Numerical study on the permeability in a tensorial form for laminar flow in anisotropic porous media

Abstract

Pore-scale flow simulations were conducted to investigate the permeability tensor of anisotropic porous media constructed using the Voronoi tessellation method. This construction method enabled the introduction of anisotropy to the media at the particle level in a random and yet controllable way. Simulations were carried out for media with different degrees of anisotropy through varying the mean aspect ratio of grain particles. The simulation results were then analyzed using the Kozeny-Carman (KC) model. The KC model describes the permeability of the anisotropic media in a tensor form with the anisotropy represented by different tortuosities along the three principal directions. The tortuosity tensor was found to be a complex function of the particle morphology, which is yet to be fully determined. However, the results presented have established the starting point for further theoretical development to formulate such a function and to build closed-form analytical permeability models for anisotropic porous media based on first principles.