Life-Cycle Gradient-Based Production Optimization Including Well-Shutoff Option with Least-Squares Support Vector Regression

Abstract

Summary In this work, we focus on well-shutoff/well-control optimization, which enables shutting off a production well or injection well to be part of the well-control optimization within a net present value (NPV) formulation that includes the operation expenditures (OPEX) if the well is not economical to produce or inject. For this purpose, we formulate an objective function for the NPV by introducing a production time fraction as the design variable to shut off a production well over its total production life, divided into a fixed number of cycles. Unlike the previous studies, we use a shutoff period within each cycle instead of shutting it off with a bottomhole pressure (BHP) control, where the BHPs for each producer are part of the optimization variables. When BHPs are considered control optimization variables with an NPV having OPEX, the NPV could be discontinuous for BHPs. To avoid this problem, we built a continuously differentiable proxy function for NPV using least-square support vector regression (LS-SVR). We use linear equality constraints so that the sums of the lengths of the cycles at each producer and injector are equal to the life of the production. Thus, we do not need to truncate the size of the last cycle, as in the previous studies, which may lead to suboptimal solutions. We use a simulator-based optimization method with stochastic simplex approximate gradient (StoSAG) and a machine learning-based (LS-SVR) optimization method to solve such an optimization problem. We update the LS-SVR proxy during optimization so that the updated proxy remains predictive toward promising regions of search space during the optimization. We compare the performance of the proposed LS-SVR-based iterative sampling refinement (ISR) method with the StoSAG-based and the finite difference (FD)-based optimization methods. To demonstrate the applicability of our proposed methodologies, we consider a synthetic example of a waterflooding process in a tight oil reservoir with two water injectors and four producers. Results show that the LS-SVR-based optimization method is at least three to seven times more computationally efficient than the StoSAG-based optimization method using a high-fidelity numerical simulator. However, we observe that the size and sampling of the training data, as well as the selection of bound constraints for the well controls, influence the performance of the LS-SVR-based optimization method. Designing multiple shutoffs and making cycle lengths unknown are found to be ineffective compared to single shutoff cases, as they yield lower NPVs.