Towards Fast GNN Surrogates for CO2 Migration in Complex Geological Formations

Rodrigo S. Luna; Thiago H. N. Coelho; Luiz S. L. Neto; Roberto M. Velho; Adriano M. A. Cortes; Renato N. Elias; Alexandre G. Evsukoff; Fernando A. Rochinha

cs.LGJun 15, 2026

Towards Fast GNN Surrogates for CO2 Migration in Complex Geological Formations

Authors: Rodrigo S. Luna, Thiago H. N. Coelho, Luiz S. L. Neto, Roberto M. Velho, Adriano M. A. Cortes, Renato N. Elias, Alexandre G. Evsukoff, Fernando A. Rochinha, +3 more

Organizations: Systems and Computer Engineering and High Performance Computing Center, NACAD - COPPE, Federal University of Rio de Janeiro · Civil Engineering and High Performance Computing Center, NACAD - COPPE, Federal University of Rio de Janeiro · Mechanical Engineering and High Performance Computing Center, NACAD - COPPE, Federal University of Rio de Janeiro · TotalEnergies

Abstract

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.

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Jul 26, 2026 · cs.LGJ/K move · Enter open · S save

Multimodal Auto-regressive Transformer Surrogate for Modeling Variable Operations and Quantifying Uncertainty in Geological Carbon Storage

Yifu Han, Louis J. Durlofsky

Department of Energy Science and Engineering, Stanford University, Stanford, CA, 94305, USA

The use of variable well perforation and injection strategies can improve the efficiency of geological carbon storage operations. We develop a new multimodal auto-regressive transformer surrogate to model these operations under geological uncertainty. A modified SEAM CO2 geomodel, which involves a faulted system with three stacked aquifers, is considered. The two injection wells are perforated in stages, from bottom to top, with the stage durations and individual well injection rates treated as control variables. The surrogate model processes three input modalities - the 3D geomodel, scalar parameters characterizing relative permeability functions, and control variables - through separate encoders. These are fused via self-attention in a transformer encoder, and a temporal decoder generates predictions auto-regressively through encoder-decoder cross-attention. The surrogate is trained, using 4000 GEOS flow simulations, to predict saturation and pressure at monitoring locations, total injected and mobile CO2 mass, and saturation footprints. For a new test set, involving randomly sampled geomodels and control variables, the surrogate achieves a median saturation MAE of 0.028 and median relative errors of 0.2-5% for the other quantities of interest. Importantly, it captures the switch from rate to bottom-hole-pressure control. The surrogate model is used within a hierarchical Markov chain Monte Carlo data assimilation procedure for a synthetic true model under three operational strategies. Substantial uncertainty reduction is achieved for key metaparameters, particularly the fault permeabilities. Posterior predictions for saturation footprints and total injected and mobile CO2 mass are also shown to be generally consistent with true model results.

Surrogate Models Multimodal Transformers

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Abstract

Explore similar work

Multimodal Auto-regressive Transformer Surrogate for Modeling Variable Operations and Quantifying Uncertainty in Geological Carbon Storage

Boundary condition fidelity for bottom-hole pressure and CO2 plume prediction in geological carbon storage

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