Acceleration of Data-Driven Proxy Models Using Physics-Based Reduced-Order-Model: Pseudo-Steady-State-Based Simulation

Abstract Injecting CO₂ into subsurface formations for large-scale geological carbon sequestration requires rapid and reliable reservoir pressure estimation for storage integrity and minimizing potential seismic activities. Although various machine/deep-learning models have been proposed for this purpose, these models typically require numerous reservoir simulations to generate adequate training data, which can be computationally expensive and potentially offset the acceleration in pressure prediction. This work utilizes a novel Pseudo-Steady-State-based Simulation (PSS-SIM) to significantly reduce training data generation cost while maintaining high performance predictions of data driven proxy models for near real time monitoring and control of carbon sequestration projects. PSS-SIM is a reduced-order modelling approach that converts 3D simulations to equivalent multi-resolution simulations using pseudo-steady-state (PSS) pressure contours as spatial coordinate. The multi-resolution grid achieves significant reduction in active cells and accelerates reservoir simulation by orders of magnitude. Our proposed method is applied to the Illinois Basin Decatur Project (IBDP), which is a large-scale CO₂ injection project into deep saline aquifer at the Illinois Basin, USA. Using PSS-SIM, training data for data-driven proxy models is generated with orders of magnitude acceleration in computational time compared to traditional fine-scale simulation. The simulated pressure from PSS-SIM is first validated against commercial reservoir simulations, demonstrating accuracy of the proposed approach. Next, Fourier Neural Operator (FNO), which solves PDEs by learning frequency-domain mappings through the Fourier transform, is trained using the PSS-SIM model simulations. The trained proxy model predicts reservoir pressure distribution from given geologic model and CO₂ injection schedule as spatial and temporal information. We account for the interactions between geologic heterogeneity and the flow field in the data-driven proxy model through the PSS pressure solution as input. The PSS contour exhibits strong correlation with pressure distribution, highlighting the effectiveness of the PSS-SIM-based proxy model. Machine/Deep learning models for geological carbon storage typically require hundreds of reservoir simulations for training data generation. The PSS-SIM reduces the generation costs by orders of magnitude for constructing data-driven proxy models. This substantial reduction in data generation costs enhances the feasibility of employing data-driven models in CCS projects, thereby enabling rapid scenario evaluations for both operational decision-making and field development planning.