Prediction of relative permeability of unsaturated porous media based on fractal theory and Monte Carlo simulation

Mass transport through porous media is an important subject to engineers and scientists in various areas including oil engineering, fuel cells, soil science, textile engineering, etc. The relative permeability and capillary pressure are the key parameters that affect liquid transport through porous media. In this paper, the Monte Carlo technique is applied to predict the relative permeability of unsaturated porous media, considering the effect of capillary pressure and tortuosity of capillaries. The relative permeability is expressed as a function of porosity, area fractal dimension of pores, fractal dimension of tortuous capillaries, degree of saturation, and capillary pressure. It is found that the phase fractal dimensions (Df,w and D f,g) strongly depend on porosity. Besides, it is shown that the capillary pressure increases with the decrease of saturation, and at low saturation the capillary pressure increases sharply with the decrease of saturation. There is no empirical constant in the proposed model, and each parameter in the model has a clear physical meaning. The predicted relative permeability obtained by the present Monte Carlo simulation is shown to have a good agreement with the experimental results reported in the literature. The proposed model improved the understanding of the physical mechanisms of liquid transport through porous media. © 2012 American Chemical Society.