Nonlinearly Constrained Life-Cycle Production Optimization Using Sequential Quadratic Programming (SQP) With Stochastic Simplex Approximated Gradients (StoSAG)

Abstract

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. When nonlinear-state constraints (e.g., field liquid production rate and field gas production rate) at each control step need to be honored, solving a large-scale production optimization problem, particularly in geological uncertainty, becomes significantly challenging. This study presents a stochastic gradient-based framework to efficiently solve a nonlinearly constrained deterministic (based on a single realization of a geological model) or a robust (based on multiple realizations of the geologic model) production optimization problem. The proposed framework is based on a novel sequential quadratic programming (SQP) method using stochastic simplex approximated gradients (StoSAG). The novelty is due to the implementation of a line-search procedure into the SQP, which we refer to as line-search sequential quadratic programming (LS-SQP). Another variant of the method, called the trust-region SQP (TR-SQP), a dual method to the LS-SQP, is also introduced. For robust optimization, we couple LS-SQP with two different constraint handling schemes; the expected value constraint scheme and minimum-maximum (min-max) constraint scheme, to avoid the explicit application of nonlinear constraints for each reservoir model. We provide the basic theoretical development that led to our proposed algorithms and demonstrate their performances in three case studies: a simple synthetic deterministic problem (a two-phase waterflooding model), a large-scale deterministic optimization problem, and a large-scale robust optimization problem, both conducted on the Brugge model. Results show that the LS-SQP and TR-SQP algorithms with StoSAG can effectively handle the nonlinear constraints in a life-cycle production optimization problem. Numerical experiments also confirm similar converged ultimate solutions for both LS-SQP and TR-SQP variants. It has been observed that TR-SQP yields shorter but more safeguarded update steps compared to LS-SQP. However, it requires slightly more objective-function evaluations. We also demonstrate the superiority of these SQP methods over the augmented Lagrangian method (ALM) in a deterministic optimization example. For robust optimization, our results show that the LS-SQP framework with any of the two different constraint handling schemes considered effectively handles the nonlinear constraints in a life-cycle robust production optimization problem. However, the expected value constraint scheme results in higher optimal NPV than the min- max constraint scheme, but at the cost of possible constraint violation for some individual geological realizations.