Gas Allocation Optimization Methods in Artificial Gas Lift

55 Pages·2017·1.989 MB·English

by  Ehsan Khamehchi, Mohammad Reza Mahdiani (auth.)

SPRINGER BRIEFS IN
PETROLEUM GEOSCIENCE & ENGINEERING
Ehsan Khamehchi
Mohammad Reza Mahdiani
Gas Allocation
Optimization
Methods in
Artificial Gas Lift
123
SpringerBriefs in Petroleum Geoscience
& Engineering
Series editors
Dorrik Stow, Heriot-Watt University, Edinburgh, UK
Mark Bentley, AGR TRACS Training Ltd, Aberdeen, UK
Jebraeel Gholinezhad, University of Portsmouth, Portsmouth, UK
Lateef Akanji, University of Aberdeen, Aberdeen, UK
Khalik Mohamad Sabil, Heriot-Watt University, Putrajaya, Malaysia
Susan Agar, ARAMCO, Houston, USA
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More information about this series at http://www.springer.com/series/15391
Ehsan Khamehchi Mohammad Reza Mahdiani
(cid:129)
Gas Allocation Optimization
fi
Methods in Arti cial Gas Lift
123
Ehsan Khamehchi Mohammad Reza Mahdiani
Faculty of Petroleum Engineering Faculty of Petroleum Engineering
Amirkabir University ofTechnology Amirkabir University ofTechnology
(TehranPolytechnic) (TehranPolytechnic)
Tehran Tehran
Iran Iran
ISSN 2509-3126 ISSN 2509-3134 (electronic)
SpringerBriefs inPetroleum Geoscience &Engineering
ISBN978-3-319-51450-5 ISBN978-3-319-51451-2 (eBook)
DOI 10.1007/978-3-319-51451-2
LibraryofCongressControlNumber:2016961272
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Preface
Usingoptimizationmethodsisofgreatimportanceindifferentaspectsofpetroleum
engineering, including production engineering and gas lift. Gas allocation opti-
mizationiscrucialinmaximizingthegasliftperformance.Therearedifferenttopics
on gas allocation optimization, which are necessary for production engineers to
know, such as the fitness function, the constraints, etc. Thus, we wrote this book
and included different points on gas allocation optimization. Here, different meth-
ods for modeling the problem, distinct optimization constraints, and various
optimizers have been discussed.
Studyingthisbookisrecommendedtoengineersandstudentswhoareinterested
in gas lift optimization.
Tehran, Iran Ehsan Khamehchi
Mohammad Reza Mahdiani
vii
Contents
1 An Introduction to Gas Lift.... .... .... .... .... .... ..... .... 1
1.1 Introduction .... .... ..... .... .... .... .... .... ..... .... 1
1.2 Formulation of the Problem . .... .... .... .... .... ..... .... 4
References.. .... .... .... ..... .... .... .... .... .... ..... .... 4
2 The Fitness Function of Gas Allocation Optimization ... ..... .... 7
2.1 Introduction .... .... ..... .... .... .... .... .... ..... .... 7
2.2 Technical Factors .... ..... .... .... .... .... .... ..... .... 8
2.2.1 Nodal Analysis..... .... .... .... .... .... ..... .... 8
2.2.2 Analytical Models... .... .... .... .... .... ..... .... 14
2.2.3 Proxy Models . ..... .... .... .... .... .... ..... .... 17
2.3 Economic Factors.... ..... .... .... .... .... .... ..... .... 18
2.4 Integrated Model .... ..... .... .... .... .... .... ..... .... 19
References.. .... .... .... ..... .... .... .... .... .... ..... .... 20
3 Constraint Optimization.. ..... .... .... .... .... .... ..... .... 25
3.1 Introduction .... .... ..... .... .... .... .... .... ..... .... 25
3.2 No Limitation... .... ..... .... .... .... .... .... ..... .... 26
3.3 Maximum Amount of Available Lift Gas... .... .... ..... .... 27
3.4 Injection and Production Limitations .. .... .... .... ..... .... 27
3.5 Stability ... .... .... ..... .... .... .... .... .... ..... .... 27
3.6 Controlling the System..... .... .... .... .... .... ..... .... 30
3.6.1 Smart Methods ..... .... .... .... .... .... ..... .... 32
References.. .... .... .... ..... .... .... .... .... .... ..... .... 33
ix
x Contents
4 Optimization Algorithms.. ..... .... .... .... .... .... ..... .... 35
4.1 Introduction .... .... ..... .... .... .... .... .... ..... .... 35
4.2 Numerical Algorithms ..... .... .... .... .... .... ..... .... 36
4.2.1 Equal Slope Optimization. .... .... .... .... ..... .... 36
4.2.2 Gradient Optimization.... .... .... .... .... ..... .... 37
4.2.3 Newton Method .... .... .... .... .... .... ..... .... 38
4.3 Heuristic Algorithms.. ..... .... .... .... .... .... ..... .... 40
References.. .... .... .... ..... .... .... .... .... .... ..... .... 44
Abbreviations
Ai Injection port size, ft2
B FVF of gas at injection point
g
C Cost of gas lift $/Mscf
g
D Injection depth, ft
i
D Tubing depth, ft
t
D Well depth, ft
well
E Orifice efficiency factor, 0.9
F , F Asheim stability factors
1 2
f Oil fraction
o
g Acceleration of gravity, ft/s2
gk The gradient of “f” at Qk
g
GLR Gas liquid ratio, SCF/STB
ID Casing inner diameter, in
c
ID Tubing inner diameter, in
t
IFT Surface tension, dyne/cm
J Productivity index, scf/s.psi
k Counter of iterations
M Apparent molecular weight
a
m Slope in equal slope method
OD Tubing outer diameter, in
t
Orificesize Orifice size, 1/64 in
P Net profit of oil $/bbl
P* Pressure reservoir from well test
P Bubble point pressure, psi
b
PI Productivity index, STB/day/psi
P Pseudo reduced pressure
pr
P Reservoir pressure, psi
R
p Tubing flow pressure at gas injection point, psi
ti
P Well head pressure, psi
wh
qfi Flow rate of reservoir fluids at injection point, ft3/s
xi