Application of path-percolation theory and Lattice-Boltzmann method to investigate structure–property relationships in porous media

In this study, path-percolation theory was applied to randomly generate porous media, and effective porosities of these domains were determined. A statistical approach was pursued to determine effective porosity with confidence levels of 95%, 97%, and 99%. Furthermore, the Lattice-Boltzmann method was applied to obtain the velocity distribution throughout the porous channels to evaluate effective tortuosity. Two dimensional lattices with nine velocity components were utilized for fluid flow simulations. A new effective diffusivity model for porous media was developed using the effective porosity and tortuosity determined by path-percolation and Lattice-Boltzmann theories, respectively. Diffusion behavior of gasses in porous media as a function of porosity is typically unpredictable when the porosity is below 0.6, but the developed diffusion model as a function of effective porosity is shown to be useful in all effective porosity ranges.