The effective application of continuous gas lift entails solving the combinatorial optimization problem of optimally allocating limited resources. This work proposes a mixed integer linear formulation for the problem of maximizing oil field profit under multiple facility constraints such as limited lift gas, fluid handling, and storage capacities. Families of valid inequalities are identified and introduced into the basic model to render a stronger formulation. Numerical experiments using commercial and non-commercial software, and comparisons with published results, show that the proposed method yields fast solution with significant average increase in oil production rate and profit.

1.
Economides
,
M. J.
,
Hill
,
A. D.
, and
Ehlig-Economides
,
C.
, 1993,
Petroleum Production Systems
,
Prentice–Hall
, Englewood Cliffs. NJ.
2.
Redden
,
J. D.
,
Sherman
,
T. A. G.
, and
Blann
,
J. R.
, 1974, “
Optimizing Gas-Lift Systems
,” Paper SPE 5150, In
Proceedings of the 49th Annual Fall Meeting of Petroleum Engineers of AIME
, October 6, Houston, TX.
3.
Kanu
,
E. P.
,
Mach
,
J.
, and
Brown
,
K. E.
, 1981, “
Economic Approach to Oil Production and Gas Allocation in Continuous Gas Lift
,”
JPT, J. Pet. Technol.
0149-2136,
33
, pp.
1887
1892
.
4.
Nishikiori
,
N.
,
Redner
,
R. A.
,
Doty
,
D. R.
, and
Schmidt
,
Z.
, 1995, “
An Improved Method for Gas Lift Allocation Optimization
,”
ASME J. Energy Resour. Technol.
0195-0738,
117
, pp.
87
92
.
5.
Alarcón
,
G. A.
,
Torres
,
C. F.
, and
Gómez
,
L. E.
, 2002, “
Global Optimization of Gas Allocation to a Group of Wells in Artificial Lift Using Nonlinear Constrained Programming
,”
ASME J. Energy Resour. Technol.
0195-0738,
124
(
4
), pp.
262
268
.
6.
Martínez
,
E. R.
,
Moreno
,
W. J.
,
Moreno
,
J. A.
, and
Maggiolo
,
R.
, 1994, “
Application of Genetic Algorithm on the Distribution of Gas Lift Injection
,” Paper SPE 26993, In
Proceedings of the Third Latin American/Caribbean Petroleum Engineering Conference
,
Buenos Aires
,
Argentina
.
7.
Buitrago
,
S.
,
Rodríguez
,
E.
, and
Espin
,
D.
, 1996, “
Global Optimization Techniques in Gas Allocation for Continuous Flow Gas Lift Systems
,” Paper SPE 35616, In
Proceedings of the Gas Technology Conference
,
Calgary, Canada.
8.
Camponogara
,
E.
, and
Nakashima
,
P. H. R.
, 2003, “
Applying Dynamic Programming to a Gas-Lift Optimization Problem
,” In
Proceedings of the Second Brazilian Congress on Research and Development in Petroleum and Gas
,
Rio de Janeiro, Brazil.
9.
Nakashima
,
P. H. R.
, and
Camponogara
,
E.
, 2004, “
Otimização da Alocação de Gás de Injeção para um Conjunto de Poços de Petróleo Operando via Gas-Lift
,” In
Anais do XV Congresso Brasileiro de Automática
,
Gramado, Brazil. In Portuguese.
10.
Nakashima
,
P. H. R.
, and
Camponogara
,
E.
, 2006, “
Optimization of Lift-Gas Allocation Using Dynamic Programming
,”
IEEE Trans. Syst. Man Cybern., Part A. Syst. Humans
1083-4427,
36
(
2
), pp.
407
414
.
11.
Camponogara
,
E.
, and
Nakashima
,
P. H. R.
, 2006, “
Solving a Gas-Lift Optimization Problem by Dynamic Programming
,”
Eur. J. Oper. Res.
0377-2217,
174
(
2
), pp.
1220
1246
.
12.
Fang
,
W. Y.
, and
Lo
,
K. K.
, 1996, “
A Generalized Well-Management Scheme for Reservoir Simulation
,”
SPE Reservoir Eng.
0885-9248,
11
(
2
), pp.
116
120
.
13.
Wang
,
P.
,
Litvak
,
M. L.
, and
Aziz
,
K.
, 2002, “
Optimization of Production From Mature Fields
,” In
Proceedings of the 17th World Petroleum Congress
,
Rio de Janeiro
, Brazil.
14.
Garey
,
M. R.
, and
Johnson
,
D. S.
, 1979,
Computers and Intractability: A Guide to the Theory of NP-Completeness
,
Freeman
, New York.
15.
Martelo
,
S.
, and
Toth
,
P.
, 1990,
Knapsack Problems: Algorithms and Computer Implementations
,
Wiley
, West Sussex, UK.
16.
Handley-Schachler
,
S.
,
McKie
,
C.
, and
Quintero
,
N.
, 2000, “
New Mathematical Techniques for the Optimization of Oil and Gas Production Systems
,” Paper SPE 65161, In
Proceedings of the SPE European Petroleum Conference
,
Paris, France.
17.
Beale
,
E. M. L.
, and
Tomlin
,
J. A.
, 1970, “
Special Facilities in a General Mathematical Programming System for Non-Convex Problems Using Ordered Sets of Variables
,” In
Proceedings of the Fifth International Conference on Operations Research
,
J.
Lawrence
, ed, pp.
447
454
.
18.
Nemhauser
,
G. L.
, and
Wolsey
,
L. A.
, 1988,
Integer and Combinatorial Optimization
,
Wiley
, New York.
19.
Nakashima
,
P. H. R.
, 2004, “
Otimização de Processos de Produção de Petróleo via Injeção Contínua de Gás
,” Ph.D. Thesis Proposal, Graduate Program in Electrical Engineering, Federal University of Santa Catarina, Florianópolis, Brazil. In Portuguese.
20.
Balas
,
E.
, 1975, “
Facets of the Knapsack Polytope
,”
Math. Program.
0025-5610,
8
, pp.
146
164
.
21.
Balas
,
E.
, and
Zemel
,
E.
, 1978, “
Facets of the Knapsack Polytope from Minimal Covers
,”
SIAM J. Appl. Math.
0036-1399,
34
, pp.
119
148
.
22.
Wolsey
,
L. A.
, 1998,
Integer Programming
,
Wiley
, New York.
23.
Camponogara
,
E.
, and
Nakashima
,
P. H. R.
, 2006, “
Optimizing Gas-Lift Production of Oil Wells: Piecewise Linear Formulation and Computational Analysis
,”
IIE Trans.
0740-817X,
38
(
2
), pp.
173
182
.
24.
ILOG Corporation
, 2003, ILOG CPLEX 9.0: Getting Started, http://www.ilog.comhttp://www.ilog.com.
25.
Makhorin
,
A.
, 2003, “
GNU Linear Programming Kit: Reference Manual
,” Department for Applied Informatics, Moscow Aviation Institute, Moscow, Russia, http://www.gnu.org/software/glpk/glpk.htmlhttp://www.gnu.org/software/glpk/glpk.html.
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