Bit Hydraulics

European Journal of Scientific Research ISSN 1450-216X Vol.57 No.1 (2011), pp.68-86 EuroJournals Publishing, Inc. 2011 http://www.eurojournals.com/ejsr.htm

Drilling Fluid Rheology and Hydraulics for Oil Fields

Sadek Z. Kassab Department of Mechanical Engineering,College of Engineering and Technology

Arab Academy for Science and Technology and Maritime Transport, Alexandria, Egypt E-mail: [email protected]

Ashraf S. Ismail Corressponding Author, Department of Engineering Mathematics and Physics

Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt E-mail: [email protected]

Marwan M. Elessawi Professional Engineer in Petroleum Company

E-mail: [email protected]

Abstract

In the present study, empirical relations for the rheology of non-Newtonian water-based mud and oil-based mud are introduced using field data from the measurements of some oil fields in the region of Belayim marine oil field. Hydraulic calculations were performed to calculate the pressure loss in the hydraulic circuit, using the empirical relations for the conventionally used modified power law, power law, Bingham plastic, as well as a newly proposed polynomial model. A good agreement between the calculated pressure losses with the reported circulating pump pressure are shown in the results.

The reported pump flow rate, and measured mud weight, used in the calculations, are represented at different true vertical depth (TVD). The calculated equivalent circulating density (ECD), hydraulic (jet) impact force, system and bit hydraulic power, and percent of pressure lost at bit, are represented at different true vertical depth (TVD). The comparison between the results in water-based mud and oil based-mud, revealed the following: The pressure losses and hydraulic power for the hydraulic circuit of oil-based mud are greater than the losses and hydraulic power for the water-based mud circuit due to the rheology difference. The impact force for water-based mud is greater than the impact force for the oil-based mud, due to difference in flow rate and nozzle sizes between the two cases. The bit hydraulic power and percent of pressure lost at bit in the oil-based mud are smaller than the water-based mud due to the difference in bit and nozzle sizes and flow rates between the two cases.

The swab and surge analysis is made to determine the safe pulling and running speeds and minimized trip times. This is done by changing the maximum or minimum time per stand and recalculating the swab and surge pressures until times per stand are found where the swab and surge pressures plus the hydrostatic pressure is approximately equal to the formation pressure and fracture pressure.

Drilling Fluid Rheology and Hydraulics for Oil Fields 69

Keywords: Drilling Fluid, Rheology, Non-Newtonian Fluid, Hydraulic System, Swab and Surge Analysis

1. Introduction Rheology and hydraulics are interrelated studies of fluid behaviour. Rheology is the study of how matter deforms and flows. It is primarily concerned with the relationship of shear stress and shear rate and the impact these have on flow characteristics inside tubular and annular spaces. Hydraulics describes how fluid flow creates and uses pressures. In drilling fluids, the flow behaviour of the fluid must be described using rheological models and equations before the hydraulic equations can be applied.

The physical properties of a drilling fluid, density and rheological properties contribute to several important aspects for successfully drilling a well, including:

Provide pressure control to prevent an influx of formation fluid. Provide energy at the bit to maximize Rate of Penetration (ROP). Provide wellbore stability through pressured or mechanically stressed zones. Suspend cuttings and weight material during static periods. Permit separation of drilled solids and gas at surface. Remove cuttings from the well.

Each well is unique, therefore it is important to control these properties with respect to the requirements for a specific well and fluid being used. The rheological properties of a fluid can affect one aspect negatively while providing a significant positive impact with respect to another aspect. A balance must be attained in order to maximize hole cleaning, minimize pump pressures and avoid fluid or formation influxes, as well as prevent loss of circulation to formations being drilled.

In the present study, the field data were collected from measurements of some oil fields in the region of Belayim marine oil field. Belayim marine oil field is located between latitudes 28 34 45 and 28 38 32 N and between longitudes 33 05 17 and 33 10 38 E in the eastern side of the Gulf of Suez, 165 km southeast of the Suez city. Gadallah et al. [2009], used gamma ray spectrometry and well log data to evaluate the spectrometry of Rudeis Formation, determine the oil bearing zones of the Rudeis Formation using gamma ray spectrometry log, and evaluate the reservoir characteristics of Rudeis Formation in Belayim marine oil field.

In the literature several studies were made on the rheology and hydraulics of drilling fluid systems. Hamed and Belhadri [2009], developed water based mud systems using two biopolymers, which are xanthan gum and scleroglucan, generally proposed for high permeability reservoirs or for complex geometries such as horizontal wells and found that non-Newtonian rheological behaviour can be described well by the three parameter in HerschelBulkley (modified power law) rheological model. Zhou and Shah [2004] investigated experimentally the rheological properties and friction pressure losses of several common well-drilling, completion, and stimulation fluids. These fluids include polymeric fluidsXanthan gum, partially hydrolyzed polyacrylamide (PHPA), guar gum, and hydroxyethyl cellulose (HEC), bentonite drilling mud, oil-based drilling mud, and guar-based fracturing slurries. Rheological measurements showed that these fluids exhibit shear thinning and thermal thinning behaviour except the bentonite drilling mud whose viscosity increased as the temperature was raised. Flow experiments using a full-scale coiled tubing test facility showed that the friction pressure loss in coiled tubing is significantly higher than in straight tubing. Zhou and Shah [2006], presented a complete set of friction factor correlations for both Newtonian and non-Newtonian fluids in laminar and turbulent flow in coiled tubing. The friction factor correlation for non-Newtonian fluids in laminar flow is based on power law model, while in turbulent flow is based on experiment considering pipe roughness. Zhou [2008] studied the hole-cleaning problem while drilling an under balanced well using an aerated non-Newtonian flow in an inclined wellbore section. He concluded that his new mechanistic model is useful for predicting minimum annular velocity and cutting bed thickness in horizontal and inclined wellbore geometry. Effects of temperature, bottom hole pressure, liquid flow

70 Sadek Z. Kassab, Ashraf S. Ismail and Marwan M. Elessawi

rate, gas injection rate, cuttings size and density, inclination angle, and rheological properties of drilling mud on hole cleaning are analyzed using this mechanistic model. Omland et al. [2006] described the effect that different salts in the internal brine phases in synthetic- and oil-based drilling fluids had on sag performance.

Birchenko et al. [2010] developed an explicit analytical model for turbulent flow in a highly deviated wellbore, to account for frictional pressure drop along the completion as an important factor in the design of horizontal wells. Gallego and Shah [2009], assumed that energy dissipation by eddies in turbulent flow of viscoelastic fluids to be the mechanism causing drag reduction, and developed generalized correlations for the prediction of drag reduction in dilute polymer solutions flowing in straight and coiled tubing on the basis of the energy dissipation of eddies in turbulent flow field and a shear rate dependent relaxation time. Kuru et al. [2005] used a transient-mechanistic model of cuttings transport with foam to revisit the classical theory of hydraulic optimization (i.e., maximum bit-hydraulic-horsepower/jet-impact-force criteria). A new methodology has been suggested to determine the optimum gas/liquid-injection rates for maximizing drilling rates when drilling with foam in vertical wells while keeping the bottomhole pressure at minimum.

Javora et al. [2008], described the field applications of new brine-based , high-density, solids-free cleaning fluids in balanced displacements in deepwater and offshore shelf wells. The new high-density fluids were based on new surfactant technology developed to ensure effective wellbore cleaning, wellbore design parameters, and displacement modelling. In addition, weighted spacers aid in reducing high pump pressures and wellbore pressure differentials. Robello Samuel [2010], concluded that well planning should include torque and drag modeling with worst-case friction factors to ensure that the drill string can be advanced, rotated, slid if oriented drilling is necessary, and pulled out of the hole. Chen et al. [2009] developed a foam-flow hydraulics model on the bases of the experimental results of foam rheology and a steady-state momentum balance equation, to predict pressure profile, equivalent circulating density (ECD), foam velocity, and foam quality along a vertical/inclined/horizontal wellbore. They indicated that it is possible to use foam to create a pressure profile within the narrow window between continuously changing pore-pressure and fracture pressure gradients.

The properties of the drilling fluid such as viscosity, gel strength, density, fluid loss control (filter cake), and sand content have effect on both the rate and efficiency of drilling wells. The penetration rate of the drill bit may be increased, drill bit life may be increased, and unplanned borehole deviation may be decreased through the suitable designing and managing of drilling fluid properties. These results offer economic benefits in terms of reducing drilling time by improving productivity during drilling and reducing costly down-time.

High solids or sand content increases the fluid density. High fluid density causes pressure in the formation of the borehole. This pressure drives the drilling fluid through the filter cake into the formation, leads to excessive drilling fluid loss to the formation, and extends well development time required to remove the mud from the formation. As the fluid density increases, the pressure required to move the fluid up the borehole also increases, leading to high mud pump pressure requirements. High solids or sand content also leads to significant abrasion in the drill tooling as the fine particles are recirculating through the mud pump and drill string. Since drilling fluid density influences drilling rate and hole stability, it can be controlled by dilution with water or remove solids to decrease or add barium to increase. The desirable limit is less than about 1080 kg/m3, and sand content less than 2% by volume [M.I. LLC., 2006].

As a general rule, viscosity should be maintained as low as possible to provide the required hole-stability and water loss control. Thin mud does the best job of cleaning the bit and optimizing the drilling rate, but thick mud are needed to remove coarse gravel from the hole. Marsh funnel viscosity readings should be taken routinely and recorded on the boring log. The measure of the capability of a drilling fluid to hold particles in suspension after flow ceases is referred to as gel strength (thixotropy). Gel strength results from the electrical charges on the individual clay platelets. The capability of keeping cuttings in suspension prevents sand locking (sticking) the tools in the borehole while drill


rods are added to the string and minimizes sediment collecting in the bottom of the hole after reaming and before going back in the hole with a sampler. Since the viscosity influences the cuttings transport, cutting settlement, and circulation pressures, it can be controlled by adding water, phosphates, or lignites to thin, and adding bentonite or polymers to thicken. The desirable viscosity limit is 34-40 sec/dm3 (Marsh funnel and measuring cup) [M.I. LLC., 2006].

Filtration refers to the ability of the drilling fluid to limit fluid loss to the formation by deposition of mud solids on the walls of the hole. The solid deposit is referred to as a filter cake. The ideal filter cake is thin with minimal intrusion into the formation. The thickness of the filter cake for a particular mud is generally a function of the permeability of the formation. The desirable limit of filter cake thickness is less than 0.2 cm, and can be controlled by controlling density and viscosity of mud.

The acidity or alkalinity (pH) of drilling fluid influences mud properties, filtration control, hole-stability, and corrosion of equipment. The pH can be increased with sodium carbonate and decreased with sodium bicarbonate. The pH desirable limit is from 8.5 to 9.5 [M.I. LLC., 2006].

Salt content such as Calcium (hard water) influences mud properties and filtration control. It can be controlled by pretreating mixing water with sodium bicarbonate. The desirable limit is less than 100 ppm calcium. For other salts, dilute salt content with fresh water or use organic polymers in the drilling fluid [M.I. LLC., 2006].

In the present study, empirical relations for the rheology of water-based mud and oil-based mud are introduced using field data from the measurements of some oil fields in the region of Belayim marine oil field. The introduced shear stress-shear rate empirical equations in the form of the power law, modified power law, Bingham plastic, and newly proposed polynomial model, are used to describe empirical relations for the apparent viscosity of the water-based and oil-based mud, in the form of power functions. Then, the hydraulic calculations have been performed, using Excel sheets, to calculate the pressure loss in the hydraulic circuit, Fig. (1), using the introduced empirical relations for apparent viscosity. In addition, the swab and surge analysis is made to determine the safe pulling and running speeds and minimized trip times.

Figure 1: Mud Circulating System and Drill String Components (courtesy of M.I. LLC., USA, 2006).


2. Drilling Fluid Rheology A rheological model is a description of the relationship between the shear stress and shear rate. Most drilling fluids are non-Newtonian fluids, and many models have been developed to describe the flow behavior of non-Newtonian fluids. Bingham Plastic, Power Law and Modified Power Law models are discussed.

2.1. Bingham Plastic Model This model describes a fluid in which a finite force is required to initiate flow (yield point) and which then exhibits a constant viscosity with increasing shear rate (plastic viscosity). The equation for the Bingham Plastic model is:

= o + PV (1) Where: = Shear stress o = Yield point or shear stress at zero shear rate (Y-intercept) PV = Plastic viscosity or rate of increase of shear stress with increasing shear rate (slope of the line) = Shear rate

2.2. Power Law Model The Power Law model attempts to solve the shortcomings of the Bingham Plastic model at low shear rates. The Power Law model is more complicated than the Bingham plastic model in that it does not assume a linear relationship between shear stress and shear rate. This model describes a fluid in which the shear stress increases as a function of the shear rate mathematically raised to some power. Mathematically, the power law model is expressed as:

= Kn (2) Where: = Shear stress


K = Consistency index = Shear rate n = Power Law index

2.3. Modified Power Law Model The API has chosen the Power Law model as the standard model. The Power Law model, however, does not fully describe drilling fluids because it does not have a yield stress and underestimates low shear rate viscosity (LSRV). The modified Power Law or Herschel- Bulkley model can be used to account for the stress required to initiate fluid movement (yield stress). Mathematically the Herschel-Bulkley model is:

= o + Kn (3) Where: = Shear stress o = Yield stress or stress to initiate flow K = Consistency index = Shear rate n = Power Law index The consistency index (K), and index (n), of power law and modified power law, in the new

empirical equations, were determined from the data fitting, instead of using the traditional equations described in references [M.I. LLC., 2006; ASME Shale Shaker Committee, 2005].

2.4. A Newly Proposed Polynomial Model In the present study, a new proposed polynomial model is introduced. In this model, we have assumed a seconed degree polynomial function to describe the shear stress-shear rate relations, in the form:

= a2 +b+c (4) Where: a, b, and c are constants. Using field data from the measurements of some oil fields in the region of Belayim marine oil

field, for water-based mud and oil-based mud, the value of o, K, n, and polynomial constants can be determined as shown in Fig. (2) for water-based mud, and Fig.(3) for oil-based mud.

Figure 2: Shear stress-shear rate relation, for water-based mud @48.88 C.

0

10

20

30

40

50

60

0 200 400 600 800 1000 1200Shear rate, (1/s)

Shea

r st

ress

, (P

a)

Polynomial model

Bingham plastic model

Power law model

Modified power law model

9229.40543.0102 25 ++=

0314.02669.7 +=

3858.02887.2 =

3858.015.22.2

=

=

=

+=

n

k

k

o

n

o


Figure 3: Shear stress-shear rate relation, for oil-based [email protected] C.

0102030405060708090

100

0 200 400 600 800 1000 1200Shear rate, (1/s)

She

ar st

ress

, (P

a.s.

)

Polynomial model


Power law model


3561.04

35.4

=

=

=

+=

n

k

k

o

n

o

9618.80719.0102 25 ++=

3561.03365.4 =

0535.0848.10 +=

2.5. Apparent (Effective) Viscosity The viscosity of a non-Newtonian fluid changes with shear. The effective viscosity () of a fluid is a fluids viscosity under specific conditions. These conditions include shear rate, pressure and temperature. By definition:

= (5)

The shear rate is dependent on the average velocity of the fluid in the geometry in which it is flowing. Thus, shear rates are higher in small geometries (inside the drillstring) and lower in larger geometries (such as casing and riser annuli). Higher shear rates usually cause a greater resistive force of shear stress. Therefore, shear stresses in the drillstring (where higher shear rates exist) exceed those in the annulus (where lower shear rates exist). The sum of pressure losses throughout the circulating system (pump pressure) is often associated with shear stress while the pump rate is associated with shear rate. The shear stress-shear rate relations described in Fig. (2) for water-based mud, and Fig.(3) for oil-based mud, substituted in Eq.(5) to calculate the apparent viscosity, and describe the results by power functions for each rheological model and compare it with the field data, in Fig. (4) for water-based mud, and Fig.(5) for oil-based mud.

Figure 4: Apparent viscosity-shear rate relation, for water-based mud @48.88 C.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 200 400 600 800 1000 1200Shear rate, (1/s)

Appa

ren

t vis

cosi

ty,

(Pa.

s.)

Polynomial model


Power law model


6198.04261.2 =

7179.00224.4 =

6142.02887.2 =

6847.06372.3 =


Figure 5: Apparent viscosity-shear rate relation, for oil-based [email protected] C.

0

0.5

1

1.5

2

2.5

0 200 400 600 800 1000 1200Shear rate, (1/s)

App

are

nt v

isco

sity

, (P

a.s

.)

Polynomial model


Power law model


6572.06042.4 =

6439.03365.4 =

6975.07867.5 =

7183.00984.7 =

The shear rate (sec1) at the wall of a cylindrical pipe may be calculated by using the following equation [M.I. LLC., 2006]:

DV8

= (6) Where: V = Average fluid velocity in the pipe (m/sec) D = Pipe diameter (m) The annular shear rate (sec1) for concentric pipes is calculated using the following equation

[M.I. LLC., 2006]:

PH DDV

=12 (7)

Where: V = Average fluid velocity in the annulus (m/sec) DH = Diameter of the hole (m) DP = Outside diameter of the pipe (m) Thus, the viscosity can be determined as shown in Fig. (4) for water-based mud, and Fig.(5) for

oil-based mud, in the pipe and annulus, by substituting the shear rate described in Eqns. (6 and 7), into the empirical relations of the viscosity.

3. Hydraulic Analysis 3.1. Hydraulic Losses Once the rheological properties for a fluid have been determined and modeled to predict flow behavior, hydraulics calculations are made to determine what effect this particular fluid will have on system pressures. The circulating system of a drilling well is made up of a number of components or intervals, each with a specific pressure drop. The sum of these interval pressure drops is equal to the total system pressure loss or the measured standpipe pressure. The total pressure loss for this system can described mathematically as:

PTotal = PSurf Equip + PDrillstring + PBit + PAnnulus (8) Each of these pressure groups is broken down into their component parts and appropriate

calculations.


3.1.1. Losses in Surface Connections (Surface Equipment) Surface pressure losses include losses between the standpipe pressure gauge and the drill pipe. This includes the standpipe, kelly hose, swivel, and Kelly or top drive, Fig. (1). To calculate the pressure loss in the surface connections, use the API pipe formula for pressure loss in the drill pipe. Common surface equipment geometries are listed in table (1) below.

Table 1: Common surface equipment geometries

Case Standpipe Hose Swivel, etc. Kelly Eq. Length 3.826-in. ID 1 12 m long, 3-in. ID

14 m long, 2-in. ID

6.1 m long, 2-in. ID

12 m long, 214-in. ID 792 m

2 12 m long, 312-in. ID 17 m long, 212-in. ID

7.6 m long, 212-in. ID

12 m long, 314-in. ID 288 m

3 14 m long, 4-in. ID 17 m long,

3-in. ID 7.6 m long, 212-in. ID

12 m long, 314-in. ID 186 m

4 14 m long, 4-in. ID 17 m long,

3-in. ID 9.1 m long,

3-in. ID 12 m long,

4-in. ID 129 m

In the present study, case 3 is chosen to represent the surface equipment geometries. Then, The following equation is used to calculate the pressure loss.

LDfVPSurfEquip

22= (9)

Where: V = Velocity (m/s) D = ID pipe (m) = Density (Mud weight) (kg/m3) L = Length (m) Before calculating the pressure loss, the Fanning friction factor ( f ) is calculated next with

different equations being used for laminar and turbulent flow. This friction factor is an indication of the resistance to fluid flow at the pipe wall. The friction factor in these calculations assumes a similar roughness for all tubular. If the Reynolds number is less than or equal to 2100:

Re16

=f (10) The Reynolds number is:

VD

=Re (11) If the Reynolds number is greater than 2100, [Birchenko et al., 2010]:

2

910

10 Re9.6log6.3

+=

Df (12)

Where: /D=relative roughness (assumed 0.0006 for pipes, and 0.00015 for annulus).

3.1.2. Losses in Pipe Drillstring The pressure loss in the drillstring is equal to the sum of the pressure losses in all of the drillstring intervals, including drill pipe, drill collars, mud motors, MWD/LWD/PWD or any other downhole tools. Drillstring (including drill collars) intervals are determined by the ID of the pipe. The length of an interval is the length of pipe that has the same internal diameter. The following equation is used to calculate the pressure loss for each drillstring interval.


LDfV

P pgDrillstrin22

= (13) The Reynolds number for inside the pipe is:

DVp

=Re (14) Where: Vp=Mud velocity in pipe D = ID drill pipe or drill collars = Apparent (Effective) viscosity If the drillstring contains a downhole motor; an MWD, LWD or PWD tool; a turbine or a

thruster, their pressure losses must be included in the system pressure losses when calculating the systems hydraulics. These pressure losses can significantly change the pressure available at the bit, as well as bypass flow around the bit. The pressure loss through MWD and LWD tools varies widely with mud weight, mud properties, flow rate, tool design, tool size and the data transmission rate. Some manufacturers publish pressure losses for their tools but these pressure losses can be conservative, because they are usually determined with water. The pressure loss through Positive Displacement Motors (PDM), thrusters and turbines is higher than the losses across MWD and LWD tools and subject to even more variables. With a PDM or thruster, increased weight on the bit increases the torque and pressure loss across the motor. The pressure drop through a turbine is proportional to the flow rate, the mud weight and the number of drive stages in the turbine. The pressure loss across motors and turbines cannot be accurately determined by formula, but, again, this pressure loss data is available from the suppliers.

3.1.3. Losses in Bit The pressure loss across the bit is calculated with the following equation:

2

2

TFAQPBit

= (15)

Where: TFA = Total Flow Area of nozzles.

3.1.4. Losses in Annular Space The pressure loss for each interval must be calculated separately and added together for the total annular pressure loss. The following equation is used to calculate the individual interval pressure losses.

LDD

fVP aannulus )(2

12

2

=

(16)

The Reynolds number for the annulus is:

)(Re 12 DDVa = (17)

Where: Va= Mud velocity in annular space D2 = ID hole or casing D1 = OD drill pipe or drill collars = Apparent (Effective) viscosity If the Reynolds number is less than or equal to 2100:

Re24

=f (18) If the Reynolds number is greater than 2100, f is calculated from Eq. 12.


3.2. Eqivalent Circulating Density (ECD) The pressure on a formation while circulating, is equal to the total annular circulating pressure losses from the point of interest to the bell nipple, plus the hydrostatic pressure of the mud. This force is expressed as the density of mud that would exert a hydrostatic pressure equivalent to this pressure. This equivalent mud weight is called the Equivalent Circulating Density (ECD).

TVDgPECD a

+= (19)

Where: =density (mud weight) Pa=total pressure losse in annular space TVD=true vertical depth g=gravity acceleration Excessive ECD may cause losses by exceeding fracture gradient on a well. It is important to

optimize rheological properties to avoid excessive ECD.

3.3. Bit Hydraulics Calculations In addition to bit pressure loss, several other hydraulics calculations are used to optimize the drilling performance. These include hydraulic power, impact force and jet velocity calculations. In many areas of the world, rock bit hydraulics can be optimized to improve rate of penetration. There are a lot of factors that effect ROP including bit size, bit type, bit features, formation type and strength, and bit hydraulics. In hard rock areas, bit/formation interaction has a greater impact on ROP than bit hydraulics. Generally, the goal is to use 50 to 65% of the maximum allowable circulating pressure to the bit. Systems are considered optimized for impact force when the pressure loss at the bit is equal to 50% of the circulating pressure. When the pressure loss at the bit is equal to approximately 65% of the circulating pressure, the system is considered optimized for hydraulic power [M.I. LLC., 2006].

3.3.1. Hydraulic Power at Bit Low hydraulic power at the bit can result in low penetration rates and poor bit performance. The bit hydraulic power cannot exceed the total system hydraulic power.

746Bit

BitQPhhp = (20)

3.3.2. Nozzle Velocity (m/s) Although more than one nozzle size may be run in a bit, the nozzle velocity will be the same for all of the nozzles. Nozzle velocities of 76.2 to 137.2 m/sec are recommended for most bits. Nozzle velocities in excess of 137.2 m/sec may erode the cutting structure of the bit.

)( 321 +++=

nnn

n AAAQV (21)

Where: Vn=nozzle velocity An=nozzle area

3.3.3. Percent Pressure Drop at the Bit It is generally desired to have 50 to 65% of surface pressure used across the bit.

100% =Total

BitBit P

PP (22)


3.3.4. Hydraulic Impact Force (IF) nQVIF = (23)

3.4. System Hydraulic Power

746Total

SystemQPhhp = (24)

3.5. Swab and Surge Analysis When the drillstring is picked up to make a connection or trip out of the well, the mud in the annulus must fall to replace the volume of pipe pulled from the well. The hydrostatic pressure is momentarily reduced while the mud is falling in the annulus. This action is referred to as swabbing and the maximum reduction in hydrostatic pressure is called the swab pressure. Swab pressures are related to the frictional pressures of the mud flowing in the annulus to displace the drillstring, not the reduction in hydrostatic pressure due to the lower mud level in the annulus. If the swab pressure is greater than the hydrostatic pressure safety margin (overbalance pressure), formation fluids will be swabbed into the wellbore. When the drillstring or casing is lowered or run into the well, mud is displaced from the well. The frictional pressure losses from the flow of mud in the annulus as it is displaced by the pipe causes pressures in excess of the hydrostatic pressure of the column of mud in the wellbore. The elevated pressures caused by running the drillstring into the well are called surge pressures. If the surge pressure plus the hydrostatic pressure exceed the fracture gradient, the formation will be fractured with resultant loss of circulation.

Swab and surge pressures are related to the muds rheological properties; the muds gel strengths; the speed at which the pipe is pulled from, or run into, the well; the annular dimensions; and the length of drillstring in the well. The rheological properties affect swab and surge pressures in the same manner as they affect annular pressure losses. Increases in either the plastic viscosity or the yield point will increase the swab and surge pressures. The velocity of the mud being displaced is different for each annular space and is directly related to the velocity of drillstring movement, whether tripping in or out of the well. Since the maximum (not average) swab and surge pressures must be less than the pressures needed to swab the well in or break the formation down, swab and surge pressures must be calculated for the maximum drillstring velocity when tripping. This is generally calculated as one-and-one-half times the average drillstring velocity.

dSperSecondsmLengthdSdSpersmV ringMaxDrillst tan

)(tan5.1)tan,/(

= (25)

The annular velocity is calculated for each interval based on the drillstring displacement for that interval. The drillstring displacement is adjusted accordingly for free flow from or into the drillstring (no float, plugged bit, etc.) or for plugged drillstring where the displacement plus capacity of the drillstring is used. The annular velocity must be calculated for each annular space. These annular velocities should be substituted into the API equations for the annular pressure losses for each interval. The swab and surge pressures are then calculated in the same manner as the ECD.

CapacityAnnularntDisplacemegDrillstrinV

smAV ringMaxDrillstSurgeSwab

=

)/( (26)

Drillstring Displacement (m3/m)=(pi/4)(OD2pipe- ID2pipe) (27) Annular Capacity (m3/m)=( pi/4) (ID2well- OD2pipe) (28) Where: IDWell = Inside diameter of open hole or casing ODPipe = Outside diameter of drill pipe or drill collars IDPipe = Inside diameter of drill pipe or drill collars


LODID

AVfP

pipewell

surgeswabannulus )(

)(2 2

=

(29)

The Reynolds number for the annulus is:

))((

Re pipewellsurgeswabODIDAV

=

(30) If the Reynolds number is less than or equal to 2100:

Re24

=f (31) If the Reynolds number is greater than 2100, f is calculated from Eq. 12.

TVDgPEQMDSwab annulus

= )( (32)

TVDgPEQMDSurge annulus

+= )( (33) The object of calculating swab and surge pressures is to determine safe pulling and running

speeds and minimized trip times. This is done by changing the maximum or minimum time per stand and recalculating the swab and surge pressures until times per stand are found where the swab and surge pressures plus the hydrostatic pressure is approximately equal to the formation pressure and fracture pressure. This time per stand is only relevant for the present length of drillstring in the well.

As pipe is removed from the hole, the drillstring length decreases and the bottom hole assembly will be pulled into large diameter casing. This will make it possible to pull each stand faster without risk of swabbing in the well. When tripping in to the well, the length of drillstring will be increasing and the annular spaces will decrease as the BHA is run into smaller diameters. This will require that the running time per stand be increased to avoid fracturing the formation. The swab and surge pressures should be calculated at either 152- or 305-m intervals [M.I. LLC., 2006].

4. Results and Discussion In the present study, empirical relations for the rheology of water-based mud and oil-based mud are introduced using field data from the measurements in the reports of some oil fields in the region of Belayim marine oil field. The rheology measurements reported at 48.88 C for water-based mud and at 65.55 C for oil-based mud. The shear stress-shear rate relations described in Fig. (2) for water-based mud, and Fig.(3) for oil-based mud, substituted in Eq.(5) to calculate the apparent viscosity, and describe the results by power functions for each rheological model and compare it with the field data, in Fig. (4), for water-based mud, and Fig. (5), for oil-based mud. At each shear rate value, the corresponding shear stress values are at different TVD; this is done for the sake of getting generalized empirical equations suitable for the all TVDs during drilling process, instead of describing equation for each TVD. In addition, the consistency index (K), and index (n), of power law and modified power law, in the new empirical equations, were determined from the data fitting, instead of using the traditional equations described in the manuals in references [M.I. LLC., 2006].

The hydraulic calculations have been performed, to calculate the pressure loss, Fig. (6), in the hydraulic circuit shown in Fig. (1), using the empirical relations for power law, modified power law, Bingham plastic, and newly proposed polynomial model. The comparison revealed that all the models give good results, but the modified power law still the best. Thus, for oil-based mud the modified power law only used and the results compared with the pump circulating pressure with good agreement.


Figure 6: Total pressure losses in the hydraulic circuit, for water-based mud and oil-based mud

Pressure losses in water-based mud hydraulic circuit

0

50

100

150

200

250

300

83.4 150 318 366.9 448.2

33.6 148.5 275.4 341.1 410.4

Depth/TVD, m

Press

ure

lo

sses

, ba

r

M. pow er law

Pump pressure

Bingham

Pow er

Polynomial

Loseese in MWD,Motor, Fittings

Pressure losses in oil-based mud hydraulic circuit

0

50

100

150

200

250

300

437.4 494.1 549.6 603 651

400.5 450 498.6 544.5 586.8

Depth/TVD, m

Pressu

re lo

sses

, ba

r

Pump pressureM. Pow er lawLosses in MWD, Motor, Fittings

The drilling assembly of the oil well, using water-based mud, till depth/TVD=366.9m/341.1m, is:

5.-in (127mmOD-109mmID)DP, 5.-in (127mmOD-76mmID)HWDP, 8.-in (203mmOD-71mmID)DC, 9.5-in MWD, and 9.5-in Mud Motor

Nozzles 20x3/16x1 1/32" Bit 23-in GTX-CG The Casing is: 30.-in @ 26.7 m (89 ft) (89 TVD) The drilling assembly of the oil well, using water-based mud, @ depth/TVD=366.9m/341.1m,

is: 5.-in DP, 5.-in HWDP , 8.-in DC, 8.5-in MWD, 8.5-in Mud Motor Nozzles 20x3/22x1 1/32" Bit 23-in GTX-CG The drilling assembly of the oil well, using oil-based mud, is: 5.-in (127mmOD-109mmID)DP, 5.-in (127mmOD-76mmID)HWDP, 8.-in (203mmOD-

71mmID)DC, 8.-in JAR, 8.-in DC, and 9.5-in BCPM Nozzles 16x3/15x6 1/32" Bit 16-in REED The Casing is: 30.-in @ 29.1 m (97 ft) (97 TVD) 18.625-in @ 426.6 m (1422 ft) (1304 TVD) The measured mud weight along with calculated ECD and, the reported pump flow rate used in

the calculations, are represented at different true vertical depth (TVD) in Figs. (7-8). Note that, the same scale is used in both figures to show clearly the comparison between their values. Fig. (7) shows that mud weight and ECD, for water-based mud are smaller than in oil-based mud. In Fig. (8), pump flow rates, for water-based mud are greater than the pump flow rates in the oil-based mud. The calculated hydraulic (jet) impact force, system and bit hydraulic power, and percent of pressure lost at bit, are represented at different true vertical depth (TVD) in the Figs. (9-11).


Figure 7: Mud weight and ECD, for water-based mud and oil-based mud.

Mud weight and ECD of water-based mud

1020

1220

1420

1620

1820

2020

83.4 150 318 366.9 448.2

33.6 148.5 275.4 341.1 410.4

Depth/TVD, m

Mu

d w

eigh

t an

d EC

D, kg

/m3

Mud WeightECD

Mud weight and ECD, oil-based mud

1020

1220

1420

1620

1820

2020

437.4 494.1 549.6 603 651

400.5 450 498.6 544.5 586.8

Depth/TVD, m

Mu

d w

eigh

t an

d EC

D, kg

/m3

Mud w eightECD

Figure 8: Pump flow rate, for water-based mud and oil-based mud.

Pump flow rate, water-based mud

0

0.01

0.02

0.03

0.04

0.05

0.06

83.4 150 318 366.9 448.2

33.6 148.5 275.4 341.1 410.4

Depth/TVD, m

Pum

p flo

w ra

te, m

3 /s

Pump flow rate, oil-based mud

0

0.01

0.02

0.03

0.04

0.05

0.06

437.4 494.1 549.6 603 651

400.5 450 498.6 544.5 586.8

Depth/TVD, m

Pum

p flo

w ra

te, m

3 /s

Figure 9: Impact force, for water-based mud and oil-based mud.

Impact force, water-based mud

0

1000

2000

3000

4000

5000

6000

83.4 150 318 366.9 448.2

33.6 148.5 275.4 341.1 410.4

Depth/TVD, m

Impa

ct fo

rce,

N

Impacy force, oil-based mud

0

1000

2000

3000

4000

5000

6000

437.4 494.1 549.6 603 651

400.5 450 498.6 544.5 586.8

Depth/TVD, m

Impa

ct fo

rce,

N


Figure 10: System and bit power, for water-based mud and oil-based mud.

System and bit power, for water-based mud

0

200

400

600

800

1000

1200

1400

1600

1800

83.4 150 318 366.9 448.2

33.6 148.5 275.4 341.1 410.4

Depth/TVD, m

Syste

m an

d bi

t ho

rsep

oer

, hp System hydraulic

horsepow erHydraulic horsepow er at bit

System and bit power for oil-based mud

0

200

400

600

800

1000

1200

1400

1600

1800

437.4 494.1 549.6 603 651

400.5 450 498.6 544.5 586.8

Depth/TVD, m

Syst

em an

d bi

t ho

rsepo

wer

, hp

System hydraulic horsepow erBit hydraulic horsepow er

Figure 11: Percent of pressure drop at bit, for water-based mud and oil-based mud.

Percent of pressure lost at bit, for water-based mud

0

5

10

15

20

25

83.4 150 318 366.9 448.2

33.6 148.5 275.4 341.1 410.4Depth/TVD, m

Perc

ent o

f pre

ssu

re lo

st at b

it,

%D

P Bit

Percent of pressure lost at bit, for oil-based mud

0

5

10

15

20

25

437.4 494.1 549.6 603 651

400.5 450 498.6 544.5 586.8

Depth/TVD, m

Perc

en

t of p

ressu

re lo

st a

t bit,

%D P

Bit

Comparison of the results, in water-based mud and oil-based mud, revealed the following. The pressure losses, Fig. (6), and hydraulic power, Fig. (10), for the hydraulic circuit of oil-based mud are greater than the losses and hydraulic power for the water-based mud circuit due to the rheology difference. The impact force, Fig. (9), for water-based mud is greater than the impact force for the oil-based mud, due to difference in flow rate and nozzle sizes between the two cases. The bit hydraulic power, Fig.(10), and percent of pressure lost at bit, Fig. (11), in the oil-based mud are smaller than the water-based mud due to the difference in bit and nozzle sizes and flow rates between the two cases.

In addition, the swab and surge analysis is made to determine the safe pulling and running speeds and minimized trip times, table (2). This is done by changing the maximum or minimum time per stand and recalculating the swab and surge pressures until times per stand are found where the swab and surge pressures plus the hydrostatic pressure is approximately equal to the formation pressure and fracture pressure. Swab and surge pressures are related to the muds rheological properties; the muds gel strengths; the speed at which the pipe is pulled from, or run into, the well; the annular dimensions, and the length of drill string in the well. In Table (2), it clear that the maximum surge EQMD is 1144.542 kg/m3 @ running speed 1 sec/stand, and maximum swab EQMD is 1134.427 kg/m3 @ pulling speed 1 sec/stand. The recommended maximum running in and pulling out speeds depend on the information about the formation pressure and fracture pressure, which are not existed with the field data used.


5. Conclusions In the present study, empirical relations for the rheology of water-based mud and oil-based mud are introduced using field data from the measurements of some oil fields in the region of Belayim marine oil field. The empirical relations for power law, modified power law, Bingham plastic, and proposed polynomial model used to calculate the pressure losses in the hydraulic circuit. A good agreement between the calculated pressure losses with the reported circulating pump pressure are shown in the results. The comparison revealed that all the models give good results, but the modified power law still the best.

Comparing the results in water-based mud and oil based-mud, the following conclusions can be drawn:

i. The pressure losses and hydraulic power for the hydraulic circuit of oil-based mud are greater than the losses and hydraulic power for the water-based mud circuit due to the rheology difference.

ii. The impact force for water-based mud is greater than the impact force for the oil-based mud, due to difference in flow rate and nozzle sizes between the two cases.

iii. The bit hydraulic power and percent of pressure lost at bit in the oil-based mud are smaller than the water-based mud due to the difference in bit and nozzle sizes and flow rates between the two cases.

The swab and surge analysis is made to determine the safe pulling and running speeds and minimized trip times. This is done by changing the maximum or minimum time per stand and recalculating the swab and surge pressures until times per stand are found where the swab and surge pressures plus the hydrostatic pressure is approximately equal to the formation pressure and fracture pressure. The recommended maximum running in and pulling out speeds depend on the information about the formation pressure and fracture pressure, which are not existed with the field data used. In future work, more detailed study including the effect of several parameters, such as annular geometry for example, on swab and surge pressures in consideration.

Table 2: Swab and surge in equivalent mud density (EQMD), for water-based mud, at Depth/TVD= 448.2 m/410.4 m.

Stand time Annular Maximum Pressure drop Swab EQMD Surge EQMDsec/stand m/s m/s bar kg/m3 kg/m3

200 0.001545 0.2025 0.037895 1138.592 1140.377180 0.001715 0.225 0.039273 1138.592 1140.496160 0.00193 0.253 0.04134 1138.473 1140.496140 0.0022 0.28925 0.042718 1138.473 1140.496120 0.002575 0.3375 0.044785 1138.354 1140.615100 0.00309 0.405 0.047541 1138.354 1140.61580 0.00385 0.50625 0.050986 1138.235 1140.73460 0.00515 0.675 0.055809 1138.116 1140.85340 0.0077 1.0125 0.063388 1137.997 1140.97220 0.01545 2.025 0.079235 1137.64 1141.44810 0.0309 4.05 0.098527 1137.164 1141.9249 0.03435 4.5 0.101283 1137.045 1141.9248 0.03865 5.0625 0.105417 1136.926 1142.0437 0.04415 5.785 0.11024 1136.807 1142.1626 0.0515 6.75 0.115752 1136.688 1142.2815 0.06185 8.1 0.122642 1136.45 1142.44 0.0773 10.125 0.13091 1136.331 1142.6383 0.10305 13.5 0.144001 1135.974 1142.9952 0.1546 20.25 0.163293 1135.26 1143.4711 0.30925 40.5 0.208767 1134.427 1144.542

Swab and surge analysisPipe velocity Bit at total depth


Nomenclature D diameter, (m)

f Fanning friction factor L Length, (m) K Consistency index, (Pa.sn.) n Power Law index PV Plastic viscosity, (Pa.s.) Q volume flow rate, (m3/s) Re Reynolds number V Velocity, (m/s) Shear rate, (1/s) Density (Mud weight), (kg/m3) Shear stress, (Pa) o Yield point, (Pa)

Abbreviation LSRV low shear rate viscosity

TVD true vertical depth DP drilling pipe DC drilling collar HWDP heavy weight drilling pipe MWD measurement while drilling LWD logging while drilling PWD pressure while drilling measurement ECD equivalent circulating density EQMD equivalent mud weight BHA bore-hole assembly ROP rate of penetration PDM positive displacement mud

References [1] Mohamed M. G., R. A., El-Terb, E. M., El-Kattan, and I. M., El-Alfy, 2009, Spectrometry and

Reservoir Characteristics of Rudeis Formation in Belayim Marine Oil Field, Gulf of Suez, Egypt, JKAU: Earth Sci., 21, No. 1, pp. 171-199.

[2] Robello Samuel, 2010, Friction factors: What are they for torque, drag, vibration, bottom hole assembly and transient surge/swab analyses?, Journal of Petroleum Science and Engineering, 73, pp. 258266.

[3] Birchenko, V.M., A.V., Usnich, and D.R., Davies, 2010, Impact of frictional pressure losses along the completion on well performance, Journal of Petroleum Science and Engineering, 73, pp. 204213.

[4] Samira Baba H., Mansour B., 2009, Rheological properties of biopolymers drilling fluids, Journal of Petroleum Science and Engineering, 67, pp. 8490.

[5] Felipe G., Subhash N. S., 2009, Friction pressure correlations for turbulent flow of drag reducing polymer solutions in straight and coiled tubing, Journal of Petroleum Science and Engineering, 65, pp. 147161.

[6] Zhou Y., Shah, S. N., 2006, New friction-factor correlations for non-Newtonian fluid flow in coiled tubing, SPE drilling and completion, March, pp. 68-76.


[7] Zhou, Y., Shah, S. N., 2004, Rheological Properties and Frictional Pressure Loss of Drilling, Completion, and Stimulation Fluids in Coiled Tubing, ASME, J. of Fluids Engineering, 126, pp. 153-161.

[8] Javora, P. H., G., Baccigalopi, J., Sanfod, C., Cordeddu, Qi Qu, G., Poole, and B., Franklin, 2008, Effective high-density wellbore cleaning fluids: brine-based and solids free, SPE drilling and completion, March, pp. 48-53.

[9] Zhou, L., 2008, Hole cleaning during underbalanced drilling in horizontal and inclined wellbore, SPE drilling and completion, September, pp. 267-273.

[10] Omland, T., T., Albertsen, K., Taugbol, A., Saasen, K., Svanes, and P., Amundsen, 2006, The effect of the synthetic- and oil-based drilling fluids internal water-phase composition on barite sag, SPE drilling and completion, June, pp. 91-97.

[11] Kuru, E., O. M., Okunsebor, and Y., Li, 2005, Hydraulic optimization of foam drilling for maximum drilling rate in vertical wells, SPE drilling and completion, December, pp. 258-267.

[12] Chen, Z., M., Duan, S. Z., Miska, M., Yu, R. M., Ahmed, and J., Hallman, 2009, Hydraulic predictions for polymer-thickened foam flow in horizontal and directional wells, SPE drilling and completion, March, pp. 40-49.

[13] M.I. LLC., 2006, Drilling Fluid Engineering Manual, M.I. LLC., USA. [14] ASME Shale Shaker Committee, 2005, Drilling Fluids Processing Handbook, Elsevier Inc.,

2005.

Bit Hydraulics

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