Summary In this paper, ensemble-based closed-loop optimization is applied to a large-scale SPE benchmark study. The Brugge field, a synthetic reservoir, is designed as a common platform to test different closed-loop reservoir management methods. The problem was designed to mimic real field management scenarios and, as a result, is by far the largest and most complex test case on closed-loop optimization. The Brugge field model consists of nine layers with a total of 44,550 active cells. It has one internal fault and seven rock regions with different relative permeability and capillary pressure functions. There are 20 producers and 10 injectors in the field. Noise corrupted production data are provided monthly. Each well has three different completions that can be controlled independently. The producing life of the reservoir is 30 years, and the objective of optimization is to maximize the net present value (NPV) at the end of 30 years. Because of the complexity of this test case, several advanced techniques are used in order to improve the solution of the ensemble-based closed-loop optimization. First, covariance localization was used to obtain good model updates with a relatively small ensemble of reservoir models. Localization alleviated the effect of spurious correlations and made it possible to incorporate large amounts of data. Second, covariance inflation was used to compensate for the tendency of small ensembles to lose variability too quickly. When covariance inflation was used together with localization, variability in the ensemble was maintained. Third, regularization was also used in the ensemble-based optimization to reduce the effect of spurious correlations and to smooth the optimized control parameters. Fourth, normalized saturations were used in the state vector because different rock regions had different relative permeability endpoint saturations. Finally, the addition of global parameters such as relative permeability curves and initial oil/water contact (IOWC) reduced the tendency for overshoot. The resulting combination of ensemble-based data assimilation and optimization performed very well on the benchmark study, achieving an NPV within 1% of the value obtained by the test organizers with known geology.
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