Closed-loop Reservoir Management using a Convolutional – Recurrent Neural Network Proxy for Robust Production Optimization

Abstract

Summary Closed-loop reservoir management (CLRM) entails continuous data collection and the repeated application of history matching followed by production optimization. In traditional CLRM procedures, high-fidelity reservoir simulation is used for all production optimization and history matching computations. This approach can be very expensive in practice, particularly when robust optimization is applied (meaning optimization is performed over multiple realizations) and a derivative-free optimization procedure is used. Therefore, a proxy that can be applied to optimize well controls over multiple geomodels in an ensemble will be particularly useful. In recent work, we developed a long short-term memory recurrent neural network (LSTM RNN) proxy to perform well control optimization, under nonlinear output constraints (e.g., maximum well water cut, maximum field water production), for a deterministic geological model ( Kim & Durlofsky, SPEJ, 2021 ). In this work, we extend this methodology to predict well-by-well production/injection rate time series for each geomodel in an ensemble, for a specified bottomhole pressure (BHP) schedule. This is achieved by incorporating a convolutional neural network (CNN) into the RNN-based proxy. In the CNN–RNN proxy, the CNN processes permeability realizations and provides initial long and short-term states for the RNN. The RNN accepts the initial states and specified BHP time-series and provides the well responses, allowing for the computation of expected NPV and constraint violations over the ensemble. The CNN-RNN proxy is incorporated into a CLRM framework and applied to a 3D system characterized by Gaussian permeability realizations. The goal is to maximize NPV for a waterflood subject to maximum water injection rates and maximum water cuts. Production optimization is achieved using the CNN–RNN proxy with a particle swarm optimization algorithm, with a filter-based treatment for constraint handling. Permeability fields are represented using principal component analysis. History matching is accomplished using a randomized maximum likelihood method with gradient-based minimization. Computational results demonstrate that the CNN–RNN proxy accurately predicts well-by-well oil and water rates, for a wide range of input BHP profiles, for each realization in the ensemble. CLRM results show that NPV for a synthetic “true model” increases over the five closed-loop cycles considered. Substantial uncertainty reduction is also achieved as CLRM progresses.