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

Abstract

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.