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

Abstract

Abstract The objective of this work is to present an efficient method based on gradient-based optimization using a least-squares support-vector regression (LS-SVR) model to solve well-shutoff and well-control optimization problems. We formulate a continuous differentiable NPV for the well shutoff optimization problem. In our approach, switching well on/off times are considered part of the design variables. Our parameterization is based on a fixed number of cycles, the length of each cycle, and the production time fraction in each cycle. The remaining fraction of each cycle is the shutoff time fraction. We use linear equality constraints so that the summation of the length of each cycle is equal to the life of the production, and thus, we do not need to truncate the length of the last cycle. We consider both the stochastic simplex gradient optimization and the machine learning-based least-squares support vector regression (LS-SVR) proxy but we update it 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 method using the LS-SVR runs coupled with iterative sampling refinement method (ISR) to update the proxy during optimization with the popular stochastic simplex approximate gradient (StoSAG) and reservoir- simulations runs for a synthetic example considering a waterflooding process in a conventional compositional oil reservoir with 2 water injectors and 4 producers. Results show that higher computational efficiency is achieved using the LS-SVR-based optimization method over the StoSAG-based optimization method using a high-fidelity numerical simulator. The proposed LS-SVR-based framework is shown to be at least 3 to 7 times computationally more efficient, depending on the cases considered than the StoSAG using a high-fidelity numerical simulator. For the waterflooding optimization example, designing multiple shutoffs and making cycle length unknown are found to be not beneficial as compared to single shutoff cases as they yield lower NPVs than single shutoff cases. 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. The well-shutoff/well-control optimization problem can be handled with the gradient-based optimization methods by introducing a production time fraction as the design variable for each cycle. This is the first LSSVR application for the well shutoff and well-control optimization problem. The proposed LS-SVR-based optimization framework has great potential to be used as an efficient tool for this type of optimization problem.