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

Multi-component fluid flow simulations in multiscale porous structures, many parts of which are likely to be under-resolved at practical resolution, often require a high-fidelity numerical model to account for the contribution of under-resolved structures to the fluid flow. In previous studies, a numerical model was proposed for viscous and capillary forces from under-resolved regions. It successfully showed comparable results in absolute permeability, capillary pressure, and relative permeability when compared to an equivalent fully resolved case up to ten times higher resolution. In this study, we show further extensions of the model to handle various types of structures and to capture detailed fluid behavior. First, we introduce the controllability of surface tension in the pseudo-potential lattice Boltzmann model while keeping the interface thickness and the spurious current at the same level. This helps to resolve more detailed interface dynamics in under-resolved regions. Second, we develop a numerical model to capture the residual fluid component in the under-resolved structure. Since it is difficult to capture such cell-sized or less-than-cell-sized fluid components with diffusive interface models, we try to consider them separately using local constitutive relations, such as the absolute and relative permeability and capillary pressure curves. Third, we introduce a tensorial resistivity model to handle under-resolved heterogeneous structures, such as a fiber bundle. After calculating the principal axis for resistivity using the Hessian and the gradient of the local porosity field, the tensorial resistivity is rotated in the proper direction. Through a series of benchmark test cases, including cases using practical rock geometries, these enhancements are validated and show significant accuracy improvements with respect to the transient interface dynamics, capture of local irreducible fluid components, and directionality effects of under-resolved structures.