Nonlinearly Constrained Life-Cycle Production Optimization With a Least-Squares Support-Vector Regression Proxy

Abstract

Summary Life-cycle production optimization is a crucial component of closed-loop reservoir management, referring to optimizing a production-driven objective function via varying well controls during a reservoir’s lifetime. However, when nonlinear constraints (such as field liquid production rate, field gas production rate, injection pressures, etc.) as functions of time need to be honored in addition to linear ones, the problem becomes significantly more challenging and computationally expensive to perform using a high-fidelity reservoir simulator with the existing gradient-based methods using the adjoint or stochastic simplex approximate gradient (StoSAG). Therefore, in this study, we present an efficient algorithm for nominal production optimization under bound, linear, and nonlinear constraints using the least-squares support-vector regression (LS-SVR), where the cost function is the net present value (NPV). We achieve computational efficiency by generating a set of output values of the NPV and nonlinear constraint functions by running the high-fidelity simulator for a broad set of input design variables (well controls) and then using the set of input/output data to train LS-SVR proxy models to replace the high-fidelity simulator when computing values of NPV and nonlinear constraint functions during iterations of sequential quadratic programming (SQP). To obtain improved (higher) estimated optimal NPV values, we use a method so-called iterative resampling with the LS-SVR proxy. With this iterative resampling method, after each proxy-based optimization, one evaluates the cost and constraint functions at the estimated optimal controls using reservoir-simulator output, and then adds this new input/output information to the training set to update the proxy models for predicting NPV and constraints. Using the updated proxies, one applies SQP optimization again. The results obtained from our new LS-SVR method are compared with those obtained from our recently developed StoSAG-based line-search sequential quadratic programming (StoSAG-LS-SQP) in which the gradients are computed from a high-fidelity simulator for the nonlinearly constrained optimization problem. We demonstrate the computational performances of the proposed methods on two small and intuitive numerical experiments and a field-scale realistic problem. All investigated cases involve multiphase flow simulated using a commercial reservoir simulator with a black-oil formulation. Different combinations of design variables including bottom-hole pressures of producers and water injection rates of the injectors are tested as feature space for LS-SVR. The nonlinear constraints are field liquid production rate and water production rate. The main conclusion of our results is that nonlinear constrained optimization with the LS-SVR iterative resampling with SQP is computationally 2 times more efficient than StoSAG-LS-SQP.