Fourier Neural Operator Surrogates for Hysteretic Multiphase Flow in Heterogeneous Geological CO2 Storage Reservoirs

Venkateshwaran Baskaran, AKM Eahsanul Haque, Numair Ahmed Siddiqui, Hariharan Ramachandran , Muthuvairavasamy Ramkumar, John Oluwadamilola Olutoki, Ida Bagus Suananda Yogi, Bamidele Abdulhakeem Adeniyi

Modeling hysteresis in heterogeneous field-scale reservoirs is essential for estimating residual CO2 trapping capacity and assessing the security of geological storage. This requires accounting for both relative permeability hysteresis and capillary pressure hysteresis, which control path-dependent multiphase flow and the spatial distribution of trapped gas. Because maximum residual gas saturation varies across lithofacies, residual trapping cannot be predicted from saturation alone when reservoir properties are spatially discontinuous. However, full-physics hysteresis-enabled simulations are computationally expensive, making large-scale storage appraisal impractical. To address this challenge, we develop 2D Fourier Neural Operator (FNO) surrogates that predict CO2 and brine saturation fields together with a hysteresis states. The models are evaluated across three complexity levels: Case F, a homogeneous system; Case D, a heterogeneous system with variable porosity and permeability but a single trapping law; and Case M, a multi-lithofacies system with five rock types. Each case is tested under relative permeability-only physics and under coupled relative permeability plus capillary pressure hysteresis. Results show that when trapping behavior is uniform, input fields and flow-condition scalars are sufficient to reproduce saturation evolution with accuracy. In contrast, when residual gas saturation varies by lithofacies, prediction accuracy deteriorates unless rock type is encoded. Adding a categorical rock-type channel restores performance across all cases, including hysteresis-state classification, but reduces robustness under coarse-to-fine grid transfer. These results show that surrogate modeling of heterogeneous CO2 storage requires representation of lithofacies-dependent trapping behavior. Petrophysical fields alone are insufficient to resolve spatially discontinuous hysteresis physics, especially when capillary pressure hysteresis is included.