An accelerated gradient algorithm for well control optimization

The simulation-assisted optimization of injection and production control settings can be considered as a way for improved management of hydrocarbon reservoirs. Although well control optimization problems are expected to have a relatively smooth landscape, they suffer from having a high number of dimensions. As a result, gradient-based algorithms are typically the preferred choice over derivative-free algorithms. Since the calculation of the exact gradient is not always feasible, recent studies into gradient-based algorithms have focused on ameliorating the accuracy of gradient approximation methods. Less attention has been paid to the framework in which these gradient approximations are utilized. The most common framework is the steepest descent with a backtracking line-search. This study aims to provide an improved framework using an adaptive moment estimation technique. The proposed method is compared to the steepest descent framework in two case studies of increasing complexity. In both frameworks, the gradient is approximated by the simultaneous perturbation stochastic approximation. The first case study is a two-dimensional heterogeneous reservoir model produced under water-flooding. The second case study investigates the injection and production settings of the three-dimensional benchmark case, the Brugge model, whilst incorporating geological uncertainty. The proposed framework showed improvements of up to 91% in convergence speeds and up to 5% in optimal value for the first case study. In addition, the proposed framework showed an improvement of up to 81% in convergence speeds and up to 2% in optimal value for the second case study over the steepest descent framework. For both case studies, the effect of the gradient approximation accuracy (perturbation number) was also investigated. The results indicated that the proposed algorithm is less sensitive to the gradient approximation accuracy than the steepest descent framework. In addition, this study investigated the effect of two popular bound constraint handling techniques in both frameworks. The results indicated that the projection method outperforms the logarithmic transformation method when applied to production optimization problem.