A fractal analytical model for Kozeny-Carman constant and permeability of roughened porous media composed of particles and converging-diverging capillaries

Seepage of particles in porous media has attracted considerable attention due to its extensive existence in nature. In this work, we have derived a novel fractal model for Kozeny-Carman (KC) constant and dimensionless permeability of roughened porous media composed of particles and converging-diverging capillaries. The model for KC constant and dimensionless permeability involves structural parameters of the media, such as porosity (phi), fractal dimensions (dT and df), relative roughness (xi), and the fluctuation amplitude (k) of capillary cross-section size. We systematically investigated the influence of the parameters above on the KC constant and the dimensionless permeability. An increase in fluctuation amplitude leads to an increase in the KC and a decrease in dimensionless permeability. In addition, the influence of the fluctuation amplitude on the KC constant and the dimensionless permeability will be more obvious with an increase in porosity. Furthermore, the effect of the fluctuation amplitude of capillary bundles on permeability satisfies the physical law. Comparisons with the experimental data in literature verifies the accuracy of the proposed fractal model. Thus, the proposed model may further reveal the physical mechanism of the fluid flow in roughened porous media, providing a better theoretical basis for various practical applications, such as petroleum engineering and fuel-cell industry.