On the theoretical calculation of tortuosity in porous media and its experimental validation

Abstract

The quantitative characterization of connectivity of pore geometry and its reconstruction of topological connectivity are two important methods to describe the laws of fluid seepage in porous media.However, the lag of theoretical work severely restricts the emergence of new geometric modeling methods.The tortuosity is one of the key carriers connecting permeability and geometric structure, and its theoretical model has not been broken through.First, combining the Hagen-Poiseuille equation and Darcy formulas, the universal expression of the tortuosity for capillary model and the pore model composed by the particles are derived.Then for the low permeability medium, combined with the formula of capillary pressure, the tortuosity expression correlated to the saturation is obtained.Furthermore, the fractal dimension of tortuosity is introduced to explain the new term of fractal coefficient based on experimental analysis.Considering the bifurcated capillary channel, a bifurcation model was established to analyze the tortuosity characteristics and the geometric relationship between the mother and sub-holes based on the energy optimization criterion was obtained.Taking the salt rock as an example, the applicability and reliability of the theoretical formula of tortuosity are verified, and the research results provide a new idea for calculating the tortuosity of porous media.

Keywords

• porous media
• seepage
• tortuosity
• fractal dimension
• bifurcated capillary