Prediction of relative permeability in unsaturated porous media with a fractal approach

Prediction of relative permeability in unsaturated porous media is important for oil and gas reservoir engineering and hydrology as well as chemical engineering. A physical conceptual model has been developed for two-phase flow in unsaturated porous media according to the fractal characteristics of pore-scale geometrical structure of natural porous media. The analytical expressions of relative permeabilities for wetting and nonwetting phases have been presented, which are the functions of wetting fluid saturation and porosity as well as fractal dimensions of the medium. Numerical simulations are also performed to determine the relationship between the relative permeability and saturation of unsaturated porous media by a fractal Monte Carlo method. The predictions by the current mathematical models have been validated by comparing with available empirical formulas, numerical results and experimental data. The present results indicate that the geometrical parameters (porosity, fractal dimension for pore size distribution and tortuosity fractal dimension) have significant effect on the multiphase flow through unsaturated porous media.