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Transcript of Hydraulic Optimization
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Hydraulic Optimization
Introduction
The main objectives of circulation during drilling are
bull To clean cuttings from the bottom of the hole and prevent re-grinding
bull To clean cuttings from the bit and prevent bit balling
bull To carry the cuttings up the annulus and out of the hole
bull To cool the bit
Maximum bottom hole cleaning is important to obtain the highest penetration rate It
is achieved by either
bull Maximum hydraulic power at the bit or
bull Maximum hydraulic impact force
In the first case it has been assumed that cutting removal from the bottom is related to
the fluid energy dissipated at the bit (bit hydraulic power) In the second case it has
been assumed that the cutting removal is optimized when the fluid impact on the
bottom is maximized (impact force on bottom) The parameters that influence the
cleaning effect in both cases are the flow rate and the nozzle area
Effective removal of cuttings from the borehole by the drilling fluid is possible onlywhen an annular velocity that creates an upward movement exceeding the
gravitational settling of the cuttings is maintained The parameters that influence the
efficiency of cutting transport are the carrying capacity of the drilling fluid the
annular clearance (referred to as the hydraulic diameter) and the flow rate The power
delivered by the rig pump is required to overcome the total hydraulic friction
throughout the circulating system Only part of this power can be used for bottom
hole cleaning because of the power losses in the system These system or parasitic
pressure losses are influenced by the drilling fluid properties the length and hydraulic
diameter of the conduit (eg string annulus and surface lines) and the flow rate
The hydraulic parameters which will affect drilling operations will be examined indetail including methods for calculating and measuring them Ideas will be extended
to consider ways of reducing pressure losses how to calculate the surface power
needed the hydraulic power developed at the bit the limits of annular velocities and
pump pressure and optimum bit hydraulics
The focus of concern in this part is the fluid behaviour of the drilling fluid as it flows
through the surface lines standpipe and hose down the drill string through the
nozzles and up the annulus When the drilling fluid is circulating it is necessary to
consider the mechanics of the drilling fluid in motion This is necessary to calculate
the pressure at any depth in pipe or annulus or the pressure on bottom The hydraulic
parameters to be considered in this Part are summarized in the accompanying figure
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Fig1 Important parameters in drilling hydraulics
No matter what the nature or stage of the project there are three effects resulting
directly from local pressure control that must be considered These are shown in
Figure 2 In this context local pressure means the pressure at the place under
consideration be it at the bottom of the hole or at any intermediate depth inside the
drill string or annulus Of these three effects it is the influence of pressure on
achieving an efficient penetration rate that is the prime interest in this Part
Figure2 Important considerations relating to pressure
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Efficient penetration occurs when proper control is exercised over a number of
conditions Drilling rate increases in direct proportion to weight on bit only when the
cuttings are effectively removed from beneath the bit The drilling fluid stream
provides the energy needed to clean both the bottom of the hole and the bit and
hydraulic conditions have to be selected to achieve this with the greatest effect It
must be stressed that the objective is to optimise the penetration rate The limitingfactors are on the one hand the hydrostatic head and the necessity to clean the hole
(lower boundaries) and on the other the prevention of losses and possibly the pump
capacity (upper boundaries) There are a number of variables over which you have
direct control the more important ones in drilling hydraulics are as follows
bull flow rate
bull pump pressure
bull nozzle size
bull drilling fluid gradient
bull drilling fluid viscosity
The main concern in this Part is with the first three of these flow rate pump pressure
and nozzle size
The hydraulic parameters
In this Topic each of nine hydraulic parameters which must be considered are
separately introduced
bull Pump volumetric output and circulation pressure (Pt )
bull Flow rate
bull Bit nozzle jet velocity
bull Annular velocity
bull Pressure losses in the system
bull Pump hydraulic power output
bull Pressure drop across the bit nozzles
bull Hydraulic power developed at the bit
bull Jet impact force
Some can be measured directly at the surface Most have to be calculated All relate to
the operational activities The well is considered as a closed system in which energyand power are conserved Therefore the total hydraulic power developed by the pump
is either dissipated within the system or is used at the bit
PUMP VOLUMETRIC OUTPUT AND CIRCULATING PRESSURE
PUMP OUTPUT
The pump volumetric output or pump output depends on the type of pump and the
size of the liners installed
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The volume output for double acting pumps is obtained with the following equation
The value of factor K in this equation is
0middot0257 when the flow rate Q is in dm3min (lmin)
0middot00679 when the flow rate Q is in galsmin
0middot000162 when the flow rate Q is in bblmin
0middot000909 when the flow rate Q is in ft3min
For single acting triplex pumps the equation to be used is
where the value of K is
0middot0386 when the flow rate Q is in dm3min (lmin)
0middot010199 when the flow rate Q is in galsmin
0middot000243 when the flow rate Q is in bblmin
0middot001364 when the flow rate Q is in ft3min
In both the equations
L = stroke in inches
D = inside diameter of liner in inches
d = outside diameter of piston rod in inches
spm = strokes per minute
nvol = volumetric efficiency as percentage
The pump or circulating pressure (Pt ) is usually measured directly at the surface with
a standpipe gauge It can also be estimated using the following
bull
the dimensions of the hole and drill stringbull rheological drilling fluid properties
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bull nozzle area
bull flow rate
The units for Pt are kPa or psi
CIRCULATING PRESSURE AND PRESSURE DROP IN THE HYDRAULICSYSTEM
Since the drilling fluid returns to the surface at atmospheric pressure (in normal
drilling operations) all the pressure developed by the pump is used between it and the
flowline
Thus Pt = Ps + P b
Where
Pt is the pump or circulating pressure (kPa or psi)
Ps is the total of all pressure losses except at the bit (kPa or psi)
P b is the pressure drop across bit nozzles (kPa or psi)
FLOW RATE (Q)
The flow rate is the volume of drilling fluid passing any point in unit time It is
usually expressed in m3s or m3min (m3sec will be used throughout this Part) In
oilfield units it is expressed in bblsmin or galsmin (gpm)
The flow rate can be measured directly with a flow meter in the surface lines usually
between pump and standpipe
BIT NOZZLE JET VELOCITY (Vn)
The jet velocity is the governing parameter in the impact-force method of maximized
bottom-hole cleaning The higher the jet velocity the better the cleaning effect The
accepted minimum value for optimized bottom hole cleaning is approximately 100
ms (350 fts)
The jet velocity is calculated from the jet nozzle area and the flow rate
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ANNULAR VELOCITY (Van)
The annular velocity is the speed with which the drilling fluid rises in the annulus and
is expressed in mmin (ftmin)
The annular drilling fluid velocity is confined by an upper and a lower limit
MAXIMUM ANNULAR VELOCITY
The upper velocity limit is determined by the effects of erosion on soft formations (or
maximum possible pump output volume) Wash-outs can easily be created in such
situations
The maximum annular velocity in sensitive formations is often limited to 30 mmin
(100 ftmin) to prevent wash-outs
MINIMUM ANNULAR VELOCITY
The lower limit is always governed by the cuttings transport capacity of the drilling
fluid
Too much build-up of cuttings in the drilling fluid will result in an increase in the
density of the fluid in the annulus The consequent increase in hydrostatic head
against exposed weak formations could cause formation break-down and loss of
circulation It could also cause stuck pipe in a deviated well (building up of cuttings
bed)
The annular velocity should therefore in relation to the cuttings generated be
sufficient to maintain densities within formation strength limits
However the minimum annular velocity is also dependent on the slip velocity (rate of
settling of the cuttings) As a result of gravity the cuttings tend to drop through the
drilling fluid Therefore when the slip velocity exceeds the annular velocity the
particles will not be carried out of the well There will be insufficient returns of large
cuttings over the shale shaker and due to regrinding erosion and deterioration the
solid content and density of the drilling fluid will increase
APPLIED ANNULAR VELOCITY
The annular velocity depends on the flow rate and the flow area the latter of which is
not constant The drill-pipe open-hole area must be considered when determining the
maximum or minimum value for the velocity This means that the actual velocity in
the drill-collar open-hole annulus may be higher than the recommended value
However that often has to be accepted The DC-OH section is comparatively short so
that the wellbore wall in soft formations will be exposed only briefly to these higher
erosive effects In harder formations erosion often becomes negligible
The annular velocity at a given flow rate can be calculated by the following equations
derived from the general equation Q = VA
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When drilling hard formations where penetration rates are low lower annular
velocities can be used In soft formations with high penetration rate often
encountered in top-hole drilling higher annular velocities will be required to remove
the cuttings from the well
Because the total pump capacity is limited sometimes it is not possible to obtainsufficient annular velocity especially in drilling large hole sizes If the fluid density is
critical because weak formations are exposed the drilling rate may have to be
adjusted to reduce the amount of cuttings generated
Generally speaking the minimum practical annular velocity is maintained above a
value of approximately 17 mmin (50 ftmin) in the very large hole sizes In the
smaller holes the more common value of 30 - 40 mmin (90 - 120 ftmin) usually
applies (the smaller hole size is usually at greater depth where the formations are
more consolidated)
Selection of an appropriate annular velocity is one of the first decisions to be takenwhen considering hydraulic conditions
Actual annular velocities are uncertain due to the irregularity of the hole size and
configuration During drilling the actual hole size is not known for this reason the bit
size is taken as the internal diameter of the hole or the last measured average caliper
hole size obtained from logs for calculation purposes
Between the maximum annular velocity and the minimum annular velocity is an
annular velocity which under the given circumstances is the best annular velocity to
be used This is called the optimum annular velocity
OPTIMUM ANNULAR VELOCITY
The optimum annular velocity is that velocity which is obtained through a flow rate
which gives an annular velocity sufficiently high to effectively remove cuttings from
the hole and having the lowest possible erosion effect on the borehole
Over time any flow results in erosion It is therefore advisable to obtain the minimum
flow rate required to effectively remove cuttings from the hole and to avoid
circulating any faster than is required to obtain this flow rate If this rate is a
calculated rate actual hole cleaning should be monitored to confirm the hole cleaningability of this flow rate
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You should be able to distinguish clearly between flow rate and annular velocity
PRESSURE LOSSES IN THE SYSTEM (Ps) (PARASITIC PRESSURE
LOSSES)
What is the system
The system is made up of all parts between the pump and the flowlines with the
exception of the bit nozzles These are excluded because pressure drop across the
nozzles is considered a useful loss of pressure It represents the change in kinetic
energy used to clean the bottom of the hole Pressure losses in the system represent
wasted energy used in overcoming friction These pressure losses are called parasitic
losses
The main sections of the circulating system which contribute to the system losses may
be summarized as follows
bull The surface lines (from pump to kelly saver sub)
bull The drill string (drill pipe and drill collars)
bull The annulus (open hole and cased hole)
In addition we will look at
bull causes of changes in circulating pressures
bull flow regimes
PRESSURE LOSSES IN SURFACE EQUIPMENT
Surface equipment consists of surface lines stand pipe kelly hose swivel and kelly
The pressure loss occurring in this equipment depends on the length and the internal
diameters of each of the items mentioned A simple practical method to find the
surface equipment pressure losses is to hang the kelly or top drive open ended in the
rotary table and pump at different rates
Table1 shows four common combinations of surface equipment The case numbers inthis table (No1 to No4) were originally intended for use with hydraulic slide rules
They are now also used to identify different surface pressure loss situations to be used
in calculations
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PRESSURE LOSSES IN THE DRILL STRING (Pf d)
The pressure loss in the drill string represents the major portion of the parasitic losses
The fluid velocities are usually high and therefore friction loss is significant as the
flow regime in most cases is turbulent The losses calculated across the drill pipe and
the drill collars are based on the Bingham Plastic Flow model
When drilling the flow pattern in the drill string is normally turbulent (With
reference to the factors above consider why this should be true) There is no exact
method of calculating pressure losses in the drill string because there is no exact
method of establishing the degree of turbulence However it is possible to estimate
pressure losses in the drill string with sufficient accuracy to select appropriate bit
nozzles for optimizing hydraulic conditions
Pressure losses in the drill string can be calculated by the following equations
You should have noticed the introduction of a new term the friction factor (f) It can
be defined in terms of Reynolds Number (and hence flow rate) and pipe roughness
and has been determined empirically
If circulating a given drilling fluid at a given depth only V and f can vary and both of
these are proportional to flow rate The equations for pressure losses in the drill string
as given above can also be expressed in the equation
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Where c is a constant incorporating the values of all the parameters which are fixed at
a given depth
N is found empirically and is not the same n as in the equations in the paragraphs on
the following pages dealing with pressure losses in the annulus The latter is called a
rheological n
c is given in SI units or API units respectively by
Where is the plastic viscosity and the other symbols are as used before Note that Nis often taken as 182
PRESSURE LOSSES IN THE ANNULUS (Pfa )
Since the annular pressure loss acts as an applied pressure on the formation this loss
should be kept as low as possible to minimise the risk of formation break down To
monitor the pressure against the formation during circulation the equivalent
circulation density (ECD) is often used which is defined as
Where
ECD = equivalent circulating density (kPam psift)
ρm = density of the drilling fluid (kPam psift)
Pan = total pressure drop in the annulus (kPa psi)
L = total length of the annulus (m ft)
The value of the annular pressure loss is relatively small compared to that developed
in the drill string and is often neglected in cases where the circulation rate is low eg
during well killing
It is more difficult to find pressure losses in the annulus because conditions are less
well defined than in the drillpipe
The following uncertainties exist
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bull the actual flow condition is not clear the flow pattern is commonly near the
transitional region
bull the hole size and shape are irregular so it is not possible to get an accurate
value for the annular velocity or the hydraulic diameter
bull the downhole viscosity is very uncertain because it varies with temperature
and flow conditionsbull pipe rotation and eccentricity effects
For efficient drilling conditions it is found that the power lost in overcoming friction
in the system absorbs approximately 30-50 of the circulation energy The remainder
will be expended at the bit It is found that the majority of the system losses are in the
drill string For medium depth drilling the annular pressure losses probably total no
more than 3 to 7 of the pump output pressure at normal circulation rates
Although pressure losses in the annulus are small they are very important because of
their effect on the exposed formations
The effects of annular pressure losses are that
bull they increase the bottom hole pressure when circulating
bull they reduce the initial severity of a kick by providing a hidden safety margin
but they increase the risks of lost circulation during killing (only while
circulating)
bull they cause formation damage if the pressure losses are due to establishing
circulation When establishing circulation the pressure drop in the annulus
increases significantly due to the initial high viscosity (gel strength) of the
drilling fluid
Much research effort has been devoted to improving knowledge of the flow
characteristics of drilling fluids particularly in order to reduce pressure losses This is
a complicated and specialized subject because of the complexity of the fluids
The following expressions provide values for annular pressure losses
Where
Pfa is the annular pressure loss (kPa) Pfa is in psi
L is the pipe length (m) L is in ft
Va is the annular velocity (ms) Va is in ftmin
d is the hydraulic diameter (dh - dp) (mm) d is in inches
n is the Power Law index of flow behaviour
(dimensionless)n is dimensionless
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n and K are derived from viscometer data
Note that K here is an approximation to that given for the Power Law model found in
the section on Drilling Fluids The number 511 results from using a specific type of
viscometer with particular values of spring constant and cylinder surface speed
With Pfa as with Pfd when drilling at a particular depth with a given drilling fluid all
values in the above equations are effectively constant except for the annular velocity(Va) But Va is directly proportional to the flow rate (Q) Thus there will be a tendency
to assume that all pressure losses in the system follow the same equation as shown
below
Where c and N are constants whose values are empirically determined in particular
cases (see under Pressure losses in the drill string)
Pressure losses can be calculated for all parts of the system using the equations givenin this Part
CAUSES OF CHANGES IN CIRCULATING PRESSURES
According to Pt = P b + Ps a change in the circulating pressure can be induced by a
change in either P b Ps or both
Increases in surface pressure
A sudden increase in circulation pressure although drilling fluid properties flow rate
and conduit length are unchanged can be caused only by an increase in P b This could be caused by one or more nozzles plugging
A gradual increase in surface pressure could be the result of several causes (excepting
hole problems)
bull Increased flow rate
bull Extending the string while deepening the hole
bull Change in drilling fluid rheological properties
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Decreases in surface pressure
A spontaneous sudden decrease in circulating pressure while conditions remain
unchanged can be caused by
bull decrease of P b resulting from the loss of a nozzle
bull a twist-off in the drill string
A gradual decrease in pressure could signal the following
bull A developing wash-out (leak) in the drill string or in pump valves
bull Reduction of hydrostatic head in the annulus caused by lighter substances (eg
gas or formation water)
bull An increase of hydrostatic head in the string
Caution Any change of the surface pressure or change in pump strokes not
deliberately instigated should be investigated immediately
To a limited extent pressure losses can be measured directly for example by
pumping through the standpipe and open kelly and through drill collars It is also a
useful exercise to observe the total circulating pressure at various flow rates
Pressure losses in the system can be derived from actual circulating pressure values
by subtracting the pressure drop at the bit which can be calculated accurately
Pressure losses in the system can also be calculated However although the
dimensions are known for all parts of the system the calculation also depends on
knowing the type of fluid flow regime in the drill string and annulus The flow may be
turbulent or laminar or of some transitional type between the two The calculations are
also based on a rheological model If the drilling fluid in use behaves slightly variant
to the model the calculation results will be less than accurate
Pressure losses within the system are minimised by reducing the fluid friction in each
part
bull surface connections losses are negligible compared with elsewhere but can bereduced by avoiding tight bends and using large diameter pipes
bull drill string reduce friction by using a larger internal diameter pipe coated with
plastic
bull drill collars increasing the internal diameter will again reduce friction but
only at the expense of decreasing their weight a balance has to be made
between these opposing effects
bull annulus losses are usually small and only become significant in deep small
diameter holes pressure losses depend on the hydraulic diameter found from
the difference between the hole size and the pipe od it is actually desirable to
reduce the pressure developed against the formations
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Flow regimes
The differences between laminar and turbulent flow are illustrated in the table
overleaf The type of flow is determined by calculating Reynolds number (Re) for the
known well conditions from the following equations
The value obtained is compared with those shown in Table2 (figures are based on
Newtonian fluid properties)
Table2 Deciding the flow condition from the Reynolds number
Inspection of the equations shows that turbulent flow is more likely with the
conditions below
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bull denser drilling fluid (ρ higher)
bull lower viscosity (micro lower)
bull higher flow rate (Q higher)
bull decreased pipe bore or hydraulic
diameter
(d lower)
PUMP HYDRAULIC POWER OUTPUT
In rig operations the amount of available hydraulic power is determined by the size
number and types of pump(s) on site However the demand in terms of output volume
(Q) and pump pressure (P) varies considerably with hole size and depth Once the
pump output or flow rate Q has been selected the available power input determines
the maximum circulating pressure (Pt) that can be achieved
This circulating pressure Pt (total pressure drop in system) is consumed partly by
friction in the fluid and the system (Ps = system pressure loss) and partly by the
pressure drop across the bit nozzles (P b = bit pressure drop) Therefore P t = Ps + P b Pt
is normally given by the pump pressure gauge
The system pressure drop has no effect on bottom-hole cleaning It is unavoidable andis also called the parasitic pressure loss
The bottom-hole cleaning action is provided by the hydraulic energy expended at the
bit Therefore the amount of hydraulic power expended at the bit is a measure for the
cleaning effectiveness (This assumes that the bit is properly matched to the formation
- if a bit designed for a hard formation is run in a soft formation no amount of power
will keep it clean )
The hydraulic power available at the surface from the pump is used to drive the
drilling fluid round the system power the bit and flush the cuttings to the surface If
you know the pump or circulating pressure (Pt ) and the flow rate (Q) then it is possible to calculate the total power available at the surface
Since Power = work done in unit time
and Work done = pressure x volume
then Power = pressure x volume pumped in unit time
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Therefore the power available at surface is given by
The power output of the pump is generally assumed to be 85 of the mechanical or
electrical power input of the pump
PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)
The pressure drop across the bit nozzles P b depends on
bull The flow rate Q
bull The total cross-sectional area of the nozzle openings A
bull The drilling fluid density ρ
Once the desired (optimum) annular velocity has been determined the flow rate (Q )
and the hydraulic power expended at the bit for a given nozzle size are fixed
Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power
expended at the bit is also fixed Both jet velocity and hydraulic power at the bit
determine the cleaning action on bottom
Pressure losses through the bit nozzles are not frictional but represent a change in
kinetic energy as the drilling fluid changes its velocity from that above the bit to that
leaving the jets The pressure expended is therefore dependent only on the drilling
fluid density and the square of the jet velocity
The pressure drop across the bit nozzles is calculated using the following equations
Where
P b is the pressure loss across the bit nozzles (kPa)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
A is the total nozzle area (mm2)
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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Fig1 Important parameters in drilling hydraulics
No matter what the nature or stage of the project there are three effects resulting
directly from local pressure control that must be considered These are shown in
Figure 2 In this context local pressure means the pressure at the place under
consideration be it at the bottom of the hole or at any intermediate depth inside the
drill string or annulus Of these three effects it is the influence of pressure on
achieving an efficient penetration rate that is the prime interest in this Part
Figure2 Important considerations relating to pressure
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Efficient penetration occurs when proper control is exercised over a number of
conditions Drilling rate increases in direct proportion to weight on bit only when the
cuttings are effectively removed from beneath the bit The drilling fluid stream
provides the energy needed to clean both the bottom of the hole and the bit and
hydraulic conditions have to be selected to achieve this with the greatest effect It
must be stressed that the objective is to optimise the penetration rate The limitingfactors are on the one hand the hydrostatic head and the necessity to clean the hole
(lower boundaries) and on the other the prevention of losses and possibly the pump
capacity (upper boundaries) There are a number of variables over which you have
direct control the more important ones in drilling hydraulics are as follows
bull flow rate
bull pump pressure
bull nozzle size
bull drilling fluid gradient
bull drilling fluid viscosity
The main concern in this Part is with the first three of these flow rate pump pressure
and nozzle size
The hydraulic parameters
In this Topic each of nine hydraulic parameters which must be considered are
separately introduced
bull Pump volumetric output and circulation pressure (Pt )
bull Flow rate
bull Bit nozzle jet velocity
bull Annular velocity
bull Pressure losses in the system
bull Pump hydraulic power output
bull Pressure drop across the bit nozzles
bull Hydraulic power developed at the bit
bull Jet impact force
Some can be measured directly at the surface Most have to be calculated All relate to
the operational activities The well is considered as a closed system in which energyand power are conserved Therefore the total hydraulic power developed by the pump
is either dissipated within the system or is used at the bit
PUMP VOLUMETRIC OUTPUT AND CIRCULATING PRESSURE
PUMP OUTPUT
The pump volumetric output or pump output depends on the type of pump and the
size of the liners installed
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The volume output for double acting pumps is obtained with the following equation
The value of factor K in this equation is
0middot0257 when the flow rate Q is in dm3min (lmin)
0middot00679 when the flow rate Q is in galsmin
0middot000162 when the flow rate Q is in bblmin
0middot000909 when the flow rate Q is in ft3min
For single acting triplex pumps the equation to be used is
where the value of K is
0middot0386 when the flow rate Q is in dm3min (lmin)
0middot010199 when the flow rate Q is in galsmin
0middot000243 when the flow rate Q is in bblmin
0middot001364 when the flow rate Q is in ft3min
In both the equations
L = stroke in inches
D = inside diameter of liner in inches
d = outside diameter of piston rod in inches
spm = strokes per minute
nvol = volumetric efficiency as percentage
The pump or circulating pressure (Pt ) is usually measured directly at the surface with
a standpipe gauge It can also be estimated using the following
bull
the dimensions of the hole and drill stringbull rheological drilling fluid properties
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bull nozzle area
bull flow rate
The units for Pt are kPa or psi
CIRCULATING PRESSURE AND PRESSURE DROP IN THE HYDRAULICSYSTEM
Since the drilling fluid returns to the surface at atmospheric pressure (in normal
drilling operations) all the pressure developed by the pump is used between it and the
flowline
Thus Pt = Ps + P b
Where
Pt is the pump or circulating pressure (kPa or psi)
Ps is the total of all pressure losses except at the bit (kPa or psi)
P b is the pressure drop across bit nozzles (kPa or psi)
FLOW RATE (Q)
The flow rate is the volume of drilling fluid passing any point in unit time It is
usually expressed in m3s or m3min (m3sec will be used throughout this Part) In
oilfield units it is expressed in bblsmin or galsmin (gpm)
The flow rate can be measured directly with a flow meter in the surface lines usually
between pump and standpipe
BIT NOZZLE JET VELOCITY (Vn)
The jet velocity is the governing parameter in the impact-force method of maximized
bottom-hole cleaning The higher the jet velocity the better the cleaning effect The
accepted minimum value for optimized bottom hole cleaning is approximately 100
ms (350 fts)
The jet velocity is calculated from the jet nozzle area and the flow rate
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ANNULAR VELOCITY (Van)
The annular velocity is the speed with which the drilling fluid rises in the annulus and
is expressed in mmin (ftmin)
The annular drilling fluid velocity is confined by an upper and a lower limit
MAXIMUM ANNULAR VELOCITY
The upper velocity limit is determined by the effects of erosion on soft formations (or
maximum possible pump output volume) Wash-outs can easily be created in such
situations
The maximum annular velocity in sensitive formations is often limited to 30 mmin
(100 ftmin) to prevent wash-outs
MINIMUM ANNULAR VELOCITY
The lower limit is always governed by the cuttings transport capacity of the drilling
fluid
Too much build-up of cuttings in the drilling fluid will result in an increase in the
density of the fluid in the annulus The consequent increase in hydrostatic head
against exposed weak formations could cause formation break-down and loss of
circulation It could also cause stuck pipe in a deviated well (building up of cuttings
bed)
The annular velocity should therefore in relation to the cuttings generated be
sufficient to maintain densities within formation strength limits
However the minimum annular velocity is also dependent on the slip velocity (rate of
settling of the cuttings) As a result of gravity the cuttings tend to drop through the
drilling fluid Therefore when the slip velocity exceeds the annular velocity the
particles will not be carried out of the well There will be insufficient returns of large
cuttings over the shale shaker and due to regrinding erosion and deterioration the
solid content and density of the drilling fluid will increase
APPLIED ANNULAR VELOCITY
The annular velocity depends on the flow rate and the flow area the latter of which is
not constant The drill-pipe open-hole area must be considered when determining the
maximum or minimum value for the velocity This means that the actual velocity in
the drill-collar open-hole annulus may be higher than the recommended value
However that often has to be accepted The DC-OH section is comparatively short so
that the wellbore wall in soft formations will be exposed only briefly to these higher
erosive effects In harder formations erosion often becomes negligible
The annular velocity at a given flow rate can be calculated by the following equations
derived from the general equation Q = VA
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When drilling hard formations where penetration rates are low lower annular
velocities can be used In soft formations with high penetration rate often
encountered in top-hole drilling higher annular velocities will be required to remove
the cuttings from the well
Because the total pump capacity is limited sometimes it is not possible to obtainsufficient annular velocity especially in drilling large hole sizes If the fluid density is
critical because weak formations are exposed the drilling rate may have to be
adjusted to reduce the amount of cuttings generated
Generally speaking the minimum practical annular velocity is maintained above a
value of approximately 17 mmin (50 ftmin) in the very large hole sizes In the
smaller holes the more common value of 30 - 40 mmin (90 - 120 ftmin) usually
applies (the smaller hole size is usually at greater depth where the formations are
more consolidated)
Selection of an appropriate annular velocity is one of the first decisions to be takenwhen considering hydraulic conditions
Actual annular velocities are uncertain due to the irregularity of the hole size and
configuration During drilling the actual hole size is not known for this reason the bit
size is taken as the internal diameter of the hole or the last measured average caliper
hole size obtained from logs for calculation purposes
Between the maximum annular velocity and the minimum annular velocity is an
annular velocity which under the given circumstances is the best annular velocity to
be used This is called the optimum annular velocity
OPTIMUM ANNULAR VELOCITY
The optimum annular velocity is that velocity which is obtained through a flow rate
which gives an annular velocity sufficiently high to effectively remove cuttings from
the hole and having the lowest possible erosion effect on the borehole
Over time any flow results in erosion It is therefore advisable to obtain the minimum
flow rate required to effectively remove cuttings from the hole and to avoid
circulating any faster than is required to obtain this flow rate If this rate is a
calculated rate actual hole cleaning should be monitored to confirm the hole cleaningability of this flow rate
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You should be able to distinguish clearly between flow rate and annular velocity
PRESSURE LOSSES IN THE SYSTEM (Ps) (PARASITIC PRESSURE
LOSSES)
What is the system
The system is made up of all parts between the pump and the flowlines with the
exception of the bit nozzles These are excluded because pressure drop across the
nozzles is considered a useful loss of pressure It represents the change in kinetic
energy used to clean the bottom of the hole Pressure losses in the system represent
wasted energy used in overcoming friction These pressure losses are called parasitic
losses
The main sections of the circulating system which contribute to the system losses may
be summarized as follows
bull The surface lines (from pump to kelly saver sub)
bull The drill string (drill pipe and drill collars)
bull The annulus (open hole and cased hole)
In addition we will look at
bull causes of changes in circulating pressures
bull flow regimes
PRESSURE LOSSES IN SURFACE EQUIPMENT
Surface equipment consists of surface lines stand pipe kelly hose swivel and kelly
The pressure loss occurring in this equipment depends on the length and the internal
diameters of each of the items mentioned A simple practical method to find the
surface equipment pressure losses is to hang the kelly or top drive open ended in the
rotary table and pump at different rates
Table1 shows four common combinations of surface equipment The case numbers inthis table (No1 to No4) were originally intended for use with hydraulic slide rules
They are now also used to identify different surface pressure loss situations to be used
in calculations
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PRESSURE LOSSES IN THE DRILL STRING (Pf d)
The pressure loss in the drill string represents the major portion of the parasitic losses
The fluid velocities are usually high and therefore friction loss is significant as the
flow regime in most cases is turbulent The losses calculated across the drill pipe and
the drill collars are based on the Bingham Plastic Flow model
When drilling the flow pattern in the drill string is normally turbulent (With
reference to the factors above consider why this should be true) There is no exact
method of calculating pressure losses in the drill string because there is no exact
method of establishing the degree of turbulence However it is possible to estimate
pressure losses in the drill string with sufficient accuracy to select appropriate bit
nozzles for optimizing hydraulic conditions
Pressure losses in the drill string can be calculated by the following equations
You should have noticed the introduction of a new term the friction factor (f) It can
be defined in terms of Reynolds Number (and hence flow rate) and pipe roughness
and has been determined empirically
If circulating a given drilling fluid at a given depth only V and f can vary and both of
these are proportional to flow rate The equations for pressure losses in the drill string
as given above can also be expressed in the equation
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Where c is a constant incorporating the values of all the parameters which are fixed at
a given depth
N is found empirically and is not the same n as in the equations in the paragraphs on
the following pages dealing with pressure losses in the annulus The latter is called a
rheological n
c is given in SI units or API units respectively by
Where is the plastic viscosity and the other symbols are as used before Note that Nis often taken as 182
PRESSURE LOSSES IN THE ANNULUS (Pfa )
Since the annular pressure loss acts as an applied pressure on the formation this loss
should be kept as low as possible to minimise the risk of formation break down To
monitor the pressure against the formation during circulation the equivalent
circulation density (ECD) is often used which is defined as
Where
ECD = equivalent circulating density (kPam psift)
ρm = density of the drilling fluid (kPam psift)
Pan = total pressure drop in the annulus (kPa psi)
L = total length of the annulus (m ft)
The value of the annular pressure loss is relatively small compared to that developed
in the drill string and is often neglected in cases where the circulation rate is low eg
during well killing
It is more difficult to find pressure losses in the annulus because conditions are less
well defined than in the drillpipe
The following uncertainties exist
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bull the actual flow condition is not clear the flow pattern is commonly near the
transitional region
bull the hole size and shape are irregular so it is not possible to get an accurate
value for the annular velocity or the hydraulic diameter
bull the downhole viscosity is very uncertain because it varies with temperature
and flow conditionsbull pipe rotation and eccentricity effects
For efficient drilling conditions it is found that the power lost in overcoming friction
in the system absorbs approximately 30-50 of the circulation energy The remainder
will be expended at the bit It is found that the majority of the system losses are in the
drill string For medium depth drilling the annular pressure losses probably total no
more than 3 to 7 of the pump output pressure at normal circulation rates
Although pressure losses in the annulus are small they are very important because of
their effect on the exposed formations
The effects of annular pressure losses are that
bull they increase the bottom hole pressure when circulating
bull they reduce the initial severity of a kick by providing a hidden safety margin
but they increase the risks of lost circulation during killing (only while
circulating)
bull they cause formation damage if the pressure losses are due to establishing
circulation When establishing circulation the pressure drop in the annulus
increases significantly due to the initial high viscosity (gel strength) of the
drilling fluid
Much research effort has been devoted to improving knowledge of the flow
characteristics of drilling fluids particularly in order to reduce pressure losses This is
a complicated and specialized subject because of the complexity of the fluids
The following expressions provide values for annular pressure losses
Where
Pfa is the annular pressure loss (kPa) Pfa is in psi
L is the pipe length (m) L is in ft
Va is the annular velocity (ms) Va is in ftmin
d is the hydraulic diameter (dh - dp) (mm) d is in inches
n is the Power Law index of flow behaviour
(dimensionless)n is dimensionless
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n and K are derived from viscometer data
Note that K here is an approximation to that given for the Power Law model found in
the section on Drilling Fluids The number 511 results from using a specific type of
viscometer with particular values of spring constant and cylinder surface speed
With Pfa as with Pfd when drilling at a particular depth with a given drilling fluid all
values in the above equations are effectively constant except for the annular velocity(Va) But Va is directly proportional to the flow rate (Q) Thus there will be a tendency
to assume that all pressure losses in the system follow the same equation as shown
below
Where c and N are constants whose values are empirically determined in particular
cases (see under Pressure losses in the drill string)
Pressure losses can be calculated for all parts of the system using the equations givenin this Part
CAUSES OF CHANGES IN CIRCULATING PRESSURES
According to Pt = P b + Ps a change in the circulating pressure can be induced by a
change in either P b Ps or both
Increases in surface pressure
A sudden increase in circulation pressure although drilling fluid properties flow rate
and conduit length are unchanged can be caused only by an increase in P b This could be caused by one or more nozzles plugging
A gradual increase in surface pressure could be the result of several causes (excepting
hole problems)
bull Increased flow rate
bull Extending the string while deepening the hole
bull Change in drilling fluid rheological properties
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Decreases in surface pressure
A spontaneous sudden decrease in circulating pressure while conditions remain
unchanged can be caused by
bull decrease of P b resulting from the loss of a nozzle
bull a twist-off in the drill string
A gradual decrease in pressure could signal the following
bull A developing wash-out (leak) in the drill string or in pump valves
bull Reduction of hydrostatic head in the annulus caused by lighter substances (eg
gas or formation water)
bull An increase of hydrostatic head in the string
Caution Any change of the surface pressure or change in pump strokes not
deliberately instigated should be investigated immediately
To a limited extent pressure losses can be measured directly for example by
pumping through the standpipe and open kelly and through drill collars It is also a
useful exercise to observe the total circulating pressure at various flow rates
Pressure losses in the system can be derived from actual circulating pressure values
by subtracting the pressure drop at the bit which can be calculated accurately
Pressure losses in the system can also be calculated However although the
dimensions are known for all parts of the system the calculation also depends on
knowing the type of fluid flow regime in the drill string and annulus The flow may be
turbulent or laminar or of some transitional type between the two The calculations are
also based on a rheological model If the drilling fluid in use behaves slightly variant
to the model the calculation results will be less than accurate
Pressure losses within the system are minimised by reducing the fluid friction in each
part
bull surface connections losses are negligible compared with elsewhere but can bereduced by avoiding tight bends and using large diameter pipes
bull drill string reduce friction by using a larger internal diameter pipe coated with
plastic
bull drill collars increasing the internal diameter will again reduce friction but
only at the expense of decreasing their weight a balance has to be made
between these opposing effects
bull annulus losses are usually small and only become significant in deep small
diameter holes pressure losses depend on the hydraulic diameter found from
the difference between the hole size and the pipe od it is actually desirable to
reduce the pressure developed against the formations
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Flow regimes
The differences between laminar and turbulent flow are illustrated in the table
overleaf The type of flow is determined by calculating Reynolds number (Re) for the
known well conditions from the following equations
The value obtained is compared with those shown in Table2 (figures are based on
Newtonian fluid properties)
Table2 Deciding the flow condition from the Reynolds number
Inspection of the equations shows that turbulent flow is more likely with the
conditions below
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bull denser drilling fluid (ρ higher)
bull lower viscosity (micro lower)
bull higher flow rate (Q higher)
bull decreased pipe bore or hydraulic
diameter
(d lower)
PUMP HYDRAULIC POWER OUTPUT
In rig operations the amount of available hydraulic power is determined by the size
number and types of pump(s) on site However the demand in terms of output volume
(Q) and pump pressure (P) varies considerably with hole size and depth Once the
pump output or flow rate Q has been selected the available power input determines
the maximum circulating pressure (Pt) that can be achieved
This circulating pressure Pt (total pressure drop in system) is consumed partly by
friction in the fluid and the system (Ps = system pressure loss) and partly by the
pressure drop across the bit nozzles (P b = bit pressure drop) Therefore P t = Ps + P b Pt
is normally given by the pump pressure gauge
The system pressure drop has no effect on bottom-hole cleaning It is unavoidable andis also called the parasitic pressure loss
The bottom-hole cleaning action is provided by the hydraulic energy expended at the
bit Therefore the amount of hydraulic power expended at the bit is a measure for the
cleaning effectiveness (This assumes that the bit is properly matched to the formation
- if a bit designed for a hard formation is run in a soft formation no amount of power
will keep it clean )
The hydraulic power available at the surface from the pump is used to drive the
drilling fluid round the system power the bit and flush the cuttings to the surface If
you know the pump or circulating pressure (Pt ) and the flow rate (Q) then it is possible to calculate the total power available at the surface
Since Power = work done in unit time
and Work done = pressure x volume
then Power = pressure x volume pumped in unit time
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Therefore the power available at surface is given by
The power output of the pump is generally assumed to be 85 of the mechanical or
electrical power input of the pump
PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)
The pressure drop across the bit nozzles P b depends on
bull The flow rate Q
bull The total cross-sectional area of the nozzle openings A
bull The drilling fluid density ρ
Once the desired (optimum) annular velocity has been determined the flow rate (Q )
and the hydraulic power expended at the bit for a given nozzle size are fixed
Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power
expended at the bit is also fixed Both jet velocity and hydraulic power at the bit
determine the cleaning action on bottom
Pressure losses through the bit nozzles are not frictional but represent a change in
kinetic energy as the drilling fluid changes its velocity from that above the bit to that
leaving the jets The pressure expended is therefore dependent only on the drilling
fluid density and the square of the jet velocity
The pressure drop across the bit nozzles is calculated using the following equations
Where
P b is the pressure loss across the bit nozzles (kPa)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
A is the total nozzle area (mm2)
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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Efficient penetration occurs when proper control is exercised over a number of
conditions Drilling rate increases in direct proportion to weight on bit only when the
cuttings are effectively removed from beneath the bit The drilling fluid stream
provides the energy needed to clean both the bottom of the hole and the bit and
hydraulic conditions have to be selected to achieve this with the greatest effect It
must be stressed that the objective is to optimise the penetration rate The limitingfactors are on the one hand the hydrostatic head and the necessity to clean the hole
(lower boundaries) and on the other the prevention of losses and possibly the pump
capacity (upper boundaries) There are a number of variables over which you have
direct control the more important ones in drilling hydraulics are as follows
bull flow rate
bull pump pressure
bull nozzle size
bull drilling fluid gradient
bull drilling fluid viscosity
The main concern in this Part is with the first three of these flow rate pump pressure
and nozzle size
The hydraulic parameters
In this Topic each of nine hydraulic parameters which must be considered are
separately introduced
bull Pump volumetric output and circulation pressure (Pt )
bull Flow rate
bull Bit nozzle jet velocity
bull Annular velocity
bull Pressure losses in the system
bull Pump hydraulic power output
bull Pressure drop across the bit nozzles
bull Hydraulic power developed at the bit
bull Jet impact force
Some can be measured directly at the surface Most have to be calculated All relate to
the operational activities The well is considered as a closed system in which energyand power are conserved Therefore the total hydraulic power developed by the pump
is either dissipated within the system or is used at the bit
PUMP VOLUMETRIC OUTPUT AND CIRCULATING PRESSURE
PUMP OUTPUT
The pump volumetric output or pump output depends on the type of pump and the
size of the liners installed
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The volume output for double acting pumps is obtained with the following equation
The value of factor K in this equation is
0middot0257 when the flow rate Q is in dm3min (lmin)
0middot00679 when the flow rate Q is in galsmin
0middot000162 when the flow rate Q is in bblmin
0middot000909 when the flow rate Q is in ft3min
For single acting triplex pumps the equation to be used is
where the value of K is
0middot0386 when the flow rate Q is in dm3min (lmin)
0middot010199 when the flow rate Q is in galsmin
0middot000243 when the flow rate Q is in bblmin
0middot001364 when the flow rate Q is in ft3min
In both the equations
L = stroke in inches
D = inside diameter of liner in inches
d = outside diameter of piston rod in inches
spm = strokes per minute
nvol = volumetric efficiency as percentage
The pump or circulating pressure (Pt ) is usually measured directly at the surface with
a standpipe gauge It can also be estimated using the following
bull
the dimensions of the hole and drill stringbull rheological drilling fluid properties
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bull nozzle area
bull flow rate
The units for Pt are kPa or psi
CIRCULATING PRESSURE AND PRESSURE DROP IN THE HYDRAULICSYSTEM
Since the drilling fluid returns to the surface at atmospheric pressure (in normal
drilling operations) all the pressure developed by the pump is used between it and the
flowline
Thus Pt = Ps + P b
Where
Pt is the pump or circulating pressure (kPa or psi)
Ps is the total of all pressure losses except at the bit (kPa or psi)
P b is the pressure drop across bit nozzles (kPa or psi)
FLOW RATE (Q)
The flow rate is the volume of drilling fluid passing any point in unit time It is
usually expressed in m3s or m3min (m3sec will be used throughout this Part) In
oilfield units it is expressed in bblsmin or galsmin (gpm)
The flow rate can be measured directly with a flow meter in the surface lines usually
between pump and standpipe
BIT NOZZLE JET VELOCITY (Vn)
The jet velocity is the governing parameter in the impact-force method of maximized
bottom-hole cleaning The higher the jet velocity the better the cleaning effect The
accepted minimum value for optimized bottom hole cleaning is approximately 100
ms (350 fts)
The jet velocity is calculated from the jet nozzle area and the flow rate
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ANNULAR VELOCITY (Van)
The annular velocity is the speed with which the drilling fluid rises in the annulus and
is expressed in mmin (ftmin)
The annular drilling fluid velocity is confined by an upper and a lower limit
MAXIMUM ANNULAR VELOCITY
The upper velocity limit is determined by the effects of erosion on soft formations (or
maximum possible pump output volume) Wash-outs can easily be created in such
situations
The maximum annular velocity in sensitive formations is often limited to 30 mmin
(100 ftmin) to prevent wash-outs
MINIMUM ANNULAR VELOCITY
The lower limit is always governed by the cuttings transport capacity of the drilling
fluid
Too much build-up of cuttings in the drilling fluid will result in an increase in the
density of the fluid in the annulus The consequent increase in hydrostatic head
against exposed weak formations could cause formation break-down and loss of
circulation It could also cause stuck pipe in a deviated well (building up of cuttings
bed)
The annular velocity should therefore in relation to the cuttings generated be
sufficient to maintain densities within formation strength limits
However the minimum annular velocity is also dependent on the slip velocity (rate of
settling of the cuttings) As a result of gravity the cuttings tend to drop through the
drilling fluid Therefore when the slip velocity exceeds the annular velocity the
particles will not be carried out of the well There will be insufficient returns of large
cuttings over the shale shaker and due to regrinding erosion and deterioration the
solid content and density of the drilling fluid will increase
APPLIED ANNULAR VELOCITY
The annular velocity depends on the flow rate and the flow area the latter of which is
not constant The drill-pipe open-hole area must be considered when determining the
maximum or minimum value for the velocity This means that the actual velocity in
the drill-collar open-hole annulus may be higher than the recommended value
However that often has to be accepted The DC-OH section is comparatively short so
that the wellbore wall in soft formations will be exposed only briefly to these higher
erosive effects In harder formations erosion often becomes negligible
The annular velocity at a given flow rate can be calculated by the following equations
derived from the general equation Q = VA
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When drilling hard formations where penetration rates are low lower annular
velocities can be used In soft formations with high penetration rate often
encountered in top-hole drilling higher annular velocities will be required to remove
the cuttings from the well
Because the total pump capacity is limited sometimes it is not possible to obtainsufficient annular velocity especially in drilling large hole sizes If the fluid density is
critical because weak formations are exposed the drilling rate may have to be
adjusted to reduce the amount of cuttings generated
Generally speaking the minimum practical annular velocity is maintained above a
value of approximately 17 mmin (50 ftmin) in the very large hole sizes In the
smaller holes the more common value of 30 - 40 mmin (90 - 120 ftmin) usually
applies (the smaller hole size is usually at greater depth where the formations are
more consolidated)
Selection of an appropriate annular velocity is one of the first decisions to be takenwhen considering hydraulic conditions
Actual annular velocities are uncertain due to the irregularity of the hole size and
configuration During drilling the actual hole size is not known for this reason the bit
size is taken as the internal diameter of the hole or the last measured average caliper
hole size obtained from logs for calculation purposes
Between the maximum annular velocity and the minimum annular velocity is an
annular velocity which under the given circumstances is the best annular velocity to
be used This is called the optimum annular velocity
OPTIMUM ANNULAR VELOCITY
The optimum annular velocity is that velocity which is obtained through a flow rate
which gives an annular velocity sufficiently high to effectively remove cuttings from
the hole and having the lowest possible erosion effect on the borehole
Over time any flow results in erosion It is therefore advisable to obtain the minimum
flow rate required to effectively remove cuttings from the hole and to avoid
circulating any faster than is required to obtain this flow rate If this rate is a
calculated rate actual hole cleaning should be monitored to confirm the hole cleaningability of this flow rate
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You should be able to distinguish clearly between flow rate and annular velocity
PRESSURE LOSSES IN THE SYSTEM (Ps) (PARASITIC PRESSURE
LOSSES)
What is the system
The system is made up of all parts between the pump and the flowlines with the
exception of the bit nozzles These are excluded because pressure drop across the
nozzles is considered a useful loss of pressure It represents the change in kinetic
energy used to clean the bottom of the hole Pressure losses in the system represent
wasted energy used in overcoming friction These pressure losses are called parasitic
losses
The main sections of the circulating system which contribute to the system losses may
be summarized as follows
bull The surface lines (from pump to kelly saver sub)
bull The drill string (drill pipe and drill collars)
bull The annulus (open hole and cased hole)
In addition we will look at
bull causes of changes in circulating pressures
bull flow regimes
PRESSURE LOSSES IN SURFACE EQUIPMENT
Surface equipment consists of surface lines stand pipe kelly hose swivel and kelly
The pressure loss occurring in this equipment depends on the length and the internal
diameters of each of the items mentioned A simple practical method to find the
surface equipment pressure losses is to hang the kelly or top drive open ended in the
rotary table and pump at different rates
Table1 shows four common combinations of surface equipment The case numbers inthis table (No1 to No4) were originally intended for use with hydraulic slide rules
They are now also used to identify different surface pressure loss situations to be used
in calculations
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PRESSURE LOSSES IN THE DRILL STRING (Pf d)
The pressure loss in the drill string represents the major portion of the parasitic losses
The fluid velocities are usually high and therefore friction loss is significant as the
flow regime in most cases is turbulent The losses calculated across the drill pipe and
the drill collars are based on the Bingham Plastic Flow model
When drilling the flow pattern in the drill string is normally turbulent (With
reference to the factors above consider why this should be true) There is no exact
method of calculating pressure losses in the drill string because there is no exact
method of establishing the degree of turbulence However it is possible to estimate
pressure losses in the drill string with sufficient accuracy to select appropriate bit
nozzles for optimizing hydraulic conditions
Pressure losses in the drill string can be calculated by the following equations
You should have noticed the introduction of a new term the friction factor (f) It can
be defined in terms of Reynolds Number (and hence flow rate) and pipe roughness
and has been determined empirically
If circulating a given drilling fluid at a given depth only V and f can vary and both of
these are proportional to flow rate The equations for pressure losses in the drill string
as given above can also be expressed in the equation
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Where c is a constant incorporating the values of all the parameters which are fixed at
a given depth
N is found empirically and is not the same n as in the equations in the paragraphs on
the following pages dealing with pressure losses in the annulus The latter is called a
rheological n
c is given in SI units or API units respectively by
Where is the plastic viscosity and the other symbols are as used before Note that Nis often taken as 182
PRESSURE LOSSES IN THE ANNULUS (Pfa )
Since the annular pressure loss acts as an applied pressure on the formation this loss
should be kept as low as possible to minimise the risk of formation break down To
monitor the pressure against the formation during circulation the equivalent
circulation density (ECD) is often used which is defined as
Where
ECD = equivalent circulating density (kPam psift)
ρm = density of the drilling fluid (kPam psift)
Pan = total pressure drop in the annulus (kPa psi)
L = total length of the annulus (m ft)
The value of the annular pressure loss is relatively small compared to that developed
in the drill string and is often neglected in cases where the circulation rate is low eg
during well killing
It is more difficult to find pressure losses in the annulus because conditions are less
well defined than in the drillpipe
The following uncertainties exist
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bull the actual flow condition is not clear the flow pattern is commonly near the
transitional region
bull the hole size and shape are irregular so it is not possible to get an accurate
value for the annular velocity or the hydraulic diameter
bull the downhole viscosity is very uncertain because it varies with temperature
and flow conditionsbull pipe rotation and eccentricity effects
For efficient drilling conditions it is found that the power lost in overcoming friction
in the system absorbs approximately 30-50 of the circulation energy The remainder
will be expended at the bit It is found that the majority of the system losses are in the
drill string For medium depth drilling the annular pressure losses probably total no
more than 3 to 7 of the pump output pressure at normal circulation rates
Although pressure losses in the annulus are small they are very important because of
their effect on the exposed formations
The effects of annular pressure losses are that
bull they increase the bottom hole pressure when circulating
bull they reduce the initial severity of a kick by providing a hidden safety margin
but they increase the risks of lost circulation during killing (only while
circulating)
bull they cause formation damage if the pressure losses are due to establishing
circulation When establishing circulation the pressure drop in the annulus
increases significantly due to the initial high viscosity (gel strength) of the
drilling fluid
Much research effort has been devoted to improving knowledge of the flow
characteristics of drilling fluids particularly in order to reduce pressure losses This is
a complicated and specialized subject because of the complexity of the fluids
The following expressions provide values for annular pressure losses
Where
Pfa is the annular pressure loss (kPa) Pfa is in psi
L is the pipe length (m) L is in ft
Va is the annular velocity (ms) Va is in ftmin
d is the hydraulic diameter (dh - dp) (mm) d is in inches
n is the Power Law index of flow behaviour
(dimensionless)n is dimensionless
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n and K are derived from viscometer data
Note that K here is an approximation to that given for the Power Law model found in
the section on Drilling Fluids The number 511 results from using a specific type of
viscometer with particular values of spring constant and cylinder surface speed
With Pfa as with Pfd when drilling at a particular depth with a given drilling fluid all
values in the above equations are effectively constant except for the annular velocity(Va) But Va is directly proportional to the flow rate (Q) Thus there will be a tendency
to assume that all pressure losses in the system follow the same equation as shown
below
Where c and N are constants whose values are empirically determined in particular
cases (see under Pressure losses in the drill string)
Pressure losses can be calculated for all parts of the system using the equations givenin this Part
CAUSES OF CHANGES IN CIRCULATING PRESSURES
According to Pt = P b + Ps a change in the circulating pressure can be induced by a
change in either P b Ps or both
Increases in surface pressure
A sudden increase in circulation pressure although drilling fluid properties flow rate
and conduit length are unchanged can be caused only by an increase in P b This could be caused by one or more nozzles plugging
A gradual increase in surface pressure could be the result of several causes (excepting
hole problems)
bull Increased flow rate
bull Extending the string while deepening the hole
bull Change in drilling fluid rheological properties
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Decreases in surface pressure
A spontaneous sudden decrease in circulating pressure while conditions remain
unchanged can be caused by
bull decrease of P b resulting from the loss of a nozzle
bull a twist-off in the drill string
A gradual decrease in pressure could signal the following
bull A developing wash-out (leak) in the drill string or in pump valves
bull Reduction of hydrostatic head in the annulus caused by lighter substances (eg
gas or formation water)
bull An increase of hydrostatic head in the string
Caution Any change of the surface pressure or change in pump strokes not
deliberately instigated should be investigated immediately
To a limited extent pressure losses can be measured directly for example by
pumping through the standpipe and open kelly and through drill collars It is also a
useful exercise to observe the total circulating pressure at various flow rates
Pressure losses in the system can be derived from actual circulating pressure values
by subtracting the pressure drop at the bit which can be calculated accurately
Pressure losses in the system can also be calculated However although the
dimensions are known for all parts of the system the calculation also depends on
knowing the type of fluid flow regime in the drill string and annulus The flow may be
turbulent or laminar or of some transitional type between the two The calculations are
also based on a rheological model If the drilling fluid in use behaves slightly variant
to the model the calculation results will be less than accurate
Pressure losses within the system are minimised by reducing the fluid friction in each
part
bull surface connections losses are negligible compared with elsewhere but can bereduced by avoiding tight bends and using large diameter pipes
bull drill string reduce friction by using a larger internal diameter pipe coated with
plastic
bull drill collars increasing the internal diameter will again reduce friction but
only at the expense of decreasing their weight a balance has to be made
between these opposing effects
bull annulus losses are usually small and only become significant in deep small
diameter holes pressure losses depend on the hydraulic diameter found from
the difference between the hole size and the pipe od it is actually desirable to
reduce the pressure developed against the formations
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Flow regimes
The differences between laminar and turbulent flow are illustrated in the table
overleaf The type of flow is determined by calculating Reynolds number (Re) for the
known well conditions from the following equations
The value obtained is compared with those shown in Table2 (figures are based on
Newtonian fluid properties)
Table2 Deciding the flow condition from the Reynolds number
Inspection of the equations shows that turbulent flow is more likely with the
conditions below
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bull denser drilling fluid (ρ higher)
bull lower viscosity (micro lower)
bull higher flow rate (Q higher)
bull decreased pipe bore or hydraulic
diameter
(d lower)
PUMP HYDRAULIC POWER OUTPUT
In rig operations the amount of available hydraulic power is determined by the size
number and types of pump(s) on site However the demand in terms of output volume
(Q) and pump pressure (P) varies considerably with hole size and depth Once the
pump output or flow rate Q has been selected the available power input determines
the maximum circulating pressure (Pt) that can be achieved
This circulating pressure Pt (total pressure drop in system) is consumed partly by
friction in the fluid and the system (Ps = system pressure loss) and partly by the
pressure drop across the bit nozzles (P b = bit pressure drop) Therefore P t = Ps + P b Pt
is normally given by the pump pressure gauge
The system pressure drop has no effect on bottom-hole cleaning It is unavoidable andis also called the parasitic pressure loss
The bottom-hole cleaning action is provided by the hydraulic energy expended at the
bit Therefore the amount of hydraulic power expended at the bit is a measure for the
cleaning effectiveness (This assumes that the bit is properly matched to the formation
- if a bit designed for a hard formation is run in a soft formation no amount of power
will keep it clean )
The hydraulic power available at the surface from the pump is used to drive the
drilling fluid round the system power the bit and flush the cuttings to the surface If
you know the pump or circulating pressure (Pt ) and the flow rate (Q) then it is possible to calculate the total power available at the surface
Since Power = work done in unit time
and Work done = pressure x volume
then Power = pressure x volume pumped in unit time
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Therefore the power available at surface is given by
The power output of the pump is generally assumed to be 85 of the mechanical or
electrical power input of the pump
PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)
The pressure drop across the bit nozzles P b depends on
bull The flow rate Q
bull The total cross-sectional area of the nozzle openings A
bull The drilling fluid density ρ
Once the desired (optimum) annular velocity has been determined the flow rate (Q )
and the hydraulic power expended at the bit for a given nozzle size are fixed
Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power
expended at the bit is also fixed Both jet velocity and hydraulic power at the bit
determine the cleaning action on bottom
Pressure losses through the bit nozzles are not frictional but represent a change in
kinetic energy as the drilling fluid changes its velocity from that above the bit to that
leaving the jets The pressure expended is therefore dependent only on the drilling
fluid density and the square of the jet velocity
The pressure drop across the bit nozzles is calculated using the following equations
Where
P b is the pressure loss across the bit nozzles (kPa)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
A is the total nozzle area (mm2)
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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The volume output for double acting pumps is obtained with the following equation
The value of factor K in this equation is
0middot0257 when the flow rate Q is in dm3min (lmin)
0middot00679 when the flow rate Q is in galsmin
0middot000162 when the flow rate Q is in bblmin
0middot000909 when the flow rate Q is in ft3min
For single acting triplex pumps the equation to be used is
where the value of K is
0middot0386 when the flow rate Q is in dm3min (lmin)
0middot010199 when the flow rate Q is in galsmin
0middot000243 when the flow rate Q is in bblmin
0middot001364 when the flow rate Q is in ft3min
In both the equations
L = stroke in inches
D = inside diameter of liner in inches
d = outside diameter of piston rod in inches
spm = strokes per minute
nvol = volumetric efficiency as percentage
The pump or circulating pressure (Pt ) is usually measured directly at the surface with
a standpipe gauge It can also be estimated using the following
bull
the dimensions of the hole and drill stringbull rheological drilling fluid properties
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bull nozzle area
bull flow rate
The units for Pt are kPa or psi
CIRCULATING PRESSURE AND PRESSURE DROP IN THE HYDRAULICSYSTEM
Since the drilling fluid returns to the surface at atmospheric pressure (in normal
drilling operations) all the pressure developed by the pump is used between it and the
flowline
Thus Pt = Ps + P b
Where
Pt is the pump or circulating pressure (kPa or psi)
Ps is the total of all pressure losses except at the bit (kPa or psi)
P b is the pressure drop across bit nozzles (kPa or psi)
FLOW RATE (Q)
The flow rate is the volume of drilling fluid passing any point in unit time It is
usually expressed in m3s or m3min (m3sec will be used throughout this Part) In
oilfield units it is expressed in bblsmin or galsmin (gpm)
The flow rate can be measured directly with a flow meter in the surface lines usually
between pump and standpipe
BIT NOZZLE JET VELOCITY (Vn)
The jet velocity is the governing parameter in the impact-force method of maximized
bottom-hole cleaning The higher the jet velocity the better the cleaning effect The
accepted minimum value for optimized bottom hole cleaning is approximately 100
ms (350 fts)
The jet velocity is calculated from the jet nozzle area and the flow rate
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ANNULAR VELOCITY (Van)
The annular velocity is the speed with which the drilling fluid rises in the annulus and
is expressed in mmin (ftmin)
The annular drilling fluid velocity is confined by an upper and a lower limit
MAXIMUM ANNULAR VELOCITY
The upper velocity limit is determined by the effects of erosion on soft formations (or
maximum possible pump output volume) Wash-outs can easily be created in such
situations
The maximum annular velocity in sensitive formations is often limited to 30 mmin
(100 ftmin) to prevent wash-outs
MINIMUM ANNULAR VELOCITY
The lower limit is always governed by the cuttings transport capacity of the drilling
fluid
Too much build-up of cuttings in the drilling fluid will result in an increase in the
density of the fluid in the annulus The consequent increase in hydrostatic head
against exposed weak formations could cause formation break-down and loss of
circulation It could also cause stuck pipe in a deviated well (building up of cuttings
bed)
The annular velocity should therefore in relation to the cuttings generated be
sufficient to maintain densities within formation strength limits
However the minimum annular velocity is also dependent on the slip velocity (rate of
settling of the cuttings) As a result of gravity the cuttings tend to drop through the
drilling fluid Therefore when the slip velocity exceeds the annular velocity the
particles will not be carried out of the well There will be insufficient returns of large
cuttings over the shale shaker and due to regrinding erosion and deterioration the
solid content and density of the drilling fluid will increase
APPLIED ANNULAR VELOCITY
The annular velocity depends on the flow rate and the flow area the latter of which is
not constant The drill-pipe open-hole area must be considered when determining the
maximum or minimum value for the velocity This means that the actual velocity in
the drill-collar open-hole annulus may be higher than the recommended value
However that often has to be accepted The DC-OH section is comparatively short so
that the wellbore wall in soft formations will be exposed only briefly to these higher
erosive effects In harder formations erosion often becomes negligible
The annular velocity at a given flow rate can be calculated by the following equations
derived from the general equation Q = VA
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When drilling hard formations where penetration rates are low lower annular
velocities can be used In soft formations with high penetration rate often
encountered in top-hole drilling higher annular velocities will be required to remove
the cuttings from the well
Because the total pump capacity is limited sometimes it is not possible to obtainsufficient annular velocity especially in drilling large hole sizes If the fluid density is
critical because weak formations are exposed the drilling rate may have to be
adjusted to reduce the amount of cuttings generated
Generally speaking the minimum practical annular velocity is maintained above a
value of approximately 17 mmin (50 ftmin) in the very large hole sizes In the
smaller holes the more common value of 30 - 40 mmin (90 - 120 ftmin) usually
applies (the smaller hole size is usually at greater depth where the formations are
more consolidated)
Selection of an appropriate annular velocity is one of the first decisions to be takenwhen considering hydraulic conditions
Actual annular velocities are uncertain due to the irregularity of the hole size and
configuration During drilling the actual hole size is not known for this reason the bit
size is taken as the internal diameter of the hole or the last measured average caliper
hole size obtained from logs for calculation purposes
Between the maximum annular velocity and the minimum annular velocity is an
annular velocity which under the given circumstances is the best annular velocity to
be used This is called the optimum annular velocity
OPTIMUM ANNULAR VELOCITY
The optimum annular velocity is that velocity which is obtained through a flow rate
which gives an annular velocity sufficiently high to effectively remove cuttings from
the hole and having the lowest possible erosion effect on the borehole
Over time any flow results in erosion It is therefore advisable to obtain the minimum
flow rate required to effectively remove cuttings from the hole and to avoid
circulating any faster than is required to obtain this flow rate If this rate is a
calculated rate actual hole cleaning should be monitored to confirm the hole cleaningability of this flow rate
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You should be able to distinguish clearly between flow rate and annular velocity
PRESSURE LOSSES IN THE SYSTEM (Ps) (PARASITIC PRESSURE
LOSSES)
What is the system
The system is made up of all parts between the pump and the flowlines with the
exception of the bit nozzles These are excluded because pressure drop across the
nozzles is considered a useful loss of pressure It represents the change in kinetic
energy used to clean the bottom of the hole Pressure losses in the system represent
wasted energy used in overcoming friction These pressure losses are called parasitic
losses
The main sections of the circulating system which contribute to the system losses may
be summarized as follows
bull The surface lines (from pump to kelly saver sub)
bull The drill string (drill pipe and drill collars)
bull The annulus (open hole and cased hole)
In addition we will look at
bull causes of changes in circulating pressures
bull flow regimes
PRESSURE LOSSES IN SURFACE EQUIPMENT
Surface equipment consists of surface lines stand pipe kelly hose swivel and kelly
The pressure loss occurring in this equipment depends on the length and the internal
diameters of each of the items mentioned A simple practical method to find the
surface equipment pressure losses is to hang the kelly or top drive open ended in the
rotary table and pump at different rates
Table1 shows four common combinations of surface equipment The case numbers inthis table (No1 to No4) were originally intended for use with hydraulic slide rules
They are now also used to identify different surface pressure loss situations to be used
in calculations
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PRESSURE LOSSES IN THE DRILL STRING (Pf d)
The pressure loss in the drill string represents the major portion of the parasitic losses
The fluid velocities are usually high and therefore friction loss is significant as the
flow regime in most cases is turbulent The losses calculated across the drill pipe and
the drill collars are based on the Bingham Plastic Flow model
When drilling the flow pattern in the drill string is normally turbulent (With
reference to the factors above consider why this should be true) There is no exact
method of calculating pressure losses in the drill string because there is no exact
method of establishing the degree of turbulence However it is possible to estimate
pressure losses in the drill string with sufficient accuracy to select appropriate bit
nozzles for optimizing hydraulic conditions
Pressure losses in the drill string can be calculated by the following equations
You should have noticed the introduction of a new term the friction factor (f) It can
be defined in terms of Reynolds Number (and hence flow rate) and pipe roughness
and has been determined empirically
If circulating a given drilling fluid at a given depth only V and f can vary and both of
these are proportional to flow rate The equations for pressure losses in the drill string
as given above can also be expressed in the equation
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Where c is a constant incorporating the values of all the parameters which are fixed at
a given depth
N is found empirically and is not the same n as in the equations in the paragraphs on
the following pages dealing with pressure losses in the annulus The latter is called a
rheological n
c is given in SI units or API units respectively by
Where is the plastic viscosity and the other symbols are as used before Note that Nis often taken as 182
PRESSURE LOSSES IN THE ANNULUS (Pfa )
Since the annular pressure loss acts as an applied pressure on the formation this loss
should be kept as low as possible to minimise the risk of formation break down To
monitor the pressure against the formation during circulation the equivalent
circulation density (ECD) is often used which is defined as
Where
ECD = equivalent circulating density (kPam psift)
ρm = density of the drilling fluid (kPam psift)
Pan = total pressure drop in the annulus (kPa psi)
L = total length of the annulus (m ft)
The value of the annular pressure loss is relatively small compared to that developed
in the drill string and is often neglected in cases where the circulation rate is low eg
during well killing
It is more difficult to find pressure losses in the annulus because conditions are less
well defined than in the drillpipe
The following uncertainties exist
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bull the actual flow condition is not clear the flow pattern is commonly near the
transitional region
bull the hole size and shape are irregular so it is not possible to get an accurate
value for the annular velocity or the hydraulic diameter
bull the downhole viscosity is very uncertain because it varies with temperature
and flow conditionsbull pipe rotation and eccentricity effects
For efficient drilling conditions it is found that the power lost in overcoming friction
in the system absorbs approximately 30-50 of the circulation energy The remainder
will be expended at the bit It is found that the majority of the system losses are in the
drill string For medium depth drilling the annular pressure losses probably total no
more than 3 to 7 of the pump output pressure at normal circulation rates
Although pressure losses in the annulus are small they are very important because of
their effect on the exposed formations
The effects of annular pressure losses are that
bull they increase the bottom hole pressure when circulating
bull they reduce the initial severity of a kick by providing a hidden safety margin
but they increase the risks of lost circulation during killing (only while
circulating)
bull they cause formation damage if the pressure losses are due to establishing
circulation When establishing circulation the pressure drop in the annulus
increases significantly due to the initial high viscosity (gel strength) of the
drilling fluid
Much research effort has been devoted to improving knowledge of the flow
characteristics of drilling fluids particularly in order to reduce pressure losses This is
a complicated and specialized subject because of the complexity of the fluids
The following expressions provide values for annular pressure losses
Where
Pfa is the annular pressure loss (kPa) Pfa is in psi
L is the pipe length (m) L is in ft
Va is the annular velocity (ms) Va is in ftmin
d is the hydraulic diameter (dh - dp) (mm) d is in inches
n is the Power Law index of flow behaviour
(dimensionless)n is dimensionless
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n and K are derived from viscometer data
Note that K here is an approximation to that given for the Power Law model found in
the section on Drilling Fluids The number 511 results from using a specific type of
viscometer with particular values of spring constant and cylinder surface speed
With Pfa as with Pfd when drilling at a particular depth with a given drilling fluid all
values in the above equations are effectively constant except for the annular velocity(Va) But Va is directly proportional to the flow rate (Q) Thus there will be a tendency
to assume that all pressure losses in the system follow the same equation as shown
below
Where c and N are constants whose values are empirically determined in particular
cases (see under Pressure losses in the drill string)
Pressure losses can be calculated for all parts of the system using the equations givenin this Part
CAUSES OF CHANGES IN CIRCULATING PRESSURES
According to Pt = P b + Ps a change in the circulating pressure can be induced by a
change in either P b Ps or both
Increases in surface pressure
A sudden increase in circulation pressure although drilling fluid properties flow rate
and conduit length are unchanged can be caused only by an increase in P b This could be caused by one or more nozzles plugging
A gradual increase in surface pressure could be the result of several causes (excepting
hole problems)
bull Increased flow rate
bull Extending the string while deepening the hole
bull Change in drilling fluid rheological properties
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Decreases in surface pressure
A spontaneous sudden decrease in circulating pressure while conditions remain
unchanged can be caused by
bull decrease of P b resulting from the loss of a nozzle
bull a twist-off in the drill string
A gradual decrease in pressure could signal the following
bull A developing wash-out (leak) in the drill string or in pump valves
bull Reduction of hydrostatic head in the annulus caused by lighter substances (eg
gas or formation water)
bull An increase of hydrostatic head in the string
Caution Any change of the surface pressure or change in pump strokes not
deliberately instigated should be investigated immediately
To a limited extent pressure losses can be measured directly for example by
pumping through the standpipe and open kelly and through drill collars It is also a
useful exercise to observe the total circulating pressure at various flow rates
Pressure losses in the system can be derived from actual circulating pressure values
by subtracting the pressure drop at the bit which can be calculated accurately
Pressure losses in the system can also be calculated However although the
dimensions are known for all parts of the system the calculation also depends on
knowing the type of fluid flow regime in the drill string and annulus The flow may be
turbulent or laminar or of some transitional type between the two The calculations are
also based on a rheological model If the drilling fluid in use behaves slightly variant
to the model the calculation results will be less than accurate
Pressure losses within the system are minimised by reducing the fluid friction in each
part
bull surface connections losses are negligible compared with elsewhere but can bereduced by avoiding tight bends and using large diameter pipes
bull drill string reduce friction by using a larger internal diameter pipe coated with
plastic
bull drill collars increasing the internal diameter will again reduce friction but
only at the expense of decreasing their weight a balance has to be made
between these opposing effects
bull annulus losses are usually small and only become significant in deep small
diameter holes pressure losses depend on the hydraulic diameter found from
the difference between the hole size and the pipe od it is actually desirable to
reduce the pressure developed against the formations
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Flow regimes
The differences between laminar and turbulent flow are illustrated in the table
overleaf The type of flow is determined by calculating Reynolds number (Re) for the
known well conditions from the following equations
The value obtained is compared with those shown in Table2 (figures are based on
Newtonian fluid properties)
Table2 Deciding the flow condition from the Reynolds number
Inspection of the equations shows that turbulent flow is more likely with the
conditions below
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bull denser drilling fluid (ρ higher)
bull lower viscosity (micro lower)
bull higher flow rate (Q higher)
bull decreased pipe bore or hydraulic
diameter
(d lower)
PUMP HYDRAULIC POWER OUTPUT
In rig operations the amount of available hydraulic power is determined by the size
number and types of pump(s) on site However the demand in terms of output volume
(Q) and pump pressure (P) varies considerably with hole size and depth Once the
pump output or flow rate Q has been selected the available power input determines
the maximum circulating pressure (Pt) that can be achieved
This circulating pressure Pt (total pressure drop in system) is consumed partly by
friction in the fluid and the system (Ps = system pressure loss) and partly by the
pressure drop across the bit nozzles (P b = bit pressure drop) Therefore P t = Ps + P b Pt
is normally given by the pump pressure gauge
The system pressure drop has no effect on bottom-hole cleaning It is unavoidable andis also called the parasitic pressure loss
The bottom-hole cleaning action is provided by the hydraulic energy expended at the
bit Therefore the amount of hydraulic power expended at the bit is a measure for the
cleaning effectiveness (This assumes that the bit is properly matched to the formation
- if a bit designed for a hard formation is run in a soft formation no amount of power
will keep it clean )
The hydraulic power available at the surface from the pump is used to drive the
drilling fluid round the system power the bit and flush the cuttings to the surface If
you know the pump or circulating pressure (Pt ) and the flow rate (Q) then it is possible to calculate the total power available at the surface
Since Power = work done in unit time
and Work done = pressure x volume
then Power = pressure x volume pumped in unit time
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Therefore the power available at surface is given by
The power output of the pump is generally assumed to be 85 of the mechanical or
electrical power input of the pump
PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)
The pressure drop across the bit nozzles P b depends on
bull The flow rate Q
bull The total cross-sectional area of the nozzle openings A
bull The drilling fluid density ρ
Once the desired (optimum) annular velocity has been determined the flow rate (Q )
and the hydraulic power expended at the bit for a given nozzle size are fixed
Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power
expended at the bit is also fixed Both jet velocity and hydraulic power at the bit
determine the cleaning action on bottom
Pressure losses through the bit nozzles are not frictional but represent a change in
kinetic energy as the drilling fluid changes its velocity from that above the bit to that
leaving the jets The pressure expended is therefore dependent only on the drilling
fluid density and the square of the jet velocity
The pressure drop across the bit nozzles is calculated using the following equations
Where
P b is the pressure loss across the bit nozzles (kPa)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
A is the total nozzle area (mm2)
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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bull nozzle area
bull flow rate
The units for Pt are kPa or psi
CIRCULATING PRESSURE AND PRESSURE DROP IN THE HYDRAULICSYSTEM
Since the drilling fluid returns to the surface at atmospheric pressure (in normal
drilling operations) all the pressure developed by the pump is used between it and the
flowline
Thus Pt = Ps + P b
Where
Pt is the pump or circulating pressure (kPa or psi)
Ps is the total of all pressure losses except at the bit (kPa or psi)
P b is the pressure drop across bit nozzles (kPa or psi)
FLOW RATE (Q)
The flow rate is the volume of drilling fluid passing any point in unit time It is
usually expressed in m3s or m3min (m3sec will be used throughout this Part) In
oilfield units it is expressed in bblsmin or galsmin (gpm)
The flow rate can be measured directly with a flow meter in the surface lines usually
between pump and standpipe
BIT NOZZLE JET VELOCITY (Vn)
The jet velocity is the governing parameter in the impact-force method of maximized
bottom-hole cleaning The higher the jet velocity the better the cleaning effect The
accepted minimum value for optimized bottom hole cleaning is approximately 100
ms (350 fts)
The jet velocity is calculated from the jet nozzle area and the flow rate
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ANNULAR VELOCITY (Van)
The annular velocity is the speed with which the drilling fluid rises in the annulus and
is expressed in mmin (ftmin)
The annular drilling fluid velocity is confined by an upper and a lower limit
MAXIMUM ANNULAR VELOCITY
The upper velocity limit is determined by the effects of erosion on soft formations (or
maximum possible pump output volume) Wash-outs can easily be created in such
situations
The maximum annular velocity in sensitive formations is often limited to 30 mmin
(100 ftmin) to prevent wash-outs
MINIMUM ANNULAR VELOCITY
The lower limit is always governed by the cuttings transport capacity of the drilling
fluid
Too much build-up of cuttings in the drilling fluid will result in an increase in the
density of the fluid in the annulus The consequent increase in hydrostatic head
against exposed weak formations could cause formation break-down and loss of
circulation It could also cause stuck pipe in a deviated well (building up of cuttings
bed)
The annular velocity should therefore in relation to the cuttings generated be
sufficient to maintain densities within formation strength limits
However the minimum annular velocity is also dependent on the slip velocity (rate of
settling of the cuttings) As a result of gravity the cuttings tend to drop through the
drilling fluid Therefore when the slip velocity exceeds the annular velocity the
particles will not be carried out of the well There will be insufficient returns of large
cuttings over the shale shaker and due to regrinding erosion and deterioration the
solid content and density of the drilling fluid will increase
APPLIED ANNULAR VELOCITY
The annular velocity depends on the flow rate and the flow area the latter of which is
not constant The drill-pipe open-hole area must be considered when determining the
maximum or minimum value for the velocity This means that the actual velocity in
the drill-collar open-hole annulus may be higher than the recommended value
However that often has to be accepted The DC-OH section is comparatively short so
that the wellbore wall in soft formations will be exposed only briefly to these higher
erosive effects In harder formations erosion often becomes negligible
The annular velocity at a given flow rate can be calculated by the following equations
derived from the general equation Q = VA
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When drilling hard formations where penetration rates are low lower annular
velocities can be used In soft formations with high penetration rate often
encountered in top-hole drilling higher annular velocities will be required to remove
the cuttings from the well
Because the total pump capacity is limited sometimes it is not possible to obtainsufficient annular velocity especially in drilling large hole sizes If the fluid density is
critical because weak formations are exposed the drilling rate may have to be
adjusted to reduce the amount of cuttings generated
Generally speaking the minimum practical annular velocity is maintained above a
value of approximately 17 mmin (50 ftmin) in the very large hole sizes In the
smaller holes the more common value of 30 - 40 mmin (90 - 120 ftmin) usually
applies (the smaller hole size is usually at greater depth where the formations are
more consolidated)
Selection of an appropriate annular velocity is one of the first decisions to be takenwhen considering hydraulic conditions
Actual annular velocities are uncertain due to the irregularity of the hole size and
configuration During drilling the actual hole size is not known for this reason the bit
size is taken as the internal diameter of the hole or the last measured average caliper
hole size obtained from logs for calculation purposes
Between the maximum annular velocity and the minimum annular velocity is an
annular velocity which under the given circumstances is the best annular velocity to
be used This is called the optimum annular velocity
OPTIMUM ANNULAR VELOCITY
The optimum annular velocity is that velocity which is obtained through a flow rate
which gives an annular velocity sufficiently high to effectively remove cuttings from
the hole and having the lowest possible erosion effect on the borehole
Over time any flow results in erosion It is therefore advisable to obtain the minimum
flow rate required to effectively remove cuttings from the hole and to avoid
circulating any faster than is required to obtain this flow rate If this rate is a
calculated rate actual hole cleaning should be monitored to confirm the hole cleaningability of this flow rate
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You should be able to distinguish clearly between flow rate and annular velocity
PRESSURE LOSSES IN THE SYSTEM (Ps) (PARASITIC PRESSURE
LOSSES)
What is the system
The system is made up of all parts between the pump and the flowlines with the
exception of the bit nozzles These are excluded because pressure drop across the
nozzles is considered a useful loss of pressure It represents the change in kinetic
energy used to clean the bottom of the hole Pressure losses in the system represent
wasted energy used in overcoming friction These pressure losses are called parasitic
losses
The main sections of the circulating system which contribute to the system losses may
be summarized as follows
bull The surface lines (from pump to kelly saver sub)
bull The drill string (drill pipe and drill collars)
bull The annulus (open hole and cased hole)
In addition we will look at
bull causes of changes in circulating pressures
bull flow regimes
PRESSURE LOSSES IN SURFACE EQUIPMENT
Surface equipment consists of surface lines stand pipe kelly hose swivel and kelly
The pressure loss occurring in this equipment depends on the length and the internal
diameters of each of the items mentioned A simple practical method to find the
surface equipment pressure losses is to hang the kelly or top drive open ended in the
rotary table and pump at different rates
Table1 shows four common combinations of surface equipment The case numbers inthis table (No1 to No4) were originally intended for use with hydraulic slide rules
They are now also used to identify different surface pressure loss situations to be used
in calculations
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PRESSURE LOSSES IN THE DRILL STRING (Pf d)
The pressure loss in the drill string represents the major portion of the parasitic losses
The fluid velocities are usually high and therefore friction loss is significant as the
flow regime in most cases is turbulent The losses calculated across the drill pipe and
the drill collars are based on the Bingham Plastic Flow model
When drilling the flow pattern in the drill string is normally turbulent (With
reference to the factors above consider why this should be true) There is no exact
method of calculating pressure losses in the drill string because there is no exact
method of establishing the degree of turbulence However it is possible to estimate
pressure losses in the drill string with sufficient accuracy to select appropriate bit
nozzles for optimizing hydraulic conditions
Pressure losses in the drill string can be calculated by the following equations
You should have noticed the introduction of a new term the friction factor (f) It can
be defined in terms of Reynolds Number (and hence flow rate) and pipe roughness
and has been determined empirically
If circulating a given drilling fluid at a given depth only V and f can vary and both of
these are proportional to flow rate The equations for pressure losses in the drill string
as given above can also be expressed in the equation
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Where c is a constant incorporating the values of all the parameters which are fixed at
a given depth
N is found empirically and is not the same n as in the equations in the paragraphs on
the following pages dealing with pressure losses in the annulus The latter is called a
rheological n
c is given in SI units or API units respectively by
Where is the plastic viscosity and the other symbols are as used before Note that Nis often taken as 182
PRESSURE LOSSES IN THE ANNULUS (Pfa )
Since the annular pressure loss acts as an applied pressure on the formation this loss
should be kept as low as possible to minimise the risk of formation break down To
monitor the pressure against the formation during circulation the equivalent
circulation density (ECD) is often used which is defined as
Where
ECD = equivalent circulating density (kPam psift)
ρm = density of the drilling fluid (kPam psift)
Pan = total pressure drop in the annulus (kPa psi)
L = total length of the annulus (m ft)
The value of the annular pressure loss is relatively small compared to that developed
in the drill string and is often neglected in cases where the circulation rate is low eg
during well killing
It is more difficult to find pressure losses in the annulus because conditions are less
well defined than in the drillpipe
The following uncertainties exist
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bull the actual flow condition is not clear the flow pattern is commonly near the
transitional region
bull the hole size and shape are irregular so it is not possible to get an accurate
value for the annular velocity or the hydraulic diameter
bull the downhole viscosity is very uncertain because it varies with temperature
and flow conditionsbull pipe rotation and eccentricity effects
For efficient drilling conditions it is found that the power lost in overcoming friction
in the system absorbs approximately 30-50 of the circulation energy The remainder
will be expended at the bit It is found that the majority of the system losses are in the
drill string For medium depth drilling the annular pressure losses probably total no
more than 3 to 7 of the pump output pressure at normal circulation rates
Although pressure losses in the annulus are small they are very important because of
their effect on the exposed formations
The effects of annular pressure losses are that
bull they increase the bottom hole pressure when circulating
bull they reduce the initial severity of a kick by providing a hidden safety margin
but they increase the risks of lost circulation during killing (only while
circulating)
bull they cause formation damage if the pressure losses are due to establishing
circulation When establishing circulation the pressure drop in the annulus
increases significantly due to the initial high viscosity (gel strength) of the
drilling fluid
Much research effort has been devoted to improving knowledge of the flow
characteristics of drilling fluids particularly in order to reduce pressure losses This is
a complicated and specialized subject because of the complexity of the fluids
The following expressions provide values for annular pressure losses
Where
Pfa is the annular pressure loss (kPa) Pfa is in psi
L is the pipe length (m) L is in ft
Va is the annular velocity (ms) Va is in ftmin
d is the hydraulic diameter (dh - dp) (mm) d is in inches
n is the Power Law index of flow behaviour
(dimensionless)n is dimensionless
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n and K are derived from viscometer data
Note that K here is an approximation to that given for the Power Law model found in
the section on Drilling Fluids The number 511 results from using a specific type of
viscometer with particular values of spring constant and cylinder surface speed
With Pfa as with Pfd when drilling at a particular depth with a given drilling fluid all
values in the above equations are effectively constant except for the annular velocity(Va) But Va is directly proportional to the flow rate (Q) Thus there will be a tendency
to assume that all pressure losses in the system follow the same equation as shown
below
Where c and N are constants whose values are empirically determined in particular
cases (see under Pressure losses in the drill string)
Pressure losses can be calculated for all parts of the system using the equations givenin this Part
CAUSES OF CHANGES IN CIRCULATING PRESSURES
According to Pt = P b + Ps a change in the circulating pressure can be induced by a
change in either P b Ps or both
Increases in surface pressure
A sudden increase in circulation pressure although drilling fluid properties flow rate
and conduit length are unchanged can be caused only by an increase in P b This could be caused by one or more nozzles plugging
A gradual increase in surface pressure could be the result of several causes (excepting
hole problems)
bull Increased flow rate
bull Extending the string while deepening the hole
bull Change in drilling fluid rheological properties
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Decreases in surface pressure
A spontaneous sudden decrease in circulating pressure while conditions remain
unchanged can be caused by
bull decrease of P b resulting from the loss of a nozzle
bull a twist-off in the drill string
A gradual decrease in pressure could signal the following
bull A developing wash-out (leak) in the drill string or in pump valves
bull Reduction of hydrostatic head in the annulus caused by lighter substances (eg
gas or formation water)
bull An increase of hydrostatic head in the string
Caution Any change of the surface pressure or change in pump strokes not
deliberately instigated should be investigated immediately
To a limited extent pressure losses can be measured directly for example by
pumping through the standpipe and open kelly and through drill collars It is also a
useful exercise to observe the total circulating pressure at various flow rates
Pressure losses in the system can be derived from actual circulating pressure values
by subtracting the pressure drop at the bit which can be calculated accurately
Pressure losses in the system can also be calculated However although the
dimensions are known for all parts of the system the calculation also depends on
knowing the type of fluid flow regime in the drill string and annulus The flow may be
turbulent or laminar or of some transitional type between the two The calculations are
also based on a rheological model If the drilling fluid in use behaves slightly variant
to the model the calculation results will be less than accurate
Pressure losses within the system are minimised by reducing the fluid friction in each
part
bull surface connections losses are negligible compared with elsewhere but can bereduced by avoiding tight bends and using large diameter pipes
bull drill string reduce friction by using a larger internal diameter pipe coated with
plastic
bull drill collars increasing the internal diameter will again reduce friction but
only at the expense of decreasing their weight a balance has to be made
between these opposing effects
bull annulus losses are usually small and only become significant in deep small
diameter holes pressure losses depend on the hydraulic diameter found from
the difference between the hole size and the pipe od it is actually desirable to
reduce the pressure developed against the formations
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Flow regimes
The differences between laminar and turbulent flow are illustrated in the table
overleaf The type of flow is determined by calculating Reynolds number (Re) for the
known well conditions from the following equations
The value obtained is compared with those shown in Table2 (figures are based on
Newtonian fluid properties)
Table2 Deciding the flow condition from the Reynolds number
Inspection of the equations shows that turbulent flow is more likely with the
conditions below
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bull denser drilling fluid (ρ higher)
bull lower viscosity (micro lower)
bull higher flow rate (Q higher)
bull decreased pipe bore or hydraulic
diameter
(d lower)
PUMP HYDRAULIC POWER OUTPUT
In rig operations the amount of available hydraulic power is determined by the size
number and types of pump(s) on site However the demand in terms of output volume
(Q) and pump pressure (P) varies considerably with hole size and depth Once the
pump output or flow rate Q has been selected the available power input determines
the maximum circulating pressure (Pt) that can be achieved
This circulating pressure Pt (total pressure drop in system) is consumed partly by
friction in the fluid and the system (Ps = system pressure loss) and partly by the
pressure drop across the bit nozzles (P b = bit pressure drop) Therefore P t = Ps + P b Pt
is normally given by the pump pressure gauge
The system pressure drop has no effect on bottom-hole cleaning It is unavoidable andis also called the parasitic pressure loss
The bottom-hole cleaning action is provided by the hydraulic energy expended at the
bit Therefore the amount of hydraulic power expended at the bit is a measure for the
cleaning effectiveness (This assumes that the bit is properly matched to the formation
- if a bit designed for a hard formation is run in a soft formation no amount of power
will keep it clean )
The hydraulic power available at the surface from the pump is used to drive the
drilling fluid round the system power the bit and flush the cuttings to the surface If
you know the pump or circulating pressure (Pt ) and the flow rate (Q) then it is possible to calculate the total power available at the surface
Since Power = work done in unit time
and Work done = pressure x volume
then Power = pressure x volume pumped in unit time
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Therefore the power available at surface is given by
The power output of the pump is generally assumed to be 85 of the mechanical or
electrical power input of the pump
PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)
The pressure drop across the bit nozzles P b depends on
bull The flow rate Q
bull The total cross-sectional area of the nozzle openings A
bull The drilling fluid density ρ
Once the desired (optimum) annular velocity has been determined the flow rate (Q )
and the hydraulic power expended at the bit for a given nozzle size are fixed
Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power
expended at the bit is also fixed Both jet velocity and hydraulic power at the bit
determine the cleaning action on bottom
Pressure losses through the bit nozzles are not frictional but represent a change in
kinetic energy as the drilling fluid changes its velocity from that above the bit to that
leaving the jets The pressure expended is therefore dependent only on the drilling
fluid density and the square of the jet velocity
The pressure drop across the bit nozzles is calculated using the following equations
Where
P b is the pressure loss across the bit nozzles (kPa)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
A is the total nozzle area (mm2)
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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ANNULAR VELOCITY (Van)
The annular velocity is the speed with which the drilling fluid rises in the annulus and
is expressed in mmin (ftmin)
The annular drilling fluid velocity is confined by an upper and a lower limit
MAXIMUM ANNULAR VELOCITY
The upper velocity limit is determined by the effects of erosion on soft formations (or
maximum possible pump output volume) Wash-outs can easily be created in such
situations
The maximum annular velocity in sensitive formations is often limited to 30 mmin
(100 ftmin) to prevent wash-outs
MINIMUM ANNULAR VELOCITY
The lower limit is always governed by the cuttings transport capacity of the drilling
fluid
Too much build-up of cuttings in the drilling fluid will result in an increase in the
density of the fluid in the annulus The consequent increase in hydrostatic head
against exposed weak formations could cause formation break-down and loss of
circulation It could also cause stuck pipe in a deviated well (building up of cuttings
bed)
The annular velocity should therefore in relation to the cuttings generated be
sufficient to maintain densities within formation strength limits
However the minimum annular velocity is also dependent on the slip velocity (rate of
settling of the cuttings) As a result of gravity the cuttings tend to drop through the
drilling fluid Therefore when the slip velocity exceeds the annular velocity the
particles will not be carried out of the well There will be insufficient returns of large
cuttings over the shale shaker and due to regrinding erosion and deterioration the
solid content and density of the drilling fluid will increase
APPLIED ANNULAR VELOCITY
The annular velocity depends on the flow rate and the flow area the latter of which is
not constant The drill-pipe open-hole area must be considered when determining the
maximum or minimum value for the velocity This means that the actual velocity in
the drill-collar open-hole annulus may be higher than the recommended value
However that often has to be accepted The DC-OH section is comparatively short so
that the wellbore wall in soft formations will be exposed only briefly to these higher
erosive effects In harder formations erosion often becomes negligible
The annular velocity at a given flow rate can be calculated by the following equations
derived from the general equation Q = VA
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When drilling hard formations where penetration rates are low lower annular
velocities can be used In soft formations with high penetration rate often
encountered in top-hole drilling higher annular velocities will be required to remove
the cuttings from the well
Because the total pump capacity is limited sometimes it is not possible to obtainsufficient annular velocity especially in drilling large hole sizes If the fluid density is
critical because weak formations are exposed the drilling rate may have to be
adjusted to reduce the amount of cuttings generated
Generally speaking the minimum practical annular velocity is maintained above a
value of approximately 17 mmin (50 ftmin) in the very large hole sizes In the
smaller holes the more common value of 30 - 40 mmin (90 - 120 ftmin) usually
applies (the smaller hole size is usually at greater depth where the formations are
more consolidated)
Selection of an appropriate annular velocity is one of the first decisions to be takenwhen considering hydraulic conditions
Actual annular velocities are uncertain due to the irregularity of the hole size and
configuration During drilling the actual hole size is not known for this reason the bit
size is taken as the internal diameter of the hole or the last measured average caliper
hole size obtained from logs for calculation purposes
Between the maximum annular velocity and the minimum annular velocity is an
annular velocity which under the given circumstances is the best annular velocity to
be used This is called the optimum annular velocity
OPTIMUM ANNULAR VELOCITY
The optimum annular velocity is that velocity which is obtained through a flow rate
which gives an annular velocity sufficiently high to effectively remove cuttings from
the hole and having the lowest possible erosion effect on the borehole
Over time any flow results in erosion It is therefore advisable to obtain the minimum
flow rate required to effectively remove cuttings from the hole and to avoid
circulating any faster than is required to obtain this flow rate If this rate is a
calculated rate actual hole cleaning should be monitored to confirm the hole cleaningability of this flow rate
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You should be able to distinguish clearly between flow rate and annular velocity
PRESSURE LOSSES IN THE SYSTEM (Ps) (PARASITIC PRESSURE
LOSSES)
What is the system
The system is made up of all parts between the pump and the flowlines with the
exception of the bit nozzles These are excluded because pressure drop across the
nozzles is considered a useful loss of pressure It represents the change in kinetic
energy used to clean the bottom of the hole Pressure losses in the system represent
wasted energy used in overcoming friction These pressure losses are called parasitic
losses
The main sections of the circulating system which contribute to the system losses may
be summarized as follows
bull The surface lines (from pump to kelly saver sub)
bull The drill string (drill pipe and drill collars)
bull The annulus (open hole and cased hole)
In addition we will look at
bull causes of changes in circulating pressures
bull flow regimes
PRESSURE LOSSES IN SURFACE EQUIPMENT
Surface equipment consists of surface lines stand pipe kelly hose swivel and kelly
The pressure loss occurring in this equipment depends on the length and the internal
diameters of each of the items mentioned A simple practical method to find the
surface equipment pressure losses is to hang the kelly or top drive open ended in the
rotary table and pump at different rates
Table1 shows four common combinations of surface equipment The case numbers inthis table (No1 to No4) were originally intended for use with hydraulic slide rules
They are now also used to identify different surface pressure loss situations to be used
in calculations
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PRESSURE LOSSES IN THE DRILL STRING (Pf d)
The pressure loss in the drill string represents the major portion of the parasitic losses
The fluid velocities are usually high and therefore friction loss is significant as the
flow regime in most cases is turbulent The losses calculated across the drill pipe and
the drill collars are based on the Bingham Plastic Flow model
When drilling the flow pattern in the drill string is normally turbulent (With
reference to the factors above consider why this should be true) There is no exact
method of calculating pressure losses in the drill string because there is no exact
method of establishing the degree of turbulence However it is possible to estimate
pressure losses in the drill string with sufficient accuracy to select appropriate bit
nozzles for optimizing hydraulic conditions
Pressure losses in the drill string can be calculated by the following equations
You should have noticed the introduction of a new term the friction factor (f) It can
be defined in terms of Reynolds Number (and hence flow rate) and pipe roughness
and has been determined empirically
If circulating a given drilling fluid at a given depth only V and f can vary and both of
these are proportional to flow rate The equations for pressure losses in the drill string
as given above can also be expressed in the equation
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Where c is a constant incorporating the values of all the parameters which are fixed at
a given depth
N is found empirically and is not the same n as in the equations in the paragraphs on
the following pages dealing with pressure losses in the annulus The latter is called a
rheological n
c is given in SI units or API units respectively by
Where is the plastic viscosity and the other symbols are as used before Note that Nis often taken as 182
PRESSURE LOSSES IN THE ANNULUS (Pfa )
Since the annular pressure loss acts as an applied pressure on the formation this loss
should be kept as low as possible to minimise the risk of formation break down To
monitor the pressure against the formation during circulation the equivalent
circulation density (ECD) is often used which is defined as
Where
ECD = equivalent circulating density (kPam psift)
ρm = density of the drilling fluid (kPam psift)
Pan = total pressure drop in the annulus (kPa psi)
L = total length of the annulus (m ft)
The value of the annular pressure loss is relatively small compared to that developed
in the drill string and is often neglected in cases where the circulation rate is low eg
during well killing
It is more difficult to find pressure losses in the annulus because conditions are less
well defined than in the drillpipe
The following uncertainties exist
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bull the actual flow condition is not clear the flow pattern is commonly near the
transitional region
bull the hole size and shape are irregular so it is not possible to get an accurate
value for the annular velocity or the hydraulic diameter
bull the downhole viscosity is very uncertain because it varies with temperature
and flow conditionsbull pipe rotation and eccentricity effects
For efficient drilling conditions it is found that the power lost in overcoming friction
in the system absorbs approximately 30-50 of the circulation energy The remainder
will be expended at the bit It is found that the majority of the system losses are in the
drill string For medium depth drilling the annular pressure losses probably total no
more than 3 to 7 of the pump output pressure at normal circulation rates
Although pressure losses in the annulus are small they are very important because of
their effect on the exposed formations
The effects of annular pressure losses are that
bull they increase the bottom hole pressure when circulating
bull they reduce the initial severity of a kick by providing a hidden safety margin
but they increase the risks of lost circulation during killing (only while
circulating)
bull they cause formation damage if the pressure losses are due to establishing
circulation When establishing circulation the pressure drop in the annulus
increases significantly due to the initial high viscosity (gel strength) of the
drilling fluid
Much research effort has been devoted to improving knowledge of the flow
characteristics of drilling fluids particularly in order to reduce pressure losses This is
a complicated and specialized subject because of the complexity of the fluids
The following expressions provide values for annular pressure losses
Where
Pfa is the annular pressure loss (kPa) Pfa is in psi
L is the pipe length (m) L is in ft
Va is the annular velocity (ms) Va is in ftmin
d is the hydraulic diameter (dh - dp) (mm) d is in inches
n is the Power Law index of flow behaviour
(dimensionless)n is dimensionless
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n and K are derived from viscometer data
Note that K here is an approximation to that given for the Power Law model found in
the section on Drilling Fluids The number 511 results from using a specific type of
viscometer with particular values of spring constant and cylinder surface speed
With Pfa as with Pfd when drilling at a particular depth with a given drilling fluid all
values in the above equations are effectively constant except for the annular velocity(Va) But Va is directly proportional to the flow rate (Q) Thus there will be a tendency
to assume that all pressure losses in the system follow the same equation as shown
below
Where c and N are constants whose values are empirically determined in particular
cases (see under Pressure losses in the drill string)
Pressure losses can be calculated for all parts of the system using the equations givenin this Part
CAUSES OF CHANGES IN CIRCULATING PRESSURES
According to Pt = P b + Ps a change in the circulating pressure can be induced by a
change in either P b Ps or both
Increases in surface pressure
A sudden increase in circulation pressure although drilling fluid properties flow rate
and conduit length are unchanged can be caused only by an increase in P b This could be caused by one or more nozzles plugging
A gradual increase in surface pressure could be the result of several causes (excepting
hole problems)
bull Increased flow rate
bull Extending the string while deepening the hole
bull Change in drilling fluid rheological properties
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Decreases in surface pressure
A spontaneous sudden decrease in circulating pressure while conditions remain
unchanged can be caused by
bull decrease of P b resulting from the loss of a nozzle
bull a twist-off in the drill string
A gradual decrease in pressure could signal the following
bull A developing wash-out (leak) in the drill string or in pump valves
bull Reduction of hydrostatic head in the annulus caused by lighter substances (eg
gas or formation water)
bull An increase of hydrostatic head in the string
Caution Any change of the surface pressure or change in pump strokes not
deliberately instigated should be investigated immediately
To a limited extent pressure losses can be measured directly for example by
pumping through the standpipe and open kelly and through drill collars It is also a
useful exercise to observe the total circulating pressure at various flow rates
Pressure losses in the system can be derived from actual circulating pressure values
by subtracting the pressure drop at the bit which can be calculated accurately
Pressure losses in the system can also be calculated However although the
dimensions are known for all parts of the system the calculation also depends on
knowing the type of fluid flow regime in the drill string and annulus The flow may be
turbulent or laminar or of some transitional type between the two The calculations are
also based on a rheological model If the drilling fluid in use behaves slightly variant
to the model the calculation results will be less than accurate
Pressure losses within the system are minimised by reducing the fluid friction in each
part
bull surface connections losses are negligible compared with elsewhere but can bereduced by avoiding tight bends and using large diameter pipes
bull drill string reduce friction by using a larger internal diameter pipe coated with
plastic
bull drill collars increasing the internal diameter will again reduce friction but
only at the expense of decreasing their weight a balance has to be made
between these opposing effects
bull annulus losses are usually small and only become significant in deep small
diameter holes pressure losses depend on the hydraulic diameter found from
the difference between the hole size and the pipe od it is actually desirable to
reduce the pressure developed against the formations
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Flow regimes
The differences between laminar and turbulent flow are illustrated in the table
overleaf The type of flow is determined by calculating Reynolds number (Re) for the
known well conditions from the following equations
The value obtained is compared with those shown in Table2 (figures are based on
Newtonian fluid properties)
Table2 Deciding the flow condition from the Reynolds number
Inspection of the equations shows that turbulent flow is more likely with the
conditions below
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bull denser drilling fluid (ρ higher)
bull lower viscosity (micro lower)
bull higher flow rate (Q higher)
bull decreased pipe bore or hydraulic
diameter
(d lower)
PUMP HYDRAULIC POWER OUTPUT
In rig operations the amount of available hydraulic power is determined by the size
number and types of pump(s) on site However the demand in terms of output volume
(Q) and pump pressure (P) varies considerably with hole size and depth Once the
pump output or flow rate Q has been selected the available power input determines
the maximum circulating pressure (Pt) that can be achieved
This circulating pressure Pt (total pressure drop in system) is consumed partly by
friction in the fluid and the system (Ps = system pressure loss) and partly by the
pressure drop across the bit nozzles (P b = bit pressure drop) Therefore P t = Ps + P b Pt
is normally given by the pump pressure gauge
The system pressure drop has no effect on bottom-hole cleaning It is unavoidable andis also called the parasitic pressure loss
The bottom-hole cleaning action is provided by the hydraulic energy expended at the
bit Therefore the amount of hydraulic power expended at the bit is a measure for the
cleaning effectiveness (This assumes that the bit is properly matched to the formation
- if a bit designed for a hard formation is run in a soft formation no amount of power
will keep it clean )
The hydraulic power available at the surface from the pump is used to drive the
drilling fluid round the system power the bit and flush the cuttings to the surface If
you know the pump or circulating pressure (Pt ) and the flow rate (Q) then it is possible to calculate the total power available at the surface
Since Power = work done in unit time
and Work done = pressure x volume
then Power = pressure x volume pumped in unit time
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Therefore the power available at surface is given by
The power output of the pump is generally assumed to be 85 of the mechanical or
electrical power input of the pump
PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)
The pressure drop across the bit nozzles P b depends on
bull The flow rate Q
bull The total cross-sectional area of the nozzle openings A
bull The drilling fluid density ρ
Once the desired (optimum) annular velocity has been determined the flow rate (Q )
and the hydraulic power expended at the bit for a given nozzle size are fixed
Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power
expended at the bit is also fixed Both jet velocity and hydraulic power at the bit
determine the cleaning action on bottom
Pressure losses through the bit nozzles are not frictional but represent a change in
kinetic energy as the drilling fluid changes its velocity from that above the bit to that
leaving the jets The pressure expended is therefore dependent only on the drilling
fluid density and the square of the jet velocity
The pressure drop across the bit nozzles is calculated using the following equations
Where
P b is the pressure loss across the bit nozzles (kPa)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
A is the total nozzle area (mm2)
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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When drilling hard formations where penetration rates are low lower annular
velocities can be used In soft formations with high penetration rate often
encountered in top-hole drilling higher annular velocities will be required to remove
the cuttings from the well
Because the total pump capacity is limited sometimes it is not possible to obtainsufficient annular velocity especially in drilling large hole sizes If the fluid density is
critical because weak formations are exposed the drilling rate may have to be
adjusted to reduce the amount of cuttings generated
Generally speaking the minimum practical annular velocity is maintained above a
value of approximately 17 mmin (50 ftmin) in the very large hole sizes In the
smaller holes the more common value of 30 - 40 mmin (90 - 120 ftmin) usually
applies (the smaller hole size is usually at greater depth where the formations are
more consolidated)
Selection of an appropriate annular velocity is one of the first decisions to be takenwhen considering hydraulic conditions
Actual annular velocities are uncertain due to the irregularity of the hole size and
configuration During drilling the actual hole size is not known for this reason the bit
size is taken as the internal diameter of the hole or the last measured average caliper
hole size obtained from logs for calculation purposes
Between the maximum annular velocity and the minimum annular velocity is an
annular velocity which under the given circumstances is the best annular velocity to
be used This is called the optimum annular velocity
OPTIMUM ANNULAR VELOCITY
The optimum annular velocity is that velocity which is obtained through a flow rate
which gives an annular velocity sufficiently high to effectively remove cuttings from
the hole and having the lowest possible erosion effect on the borehole
Over time any flow results in erosion It is therefore advisable to obtain the minimum
flow rate required to effectively remove cuttings from the hole and to avoid
circulating any faster than is required to obtain this flow rate If this rate is a
calculated rate actual hole cleaning should be monitored to confirm the hole cleaningability of this flow rate
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You should be able to distinguish clearly between flow rate and annular velocity
PRESSURE LOSSES IN THE SYSTEM (Ps) (PARASITIC PRESSURE
LOSSES)
What is the system
The system is made up of all parts between the pump and the flowlines with the
exception of the bit nozzles These are excluded because pressure drop across the
nozzles is considered a useful loss of pressure It represents the change in kinetic
energy used to clean the bottom of the hole Pressure losses in the system represent
wasted energy used in overcoming friction These pressure losses are called parasitic
losses
The main sections of the circulating system which contribute to the system losses may
be summarized as follows
bull The surface lines (from pump to kelly saver sub)
bull The drill string (drill pipe and drill collars)
bull The annulus (open hole and cased hole)
In addition we will look at
bull causes of changes in circulating pressures
bull flow regimes
PRESSURE LOSSES IN SURFACE EQUIPMENT
Surface equipment consists of surface lines stand pipe kelly hose swivel and kelly
The pressure loss occurring in this equipment depends on the length and the internal
diameters of each of the items mentioned A simple practical method to find the
surface equipment pressure losses is to hang the kelly or top drive open ended in the
rotary table and pump at different rates
Table1 shows four common combinations of surface equipment The case numbers inthis table (No1 to No4) were originally intended for use with hydraulic slide rules
They are now also used to identify different surface pressure loss situations to be used
in calculations
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PRESSURE LOSSES IN THE DRILL STRING (Pf d)
The pressure loss in the drill string represents the major portion of the parasitic losses
The fluid velocities are usually high and therefore friction loss is significant as the
flow regime in most cases is turbulent The losses calculated across the drill pipe and
the drill collars are based on the Bingham Plastic Flow model
When drilling the flow pattern in the drill string is normally turbulent (With
reference to the factors above consider why this should be true) There is no exact
method of calculating pressure losses in the drill string because there is no exact
method of establishing the degree of turbulence However it is possible to estimate
pressure losses in the drill string with sufficient accuracy to select appropriate bit
nozzles for optimizing hydraulic conditions
Pressure losses in the drill string can be calculated by the following equations
You should have noticed the introduction of a new term the friction factor (f) It can
be defined in terms of Reynolds Number (and hence flow rate) and pipe roughness
and has been determined empirically
If circulating a given drilling fluid at a given depth only V and f can vary and both of
these are proportional to flow rate The equations for pressure losses in the drill string
as given above can also be expressed in the equation
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Where c is a constant incorporating the values of all the parameters which are fixed at
a given depth
N is found empirically and is not the same n as in the equations in the paragraphs on
the following pages dealing with pressure losses in the annulus The latter is called a
rheological n
c is given in SI units or API units respectively by
Where is the plastic viscosity and the other symbols are as used before Note that Nis often taken as 182
PRESSURE LOSSES IN THE ANNULUS (Pfa )
Since the annular pressure loss acts as an applied pressure on the formation this loss
should be kept as low as possible to minimise the risk of formation break down To
monitor the pressure against the formation during circulation the equivalent
circulation density (ECD) is often used which is defined as
Where
ECD = equivalent circulating density (kPam psift)
ρm = density of the drilling fluid (kPam psift)
Pan = total pressure drop in the annulus (kPa psi)
L = total length of the annulus (m ft)
The value of the annular pressure loss is relatively small compared to that developed
in the drill string and is often neglected in cases where the circulation rate is low eg
during well killing
It is more difficult to find pressure losses in the annulus because conditions are less
well defined than in the drillpipe
The following uncertainties exist
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bull the actual flow condition is not clear the flow pattern is commonly near the
transitional region
bull the hole size and shape are irregular so it is not possible to get an accurate
value for the annular velocity or the hydraulic diameter
bull the downhole viscosity is very uncertain because it varies with temperature
and flow conditionsbull pipe rotation and eccentricity effects
For efficient drilling conditions it is found that the power lost in overcoming friction
in the system absorbs approximately 30-50 of the circulation energy The remainder
will be expended at the bit It is found that the majority of the system losses are in the
drill string For medium depth drilling the annular pressure losses probably total no
more than 3 to 7 of the pump output pressure at normal circulation rates
Although pressure losses in the annulus are small they are very important because of
their effect on the exposed formations
The effects of annular pressure losses are that
bull they increase the bottom hole pressure when circulating
bull they reduce the initial severity of a kick by providing a hidden safety margin
but they increase the risks of lost circulation during killing (only while
circulating)
bull they cause formation damage if the pressure losses are due to establishing
circulation When establishing circulation the pressure drop in the annulus
increases significantly due to the initial high viscosity (gel strength) of the
drilling fluid
Much research effort has been devoted to improving knowledge of the flow
characteristics of drilling fluids particularly in order to reduce pressure losses This is
a complicated and specialized subject because of the complexity of the fluids
The following expressions provide values for annular pressure losses
Where
Pfa is the annular pressure loss (kPa) Pfa is in psi
L is the pipe length (m) L is in ft
Va is the annular velocity (ms) Va is in ftmin
d is the hydraulic diameter (dh - dp) (mm) d is in inches
n is the Power Law index of flow behaviour
(dimensionless)n is dimensionless
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n and K are derived from viscometer data
Note that K here is an approximation to that given for the Power Law model found in
the section on Drilling Fluids The number 511 results from using a specific type of
viscometer with particular values of spring constant and cylinder surface speed
With Pfa as with Pfd when drilling at a particular depth with a given drilling fluid all
values in the above equations are effectively constant except for the annular velocity(Va) But Va is directly proportional to the flow rate (Q) Thus there will be a tendency
to assume that all pressure losses in the system follow the same equation as shown
below
Where c and N are constants whose values are empirically determined in particular
cases (see under Pressure losses in the drill string)
Pressure losses can be calculated for all parts of the system using the equations givenin this Part
CAUSES OF CHANGES IN CIRCULATING PRESSURES
According to Pt = P b + Ps a change in the circulating pressure can be induced by a
change in either P b Ps or both
Increases in surface pressure
A sudden increase in circulation pressure although drilling fluid properties flow rate
and conduit length are unchanged can be caused only by an increase in P b This could be caused by one or more nozzles plugging
A gradual increase in surface pressure could be the result of several causes (excepting
hole problems)
bull Increased flow rate
bull Extending the string while deepening the hole
bull Change in drilling fluid rheological properties
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Decreases in surface pressure
A spontaneous sudden decrease in circulating pressure while conditions remain
unchanged can be caused by
bull decrease of P b resulting from the loss of a nozzle
bull a twist-off in the drill string
A gradual decrease in pressure could signal the following
bull A developing wash-out (leak) in the drill string or in pump valves
bull Reduction of hydrostatic head in the annulus caused by lighter substances (eg
gas or formation water)
bull An increase of hydrostatic head in the string
Caution Any change of the surface pressure or change in pump strokes not
deliberately instigated should be investigated immediately
To a limited extent pressure losses can be measured directly for example by
pumping through the standpipe and open kelly and through drill collars It is also a
useful exercise to observe the total circulating pressure at various flow rates
Pressure losses in the system can be derived from actual circulating pressure values
by subtracting the pressure drop at the bit which can be calculated accurately
Pressure losses in the system can also be calculated However although the
dimensions are known for all parts of the system the calculation also depends on
knowing the type of fluid flow regime in the drill string and annulus The flow may be
turbulent or laminar or of some transitional type between the two The calculations are
also based on a rheological model If the drilling fluid in use behaves slightly variant
to the model the calculation results will be less than accurate
Pressure losses within the system are minimised by reducing the fluid friction in each
part
bull surface connections losses are negligible compared with elsewhere but can bereduced by avoiding tight bends and using large diameter pipes
bull drill string reduce friction by using a larger internal diameter pipe coated with
plastic
bull drill collars increasing the internal diameter will again reduce friction but
only at the expense of decreasing their weight a balance has to be made
between these opposing effects
bull annulus losses are usually small and only become significant in deep small
diameter holes pressure losses depend on the hydraulic diameter found from
the difference between the hole size and the pipe od it is actually desirable to
reduce the pressure developed against the formations
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Flow regimes
The differences between laminar and turbulent flow are illustrated in the table
overleaf The type of flow is determined by calculating Reynolds number (Re) for the
known well conditions from the following equations
The value obtained is compared with those shown in Table2 (figures are based on
Newtonian fluid properties)
Table2 Deciding the flow condition from the Reynolds number
Inspection of the equations shows that turbulent flow is more likely with the
conditions below
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bull denser drilling fluid (ρ higher)
bull lower viscosity (micro lower)
bull higher flow rate (Q higher)
bull decreased pipe bore or hydraulic
diameter
(d lower)
PUMP HYDRAULIC POWER OUTPUT
In rig operations the amount of available hydraulic power is determined by the size
number and types of pump(s) on site However the demand in terms of output volume
(Q) and pump pressure (P) varies considerably with hole size and depth Once the
pump output or flow rate Q has been selected the available power input determines
the maximum circulating pressure (Pt) that can be achieved
This circulating pressure Pt (total pressure drop in system) is consumed partly by
friction in the fluid and the system (Ps = system pressure loss) and partly by the
pressure drop across the bit nozzles (P b = bit pressure drop) Therefore P t = Ps + P b Pt
is normally given by the pump pressure gauge
The system pressure drop has no effect on bottom-hole cleaning It is unavoidable andis also called the parasitic pressure loss
The bottom-hole cleaning action is provided by the hydraulic energy expended at the
bit Therefore the amount of hydraulic power expended at the bit is a measure for the
cleaning effectiveness (This assumes that the bit is properly matched to the formation
- if a bit designed for a hard formation is run in a soft formation no amount of power
will keep it clean )
The hydraulic power available at the surface from the pump is used to drive the
drilling fluid round the system power the bit and flush the cuttings to the surface If
you know the pump or circulating pressure (Pt ) and the flow rate (Q) then it is possible to calculate the total power available at the surface
Since Power = work done in unit time
and Work done = pressure x volume
then Power = pressure x volume pumped in unit time
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Therefore the power available at surface is given by
The power output of the pump is generally assumed to be 85 of the mechanical or
electrical power input of the pump
PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)
The pressure drop across the bit nozzles P b depends on
bull The flow rate Q
bull The total cross-sectional area of the nozzle openings A
bull The drilling fluid density ρ
Once the desired (optimum) annular velocity has been determined the flow rate (Q )
and the hydraulic power expended at the bit for a given nozzle size are fixed
Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power
expended at the bit is also fixed Both jet velocity and hydraulic power at the bit
determine the cleaning action on bottom
Pressure losses through the bit nozzles are not frictional but represent a change in
kinetic energy as the drilling fluid changes its velocity from that above the bit to that
leaving the jets The pressure expended is therefore dependent only on the drilling
fluid density and the square of the jet velocity
The pressure drop across the bit nozzles is calculated using the following equations
Where
P b is the pressure loss across the bit nozzles (kPa)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
A is the total nozzle area (mm2)
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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You should be able to distinguish clearly between flow rate and annular velocity
PRESSURE LOSSES IN THE SYSTEM (Ps) (PARASITIC PRESSURE
LOSSES)
What is the system
The system is made up of all parts between the pump and the flowlines with the
exception of the bit nozzles These are excluded because pressure drop across the
nozzles is considered a useful loss of pressure It represents the change in kinetic
energy used to clean the bottom of the hole Pressure losses in the system represent
wasted energy used in overcoming friction These pressure losses are called parasitic
losses
The main sections of the circulating system which contribute to the system losses may
be summarized as follows
bull The surface lines (from pump to kelly saver sub)
bull The drill string (drill pipe and drill collars)
bull The annulus (open hole and cased hole)
In addition we will look at
bull causes of changes in circulating pressures
bull flow regimes
PRESSURE LOSSES IN SURFACE EQUIPMENT
Surface equipment consists of surface lines stand pipe kelly hose swivel and kelly
The pressure loss occurring in this equipment depends on the length and the internal
diameters of each of the items mentioned A simple practical method to find the
surface equipment pressure losses is to hang the kelly or top drive open ended in the
rotary table and pump at different rates
Table1 shows four common combinations of surface equipment The case numbers inthis table (No1 to No4) were originally intended for use with hydraulic slide rules
They are now also used to identify different surface pressure loss situations to be used
in calculations
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PRESSURE LOSSES IN THE DRILL STRING (Pf d)
The pressure loss in the drill string represents the major portion of the parasitic losses
The fluid velocities are usually high and therefore friction loss is significant as the
flow regime in most cases is turbulent The losses calculated across the drill pipe and
the drill collars are based on the Bingham Plastic Flow model
When drilling the flow pattern in the drill string is normally turbulent (With
reference to the factors above consider why this should be true) There is no exact
method of calculating pressure losses in the drill string because there is no exact
method of establishing the degree of turbulence However it is possible to estimate
pressure losses in the drill string with sufficient accuracy to select appropriate bit
nozzles for optimizing hydraulic conditions
Pressure losses in the drill string can be calculated by the following equations
You should have noticed the introduction of a new term the friction factor (f) It can
be defined in terms of Reynolds Number (and hence flow rate) and pipe roughness
and has been determined empirically
If circulating a given drilling fluid at a given depth only V and f can vary and both of
these are proportional to flow rate The equations for pressure losses in the drill string
as given above can also be expressed in the equation
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Where c is a constant incorporating the values of all the parameters which are fixed at
a given depth
N is found empirically and is not the same n as in the equations in the paragraphs on
the following pages dealing with pressure losses in the annulus The latter is called a
rheological n
c is given in SI units or API units respectively by
Where is the plastic viscosity and the other symbols are as used before Note that Nis often taken as 182
PRESSURE LOSSES IN THE ANNULUS (Pfa )
Since the annular pressure loss acts as an applied pressure on the formation this loss
should be kept as low as possible to minimise the risk of formation break down To
monitor the pressure against the formation during circulation the equivalent
circulation density (ECD) is often used which is defined as
Where
ECD = equivalent circulating density (kPam psift)
ρm = density of the drilling fluid (kPam psift)
Pan = total pressure drop in the annulus (kPa psi)
L = total length of the annulus (m ft)
The value of the annular pressure loss is relatively small compared to that developed
in the drill string and is often neglected in cases where the circulation rate is low eg
during well killing
It is more difficult to find pressure losses in the annulus because conditions are less
well defined than in the drillpipe
The following uncertainties exist
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bull the actual flow condition is not clear the flow pattern is commonly near the
transitional region
bull the hole size and shape are irregular so it is not possible to get an accurate
value for the annular velocity or the hydraulic diameter
bull the downhole viscosity is very uncertain because it varies with temperature
and flow conditionsbull pipe rotation and eccentricity effects
For efficient drilling conditions it is found that the power lost in overcoming friction
in the system absorbs approximately 30-50 of the circulation energy The remainder
will be expended at the bit It is found that the majority of the system losses are in the
drill string For medium depth drilling the annular pressure losses probably total no
more than 3 to 7 of the pump output pressure at normal circulation rates
Although pressure losses in the annulus are small they are very important because of
their effect on the exposed formations
The effects of annular pressure losses are that
bull they increase the bottom hole pressure when circulating
bull they reduce the initial severity of a kick by providing a hidden safety margin
but they increase the risks of lost circulation during killing (only while
circulating)
bull they cause formation damage if the pressure losses are due to establishing
circulation When establishing circulation the pressure drop in the annulus
increases significantly due to the initial high viscosity (gel strength) of the
drilling fluid
Much research effort has been devoted to improving knowledge of the flow
characteristics of drilling fluids particularly in order to reduce pressure losses This is
a complicated and specialized subject because of the complexity of the fluids
The following expressions provide values for annular pressure losses
Where
Pfa is the annular pressure loss (kPa) Pfa is in psi
L is the pipe length (m) L is in ft
Va is the annular velocity (ms) Va is in ftmin
d is the hydraulic diameter (dh - dp) (mm) d is in inches
n is the Power Law index of flow behaviour
(dimensionless)n is dimensionless
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n and K are derived from viscometer data
Note that K here is an approximation to that given for the Power Law model found in
the section on Drilling Fluids The number 511 results from using a specific type of
viscometer with particular values of spring constant and cylinder surface speed
With Pfa as with Pfd when drilling at a particular depth with a given drilling fluid all
values in the above equations are effectively constant except for the annular velocity(Va) But Va is directly proportional to the flow rate (Q) Thus there will be a tendency
to assume that all pressure losses in the system follow the same equation as shown
below
Where c and N are constants whose values are empirically determined in particular
cases (see under Pressure losses in the drill string)
Pressure losses can be calculated for all parts of the system using the equations givenin this Part
CAUSES OF CHANGES IN CIRCULATING PRESSURES
According to Pt = P b + Ps a change in the circulating pressure can be induced by a
change in either P b Ps or both
Increases in surface pressure
A sudden increase in circulation pressure although drilling fluid properties flow rate
and conduit length are unchanged can be caused only by an increase in P b This could be caused by one or more nozzles plugging
A gradual increase in surface pressure could be the result of several causes (excepting
hole problems)
bull Increased flow rate
bull Extending the string while deepening the hole
bull Change in drilling fluid rheological properties
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Decreases in surface pressure
A spontaneous sudden decrease in circulating pressure while conditions remain
unchanged can be caused by
bull decrease of P b resulting from the loss of a nozzle
bull a twist-off in the drill string
A gradual decrease in pressure could signal the following
bull A developing wash-out (leak) in the drill string or in pump valves
bull Reduction of hydrostatic head in the annulus caused by lighter substances (eg
gas or formation water)
bull An increase of hydrostatic head in the string
Caution Any change of the surface pressure or change in pump strokes not
deliberately instigated should be investigated immediately
To a limited extent pressure losses can be measured directly for example by
pumping through the standpipe and open kelly and through drill collars It is also a
useful exercise to observe the total circulating pressure at various flow rates
Pressure losses in the system can be derived from actual circulating pressure values
by subtracting the pressure drop at the bit which can be calculated accurately
Pressure losses in the system can also be calculated However although the
dimensions are known for all parts of the system the calculation also depends on
knowing the type of fluid flow regime in the drill string and annulus The flow may be
turbulent or laminar or of some transitional type between the two The calculations are
also based on a rheological model If the drilling fluid in use behaves slightly variant
to the model the calculation results will be less than accurate
Pressure losses within the system are minimised by reducing the fluid friction in each
part
bull surface connections losses are negligible compared with elsewhere but can bereduced by avoiding tight bends and using large diameter pipes
bull drill string reduce friction by using a larger internal diameter pipe coated with
plastic
bull drill collars increasing the internal diameter will again reduce friction but
only at the expense of decreasing their weight a balance has to be made
between these opposing effects
bull annulus losses are usually small and only become significant in deep small
diameter holes pressure losses depend on the hydraulic diameter found from
the difference between the hole size and the pipe od it is actually desirable to
reduce the pressure developed against the formations
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Flow regimes
The differences between laminar and turbulent flow are illustrated in the table
overleaf The type of flow is determined by calculating Reynolds number (Re) for the
known well conditions from the following equations
The value obtained is compared with those shown in Table2 (figures are based on
Newtonian fluid properties)
Table2 Deciding the flow condition from the Reynolds number
Inspection of the equations shows that turbulent flow is more likely with the
conditions below
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bull denser drilling fluid (ρ higher)
bull lower viscosity (micro lower)
bull higher flow rate (Q higher)
bull decreased pipe bore or hydraulic
diameter
(d lower)
PUMP HYDRAULIC POWER OUTPUT
In rig operations the amount of available hydraulic power is determined by the size
number and types of pump(s) on site However the demand in terms of output volume
(Q) and pump pressure (P) varies considerably with hole size and depth Once the
pump output or flow rate Q has been selected the available power input determines
the maximum circulating pressure (Pt) that can be achieved
This circulating pressure Pt (total pressure drop in system) is consumed partly by
friction in the fluid and the system (Ps = system pressure loss) and partly by the
pressure drop across the bit nozzles (P b = bit pressure drop) Therefore P t = Ps + P b Pt
is normally given by the pump pressure gauge
The system pressure drop has no effect on bottom-hole cleaning It is unavoidable andis also called the parasitic pressure loss
The bottom-hole cleaning action is provided by the hydraulic energy expended at the
bit Therefore the amount of hydraulic power expended at the bit is a measure for the
cleaning effectiveness (This assumes that the bit is properly matched to the formation
- if a bit designed for a hard formation is run in a soft formation no amount of power
will keep it clean )
The hydraulic power available at the surface from the pump is used to drive the
drilling fluid round the system power the bit and flush the cuttings to the surface If
you know the pump or circulating pressure (Pt ) and the flow rate (Q) then it is possible to calculate the total power available at the surface
Since Power = work done in unit time
and Work done = pressure x volume
then Power = pressure x volume pumped in unit time
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Therefore the power available at surface is given by
The power output of the pump is generally assumed to be 85 of the mechanical or
electrical power input of the pump
PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)
The pressure drop across the bit nozzles P b depends on
bull The flow rate Q
bull The total cross-sectional area of the nozzle openings A
bull The drilling fluid density ρ
Once the desired (optimum) annular velocity has been determined the flow rate (Q )
and the hydraulic power expended at the bit for a given nozzle size are fixed
Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power
expended at the bit is also fixed Both jet velocity and hydraulic power at the bit
determine the cleaning action on bottom
Pressure losses through the bit nozzles are not frictional but represent a change in
kinetic energy as the drilling fluid changes its velocity from that above the bit to that
leaving the jets The pressure expended is therefore dependent only on the drilling
fluid density and the square of the jet velocity
The pressure drop across the bit nozzles is calculated using the following equations
Where
P b is the pressure loss across the bit nozzles (kPa)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
A is the total nozzle area (mm2)
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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PRESSURE LOSSES IN THE DRILL STRING (Pf d)
The pressure loss in the drill string represents the major portion of the parasitic losses
The fluid velocities are usually high and therefore friction loss is significant as the
flow regime in most cases is turbulent The losses calculated across the drill pipe and
the drill collars are based on the Bingham Plastic Flow model
When drilling the flow pattern in the drill string is normally turbulent (With
reference to the factors above consider why this should be true) There is no exact
method of calculating pressure losses in the drill string because there is no exact
method of establishing the degree of turbulence However it is possible to estimate
pressure losses in the drill string with sufficient accuracy to select appropriate bit
nozzles for optimizing hydraulic conditions
Pressure losses in the drill string can be calculated by the following equations
You should have noticed the introduction of a new term the friction factor (f) It can
be defined in terms of Reynolds Number (and hence flow rate) and pipe roughness
and has been determined empirically
If circulating a given drilling fluid at a given depth only V and f can vary and both of
these are proportional to flow rate The equations for pressure losses in the drill string
as given above can also be expressed in the equation
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Where c is a constant incorporating the values of all the parameters which are fixed at
a given depth
N is found empirically and is not the same n as in the equations in the paragraphs on
the following pages dealing with pressure losses in the annulus The latter is called a
rheological n
c is given in SI units or API units respectively by
Where is the plastic viscosity and the other symbols are as used before Note that Nis often taken as 182
PRESSURE LOSSES IN THE ANNULUS (Pfa )
Since the annular pressure loss acts as an applied pressure on the formation this loss
should be kept as low as possible to minimise the risk of formation break down To
monitor the pressure against the formation during circulation the equivalent
circulation density (ECD) is often used which is defined as
Where
ECD = equivalent circulating density (kPam psift)
ρm = density of the drilling fluid (kPam psift)
Pan = total pressure drop in the annulus (kPa psi)
L = total length of the annulus (m ft)
The value of the annular pressure loss is relatively small compared to that developed
in the drill string and is often neglected in cases where the circulation rate is low eg
during well killing
It is more difficult to find pressure losses in the annulus because conditions are less
well defined than in the drillpipe
The following uncertainties exist
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bull the actual flow condition is not clear the flow pattern is commonly near the
transitional region
bull the hole size and shape are irregular so it is not possible to get an accurate
value for the annular velocity or the hydraulic diameter
bull the downhole viscosity is very uncertain because it varies with temperature
and flow conditionsbull pipe rotation and eccentricity effects
For efficient drilling conditions it is found that the power lost in overcoming friction
in the system absorbs approximately 30-50 of the circulation energy The remainder
will be expended at the bit It is found that the majority of the system losses are in the
drill string For medium depth drilling the annular pressure losses probably total no
more than 3 to 7 of the pump output pressure at normal circulation rates
Although pressure losses in the annulus are small they are very important because of
their effect on the exposed formations
The effects of annular pressure losses are that
bull they increase the bottom hole pressure when circulating
bull they reduce the initial severity of a kick by providing a hidden safety margin
but they increase the risks of lost circulation during killing (only while
circulating)
bull they cause formation damage if the pressure losses are due to establishing
circulation When establishing circulation the pressure drop in the annulus
increases significantly due to the initial high viscosity (gel strength) of the
drilling fluid
Much research effort has been devoted to improving knowledge of the flow
characteristics of drilling fluids particularly in order to reduce pressure losses This is
a complicated and specialized subject because of the complexity of the fluids
The following expressions provide values for annular pressure losses
Where
Pfa is the annular pressure loss (kPa) Pfa is in psi
L is the pipe length (m) L is in ft
Va is the annular velocity (ms) Va is in ftmin
d is the hydraulic diameter (dh - dp) (mm) d is in inches
n is the Power Law index of flow behaviour
(dimensionless)n is dimensionless
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n and K are derived from viscometer data
Note that K here is an approximation to that given for the Power Law model found in
the section on Drilling Fluids The number 511 results from using a specific type of
viscometer with particular values of spring constant and cylinder surface speed
With Pfa as with Pfd when drilling at a particular depth with a given drilling fluid all
values in the above equations are effectively constant except for the annular velocity(Va) But Va is directly proportional to the flow rate (Q) Thus there will be a tendency
to assume that all pressure losses in the system follow the same equation as shown
below
Where c and N are constants whose values are empirically determined in particular
cases (see under Pressure losses in the drill string)
Pressure losses can be calculated for all parts of the system using the equations givenin this Part
CAUSES OF CHANGES IN CIRCULATING PRESSURES
According to Pt = P b + Ps a change in the circulating pressure can be induced by a
change in either P b Ps or both
Increases in surface pressure
A sudden increase in circulation pressure although drilling fluid properties flow rate
and conduit length are unchanged can be caused only by an increase in P b This could be caused by one or more nozzles plugging
A gradual increase in surface pressure could be the result of several causes (excepting
hole problems)
bull Increased flow rate
bull Extending the string while deepening the hole
bull Change in drilling fluid rheological properties
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Decreases in surface pressure
A spontaneous sudden decrease in circulating pressure while conditions remain
unchanged can be caused by
bull decrease of P b resulting from the loss of a nozzle
bull a twist-off in the drill string
A gradual decrease in pressure could signal the following
bull A developing wash-out (leak) in the drill string or in pump valves
bull Reduction of hydrostatic head in the annulus caused by lighter substances (eg
gas or formation water)
bull An increase of hydrostatic head in the string
Caution Any change of the surface pressure or change in pump strokes not
deliberately instigated should be investigated immediately
To a limited extent pressure losses can be measured directly for example by
pumping through the standpipe and open kelly and through drill collars It is also a
useful exercise to observe the total circulating pressure at various flow rates
Pressure losses in the system can be derived from actual circulating pressure values
by subtracting the pressure drop at the bit which can be calculated accurately
Pressure losses in the system can also be calculated However although the
dimensions are known for all parts of the system the calculation also depends on
knowing the type of fluid flow regime in the drill string and annulus The flow may be
turbulent or laminar or of some transitional type between the two The calculations are
also based on a rheological model If the drilling fluid in use behaves slightly variant
to the model the calculation results will be less than accurate
Pressure losses within the system are minimised by reducing the fluid friction in each
part
bull surface connections losses are negligible compared with elsewhere but can bereduced by avoiding tight bends and using large diameter pipes
bull drill string reduce friction by using a larger internal diameter pipe coated with
plastic
bull drill collars increasing the internal diameter will again reduce friction but
only at the expense of decreasing their weight a balance has to be made
between these opposing effects
bull annulus losses are usually small and only become significant in deep small
diameter holes pressure losses depend on the hydraulic diameter found from
the difference between the hole size and the pipe od it is actually desirable to
reduce the pressure developed against the formations
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Flow regimes
The differences between laminar and turbulent flow are illustrated in the table
overleaf The type of flow is determined by calculating Reynolds number (Re) for the
known well conditions from the following equations
The value obtained is compared with those shown in Table2 (figures are based on
Newtonian fluid properties)
Table2 Deciding the flow condition from the Reynolds number
Inspection of the equations shows that turbulent flow is more likely with the
conditions below
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bull denser drilling fluid (ρ higher)
bull lower viscosity (micro lower)
bull higher flow rate (Q higher)
bull decreased pipe bore or hydraulic
diameter
(d lower)
PUMP HYDRAULIC POWER OUTPUT
In rig operations the amount of available hydraulic power is determined by the size
number and types of pump(s) on site However the demand in terms of output volume
(Q) and pump pressure (P) varies considerably with hole size and depth Once the
pump output or flow rate Q has been selected the available power input determines
the maximum circulating pressure (Pt) that can be achieved
This circulating pressure Pt (total pressure drop in system) is consumed partly by
friction in the fluid and the system (Ps = system pressure loss) and partly by the
pressure drop across the bit nozzles (P b = bit pressure drop) Therefore P t = Ps + P b Pt
is normally given by the pump pressure gauge
The system pressure drop has no effect on bottom-hole cleaning It is unavoidable andis also called the parasitic pressure loss
The bottom-hole cleaning action is provided by the hydraulic energy expended at the
bit Therefore the amount of hydraulic power expended at the bit is a measure for the
cleaning effectiveness (This assumes that the bit is properly matched to the formation
- if a bit designed for a hard formation is run in a soft formation no amount of power
will keep it clean )
The hydraulic power available at the surface from the pump is used to drive the
drilling fluid round the system power the bit and flush the cuttings to the surface If
you know the pump or circulating pressure (Pt ) and the flow rate (Q) then it is possible to calculate the total power available at the surface
Since Power = work done in unit time
and Work done = pressure x volume
then Power = pressure x volume pumped in unit time
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Therefore the power available at surface is given by
The power output of the pump is generally assumed to be 85 of the mechanical or
electrical power input of the pump
PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)
The pressure drop across the bit nozzles P b depends on
bull The flow rate Q
bull The total cross-sectional area of the nozzle openings A
bull The drilling fluid density ρ
Once the desired (optimum) annular velocity has been determined the flow rate (Q )
and the hydraulic power expended at the bit for a given nozzle size are fixed
Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power
expended at the bit is also fixed Both jet velocity and hydraulic power at the bit
determine the cleaning action on bottom
Pressure losses through the bit nozzles are not frictional but represent a change in
kinetic energy as the drilling fluid changes its velocity from that above the bit to that
leaving the jets The pressure expended is therefore dependent only on the drilling
fluid density and the square of the jet velocity
The pressure drop across the bit nozzles is calculated using the following equations
Where
P b is the pressure loss across the bit nozzles (kPa)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
A is the total nozzle area (mm2)
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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Where c is a constant incorporating the values of all the parameters which are fixed at
a given depth
N is found empirically and is not the same n as in the equations in the paragraphs on
the following pages dealing with pressure losses in the annulus The latter is called a
rheological n
c is given in SI units or API units respectively by
Where is the plastic viscosity and the other symbols are as used before Note that Nis often taken as 182
PRESSURE LOSSES IN THE ANNULUS (Pfa )
Since the annular pressure loss acts as an applied pressure on the formation this loss
should be kept as low as possible to minimise the risk of formation break down To
monitor the pressure against the formation during circulation the equivalent
circulation density (ECD) is often used which is defined as
Where
ECD = equivalent circulating density (kPam psift)
ρm = density of the drilling fluid (kPam psift)
Pan = total pressure drop in the annulus (kPa psi)
L = total length of the annulus (m ft)
The value of the annular pressure loss is relatively small compared to that developed
in the drill string and is often neglected in cases where the circulation rate is low eg
during well killing
It is more difficult to find pressure losses in the annulus because conditions are less
well defined than in the drillpipe
The following uncertainties exist
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bull the actual flow condition is not clear the flow pattern is commonly near the
transitional region
bull the hole size and shape are irregular so it is not possible to get an accurate
value for the annular velocity or the hydraulic diameter
bull the downhole viscosity is very uncertain because it varies with temperature
and flow conditionsbull pipe rotation and eccentricity effects
For efficient drilling conditions it is found that the power lost in overcoming friction
in the system absorbs approximately 30-50 of the circulation energy The remainder
will be expended at the bit It is found that the majority of the system losses are in the
drill string For medium depth drilling the annular pressure losses probably total no
more than 3 to 7 of the pump output pressure at normal circulation rates
Although pressure losses in the annulus are small they are very important because of
their effect on the exposed formations
The effects of annular pressure losses are that
bull they increase the bottom hole pressure when circulating
bull they reduce the initial severity of a kick by providing a hidden safety margin
but they increase the risks of lost circulation during killing (only while
circulating)
bull they cause formation damage if the pressure losses are due to establishing
circulation When establishing circulation the pressure drop in the annulus
increases significantly due to the initial high viscosity (gel strength) of the
drilling fluid
Much research effort has been devoted to improving knowledge of the flow
characteristics of drilling fluids particularly in order to reduce pressure losses This is
a complicated and specialized subject because of the complexity of the fluids
The following expressions provide values for annular pressure losses
Where
Pfa is the annular pressure loss (kPa) Pfa is in psi
L is the pipe length (m) L is in ft
Va is the annular velocity (ms) Va is in ftmin
d is the hydraulic diameter (dh - dp) (mm) d is in inches
n is the Power Law index of flow behaviour
(dimensionless)n is dimensionless
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n and K are derived from viscometer data
Note that K here is an approximation to that given for the Power Law model found in
the section on Drilling Fluids The number 511 results from using a specific type of
viscometer with particular values of spring constant and cylinder surface speed
With Pfa as with Pfd when drilling at a particular depth with a given drilling fluid all
values in the above equations are effectively constant except for the annular velocity(Va) But Va is directly proportional to the flow rate (Q) Thus there will be a tendency
to assume that all pressure losses in the system follow the same equation as shown
below
Where c and N are constants whose values are empirically determined in particular
cases (see under Pressure losses in the drill string)
Pressure losses can be calculated for all parts of the system using the equations givenin this Part
CAUSES OF CHANGES IN CIRCULATING PRESSURES
According to Pt = P b + Ps a change in the circulating pressure can be induced by a
change in either P b Ps or both
Increases in surface pressure
A sudden increase in circulation pressure although drilling fluid properties flow rate
and conduit length are unchanged can be caused only by an increase in P b This could be caused by one or more nozzles plugging
A gradual increase in surface pressure could be the result of several causes (excepting
hole problems)
bull Increased flow rate
bull Extending the string while deepening the hole
bull Change in drilling fluid rheological properties
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Decreases in surface pressure
A spontaneous sudden decrease in circulating pressure while conditions remain
unchanged can be caused by
bull decrease of P b resulting from the loss of a nozzle
bull a twist-off in the drill string
A gradual decrease in pressure could signal the following
bull A developing wash-out (leak) in the drill string or in pump valves
bull Reduction of hydrostatic head in the annulus caused by lighter substances (eg
gas or formation water)
bull An increase of hydrostatic head in the string
Caution Any change of the surface pressure or change in pump strokes not
deliberately instigated should be investigated immediately
To a limited extent pressure losses can be measured directly for example by
pumping through the standpipe and open kelly and through drill collars It is also a
useful exercise to observe the total circulating pressure at various flow rates
Pressure losses in the system can be derived from actual circulating pressure values
by subtracting the pressure drop at the bit which can be calculated accurately
Pressure losses in the system can also be calculated However although the
dimensions are known for all parts of the system the calculation also depends on
knowing the type of fluid flow regime in the drill string and annulus The flow may be
turbulent or laminar or of some transitional type between the two The calculations are
also based on a rheological model If the drilling fluid in use behaves slightly variant
to the model the calculation results will be less than accurate
Pressure losses within the system are minimised by reducing the fluid friction in each
part
bull surface connections losses are negligible compared with elsewhere but can bereduced by avoiding tight bends and using large diameter pipes
bull drill string reduce friction by using a larger internal diameter pipe coated with
plastic
bull drill collars increasing the internal diameter will again reduce friction but
only at the expense of decreasing their weight a balance has to be made
between these opposing effects
bull annulus losses are usually small and only become significant in deep small
diameter holes pressure losses depend on the hydraulic diameter found from
the difference between the hole size and the pipe od it is actually desirable to
reduce the pressure developed against the formations
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Flow regimes
The differences between laminar and turbulent flow are illustrated in the table
overleaf The type of flow is determined by calculating Reynolds number (Re) for the
known well conditions from the following equations
The value obtained is compared with those shown in Table2 (figures are based on
Newtonian fluid properties)
Table2 Deciding the flow condition from the Reynolds number
Inspection of the equations shows that turbulent flow is more likely with the
conditions below
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bull denser drilling fluid (ρ higher)
bull lower viscosity (micro lower)
bull higher flow rate (Q higher)
bull decreased pipe bore or hydraulic
diameter
(d lower)
PUMP HYDRAULIC POWER OUTPUT
In rig operations the amount of available hydraulic power is determined by the size
number and types of pump(s) on site However the demand in terms of output volume
(Q) and pump pressure (P) varies considerably with hole size and depth Once the
pump output or flow rate Q has been selected the available power input determines
the maximum circulating pressure (Pt) that can be achieved
This circulating pressure Pt (total pressure drop in system) is consumed partly by
friction in the fluid and the system (Ps = system pressure loss) and partly by the
pressure drop across the bit nozzles (P b = bit pressure drop) Therefore P t = Ps + P b Pt
is normally given by the pump pressure gauge
The system pressure drop has no effect on bottom-hole cleaning It is unavoidable andis also called the parasitic pressure loss
The bottom-hole cleaning action is provided by the hydraulic energy expended at the
bit Therefore the amount of hydraulic power expended at the bit is a measure for the
cleaning effectiveness (This assumes that the bit is properly matched to the formation
- if a bit designed for a hard formation is run in a soft formation no amount of power
will keep it clean )
The hydraulic power available at the surface from the pump is used to drive the
drilling fluid round the system power the bit and flush the cuttings to the surface If
you know the pump or circulating pressure (Pt ) and the flow rate (Q) then it is possible to calculate the total power available at the surface
Since Power = work done in unit time
and Work done = pressure x volume
then Power = pressure x volume pumped in unit time
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Therefore the power available at surface is given by
The power output of the pump is generally assumed to be 85 of the mechanical or
electrical power input of the pump
PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)
The pressure drop across the bit nozzles P b depends on
bull The flow rate Q
bull The total cross-sectional area of the nozzle openings A
bull The drilling fluid density ρ
Once the desired (optimum) annular velocity has been determined the flow rate (Q )
and the hydraulic power expended at the bit for a given nozzle size are fixed
Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power
expended at the bit is also fixed Both jet velocity and hydraulic power at the bit
determine the cleaning action on bottom
Pressure losses through the bit nozzles are not frictional but represent a change in
kinetic energy as the drilling fluid changes its velocity from that above the bit to that
leaving the jets The pressure expended is therefore dependent only on the drilling
fluid density and the square of the jet velocity
The pressure drop across the bit nozzles is calculated using the following equations
Where
P b is the pressure loss across the bit nozzles (kPa)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
A is the total nozzle area (mm2)
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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bull the actual flow condition is not clear the flow pattern is commonly near the
transitional region
bull the hole size and shape are irregular so it is not possible to get an accurate
value for the annular velocity or the hydraulic diameter
bull the downhole viscosity is very uncertain because it varies with temperature
and flow conditionsbull pipe rotation and eccentricity effects
For efficient drilling conditions it is found that the power lost in overcoming friction
in the system absorbs approximately 30-50 of the circulation energy The remainder
will be expended at the bit It is found that the majority of the system losses are in the
drill string For medium depth drilling the annular pressure losses probably total no
more than 3 to 7 of the pump output pressure at normal circulation rates
Although pressure losses in the annulus are small they are very important because of
their effect on the exposed formations
The effects of annular pressure losses are that
bull they increase the bottom hole pressure when circulating
bull they reduce the initial severity of a kick by providing a hidden safety margin
but they increase the risks of lost circulation during killing (only while
circulating)
bull they cause formation damage if the pressure losses are due to establishing
circulation When establishing circulation the pressure drop in the annulus
increases significantly due to the initial high viscosity (gel strength) of the
drilling fluid
Much research effort has been devoted to improving knowledge of the flow
characteristics of drilling fluids particularly in order to reduce pressure losses This is
a complicated and specialized subject because of the complexity of the fluids
The following expressions provide values for annular pressure losses
Where
Pfa is the annular pressure loss (kPa) Pfa is in psi
L is the pipe length (m) L is in ft
Va is the annular velocity (ms) Va is in ftmin
d is the hydraulic diameter (dh - dp) (mm) d is in inches
n is the Power Law index of flow behaviour
(dimensionless)n is dimensionless
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n and K are derived from viscometer data
Note that K here is an approximation to that given for the Power Law model found in
the section on Drilling Fluids The number 511 results from using a specific type of
viscometer with particular values of spring constant and cylinder surface speed
With Pfa as with Pfd when drilling at a particular depth with a given drilling fluid all
values in the above equations are effectively constant except for the annular velocity(Va) But Va is directly proportional to the flow rate (Q) Thus there will be a tendency
to assume that all pressure losses in the system follow the same equation as shown
below
Where c and N are constants whose values are empirically determined in particular
cases (see under Pressure losses in the drill string)
Pressure losses can be calculated for all parts of the system using the equations givenin this Part
CAUSES OF CHANGES IN CIRCULATING PRESSURES
According to Pt = P b + Ps a change in the circulating pressure can be induced by a
change in either P b Ps or both
Increases in surface pressure
A sudden increase in circulation pressure although drilling fluid properties flow rate
and conduit length are unchanged can be caused only by an increase in P b This could be caused by one or more nozzles plugging
A gradual increase in surface pressure could be the result of several causes (excepting
hole problems)
bull Increased flow rate
bull Extending the string while deepening the hole
bull Change in drilling fluid rheological properties
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Decreases in surface pressure
A spontaneous sudden decrease in circulating pressure while conditions remain
unchanged can be caused by
bull decrease of P b resulting from the loss of a nozzle
bull a twist-off in the drill string
A gradual decrease in pressure could signal the following
bull A developing wash-out (leak) in the drill string or in pump valves
bull Reduction of hydrostatic head in the annulus caused by lighter substances (eg
gas or formation water)
bull An increase of hydrostatic head in the string
Caution Any change of the surface pressure or change in pump strokes not
deliberately instigated should be investigated immediately
To a limited extent pressure losses can be measured directly for example by
pumping through the standpipe and open kelly and through drill collars It is also a
useful exercise to observe the total circulating pressure at various flow rates
Pressure losses in the system can be derived from actual circulating pressure values
by subtracting the pressure drop at the bit which can be calculated accurately
Pressure losses in the system can also be calculated However although the
dimensions are known for all parts of the system the calculation also depends on
knowing the type of fluid flow regime in the drill string and annulus The flow may be
turbulent or laminar or of some transitional type between the two The calculations are
also based on a rheological model If the drilling fluid in use behaves slightly variant
to the model the calculation results will be less than accurate
Pressure losses within the system are minimised by reducing the fluid friction in each
part
bull surface connections losses are negligible compared with elsewhere but can bereduced by avoiding tight bends and using large diameter pipes
bull drill string reduce friction by using a larger internal diameter pipe coated with
plastic
bull drill collars increasing the internal diameter will again reduce friction but
only at the expense of decreasing their weight a balance has to be made
between these opposing effects
bull annulus losses are usually small and only become significant in deep small
diameter holes pressure losses depend on the hydraulic diameter found from
the difference between the hole size and the pipe od it is actually desirable to
reduce the pressure developed against the formations
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Flow regimes
The differences between laminar and turbulent flow are illustrated in the table
overleaf The type of flow is determined by calculating Reynolds number (Re) for the
known well conditions from the following equations
The value obtained is compared with those shown in Table2 (figures are based on
Newtonian fluid properties)
Table2 Deciding the flow condition from the Reynolds number
Inspection of the equations shows that turbulent flow is more likely with the
conditions below
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bull denser drilling fluid (ρ higher)
bull lower viscosity (micro lower)
bull higher flow rate (Q higher)
bull decreased pipe bore or hydraulic
diameter
(d lower)
PUMP HYDRAULIC POWER OUTPUT
In rig operations the amount of available hydraulic power is determined by the size
number and types of pump(s) on site However the demand in terms of output volume
(Q) and pump pressure (P) varies considerably with hole size and depth Once the
pump output or flow rate Q has been selected the available power input determines
the maximum circulating pressure (Pt) that can be achieved
This circulating pressure Pt (total pressure drop in system) is consumed partly by
friction in the fluid and the system (Ps = system pressure loss) and partly by the
pressure drop across the bit nozzles (P b = bit pressure drop) Therefore P t = Ps + P b Pt
is normally given by the pump pressure gauge
The system pressure drop has no effect on bottom-hole cleaning It is unavoidable andis also called the parasitic pressure loss
The bottom-hole cleaning action is provided by the hydraulic energy expended at the
bit Therefore the amount of hydraulic power expended at the bit is a measure for the
cleaning effectiveness (This assumes that the bit is properly matched to the formation
- if a bit designed for a hard formation is run in a soft formation no amount of power
will keep it clean )
The hydraulic power available at the surface from the pump is used to drive the
drilling fluid round the system power the bit and flush the cuttings to the surface If
you know the pump or circulating pressure (Pt ) and the flow rate (Q) then it is possible to calculate the total power available at the surface
Since Power = work done in unit time
and Work done = pressure x volume
then Power = pressure x volume pumped in unit time
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Therefore the power available at surface is given by
The power output of the pump is generally assumed to be 85 of the mechanical or
electrical power input of the pump
PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)
The pressure drop across the bit nozzles P b depends on
bull The flow rate Q
bull The total cross-sectional area of the nozzle openings A
bull The drilling fluid density ρ
Once the desired (optimum) annular velocity has been determined the flow rate (Q )
and the hydraulic power expended at the bit for a given nozzle size are fixed
Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power
expended at the bit is also fixed Both jet velocity and hydraulic power at the bit
determine the cleaning action on bottom
Pressure losses through the bit nozzles are not frictional but represent a change in
kinetic energy as the drilling fluid changes its velocity from that above the bit to that
leaving the jets The pressure expended is therefore dependent only on the drilling
fluid density and the square of the jet velocity
The pressure drop across the bit nozzles is calculated using the following equations
Where
P b is the pressure loss across the bit nozzles (kPa)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
A is the total nozzle area (mm2)
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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n and K are derived from viscometer data
Note that K here is an approximation to that given for the Power Law model found in
the section on Drilling Fluids The number 511 results from using a specific type of
viscometer with particular values of spring constant and cylinder surface speed
With Pfa as with Pfd when drilling at a particular depth with a given drilling fluid all
values in the above equations are effectively constant except for the annular velocity(Va) But Va is directly proportional to the flow rate (Q) Thus there will be a tendency
to assume that all pressure losses in the system follow the same equation as shown
below
Where c and N are constants whose values are empirically determined in particular
cases (see under Pressure losses in the drill string)
Pressure losses can be calculated for all parts of the system using the equations givenin this Part
CAUSES OF CHANGES IN CIRCULATING PRESSURES
According to Pt = P b + Ps a change in the circulating pressure can be induced by a
change in either P b Ps or both
Increases in surface pressure
A sudden increase in circulation pressure although drilling fluid properties flow rate
and conduit length are unchanged can be caused only by an increase in P b This could be caused by one or more nozzles plugging
A gradual increase in surface pressure could be the result of several causes (excepting
hole problems)
bull Increased flow rate
bull Extending the string while deepening the hole
bull Change in drilling fluid rheological properties
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Decreases in surface pressure
A spontaneous sudden decrease in circulating pressure while conditions remain
unchanged can be caused by
bull decrease of P b resulting from the loss of a nozzle
bull a twist-off in the drill string
A gradual decrease in pressure could signal the following
bull A developing wash-out (leak) in the drill string or in pump valves
bull Reduction of hydrostatic head in the annulus caused by lighter substances (eg
gas or formation water)
bull An increase of hydrostatic head in the string
Caution Any change of the surface pressure or change in pump strokes not
deliberately instigated should be investigated immediately
To a limited extent pressure losses can be measured directly for example by
pumping through the standpipe and open kelly and through drill collars It is also a
useful exercise to observe the total circulating pressure at various flow rates
Pressure losses in the system can be derived from actual circulating pressure values
by subtracting the pressure drop at the bit which can be calculated accurately
Pressure losses in the system can also be calculated However although the
dimensions are known for all parts of the system the calculation also depends on
knowing the type of fluid flow regime in the drill string and annulus The flow may be
turbulent or laminar or of some transitional type between the two The calculations are
also based on a rheological model If the drilling fluid in use behaves slightly variant
to the model the calculation results will be less than accurate
Pressure losses within the system are minimised by reducing the fluid friction in each
part
bull surface connections losses are negligible compared with elsewhere but can bereduced by avoiding tight bends and using large diameter pipes
bull drill string reduce friction by using a larger internal diameter pipe coated with
plastic
bull drill collars increasing the internal diameter will again reduce friction but
only at the expense of decreasing their weight a balance has to be made
between these opposing effects
bull annulus losses are usually small and only become significant in deep small
diameter holes pressure losses depend on the hydraulic diameter found from
the difference between the hole size and the pipe od it is actually desirable to
reduce the pressure developed against the formations
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Flow regimes
The differences between laminar and turbulent flow are illustrated in the table
overleaf The type of flow is determined by calculating Reynolds number (Re) for the
known well conditions from the following equations
The value obtained is compared with those shown in Table2 (figures are based on
Newtonian fluid properties)
Table2 Deciding the flow condition from the Reynolds number
Inspection of the equations shows that turbulent flow is more likely with the
conditions below
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bull denser drilling fluid (ρ higher)
bull lower viscosity (micro lower)
bull higher flow rate (Q higher)
bull decreased pipe bore or hydraulic
diameter
(d lower)
PUMP HYDRAULIC POWER OUTPUT
In rig operations the amount of available hydraulic power is determined by the size
number and types of pump(s) on site However the demand in terms of output volume
(Q) and pump pressure (P) varies considerably with hole size and depth Once the
pump output or flow rate Q has been selected the available power input determines
the maximum circulating pressure (Pt) that can be achieved
This circulating pressure Pt (total pressure drop in system) is consumed partly by
friction in the fluid and the system (Ps = system pressure loss) and partly by the
pressure drop across the bit nozzles (P b = bit pressure drop) Therefore P t = Ps + P b Pt
is normally given by the pump pressure gauge
The system pressure drop has no effect on bottom-hole cleaning It is unavoidable andis also called the parasitic pressure loss
The bottom-hole cleaning action is provided by the hydraulic energy expended at the
bit Therefore the amount of hydraulic power expended at the bit is a measure for the
cleaning effectiveness (This assumes that the bit is properly matched to the formation
- if a bit designed for a hard formation is run in a soft formation no amount of power
will keep it clean )
The hydraulic power available at the surface from the pump is used to drive the
drilling fluid round the system power the bit and flush the cuttings to the surface If
you know the pump or circulating pressure (Pt ) and the flow rate (Q) then it is possible to calculate the total power available at the surface
Since Power = work done in unit time
and Work done = pressure x volume
then Power = pressure x volume pumped in unit time
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Therefore the power available at surface is given by
The power output of the pump is generally assumed to be 85 of the mechanical or
electrical power input of the pump
PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)
The pressure drop across the bit nozzles P b depends on
bull The flow rate Q
bull The total cross-sectional area of the nozzle openings A
bull The drilling fluid density ρ
Once the desired (optimum) annular velocity has been determined the flow rate (Q )
and the hydraulic power expended at the bit for a given nozzle size are fixed
Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power
expended at the bit is also fixed Both jet velocity and hydraulic power at the bit
determine the cleaning action on bottom
Pressure losses through the bit nozzles are not frictional but represent a change in
kinetic energy as the drilling fluid changes its velocity from that above the bit to that
leaving the jets The pressure expended is therefore dependent only on the drilling
fluid density and the square of the jet velocity
The pressure drop across the bit nozzles is calculated using the following equations
Where
P b is the pressure loss across the bit nozzles (kPa)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
A is the total nozzle area (mm2)
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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Decreases in surface pressure
A spontaneous sudden decrease in circulating pressure while conditions remain
unchanged can be caused by
bull decrease of P b resulting from the loss of a nozzle
bull a twist-off in the drill string
A gradual decrease in pressure could signal the following
bull A developing wash-out (leak) in the drill string or in pump valves
bull Reduction of hydrostatic head in the annulus caused by lighter substances (eg
gas or formation water)
bull An increase of hydrostatic head in the string
Caution Any change of the surface pressure or change in pump strokes not
deliberately instigated should be investigated immediately
To a limited extent pressure losses can be measured directly for example by
pumping through the standpipe and open kelly and through drill collars It is also a
useful exercise to observe the total circulating pressure at various flow rates
Pressure losses in the system can be derived from actual circulating pressure values
by subtracting the pressure drop at the bit which can be calculated accurately
Pressure losses in the system can also be calculated However although the
dimensions are known for all parts of the system the calculation also depends on
knowing the type of fluid flow regime in the drill string and annulus The flow may be
turbulent or laminar or of some transitional type between the two The calculations are
also based on a rheological model If the drilling fluid in use behaves slightly variant
to the model the calculation results will be less than accurate
Pressure losses within the system are minimised by reducing the fluid friction in each
part
bull surface connections losses are negligible compared with elsewhere but can bereduced by avoiding tight bends and using large diameter pipes
bull drill string reduce friction by using a larger internal diameter pipe coated with
plastic
bull drill collars increasing the internal diameter will again reduce friction but
only at the expense of decreasing their weight a balance has to be made
between these opposing effects
bull annulus losses are usually small and only become significant in deep small
diameter holes pressure losses depend on the hydraulic diameter found from
the difference between the hole size and the pipe od it is actually desirable to
reduce the pressure developed against the formations
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Flow regimes
The differences between laminar and turbulent flow are illustrated in the table
overleaf The type of flow is determined by calculating Reynolds number (Re) for the
known well conditions from the following equations
The value obtained is compared with those shown in Table2 (figures are based on
Newtonian fluid properties)
Table2 Deciding the flow condition from the Reynolds number
Inspection of the equations shows that turbulent flow is more likely with the
conditions below
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bull denser drilling fluid (ρ higher)
bull lower viscosity (micro lower)
bull higher flow rate (Q higher)
bull decreased pipe bore or hydraulic
diameter
(d lower)
PUMP HYDRAULIC POWER OUTPUT
In rig operations the amount of available hydraulic power is determined by the size
number and types of pump(s) on site However the demand in terms of output volume
(Q) and pump pressure (P) varies considerably with hole size and depth Once the
pump output or flow rate Q has been selected the available power input determines
the maximum circulating pressure (Pt) that can be achieved
This circulating pressure Pt (total pressure drop in system) is consumed partly by
friction in the fluid and the system (Ps = system pressure loss) and partly by the
pressure drop across the bit nozzles (P b = bit pressure drop) Therefore P t = Ps + P b Pt
is normally given by the pump pressure gauge
The system pressure drop has no effect on bottom-hole cleaning It is unavoidable andis also called the parasitic pressure loss
The bottom-hole cleaning action is provided by the hydraulic energy expended at the
bit Therefore the amount of hydraulic power expended at the bit is a measure for the
cleaning effectiveness (This assumes that the bit is properly matched to the formation
- if a bit designed for a hard formation is run in a soft formation no amount of power
will keep it clean )
The hydraulic power available at the surface from the pump is used to drive the
drilling fluid round the system power the bit and flush the cuttings to the surface If
you know the pump or circulating pressure (Pt ) and the flow rate (Q) then it is possible to calculate the total power available at the surface
Since Power = work done in unit time
and Work done = pressure x volume
then Power = pressure x volume pumped in unit time
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Therefore the power available at surface is given by
The power output of the pump is generally assumed to be 85 of the mechanical or
electrical power input of the pump
PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)
The pressure drop across the bit nozzles P b depends on
bull The flow rate Q
bull The total cross-sectional area of the nozzle openings A
bull The drilling fluid density ρ
Once the desired (optimum) annular velocity has been determined the flow rate (Q )
and the hydraulic power expended at the bit for a given nozzle size are fixed
Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power
expended at the bit is also fixed Both jet velocity and hydraulic power at the bit
determine the cleaning action on bottom
Pressure losses through the bit nozzles are not frictional but represent a change in
kinetic energy as the drilling fluid changes its velocity from that above the bit to that
leaving the jets The pressure expended is therefore dependent only on the drilling
fluid density and the square of the jet velocity
The pressure drop across the bit nozzles is calculated using the following equations
Where
P b is the pressure loss across the bit nozzles (kPa)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
A is the total nozzle area (mm2)
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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Flow regimes
The differences between laminar and turbulent flow are illustrated in the table
overleaf The type of flow is determined by calculating Reynolds number (Re) for the
known well conditions from the following equations
The value obtained is compared with those shown in Table2 (figures are based on
Newtonian fluid properties)
Table2 Deciding the flow condition from the Reynolds number
Inspection of the equations shows that turbulent flow is more likely with the
conditions below
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bull denser drilling fluid (ρ higher)
bull lower viscosity (micro lower)
bull higher flow rate (Q higher)
bull decreased pipe bore or hydraulic
diameter
(d lower)
PUMP HYDRAULIC POWER OUTPUT
In rig operations the amount of available hydraulic power is determined by the size
number and types of pump(s) on site However the demand in terms of output volume
(Q) and pump pressure (P) varies considerably with hole size and depth Once the
pump output or flow rate Q has been selected the available power input determines
the maximum circulating pressure (Pt) that can be achieved
This circulating pressure Pt (total pressure drop in system) is consumed partly by
friction in the fluid and the system (Ps = system pressure loss) and partly by the
pressure drop across the bit nozzles (P b = bit pressure drop) Therefore P t = Ps + P b Pt
is normally given by the pump pressure gauge
The system pressure drop has no effect on bottom-hole cleaning It is unavoidable andis also called the parasitic pressure loss
The bottom-hole cleaning action is provided by the hydraulic energy expended at the
bit Therefore the amount of hydraulic power expended at the bit is a measure for the
cleaning effectiveness (This assumes that the bit is properly matched to the formation
- if a bit designed for a hard formation is run in a soft formation no amount of power
will keep it clean )
The hydraulic power available at the surface from the pump is used to drive the
drilling fluid round the system power the bit and flush the cuttings to the surface If
you know the pump or circulating pressure (Pt ) and the flow rate (Q) then it is possible to calculate the total power available at the surface
Since Power = work done in unit time
and Work done = pressure x volume
then Power = pressure x volume pumped in unit time
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Therefore the power available at surface is given by
The power output of the pump is generally assumed to be 85 of the mechanical or
electrical power input of the pump
PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)
The pressure drop across the bit nozzles P b depends on
bull The flow rate Q
bull The total cross-sectional area of the nozzle openings A
bull The drilling fluid density ρ
Once the desired (optimum) annular velocity has been determined the flow rate (Q )
and the hydraulic power expended at the bit for a given nozzle size are fixed
Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power
expended at the bit is also fixed Both jet velocity and hydraulic power at the bit
determine the cleaning action on bottom
Pressure losses through the bit nozzles are not frictional but represent a change in
kinetic energy as the drilling fluid changes its velocity from that above the bit to that
leaving the jets The pressure expended is therefore dependent only on the drilling
fluid density and the square of the jet velocity
The pressure drop across the bit nozzles is calculated using the following equations
Where
P b is the pressure loss across the bit nozzles (kPa)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
A is the total nozzle area (mm2)
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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bull denser drilling fluid (ρ higher)
bull lower viscosity (micro lower)
bull higher flow rate (Q higher)
bull decreased pipe bore or hydraulic
diameter
(d lower)
PUMP HYDRAULIC POWER OUTPUT
In rig operations the amount of available hydraulic power is determined by the size
number and types of pump(s) on site However the demand in terms of output volume
(Q) and pump pressure (P) varies considerably with hole size and depth Once the
pump output or flow rate Q has been selected the available power input determines
the maximum circulating pressure (Pt) that can be achieved
This circulating pressure Pt (total pressure drop in system) is consumed partly by
friction in the fluid and the system (Ps = system pressure loss) and partly by the
pressure drop across the bit nozzles (P b = bit pressure drop) Therefore P t = Ps + P b Pt
is normally given by the pump pressure gauge
The system pressure drop has no effect on bottom-hole cleaning It is unavoidable andis also called the parasitic pressure loss
The bottom-hole cleaning action is provided by the hydraulic energy expended at the
bit Therefore the amount of hydraulic power expended at the bit is a measure for the
cleaning effectiveness (This assumes that the bit is properly matched to the formation
- if a bit designed for a hard formation is run in a soft formation no amount of power
will keep it clean )
The hydraulic power available at the surface from the pump is used to drive the
drilling fluid round the system power the bit and flush the cuttings to the surface If
you know the pump or circulating pressure (Pt ) and the flow rate (Q) then it is possible to calculate the total power available at the surface
Since Power = work done in unit time
and Work done = pressure x volume
then Power = pressure x volume pumped in unit time
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Therefore the power available at surface is given by
The power output of the pump is generally assumed to be 85 of the mechanical or
electrical power input of the pump
PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)
The pressure drop across the bit nozzles P b depends on
bull The flow rate Q
bull The total cross-sectional area of the nozzle openings A
bull The drilling fluid density ρ
Once the desired (optimum) annular velocity has been determined the flow rate (Q )
and the hydraulic power expended at the bit for a given nozzle size are fixed
Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power
expended at the bit is also fixed Both jet velocity and hydraulic power at the bit
determine the cleaning action on bottom
Pressure losses through the bit nozzles are not frictional but represent a change in
kinetic energy as the drilling fluid changes its velocity from that above the bit to that
leaving the jets The pressure expended is therefore dependent only on the drilling
fluid density and the square of the jet velocity
The pressure drop across the bit nozzles is calculated using the following equations
Where
P b is the pressure loss across the bit nozzles (kPa)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
A is the total nozzle area (mm2)
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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Therefore the power available at surface is given by
The power output of the pump is generally assumed to be 85 of the mechanical or
electrical power input of the pump
PRESSURE DROP ACROSS THE BIT NOZZLES (Pb)
The pressure drop across the bit nozzles P b depends on
bull The flow rate Q
bull The total cross-sectional area of the nozzle openings A
bull The drilling fluid density ρ
Once the desired (optimum) annular velocity has been determined the flow rate (Q )
and the hydraulic power expended at the bit for a given nozzle size are fixed
Since the jet velocity (Vn) is directly related to the flow rate the hydraulic power
expended at the bit is also fixed Both jet velocity and hydraulic power at the bit
determine the cleaning action on bottom
Pressure losses through the bit nozzles are not frictional but represent a change in
kinetic energy as the drilling fluid changes its velocity from that above the bit to that
leaving the jets The pressure expended is therefore dependent only on the drilling
fluid density and the square of the jet velocity
The pressure drop across the bit nozzles is calculated using the following equations
Where
P b is the pressure loss across the bit nozzles (kPa)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
A is the total nozzle area (mm2)
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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Cn is the nozzle coefficient (dimensionless)
The nozzle coefficient for jet nozzles is usually taken as 0middot95
Where
P b is in psi
ρ is in psift
Q is in gpm
A is in inch2
Cn is dimensionless
HYDRAULIC POWER DEVELOPED AT THE BIT
As stated Pt = Ps + P b where the symbols have their previous meanings
It was later shown that the total power available is given by or
according to the system of units where the symbols again have their previous
meanings
Similarly the power lost in the system is given by or
But the power generated at the pump must either be lost in the system or used at the
bit so the hydraulic power developed at the bit is given in SI units and oilfield units
respectively by
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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Since Pt - Ps = P b then the hydraulic power developed at the bit is also given by
JET IMPACT FORCE (I) BELOW THE BIT
Consideration may also be given to the actual force with which the drilling fluid
jetting from the bit strikes against the formation This is called the jet impact force (I)
The jet impact force can be calculated using the following equations
Where
I is the jet impact force (N)
ρ is the drilling fluid gradient (kPam)
Q is the flow rate (m3s)
Vn is the jet velocity (ms)
and
Where
I is in lbf
ρ is in psift
Q is in gpm
Vn is in fts
These equations can be modified by substituting for Vn
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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You should note the following points
bull the result obtained does not take into account the extremely complicated flow
conditions at the bottom of the hole
bull impact force is an important measure of the hole cleaning effort which is
applied on bottombull impact force theory is very important in the design and operation of extended-
nozzle and high-impact jet bits
SUMMARY
In this topic nine important hydraulic parameters have been described The important
equations from this section are listed below and these indicate how the parameters are
related Note in particular the importance of the flow rate and the nozzle area
Evaluation of the parasitic pressure losses
This Topic will provide some theoretical background information to explain how the
parasitic pressure losses can be related to the flow rate It will deal with
bull Aspects of fluid flow
bull Practical application
bull Determination of c and N
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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ASPECTS OF FLUID FLOW
The movement of fluid through a conduit is caused by an external force provided in
this case by a pump This force must overcome the internal fluid friction and the
friction between fluid and conduit which results in the pressure drop It and the
pressure drop is a function of
bull The flow rate
bull The fluid properties
o fluid density
o viscosity
bull The type of conduit and its dimensions
o length
o flow area ie hydraulic diameter
o roughness of the system wall
bull The flow regime
Basically these parameters are related as follows
(1)
and since and then (2)
The friction factor f in equations (1) and (2) is a function of the drilling fluid
properties flow regime and Reynolds number and is expressed as follows
(3)
where the friction factor coefficients are functions of the plastic viscosity (PV) and
yield point (YP) of the drilling fluid
The magnitude of the Re number determines the flow regime which under most
drilling conditions will be turbulent inside the drill string and laminar in the annulus
In its most general form the Reynolds number (Re) is determined by the equations
(4)
In equations (1) to (4)
P = pressure drop (kPa) (psi)
k 1234 = conversion factors
ρ = drilling fluid gradient (kPam) (psift)
V = average fluid velocity (ms) (fts)
Q = flow rate (m3
s) (ft3
s or gallmin)L = length of conduit (m) (ft)
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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d = hydraulic diameter of conduit
for the annulus d = ID hole - OD pipe and for pipe d = ID) (mm)
(inch)
f = flow friction factor
η = effective viscosity (Pa-s) (cP)ab = friction factor coefficients
As stated previously once drilling has started with a particular drilling assembly and
bit the circulating pressure is composed of two parts
The bit pressure drop can be calculated accurately as explained
The system pressure drop could be calculated by substituting equations (4) and (3) in
equation (2) A rather complicated equation then evolves which can be simplified to
The following variables are included in this general expression for the parasitic
pressure losses
In cρ η L d
In N friction factor coefficient b
PRACTICAL APPLICATION
The effect of changes in depth circulating rate and drilling fluid gradient on the
circulating pressure will now be explained
While drilling a section of hole with one bit (a certain bit run) the circulating rate is
determined by the annular velocity which is usually kept constant The drilling fluid
properties are normally also kept steady during such a period (as long as no changesare required as a result of hole condition or formation pressures) The only variable
that changes is the string length L
For pressure drop calculations the drill string is divided into two sections iedrill
pipe and drill collars which are considerably different in both internal and external
diameters During a bit run the length of the drill collars does not change
Depending on the ratio of LdpLdc and the magnitude of the increase in Ldp the
following approximation may be used to determine the change in Ps
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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If however the increase in hole depth during one bit run is considerable the changein Ps should be determined more accurately by pump tests as described in the
following section
During well control operations however a reduced circulating rate is used and at the
same time the drilling fluid gradient is changed
The effect of a change in drilling fluid gradient ρ on P b is proportional and for
practical purposes the same proportional change is applied to Ps
Scrutinizing the theoretical equations in the previous section the change in P s is not
exactly proportional The friction factor changes with ρ via the Re-number Howeverfrom practical experience neglecting this inaccuracy is justified and therefore the
following proportional relation is used
DETERMINATION OF c AND N
Theoretically the value of the exponent N and the factor c can be calculated from
two standpipe pressure readings observed at two different pump rates
knowing that
Since the value of N can be solved by the ratio
Therefore it follows that or
(The value of N is often quoted as 182 in literature Where insufficient information is
available to make the calculation 182 can be assumed to make an estimate of the
pressures which can be expected
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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As soon as operations allow pressure readings should be taken and N calculated)
c can be determined from the equation
As small inaccuracies in pressure readings and pump stroke counts can result in
considerable errors in N and c it is recommended to monitor pressures at more
than just two pump rates These readings should cover the expected range of both
drilling and well killing pump rates
Operating limits
Decisions regarding hydraulic parameters may be necessary before the hole is drilled
In this Topic attention is focused upon the annular velocity pump pressure and flow
rate Knowledge of their allowable maximum and minimum values is important in the
process of establishing the optimum values of the variables under your control at the
surface
When considering the operating limits there are three important processes
bull DECIDING the limits for the annular velocity pressure and flow rate
bull CONSIDERING special hydraulic conditions Is the hole abnormally deep Is
the hole to be of unusual diameter Will there be high temperatures Will it be
a deviated hole What is the hydraulic capacity of the rig
bull REVIEWING the hydraulic parameters when there are hole problems
SELECTING THE ANNULAR VELOCITY
As a first step the most suitable annular velocity should be decided The purpose here
is not to show how a precise value is selected but to indicate the factors that affect the
minimum and maximum values of the annular velocity that can be selected
SELECTING THE PUMP PRESSURE AND FLOW RATE
It is normal practice to operate circulating pumps at a constant pressure The pressure
used is either the rated delivery pressure (inclusive of a safety factor) for the size of
liner installed or a rate selected to minimize pump maintenance if this still allows
good hole cleaning and adequate power at the bit
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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MAINTENANCE COSTS
These increase sharply above a critical operating pressure If used above this pressure
wear on components suddenly increases out of proportion to the increased outputAdditionally maintenance has to be carried out more frequently increasing rig
downtime Table 3 lists the maximum normal running pressures for most duplex and
triplex pumps (however the manufacturers instructions are the determining factor)
These values only apply to rig surface equipment that is suitably rated
Table 3 Maximum normal running pump pressures
LINER SIZE
This should be selected to minimize the need for changing liners through the project
They should also be such that they provide both an adequate flow rate for the surface
hole and the pressure needed at depth
MINIMUM VALUE OF ANNULAR VELOCITY
The minimum value of the annular velocity is governed by the ability of the drilling
fluid to clean the well If the well is not efficiently cleaned there will be cuttings build
up leading to increased hydrostatic and ECD pressures which might cause drilling
fluid losses to the formation In inclined holes a significant amount of the cuttings
might drop to the lower side of the hole and form a cuttings bed When the annular
velocity is not sufficient the cuttings bed will grow thereby increasing the risk of
differential and mechanical sticking of the drill string
Vertical wells
In vertical sections (in practice those with an inclination of up to plusmn25deg) the cuttings
suspension will be homogeneously distributed over the entire cross section of the
annulus Given that cuttings settle relative to the upward flowing mud then as long as
the fluid velocity is greater than the cuttings settling velocity transport will occur
Figure 223 shows how the cutting velocity varies with annular velocity for different
drilling fluid thicknesses Four coloured areas are shown corresponding to different
amounts of cuttings being removed
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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Figure3 The relationship between annular velocity drilling fluid and cuttings velocity
Thick drilling fluid will lift more than 75 of the cuttings at all speeds thin drilling
fluid will carry more than 50 if the annular velocity exceeds about 02 ms (30
ftmin) Water even at annular velocities of 03 ms (66 ftmin) will carry away only
slightly more than 25 In other words drilling fluid thickness (viscosity and gel
strength) is an important factor
A practical method of estimating the minimum annular velocity to ensure hole
cleaning is based on Fullertons approximation which assumes that the diameter of
the cuttings is 6middot35 mm (0middot25) that their density is 2510 kgm3 (157 lbsft3) andthat the annular fluid velocity should be not less than twice the cuttings settling
velocity
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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The approximation is
Note drill string rotation does not benefit transport much in these well sections
because it does not effect the distribution of cuttings over the wellbore cross section
Penetration rate and hole size must also be considered In large diameter shallow
holes it may not be possible to achieve the necessary minimum velocity and special
precautions may be necessary to ensure that the hole is properly cleaned At such
depths penetration rates are likely to be high anyway so there may be less emphasis
on the need for optimum hydraulics
Fig 4
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
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where k is a constant
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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Inclined sections
In intermediate inclined sections (plusmn 25deg to plusmn 50deg) cuttings tend to settle towards the
low side of the wellbore and form an unstable deposit As the deposit grows it will
avalanche downhole with increasing velocity When the velocity becomes too high
the deposit breaks up and re-suspends in the flow (see also Figure4) The most
important factors to enhance transport are
bull Annular drilling fluid velocity increase (see also under vertical sections)
bull Drill string rotation ampendash faster is better Drill string rotation results in a
more homogeneous distribution of cuttings over the cross section of the
annulus and consequently enhances transport
bull Viscosity increase A viscosity increase will usually enhance transport in
intermediate inclined sections but the effect is less pronounced compared tothe effect in vertical sections
Highly inclined sections
In highly inclined sections (plusmn 50deg to horizontal) a large part of the cuttings will not
stay in suspension but will settle towards the lower side of the hole to form a
stationary cuttings bed As the height of the deposit grows the area of the annulus
open to flow decreases leading to an increase in the average drilling fluid velocity
above the bed At a certain bed height the velocity of the fluid above the bed (and the
associated stresses on the bed surface) will exceed a critical value above which
cuttings are continuously picked up eroded and transported upwards Under theseconditions a steady state constant bed height will develop (See also Figure4)
Operational problems can be minimized by setting the operational variables in such a
way that cuttings accumulation is minimized The following parameters have the most
impact on cuttings transport in highly inclined well sections
bull Annular drilling fluid velocity (flowrate) higher is better
bull Drill string rotational velocity faster is better (see also above) The impact of
rotation on cuttings accumulation can be very large In troublesome wells
avoid slidingorient mode drilling Consider the use of rotary steerable
systemsbull Drilling fluid viscosity It is difficult to give a general guideline about the level
of drilling fluid viscosity In horizontal well sections transport is obtained by
erosion of the bed surface Erosion can be optimized by a high shear stress at
the surface of the deposit (which requires a high viscosity) or by increasing
turbulence intensity (turbulence is intensified by a viscosity decrease)
Furthermore the resistance to erosion of a cuttings bed depends on the
consistency of the (stationary) drilling fluid in the pores between the cuttings
A high gel strength or yield point tends to glue the particles together High
yield points should therefore be avoided
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
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7182019 Hydraulic Optimization
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
Eng Fayez Amin Makkar 31
7182019 Hydraulic Optimization
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MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
Eng Fayez Amin Makkar 32
7182019 Hydraulic Optimization
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Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
Eng Fayez Amin Makkar 33
7182019 Hydraulic Optimization
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where k is a constant
Eng Fayez Amin Makkar 34
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Eng Fayez Amin Makkar 35
7182019 Hydraulic Optimization
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
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Appendix 5
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These conflicting mechanisms usually mean that medium viscosity fluids should
preferably be avoided It is usually better to choose either a high or a low viscosity
drilling fluid Which one is preferable depends on the specific case and can only be
evaluated using cuttings transport software
Note The optimum viscosity to clean horizontal sections is often not the optimumviscosity to clean the vertical or intermediate inclined sections The viscosity choice
will therefore always be a compromise
MAXIMUM VALUE OF ANNULAR VELOCITY
Erosion of the formation face will occur over time as the drilling fluid flows over it
However the rate of erosion is only slightly influenced by the actual annular velocity
Far more important is the flow type Turbulent flow is more erosive than laminar
flow hence the need to calculate the Reynolds Number Also important is the
formation type the softer the formation the faster it erodes
Once the range of acceptable values for the annular velocity is known it is then
possible to consider the selection of pump pressure and flow rate
Optimum bit hydraulics
This Topic discusses optimized drilling performance in general and two possible
approaches to obtaining optimum conditions at the bit These are to maximize the
hydraulic power at the bit or to maximize the jet impact force
OPTIMUM DRILLING PERFORMANCE
Opinions vary both as to what the optimum conditions are and how they can be
achieved There is agreement that the aim is to achieve the best penetration rate All
efforts should be made to minimize costs per foot The first factor affecting the costs
is the rate of penetration It is a well known fact that if bottom hole andor bit cleaning
is inadequate drilling progress will be jeopardized
Optimum drilling performance therefore is closely related to optimum use of the
available hydraulic power within the constraints posed by the drilling fluids and the
hole condition Optimization can be effected only when during drilling the hydraulicforce and energy at the bit is in the first place sufficient to remove cuttings
effectively as they are produced by the bit In roller cone bits the bit teeth crush the
rock as shown in Figure 225 and the hydraulic forces have to remove these cuttings
from the hole bottom Significant fluid forces are required since the cuttings are
pushed against the hole bottom due to the difference between the borehole pressure
BHP and the pore pressure Po in the formation (BHP gt Po) This effect is called the
chip hold-down effect It causes regrinding of the cuttings which greatly reduces the
rate of penetration
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
Eng Fayez Amin Makkar 29
7182019 Hydraulic Optimization
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
Eng Fayez Amin Makkar 30
7182019 Hydraulic Optimization
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bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
Eng Fayez Amin Makkar 31
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3252
MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
Eng Fayez Amin Makkar 32
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3352
Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
Eng Fayez Amin Makkar 33
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3452
where k is a constant
Eng Fayez Amin Makkar 34
7182019 Hydraulic Optimization
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Eng Fayez Amin Makkar 35
7182019 Hydraulic Optimization
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It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
Eng Fayez Amin Makkar 36
7182019 Hydraulic Optimization
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Appendix 1
SOLUTION IN FIELD UNITS
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Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
Eng Fayez Amin Makkar 39
7182019 Hydraulic Optimization
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Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 40
7182019 Hydraulic Optimization
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Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 41
7182019 Hydraulic Optimization
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Appendix 5
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Figure5 Cutting action of a roller cone bit
Soft formation roller cone bits have therefore been designed not only to crush the
rock but also to remove the cuttings from the hole bottom by a dragging action of the
teeth (this would cause mechanical failure of the bit teeth or inserts in harder
formations) In these formations part of the hydraulic power should therefore be used
to remove the rock from between the teeth and to prevent clogging of the bit
Penetration rate can be reduced significantly if the layer of rock cuttings on the cones
of the bit is so thick that it can hamper the penetration of the teeth into the formation
This process is called bit balling and can be so severe in some soft and sticky
formations that the rate of penetration reduces to almost zero after only a few metresof drilling In large size bits bit balling can often be prevented by adding a nozzle into
the centre of the bit
PDC bits have a very different cutting action than roller cone bits as shown in
Figure6 The PDC cutters drag through the rock continuously the cuttings are
therefore immediately removed from the hole bottom Hydraulic forces now have to
break the cuttings and remove them from the bit face
Figure 226 Cutting action of a PDC bit
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7182019 Hydraulic Optimization
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If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
Eng Fayez Amin Makkar 30
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3152
bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
Eng Fayez Amin Makkar 31
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3252
MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
Eng Fayez Amin Makkar 32
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3352
Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
Eng Fayez Amin Makkar 33
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3452
where k is a constant
Eng Fayez Amin Makkar 34
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3552
Eng Fayez Amin Makkar 35
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3652
It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
Eng Fayez Amin Makkar 36
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3752
Appendix 1
SOLUTION IN FIELD UNITS
Eng Fayez Amin Makkar 37
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3852
Eng Fayez Amin Makkar 38
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3952
Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
Eng Fayez Amin Makkar 39
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4052
Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 40
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4152
Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 41
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4252
Appendix 5
Eng Fayez Amin Makkar 42
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4352
Eng Fayez Amin Makkar 43
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4452
Eng Fayez Amin Makkar 44
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4552
Eng Fayez Amin Makkar 45
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4652
Eng Fayez Amin Makkar 46
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4752
Eng Fayez Amin Makkar 47
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4852
Eng Fayez Amin Makkar 48
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4952
Eng Fayez Amin Makkar 49
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5052
Eng Fayez Amin Makkar 50
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5152
Eng Fayez Amin Makkar 51
7182019 Hydraulic Optimization
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7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3052
If this is not done properly the cuttings will be pushed upwards towards the bit face
where they might stick to the bit surface This will also ball up (part of) the bit which
can again reduce the rate of penetration significantly In drag bits the available
hydraulic power should therefore be used to clean the cutters and the bit surface PDC
bit designs for soft and sticky formations should achieve high fluid velocities along all
cutters and along the surface of the bit Bits with large waterways have proven tosignificantly reduce the risk of bit balling
The remainder of this paragraph will be limited to optimization of bottom hole
cleaning for roller cone bits
In general two theories on the subject of bottom hole cleaning are supported
bull Bit hydraulic power It is assumed that chip removal depends on the fluid
energy dissipated at the bit Therefore the hydraulic power at the bit should be
maximized
bull Jetting (impact) force It is assumed that the bottom is cleaned best when thedrilling fluid hits the rock at maximum force Therefore the hydraulic impact
force should be maximized
The magnitudes of both impact force and hydraulic power expended at the bit vary
according to the following factors
bull Diameter and number of nozzles fitted at the bit
bull Circulating rate through the bit
bull The drilling fluid density or drilling fluid gradient
There are a number of limitations or constraints for any given circulating system
which directly affect optimization These constraints are
bull Upper and lower limits set on annular velocity
bull Maximum pumping speed and therefore circulating rate with the pumps
available on the rig
bull Maximum practical operating pressure often dictated by the pump liner size
fitted or the pressure rating of the surface equipment
The pump output and standpipe pressure can be determined accurately for any given
drilling situation The standpipe pressure as has been explained is considered to bethe sum of all the friction losses in and around the drill string The pressure drop at the
bit is included in the total sum
To simplify a direct approach to optimizing drilling hydraulics the pressure drop at
the bit is separated as the only useful pressure drop System or parasitic pressure
losses in and around the drill string are however unavoidable The only direct control
over the hydraulic energy expended at the bit is by keeping the system losses to a
minimum or in proper relation to the useful pressure drop across the bit
This can be achieved by
bull Proper selection of nozzle sizes
Eng Fayez Amin Makkar 30
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3152
bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
Eng Fayez Amin Makkar 31
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3252
MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
Eng Fayez Amin Makkar 32
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3352
Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
Eng Fayez Amin Makkar 33
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3452
where k is a constant
Eng Fayez Amin Makkar 34
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3552
Eng Fayez Amin Makkar 35
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3652
It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
Eng Fayez Amin Makkar 36
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3752
Appendix 1
SOLUTION IN FIELD UNITS
Eng Fayez Amin Makkar 37
7182019 Hydraulic Optimization
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Eng Fayez Amin Makkar 38
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3952
Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
Eng Fayez Amin Makkar 39
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4052
Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 40
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4152
Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 41
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4252
Appendix 5
Eng Fayez Amin Makkar 42
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4352
Eng Fayez Amin Makkar 43
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4452
Eng Fayez Amin Makkar 44
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4552
Eng Fayez Amin Makkar 45
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4652
Eng Fayez Amin Makkar 46
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4752
Eng Fayez Amin Makkar 47
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4852
Eng Fayez Amin Makkar 48
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4952
Eng Fayez Amin Makkar 49
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5052
Eng Fayez Amin Makkar 50
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5152
Eng Fayez Amin Makkar 51
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7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3152
bull Operating at optimum flow rate but within rated pressure
In the latter case it should be remembered that operating rig pumps at high pressure
ratings will be uneconomical with regard to spare parts and fuel consumption
The two approaches will now be considered in more detail In the first approach the
assumption is that the best penetration rate is achieved if cuttings are removed
efficiently from below the bit It is then assumed that the most efficient cutting
removal is achieved by maximizing the hydraulic power available at the bit In the
second approach the assumption is that the formation is best removed by maximizing
the jet impact force These two approaches are summarized in the following Table
The most popular approach is that of maximizing the hydraulic power developed at
the bit although with some formations notably soft formations maximizing hydraulicimpact force is preferred There are other approaches including maximizing the jet
velocity and optimizing the fluid energy with respect to the bit diameter These
approaches are seldom used hence they are not considered here
Each of the two main approaches the maximum hydraulic power at the bit and the
maximum jet impact force will be examined in turn The procedure for optimizing
drilling hydraulics using the two approaches is summarized in the flowchart below
Eng Fayez Amin Makkar 31
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3252
MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
Eng Fayez Amin Makkar 32
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3352
Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
Eng Fayez Amin Makkar 33
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3452
where k is a constant
Eng Fayez Amin Makkar 34
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3552
Eng Fayez Amin Makkar 35
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3652
It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
Eng Fayez Amin Makkar 36
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3752
Appendix 1
SOLUTION IN FIELD UNITS
Eng Fayez Amin Makkar 37
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3852
Eng Fayez Amin Makkar 38
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3952
Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
Eng Fayez Amin Makkar 39
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4052
Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 40
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4152
Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 41
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4252
Appendix 5
Eng Fayez Amin Makkar 42
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4352
Eng Fayez Amin Makkar 43
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4452
Eng Fayez Amin Makkar 44
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4552
Eng Fayez Amin Makkar 45
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4652
Eng Fayez Amin Makkar 46
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4752
Eng Fayez Amin Makkar 47
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4852
Eng Fayez Amin Makkar 48
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4952
Eng Fayez Amin Makkar 49
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5052
Eng Fayez Amin Makkar 50
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5152
Eng Fayez Amin Makkar 51
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5252
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3252
MAXIMUM HYDRAULIC POWER AT THE BIT
An expression was found for the hydraulic power at the bit in terms of the pump or
circulating pressure the pressure losses in the system and the flow rate
Thus in order to maximize the hydraulic power at the bit we have to ensure that this
expression has a maximum value
It was said that it is normal practice to operate circulating pumps at a constant
pressure So in the expression for the hydraulic power at the bit Pt will be effectively
constant for a particular well Thus the only variable on the right hand side of the
expression is Q the flow rate Therefore the maximum hydraulic power will be
developed at the bit when its derivative with respect to the flow rate is zero
ie Maximum hydraulic power at the bit is when
Eng Fayez Amin Makkar 32
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3352
Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
Eng Fayez Amin Makkar 33
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3452
where k is a constant
Eng Fayez Amin Makkar 34
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3552
Eng Fayez Amin Makkar 35
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3652
It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
Eng Fayez Amin Makkar 36
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3752
Appendix 1
SOLUTION IN FIELD UNITS
Eng Fayez Amin Makkar 37
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3852
Eng Fayez Amin Makkar 38
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3952
Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
Eng Fayez Amin Makkar 39
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4052
Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 40
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4152
Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 41
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4252
Appendix 5
Eng Fayez Amin Makkar 42
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4352
Eng Fayez Amin Makkar 43
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4452
Eng Fayez Amin Makkar 44
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4552
Eng Fayez Amin Makkar 45
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4652
Eng Fayez Amin Makkar 46
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4752
Eng Fayez Amin Makkar 47
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4852
Eng Fayez Amin Makkar 48
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4952
Eng Fayez Amin Makkar 49
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5052
Eng Fayez Amin Makkar 50
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5152
Eng Fayez Amin Makkar 51
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5252
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3352
Differentiating
Thus maximum hydraulic power at the bit is when
that is when
But since the hydraulic power at the bit will be a maximum
when
To obtain a similar relationship between the power at the bit and the system losses P s
from the equation can be substituted in the above to give
MAXIMUM JET IMPACT FORCE
When maximizing the hydraulic power at the bit the method was as follows
bull Obtain an expression for the hydraulic power at the bit in terms of one
variable Q (This was possible because the pump operating pressure was taken
to be fixed)bull Differentiate with respect to Q and equate the derivative to zero
bull Obtain an expression for Ps in terms of Pt and N
bull Obtain an expression for P b in terms of Pt and N
By a worked example it was then possible to show that given values of Pt and
calculated Q and N led to a value of P b The method is essentially the same for
maximizing the jet impact force Thus the first step is to obtain an expression for the
jet impact force in terms of the flow rate Q
In the jet impact force is given by
If we consider that for a given situation the drilling fluid gradient is constant then
the expression for the jet impact force can be written as
Eng Fayez Amin Makkar 33
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3452
where k is a constant
Eng Fayez Amin Makkar 34
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3552
Eng Fayez Amin Makkar 35
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3652
It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
Eng Fayez Amin Makkar 36
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3752
Appendix 1
SOLUTION IN FIELD UNITS
Eng Fayez Amin Makkar 37
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3852
Eng Fayez Amin Makkar 38
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3952
Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
Eng Fayez Amin Makkar 39
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4052
Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 40
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4152
Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 41
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4252
Appendix 5
Eng Fayez Amin Makkar 42
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4352
Eng Fayez Amin Makkar 43
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4452
Eng Fayez Amin Makkar 44
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4552
Eng Fayez Amin Makkar 45
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4652
Eng Fayez Amin Makkar 46
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4752
Eng Fayez Amin Makkar 47
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4852
Eng Fayez Amin Makkar 48
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4952
Eng Fayez Amin Makkar 49
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5052
Eng Fayez Amin Makkar 50
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5152
Eng Fayez Amin Makkar 51
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5252
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3452
where k is a constant
Eng Fayez Amin Makkar 34
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3552
Eng Fayez Amin Makkar 35
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3652
It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
Eng Fayez Amin Makkar 36
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3752
Appendix 1
SOLUTION IN FIELD UNITS
Eng Fayez Amin Makkar 37
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3852
Eng Fayez Amin Makkar 38
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3952
Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
Eng Fayez Amin Makkar 39
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4052
Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 40
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4152
Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 41
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4252
Appendix 5
Eng Fayez Amin Makkar 42
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4352
Eng Fayez Amin Makkar 43
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4452
Eng Fayez Amin Makkar 44
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4552
Eng Fayez Amin Makkar 45
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4652
Eng Fayez Amin Makkar 46
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4752
Eng Fayez Amin Makkar 47
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4852
Eng Fayez Amin Makkar 48
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4952
Eng Fayez Amin Makkar 49
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5052
Eng Fayez Amin Makkar 50
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5152
Eng Fayez Amin Makkar 51
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5252
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3552
Eng Fayez Amin Makkar 35
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3652
It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
Eng Fayez Amin Makkar 36
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3752
Appendix 1
SOLUTION IN FIELD UNITS
Eng Fayez Amin Makkar 37
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3852
Eng Fayez Amin Makkar 38
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3952
Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
Eng Fayez Amin Makkar 39
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4052
Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 40
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4152
Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 41
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4252
Appendix 5
Eng Fayez Amin Makkar 42
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4352
Eng Fayez Amin Makkar 43
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4452
Eng Fayez Amin Makkar 44
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4552
Eng Fayez Amin Makkar 45
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4652
Eng Fayez Amin Makkar 46
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4752
Eng Fayez Amin Makkar 47
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4852
Eng Fayez Amin Makkar 48
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4952
Eng Fayez Amin Makkar 49
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5052
Eng Fayez Amin Makkar 50
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5152
Eng Fayez Amin Makkar 51
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5252
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3652
It is now possible to obtain an expression for P b in terms of Pt and N when the jet
impact force is maximized
Reduced drilling hydraulics
So far we have been concerned to achieve optimum hydraulic conditions in order to
drill at the best possible speed without reservations However sometimes there are
factors present that prevent the use of optimum hydraulics In such cases reduceddrilling hydraulics are used even though it is known that maximum penetration rates
will not be achieved
The occasions when reduced drilling hydraulics are used include the following
bull when drilling poorly consolidated formations
bull when losses are anticipated
bull when large nozzles are being used or nozzles have been omitted to allow the
use of lost circulation material
bull when using hydraulic motors
bull when using special deviation tools eg MWD
The major concern is with poorly consolidated formations
In these formations erosion by the drilling fluid can occur and the hole may be
enlarged greatly above its nominal size Once a washout is started conditions can
deteriorate rapidly and large quantities of formation slough into the hole Eventually
the hole can collapse and bridging off results
Large washouts also contribute to mechanical problems with the drill string
(vibration) They interfere with logging and with running casing Large irregular holes
make successful primary cementation difficult if not impossible and therefore reduceisolation between potentially productive reservoirs An inadequate cement column in
these situations often later proves very costly since lost production frequently occurs
as a result of remedial action It is better to drill an in-gauge hole using reduced
drilling hydraulics than a hole that was drilled in record time but which needs some
remedial repair work later in its life time
Hole enlargement in these cases can be avoided by
bull ensuring that annular flow conditions are kept in the laminar range
bull limiting the annular velocity to a specified value
bull limiting jet velocity to a locally determined empirical value
Eng Fayez Amin Makkar 36
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3752
Appendix 1
SOLUTION IN FIELD UNITS
Eng Fayez Amin Makkar 37
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3852
Eng Fayez Amin Makkar 38
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3952
Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
Eng Fayez Amin Makkar 39
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4052
Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 40
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4152
Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 41
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4252
Appendix 5
Eng Fayez Amin Makkar 42
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4352
Eng Fayez Amin Makkar 43
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4452
Eng Fayez Amin Makkar 44
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4552
Eng Fayez Amin Makkar 45
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4652
Eng Fayez Amin Makkar 46
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4752
Eng Fayez Amin Makkar 47
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4852
Eng Fayez Amin Makkar 48
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4952
Eng Fayez Amin Makkar 49
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5052
Eng Fayez Amin Makkar 50
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5152
Eng Fayez Amin Makkar 51
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5252
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3752
Appendix 1
SOLUTION IN FIELD UNITS
Eng Fayez Amin Makkar 37
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3852
Eng Fayez Amin Makkar 38
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3952
Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
Eng Fayez Amin Makkar 39
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4052
Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 40
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4152
Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 41
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4252
Appendix 5
Eng Fayez Amin Makkar 42
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4352
Eng Fayez Amin Makkar 43
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4452
Eng Fayez Amin Makkar 44
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4552
Eng Fayez Amin Makkar 45
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4652
Eng Fayez Amin Makkar 46
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4752
Eng Fayez Amin Makkar 47
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4852
Eng Fayez Amin Makkar 48
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4952
Eng Fayez Amin Makkar 49
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5052
Eng Fayez Amin Makkar 50
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5152
Eng Fayez Amin Makkar 51
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5252
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3852
Eng Fayez Amin Makkar 38
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3952
Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
Eng Fayez Amin Makkar 39
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4052
Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 40
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4152
Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 41
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4252
Appendix 5
Eng Fayez Amin Makkar 42
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4352
Eng Fayez Amin Makkar 43
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4452
Eng Fayez Amin Makkar 44
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4552
Eng Fayez Amin Makkar 45
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4652
Eng Fayez Amin Makkar 46
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4752
Eng Fayez Amin Makkar 47
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4852
Eng Fayez Amin Makkar 48
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4952
Eng Fayez Amin Makkar 49
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5052
Eng Fayez Amin Makkar 50
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5152
Eng Fayez Amin Makkar 51
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5252
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 3952
Appendix 2
SOLUTION IN FIELD UNITS
For drilling fluid density of 0aacute676 psift and drilling a 1214 hole the minimum flowrate is 485 gpm
for optimum circulation will be (1aacute44 + 1) x 1274 = 3109 psi
Maximum pump pressure is given as 3250 psi Therefore the Maximum hydraulic
power at the bit method can be used
3 times 13 nozzles gives the closest match with 0aacute3889 inch2
The actual pressure drop over the nozzles will be
Bit hydraulic horsepower
Total hydraulic horsepower
ANNULAR VELOCITY
Eng Fayez Amin Makkar 39
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4052
Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 40
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4152
Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 41
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4252
Appendix 5
Eng Fayez Amin Makkar 42
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4352
Eng Fayez Amin Makkar 43
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4452
Eng Fayez Amin Makkar 44
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4552
Eng Fayez Amin Makkar 45
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4652
Eng Fayez Amin Makkar 46
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4752
Eng Fayez Amin Makkar 47
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4852
Eng Fayez Amin Makkar 48
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4952
Eng Fayez Amin Makkar 49
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5052
Eng Fayez Amin Makkar 50
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5152
Eng Fayez Amin Makkar 51
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5252
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4052
Appendix 3
Determining c and N
DATA
Before starting a trip out at 3150 m (9460 ft) to change the bit 311 mm with 3 x
11middot1 mm (1214 with 3 x 1432) nozzles the following readings were taken
Pump rate Circulating pressure
spm kPa psi
160 24000 3480
135 18200 2640
110 12480 1810
88 8480 1230
Drill string in use127 mm (5) 29middot0 kgm (19middot5 lbft) G105 drill pipe and 192 m of
210 mm x 76middot2 mm (630 x 814 x 3) drill collars The 339middot7 mm (1338) 79middot5
daNm (54middot5 lbft) N80 casing is set at 1524 m (5000)
Mud pumps two single-acting triplex pumps with 6 liner 10 stroke 97middot5
volumetric efficiency
The drilling fluid gradient in use is 15middot29 kPam (0middot676 psift) with of 16 cPand of 11 lbs100 ft2
REQUIRED
Calculate for each circulation rate (Q)
Calculate N and c for a minimum of three combinations and obtain the average
SOLUTIONS
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 40
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4152
Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 41
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4252
Appendix 5
Eng Fayez Amin Makkar 42
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4352
Eng Fayez Amin Makkar 43
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4452
Eng Fayez Amin Makkar 44
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4552
Eng Fayez Amin Makkar 45
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4652
Eng Fayez Amin Makkar 46
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4752
Eng Fayez Amin Makkar 47
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4852
Eng Fayez Amin Makkar 48
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4952
Eng Fayez Amin Makkar 49
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5052
Eng Fayez Amin Makkar 50
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5152
Eng Fayez Amin Makkar 51
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5252
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4152
Appendix 4
Determination of other parameters
DATA
Use the data of Appendix 1
REQUIRED
bull For max hydraulic horsepower at the bit calculate and assuming the
maximum pump pressure to be used is 22500 kPa (3250 psi)
bull Determine the size of the nozzles for the next bit to obtain optimum
hydraulicsbull Calculate bit and total hydraulic horsepower for the next bit run
bull Calculate annular velocity around drill pipe 127 mm (5)
bull Calculate nozzle velocity
SOLUTION
FOR MAXIMUM HYDRAULIC POWER AT THE BIT
We have seen that the optimum flow rate is determined by the carrying capacity of the
drilling fluid and the degree of erosion the flow will give in the open hole We have
established that the optimum flow rate is the minimum rate required to clean the holeFullertons approximation will give us the minimum annular velocity required to clean
the hole Knowing this velocity drill pipe size and hole size the optimum flow rate
can then be obtained
The solutions are given in SI units and in Field units
Eng Fayez Amin Makkar 41
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4252
Appendix 5
Eng Fayez Amin Makkar 42
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4352
Eng Fayez Amin Makkar 43
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4452
Eng Fayez Amin Makkar 44
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4552
Eng Fayez Amin Makkar 45
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4652
Eng Fayez Amin Makkar 46
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4752
Eng Fayez Amin Makkar 47
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4852
Eng Fayez Amin Makkar 48
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4952
Eng Fayez Amin Makkar 49
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5052
Eng Fayez Amin Makkar 50
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5152
Eng Fayez Amin Makkar 51
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 5252
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4252
Appendix 5
Eng Fayez Amin Makkar 42
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4352
Eng Fayez Amin Makkar 43
7182019 Hydraulic Optimization
httpslidepdfcomreaderfullhydraulic-optimization 4452
Eng Fayez Amin Makkar 44
7182019 Hydraulic Optimization
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