Determination of Characteristic Transport Coefficients of Porous Media from Volumetric Images using the Diffuse Interface Method

Abstract

Transport in engineered materials such as electrodes, membranes, filters, and natural materials such as rock, sand, soil can be modeled as transport in porous media. Direct Numerical Simulations (DNS) on volumetric images of porous media are commonly done using the Lattice Boltzmann Method (LBM), but this presents various challenges such as long the computational time required to reach steady-state, fixed grid coarseness, and limited availability of reliable LBM software, commercial or otherwise. Traditional finite element based methods require conformal meshes of porous domains that are able to accurately capture fluid/solid interfaces, but at the cost of significant computational complexity and user interaction in order to create the mesh. To address these challenges, this work presents the application of a diffuse-interface finite element method that approximates a phase-field from volumetric images of porous media without user interaction and enables the use of a simple structured grid/mesh for traditional finite element-based fluid mechanics methods. The presented diffuse interface method (DIM) is automated and non-iterative, enabling the direct calculation of three characteristic coefficients from input images: tortuosity, permeability, and inertial constant by simulating Fickian mass diffusion and single component incompressible Navier Stokes equation from low to high range of inlet velocity. Three different 2D test images with varying porosities are used to demonstrate the use of DIM. The method is compared to traditional FEM implementation using conformal meshes with respect to the agreement with the determination of the characteristic coefficients, numerical accuracy, and computational requirements (time). Different parameters affecting the accuracy of DIM were identified and ideal parameters were determined. At ideal parameters, the relative error in tortuosity less than 0.75%, the relative error in permeability less than 1%, and relative error in inertial constant less than 3% were achieved for all three images. Though, DIM was found to be slower than traditional FEM implementation calls for optimized solvers for fluid flow on structured meshes to speed up the DIM simulations. The developed method provides an automated approach for computing effective transport properties from volumetric images of porous media.