Permeability of Partially to Fully Randomized Arrays of Square Obstacles: A Lattice Boltzmann Approach

Abstract

Porous media consisting of monodisperse square obstacles were computationally studied using the lattice Boltzmann method in the Darcy regime. Different random arrays of obstacles were generated from the ordered arrays of obstacles using a new algorithm for controlled randomization. The porosity lies in the dilute to moderately dense range of 0.85-0.69. By proper nondimensionalization of the randomization parameter, it was demonstrated that the normalized permeability linearly depends on this parameter within slight randomizations through all porosities. Further randomization breaks the linear dependence, where the normalized permeability undergoes a sharp transition to a plateau at smaller porosities and a continuous transition at larger porosities. The plateau values of the normalized permeability linearly depend on the porosity. Interstitial flow maps show an immediate breakdown of spatial velocity distribution in ordered configurations starting with randomization and manifesting major flow channeling at higher randomizations, which can explain the transition types for permeability.