Managing geological uncertainty in expensive reservoir simulation optimization

A method to manage geological uncertainty as part of an expensive simulation-based optimization process is presented. When the number of realizations representing the uncertainty is high, the computational cost to optimize the system can be considerable, and often prohibitively, as each forward evaluation is expensive to evaluate. To overcome this limitation, an iterative procedure is developed that selects a subset of realizations, based on a binary nonlinear optimization subproblem, to match the statistical properties of the target function at known sample points. This results in a reduced-order model that is optimized in place of the full system at a much lower computational cost. The result is validated over the ensemble of all realizations giving rise to one new sample point per iteration. The process repeats until the stipulated stopping conditions are met. Demonstration of the proposed method on a publicly available realistic reservoir model with 50 realizations shows that comparable results to full optimization can be obtained but far more efficiently.