Optimization models for petroleum field exploitation

This paper presents a mixed integer programming model for op- timal development of an oil field under uncertain future oil price. Based on a two-dimensional reservoir description, the model sug- gests decisions concerning both design and operation, and the objective is to maximize the expected net present value of the oil field. A finite set of oil price scenarios with associated prob- abilities is given, and the scenario and policyaggregation tech- nique developed by Rockafellar and Wets is used for solving the problem. This technique is developed for the case of continu- ous variables, and in this paper we discuss different methods for adapting the scenario aggregation approach to the case of mixed integer problems. This is done by utilizing the interaction be- tween the continuous (production) and integer (design) variables. We present numerical experiments, and conclude that scenario aggregation may be a suitable technique also for mixed integer problems. lAccepted for publication in Journal of the Operational Research Society ~ 101 102 Oil Field Optimization under Price Uncertainty

[1]  B. L. Foster,et al.  Maximization in the Oil Industry--A Survey , 1964 .

[2]  Xi-Ren Cao,et al.  Perturbation analysis of discrete event dynamic systems , 1991 .

[3]  T. E. Baker,et al.  A History of Mathematical Programming in the Petroleum Industry , 1990 .

[4]  W. G. Lesso,et al.  Models for the Minimum Cost Development of Offshore Oil Fields , 1972 .

[5]  Leon S. Lasdon,et al.  Development Planning and Management of Petroleum Reservoirs Using Tank Models and Nonlinear Programming , 1984, Oper. Res..

[6]  Kjetil K. Haugen,et al.  A Stochastic Dynamic Programming model for scheduling of offshore petroleum fields with resource uncertainty , 1996 .

[7]  Leen Stougie,et al.  Solving stochastic programs with integer recourse by enumeration: A framework using Gröbner basis , 1995, Math. Program..

[8]  Georg Ch. Pflug.  On-Line Optimization of Simulated Markovian Processes , 1990, Math. Oper. Res..

[9]  T W Jonsbråten,et al.  Oil field optimization under price uncertainty , 1998, J. Oper. Res. Soc..

[10]  K. Jörnsten.  Sequencing offshore oil and gas fields under uncertainty , 1992 .

[11]  Leen Stougie,et al.  Approximation in Stochastic integer programming , 2003 .

[12]  Tom R. Douglass.  Linear programming optimizes unit negotiations , 1986 .

[13]  A. S. Manne.  A LINEAR PROGRAMMING MODEL OF THE U. S. PETROLEUM REFINING INDUSTRY , 1958 .

[14]  M. D. Devine.  Note—A Model for Minimizing the Cost of Drilling Dual Completion Oil Wells , 1973 .

[15]  G. E. Slater,et al.  Optimization of Petroleum and Natural Gas Production—A Survey , 1977 .

[16]  John M. Bohannon,et al.  A Linear Programming Model for Optimum Development of Multi-Reservoir Pipeline Systems , 1970 .

[17]  W. Garvin,et al.  Applications of Linear Programming in the Oil Industry , 1957 .

[18]  Les Frair,et al.  Economic Optimization of Offshore Petroleum Development , 1975 .

[19]  Robert A. Wattenbarger,et al.  Maximizing Seasonal Withdrawals from Gas Storage Reservoirs , 1970 .

[20]  Gary D. Libecap,et al.  Contracting for Property Rights: Series editors' preface , 1990 .

[21]  K. Aziz,et al.  Petroleum Reservoir Simulation , 1979 .

[22]  Morten W. Lund,et al.  THE VALUE OF FLEXIBILITY IN OFFSHORE OIL FIELD DEVELOPMENT PROJECTS , 1997 .

[23]  K. Pinder,et al.  Optimization of a Simulation Model of a Chemical Plant , 1972 .

[24]  Kurt Jörnsten,et al.  Modelling petroleum fields with movable platforms , 1991 .

[25]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[26]  Zvi Artstein,et al.  Sensors and Information in Optimization Under Stochastic Uncertainty , 1993, Math. Oper. Res..

[27]  Marielle Christiansen,et al.  Well management in the North Sea , 1993, Ann. Oper. Res..

[28]  Dag Haugland,et al.  Mathematical and computer modelling reports: Models for petroleum field exploitation , 1988 .

[29]  E. M. L. Beale.  A mathematical programming model for the long term development of an off-shore gas field , 1983, Discret. Appl. Math..

[30]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

[31]  J. S. Aronofsky,et al.  A Linear Programming Model for Scheduling Crude Oil Production , 1958 .

[32]  Kurt Jörnsten,et al.  A mathematical programming model for the development of petroleum fields and transport systems , 1989 .

[33]  Veijo Kaitala,et al.  Game Theory Models of Fisheries Management — a Survey , 1986 .

[34]  Gilbert Laporte,et al.  The integer L-shaped method for stochastic integer programs with complete recourse , 1993, Oper. Res. Lett..

[35]  John D. Huppler.  Scheduling Gas Field Production for Maximum Profit , 1974 .

[36]  David L. Woodruff,et al.  A class of stochastic programs withdecision dependent random elements , 1998, Ann. Oper. Res..

[37]  Gary L. Lilien.  A Note on Offshore Oil Field Development Problems and Suggested Solutions , 1973 .

[38]  D. W. Peaceman.  Interpretation of Well-Block Pressures in Numerical Reservoir Simulation(includes associated paper 6988 ) , 1978 .

[39]  James L. Smith.  The Common Pool, Bargaining, and the Rule of Capture , 1987 .

[40]  E. Silver,et al.  Application of the scenario aggregation approach to a two-stage, stochastic, common component, inventory problem with a budget constraint , 1993 .

[41]  Petter Bjerksund,et al.  Managing Investment Opportunities under Price Uncertainty: From "Last Chance" to "Wait and See" Strategies , 1990 .

[42]  D. Babayev.  Mathematical Models for Optimal Timing of Drilling on Multilayer Oil and Gas Fields , 1975 .

[43]  Alexei A. Gaivoronski,et al.  Stochastic optimization techniques for finding optimal submeasures , 1986 .

[44]  Celso C. Ribeiro,et al.  Location and sizing of offshore platforms for oil exploration , 1992 .

[45]  Rüdiger Schultz,et al.  Dual decomposition in stochastic integer programming , 1999, Oper. Res. Lett..

[46]  John H. Doveton,et al.  Probability methods in oil exploration , 1977 .

[47]  A. Williams,et al.  The Use of Linear Programming and Mathematical Models in Under-Ground Oil Production , 1962 .

[48]  Roger J.-B. Wets,et al.  The aggregation principle in scenario analysis stochastic optimization , 1989 .

[49]  Sevgi Dogru.  Selection of optimal platform locations , 1987 .

[50]  Eduardo S. Schwartz,et al.  Investment Under Uncertainty. , 1994 .

[51]  A. Charnes,et al.  Management Models and Industrial Applications of Linear Programming , 1961 .

[52]  R. Tyrrell Rockafellar,et al.  Scenarios and Policy Aggregation in Optimization Under Uncertainty , 1991, Math. Oper. Res..

[53]  J Figueira,et al.  Stochastic Programming , 1998, J. Oper. Res. Soc..

[54]  Peter Kall,et al.  Stochastic Programming , 1995 .

[55]  Alexei A. Gaivoronski,et al.  Linearization methods for optimization of functionals which depend on probability measures , 1986 .

[56]  D. W. Peaceman.  Fundamentals of numerical reservoir simulation , 1977 .

[57]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[58]  R. Bellman.  Dynamic programming. , 1957, Science.

[59]  Roger J.-B. Wets,et al.  Computing Bounds for Stochastic Programming Problems by Means of a Generalized Moment Problem , 1987, Math. Oper. Res..

[60]  A. Roth.  Axiomatic models of bargaining , 1979 .

[61]  M. Padberg,et al.  Solving airline crew scheduling problems by branch-and-cut , 1993 .

[62]  David L. Woodruff,et al.  Progressive hedging and tabu search applied to mixed integer (0,1) multistage stochastic programming , 1996, J. Heuristics.

[63]  J. A. Ventura,et al.  Restricted simplicial decomposition: computation and extensions , 1987 .

[64]  Jason H. Goodfriend,et al.  Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method , 1995 .

[65]  A. Charnes,et al.  BLENDING AVIATION GASOLINES-A STUDY IN PROGRAMMING INTERDEPENDENT ACTIVITIES IN AN INTEGRATED OIL COMPANY' , 1952 .

[66]  H. D. Attra,et al.  Application of Optimizing Techniques for Studying Field Producing Operations , 1961 .

[67]  Gary D. Libecap,et al.  The Influence of Private Contractual Failure on Regulation: The Case of Oil Field Unitization , 1985, Journal of Political Economy.

[68]  Frederick S. Hillier,et al.  Introduction of Operations Research , 1967 .

[69]  D. Green,et al.  A Method for Determining the Optimum Location of Wells in a Reservoir Using Mixed-Integer Programming , 1974 .

[70]  M. King Hubbert,et al.  The theory of ground-water motion and related papers , 1969 .

[71]  Kamy Sepehrnoori,et al.  Optimal Hydrocarbon Reservoir Production Policies , 1986, Oper. Res..