On optimization algorithms for the reservoir oil well placement problem

Abstract

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 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.

A New Hybrid Approach Using the Simultaneous Perturbation Stochastic Approximation Method for the Optimal Allocation of Electrical Energy Storage Systems

“…The constant a k is included to accelerate the convergence, and it depends on the expected maximum number of iterations, the expected step size, and the starting values of the optimization variables; ∆ k is the random perturbation vector (with dimension q), the components of which are independently generated following a Bernoulli (±1) distribution [25]; the constant c k is a positive number. More details about the values of the constants and on the generation of the perturbation vector are in [25].…”

“…More details about the values of the constants and on the generation of the perturbation vector are in [25].…”

A review of closed-loop reservoir management

“…Based on the simultaneous perturbation idea, Spall further provided a second-order SPSA method, which estimates the Hessian matrix at each iteration. Later Bangerth et al (2006) described an integer SPSA method and used this modified SPSA method to solve well placement optimization problems. To the best of our knowledge, this is the first time that SPSA has been used in optimal control problems.…”

Joint optimization of oil well placement and controls

“…Examples include genetic algorithms (Goldberg, 1989;Güyagüler et al, 2000;Yeten et al, 2003), stochastic perturbation methods (Bangerth et al, 2006), and particle swarm optimization (Clerc, 2006;Onwunalu and Durlofsky, 2010;Echeverría Ciaurri et al, 2011b). Due to their random component, these search procedures can avoid being trapped in some unsatisfactory local optima.…”

“…Other approaches have mimicked a more traditional approach of computing finite differences. Bangerth et al (2006), e.g., uses stochastic perturbation of well location variables to obtain derivative information that may then be used within a standard solver. Complementary references can be found in Chapter 2.…”