Efficient Robust Production Optimization with Reduced Sampling

Abstract

Summary Model-based robust production optimization is performed by propagating the uncertainty in the reservoir model description through the nonlinear fluid flow dynamics to predict the stochastic production response and the objective function of interest. Propagation of uncertainty is often accomplished through Monte Carlo simulation by sampling from the distribution of uncertain input parameters and computing the corresponding value of the objective function after performing reservoir simulation. The computational burden of performing hundreds of reservoir simulation runs to characterize the distribution of the objective function (or its point statistics) over the sampled input parameters makes the process prohibitive for large-scale deployment. To reduce the computational load of robust production optimization under geologic uncertainty, we propose an efficient stochastic production optimization algorithm based on a reduced sampling strategy. In this approach, at each iteration of the optimization procedure, instead of evaluating the objective function and its gradient over a large number of fixed realizations, we approximate them by using a small subset of model realizations that are selected randomly. This approximation leads to solving a series of “small” subproblems that require significantly fewer reservoir simulation runs, thereby reducing the computational complexity of the robust optimization workflow. Because the samples are selected randomly, over several iterations of the optimization process, a large number of samples are included. For a fixed set of realization, the proposed approach results in each sample being used multiple times during the optimization process. The proposed method is applied to several numerical examples, including a field-scale reservoir model, to show its computational efficiency over traditional robust production optimization under geologic uncertainty.