Archie's equation is an empirical electrical conductivity‐porosity model that has been used to predict the formation factor of porous rock for more than 70 years. However, the physical interpretation of its parameters, e.g., the cementation exponent m, remains questionable. In this study, a theoretical electrical conductivity equation is derived based on the fractal characteristics of porous media. The proposed model is expressed in terms of the tortuosity fractal dimension (D_T), the pore fractal dimension (D_f), the electrical conductivity of the pore liquid, and the porosity. The empirical parameter m is then determined from physically based parameters, such as D_T and D_f. Furthermore, a distinct interrelationship between D_T and D_f is obtained. We find a reasonably good match between the predicted formation factor by our model and experimental data.

This project was supported by the National Natural Science Foundation of China (Nos. 41572116, 51576114, ​41630317), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (No. CUG160602) and the Natural Science Foundation of Fujian Province of China (No. 2016J01254). The authors of the figures that used in presented review are also highly appreciated.Peer reviewedPostprin