Ensemble Surrogates and NSGA-II with Active Learning for Multi-Objective Optimization of WAG Injection in CO₂-EOR

CO₂-enhanced oil recovery (CO₂-EOR) with water-alternating-gas (WAG) injection offers the dual benefit of boosted oil production and CO₂ storage, addressing both energy needs and climate goals. However, designing CO₂-WAG schemes is challenging; maximizing oil recovery, CO₂ storage, and economic returns (net present value, NPV) simultaneously under a limited simulation budget leads to conflicting trade-offs. We propose a novel closed-loop multi-objective framework that integrates high-fidelity reservoir simulation with stacking surrogate modeling and active learning for multi-objective CO₂-WAG optimization. A high-diversity stacking ensemble surrogate is constructed to approximate the reservoir simulator. It fuses six heterogeneous models (gradient boosting, Gaussian process regression, polynomial ridge regression, k-nearest neighbors, generalized additive model, and radial basis SVR) via a ridge-regression meta-learner, with original control variables included to improve robustness. This ensemble surrogate significantly reduces per-evaluation cost while maintaining accuracy across the parameter space. During optimization, an NSGA-II genetic algorithm searches for Pareto-optimal CO₂-WAG designs by varying key control parameters (water and CO₂ injection rates, slug length, and project duration). Crucially, a decision-space diversity-controlled active learning scheme (DCAF) iteratively refines the surrogate: it filters candidate designs by distance to existing samples and selects the most informative points for high-fidelity simulation. This closed-loop cycle of “surrogate prediction → high-fidelity correction → model update” improves surrogate fidelity and drives convergence toward the true Pareto front. We validate the framework of the SPE5 benchmark reservoir under CO₂-WAG conditions. Results show that the integrated “stacking + NSGA-II + DCAF” approach closely recovers the true tri-objective Pareto front (oil recovery, CO₂ storage, NPV) while greatly reducing the number of expensive simulator runs. The method’s novelty lies in combining diverse stacking ensembles, NSGA-II, and active learning into a unified CO₂-EOR optimization workflow. It provides practical guidance for economically aware, low-carbon reservoir management, demonstrating a data-efficient paradigm for coordinated production, storage, and value optimization in CO₂-WAG EOR.