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Production optimization under geological uncertainty is computationallyexpensive, as a large number of well control schedules must be evaluated overmultiple geological realizations. In this work, a convolutional-recurrentneural network (CNN-RNN) proxy model is developed to predict well-by-well oiland water rates, for given time-varying well bottom-hole pressure (BHP)schedules, for each realization in an ensemble. This capability enables theestimation of the objective function and nonlinear constraint values requiredfor robust optimization. The proxy model represents an extension of a recentlydeveloped long short-term memory (LSTM) RNN proxy designed to predict wellrates for a single geomodel. A CNN is introduced here to processes permeabilityrealizations, and this provides the initial states for the RNN. The CNN-RNNproxy is trained using simulation results for 300 different sets of BHPschedules and permeability realizations. We demonstrate proxy accuracy foroil-water flow through multiple realizations of 3D multi-Gaussian permeabilitymodels. The proxy is then incorporated into a closed-loop reservoir management(CLRM) workflow, where it is used with particle swarm optimization and afilter-based method for nonlinear constraint satisfaction. History matching isachieved using an adjoint-gradient-based procedure. The proxy model is shown toperform well in this setting for five different (synthetic) `true' models.Improved net present value along with constraint satisfaction and uncertaintyreduction are observed with CLRM. For the robust production optimization steps,the proxy provides O(100) runtime speedup over simulation-based optimization.

Convolutional-Recurrent Neural Network Proxy for Robust Optimization and Closed-Loop Reservoir Management