Tortuosity of porous media: Image analysis and physical simulation

Abstract

Tortuosity is widely used as a critical parameter to predict transport properties of porous media, such as rocks and soils. But unlike other standard microstructural properties, the concept of tortuosity is vague with multiple definitions and various evaluation methods introduced in different contexts. Hydraulic, electrical, diffusional, and thermal tortuosities are defined to describe different transport processes in porous media, while geometrical tortuosity is introduced to characterize the morphological property of porous microstructures. In particular, the rapid development of microscopy imaging techniques has made digital microstructures of porous media increasingly accessible, from which geometrical and physical tortuosities can be evaluated using various image analysis and numerical simulation methods. These tortuosities are defined differently and can differ greatly in value, but in many works of literature, they are used interchangeably. To address this situation, we systematically examine geometrical, hydraulic, electrical, diffusional, and thermal tortuosities from the viewpoints of the definition and evaluation method. For the same porous medium, visible discrepancies are found in the evaluated geometrical and physical tortuosities, depending on the specific definition and the evaluation method adopted. This observation makes it questionable to directly use the geometrical tortuosity as a substitute for physical tortuosities, a common practice in the literature. Thus, the correlations between geometrical and physical tortuosities are further analyzed, which also takes into account the influence of both image size and resolution. From the correlation analysis, phenomenological relations between geometrical and physical tortuosities are established, so that the latter can be accurately predicted by using the former which is much cheaper to evaluate from digital microstructures.