Lower and Upper Bounds for Hydraulic Tortuosity of Porous Materials

Single-phase fluid flow in porous media is always direction dependent owing to the tortuosity associated with the internal structures of materials that exhibit inherent anisotropy. This paper presents an approach to determining the tortuosity and permeability of porous materials using a structural measure quantifying the directional distribution of pore voids. The approach uses volume averaging methods 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, which is derived from the macroscopic momentum balance equation of fluid, is expressed as a function of the tortuosity tensor and the internal structure of the material. The analytical results are in good agreement with published data in the literature.