A Recurrent Neural Network–Based Proxy Model for Well-Control Optimization with Nonlinear Output Constraints

Summary In well-control optimization problems, the goal is to determine the time-varying well settings that maximize an objective function, which is often the net present value (NPV). Various proxy models have been developed to predict NPV for a set of inputs such as time-varying well bottomhole pressures (BHPs). However, when nonlinear output constraints (e.g., maximum well/field water production rate or minimum well/field oil rate) are specified, the problem is more challenging because well rates as a function of time are required. In this work, we develop a recurrent neural network (RNN)–based proxy model to treat constrained production optimization problems. The network developed here accepts sequences of BHPs as inputs and predicts sequences of oil and water rates for each well. A long-short-term memory (LSTM) cell, which is capable of learning long-term dependencies, is used. The RNN is trained using well-rate results from 256 full-order simulation runs that involve different injection and production-well BHP schedules. After detailed validation against full-order simulation results, the RNN-based proxy is used for 2D and 3D production optimization problems. Optimizations are performed using a particle swarm optimization (PSO) algorithm with a filter-basednonlinear-constraint treatment. The trained proxy is extremely fast, although optimizations that apply the RNN-based proxy at all iterations are found to be suboptimal relative to full simulation-based (standard) optimization. Through use of a few additional simulation-based PSO iterations after proxy-based optimization, we achieve NPVs comparable with those from simulation-based optimization but with speedups of 10 or more (relative to performing five simulation-based optimization runs). It is important to note that because the RNN-based proxy provides full well-rate time sequences, optimization constraint types or limits, as well as economic parameters, can be varied without retraining.