The mapping relationships between the conductivity properties are not only of great importance for understanding the transport phenomenon in porous material, but also benefit the prediction of transport parameters. Therefore, a fractal pore-scale model with capillary bundle is applied to study the fluid flow and heat conduction as well as gas diffusion through saturated porous material, and calculate the conductivity properties including effective permeability, thermal conductivity and diffusion coefficient. The results clearly show that the correlations between the conductivity properties of saturated porous material are prominent and depend on the way the pore structure changes. By comparing with available experimental results and 2D numerical simulation on Sierpinski carpet models, the proposed mapping relationships among transport properties are validated. The present mapping method provides a new window for understanding the transport processes through porous material, and sheds light on oil and gas resources, energy storage, carbon dioxide sequestration and storage as well as fuel cell etc.

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The through-plane permeability is of great importance for understanding the transport phenomenon in anisotropic fibrous porous material. In this paper, a novel pore-scale model based on the equilateral triangle representative unit cell (RUC) and capillary bundle model is developed for the fluid flow through the anisotropic fibrous porous material according to fractal theory, and the effective through-plane permeability is presented accordingly. The digital structures of the fibrous porous material are generated by a fractal stochastic method (FSM), and the single-phase fluid flow through the 3D-reconstructed model is simulated by using the finite element method (FEM). It was found that the effective through-plane permeability depends on the fiber column size, porosity, and fractal dimensions for pore and tortuosity. The results show that the predicted through-plane permeability by the present fractal model indicates good agreement with numerical results and available experimental data as well as empirical formulas. The dimensionless through-plane permeability is positively correlated with the porosity and negatively correlated with the fractal dimensions for pore and tortuosity at certain porosity.