On optimization algorithms for the reservoir oil well placement problem

Determining optimal locations and operation parameters for wells in oil and gas reservoirs has a potentially high economic impact. Finding these optima depends on a complex combination of geological, petrophysical, flow regimen, and economical parameters that are hard to grasp intuitively. On the other hand, automatic approaches have in the past been hampered by the overwhelming computational cost of running thousands of potential cases using reservoir simulators, given that each of these runs can take on W. Bangerth (B) Department of Mathematics, Texas A&MUniversity, College Station, TX 77843, USA e-mail: [email protected] W. Bangerth Institute for Geophysics, The University of Texas at Austin, Austin, TX 78712, USA H. Klie ·M. F. Wheeler Center for Subsurface Modeling, Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX 78712, USA H. Klie e-mail: [email protected] M. F. Wheeler e-mail: [email protected] P. L. Stoffa ·M. K. Sen Institute for Geophysics, John A. and Katherine G. Jackson School of Geosciences, University of Texas at Austin, Austin, TX 78712, USA P. L. Stoffa e-mail: [email protected] M. K. Sen e-mail: [email protected] the order of hours. Therefore, the key issue to such automatic optimization is the development of algorithms that find good solutions with a minimum number of function evaluations. In this work, we compare and analyze the efficiency, effectiveness, and reliability of several optimization algorithms for the well placement problem. In particular, we consider the simultaneous perturbation stochastic approximation (SPSA), finite difference gradient (FDG), and very fast simulated annealing (VFSA) algorithms. None of these algorithms guarantees to find the optimal solution, but we show that both SPSA and VFSA are very efficient in finding nearly optimal solutions with a high probability. We illustrate this with a set of numerical experiments based on real data for single and multiple well placement problems.