Gradient-based Production Optimization with Economic Constraints

Abstract

This work develops an analytical framework to study the effects of enforcing simulator-based constraints while performing gradient-based production optimization. In particular, this work studies how the enforcement of this type of constraints affects the consistency of the adjoint-based gradient and the performance of a gradient-based algorithm. In reservoir management, production optimization is commonly performed using gradient-based algorithms that rely on the efficient computation of control gradients through an adjoint formulation. Often, production optimization is implicitly coupled with economic constraints, which typically are implemented through well performance limits enforced within the reservoir simulator. We show that enforcing simulator-based economic constraints triggers nondifferentiable unscheduled changes in both the well model equations and in the functions defining the economic criteria. These discontinuities lead to inconsistencies within the adjoint gradient formulation that eventually translate into decreased algorithmic performance. The analytical framework developed in this study allows us to devise an efficient implementation of the simulator-based constraints that provides gradients that are consistent with the adjoint formulation. These analytical results are described using the theoretical framework developed in this paper, and implemented for a production optimization test case where they are shown to outperform common modes of economic constraint enforcement.