Recurrent Transformer U-Net Surrogate for Flow Modeling and Data Assimilation in Subsurface Formations with Faults

Many subsurface formations, including some of those under consideration for large-scale geological carbon storage, include extensive faults that can strongly impact fluid flow. In this study, we develop a new recurrent transformer U-Net surrogate model to provide very fast predictions for pressure and CO2 saturation in realistic faulted subsurface aquifer systems. The geomodel includes a target aquifer (into which supercritical CO2 is injected), surrounding regions, caprock, two extensive faults, and two overlying aquifers. The faults can act as leakage pathways between the three aquifers. The heterogeneous property fields in the target aquifer are characterized by hierarchical uncertainty, meaning both the geological metaparameters (e.g., mean and standard deviation of log-permeability) and the detailed cell properties of each realization, are uncertain. Fault permeabilities are also treated as uncertain. The model is trained with simulation results for (up to) 4000 randomly sampled realizations. Error assessments show that this model is more accurate than a previous recurrent residual U-Net, and that it maintains accuracy for qualitatively different leakage scenarios. The new surrogate is then used for global sensitivity analysis and data assimilation. A hierarchical Markov chain Monte Carlo data assimilation procedure is applied. Different monitoring strategies, corresponding to different amounts and types of observed data collected at monitoring wells, are considered for three synthetic true models. Detailed results demonstrate the degree of uncertainty reduction achieved with the various monitoring strategies. Posterior results for 3D saturation plumes and leakage volumes indicate the benefits of measuring pressure and saturation in all three aquifers.