Correcting the Micro-Continuum Approach for the Direct Numerical Simulation of the Absolute Permeability of Porous Media

This study corrects the micro-continuum model to improve the accuracy of simulating porous media flows. The correction includes adding the second Brinkman term to the averaged momentum balance equation and discretizing the gradients of this term using the Gaussian scheme with a harmonic interpolation in the finite-volume method. The corrected micro-continuum model better applies the no-slip immersed boundary condition at the solid–fluid interface. We compared the absolute permeability obtained from direct numerical simulation of the flow in different 2D and 3D porous media using the corrected and uncorrected micro-continuum models and the Navier–Stokes model. Considering all flow simulations on coarse meshes of 2D and 3D porous media, we observed errors of up to 54.2% in determining absolute permeability with the micro-continuum model without correction, which is reduced to a maximum of 4.3% using the corrected micro-continuum model. Due to this gain of accuracy, the corrected micro-continuum model with a coarse mesh can be as accurate as the uncorrected micro-continuum model in a much finer mesh. For the 2D bed of particles, this led to a speedup of 8483. Besides, we developed a methodology to compare the relative errors in the absolute permeability in 2D and 3D porous media using the number of mesh cells in the mean throat diameter. Our analysis indicates that meshes from 3D microtomography are usually coarse enough to require the corrected micro-continuum model in its flow simulation.