Enhanced numerical models for two-component fluid flow in multiscale porous structures

Abstract: Multi-component fluid flow simulations in multi-scale porous structures often involve regions that are under-resolved at practical computational resolutions. Accurately capturing the contributions from these unresolved regions is critical. Previous studies proposed a model to account for viscous and capillary forces in under-resolved regions, showing permeability, capillary pressure, and relative permeability comparable to fully resolved high-resolution cases. In this study, we extend the model to handle diverse structures and capture detailed fluid behavior. We introduce controllable surface tension in a pseudo-potential lattice Boltzmann model while keeping interface thickness and spurious currents constant, improving interface dynamics resolution. A method is developed to capture residual fluid components smaller than cell size using local constitutive relations, including absolute and relative permeability and capillary pressure curves. Additionally, a tensorial resistivity model is implemented for heterogeneous structures such as fiber bundles, aligning resistivity along principal axes determined from the Hessian and gradient of local porosity fields. Benchmark tests, including practical rock geometries, validate these enhancements, demonstrating improved transient interface dynamics, accurate capture of irreducible fluid components, and correct directional effects in under-resolved structures.