Abstract
In gas-lifted oil fields, high pressure gas is injected at the bottom of the production tubing of the wells to artificially lift oil to the surface. Lift-gas should enter each well at a certain mass flow and pressure, giving rise to the problem of deciding which compressors (facilities) should be installed and how they supply the demands of the wells (clients). This compressor scheduling is a mixed-integer, nonconvex, nonlinear programming problem that generalizes the standard facility location problem. By piecewise-linearizing the performance curve of each compressor—a function relating output mass flow and discharge pressure, the problem is recast as a mixed-integer linear program. This paper presents this linear reformulation, proposes families of valid inequalities, and reports on results from the application of these inequalities to solve representative instances of the compressor scheduling problem.
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Abhishek K, Leyffer S, Linderoth JT (March 2008) FilMINT: An outer-approximation-based solver for nonlinear mixed integer programs. Technical Report ANL/MCS-P1374-0906, Mathematics and Computer Science Division, Argonne National Laboratory
An S, Li Q, Gedra TW (September 2003) Natural gas and electricity optimal power flow. In: Proceedings of the IEEE/PES transmission and distribution conference, Dallas, TX, pp. 138–143
Balas E (1975) Facets of the knapsack polytope. Math Program 8(1):146–164
Balas E, Zemel E (1978) Facets of the knapsack polytope from minimal covers. SIAM J Appl Math 34(1):119–148
Bonami P, Biegler LT, Conn AR, Cornuéjols G, Grossmann IE, Laird CD, Lee J, Lodi A, Margot F, Sawaya N, Waechter A (October 2005) An algorithmic framework for convex mixed integer nonlinear programs. Technical Report RC23771, IBM Research Division
Boyd EA (1994) Fenchel cutting planes for integer programs. Oper Res 42(1):53–64
Camponogara E, de Castro MP (June 2008) Cover-based cutting planes for a compressor scheduling problem: a computational study. In: Proceedings of the international conference on engineering optimization, Rio de Janeiro, Brazil
Camponogara E, de Castro MP, Plucenio A (2006) The facility location problem: model, algorithm, and application to compressor allocation. In: Proceedings of the IFAC international symposium on advanced control of chemical processes. Elsevier, Amsterdam
Camponogara E, de Castro MP, Plucenio A (September 2007) Compressor scheduling in oil fields: a piecewise-linear formulation. In: Proceedings of the IEEE conference on automation science and engineering, Scottsdale, AZ, pp 436–441
Camponogara E, de Conto AM (2009) Lift-gas allocation under precedence constraints: MILP formulation and computational analysis. IEEE Trans Automa Sci Eng 6(3):544–551
Camponogara E, Nakashima PHR (2006) Optimizing gas-lift production of oil wells: piecewise linear formulation and computational analysis. IIE Trans 38(2):173–182
Camponogara E, Plucenio A, Teixeira AF, Campos SRV (2008) An automation system for gas-lifted oil wells: model identification, control, and optimization. J Petrol Sci Eng (submitted)
Cornuéjols G, Sridharan R, Thizy J-M (1991) A comparison of heuristics and relaxations for the capacitated plant location problem. Eur J Oper Res 50:280–297
Dutta-Roy K, Barua S, Heiba A (March 1997) Computer-aided gas field planning and optimization. In: Proceedings of the SPE production operations symposium, Oklahoma City
Floudas CA (1995) Nonlinear and mixed-integer optimization: fundamentals and applications. Oxford University Press, New York
Fourer R, Gay DM, Kernighan BW (2002) AMPL: A modeling language for mathematical programming. Duxbury, N. Scituate
Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, New York
Holmström K, Göran AO, Edvall MM (February 2007) User’s guide for TOMLAB/MINLP. Technical report, Tomlab Optimization Inc., San Diego, CA
Horst R, Pardalos PM, Van Thoai N (2000) Introduction to global optimization (nonconvex optimization and its applications). Springer, Berlin
Horst R, Tuy H (2003) Global optimization: deterministic approaches. Springer, Berlin
ILOG Incorporated, Mountain View, CA. ILOG CPLEX 9.0: Getting Started 2003
Jahn F, Cook M, Graham M (2003) Hydrocarbon exploration and production. Elsevier, Amsterdam
Leung JM, Magnanti TL (1989) Valid inequalities and facets of the capacitated plant location problem. Math Program 44(1–3):271–291
Leyffer S (1998) User manual for MINLP-BB. Technical report, University of Dundee, 1998
Murray R, Edwards C, Gibbons K, Jakeman S, de Jonge G, Kimminau S, Ormerod L, Roy C, Vachon G (April 2006) Making our mature fields smarter—an industry wide position paper from the 2005 SPE forum. In: Proc of the SPE intelligent energy conference and exhibition, Amsterdam, The Netherlands. Paper SPE 100024
Nadar MS, McKie C (June 2004) Benefits of detailed compressor modelling in optimising production from gas-lifted fields. In: Proceedings of the 2nd Middle East artificial lift forum, Dubai, pp 46–47
Nakashima PHR, Camponogara E (2006) Optimization of lift-gas allocation using dynamic programming. IEEE Trans Syst Man Cybernet Part A 36(2):407–414
Nemhauser GL, Wolsey LA (1988) Integer and combinatorial optimization. Wiley, New York
Padberg M (2000) Approximating separable nonlinear functions via mixed zero-one programs. Oper Res Lett 27(1):1–5
Sherali HD (2001) On mixed-integer zero-one representations for separable lower-semicontinuous piecewise-linear functions. Oper Res Lett 28(4):155–160
Smith A, Law F, Sillner R (1998) Scheduling, maintenance software helps reduce pipeline costs, downtime. Oil Gas J 96(43):69–74
Tomlin J (1988) Special ordered sets and an application to gas supply operations planning. Math Program 42(1–3):69–84
Yeten B, Brouwer DR, Durlofsky LJ, Aziz K (2004) Decision analysis under uncertainty for smart well deployment. J Petrol Sci Eng 44(1–2):183–199
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This work was supported in part by Agência Nacional do Petróleo, Gás Natural e Biocombustíveis (ANP) under grant PRH-34/aciPG/ANP and by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under grants 479157/2006-5 and 473841/2007-0.
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Camponogara, E., de Castro, M.P., Plucenio, A. et al. Compressor scheduling in oil fields. Optim Eng 12, 153–174 (2011). https://doi.org/10.1007/s11081-009-9093-3
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DOI: https://doi.org/10.1007/s11081-009-9093-3