Model-based optimization of production

systems

Cleide Rosemine Gany

Vieira

Petroleum Engineering
Submission date: July 2015
Supervisor: Milan Stanko, IPT

Norwegian University of Science and Technology

Department of Petroleum Engineering and Applied Geophysics
Model-Based Optimisation of Production
Systems

Cleide Vieira

Master’s Thesis
Submission date: July 2015
Supervisor: Milan Stanko, IPT

Norwegian University of Science and Technology

Department of Petroleum Engineering and Applied Geophysics
 Model-Based Optimisation of
Production Systems
Case Study: Gas-Lift Method

By

Cleide Vieira

Master’s Thesis in Petroleum Engineering

Supervisor: Dr. Milan Stanko

Co-supervisors: Prof. Abraham Temu

Trondheim, July 2015

Norwegian University of Science and Technology

Faculty of Engineering Science and Technology
Department of Petroleum Engineering and Applied Geophysics
 Abstract

Gas lifted method is one of the artificial lift technique used in the oil and gas industry.
This method is applied most in oil well to improve the oil recovery by lowering the bottom
hole pressure.
Normally in the field there are multi-gas lifted wells that requires certain amount of
gas to be injected to achieve the maximum oil production. Generally the amount of gas
available is limited, therefore is has to be allocated per well in the best way possible
to achieve maximum oil production in the system. The problem of determining gas lift
allocation per well to ensure maximum oil production can be formulated and solved as a
mathematical optimization.
The results of the optimisation is a optimum gas injection rate that yield the maximum
oil production for group of wells, this is important because excessive gas injected into the
well can reduce the oil production and increases operation cost.
For a group of gas lifted wells there are two possible methods to perform the optimi-
sation. Method 1, by assuming that the well operating conditions (i.e. wellhead pressure)
of each well in the system will not be affected by the neighbouring wells and using pre-
computed gas lift performance curves of each well. In method 2, the case is usually solved
using a mathematical optimisation routine and a model of the entire production system.
To achieve the main goal of the present thesis, optimisation for an ideal production
network with five gas lifted wells has been modelled in Excel with data generated in
PROSPER for the case of method 1 and in GAP optimisation software for the case of
method 2. Therefore a deviation between the methods were calculated and presented in
percentage for better analyses and observations. Through the results presented in this
thesis the value of the total oil production found using method 1 can in some cases be
close to the value in GAP optimisation (method 2), but in another hand the injected
gas per well differ from each other in the same system. The deviation found for the case
of injected gas per well increases proportional with the amount of gas available in the
system.
For the optimisation using method 2, three different model schematic were created,
and the model without an pipeline showed to be the system with more oil production,
due to the location of the separator that does not contribute for the pressure loss in the
system. The second model (GAP-2) have the lower production in comparison with all the
model, cause by the pipeline length distance (12km) that affect the pressure loss during
the production.
In method 1 two different techniques were used for the optimisation, the piecewise-
linear optimisation and the curve fitting. The calculation shows that the piecewise-linear
has high deviation value compared with the curve fitting technique, being better to use
the curve fitting to calculate the optimisation when the constant wellhead assumption is
used. Curve fitting techniques two equations were used to fit the gas lift performance
curve data (generated in PROSPER), the Alaracón et al. and Rashid et al. The Rashid
et al. equation was observed to be the best representative of the gas lift curve in all the
scenarios and the deviation tended to be lower than one found using the other equation.
If the number of iteration and time taken for each system to reach the optimum
point is considered, the curve fitting technique using Rashid et. al. equation takes less
time and iteration number comparing with other techniques in method 1. For the case
of optimisation using method 2 those values change in all scenarios and model, is not
constant trend.
 The study shows that, if a optimisation using method 1 is done for a system with
wells having high values of gas injection (more than 10 scf/D) to achieve the maximum
oil production, the deviation between the methods (Excel and GAP models) will be
more than 10%. This also when the data generated from PROSPER have more than
2000 STB/D as maximum oil production per well. If the data generated containing gas
injection greater than zero at the beginning of GLPC is used in method 1 optimisation
the deviation can be more than 30% when all wells in the system present the same
characteristic.
The deviation calculated between the method 1 and method 2 is lower for the system
using the third model schematic in GAP where pipelines were added. The total oil
production is lower than the first model and greater than the second model, making the
value more approximated to the optimum found in method 1.
In optimisation using method 1 if the wells data from gas lift performance curve
present low oil production and gas injection, the value of coefficients in equation of
Alaracón and Rashid are almost the same and the deviation calculated using this well
will be lower. For wells having the value of coefficient different the deviation calculated
will be high, this is the case of well with gas injection greater than zero at the beginning
in the gas lift performance curve.

II
Acknowledgment

First and foremost, I have to thank my at NTNU supervisors, Dr. Milan Stanko and
Prof. Michael Golan for the opportunity of being part of the students assisted by them.
Extend my thanks to the co-supervisor at University of Dar-es-salaam Prof. Abraham
Temu for the assistance given to me during my stay in Tanzania. Without their assistance
and dedicated involvement in every step throughout the process, this paper would have
never been accomplished. I would like to thank you very much for your support and
understanding over these semester.
I would like to be grateful for the people in Statoil Tanzania that was supporting me
in all ways, in special to Dr. Richard, Mr. Tore and Miss Ghati.
Getting through my dissertation required more than academic support, and I have
many people to thanks, but I cannot begin without saying a huge thank you to my fellows
from ANTHEI 2013-2015. Has been a new experience day-by-day with their personal and
professional support during the time I spent in Tanzania.
I cannot forget the most important, my family, without them this could not be possible
in any way. Special to my mother and my brothers, for offered me their encouragement
through phone calls every day to make sure that I can handle the most difficult challenge
that I was facing being far of them.
For all and everyone I say:

-Thank you-

I
Contents

Abstract I

Acknowledgement II

List of Figures IV

List of Tables VII

Nomenclature IX

1 Introduction 1
1.1 Project Main Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Specific Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Project Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Literature Reviews 5
2.1 Wells Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Inflow Performance Relationship . . . . . . . . . . . . . . . . . . . 5
2.1.2 Vertical Lift Performance . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.3 Well Deliverability . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.4 Productivity Index . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Gas Lift System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 General Classification of Gas Lift . . . . . . . . . . . . . . . . . . 10
2.2.2 Principle of Gas Lift . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.3 Advantages and Disadvantages of Gas Lift . . . . . . . . . . . . . 12

3 Optimisation in Gas Lift Well System 13

3.1 Mathematical Allocation Problem for Gas Lift System . . . . . . . . . . 13
3.2 Gas Lift Performance Curve . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3 Maximum Production and Economical Region . . . . . . . . . . . . . . . 15
3.4 Optimisation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.4.1 Optimisation using Individual Gas Lift Performance Curve . . . . 17
3.4.2 Model-based Optimisation . . . . . . . . . . . . . . . . . . . . . . 18

4 Methodology 19
4.1 Gas Lift Performance Curve Elaboration . . . . . . . . . . . . . . . . . . 19
4.2 Optimisation using Individual Gas Lift Performance Curve . . . . . . . . 20
4.2.1 Curve Fitting Technique . . . . . . . . . . . . . . . . . . . . . . . 20
4.2.2 Piecewise-Linear Optimisation . . . . . . . . . . . . . . . . . . . . 21
4.3 Model-Based Optimisation using GAP . . . . . . . . . . . . . . . . . . . 22
4.4 Comparison of the Total Oil Production . . . . . . . . . . . . . . . . . . 24

II
5 Simulation Results and Discussions 25
5.1 Case 1: Five Wells with Same Layout . . . . . . . . . . . . . . . . . . . . 25
5.1.1 Systems with Well Layout 1 . . . . . . . . . . . . . . . . . . . . . 26
5.1.2 Systems with Well Layout 2 . . . . . . . . . . . . . . . . . . . . . 31
5.1.3 System with Well Layout 3 . . . . . . . . . . . . . . . . . . . . . . 37
5.2 Case 2: Five wells with Different Layout . . . . . . . . . . . . . . . . . . 38
5.2.1 System 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.2.2 System 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.2.3 System 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.2.4 System 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

6 Conclusions and Recommendation 41

Bibliography 43

Appendices 45
A Well Modelling in PROSPER . . . . . . . . . . . . . . . . . . . . . . . . 46
B Well Data Design in PROSPER . . . . . . . . . . . . . . . . . . . . . . . 56
C Optimisation Modelling in GAP . . . . . . . . . . . . . . . . . . . . . . . 59
D Results from the Simulations and Calculated . . . . . . . . . . . . . . . 66

III
List of Figures

1.1 Subject Oriented Literature Review . . . . . . . . . . . . . . . . . . . . 3

1.2 Optimisation of gas lift system . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Methodology procedure optimisation . . . . . . . . . . . . . . . . . . . . 4

2.1 Straight-line IPR. [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Inflow performance relationship for a gas reservoir.[4] . . . . . . . . . . . 6
2.3 Typical inflow performance curves. [4] . . . . . . . . . . . . . . . . . . . 6
2.4 Well Deliverability using different artificial lift methods.[4] . . . . . . . . 8
2.5 Natural flow condition [2] . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.6 Examples of well deliverability.[4] . . . . . . . . . . . . . . . . . . . . . . 9
2.7 General gas lift system.[2] . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.8 General classification of gas lift . . . . . . . . . . . . . . . . . . . . . . . 11
2.9 Simple gas lift schematic [2] . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.1 Typical Forms of Gas lift performance curve [11] . . . . . . . . . . . . . . 15

3.2 Gas allocation between wells for maximum production with limited gas-
injection rate.[2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Data for the GLPC used in the piecewise-linear optimisation . . . . . . 18

4.1 GLPC generated from PROSPER . . . . . . . . . . . . . . . . . . . . . . 19

4.2 Matlab menu bar tool screen . . . . . . . . . . . . . . . . . . . . . . . . 20
4.3 Matlab curve fitting tool . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.4 Excel Solver for curve fitting technique . . . . . . . . . . . . . . . . . . . 21
4.5 Excel Solver for piecewise-linear programming method . . . . . . . . . . 22
4.6 Gas lift network design in GAP - integrated model schematic 1 . . . . . . 23
4.7 Gas lift network design in GAP - integrated model schematic 2 . . . . . . 23
4.8 Gas lift network design in GAP - integrated model schematic 3 . . . . . . 24

5.1 GLPC for different reservoir pressures layout 1 . . . . . . . . . . . . . . . 26

5.2 Deviation between GAP-1 and Piecewise method for different systems lay-
out1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.3 Deviation between GAP-2 and Piecewise method for different systems lay-
out 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.4 Deviation between GAP-3 and Piecewise method for different systems lay-
out 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.5 Deviation between GAP-1 and curve fitting method using Alarcón equation
for different systems layout 1 . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.6 Deviation between GAP-2 and curve fitting method using Alarcón equation
for different systems layout 1 . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.7 Deviation between GAP-3 and curve fitting method using Alarcón equation
for different systems layout 1 . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.8 Difference error between GAP-1 and curve fitting method using Rashid
equation for different systems layout 1 . . . . . . . . . . . . . . . . . . . 30

IV
5.9 Difference error between GAP-2 and curve fitting method using Rashid
equation for different systems layout 1 . . . . . . . . . . . . . . . . . . . 30
5.10 Difference error between GAP-2 and curve fitting method using Rashid
equation for different systems layout 1 . . . . . . . . . . . . . . . . . . . 31
5.11 GLPC for different reservoir pressures layout 2 . . . . . . . . . . . . . . . 32
5.12 Deviation between GAP-1 and piecewise method for different layout2 . . 33
5.13 Deviation between GAP-2 and piecewise method for different layout2 . . 33
5.14 Deviation between GAP-3 and piecewise method for different systems lay-
out 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.15 Deviation between GAP-1 and curve fitting method using Alarcón equation
for different systems layout 2 . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.16 Deviation between GAP-2 and curve fitting method using Alarcón equation
for different systems layout 2 . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.17 Deviation between GAP-3 and curve fitting method using Alarcón equation
for different systems layout 2 . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.18 Deviation between GAP-1 and curve fitting method using Rashid equation
for different systems layout 2 . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.19 Deviation between GAP-2 and curve fitting method using Rashid equation
for different systems layout 2 . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.20 Deviation between GAP-3 and curve fitting method using Rashid equation
for different systems layout 2 . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.21 GLPC for system 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.22 GLPC for system 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.23 GLPC for system 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

A.1 System Summary for well . . . . . . . . . . . . . . . . . . . . . . . . . . 46

A.2 Screen to insert the PVT Data . . . . . . . . . . . . . . . . . . . . . . . 47
A.3 Match Data screen to enter the laboratory data . . . . . . . . . . . . . . 47
A.4 Match Data screen to enter the laboratory data . . . . . . . . . . . . . . 47
A.5 Screen to select the equipment’s . . . . . . . . . . . . . . . . . . . . . . . 48
A.6 Screen to insert the deviation survey data . . . . . . . . . . . . . . . . . 48
A.7 Screen to insert the surface equipment data . . . . . . . . . . . . . . . . 49
A.8 Screen to insert the Down-hole equipment data . . . . . . . . . . . . . . 49
A.9 Screen to insert the geothermal gradient data . . . . . . . . . . . . . . . 49
A.10 Screen to insert the average heat capacity data . . . . . . . . . . . . . . . 50
A.11 Screen to insert the gauge details . . . . . . . . . . . . . . . . . . . . . . 50
A.12 Equipment summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
A.13 Downhole Draw of the Well . . . . . . . . . . . . . . . . . . . . . . . . . 51
A.14 Screen for inputting IPR data . . . . . . . . . . . . . . . . . . . . . . . . 52
A.15 Entering data for the Darcy model . . . . . . . . . . . . . . . . . . . . . 52
A.16 Entering Data for Skin models . . . . . . . . . . . . . . . . . . . . . . . . 53
A.17 Entering Data for sand control . . . . . . . . . . . . . . . . . . . . . . . . 53
A.18 Entering Data for the properties of gas injected . . . . . . . . . . . . . . 54
A.19 Entering the well design criteria . . . . . . . . . . . . . . . . . . . . . . . 54
A.20 The design rate and valve depths . . . . . . . . . . . . . . . . . . . . . . 55

C.1 System Options screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

C.2 Components/equipment toll-bar . . . . . . . . . . . . . . . . . . . . . . 60
C.3 Well Specification Screen . . . . . . . . . . . . . . . . . . . . . . . . . . 60
C.4 Generate IPR and VLP screen . . . . . . . . . . . . . . . . . . . . . . . 60
C.5 IPR generate screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
C.6 VLP generate screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

V
C.7 Generate data for VLP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
C.8 Pipeline definition screen . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
C.9 Pipeline environment screen . . . . . . . . . . . . . . . . . . . . . . . . . 63
C.10 Pipeline description screen . . . . . . . . . . . . . . . . . . . . . . . . . . 63
C.11 Gas available screen input . . . . . . . . . . . . . . . . . . . . . . . . . . 64
C.12 Separator pressure screen input . . . . . . . . . . . . . . . . . . . . . . . 64
C.13 Optimisation screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
C.14 Summary results screen . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

VI
List of Tables

2.1 Advantages and disadvantages of gas lift method. [2] . . . . . . . . . . . 12

5.1 Well data for the well and flowline system . . . . . . . . . . . . . . . . . 25

5.2 Equation coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

B.1 IPR data for Well 1 and Well 2 . . . . . . . . . . . . . . . . . . . . . . . 56

B.2 PVT Data for Well 1 and Well 2 . . . . . . . . . . . . . . . . . . . . . . . 56
B.3 Temperature and pressure in the lab test Well 1 . . . . . . . . . . . . . . 56
B.4 Parameters measured in the Lab . . . . . . . . . . . . . . . . . . . . . . . 56
B.5 Temperature and pressure in the lab test Well 2 . . . . . . . . . . . . . . 57
B.6 Parameters measured in the Lab . . . . . . . . . . . . . . . . . . . . . . . 57
B.7 Completion Data well 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
B.8 Completion Data well 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
B.9 Input Parameters for the gas lift design . . . . . . . . . . . . . . . . . . . 58
B.10 Design options for a valve . . . . . . . . . . . . . . . . . . . . . . . . . . 58
B.11 Valve selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

D.1 Data from PROSPER for different reservoir pressure layout 1 . . . . . . 66

D.2 Equation coefficient in layout 1 . . . . . . . . . . . . . . . . . . . . . . . 67
D.3 Data from PROSPER for different reservoir pressure layout 2 . . . . . . 67
D.4 Equation coefficient in layout 2 . . . . . . . . . . . . . . . . . . . . . . . 68
D.5 Data from PROSPER for layout well 3 . . . . . . . . . . . . . . . . . . . 68
D.6 Data generated in PROSPER for system 1 . . . . . . . . . . . . . . . . . 69
D.7 Equation coefficient in system 1 . . . . . . . . . . . . . . . . . . . . . . . 69
D.8 Data generated in PROSPER for system 2 . . . . . . . . . . . . . . . . . 70
D.9 Equation coefficient in system 2 . . . . . . . . . . . . . . . . . . . . . . . 70
D.10 Data generated in PROSPER for system 3 . . . . . . . . . . . . . . . . . 71
D.11 Equation coefficient in system 3 . . . . . . . . . . . . . . . . . . . . . . . 71
D.12 Optimum oil production for system 1-1 . . . . . . . . . . . . . . . . . . . 72
D.13 Optimum oil production for system 1-2 . . . . . . . . . . . . . . . . . . . 73
D.14 Optimum oil production for system 1-3 . . . . . . . . . . . . . . . . . . . 73
D.15 Optimum oil production for system 1-4 . . . . . . . . . . . . . . . . . . . 74
D.16 Optimum oil production for system 1-5 . . . . . . . . . . . . . . . . . . . 74
D.17 Optimum oil production for system 2-1 . . . . . . . . . . . . . . . . . . . 75
D.18 Optimum oil production for system 2-2 . . . . . . . . . . . . . . . . . . . 75
D.19 Optimum oil production for system 2-3 . . . . . . . . . . . . . . . . . . . 76
D.20 Optimum oil production for system 2-4 . . . . . . . . . . . . . . . . . . . 76
D.21 Optimum oil production for system 2-5 . . . . . . . . . . . . . . . . . . . 77
D.22 Optimum value found using different methods of optimisation layout well 3 77
D.23 Optimum value found using different methods of optimisation system 1 . 78
D.24 Optimum value found using different methods of optimisation system 2 . 79
D.25 Optimum value found using different methods of optimisation system 3 . 79
D.26 Optimum value found using different methods of optimisation system 4 . 80

VII
D.27 Difference between GAP-1, GAP-2 and GAP-3 with and piecewise method
for different system layout 1 . . . . . . . . . . . . . . . . . . . . . . . . . 80
D.28 Difference between GAP-1,GAP-2 and GAP-3 with and curve fitting using
Alaracón equation for different system layout 1 . . . . . . . . . . . . . . 81
D.29 Difference between GAP-1, GAP-2 and GAP-3 with curve fitting Rashid
equation for different system layout 1 . . . . . . . . . . . . . . . . . . . . 82
D.30 Difference between GAP-1, GAP-2 and GAP-3 with piecewise method for
different system layout well 2 . . . . . . . . . . . . . . . . . . . . . . . . 83
D.31 Difference between GAP-1, GAP-2 and GAP-3 with curve fitting using
Alaracón equation for different system layout well 2 . . . . . . . . . . . . 84
D.32 Difference between GAP-1, GAP-2 and GAP-3 with curve fitting using
Rashid equation for different system layout well 2 . . . . . . . . . . . . . 85
D.33 Difference between GAP and the excel method . . . . . . . . . . . . . . . 86
D.34 Difference between GAP and the excel method system 1 . . . . . . . . . 86
D.35 Difference between GAP and the excel method system 2 . . . . . . . . . 87
D.36 Difference between GAP and the excel method system 3 . . . . . . . . . 87
D.37 Difference between GAP and the excel method system 4 . . . . . . . . . 89

VIII
Nomenclature

Abbreviations
AOFP Absolute open flow pressure
ANTHEI Angola Norway Tanzania high education initiative
ESP Electric submersible pump
GAP General allocation package
GL Gas lift
GLPC Gas lift performance curve
GLR Gas-Liquid ratio
GOR Gas-Oil ratio
IPR Inflow performance relationship
MD Measured depth
NTNU Norwegian university of science and technology
PETEX Petroleum experts limited
PI Production index
Pr Reservoir pressure
PROSPER Production and system performance
scf Standard cubic feet
SG Specific gravity
SQP Sequential quadratic programming
STB Stock tank barrel
VLP Vertical lift performance
UDSM University of Dar-es-Salaam
WHP Wellhead pressure
WOR Water Oil ratio

Symbols
qo Produced oil rate
qg Gas injection rate

Subscripts
bp Bubble point
g Gas
in Intake
inj Injection
o Oil
r Reservoir
T Total
wf Well flow

IX
Chapter 1

Introduction

In the petroleum industry one of the major objectives is to maximise and/or prolong the
oil production within the technical and financial limits existent. To ensure that the aim
is reached many technologies such as artificial lift has been developed.
Different artificial lift methods such as sucker rod pump, progressive cavity pump, gas-
lift injection, jet pump and electric submersible pumps (ESP) have been used in most of
the fields all over the world to increase the oil and/or gas production rate considered not
economical, thus maximising recovery and prolonging field life. For this thesis work, the
main focus is production networks with gas-lifted wells.
In most of the cases during the lift process, gas at high pressure is injected into the
tubing string, through the gas lift valve at the bottom of the well. The injection can
be at fixed or variable points where the gas will be mixed to the fluid coming from
the reservoir, resulting in reduction of total pressure losses in the tubing (bottom-hole
pressure). This reduction of pressure is due to the light fluid or reduction of the mixture
density circulating in the column, therefore large amount of fluid will flow along the
production tubing to the surface increasing the oil production. However at some point
if large amount of gas is injected the oil production will decrease, this happen when
the friction pressure loss increase up to certain point where the gas phase moves faster
than the liquid, leaving behind the fluid coming from the reservoir. Therefore, there is
optimum limit of injection for a particular well, where the oil production start to decline
or at maximum oil production point.
Any artificial lift system can be divided into two main parts when the design and
the analyses are taking place. The first is the inflow performance relationship (IPR),
which represent the ability of the reservoir to deliver fluid to the production tubing. The
second includes the entire piping system and artificial lift system itself, so it is possible to
determine the vertical lift performance (VLP) for a certain wellhead pressure, afterwards
the flow rate of a well can be known by the intersection between the IPR and VLP curve.
The final choice for the lift equipment and method in most of the case is influenced by
many reasons as corrosion, sand and solids production, well deviation angle, oil viscosity
and gravity, cost, surface facilities, location and others. However the main factors are the
production rate, down hole flowing pressure and the gas-liquid ratio.
The primary constraint when gas-lifted method is chosen to boost up the fluid to the
surface, is the total amount of gas available to be injected into the well that in some
cases is insufficient or limited. Thus, it is necessary to allocate the amount of gas in some
optimal way that yields the maximum oil production from the field. The optimum allo-
cation process is a challenging problem that has been addressed extensively in the past
in many studies. It constitutes an optimisation problem that can be solved in principle,
using simple mathematical optimisation techniques such as the simplex (linear program-
ming) method and equal slope,and others much more complex as sequential quadratic

1
programming (SQP).
For a group of gas lifted wells producing through the same surface, depending on the
conditions of the network and the piping layout, there is usually hydraulic interdepen-
dency. That is what changes in the operating conditions of one well and will probably
affect the pressures conditions and production rates of the rest wells in the network. For
this it is possible to perform a model-base optimisation into two different methods:
1. Using the relationship between the gas injected and the oil produced, denominated
as gas lift performance curve for each well. This curve is calculated without taking
into account the effect of other wells.

2. Perform a full optimisation using a software without using the gas lift performance
curve.
The first method use the individual gas lift performance curve, calculated assuming
the constant wellhead pressure. The curve can be fitted to an equation or use linear
interpolation between the points and execute mathematical optimisation.
On the other hand the second method employs a numerical model of the production
system where mathematical optimisation is performed using an algorithm, and this re-
quire multiple model evaluation an example of this, is GAP software developed by the
petroleum experts limited (PETEX). This method is sometimes expensive and challeng-
ing in the petroleum industry, specially for systems with hundreds of wells.
This thesis work is an extension of the specialization project, that carries the model-
based optimisation done using:

a) Gas lift performance curve equation fitting and non-linear optimisation;

b) Linear interpolation in gas lift performance curve and linear optimisation;

c) Model-based optimisation in GAP software.

In the end a comparison aimed to see if the optimisation using method one is a good
approximation of method two (GAP) was taken. Additional document file is provide
with the information about the number of iteration and time taken for each method used
in this study. Also for the case of deviation calculated for gas injection per well found in
both methods.

1.1 Project Main Objective

The main objective of the thesis work is to estimate and compare the maximum oil
production and the allocation of gas lift for a system of gas-lifted wells by performing the
optimisation using individual well performance curve and model based optimisation.

1.2 Specific Objectives

The specific objective of this project are:
a) Understand how to generate the GLPC for different conditions;

b) Identify the behaviour of the curve for different wells layout;

c) Perform optimisation using GLPC in the piecewise linear optimisation;

d) Perform optimisation using GLPC fitting and non-linear optimisation;

2
e) Perform optimisation without the GLPC in GAP software;

f) Compare the optimum oil production obtained in different methods.

1.3 Project Outline

The present thesis work contain 6 chapters. In the first chapter a brief introduction is
presented to give a general view to the reader to know what the report will talk about,
this includes the main and specific objectives of the work.
The second chapter involves a review of the literature in the relevant topics to this
study. This part of the thesis was meant to understand the fundamentals and the physics
of the artificial lift systems giving a special attention in gas-lift well system. An overview
of gas lift was carried where classification, principle, advantages and disadvantage were
described to give more knowledge about this artificial lift method. Figure 1.1 presents
all threads in the first part that are also presented in Chapter 2.
In addition, the familiarization with the PETEX software: PROSPER and GAP was
done for optimisation part in the work.

Figure 1.1: Subject Oriented Literature Review

The optimisation in gas lift well systems was carried out in Chapter 3. The chapter
explains the theoretical part of the optimisation used to achieve the aim of the thesis
(Figure 1.2).

Figure 1.2: Optimisation of gas lift system

3
 In chapter 4 the methodology (Figure 1.3) used to perform the objectives is presented
by using the theoretical part explained in the previous chapter.

Figure 1.3: Methodology procedure optimisation

In Chapter 5 results of the simulation done in Excel and GAP are presented and
discussed. Different cases and scenarios were created to identify when the values of the
total oil production are close to each other using different optimisation methods.

Lastly in Chapter 6 the conclusion and recommendation for the thesis are presented.

4
Chapter 2

Literature Reviews

2.1 Wells Performance

For production optimisation in the gas lift well system, it is necessary to have the con-
ceptions of inflow and outflow (vertical lift) performance of the wells to see how the well
behave for a specific characteristics and conditions. In the following section some rel-
evant theoretical concepts that have been considered necessary for the thesis work are
presented.

2.1.1 Inflow Performance Relationship

Inflow performance relationship (IPR) or backpressure curve (used by the engineers deal-
ing with gas wells) is the ability of the reservoir to deliver the fluid into the wellbore or
production tubing. With IPR is possible to define how much fluid can flow from the
reservoir into the wellbore at given conditions.

The simplest and most widely used IPR equation is the straight-line. The IPR (Fig-
ure 2.1) represents the directly proportionality of the rate with the pressure drawdown
(difference between the reservoir pressure and the wellbore flowing pressure) assuming
the fluid in the reservoir is undersaturated oil .

Figure 2.1: Straight-line IPR. [2]

Several equations have been developed so that the saturated oil or two phase flow
can be represented. In 1935 Rawlins and Schellhardt introduced the first mathematical

5
expression known as a back-pressure equation, commonly used in gas reservoir.[3]
The equation (2.1) can be afterwards represented as a graph (Figure 2.2).

q = C(p2r − p2wf )n (2.1)

Where C is the inflow back pressure coefficient and n is the back pressure exponent
that ranges between 0.5 and 1.

Figure 2.2: Inflow performance relationship for a gas reservoir.[4]

Some factors as rock properties, fluid properties, reservoir pressure, well geometry
and well flowing pressure can affect the nature of the IPR curve (Figure 2.3).

Figure 2.3: Typical inflow performance curves. [4]

6
2.1.2 Vertical Lift Performance
Vertical lift performance (VLP) is the ability to deliver the fluid to the surface, from the
bottom of the well at required wellhead pressure. With VLP curve it is possible to define
how much fluid can be lifted by the well at given operation conditions.

As the fluid flows through the production string to the surface, the pressure drop may
occur due to gravity, acceleration and friction factor. A simple and accurate equation for
a vertical flow of dry gas wells has been recommended by Golan and Whitson (1995).[2]
" #0.5
sD5 (p2in − es p2wf )
qg = 200, 000 (2.2)
γg T ZHfM (es − 1)
Where:
qg = gas flow rate, scf/day
Z = average gas compressibility factor
T = average temperature, ◦ R
fM = Moody friction factor
γg = gas gravity, air=1
pin = flowing tubing intake pressure, psia
pwf = flowing wellhead pressure, psia
H = vertical depth, ft
D = tubing diameter, in
s = 0.0375γg H/T Z.

In cases of gas well assumption that the flow is turbulent, the friction factor results
in the following expression:

fm = 2 log[3.7/(ε/D)]−2 (2.3)
Where ε is the absolute pipe roughness and ε = 0.0006in for most commercial pipe.
The friction factor in equation 2.3 is the best fit for the fully turbulent region of the
Moody diagram and is sufficient accurate for most engineering calculations.[2]

Like IPR some factors also affect the nature of the VLP curve such as production
rate, well depth, Gas-Oil ratio (GOR), Gas-Liquid ratio (GLR), tubing diameter and
Water-Oil ratio (WOR). Figure 2.4 represents the comparison for rate of different lift
methods properly that can change with the condition of the well, and the intersection of
each VLP with the IPR curve determine the flow rate for a particular lift method. The
procedures for preparation of these VLP curves has been presented by Agena.[5]

7
 Figure 2.4: Well Deliverability using different artificial lift methods.[4]

Analysis of a VLP of a well is an important part of the well design. It allows selecting
the well completion correctly corresponding to lifting methods and to evaluate wells
performance.[6]

2.1.3 Well Deliverability

Well deliverability is the stable rate that a particular well can produce, resulting of the
combination of the IPR and VLP, where the intersection of the curves is the operation
point or natural flow point (Figure 2.5).

Figure 2.5: Natural flow condition [2]

In Figure 2.6 some examples of well deliverability that can be found in the fields are

8
presented. The curve changes with the condition in the field from there it is possible to
see if it will be necessary to apply some methods to ensure that the well will not be dead
after a couple of years.

(a) Flowing at rate 2 (b) Dead Well

(c) Stable flow rate (d) Dead well

Figure 2.6: Examples of well deliverability.[4]

2.1.4 Productivity Index

Productivity index (PI) is one of the important characteristics of a well inflow performance
[6]. It is also defined as the flow rate per unit of pressure drop. Dependent of the reservoir
and fluid properties, PI serves also to indicate the potential production of the well.
q 2πkh 1
PI = = (2.4)
(p̄ − pwf ) µB ln(re − rw ) + S
Where:
p̄ = average reservoir pressure, psig
k = Permeability, md
q = Surface volumetric rate, STB/D
h = Thickness, ft
re = Drainage radius, ft
rw = Wellbore radius, ft
S = Skin factor
B = Formation volume factor, bbl/STB
µ = Fluid viscosity, cp
pwf = Well flowing pressure, psia

Once the PI is known, the equation can be re-arranged to determine the deliverability
rate straight forward:

9
 q = P I(p̄ − pwf ) (2.5)
The equation (2.5) is only valid for a well with the reservoir pressure (pR ) below the
bubble point pressure (pbp ). For well with the pR above the pbp , i.e., saturated reservoir
or gas wells, the relationship is not as straight forward. In these situations either an IPR
(for oil) or absolute open flow (for gas) analysis should be performed.

2.2 Gas Lift System

Gas lift (GL) is a lifting method that consists in injecting compressed gas at the bottom of
the well through the casing annulus or production string, in order to reduce the pressure
drop in the column by reducing the density of the fluid and making the well produce a
desired rate of oil.
As one of the most common artificial lift employed all over the world, gas lift injection
is required when the reservoir pressure us not enough to maintain economical production
rates. The typical general GL system is shown in Figure 2.7.

Figure 2.7: General gas lift system.[2]

2.2.1 General Classification of Gas Lift

The oil world has two different ways of lifting the oil or gas to the surface, by using the
continuous gas lift and the intermittent gas lift (Figure 2.8).

10
 I. Continuous gas lift - is injected continuously in the casing annulus. Recommended
for a well with high bottom hole pressures (BHP) and high volume (high PI) and
where major pumping problems will occur.

II. Intermittent gas lift - is injected periodically into the annulus of the well. Rec-
ommended for a well that produces low volumes due to low BHP or low PI.

The system allows the fluids to accumulate in the column, which is quickly displaced
to the surface by the gas that have been injected and controlled by the gas lift valve
located at the bottom of the well under the fluid accumulated.

The frequency of gas injection is determined with the amount of time it takes for the
fluid to enter the wellbore and tubing plus the duration of the gas injection required to
displace it to the surface.[6]

Figure 2.8: General classification of gas lift

2.2.2 Principle of Gas Lift

When the well does not have enough energy, the IPR and VLP do not intersect and
the production stops. In order to avoid this, compressed gas is injected into the casing
through the valve at the surface and flows from the annulus to the production tubing
through a injection valve close to the bottom of the well. Therefore the density above
the injection point decreases, then the gas expanded in the tubing will push the liquid
ahead, which further the fluid column weight will also be reduced. Displacement of liquid
slugs by large bubbles of gas act as piston to push the produced fluids to the surface, this
causes liquid to flow to the surface.[6]

For the well to be able to produce the maximum or the desired yield of oil, basic
requirement as a sufficient adequate and good-quality of gas should be injected with
enough pressure at the appropriate place and rate where the flow system exists. Suppliers
are therefore needed throughout the producing life of the field and the injection gas may
come from production operation or outside sources. Often sufficient supply and pressure
are available from the high separator pressure; if the available operator pressure is not
high enough a compressor will be needed.

11
 Figure 2.9 represents the conventional GL, where it is referred to the gas injection
depth, gas injection rate, surface injection pressure and production rate.[7] Note that
oil production by gas lift can be controlled by changing gas volumes, injection depth,
wellhead pressure and tubing size.

Figure 2.9: Simple gas lift schematic [2]

2.2.3 Advantages and Disadvantages of Gas Lift

As a method to lift the fluid to the surface facilities, gas lift have advantages and disad-
vantages mentioned in the Table 2.1.

Table 2.1: Advantages and disadvantages of gas lift method. [2]

Advantages Disadvantages
Can produce high rate from high- High initial investment
productivity wells
Flexible,easy to change rate Limited reservoir pressure drawdown
Can handle large volume of solids with minor Some difficulty in analysing property without
problems engineering supervision
Unobtrusive in urban locations Gas freezing and hydrate problems
Power sources can be remotely located Problems with dirty surface lines
Easy to obtain downhole pressures and gra- Not efficient for small fields or one-well lease
dients if compression equipment is required
Lifting gassy wells with no problem Cannot effectively produce deep well to
abandonment
Sometimes serviceable with wireline unit Difficult to lift emulsions and viscous crude
Crooked holes present no problem Not efficient in lifting small field or one-well
leases
Corrosion is not usually as adverse Casing must withstand lift pressure
Applicable offshore-platforms and subsea Safety problem with high pressure gas
completions

12
Chapter 3

Optimisation in Gas Lift Well

System

In the petroleum industry there are many factors and process that must be optimised
before and during the life field. For a gas lifted wells system there is usually a limited
amount of gas available for injection and it is desirable to allocate it in such a manner
that the gas injected will yield the highest oil production possible.
In the gas lifted wells system the problem of optimising typically uses the economical
objective function which aims to:
• Maximise the oil production
• Maximise the profit
• Minimise the production cost
In this chapter some important concepts about the optimisation in gas lift network system
is considered.

3.1 Mathematical Allocation Problem for Gas Lift

System
For a operating using some artificial lift, an optimisation method is indispensable to
prevent the inappropriate use of available resources. Optimisation normally is composed
by the objective function and the constraints function. Both of them can be constructed
in easy or sometimes difficult ways depending on the circumstances. The choice of the
objective function is one of the important steps in optimisation and a bad choice make
the work meaningless. In the present study the objective function in the gas lift system
during the allocation of the gas injected rate is to maximise the total oil production rate
from the gas lift wells system using the amount of gas injection as the constraint.[8]
Other constraints that are considered significant in gas lift application include com-
pressor operation limits (maximum speed, horsepower, surge/stonewall, clearance volume
limits for reciprocating engines, etc.), production ceiling contracts, water handling facil-
ities (especially offshore), and allowable operating pressures.[9]
The problem of gas allocation optimisation can be formulated mathematically as
follows:
Maximise non-linear function of total oil production for a network well system
n
X
QoT = qoi = f (Qg ) (3.1)
i=1

13
 The total oil production QoT which is the sum of the individual oil production
rates, qoi , can be considered as a function of the flow of gas injected, Qg , where Qg =
(qg1 , · · · , qgn )T is the n-dimensional vector. Equation (3.1) is subject to the following
constrains:
n
X
QgT = qgi ≤ Qg, Available (3.2)
i=1

qgi ≥ qgi, min (3.3)

qgi ≤ qgi, max (3.4)

qgi ≥ 0 (3.5)
Where i = number of well 1, 2, · · · , n.
The constraints defined by the Equation (3.2) indicates that the sum of the individual
gas injection rates should be less than or equal to the total gas available for the system.
Equation (3.3) and (3.4) ensure that each gas injection rate must not be less than
the minimum and greater than the gas injection rate corresponding to the maximum
individual oil production rate. Therefore, the gas injection rates should always satisfy
the set of constraints defined by Equations (3.2) - (3.4) during the optimisation process.
Other constrains can be added in the future to the optimisation technique, such as water
cut and minimum economic performance for each well.

3.2 Gas Lift Performance Curve

The aim of the gas lift system is to deliver the fluid at the wellhead pressure while
bottom-hole pressure is maintained lower enough so that the fluid flows easily to the sur-
face. Therefore larger amount of fluid will flow along the production tubing and the gas
will lower the oil production, due to the effects of friction pressure loss and acceleration
in two phase flow.

The bottom-hole pressure will increase up to certain point where the gas phase moves
faster than the liquid, leaving behind the fluid coming from the reservoir. This will also
cause low amount of liquid flowing though the tubing. The phenomenon results in a
relationship between the gas injection rate and the oil production rate or what is called
gas lift performance curve (GLPC) and is essential for optimisation.

The GLPC can be obtained numerically by simulation as the nodal analysis or by

measuring the rate of gas injection and the rate of oil production in oil field.[10]

In Figure 3.1(a) some of the typical forms for a GLPC are represented, where the
curve A is for a well with an uneconomic oil production rate that gas lift leads to increase
in oil rate, and the well is capable of producing naturally. Curve B is related to a well that
cannot produce without gas lift system. Curve C and D behave as well not producing
without an initial amount of gas, but at this point, well C has a value for oil production
rate.[11]

14
 (a) (b)

Figure 3.1: Typical Forms of Gas lift performance curve [11]

The optimum limit of gas available to be injected into the well should be used to
achieve the maximum oil produced. This limit can be economical, where the value of the
injected gas does not exceed the price of the extra oil produced discussed by Kanu et al.
[12] and presented in Figure 3.1(b).
When some points of the curve are known or may be obtained from the field tests,
some methods of tuning the curves and fitting model are used to approximate the oil
production at the surface as a function of the gas injected into the well.

3.3 Maximum Production and Economical Region

The analysis of the GLPC (Figure 3.1(b)) shows that the oil production has a quick
increase at the beginning of the curve with the injection of gas due to the density factor
in the column that affect the gravity pressure lost. After sometimes opposite situation is
visible where any injection of gas into the well result in less oil production at the surface,
where the friction factor is greater than the density. With this it is possible to conclude
that, GLPC have two important points to be take in consideration.

The maximum point is the one which any increase in gas injected does not increase the
oil produced and with this the oil production start to decrease. This limit or maximum
point of oil production is achieved when the derivative of the function in the performance
curve is equal to zero.
∂qop
=0 (3.6)
∂qgi
The economical region is where the outputs from gas lift maximise the revenue of the
well in production. To find the economical point for the gas lift system, a tangent line
should be determined in the economical region, where the tangent curve is the economical
region.
Conceptually, the optimum economical production value is reached by the time that
additional earnings for the extra oil produced does not compensate the expenses in com-
press the gas to inject into the well. The Equation (3.7) represent the time at which this
is achieved.

∆qop (P − Cext ) = ∆qgi Cgi (3.7)

15
 Where:
Cgi = Cost for compressing the gas;
Cext = Cost to produce the oil;
P= Oil price.

Therefore, there are two possibilities for solving the optimisation program for gas lift,
one where the objective is on maximising the oil production and another on the maximum
profit or minimise the expenses. The choice of maximising the profit seems more obvious,
but this choice may not be so simple to implement, because it requires the estimation of
the cost of compressing gas.

Figure 3.2 illustrates the application of the maximum rate approach for the simple
case of two wells. A procedure formulated by the Clegg (1982) [2] suggest that maximum
total production from the two wells is the sum of the rates qo1 and qo2 , where the two
performance curves have equal slopes m1 = m2 and the total available injection gas equals
qg1 + qg2 .

Figure 3.2: Gas allocation between wells for maximum production with limited gas-
injection rate.[2]

For this discussion wellhead pressure is assumed to be constant, the assumption is

valid if the wells are near to the production separator or if the separators are working at
constant pressure.

3.4 Optimisation Method

For a gas lift optimisation problem there is two main methods used to solve this problem.
The first one is using the individual well performance curve and another without using
the performance curve (model-based optimisation). For this thesis work the methods
were used to calculate the maximum oil production for a particular system.

16
3.4.1 Optimisation using Individual Gas Lift Performance Curve
This optimisation was done using two different methods, a non-linear function using a
curve fitting technique and linear function using a piecewise-linear optimisation.

3.4.1.1 Curve Fitting Technique

In subsection 3.2 it was mentioned that the GLPC can be obtained from numerical
simulations, and when only some points of the curve are known or may be obtained
from field experiments, methods are employed to adjustment of the curve. For classical
optimisation problems the GLPC could be approximated by the third-order polynomial
equation. But the model is considered more easily treatable, and has large error based
on least squares techniques.

2 3
qop = a0 + c1 qgi + c2 qgi + c3 qgi (3.8)
Later on Alarcón et al.[13] made a comparative analysis of the mathematical curve
proposed for the GLPC using the polynomial model, ending with a proposed curve that is
represented by second-order polynomial plus a logarithmic term. It was discovered that
the model is more accurate than the third-order polynomial, although it has an important
disadvantage. This model can cover discontinuous points of the GLPC but fails to match
the trend of curve beyond the maximum point. [11]
2
qop = c1 + c2 qgi + c3 qgi + c4 Ln(qgi + 1) (3.9)
Where c1 , c2 , c3 , c4 are the constant that characterize the well.
Another representation of the GLPC was proposed by Nakashima and Camponogara[14],
by using the composition of two exponential terms:
qop = α1 (2 − e−β1 qgi ) − α2 eβ2 qgi (3.10)
In 2011 Rashid et al.[11] proposed an equation model, considering the variable deci-
sions the flow, gas lift and the opening of the production choke, which is represented as
a discreet variable.
√
qop = c1 + c2 qgi + c3 qgi (3.11)
Some previous work used those equations as the main study to compare them and
establish which one best fits and represents the GLPC. Equations by Alaracon et al.[13]
and Rashid et al.[11] best fit in most of the cases for different operating conditions. This
comparison was done using the least squares techniques, where the R2 should approach
1 to become the best fitting equation. Therefore, those two equations were used for
the optimisation of the gas lift system built in Excel, after finding the coefficient of the
equation using the curve fitting tool in MATLAB (Chapter 4, Figure 4.2 and 4.3).

3.4.1.2 Piecewise-Linear Optimisation

Several kinds of linear programming problems use functions that are not really linear,
but can be approximated by a series of linear segments that follow the gradient of the
function. These ”piecewise-linear” terms are easy to imagine, but can be hard to describe
in conventional algebraic notation.
In this work a piecewise-linear optimisation of a non-linear function is computed in
Excel using linear programming with binary integer variable y and z inside the Solver
tool to find the maximum total oil production for a network system of five gas lifted wells.

In order to know and understand how the piecewise-linear programming works as a

linear optimisation, some description are presented:

17
 • An optimisation variable is added for each data point n in the gas lift performance
curve (zj in Figure 3.3).

Figure 3.3: Data for the GLPC used in the piecewise-linear optimisation

The variable will be multiplied with the coordinates of each point, i.e. the gas
injection rate and the oil produced. Afterwards a summation of the product between
the coordinates of each point and the variable is calculated.
n
X
qopi = qoj zj (3.12)
j=1

n
X
qgi = qgj zj (3.13)
j=1

Where i= number of the well and j = number of data points in the GLPC

• The value of the variable zi might vary between 0 and 1.

• To honour the adjacency condition, addition binary variables (yj ) have to be in-
cluded. And only one of the adjacent variable is allowed to be different from zero.

• The sum of all variables has to be equal to 1 and will be added as additional
constraints.

• The optimiser uses the Simplex method and Branch and Bound in Excel Tool.

3.4.2 Model-based Optimisation

The optimisation for a system using the model-based optimisation is done normally by
using a computational software that takes into account the changes in the operation
conditions during the production.
In this work three model schematic GAP software were used to allocate the amount
of gas to be inject in each well in the system (described in Chapter 4 in section 4.3).

18
Chapter 4

Methodology

In this chapter the methodology used to achieve the aim of this thesis work are presented.

4.1 Gas Lift Performance Curve Elaboration

Gas lift performance curve is important during the optimisation in a systems using gas lift
well. In this work some wells were modelled in PROSPER, which is a well performance,
design and optimisation program which is part of the Integrated Production Modelling
Tool kit (IPM). The step by step in appendices A shows how to design a gas lift well
using PROSPER.
After modelling the well in PROSPER, the GLPC was generated (Figure 4.1) and
the data points (gas injected and oil produced) were exported into Excel and then used
in the optimisation using individual performance curve.

Figure 4.1: GLPC generated from PROSPER

19
4.2 Optimisation using Individual Gas Lift Perfor-
mance Curve
In this optimisation method the data generated and exported from PROSPER were
used. The simple system with five gas lift wells were modelled and the optimisation were
performed using Solver Tool in Excel.

4.2.1 Curve Fitting Technique

As described in section 3.4, there are many equations that can be used to represent the
behaviour of the lift performance curve. For this thesis work two equations were chosen,
the choice was based on the previous studies, where the equation should best fit in the
data presented. In the specific case the equation from Alarcón et al.[11] and Rashid et
al.[13] were used.
In order to use the equation in the curve fitting technique, the coefficients should
be found first. This can be found using different methods, example interation, here
MATLAB curve fitting tool was used.
Figure 4.2 shows the MATLAB menu bar where the curve fitting application can be
selected. In Figure 4.3 the coefficients of the equations and the R2 are automatically
calculated, after import the data and introduce the equation in the custom equation
window.

Figure 4.2: Matlab menu bar tool screen

Figure 4.3: Matlab curve fitting tool

20
 With the known equation coefficients, a simple excel sheet was built for the optimi-
sation. For both equations a Solver Tool was used (Figure 4.4) where mathematical
allocation algorithm problem for gas lift system were introduced with the set objective
of maximising the total oil production, subjected to the constraints defined in the op-
timisation algorithm. For this optimisation technique a GRG non-linear method was
selected.

Figure 4.4: Excel Solver for curve fitting technique

4.2.2 Piecewise-Linear Optimisation

The optimisation using the piecewise-linear programming was performed after the data
is generated in PROSPER. Like in the previous process a simple excel sheet was built
and Solver tool used for the optimisation (Figure 4.5).
Different from the curve fitting technique the non-linear function was subjected to
the constraints represented in the mathematical algorithm for gas lift system and the
piecewise-linear programming. The optimisation technique selected in Solver was Sim-
plex.

21
 Figure 4.5: Excel Solver for piecewise-linear programming method

4.3 Model-Based Optimisation using GAP

Petroleum Experts General Allocation Package (GAP) is a multiphase flow simulator
that is able to model and optimise production and injection networks. There are several
optimisation techniques available in the literature, some are simple as simplex (linear
programming) and equal slope, while other are more complex like sequential quadratic
programming (SQP). In GAP the method used is the SQP.[1]

In this work, optimisation using GAP was performed to determine the optimum
amount of gas to be injected in each well that yields the maximum oil production. The
step by step optimisation using GAP is described in appendices C. For the optimisation
using GAP three integrated model schematic were created.
Figure 4.6 shows the first model system with five gas lifted wells producing to a
common junction and the separator that is located near the wells.

22
 Figure 4.6: Gas lift network design in GAP - integrated model schematic 1

Figure 4.7 shows the second model system with five gas lifted wells producing to a
common junction, then a long pipeline with a length of 12km and the separator.

Figure 4.7: Gas lift network design in GAP - integrated model schematic 2

Figure 4.8 shows the last model system with five gas lifted wells, each well producing to
its own junction, then a pipe (1km) and then a junction where all pipes are commingled,
then a long pipeline (4km) and a separator.

23
 Figure 4.8: Gas lift network design in GAP - integrated model schematic 3

4.4 Comparison of the Total Oil Production

After performing the optimisation for the production system containing five gas lifted
wells using the individual GLPC and the model-based optimisation in GAP, there is an
interest of knowing if the optimum oil production calculated in each method are close to
each other.

To make this comparison, calculations using Equation (4.1) were performed. The
equation represents the deviation between the total oil production in the system and the
amount of injected gas per well found by using a model-based optimisation GAP and
the individual well performance curve optimisation. This deviation was represented as
absolute percentage of error for the values of total oil production.
 
 M ethod 2 − M ethod 1 
%Error = (  ) × 100 (4.1)
M ethod 2
Where
Method 1 = optimisation using individual well performance
Method 2 = model-based optimisation in GAP

If the deviation value in both case of total oil production and injected gas per well is
more than 100% it indicates that the optimum point found by method 2 is completely
different by the optimum found in method 1.

24
Chapter 5

Simulation Results and Discussions

In this chapter the simulation results for the cases studies are presented and discussed.
This includes the GLPC generated, the mathematical optimisation for a group of gas
lifted wells using individual GLPC and GAP Software optimisation. Comparison of the
total oil production and the injected gas per well found for those methods were done to
see if they are close from each other. Comparison also aimed to see if it is possible to
perform the optimisation using method 1 as a start point to the method 2 or even to use
for a practical propose when performing a method 2 is expensive. The method 1 assumes
that there is no change in the operation conditions for a particular well due to the effect
of neighbour wells and in method 2 this assumption is not valid.
The wells were modelled in PROSPER and the GLPC data were generated and ex-
ported, then used in optimisation using method 1. For GAP optimisation the well mod-
elled is used as input file.

5.1 Case 1: Five Wells with Same Layout

In this case a system of wells was created using the same layout design in PROSPER,
i.e., same PVT and IPR properties, well completion and gas lift well design. Using the
same system, different reservoir pressure were tested to see the effect in the GLPC and
in the optimisation process.
For this case two different layout wells with different properties (Table 5.1) were
studied, to see if the observation in one well will be the same for different well properties.

Table 5.1: Well data for the well and flowline system
Parameter Unit Layout 1 Layout 2
Reservoir Pressure psig 3026 3700
o
Oil gravity API 39 37
Gas specific gravity 0.798 0.76
PI STB/D/psi 5 5
Water salinity ppm 100000 23000
GOR scf/STB 500 800
o
Bottom hole temperature F 250 210
Well head pressure psig 200 250
Well depth ft 8000 9000
Tubing ID in 4.05 4.05
Operation valve depth ft 7800 8000
Injection gas gravity 0.7 0.7
Water cut % 15 40

25
5.1.1 Systems with Well Layout 1
Before the optimisation using different methods, it is necessary to have a look at the
GLPC to see how the well will behave in different operation conditions.
Figure 5.1 present the GLPC for layout well 1. It is observed that for any changes
in reservoir pressure the GLPC also changes for the well designed and for all the GLPC
there is no need of an initial volume of gas injection to produce oil.
When the reservoir pressure increases the oil produced also increases, due to the
wellhead pressure that doesn’t change during the gas lift design. Then with the same
wellhead pressure once the reservoir pressure changes the GLPC will also change.

Figure 5.1: GLPC for different reservoir pressures layout 1

The GLPC is generated automatically in PROSPER, it depends on many factors as

water cut, wellhead pressure, GOR and other data supplied in the gas lift design screen
and PVT data (Appendices A, Figure A.2 and A.18).
Table D.1 shows that the oil production in layout 1 for different reservoir pressure
do not reach more than 2000 STB/D, and the gas injection to reach the maximum oil
production is less than 10 scf/D.

5.1.1.1 Total Oil Production Optimisation

After creating the individual wells GLPC (Table D.1), ideal systems with five gas lifted
wells were create and optimised using method 1. During the optimisation each GLPC was
representing a system, this means that for a particular system data from well 1 = well 2 =
well 3 = well 4 = well 5. The optimum oil production found using different techniques are
presented in Table D.12 to D.16 in appendices D for a wells with layout 1. Then the val-
ues were used to compute the deviation between the methods and represented into graph.

Figure 5.2 to Figure 5.4 represents the deviation between the total oil production
calculated using GAP-1, GAP-2 and GAP-3 with the piecewise-linear optimisation tech-

26
nique respectively. The figures shows that when the reservoir pressure increased the
deviation between the values also increased.

Figure 5.2: Deviation between GAP-1 and Piecewise method for different systems layout1

For the case in Figure 5.3 and 5.4 the deviation value for the systems is less than the
deviation found when the model GAP-1 is compared.

Figure 5.3: Deviation between GAP-2 and Piecewise method for different systems layout
1

27
Figure 5.4: Deviation between GAP-3 and Piecewise method for different systems layout
1

Figure 5.5 to Figure 5.7 represents the deviation between the total oil production cal-
culated using GAP-1, GAP-2 and GAP-3 with the curve fitting technique (using Alaracón
equation) respectively. The deviation has the same behaviour as seen in piecewise tech-
nique.

Figure 5.5: Deviation between GAP-1 and curve fitting method using Alarcón equation
for different systems layout 1

28
Figure 5.6: Deviation between GAP-2 and curve fitting method using Alarcón equation
for different systems layout 1

Figure 5.7: Deviation between GAP-3 and curve fitting method using Alarcón equation
for different systems layout 1

Figure 5.8 to Figure 5.10 represents the deviation between the total oil production cal-
culated using GAP-1, GAP-2 and GAP-3 with the curve fitting technique (using Rashid
equation) respectively.

29
Figure 5.8: Difference error between GAP-1 and curve fitting method using Rashid equa-
tion for different systems layout 1

Figure 5.9: Difference error between GAP-2 and curve fitting method using Rashid equa-
tion for different systems layout 1

30
Figure 5.10: Difference error between GAP-2 and curve fitting method using Rashid
equation for different systems layout 1

Comparing the graphs it is possible to observe that the trend are not equal when
using different techniques in the individual GLPC optimisation methods. The deviation
calculated between the different model schematic in GAP and the curve fitting technique
using Rashid et. al. equation is less comparing with other techniques in general(Table
D.27 to D.29).
The total number of iteration and total time used in curve fitting technique using
Rashid et al. equation is less comparing with other methods.
In the model GAP-2 the deviation calculated using curve fitting technique is almost
the same for both equation. The total oil production is small comparing with the model
GAP-1 and GAP-3 (Table D.12 to Table D.16), this can be cause by the long distance of
the pipeline from the junction to the separator.

5.1.2 Systems with Well Layout 2

Figure 5.11 represent the GLPC for the case of layout well 2. For the present layout
the performance curve behaves in the same way as layout well 1, where the GLPC have
different response for different reservoir pressure. The oil production also increases with
the increases in reservoir pressure.

31
 Figure 5.11: GLPC for different reservoir pressures layout 2

For this layout the initial amount of gas lift is required when the well have low reservoir
pressure in order to produce oil.
Table D.3 shows that the oil production is very high more than 2000 STB/D when
the reservoir pressure increases. In comparison with layout 1 the produced oil does not
increase to much with increase in reservoir pressure. The gas injection need to reach the
maximum oil production is more than 10 scf/D for all the reservoir pressure.
Generally, the difference in oil production and gas injected in the well is due to
the different parameters introduced during the well design, that makes the GLPC data
different for a particular case.

5.1.2.1 Total Oil Production Optimisation

For layout 2 the same studies was done to see if the observation in layout 1 can be
seen for different systems. Figures 5.12 to 5.18 shows that for a different well design the
observations are not the same as in layout 1, because when the reservoir pressure increase
the deviation decreases. Figure 5.12 to Figure 5.14 represents the deviation between the
total oil production calculated using GAP-1, GAP-2 and GAP-3 with the piecewise-linear
optimisation technique respectively.

32
Figure 5.12: Deviation between GAP-1 and piecewise method for different layout2

Figure 5.13: Deviation between GAP-2 and piecewise method for different layout2

33
Figure 5.14: Deviation between GAP-3 and piecewise method for different systems layout
2

Figure 5.15 to Figure 5.17 represents the deviation between the total oil produc-
tion calculated using GAP-1, GAP-2 and GAP-3 with the curve fitting technique (using
Alaracón equation) respectively.

Figure 5.15: Deviation between GAP-1 and curve fitting method using Alarcón equation
for different systems layout 2

34
Figure 5.16: Deviation between GAP-2 and curve fitting method using Alarcón equation
for different systems layout 2

Figure 5.17: Deviation between GAP-3 and curve fitting method using Alarcón equation
for different systems layout 2

Figure 5.18 to Figure 5.20 represents the deviation between the total oil produc-
tion calculated using GAP-1, GAP-2 and GAP-3 with the curve fitting technique (using
Rashid equation) respectively.

35
Figure 5.18: Deviation between GAP-1 and curve fitting method using Rashid equation
for different systems layout 2

Figure 5.19: Deviation between GAP-2 and curve fitting method using Rashid equation
for different systems layout 2

36
Figure 5.20: Deviation between GAP-3 and curve fitting method using Rashid equation
for different systems layout 2

Comparing the graphs it is possible to observe that the trend are not equal when using
different techniques in the individual GLPC optimisation methods, the same happened
for layout 1. The deviation calculated between the different model schematic in GAP
and the piecewise-linear optimisation is high comparing with other techniques in general
(Table D.30 to D.32).
The total number of iteration and total time used in piecewise-linear optimisation is
greater than other methods.
During deviation calculation for layout 2, it was observed that for lower reservoir
pressure the deviation tends to be very high (more than 20%) in comparison with all the
GAP model schematic. Therefore, some analyses were done with the values in appendices
D to identify why this happen.
Table D.3 shows that, for the system 2-1; Pr = 2000psig an initial gas injection rate is
needed so that the well can produce. In Table D.4 system 2-1, the ALaracón and Rashid
equation first coefficient value are different from each other, this is not observed for all
the systems created with this layout.

5.1.3 System with Well Layout 3

The following system was created to see if the deviation value is affected when the first
coefficient value for the equation used in the curve fitting technique are different.

In Table D.5 data of the GLPC generated in PROSPER are presented where the initial
gas injected is greater than zero (0.26 scf/D). This data were used in all the optimisation
methods. During the optimisation in Excel for the case of curve fitting technique the
coefficient of the equations used were calculated as shows in Table 5.2. Where is possible
to see that the value of C1 is different in both equation and this may affect optimum oil
production found in this system.

37
 Table 5.2: Equation coefficient
Equation C1 C2 C3 C4
Alaracón 138 -299 9.239 1339
Rashid -106.6 1066 -196

If the above case is compared with the system 2-1 (Table D.33) when the reservoir
pressure is 2000 psig in layout 2, the deviation is 58.94% and other 40.56% using Rashid
equation in the curve fitting technique. This difference is due to the different in the oil
production rate, the well starting with gas injection rate equal to 0.26 scf/D have high oil
production rate comparing with the well starting with 0.67 scf/D. In system 2-1 oil pro-
duction doesn’t increase to much with the gas injection, comparing with the case above
where the oil production increases almost 950STB/D with the gas injection.

Generally, if two systems with well having the initial gas injection greater than zero,
the deviation will be high for the well with high oil production.

5.2 Case 2: Five wells with Different Layout

In this section four different scenarios were create, where each of them contain a network
system of five gas lifted wells different form each other, i.e., the wells have different PVT
and IPR properties, wells completion and gas lift well design.

5.2.1 System 1
In Figure 5.21 it is possible to see that each well have difference response in the GLPC,
where two wells have high oil production comparing with other and the wells are producing
without an initial volume of gas injection.

Figure 5.21: GLPC for system 1

38
 Form the table D.7 the coefficients for the equation used, doesn’t differ to much form
each other, but there are not the same because the gas injection and the oil production
for some of the wells are high. For well 4 and 5 when the gas injection rate is lower the
coefficient are almost the same.
Table D.34 shows that in case for comparison with the GAP-1 the deviation is around
9%. For GAP-2 the deviation value is very low because the optimum found in method
1 is almost the same as method 2. For the case of gas injected per well the deviation
is high comparing with the deviation calculated between method 1 and the GAP-1 and
GAP-3.

5.2.2 System 2
Figure 5.22 represent the GLPC for the system 2. The wells are producing at gas injection
rate greater than 10 scf/D and the oil production rate is lower less than 2000 STB/D.

Figure 5.22: GLPC for system 2

Table D.8 shows the data used in the optimisation calculation, it’s possible to see that
for well 1 and well 2 the gas injected at the beginning of GLPC is greater than zero. This
may affect the total oil production of the system calculated using the method 1.
Table D.9 shows that the first coefficient for the equations used are different for each
other in all the well. Note that in well 2 the difference between the coefficient are high
comparing with another well and this is the well that need the initial gas injection rate
greater than zero. The deviation between the method 1 and all GAP model schematic is
higher than 10%.

5.2.3 System 3
The GLPC for the system 3 are presented in the Figure 5.23. The system contain the well
with almost the same performance lift curve, the wells are producing at lower production
rate (less than 2000 STB/D) and the initial gas injection rate is zero.

39
 In Table D.11 the first coefficient for all the wells are similar for both equations used
in the optimisation. The deviation value is lower in average of 4% for all GAP model
schematic. The system have the lowest deviation value comparing with other systems
(Table D.3.6).

Figure 5.23: GLPC for system 3

5.2.4 System 4
The fourth system optimisation method 1 were done using the GLPC data for the wells
in Table D.3. Well 1 of the system start with the value greater than zero and there is
difference between the first coefficient in the equations (Table D.4).
The deviation between the method 1 and GAP-2 is very low comparing with another
models( Table D.37).
If a comparison of the system 2 in section 5.2.2 the deviation is also lower when the
GAP-2 is compared and the system also contain a well with gas injection rate greater
than zero.
It was noted that for the system 2 the deviation value is greater than the deviation
in system 4, due to the distance between the first coefficient equation.
The well in system 2 the coefficients are 177% distant from each other, and in the
system the coefficients for the well are distant in 166%, having as base the value Alaracón
equation coefficient.

40
Chapter 6

Conclusions and Recommendation

Conclusions
The optimisation of gas lifted well system is important because excessive gas injection
reduces oil production and increases operation cost. Sometimes this optimisation is ex-
pensive when computational optimisation methods are chosen or recommended, then two
different methods of optimisation were study to identify when the optimum oil production
value for both are close to each other.
The present work was developed based on the network system of five gas lifted wells
and different cases were modelled. Before the optimization calculation some simulation
were done in PROSPER to find the GLPC. With this some conclusion can be taken as:

• Gas lift performance curve is a non-linear function of gas injected and oil produced
for a particular well.

• The shape of the GLPC generated changes when some parameters as water cut,
reservoir pressure, wellhead pressure, GOR and well equipment size are changed.

• Depending on the gas lift well design in PROSPER the gas lift performance curve
have different response.

• For a particular well, when the value of the reservoir pressure increase the oil pro-
duction rate also increase, because the wellhead pressure remains constant during
the gas lift well design in PROSPER.

• For a well with high oil rate production more gas injection is needed to reach the
maximum oil production of the same well.

After GLPC behaviour analysis in different condition, the data were used for the
optimisation in method 1 and another using GAP (method 2). Therefore a comparison
for the methods were presented in perceptual deviation calculation. Then it was possible
to conclude that:

• The value of the optimum oil production for a group of well found using curve
fitting technique is better approximation of the GAP optimisation values than using
piecewise-linear optimisation.

• For a system containing well producing high amount of oil the perceptual deviation
is high, i.e., the value optimum found using curve fitting or piecewise-linear pro-
gramming differ more that 10% with a simple model in GAP ( without any facilities
system or pipeline).

41
 • For a system with wells having lower gas injection and oil production rate in the
GLPC generated the deviation is lower than 10%.

• For a system having a well that needs a gas injection greater than zero at the
beginning the deviation is bigger than systems with initial data for gas injection
equal to zero.

• If a system have one or more wells with initial gas injection rate greater than zero
in GLPC the deviation is very lower (less than 5%) when GAP-2 model is used
for comparison. Because the total oil for the GAP-2 model schematic is lower and
approaches more to the value found using method 1.

• Using the first coefficient for the Alaracón et al. and Rashid et al. equation is
possible to predict if the perceptual deviation between the total oil production
using method 1 and method 2 is high or lower.

• The difference between the first coefficients of the Alaracón and Rashid can be one
of the factor that may show the percentage of the deviation for a specific system.
If the system have more than one well with different values in the first coefficient
bigger will be the deviation more than 20% if the model in GAP has no facility
system.

• For a system with wells having the first coefficient for the equations more close, less
will be the deviation between the optimisation using GAP and method 1.

• Curve fitting technique using Rashid et. al. equation takes less time and iteration
number comparing with other techniques in method 1.

• The optimisation for the system using the model schematic GAP-3 takes more time
comparing with the another model, due to the number of pipelines in the system.
This case the pressure loss changes and more time is necessary to converge the
value.

• Deviation found for the case of injected gas per well increases proportional with the
amount of gas available.

Recommendations
Since the gas lift method is one of the most used methods to solve production problem
in the oil industries, it is highly recommended a study in the profit optimisation to see if
this artificial methods is suitable for a certain system. For this specific case of gas lifted
well a research in a system with more than five well and containing a facilities equipments
as pipeline, compressor, etc is also recommended to see if the observations will be the
same as in the present report.
The final general recommendation is for further studies having another artificial meth-
ods as a goal for the optimisation using the approach of constant wellhead pressure.

42
Bibliography

[1] Petroleum Experts Limited, GAP User Manual, Multiphase Production Optimisa-
tion, Version 10, (June 2014).

[2] Golan M. and Curtis W.,”Well performance”, Norwegian University of Science and
Technology(NTNU), 2nd edition, Norway, (August 1995)

[3] Mwita, G., ”Field development evaluation study using integrated modelling”, Msc
thesis, NTNU, Trondheim (2014)

[4] Brown, Kermit E., ”Overview of Artificial Lift System”, Journal of Petroleum Tech-
nology, Society of Petroleum Engineers of AIME (SPE-9979), U. of Tulsa (1982)

[5] Agena, B., ” Preparation of Tubing Intake Curves for Artificial Lift System”, MS
thesis, U. of Tulsa (1982)

[6] Ibrahim, Abu T., ”Optimization of Gas Lift System in Varg Field”,MS thesis, U. of
Stavanger (2007)

[7] Lake,F. W. ” Relation of Air-gas lift to Gas-Oil ratios and effect on ultimate pro-
duction.”, Trans., AIME 77 (1927) 173-188.

[8] Pudjo Sukamo et al., ”New Approach on Gas Lift Wells Optimization With Limited
Available Gas Injected”, IATMI 2006-TS-47, Indonesia (15-17 November 2006)

[9] Dutta-Roy K. and Kattapuram J., ”A new approach to gas-lift allocation optimiza-
tion”,Journal of Petroleum Technology, Society of Petroleum Engineers of AIME,
California (1997)

[10] Mach, J., Proano, E.,Brown,K.,” A nodal approach for applying systems analysis to
the following and artificial lift of oil or gas well.”,Society of Petroleum Engineers,
Paper SPE 8025,(1979)

[11] H.Hamedi, F.Rashidi and E. Khamehchi,” A Novel Approach to the Gas-Lift Allo-
cation Optimization Problem”,Petroleum Science and Technology, Taylor & Francis
Group, Iran (2011)

[12] Kanu, E.P., Mach J.,and Brown,K.E.,”Economic approach to oil production and gas
allocation in continuous gas lift”, Journal of Petroleum Technology,(October 1981)

[13] Alarcón, G.;Torres, C.;Gomez,L., ”Global optimization of gas allocation to a group

of wells in artificial lift using non-linear constrained programming”,ASME Journal
of Energy Resources Technology, v 124, p. 262-268, (December 2002)

[14] Nakashima, P.; Camponogara, E.,”Solving a gas-lift optimization problem by dy-

namic programming.” IEEE Transactions on Systems, Man, and Cybernetics Part
A, v. 36, n. 2,(2006), p. 407 414

43
[15] Petroleum Experts Limited, Prosper User Manual, Single Well Systems Analysis,
Version 13, (June 2014)

[16] James A. Carroll and Roland N. Horne,”Multivarite Optimization of Production

Systems”, Journal of Petroleum Technology, Dallas Society of Petroleum Engineers
(SPE-22847), (July 1992)

[17] Akpan, Stella E.,” Well Placement for Maximum Production in the Norwegian Sea”,
Msc Thesis, NTNU, Trondheim (2012) pp. 99-100

[18] Deni Saepudin et al., International Journal of Mathematics and Mathematical Sci-
ences, volume 2007, Article ID 81519, (March 2007)

[19] J.Redden, T. Sherman ,and J.Blann,”Optimization gas-lift systems”, in Proceedings

of the SPE Fall AIME Meetings, pp.1-13, Dallas, Tex, USA (October 1974)

[20] S.Ayatollahi, A.Bahadori,and A. Moshfeghian,”Method optimises Aghajari oil field

gas lift”, Oil and Gas Journal, vol.99, no.21,(2001) pp.47-49

[21] Samprit Chatterjee and Ali S. Hadi, ” Regression Analysis by examples”, copyright
John
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44
Appendices

45
Appendix A

Well Modelling in PROSPER

PROSPER mean PROduction and System PERformance analysis software from Petroleum
Experts Limiters.PROSPER can assist the production or reservoir engineer to predict
tubing and pipeline hydraulics and temperatures with accuracy and speed.[15] Prosper
is powerful sensitivity calculation features, can enables the handling of an already exist-
ing project, as well as the future utilization of equipment that make a difference in the
project.
The following sub-chapter summarize how to build a well using the software PROS-
PER was described using the PROSPER software manual.[15]

A.1 Setting Up the Model

In order to design a gas lifted well, the gas lift option should be enable in the Op-
tions|Options screen:

Figure A.1: System Summary for well

For this design, Gas Lift (Continuous) and Friction Loss in Annulus from the drop
down menus. considering that during the gas flowing trough the annulus there is no
pressure loss due to the friction.

A.2 Insetting PVT Data

The PVT data screen had been entered to describe the reservoir fluid properties. This
value can be given by the laboratories tests.

46
 Figure A.2: Screen to insert the PVT Data

A.2.1 PVT Matching

When some test are done or data are available for a particular field, this data can be
used and matched during the gas lift design.

Figure A.3: Match Data screen to enter the laboratory data

A.2.1.1 Matching the correlations

After introduced the data a correlation for should be found, this can be done by selecting
Match in the screen and then see the parameter 1 should the approximately 1 and the
parameter 2 small number or zero.

Figure A.4: Match Data screen to enter the laboratory data

47
A.3 Defining the Annulus
As the pressure drop due to the gas travelling in the annulus, the annulus definition should
be considered. This can be done by selecting System|Equipment(Tubing etc). Select
All|Edit to be able to introduced the values for each section.

Figure A.5: Screen to select the equipment’s

A.3.1 Deviation Survey

This section is to introduce that represents the refletion of the path the well takes to
surface.

Figure A.6: Screen to insert the deviation survey data

A.3.2 Surface Equipment

This section is felled if there is any surface equipment in the model.

48
 Figure A.7: Screen to insert the surface equipment data

A.3.3 Down-hole Equipment

Figure A.8: Screen to insert the Down-hole equipment data

The screen is used input the values that specify the path through which the fluid will
travel to surface.

A.3.4 Geothermal Gradient

In this section the temperature gradient of surrounding rock or atmosphere around the
well.

Figure A.9: Screen to insert the geothermal gradient data

49
 Overall heat transfer coefficient = 8 BTU/hr/f t2 /o F

A.3.5 Average Heat Capacities

A default values for the heat capacities of the fluids will be used for this well but they
can be altered if necessary.

Figure A.10: Screen to insert the average heat capacity data

A.3.6 Gauge Details

If the gauge depths are specified for model, the value can be added in the screen below.

Figure A.11: Screen to insert the gauge details

A.3.7 Equipment Summary

Figure A.12: Equipment summary

50
Once the annulus has been defined, select Done to return to the Equipment screen and
then Done to return to the main screen.

A.3.7.1 Draw Downhole

It is possible to see a drawing of the down-hole equipment by selecting Draw Downhole.

Figure A.13: Downhole Draw of the Well

A.4 Inputting IPR Data

The inflow from the reservoir and into the bottom of the well is defined in the IPR section.
This can be done by selecting System|Inflow Performance to input the data in the
screen.

51
 Figure A.14: Screen for inputting IPR data

A.4.1 Entering Data for the Darcy Model

Figure A.15: Entering data for the Darcy model

52
A.4.2 Entering Data for Skin Models

Figure A.16: Entering Data for Skin models

A.4.3 Entering Data for Sand Control

Figure A.17: Entering Data for sand control

53
A.5 Designing a Gas Lifted System
Before the design is carried out, the gas lift gas properties should be set. This can be
done in the System|Gas Lift Data screen:

Figure A.18: Entering Data for the properties of gas injected

In this case a gas lift method is at fixed depth of injection. To return to the main
screen press Done.

A.5.1 Entering the Design Criteria

To enter the design criteria to be used for the well, select Design| Gas|New Well:

Figure A.19: Entering the well design criteria

Enter the design data shown above and select Next.

54
A.5.2 Finding the design Rate and the Valve Depths
Find the design rate is the first step to use during the design. This can be done by
selecting Get Rate.
This will calculate the gas lift performance curve of produced oil rate against gas
injection rate. The Design Rate will be calculated on the basis of the constraints placed
in the previous screen, Represented in plot that can be seen by selecting the Plot.
With the design rate found, the valve depth can be calculated by selecting Design.

Figure A.20: The design rate and valve depths

55
Appendix B

Well Data Design in PROSPER

B.1 IPR

Table B.1: IPR data for Well 1 and Well 2

Parameter Unit Well 1 Well 2
Reservoir Pressure psig 3026 3700
o
Reservoir Temperature F 250 210
Total GOR scf/STB 800 500

B.2 PVT Data

This is the preliminary PVT data which has been received from the lab to characterise
the fluid as well as results from a flash calculation.

Table B.2: PVT Data for Well 1 and Well 2

Parameter Unit Well 1 Well 2
GOR scf/STB 500 800
o
Oil gravity API 39 37
Gas specific gravity air=1 0.798 0.76
Water salinity ppm 100000 23000
Mole H2S % 0 0
Mole CO2 % 0 0
Mole N2 % 0 0

Flash Experiment Data

Table B.3: Temperature and pressure in the lab test Well 1

Temperature of test 250o F
Bubble Point at test temperature 2200psi

Table B.4: Parameters measured in the Lab

Pressure GOR Oil FVF Viscosuty
psig scf/STB STB/RB cp
2200 500 1.32 0.4

56
 Table B.5: Temperature and pressure in the lab test Well 2
Temperature of test 210o F
Bubble Point at test temperature 3500psi

Table B.6: Parameters measured in the Lab

Pressure GOR Oil FVF Viscosuty
psig scf/STB STB/RB cp
4000 800 1.42 0.364
3500 800 1.432 0.35
3000 655 1.352 0.403
2400 500 1.273 0.48
1000 190 1.12 0.7205

B.3 Completion Data

The following data describes the casing and the annulus within the wells

Table B.7: Completion Data well 1

MD Tubing In Tubing In Casing In Casing In
Type
Diam. Rough- Diam. Rough-
ness ness
(ft) (Inches) (Inches) (Inches) (Inches)
Xmas Tree 600
Tubing 2999.9 5.01 0.0006
SSSV 3.72
Tubing 7900 5.01 0.0006
Casing 8000 6.40 0.0006

Table B.8: Completion Data well 2

MD Tubing Tubing Tubing Casing Casing Rate
Type
Inside Outside Inside/ Inside Inside Mul-
Diameter Diameter Outside Diameter Rough- ti-
Rough- ness plier
ness
(ft) (Inches) (Inches) (Inches) (Inches) (Inches)
Xmas Tree 600 1
Tubing 1000 4.052 4.8 0.0006 6.4 0.0006 1
SSSV 3.72 1
Tubing 8900 4.052 4.8 0.0006 6.4 0.0006 1
Casing 9000 6.4 0.0006 1

57
B.4 Gas Lift Design Criteria
The following criteria has been set for the gas lift design.

Table B.9: Input Parameters for the gas lift design

Parameters Unit Well 1 Well 2
Design Rate Method Calculated From Max Prod.
Maximum Liquid Rate STB/day 6500 1500
Maximum Gas Available MMscf/day 5 10
Maximum Gas During Unloading MMscf/day 5 10
Flowing Top Node Pressure psig 600 200
Unloading Top Node Pressure psig 600 200
Operating Injection Pressure psig 2000 1000
Kick Off Injection pressure psig 2000 1000
Desired dp across valve psi 100 100
Maximum depth of injection ft 8000 7800
Water cut % 15 40
Minimum Spacing ft 250 250
Static gradient of load fluid psi/ft 0.45 0.41
Minimum transfer dp % 25 0
Safety for closure of last unloading valve psi 0 50
Minimum CHP decrease per valve psi 50 50

Table B.10: Design options for a valve

Design options for a valve
Valve type Casing sensitive
Valve Setting All valve PVo=gas pressure
Injection point Injection point ORIFICE
Dome pressure correlation above 1200psig Yes
Valve spacing procedure Normal
Check rate conformance with IPR Yes
Vertical lift correlation Petroleum Experts 2
Surface pipe correlation Beggs and Brill
Use IPR for unloading Yes
Orifice sizing on Calculated dp @ orifice

Table B.11: Valve selection

Valve Selection
Manufacturer Camco
Valve type R-20
Valve spec Normal

58
Appendix C

Optimisation Modelling in GAP

GAP is used to simulate and perform a non-linear optimisation to allocate the gas for gas
lifted wells to maximise the revenue or oil/gas production while honouring constraints at
any level in the system. The following sub-chapter summarize how to build a optimisation
modelling in GAP was described using the GAP software manual.[? ]

C.1 Define GAP System Options

This option allows setting up overall system parameters.

Figure C.1: System Options screen

C.2 Define GAP Model Schematically

This section is need to design the system. This include all components or elements used
in the model. The properties of the components are entered using PROSPER and can
be easily added and deleted.

59
 Figure C.2: Components/equipment toll-bar

C.3 Define the Well

In this step the physical characteristics of the well shall be specified.

Figure C.3: Well Specification Screen

C.4 Calculate the Well IPR and VLP

The IPR and VLP data can be automatically generate in this section. From the main
GAP menu Select Generate|Generate Well IPRs or VLPs with PROSPER|All|Generate

Figure C.4: Generate IPR and VLP screen

60
 Figure C.5: IPR generate screen

Figure C.6: VLP generate screen

The VLP curve is generate to a specific ranges of data. PROSPER is called up to

load the sensitivity values already stored within it. The following sensitivity values:

Figure C.7: Generate data for VLP

The VLP can also be generated within the PROSPER software and then imported to
GAP. In case of Pipeline the definition is needed.

61
C.5 Define the Pipelines
To define the pipelines acess the pipe summary screen below by double-clicking on the
link that joins the WH and the junction or junction and setpoint.

Figure C.8: Pipeline definition screen

Make the following changes:

Pipeline model : GAP Internal Correlation
Correlation : Petroleum Experts 5
Gravity Coefficient : 1
Friction Coefficient : 1

Environment

In the screen select Environment to have access to the pipeline environment and
make the following changes:
Surface Temperature : 50 deg/F
Overrall Heat Transfer Coefficient : 8 Btu/h/ft
Oil Heat Capacity : 0.53 Btu/lb/F (default)
Gas Heat Capacity : 0.51 Btu/lb/F (default)
Water Heat Capacity : 1 Btu/lb/F (default)

62
 Figure C.9: Pipeline environment screen

Pipeline Description

Select the Description to define the pipeline dimensions in the screen.

Figure C.10: Pipeline description screen

Once the data has been entered click Validate to check if the data entered is valid or
not. After this click on OK to retorn to the GAP main screen.
Repeat this procedure for all the wells lines in the system.

C.6 Calculate Production Given total lift available

To perform the optimisation from the system given a total amount of gas lift available,
click on |Solve Network in the main menu and the enter different amount of gas avail-
able.

63
 Figure C.11: Gas available screen input

Then | Next and production will be determined for the separator pressure introduced
in the screen.

Figure C.12: Separator pressure screen input

Then click on |Next|Calculate check box Optimise with all Constraints before
the calculation is started.

64
 Figure C.13: Optimisation screen

C.7 Result analysis

To see and export the result of the optimised injection of increasing of lift gas, click on
Results|Summary|All Wells

Figure C.14: Summary results screen

65
Appendix D

Results from the Simulations and

Calculated

D.1 Data generate from PROSPER

D.1.1 Same layout 1: For different reservoir pressure
For the calculation each data were used five times, i.e. the gas lift performance data in
well 1 = well 2 = well 3 = well 4 = well 5.

Table D.1: Data from PROSPER for different reservoir pressure layout 1
S 1-1; PR=2000psig S 1-2; PR=3026psig S 1-3; PR=3450psig
Qg,MMscf/D Qo,STB/D Qg,MMscf/D Qo,STB/D Qg,MMscf/D Qo,STB/D
1.7479E-08 368.23 0.00 782.58 0.00 1027.88
0.67 555.42 1.09 1050.55 0.60 1203.87
0.95 561.73 1.54 1058.09 0.86 1219.56
1.35 568.38 2.17 1064.97 1.21 1229.99
1.91 576.83 3.05 1071.57 1.71 1238.35
2.72 586.27 4.30 1078.28 2.40 1245.43
3.87 595.56 6.05 1084.36 3.38 1251.70
5.52 606.50 8.47 1083.80 4.76 1257.53
7.72 606.00 6.68 1261.46
9.31 1256.60
S 1-4; PR=4000psig S 1-5; PR=6200psig
Qg,MMscf/D Qo,STB/D Qg,MMscf/D Qo,STB/D
0.00 1235.64 0.00 1789.63
0.71 1408.42 0.97 1940.12
1.00 1423.60 1.37 1953.11
1.41 1433.90 1.93 1961.88
1.99 1443.12 2.71 1969.87
2.80 1450.30 3.81 1976.17
3.93 1456.07 5.35 1980.43
5.52 1460.41 7.49 1981.24
7.73 1460.37 10.43 1970.41
*
S 1-n: where 1 is the layout well and n the number of system created by changing the reservoir pressure

66
 Table D.2: Equation coefficient in layout 1
System Equation C1 C2 C3 C4
Alaracón 384.3 -198.8 10.83 516.5
1-1 Rashid 383.4 216.7 -51.04
Alaracón 790.2 -220.5 10.69 623.3
1-2 Rashid 794.8 281.7 -64.9
Alaracón 1050 -160.3 7.443 455.4
1-3 Rashid 1048 207.8 -47.56
Alaracón 1246 -190.5 10.12 502.1
1-4 Rashid 1247 214.8 -51.42
Alaracón 1797 -93.15 3.559 313
1-5 Rashid 1798 165.9 -35.68

D.1.2 Same layout 2 : For different reservoir pressure

For the calculation each data were used five times, i.e. the gas lift performance data in
well 1 = well 2 = well 3 = well 4 = well 5.

Table D.3: Data from PROSPER for different reservoir pressure layout 2
S 2-1; PR=2000psig S 2-2; PR=3100psig S 2-3; PR=3700psig
Qg,MMscf/D Qo,STB/D Qg,MMscf/D Qo,STB/D Qg,MMscf/D Qo,STB/D
0.67 459.71 0.00 776.38 0.00 2778.33
1.10 670.51 0.48 1810.77 1.32 3834.55
2.03 883.73 0.81 2198.96 1.97 4077.07
3.17 982.74 1.31 2526.32 2.89 4281.73
4.82 1068.45 2.05 2830.86 4.21 4458.22
7.10 1124.60 3.14 3091.06 6.08 4593.53
10.17 1150.23 4.66 3274.17 8.64 4663.35
14.17 1145.37 6.69 3357.27 12.07 4655.13
9.41 3376.72
13.13 3364.91
S 2-4; PR=4500psig S 2-5; PR=6200psig
Qg,MMscf/D Qo,STB/D Qg,MMscf/D Qo,STB/D
0.00 4892.29 0.00 8104.70
0.88 5293.62 1.38 8296.55
1.26 5407.57 1.95 8356.48
1.81 5548.31 2.75 8426.24
2.61 5711.83 3.89 8504.75
3.75 5857.90 5.49 8574.66
5.37 5991.09 7.74 8632.10
7.64 6089.24 10.86 8652.93
10.78 6133.31 15.17 8632.16
14.96 6080.37
*
S 2-n: where 2 is the layout well and n the number of system created by changing the reservoir pressure

67
 Table D.4: Equation coefficient in layout 2
System Equation C1 C2 C3 C4
Alaracon 82.66 -190.4 4.822 1029
2-1 Rashid -57.51 807.9 -131.8
Alaracon 885 -646.9 19.25 2903
2-2 Rashid 761.1 1861 -320.8
Alaracon 2784 -267.4 6.078 1641
2-3 Rashid 2762 1201 -188
Alaracon 4885 -28.58 -1.435 700.9
2-4 Rashid 4816 692.6 -90.74
Alaracon 8100 28.32 -1.974 198.5
2-5 Rashid 8073 270.3 -30.12

D.1.3 Same layout well 3

Table D.5: Data from PROSPER for layout well 3

Well 1
Qg,MMscf/D Qo,STB/D
0.2581 345.75
0.40 481.47
0.88 752.24
1.58 964.07
2.60 1131.36
3.93 1222.76
5.76 1280.99
8.17 1298.57
11.43 1296.73

68
D.1.4 Different layout system 1

Table D.6: Data generated in PROSPER for system 1

Well 1 Well 2 Well 3
Qg,MMscf/D Qo,STB/D Qg,MMscf/D Qo,STB/D Qg,MMscf/D Qo,STB/D
5.06E-04 595.07 0.00 2778.33 0.00 3722.41
0.61 927.47 1.32 3834.55 0.69 4137.82
0.99 1071.03 1.97 4077.07 0.99 4246.06
1.57 1214.56 2.89 4281.73 1.43 4371.94
2.46 1354.76 4.21 4458.22 2.06 4504.68
3.73 1468.87 6.08 4593.53 2.97 4637.96
5.51 1550.86 8.64 4663.35 4.26 4751.86
7.83 1572.68 12.07 4655.13 6.06 4826.34
10.89 1563.04 8.53 4855.58
11.84 4812.57
Well 4 Well 5
Qg,MMscf/D Qo,STB/D Qg,MMscf/D Qo,STB/D
0.00 782.58 0.00 817.30
1.09 1050.55 1.09 1054.28
1.54 1058.09 1.54 1061.60
2.17 1064.97 2.17 1068.31
3.05 1071.57 3.06 1074.75
4.30 1078.28 4.31 1081.33
6.05 1084.36 6.07 1087.23
8.47 1083.80 8.49 1086.40

Table D.7: Equation coefficient in system 1

Well Equation C1 C2 C3 C4
Alaracon 594.9 -145.8 3.011 888.3
1 Rashid 537.3 675.3 -108.6
Alaracon 2784 -267.4 6.078 1641
2 Rashid 2762 1201 -188
Alaracon 3729 -128.1 1.672 927.8
3 Rashid 3669 745.4 -117
Alaracon 790.2 -220.5 10.69 623.3
4 Rashid 794.8 281.7 -64.9
Alaracon 824 -191.7 9.233 546.8
5 Rashid 827.8 249.6 -57.11

69
D.1.5 Different layout system 2

Table D.8: Data generated in PROSPER for system 2

Well 1 Well 2 Well 3
Qg,MMscf/D Qo,STB/D Qg,MMscf/D Qo,STB/D Qg,MMscf/D Qo,STB/D
5.03E-04 593.25 0.26 345.75 0.00 471.80
0.61 925.00 0.40 481.47 0.48 959.09
0.99 1068.85 0.88 752.24 0.76 1080.34
1.57 1213.30 1.58 964.07 1.18 1203.76
2.46 1354.50 2.60 1131.36 1.83 1333.98
3.73 1466.92 3.93 1222.76 2.79 1454.94
5.50 1547.77 5.76 1280.99 4.17 1550.50
7.82 1569.98 8.17 1298.57 6.08 1616.22
10.87 1560.12 11.43 1296.73 8.64 1639.78
11.95 1618.93
Well 4 Well 5
Qg,MMscf/D Qo,STB/D Qg,MMscf/D Qo,STB/D
0.00 417.90 0.00 478.81
0.41 812.32 0.42 840.71
0.64 916.59 0.65 935.66
1.02 1036.97 1.02 1044.44
1.59 1161.99 1.59 1158.19
2.45 1273.50 2.42 1258.95
3.67 1365.13 3.62 1345.77
5.36 1423.46 5.25 1394.46
7.63 1447.57 7.43 1408.77
10.60 1436.65 10.29 1394.30

Table D.9: Equation coefficient in system 2

Well Equation C1 C2 C3 C4
Alaracon 592.8 -147.6 3.083 892.3
1 Rashid 535.4 676.4 -109
Alaracon 138 -299 9.239 1339
2 Rashid -106.6 1066 -196
Alaracon 533 -284.2 8.838 1264
3 Rashid 473.1 820 -142.4
Alaracon 468.1 -294.8 10.16 1209
4 Rashid 407.5 758.5 -136.6
Alaracon 519.2 -275.6 9.479 1121
5 Rashid 464.4 703.7 -129.4

70
D.1.6 Different layout system 3

Table D.10: Data generated in PROSPER for system 3

Well 1 Well 2 Well 3
Qg,MMscf/D Qo,STB/D Qg,MMscf/D Qo,STB/D Qg,MMscf/D Qo,STB/D
1.7479E-08 368.23 0.00 782.58 0.00 1027.88
0.67 555.42 1.09 1050.55 0.60 1203.87
0.95 561.73 1.54 1058.09 0.86 1219.56
1.35 568.38 2.17 1064.97 1.21 1229.99
1.91 576.83 3.05 1071.57 1.71 1238.35
2.72 586.27 4.30 1078.28 2.40 1245.43
3.87 595.56 6.05 1084.36 3.38 1251.70
5.52 606.50 8.47 1083.80 4.76 1257.53
7.72 606.00 6.68 1261.46
9.31 1256.60
Well 4 Well 5
Qg,MMscf/D Qo,STB/D Qg,MMscf/D Qo,STB/D
0.00 1126.37 0.00 1397.49
0.65 1300.79 0.79 1565.41
0.93 1316.23 1.11 1580.58
1.31 1326.62 1.57 1590.59
1.84 1335.17 2.20 1599.36
2.59 1342.82 3.10 1606.46
3.64 1348.87 4.35 1611.77
5.12 1353.86 6.11 1615.09
7.178 1355.90 8.532 1611.72
9.99 1347.89

Table D.11: Equation coefficient in system 3

Well Equation C1 C2 C3 C4
Alaracon 384.3 -198.8 10.83 516.5
1 Rashid 383.4 216.7 -51.04
Alaracon 790.2 -220.5 10.69 623.3
2 Rashid 794.8 281.7 -64.9
Alaracon 1050 -160.3 7.443 455.4
3 Rashid 1048 207.8 -47.56
Alaracon 1147 -140 6.019 420.3
4 Rashid 1145 201.4 -45.07
Alaracon 1407 -153.7 7.373 436.9
5 Rashid 1408 200.8 -46.3

71
D.2 Optimisation Value of Total Oil Production
D.2.1 Same layout well 1 : For different reservoir pressure

Table D.12: Optimum oil production for system 1-1

System 1-1
Piecewise Alarcon Rashid
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 2889.16 10.00 2987.27 10.00 2938.90
20.00 20.00 2982.01 13.28 3011.30 20.00 3063.20
25.00 25.00 3015.17 13.28 3011.30 22.53 3067.05
30.00 27.61 3032.49 13.28 3011.30 22.53 3067.05
35.00 27.61 3032.49 13.28 3011.30 22.53 3067.05
40.00 27.61 3032.49 13.28 3011.30 22.53 3067.05
45.00 27.61 3032.49 13.28 3011.30 22.53 3067.05
GAP-1 GAP-2 GAP-3
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 2885.00 10.00 2851.00 10.00 2869.00
20.00 20.00 3028.50 20.00 2939.50 20.00 2986.50
25.00 22.25 3057.50 21.36 2949.90 21.91 3004.00
30.00 22.25 3057.50 21.32 2948.00 21.90 3004.00
35.00 22.25 3057.50 21.32 2948.00 21.93 3004.50
40.00 22.23 3057.50 21.32 2948.00 21.92 3004.50
45.00 22.25 3057.50 21.32 2948.00 21.93 3004.50

72
 Table D.13: Optimum oil production for system 1-2
System 1-2
Piecewise Alarcon Rashid
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 5315.78 10.00 5383.63 10.00 5316.92
20.00 20.00 5383.38 14.85 5444.98 20.00 5493.00
25.00 25.00 5403.57 14.85 5444.98 23.55 5502.41
30.00 30.00 5420.91 14.85 5444.98 23.55 5502.41
35.00 30.26 5421.80 14.85 5444.98 23.55 5502.41
40.00 30.26 5421.80 14.85 5444.98 23.55 5502.41
45.00 30.26 5421.80 14.85 5444.98 23.55 5502.41
GAP-1 GAP-2 GAP-3
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 5601.00 10.00 5548.50 10.00 5576.00
20.00 20.00 5685.50 18.78 5566.50 20.00 5630.00
25.00 25.00 5699.50 20.12 5570.50 25.00 5623.50
30.00 30.00 5709.00 19.11 5569.50 23.14 5627.50
35.00 35.00 5718.50 19.11 5569.50 23.13 5627.50
40.00 40.00 5727.50 20.33 5568.50 23.13 5627.50
45.00 41.40 5730.00 20.33 5568.50 23.13 5627.50

Table D.14: Optimum oil production for system 1-3

System 1-3
Piecewise Alarcon Rashid
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 6206.67 10.00 6297.40 10.00 6233.77
20.00 20.00 6271.63 14.38 6337.59 20.00 6366.80
25.00 25.00 6290.15 14.38 6337.59 23.86 6374.90
30.00 30.00 6300.37 14.38 6337.59 23.86 6374.90
35.00 31.47 6303.37 14.38 6337.59 23.86 6374.90
40.00 31.47 6303.37 14.38 6337.59 23.86 6374.90
45.00 31.47 6303.37 14.38 6337.59 23.86 6374.90
GAP-1 GAP-2 GAP-3
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 6582.50 10.00 6521.00 10.00 6554.00
20.00 20.00 6666.00 16.31 6541.00 20.00 6604.00
25.00 24.34 6691.00 18.47 6537.50 23.77 6611.50
30.00 24.34 6691.00 18.47 6537.50 23.78 6611.50
35.00 24.34 6691.00 18.47 6537.50 23.77 6611.50
40.00 24.32 6691.00 18.47 6537.50 23.77 6611.50
45.00 24.32 6691.00 18.47 6537.50 23.77 6611.50

73
 Table D.15: Optimum oil production for system 1-4
System 1-4
Piecewise Alarcon Rashid
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 7216.10 10.00 7285.47 10.00 7239.67
20.00 20.00 7281.27 13.45 7311.70 20.00 7354.60
25.00 25.00 7294.92 13.45 7311.70 21.81 7356.62
30.00 27.61 7302.05 13.45 7311.70 21.81 7356.62
35.00 27.61 7302.05 13.45 7311.70 21.81 7356.62
40.00 27.61 7302.05 13.45 7311.70 21.81 7356.62
45.00 27.61 7302.05 13.45 7311.70 21.81 7356.62
GAP-1 GAP-2 GAP-3
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 7695.00 10.00 7625.00 10.00 7661.50
20.00 20.00 7778.00 19.30 7634.90 20.00 7710.00
25.00 25.00 7798.50 17.71 7643.00 25.00 7709.50
30.00 28.39 7812.00 17.71 7643.00 19.92 7710.00
35.00 28.22 7811.50 17.71 7643.00 19.92 7710.00
40.00 28.22 7811.50 17.71 7643.00 24.94 7707.50
45.00 28.22 7811.50 17.71 7643.00 23.68 7709.50

Table D.16: Optimum oil production for system 1-5

System 1-5
Piecewise Alarcon Rashid
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 9812.91 10.00 9844.01 10.00 9806.29
20.00 20.00 9883.45 18.35 9927.29 20.00 9935.40
25.00 25.00 9897.31 18.35 9927.29 25.00 9952.82
30.00 30.00 9903.38 18.35 9927.29 27.02 9954.22
35.00 35.00 9905.27 18.35 9927.29 27.02 9954.22
40.00 37.46 9906.20 18.35 9927.29 27.02 9954.22
45.00 37.46 9906.20 18.35 9927.29 27.02 9954.22
GAP-1 GAP-2 GAP-3
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 10578.00 10.00 10499.50 10.00 10541.00
20.00 20.00 10655.00 18.66 10508.50 19.41 10583.50
25.00 25.00 10661.50 18.97 10505.70 19.85 10582.00
30.00 30.00 10668.00 18.60 10508.50 19.66 10583.00
35.00 35.00 10674.50 18.60 10508.50 19.66 10583.00
40.00 38.64 10679.00 18.60 10508.50 19.66 10583.00
45.00 38.76 10679.50 18.60 10508.50 19.66 10583.00

74
D.2.2 Layout well 2 : For different Reservoir Pressure

Table D.17: Optimum oil production for system 2-1

System 2-1
Piecewise Alarcon Rashid
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 4380.56 10.00 4258.10 10.00 4107.17
20.00 20.00 5130.09 20.00 5271.62 20.00 5155.45
25.00 25.00 5364.62 25.00 5474.65 25.00 5450.05
30.00 30.00 5487.66 30.00 5580.97 30.00 5653.16
35.00 35.00 5610.70 35.00 5629.42 35.00 5786.96
40.00 40.00 5660.61 40.00 5645.06 40.00 5865.88
45.00 45.00 5702.40 42.20 5646.16 45.00 5899.95
GAP-1 GAP-2 GAP-3
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 8471.00 10.00 7828.10 10.00 7752.80
20.00 20.00 9062.00 20.00 7935.30 20.00 7821.40
25.00 24.61 9223.00 19.86 7939.30 19.86 7820.80
30.00 24.61 9223.00 20.16 7934.90 20.16 7821.50
35.00 24.61 9223.00 20.65 7936.30 20.90 7802.00
40.00 24.61 9223.00 20.00 7935.60 20.44 7818.00
45.00 24.61 9223.00 21.09 7930.30 14.67 7820.80

Table D.18: Optimum oil production for system 2-2

System 2-2
Piecewise Alarcon Rashid
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 14043.27 10.00 14287.36 10.00 13756.76
20.00 20.00 15974.24 20.00 16387.99 20.00 15999.50
25.00 25.00 16441.12 25.00 16666.14 25.00 16592.11
30.00 30.00 16645.98 29.72 16728.05 30.00 16974.00
35.00 35.00 16797.57 29.72 16728.05 35.00 17196.22
40.00 40.00 16833.21 29.72 16728.05 40.00 17292.01
45.00 45.00 16868.86 29.72 16728.05 42.07 17300.36
GAP-1 GAP-2 GAP-3
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 19424.50 10.00 17173.50 10.00 18153.00
20.00 20.00 20150.50 20.00 17441.00 20.00 18578.10
25.00 25.00 20338.00 23.27 17522.60 24.90 18709.40
30.00 27.24 20418.50 23.30 17523.70 24.92 18710.10
35.00 27.20 20418.00 23.38 17525.00 24.92 18710.20
40.00 27.23 20418.50 23.31 17523.70 24.94 18710.60
45.00 27.24 20418.50 23.27 17522.50 24.96 18710.50

75
 Table D.19: Optimum oil production for system 2-3
System 2-3
Piecewise Alarcon Rashid
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 20423.52 10.00 20381.67 10.00 20422.35
20.00 20.00 22149.28 20.00 22263.68 20.00 22060.00
25.00 25.00 22576.90 25.00 22696.14 25.00 22537.59
30.00 30.00 22939.85 30.00 22958.23 30.00 22879.19
35.00 35.00 23093.58 35.00 23111.93 35.00 23117.74
40.00 40.00 23229.95 40.00 23197.19 40.00 23274.70
45.00 43.18 23316.75 45.00 23241.30 45.00 23365.00
GAP-1 GAP-2 GAP-3
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 25765.50 10.00 22494.50 10.00 23871.00
20.00 20.00 26501.50 20.00 22814.70 20.00 24315.60
25.00 25.00 26595.00 19.75 22816.20 25.00 24339.10
30.00 30.00 26685.00 30.00 22816.50 30.00 24419.00
35.00 35.00 26772.50 26.25 22790.80 32.63 24482.00
40.00 35.66 26784.00 29.78 22816.20 32.62 24481.50
45.00 35.67 26784.00 30.24 22816.90 32.53 24479.60

Table D.20: Optimum oil production for system 2-4

System 2-4
Piecewise Alarcon Rashid
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 27933.28 10.00 27960.59 10.00 28070.02
20.00 20.00 29392.04 20.00 29378.88 20.00 29191.20
25.00 25.00 29803.21 25.00 29810.35 25.00 29555.00
30.00 30.00 30091.52 30.00 30128.74 30.00 29840.38
35.00 35.00 30307.59 35.00 30360.53 35.00 30066.34
40.00 40.00 30471.40 40.00 30522.77 40.00 30245.24
45.00 45.00 30541.71 45.00 30627.13 45.00 30385.70
GAP-1 GAP-2 GAP-3
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 33264.00 10.00 29018.20 10.00 30768.00
20.00 20.00 33854.00 20.00 29273.00 20.00 31179.60
25.00 25.00 34001.50 19.56 29287.50 25.00 31184.00
30.00 30.00 34028.00 22.42 29200.20 26.94 31188.00
35.00 35.00 34054.50 25.67 29132.10 35.00 31192.30
40.00 40.00 34080.00 28.92 29076.70 40.00 31205.50
45.00 45.00 34105.50 32.17 29046.70 41.27 31206.60

76
 Table D.21: Optimum oil production for system 2-5
System 2-5
Piecewise Alarcon Rashid
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 41804.19 10.00 41834.09 10.00 41975.11
20.00 20.00 42547.88 20.00 42505.85 20.00 42465.60
25.00 25.00 42766.27 25.00 42739.57 25.00 42634.05
30.00 30.00 42938.46 30.00 42925.60 30.00 42771.89
35.00 35.00 43066.25 35.00 43071.42 35.00 42886.53
40.00 40.00 43169.26 40.00 43181.87 40.00 42982.82
45.00 45.00 43202.62 45.00 43260.25 45.00 43064.10
GAP-1 GAP-2 GAP-3
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 46262.00 10.00 42234.00 10.00 43679.50
20.00 20.00 46575.00 19.30 42262.10 20.00 43881.50
25.00 25.00 46653.50 19.75 42260.00 25.00 43948.10
30.00 30.00 46730.50 23.88 42251.50 29.35 44008.50
35.00 31.12 46747.50 26.25 42247.50 30.63 43978.50
40.00 31.00 46745.50 29.50 42209.50 29.35 44008.50
45.00 31.00 46745.50 27.97 42253.70 29.49 44005.00

D.2.3 Same layout well 3

Table D.22: Optimum value found using different methods of optimisation layout well 3
Initial Gas injection greater than zero
Piecewise Alarcon Rashid GAP
Gas Ava. Qg Qo Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 5166.36 10.00 5239.99 10.00 5044.76 10.00 14394.00
20.00 20.00 6125.34 20.00 6224.31 20.00 6207.00 20.00 15016.00
25.00 25.00 6284.20 25.00 6365.70 25.00 6485.24 25.00 15289.50
30.00 30.00 6413.68 30.00 6410.89 30.00 6642.78 30.00 15544.00
35.00 35.00 6450.08 32.18 6414.07 35.00 6708.85 35.00 15779.50
40.00 40.00 6486.48 32.18 6414.07 36.98 6714.17 40.00 16000.00
45.00 40.87 6492.85 32.18 6414.07 36.98 6714.17 45.00 16209.50

77
D.2.4 Different layout system 1

Table D.23: Optimum value found using different methods of optimisation system 1
System 1
Piecewise Alarcon Rashid
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 12305.82 10.00 12307.95 10.00 12240.34
20.00 20.00 13080.14 20.00 13075.22 20.00 12971.25
25.00 25.00 13180.49 25.00 13200.84 25.00 13149.45
30.00 30.00 13229.85 30.00 13248.57 30.00 13256.16
35.00 35.00 13256.06 34.52 13261.98 35.00 13310.34
40.00 37.11 13263.20 34.52 13261.98 39.50 13324.41
45.00 37.11 13263.20 34.52 13261.98 39.50 13324.41
GAP-1 GAP-2 GAP-3
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 14120.50 10.00 13085.90 10.00 13493.30
20.00 20.00 14398.60 20.00 13126.40 20.00 13659.30
25.00 25.00 14482.90 16.54 13166.30 25.00 13661.70
30.00 29.51 14486.90 17.42 13217.40 25.76 13691.30
35.00 33.19 14497.30 17.93 13254.00 19.66 13673.70
40.00 32.91 14496.90 19.41 13239.40 21.48 13676.20
45.00 33.07 14496.40 19.41 13239.40 21.89 13674.00

78
D.2.5 Different layout system 2

Table D.24: Optimum value found using different methods of optimisation system 2
System 2
Piecewise Alarcon Rashid
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 6129.43 10.00 6217.80 10.00 6053.42
20.00 20.00 6991.44 20.00 7085.38 20.00 6975.71
25.00 25.00 7172.07 25.00 7215.89 25.00 7210.99
30.00 30.00 7284.59 30.00 7260.73 30.00 7357.16
35.00 35.00 7331.88 32.60 7264.98 35.00 7436.25
40.00 39.69 7364.67 32.60 7264.98 40.00 7462.56
45.00 39.69 7364.67 32.60 7264.98 40.41 7462.71
GAP-1 GAP-2 GAP-3
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 9768.30 10.00 8377.40 10.00 9131.50
20.00 20.00 10378.60 20.00 8628.90 20.00 9402.80
25.00 25.00 10682.80 25.00 8646.40 25.00 9220.60
30.00 30.00 10902.70 30.00 8845.10 30.00 9640.80
35.00 35.00 11102.50 35.00 8914.70 35.00 9863.70
40.00 40.00 11284.80 40.00 9102.90 40.00 9932.80
45.00 45.00 11443.30 44.42 9249.10 45.00 10130.00

D.2.6 Different layout system 3

Table D.25: Optimum value found using different methods of optimisation system 3
System 3
Piecewise Alarcon Rashid
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 5817.11 10.00 5896.71 10.00 5838.51
20.00 20.00 5892.04 14.57 5940.59 20.00 5976.79
25.00 25.00 5911.31 14.57 5940.59 23.68 5984.58
30.00 30.00 5921.78 14.57 5940.59 23.68 5984.58
35.00 31.54 5923.31 14.57 5940.59 23.68 5984.58
40.00 31.54 5923.31 14.57 5940.59 23.68 5984.58
45.00 31.54 5923.31 14.57 5940.59 23.68 5984.58
GAP-1 GAP-2 GAP-3
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 6147.30 10.00 6091.80 10.00 6121.50
20.00 19.99 6247.10 18.19 6118.20 20.00 6185.50
25.00 25.00 6265.70 20.09 6121.70 24.65 6184.10
30.00 29.90 6273.90 20.09 6121.70 26.48 6171.60
35.00 30.60 6272.80 20.09 6121.70 26.48 6171.60
40.00 31.97 6272.10 20.09 6121.70 26.48 6171.60
45.00 30.96 6273.60 20.09 6121.70 26.48 6171.60

79
D.2.7 Different layout system 4

Table D.26: Optimum value found using different methods of optimisation system 4
System 4
Piecewise Alarcon Rashid
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 21926.74 10.00 22003.56 10.00 21916.37
20.00 20.00 23047.98 20.00 23211.13 20.00 23098.72
25.00 25.00 23326.52 25.00 23513.77 25.00 23428.47
30.00 30.00 23553.20 30.00 23712.71 30.00 23663.45
35.00 35.00 23737.29 35.00 23836.92 35.00 23831.69
40.00 40.00 23872.99 40.00 23904.49 40.00 23951.13
45.00 45.00 23941.25 45.00 23931.52 45.00 24033.87
GAP-1 GAP-2 GAP-3
Gas Ava. Qg Qo Qg Qo Qg Qo
MMscf/D MMscf/D STB/D MMscf/D STB/D MMscf/D STB/D
10.00 10.00 26732.50 10.00 23605.70 10.00 24880.90
20.00 20.00 27261.60 20.00 23758.50 20.00 25159.90
25.00 25.00 27368.20 25.00 23623.10 25.00 25176.10
30.00 30.00 27440.00 23.71 23649.30 30.00 25167.10
35.00 32.54 27450.90 21.98 23680.20 33.43 25129.80
40.00 32.63 27453.30 23.52 23631.60 33.10 25136.10
45.00 32.61 27453.30 24.52 23596.60 34.82 25070.20

D.3 Perceptual Error Calculation Value

D.3.1 Same layout well 1:For different Reservoir Pressure

Table D.27: Difference between GAP-1, GAP-2 and GAP-3 with and piecewise method
for different system layout 1
Piecewise - GAP 1
System
Gas Ava. 1-1 1-2 1-3 1-4 1-5
10 0.14% 5.09% 5.71% 6.22% 7.23%
20 1.54% 5.31% 5.92% 6.39% 7.24%
25 1.38% 5.19% 5.99% 6.46% 7.17%
30 0.82% 5.05% 5.84% 6.53% 7.17%
35 0.82% 5.19% 5.79% 6.52% 7.21%
40 0.82% 5.34% 5.79% 6.52% 7.24%
45 0.82% 5.38% 5.79% 6.52% 7.24%
Average 0.91% 5.22% 5.83% 6.45% 7.21%

80
 Piecewise - GAP 2
System
Gas Ava. 1-1 1-2 1-3 1-4 1-5
10 1.34% 4.19% 4.82% 5.36% 6.54%
20 1.45% 3.29% 4.12% 4.63% 5.95%
25 2.21% 3.00% 3.78% 4.55% 5.79%
30 2.87% 2.67% 3.63% 4.46% 5.76%
35 2.87% 2.65% 3.58% 4.46% 5.74%
40 2.87% 2.63% 3.58% 4.46% 5.73%
45 2.87% 2.63% 3.58% 4.46% 5.73%
Average 2.35% 3.01% 3.87% 4.63% 5.89%
Piecewise - GAP 3
System
Gas Ava. 1-1 1-2 1-3 1-4 1-5
10 0.70% 4.67% 5.30% 5.81% 6.91%
20 0.15% 4.38% 5.03% 5.56% 6.61%
25 0.37% 3.91% 4.86% 5.38% 6.47%
30 0.95% 3.67% 4.71% 5.29% 6.42%
35 0.93% 3.66% 4.66% 5.29% 6.40%
40 0.93% 3.66% 4.66% 5.26% 6.40%
45 0.93% 3.66% 4.66% 5.29% 6.40%
Average 0.71% 3.94% 4.84% 5.41% 6.52%

Table D.28: Difference between GAP-1,GAP-2 and GAP-3 with and curve fitting using
Alaracón equation for different system layout 1
Alaracon et al. - GAP 1
System
Gas Ava. 1-1 1-2 1-3 1-4 1-5
10 3.54% 3.88% 4.33% 5.32% 6.94%
20 0.57% 4.23% 4.93% 6.00% 6.83%
25 1.51% 4.47% 5.28% 6.24% 6.89%
30 1.51% 4.62% 5.28% 6.40% 6.94%
35 1.51% 4.78% 5.28% 6.40% 7.00%
40 1.51% 4.93% 5.28% 6.40% 7.04%
45 1.51% 4.97% 5.28% 6.40% 7.04%
Average 1.67% 4.56% 5.10% 6.17% 6.95%
Alaracon et al. - GAP 2
System
Gas Ava. 1-1 1-2 1-3 1-4 1-5
10 4.78% 2.97% 3.43% 4.45% 6.24%
20 2.44% 2.18% 3.11% 4.23% 5.53%
25 2.08% 2.25% 3.06% 4.33% 5.51%
30 2.15% 2.24% 3.06% 4.33% 5.53%
35 2.15% 2.24% 3.06% 4.33% 5.53%
40 2.15% 2.22% 3.06% 4.33% 5.53%
45 2.15% 2.22% 3.06% 4.33% 5.53%
Average 2.56% 2.33% 3.12% 4.34% 5.63%

81
 Alaracon et al. - GAP 3
System
Gas Ava. 1-1 1-2 1-3 1-4 1-5
10 4.12% 3.45% 3.92% 4.91% 6.61%
20 0.83% 3.29% 4.03% 5.17% 6.20%
25 0.24% 3.17% 4.14% 5.16% 6.19%
30 0.24% 3.24% 4.14% 5.17% 6.20%
35 0.23% 3.24% 4.14% 5.17% 6.20%
40 0.23% 3.24% 4.14% 5.14% 6.20%
45 0.23% 3.24% 4.14% 5.16% 6.20%
Average 0.87% 3.27% 4.09% 5.12% 6.25%

Table D.29: Difference between GAP-1, GAP-2 and GAP-3 with curve fitting Rashid
equation for different system layout 1
Rashid et al. - GAP 1
System
Gas Ava. 1-1 1-2 1-3 1-4 1-5
10 1.87% 5.07% 5.30% 5.92% 7.30%
20 1.15% 3.39% 4.49% 5.44% 6.75%
25 0.31% 3.46% 4.72% 5.67% 6.65%
30 0.31% 3.62% 4.72% 5.83% 6.69%
35 0.31% 3.78% 4.72% 5.82% 6.75%
40 0.31% 3.93% 4.72% 5.82% 6.79%
45 0.31% 3.97% 4.72% 5.82% 6.79%
Average 0.65% 3.89% 4.77% 5.76% 6.82%
Rashid et al. - GAP 2
System
Gas Ava. 1-1 1-2 1-3 1-4 1-5
10 3.08% 4.17% 4.40% 5.05% 6.60%
20 4.21% 1.32% 2.66% 3.67% 5.45%
25 3.97% 1.22% 2.49% 3.75% 5.26%
30 4.04% 1.20% 2.49% 3.75% 5.27%
35 4.04% 1.20% 2.49% 3.75% 5.27%
40 4.04% 1.19% 2.49% 3.75% 5.27%
45 4.04% 1.19% 2.49% 3.75% 5.27%
Average 3.92% 1.64% 2.79% 3.92% 5.49%
Rashid et al. - GAP 3
System
Gas Ava. 1-1 1-2 1-3 1-4 1-5
10 2.44% 4.65% 4.89% 5.51% 6.97%
20 2.57% 2.43% 3.59% 4.61% 6.12%
25 2.10% 2.15% 3.58% 4.58% 5.95%
30 2.10% 2.22% 3.58% 4.58% 5.94%
35 2.08% 2.22% 3.58% 4.58% 5.94%
40 2.08% 2.22% 3.58% 4.55% 5.94%
45 2.08% 2.22% 3.58% 4.58% 5.94%
Average 2.21% 2.59% 3.77% 4.71% 6.11%

82
D.3.2 Same layout well 2: For different Reservoir Pressure

Table D.30: Difference between GAP-1, GAP-2 and GAP-3 with piecewise method for
different system layout well 2
Piecewise - GAP 1
System
Gas Ava. 2-1 2-2 2-3 2-4 2-5
10 48.29% 27.70% 20.73% 16.03% 9.64%
20 43.39% 20.73% 16.42% 13.18% 8.65%
25 41.83% 19.16% 15.11% 12.35% 8.33%
30 40.50% 18.48% 14.03% 11.57% 8.11%
35 39.17% 17.73% 13.74% 11.00% 7.87%
40 38.63% 17.56% 13.27% 10.59% 7.65%
45 38.17% 17.38% 12.95% 10.45% 7.58%
Average 41.42% 19.82% 15.18% 12.17% 8.26%
Piecewise - GAP 2
System
Gas Ava. 2-1 2-2 2-3 2-4 2-5
10 44.04% 18.23% 9.21% 3.74% 1.02%
20 35.35% 8.41% 2.92% 0.41% 0.68%
25 32.43% 6.17% 1.05% 1.76% 1.20%
30 30.84% 5.01% 0.54% 3.05% 1.63%
35 29.30% 4.15% 1.33% 4.04% 1.94%
40 28.67% 3.94% 1.81% 4.80% 2.27%
45 28.09% 3.73% 2.19% 5.15% 2.25%
Average 32.68% 7.09% 2.72% 3.28% 1.57%
Piecewise - GAP 3
System
Gas Ava. 2-1 2-2 2-3 2-4 2-5
10 43.50% 22.64% 14.44% 6.63% 4.29%
20 34.41% 14.02% 8.91% 5.73% 3.04%
25 31.41% 12.12% 7.24% 4.43% 2.69%
30 29.84% 11.03% 6.06% 3.52% 2.43%
35 28.09% 10.22% 5.67% 2.84% 2.07%
40 27.60% 10.03% 5.11% 2.35% 1.91%
45 27.09% 9.84% 4.75% 2.13% 1.82%
Average 31.70% 12.84% 7.45% 3.95% 2.61%

83
Table D.31: Difference between GAP-1, GAP-2 and GAP-3 with curve fitting using
Alaracón equation for different system layout well 2
Alaracon et al. - GAP 1
System
Gas Ava. 2-1 2-2 2-3 2-4 2-5
10 49.73% 26.45% 20.90% 15.94% 9.57%
20 41.83% 18.67% 15.99% 13.22% 8.74%
25 40.64% 18.05% 14.66% 12.33% 8.39%
30 39.49% 18.07% 13.97% 11.46% 8.14%
35 38.96% 18.07% 13.67% 10.85% 7.86%
40 38.79% 18.07% 13.39% 10.44% 7.62%
45 38.78% 18.07% 13.23% 10.20% 7.46%
Average 41.18% 19.35% 15.11% 12.06% 8.25%
Alaracon et al. - GAP 2

System
Gas Ava. 2-1 2-2 2-3 2-4 2-5
10 45.60% 16.81% 9.39% 3.64% 0.95%
20 33.57% 6.04% 2.42% 0.36% 0.58%
25 31.04% 4.89% 0.53% 1.79% 1.13%
30 29.67% 4.54% 0.62% 3.18% 1.60%
35 29.07% 4.55% 1.41% 4.22% 1.95%
40 28.86% 4.54% 1.67% 4.97% 2.30%
45 28.80% 4.53% 1.86% 5.44% 2.38%
Average 32.37% 6.56% 2.56% 3.37% 1.56%
Alaracon et al. - GAP 3
System
Gas Ava. 2-1 2-2 2-3 2-4 2-5
10 49.73% 26.45% 20.90% 15.94% 9.57%
20 32.60% 11.79% 8.44% 5.78% 3.13%
25 30.00% 10.92% 6.75% 4.40% 2.75%
30 28.65% 10.59% 5.98% 3.40% 2.46%
35 27.85% 10.59% 5.60% 2.67% 2.06%
40 27.79% 10.60% 5.25% 2.19% 1.88%
45 27.81% 10.60% 5.06% 1.86% 1.69%
Average 32.06% 13.08% 8.28% 5.18% 3.36%

84
Table D.32: Difference between GAP-1, GAP-2 and GAP-3 with curve fitting using
Rashid equation for different system layout well 2
Rashid et al. - GAP 1
System
Gas Ava. 2-1 2-2 2-3 2-4 2-5
10 51.51% 29.18% 20.74% 15.61% 9.27%
20 43.11% 20.60% 16.76% 13.77% 8.82%
25 40.91% 18.42% 15.26% 13.08% 8.62%
30 38.71% 16.87% 14.26% 12.31% 8.47%
35 37.26% 15.78% 13.65% 11.71% 8.26%
40 36.40% 15.31% 13.10% 11.25% 8.05%
45 36.03% 15.27% 12.77% 10.91% 7.88%
Average 40.56% 18.78% 15.22% 12.66% 8.48%
Rashid et al. - GAP 2
System
Gas Ava. 2-1 2-2 2-3 2-4 2-5
10 47.53% 19.90% 9.21% 3.27% 0.61%
20 35.03% 8.27% 3.31% 0.28% 0.48%
25 31.35% 5.31% 1.22% 0.91% 0.89%
30 28.76% 3.14% 0.27% 2.19% 1.23%
35 27.08% 1.88% 1.43% 3.21% 1.51%
40 26.08% 1.32% 2.01% 4.02% 1.83%
45 25.60% 1.27% 2.40% 4.61% 1.92%
Average 31.63% 5.87% 2.84% 2.64% 1.21%
Rashid et al. - GAP 3
System
Gas Ava. 2-1 2-2 2-3 2-4 2-5
10 47.02% 24.22% 14.45% 6.17% 3.90%
20 34.09% 13.88% 9.28% 6.38% 3.23%
25 30.31% 11.32% 7.40% 5.22% 2.99%
30 27.72% 9.28% 6.31% 4.32% 2.81%
35 25.83% 8.09% 5.57% 3.61% 2.48%
40 24.97% 7.58% 4.93% 3.08% 2.33%
45 24.56% 7.54% 4.55% 2.63% 2.14%
Average 30.64% 11.70% 7.50% 4.49% 2.84%

85
D.3.3 Same layout system well 3

Table D.33: Difference between GAP and the excel method

Gas Ava. Piecewise-Lin Alaracon et al. Rashid et al.
10 64.11% 63.60% 64.95%
20 59.21% 58.55% 58.66%
25 58.90% 58.37% 57.58%
30 58.74% 58.76% 57.26%
35 59.12% 59.35% 57.48%
40 59.46% 59.91% 58.04%
45 59.94% 60.43% 58.58%
Average 59.93% 59.85% 58.94%

D.3.4 Different layout system 1

Table D.34: Difference between GAP and the excel method system 1
Piecewise-Linear
Gas Ava. GAP-1 GAP - 2 GAP - 3
10 12.85% 5.96% 8.80%
20 9.16% 0.35% 4.24%
25 8.99% 0.11% 3.52%
30 8.68% 0.09% 3.37%
35 8.56% 0.02% 3.05%
40 8.51% 0.18% 3.02%
45 8.51% 0.18% 3.00%
Average 9.32% 0.98% 4.14%
Alaracon et al.
Gas Ava. GAP-1 GAP - 2 GAP - 3
10 12.84% 5.94% 8.78%
20 9.19% 0.39% 4.28%
25 8.85% 0.26% 3.37%
30 8.55% 0.24% 3.23%
35 8.52% 0.06% 3.01%
40 8.52% 0.17% 3.03%
45 8.52% 0.17% 3.01%
Average 9.28% 1.03% 4.10%
Rashid et al.
Gas Ava. GAP-1 GAP - 2 GAP - 3
10 13.32% 6.46% 9.29%
20 9.91% 1.18% 5.04%
25 9.21% 0.13% 3.75%
30 8.50% 0.29% 3.18%
35 8.19% 0.43% 2.66%
40 8.09% 0.64% 2.57%
45 8.08% 0.64% 2.56%
Average 9.33% 1.40% 4.15%

86
D.3.5 Different layout system 2
Table D.35: Difference between GAP and the excel method system 2
Piecewise-Linear
Gas Ava. GAP-1 GAP - 2 GAP - 3
10 37.25% 26.83% 32.88%
20 32.64% 18.98% 25.65%
25 32.86% 17.05% 22.22%
30 33.19% 17.64% 24.44%
35 33.96% 17.76% 25.67%
40 34.74% 19.10% 25.86%
45 35.64% 20.37% 27.30%
Average 34.33% 19.68% 26.29%
Alaracon et al.
Gas Ava. GAP-1 GAP - 2 GAP - 3
10 36.35% 25.78% 31.91%
20 31.73% 17.89% 24.65%
25 32.45% 16.54% 21.74%
30 33.40% 17.91% 24.69%
35 34.56% 18.51% 26.35%
40 35.62% 20.19% 26.86%
45 36.51% 21.45% 28.28%
Average 34.38% 19.75% 26.35%
Rashid et al.
Gas Ava. GAP-1 GAP - 2 GAP - 3
10 38.03% 27.74% 33.71%
20 32.79% 19.16% 25.81%
25 32.50% 16.60% 21.79%
30 32.52% 16.82% 23.69%
35 33.02% 16.58% 24.61%
40 33.87% 18.02% 24.87%
45 34.79% 19.31% 26.33%
Average 33.93% 19.18% 25.83%

D.3.6 Different layout system 3

Table D.36: Difference between GAP and the excel method system 3
Piecewise-Linear
Gas Ava. GAP-1 GAP - 2 GAP - 3
10 5.37% 4.51% 4.97%
20 5.68% 3.70% 4.74%
25 5.66% 3.44% 4.41%
30 5.61% 3.27% 4.05%
35 5.57% 3.24% 4.02%
40 5.56% 3.24% 4.02%
45 5.58% 3.24% 4.02%
Average 5.58% 3.52% 4.32%

87
 Alaracon et al.
Gas Ava. GAP-1 GAP - 2 GAP - 3
10 4.08% 3.20% 3.67%
20 4.91% 2.90% 3.96%
25 5.19% 2.96% 3.94%
30 5.31% 2.96% 3.74%
35 5.30% 2.96% 3.74%
40 5.29% 2.96% 3.74%
45 5.31% 2.96% 3.74%
Average 5.05% 2.99% 3.79%
Rashid et al.
Gas Ava. GAP-1 GAP - 2 GAP - 3
10 5.02% 4.16% 4.62%
20 4.33% 2.31% 3.37%
25 4.49% 2.24% 3.23%
30 4.61% 2.24% 3.03%
35 4.59% 2.24% 3.03%
40 4.58% 2.24% 3.03%
45 4.61% 2.24% 3.03%
Average 4.60% 2.52% 3.33%

88
D.3.7 Different layout system 4

Table D.37: Difference between GAP and the excel method system 4
Piecewise-Linear
Gas Ava. GAP-1 GAP - 2 GAP - 3
10 17.95% 7.08% 11.84%
20 15.19% 2.69% 8.11%
25 14.35% 0.77% 6.89%
30 13.80% 0.02% 6.01%
35 13.31% 0.49% 5.30%
40 12.95% 1.13% 4.93%
45 12.79% 1.47% 4.49%
Average 14.33% 1.95% 6.80%
Alaracon et al.
Gas Ava. GAP-1 GAP - 2 GAP - 3
10 17.69% 6.79% 11.56%
20 14.86% 2.30% 7.75%
25 14.08% 0.46% 6.60%
30 13.58% 0.27% 5.78%
35 13.17% 0.66% 5.14%
40 12.93% 1.15% 4.90%
45 12.83% 1.41% 4.55%
Average 14.16% 1.86% 6.61%
Rashid et al.
Gas Ava. GAP-1 GAP - 2 GAP - 3
10 18.02% 7.16% 11.91%
20 15.27% 2.78% 8.19%
25 14.40% 0.82% 6.94%
30 13.76% 0.06% 5.97%
35 13.18% 0.64% 5.17%
40 12.76% 1.35% 4.71%
45 12.46% 1.85% 4.13%
Average 14.26% 2.09% 6.72%

89