Robust Waterflooding Optimization of Multiple Geological Scenarios

Dynamic optimization of water flooding using optimal control theory has a 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 impact 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 3dimensional reservoir in a fluvial depositional environment with known main flow direction. We optimized the rates of the 8 injection and 4 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 where 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, it 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 NPV's, 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 nominal optimization strategies.

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