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