Robust Waterflooding Optimization of Multiple Geological Scenarios

Abstract

Summary Dynamic optimization of waterflooding using optimal control theory has significant potential to increase ultimate recovery, as has been shown in various studies. However, optimal control strategies often lack robustness to geological uncertainties. We present an approach to reduce the effect of geological uncertainties in the field-development phase known as robust optimization (RO). RO uses a set of realizations that reflect the range of possible geological structures honoring the statistics of the geological uncertainties. In our study, we used 100 realizations of a 3D reservoir in a fluvial depositional environment with known main-flow direction. We optimized the rates of the eight injection and four production wells over the life of the reservoir, with the objective to maximize the average net present value (NPV). We used a gradient-based optimization method in which the gradients are obtained with an adjoint formulation. We compared the results of the RO procedure to two alternative approaches: a nominal-optimization (NO) and a reactive-control approach. In the reactive approach, each production well is shut in when production is no longer profitable. The NO procedure is based on a single realization. In our study, the NO procedure is performed on each of the 100 realizations in the set individually, resulting in 100 different NO-production strategies. The control strategies were applied to each realization, from which the average NPVs, the standard deviation, the cumulative-distribution functions, and the probability-density functions were determined. The RO results displayed a much smaller variance than the alternatives, indicating an increased robustness to geological uncertainty. Moreover, the RO procedure significantly improved the expected NPV compared to the alternative methods (on average 9.5% higher than using reactive-control and 5.9% higher than the average of the NO strategies).