Investigating the Characterization of Pore Size Distribution and Permeability, Capillary Water Absorption in Porous Media Based on Entropy Theory

The performance of porous media, such as capillary water migration and permeability, is significantly influenced by the complexity of the pore structure. The pore complexity can be characterized by the fractal dimension of the pore structure ($D_f$) and the fractal dimension of pore tortuosity ($D_T$). In this study, the entropy theory was employed to evaluate the complexity of the pore size distribution in porous media. By considering T₂ and porosity, the entropy measures for the pore size distribution entropy (H_P), global entropy (H_G) and relative entropy (H_R) were calculated. Furthermore, the relationships between these three types of entropy and $D_f$, tortuosity, $D_T$, permeability, and capillary absorption coefficient ($\vartheta$) were investigated. Our findings demonstrate that H_P exhibits a quadratic increase with $D_f$. Pore tortuosity decreases as a power function of H_G while increasing as a power function of H_R. $D_T$ decreases as an exponential function with H_G while increasing as an exponential function with H_R. Moreover, the permeability varied as a quadratic function with the H_P, and the$\vartheta$increased as an exponential and logarithmic function with the porosity and H_G, respectively. This study highlights the feasibility and reliability of employing entropy theory to characterize microscopic pore structure features and hydraulic properties.