A NOVEL MONTE CARLO SIMULATION ON THE ELECTRICAL CONDUCTIVITY OF FRACTAL POROUS MEDIA

The electrical conductivity of porous media has received more and more attention in the fields of geophysics and petroleum engineering. In this study, a Monte Carlo method, combined with fractal geometry theory and the probability model for pore size distribution, is employed to predict the electrical conductivity of porous media, considering the effect of surface electrical conductivity. The electrical conductivity is explicitly expressed as a function of several factors, including porosity, the electrical conductivity of pore fluid in porous media, tortuosity fractal dimension, specific surface electrical conductivity, length of representative elementary volume (REV), and random pore size. The predictions obtained using the Fractal-Monte Carlo (FMC) method show good agreement with reported experimental data. Additionally, a numerical model for the formation factor is developed by neglecting surface electrical conductivity, and the simulated results align well with predictions from Archie’s law and other existing models. Furthermore, the results indicate that electrical conductivity increases with increasing porosity, while it decreases with increasing tortuosity fractal dimension. The proposed FMC method is both simple and efficient for calculating electrical conductivity and shows significant potential for predicting other transport properties of porous media.