Life-Cycle Production Optimization of the CO2-Water-Alternating-Gas Injection Process Using Least-Squares Support-Vector Regression (LS-SVR) Proxy

In this study, we present a framework for efficient estimation of the optimal CO2-WAG parameters for robust production-optimization problems by replacing a high-fidelity model with a least-squares support vector regression (LS-SVR) model. We provide insight and information on proper training of the LS-SVR proxy model for the CO2-WAG life-cycle production optimization problem. Given a set of training points generated from high-fidelity model-based simulation results, an LS-SVR-based proxy model is built to approximate a reservoir-simulation model. The estimated optimal design parameters are then found by maximizing NPV using the LS-SVR proxy as the forward model within an iterative-sampling-refinement optimization algorithm that is designed specifically to promote the accuracy of the proxy model for robust production optimization. As an optimization tool, the sequential quadratic programming (SQP) method is used. CO2-WAG design variables are CO2 injection and water injection rates for each injection well at each cycle, production BHP for each production well at each WAG half-cycle, and inflow control valve (ICV) for each well at each WAG half-cycle and at each valve. We study different scenarios where we fix some of the design variables to investigate the importance of design variables on life-cycle production optimization of the CO2-WAG problem. We compare the performance of the proposed method using the LS-SVR runs with the popular stochastic simplex approximate gradient (StoSAG) and reservoir-simulations runs for a synthetic example considering a three-layer, channelized reservoir with 4 injectors and 9 producers. Results show that the proposed LS-SVR-based optimization framework is at least 3 to 6 times computationally more efficient, depending on the cases considered, than the StoSAG using a high-fidelity numerical simulator. However, we observe that the size and sampling of the training data, as well as the selection of well controls and their bound constraints for the well controls, seem to be influential on the performance of the LS-SVR-based optimization method. This is the first LS-SVR application to the CO2-WAG optimal well-control problem. The proposed LS-SVR-based optimization framework has great potential to be used as an efficient tool for the CO2-WAG optimization problem.