A FRACTAL MODEL FOR EFFECTIVE THERMAL CONDUCTIVITY OF DUAL-POROSITY MEDIA WITH RANDOMLY DISTRIBUTED TREE-LIKE NETWORKS

It is very difficult to characterize the transport properties of porous media due to the disorder of pores distribution in porous media. In this paper, we study heat conduction through porous media with randomly fractures which are considered as tree-like networks. An expression for effective thermal conductivity (ETC) of saturated dual-porosity media is derived based on the fractal characteristics of pores diameter and fractures size. It is shown that the ETC is a function of structure parameters of the fractal dimension (D-g), the porosity (phi(g)), the tortuous fractal dimension (D-t) and the maximum diameter (lambda(max)) for the porous matrix; the fractal dimension (D-f), the porosity (phi f), the maximum diameter (d(0max)), the diameter ratio (beta), the length ratio (alpha) and the branching levels (n) for the fracture networks. The dependence of structure parameters on the ETC is studied in detail. The results of our model are compared with the available experiments, which show good agreement. The proposed model for the ETC does not contain empirical parameters. The model is useful for predicting the heat conduction of materials.