production system optmization for submersible pump lifted wells a case study

8/8/2019 Production System Optmization for Submersible Pump Lifted Wells a Case Study

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Approval of the Graduate School of Natural and Applied Sciences

Prof . Dr. Canan ZGEN

Director

I certify that this thesis satisfies all the requirements as a thesis for the degree of

Master of Science.

Prof. Dr. Birol DEMRAL

Head of Department

This is to certify that we have read this thesis and that in our opinion it is fully

adequate, in scope and quality, as a thesis for the degree of Master of Science.

Prof. Dr. A .Suat Bac

Supervisor

Examining Committee Members

Prof. Dr. Birol DEMRAL (Chair Person)

Prof. Dr. A. Suat BACI

Prof. Dr. Fevzi GMRAH

Prof. Dr. Mustafa V. KK

Prof. Dr. Nurkan KARAHANOLU


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ABSTRACT

PRODUCTION SYSTEM OPTIMIZATION FOR SUBMERSIBLE

PUMP LIFTED WELLS : A CASE STUDY

GLER, Nuri Ozan

M.S. Department of Petroleum and Natural Gas Engineering

Supervisor: Prof. Dr. A. Suat Bac

April, 2004, 173 Pages

A computer program has been written to perform production

optimization in submersible pump lifted wells. Production optimization wasachieved by the principles of Nodal Analysis Technique which was applied

between the reservoir and the wellhead ignoring the surface choke and

separator. Computer program has been written according to two lifting

environment, which are: pumping with only liquid and pumping with both

liquid and gas. Program played an important role in the study by overcoming

difficult iterations existing in the pumping liquid and gas case due to

variation of liquid volume between pump intake and discharge pressure.

Hagedorn and Brown vertical multiphase flow correlation was utilized in theprogram to determine the pressure at required depth. However, Griffith

Correlation was also used in the program since Hagedorn and Brown

Correlation failed to give accurate results at bubble flow.


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A case study was done by evaluating the 10 wells located in

Diyarbakr-GK field which are all submersible pump lifted. Well, reservoir,

fluid and lift-system data was transferred to already written computer

program. Output of the computer program for both cases was used to

calculate accurately the optimum production rates, required horsepower,number of pump stages and the relation between these parameters with

each other. The sensitivity variable selected is the number of pump stages.

At the end of the study, by comparing the actual operating data and the

computer-based optimized data, it was observed that 3 wells: W-16, W-17,

and W-24 were producing completely within their optimum range, 5 wells:

W-07, W-08, W-25, W-27 and W-28 were not producing at their optimum

range but their production parameters can said to be acceptable , 1 well: W-

22 was producing inefficiently and should be re-designed to reach optimum

conditions. It was realized that W-15 has insufficient data to make

necessary interpretations.

Keywords: Production optimization, nodal system analysis technique,

electrical submersible pump, artificial lift, Hagedorn and Brown correlation,

Griffith correlation.


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Yazlan bu programn pratie geirilmesi asndan Diyarbakr GK

sahasndaki dalg pompalarla retim yaplan 10 kuyu incelemeye

alnmtr. Bu kuyularn rezervuar, akkan ve retim verileri hazr olan

bilgisayar programna aktarlmtr. Daha nce belirtilen iki pompalama

ortamn kapsayan bu programn kts optimum retim debisi, gerekenbeygirgc ve pompa kademe saysnn belirlenmesi iin kullanlmtr. Bu

hesaplamalarda hassas deiken olarak pompa kademe says seilmitir.

almann sonunda GK sahas verileri ile programdan karlan optimize

deerler karlatrlm ve dalg pompalarla retim yaplan 10 kuyudan

3nn: W-16, W-17, ve W-24n optimum deer snrlar ierisinde retim

yapt, kuyulardan 5inin W-07, W-08, W-25, W-27, W-28, optimum

deerler ierisinde olmasa bile kabul edilebilir ve geerli saylabilir

snrlarda retim yapt, 1 kuyunun, W-22, optimum snrlar dnda ve

verimsiz bir ekilde retime devam ettirildii saptanmtr. W-15in verileri

herhangi bir yorum yapmak iin yetersiz kalmtr.

Kelimeler: retim optimizasyonu, sistem analiz teknii, dalg pompa, yapay

retim, Hagedorn ve Brown Korelasyonu, Griffith Korelasyonu


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To my family,

idem, Yurdahan and Sanem Gler


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ACKNOWLEDGEMENTS

The author would like to thank his supervising professor, Dr. Suat

Bac, for his precious assistance throughout this study and also N.V.

Turkse Perenco for their cooperation.


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TABLE OF CONTENTS

ABSTRACT .. iii

ZET . v

ACKNOWLEDGEMENTS .. viii

TABLE OF CONTENTS . ix

LIST OF TABLES xiii

LIST OF FIGURES . xv

NOMENCLATURE .. xviii

CHAPTER

1. INTRODUCTION . 1

2. ELECTRICAL SUBMERSIBLE PUMPS .. 4

2.1 Introduction ... 4

2.2 Pump Performance Curves 8

2.3 Pump Intake Curves ... 13


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2.3.1 Pumping Liquid Only 13

2.3.1.1 Procedure for the Preparation

of Tubing Intake Curves for

Liquid Only .. 14

2.3.2 Pumping Liquid and Gas ... 16

2.3.2.1 Determination of the Number

of Stages . 16

2.3.2.2 Determination of Horsepower .. 19

2.3.2.3 Pump Selection .. 20

2.3.2.4 Procedure for the Preparation

of Intake Curves for Wells

Pumping Gas 21

3. NODAL ANALYSIS APPROACH . 23

3.1 Introduction .. 23

3.2 Application of Nodal Analysis to Electrical

Submersible Pumping Wells .. 29

3.3 Description of the Computer

Program 31

3.3.1 Pumping Liquid 31

3.3.2 Pumping Liquid and Gas 32

4. STATEMENT OF THE PROBLEM 34


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5. HAGEDORN AND BROWN VERTICAL

MULTIPHASE FLOW CORRELATION

SUPPORTED BY GRIFFITH CORRELATION .. 36

5.1 Introduction .. 365.2 Hagedorn and Brown Method 38

5.3 Procedure for Calculating a Vertical Pressure

Traverse by the Method of Hagedorn and

Brown . 39

5.4 Griffith Correlation (Bubble Flow) . 49

6. DESCRIPTION OF THE GK FIELD . 51


6.2 Geology 52

6.3 Reservoir, Fluid, and Lift System

Properties . 53

6.4 Production History .. 54

7. RESULTS AND DISCUSSION . 57


7.2 Results and Discussion .. 58

7.2.1 Construction of Vertical Flowing

Pressure Gradient Curves Using

Computer Program Output . 58

7.2.2 Sensitivity Analysis by Using the

Computer Program Output 64


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7.2.3 Construction of Possible Production

Rate versus Stage and Horsepower

Chart for GK Field Wells by Using

the Pumping Liquid and Gas

Computer Algorithm ... 677.2.4 Comparison of Theorotical and

Actual Production Parameters and

Suggestion for Optimum Pump

Operating Conditions by Inspecting

Possible Production Rate versus

Stage and Hordepower Chart 77

8. CONCLUSION AND RECOMMENDATIONS . 81

REFERENCES 83

APPENDIX

A Pumping Liquid and Gas Computer Program . 85

B Pumping Only Liquid Computer Program 101

C Subprograms 109

D Sample Calculation of W-08 .. 128


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LIST OF TABLES

TABLE

6.1 Reservoir and Fluid Properties of GK Field .... 53

6.2 Submersible Pump Lifted Wells Operated

in GK Field and Their Efficiency Ranges . 54

6.3 Gross Production Rate of the Wells in GK

Field and Required Pump Stages .. 56

7.1 Comparison of Computer-Based Vertical

Flowing Pressures with Beggs&Brill

Correlation at Selected Depths .... 63

7.2 Effect of Oil Density on Flowing Bottomhole

Pressures at Selected Depths .. 64

7.3 Effect of GLR on Flowing Bottomhole

Pressures . 65

7.4 Effect of WOR on Flowing BottomholePressures at Selected Depths... 65


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7.5 Results Obtained After The Comparison

of Actual and Computer-Based Data

for GK Field .. 79

D1 Well, Fluid, Reservoir and Lift-SystemData Used In Calculations for W-08 . 129

D2 Production History of W-08 130

D3 Intake Pressures at Assumed Rates for W-08 161

D4 Horsepower Requirements for Possible

Rates from W-08 . 171

D5 Relation of Production Parameters

With Each Other .. 173


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xv

LIST OF FIGURES

FIGURES

2.1 A Typical Submersible Pump Installation 6

2.2 Submersible Pump Schematic .. 7

2.3 Pressure Traverses for Pump on Bottom 7

2.4 A Typical Pump Performance Curve (GN 3200) 9

3.1 Pressure Losses In a Production System 25

3.2 Tubing Intake Curves for Artificial Lift Systems . 26

5.1 Schematic Diagram of Possible Flow

Patterns in Two-Phase Pipelines .. 37

6.1 Generalized IPR Curve .. 55

7.1 Pressure Traverse Curve (WC = 0) . 59

7.2 Pressure Traverse Curve (WC = 0.5) .. 60


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7.3 Pressure Traverse Curve (WC = 1.0) 61

7.4 Graphical Analysis of Effect of GLR on

Flowing Bottomhole Pressures for W-08 . 66

7.5 Graphical Analysis of Effect of WOR on

Flowing Bottomhole Pressures for W-08 . 66

7.6 Possible Production Rate vs Stages and

Horsepower for W-07 . 68
















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NOMENCLATURE

Symbol Description Unit

A area of tubing ft2

B formation volume factor rbbl/stb

CNL viscosity number coefficient

d tubing inner diameter in

Es fraction of free gas

f friction factor

fo fraction of oil flowing

Gf gradient of the pumped fluid psi/ft

GLR gas liquid ratio scf/stb

GOR gas oil ratio scf/stb

h head per stage ft/stage

HL liquid hold-up

hp horsepower per stage hp/stage

HP horsepower hp

J productivity index stb/d/psi

m mass associated with one bbl

of stock tank liquid lbm/stbl

Nd pipe diameter number

NGV gas velocity numberNL liquid viscosity number

NLV liquid velocity number

(NRE)TP two-phase Reynolds number


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Symbol Description Unit

P pressure psi

q flow rate stb/d

Rs solution gas oil ratio scf/stbSt pump stage

T average flowing temperature F

V capacity stb/d

VF volume factor

w mass flow rate lbmday

W weight of the capacity lb/day

WC water cut

z gas compressibility

increment

viscosity cp

velocity ft/sec

density lb/cuft

hold-up correlating function secondary correction factor

liquid surface tension dyne/cm

specific gravity

Subscription Description

b bubble point

dn pump discharge (downstream)

f fluid

g gas


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Subscription Description

l liquid

m mixture

o oilpc pseudo critical

pr pseudo reduced

R reservoir

sc standard condition

sg superficial gas

sl superficial liquid

sep separator

up pump intake (upstream)

w water

wf flowing well

wh wellhead

2 discharge

3 intake


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CHAPTER I

INTRODUCTION

The electrical submersible pumping system can said to be an

attractive artificial lift technique in reservoirs having high water-cut and low

gas-oil ratio. Currently, it is considered as an effective and economical

means of lifting large volumes of fluid from great depths under a variety of

well conditions. Pumping equipment is capable of producing as high as60,000 b/d and as low as 200 b/d. The oil cut may also vary within very wide

limits, from negligible amounts to 100 %. The pump performs at highest

efficiency when pumping liquid only; it can handle free gas with the liquid

but high volumes of free gas causes inefficient operation and gas lock

problems. The first submersible pumping unit was installed in an oil well in

1928 and since that time the concept has proven itself throughout the oil-

producing world1. A submersible pumping unit consists of an electric motor,

a seal section, an intake section, a multistage centrifugal pump, an electric

cable, a surface installed switchboard, a junction box and transformers.

Additional miscellaneous components also present in order to secure the

cable alongside the tubing and wellhead supports. Pressure sentry for

sensing bottom-hole pressure, check and bleeder valves are the optional

equipment that can be taken into consideration. Under normal operating

conditions, submersible pumping unit can be expected to give from 1 to 3

years of good operating life with some units operating over 10 years.

Despite this advantage, many submersible pump lifted oil and gas wells

produce at rates different than optimum. This fact makes necessary to apply

production optimization techniques to wells having low production rates.

Nodal Analysis has been applied to artificial lift method for many years to


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analyze the performance of the systems composed of interacting

components. It is a process of determining the effect of each component in

the production system on the total system performance. The analysis can

improve the completion design, well productivity and producing efficiency,

all of which lead to increased profitability from oil and gas investments. TheNodal analysis technique is essentially a simulator of the producing well

system. The system includes all flow between the reservoir and the

separator. As the entire system is simulated, each of the components is

modelled using various correlations or equations to determine the pressure

loss through that component as a function of flow rate. The summation of

these individual losses make up the total pressure loss through the entire

system for a given flow rate. The production rate or deliverability of a well

can be severely restricted by the poor performance of just one component in

the system. If the effect of each component on the performance of the total

system can be isolated, the efficiency of the system can be optimized in the

most economical way. When performing a Nodal analysis, we divide the

production system into its components, i.e., reservoir, perforations, tubing,

surface choke, flowline and separator. Then we pick a problem area in this

production system as a node. This node acts as the intersection point

between the inflow and outflow performances. Different inflow and outflow

performance curves intersect on the same plot and give the design

considerations for different arrangements2. Optimization and design of

submersible pump lifted wells pumping only liquid are generally straight-

forward however pumping gas with the liquid is complicated because of the

high compressibility of gas. In this case, volume of the produced fluid rate

shows a significant variation between the pump intake and discharge

pressures, consequently considerable amount of iterations should be

performed to determine the volume factor at any pressure between the

intake and discharge pressures. Thus, computer program should be written

to overcome these iterations. Optimization of wells with Nodal Analysis

requires pressure gradient correlation in order to reach a solution so it is


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necessary to use a vertical multiphase flow correlation method in the

computer program. In this study, Hagedorn and Brown vertical multiphase

flow correlation3 has been used to determine the pressure and pressure

losses at required depth. However, during the study it was observed that

Hagedorn and Brown Correlation failed to give accurate output at bubbleflow. Thus, Griffith Correlation4 was constructed at bubble flow to obtain

accurate results.

The purpose of this study was to write a general computer program

that gives simultaneously the possible production rates for submersible

pump lifted wells and also the optimum required horsepower and number of

pump stages at these possible rates both considering pumping liquid and

pumping gas with liquid. In addition to that objective, comparison made by

using the production data of wells located in the GK field will assist us in

suggesting optimum pump operating conditions.


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CHAPTER II

ELECTRICAL SUBMERSIBLE PUMPS

2.1 Introduction

Many high volume wells are equipped with electric submersible pumps

(ESP) to lift the liquid and decrease the flowing bottom hole pressure. A

submersible pump is a multistage centrifugal pump that is driven by an

electric motor located in the well below the pump. Electrical power is

supplied by means of a cable from the surface.

The pump and motor are suspended on the tubing at a certain depth in

the well. The annulus is either vented or tied into the wells flowline, so that

as much gas as possible is separated from the liquid before it enters the

pump. In some cases, a centrifugal separator will be placed between the

pump and motor for obtaining maximum gas-liquid separation. A typical

submersible pump installation is given in Figure 2.1. A schematic of a well

equipped with a submersible pump is given in Figure 2.2, along with the

pressure traverse in the well. From the figure it can be seen that, initially,

flowing pressure of submersible pump lifted well is not sufficient to lift the

fluid (depleted well). This insufficient pressure (Pup) which we define as

intake pressure starts to increase at pump setting depth by required pump

stages and finally reaches to discharge pressure (Pdn) generated by the

pump which will assist fluid to flow throughout the surface. Figure 2.3 is a

typical pressure traverses for pump on bottom. Discharge pressure of the

pump will be defined as P2, and also intake pressure will be defined as P3

throughout the study. From figure, the effective lift point is that depth at


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which the flowing bottomhole pressure is capable of supporting the fluids in

the tubing string.

The pump performs highest efficiency when pumping liquid only. It can

and does handle free gas along with the liquid. The manner in which the

pump handle gas is not completely understood; however high volumes offree gas are known to cause inefficient operation.


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Figure 2.1 A Typical Submersible Pump Installation


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Figure 2.2 Submersible Pump Schematic

Figure 2.3 Pressure Traverses for Pump on Bottom


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2.2 Pump Performance Curves

Pumps are divided into groups according to the minimum casing size

into which the pump can be run. But even within the same group, each

pump performs differently. A typical pump performance curve5 is given inFigure 2.4.

The performance curves of a submersible electrical pump represent the

variation of head, horsepower, and efficiency with capacity. Capacity refers

to the volume of the produced flow rate, which may include free and/or

dissolved gas. These curves are for a fixed power cycle normally 50 or 60

cycle and can be changed with variable frequency controllers6.

j

j

j

j

j


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j

j

j

j

j

Figure2.3

ATypicalPumpPerformanceC

urve(GN3200)

Figure2.4

ATypicalPumpPerformance

Curve(GN3200)5


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The head (in feet per stage) developed by a centrifugal pump is the

same regardless of the type or specific gravity of the fluid pumped. But

when converting this head to pressure, it must be multiplied by the gradient

of the fluid in question. Therefore, the following can be stated:

Pressure developed by pump = head per stage gradient of fluid

number of stages

When pumping gas with the liquid, the capacity and, consequently, the

head per stage as well as the gradient vary as the pressure of the liquid

elevated from the intake value P3 to the discharge value P2. Thus, the above

equation can be written as follows6:

)()()( StdVGVhdP f = (1)

where:

dP = the differential pressure developed by the pump, psi

h = the head per stage, ft/stage

Gf= the gradient of the pumped fluid, psi/ft

d(St) = the differential number of stages

Note that parentheses are included to indicate that h and Gfare functions

of the capacity V, which is:

VFqV sc= (2)

The gradient of fluid at any pressure and temperature is given by:

)(433.0)( VVG ff = (3)

but:


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V

WVf

350)( = (4)

where W is the weight of the capacity V at any pressure and temperature,

which is equal to the weight at standard conditions. Hence:

V

qV

fscsc

f350

)(

= (5)

Substituting equation 5 into 3 gives:

V

qVG

fscsc

f

)

350

433.0()( = (6)

fsc is the weight of 1 bbl of liquid plus pumped gas (per 1bbl of liquid) at

standard conditions, or:

gscoscwscfsc GLRGIPwcwc ))(()1(350350 ++= (7)

where gsc is the density of gas (in lb/scf) at standard conditions.

Substituting Equation 6 into Equation 1 gives:

dPVh

V

qStd

fscsc )()

433.0

350()(

= (8)

The total number of stages is obtained by integrating the above equation

between the intake and discharge pressures:

=2

3)(

)433.0350()(

0

P

Pfscsc

St

dPVhV

qStd

(9)

or:


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=2

3)(

)3141.808

(

P

Pfscsc

dPVh

V

qSt

(10)

The pump performance curves give the horsepower per stage based on

a fluid specific gravity equal to 1.0. This horsepower must be multiplied by

the specific gravity of the fluid under consideration. Thus the following can

be stated:

(horsepower requirements) = (horsepower per stage) (specific gravity of

fluid) (number of stages)

Since the horsepower per stage, the specific gravity of fluid, and the

number of stages depend on the capacity V, which varies between the

intake and the discharge pressures, the above equation can be written as

follows:

)()()()( StdVVhHPd fp = (11)

Substituting Equations 5 and 8 into the above equation gives:

=)(HPd ( dPVh

Vhp

)(

)()

433.0

1(12)

The total horsepower requirement is obtained by integrating the above

equation between the intake and the discharge pressures:

=

2

)(

)()

433.0

1()(

0

P

P

pHP

dPVh

VhHPd (13)

or:


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=2

3)(

)()

433.0

1(

P

P

pdP

Vh

VhHP (14)

For each pump, there is a capacity range within which the pump

performs at or near its peak efficency. The volume range of the selected

rate between the intake and the discharge pressures should, therefore,

remain within the efficiency range of the pump. This range, of course, can

be changed by using a variable frequency controller.

2.3 Pump Intake Curves

Predicting intake curves for submersible pumps is considered for two

cases: (1) pumping only liquid, and (2) pumping liquid and gas. For both

cases, it is assumed that the pump is set at the bottom of well and the

wellhead pressure and tubing size are fixed. For case 2, it is assumed that

all associated gas is pumped with the liquid. The sensitivity variable

selected is the number of stages6.

2.3.1 Pumping Liquid Only

Since the liquids are only slightly compressible, the volume of the

production rate can be considered constant and equal to the surface rate

qsc. Hence, the head per stage will also be constant, and Equation 10 can

be integrated to give6:

))(3141.808

( 32 PPh

Stfsc

=

(15)

Solving Equation 15 for 3P gives:


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14

Sth

PPfsc

)3141.808

(23

= (16)

Equation 14 also can be integrated to give:

)()433.0

1( 32 PP

h

hHP

p = (17)

Substituting Equation 15 into the above equation yields:

SthHP fscp= (18)

Pump selection is limited by the casing size. Another constraint is the

desired production rate. If the objective is to maximize the production rate,

the proper procedure is to select a pump whose efficiency range includes

rates that are close to the maximum rate of the well.

2.3.1.1 Procedure For The Preparation of Tubing Intake

Curves for Liquid Only

A step-wise procedure for predicting intake curves for the case

when only liquid is pumped follows6:

(1) Select a suitable pump as dictated by the casing size and the flow

capacity of the well

(2) Calculate fsc from Equation 7 (GLR=0) and fsc from Equation 5.

(3) Assume various production rates and, for each of these rates, do the

following:(a) Read the head per stage from the pump performance curves and

calculate the quantity (fsch/808.3141).


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2.3.2 Pumping Liquid and Gas

Because of the high compressibility of gas, the volume of the

produced flow rate V may undergo a significant variation as the pressure of

the fluid changes from the intake value to the discharge value. At anypressure point between the intake and discharge, if all gas is pumped with

the liquid, the volume factor is determined from6:

[ ] gso BRwcGLRBwcwcVF )1()1( ++= (19)

if a certain percentage of the gas is vented:

[ ] gso BRwcGLRGIPBwcwcVF )1()1( ++= (20)

In either case, the volume of the flow rate is given by:

VFqV sc= (21)

2.3.2.1 Determination Of The Number of Stages

Because V and, consequently, h vary as the fluid passes through

the pump, direct integration of Equation 10 is possible only if the integrand

V/h(V) can be reduced to a simple function of pressure. But this is difficult

because VF is a very complicated function of pressure. For this reason,

numerical integration methods are recommended.

The existence of gas at the intake section of the pump implies that

the intake pressure is below the bubble point of the crude (saturated crude).

If that is the case and if the required discharge pressure is above the bubble

point, Equation 10 should be broken down into two integrals as follows6:


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+=2

3)()(

P

Psc

P

Psc b

b

dPVh

V

q

AdP

Vh

V

q

ASt (22)

where A = 808.3141/fsc = constant (23)

For performing numerical integration, Equation 22 can be written in a

more convenient form as follows:

= =

+=m

i

n

mj

j

j

j

sc

i

i

i

sc

Ph

V

q

AP

h

V

q

ASt

1

,3,3 (24)

where:

P3,i = any intake pressure above the bubble point

P3,j = any intake pressure below the bubble point

P3,o = discharge pressure (P2)

P3,m = bubble point pressure (Pb)

P3,i = P3,i=P3,i-1-P3,i

P3,j = P3,j=P3,j-1-P3,j

ii hV / and jj hV / = average quantities evaluated at the average pressures

iP,3 and jP,3 , respectively.

where:

2/)( ,31,3,3 iii PPP +=

and

2/)( ,31,3,3 jjj PPP +=

The main reason for breaking down the number of stages into two

summations is the fact that V and, consequently, h undergo only slight

change above the bubble point; hence, P3,i can be taken much larger than


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P3,j. In fact, satisfactory results are obtained even if P3 is taken as the

difference between Pb and P2 and the quantity hV / is evaluated at the

midpoint.

When using a computer solution, it is easier to divide the interval

between the intake and the discharge pressure into equal increments by

taking P3 constant. For this case, Equation 24 can be written as:

=

=

n

i i

i

sc

ih

V

q

PASt

1

3 )( (25)

where:

P3,0

= discharge pressure (P2)

P3,n = intake pressure (P3)

n = (P2-P3)/P3

P3,i = P3,i-1- P3

The quantity ii hV / is evaluated at the average pressure given by:

2/)( ,31,3,3 iii PPP += (26)

In reality, any pressure P3,I can be considered an intake pressure. To

illustrate this point, Equation 25 can be written in the following form:

=

=n

i

ii StSt1

)( (27)

where:

i

i

sc

ih

V

q

PASt )()( 3

= (28)


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Therefore, inorder to obtain an intake pressure P3,i , we have:

i

i

sc h

V

q

PAStSt )()( 311

== (29)

In order to obtain P3,2, we have:

)()()(

2

2

1

13

212h

V

h

V

q

PAStStSt

sc

+

=+= (30)

And in order to obtain P3,n, we have:

=nSt nStStSt )(...)()( 21 +++ (31)

= )(( 3

scq

PA)...

2

2

1

1

n

n

h

V

h

V

h

V+++ (32)

2.3.2.2 Determination of Horsepower

The horsepower requirement is obtained by integrating Equation14 between the intake and the discharge pressures. Since the integrand

hp(V)/h(V) can not be reduced to a simple function of pressure, direct

integration is not possible, and numerical methods must be used.

If the interval between the intake and the discharge pressure is divided

into equal increments by taking P3 constant, Equation 14 can be written as

follows6:

=

=

n

i i

i

ih

hpPHP

1

3 )433.0

( (33)


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If(HP)I is defined as:

=

=

n

i i

ii

h

hpPHP

1

3 )433.0

()( (34)

then Equation 33 can be written as:

=

=n

i

ii HPHP1

)( (35)

2.3.2.3 Pump Selection

As mentioned previously, pump selection is limited by the casing

size and flow capacity of the well. Another constraint that must be taken into

account when pumping gas with the liquid is the volume range of the flow

rate. Because of the high compressibility of the gas, the difference between

the intake and discharge volumes may be too great to be contained within

the efficiency range of one pump. For this reason, the following procedure

for pump selection is suggested6:

(1) Prepare IPR curves in stbl/d and b/d to the same scale on the same

graph.

(2) Enter the b/d IPR curve at the upper limit of the efficiency range of

several pumps that are suitable from a casing-size standpoint. Move

horizontally to the stbl/d IPR curve and read the intake rate in stbl/d.

(3) For each intake rate determined in step 2, do the following:

(a) Determine the required discharge pressure from a two-phase flow

correlation.(b) Calculate VF at the discharge pressure, then calculate the discharge

volume.


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(4) Select the pump for which the discharge volume is greater than or equal

to the lower limit of its efficency range.

If more than one pump is found to be suitable, choose the one with the

highest capacity.

2.3.2.4 Procedure for the Preparation of Intake Curves for

Wells Pumping Gas

A step-wise procedure for predicting tubing intake curves for the

case in which gas is with the liquid is given as follows 6:

(1) Select a suitable pump as outlined previously.

(2) Calculate fsc from Equation 7 and calculate the constant A from

Equation 23.

(3) Assume several production rates in stbl/d and, for each of these rates,

do the following:

(a) Determine the required discharge pressure (P3,0) from a two-phase

flow correlation.

(b) Choose P3 and calculate the quantity (AP3/qsc)

(c) Calculate1,3

P and 1,3P .

(d) Determine 1VF at 1,3P , then calculate 1V .

(e) Read 1h at 1V from the pump performance curves.

(f) Calculate the required number of stages to obtain the intake pressure

P3,1 from Equation 25.

(g) Repeat steps c-f for P3,2, P3,3 through P3,i until a convenient intake

pressure is reached. Tabulate the intake pressure versus the number

of stages.

(4) By interpolating or plotting, obtain intake pressure for assumes rates for

an identical number of stages.


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(5) Plot the intake pressure (obtained in step 4) versus the assumed

production rates for the various number of stages. Plot the stbl/d IPR

curve to the same scale on the same graph.

(6) Read the rates at the intersection of the pump intake curves with the IPR

curve.(7) For each rate, calculate the horsepower requirement from Equation 33.

Calculation of horsepower requirements is similar to the calculation of

the number of stages.

(8) Plot the rate versus the number of stages and horsepower requirements.

Impose the efficiency range of the pump on the same graph.

(9) Select a suitable rate.


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23

CHAPTER III

NODAL ANALYSIS APPROACH

3.1 Introduction

The systems analysis approach, often called NODALTM Analysis, has

been applied for many years to analyze the performance of systems

composed of interacting components. Electrical circuits, complex pipelinenetworks and centrifugal pumping systems are all analyzed using this

method. Its application to well producing systems was first proposed by

Gilbert7 in 1954 and discussed by Nind8 in 1964 and Brown9 in 1978.

The production system can be relatively simple or can include many

components in which energy or pressure losses occur. Figure 3.1 illustrates

a number of the components in which pressure losses occur.

The procedure consists of selecting a division point or node in the well

and dividing the system at this point. All of the components upstream of the

node comprise the inflow section, while the outflow section consists of all of

the components downstream of the node. A relationship between flow rate

and pressure drop must be available for each component in the system. The

flow rate through the system can be determined once the following

requirements are satisfied2:

1 Flow into the node equals flow out of the node

2 Only one pressure can exist at a node.

At a particular time in the life of the well, there are always two pressures

that remain fixed and are not functions of flow rate. One of these pressures


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is the average reservoir pressure, Rp , and the other is the system

outlet pressure. The outlet pressure is usually the seperator pressure, psep,

but if the well is controlled by a surface choke the fixed outlet pressure may

be the wellhead pressure pwh.

Once the node is selected, the node pressure is calculated from both

directions starting at the fixed pressures.

Inflow to the node:

ppR (upstream components) = nodep (36)

Outflow from the node:

ppsep + (downstream component) = nodep (37)

The pressure drop, p , in any component varies with flow rate, q .

Therefore, a plot of node pressure versus flow rate will produce two curves,

the intersection of which will give the conditions satisfying requirements 1

and 2, given previously.

The effect of a change in any of the components can be analyzed by

recalculating the node pressure versus flow rate using the new

characteristics of the component that was changed. If a change was made

in an upstream component, the outflow curve will remain unchanged.

However, if either curve is changed, the intersection will be shifted, and a

new flow capacity and node pressure will exist. The curves will also be

shifted if either of the fixed pressures is changed, which may occur with

depletion or a change in separation conditions.

Figure 3.2 illustrates the comparison of intake curves for artificial lift

methods. It can be observed from the figure that electrical submersible


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pump keeps the bottomhole pressure low, thus, creates large amount of

pressure drawdown to reach high production rates.

Figure 3.1 Pressure Losses In a Production System2


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Figure 3.2 Tubing Intake Curves for Artificial Lift Systems6

Inflow to node:

whtubingresR pppp = (38)

Outflow from node:

whflowlinesep ppp =+ (39)

The effect of increasing the tubing size, as long as the tubing is not too

large, is to give a higher node or wellhead pressure for a given flow rate,

because the pressure drop in the tubing will be decreased. This shifts theinflow curve upward and the intersection to the right.

A larger flowline will reduce the pressure drop in the flowline, shifting the

outflow down and the intersection to the right. The effect of a change in any


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component in the system can be isolated in this manner. Also, the effect of

declining reservoir pressure or changing separator can be determined.

A more frequently used analysis procedure is to select the node

between the reservoir and piping system. The inflow and outflow

expressions for the simple system will then be:

Inflow to node:

wfresR ppp = (40)

Outflow from node:

wftubingflowlinesep pppp =++ (41)

A producing system may be optimized by selecting the combination of

component characteristics that will give the maximum production rate for the

lower cost. Although the overall pressure drop available for a system,

sepR pp , might be fixed at a particular time, the producing capacity of the

system depends on where the pressure drop occurs. If too much pressure

drop occurs in one component or module, there may be insufficient pressure

drop remaining for efficient performance of the other modules.

Even though the reservoir may be capable of producing a large amount

of fluid, if too much pressure drop occurs in the tubing, the well performance

suffers. For this type of well completion, it is obvious that increasing

reservoir performance by stimulation would be a waste of effort unless

larger tubing were installed.

If tubing is too large, the velocity of the fluid moving up the tubing may

be too low to effectively lift the liquids to the surface. This could be caused

by either large tubing or low production rates.The fluid velocity is the

production rate divided by the area of the tubing.


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As tubing size is increased, the friction losses decrease, which results in

a lower wfp and, therefore, a larger inflow. However, as the tubing size is

further increased, the well begins loading with liquid and the flow becomes

intermittent or unstable. As the liquid level in the well builds the well will

eventually die.

Once a well that is producing liquids along with the gas reaches the

stage in which it will no longer flow naturally, it will usually be placed on

artificial lift.

The nodal systems analysis approach may used to analyze many

producing oil and gas well problems. The procedure can be applied to both

flowing and artificial lift wells, if the effect of artificial lift method on the

pressure can be expressed as a function of flow rate. The procedure can

also be applied to the analysis of injection well performance by appropriate

modification of the inflow and outflow expressions. A partial list of possible

applications is given as follows2:

1. Selecting tubing size

2. Selecting flowline size

3. Gravel pack design

4. Surface choke sizing

5. Subsurface safety valve sizing

6. Analyzing an existing system for abnormal flow restrictions

7. Artificial lift design

8. Well stimulation evaluation

9. Determinig the effect of compression on gas well performance

10. Analyzing the effects of perforating density

11. Predicting the effect of depletion on producing capacity

12. Allocating injection gas among gas lift wells13. Analyzing a multiwell producing system

14. Relating field performance to time


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3.2 Application of Nodal Analysis to Electrical Submersible Pumping

Wells

To perform a nodal analysis on a submersible pumping well, the node is

selected at the pump. The pump can be handled as an independentcomponent in the system in a manner similar to that used in gravel-packed

completions. The node pressure is either the pump intake pressure upp or

the pump discharge pressure dnp . The pressure gain that the pump must

generate for a particular producing rate is updn ppp = . The pressure

traverse below the pump will be calculated based on the formation

gas/liquid ratio and the casing size. The traverse in the tubing above the

pump will be based on the gas/liquid ratio entering the pump and the tubingsize. The inflow and outflow expressions are2:

Inflow:

upcsgresR pbelowpumpppp = )(

Outflow:

(tubflowlinesep ppp ++ dnpabovepump =)

The following procedure may be used to estimate the pressure gain and

power required to achieve a particular producing capacity.

Inflow:

1. Select a value for liquid producing rate Lq .

2. Determine the required wfp for this Lq .using the reservoir performance

procedures.

3. Determine the pump suction pressure upp using the casing diameter and

the total producing GLR to calculate the pressure drop below the pump.

4. Repeat for a range of liquid producing rates and plot upp versus. Lq .


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Outflow:

1. Select a value for Lq .

2. Determine the appropriate GLR for tubing and flowline pressure drop

calculations.

a. Determine upp and fluid temperature at the pump at this Lq value from

inflow calculations.

b. Determine dissolved gas sR at this pressure and temperature.

c. Estimate fraction of free gas sE , separated at the pump. This will be

dependent whether or not a downhole separator is to be used. If not use

5.0=sE .

d. Calculate the GLR downstream of the pump from

))(1( sototalsdn RfREGLR = = (42)

where:

=totalR total producing gas/liquid ratio,

sR = solution gas/oil ratio at suction conditions, and

=of fraction of oil flowing

3. Determine dnp using GLRdn to calculate the pressure drop in the tubing

and the flowline if the casing gas is vented. If the casing tied into the

flowline, the total GLR will be used to determine the pressure drop in the

flowline.

4. Repeat for a range of Lq and plot dnp vs Lq on the same graph.

5. Select various producing rates and determine the pressure gain prequired to achieve an intersection of the inflow and outflow curves at

these rates. The suction and discharge pressures can also be

determined for each rate.


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6. Calculate the power requirement, pump size, number of stages, etc., at

each producing rate.

The required horsepower can be calculated from:

)(1072.15

wwoo BqBqpHP += (43)

where:

HP = horsepower required

p = pressure gain, psi

qo = oil rate, STB/day

qw = water rate, STB/day

Bo = oil formation volume factor at suction conditions, bbl/STB, and

Bw = water formation volume factor at suction conditions

The pressure gain can be converted to head gain if necessary for pump

selection. This is accomplished by dividing the pressure gain by the density

of fluid being pumped. The actual plotting of the data is not required if the

pump is to be selected for specific rates, as all the necessary information is

calculated before plotting.

3.3 Description of the Computer Program

3.3.1 Pumping Only Liquid

A two-stage computer program in Fortran Code has been written and

also EXCEL Worksheet was used to support the program.

At the first stage, program input consists of well, fluid, reservoir, and lift-system data. Once these conditions were satisfied, program initially gives

the pressure at pump setting depth (discharge pressure) by applying

Hagedorn and Brown3 vertical multiphase correlation. In addition to


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Code has been written and also EXCEL Worksheet was used to support the

program. Input parameters of the program are same with pumping only

liquid program, however, GOR value should be entered since free gas

exists. At first stage, program calculates VF at pressure interval between

200 5000 psi. Afterwards, by following same steps with pumping onlyliquid program, discharge pressure is calculated by Hagedorn and Brown3

Vertical Multiphase Flow Correlation (existing as a subprogram in the

algorithm) and program starts to make iterations by decreasing pressure 50

psi at every iteration in order to calculate volume (h), h (head per stage) and

number of stage (St) values at desired production rate. As explained

previously, program computes Griffith4 Correlation when bubble flow

conditions were formed. Program then calculates the intake pressure at

various numbers of stages to let us construct tubing intake curve on the

same graph as the IPR curve. At the second stage of the program, user

should again enter possible production rates to programs, which are

obtained manually by intersecting intake curve and IPR curve. This

procedure cannot be achieved by program as explained before. At this

point, program starts to make iterations to calculate horsepower per stage

and total horsepower requirement at every 50 psi pressure drop until it

reaches to intake pressure. This data will help us to construct Possible

Production Rate versus Stages and Horsepower Figure in order us to make

necessary evaluation. It should be kept in mind that pump selection is

achieved manually by entering to input, in other words program does not

include an algorithm that automatically selects a suitable pump for that well.


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CHAPTER IV

STATEMENT OF THE PROBLEM

The objective of this study is to perform a production engineering

study at GK oil field in Southeastern Turkey. The main goal of the study is to

achieve production optimization of 10 electrical submersible pump lifted

wells currently operating in this field. Desired conclusion will be reachedafter determining the optimum pump stages and horsepower requirement

for a possible production rate by a theorotical study and compare it with

actual field submersible pump operating data. The study will let us to

suggest optimum submersible pump running conditions for each well to

continue production in a more economical and cost saving approach.

Following steps were considered during the study to reach the aim:

writing computer program that applies vertical multiphase flow

correlation and computes the parameters that were required for the

optimization

collecting and evaluating the actual reservoir, well, fluid and lifting

data that the case study was performed

entering field data to computer program and taking the output for

two pumping conditions


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preparing necessary figures and charts concerning pump stages,

production rate and horsepower requirement using the computer

output

comparison of actual field values and theorotical values and

making necessary suggestions


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CHAPTER V

HAGEDORN AND BROWN VERTICAL MULTIPHASE FLOW

CORRELATION SUPPORTED BY GRIFFITH CORRELATION

5.1 Introduction

The use of multiphase flow pipeline pressure drop correlations is very

important in applying nodal analysis.

The correlations that are most widely used at the present time for

vertical multiphase flow are as follows:

1. Hagedorn and Brown3

2. Duns and Ros10

3. Ros and Gray11

4. Orkiszewski12

5. Beggs and Brill13

6. Aziz14

These are found to calculate pressure drop very well in certain wells

and certain fields. However, one may be much better than the other under

certain conditions and field pressure surveys are the only way to find out.

Without any knowledge in a particular field, it would be recommended

beginning initial work with the correlations as listed in the above order.

In the literature it is recommended to from a hybrid by using the most

dependable parts of the four models. As an example, the commercial

vertical multiphase flow model (MTRAN) that was developed by Scientific

Software Incorporation uses the following sections:


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1. Duns and Ros10 flow map

2. Use Orkiszewski12 for bubble flow

3. Use Hagedorn and Brown3 for slug flow

4. Use Duns and Ros10 for transitional and mist flow

Figure 5.1 illustrates the schematic diagram of possible flow patterns in

two-phase pipelines to visualize the flow systems that above correlations

used for.

Figure 5.1 Schematic Diagram of Possible Flow Patterns in Two-PhasePipelines6


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5.2 Hagedorn and Brown Method

The Hagedorn and Brown3 method was developed by obtaining

experimental pressure drop and flow rate data from a 1500 ft deep

instrumented well. Pressures were measured for flow in tubing sizes ranging

from 1 to 2 7/8 in O.D. A wide range of liquid rates and gas/liquid ratios

was included, and the effects of liquid viscosity were studied by using water

and oil as the liquid phase. The oils used had viscosities at stock tank

conditions of 10, 35 and 110 cp. Later two adjustments were made to

improve this correlation. When bubble flow existed, the Griffith4 Correlation

was used and when the no slip holdup was greater than the holdup value,

the no slip holdup was used2.

Neither liquid holdup nor flow pattern was measured during the

Hagedorn and Brown study, although a correlation for the calculated liquid

holdup is presented. The correlations were developed by assuming that the

two-phase friction factor could be obtained from the Moody diagram based

on a two-phase Reynolds number. This Reynolds Number requires a value

for LH in the viscosity term.

The Hagedorn and Brown method has been found to give good

results over a wide range of well conditions and is one of the most widely

used well flow correlations in the industry2

. However, the original Hagedornand Brown correlation has several weaknesses: At first, it is not very

accurate in bubble flow. Moreover, calculated slip holdup is sometimes

below no-slip holdup and also the acceleration term is too dominant.

Thompson added that, the modified Hagedorn and Brown Correlation

tended to overpredict pressure loss in bubble flow (Griffith), while it tended

to underpredict slug flow. The Hagedorn and Brown Correlation gives best

results for wellbores with low to moderate liquid volume fractions (high gas-

liquid ratios) and relatively high mixture velocities (annular-mist or frothflow).

The selection of appropriate correlation for a given production system

is important to reach to an accurate solution. In this study, Hagedorn and


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40

psi. This type of calculation is practically forbidden by long hand but lends

itself readily to machine computation. If starting from bottom with pressures

in excess of 1,000 psi, the pressure decrements may be as great as 200

psi.

2. Calculate the specific gravity of the oil, o:

o=API+5.1315.141

(47)

3. Find total mass associated with one bbl of stock tank liquid:

m = o (350) (WOR+11 ) + w (350) (

WOR

WOR

+1) + (0.0764) (GLR) g (48)

4. Calculate the mass flow rate:

w = q m (49)

5. Obtain Rs at P and T by Standings16 Correlation :

Rs = g ( )(00091.0

)(0125.0

10

10

18 T

APIP )1/0.83 (50)

where Rs = scf/bbl

Lasaters17 equation can also be used and it is more accurate than

Standings correlation especially at higher API. The equation of Lasaters

correlation is as follows:


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Rs = CY

Y

M g

g

o

o )1

)())(350)(3.379(

(

(51)

where:

Mo = molecular weight

T = R

The value of C is 1.0 unless a correction factor is necessary to make the

equation check with actual field cases.

6. Obtain Bo according to calculated Rs value:

a) If bPP :

TRFo

g

s 25.1)(5.0 +=

(52)

175.1000147.0972.0 FBob += (53)

b) If bPP

))(( PPc

oboboeBB

= (54)

7. Calculate the density of liquid phase:

L = [ ] [ ])1

)(4.62()1

1(614.5/)0764.0()4.62(

WOR

WOR

WORB

Rw

o

gso

++

++ (55)


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8. Assuming T= constant, find a value ofZ for a constant T, p and g. If

T is to be a variable, then a single trial and error solution develops.

Although the temperature gradient may be known, the depth at which

the pressure increment occurs is not known and, therefore, the

temperature at the next pressure point is not known.

4.688852.17292.17 2 += ggpcP (56)

94.17293.3088324.1 2 ++= ggpcT (57)

pcpr P

P

P = (58)

pc

prT

TT = (59)

101.036.0)92.0(39.1 5.0 = prpr TTA (60)

6

))1(9(

2 )10

32.0()037.0

)86.0(

066.0()02362.0( prTpr

pr

prpr PPT

PTBpr

+

+= (61)

)log(32.0132.0 prTC = (62)

)1824.049.03106.0( 2

10 prprTT

D+= (63)

a) If 100B


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D

prBCP

e

AAz +

+=1

(64)

b) If 100B

D

prCPAz += (65)

9. Calculate the average density of the gas phase

g = )1

)(520

)(7.14

)(0764.0(ZT

pg (66)

10. Calculate the average viscosity of the oil from appropriate correlations.

As noted, a knowledge of fluid properties of the oil, p , and / or T is

required.

a) If bPP

)04658.09824.6(163.1 APIeTX = (67)

110 = XoD (68)

515.0)100(715.10+= sRA (69)

338.0)150(44.5

+= sRB (70)

B

oDo A = (71)

b) Ifb

PP

)(

143

2 PCCC

ePCB+= (72)


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where:

C1 = 2.6

C2 = 1.187

C3 = -11.513

C4 = -8.9810-5B

oDb A =

B

b

boP

P)( = (73)

where:

b = viscosity of the reservoir liquid at the bubble point, cp

oD = dead oil viscosity, cp

11. Determine the average water viscosity from correlation below:

)10982.110479.1003.1( 252 TT

W e += (74)

12. Calculate the liquid mixture viscosity:

L = o +

+ WOR11

w

+ WORWOR

1(75)

This can only be an approximation since the viscosity of two immiscible

liquids is quite complex.

12. Assuming constant surface tensions at each pressure point, calculate

the liquid mixture surface tension.


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L = o (WOR+11

) + w (WOR

WOR

+1) (76)

Again, this represents only an approximation of the surface tension of

the liquid phase.

13. Calculate the liquid viscosity number:

NL = 0.15726L( 31

LL)1/4 (77)

14. Determine CNL from the previously formed equation of CNL versus NL

graph.

002.002.08612.0069.1022.4804.106222.87 23456 ++++= LLLLLLL NNNNNNCN (78)

15. Calculate the area of tubing, Ap.

Ap =4

2d(79)

16. Obtain Bo at Tp,

17. Assuming Bw = 1.0, calculate the superficial liquid velocity sL , ft/sec:

sL =

+

++

)1()

1

1(

86400

61.5

WOR

WORB

WORB

A

qwo

p

L (80)

18. Calculate the liquid velocity number, NLV:


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NLV = 1.9384/1)(

L

LsL

(81)

19. Calculate the superficial gas velocity, sg :

sg =

+

1520

7.14

86400

1

1

ZT

pA

WORRGLRq

p

sL

(82)

20. Determine the gas velocity number, NGV:

NGV =1.938 sg

4/1

L

L

(83)

21. Find the pipe diameter number, Nd:

Nd = 120.872dL

L

(84)

22. Calculate the holdup correlating function :

=

d

L

gV

LV

N

CNp

N

N10.0

575.0 7.14 (85)

23. Obtain

LH from the correlation determined before:

LH = 11.02.182310210103104102 2639411513615 ++++ (86)


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24. Determine the secondary correction factor correlating parameter, :

=

14.2

380.0

d

Lgv

N

NN(87)

25. Obtain from the previously formed equation of versus graph.

= 7611.112.15710765300129104103108 23465767 +++ (88)

26. Calculate a value for HL:

HL = [ ]

LH (89)

For low viscosities there will be no correction and = 1.00.

27. In order to obtain a friction factor, determine a value for the two-phase

Reynolds number, (NRe)TP:

))()((

102.2)(

)1(

2

ReLL H

g

H

L

TPd

wN

=

(90)

28. Determine a value for/d. If the value of is not known, a good value to

use is 0.00015 ft which is an average value given for commercial steel.

29. Obtain the friction factor from the Jain18 Equation:

)25.21

log(214.11

9.0

ReNdf+=

(91)


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30. Calculate the average two-phase density of the mixtures m by two

methods.

(a) Using the value of HL, calculate m as follows:

m = )1( LgLL HH + (92)

(b) Calculate a value of m assuming no slippage.

31. Calculate the two-phase mixture velocity at both p1 and p2.

m1=sL1+sg1 (93)

m2=sL2+sg2 (94)

32. Determine a value for (m2)

(m2) = [ ]2 221 mm (95)

33. Calculate h corresponding to p = p1 p2

h =

m

m

c

m

m

d

fw

gp

511

2

2

109652.2

)2(144

+

(96)

34. Starting with p2 and the known depth at p2, assume another pressure

point and repeat the procedures until reaching total depth, or until reaching

the surface depending upon whether you are starting from the bottom or top

of tube.


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5.4 GRIFFITH CORRELATION (BUBBLE FLOW)

The void fraction of gas (Hg) in bubble flow can be expressed as:

Hg=

++

ps

g

ps

t

ps

t

Av

q

Av

q

Av

q 4)1(1

2

1 2 (97)

where :

vs = slip velocity (bubble rise velocity), ft/sec

Griffith suggested that a good approximation of an average vs is 0.8

ft/sec. The average flowing density can be computed as:

= gggL HH + )1( (98)

The friction gradient is:

hcLLf dgvf 2/2

= (99)

where:

[ ])1( gpL

LHA

q

= (100)

The Reynolds number is calculated as:

L

LhL vdN

1488Re = (101)

where:


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dh = hydraulic pipe diameter, ft

L = liquid viscosity, cp

Vertical pressure gradient curves (for three different reservoir

conditions) obtained from the computer program by following the above

steps were given at Chapter 7.


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CHAPTER VI

DESCRIPTION OF THE GK FIELD

6.1 Introduction

The selected field is located on South East Anatolian. The field was

discovered in 1961 and has been on production since then. Currently, there

are a total of 29 wells with 12 producers, 13 closed-in, 2 dumpflooders and2 injection wells. The main drive mechanism of the field is rock and fluid

expansion, there also exists a weak aquifer at the system but not sufficient

to create a producing force.

The field started its production life as a dry and natural flowing field. A

steep pressure decline in wells was observed during late 1961 and early

1962. It was decided that the field pressure should be maintained by water

injection through peripheral wells 3 and 5 on the Eastern and Western

flanks of the field to keep the production wells on natural flow. In 1966,water cut increased and killed natural flow. In 1967, as a result of high field

offtake, pressure in producers began to decline rapidly. Thus, in August

1967, water injection was stopped to observe production declines in the field

and artificial lift system was installed. After realising that recovery is

constrained by pressure decline rather than the watercut development in

1986 dumpflooding started. In June 1997 from two wells re-injection

started19.


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6.2 Geology

The field is an elongated structure in an approximate EastWest

direction. Up to date 29 wells have been drilled and two wells are located

outside the field (Well-9 and Well-10). The field is a frontal thrust structureconsisting of an anticline on the leading edge of the thrust block. The

reservoir rock has been divided into Mardin Units, I, II, III and IV. These

units are further subdivided based on lithology (limestone and dolomite) and

porosity classes.

There is a main continues East-West trending normal fault. This main

fault separates two blocks as Main Block and Northern Block and there is an

another block called Western Block. The unique pressure response of the

W-14 with respect to the rest of the field (pressure measured in W-14

showed slight depletion of only a few hundred psi, when the average

reservoir pressure in the rest of the field was more than 1000 psi) may show

the existence of a barrier between W-14 and W-11 due to either a fault or

reservoir rock quality deterioration (a permeability barrier) between those

wells. The reservoir deterioration between the wells on the other hand, can

not be confirmed due to shallow completion of the W-11 which prevents the

correlation of two wells because of the long distance between these two

wells, the deterioration of the reservoir quality is still quite possible.

The units having the highest porosities are the dolomite in Unit I and the

high porosity limestone close to the bottom of the Unit II. The average

porosities of this dolomite unit varies between 15% and 20% and the

average permeabilities between 6 mD-50mD based on core measurements.

Intercrystalline and vuggy porosities, and some solution channels and

fractures were also observed on the core samples.

Unit II is described as limestone-dolomitic limestone. Cores indicated

that it has vuggy porosity and solution channels, and some sub-vertical/sub-

horizontal fractures also exist. The average porosity is 10%-15% with air

permeabilities between 0.3 mD-1.5 mD based on core measurements.


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54

TABLE 6.2 SUBMERSIBLE PUMP LIFTED WELLS OPERATED IN

GK FIELD AND THEIR EFFICIENCY RANGES

WELL PUMP USEDEFFICIENCY

RANGE (bbl/d)

W-07 DN440 83 - 458

W-08 DN675 267 - 692

W-15 GN2000 1300 - 2650

W-16 GN1600 833 - 1792

W-17 GN1600 833 -1792

W-22 DN440 83 - 458

W-24 DN1100 500 - 1125

W-25 GN3200 1834 - 3417

W-27 DN675 267 - 692

W-28 DN675 267 - 692

6.4 Production History

Production rates and bottomhole pressures recorded for the producer

wells between the years 1961 and 1999 gives the generalized IPR curve

showed in Figure 6.1. This figure is the combination of 66 well test data from

12 different producer wells and by inspecting the figure, it can be observed

that the (qo)max is 1378 bbl/d or 1385 stb/d and flow rate at bubble point

pressure, (qo)b, is 1340 bbl/d or 1347 stb/d.


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0

500

1000

1500

2000

2500

3000

0 200 400 600 800 1000 1200 1400 1600

q (BBL/D or STB/D)

Pwf(psi)

BBL/D

STB/D

Figure 6.1 Generalized IPR Curve

The gross rate of each submersible pump lifted producer well during

the production period and required pump stages used in the field are given

in Table 6.3.


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TABLE 6.3 GROSS PRODUCTION RATE OF THE WELLS IN GK FIELD

AND REQUIRED PUMP STAGES

Well Gross Rate (bbl/d) Pump Stages

W-07 180 356

W-08 740 238

W-15 1180 216

W-16 1350 180

W-17 1270 181

W-22 70 320

W-24 1000 332

W-25 1620 239

W-27 400 338

W-28 530 338


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CHAPTER VII

RESULTS AND DISCUSSION

7.1 INTRODUCTION

Calculations are based on the steps that are summarized in Chapter 2

at sections 2.3.1.1 for pumping liquid and 2.3.2.4 for pumping liquid and

gas. These calculations were done for the 10 submersible pump lifted wellsindicated in Table 6.2 and by using the pumps that were actually operated in

the GK field. Detailed sample calculation for W-08 and the output of

computer program can be observed in Appendix B.

Results of the study can be categorized into five different parts:

a. Construction of vertical flowing pressure gradient (pressure traverse)

curves according to computer program output and comparing theresults with Beggs&Brill13 Correlation

b. Performing Sensitivity Analysis based on effect of of oil density, GLR

and WOR on flowing bottomhole pressure by using the computer

program output

c. Construction of possible production rate versus stage and

horsepower chart for each well (GLR = 15 scf / STB) by using the

pumping liquid and gas computer algorithm

d. Comparison of theoretical and actual production parameters andsuggestion for optimum pump operating conditions by inspecting

possible production rate versus stage and horsepower chart


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59

100400 300

500

0200

GAS-LIQ

UIDRATIO

,scf/STB

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

0 400 800 1200 1600 2000 2400 2800 3200 3600 4000

Pressure (psi)

Depth(ft)

Tubing Size, in : 2.441

Liquid Rate, STBL/D : 100Water Fraction : 0

Gas Gravity : 0.70

Oil API Gravity : 38

Water Specific Gravity : 1.02

Average Flowing Temp., F : 170

Correlation : Hagedorn&Brown

Griffith Correlation (bubble flow)

Figure 7.1 Pressure Traverse Curve (WC = 0)


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60

1002000

500

300400

GAS-LIQ

UIDRATIO

,scf/STB

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

0 400 800 1200 1600 2000 2400 2800 3200 3600 4000 4400

Pressure (psi)

Depth(ft)

Tubing Size, in : 2.441

Liquid Rate, STBL/D : 100Water Fraction : 0.5

Gas Gravity : 0.70






Figure 7.2 Pressure Traverse Curve (WC = 0.5)


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500

400 300

200 100 0

GAS-LIQ

UIDRATIO

,SCF/S

TBL

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

0 400 800 1200 1600 2000 2400 2800 3200 3600 4000 4400 4800

Pressure (psi)

Depth(ft)

Tubing Size, in : 2.441Liquid Rate, STBL/D : 100

Water Fraction : 1.0

Gas Gravity : 0.70






Figure 7.3 Pressure Traverse Curve (WC = 1.0)


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A comparison was made between pressure traverse curves prepared

by Beggs&Brill13 and curves constructed with computer output in order to

test the accuracy of correlation used in the program algorithm. Table 7.1

briefly indicates the pressures at selected depths with respect to two

conditions. Inspecting Table 7.1, we can understand that computer-basedpressures and the Beggs&Brill correlation values are very close to each

other. This means that vertical multiphase flow correlation within the

program is giving reliable output and encurages us about the accuracy of

rest of the study. It should be kept in mind that values determined from

Beggs&Brill correlation are recorded at slightly different reservoir and fluid

conditions than GK field parameters, that is, gas gravity is 0.65, oil API

gravity is 35 and average flowing temperature is 150 F. Another point that

should be taken into account during the comparison is that when GLR

increases, difference between pressure values of computer output and

Beggs&Brill values are also increases. This behaviour can be interpreted as

reliability of Hagedorn and Brown flow correlation supported by Griffith

Correlation should be re-tested at high GLR reservoirs.


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TABLE 7.1 COMPARISON of COMPUTER-BASED VERTICAL FLOWING PRESSUR

BEGGS&BRILL CORRELATION AT SELECTED DEPTHS

Water Fraction

0 0.5

GLR (scf/STB) GLR (scf/STB) GLR (

0 100 0 100 0

Pressure (psi) Pressure (psi) Press

Depth (ft) Output Beggs&Brill Output Beggs&Brill Output Beggs&Brill Output Beggs&Brill Output Beggs&Brill

4000 1440 1400 1050 1040 1590 1600 1220 1140 1680 1800

6000 2160 2090 1770 1750 2380 2400 2040 1960 2560 2720

8000 2870 2800 2480 2440 3190 3190 2820 2750 3440 3610

10000 3580 3500 3190 3130 3985 4000 3610 3560 4320 4540


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7.2.2 Sensitivity Analysis by Using the Computer Program Output

Having a chance of changing all variables related to Hagedorn and

Brown vertical multiphase flow correlation within the program, sensitivity

analysis was performed by observing the effect of oil density, GLR andWOR on flowing bottomhole pressure. Results were summarized in Table

7.2, 7.3 and 7.4. Reservoir and fluid data of W-08 was used during the

study. After making necessary observations for the output, it can be

observed that the increase in oil density and GLR creates a slight decrease

in bottomhole pressure, and an increase in WOR causes an increase in

flowing bottomhole pressure.

TABLE 7.2 EFFECT of OIL DENSITY on FLOWING BOTTOMHOLE

PRESSURES AT SELECTED DEPTHS

Well Depth (ft)

API4000 6000 8000 10000

10 2000 2880 3760 4620

15 2000 2880 3760 4620

20 1990 2870 3760 4610

25 1990 2870 3750 4610

30 1990 2870 3750 4610

35 1990 2870 3750 4600

40 1990 2870 3740 4600


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GLR=0 scf/stbl

GLR=100

GLR=200GLR=300

GLR=400GLR=500

IPR

0

500

1000

1500

2000

2500

3000

0 200 400 600 800 1000 1200

q (BBL/D or STB/D)

Pwf(psi) BBL/D

STB/D

Figure 7.4 Graphical Analysis of Effect of GLR on Flowing

Bottomhole Pressure for W-08

WOR=0.5

IPR

WOR =0

WOR=1.0

0

500

1000

1500

2000

2500

3000

0 200 400 600 800 1000 1200

q (BBL/D or STB/D)

Pwf(psi)

BBL/D

STB/D

Figure 7.5 Graphical Analysis of Effect of WOR on Flowing

Bottomhole Pressure for W-08


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7.2.3 Construction of Possible Production Rate versus Stage

and Horsepower Chart for GK Field Wells by Using

the Pumping Liquid and Gas Computer Algorithm

Possible production rate versus stage and horsepower chart wasprepared for each electrical submersible pump lifted wells in GK field by

considering the intake pressures obtained from computer program at

selected flow rates. These charts can said to be the final step of the study

and helped us to make necessary suggestions for optimum pump operating

conditions. In below figures, actual value point is the real production rate of

the well in GK field and the number of pump stages used for that well. It

should be noted that actual horsepower requirement data for these wells

are not available. On Figures 7.6 to 7.14, the efficiency range of the pumps

used and also suggested flow rate and corresponding horsepower

requirement and number of pump stages can be observed.


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HP

Stages

Efficiency Range

Actual

Suggested HP

0

50

100

150

200

250

300

350

400

450

500

550

600

0 50 100 150 200 250 300

Stages or Horsepower

PossibleRate(STB/D)

FIGURE 7.6 Possible Production Rate vs Stages and Horsepower fo


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69

HP

Effic

Stages

Actual Value (St)Suggested HP

Suggested Stage

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

13001400

0 50 100 150 200 250 300


Pos

sibleRate(STB/D)

FIGURE 7.7 Possible Production Rate vs Stages and Horsepower


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70

HP

Efficiency Range

Stages

Actual Value(St)

Suggested Stage

Suggested HP

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

0 100 200 300 400 500 600


PossibleRate(STB/D)

FIGURE 7.8 Possible Production Rate vs Stages and Horsepower for


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HP

Efficiency RaActual Value (St)

Suggested HP Suggested Stage

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 100 200 300 400


PossibleRate(STB/D)

FIGURE 7.9 Possible Production Rate vs Stages and Horsepower for


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72

HP

Stages

Actual Value (St)

Suggested HP Suggested Stage

0

200

400

600

800

1000

1200

1400

1600

1800

0 100 200 300 400


Possib

leRate(STB/D)



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73

HP

Efficiency Range

Suggested HP

Suggested Stage

0

200

400

600

800

1000

1200

1400

1600

1800

0 50 100 150 200 250 300


Possib

leRate(STB/D)



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HPStages

Efficiency Range

Actual Value(St)

Suggested HP

Suggested Stage

0

500

1000

1500

2000

2500

3000

3500

0 100 200 300 400 500


PossibleRate(STB/D)



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Efficiency Range

Suggested Stage

Suggested HP

0

100

200

300

400

500600

700

800

900

1000

1100

1200

1300

1400

0 50 100 150 200 250 300Stages or Horsepower

PossibleRate(STB/D)



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Efficiency Range

Actual VaSuggested HP

Suggested Stage

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400

0 50 100 150 200 250 300


Possib

leRate(STB/D)



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W-17 is operated with 1270 stb/d with 181 stages. This rate indicates

that the pump is used efficiently (833-1792 bpd). Besides, observing Figure

7.9, operating production rate and pump stage values are said to be at

optimum range, and the actual and theoretical values are close to each

other. Thus, a production rate of 1400 stb/d and a corresponding HPrequirement of 100 HP and 220 pump stages can be offered in theorotical

circumst

production system optmization for submersible pump lifted wells a case study

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