Fast and Inexpensive 2D-Micrograph based Method of Permeability Estimation through Micro-Macro Coupling in Porous Media

The closure formulation, developed as a part of the derivation of Darcy's law proposed by Whitaker (1998), is used to develop a method based on two-dimensional (2D) micrographs for estimating the full in-plane (2D) permeability tensor of a porous medium without requiring multiple flow simulations in different directions. The governing equations were solved in the pore space of a representative elementary volume (REV) using the finite-element (FE) method via COMSOL Multiphysics software. The permeabilities of two distinct porous media created from cellulose nanofibers (CNF) and sintered polymer beads were then estimated numerically. In order to use real micrographs in such simulations, scanning electron microscopy (SEM) pictures of the CNF and polymer-wick porous media were considered. The mesh-size independence studies were conducted to find the appropriate FE mesh for computations. A falling-head permeameter was used for measuring the experimental permeability in order to test the accuracy of the permeability results obtained by numerical simulation. Unequal diagonal terms of the permeability tensor pointed to the presence of anisotropicity in CNF; such characterization is a benefit of the proposed method. A good agreement between the numerical permeability results and the experimental results confirmed the accuracy of the proposed micro-macro coupling based method in estimating this crucial property using 2D micrographs. This 2D closure formulation based permeability estimation, which is faster, less expensive, and less troublesome than its three-dimensional (3D) counterpart, has the potential to emerge as a powerful characterization tool in the arsenal of porous-media scientists and researchers.