Optimization for submersible pump

PRODUCTION SYSTEM OPTIMIZATION FOR SUBMERSIBLE PUMP

LIFTED WELLS : A CASE STUDY

A THESIS SUBMITTED TO

THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES

OF

THE MIDDLE EAST TECHNICAL UNIVERSITY

BY

NURİ OZAN GÜLER

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

IN

THE DEPARTMENT OF PETROLEUM AND NATURALGAS ENGINEERING

APRIL 2004

Approval of the Graduate School of Natural and Applied Sciences

Prof . Dr. Canan ÖZGEN

Director

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

Master of Science.

Prof. Dr. Birol DEMİRAL

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 Bağcı

Supervisor

Examining Committee Members

Prof. Dr. Birol DEMİRAL (Chair Person)

Prof. Dr. A. Suat BAĞCI

Prof. Dr. Fevzi GÜMRAH

Prof. Dr. Mustafa V. KÖK

Prof. Dr. Nurkan KARAHANOĞLU

iii

ABSTRACT

PRODUCTION SYSTEM OPTIMIZATION FOR SUBMERSIBLE

PUMP LIFTED WELLS : A CASE STUDY

GÜLER, Nuri Ozan

M.S. Department of Petroleum and Natural Gas Engineering

Supervisor: Prof. Dr. A. Suat Bağcı

April, 2004, 173 Pages

A computer program has been written to perform production

optimization in submersible pump lifted wells. Production optimization was

achieved 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 the

program 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.

iv

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

Diyarbakır-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.

v

ÖZET

DALGIÇ POMPALARLA ÜRETİMİ YAPILAN KUYULARIN SİSTEM

OPTİMİZASYONU: ÖRNEK SAHA ÇALIŞMASI

GÜLER, Nuri Ozan

M.Sc., Petrol ve Doğal Gaz Mühendisliği Bölümü

Danışman: Prof. Dr. A. Suat Bağcı

Nisan, 2004, 173 Sayfa

Dalgıç pompalarla üretim yapılan kuyuların optimizasyonu için

bilgisayar programı yazılmıştır. Üretim optimizasyonu Nodal Analizi

Tekniğiyle gerçekleştirilmiş ve rezervuar ile kuyubaşı arasında, kuyubaşı

sonrası yüzey donanımı ve separatör dikkate alınmadan uygulanmıştır.

Program iki üretim ortamına göre yazılmıştır, bunlar: sadece sıvı ile hem sıvı

hem gaz üretim ortamlarıdır. Bu bilgisayar programı, sözü edilen sıvı ile gaz

pompalanması sırasındaki pompa emiş ve çıkış basıncı arasında sistemdeki

gaz’dan dolayı oluşan sıvı hacmi değişimlerinin hesaplamasında ortaya

çıkan iterasyonların çözümü açısından önemli bir rol oynamaktadır.

Programda istenilen derinlikteki basınç değerlerini hesaplamak amacıyla

Hagedorn ve Brown korelasyonu kullanılmıştır. Hagedorn ve Brown

Korelasyonunun yetersiz kaldığı akış rejimlerinde Griffith Korelasyonu

kullanılarak sonuca ulaşılmıştır.

vi

Yazılan bu programın pratiğe geçirilmesi açısından Diyarbakır – GK

sahasındaki dalgıç pompalarla üretim yapılan 10 kuyu incelemeye

alınmıştır. Bu kuyuların rezervuar, akışkan ve üretim verileri hazır olan

bilgisayar programına aktarılmıştır. Daha önce belirtilen iki pompalama

ortamını kapsayan bu programın çıktısı optimum üretim debisi, gereken

beygirgücü ve pompa kademe sayısının belirlenmesi için kullanılmıştır. Bu

hesaplamalarda hassas değişken olarak pompa kademe sayısı seçilmiştir.

Çalışmanın sonunda GK sahası verileri ile programdan çıkarılan optimize

değerler karşılaştırılmış ve dalgıç pompalarla üretim yapılan 10 kuyudan

3’ünün: W-16, W-17, ve W-24’ün optimum değer sınırları içerisinde üretim

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

değerler içerisinde olmasa bile kabul edilebilir ve geçerli sayılabilir

sınırlarda üretim yaptığı, 1 kuyunun, W-22, optimum sınırlar dışında ve

verimsiz bir şekilde üretime devam ettirildiği saptanmıştır. W-15’in verileri

herhangi bir yorum yapmak için yetersiz kalmıştır.

Kelimeler: Üretim optimizasyonu, sistem analiz tekniği, dalgıç pompa, yapay

üretim, Hagedorn ve Brown Korelasyonu, Griffith Korelasyonu

vii

To my family,

Çiğdem, Yurdahan and Sanem Güler

viii

ACKNOWLEDGEMENTS

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

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

Turkse Perenco for their cooperation.

ix

TABLE OF CONTENTS

ABSTRACT ……………………………………………………………….. iii

ÖZET ………………………………………………………………….…… 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

x

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

xi

5. HAGEDORN AND BROWN VERTICAL

MULTIPHASE FLOW CORRELATION

SUPPORTED BY GRIFFITH CORRELATION ……….. 36

5.1 Introduction ……………………………………….. 36

5.2 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

6.1 Introduction ……………………………………….. 51

6.2 Geology …………………………………………… 52

6.3 Reservoir, Fluid, and Lift System

Properties …………………………………………. 53

6.4 Production History ……………………………….. 54

7. RESULTS AND DISCUSSION …………….…………… 57

7.1 Introduction ……………………………………….. 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

xii

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 ……………….…….. 67

7.2.4 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

xiii

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 Bottomhole

Pressures at Selected Depths…………………..….…… 65

xiv

7.5 Results Obtained After The Comparison

of Actual and Computer-Based Data

for GK Field ……………………………………………..… 79

D1 Well, Fluid, Reservoir and Lift-System

Data 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

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

xvi

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


Horsepower for W-08 ……………………………………. 69


Horsepower for W-16 ……………………………………. 70


Horsepower for W-17 ……………………………………. 71


Horsepower for W-22 ………………………………….… 72


Horsepower for W-24 ……………………………………. 73


Horsepower for W-25 ……………………………………. 74


Horsepower for W-27 ……………………………………. 75

xvii


Horsepower for W-28 ……………………………………. 76

D1 IPR Curve for W-08 ……………………………………… 131

D2 Intake Curves for W-08 ………………………………….. 162

D3 Possible Production Rate vs Stages and

Horsepower for W-08 ……………………………………. 172

xviii

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 number

NL liquid viscosity number

NLV liquid velocity number

(NRE)TP two-phase Reynolds number

xix

Symbol Description Unit

P pressure psi

q flow rate stb/d

Rs solution gas oil ratio scf/stb

St 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

µ viscosity cp

ν velocity ft/sec

ρ density lb/cuft

φ hold-up correlating function

ψ secondary correction factor

σ liquid surface tension dyne/cm

γ specific gravity

Subscription Description

b bubble point

dn pump discharge (downstream)

f fluid

g gas

xx

Subscription Description

l liquid

m mixture

o oil

pc 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

1

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 as

60,000 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

2

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. The

Nodal 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

3

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 bubble

flow. 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.

4

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 well’s 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

5

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 of

free gas are known to cause inefficient operation.

6

Figure 2.1 A Typical Submersible Pump Installation

7

Figure 2.2 Submersible Pump Schematic

Figure 2.3 Pressure Traverses for Pump on Bottom

8

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 in

Figure 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.

kjkjkjkjkj

9

kjkjkjkjkj

Figu

re 2

.3

A T

ypic

al P

ump

Per

form

ance

Cur

ve (G

N32

00)

Figu

re 2

.4

A T

ypic

al P

ump

Per

form

ance

Cur

ve (G

N32

00)5

10

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 Gf are 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 γ= (3)

but:

11

VWVf 350

)( =γ (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:

Vq

V fscscf 350

)(ρ

γ = (5)

Substituting equation 5 into 3 gives:

Vq

VG fscscf

ρ)

350433.0()( = (6)

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

standard conditions, or:

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

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

Substituting Equation 6 into Equation 1 gives:

dPVhV

qStd

fscsc )()

433.0350()(

ρ= (8)

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

between the intake and discharge pressures:

∫∫ =2

3)(

)433.0

350()(0

P

Pfscsc

St

dPVhV

qStd

ρ (9)

or:

12

∫=2

3)(

)3141.808(P

Pfscsc

dPVhV

qSt

ρ (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 ××= γ (11)

Substituting Equations 5 and 8 into the above equation gives:

=)(HPd ( dPVhVhp)()(

)433.01 (12)

The total horsepower requirement is obtained by integrating the above

equation between the intake and the discharge pressures:

∫∫ =2

)()(

)433.01()(

0

P

P

pHP

dPVhVh

HPd (13)

or:

13

∫=2

3)()(

)433.01(

P

P

p dPVhVh

HP (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

−=ρ

(15)

Solving Equation 15 for 3P gives:

14

Sth

PP fsc )3141.808

(23

ρ−= (16)

Equation 14 also can be integrated to give:

)()433.01( 32 PP

hh

HP p −= (17)

Substituting Equation 15 into the above equation yields:

SthHP fscpγ= (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 fscρ from Equation 7 (GLR=0) and fscγ 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 (ρfsch/808.3141).

15

(b) Determine the required discharge pressure from a pressure gradient

correlation.

(c) Assume various numbers of stages and, for each of these numbers,

calculate the intake pressure from Equation 16.

(4) Plot the intake pressures vs rate for each assumed number of stages on

the same graph as the IPR curve and to the same scale.

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

curve.

(6) For each rate, read the horsepower per stage from the pump

performance curves; then calculate the total horsepower requirement

from Equation 18.

(7) Plot the rates vs the number of stages and horsepower requirements.

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

(8) Select a suitable rate.

Whether pumping only liquid or pumping gas with the liquid, the selected

rate must satisfy the following criteria:

(a) Its volume range between the intake and the discharge pressures

must remain within the efficiency range of the pump.

(b) It must be economically feasible.

As the number of stages and, consequently, the production rate

increase, the effect of friction in the tubing string becomes significant,

causing the discharge pressure to increase. As a result, the gain in the

production rate per one stage continues to diminish until it becomes

insignificant.

16

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 any

pressure 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:

17

∫∫ +=2

3)()(

P

Psc

P

Psc b

b

dPVhV

qAdP

VhV

qASt (22)

where A = 808.3141/ρfsc = constant (23)

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

more convenient form as follows:

∑ ∑= =

∆+∆=m

i

n

mjj

j

j

sci

i

i

sc

PhV

qAP

hV

qASt

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

18

∆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

sci h

VqPA

St1

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

iii StSt

1)( (27)

where:

i

i

sci h

VqPA

St )()( 3∆=∆ (28)

19

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

i

i

sc hV

qPA

StSt )()( 311

∆=∆= (29)

In order to obtain P3,2, we have:

)()()(2

2

1

13212 h

VhV

qPA

StStStsc

+∆

=∆+∆= (30)

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

=nSt nStStSt )(...)()( 21 ∆++∆+∆ (31)

= )(( 3

scqPA∆

)...2

2

1

1

n

n

hV

hV

hV

+++ (32)

2.3.2.2 Determination of Horsepower

The horsepower requirement is obtained by integrating Equation

14 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

ii h

hpPHP

1

3 )433.0

( (33)

20

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

iii HPHP

1)( (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.

21

(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 follows6:

(1) Select a suitable pump as outlined previously.

(2) Calculate ρfsc 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 (A∆P3/qsc)

(c) Calculate 1,3P 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.

22

(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.

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 pipeline

networks 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

24

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

25

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

26

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 the

inflow 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

27

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.

28

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 wells

13. Analyzing a multiwell producing system

14. Relating field performance to time

29

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 independent

component 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 tubing

size. 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 .

30

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 ∆p

required 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.

31

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

each producing rate.

The required horsepower can be calculated from:

)(1072.1 5wwoo 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

32

Hagedorn and Brown Correlation, Griffith4 Correlation was also used at

bubble flow to obtain accurate results. Steps followed in the correlation can

be observed in details at Chapter 4. During this process, program takes Pwh

as initial pressure and calculates depth increment at every 10 psi pressure

increase (pressure interval was taken low to reach an accurate solution) and

finally stores the pressure (discharge pressure) when depth reaches to total

pump setting depth. After recording discharge value program simply

calculates intake pressures at assumed flow rates and number of pump

stages. Head per stage data was required during these calculations and this

was achieved by constructing equation of each pump performance curve

and transferring it to program. These intake pressures are necessary to

construct intake curves on the same graph as the IPR curve. At the second

stage of the program, user should enter possible production rates to

programs, which are obtained manually by intersecting intake curve and IPR

curve. This procedure cannot be achieved by program since curve trendline

equation changes at every different input value and there is no chance of

data transfer between EXCEL Worksheet and the program. At the last step,

program calculates HP requirement at every possible rate, which will help

us to construct Possible Production Rate versus Stages and Horsepower

Figure. It should be kept in mind that pump selection is achieved manually

by entering to input, in other words program does not comprise an algorithm

that automatically selects a suitable pump for that well.

3.3.2 Pumping Liquid and Gas

Pumping gas with the liquid causes produced fluid rate V to undergo a

significant variation between the intake and discharge pressures. This is

due to high compressibility of gas. At any pressure point between the intake

and discharge, the volume factor should be determined. This process can

only be achieved by making huge amounts of iteration, which leads to

necessity of a computer program. A two-stage computer program in Fortran

33

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 only

liquid 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.

34

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 reached

after 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

35

• 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

36

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:

37

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-Phase

Pipelines6

38

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 ¼ 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 Hagedorn

and 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 froth

flow).

The selection of appropriate correlation for a given production system

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

39

Brown correlation was selected to calculate pressure drop for flow in the

vertical tubing. However, during the execution of the correlation in this

study, Griffith modification was also used when bubble flow conditions were

satisfied since Hagedorn and Brown method shows weaknesses at bubble

flow. 5.3 PROCEDURE FOR CALCULATING A VERTICAL PRESSURE

TRAVERSE BY THE METHOD OF HAGEDORN AND BROWN

The general equation of Hagedorn and Brown correlation is15:

144hgV

dfw

hp c

m

mm

m ∆

∆+

×+=

∆∆

)2

(

109652.2

2

511

2

ρρ

ρ (44)

Solving for the depth increment, h∆

h∆ =

mm

c

mm

dfw

gV

p

ρρ

ρ

×××+

∆−∆

511

2

2

109652.2

)2

(144 (45)

Start with a known pressure p1, assume a value for p2 and calculate the

depth increment. 1. Calculate the average pressure between the two pressure points,psia

p 7.142

21 ++

=pp

(46)

Depending upon the requirements of the problem,i.e., whether or not a

flowing bottom-hole pressure is to be determined from surface information,

or whether the calculations are to start from total depth and come up the

pipe, the starting pressure must be known. Pressure increments or

decrements must then be assumed from which the distance between

pressure points (1) and (2) will be calculated.

As a word of precaution, if starting from the surface with a pressure

lower than 100 psi, increments of 25 psi should be taken until reaching 400

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, γo:

γo=API°+5.131

5.141 (47)

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

m = γo (350) (WOR+11 ) + γw (350) (

WORWOR+1

) + (0.0764) (GLR) γg (48)

4. Calculate the mass flow rate:

w = q m (49)

5. Obtain Rs at P and T by Standing’s16 Correlation :

Rs = γg ( )(00091.0

)(0125.0

1010

18 T

APIP× )1/0.83 (50)

where Rs = scf/bbl

Lasater’s17 equation can also be used and it is more accurate than

Standing’s correlation especially at higher °API. The equation of Lasater’s

correlation is as follows:

41

Rs = CYY

M g

g

o

o )1

)())(350)(3.379(

(−

γ (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

gs 25.1)( 5.0 +=

γγ

(52)

175.1000147.0972.0 FBob += (53)

b) If bPP⟩

))(( PPc

oboboeBB −= (54)

7. Calculate the density of liquid phase:

ρL = [ ] [ ])1

)(4.62()1

1(614.5/)0764.0()4.62(

WORWOR

WORBR

wo

gso

++

+

+γ

γγ(55)

42

8. Assuming T = constant, find a value of Z for a constant T , p and γg. 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 γγ (56)

94.17293.3088324.1 2 ++= ggpcT γγ (57)

pcpr P

PP = (58)

pcpr T

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( prTprpr

prpr PPT

PTBpr −

+−−

+−= (61)

)log(32.0132.0 prTC −= (62)

)1824.049.03106.0( 2

10 prpr TTD +−= (63)

a) If 100⟨B

43

DprB CP

eAAz +

−+=

1 (64)

b) If 100⟩B

DprCPAz += (65)

9. Calculate the average density of the gas phase

gρ = )1)(520)(7.14

)(0764.0(ZT

pgγ (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 −= XoDµ (68)

515.0)100(715.10 −+= sRA (69)

338.0)150(44.5 −+= sRB (70)

BoDo Aµµ = (71)

b) If bPP ≥

)(

1432 PCCC

ePCB += (72)

44

where:

C1 = 2.6

C2 = 1.187

C3 = -11.513

C4 = -8.98×10-5

BoDb Aµµ =

B

bbo PP )(µµ = (73)

where:

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

µoD = dead oil viscosity, cp

11. Determine the average water viscosity from correlation below:

)10982.110479.1003.1( 252 TT

W e−− ×+×−=µ (74)

12. Calculate the liquid mixture viscosity:

µL = µo +

+WOR11

µw

+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.

45

σL = σo (WOR+11 ) + σw (

WORWOR+1

) (76)

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

the liquid phase.

13. Calculate the liquid viscosity number:

NL = 0.15726µL( 3

1

LLσρ)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

2dπ (79)

16. Obtain Bo at Tp,

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

sLν =

++

+)

1()

11(

8640061.5

WORWORB

WORB

Aq

wop

L (80)

18. Calculate the liquid velocity number, NLV:

46

NLV = 1.938 4/1)(L

LsL σ

ρν (81)

19. Calculate the superficial gas velocity, sgν :

sgν =

+−

15207.14

864001

1ZT

pAWOR

RGLRq

p

sL

(82)

20. Determine the gas velocity number, NGV:

NGV =1.938 sgν4/1

L

L

σρ

(83)

21. Find the pipe diameter number, Nd:

Nd = 120.872dL

L

σρ

(84)

22. Calculate the holdup correlating function φ :

=

d

L

gV

LV

NCNp

NN

10.0

575.0 7.14φ (85)

23. Obtain ψLH from the correlation determined before:

ψLH = 11.02.182310210103104102 2639411513615 ++×−+×−×+×− φφφφφφ (86)

47

24. Determine the secondary correction factor correlating parameter, φ:

φ =

14.2

380.0

d

Lgv

NNN

(87)

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

ψ = 7611.112.15710765300129104103108 23465767 +−+−×+×−× φφφφφφ (88)

26. Calculate a value for HL:

HL = [ ]ψψ

LH (89)

For low viscosities there will be no correction and ψ = 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

Re LL Hg

HL

TP dwN−

−×=

µµ (90)

28. Determine a value for ε/d. If the value of ε 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:

)25.21log(214.119.0

ReNdf+−=

ε (91)

48

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

methods.

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

mρ = )1( LgLL HH −+ ρρ (92)

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

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

νm1=νsL1+νsg1 (93)

νm2=νsL2+νsg2 (94)

32. Determine a value for ∆ (νm2)

∆ (νm2) = [ ]2

22

1 mm νν − (95)

33. Calculate ∆h corresponding to ∆p = p1 – p2

∆h =

mm

c

mm

dfw

gp

ρρ

νρ

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.

49

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

Avq

Avq

Avq 4

)1(121 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:

ρ = gggL HH ρρ +− )1( (98)

The friction gradient is:

hcLLf dgvf 2/2ρτ = (99)

where:

[ ])1( gp

LL HA

q−

=ν (100)

The Reynolds number is calculated as:

L

LhLvdNµ

ρ1488Re = (101)

where:

50

dh = hydraulic pipe diameter, ft

µL = 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.

51

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 and

2 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.

52

6.2 Geology

The field is an elongated structure in an approximate East–West

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 structure

consisting 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.

53

All of the producing wells produce from Unit I and II, the dumpflooders

W-3, W-5, W-19 inject the water into Unit I and injectors W-11 and W-18

inject to Unit I and II.

6.3 Reservoir,Fluid and Lift-System Properties

In the absence of PVT sampling, reservoir fluid properties have been, to

large extent, derived from correlations. Estimated values for key parameters

are listed in Table 6.1.

TABLE 6.1 RESERVOIR AND FLUID PROPERTIES OF

GK FIELD

° API 38

GOR, scf/STB 15

γgsc 0.7

γwsc 1.02

γosc 0.83

Pb, psi 160

PR (initial), psi 2400

Tav, °F 170

10 of 12 producer wells were lifted with electrical submersible pumps.

These wells and the series of pumps operated are given in Table 6.2.

54

TABLE 6.2 SUBMERSIBLE PUMP LIFTED WELLS OPERATED IN

GK FIELD AND THEIR EFFICIENCY RANGES

WELL

PUMP USED

EFFICIENCY 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.

55

0

500

1000

1500

2000

2500

3000

0 200 400 600 800 1000 1200 1400 1600q (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.

56

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

57

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 wells

indicated 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 the

results 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 and

suggestion for optimum pump operating conditions by inspecting

possible production rate versus stage and horsepower chart

58

7.2 RESULTS and DISCUSSION

7.2.1 Construction of Vertical Flowing Pressure Gradient Curves Using Computer Program Output

Hagedorn and Brown3 subprogram supported with Griffith4

Correlation gives program user a chance to construct the vertical flowing

pressure gradient curves at any flow rate and at the desired reservoir, fluid

and well conditions. Pressure traverse curves for a flow rate of 100 stb/d

and with a water-cut of 0, 0.5 and 1.0 were constructed respectively

according to GK field data and by the help of computer program output.

These curves can be observed at Figure 7.1, 7.2 and 7.3.

59

100400 300

500

0200

GAS-LIQUID RATIO, 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)

Dep

th (f

t)Tubing Size, in : 2.441Liquid Rate, STBL/D : 100Water Fraction : 0Gas Gravity : 0.70Oil API Gravity : 38Water Specific Gravity : 1.02Average Flowing Temp., F : 170Correlation : Hagedorn&BrownGriffith Correlation (bubble flow)

Figure 7.1 Pressure Traverse Curve (WC = 0)

60

1002000

500

300400

GAS-LIQUID RATIO, 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)

Dep

th (f

t)Tubing Size, in : 2.441Liquid Rate, STBL/D : 100Water Fraction : 0.5Gas Gravity : 0.70Oil API Gravity : 38Water Specific Gravity : 1.02Average Flowing Temp., F : 170Correlation : Hagedorn&BrownGriffith Correlation (bubble flow)

Figure 7.2 Pressure Traverse Curve (WC = 0.5)

61

500

400 300

200 100 0

GAS-LIQUID RATIO, SCF/STBL

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)

Dep

th (f

t)Tubing Size, in : 2.441Liquid Rate, STBL/D : 100Water Fraction : 1.0Gas Gravity : 0.70Oil API Gravity : 38Water Specific Gravity : 1.02Average Flowing Temp., F : 170Correlation : Hagedorn&BrownGriffith Correlation (bubble flow)

Figure 7.3 Pressure Traverse Curve (WC = 1.0)

62

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-based

pressures 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.

63

TABLE 7.1 COMPARISON of COMPUTER-BASED VERTICAL FLOWING PRESSURES with

BEGGS&BRILL CORRELATION AT SELECTED DEPTHS

Water Fraction

0 0.5 1.0

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

0 100 0 100 0 100

Pressure (psi) Pressure (psi) Pressure (psi)

Depth (ft) Output Beggs&Brill 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 1400 1280

6000 2160 2090 1770 1750 2380 2400 2040 1960 2560 2720 2280 2180

8000 2870 2800 2480 2440 3190 3190 2820 2750 3440 3610 3180 3080

10000 3580 3500 3190 3130 3985 4000 3610 3560 4320 4540 4080 3090

64

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 and

WOR 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) API

4000 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

65

TABLE 7.3 EFFECT of GLR on FLOWING BOTTOMHOLE PRESSURES

Q = 100 STB/D

GLR Wellhead Pressure (psi) Flowing Bottomhole Pressure (psi)

0 250 2480

100 250 2190

200 250 1960

300 250 1860

400 250 1800

500 250 1720

TABLE 7.4 EFFECT of WOR on FLOWING BOTTOMHOLE

PRESSURES AT SELECTED DEPTHS

Flowing Bottomhole Pressure (psi) Well Depth (ft)

WOR 0% WOR 50% WOR 100%

4000 1640 1820 2000

6000 2350 2620 2880

8000 3070 3420 3770

Figure 7.4 and 7.5 indicate a graphical analysis for the effect of GLR

and WOR on flowing botomhole pressure respectively. It can be observed

that flow rates that were selected show no or negligible effect on flowing

bottomhole pressures.

66

GLR=0 scf/stblGLR=100 GLR=200

GLR=300GLR=400

GLR=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

67

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 was

prepared 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.

68

HP

Stages

Efficiency Range

Actual Value (St)

Suggested HP Suggested Stage

0

50

100

150

200

250

300

350

400

450

500

550

600

0 50 100 150 200 250 300 350 400 450Stages or Horsepower

Poss

ible

Rat

e (S

TB/D

)

FIGURE 7.6 Possible Production Rate vs Stages and Horsepower for W-07

69

HP

Efficiency RangeStages

Actual Value (St)Suggested HP

Suggested Stage

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400


Poss

ible

Rat

e (S

TB/D

)


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

0 100 200 300 400 500 600 700 800Stages or Horsepower

Poss

ible

Rat

e (S

TB/D

)


71

HP Stages

Efficiency RangeActual Value (St)


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 100 200 300 400 500 600

Stages or Horsepower

Poss

ible

Rat

e (S

TB/D

)


72

HP

Efficiency Range

Stages

Actual Value (St)


0

200

400

600

800

1000

1200

1400

1600

1800

0 100 200 300 400 500 600Stages or Horsepower

Poss

ible

Rat

e (S

TB/D

)


73

HP

Efficiency Range

Stages

Actual Value (St)Suggested HPSuggested Stage

0

200

400

600

800

1000

1200

1400

1600

1800


Poss

ible

Rat

e (S

TB/D

)


74

HP Stages

Efficiency Range

Actual Value(St)

Suggested HP

Suggested Stage

0

500

1000

1500

2000

2500

3000

3500

0 100 200 300 400 500 600 700Stages or Horsepower

Poss

ible

Rat

e (S

TB/D

)


75

HP

Efficiency Range

Stages

Actual Value (St)

Suggested Stage

Suggested HP

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400


Poss

ible

Rat

e (S

TB/D

)


76

HP

Stages

Efficiency Range


Suggested Stage

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

1400


Poss

ible

Rat

e (S

TB/D

)


77

7.2.4 Comparison of Theoretical and Actual Production Parameters and Suggestion for Optimum Pump Operating Conditions by

Inspecting Possible Production Rate versus Stage and Horsepower Chart

Inspection of Possible Production Rate versus Stage and

Horsepower charts for GK field wells let us to make following interpretations:

Actual operating rate of W-07 is 180 stb/d with 356 stages. This

operating rate is within the efficiency range (83-458 bpd) of the pump used

(DN 440), however from the Figure 7.6 it can be observed that beyond 100

stb/d, the horsepower requirement and the number of pump stages increase

very fast without a significant gain in the production rate. A production rate

of 90 stb/d with a horsepower requirement of 40 HP, and a pump stages of

450 can said to be ideal considering the chart.

W-08 is operated with 740 stb/d with 238 stages. This production rate

is higher than the upper limit of pump efficiency range (267-692 bpd). On

the other hand, by examining Figure 7.7, 740 stb/d rate at 238 stages seem

to be a good choice, since HP and pump stage curve slope increases

significantly with an increase in production rate. A production rate of 680

stb/d and a corresponding horsepower requirement of 35 HP and 230 pump

stages can be suggested which are close to actual operating values. 680

stb/d production rate is useful since it is within the upper limit of efficiency

range and providing maximum production rate from W-08.

W-15 cannot be interpreted due to lack of required data.

W-16 is operated with 1350 stb/d with a pump stage of 180. The rate

is within the efficiency range of the pump (833-1792 bpd) and the

corresponding pump stages and HP requirement can said to be economical

by observing Figure 7.8. A production rate of 1200 stb/d with a 70 HP and

160 pump stages can be a perfect design and it should be noted that the

actual production rate and pump stage values are nearly equal to theoretical

values.

78

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 HP

requirement of 100 HP and 220 pump stages can be offered in theorotical

circumstances.

W-22 produces with a low rate, 70 stb/d, with 320 stages. Figure 7.10

shows that the rate is below pump efficiency range (83-458 bpd) and also

320 stages is useless since HP requirement increases significantly,

however production rate increases slightly. This well can said to be

operated inefficiently. 390 stb/d production rate can be selected with a 18

HP requirement and a pump stages of 212.

W-24 produces 1000 stb/d within upper limit of pump efficiency range

(500-1125 bpd). Pump stage value is 332, and entire actual operating data,

is acceptable. Suggested values can be given as 1050 stb/d production rate

with a 32 HP and 270 pump stages.

W-25 is operated with 1620 stb/d with 239 stages. Figure 7.12 shows

that the actual operating production rate can be selected higher, especially

within efficiency range (1834-3417 bpd) of the pump. 1900 stb/d production

rate with a 310 HP and a pump stage of 400 can be suggested for this well

but it should be noted that horsepower requirement is too high to be

operated in field conditions.

W-27 has a production rate of 400 stb/d and a pump stage of 338.

Examining Figure 7.13, it can be concluded that the pump is operating at its

optimum range (267-692 bpd). Operating with 650 stb/d with a 25 HP and

170 pump stages can be economical.

W-28 operates with 530 stb/d within its pump efficiency range (267-

692 bpd) with 338 stages 680 stb/d production rate with a 28 HP and 192

pump stages can be a good selection.

79

TABLE 7.5. RESULTS OBTAINED AFTER the COMPARISON of ACTUAL

and COMPUTER-BASED DATA for GK FIELD

WELL Actual Flow Rate

(stb/d)

Actual Pump Stages

Actual HP Suggested Flow Rate

(stb/d) Suggested

Pump Stages

Suggested HP RESULT

W-07 180 356 N/A 90 450 40 not completely optimum but can be acceptable


W-15 1180 216 N/A N/A N/A N/A N/A

W-16 1350 180 N/A 1200 160 70 completely optimum


W-22 70 320 N/A 390 212 18 inefficient production





80

where:

NA = not applicable due to lack of required data

81

CHAPTER VIII

CONCLUSIONS AND RECOMMENDATIONS

System Nodal Analysis is an useful method in designing and optimizing

a production system having interacting components. Application of Nodal

Analysis technique to electrical submersible pumps lets production

engineers to run the pump more efficiently by selecting optimum flow rate

and corresponding number of pump stages and horsepower requirement.

System optimization is especially important when dealing with gas with

liquid rather than producing and pumping only liquid. In these cases, system

analysis should be supported by a computer program to overcome large

iterations due to production volume change between pump discharge and

intake pressures. It should be noted that GK field has a low GOR (15

scf/STB) which allows straight-forward pump designs without a need of

detailed optimization procedures. This study is useful especially for high

GOR submersible pump lifted wells. A computer program is also necessary

to predict pressure at required depth simultaneously by using vertical

multiphase flow correlation. It can be observed from the results that

Hagedorn and Brown correlation generally gave acceptable program output

when compared with Beggs&Brill Correlation, however failed to give

accurate values at bubble flow. During the study, Griffith Correlation was

used when bubble flow conditions were met. Results indicated that when

dealing with high GLR wells by the help of the computer program, Hagedorn

and Brown Correlation showed tendency to give less accurate output. In this

study, sensitivity analysis was also performed based on the effect of oil

gravity, WOR and GLR on flowing bottomhole pressure which was

evaluated with graphical analysis.

Evaluation of possible production rate versus stage and horsepower

chart showed that within 10 submersible pump lifted wells, 3 wells, W-16,

82

W-17, and W-24 were operated at their optimum range. 5 wells, W-07, W-

08, W-25, W-27, and W-28, were not operated completely at optimum

operating conditions but can said to be acceptable. 1 well, W-22, was

operated inefficiently which should be re-designed to reach optimum

parameters. W–15 could not be interpreted due to lack of required

production data. The study gave the writer a chance to suggest optimum

operating parameters for each well. Finally, it should be kept in mind that

actual production rates for the wells in GK field can be different from the

optimized values because of the commercial production needs of the oil

companies.

83

REFERENCES

1. Brown, K.E., “The Technology of Artificial Lift Methods”, Vol. 2b,

PennWell Publishing Company, Tulsa, Oklahoma, 1980.

2. Beggs, H.D., “Production Optmization Using Nodal Analysis”, OGCI

Publications, Tulsa, Oklahoma, 1991.

3. Hagedorn, Alton R., Brown, K.E., “Experimental Study of Pressure

Gradients Occuring During Continuous Two-phase Flow in Small

Diameter Vertical Conduits”, Journal of Petroleum Technology, April

1965, p.475

4. Griffith, P., ‘’Two-Phase Flow In Pipes’’, Summer Program, M.I.T., 1962.

5. Reda Pump Company Pte. Ltd., 1992

6. Brown, K.E., “The Technology of Artificial Lift Methods”, Vol. 4, PennWell

Publishing Company, Tulsa, Oklahoma, 1984.

7. Gilbert, W.E., ‘’Flowing and Gas-Lift Well Performance’’, API

Drill.Prod.Practice,1954.

8. Nind, T.E.W., ‘’Principles of Oil Well Production’’, McGraw-Hill, 1964.

9. Brown, K.E., Beggs, H.D., ‘’ The Technology of Artificial Lift Methods”,

Vol. 1, Petroleum Publishing Company, Tulsa, Oklahoma, 1978

84

10. Duns, H.Jr., Ros, N.C.J., ‘’Vertical Flow of Gas and Liquid Mixtures in

Wells’’, 6th World Petroleum Congress, Frankfurt, Germany.

11. Gray, H.E., ‘’Vertical Flow Correlations in Gas Wells’’, User Manual for

API 14B Subsurface Control Safety Valve Sizing Computer Program

App.B., June 1974

12. Orkizewski, J. “Predicting Two-Phase Pressure Drops in Vertical Pipe”,

Journal of Petroleum Technology, June 1967

13. Beggs, H.D., Brill, J.P. “A Study of Two Phase Flow in Inclined Pipes”,

Journal of Petroleum Technology, May 1973

14. Aziz, K., Govier, G.W., and Fogarasi, M., “Pressure Drop in Wells

Producing Oil and Gas”, Journal of Canadian Petroleum Technology,

July-September 1972

15. Brown, K.E., “The Technology of Artificial Lift Methods”, Vol. 1,

Petroleum Publishing Company, Tulsa, 1977

16. Standing, M.B., ‘’Volumetric and Phase Behavior of Oilfield Hydrocarbon

Systems’’, NewYork, Reinhold Publishing Corp., 1952

17. Lasater, J.A., ‘’Bubble Point Pressure Correlation’’, Transactions of the

AIME, 1958, pg379

18. Jain, A.K., “Accurate Explicit Equation for Friction Factor”,

J.Hydl.Div.ASCE, NoHY5, May, 1976

19. Private Communication with N.V. Turkse Perenco, 2003

85

APPENDIX A

PUMPING LIQUID AND GAS COMPUTER PROGRAM

1. Nomenclature

2. Flow Chart 3. Main Program

86

PUMPING LIQUID AND GAS A1 Nomenclature: A1.1 Simple Variables Used In The Program A,B,C,D terms used in z factor calculation

API API value of the oil

AREA area of the tubing, ft2

AVALUE constant used in determination of the number of pump stages

BHT bottomhole temperature, °F

BO formation volume factor of oil, rbbl/STB

BOB formation volume factor of oil at bubble point pressure,

rbbl/STB

CNL viscosity number coefficient

CO coefficient of isothermal compressibility

DELP pressure increment, psi

DENAV average density of the gas phase, lb/ft3

DENF weight of 1 bbl liquid plus pumped gas at standard conditions,

lb/stbl

DENGAS gas density at standard conditions, lb/scf

DENLIQ density of the liquid phase, lb/ft3

DENMIX average two phase density of the mixture, lb/ft3

DIA inner diameter of tubing, in.

DIANUM pipe diameter number

DIST distance used in Hagedorn and Brown correlation, ft

DOV dead oil viscosity, cp

ED pipe roughness

87

F term used in calculating formation volume factor of oil

FF friction factor

GLR gas liquid ratio, scf/STB

GOR gas oil ratio, scf/STB

HEADCAP head per stage, ft/stage

HOLDCOF holdup correlating function

HOLDUP liquid holdup

HOLOSEC liquid holdup over secondary correction factor

HPLOAD horsepower per stage, HP/stage

PAV average pressure between P1 and P2

PBUB bubble point pressure, psi

PPC pseudo critical pressure

PPR pseudo reduced pressure

P1 initial pressure (wellhead pressure in this case), psi

P2 final pressure, psi

Q flow rate term used in pump head capacity subprogram,

STB/D

QOIL oil flow rate, STB/D

QOPTM flow rate term used in pump horsepower subprogram, STB/D

QWATER water flow rate, STB/D

RS solution gas oil ratio, scf/STB

RS1 solution gas oil ratio at initial condition, scf/STB

RS2 solution gas oil ratio at final condition, scf/STB

SCF secondary correction factor

SECORF secondary correction factor correlating parameter

SGGAS specific gravity of gas

SGOIL specific gravity of oil

SGWATER specific gravity of water

T average flowing temperature, °F

TD total depth of the well, ft

TENLIQ liquid mixture surface tension, dynes/cm

88

TPC pseudo critical temperature

TPR pseudo reduced temperature

VELNGAS gas velocity number

VELNLIQ liquid velocity number

VISAV average viscosity between initial and final condition, cp

VISGAS gas viscosity (assumed constant), cp

VISNLIQ liquid viscosity number

VISO1 oil viscosity at initial condition, cp

VISO2 oil viscosity at final condition, cp

VISWAT average water viscosity, cp

VSG superficial gas velocity, ft/sec

VSL superficial liquid velocity, ft/sec

W mass flow rate, lb/day

WM mass associated with one barrel of stock tank liquid, lb/STBL

WC water cut

WOR water oil ratio

A1.2. Arrays Used In The Program BE array showing factor ‘B’ used in z factor calculation

HP array showing the calculation of required pump horsepower

P array showing VF data at various pressures

PR array showing the calculation of number of pump stages

ST array showing the intake pressures at various pump stages

ZE array showing z factor

89

A2 Flow Chart

MAIN PROGRAM

START

Input: Well, fluid, reservoir, and lift-

system data

Calculate: Rs, Bo, Bg and VF at various

pressures (200 – 5000 psi)

CALL HAGBROWN (pressure gradient correlation)

Store discharge pressure at pump depth. Apply Griffith Correlation if

bubble flow exists

Begin with first iteration. At every iteration decrease the pressure 50 psi (∆P) starting from the discharge pressure

A

Calculate: Average pressure

Pav = 2

finalinitial PP +

Output: file name is Table1

volume factor data at various

pressures

90

Calculate: volume factor at the average pressure by making interpolation

and volume of fluid according to volume

factor value

According to input lift data: CALL DN440H for pump DN440 CALL DN675H for pump DN675 CALL DN1100H for pump DN1100 CALL GN1600H for pump GN1600 CALL GN2000H for pump GN2000 CALL GN3200H for pump GN3200 Store head per stage at volume of

fluid

Calculate: stage increment and total number of

stages

If average pressure is less

than 200 psi

A F


iterations to calculate total

number of pump stages at various

pressures

T

91

Input: number of pump stages (7 values) at

which intake pressure will be calculated

Calculate: intake pressures at selected

pump stages by interpolation


intake pressure values at

selected pump stages

Input: possible (optimized) production rate and

corresponding intake pressure determined from

EXCEL Worksheet

CALL HAGBROWN Store discharge pressure at possible (optimum) flow rate.

Apply Griffith Correlation if bubble flow exists

Begin with first iteration. At every iteration decrease the

pressure 50 psi (∆P) starting from the discharge

pressure

B

92


Pav = 2

finalinitial PP +

Calculate: volume factor at the average pressure by making interpolation and

volume of fluid according to volume factor value

According to input lift data: CALL DN440HP for pump DN440 CALL DN675HP for pump DN675

CALL DN1100HP for pump DN1100 CALL GN1600HP for pump GN1600 CALL GN2000HP for pump GN2000 CALL GN3200HP for pump GN3200

Store horsepower per stage at volume of fluid

According to input lift data: CALL DN440H for pump DN440 CALL DN675H for pump DN675

CALL DN1100H for pump DN1100 CALL GN1600H for pump GN1600 CALL GN2000H for pump GN2000 CALL GN3200H for pump GN3200

Store head per stage at volume of fluid

Calculate: horsepower increment and total

required horsepower

93

If average pressure is less than

intake pressure

FB

Output: file name is Table4 iterations to calculate total horsepower requirement

between intake and discharge pressures

STOP

T

94

A3 Main Program

C **********LIQUID AND GAS CASE MAIN PROGRAM**********

DIMENSION P(25,5),BE(25),ZE(25),PR(100,8),ST(10,10),HP(100,9)

REAL HEAD,XY,YX,HPPERST

C **********OPEN FILE**********

OPEN (15,FILE='TABLE1.FOR')




C **********INPUT DATA**********

PRINT *,'SELECT YOUR PUMP'

PRINT *,'TYPE 1 FOR DN440'



PRINT *,'TYPE 4 FOR GN1600'



READ *,SELECT

IF (SELECT.EQ.1) PRINT *,'YOU CHOOSE DN440'



IF (SELECT.EQ.4) PRINT *,'YOU CHOOSE GN1600'



PRINT *,'ENTER WATERCUT'

READ *,WC

PRINT *,'ENTER SPECIFIC GRAVITY OF WATER'

READ *,SGWAT

PRINT *,'ENTER SPECIFIC GRAVITY OF OIL'

READ *,SGOIL

95

PRINT *,'ENTER GOR'

READ *,GOR

PRINT *,'ENTER SPECIFIC GRAVITY OF GAS'

READ *,SGGAS

PRINT *,'ENTER VISCOSITY OF GAS'

READ *,VISGAS

PRINT *,'ENTER WELLHEAD PRESSURE'

READ *,P1

PRINT *,'ENTER PRESSURE INTERVAL'

READ *,DELP

PRINT *,'ENTER BOTTOMHOLE TEMPERATURE'

READ *,BHT

PRINT *,'ENTER BUBBLE POINT PRESSURE'

READ *,PBUB

PRINT *,'ASSUME A LIQUID FLOW RATE'

READ *,QLIQ

PRINT *,'ENTER INNER DIAMETER OF TUBING'

READ *,DIA

PRINT *,'ENTER TOTAL DEPTH'

READ *,TD

**********CALCULATION OF VF DATA ATVARIOUS PRESSURES*****

T=BHT

QWATER=QLIQ*WC

QOIL=QLIQ-QWATER

GLR=GOR/(1/(1-WC))

DENGAS=SGGAS*0.0763

DENF=350*WC*SGWAT+350*(1-WC)*SGOIL+GLR*DENGAS

PRINT *,'FLUID DENSITY IS',DENF

AVALUE=808.3141/DENF

API=(141.5/SGOIL-131.5)

P2=P1+DELP

96

PAV=(P1+P2)/2+14.7

PPC=-17.292*SGGAS**2-17.852*SGGAS+688.4

TPC=1.8324*SGGAS**2+308.93*SGGAS+172.94

TPR=(T+460)/TPC

PPR=PAV/PPC

A=1.39*(TPR-0.92)**0.5-0.36*TPR-0.101

B=(0.62-0.23*TPR)*PPR+(0.066/(TPR-0.86)-0.037)*PPR**2

+ +(0.32/10**(9*(TPR-1)))*PPR**6

C=(0.132-0.32*ALOG10(TPR))

D=10**(0.3106-0.49*TPR+0.1824*TPR**2)

DO 10 I=2,26

P(I-1,1)=200+200*(I-2)

P(I-1,2)=SGGAS*((P(I-1,1)/18)*(10**(0.0125*API)/10**(0.00091*T)))

+ **(1/0.83)

IF (P(I-1,1).GE.PBUB) P(I-1,2)=GOR

IF (P(I-1,1).LT.PBUB) THEN

P(I-1,3)=0.972+0.000147*(P(I-1,2)

+ *(SGGAS/SGOIL)**0.5+1.25*T)**1.175

ELSE

P(I-1,3)=(0.972+0.000147*(P(I-1,2)*(SGGAS/SGOIL)**0.5+1.25*T)

+ **1.175)*EXP(((-1433+5*P(I-1,2)+17.2*T-1180*SGGAS+12.61*API)

+ /(10**5*P(I-1,1))*(PBUB-P(I-1,1))))

END IF

BE(I-1)=(0.62-0.23*TPR)*(P(I-1,1)/(-17.292*SGGAS**2-17.852*SGGAS

+ +688.4))+(0.066/(TPR-0.86)-0.037)*(P(I-1,1)/(-17.292*SGGAS

+ **2-17.852*SGGAS+688.4))**2+(0.32/10**(9*(TPR-1)))*(P(I-1,1)

+ /(-17.292*SGGAS**2-17.852*SGGAS+688.4))**6

IF (BE(I-1).LT.100) ZE(I-1)=A+(1-A)/EXP(BE(I-1))+C

+ *(P(I-1,1)/(-17.292*SGGAS**2-17.852*SGGAS+688.4))**D

IF (BE(I-1).GT.100) ZE(I-1)=A+C*(P(I-1,1)/(-17.292*SGGAS

+ **2-17.852*SGGAS+688.4))**D

97

P(I-1,4)=0.00504*(T+460)*ZE(I-1)/P(I-1,1)

IF (P(I-1,2).EQ.GOR) P(I-1,4)=0

P(I-1,5)=WC+(1-WC)*P(I-1,3)+(GLR-(1-WC)*P(I-1,2))*P(I-1,4)

20 FORMAT (25(2X,F9.4))

WRITE (15,20) (P(I-1,J),J=1,5)

10 CONTINUE

C ******************CALCULATION OF NUMBER OF STAGES********

SUMST=0

PR(1,1)=0

CALL HAGBROWN (QOIL,QWATER,WC,GLR,GOR,WOR,WM,W,API,

+ RS,BO,DENLIQ,SGGAS,SGWAT,SGOIL,DELP,P1,P2,PBUB,VISO1,

+VISO2,DIA,VISGAS,TD)

PR(1,2)=P2

SS=((PR(1,2)-200)/50)+1

NL=AINT(SS)

DO 21 I=2,NL

PR(I,1)=I-1.0

PR(I,2)=PR(I-1,2)-50

IF (PR(I,2).LT.200) GO TO 70

PR(I,3)=(PR(I,2)+PR(I-1,2))/2

DO 25 J=1,25

IF (PR(I,3).EQ.P(J,1)) PR(I,4)=P(J,5)

X=PR(I,3)-P(J,1)

IF (X.LT.200.AND.X.GT.0) PR(I,4)=P(J,5)+(P(J+1,5)-P(J,5))

+ *((PR(I,3)-P(J,1))/(P(J+1,1)-P(J,1)))

25 CONTINUE

PR(I,5)=PR(I,4)*(QWATER+QOIL)

XY=PR(I,5)

IF (SELECT.EQ.1) CALL DN440H(XY,HEAD)



98

IF (SELECT.EQ.4) CALL GN1600H(XY,HEAD)



PR(I,6)=HEAD

PR(I,7)=50*AVALUE*(PR(I,4)/PR(I,6))

SUMST=SUMST+PR(I,7)

PR(I,8)=SUMST

36 FORMAT (25(1X,F7.2))

WRITE (35,36) (PR(I,J),J=1,8)

21 CONTINUE

C ******************INTAKE PRESSURE DATA*******************

70 PRINT *,'ENTER THE NUMBER OF STAGE VALUES'

READ *,(ST(K,1),K=1,7)

M=1

48 N=2

49 IF (PR(N,8).GT.ST(M,1)) GO TO 52

N=N+1

IF (N.GT.NL) GO TO 53

GO TO 49

52 ST(M,2)=PR(N-1,2)+(ST(M,1)-PR(N-1,8))/(PR(N,8)-PR(N-1,8))

+ *(PR(N,2)-PR(N-1,2))

53 M=M+1

IF (M.EQ.8) GO TO 51

GO TO 48

51 DO 100 NS=1,7

37 FORMAT (7(1X,F7.2))

WRITE (41,37) (ST(NS,LN),LN=1,2)

100 CONTINUE

C **********CALCULATION OF HORSEPOWER REQUIREMENT*******

PRINT *,'ENTER THE INTAKE PRESSURE AT OPTIMUM FLOW RATE'

READ *,PINT

99

PRINT *,'ENTER THE OPTIMUM FLOW RATE AT ASSUMED STAGE'

READ *,QOPT

QWATER=QOPT*WC

QOIL=QOPT-QWATER

SUMHP=0

HP(1,1)=0

CALL HAGBROWN (QOIL,QWATER,WC,GLR,GOR,WOR,WM,W,API,

+ RS,BO,DENLIQ,SGGAS,SGWAT,SGOIL,DELP,P1, P2, T, PBUB,

+VISO1, VISO2,DIA,VISGAS,TD)

HP(1,2)=P2

PRINT *,P2

TT=((P2-PINT)/50)+2

NT=AINT(TT)

DO 38 I=2,NT

HP(I,1)=I-1

HP(I,2)=HP(I-1,2)-50

IF (HP(I,2).LE.PINT) HP(I,2)=PINT

HP(I,3)=(HP(I,2)+HP(I-1,2))/2

DO 39 J=1,25

IF (HP(I,3).EQ.P(J,1)) HP(I,4)=P(J,5)

XX=HP(I,3)-P(J,1)

IF (XX.LT.200.AND.XX.GT.0) HP(I,4)=P(J,5)+(P(J+1,5)-P(J,5))

+ *((HP(I,3)-P(J,1))/(P(J+1,1)-P(J,1)))

39 CONTINUE

HP(I,5)=HP(I,4)*QOPT

YX=HP(I,5)

IF (SELECT.EQ.1) CALL DN440HP(YX,HPPERST)



IF (SELECT.EQ.4) CALL GN1600HP(YX,HPPERST)


100


HP(I,6)=HPPERST

IF (SELECT.EQ.1) CALL DN440H(YX,HEAD)



IF (SELECT.EQ.4) CALL GN1600H(YX,HEAD)



HP(I,7)=HEAD

HP(I,8)=115.47*HP(I,6)/HP(I,7)

SUMHP=SUMHP+HP(I,8)

HP(I,9)=SUMHP

32 FORMAT (25(1X,F7.2))

WRITE (31,32) (HP(I,J),J=1,9)

38 CONTINUE

STOP

END

101

APPENDIX B

PUMPING ONLY LIQUID COMPUTER PROGRAM

1. Nomenclature

2. Flow Chart 3. Main Program

102

PUMPING ONLY LIQUID

B1 Nomenclature: B1.1 Simple Variables Used In The program

Simple variables used in this program are included in the nomenclature

of pumping liquid and gas case.

B1.2 Arrays Used In The Program

HP array showing the calculation of required pump horsepower

LIQT array showing the intake pressures at various pump stages

QOPT array showing the optimum (possible) production rates

STL array showing the selected pump stages

103

B2 Flow Chart

MAIN PROGRAM

START

Input: Well, fluid, reservoir, and lift-

system data

Calculate: gas density at standard conditions, weight of 1 bbl liquid plus pumped gas at standard conditions and specific gravity of fluid

CALL HAGBROWN (pressure gradient correlation) Store discharge pressure at pump depth. Apply Griffith

Correlation if bubble flow exist

According to input lift data: CALL DN440H for pump DN440 CALL DN675H for pump DN675 CALL DN1100H for pump DN1100 CALL GN1600H for pump GN1600 CALL GN2000H for pump GN2000 CALL GN3200H for pump GN3200 Store head per stage at assumed production rate


intake pressures at selected pump

stages

104

According to input lift data: CALL DN440HP for pump DN440 CALL DN675HP for pump DN675

CALL DN1100HP for pump DN1100 CALL GN1600HP for pump GN1600 CALL GN2000HP for pump GN2000 CALL GN3200HP for pump GN3200

Store horsepower per stage at possible (optimized) production rate that is

calculated from EXCEL Worksheet

Calculate: HP and ∆qp/∆St values


Horsepower requirement for possible (optimized)

rates

STOP

105

B3 Main Program C **********ONLY LIQUID CASE MAIN PROGRAM**********

REAL LIQT(10,10),STL(10),HP(10,10),QOPT(10)

C **********OPEN FILE**********



C **********INPUT DATA**********

PRINT *,'SELECT YOUR PUMP'







READ *,SELECT







PRINT *,'ENTER WATERCUT'

READ *,WC

PRINT *,'ENTER SPECIFIC GRAVITY OF WATER'

READ *,SGWAT

PRINT *,'ENTER SGOIL'

READ *,SGOIL

PRINT *,'ENTER GOR'

READ *,GLR

PRINT *,'ENTER SPECIFIC GRAVITY OF GAS'

106

READ *,SGGAS

PRINT *,'ENTER VISCOSITY OF GAS'

READ *,VISGAS

PRINT *,'ENTER WELLHEAD PRESSURE'

READ *,P1

PRINT *,'ENTER PRESSURE INTERVAL'

READ *,DELP

PRINT *,'ENTER BOTTOMHOLE TEMPERATURE'

READ *,T

PRINT *,'ENTER BUBBLE POINT PRESSURE'

READ *,PBUB

PRINT *,'ENTER A LIQUID FLOW RATE'

READ *,QLIQ

PRINT *,'ENTER INNER DIAMETER OF TUBING'

READ *,DIA

PRINT *,'ENTER TOTAL DEPTH'

READ *,TD

PRINT *,'ASSUME NUMBER OF STAGES (7 VALUES)'

READ *,(STL(I),I=1,7)

DATA WC/0/ ,SGWAT/1.02/ ,SGOIL/0.83/ ,SGGAS/0.7/

DATA P1/1/ ,DELP/10/ ,BHT/170/ ,PBUB/160/ ,QLIQ/100/

DATA GLR/100/ ,VISGAS/0.018/ ,TD/1000/ ,DIA/2.441/

C **********CALCULATION OF INTAKE PRESSURE**********

T=BHT

QWATER=QLIQ*WC

QOIL=QLIQ-QWATER

DENGAS=SGGAS*0.0763

DENF=350*WC*SGWAT+350*(1-WC)*SGOIL+GLR*DENGAS

SGFLUID=DENF/350

DO 13 I=1,7

QASS=QWATER+QOIL

107

LIQT(I,1)=QASS

IF (SELECT.EQ.1) CALL DN440H(QASS,HEAD)



IF (SELECT.EQ.4) CALL GN1600H(QASS,HEAD)



LIQT(I,2)=HEAD

IF (I.GT.1) GO TO 14

CALL HAGBROWN(QOIL,QWATER,WC,GLR,GOR,WOR,WM,W,API,

+ RS,BO,DENLIQ,SGGAS,SGWAT,SGOIL,DELP,P1,P2,T,PBUB,

+ VISO1,VISO2,DIA,VISGAS,TD)

14 LIQT(I,3)=P2

LIQT(I,4)=STL(I)

LIQT(I,5)=LIQT(I,3)-((DENF*LIQT(I,2))/808.3141)*LIQT(I,4)

12 FORMAT (7(1X,F9.3))

WRITE (11,12) (LIQT(I,J),J=1,5)

13 CONTINUE

C **********HORSEPOWER REQUIREMENT**********

PRINT *,'ENTER OPTIMUM FLOW RATES AT EACH

+ ASSUMED STAGES RESPECTIVELY'

DO 16 I=1,7

READ *,QOPT(I)

HP(I,1)=STL(I)

HP(I,2)=QOPT(I)

ZX=QOPT(I)

IF (SELECT.EQ.1) CALL DN440HP(ZX,HPMOTOR)



IF (SELECT.EQ.4) CALL GN1600HP(ZX,HPMOTOR)


108


HP(I,3)=HPMOTOR

HP(I,4)=SGFLUID*HP(I,3)*HP(I,1)

HP(I,5)=(HP(I,2)-HP(I-1,2))/(HP(I,1)-HP(I-1,1))

17 FORMAT (7(1X,F9.3))

WRITE (15,17) (HP(I,J),J=1,5)

16 CONTINUE

STOP

END

109

APPENDIX C

SUBPROGRAMS

1. Nomenclature

2. Flow Chart 3. Program Listing

110

SUBPROGRAMS

C1 Nomenclature: C1.1 Simple Variables Used In The program

Simple variables used in subprograms are included in the nomenclature

of pumping liquid and gas case.

C1.2 Arrays Used In The Program

Arrays used in subprograms are included in the nomenclature of

pumping liquid and gas case.

Subprograms written for entire program are:

1. HAGBROWN SUBPROGRAM

2. DN440HP, DN675HP, DN1100HP, GN1600HP, GN2000HP,

GN3200HP SUBPROGRAMS

3. RSOL, FVF, ZF, VISCOS, WATVIS, VSOL, VSOG, FFACTOR

SUBPROGRAMS

where:

RSOL = solution-gas oil ratio (Standings correlation)

FVF = formation volume factor of oil (Standings correlation)

ZF = compressibility of gas (Standings Modification to the Beggs

& Brill correlation)

VISCOS = viscosity of oil (Beggs & Robinson correlation)

WATVIS = water viscosity (Brill & Beggs correlation)

111

VSOL = superficial liquid velocity (Hagedorn & Brown correlation)

VSOG = superficial gas velocity (Hagedorn & Brown correlation)

FF = friction factor (Jain Equation)

112

C2 Flow Chart

HAGBROWN SUBPROGRAM

START

Calculate: Mass associated with one bbl of stock tank

liquid,mass flow rate, density of the liquid phase, water-oil

ratio, gas oil ratio

Beginning with wellhead pressure (correlation from top of the well to bottom), incrementation of pressure 10 psi in every iteration


Pav = 2

finalinitial PP +

Total Depth = 0

C

113

Calculate: z factor, average density of the gas phase, solution gas-oil

ratio, average viscosity of oil, average water viscosity, liquid mixture viscosity, liquid mixture surface tension, liquid viscosity

number, viscosity number coefficient

Calculate: average mixture density, average

mixture velocity,

Calculate: area of tubing, superficial liquid velocity, liquid velocity

number, superficial gas velocity, gas velocity number, pipe diameter

number, holdup correlating function,HL/ψ, two-phase Reynolds number,

pipe roughness, friction factor

If Bubble

flow exists

Calculate: void fraction of gas, average flowing density, friction

gradient, Reynolds Number

T

F Calculate depth increment (∆h) by Griffith Approach

D

114

If

Well Depth = Total Depth

(or 50± ft)

Calculate depth increment (∆h) and Total Depth Total Depth = Depth increment (∆h) + Total Depth

T

Output: pressure at required depth (discharge pressure)

CF

RETURN

D

115

C3 Program Listing

HAGBROWN SUBPROGRAM

C **********HAGBROWN SUBPROGRAM**********

SUBROUTINE HAGBROWN (QOIL, QWATER,WC, GLR,GOR, WOR,

+WM, W,API, RS, BO, DENLIQ,SGGAS, SGWAT,SGOIL, DELP,P1,P2,

+T, PBUB, VISO1,VISO2, DIA,VISGAS,TD)

GOR=GLR*1/(1-WC)

QLIQ=QOIL+QWATER

WOR=QWATER/QOIL

WM=SGOIL*350*(1/(1+WOR))+SGWAT*350*(WOR/(1+WOR))+

+0.0764*GLR*SGGAS

W=WM*(QWATER+QOIL)

BHT=T

SUM=0

3 P2=P1+DELP

PRINT*,'P2 (psi) =',P2

PAV=(P1+P2)/2+14.7

API=(141.5/SGOIL-131.5)

CALL RSOL(SGGAS,PAV,API,T,RS)

IF (PAV.GT.PBUB) RS=GOR

CALL FVF(PAV,PBUB,RS,T,SGGAS,SGOIL,API,BO)

DENLIQ=((SGOIL*62.4+(RS*SGGAS*0.0764)/5.614)/(BO))*(1/

(1+WOR))+ (SGWAT*62.4*(WOR/(1+WOR)))

PRINT *,'THE DENSITY OF THE LIQUID PHASE (lb/cuft) = ',DENLIQ

CALL ZF(SGGAS,T,PAV,Z)

PRINT *,Z

DENAV=SGGAS*0.0764*(PAV/14.7)*(520/(T+460))*(1/Z)

PRINT*,DENAV

CALL RSOL(SGGAS,P1,API,T,RS1)

116

CALL RSOL(SGGAS,P2,API,T,RS2)

IF (RS.EQ.0) RS1=0

IF (RS.EQ.0) RS2=0

IF (PAV.GT.PBUB) RS1=GOR

IF (PAV.GT.PBUB) RS2=GOR

CALL FVF(P1,PBUB,RS1,T,SGGAS,SGOIL,API,BO1)

CALL FVF(P2,PBUB,RS2,T,SGGAS,SGOIL,API,BO2)

PRINT*,BO1,BO2,RS1,RS2,T

CALL VISCOS(P1,PBUB,T,API,RS1,VISO1)

CALL VISCOS(P2,PBUB,T,API,RS2,VISO2)

VISAV=(VISO1+VISO2)/2

PRINT *,'AVERAGE VISCOSITY (cp) = ',VISAV

C ONE VALUE (NO AVERAGE) FOR VISCOSITY OF WATER-NO

SALINITY

CALL WATVIS(T,VISWAT)

VISLIQ=VISAV*(1/(1+WOR))+VISWAT*(WOR/(1+WOR))

PRINT *,'LIQUID MIXTURE VISCOSITY (cp) = ',VISLIQ

C ASSUME CONSTANT SURFACE TENSION OF OIL AND

WATER(30&70 DYNES/CM)

TENLIQ=30*(1/(1+WOR))+70*(WOR/(1+WOR))

PRINT *,'LIQUID MIXTURE SURFACE TENSION (dynes/cm) = '

TENLIQ

VISNLIQ=0.15726*VISLIQ*(1/(DENLIQ*TENLIQ**3))**(0.25)

PRINT *,'LIQUID VISCOSITY NUMBER = ',VISNLIQ

CNL=87.222*VISNLIQ**6-106.04*VISNLIQ**5+48.22*VISNLIQ**4-

+10.069

+*VISNLIQ**3+0.8612*VISNLIQ**2+0.02*VISNLIQ+0.002

PRINT*,'CNL = ',CNL

AREA=((3.14159*DIA**2)/4)/144

PRINT *,'AREA OF TUBING (sq ft) = ',AREA

117

C FORMATION VOLUME FACTOR OF WATER IS TAKEN AS 1.0

(Bw=1.0)

CALL VSOL(QLIQ,AREA,BO,WOR,VSL)

CALL VSOL(QLIQ,AREA,BO1,WOR,VSL1)

CALL VSOL(QLIQ,AREA,BO2,WOR,VSL2)

PRINT *,'SUPERFICIAL LIQUID VELOCITY (ft/sec) = ',VSL

VELNLIQ=1.938*VSL*(DENLIQ/TENLIQ)**(1/4)

PRINT *,'LIQUID VELOCITY NUMBER = ',VELNLIQ

CALL VSOG(QLIQ,GLR,RS,WOR,AREA,PAV,T,Z,VSG)

CALL VSOG(QLIQ,GLR,RS1,WOR,AREA,P1,T,Z,VSG1)

CALL VSOG(QLIQ,GLR,RS2,WOR,AREA,P2,T,Z,VSG2)

PRINT *,'SUPERFICIAL GAS VELOCITY (ft/sec) = ',VSG

VELNGAS=1.938*VSG*(DENLIQ/TENLIQ)**(1/4)

PRINT *,'GAS VELOCITY NUMBER = ',VELNGAS

AZ=1.071-(0.2218*(VSL+VSG)**2)/DIA

IF (AZ.GE.0.13) AZ=AZ

IF (AZ.LT.0.13) AZ=0.13

PRINT *,AZ

BZ=VSG/(VSL+VSG)

S=BZ-AZ

IF (S.GE.0) GO TO 22

IF (S.LT.0) PRINT *,'CONTINUE WITH GRIFFITH CORRELATION'

C *********GRIFFITH CORRELATION FOR BUBBLE FLOW************

VS=0.8

HOLDUP=1-0.5*(1+(VSL+VSG)/VS-SQRT((1+(VSL+VSG)/VS)**2-

+4*VSG/VS))

HLNS=VSL/(VSL+VSG)

IF (HOLDUP.LT.HLNS) HOLDUP=HLNS

DENMIX=DENLIQ*HOLDUP+DENAV*(1-HOLDUP)

REY=1488*DENLIQ*(VSL/HOLDUP)*DIA/VISLIQ

CALL FFACTOR(REY,DIA,FF)

118

FGR=FF*DENLIQ*(VSL/HOLDUP)**2/(2*32.2*DIA*144)

GO TO 23

C *****************************************************

22 PRINT *,'CONTINUE WITH HAGEDORN&BROWN CORRELATION'

DIANUM=120.872*DIA/12*SQRT(DENLIQ/TENLIQ)

PRINT *,'PIPE DIAMETER NUMBER = ',DIANUM

IF (PAV.GE.PBUB) GO TO 50

HOLDCOF=(VELNLIQ/VELNGAS**0.575)*((((P1+P2)/2)/14.7)**0.10)

+ *(CNL/DIANUM)

PRINT *,HOLDCOF

HOLOSEC=-2*10**15*HOLDCOF**6+4*10**13*HOLDCOF**5-3*10**11

+ *HOLDCOF**4+10**9*HOLDCOF**3-2*10**6*HOLDCOF**2+1823.2

+ *HOLDCOF+0.1078

IF (HOLOSEC.GT.1) HOLOSEC=1

PRINT *,HOLOSEC

SECORF=(VELNGAS*VISNLIQ**0.380)/(DIANUM**2.14)

PRINT *,SECORF

SCF=8*10**7*SECORF**6-3*10**7*SECORF**5+4*10**6*SECORF**4

+ -300129*SECORF**3+10765**SECORF**2-157.12*SECORF+1.7611

IF (SECORF.LE.0.01) SCF=1

PRINT *,SCF

HOLDUP=HOLOSEC*SCF

GO TO 60

50 HOLDUP=1

60 PRINT *,'LIQUID HOLD-UP = ',HOLDUP

REY=(2.2E-2*W)/((DIA/12)*(VISLIQ**HOLDUP)

+ *(VISGAS**(1-HOLDUP)))

PRINT *,'TWO-PHASE REYNOLDS NUMBER = ',REY

CALL FFACTOR(REY,DIA,FF)

PRINT *,'FRICTION FACTOR = ',FF

DENMIX=DENLIQ*HOLDUP+DENAV*(1-HOLDUP)

119

VMIX1=VSL1+VSG1

VMIX2=VSL2+VSG2

VDIF=VMIX1**2-VMIX2**2

PRINT *,'TWO-PHASE DENSITY OF THE MIXTURE (lb/cuft) =

+',DENMIX

DIST=(144*ABS(P2-P1)-DENMIX*(VDIF/64.4))/

+ (DENMIX+(FF*W**2)/2.9652E11*(DIA/12)**5*DENMIX)

GO TO 24

23 DIST=144*(ABS(P2-P1)*(1-((W/86400)*VSG *AREA)/ (4637* AREA**2

+ *PAV)))/(DENMIX+FGR)

24 PRINT*,'DISTANCE (ft)= ',DIST

SUM=SUM+DIST

C ****TEMPERATURE GRADIENT IS TAKEN AS 1.5F/100 FT******

T=BHT-SUM/100*1.5

PRINT *,'TOTAL DEPTH CALCULATED = ',SUM

PRINT*,VISO1,VISO2,P1,P2

IF (ABS(SUM-TD).LT.50) GO TO 2

P1=P2

GO TO 3

2 DISPR=P2

PRINT *,'DISCHARGE PRESSURE (psi) =',PDISPR

120

DN440HP, DN675HP, DN1100HP, GN1600HP, GN2000HP, GN3200HP

SUBPROGRAMS

C ********PUMP PERFORMANCE CURVES SUBPROGRAM********

C **********DN440*********

SUBROUTINE DN440HP(QOPTM,HPLOAD)

REAL QOPTM,HPLOAD

HPLOAD=-1E-07*QOPTM**2+6E-5*QOPTM+0.0661

RETURN

END

C **********DN675*********


REAL QOPTM,HPLOAD

HPLOAD=-1E-07*QOPTM**2+0.0002*QOPTM+0.0561

RETURN

END

C **********DN1100***************


REAL QOPTM,HPLOAD


RETURN

END

C ***********GN1600***************

SUBROUTINE GN1600HP(QOPTM,HPLOAD)

REAL QOPTM,HPLOAD


RETURN

END

C ***********GN2000***************


121

REAL QOPTM,HPLOAD

HPLOAD=6E-08*Q**2+0.0003*Q+0.5697

RETURN

END

C ************GN3200***************


REAL QOPTM,HPLOAD

HPLOAD=-6E-09*QOPTM**2+9E-05*QOPTM+0.625

RETURN

END

122

DN440H, DN675H, DN1100H, GN1600H, GN2000H, GN3200H

SUBPROGRAMS

C ********PUMP PERFORMANCE CURVES SUBPROGRAM********

C **********DN440*********

SUBROUTINE DN440H(Q,HEADCAP)

REAL Q,HEADCAP

HEADCAP=-2E-16*Q**6+4E-13*Q**5-3E-10*Q**4+5E-08*

+ Q**3-6E-05*Q**2+0.0047*Q+19.751

RETURN

END

C **********DN675*********


HEADCAP=-3E-5*Q**2+0.0027*Q+23.11

RETURN

END

C **********DN1100***************


HEADCAP=-1E-05*Q**2+0.0077*Q+19.464

RETURN

END

C ***********GN1600***************

SUBROUTINE GN1600H(Q,HEADCAP)

HEADCAP=-9E-06*Q**2+0.0065*Q+38.134

RETURN

END

C ***********GN2000***************


HEADCAP=-5E-06*Q**2+0.0035*Q+50.676

RETURN

END

123

C ************GN3200***************


HEADCAP=-1E-06*Q**2-0.0015*Q+38.79

RETURN

END

124

RSOL, FVF, ZF, VISCOS, WATVIS, VSOL, VSOG, FFACTOR

SUBPROGRAMS

C *****FLUID PROPERTIES CORRELATION SUBPROGRAMS****

C ***********SOLUTION-GAS OIL RATIO**************

C ***********STANDINGS CORRELATION****************

SUBROUTINE RSOL(SGAS,P,APIO,TEMP,RSO)

RSO=SGAS*((P/18)*(10**(0.0125*APIO)/10

+ **(0.00091*TEMP)))**(1/0.83)

RETURN

END

C *********FORMATION VOLUME FACTOR OF OIL*********

C ***********STANDINGS CORRELATION****************

SUBROUTINE FVF(P,PBUBB,RSO,TEMP,SGAS,SOIL,APIO,FVFO)

CO=(-1433+5*RSO+17.2*TEMP-1180*SGAS+12.61*APIO)/(10**5*P)

IF (P.LT.PBUBB) THEN

F=RSO*(SGAS/SOIL)**0.5+1.25*TEMP

FVFO=0.972+0.000147*F**1.175

ELSE

F=RSO*(SGAS/SOIL)**0.5+1.25*TEMP

BOB=0.972+0.000147*F**1.175

FVFO=BOB*EXP(CO*(PBUBB-P))

END IF

RETURN

END

125

C *********COMPRESSIBILITY OF GAS*****************

C ****STANDINGS MODIFICATION TO THE BEGS&BRILL

CORRELATION*****

SUBROUTINE ZF(SGAS,TEMP,P,ZFAC)

PPC=-17.292*SGAS**2-17.852*SGAS+688.4

TPC=1.8324*SGAS**2+308.93*SGAS+172.94

TPR=(TEMP+460)/TPC

PPR=P/PPC

A=1.39*(TPR-0.92)**0.5-0.36*TPR-0.101

B=(0.62-0.23*TPR)*PPR+(0.066/(TPR-0.86)-0.037)*PPR**2

+ +(0.32/10**(9*(TPR-1)))*PPR**6

C=(0.132-0.32*ALOG10(TPR))

D=10**(0.3106-0.49*TPR+0.1824*TPR**2)

IF (B.LT.100) ZFAC=A+(1-A)/EXP(B)+C*PPR**D

IF (B.GT.100) ZFAC=A+C*PPR**D

RETURN

END

C ********VISCOSITY OF OIL*********************

C ********BEGGS&ROBINSON CORRELATION***************

SUBROUTINE VISCOS(P,PBUBB,TEMP,APIO,RSO,VISOIL)

IF (P.LE.PBUBB) THEN

X=(TEMP**(-1.163))*EXP(6.9824-0.04658*APIO)

DOV=10**X-1

AA=10.715*(RSO+100)**(-0.515)

BB=5.44*(RSO+150)**(-0.338)

VISOIL=AA*DOV**BB

ELSE

BBB=2.6*P**1.187*EXP(-11.513+(-8.98E-5*P))

X=(TEMP**(-1.163))*EXP(6.9824-0.04658*APIO)

DOV=10**X-1

126

AA=10.715*(RSO+100)**(-0.515)

BB=5.44*(RSO+150)**(-0.338)

VISBUB=AA*DOV**BB

VISOIL=VISBUB*(P/PBUBB)**BBB

ENDIF

RETURN

END

C *************WATER VISCOSITY*************

C *************BRILL&BEGGS CORRELATION*******

SUBROUTINE WATVIS(TEMP,VISW)

VISW=EXP(1.003-1.479E-2*TEMP+1.982E-5*TEMP**2)

RETURN

END

C *************SUPERFICIAL LIQUID VELOCITY******

C *************HAGEDORN&BROWN CORRELATION**********

SUBROUTINE VSOL(QLIQD,TAREA,FVF,WORAT,VSLIQ)

VSLIQ=((5.61*QLIQD)/(86400*TAREA))*(FVF*(1/(1+WORAT))+1.0

+ *(WORAT/(1+WORAT)))

RETURN

END

C *************SUPERFICIAL GAS VELOCITY******

C *************HAGEDORN&BROWN CORRELATION**********

SUBROUTINE VSOG(QLIQD,GLRAT,RSO,WORAT,TAREA,

P,TEMP,ZFAC, VSGAS)

VSGAS=((QLIQD*(GLRAT-RSO*(1/(1+WORAT))))/ (86400*TAREA))

+*(14.7/P)

+ *((TEMP+460)/520)*(ZFAC/1)

RETURN

127

END

C *****************FRICTION FACTOR*********************************

C *****************JAIN EQUATION******************

SUBROUTINE FFACTOR(REYN,DIAM,FFR)

EDP=0.00015*12/DIAM

IF (REYN.GT.2000) GO TO 5

FFR=64/REYN

5 FGI=0.0056+0.5/REYN**0.32

I=1

6 DEN=1.14-2*ALOG10(EDP+9.34/(REYN*SQRT(FGI)))

FFR=(1/DEN)**2

DIFF=ABS(FGI-FFR)

IF (DIFF.LE.0.0001) GO TO 7

FGI=(FGI+FFR)/2

I=I+1

IF (I.LT.10) GO TO 6

7 FFR=FGI

RETURN

END

128

APPENDIX D

SAMPLE CALCULATION

W-08

Pumping Liquid and Gas (GOR = 15 scf /STB)

129

TABLE D1 WELL, FLUID, RESERVOIR AND LIFT-SYSTEM DATA

USED IN CALCULATIONS FOR W-08

W-08

Depth, ft 5800

Casing size, in. 7

Tubing size, in. 2.441

Wellhead pressure, psi 250

Wellhead temperature, °F 110

API 38

γosc 0.83

γgsc 0.7

Water Cut 96.5%

γwsc 1.02

GOR, scf/stbo 15

Pb, psi 160

Pr, psi 2400

J (above Pb), stbl/d/psi -

qmax, bbl/d 1132

Average flowing temperature, °F 170

130

TABLE D2 PRODUCTION HISTORY OF W-08

DATE

Pr (psi)

DAYS ON PRODUCTION

(bbls)

VOLUME PRODUCED

(bbls)

q (bbl/day)

2400 0

Dec.62 2224 12 4984 415

May63 2052 26 12606 485

Aug.63 2055 31 14745 476

Dec.63 2071 18 9096 505

April64 2220 24 11990 500

Nov.64 2074 30 15457 515

March65 2247 2 821 411

Jan.66 2222 2 1075 538

March66 2243 25 3373 135

Sept.67 2090 10 5630 563

March68 1970 7 2839 406

April70 1340 25 18811 752

Dec.73 742 30 20573 686

Nov.84 304 27 2535 94

July91 614 29 1753 60

Sept.93 742

April98 1903 29 1008 35

Oct.99 1716

131

FIGURE D1 IPR Curve for W-08

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

2750

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

q (BBL/D or ST B/D)

Pwf (

psi)

BBL/D

ST B/D

132

The units of the computer program production parameter output are

given below:

Flow Rate (Q) : stb/d

Formation Volume Factor of Oil (Bo): rbbl/stb

Formation Volume Factor of Gas (Bg):rbbl/scf

Head per stage (h) : ft/stage

Horsepower per stage (hp) : HP/stage

Horsepower Requirement (HP) : HP

Intake Pressure (P3) : psi

Pressure (P): psi

Solution Gas-Oil Ratio (Rs): scf/bbl

Volume of the Produced Fluid (V) : bbl/d

Volume Factor (VF) : bbl/stbl

133

VF DATA AT VARIOUS PRESSURES FOR THE FLUID OF W-08

P Rs Bo Bg VF 200.0000 15.0000 1.0553 0.0000 1.0019

400.0000 15.0000 1.0501 0.0000 1.0018

600.0000 15.0000 1.0484 0.0000 1.0017

800.0000 15.0000 1.0475 0.0000 1.0017

1000.0000 15.0000 1.0470 0.0000 1.0016

1200.0000 15.0000 1.0467 0.0000 1.0016

1400.0000 15.0000 1.0464 0.0000 1.0016

1600.0000 15.0000 1.0462 0.0000 1.0016

1800.0000 15.0000 1.0461 0.0000 1.0016

2000.0000 15.0000 1.0460 0.0000 1.0016

2200.0000 15.0000 1.0459 0.0000 1.0016

2400.0000 15.0000 1.0458 0.0000 1.0016

2600.0000 15.0000 1.0457 0.0000 1.0016

2800.0000 15.0000 1.0457 0.0000 1.0016

3000.0000 15.0000 1.0456 0.0000 1.0016

3200.0000 15.0000 1.0456 0.0000 1.0016

3400.0000 15.0000 1.0456 0.0000 1.0016

3600.0000 15.0000 1.0455 0.0000 1.0016

3800.0000 15.0000 1.0455 0.0000 1.0016

4000.0000 15.0000 1.0455 0.0000 1.0016

4200.0000 15.0000 1.0454 0.0000 1.0016

4400.0000 15.0000 1.0454 0.0000 1.0016

4600.0000 15.0000 1.0454 0.0000 1.0016

4800.0000 15.0000 1.0454 0.0000 1.0016

5000.0000 15.0000 1.0454 0.0000 1.0016

134

CALCULATION OF NUMBER OF STAGES FOR W-08 (Q = 100 STB/D)

i P3,I P3,I VFi Vi hi ∆Sti Sti

1.00 2730.00 2755.00 1.00 100.16 23.08 4.94 4.94

2.00 2680.00 2705.00 1.00 100.16 23.08 4.94 9.89

3.00 2630.00 2655.00 1.00 100.16 23.08 4.94 14.83

4.00 2580.00 2605.00 1.00 100.16 23.08 4.94 19.78

5.00 2530.00 2555.00 1.00 100.16 23.08 4.94 24.72

6.00 2480.00 2505.00 1.00 100.16 23.08 4.94 29.67

7.00 2430.00 2455.00 1.00 100.16 23.08 4.94 34.61

8.00 2380.00 2405.00 1.00 100.16 23.08 4.94 39.56

9.00 2330.00 2355.00 1.00 100.16 23.08 4.94 44.50

10.00 2280.00 2305.00 1.00 100.16 23.08 4.94 49.45

11.00 2230.00 2255.00 1.00 100.16 23.08 4.94 54.39

12.00 2180.00 2205.00 1.00 100.16 23.08 4.94 59.34

13.00 2130.00 2155.00 1.00 100.16 23.08 4.94 64.28

14.00 2080.00 2105.00 1.00 100.16 23.08 4.94 69.23

15.00 2030.00 2055.00 1.00 100.16 23.08 4.94 74.17

16.00 1980.00 2005.00 1.00 100.16 23.08 4.94 79.12

17.00 1930.00 1955.00 1.00 100.16 23.08 4.94 84.06

18.00 1880.00 1905.00 1.00 100.16 23.08 4.94 89.01

19.00 1830.00 1855.00 1.00 100.16 23.08 4.94 93.95

20.00 1780.00 1805.00 1.00 100.16 23.08 4.94 98.90

21.00 1730.00 1755.00 1.00 100.16 23.08 4.94 103.84

22.00 1680.00 1705.00 1.00 100.16 23.08 4.94 108.79

23.00 1630.00 1655.00 1.00 100.16 23.08 4.94 113.73

24.00 1580.00 1605.00 1.00 100.16 23.08 4.94 118.68

25.00 1530.00 1555.00 1.00 100.16 23.08 4.94 123.62

26.00 1480.00 1505.00 1.00 100.16 23.08 4.94 128.57

27.00 1430.00 1455.00 1.00 100.16 23.08 4.95 133.51

28.00 1380.00 1405.00 1.00 100.16 23.08 4.95 138.46

135

29.00 1330.00 1355.00 1.00 100.16 23.08 4.95 143.40

30.00 1280.00 1305.00 1.00 100.16 23.08 4.95 148.35

31.00 1230.00 1255.00 1.00 100.16 23.08 4.95 153.29

32.00 1180.00 1205.00 1.00 100.16 23.08 4.95 158.24

33.00 1130.00 1155.00 1.00 100.16 23.08 4.95 163.18

34.00 1080.00 1105.00 1.00 100.16 23.08 4.95 168.13

35.00 1030.00 1055.00 1.00 100.16 23.08 4.95 173.07

36.00 980.00 1005.00 1.00 100.16 23.08 4.95 178.02

37.00 930.00 955.00 1.00 100.16 23.08 4.95 182.96

38.00 880.00 905.00 1.00 100.17 23.08 4.95 187.91

39.00 830.00 855.00 1.00 100.17 23.08 4.95 192.85

40.00 780.00 805.00 1.00 100.17 23.08 4.95 197.80

41.00 730.00 755.00 1.00 100.17 23.08 4.95 202.74

42.00 680.00 705.00 1.00 100.17 23.08 4.95 207.69

43.00 630.00 655.00 1.00 100.17 23.08 4.95 212.64

44.00 580.00 605.00 1.00 100.17 23.08 4.95 217.58

45.00 530.00 555.00 1.00 100.17 23.08 4.95 222.53

46.00 480.00 505.00 1.00 100.17 23.08 4.95 227.47

47.00 430.00 455.00 1.00 100.17 23.08 4.95 232.42

48.00 380.00 405.00 1.00 100.18 23.08 4.95 237.36

49.00 330.00 355.00 1.00 100.18 23.08 4.95 242.31

50.00 280.00 305.00 1.00 100.18 23.08 4.95 247.25

51.00 230.00 255.00 1.00 100.19 23.08 4.95 252.20

136

INTAKE PRESSURES AT SELECTED PUMP STAGES FOR W-08 (Q = 100 STB/D)

St P3 150.00 1263.30

175.00 1010.52

200.00 757.75

250.00 252.25

300.00 -

350.00 -

400.00 -

137



1.00 2730.00 2755.00 1.00 150.24 22.84 5.00 5.00

2.00 2680.00 2705.00 1.00 150.24 22.84 5.00 9.99

3.00 2630.00 2655.00 1.00 150.24 22.84 5.00 14.99

4.00 2580.00 2605.00 1.00 150.24 22.84 5.00 19.99

5.00 2530.00 2555.00 1.00 150.24 22.84 5.00 24.99

6.00 2480.00 2505.00 1.00 150.24 22.84 5.00 29.98

7.00 2430.00 2455.00 1.00 150.24 22.84 5.00 34.98

8.00 2380.00 2405.00 1.00 150.24 22.84 5.00 39.98

9.00 2330.00 2355.00 1.00 150.24 22.84 5.00 44.97

10.00 2280.00 2305.00 1.00 150.24 22.84 5.00 49.97

11.00 2230.00 2255.00 1.00 150.24 22.84 5.00 54.97

12.00 2180.00 2205.00 1.00 150.24 22.84 5.00 59.96

13.00 2130.00 2155.00 1.00 150.24 22.84 5.00 64.96

14.00 2080.00 2105.00 1.00 150.24 22.84 5.00 69.96

15.00 2030.00 2055.00 1.00 150.24 22.84 5.00 74.96

16.00 1980.00 2005.00 1.00 150.24 22.84 5.00 79.95

17.00 1930.00 1955.00 1.00 150.24 22.84 5.00 84.95

18.00 1880.00 1905.00 1.00 150.24 22.84 5.00 89.95

19.00 1830.00 1855.00 1.00 150.24 22.84 5.00 94.94

20.00 1780.00 1805.00 1.00 150.24 22.84 5.00 99.94

21.00 1730.00 1755.00 1.00 150.24 22.84 5.00 104.94

22.00 1680.00 1705.00 1.00 150.24 22.84 5.00 109.94

23.00 1630.00 1655.00 1.00 150.24 22.84 5.00 114.93

24.00 1580.00 1605.00 1.00 150.24 22.84 5.00 119.93

25.00 1530.00 1555.00 1.00 150.24 22.84 5.00 124.93

26.00 1480.00 1505.00 1.00 150.24 22.84 5.00 129.92

27.00 1430.00 1455.00 1.00 150.24 22.84 5.00 134.92

138

28.00 1380.00 1405.00 1.00 150.24 22.84 5.00 139.92

29.00 1330.00 1355.00 1.00 150.24 22.84 5.00 144.92

30.00 1280.00 1305.00 1.00 150.24 22.84 5.00 149.91

31.00 1230.00 1255.00 1.00 150.24 22.84 5.00 154.91

32.00 1180.00 1205.00 1.00 150.25 22.84 5.00 159.91

33.00 1130.00 1155.00 1.00 150.25 22.84 5.00 164.91

34.00 1080.00 1105.00 1.00 150.25 22.84 5.00 169.90

35.00 1030.00 1055.00 1.00 150.25 22.84 5.00 174.90

36.00 980.00 1005.00 1.00 150.25 22.84 5.00 179.90

37.00 930.00 955.00 1.00 150.25 22.84 5.00 184.89

38.00 880.00 905.00 1.00 150.25 22.84 5.00 189.89

39.00 830.00 855.00 1.00 150.25 22.84 5.00 194.89

40.00 780.00 805.00 1.00 150.25 22.84 5.00 199.89

41.00 730.00 755.00 1.00 150.25 22.84 5.00 204.88

42.00 680.00 705.00 1.00 150.25 22.84 5.00 209.88

43.00 630.00 655.00 1.00 150.25 22.84 5.00 214.88

44.00 580.00 605.00 1.00 150.25 22.84 5.00 219.88

45.00 530.00 555.00 1.00 150.26 22.84 5.00 224.87

46.00 480.00 505.00 1.00 150.26 22.84 5.00 229.87

47.00 430.00 455.00 1.00 150.26 22.84 5.00 234.87

48.00 380.00 405.00 1.00 150.26 22.84 5.00 239.87

49.00 330.00 355.00 1.00 150.27 22.84 5.00 244.87

50.00 280.00 305.00 1.00 150.28 22.84 5.00 249.86

51.00 230.00 255.00 1.00 150.28 22.84 5.00 254.86

139


St P3 150.00 1279.14

175.00 1029.00

200.00 778.87

250.00 278.64

300.00 -

350.00 -

400.00 -

140



1.00 2730.00 2755.00 1.00 200.32 22.45 5.08 5.08

2.00 2680.00 2705.00 1.00 200.32 22.45 5.08 10.17

3.00 2630.00 2655.00 1.00 200.32 22.45 5.08 15.25

4.00 2580.00 2605.00 1.00 200.32 22.45 5.08 20.33

5.00 2530.00 2555.00 1.00 200.32 22.45 5.08 25.42

6.00 2480.00 2505.00 1.00 200.32 22.45 5.08 30.50

7.00 2430.00 2455.00 1.00 200.32 22.45 5.08 35.58

8.00 2380.00 2405.00 1.00 200.32 22.45 5.08 40.67

9.00 2330.00 2355.00 1.00 200.32 22.45 5.08 45.75

10.00 2280.00 2305.00 1.00 200.32 22.45 5.08 50.83

11.00 2230.00 2255.00 1.00 200.32 22.45 5.08 55.92

12.00 2180.00 2205.00 1.00 200.32 22.45 5.08 61.00

13.00 2130.00 2155.00 1.00 200.32 22.45 5.08 66.08

14.00 2080.00 2105.00 1.00 200.32 22.45 5.08 71.17

15.00 2030.00 2055.00 1.00 200.32 22.45 5.08 76.25

16.00 1980.00 2005.00 1.00 200.32 22.45 5.08 81.33

17.00 1930.00 1955.00 1.00 200.32 22.45 5.08 86.42

18.00 1880.00 1905.00 1.00 200.32 22.45 5.08 91.50

19.00 1830.00 1855.00 1.00 200.32 22.45 5.08 96.58

20.00 1780.00 1805.00 1.00 200.32 22.45 5.08 101.67

21.00 1730.00 1755.00 1.00 200.32 22.45 5.08 106.75

22.00 1680.00 1705.00 1.00 200.32 22.45 5.08 111.83

23.00 1630.00 1655.00 1.00 200.32 22.45 5.08 116.92

24.00 1580.00 1605.00 1.00 200.32 22.45 5.08 122.00

25.00 1530.00 1555.00 1.00 200.32 22.45 5.08 127.09

26.00 1480.00 1505.00 1.00 200.33 22.45 5.08 132.17

27.00 1430.00 1455.00 1.00 200.33 22.45 5.08 137.25

141

28.00 1380.00 1405.00 1.00 200.33 22.45 5.08 142.34

29.00 1330.00 1355.00 1.00 200.33 22.45 5.08 147.42

30.00 1280.00 1305.00 1.00 200.33 22.45 5.08 152.50

31.00 1230.00 1255.00 1.00 200.33 22.45 5.08 157.59

32.00 1180.00 1205.00 1.00 200.33 22.45 5.08 162.67

33.00 1130.00 1155.00 1.00 200.33 22.45 5.08 167.75

34.00 1080.00 1105.00 1.00 200.33 22.45 5.08 172.84

35.00 1030.00 1055.00 1.00 200.33 22.45 5.08 177.92

36.00 980.00 1005.00 1.00 200.33 22.45 5.08 183.00

37.00 930.00 955.00 1.00 200.33 22.45 5.08 188.09

38.00 880.00 905.00 1.00 200.33 22.45 5.08 193.17

39.00 830.00 855.00 1.00 200.33 22.45 5.08 198.25

40.00 780.00 805.00 1.00 200.33 22.45 5.08 203.34

41.00 730.00 755.00 1.00 200.33 22.45 5.08 208.42

42.00 680.00 705.00 1.00 200.34 22.45 5.08 213.51

43.00 630.00 655.00 1.00 200.34 22.45 5.08 218.59

44.00 580.00 605.00 1.00 200.34 22.45 5.08 223.67

45.00 530.00 555.00 1.00 200.34 22.45 5.08 228.76

46.00 480.00 505.00 1.00 200.35 22.45 5.08 233.84

47.00 430.00 455.00 1.00 200.35 22.45 5.08 238.93

48.00 380.00 405.00 1.00 200.35 22.45 5.08 244.01

49.00 330.00 355.00 1.00 200.36 22.45 5.08 249.09

50.00 280.00 305.00 1.00 200.37 22.45 5.08 254.18

51.00 230.00 255.00 1.00 200.38 22.45 5.08 259.26

142


St P3 150.00 1305.12

175.00 1059.00

200.00 813.47

250.00 322.89

300.00 -

350.00 -

400.00 -

143



1.00 2730.00 2755.00 1.00 300.48 21.21 5.38 5.38

2.00 2680.00 2705.00 1.00 300.48 21.21 5.38 10.76

3.00 2630.00 2655.00 1.00 300.48 21.21 5.38 16.14

4.00 2580.00 2605.00 1.00 300.48 21.21 5.38 21.52

5.00 2530.00 2555.00 1.00 300.48 21.21 5.38 26.90

6.00 2480.00 2505.00 1.00 300.48 21.21 5.38 32.28

7.00 2430.00 2455.00 1.00 300.48 21.21 5.38 37.65

8.00 2380.00 2405.00 1.00 300.48 21.21 5.38 43.03

9.00 2330.00 2355.00 1.00 300.48 21.21 5.38 48.41

10.00 2280.00 2305.00 1.00 300.48 21.21 5.38 53.79

11.00 2230.00 2255.00 1.00 300.48 21.21 5.38 59.17

12.00 2180.00 2205.00 1.00 300.48 21.21 5.38 64.55

13.00 2130.00 2155.00 1.00 300.48 21.21 5.38 69.93

14.00 2080.00 2105.00 1.00 300.48 21.21 5.38 75.31

15.00 2030.00 2055.00 1.00 300.48 21.21 5.38 80.69

16.00 1980.00 2005.00 1.00 300.48 21.21 5.38 86.07

17.00 1930.00 1955.00 1.00 300.48 21.21 5.38 91.45

18.00 1880.00 1905.00 1.00 300.48 21.21 5.38 96.83

19.00 1830.00 1855.00 1.00 300.48 21.21 5.38 102.20

20.00 1780.00 1805.00 1.00 300.49 21.21 5.38 107.58

21.00 1730.00 1755.00 1.00 300.49 21.21 5.38 112.96

22.00 1680.00 1705.00 1.00 300.49 21.21 5.38 118.34

23.00 1630.00 1655.00 1.00 300.49 21.21 5.38 123.72

24.00 1580.00 1605.00 1.00 300.49 21.21 5.38 129.10

25.00 1530.00 1555.00 1.00 300.49 21.21 5.38 134.48

26.00 1480.00 1505.00 1.00 300.49 21.21 5.38 139.86

144

27.00 1430.00 1455.00 1.00 300.49 21.21 5.38 145.24

28.00 1380.00 1405.00 1.00 300.49 21.21 5.38 150.62

29.00 1330.00 1355.00 1.00 300.49 21.21 5.38 156.00

30.00 1280.00 1305.00 1.00 300.49 21.21 5.38 161.38

31.00 1230.00 1255.00 1.00 300.49 21.21 5.38 166.76

32.00 1180.00 1205.00 1.00 300.49 21.21 5.38 172.14

33.00 1130.00 1155.00 1.00 300.49 21.21 5.38 177.52

34.00 1080.00 1105.00 1.00 300.49 21.21 5.38 182.89

35.00 1030.00 1055.00 1.00 300.49 21.21 5.38 188.27

36.00 980.00 1005.00 1.00 300.49 21.21 5.38 193.65

37.00 930.00 955.00 1.00 300.50 21.21 5.38 199.03

38.00 880.00 905.00 1.00 300.50 21.21 5.38 204.41

39.00 830.00 855.00 1.00 300.50 21.21 5.38 209.79

40.00 780.00 805.00 1.00 300.50 21.21 5.38 215.17

41.00 730.00 755.00 1.00 300.50 21.21 5.38 220.55

42.00 680.00 705.00 1.00 300.50 21.21 5.38 225.93

43.00 630.00 655.00 1.00 300.51 21.21 5.38 231.31

44.00 580.00 605.00 1.00 300.51 21.21 5.38 236.69

45.00 530.00 555.00 1.00 300.51 21.21 5.38 242.07

46.00 480.00 505.00 1.00 300.52 21.21 5.38 247.45

47.00 430.00 455.00 1.00 300.52 21.21 5.38 252.83

48.00 380.00 405.00 1.00 300.53 21.21 5.38 258.21

49.00 330.00 355.00 1.00 300.54 21.21 5.38 263.59

50.00 280.00 305.00 1.00 300.55 21.21 5.38 268.97

51.00 230.00 255.00 1.00 300.57 21.21 5.38 274.35

145


St P3 150.00 1386.12

175.00 1154.00

200.00 921.74

250.00 457.98

300.00 -

350.00 -

400.00 -

146



1.00 2730.00 2755.00 1.00 400.64 19.38 5.89 5.89

2.00 2680.00 2705.00 1.00 400.64 19.38 5.89 11.78

3.00 2630.00 2655.00 1.00 400.64 19.38 5.89 17.67

4.00 2580.00 2605.00 1.00 400.64 19.38 5.89 23.56

5.00 2530.00 2555.00 1.00 400.64 19.38 5.89 29.44

6.00 2480.00 2505.00 1.00 400.64 19.38 5.89 35.33

7.00 2430.00 2455.00 1.00 400.64 19.38 5.89 41.22

8.00 2380.00 2405.00 1.00 400.64 19.38 5.89 47.11

9.00 2330.00 2355.00 1.00 400.64 19.38 5.89 53.00

10.00 2280.00 2305.00 1.00 400.64 19.38 5.89 58.89

11.00 2230.00 2255.00 1.00 400.64 19.38 5.89 64.78

12.00 2180.00 2205.00 1.00 400.64 19.38 5.89 70.67

13.00 2130.00 2155.00 1.00 400.64 19.38 5.89 76.56

14.00 2080.00 2105.00 1.00 400.64 19.38 5.89 82.45

15.00 2030.00 2055.00 1.00 400.64 19.38 5.89 88.33

16.00 1980.00 2005.00 1.00 400.65 19.38 5.89 94.22

17.00 1930.00 1955.00 1.00 400.65 19.38 5.89 100.11

18.00 1880.00 1905.00 1.00 400.65 19.38 5.89 106.00

19.00 1830.00 1855.00 1.00 400.65 19.38 5.89 111.89

20.00 1780.00 1805.00 1.00 400.65 19.38 5.89 117.78

21.00 1730.00 1755.00 1.00 400.65 19.38 5.89 123.67

22.00 1680.00 1705.00 1.00 400.65 19.38 5.89 129.56

23.00 1630.00 1655.00 1.00 400.65 19.38 5.89 135.45

24.00 1580.00 1605.00 1.00 400.65 19.38 5.89 141.34

25.00 1530.00 1555.00 1.00 400.65 19.38 5.89 147.23

26.00 1480.00 1505.00 1.00 400.65 19.38 5.89 153.11

147

27.00 1430.00 1455.00 1.00 400.65 19.38 5.89 159.00

28.00 1380.00 1405.00 1.00 400.65 19.38 5.89 164.89

29.00 1330.00 1355.00 1.00 400.65 19.38 5.89 170.78

30.00 1280.00 1305.00 1.00 400.65 19.38 5.89 176.67

31.00 1230.00 1255.00 1.00 400.65 19.38 5.89 182.56

32.00 1180.00 1205.00 1.00 400.65 19.38 5.89 188.45

33.00 1130.00 1155.00 1.00 400.66 19.38 5.89 194.34

34.00 1080.00 1105.00 1.00 400.66 19.38 5.89 200.23

35.00 1030.00 1055.00 1.00 400.66 19.38 5.89 206.12

36.00 980.00 1005.00 1.00 400.66 19.38 5.89 212.01

37.00 930.00 955.00 1.00 400.66 19.38 5.89 217.90

38.00 880.00 905.00 1.00 400.66 19.38 5.89 223.79

39.00 830.00 855.00 1.00 400.66 19.38 5.89 229.68

40.00 780.00 805.00 1.00 400.67 19.38 5.89 235.56

41.00 730.00 755.00 1.00 400.67 19.38 5.89 241.45

42.00 680.00 705.00 1.00 400.67 19.38 5.89 247.34

43.00 630.00 655.00 1.00 400.68 19.38 5.89 253.23

44.00 580.00 605.00 1.00 400.68 19.38 5.89 259.12

45.00 530.00 555.00 1.00 400.68 19.38 5.89 265.01

46.00 480.00 505.00 1.00 400.69 19.38 5.89 270.90

47.00 430.00 455.00 1.00 400.70 19.38 5.89 276.79

48.00 380.00 405.00 1.00 400.70 19.38 5.89 282.68

49.00 330.00 355.00 1.00 400.72 19.37 5.89 288.57

50.00 280.00 305.00 1.00 400.74 19.37 5.89 294.46

51.00 230.00 255.00 1.00 400.75 19.37 5.89 300.36

148


St P3 150.00 1507.32

175.00 1294.00

200.00 1082.47

250.00 658.18

300.00 233.78

350.00 -

400.00 -

149



1.00 2730.00 2755.00 1.00 500.80 16.94 6.74 6.74

2.00 2680.00 2705.00 1.00 500.80 16.94 6.74 13.47

3.00 2630.00 2655.00 1.00 500.80 16.94 6.74 20.21

4.00 2580.00 2605.00 1.00 500.80 16.94 6.74 26.95

5.00 2530.00 2555.00 1.00 500.80 16.94 6.74 33.68

6.00 2480.00 2505.00 1.00 500.80 16.94 6.74 40.42

7.00 2430.00 2455.00 1.00 500.80 16.94 6.74 47.16

8.00 2380.00 2405.00 1.00 500.80 16.94 6.74 53.89

9.00 2330.00 2355.00 1.00 500.80 16.94 6.74 60.63

10.00 2280.00 2305.00 1.00 500.80 16.94 6.74 67.37

11.00 2230.00 2255.00 1.00 500.80 16.94 6.74 74.10

12.00 2180.00 2205.00 1.00 500.81 16.94 6.74 80.84

13.00 2130.00 2155.00 1.00 500.81 16.94 6.74 87.58

14.00 2080.00 2105.00 1.00 500.81 16.94 6.74 94.31

15.00 2030.00 2055.00 1.00 500.81 16.94 6.74 101.05

16.00 1980.00 2005.00 1.00 500.81 16.94 6.74 107.79

17.00 1930.00 1955.00 1.00 500.81 16.94 6.74 114.52

18.00 1880.00 1905.00 1.00 500.81 16.94 6.74 121.26

19.00 1830.00 1855.00 1.00 500.81 16.94 6.74 128.00

20.00 1780.00 1805.00 1.00 500.81 16.94 6.74 134.73

21.00 1730.00 1755.00 1.00 500.81 16.94 6.74 141.47

22.00 1680.00 1705.00 1.00 500.81 16.94 6.74 148.21

23.00 1630.00 1655.00 1.00 500.81 16.94 6.74 154.95

24.00 1580.00 1605.00 1.00 500.81 16.94 6.74 161.68

25.00 1530.00 1555.00 1.00 500.81 16.94 6.74 168.42

150

26.00 1480.00 1505.00 1.00 500.81 16.94 6.74 175.16

27.00 1430.00 1455.00 1.00 500.81 16.94 6.74 181.89

28.00 1380.00 1405.00 1.00 500.81 16.94 6.74 188.63

29.00 1330.00 1355.00 1.00 500.82 16.94 6.74 195.37

30.00 1280.00 1305.00 1.00 500.82 16.94 6.74 202.10

31.00 1230.00 1255.00 1.00 500.82 16.94 6.74 208.84

32.00 1180.00 1205.00 1.00 500.82 16.94 6.74 215.58

33.00 1130.00 1155.00 1.00 500.82 16.94 6.74 222.32

34.00 1080.00 1105.00 1.00 500.82 16.94 6.74 229.05

35.00 1030.00 1055.00 1.00 500.82 16.94 6.74 235.79

36.00 980.00 1005.00 1.00 500.82 16.94 6.74 242.53

37.00 930.00 955.00 1.00 500.83 16.94 6.74 249.26

38.00 880.00 905.00 1.00 500.83 16.94 6.74 256.00

39.00 830.00 855.00 1.00 500.83 16.94 6.74 262.74

40.00 780.00 805.00 1.00 500.83 16.94 6.74 269.48

41.00 730.00 755.00 1.00 500.84 16.94 6.74 276.21

42.00 680.00 705.00 1.00 500.84 16.94 6.74 282.95

43.00 630.00 655.00 1.00 500.84 16.94 6.74 289.69

44.00 580.00 605.00 1.00 500.85 16.94 6.74 296.43

45.00 530.00 555.00 1.00 500.86 16.94 6.74 303.16

46.00 480.00 505.00 1.00 500.86 16.94 6.74 309.90

47.00 430.00 455.00 1.00 500.87 16.94 6.74 316.64

48.00 380.00 405.00 1.00 500.88 16.94 6.74 323.38

49.00 330.00 355.00 1.00 500.90 16.94 6.74 330.12

50.00 280.00 305.00 1.00 500.92 16.93 6.74 336.86

51.00 230.00 255.00 1.00 500.94 16.93 6.74 343.60

151


St P3 150.00 1667.22

175.00 1481.00

200.00 1296.97

250.00 925.48

300.00 554.18

350.00 -

400.00 -

152



1.00 2730.00 2755.00 1.00 600.96 13.90 8.21 8.21

2.00 2680.00 2705.00 1.00 600.96 13.90 8.21 16.42

3.00 2630.00 2655.00 1.00 600.96 13.90 8.21 24.63

4.00 2580.00 2605.00 1.00 600.96 13.90 8.21 32.84

5.00 2530.00 2555.00 1.00 600.96 13.90 8.21 41.05

6.00 2480.00 2505.00 1.00 600.96 13.90 8.21 49.26

7.00 2430.00 2455.00 1.00 600.96 13.90 8.21 57.47

8.00 2380.00 2405.00 1.00 600.96 13.90 8.21 65.68

9.00 2330.00 2355.00 1.00 600.96 13.90 8.21 73.89

10.00 2280.00 2305.00 1.00 600.97 13.90 8.21 82.10

11.00 2230.00 2255.00 1.00 600.97 13.90 8.21 90.31

12.00 2180.00 2205.00 1.00 600.97 13.90 8.21 98.52

13.00 2130.00 2155.00 1.00 600.97 13.90 8.21 106.73

14.00 2080.00 2105.00 1.00 600.97 13.90 8.21 114.95

15.00 2030.00 2055.00 1.00 600.97 13.90 8.21 123.16

16.00 1980.00 2005.00 1.00 600.97 13.90 8.21 131.37

17.00 1930.00 1955.00 1.00 600.97 13.90 8.21 139.58

18.00 1880.00 1905.00 1.00 600.97 13.90 8.21 147.79

19.00 1830.00 1855.00 1.00 600.97 13.90 8.21 156.00

20.00 1780.00 1805.00 1.00 600.97 13.90 8.21 164.21

21.00 1730.00 1755.00 1.00 600.97 13.90 8.21 172.42

22.00 1680.00 1705.00 1.00 600.97 13.90 8.21 180.63

23.00 1630.00 1655.00 1.00 600.97 13.90 8.21 188.84

24.00 1580.00 1605.00 1.00 600.97 13.90 8.21 197.05

153

25.00 1530.00 1555.00 1.00 600.97 13.90 8.21 205.26

26.00 1480.00 1505.00 1.00 600.98 13.90 8.21 213.47

27.00 1430.00 1455.00 1.00 600.98 13.90 8.21 221.68

28.00 1380.00 1405.00 1.00 600.98 13.90 8.21 229.89

29.00 1330.00 1355.00 1.00 600.98 13.90 8.21 238.10

30.00 1280.00 1305.00 1.00 600.98 13.90 8.21 246.32

31.00 1230.00 1255.00 1.00 600.98 13.90 8.21 254.53

32.00 1180.00 1205.00 1.00 600.98 13.90 8.21 262.74

33.00 1130.00 1155.00 1.00 600.98 13.90 8.21 270.95

34.00 1080.00 1105.00 1.00 600.99 13.90 8.21 279.16

35.00 1030.00 1055.00 1.00 600.99 13.90 8.21 287.37

36.00 980.00 1005.00 1.00 600.99 13.90 8.21 295.58

37.00 930.00 955.00 1.00 600.99 13.90 8.21 303.79

38.00 880.00 905.00 1.00 600.99 13.90 8.21 312.00

39.00 830.00 855.00 1.00 601.00 13.90 8.21 320.22

40.00 780.00 805.00 1.00 601.00 13.90 8.21 328.43

41.00 730.00 755.00 1.00 601.00 13.90 8.21 336.64

42.00 680.00 705.00 1.00 601.01 13.90 8.21 344.85

43.00 630.00 655.00 1.00 601.01 13.90 8.21 353.06

44.00 580.00 605.00 1.00 601.02 13.90 8.21 361.28

45.00 530.00 555.00 1.00 601.03 13.90 8.21 369.49

46.00 480.00 505.00 1.00 601.04 13.90 8.21 377.70

47.00 430.00 455.00 1.00 601.04 13.90 8.21 385.91

48.00 380.00 405.00 1.00 601.05 13.89 8.21 394.13

49.00 330.00 355.00 1.00 601.08 13.89 8.21 402.34

50.00 280.00 305.00 1.00 601.10 13.89 8.22 410.56

51.00 230.00 255.00 1.00 601.13 13.89 8.22 418.77

154


St P3 150.00 1867.12

175.00 1714.30

200.00 1562.56

250.00 1258.12

300.00 953.28

350.00 649.45

400.00 345.74

155



1.00 2730.00 2755.00 1.00 701.12 10.26 11.13 11.13

2.00 2680.00 2705.00 1.00 701.12 10.26 11.13 22.25

3.00 2630.00 2655.00 1.00 701.12 10.26 11.13 33.38

4.00 2580.00 2605.00 1.00 701.12 10.26 11.13 44.50

5.00 2530.00 2555.00 1.00 701.12 10.26 11.13 55.63

6.00 2480.00 2505.00 1.00 701.12 10.26 11.13 66.76

7.00 2430.00 2455.00 1.00 701.12 10.26 11.13 77.88

8.00 2380.00 2405.00 1.00 701.13 10.26 11.13 89.01

9.00 2330.00 2355.00 1.00 701.13 10.26 11.13 100.13

10.00 2280.00 2305.00 1.00 701.13 10.26 11.13 111.26

11.00 2230.00 2255.00 1.00 701.13 10.26 11.13 122.39

12.00 2180.00 2205.00 1.00 701.13 10.26 11.13 133.51

13.00 2130.00 2155.00 1.00 701.13 10.26 11.13 144.64

14.00 2080.00 2105.00 1.00 701.13 10.26 11.13 155.77

15.00 2030.00 2055.00 1.00 701.13 10.26 11.13 166.89

16.00 1980.00 2005.00 1.00 701.13 10.26 11.13 178.02

17.00 1930.00 1955.00 1.00 701.13 10.26 11.13 189.14

18.00 1880.00 1905.00 1.00 701.13 10.26 11.13 200.27

19.00 1830.00 1855.00 1.00 701.13 10.26 11.13 211.40

20.00 1780.00 1805.00 1.00 701.13 10.26 11.13 222.52

21.00 1730.00 1755.00 1.00 701.13 10.26 11.13 233.65

22.00 1680.00 1705.00 1.00 701.13 10.26 11.13 244.78

23.00 1630.00 1655.00 1.00 701.13 10.26 11.13 255.90

24.00 1580.00 1605.00 1.00 701.14 10.26 11.13 267.03

156

25.00 1530.00 1555.00 1.00 701.14 10.26 11.13 278.16

26.00 1480.00 1505.00 1.00 701.14 10.26 11.13 289.28

27.00 1430.00 1455.00 1.00 701.14 10.26 11.13 300.41

28.00 1380.00 1405.00 1.00 701.14 10.26 11.13 311.54

29.00 1330.00 1355.00 1.00 701.14 10.26 11.13 322.67

30.00 1280.00 1305.00 1.00 701.14 10.26 11.13 333.79

31.00 1230.00 1255.00 1.00 701.14 10.25 11.13 344.92

32.00 1180.00 1205.00 1.00 701.15 10.25 11.13 356.05

33.00 1130.00 1155.00 1.00 701.15 10.25 11.13 367.17

34.00 1080.00 1105.00 1.00 701.15 10.25 11.13 378.30

35.00 1030.00 1055.00 1.00 701.15 10.25 11.13 389.43

36.00 980.00 1005.00 1.00 701.15 10.25 11.13 400.56

37.00 930.00 955.00 1.00 701.16 10.25 11.13 411.69

38.00 880.00 905.00 1.00 701.16 10.25 11.13 422.81

39.00 830.00 855.00 1.00 701.16 10.25 11.13 433.94

40.00 780.00 805.00 1.00 701.17 10.25 11.13 445.07

41.00 730.00 755.00 1.00 701.17 10.25 11.13 456.20

42.00 680.00 705.00 1.00 701.18 10.25 11.13 467.33

43.00 630.00 655.00 1.00 701.18 10.25 11.13 478.46

44.00 580.00 605.00 1.00 701.19 10.25 11.13 489.59

45.00 530.00 555.00 1.00 701.20 10.25 11.13 500.72

46.00 480.00 505.00 1.00 701.21 10.25 11.13 511.85

47.00 430.00 455.00 1.00 701.22 10.25 11.13 522.98

48.00 380.00 405.00 1.00 701.23 10.25 11.13 534.11

49.00 330.00 355.00 1.00 701.26 10.25 11.13 545.25

50.00 280.00 305.00 1.00 701.29 10.25 11.14 556.38

51.00 230.00 255.00 1.00 701.32 10.25 11.14 567.52

157


St P3 150.00 2106.22

175.00 1994.70

200.00 1881.12

250.00 1657.83

300.00 1432.16

350.00 1207.67

400.00 983.24

158



1.00 2730.00 2755.00 1.00 801.28 6.01 18.98 18.98

2.00 2680.00 2705.00 1.00 801.28 6.01 18.98 37.96

3.00 2630.00 2655.00 1.00 801.28 6.01 18.98 56.94

4.00 2580.00 2605.00 1.00 801.28 6.01 18.98 75.92

5.00 2530.00 2555.00 1.00 801.28 6.01 18.98 94.90

6.00 2480.00 2505.00 1.00 801.28 6.01 18.98 113.88

7.00 2430.00 2455.00 1.00 801.29 6.01 18.98 132.86

8.00 2380.00 2405.00 1.00 801.29 6.01 18.98 151.84

9.00 2330.00 2355.00 1.00 801.29 6.01 18.98 170.82

10.00 2280.00 2305.00 1.00 801.29 6.01 18.98 189.81

11.00 2230.00 2255.00 1.00 801.29 6.01 18.98 208.79

12.00 2180.00 2205.00 1.00 801.29 6.01 18.98 227.77

13.00 2130.00 2155.00 1.00 801.29 6.01 18.98 246.75

14.00 2080.00 2105.00 1.00 801.29 6.01 18.98 265.73

15.00 2030.00 2055.00 1.00 801.29 6.01 18.98 284.71

16.00 1980.00 2005.00 1.00 801.29 6.01 18.98 303.69

17.00 1930.00 1955.00 1.00 801.29 6.01 18.98 322.67

18.00 1880.00 1905.00 1.00 801.29 6.01 18.98 341.66

19.00 1830.00 1855.00 1.00 801.29 6.01 18.98 360.64

20.00 1780.00 1805.00 1.00 801.29 6.01 18.98 379.62

21.00 1730.00 1755.00 1.00 801.29 6.01 18.98 398.60

22.00 1680.00 1705.00 1.00 801.30 6.01 18.98 417.59

23.00 1630.00 1655.00 1.00 801.30 6.01 18.98 436.57

24.00 1580.00 1605.00 1.00 801.30 6.01 18.98 455.55

159

25.00 1530.00 1555.00 1.00 801.30 6.01 18.98 474.53

26.00 1480.00 1505.00 1.00 801.30 6.01 18.98 493.52

27.00 1430.00 1455.00 1.00 801.30 6.01 18.98 512.50

28.00 1380.00 1405.00 1.00 801.30 6.01 18.98 531.48

29.00 1330.00 1355.00 1.00 801.30 6.01 18.98 550.47

30.00 1280.00 1305.00 1.00 801.31 6.01 18.98 569.45

31.00 1230.00 1255.00 1.00 801.31 6.01 18.98 588.44

32.00 1180.00 1205.00 1.00 801.31 6.01 18.98 607.42

33.00 1130.00 1155.00 1.00 801.31 6.01 18.99 626.41

34.00 1080.00 1105.00 1.00 801.31 6.01 18.99 645.39

35.00 1030.00 1055.00 1.00 801.32 6.01 18.99 664.38

36.00 980.00 1005.00 1.00 801.32 6.01 18.99 683.36

37.00 930.00 955.00 1.00 801.32 6.01 18.99 702.35

38.00 880.00 905.00 1.00 801.33 6.01 18.99 721.34

39.00 830.00 855.00 1.00 801.33 6.01 18.99 740.33

40.00 780.00 805.00 1.00 801.33 6.01 18.99 759.31

41.00 730.00 755.00 1.00 801.34 6.01 18.99 778.30

42.00 680.00 705.00 1.00 801.34 6.01 18.99 797.29

43.00 630.00 655.00 1.00 801.35 6.01 18.99 816.29

44.00 580.00 605.00 1.00 801.36 6.01 18.99 835.28

45.00 530.00 555.00 1.00 801.37 6.01 18.99 854.27

46.00 480.00 505.00 1.00 801.38 6.01 19.00 873.27

47.00 430.00 455.00 1.00 801.39 6.01 19.00 892.27

48.00 380.00 405.00 1.00 801.40 6.01 19.00 911.27

49.00 330.00 355.00 1.00 801.44 6.00 19.01 930.28

50.00 280.00 305.00 1.00 801.47 6.00 19.01 949.29

51.00 230.00 255.00 1.00 801.51 6.00 19.02 968.31

160


St P3 150.00 2385.22

175.00 2319.70

200.00 2253.12

250.00 2122.83

300.00 1990.16

350.00 1858.67

400.00 1726.24

161

TABLED3 INTAKE PRESSURES AT ASSUMED RATES FOR W-08

P3 for Assumed Number of Stages Assumed Flow Rate, qL ,

STB/D 150 175 200 250 300 350 400

100 1263 1011 758 252 - - -

150 1279 1029 779 279 - - -

200 1305 1059 813 322 - - -

300 1386 1154 921 457 - - -

400 1507 1294 1082 658 233 - -

500 1667 1481 1296 925 554 - -

600 1867 1714 1562 1258 953 649 345

700 2106 1994 1881 1657 1432 1207 983

800 2385 2319 2253 2122 1990 1858 1726

162

Figure D2 Intake Curves for W-08

IPR

Stage=150

200

175

250 300 4003500

500

1000

1500

2000

2500

3000

0 200 400 600 800 1000 1200

q (BBL/D or ST B/D)

Pwf (

psi)

163

CALCULATION OF HORSEPOWER FOR W-08 (Qp = 598 stb/d, Stage = 150)

i P3,I P3,I VFi Vi hpi hi ∆HPi HPi

1.00 2730.00 2755.00 1.00 598.96 0.14 13.96 1.16 1.16

2.00 2680.00 2705.00 1.00 598.96 0.14 13.96 1.16 2.32

3.00 2630.00 2655.00 1.00 598.96 0.14 13.96 1.16 3.47

4.00 2580.00 2605.00 1.00 598.96 0.14 13.96 1.16 4.63

5.00 2530.00 2555.00 1.00 598.96 0.14 13.96 1.16 5.79

6.00 2480.00 2505.00 1.00 598.96 0.14 13.96 1.16 6.95

7.00 2430.00 2455.00 1.00 598.96 0.14 13.96 1.16 8.10

8.00 2380.00 2405.00 1.00 598.96 0.14 13.96 1.16 9.26

9.00 2330.00 2355.00 1.00 598.96 0.14 13.96 1.16 10.42

10.00 2280.00 2305.00 1.00 598.96 0.14 13.96 1.16 11.58

11.00 2230.00 2255.00 1.00 598.96 0.14 13.96 1.16 12.74

12.00 2180.00 2205.00 1.00 598.96 0.14 13.96 1.16 13.89

13.00 2130.00 2155.00 1.00 598.96 0.14 13.96 1.16 15.05

14.00 2080.00 2105.00 1.00 598.96 0.14 13.96 1.16 16.21

15.00 2030.00 2055.00 1.00 598.96 0.14 13.96 1.16 17.37

16.00 1980.00 2005.00 1.00 598.96 0.14 13.96 1.16 18.52

17.00 1930.00 1955.00 1.00 598.97 0.14 13.96 1.16 19.68

18.00 1880.00 1905.00 1.00 598.97 0.14 13.96 1.16 20.84

19.00 1870.00 1875.00 1.00 598.97 0.14 13.96 1.16 22.00

164



1.00 2730.00 2755.00 1.00 632.01 0.14 12.83 1.28 1.28

2.00 2680.00 2705.00 1.00 632.01 0.14 12.83 1.28 2.57

3.00 2630.00 2655.00 1.00 632.01 0.14 12.83 1.28 3.85

4.00 2580.00 2605.00 1.00 632.01 0.14 12.83 1.28 5.13

5.00 2530.00 2555.00 1.00 632.01 0.14 12.83 1.28 6.41

6.00 2480.00 2505.00 1.00 632.01 0.14 12.83 1.28 7.70

7.00 2430.00 2455.00 1.00 632.01 0.14 12.83 1.28 8.98

8.00 2380.00 2405.00 1.00 632.01 0.14 12.83 1.28 10.26

9.00 2330.00 2355.00 1.00 632.01 0.14 12.83 1.28 11.54

10.00 2280.00 2305.00 1.00 632.02 0.14 12.83 1.28 12.83

11.00 2230.00 2255.00 1.00 632.02 0.14 12.83 1.28 14.11

12.00 2180.00 2205.00 1.00 632.02 0.14 12.83 1.28 15.39

13.00 2130.00 2155.00 1.00 632.02 0.14 12.83 1.28 16.68

14.00 2080.00 2105.00 1.00 632.02 0.14 12.83 1.28 17.96

15.00 2030.00 2055.00 1.00 632.02 0.14 12.83 1.28 19.24

16.00 1980.00 2005.00 1.00 632.02 0.14 12.83 1.28 20.52

17.00 1930.00 1955.00 1.00 632.02 0.14 12.83 1.28 21.81

18.00 1880.00 1905.00 1.00 632.02 0.14 12.83 1.28 23.09

19.00 1830.00 1855.00 1.00 632.02 0.14 12.83 1.28 24.37

20.00 1792.00 1811.00 1.00 632.02 0.14 12.83 1.28 25.65

165



1.00 2730.00 2755.00 1.00 659.06 0.14 11.86 1.41 1.41

2.00 2680.00 2705.00 1.00 659.06 0.14 11.86 1.41 2.81

3.00 2630.00 2655.00 1.00 659.06 0.14 11.86 1.41 4.22

4.00 2580.00 2605.00 1.00 659.06 0.14 11.86 1.41 5.63

5.00 2530.00 2555.00 1.00 659.06 0.14 11.86 1.41 7.03

6.00 2480.00 2505.00 1.00 659.06 0.14 11.86 1.41 8.44

7.00 2430.00 2455.00 1.00 659.06 0.14 11.86 1.41 9.85

8.00 2380.00 2405.00 1.00 659.06 0.14 11.86 1.41 11.25

9.00 2330.00 2355.00 1.00 659.06 0.14 11.86 1.41 12.66

10.00 2280.00 2305.00 1.00 659.06 0.14 11.86 1.41 14.07

11.00 2230.00 2255.00 1.00 659.06 0.14 11.86 1.41 15.47

12.00 2180.00 2205.00 1.00 659.06 0.14 11.86 1.41 16.88

13.00 2130.00 2155.00 1.00 659.06 0.14 11.86 1.41 18.29

14.00 2080.00 2105.00 1.00 659.06 0.14 11.86 1.41 19.69

15.00 2030.00 2055.00 1.00 659.06 0.14 11.86 1.41 21.10

16.00 1980.00 2005.00 1.00 659.06 0.14 11.86 1.41 22.51

17.00 1930.00 1955.00 1.00 659.06 0.14 11.86 1.41 23.92

18.00 1880.00 1905.00 1.00 659.06 0.14 11.86 1.41 25.32

19.00 1830.00 1855.00 1.00 659.06 0.14 11.86 1.41 26.73

20.00 1780.00 1805.00 1.00 659.06 0.14 11.86 1.41 28.14

21.00 1730.00 1755.00 1.00 659.06 0.14 11.86 1.41 29.54

22.00 1725.00 1727.50 1.00 659.07 0.14 11.86 1.41 30.95

166



1.00 2730.00 2755.00 1.00 695.11 0.15 10.49 1.62 1.62

2.00 2680.00 2705.00 1.00 695.11 0.15 10.49 1.62 3.23

3.00 2630.00 2655.00 1.00 695.11 0.15 10.49 1.62 4.85

4.00 2580.00 2605.00 1.00 695.11 0.15 10.49 1.62 6.46

5.00 2530.00 2555.00 1.00 695.11 0.15 10.49 1.62 8.08

6.00 2480.00 2505.00 1.00 695.11 0.15 10.49 1.62 9.69

7.00 2430.00 2455.00 1.00 695.12 0.15 10.49 1.62 11.31

8.00 2380.00 2405.00 1.00 695.12 0.15 10.49 1.62 12.93

9.00 2330.00 2355.00 1.00 695.12 0.15 10.49 1.62 14.54

10.00 2280.00 2305.00 1.00 695.12 0.15 10.49 1.62 16.16

11.00 2230.00 2255.00 1.00 695.12 0.15 10.49 1.62 17.77

12.00 2180.00 2205.00 1.00 695.12 0.15 10.49 1.62 19.39

13.00 2130.00 2155.00 1.00 695.12 0.15 10.49 1.62 21.01

14.00 2080.00 2105.00 1.00 695.12 0.15 10.49 1.62 22.62

15.00 2030.00 2055.00 1.00 695.12 0.15 10.49 1.62 24.24

16.00 1980.00 2005.00 1.00 695.12 0.15 10.49 1.62 25.85

17.00 1930.00 1955.00 1.00 695.12 0.15 10.49 1.62 27.47

18.00 1880.00 1905.00 1.00 695.12 0.15 10.49 1.62 29.08

19.00 1830.00 1855.00 1.00 695.12 0.15 10.49 1.62 30.70

20.00 1780.00 1805.00 1.00 695.12 0.15 10.49 1.62 32.32

21.00 1730.00 1755.00 1.00 695.12 0.15 10.49 1.62 33.93

22.00 1680.00 1705.00 1.00 695.12 0.15 10.49 1.62 35.55

23.00 1632.00 1656.00 1.00 695.12 0.15 10.49 1.62 37.16

167



1.00 2730.00 2755.00 1.00 721.15 0.15 9.46 1.81 1.81

2.00 2680.00 2705.00 1.00 721.15 0.15 9.46 1.81 3.62

3.00 2630.00 2655.00 1.00 721.16 0.15 9.46 1.81 5.43

4.00 2580.00 2605.00 1.00 721.16 0.15 9.46 1.81 7.25

5.00 2530.00 2555.00 1.00 721.16 0.15 9.46 1.81 9.06

6.00 2480.00 2505.00 1.00 721.16 0.15 9.46 1.81 10.87

7.00 2430.00 2455.00 1.00 721.16 0.15 9.46 1.81 12.68

8.00 2380.00 2405.00 1.00 721.16 0.15 9.46 1.81 14.49

9.00 2330.00 2355.00 1.00 721.16 0.15 9.46 1.81 16.30

10.00 2280.00 2305.00 1.00 721.16 0.15 9.46 1.81 18.11

11.00 2230.00 2255.00 1.00 721.16 0.15 9.46 1.81 19.93

12.00 2180.00 2205.00 1.00 721.16 0.15 9.46 1.81 21.74

13.00 2130.00 2155.00 1.00 721.16 0.15 9.45 1.81 23.55

14.00 2080.00 2105.00 1.00 721.16 0.15 9.45 1.81 25.36

15.00 2030.00 2055.00 1.00 721.16 0.15 9.45 1.81 27.17

16.00 1980.00 2005.00 1.00 721.16 0.15 9.45 1.81 28.98

17.00 1930.00 1955.00 1.00 721.16 0.15 9.45 1.81 30.79

18.00 1880.00 1905.00 1.00 721.16 0.15 9.45 1.81 32.61

19.00 1830.00 1855.00 1.00 721.16 0.15 9.45 1.81 34.42

20.00 1780.00 1805.00 1.00 721.16 0.15 9.45 1.81 36.23

21.00 1730.00 1755.00 1.00 721.17 0.15 9.45 1.81 38.04

22.00 1680.00 1705.00 1.00 721.17 0.15 9.45 1.81 39.85

23.00 1630.00 1655.00 1.00 721.17 0.15 9.45 1.81 41.66

24.00 1580.00 1605.00 1.00 721.17 0.15 9.45 1.81 43.47

25.00 1559.00 1569.50 1.00 721.17 0.15 9.45 1.81 45.29

168



1.00 2730.00 2755.00 1.00 743.19 0.15 8.55 2.02 2.02

2.00 2680.00 2705.00 1.00 743.19 0.15 8.55 2.02 4.04

3.00 2630.00 2655.00 1.00 743.19 0.15 8.55 2.02 6.06

4.00 2580.00 2605.00 1.00 743.19 0.15 8.55 2.02 8.08

5.00 2530.00 2555.00 1.00 743.19 0.15 8.55 2.02 10.10

6.00 2480.00 2505.00 1.00 743.19 0.15 8.55 2.02 12.12

7.00 2430.00 2455.00 1.00 743.19 0.15 8.55 2.02 14.14

8.00 2380.00 2405.00 1.00 743.19 0.15 8.55 2.02 16.16

9.00 2330.00 2355.00 1.00 743.19 0.15 8.55 2.02 18.18

10.00 2280.00 2305.00 1.00 743.19 0.15 8.55 2.02 20.20

11.00 2230.00 2255.00 1.00 743.19 0.15 8.55 2.02 22.22

12.00 2180.00 2205.00 1.00 743.19 0.15 8.55 2.02 24.24

13.00 2130.00 2155.00 1.00 743.20 0.15 8.55 2.02 26.26

14.00 2080.00 2105.00 1.00 743.20 0.15 8.55 2.02 28.28

15.00 2030.00 2055.00 1.00 743.20 0.15 8.55 2.02 30.30

16.00 1980.00 2005.00 1.00 743.20 0.15 8.55 2.02 32.32

17.00 1930.00 1955.00 1.00 743.20 0.15 8.55 2.02 34.34

18.00 1880.00 1905.00 1.00 743.20 0.15 8.55 2.02 36.36

19.00 1830.00 1855.00 1.00 743.20 0.15 8.55 2.02 38.38

20.00 1780.00 1805.00 1.00 743.20 0.15 8.55 2.02 40.40

21.00 1730.00 1755.00 1.00 743.20 0.15 8.55 2.02 42.42

22.00 1680.00 1705.00 1.00 743.20 0.15 8.55 2.02 44.44

23.00 1630.00 1655.00 1.00 743.20 0.15 8.55 2.02 46.46

24.00 1580.00 1605.00 1.00 743.20 0.15 8.55 2.02 48.48

25.00 1530.00 1555.00 1.00 743.20 0.15 8.55 2.02 50.50

26.00 1496.00 1513.00 1.00 743.21 0.15 8.55 2.02 52.52

169

CALCULATION OF HORSEPOWER FOR W-08

(Qp = 760 stb/d, Stage = 400)


1.00 2730.00 2755.00 1.00 761.22 0.15 7.78 2.23 2.23

2.00 2680.00 2705.00 1.00 761.22 0.15 7.78 2.23 4.46

3.00 2630.00 2655.00 1.00 761.22 0.15 7.78 2.23 6.70

4.00 2580.00 2605.00 1.00 761.22 0.15 7.78 2.23 8.93

5.00 2530.00 2555.00 1.00 761.22 0.15 7.78 2.23 11.16

6.00 2480.00 2505.00 1.00 761.22 0.15 7.78 2.23 13.39

7.00 2430.00 2455.00 1.00 761.22 0.15 7.78 2.23 15.62

8.00 2380.00 2405.00 1.00 761.22 0.15 7.78 2.23 17.85

9.00 2330.00 2355.00 1.00 761.22 0.15 7.78 2.23 20.09

10.00 2280.00 2305.00 1.00 761.22 0.15 7.78 2.23 22.32

11.00 2230.00 2255.00 1.00 761.22 0.15 7.78 2.23 24.55

12.00 2180.00 2205.00 1.00 761.22 0.15 7.78 2.23 26.78

13.00 2130.00 2155.00 1.00 761.22 0.15 7.78 2.23 29.01

14.00 2080.00 2105.00 1.00 761.22 0.15 7.78 2.23 31.24

15.00 2030.00 2055.00 1.00 761.23 0.15 7.78 2.23 33.48

16.00 1980.00 2005.00 1.00 761.23 0.15 7.78 2.23 35.71

17.00 1930.00 1955.00 1.00 761.23 0.15 7.78 2.23 37.94

18.00 1880.00 1905.00 1.00 761.23 0.15 7.78 2.23 40.17

19.00 1830.00 1855.00 1.00 761.23 0.15 7.78 2.23 42.40

20.00 1780.00 1805.00 1.00 761.23 0.15 7.78 2.23 44.64

21.00 1730.00 1755.00 1.00 761.23 0.15 7.78 2.23 46.87

22.00 1680.00 1705.00 1.00 761.23 0.15 7.78 2.23 49.10

23.00 1630.00 1655.00 1.00 761.23 0.15 7.78 2.23 51.33

24.00 1580.00 1605.00 1.00 761.23 0.15 7.78 2.23 53.56

25.00 1530.00 1555.00 1.00 761.23 0.15 7.78 2.23 55.79

170

26.00 1480.00 1505.00 1.00 761.24 0.15 7.78 2.23 58.03

27.00 1443.00 1461.50 1.00 761.24 0.15 7.78 2.23 60.26

171

TABLE D4 HORSEPOWER REQUIREMENTS FOR POSSIBLE

RATES FROM W-08

St qp (STB/D) P3 (psi) P2 (psi) HP ∆qp/∆St

150 598 1870 2780 23 1,32

175 631 1792 2780 27 1,08

200 658 1725 2780 32 0,72

250 694 1632 2780 39 0,52

300 720 1559 2780 49 0,44

350 742 1496 2780 57 0,36

400 760 1443 2780 66 -

172

HP

Efficiency RangeStages


Suggested Stage

0100200300400500600700800900

10001100120013001400


Poss

ible

Rat

e (S

TB/D

)

FIGURE D3 Possible Production Rate vs Stages and Horsepower for W-08

173

TABLE D5 Relation of Production Parameters With Each Other

Comments

Wellhead Pressure, Pwh

A high wellhead pressure means a high pump discharge pressure. More the pump increases the pressure from intake to discharge value, more the pressure will be in the wellhead

Intake Pressure, Pintake

Assuming a constant discharge pressure , intake pressure increases with an increase in production rate and decreases with an increase in number of pump stages

Discharge Pressure, Pdischarge

Discharge pressure is a function of production rate, and pressure in the wellhead. These parameters are directly proportional with discharge pressure

Pressure gain, ∆Pgain

Pressure gained by pump (Pdischarge- Pintake) increases with an increase in number of pump stage however in this case pump requires more horsepower

Pressure loss ∆Ploss

Pressure loss in the tubing is directly related to production rate. High production rates results in high-pressure losses.

Production Rate, q

An increase in production rate results in increase in pressure loss due to friction and related to that increase in discharge pressure Also an increase in production rate decreases the pump head (per stage) which causes a decrease in intake pressure and thus a decrease in pressure gain by pump

Number of Stages

If number of pump stages will be increased then intake pressure will decrease, that means pump will gain more pressure but at the same time pump will require more horsepower

HP Required

High horsepower requirement means number of pump stages will be more and pressure gain will be high, i.e, pump will increase the intake pressure to higher discharge pressure for lifting the fluid

Business

Optimization for submersible pump