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Approval of the Graduate School of Natural and Applied Sciences
Prof . Dr. Canan ZGEN
Director
I certify that this thesis satisfies all the requirements as a thesis for the degree of
Master of Science.
Prof. Dr. Birol DEMRAL
Head of Department
This is to certify that we have read this thesis and that in our opinion it is fully
adequate, in scope and quality, as a thesis for the degree of Master of Science.
Prof. Dr. A .Suat Bac
Supervisor
Examining Committee Members
Prof. Dr. Birol DEMRAL (Chair Person)
Prof. Dr. A. Suat BACI
Prof. Dr. Fevzi GMRAH
Prof. Dr. Mustafa V. KK
Prof. Dr. Nurkan KARAHANOLU
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iii
ABSTRACT
PRODUCTION SYSTEM OPTIMIZATION FOR SUBMERSIBLE
PUMP LIFTED WELLS : A CASE STUDY
GLER, Nuri Ozan
M.S. Department of Petroleum and Natural Gas Engineering
Supervisor: Prof. Dr. A. Suat Bac
April, 2004, 173 Pages
A computer program has been written to perform production
optimization in submersible pump lifted wells. Production optimization wasachieved by the principles of Nodal Analysis Technique which was applied
between the reservoir and the wellhead ignoring the surface choke and
separator. Computer program has been written according to two lifting
environment, which are: pumping with only liquid and pumping with both
liquid and gas. Program played an important role in the study by overcoming
difficult iterations existing in the pumping liquid and gas case due to
variation of liquid volume between pump intake and discharge pressure.
Hagedorn and Brown vertical multiphase flow correlation was utilized in theprogram to determine the pressure at required depth. However, Griffith
Correlation was also used in the program since Hagedorn and Brown
Correlation failed to give accurate results at bubble flow.
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iv
A case study was done by evaluating the 10 wells located in
Diyarbakr-GK field which are all submersible pump lifted. Well, reservoir,
fluid and lift-system data was transferred to already written computer
program. Output of the computer program for both cases was used to
calculate accurately the optimum production rates, required horsepower,number of pump stages and the relation between these parameters with
each other. The sensitivity variable selected is the number of pump stages.
At the end of the study, by comparing the actual operating data and the
computer-based optimized data, it was observed that 3 wells: W-16, W-17,
and W-24 were producing completely within their optimum range, 5 wells:
W-07, W-08, W-25, W-27 and W-28 were not producing at their optimum
range but their production parameters can said to be acceptable , 1 well: W-
22 was producing inefficiently and should be re-designed to reach optimum
conditions. It was realized that W-15 has insufficient data to make
necessary interpretations.
Keywords: Production optimization, nodal system analysis technique,
electrical submersible pump, artificial lift, Hagedorn and Brown correlation,
Griffith correlation.
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vi
Yazlan bu programn pratie geirilmesi asndan Diyarbakr GK
sahasndaki dalg pompalarla retim yaplan 10 kuyu incelemeye
alnmtr. Bu kuyularn rezervuar, akkan ve retim verileri hazr olan
bilgisayar programna aktarlmtr. Daha nce belirtilen iki pompalama
ortamn kapsayan bu programn kts optimum retim debisi, gerekenbeygirgc ve pompa kademe saysnn belirlenmesi iin kullanlmtr. Bu
hesaplamalarda hassas deiken olarak pompa kademe says seilmitir.
almann sonunda GK sahas verileri ile programdan karlan optimize
deerler karlatrlm ve dalg pompalarla retim yaplan 10 kuyudan
3nn: W-16, W-17, ve W-24n optimum deer snrlar ierisinde retim
yapt, kuyulardan 5inin W-07, W-08, W-25, W-27, W-28, optimum
deerler ierisinde olmasa bile kabul edilebilir ve geerli saylabilir
snrlarda retim yapt, 1 kuyunun, W-22, optimum snrlar dnda ve
verimsiz bir ekilde retime devam ettirildii saptanmtr. W-15in verileri
herhangi bir yorum yapmak iin yetersiz kalmtr.
Kelimeler: retim optimizasyonu, sistem analiz teknii, dalg pompa, yapay
retim, Hagedorn ve Brown Korelasyonu, Griffith Korelasyonu
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vii
To my family,
idem, Yurdahan and Sanem Gler
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viii
ACKNOWLEDGEMENTS
The author would like to thank his supervising professor, Dr. Suat
Bac, for his precious assistance throughout this study and also N.V.
Turkse Perenco for their cooperation.
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ix
TABLE OF CONTENTS
ABSTRACT .. iii
ZET . v
ACKNOWLEDGEMENTS .. viii
TABLE OF CONTENTS . ix
LIST OF TABLES xiii
LIST OF FIGURES . xv
NOMENCLATURE .. xviii
CHAPTER
1. INTRODUCTION . 1
2. ELECTRICAL SUBMERSIBLE PUMPS .. 4
2.1 Introduction ... 4
2.2 Pump Performance Curves 8
2.3 Pump Intake Curves ... 13
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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
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5. HAGEDORN AND BROWN VERTICAL
MULTIPHASE FLOW CORRELATION
SUPPORTED BY GRIFFITH CORRELATION .. 36
5.1 Introduction .. 365.2 Hagedorn and Brown Method 38
5.3 Procedure for Calculating a Vertical Pressure
Traverse by the Method of Hagedorn and
Brown . 39
5.4 Griffith Correlation (Bubble Flow) . 49
6. DESCRIPTION OF THE GK FIELD . 51
6.1 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
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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 ... 677.2.4 Comparison of Theorotical and
Actual Production Parameters and
Suggestion for Optimum Pump
Operating Conditions by Inspecting
Possible Production Rate versus
Stage and Hordepower Chart 77
8. CONCLUSION AND RECOMMENDATIONS . 81
REFERENCES 83
APPENDIX
A Pumping Liquid and Gas Computer Program . 85
B Pumping Only Liquid Computer Program 101
C Subprograms 109
D Sample Calculation of W-08 .. 128
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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 BottomholePressures at Selected Depths... 65
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xiv
7.5 Results Obtained After The Comparison
of Actual and Computer-Based Data
for GK Field .. 79
D1 Well, Fluid, Reservoir and Lift-SystemData Used In Calculations for W-08 . 129
D2 Production History of W-08 130
D3 Intake Pressures at Assumed Rates for W-08 161
D4 Horsepower Requirements for Possible
Rates from W-08 . 171
D5 Relation of Production Parameters
With Each Other .. 173
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xv
LIST OF FIGURES
FIGURES
2.1 A Typical Submersible Pump Installation 6
2.2 Submersible Pump Schematic .. 7
2.3 Pressure Traverses for Pump on Bottom 7
2.4 A Typical Pump Performance Curve (GN 3200) 9
3.1 Pressure Losses In a Production System 25
3.2 Tubing Intake Curves for Artificial Lift Systems . 26
5.1 Schematic Diagram of Possible Flow
Patterns in Two-Phase Pipelines .. 37
6.1 Generalized IPR Curve .. 55
7.1 Pressure Traverse Curve (WC = 0) . 59
7.2 Pressure Traverse Curve (WC = 0.5) .. 60
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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
7.7 Possible Production Rate vs Stages and
Horsepower for W-08 . 69
7.8 Possible Production Rate vs Stages and
Horsepower for W-16 . 70
7.9 Possible Production Rate vs Stages and
Horsepower for W-17 . 71
7.10 Possible Production Rate vs Stages and
Horsepower for W-22 . 72
7.11 Possible Production Rate vs Stages and
Horsepower for W-24 . 73
7.12 Possible Production Rate vs Stages and
Horsepower for W-25 . 74
7.13 Possible Production Rate vs Stages and
Horsepower for W-27 . 75
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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 numberNL liquid viscosity number
NLV liquid velocity number
(NRE)TP two-phase Reynolds number
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xix
Symbol Description Unit
P pressure psi
q flow rate stb/d
Rs solution gas oil ratio scf/stbSt pump stage
T average flowing temperature F
V capacity stb/d
VF volume factor
w mass flow rate lbmday
W weight of the capacity lb/day
WC water cut
z gas compressibility
increment
viscosity cp
velocity ft/sec
density lb/cuft
hold-up correlating function secondary correction factor
liquid surface tension dyne/cm
specific gravity
Subscription Description
b bubble point
dn pump discharge (downstream)
f fluid
g gas
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xx
Subscription Description
l liquid
m mixture
o oilpc pseudo critical
pr pseudo reduced
R reservoir
sc standard condition
sg superficial gas
sl superficial liquid
sep separator
up pump intake (upstream)
w water
wf flowing well
wh wellhead
2 discharge
3 intake
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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 as60,000 b/d and as low as 200 b/d. The oil cut may also vary within very wide
limits, from negligible amounts to 100 %. The pump performs at highest
efficiency when pumping liquid only; it can handle free gas with the liquid
but high volumes of free gas causes inefficient operation and gas lock
problems. The first submersible pumping unit was installed in an oil well in
1928 and since that time the concept has proven itself throughout the oil-
producing world1. A submersible pumping unit consists of an electric motor,
a seal section, an intake section, a multistage centrifugal pump, an electric
cable, a surface installed switchboard, a junction box and transformers.
Additional miscellaneous components also present in order to secure the
cable alongside the tubing and wellhead supports. Pressure sentry for
sensing bottom-hole pressure, check and bleeder valves are the optional
equipment that can be taken into consideration. Under normal operating
conditions, submersible pumping unit can be expected to give from 1 to 3
years of good operating life with some units operating over 10 years.
Despite this advantage, many submersible pump lifted oil and gas wells
produce at rates different than optimum. This fact makes necessary to apply
production optimization techniques to wells having low production rates.
Nodal Analysis has been applied to artificial lift method for many years to
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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. TheNodal analysis technique is essentially a simulator of the producing well
system. The system includes all flow between the reservoir and the
separator. As the entire system is simulated, each of the components is
modelled using various correlations or equations to determine the pressure
loss through that component as a function of flow rate. The summation of
these individual losses make up the total pressure loss through the entire
system for a given flow rate. The production rate or deliverability of a well
can be severely restricted by the poor performance of just one component in
the system. If the effect of each component on the performance of the total
system can be isolated, the efficiency of the system can be optimized in the
most economical way. When performing a Nodal analysis, we divide the
production system into its components, i.e., reservoir, perforations, tubing,
surface choke, flowline and separator. Then we pick a problem area in this
production system as a node. This node acts as the intersection point
between the inflow and outflow performances. Different inflow and outflow
performance curves intersect on the same plot and give the design
considerations for different arrangements2. Optimization and design of
submersible pump lifted wells pumping only liquid are generally straight-
forward however pumping gas with the liquid is complicated because of the
high compressibility of gas. In this case, volume of the produced fluid rate
shows a significant variation between the pump intake and discharge
pressures, consequently considerable amount of iterations should be
performed to determine the volume factor at any pressure between the
intake and discharge pressures. Thus, computer program should be written
to overcome these iterations. Optimization of wells with Nodal Analysis
requires pressure gradient correlation in order to reach a solution so it is
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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 bubbleflow. Thus, Griffith Correlation4 was constructed at bubble flow to obtain
accurate results.
The purpose of this study was to write a general computer program
that gives simultaneously the possible production rates for submersible
pump lifted wells and also the optimum required horsepower and number of
pump stages at these possible rates both considering pumping liquid and
pumping gas with liquid. In addition to that objective, comparison made by
using the production data of wells located in the GK field will assist us in
suggesting optimum pump operating conditions.
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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 wells flowline, so that
as much gas as possible is separated from the liquid before it enters the
pump. In some cases, a centrifugal separator will be placed between the
pump and motor for obtaining maximum gas-liquid separation. A typical
submersible pump installation is given in Figure 2.1. A schematic of a well
equipped with a submersible pump is given in Figure 2.2, along with the
pressure traverse in the well. From the figure it can be seen that, initially,
flowing pressure of submersible pump lifted well is not sufficient to lift the
fluid (depleted well). This insufficient pressure (Pup) which we define as
intake pressure starts to increase at pump setting depth by required pump
stages and finally reaches to discharge pressure (Pdn) generated by the
pump which will assist fluid to flow throughout the surface. Figure 2.3 is a
typical pressure traverses for pump on bottom. Discharge pressure of the
pump will be defined as P2, and also intake pressure will be defined as P3
throughout the study. From figure, the effective lift point is that depth at
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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 offree gas are known to cause inefficient operation.
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6
Figure 2.1 A Typical Submersible Pump Installation
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7
Figure 2.2 Submersible Pump Schematic
Figure 2.3 Pressure Traverses for Pump on Bottom
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2.2 Pump Performance Curves
Pumps are divided into groups according to the minimum casing size
into which the pump can be run. But even within the same group, each
pump performs differently. A typical pump performance curve5 is given inFigure 2.4.
The performance curves of a submersible electrical pump represent the
variation of head, horsepower, and efficiency with capacity. Capacity refers
to the volume of the produced flow rate, which may include free and/or
dissolved gas. These curves are for a fixed power cycle normally 50 or 60
cycle and can be changed with variable frequency controllers6.
j
j
j
j
j
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9
j
j
j
j
j
Figure2.3
ATypicalPumpPerformanceC
urve(GN3200)
Figure2.4
ATypicalPumpPerformance
Curve(GN3200)5
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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 Gfare functions
of the capacity V, which is:
VFqV sc= (2)
The gradient of fluid at any pressure and temperature is given by:
)(433.0)( VVG ff = (3)
but:
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V
WVf
350)( = (4)
where W is the weight of the capacity V at any pressure and temperature,
which is equal to the weight at standard conditions. Hence:
V
qV
fscsc
f350
)(
= (5)
Substituting equation 5 into 3 gives:
V
qVG
fscsc
f
)
350
433.0()( = (6)
fsc is the weight of 1 bbl of liquid plus pumped gas (per 1bbl of liquid) at
standard conditions, or:
gscoscwscfsc GLRGIPwcwc ))(()1(350350 ++= (7)
where gsc is the density of gas (in lb/scf) at standard conditions.
Substituting Equation 6 into Equation 1 gives:
dPVh
V
qStd
fscsc )()
433.0
350()(
= (8)
The total number of stages is obtained by integrating the above equation
between the intake and discharge pressures:
=2
3)(
)433.0350()(
0
P
Pfscsc
St
dPVhV
qStd
(9)
or:
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12
=2
3)(
)3141.808
(
P
Pfscsc
dPVh
V
qSt
(10)
The pump performance curves give the horsepower per stage based on
a fluid specific gravity equal to 1.0. This horsepower must be multiplied by
the specific gravity of the fluid under consideration. Thus the following can
be stated:
(horsepower requirements) = (horsepower per stage) (specific gravity of
fluid) (number of stages)
Since the horsepower per stage, the specific gravity of fluid, and the
number of stages depend on the capacity V, which varies between the
intake and the discharge pressures, the above equation can be written as
follows:
)()()()( StdVVhHPd fp = (11)
Substituting Equations 5 and 8 into the above equation gives:
=)(HPd ( dPVh
Vhp
)(
)()
433.0
1(12)
The total horsepower requirement is obtained by integrating the above
equation between the intake and the discharge pressures:
=
2
)(
)()
433.0
1()(
0
P
P
pHP
dPVh
VhHPd (13)
or:
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13
=2
3)(
)()
433.0
1(
P
P
pdP
Vh
VhHP (14)
For each pump, there is a capacity range within which the pump
performs at or near its peak efficency. The volume range of the selected
rate between the intake and the discharge pressures should, therefore,
remain within the efficiency range of the pump. This range, of course, can
be changed by using a variable frequency controller.
2.3 Pump Intake Curves
Predicting intake curves for submersible pumps is considered for two
cases: (1) pumping only liquid, and (2) pumping liquid and gas. For both
cases, it is assumed that the pump is set at the bottom of well and the
wellhead pressure and tubing size are fixed. For case 2, it is assumed that
all associated gas is pumped with the liquid. The sensitivity variable
selected is the number of stages6.
2.3.1 Pumping Liquid Only
Since the liquids are only slightly compressible, the volume of the
production rate can be considered constant and equal to the surface rate
qsc. Hence, the head per stage will also be constant, and Equation 10 can
be integrated to give6:
))(3141.808
( 32 PPh
Stfsc
=
(15)
Solving Equation 15 for 3P gives:
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14
Sth
PPfsc
)3141.808
(23
= (16)
Equation 14 also can be integrated to give:
)()433.0
1( 32 PP
h
hHP
p = (17)
Substituting Equation 15 into the above equation yields:
SthHP fscp= (18)
Pump selection is limited by the casing size. Another constraint is the
desired production rate. If the objective is to maximize the production rate,
the proper procedure is to select a pump whose efficiency range includes
rates that are close to the maximum rate of the well.
2.3.1.1 Procedure For The Preparation of Tubing Intake
Curves for Liquid Only
A step-wise procedure for predicting intake curves for the case
when only liquid is pumped follows6:
(1) Select a suitable pump as dictated by the casing size and the flow
capacity of the well
(2) Calculate fsc from Equation 7 (GLR=0) and fsc from Equation 5.
(3) Assume various production rates and, for each of these rates, do the
following:(a) Read the head per stage from the pump performance curves and
calculate the quantity (fsch/808.3141).
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2.3.2 Pumping Liquid and Gas
Because of the high compressibility of gas, the volume of the
produced flow rate V may undergo a significant variation as the pressure of
the fluid changes from the intake value to the discharge value. At anypressure point between the intake and discharge, if all gas is pumped with
the liquid, the volume factor is determined from6:
[ ] gso BRwcGLRBwcwcVF )1()1( ++= (19)
if a certain percentage of the gas is vented:
[ ] gso BRwcGLRGIPBwcwcVF )1()1( ++= (20)
In either case, the volume of the flow rate is given by:
VFqV sc= (21)
2.3.2.1 Determination Of The Number of Stages
Because V and, consequently, h vary as the fluid passes through
the pump, direct integration of Equation 10 is possible only if the integrand
V/h(V) can be reduced to a simple function of pressure. But this is difficult
because VF is a very complicated function of pressure. For this reason,
numerical integration methods are recommended.
The existence of gas at the intake section of the pump implies that
the intake pressure is below the bubble point of the crude (saturated crude).
If that is the case and if the required discharge pressure is above the bubble
point, Equation 10 should be broken down into two integrals as follows6:
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17
+=2
3)()(
P
Psc
P
Psc b
b
dPVh
V
q
AdP
Vh
V
q
ASt (22)
where A = 808.3141/fsc = constant (23)
For performing numerical integration, Equation 22 can be written in a
more convenient form as follows:
= =
+=m
i
n
mj
j
j
j
sc
i
i
i
sc
Ph
V
q
AP
h
V
q
ASt
1
,3,3 (24)
where:
P3,i = any intake pressure above the bubble point
P3,j = any intake pressure below the bubble point
P3,o = discharge pressure (P2)
P3,m = bubble point pressure (Pb)
P3,i = P3,i=P3,i-1-P3,i
P3,j = P3,j=P3,j-1-P3,j
ii hV / and jj hV / = average quantities evaluated at the average pressures
iP,3 and jP,3 , respectively.
where:
2/)( ,31,3,3 iii PPP +=
and
2/)( ,31,3,3 jjj PPP +=
The main reason for breaking down the number of stages into two
summations is the fact that V and, consequently, h undergo only slight
change above the bubble point; hence, P3,i can be taken much larger than
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P3,j. In fact, satisfactory results are obtained even if P3 is taken as the
difference between Pb and P2 and the quantity hV / is evaluated at the
midpoint.
When using a computer solution, it is easier to divide the interval
between the intake and the discharge pressure into equal increments by
taking P3 constant. For this case, Equation 24 can be written as:
=
=
n
i i
i
sc
ih
V
q
PASt
1
3 )( (25)
where:
P3,0
= discharge pressure (P2)
P3,n = intake pressure (P3)
n = (P2-P3)/P3
P3,i = P3,i-1- P3
The quantity ii hV / is evaluated at the average pressure given by:
2/)( ,31,3,3 iii PPP += (26)
In reality, any pressure P3,I can be considered an intake pressure. To
illustrate this point, Equation 25 can be written in the following form:
=
=n
i
ii StSt1
)( (27)
where:
i
i
sc
ih
V
q
PASt )()( 3
= (28)
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19
Therefore, inorder to obtain an intake pressure P3,i , we have:
i
i
sc h
V
q
PAStSt )()( 311
== (29)
In order to obtain P3,2, we have:
)()()(
2
2
1
13
212h
V
h
V
q
PAStStSt
sc
+
=+= (30)
And in order to obtain P3,n, we have:
=nSt nStStSt )(...)()( 21 +++ (31)
= )(( 3
scq
PA)...
2
2
1
1
n
n
h
V
h
V
h
V+++ (32)
2.3.2.2 Determination of Horsepower
The horsepower requirement is obtained by integrating Equation14 between the intake and the discharge pressures. Since the integrand
hp(V)/h(V) can not be reduced to a simple function of pressure, direct
integration is not possible, and numerical methods must be used.
If the interval between the intake and the discharge pressure is divided
into equal increments by taking P3 constant, Equation 14 can be written as
follows6:
=
=
n
i i
i
ih
hpPHP
1
3 )433.0
( (33)
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20
If(HP)I is defined as:
=
=
n
i i
ii
h
hpPHP
1
3 )433.0
()( (34)
then Equation 33 can be written as:
=
=n
i
ii HPHP1
)( (35)
2.3.2.3 Pump Selection
As mentioned previously, pump selection is limited by the casing
size and flow capacity of the well. Another constraint that must be taken into
account when pumping gas with the liquid is the volume range of the flow
rate. Because of the high compressibility of the gas, the difference between
the intake and discharge volumes may be too great to be contained within
the efficiency range of one pump. For this reason, the following procedure
for pump selection is suggested6:
(1) Prepare IPR curves in stbl/d and b/d to the same scale on the same
graph.
(2) Enter the b/d IPR curve at the upper limit of the efficiency range of
several pumps that are suitable from a casing-size standpoint. Move
horizontally to the stbl/d IPR curve and read the intake rate in stbl/d.
(3) For each intake rate determined in step 2, do the following:
(a) Determine the required discharge pressure from a two-phase flow
correlation.(b) Calculate VF at the discharge pressure, then calculate the discharge
volume.
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(4) Select the pump for which the discharge volume is greater than or equal
to the lower limit of its efficency range.
If more than one pump is found to be suitable, choose the one with the
highest capacity.
2.3.2.4 Procedure for the Preparation of Intake Curves for
Wells Pumping Gas
A step-wise procedure for predicting tubing intake curves for the
case in which gas is with the liquid is given as follows 6:
(1) Select a suitable pump as outlined previously.
(2) Calculate fsc from Equation 7 and calculate the constant A from
Equation 23.
(3) Assume several production rates in stbl/d and, for each of these rates,
do the following:
(a) Determine the required discharge pressure (P3,0) from a two-phase
flow correlation.
(b) Choose P3 and calculate the quantity (AP3/qsc)
(c) Calculate1,3
P and 1,3P .
(d) Determine 1VF at 1,3P , then calculate 1V .
(e) Read 1h at 1V from the pump performance curves.
(f) Calculate the required number of stages to obtain the intake pressure
P3,1 from Equation 25.
(g) Repeat steps c-f for P3,2, P3,3 through P3,i until a convenient intake
pressure is reached. Tabulate the intake pressure versus the number
of stages.
(4) By interpolating or plotting, obtain intake pressure for assumes rates for
an identical number of stages.
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(5) Plot the intake pressure (obtained in step 4) versus the assumed
production rates for the various number of stages. Plot the stbl/d IPR
curve to the same scale on the same graph.
(6) Read the rates at the intersection of the pump intake curves with the IPR
curve.(7) For each rate, calculate the horsepower requirement from Equation 33.
Calculation of horsepower requirements is similar to the calculation of
the number of stages.
(8) Plot the rate versus the number of stages and horsepower requirements.
Impose the efficiency range of the pump on the same graph.
(9) Select a suitable rate.
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23
CHAPTER III
NODAL ANALYSIS APPROACH
3.1 Introduction
The systems analysis approach, often called NODALTM Analysis, has
been applied for many years to analyze the performance of systems
composed of interacting components. Electrical circuits, complex pipelinenetworks and centrifugal pumping systems are all analyzed using this
method. Its application to well producing systems was first proposed by
Gilbert7 in 1954 and discussed by Nind8 in 1964 and Brown9 in 1978.
The production system can be relatively simple or can include many
components in which energy or pressure losses occur. Figure 3.1 illustrates
a number of the components in which pressure losses occur.
The procedure consists of selecting a division point or node in the well
and dividing the system at this point. All of the components upstream of the
node comprise the inflow section, while the outflow section consists of all of
the components downstream of the node. A relationship between flow rate
and pressure drop must be available for each component in the system. The
flow rate through the system can be determined once the following
requirements are satisfied2:
1 Flow into the node equals flow out of the node
2 Only one pressure can exist at a node.
At a particular time in the life of the well, there are always two pressures
that remain fixed and are not functions of flow rate. One of these pressures
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is the average reservoir pressure, Rp , and the other is the system
outlet pressure. The outlet pressure is usually the seperator pressure, psep,
but if the well is controlled by a surface choke the fixed outlet pressure may
be the wellhead pressure pwh.
Once the node is selected, the node pressure is calculated from both
directions starting at the fixed pressures.
Inflow to the node:
ppR (upstream components) = nodep (36)
Outflow from the node:
ppsep + (downstream component) = nodep (37)
The pressure drop, p , in any component varies with flow rate, q .
Therefore, a plot of node pressure versus flow rate will produce two curves,
the intersection of which will give the conditions satisfying requirements 1
and 2, given previously.
The effect of a change in any of the components can be analyzed by
recalculating the node pressure versus flow rate using the new
characteristics of the component that was changed. If a change was made
in an upstream component, the outflow curve will remain unchanged.
However, if either curve is changed, the intersection will be shifted, and a
new flow capacity and node pressure will exist. The curves will also be
shifted if either of the fixed pressures is changed, which may occur with
depletion or a change in separation conditions.
Figure 3.2 illustrates the comparison of intake curves for artificial lift
methods. It can be observed from the figure that electrical submersible
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pump keeps the bottomhole pressure low, thus, creates large amount of
pressure drawdown to reach high production rates.
Figure 3.1 Pressure Losses In a Production System2
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Figure 3.2 Tubing Intake Curves for Artificial Lift Systems6
Inflow to node:
whtubingresR pppp = (38)
Outflow from node:
whflowlinesep ppp =+ (39)
The effect of increasing the tubing size, as long as the tubing is not too
large, is to give a higher node or wellhead pressure for a given flow rate,
because the pressure drop in the tubing will be decreased. This shifts theinflow curve upward and the intersection to the right.
A larger flowline will reduce the pressure drop in the flowline, shifting the
outflow down and the intersection to the right. The effect of a change in any
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component in the system can be isolated in this manner. Also, the effect of
declining reservoir pressure or changing separator can be determined.
A more frequently used analysis procedure is to select the node
between the reservoir and piping system. The inflow and outflow
expressions for the simple system will then be:
Inflow to node:
wfresR ppp = (40)
Outflow from node:
wftubingflowlinesep pppp =++ (41)
A producing system may be optimized by selecting the combination of
component characteristics that will give the maximum production rate for the
lower cost. Although the overall pressure drop available for a system,
sepR pp , might be fixed at a particular time, the producing capacity of the
system depends on where the pressure drop occurs. If too much pressure
drop occurs in one component or module, there may be insufficient pressure
drop remaining for efficient performance of the other modules.
Even though the reservoir may be capable of producing a large amount
of fluid, if too much pressure drop occurs in the tubing, the well performance
suffers. For this type of well completion, it is obvious that increasing
reservoir performance by stimulation would be a waste of effort unless
larger tubing were installed.
If tubing is too large, the velocity of the fluid moving up the tubing may
be too low to effectively lift the liquids to the surface. This could be caused
by either large tubing or low production rates.The fluid velocity is the
production rate divided by the area of the tubing.
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As tubing size is increased, the friction losses decrease, which results in
a lower wfp and, therefore, a larger inflow. However, as the tubing size is
further increased, the well begins loading with liquid and the flow becomes
intermittent or unstable. As the liquid level in the well builds the well will
eventually die.
Once a well that is producing liquids along with the gas reaches the
stage in which it will no longer flow naturally, it will usually be placed on
artificial lift.
The nodal systems analysis approach may used to analyze many
producing oil and gas well problems. The procedure can be applied to both
flowing and artificial lift wells, if the effect of artificial lift method on the
pressure can be expressed as a function of flow rate. The procedure can
also be applied to the analysis of injection well performance by appropriate
modification of the inflow and outflow expressions. A partial list of possible
applications is given as follows2:
1. Selecting tubing size
2. Selecting flowline size
3. Gravel pack design
4. Surface choke sizing
5. Subsurface safety valve sizing
6. Analyzing an existing system for abnormal flow restrictions
7. Artificial lift design
8. Well stimulation evaluation
9. Determinig the effect of compression on gas well performance
10. Analyzing the effects of perforating density
11. Predicting the effect of depletion on producing capacity
12. Allocating injection gas among gas lift wells13. Analyzing a multiwell producing system
14. Relating field performance to time
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3.2 Application of Nodal Analysis to Electrical Submersible Pumping
Wells
To perform a nodal analysis on a submersible pumping well, the node is
selected at the pump. The pump can be handled as an independentcomponent in the system in a manner similar to that used in gravel-packed
completions. The node pressure is either the pump intake pressure upp or
the pump discharge pressure dnp . The pressure gain that the pump must
generate for a particular producing rate is updn ppp = . The pressure
traverse below the pump will be calculated based on the formation
gas/liquid ratio and the casing size. The traverse in the tubing above the
pump will be based on the gas/liquid ratio entering the pump and the tubingsize. The inflow and outflow expressions are2:
Inflow:
upcsgresR pbelowpumpppp = )(
Outflow:
(tubflowlinesep ppp ++ dnpabovepump =)
The following procedure may be used to estimate the pressure gain and
power required to achieve a particular producing capacity.
Inflow:
1. Select a value for liquid producing rate Lq .
2. Determine the required wfp for this Lq .using the reservoir performance
procedures.
3. Determine the pump suction pressure upp using the casing diameter and
the total producing GLR to calculate the pressure drop below the pump.
4. Repeat for a range of liquid producing rates and plot upp versus. Lq .
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Outflow:
1. Select a value for Lq .
2. Determine the appropriate GLR for tubing and flowline pressure drop
calculations.
a. Determine upp and fluid temperature at the pump at this Lq value from
inflow calculations.
b. Determine dissolved gas sR at this pressure and temperature.
c. Estimate fraction of free gas sE , separated at the pump. This will be
dependent whether or not a downhole separator is to be used. If not use
5.0=sE .
d. Calculate the GLR downstream of the pump from
))(1( sototalsdn RfREGLR = = (42)
where:
=totalR total producing gas/liquid ratio,
sR = solution gas/oil ratio at suction conditions, and
=of fraction of oil flowing
3. Determine dnp using GLRdn to calculate the pressure drop in the tubing
and the flowline if the casing gas is vented. If the casing tied into the
flowline, the total GLR will be used to determine the pressure drop in the
flowline.
4. Repeat for a range of Lq and plot dnp vs Lq on the same graph.
5. Select various producing rates and determine the pressure gain prequired to achieve an intersection of the inflow and outflow curves at
these rates. The suction and discharge pressures can also be
determined for each rate.
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6. Calculate the power requirement, pump size, number of stages, etc., at
each producing rate.
The required horsepower can be calculated from:
)(1072.15
wwoo BqBqpHP += (43)
where:
HP = horsepower required
p = pressure gain, psi
qo = oil rate, STB/day
qw = water rate, STB/day
Bo = oil formation volume factor at suction conditions, bbl/STB, and
Bw = water formation volume factor at suction conditions
The pressure gain can be converted to head gain if necessary for pump
selection. This is accomplished by dividing the pressure gain by the density
of fluid being pumped. The actual plotting of the data is not required if the
pump is to be selected for specific rates, as all the necessary information is
calculated before plotting.
3.3 Description of the Computer Program
3.3.1 Pumping Only Liquid
A two-stage computer program in Fortran Code has been written and
also EXCEL Worksheet was used to support the program.
At the first stage, program input consists of well, fluid, reservoir, and lift-system data. Once these conditions were satisfied, program initially gives
the pressure at pump setting depth (discharge pressure) by applying
Hagedorn and Brown3 vertical multiphase correlation. In addition to
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Code has been written and also EXCEL Worksheet was used to support the
program. Input parameters of the program are same with pumping only
liquid program, however, GOR value should be entered since free gas
exists. At first stage, program calculates VF at pressure interval between
200 5000 psi. Afterwards, by following same steps with pumping onlyliquid program, discharge pressure is calculated by Hagedorn and Brown3
Vertical Multiphase Flow Correlation (existing as a subprogram in the
algorithm) and program starts to make iterations by decreasing pressure 50
psi at every iteration in order to calculate volume (h), h (head per stage) and
number of stage (St) values at desired production rate. As explained
previously, program computes Griffith4 Correlation when bubble flow
conditions were formed. Program then calculates the intake pressure at
various numbers of stages to let us construct tubing intake curve on the
same graph as the IPR curve. At the second stage of the program, user
should again enter possible production rates to programs, which are
obtained manually by intersecting intake curve and IPR curve. This
procedure cannot be achieved by program as explained before. At this
point, program starts to make iterations to calculate horsepower per stage
and total horsepower requirement at every 50 psi pressure drop until it
reaches to intake pressure. This data will help us to construct Possible
Production Rate versus Stages and Horsepower Figure in order us to make
necessary evaluation. It should be kept in mind that pump selection is
achieved manually by entering to input, in other words program does not
include an algorithm that automatically selects a suitable pump for that well.
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CHAPTER IV
STATEMENT OF THE PROBLEM
The objective of this study is to perform a production engineering
study at GK oil field in Southeastern Turkey. The main goal of the study is to
achieve production optimization of 10 electrical submersible pump lifted
wells currently operating in this field. Desired conclusion will be reachedafter determining the optimum pump stages and horsepower requirement
for a possible production rate by a theorotical study and compare it with
actual field submersible pump operating data. The study will let us to
suggest optimum submersible pump running conditions for each well to
continue production in a more economical and cost saving approach.
Following steps were considered during the study to reach the aim:
writing computer program that applies vertical multiphase flow
correlation and computes the parameters that were required for the
optimization
collecting and evaluating the actual reservoir, well, fluid and lifting
data that the case study was performed
entering field data to computer program and taking the output for
two pumping conditions
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preparing necessary figures and charts concerning pump stages,
production rate and horsepower requirement using the computer
output
comparison of actual field values and theorotical values and
making necessary suggestions
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CHAPTER V
HAGEDORN AND BROWN VERTICAL MULTIPHASE FLOW
CORRELATION SUPPORTED BY GRIFFITH CORRELATION
5.1 Introduction
The use of multiphase flow pipeline pressure drop correlations is very
important in applying nodal analysis.
The correlations that are most widely used at the present time for
vertical multiphase flow are as follows:
1. Hagedorn and Brown3
2. Duns and Ros10
3. Ros and Gray11
4. Orkiszewski12
5. Beggs and Brill13
6. Aziz14
These are found to calculate pressure drop very well in certain wells
and certain fields. However, one may be much better than the other under
certain conditions and field pressure surveys are the only way to find out.
Without any knowledge in a particular field, it would be recommended
beginning initial work with the correlations as listed in the above order.
In the literature it is recommended to from a hybrid by using the most
dependable parts of the four models. As an example, the commercial
vertical multiphase flow model (MTRAN) that was developed by Scientific
Software Incorporation uses the following sections:
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1. Duns and Ros10 flow map
2. Use Orkiszewski12 for bubble flow
3. Use Hagedorn and Brown3 for slug flow
4. Use Duns and Ros10 for transitional and mist flow
Figure 5.1 illustrates the schematic diagram of possible flow patterns in
two-phase pipelines to visualize the flow systems that above correlations
used for.
Figure 5.1 Schematic Diagram of Possible Flow Patterns in Two-PhasePipelines6
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5.2 Hagedorn and Brown Method
The Hagedorn and Brown3 method was developed by obtaining
experimental pressure drop and flow rate data from a 1500 ft deep
instrumented well. Pressures were measured for flow in tubing sizes ranging
from 1 to 2 7/8 in O.D. A wide range of liquid rates and gas/liquid ratios
was included, and the effects of liquid viscosity were studied by using water
and oil as the liquid phase. The oils used had viscosities at stock tank
conditions of 10, 35 and 110 cp. Later two adjustments were made to
improve this correlation. When bubble flow existed, the Griffith4 Correlation
was used and when the no slip holdup was greater than the holdup value,
the no slip holdup was used2.
Neither liquid holdup nor flow pattern was measured during the
Hagedorn and Brown study, although a correlation for the calculated liquid
holdup is presented. The correlations were developed by assuming that the
two-phase friction factor could be obtained from the Moody diagram based
on a two-phase Reynolds number. This Reynolds Number requires a value
for LH in the viscosity term.
The Hagedorn and Brown method has been found to give good
results over a wide range of well conditions and is one of the most widely
used well flow correlations in the industry2
. However, the original Hagedornand Brown correlation has several weaknesses: At first, it is not very
accurate in bubble flow. Moreover, calculated slip holdup is sometimes
below no-slip holdup and also the acceleration term is too dominant.
Thompson added that, the modified Hagedorn and Brown Correlation
tended to overpredict pressure loss in bubble flow (Griffith), while it tended
to underpredict slug flow. The Hagedorn and Brown Correlation gives best
results for wellbores with low to moderate liquid volume fractions (high gas-
liquid ratios) and relatively high mixture velocities (annular-mist or frothflow).
The selection of appropriate correlation for a given production system
is important to reach to an accurate solution. In this study, Hagedorn and
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psi. This type of calculation is practically forbidden by long hand but lends
itself readily to machine computation. If starting from bottom with pressures
in excess of 1,000 psi, the pressure decrements may be as great as 200
psi.
2. Calculate the specific gravity of the oil, o:
o=API+5.1315.141
(47)
3. Find total mass associated with one bbl of stock tank liquid:
m = o (350) (WOR+11 ) + w (350) (
WOR
WOR
+1) + (0.0764) (GLR) g (48)
4. Calculate the mass flow rate:
w = q m (49)
5. Obtain Rs at P and T by Standings16 Correlation :
Rs = g ( )(00091.0
)(0125.0
10
10
18 T
APIP )1/0.83 (50)
where Rs = scf/bbl
Lasaters17 equation can also be used and it is more accurate than
Standings correlation especially at higher API. The equation of Lasaters
correlation is as follows:
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Rs = CY
Y
M g
g
o
o )1
)())(350)(3.379(
(
(51)
where:
Mo = molecular weight
T = R
The value of C is 1.0 unless a correction factor is necessary to make the
equation check with actual field cases.
6. Obtain Bo according to calculated Rs value:
a) If bPP :
TRFo
g
s 25.1)(5.0 +=
(52)
175.1000147.0972.0 FBob += (53)
b) If bPP
))(( PPc
oboboeBB
= (54)
7. Calculate the density of liquid phase:
L = [ ] [ ])1
)(4.62()1
1(614.5/)0764.0()4.62(
WOR
WOR
WORB
Rw
o
gso
++
++ (55)
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8. Assuming T= constant, find a value ofZ for a constant T, p and g. If
T is to be a variable, then a single trial and error solution develops.
Although the temperature gradient may be known, the depth at which
the pressure increment occurs is not known and, therefore, the
temperature at the next pressure point is not known.
4.688852.17292.17 2 += ggpcP (56)
94.17293.3088324.1 2 ++= ggpcT (57)
pcpr P
P
P = (58)
pc
prT
TT = (59)
101.036.0)92.0(39.1 5.0 = prpr TTA (60)
6
))1(9(
2 )10
32.0()037.0
)86.0(
066.0()02362.0( prTpr
pr
prpr PPT
PTBpr
+
+= (61)
)log(32.0132.0 prTC = (62)
)1824.049.03106.0( 2
10 prprTT
D+= (63)
a) If 100B
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D
prBCP
e
AAz +
+=1
(64)
b) If 100B
D
prCPAz += (65)
9. Calculate the average density of the gas phase
g = )1
)(520
)(7.14
)(0764.0(ZT
pg (66)
10. Calculate the average viscosity of the oil from appropriate correlations.
As noted, a knowledge of fluid properties of the oil, p , and / or T is
required.
a) If bPP
)04658.09824.6(163.1 APIeTX = (67)
110 = XoD (68)
515.0)100(715.10+= sRA (69)
338.0)150(44.5
+= sRB (70)
B
oDo A = (71)
b) Ifb
PP
)(
143
2 PCCC
ePCB+= (72)
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where:
C1 = 2.6
C2 = 1.187
C3 = -11.513
C4 = -8.9810-5B
oDb A =
B
b
boP
P)( = (73)
where:
b = viscosity of the reservoir liquid at the bubble point, cp
oD = dead oil viscosity, cp
11. Determine the average water viscosity from correlation below:
)10982.110479.1003.1( 252 TT
W e += (74)
12. Calculate the liquid mixture viscosity:
L = o +
+ WOR11
w
+ WORWOR
1(75)
This can only be an approximation since the viscosity of two immiscible
liquids is quite complex.
12. Assuming constant surface tensions at each pressure point, calculate
the liquid mixture surface tension.
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L = o (WOR+11
) + w (WOR
WOR
+1) (76)
Again, this represents only an approximation of the surface tension of
the liquid phase.
13. Calculate the liquid viscosity number:
NL = 0.15726L( 31
LL)1/4 (77)
14. Determine CNL from the previously formed equation of CNL versus NL
graph.
002.002.08612.0069.1022.4804.106222.87 23456 ++++= LLLLLLL NNNNNNCN (78)
15. Calculate the area of tubing, Ap.
Ap =4
2d(79)
16. Obtain Bo at Tp,
17. Assuming Bw = 1.0, calculate the superficial liquid velocity sL , ft/sec:
sL =
+
++
)1()
1
1(
86400
61.5
WOR
WORB
WORB
A
qwo
p
L (80)
18. Calculate the liquid velocity number, NLV:
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NLV = 1.9384/1)(
L
LsL
(81)
19. Calculate the superficial gas velocity, sg :
sg =
+
1520
7.14
86400
1
1
ZT
pA
WORRGLRq
p
sL
(82)
20. Determine the gas velocity number, NGV:
NGV =1.938 sg
4/1
L
L
(83)
21. Find the pipe diameter number, Nd:
Nd = 120.872dL
L
(84)
22. Calculate the holdup correlating function :
=
d
L
gV
LV
N
CNp
N
N10.0
575.0 7.14 (85)
23. Obtain
LH from the correlation determined before:
LH = 11.02.182310210103104102 2639411513615 ++++ (86)
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24. Determine the secondary correction factor correlating parameter, :
=
14.2
380.0
d
Lgv
N
NN(87)
25. Obtain from the previously formed equation of versus graph.
= 7611.112.15710765300129104103108 23465767 +++ (88)
26. Calculate a value for HL:
HL = [ ]
LH (89)
For low viscosities there will be no correction and = 1.00.
27. In order to obtain a friction factor, determine a value for the two-phase
Reynolds number, (NRe)TP:
))()((
102.2)(
)1(
2
ReLL H
g
H
L
TPd
wN
=
(90)
28. Determine a value for/d. If the value of is not known, a good value to
use is 0.00015 ft which is an average value given for commercial steel.
29. Obtain the friction factor from the Jain18 Equation:
)25.21
log(214.11
9.0
ReNdf+=
(91)
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30. Calculate the average two-phase density of the mixtures m by two
methods.
(a) Using the value of HL, calculate m as follows:
m = )1( LgLL HH + (92)
(b) Calculate a value of m assuming no slippage.
31. Calculate the two-phase mixture velocity at both p1 and p2.
m1=sL1+sg1 (93)
m2=sL2+sg2 (94)
32. Determine a value for (m2)
(m2) = [ ]2 221 mm (95)
33. Calculate h corresponding to p = p1 p2
h =
m
m
c
m
m
d
fw
gp
511
2
2
109652.2
)2(144
+
(96)
34. Starting with p2 and the known depth at p2, assume another pressure
point and repeat the procedures until reaching total depth, or until reaching
the surface depending upon whether you are starting from the bottom or top
of tube.
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5.4 GRIFFITH CORRELATION (BUBBLE FLOW)
The void fraction of gas (Hg) in bubble flow can be expressed as:
Hg=
++
ps
g
ps
t
ps
t
Av
q
Av
q
Av
q 4)1(1
2
1 2 (97)
where :
vs = slip velocity (bubble rise velocity), ft/sec
Griffith suggested that a good approximation of an average vs is 0.8
ft/sec. The average flowing density can be computed as:
= gggL HH + )1( (98)
The friction gradient is:
hcLLf dgvf 2/2
= (99)
where:
[ ])1( gpL
LHA
q
= (100)
The Reynolds number is calculated as:
L
LhL vdN
1488Re = (101)
where:
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dh = hydraulic pipe diameter, ft
L = liquid viscosity, cp
Vertical pressure gradient curves (for three different reservoir
conditions) obtained from the computer program by following the above
steps were given at Chapter 7.
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CHAPTER VI
DESCRIPTION OF THE GK FIELD
6.1 Introduction
The selected field is located on South East Anatolian. The field was
discovered in 1961 and has been on production since then. Currently, there
are a total of 29 wells with 12 producers, 13 closed-in, 2 dumpflooders and2 injection wells. The main drive mechanism of the field is rock and fluid
expansion, there also exists a weak aquifer at the system but not sufficient
to create a producing force.
The field started its production life as a dry and natural flowing field. A
steep pressure decline in wells was observed during late 1961 and early
1962. It was decided that the field pressure should be maintained by water
injection through peripheral wells 3 and 5 on the Eastern and Western
flanks of the field to keep the production wells on natural flow. In 1966,water cut increased and killed natural flow. In 1967, as a result of high field
offtake, pressure in producers began to decline rapidly. Thus, in August
1967, water injection was stopped to observe production declines in the field
and artificial lift system was installed. After realising that recovery is
constrained by pressure decline rather than the watercut development in
1986 dumpflooding started. In June 1997 from two wells re-injection
started19.
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6.2 Geology
The field is an elongated structure in an approximate EastWest
direction. Up to date 29 wells have been drilled and two wells are located
outside the field (Well-9 and Well-10). The field is a frontal thrust structureconsisting of an anticline on the leading edge of the thrust block. The
reservoir rock has been divided into Mardin Units, I, II, III and IV. These
units are further subdivided based on lithology (limestone and dolomite) and
porosity classes.
There is a main continues East-West trending normal fault. This main
fault separates two blocks as Main Block and Northern Block and there is an
another block called Western Block. The unique pressure response of the
W-14 with respect to the rest of the field (pressure measured in W-14
showed slight depletion of only a few hundred psi, when the average
reservoir pressure in the rest of the field was more than 1000 psi) may show
the existence of a barrier between W-14 and W-11 due to either a fault or
reservoir rock quality deterioration (a permeability barrier) between those
wells. The reservoir deterioration between the wells on the other hand, can
not be confirmed due to shallow completion of the W-11 which prevents the
correlation of two wells because of the long distance between these two
wells, the deterioration of the reservoir quality is still quite possible.
The units having the highest porosities are the dolomite in Unit I and the
high porosity limestone close to the bottom of the Unit II. The average
porosities of this dolomite unit varies between 15% and 20% and the
average permeabilities between 6 mD-50mD based on core measurements.
Intercrystalline and vuggy porosities, and some solution channels and
fractures were also observed on the core samples.
Unit II is described as limestone-dolomitic limestone. Cores indicated
that it has vuggy porosity and solution channels, and some sub-vertical/sub-
horizontal fractures also exist. The average porosity is 10%-15% with air
permeabilities between 0.3 mD-1.5 mD based on core measurements.
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TABLE 6.2 SUBMERSIBLE PUMP LIFTED WELLS OPERATED IN
GK FIELD AND THEIR EFFICIENCY RANGES
WELL PUMP USEDEFFICIENCY
RANGE (bbl/d)
W-07 DN440 83 - 458
W-08 DN675 267 - 692
W-15 GN2000 1300 - 2650
W-16 GN1600 833 - 1792
W-17 GN1600 833 -1792
W-22 DN440 83 - 458
W-24 DN1100 500 - 1125
W-25 GN3200 1834 - 3417
W-27 DN675 267 - 692
W-28 DN675 267 - 692
6.4 Production History
Production rates and bottomhole pressures recorded for the producer
wells between the years 1961 and 1999 gives the generalized IPR curve
showed in Figure 6.1. This figure is the combination of 66 well test data from
12 different producer wells and by inspecting the figure, it can be observed
that the (qo)max is 1378 bbl/d or 1385 stb/d and flow rate at bubble point
pressure, (qo)b, is 1340 bbl/d or 1347 stb/d.
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0
500
1000
1500
2000
2500
3000
0 200 400 600 800 1000 1200 1400 1600
q (BBL/D or STB/D)
Pwf(psi)
BBL/D
STB/D
Figure 6.1 Generalized IPR Curve
The gross rate of each submersible pump lifted producer well during
the production period and required pump stages used in the field are given
in Table 6.3.
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TABLE 6.3 GROSS PRODUCTION RATE OF THE WELLS IN GK FIELD
AND REQUIRED PUMP STAGES
Well Gross Rate (bbl/d) Pump Stages
W-07 180 356
W-08 740 238
W-15 1180 216
W-16 1350 180
W-17 1270 181
W-22 70 320
W-24 1000 332
W-25 1620 239
W-27 400 338
W-28 530 338
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CHAPTER VII
RESULTS AND DISCUSSION
7.1 INTRODUCTION
Calculations are based on the steps that are summarized in Chapter 2
at sections 2.3.1.1 for pumping liquid and 2.3.2.4 for pumping liquid and
gas. These calculations were done for the 10 submersible pump lifted wellsindicated in Table 6.2 and by using the pumps that were actually operated in
the GK field. Detailed sample calculation for W-08 and the output of
computer program can be observed in Appendix B.
Results of the study can be categorized into five different parts:
a. Construction of vertical flowing pressure gradient (pressure traverse)
curves according to computer program output and comparing theresults with Beggs&Brill13 Correlation
b. Performing Sensitivity Analysis based on effect of of oil density, GLR
and WOR on flowing bottomhole pressure by using the computer
program output
c. Construction of possible production rate versus stage and
horsepower chart for each well (GLR = 15 scf / STB) by using the
pumping liquid and gas computer algorithm
d. Comparison of theoretical and actual production parameters andsuggestion for optimum pump operating conditions by inspecting
possible production rate versus stage and horsepower chart
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100400 300
500
0200
GAS-LIQ
UIDRATIO
,scf/STB
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
0 400 800 1200 1600 2000 2400 2800 3200 3600 4000
Pressure (psi)
Depth(ft)
Tubing Size, in : 2.441
Liquid Rate, STBL/D : 100Water Fraction : 0
Gas Gravity : 0.70
Oil API Gravity : 38
Water Specific Gravity : 1.02
Average Flowing Temp., F : 170
Correlation : Hagedorn&Brown
Griffith Correlation (bubble flow)
Figure 7.1 Pressure Traverse Curve (WC = 0)
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60
1002000
500
300400
GAS-LIQ
UIDRATIO
,scf/STB
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
0 400 800 1200 1600 2000 2400 2800 3200 3600 4000 4400
Pressure (psi)
Depth(ft)
Tubing Size, in : 2.441
Liquid Rate, STBL/D : 100Water Fraction : 0.5
Gas Gravity : 0.70
Oil API Gravity : 38
Water Specific Gravity : 1.02
Average Flowing Temp., F : 170
Correlation : Hagedorn&Brown
Griffith Correlation (bubble flow)
Figure 7.2 Pressure Traverse Curve (WC = 0.5)
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500
400 300
200 100 0
GAS-LIQ
UIDRATIO
,SCF/S
TBL
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
0 400 800 1200 1600 2000 2400 2800 3200 3600 4000 4400 4800
Pressure (psi)
Depth(ft)
Tubing Size, in : 2.441Liquid Rate, STBL/D : 100
Water Fraction : 1.0
Gas Gravity : 0.70
Oil API Gravity : 38
Water Specific Gravity : 1.02
Average Flowing Temp., F : 170
Correlation : Hagedorn&Brown
Griffith Correlation (bubble flow)
Figure 7.3 Pressure Traverse Curve (WC = 1.0)
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A comparison was made between pressure traverse curves prepared
by Beggs&Brill13 and curves constructed with computer output in order to
test the accuracy of correlation used in the program algorithm. Table 7.1
briefly indicates the pressures at selected depths with respect to two
conditions. Inspecting Table 7.1, we can understand that computer-basedpressures and the Beggs&Brill correlation values are very close to each
other. This means that vertical multiphase flow correlation within the
program is giving reliable output and encurages us about the accuracy of
rest of the study. It should be kept in mind that values determined from
Beggs&Brill correlation are recorded at slightly different reservoir and fluid
conditions than GK field parameters, that is, gas gravity is 0.65, oil API
gravity is 35 and average flowing temperature is 150 F. Another point that
should be taken into account during the comparison is that when GLR
increases, difference between pressure values of computer output and
Beggs&Brill values are also increases. This behaviour can be interpreted as
reliability of Hagedorn and Brown flow correlation supported by Griffith
Correlation should be re-tested at high GLR reservoirs.
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TABLE 7.1 COMPARISON of COMPUTER-BASED VERTICAL FLOWING PRESSUR
BEGGS&BRILL CORRELATION AT SELECTED DEPTHS
Water Fraction
0 0.5
GLR (scf/STB) GLR (scf/STB) GLR (
0 100 0 100 0
Pressure (psi) Pressure (psi) Press
Depth (ft) Output Beggs&Brill Output Beggs&Brill Output Beggs&Brill Output Beggs&Brill Output Beggs&Brill
4000 1440 1400 1050 1040 1590 1600 1220 1140 1680 1800
6000 2160 2090 1770 1750 2380 2400 2040 1960 2560 2720
8000 2870 2800 2480 2440 3190 3190 2820 2750 3440 3610
10000 3580 3500 3190 3130 3985 4000 3610 3560 4320 4540
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7.2.2 Sensitivity Analysis by Using the Computer Program Output
Having a chance of changing all variables related to Hagedorn and
Brown vertical multiphase flow correlation within the program, sensitivity
analysis was performed by observing the effect of oil density, GLR andWOR on flowing bottomhole pressure. Results were summarized in Table
7.2, 7.3 and 7.4. Reservoir and fluid data of W-08 was used during the
study. After making necessary observations for the output, it can be
observed that the increase in oil density and GLR creates a slight decrease
in bottomhole pressure, and an increase in WOR causes an increase in
flowing bottomhole pressure.
TABLE 7.2 EFFECT of OIL DENSITY on FLOWING BOTTOMHOLE
PRESSURES AT SELECTED DEPTHS
Well Depth (ft)
API4000 6000 8000 10000
10 2000 2880 3760 4620
15 2000 2880 3760 4620
20 1990 2870 3760 4610
25 1990 2870 3750 4610
30 1990 2870 3750 4610
35 1990 2870 3750 4600
40 1990 2870 3740 4600
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GLR=0 scf/stbl
GLR=100
GLR=200GLR=300
GLR=400GLR=500
IPR
0
500
1000
1500
2000
2500
3000
0 200 400 600 800 1000 1200
q (BBL/D or STB/D)
Pwf(psi) BBL/D
STB/D
Figure 7.4 Graphical Analysis of Effect of GLR on Flowing
Bottomhole Pressure for W-08
WOR=0.5
IPR
WOR =0
WOR=1.0
0
500
1000
1500
2000
2500
3000
0 200 400 600 800 1000 1200
q (BBL/D or STB/D)
Pwf(psi)
BBL/D
STB/D
Figure 7.5 Graphical Analysis of Effect of WOR on Flowing
Bottomhole Pressure for W-08
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7.2.3 Construction of Possible Production Rate versus Stage
and Horsepower Chart for GK Field Wells by Using
the Pumping Liquid and Gas Computer Algorithm
Possible production rate versus stage and horsepower chart wasprepared for each electrical submersible pump lifted wells in GK field by
considering the intake pressures obtained from computer program at
selected flow rates. These charts can said to be the final step of the study
and helped us to make necessary suggestions for optimum pump operating
conditions. In below figures, actual value point is the real production rate of
the well in GK field and the number of pump stages used for that well. It
should be noted that actual horsepower requirement data for these wells
are not available. On Figures 7.6 to 7.14, the efficiency range of the pumps
used and also suggested flow rate and corresponding horsepower
requirement and number of pump stages can be observed.
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HP
Stages
Efficiency Range
Actual
Suggested HP
0
50
100
150
200
250
300
350
400
450
500
550
600
0 50 100 150 200 250 300
Stages or Horsepower
PossibleRate(STB/D)
FIGURE 7.6 Possible Production Rate vs Stages and Horsepower fo
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HP
Effic
Stages
Actual Value (St)Suggested HP
Suggested Stage
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
13001400
0 50 100 150 200 250 300
Stages or Horsepower
Pos
sibleRate(STB/D)
FIGURE 7.7 Possible Production Rate vs Stages and Horsepower
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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
Stages or Horsepower
PossibleRate(STB/D)
FIGURE 7.8 Possible Production Rate vs Stages and Horsepower for
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HP
Efficiency RaActual Value (St)
Suggested HP Suggested Stage
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 100 200 300 400
Stages or Horsepower
PossibleRate(STB/D)
FIGURE 7.9 Possible Production Rate vs Stages and Horsepower for
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HP
Stages
Actual Value (St)
Suggested HP Suggested Stage
0
200
400
600
800
1000
1200
1400
1600
1800
0 100 200 300 400
Stages or Horsepower
Possib
leRate(STB/D)
FIGURE 7.10 Possible Production Rate vs Stages and Horsepower fo
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HP
Efficiency Range
Suggested HP
Suggested Stage
0
200
400
600
800
1000
1200
1400
1600
1800
0 50 100 150 200 250 300
Stages or Horsepower
Possib
leRate(STB/D)
FIGURE 7.11 Possible Production Rate vs Stages and Horsepower fo
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HPStages
Efficiency Range
Actual Value(St)
Suggested HP
Suggested Stage
0
500
1000
1500
2000
2500
3000
3500
0 100 200 300 400 500
Stages or Horsepower
PossibleRate(STB/D)
FIGURE 7.12 Possible Production Rate vs Stages and Horsepower fo
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Efficiency Range
Suggested Stage
Suggested HP
0
100
200
300
400
500600
700
800
900
1000
1100
1200
1300
1400
0 50 100 150 200 250 300Stages or Horsepower
PossibleRate(STB/D)
FIGURE 7.13 Possible Production Rate vs Stages and Horsepower fo
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Efficiency Range
Actual VaSuggested HP
Suggested Stage
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0 50 100 150 200 250 300
Stages or Horsepower
Possib
leRate(STB/D)
FIGURE 7.14 Possible Production Rate vs Stages and Horsepower fo
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W-17 is operated with 1270 stb/d with 181 stages. This rate indicates
that the pump is used efficiently (833-1792 bpd). Besides, observing Figure
7.9, operating production rate and pump stage values are said to be at
optimum range, and the actual and theoretical values are close to each
other. Thus, a production rate of 1400 stb/d and a corresponding HPrequirement of 100 HP and 220 pump stages can be offered in theorotical
circumst
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