A data-driven multiscale model for two-phase flow in porous media

A data-driven multiscale framework for modeling two-phase flow in porous media is presented. The approach couples a Darcy-scale two-phase flow model with high-fidelity pore-scale simulations through closure relations that are learned directly from microscale data. Pore-scale simulations are performed on representative geometries, and the resulting closure quantities are approximated using a surrogate model to enable efficient evaluation during macroscale computations. Unlike standard constitutive formulations based solely on saturation-dependent relations, the proposed framework yields closures that depend on the full set of microscale parameters varied during data generation, allowing a richer representation of flow behavior. Numerical results in two and three dimensions, obtained for simplified packed-bed geometries, demonstrate that the resulting multiscale coupling is numerically stable and produces physically consistent macroscale predictions. These results establish the feasibility of data-driven closure modeling for two-phase Darcy flow and provide a foundation for systematically incorporating pore-scale physics into continuum-scale simulations.