A fractal model for relative permeability of unsaturated porous media with capillary pressure effect

A fractal relative permeability model is derived which takes into account the capillary pressure difference effect. The proposed model is expressed as a function of saturation, fractal dimensions, fluid properties and capillary pressure difference, and there is no empirical constant introduced in the proposed model. The effect of the capillary pressure difference on the relative permeability is analyzed, and the results indicate that the capillary pressure difference has the significant influence on the relative permeability at low saturation. The predicted relative permeabilities are compared with the available experimental data. Good agreement is found between the present model predictions and the available experimental data.