Towards Fast GNN Surrogates for CO2 Migration in Complex Geological Formations

This chapter discusses how a data-driven machine learning approach can reproduce key aspects of the physical behavior of multiphase flows in complex geological formations. We propose an end-to-end graph neural surrogate tailored to CO$_2$ plume migration forecasting in geological storage. The method is evaluated on the SPE11A benchmark, a well-known industry test case designed to assess CO$_2$ storage scenarios and characterized by sharp gas-water interfaces, strong advective transport, and rapid convective mixing with fingering development. The benchmark is reformulated as a graph in which nodes represent computational cells and edges encode transmissibility-based interactions enriched with geometric attributes. Directional transport arising from grid geometry, permeability contrasts, and geological heterogeneity is captured through an anisotropic message-passing mechanism, where interaction weights are computed via geometry-conditioned edge embeddings, biasing message aggregation toward physically relevant transport directions. Temporal evolution is modeled in latent space using an autoregressive residual formulation trained with multi-step supervision. The proposed model produces competitive forecasts of gas saturation and liquid-phase density, which are key indicators for CO$_2$ storage monitoring, with cumulative errors that remain moderate over extended forecasting horizons.

Closed-Loop CO2 Storage Control With History-Based Reinforcement Learning and Latent Model-Based Adaptation

Closed-loop management of geological CO2 storage requires control policies that adapt to uncertain reservoir behavior while relying on observations that are realistically available during operation. This work formulates CO2 injection and brine-production control as a partially observable sequential decision problem and studies deployable deep reinforcement-learning controllers trained with high-fidelity reservoir simulation. We first compare privileged-state, well-only, history-conditioned, masking-curriculum, and asymmetric teacher-student model-free policies in order to quantify the value of temporal well-response information and training-time privileged simulator states. We then evaluate a latent model-based adaptation pipeline that reuses nominal latent dynamics and retunes controllers under known injector failure, leakage-induced dynamics and reward shift, and compartmentalized reservoir connectivity. The results show that history-conditioned policies recover nearly all of the privileged-state performance while using only deployable well-level information, and that latent model-based retuning outperforms direct model-free retuning under the same scenario-specific real-simulator budget in the abnormal operating cases. The proposed framework therefore provides a simulator-budget-aware alternative to repeated online history matching and re-optimization for closed-loop CO2 storage control.