Description of tortuosity and hydraulic conductivity of anisotropic porous materials

Single-phase fluid flow in porous media is usually direction dependent owing to the tortuosity associated with the internal structures of materials that exhibit inherent anisotropy. This paper presents an approach to determine the tortuosity and permeability of porous materials using a structural measure quantifying the anisotropic distribution of pore voids. The approach uses a volume averaging method through which the macroscopic tortuosity tensor is related to both the average porosity and the directional distribution of pore spaces. Depending on the estimate for the drag on the fluid-solid interfaces, the upper and lower bounds of tortuosity are determined. The permeability tensor is derived from the macroscopic momentum balance equation of fluid in a porous medium and expressed as a function of the tortuosity tensor and the internal structure of the material. The analytical results generally agree with experimental data in the literature.