Improved micro-continuum approach for capillary-dominated multiphase flow with reduced spurious velocity

A diverse range of multiphase flow and transport occurs in multiscale porous media. The multiphase micro-continuum Darcy-Brinkmann-Stokes (DBS) model has been developed to simulate the multiphase flow at both the pore and continuum scales via single-field equations. However, the unacceptable spurious velocities produced by the conventional micro-continuum DBS model present challenges to the modeling of capillary-dominated flow dynamics. This study improves the micro-continuum DBS model to mitigate these spurious velocities at the gas-liquid interface and contact-line regions. A hybrid interpolation scheme is proposed to improve the computational accuracy of the interface curvature and reduce the spurious velocity around the gas-liquid interface by 1-2 orders of magnitude. At the porous boundary, the normal to the gas-liquid interface is corrected, and the normal to the solid-fluid interface is smoothed to guarantee the prescribed wettability condition and decrease the spurious velocities at the contact-line region by an order of magnitude. A series of static and dynamic benchmark cases are investigated to demonstrate that the improved DBS model can simulate capillary-dominated multiphase flows with negligible spurious velocities at capillary numbers as low as 10-4 in both simple and complex geometries. The improved DBS model can combine x-ray computed micro-tomography images to perform multiscale simulations of capillary-dominated multiphase flow and understand the effect of sub-resolution porosity on fluid dynamics in naturally multiscale rocks.