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.

Micro‐Continuum Modeling: An Hybrid‐Scale Approach for Solving Coupled Processes in Porous Media

“…Therefore, their studies were limited to relative permeabilities and did not focus on the capillary pressure curve. Recent improvements that filtered the spurious velocities due to the computation of the fluid-fluid interface curvature should leverage this limitation (Liu et al, 2022). The a priori characterization of two-phase sub-grid models remains an open Water Resources Research 10.1029/2023WR035908 challenge.…”

Pore-Scale Modeling of Methane Hydrate Dissociation Using a Multiphase Micro-Continuum Framework

“…frameworks to describe the two-phase flow at both the pore and cont Carrillo [34] later improved the multiphase micro-continuum model wit derivation to asymptotically match the scale-dependent multiphase model proposed corrections to mitigate spurious velocities at the gas-liquid contact-line regions [35]. Thanks to these efforts, the multiphase micro-con shows the potential to simulate multiphase flow across multiscale por summary, the DBS model demonstrates a strong ability to simulate multi flows in porous media, which is expected to enable numerical simulations dissociation process.…”

“…Following the numerical work by Soulaine et al [33], Liu et al [35], Maes et al [37], and Yang et al [27], the single-field governing equations can be written as…”

“…Numerically, the face-centered interface norm n lg, f is employed to calculate the term ∇ • n lg (the magnitude of the interface curvature) based on the Gaussian scheme. In order to improve the numerical accuracy of the interface curvature and reduce the spurious velocity around the gas-liquid interface, a hybrid scheme is used to compute n lg, f as follows [35]:…”

“…Horgue [32] and Soulaine [33] proposed two-phase micro-continuum DBS frameworks to describe the two-phase flow at both the pore and continuum scales. Carrillo [34] later improved the multiphase micro-continuum model with a theoretical derivation to asymptotically match the scale-dependent multiphase model, and Liu et al proposed corrections to mitigate spurious velocities at the gas-liquid interface and contact-line regions [35]. Thanks to these efforts, the multiphase micro-continuum model shows the potential to simulate multiphase flow across multiscale porous media.…”