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Use of retrospective optimization for placement of oil wells under uncertainty

Published: 05 December 2010 Publication History

Abstract

Determining well locations in oil reservoirs under geological uncertainty remains a challenging problem in field development. Well placement problems are integer optimization problems because a reservoir is discretized into grid blocks and the well locations are defined by block indices (i, j, k) in the discrete model. Reservoir simulators are used to evaluate reservoir production given a well placement. In the presence of reservoir uncertainty, we simulate multiple model realizations to estimate the expected field performance for a certain well placement. Most existing methods for well placement optimization problems are random-search based algorithms.
We present a retrospective optimization (RO) algorithm that uses Hooke-Jeeves search for well location optimization under uncertainty. The RO framework generates a sequence of sample-path problems with increasing sample sizes. Embedded in RO, the Hooke-Jeeves search solves each sample-path problem for a local optimizer given a discrete neighborhood definition. The numerical results show that the RO algorithm efficiently finds a solution yielding a 70% increase (compared to a solution suggested from heuristics) in the expected net present value (NPV) over 30 years of reservoir production for the problem considered.

References

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Bangerth, W., H. Klie, M. F. Wheeler, P. L. Stoffa, and M. K. Sen. 2006. On optimization algorithms for the reservoir oil well placement problem. Computational Geosciences 10:303--319.
[2]
Chen, H., and B. W. Schmeiser. 2001. Stochastic root finding via retrospective approximation. IIE Transactions 33:259--275.
[3]
Hooke, R, and T. A. Jeeves. 1961. "Direct search" solution of numerical and statistical problems. Journal of the ACM 8:212--229.
[4]
Jin, J., and B. W. Schmeiser. 2003. Simulation-based retrospective optimization of stochastic systems. In Proceedings of the 2003 Winter Simulation Conference. New Orleans, Louisiana.
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Kleywegt, A. J., A. Shapiro, and T. H. de Mello. 2001. The sample average approximation method for stochastic discrete optimization. SIAM Journal on Optimization 12:479--502.
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Onwunalu, J. E., and L. J. Durlofsky. 2010. Application of a particle swarm optimization algorithm for determining optimum well location and type. Computational Geosciences 14:183--198.
[7]
Peters, E., R. J. Arts, G. K. Brouwer, and C. R. Geel. 2009. Results of the Brugge benchmark study for flooding optimization and history matching. In Paper SPE 119094 presented at the SPE Reservoir Simulation Symposium. The Woodlands, Texas.
[8]
Sarma, P., and W. H. Chen. 2008. Efficient well placement optimization with gradient-based algorithms and adjoint models. In Paper SPE 112257 presented at the SPE Intelligent Energy Conference and Exhibition. Amsterdam, The Netherlands.
[9]
Wang, H., and B. W. Schmeiser. 2008. Discrete stochastic optimization using linear interpolation. In Proceedings of the 2008 Winter Simulation Conference, ed. S. J. Mason, R. R. Hill, L. Mönch, O. Rose, T. Jefferson, and J. W. Fowler. Washington D. C., USA.
[10]
Yeten, B. 2003. Optimum deployment of nonconventional wells. Ph.D. thesis, Stanford University.

Cited By

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  • (2015)Hierarchical stochastic modeling and optimization for petroleum field development under geological uncertaintyComputers and Industrial Engineering10.1016/j.cie.2014.11.00780:C(23-32)Online publication date: 1-Feb-2015
  • (2013)Mixed integer simulation optimization for petroleum field development under geological uncertaintyProceedings of the 2013 Winter Simulation Conference: Simulation: Making Decisions in a Complex World10.5555/2675983.2676117(1057-1067)Online publication date: 8-Dec-2013

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cover image ACM Conferences
WSC '10: Proceedings of the Winter Simulation Conference
December 2010
3519 pages
ISBN:9781424498642

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Winter Simulation Conference

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Published: 05 December 2010

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WSC10
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WSC10: Winter Simulation Conference
December 5 - 8, 2010
Maryland, Baltimore

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WSC '10 Paper Acceptance Rate 184 of 281 submissions, 65%;
Overall Acceptance Rate 3,413 of 5,075 submissions, 67%

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Cited By

View all
  • (2015)Hierarchical stochastic modeling and optimization for petroleum field development under geological uncertaintyComputers and Industrial Engineering10.1016/j.cie.2014.11.00780:C(23-32)Online publication date: 1-Feb-2015
  • (2013)Mixed integer simulation optimization for petroleum field development under geological uncertaintyProceedings of the 2013 Winter Simulation Conference: Simulation: Making Decisions in a Complex World10.5555/2675983.2676117(1057-1067)Online publication date: 8-Dec-2013

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