Data-Driven Modeling of Hysteresis in Porous Media: Neural-Network Surrogates Coupled with the OPM Flow Reservoir Simulator

Abstract Relative permeability hysteresis in porous media presents a significant challenge for accurate reservoir simulation due to its path-dependent nature. Traditional empirical and geometric models often fall short in capturing the complexity of hysteresis, especially under cyclic drainage and imbibition conditions. This study investigates the use of machine learning (ML), specifically neural networks, as surrogate models to approximate relative permeability relationships, including hysteresis effects, with high fidelity for applications in reservoir simulations. Focusing on two-phase oil–water systems, the study uses separate training datasets derived from classical hysteresis models (Killough and Carlson) and pore-scale simulation results from a workflow using level set and lattice Boltzmann models (LS-LBM) to generate training data. The proposed ML models incorporate saturation history to predict relative permeability. Three surrogate models are developed: ML-Killough and ML-Carlson, trained on synthetic/model-generated datasets, and ML-LS-LBM, trained on a physics-based dataset. To demonstrate practical applicability, the proposed ML surrogates are applied to a core-scale simulation case implemented in the OPM Flow reservoir simulator. Results demonstrate that the ML surrogates accurately reproduce scanning curves and nonlinear hysteresis effects, perform well on test data drawn from the same distribution, and maintain physical consistency. Their differentiable structure and computationally efficient inference make them suitable for integration into full-field reservoir simulators, offering a promising alternative for simulation-time prediction in enhanced oil recovery and CO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> storage applications.