A novel micro-continuum lattice Boltzmann approach for multiscale modeling immiscible two-phase flow in porous media

Immiscible two-phase flow in porous media is crucial in various industrial processes, necessitating a robust numerical tool to capture this complex multiscale behavior. This paper aims to introduce a novel micro-continuum multiphase solver, abbreviated as DBS-CG, which integrates lattice Boltzmann method with the Darcy-Brinkman-Stokes approach via embedding a volume-averaging scheme into the color-gradient model. The fluid-solid interactions in free and porous regions are effectively reproduced by the continuum surface force and micro-capillary force incorporated in DBS-CG. Validations against analytical solutions and numerical experiments confirm that DBS-CG is capable of monolithic modeling the trans-scale immiscible flow in spatially fluctuated porosity fields. Additionally, the water-oil displacement processes in mix-wetted and fractured-vuggy porous systems are tentatively investigated by DBS-CG, where various fingering patterns and preferential flow paths under different structural conditions and fluid properties are discussed. Non-monotonic trends of the recovery efficiency indicate that this multiphase process is competitively manipulated by the capillary or Darcy drag forces in microporous regions and inertial or viscous forces in solid-free regions, and thus, the moderate wettability and sedimentation are more beneficial for oil extraction.