A validation of Whitaker's closure formulation based method for estimating flow permeability in anisotropic porous media

Abstract

Advances in computational power and scanning technology has allowed one to estimate the flow permeability in porous media directly from 2-D and 3-D micrographs. So, unit cells representing 2-D/3-D porous media were constructed from rectangles/rectangular solids and ellipses/ellipsoids. Anisotropy was created by marginally aligning the randomly distributed particles with varying aspect ratio along certain directions. Pore-scale flow simulations were performed to rigorously test the capability of the closure formulation method, result of upscaling through the volume averaging method, to predict the permeability tensors for anisotropic porous models. The results were compared with the Stokes–Darcy approach based on the Darcy's law and employing multiple 1-D Stokes-flow simulations along different orientations to arrive at the permeability tensor. Our closure-formulation implementation, validated through comparison with a published result, was shown to be in good agreement with the results of the Stokes–Darcy flow technique for the 2-D and 3-D models. The closure formulation method was shown to be much faster for 3-D unit-cell geometries. © 2022 Elsevier Ltd