A hybrid CNN-transformer surrogate model for the multi-objective robust optimization of geological carbon sequestration

The optimization of well controls over time constitutes an essential step in the design of cost-effective and safe geological carbon sequestration (GCS) projects. However, the computational expense of these optimization problems, due to the extensive number of simulation evaluations, presents significant challenges for real-time decision-making. In this paper, we propose a hybrid CNN-Transformer surrogate model to accelerate the well control optimization in GCS applications. The surrogate model encompasses a Convolution Neural Network (CNN) encoder to compress high-dimensional geological parameters, a Transformer processor to learn global patterns inherent in the well controls over time, and a CNN decoder to map the latent variables to the target solution variables. The surrogate model is trained to predict the spatiotemporal evolution of CO₂ saturation and pressure within 3D heterogeneous permeability fields under dynamic CO₂ injection rates. Results demonstrate that the surrogate model exhibits satisfactory performance in the context of prediction accuracy, computation efficiency, data scalability, and out-of-distribution generalizability. The surrogate model is further integrated with Multi-Objective Robust Optimization (MORO). Pareto optimal well controls are determined based on Non-dominated Sorting-based Genetic Algorithm II (NSGA-II), which maximize the storage efficiency and minimize the induced over-pressurization across an ensemble of uncertain geological realizations. The surrogate-based MORO reduces computational time by 99.99 % compared to simulation-based optimization. The proposed workflow not only highlights the feasibility of applying the CNN-Transformer model for complex subsurface flow systems but also provides a practical solution for real-time decision-making in GCS projects.