Use of retrospective optimization for placement of oil wells under uncertainty

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.