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Chapter 1

Introduction to Artificial Lift

1.0 INTRODUCTION

In the extraordinary process of formation of oil and gas deep under the earth

crust, followed by their migration and accumulation as oil and gas reserve, a

great amount of energy is stored in them. This energy is in the form of dissolvedgas in oil, pressure of free gas, water and overburden pressure. When a well is

drilled to tap the oil and gas to the surface, it is a general phenomenon that oil

and gas comes to the surface vigorously by virtue of the energy stored in them.

Over the years/months of production, the decline of energy takes place and at

one point of time, the existing energy is found insufficient to lift the ade uate

uantity of oil to the surface. !rom that time onwards, man"made effort is

re uired and this is what is known as artificial lift. In other words artificial lift is a

supplement to natural energy for lifting well fluid to the surface. Therefore, the

flow of oil from the reservoir to the surface can be fundamentally dichotomi#ed as

self flow period and artificial lift period.

1.2 PATH !"CTOR! IN#LU"NCIN$ TH" %"LL P"R#OR&ANC"

$roadly four main sectors influence the well performance '#i( 1.1) . The first

and second is the reservoir component from the periphery of drainage area toaround the wellbore and then from around the well bore to the wellbore which

represent the wells ability to give up fluids into the well bore. The third component

of flow path is the entire tubing in the vertical/inclined/hori#ontal path which

include all systems like, downhole artificial lift e uipment, sub"surface safety

valves, non return valves etc. The fourth component includes the surface flow

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path which consists of length and diameter of flowline, valves, bends, wellhead,

chokes, manifold, separator etc.

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#i( 1.1

%ny change in the relevant parameters in any of the four sectors, influences the

parameters of other sectors. The re uired changes of parameters should bemade till the flow gets steady. The individual sectors of flow"path area have been

discussed as under.

This can also be simplified into two basic categories i.e. Inflow and outflow

performance. %ll flow in the reservoir up to wellbore is designated as inflow

performance and all flow from the wellbore up the tubing and into the flow lines

and production facilities is designated as outflow performance.

The inflow performance is controlled by reservoir characteristics vi#. reservoir

pressure, productivity index and fluid composition. While, outflow performance is

governed by the si#e and type of the production e uipment. It is very important

to accurately estimate the well inflow performance as all future plans depend on

the well&s inflow performance. 'imilarly, it is very essential to design a suitable

outflow system in order to exploit the well&s inflow capabilities. In any given well,

outflow performance and inflow performance must be e ual. In other words, we

can produce no more fluid from the reservoir than we can lift to the surface and

vice versa.

1.* IN#LO% P"R#OR&ANC" PR"DICTION+

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(o definite shape of flow conduit can be conceptualised in this sector of flow

through porous medium. 'o, it is largely an area of concern for

determining the flow parameters. In order to understand this, the

fundamental concept of )eservoir engineering which includes

reservoir drive mechanism and *.I. +*roductivity Index of

individual wells are dealt. The productivity index is the measure of

the ability of well to produce fluid into the wellbore at a given

reservoir pressure. -athematically, it can be expressed as "

α +*r " * wl

Where 0 Total uantity of fluid

* r 0 )eservoir pressure

* wf 0 !lowing bottomhole pressure in the wellbore againstsand face

Therefore, 0 1onstant x +* r " * wf

This constant is the productivity index +*I of the well and is generally

abbreviated as 23 , '#i( 1.2). In other words,

3 0 * r " * wf

#i( 1.2

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In fact, 3 is not a constant value but it varies with the type of reservoir, type of

drive mechanism, production rate, time of production, cumulative production,

perforation density, skin, sand bridging, gas coning, infill wells on production etc.

#i( 1.*

In order to define *.I more correctly, the concept of inflow performance

relationship +I*) is introduced '#i( 1.*) to define the li uid inflow in the

wellbore. It is basically a straight line or a curve drawn in the two"dimensional

plane, where - axis is / the flow rate and "axis is P f / flowing bottom hole

pressure. Therefore, the concept that 3 is always a constant is not correct. *I

here can be described as 4ust a point on I*) curve. The following are some of

the typical I*)s being mainly influenced by different reservoir drive mechanisms.

1.*.1 IPR IN CA!" O# ACTI " %AT"R DRI " ' #i( 1.3 )

#i( 1.3

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Out of all types of reservoir drives, water drive is regarded as the strongest.

5owever, the intensity differs in different types of water drive reservoirs. 'ome

are moderately weak and some are strong, like edge water drive is weaker than

bottom water drive. In bottom water drive, when the oil pool is underlain with a

large a uifer of dynamic source, reservoir pressure is generally not mellowed at

all with the advancing years of production" that is, the reservoir pressure

practically remains constant and is not influenced by cumulative production. In

this case, the I*) curve will simply be a straight line i.e. the I*) curve will

provide only one value of *I.

1.*.2 IPR IN CA!" O# !OLUTION $A! DRI " ' #i( 1.4 )

In this particular type of drive the driving mechanism is the gas coming out of thesolution flows along the oil. The gas comes out of the solution but doesn&t move

upward to form a gas cap. 6as bubbles formed in the oil phase remains in the oil

phase remains in the oil phase resulting in the simultaneous flow of both oil and

gas. Oil production is thus the result of the volumetric expansion of the solution

gas and volumetric expulsion of oil. This type of reservoir drive approaches a gas

liberation process.

This type of drive is also called as internal gas drive or depletion drive. This is

the least effective drive mechanism.

If excessive draw"down is created,

it results in increase of permeability

to gas and correspondingly

decrease of permeability to li uid,

thereby, ability of well to deliver

li uids is greatly reduced.6enerally, the reservoir pressure

for this type of reservoir declines at

a very fast rate and accordingly it

influences the pattern of I *) curve

.

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#i( 1.41.*.* IPR IN CA!" O# $A! CAP "-PAN!ION DRI " '#i(.1.5)

This drive mechanism is also called segregation drive because of the state of

segregation of oil #one from gas #one, where oil #one is overlain by gas #one

called gas cap. %lso, as production continues, the gas cap swells and because of

this the drive is also known as gas cap expansion drive.

This type of reservoir drive

mechanism is more effective than

solution gas drive and less

effective than water drive.

Therefore, the profile of I*) curve

for gas cap expansion drive liessomewhere in between those for

solution gas drive and water drive.

#i( 1.51.*.3 IPR %H"N P r 6 7U77L" POINT PR"!!UR" '!ATURATION

PR"!!UR") #i( 1.8

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#i( 1.8

7pto a point $ in the profile, %$ is a straight line representing constant *I. %t $,

the gas separation starts in the reservoir. With more drawdown i.e. by further

dropping"in of bottomhole pressure, more and more gas will come out and this

affects the flow of li uid due to generation of more gas around the wellbore .

1.*.4 CHAN$" O# PI %ITH CU&ULATI " R"CO "R'P"RC"NTA$" O# ORI$INAL OIL IN PLAC") %ITH TI&"

The pattern of I*) curves with cumulative recovery, that is percentage of oil in

place can be best described when a reservoir is allowed to produce over

the

years without any pressure maintenance either with the help of water in4ection or gas in4ection which results in continuous decrease of reservoir pressure.

% series of I*) curves '#i( 1.9) with time are obtained where reservoir

pressure indicates a downward trend. The successive I*)s tend to approach the

origin +8,8 of the producing rate " pressure axis. This type of I*) curves trend

indicate that the reservoir is attaining fast the state of senescence, as such,

reservoir pressure has overbearing effect on the inflow of li uid in the wellbore .

#i( 1.9

1.3 O$"L:! %OR; ON

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% publication by 9ogel in l:;< offered an extra ordinary solution in determining

the Inflow *erformance 1urve for a solution gas drive reservoir for flow below the

bubble point or gas cap drive reservoir or any other types of reservoir having

reservoir pressure below bubble point pressure. 9ogel&s performance curve is

generated in the following manner.

!rom general I *) e uation i.eo

3 0 =====..+>* r " * wf

When * wf is #ero, the o become maximum and is denoted as max.

max.Then 3 0

* r " 8

max.or 3 0 ======.. + ? * r @ividing e uation +> by +?

3 8 * r 0 x

3 * r A * wf max

8 * r A * wf or 0

max * r

8 * r * wf

or 0max * r * r

o * wf or """""""""" 0 > " """"""" , It is a straight line form of e uation.

max * r

'ince I*) curve below bubble point is not a straight line, he created a parabolic

e uation from the above.

5e distributed * wf in the following manner* r

?8B of * wf C

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Therefore, the new e uation is established as "

o * wf * wf ?

0 > A 8.? " 8.<max * r * r

This is known as 9ogel&s e uation.

5e then plotted dimensioniess I*)s in two dimensional plane '#i( 1.=)

o * wfWhere D " axis represents and E " axis represents + both are

max *r

@imensionless uantity

o * wf

The minimum and maximum values of and in each case is 8 andmax * r

* wf o * wf o>.8 . When, """"" 0 >, """""" 0 8 and when, """"" 0 8, """"""" 0 >. * r max * r max

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#i( 1.=

1.4 !TANDIN$:! "-T"N!ION O# O$"L:! IPR #OR DA&A$"D OR

I&PRO "D %"LL

While deriving the e uation, 9ogel assumed that flow efficiency is >.88 which

implies that there was no damage or improvement in the well. 'tanding extended

the 9ogelFs e uation by proposing the comparision chart where he has

indicated flow efficiency either more or less than one.

%ccording to him, flow efficiency is defined as

Ideal drawdown * r " * > wf Gin actual drawdown Hskin&!. . 0 0 has not been consideredJ %ctual drawdown * r A * wf

Where * >wf 0 * wf K +@* skin

+@* skin defined by 9an verdingen is as below

' µ+@* skin 0

? π kh

Where,

h 0 *ay thickness

0 !low rate

µ 0 9iscosity

k 0 *ermeability

' 0 'kin factor

' 0 K indicates damage

' 0 8 indicates no damage / no improvement.' 0 " indicates improvement

Therefore,

o/ max 0 >" 8.? ( * >wf / * r ) " 8.< ( * >wf /* r )?

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Where * >wf 0 * r " !. . +* r A * wf

G 'ince, from e uation +> , !. . +* r " * wf , 0 * r A * >wf or * >wf 0 * r A !. . +* r A * wf J

!low efficiency value has to be either obtained or assumed.

1.5 #"T;O ICH IPR ">UATION

!etkovich opined that oil well also behaves like gas wells so that I*) e uation

being used for gas well will also be applicable for oil wells.

Therefore the e uation used for gas wells is also the same as that for oil wells.

i.e. 8 0 1 + * r ? A * wf ? n

!or determining the value of 1, at least one flow test data is re uired. Let oneflow test data be o corresponding to the flowing bottom hole pressure * wf .

oThen 1 0

+*r ? " * wf ? n

!or convenience, n is taken as one.

I*)s with different e uations are depicted below '#i( 1.10)

#i( 1.10

1.8 PR"PARATION O# #UTUR" IPR CUR "!

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!or the planning of future re uirement of artificial lift and other surface and

downhole infrastructure it is imperative to know the future production potential of

oil wells. Therefore generation of future I*) curves assumes a paramount

importance.

1ombination of !etkovich and 9ogel procuedure for the generation of future I*)

curves is being commonly used.

!etkovich has proposed the future I*) e uation by correlating the current

reservoir pressure with the productivity indices of the present and future as

* r? 8? 0 3 8> +*r? ? " * wf ? n * r> * r? is the future reservoir pressure and pr> is the present reservoir pressure.

ckmier put forward that the !etkovich e uation of the current and future I*)s

for max for both the times can be obtained in the following way.

max 0 3 8> +*r ? " * wf ? n2.0 OUT#LO% P"R#OR&ANC" PR"DICTION+

Outflow performance of a well depends on many factors like fluid characteristics,

conduit si#e, wellhead back pressure, well depth, pipe roughness etc. fforts to

predict well outflow performance have been going on for many years which

resulted in much research and development work being done in the area of

-ultiphase !low. @ifferent multiphase flow correlations have been developed

which help in predicting the pressure losses + pressure vs depth / length in a

vertical / hori#ontal pipe column of multiphase fluid + more than on phase i.e. oil"

gas, water"gas or oil"water"gas taking into account the fluid characteristics

along with the conduit configuration and other factors affecting the flow.

-ultiphase flow is discussed in the subse uent chapters.

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A

Tubing intake pressure / outflow pressure is the pressure re uired at the bottom

of the tubing to pump a re uired amount of li uid at a given well head pressure. It

depends on the following factors

• Tubing si#e• Tubing head

pressure• Water 1ut• 6L)• @epth

% typical tubing intake curve

is shown in #i( 1.11

#i( 1.11 %ny point % on the TI1 represents the pressure re uired at the bottom of the

tubing to produce given li uid through the given tubing si#e against a defined

wellhead pressure.

*.0 IN#LO% AND OUT#LO% &ATCHIN$+

#i(

1.12

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%s mentioned earlier, for any given well, outflow performance and inflow

performance must be e ual i.e.the point of intersection % of both these curves

gives the given production rate '#i( 1.12). In other words, the point % on the I*)

curve indicates the pressure re uired to produce the given rate into the wellbore.

Whereas, the same point % on the outflow +TI1 curve indicates the pressure

re uired at the bottom of the tubing to produce the same fluid from wellbore up

the tubing to the pipelines and surface facilities.

3.0 ARTI#ICIAL LI#T+

%s the well flows, over a period, there could be a condition when the well inflow

pressure is not sufficient to lift the desired li uid up the tubing. This could be due

to reasons like drop in reservoir pressure, increase in water"cut etc. 7nder thoseconditions, when a self"flowing oil well ceases to flow or is not able to deliver the

re uired uantity to the surface, the additional energy is supplemented either by

mechanical means or by in4ecting compressed gas. This is called artificial lift and

the purpose of artificial lift is to create a steady low pressure or reduced pressure

in the well bore against the sand face, so as to allow the well fluid to come into

the well bore continuously. In this process, a steady stream of production to

surface would result.

In other words, maintaining a re uired and steady low pressure against the sand

face, which we call steady flowing bottom hole pressure, is the fundamental basis

for the design of any artificial lift installation.

4.0 &ULTIPHA!" #LO%

4.1 INTRODUCTION

'ingle phase flow refers to one fluid medium only and whenever there is more

than one fluid medium, for example oil, water and gas, it is termed as multiphase

medium of fluid flow. In petroleum industry vertical / deviated tubing, hori#ontalpipes and inclined pipes are commonly encountered. % typical overall production

system is shown below . #i( 1.1*

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#i( 1.1*

It is, in this respect, a necessity to predict pressure gradients at certain intervals

in the tubing or flowline to correctly predict the pressure, flow rates, etc. This

facilitates, inter"alia, optimum tubing string and flowline design and the designing

of artificial lift for the production of oil.

#i( 1.13

To simplify the whole problem, at the outset, it is convenient to divide multiphase

flow into two broad categories, vi#. hori#ontal on the surface and vertical in the

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well '#i( 1.13). The material difference between these two categories is the effect

of gravity in association with the specific character of the flow or the specific flow

regime.

4.2 HORI?ONTAL #LO%

When more than one phase is present, the pressure loss accounts for the

interaction between the phases in addition to the pipe wall friction which is

normally the case in single phase pipe flow. There are other forces present, vi#.

rotational forces perpendicular to direction of flow as well as the accumulation of

li uid in certain areas in the line resulting in momentum losses. $ecause of all

the above complexities, the pressure loss calculation has to be made taking into

consideration the various flow regimes.

The number of flow regimes may be divided into two broad divisions

>. Where one phase is continuous.

?. Where both phases are continuous.

$ubble, and spray are the examples where only one phase is continuous. Li uidis the continuous phase in bubble flow and gas is the continuous phase in the

other, I,e, spray flow. %ll other flow regimes have both phases as continuous in

various degrees.

%n attempt has been made by @r. 'hoham to define an acceptable set of flow

patterns in multiphase flow in hori#ontal and near hori#ontal flow conduit. 5e has

classified the various flow regimes in four principal divisions.

>. 'tratified flow.

?. Intermittent flow.

M. %nnular flow.

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N. @ispersed bubble flow.

4.2.1 !TRATI#I"D #LO%

'tratified flow is further sub divided into two groups

i 'tratified smooth flow. #i( 1.14

#i( 1.14

ii 'tratified wavy flow. #i( 1.15

#i( 1.15

This flow pattern develops at low gas and li uid rates. Two phases become

distinct and they are separated by gravity. The li uid phase occupies bottom of

the pipe and gas occupies the top. The transformation from stratified smooth flow

to stratified wavy flow occurs at relatively higher gas flow rates.

4.2.2 INT"R&ITT"NT #LO%

Intermittent flow is again sub divided into two categories

i) 'lug flow. #i( 1.18

#i( 1.18

ii longated bubble flow . #i( 1.19

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#i( 1.19

Intermittent flow is basically an intermittent flow of li uid and gas i.e. it is

characteri#ed by alternate flow of li uid and gas.

The slug flow or plug flow of li uid occurs when entire pipe cross"sectional area

is separated by gas pockets at intervals as well as the conduit contains a

stratified li uid layer flowing along the bottom of pipe. $asically the flow

behaviour of slug and elongated bubble are same with respect to flow mechanism

and as such they cannot be distinguished. 5owever, the elongated bubble patterncan be considered to be limiting case of slug flow when the li uid slug is free of

entrained bubbles. Therefore, elongated bubble flow occurs earlier than the

slug/plug flow, when relatively the gas rates are low. %s the gas rate increases,

the flow at the front of slug takes the form of an eddy due to picking up of slow

moving li uid and this is designated as slug flow. The occurance of slug flow is

detrimental to fluid flow in the pipe, because this may create severe flow

disturbance and fluid hammering in line. This also results in additional pressure

losses.

4.2.* ANNULAR #LO% #i( 1.1=

#i( 1.1=

In the annular flow, gas occupies the central portion like a cylinder and li uidremains near the pipe wall. This flow occurs generally at very high gas flow

rates. The gas flows in the form of a core with high velocity which may contain

entrained li uid droplets whereas li uid flows as a thin film around the pipe wall.

The li uid film at the bottom is usually thicker than that at the top.

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4.* "RTICAL @ INCLIN"D #LO% PATT"RN!

%s given by @r. 'hoham, four possible flow regimes have been described. They

are

>. $ubble flow.

?. 'lug flow.

M. 1hurn flow.

N. %nnular flow.

In the case of vertical and inclined flow, the stratified regime as in the case of hori#ontal flow is absent and a new flow pattern is observed which is called churn

flow.

4.*.1 7U77L" #LO% #i( 1.21

$ubble flow occurs at relatively low li uid rates. The gas phase is

dispersed as small discrete bubbles in a continuous li uid phase and

in this case the distribution is approximately homogenous throughout

the pipe section.

The bubble flow regime is sub divided into two categories

i $ubbly flow. #i( 1.21ii @ispersed bubble flow.

$ubbly flow occurs at relatively low li uid rates and is characteri#ed by slippage

between the gas and li uid phases.

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@ispersed bubble flow occurs at relatively high li uid rates and is characteri#ed

by no slippage between gas and li uid phases and in this condition, the li uid

phase carries the gas bubbles.

4.*.2 !LU$ #LO% #i( 1.22

'lug flow regime in vertical / inclined pipe is symmetric about the pipe

axis. 6as phase appears in the form of large bullet shaped gas pocket

with a diameter almost e ual to the pipe diameter. This gas pocket is

termed as 2Taylor $ubble2. The flow consists of alternate Taylor bubbles

and li uid slugs in the pipe cross" section. % thin li uid film trapped

between the Taylor bubble and the pipe wall flows downward. The filmpenetrates into the next li uid slug below it and creates a mixing #one

aerated by small gas bubbles.

#i( 1.22

4.*.* CHURN #LO% #i( 1.2*

1hurn flow is similar to slug flow but it appears more chaotic with no

clear boundaries between the two phases. The flow patterns are more

symmetric around the axial direction and less dominated by gravity.This flow pattern is characteri#ed by oscillatory motion. This type of

pattern occurs at high flow rates where the li uid slug bridging the pipe

become shorter and frothy. The slugs are blown through by gas phase

and thus they break and fall backwards and subse uently merge with

the following slug. %s a result, the bullet shaped 2Taylor bubble2 is

distorted and churning occurs, as such, it is named churn flow. #i( 1.2*

4.*.3 ANNULAR #LO% #i( 1.23

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In this type of flow, the li uid film thickness is more or less uniform around the

pipe wall and this li uid film moves at a slow rate. There are also li uid droplets

which are entrained in the gas core.

This type of flow is characteri#ed by a fast moving gas core and the

interface between the gas core and li uid film is highly wavy due to

high interfacial stress.

In case of vertical downward flow, the annular flow regime exist even

at very low gas rates in the form of falling film. The slug regime is,

however, very similar to that of upward annular flow except that the

2Taylor bubble2 becomes unstable and are eccentrically located withrespect to the pipe axis.

#i( 1.23

4.3 #LO% CORR"LATION!

%. 5ori#ontal flow correlations.

$. Inclined flow correlations.

1. 9ertical flow correlations.

4.3.1 HORI?ONTAL #LO% CORR"LATION!

In hori#ontal section, flow characteristic depends on factors like

>. !low rates of gas and li uid.

?. 6as li uid ratio.

M. *hysical properties of gas and li uids.

N. Line diameter.

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P. Interfacial energies and shear forces between the separate phases

present.

In hori#ontal flow, the total pressure loss is the sum of the frictional and total

kinetic losses with respect to various flow patterns. The pressure losses for

multiphase flow differ significantly from those encountered in single phase flow.

% great aberration in flow is observed in case of very viscous emulsified flow.

-any investigators of hori#ontal multiphase flow pattern have chosen their

separate experimental data into various groups that match the various flow

regimes as described earlier and accordingly they have offered their correlations

for prediction. There is a great deal of discrepancy in all of this kind of work andgenerally the 4ustification as offered by different authors are not enough to

convince fully the degree of influence of different flow patterns on pressure

losses occurring at various sections of the pipe.

In fact, no line is truly hori#ontal. Therefore multiphase flow occurs likely in

uphill, downhill as well as in hori#ontal direction. %ny dip or change in the

flowline profile from a hori#ontal position will effect a change in the flow pattern.

Li uid builds up in the low spots wherever they are and this ultimately decreases

the area available for flow. In that portion, velocity normally becomes high. %lso,

when the li uid is lifted over the hill, li uid also get collected in low spots. The

collected li uid at times overflows and contributes to build up of li uid in the next

lower spot. % portion of this li uid, in turn, is again lifted up. Therefore there is a

li uid surging process taking place repeatedly. This causes unstable fluid flow

and pressure loss. Thus excess pressure drop in the line operating below the

designed capacity is witnessed.

Therefore, in selecting multiphase flow system, there is a re uirement of keeping

high velocity so that li uid segregation and accumulation will be minimal. In

order to achieve this, excessive oversi#ing of line must be avoided in the case

of multiphase fluid transportation on the surface.

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The first known work in the

development of multiphase hori#ontal

flow was done in >:N: by Lockhart C

-artinelli. 1ommonly used

correlations for hori#ontal multiphase flow are

#i( 1.24

>. Lockhart and -artinelli.?. $aker.

M. %ndrews et al.

N. @ukler et al.

P. aton et al.

;. $eggs C $rill.

LOC;HART &ARTIN"LLI

Lockhart C -artinelli presented a very good work on hori#ontal multiphase flow

correlations which has been widely used by industries. This correlation is

considered fairly accurate for very low gas and li uid rates and for small conduit

si#es.

7A;"R

$aker has dealt with the multiphase flow in hori#ontal pipes specially in hilly

terrain. While using his method the slug and annular flow regions are found to be

more accurate. 5is method is better for pipe si#es greater than ; inches. %lso,

his work is found to be suitable whenever there is a case of slug flow. $aker has

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tried to present different e uations for each flow pattern and that is the main

difference between $aker and Lockhart C -artinelliFs approach.

ANDR"%! "T AL

%ndrews et al, presented a correlation to determine the pressure loss in ?.8;

inches I.@. steel pipe at field conditions. 5e had conducted the tests with water,

distillates, crude oil and natural gas. 5e found that his correlation with the

distillate data came close to the water curve but the oil curve deviated at high

)eynoldFs numbers. %lso he found that in case of turbulent flow, frictional losses

appear abnormally high at the lower )eynold numbers. 5is correlation is found

more suitable for ? inches pipe and for viscosities less than >8 " >P cp.

DU;L"R "T AL

@ukler et al, accumulated a huge data bank where more than ?8,888

measurements have been taken. 5e actually segregated his work in two

categories.

%t the outset, he tried to depict a comparison of different correlations vi#. $aker,

$ankoff, Lockhart C -artinelli, Eagi etc. The second part was the development of

a new correlation, through the concept of above similarity analysis. While

developing his correlation, he identified forces due to pressure, viscous shear

forces, forces due to gravity, and forces due to inertia or acceleration of the fluid.

Thereafter the correlation was presented in the form of two cases vi#. 1ase > C

1ase II, which are as follows "

CaBe I Du ler There is no slip between phases and a homogeneous flow is assumed to exist "

In 1ase I " @ukler, the two phase mixture was considered e uivalent to single

phase. 'o, this method is very simple to use and re uires no flow pattern

calculation since it is essentially a single phase pressure drop calculation.

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%lthough, most hori#ontal flow is highly unsteady, the assumption taken here is of

steady state flow where the hold" up is defined as the ratio of li uid superficial

velocity to total superficial velocity.

CaBe II Du ler

In this case, slip occurs but the ratio of each phase velocity to average is

assumed constant "

1ase " II @ukler, i.e. the constant slip method, is one of the most accepted

method as of today, for a wide range of conditions. The correlation of @ukler can

also handle viscous effects to a great extent. % wide range of conditions here

means a wide range of pipe si#es, a wide range of flow rates and a wide range of other related parameters. This correlation has been found to be more suitable

for the large pipes.

"ATON "T AL

aton et al conducted an extensive field study covering various gas and li uid

rates in long tubes. The diameter of tubes were ? inches and N inches. 5e

varied the li uid rates from P8 to ?P88 $*@ in ? inch line and P8 " P888 $*@ in N

inch line. !or each li uid rate, he varied the gas li uid ratio from bare minimum

to maximum as allowed by the system. One of the most important contributions

of aton was 2li uid hold"up correlation2. This hold"up related to fluid properties,

flow rate and the flow pattern in the line. aton applied a similar dimensional

analysis to this problem as had been done by )os and also by 5agedorn C

$rown for vertical flow. This correlation has a limitation and does not apply when

the flow degenerates to single phase.

7"$$! 7RILL

The $eggs C $rill method is suitable for a wide range of conditions and is

considered realistic in approach. This method has been extensively tested for

large diameter pipes. !or each pipe si#e, li uid and gas rates were varied and all

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5e then studied the deviation component. 5e treated the uphill section in the

similar manner as it would have been a vertical column containing same amount

of li uid. !lanigan used a dimensionless factor in the pressure drop e uation of

the vertical flow.

7"$$! 7RILL CORR"LATION

$eggs C $rill conducted gas"li uid two phase flow experiments in inclined pipe

and studied the effect of inclination angle on li uid hold"up and pressure drop.

They subse uently developed empirical correlation for li uid hold up and

frictional factor as functions of flow properties and inclination angle. They came

out with different correlations for li uid hold" up for three flow regimes, however,they observed that friction factor was not dependent on flow regime. They

observed that

> Li uid hold up and pressure drop were different with the change of

inclination angle.

? In inclined two phase flow, the li uid hold up increased to a maximum at

KP8 degrees and a minimum at "P8 degrees from hori#ontal.

M *ressure recovery in the down hill section was noticed and the same

should be considered in pipe line design.

4.3.* PRACTICAL APPLICATION! O# HORI?ONTAL @ INCLIN"D

&ULTIPHA!" #LO%

In this respect, it is a primary re uirement that a well should produce against a

minimum wellhead pressure possible to make the well flow to its capacity. $ut on

many occasions, the well produces against a higher well head pressure which at

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times is excessive. This can be considered a serious problem. Therefore the

practical application of hori#ontal multiphase correlation for the self flowing or lift

wells is to arrive at the minimum necessary well head pressure for pushing the

fluids in the surface lines up to the separator against the predetermined separator

pressure. If this flowline diameter is very small then a high wellhead pressure is

re uired to flow the fluid from wellhead to separator. %gain, on the other hand, if

the flowline diameter is bigger, then chances of fluctuating pressure loss and

li uid surging increase. Therefore by using a proper hori#ontal flow correlation,

the optimum surface flowline diameter and length can be selected.

EFFECT OF VARIABLES

"ffect of line Bi e #i( 1.25It is clearly seen that pressure loss for a given

length of flow line decreases very rapidly with

increasing of diameter. It is generally more

sharp when diameters are less and less rapid for

higher diameters.

#i( 1.25

"ffect of flo rate

The effect of flow rate with a wide range of

different diameter pipelines have been shown

in the #i( 1.28 !or a fixed diameter, more is the

uantity of flow, more is the pressure drop.

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#i( 1.28

"ffect of $aB li uid ratioB

'ince, in hori#ontal flow, no fluids are being lifted

vertically the presence of gas merely

represents additional fluids to be moved in thehori#ontal line. This in other words, means

more and more gas in the fluid causes

increasing gas"li uid"ratio + 6L) and this

increase in 6L), in turn, causes increase in

pressure drop. #i( 1.29 shows how

approximately gas li uid ratios effect

pressure drop in the line.

#i(

1.29

@ifferent published graphs are available for different pipe si#es, and li uid flow

rates with approximate water specific gravity at >.8Q, gas specific gravity at 8.;P

and average flowing temperature at >N8 8 !. The other sets of published graphs at

different conditions like average flowing temperature of >?8 o! etc. are also

available.

"ffect of %ater oil ratio

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The effect of water"oil"ratio or in other words the density of the mixed fluid is not

an important factor for hori#ontal flow.

"ffect of EiBcoBitF

9iscous crudes offer more of a problem in hori#ontal flow than they do in vertical

multiphase flow. The reason for this is that generally the crudes are cooler in the

surface flowline and hence more viscous. The Fig. #i( 1.2= depicts an

approximate effect of change of viscosity on pressure drop

for a given length of line.

#i( 1.2=

4.3.3 "RTICAL #LO% CORR"LATION! #i( 1.*0

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#i( 1.*0

9ertical multiphase flow pressure traverse is extremely important to select the

completion string, predicting flow rates and design of %rtificial Lift installation.

It is essentially sum of three contributing factors vi#.

" 'tatic gradient or hydrostatic gradient.

" !riction pressure gradient or simply friction gradient.

" %cceleration pressure gradient or simply acceleration gradient.

The other factors like viscosity, surface tension, density have also been included

upto a certain specific limit.

The historical development of the vertical multiphase flow was started as early as

>:>N but its impact was greatly felt after 6ilbertFs work.

W. . 6ilbert did considerable amount of work in >:M: and >:N8 on multiphase

flow although he could publish the result only in >:PN. 6ilbert had a very

important contribution in presenting grapghically pressure vs. depth values which

are known as the gradient curves.

*oettmann"1arpenterFs contribution in this area was also uni ue. They published

their correlation in the form of a set of gradient curves in >:P?. It was regarded

that their approach was probably the first fundamental and mathematical pattern

towards a wide range of flowing conditions.

'ubse uent authors used their correlations and plotted the gradient curves with

different ranges of flow rates for different conduit si#es.

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The most important correlations for predicting pressure loss in vertical flow are

> @uns and )os.

? Orkis#ewski.

M 5agedorn and $rown.N Winkler and 'mith.

P $eggs and $rill.

; 6ovier and %#i#.

These correlations are, in general, used 4udiciously for all pipe si#es and for any

field.There are several other correlations and most of them are limited to only onepipe si#e. #i( 1.*1

#i( 1.*1

DUN! AND RO!

@uns and )os did an extensive laboratory investigation using different field data.

@uns and )os in their investigations assumed a pressure difference and after

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calculating various re uired properties of fluids, they selected a flow regime. @ue

to the different flow regimes, the li uid hold up and friction factor also were

different. They finally came out after calculating slip velocity, li uid hold"up,

friction factor, friction gradient, static gradient, acceleration gradient etc. to

determine the vertical length corresponding to the assumed pressure difference.

This calculated length was compared to actual length and by iterative procedure

actual pressure drop was found out. Li uid hold"up and pressure gradient

depend on the gas flow rate to a large extent. %s per @uns and )os, the bubble

flow prevailed at low gas flow rates and li uid then was the continuous phase.

This kind of flow pattern made the pressure gradient almost e ual to the

hydrostatic gradient of the li uid. $ut when the gas rate was made to increase,bubbles grew in number. $ubbles then at different locations merged and formed

into bubbles of bigger shape, which finally turned into bullet patterned gas plugs.

These plugs then subse uently became unstable and collapsed when gas flow

rate further increased. !inally, the flow pattern became alternating li uid and gas

slug which are known as slug flow. %t still higher flow rates of gas, the slug flow

pattern became mist flow and in this situation gas, instead of li uid became the

continuous phase and li uid got dispersed and entrained in the gas medium. %s

per @uns and )os, the wall friction remained essentially negligible throughout the

changing of flow patterns upto slug flow. $ut the wall friction became very

significant for the mist flow and the wall friction further increased sharply with the

increase of gas flow rates. %s had been exercised by other authors, @uns and

)os also used superficial velocities + which means each phase is flowing

separately in the pipe . %ccording to them, when the surperficial velocity of li uid

exceeded >;8 cms/second, it became very difficult to observe the various flow

patterns. ven plug flow remained non"existent. %ctually, then the pattern

became turbulent with li uid being frothy with dispersed gas bubbles entrained in

it. $ut again at the same time if the gas flow rate was made to increase, the

li uid got segregated and caused slug flow. !inally, this flow pattern changed to

mist flow when superficial velocity of gas. exceeded P888 cms/ second.

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@uns and )os had divided the flow regimes into mainly three regions depending

on the amount of gas present.

>. The li uid phase was continuous. $ubble flow, plug flow and part of the

froth flow existed.

?. There was alternate phases of li uid and gas flow so this region covered

slug flow and froth flow regime.

M. The gas was in a continuous phase and there was mist flow.

@uns and )os used these three regions and friction factor as well as li uid hold"

up separately for each region and developed the correlations.

They used four dimensionless groups such as gas velocity number, li uid velocity

number, diameter number and li uid viscosity number.

@uns and )os correlation is one of the best for multiphase flow as this covers all

ranges of flow. 5owever, this correlation is not accurate for stable emulsion.

OR;I!?"%!;I

Orkis#ewskiFs correlation was based on the analysis of many published

correlations and he came out with some discriminatory features like considering

li uid hold"up in consideration to density and friction losses with respect to

different flow regimes. In order to simplify his approach, he had considered the

whole aspect in three separate categories. In the first category, the li uid hold up

was not considered in with density. The li uid hold up and wall friction losseswere expressed by using the empirically correlated friction factors and he did not

make any distinction between flow regimes. In the second category he used

li uid hold"up in density calculation and he arrived at the friction losses based

mainly on composite properties of li uids and gas. 5owever here also he did not

make any distinction between any flow regimes. In the third and last category, he

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used li uid hold"up in the density computation and the li uid hold"up was

calculated from the concept of slip velocity. !riction losses were then calculated

by the properties of the continuous phase and in this category flow regimes were

taken into consideration.

Orkis#ewski emphasi#ed that li uid hold up was the result of physical

phenomena and that the pressure gradient was related to the distribution fashion

of li uid and the gas phase. 5e then recogni#ed the four types of flow patterns

vi#. bubble, slug, transition and mixed. 5e prepared separate correlations for

each to establish slippage velocity and friction. 5e took help of the work done by

6riffith and Wallis in establishing his correlation for a slug flow and he used

basically @uns and )os correlation for transition and mist flow.

HA$"DORN AND 7RO%N

5agedorn and $rown came out with generali#ed correlation which included

almost all practical ranges of flow rates, a wide range of gas"li uid"ratios,

normally all the available tubing si#es and the effect of fluid properties. This

study also included all of the prior works done on the effect of the li uid viscosity.

5agedorn and $rown also incorporated a kinetic energy term which was

considered to be very significant in small diameter pipes in the region where the

fluid was having low density. They used 6riffith correlation when bubble flow

existed. The li uid hold"up was checked to make sure that it exceeded the hold"

up for no slippage to occur.

5agedorn and $rown on a similar line to that of @uns and )os showed that the

li uid hold up was principally related to four dimensionless parameters like li uidvelocity number, gas velocity number, diameter number, and li uid viscosity

number. They used the regression analysis techni ue to relate the above four

dimensionless groups as well as pressure terms. The 5agedorn"$rown li uid

hold"up correlation is a pseudo hold"up correlation. 5old"up was not actually

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measured but back calculated after knowing the total pressure loss and by using

a friction factor obtained from two phase )eynoldFs number.

%IN;L"R AND !&ITH

Work of building the fluid gradient curves by Winkler and 'mith was the

extension of work by *oettmann C 1arpenter, as mentioned in the foregoing

discussion. Winkler and 'mith, in order to give their gradient curves a universal

application, selected some average li uid and gas conditions with corresponding

*9T characteristics and thereafter demonstrated the effect of each possible

variable upon the gradient curve like effect of tubing si#e, effect of flow rate, effect

of gas"li uid ratio, effect of oil C water gravity, effect of gas gravity, effect of welltemperature, effect of solution gas"oil"ratio etc. These effects were with certain

assumptions like no paraffin or scale build"up in the tubing wall, no loading of

fluid in the bottom of the tubing or the breaking out of gas from the fluid. %s per

Winkler and 'mith, a variation of one factor would not seriously affect the fluid

gradient curve, but when a large number of variables pointed in the same

direction, an appreciable error would be introduced into the gradient curves.

1onsidering all such aspects, @uns and )os, 5agedom and $rown, Winkler and

'mith and others published fluid gradient curves with the consideration of the

most common field conditions such as Tubing I.@. +>.;>82, >.::P2, ?.NN2, ?.::?2

etc. oil gravity as MP 8 %*I, gas gravity as 8.;P water specific gravity as >.8N8 O!, >:8 O! etc., surface gas pressure as >N.;P

psia, surface gas temperature base as ;8 8! and surface compressibility factor, R

as >.8. %ll the curves were drawn for each condition such as 2all oil2, 2all water2

and 2P8B oil and P8B water2.7"$$! AND 7RILL

$eggs and $rill developed the correlation by doing experimentation on a small

scale test facility. This small scale test facility consisted of > inch and >.P inches

sections of acrylic pipe of :8 ft long which was set up in Tulsa 7niversity fluid flow

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section. The pipe could also be inclined at any angle from the vertical position to

hori#ontal. The following parameters were studied " gas flow rate, li uid flow rate,

average system pressure, pipe diameter +as in the set up, i.e., > 2 and >.P2 , li uid

hold up, pressure gradient, inclination angle and hori#ontal flow patterns. The

fluids used were water and air. Li uid hold up and pressure gradients were noted

at every step. The original flow pattern was modified to include a transition #one

between the segregated and intermittent flow regimes.

$O I"R AND A?I?

6ovier and %#i# correlation was flow regime dependent. They came out with a

new method for the bubble and slug flow regimes in vertical two phase flow. !or mist flow they preferred @uns and )os method. 6ovier and %#i# correlation

performed with accuracy.

4.4 PR"!!UR" !. D"PTH #LUID $RADI"NT CUR "!

In order to have access to the multiphase correlation by the oil field design

engineers, multiphase correlations as developed by different authors areavailable in two forms

i In the form of a set of pressure"depth working curves.

ii In the form of computer solutions.

$oth are very useful. 1omputer solution provides the design in no time. 5owever,

field engineers can ac uire a fair idea when they apply working curves to solve

problems.

There are several publications of multiphase flowing pressure curves vi#. +>

Winkler and 'mith curves in 6as lift -anual of 1amco, Inc., +? 5agedorn and

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$rown curves in the book titled S %rtificial Lift -ethods S by ermit . $rown,

*rentice 5all, Inc., +M 7.'. Industries curves in 5andbook of 6as lift, etc.

These correlations are useful for

+i 'electing tubing si#es.

+ii To predict when the well will cease to flow i.e. when the well re uires

additional gas to be in4ected at some point in the tubing to make it flow at

the desired rate.

+iii @esigning of artificial lift system.

+iv @etermining flowing bottom hole pressures from the wellhead pressuresand vise versa.

+v *redicting maximum flow rates possible.

%ll the correlations are based on certain common assumptions like - !luid must be free from emulsion.

- !luid must be free from scale/paraffin build up.

- -ashed or kinked 4oints should not exist in the tubing.

- !low patterns should be relatively stable.

- (o severe slugging should occur.

- !luid + oil should not be very viscous.