Predicting the electrical conductivity of porous media is of significant importance for applications in oil reservoirs, rock physics, and fuel cells. For studying the electrical conductivity in porous media, this paper proposes a cuboid embedded with multiple sets of tree-like fractal networks to represent a portion of porous media. Analytical expressions for the electrical conductivity are then derived using the fractal theory. The influences of various structural parameters on electrical conductivity are examined in detail, revealing the transport properties of fluids in porous media composed of converging-diverging capillaries. The study found that an increase in the branching level implies more difficult ion migration, leading to a decrease in electrical conductivity of the porous media. Furthermore, decreasing length ratio or increasing diameter ratio enhances electrical conductivity. Simultaneously, an increase in the pore distribution fractal dimension leads to a decrease in electrical conductivity. Comparison of the predicted results with those from other models achieves good agreement, thereby validating the proposed model. These findings may contribute to a deeper interpretation of the transport properties in porous media.
Feng et al. (Fri,) studied this question.