Fractal-based analysis of stress-induced dynamic evolution in geometry and permeability of porous media

Accurate description of cavity geometric structure and quantitative estimation of the permeability of porous media are crucial for understanding fluid flow and mass transport in various geosciences and geological engineering. A permeability fractal model was constructed by combining fractal theory, Poiseuille's law of flow, and Darcy's law, taking into account the characteristic parameters of three-dimensional (3D) pore and fracture network structure. The mechanical response of tortuous capillaries was analyzed theoretically to elucidate the dynamic evolution of geometry and permeability in porous media. In addition, the geometric parameter sensitivity of the stresses is analyzed in relation to the geologic reservoir. Results indicate that: (i) an incremental rise in stress results in increases in fractal dimension, porosity, and pore quantity of the porous medium while concurrently inducing a decline in the average pore radius; (ii) the permeability obtained based on the mathematical model this study proposed and the digital core reconstruction shows a good agreement; this validates the fractal permeability. Mathematical model of stress can be used to describe the relationship between stress and the microstructure of porous media; and (iii) during the uniaxial strain process of porous media, the effective surface porosity uniformly influences permeability across all directions, adhering to the same principle. As effective surface porosity diminishes, the sensitivity of permeability to strain intensifies. Conversely, the sensitivity of permeability to strain perpendicular to the compression direction diminishes with increasing tortuosity, while the sensitivity of permeability to strain parallel to the compression direction escalates with rising tortuosity.