An efficient adaptive algorithm for robust control optimization using StoSAG

There is significant geological uncertainty in the reservoir description due to the limited knowledge about the underground formation. The common approach is to use multiple plausible geostatistical realizations of the reservoir model in order to quantify the uncertainty, however, usually a small ensemble of realizations is utilized in the robust optimization due to the computational cost. This may results in erroneous estimation of uncertainty in the predicted optimal reservoir production performance. We propose an efficient algorithm for robust optimization where a large number of representative realizations are considered. The algorithm proposed in this work assumes confidence in a subset of realizations for representing the full-set of realizations in the neighbourhood of the current control estimate. The subset is chosen based on a ranking method and modified adaptively throughout the optimization iterations. The optimizer in this paper is the steepest ascent method using the Stochastic Simplex Approximate Gradient (StoSAG), but the proposed algorithm is suitable to be combined with other optimization algorithms. Three synthetic reservoir examples generated with different geostatistical modelling methods are tested to validate the proposed algorithm. All three examples show that compared with a full-set robust optimization, the proposed adaptive robust optimization algorithm not only improves the optimization convergence rate, but also find a higher optimal NPV when the optimization is terminated at a maximum affordable simulation cost using the stochastic simplex gradient.