Abstract
This study presents an efficient gradient-based production optimization method that uses a deep-learning-based proxy model for the prediction of state variables (such as pressures and saturations) and well outputs (such as bottomhole pressures and injection rates) to solve nonlinearly constrained optimization with geological uncertainty. The surrogate model is the Embed-to-control Observe (E2CO) deep-learning proxy model, consisting of four blocks of neural networks: encoder, transition, transition output, and decoder. The use of a transition output block in E2CO networks provides the capability of predicting reservoir system output directly from the input state variables without using any explicit well-model equations. The proxy model is coupled with a powerful stochastic-gradient-based line-search sequential quadratic programming (LS-SQP) workflow to handle robust production optimization in the presence of nonlinear state constraints. A portion of the SPE10 benchmark reservoir model with channelized heterogeneous permeability under waterflooding is used for demonstrating the prediction and optimization performances of the proposed E2CO-based framework. The results from this framework are directly and quantitatively compared with the ones simulated using a commercial high-fidelity reservoir simulator.
