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
.
k
j
k
j
k
j
k
j
k
j

9
k
j
k
j
k
j
k
j
k
j
Figure2.3ATypicalPumpPerformanceCurve(GN3200)Figure2.4ATypicalPumpPerformanceCurve(GN3200)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
V
W
Vf
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:
V
q
V
fscsc
f
350
)(
ρ
γ = (5)
Substituting equation 5 into 3 gives:
V
q
VG
fscsc
f
ρ
)
350
433.0
()( = (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:
dP
Vh
V
q
Std
fscsc )(
)
433.0
350
()(
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
dP
Vh
V
q
Std
ρ
(9)
or:

12
∫=
2
3
)(
)
3141.808
(
P
Pfscsc
dP
Vh
V
q
St
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 ( dP
Vh
Vhp
)(
)(
)
433.0
1
(12)
The total horsepower requirement is obtained by integrating the above
equation between the intake and the discharge pressures:
∫∫ =
2
)(
)(
)
433.0
1
()(
0
P
P
p
HP
dP
Vh
Vh
HPd (13)
or:

13
∫=
2
3
)(
)(
)
433.0
1
(
P
P
p
dP
Vh
Vh
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
.
2.3.1Pumping 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 PP
h
St
fsc
−=
ρ
(15)
Solving Equation 15 for 3P gives:

14
St
h
PP
fsc
)
3141.808
(23
ρ
−= (16)
Equation 14 also can be integrated to give:
)()
433.0
1
( 32 PP
h
h
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
2.3.2Pumping 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
dP
Vh
V
q
A
dP
Vh
V
q
A
St (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
mj
j
j
j
sc
i
i
i
sc
P
h
V
q
A
P
h
V
q
A
St
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
sc
i
h
V
q
PA
St
1
3
)( (25)
where:
P3,0 = discharge pressure (P2)
P3,n = intake pressure (P3)
n = (P2-P3)/∆P3
P3,i = P3,i-1 - ∆P3
The quantity ii hV / is evaluated at the average pressure given by:
2/)( ,31,3,3 iii PPP += − (26)
In reality, any pressure P3,I can be considered an intake pressure. To
illustrate this point, Equation 25 can be written in the following form:
∑=
∆=
n
i
ii StSt
1
)( (27)
where:
i
i
sc
i
h
V
q
PA
St )()( 3∆
=∆ (28)

19
Therefore, inorder to obtain an intake pressure P3,i , we have:
i
i
sc h
V
q
PA
StSt )()( 3
11
∆
=∆= (29)
In order to obtain P3,2, we have:
)()()(
2
2
1
13
212
h
V
h
V
q
PA
StStSt
sc
+
∆
=∆+∆= (30)
And in order to obtain P3,n, we have:
=nSt nStStSt )(...)()( 21 ∆++∆+∆ (31)
= )(( 3
scq
PA∆
)...
2
2
1
1
n
n
h
V
h
V
h
V
+++ (32)
2.3.2.2 Determination of Horsepower
The horsepower requirement is obtained by integrating 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
i
i
h
hpP
HP
1
3
)
433.0
( (33)

20
If ∆(HP)I is defined as:
∑=
∆
=∆
n
i i
i
i
h
hpP
HP
1
3
)
433.0
()( (34)
then Equation 33 can be written as:
∑=
∆=
n
i
ii 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 5
wwoo BqBqpHP +∆×= −
(43)
where:
HP = horsepower required
∆p = pressure gain, psi
qo = oil rate, STB/day
qw = water rate, STB/day
Bo = oil formation volume factor at suction conditions, bbl/STB, and
Bw = water formation volume factor at suction conditions
The pressure gain can be converted to head gain if necessary for pump
selection. This is accomplished by dividing the pressure gain by the density
of fluid being pumped. The actual plotting of the data is not required if the
pump is to be selected for specific rates, as all the necessary information is
calculated before plotting.
3.3 Description of the Computer Program
3.3.1 Pumping Only Liquid
A two-stage computer program in Fortran Code has been written and
also EXCEL Worksheet was used to support the program.
At the first stage, program input consists of well, fluid, reservoir, and lift-
system data. Once these conditions were satisfied, program initially gives
the pressure at pump setting depth (discharge pressure) by applying
Hagedorn and Brown3
vertical multiphase correlation. In addition to

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
:
144
h
g
V
d
fw
h
p c
m
m
m
m
∆
∆
+
×
+=
∆
∆
)
2
(
109652.2
2
511
2
ρ
ρ
ρ (44)
Solving for the depth increment, h∆
h∆ =
m
m
c
m
m
d
fw
g
V
p
ρ
ρ
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 7.14
2
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+1
1
) + γw (350) (
WOR
WOR
+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
10
10
18 T
API
P
× )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 = C
Y
Y
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〈 :
TRF
o
g
s 25.1)( 5.0
+=
γ
γ
(52)
175.1
000147.0972.0 FBob += (53)
b) If bPP〉
))(( PPc
obo
bo
eBB −
= (54)
7. Calculate the density of liquid phase:
ρL = [ ] [ ])
1
)(4.62()
1
1
(
614.5/)0764.0()4.62(
WOR
WOR
WORB
R
w
o
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)
pc
pr
P
P
P = (58)
pc
pr
T
T
T = (59)
101.036.0)92.0(39.1 5.0
−−−= prpr TTA (60)
6
))1(9(
2
)
10
32.0
()037.0
)86.0(
066.0
()02362.0( prTpr
pr
prpr PP
T
PTB
pr −
+−
−
+−= (61)
)log(32.0132.0 prTC −= (62)
)1824.049.03106.0( 2
10 prpr TT
D
+−
= (63)
a) If 100〈B

43
D
prB
CP
e
A
Az +
−
+=
1
(64)
b) If 100〉B
D
prCPAz += (65)
9. Calculate the average density of the gas phase
gρ = )
1
)(
520
)(
7.14
)(0764.0(
ZT
p
gγ (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 API
eTX −−
= (67)
110 −= X
oDµ (68)
515.0
)100(715.10 −
+= sRA (69)
338.0
)150(44.5 −
+= sRB (70)
B
oDo Aµµ = (71)
b) If bPP ≥
)(
1
43
2 PCCC
ePCB +
= (72)

44
where:
C1 = 2.6
C2 = 1.187
C3 = -11.513
C4 = -8.98×10-5
B
oDb Aµµ =
B
b
bo
P
P
)(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 +





+ WOR1
1
µw 





+ WOR
WOR
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+1
1
) + σw (
WOR
WOR
+1
) (76)
Again, this represents only an approximation of the surface tension of
the liquid phase.
13. Calculate the liquid viscosity number:
NL = 0.15726µL( 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
2
dπ
(79)
16. Obtain Bo at Tp,
17. Assuming Bw = 1.0, calculate the superficial liquid velocity sLν , ft/sec:
sLν = 





+
+
+
)
1
()
1
1
(
86400
61.5
WOR
WOR
B
WOR
B
A
q
wo
p
L
(80)
18. Calculate the liquid velocity number, NLV:

46
NLV = 1.938 4/1
)(
L
L
sL
σ
ρ
ν (81)
19. Calculate the superficial gas velocity, sgν :
sgν = 


































+
−
1520
7.14
86400
1
1
ZT
pA
WOR
RGLRq
p
sL
(82)
20. Determine the gas velocity number, NGV:
NGV =1.938 sgν
4/1






L
L
σ
ρ
(83)
21. Find the pipe diameter number, Nd:
Nd = 120.872d
L
L
σ
ρ
(84)
22. Calculate the holdup correlating function φ :






















=
d
L
gV
LV
N
CNp
N
N
10.0
575.0
7.14
φ (85)
23. Obtain
ψ
LH
from the correlation determined before:
ψ
LH
= 11.02.182310210103104102 2639411513615
++×−+×−×+×− φφφφφφ (86)

47
24. Determine the secondary correction factor correlating parameter, φ:
φ =








14.2
380.0
d
Lgv
N
NN
(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 = [ ]ψ
ψ 




 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 H
g
H
L
TP
d
w
N −
−
×
=
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:
)
25.21
log(214.1
1
9.0
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 ∆ (νm
2
)
∆ (νm
2
) = [ ]2
2
2
1 mm νν − (95)
33. Calculate ∆h corresponding to ∆p = p1 – p2
∆h =
m
m
c
m
m
d
fw
g
p
ρ
ρ
ν
ρ
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
Av
q
Av
q
Av
q 4
)1(1
2
1 2
(97)
where :
vs = slip velocity (bubble rise velocity), ft/sec
Griffith suggested that a good approximation of an average vs is 0.8
ft/sec. The average flowing density can be computed as:
ρ = gggL HH ρρ +− )1( (98)
The friction gradient is:
hcLLf dgvf 2/
2
ρτ = (99)
where:
[ ])1( gp
L
L
HA
q
−
=ν (100)
The Reynolds number is calculated as:
L
L
hL
v
dN
µ
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 1600
q (BBL/D or STB/D)
Pwf(psi)
BBL/D
STB/D
Figure 6.1 Generalized IPR Curve
The gross rate of each submersible pump lifted producer well during
the production period and required pump stages used in the field are given
in Table 6.3.

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)
Depth(ft)
Tubing Size, in : 2.441
Liquid Rate, STBL/D : 100
Water Fraction : 0
Gas Gravity : 0.70
Oil API Gravity : 38
Water Specific Gravity : 1.02
Average Flowing Temp., F : 170
Correlation : Hagedorn&Brown
Griffith Correlation (bubble flow)
Figure 7.1 Pressure Traverse Curve (WC = 0)

60
100200
0
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)
Depth(ft)
Tubing Size, in : 2.441
Water Fraction : 0.5
Gas Gravity : 0.70
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)
Depth(ft) Tubing Size, in : 2.441
Water Fraction : 1.0
Gas Gravity : 0.70
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/stbl
GLR=100
GLR=200
GLR=300
GLR=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 50 100 150 200 250 300 350 400 450
Stages or Horsepower
PossibleRate(STB/D)
FIGURE 7.6 Possible Production Rate vs Stages and Horsepower for W-07

69
HP
Efficiency Range
Stages
Actual Value (St)Suggested HP
Suggested Stage
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0 50 100 150 200 250 300 350 400 450
PossibleRate(STB/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
0 100 200 300 400 500 600 700 800
PossibleRate(STB/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
PossibleRate(STB/D)

72
HP
Efficiency Range
Stages
Actual Value (St)
0
200
400
600
800
1000
1200
1400
1600
1800
0 100 200 300 400 500 600
PossibleRate(STB/D)

73
HP
Efficiency Range
Stages
Suggested Stage
0
200
400
600
800
1000
1200
1400
1600
1800
0 50 100 150 200 250 300 350 400 450
PossibleRate(STB/D)

74
HP
Stages
Efficiency Range
Actual Value(St)
Suggested HP
Suggested Stage
0
500
1000
1500
2000
2500
3000
3500
0 100 200 300 400 500 600 700
PossibleRate(STB/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
0 50 100 150 200 250 300 350 400 450
PossibleRate(STB/D)

76
HP
Stages
Efficiency Range
Suggested Stage
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0 50 100 150 200 250 300 350 400 450
PossibleRate(STB/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-08 740 238 N/A 680 230 35
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
W-25 1620 239 N/A 1900 400 310
acceptable
W-27 400 338 N/A 650 170 25
acceptable
W-28 530 338 N/A 680 192 28
acceptable

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 GN1600H for pump GN1600
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
Output: file name
is Table2
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
Output: file name
is Table3
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
Calculate: Average
pressure
Pav =
2
finalinitial PP +
Calculate: volume factor at
the average pressure by
making interpolation and
volume of fluid according to
volume factor value
CALL DN440HP for pump DN440
CALL GN1600HP for pump GN1600
Store horsepower per stage at volume
of fluid
Store head per stage at volume of fluid
Calculate: horsepower
increment and total
required horsepower

93
If average
pressure is
less than
intake
pressure
F
B
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

Optimization for submersible pump

Optimization for submersible pump

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