A FRACTAL-MONTE CARLO APPROACH TO SIMULATE ELECTRICAL CONDUCTIVITY OF POROUS MEDIA WITH ROUGH SURFACES

The study of electrical conductivity in porous media has become increasingly important in wide fields such as geophysics and oil engineering. In this work, a probability model for electrical conductivity of porous media with rough surfaces is proposed combining Monte Carlo simulations with fractal geometry theory. The electrical conductivity is expressed as an expression of the relative roughness [Formula: see text], porosity [Formula: see text], the electrical conductivity of the pore fluid in porous media [Formula: see text], the tortuosity fractal dimension [Formula: see text], the surface electrical conductivity [Formula: see text], and capillary size [Formula: see text]. The predicted results using the fractal-Monte Carlo (FMC) approach show that electrical conductivity increases with a decrease in the relative roughness and the tortuosity fractal dimension, while it increases with an increase in porosity, the electrical conductivity of the pore fluid in porous media, and surface electrical conductivity. The validity of the proposed model is demonstrated by the good agreement between the predictions of the FMC approach and those of established models. In addition, a functional form for the formation factor of porous media with rough surfaces is obtained without considering surface electrical conductivity. The formation factor simulated using the FMC approach is found to increase as porosity decreases and relative roughness increases.