A fractal model for spherical seepage in porous media

The characters of spherical/radial seepage in porous media have attracted steadily attention in many sciences and technologies such as in oil/water exploration, nuclear waste disposal, and heat and mass transfer in aerospace materials, biological tissue and organs. Considering the effects of capillary pressure, in this work we study the effective radial permeability and relative permeability for spherical seepage in porous media by applying the fractal theory and technique for porous media. The proposed models are related to the structural parameters of porous media, such as fractal dimensions, porosity, tortuosity and fluid properties. The validity of the proposed model is verified by comparing the model predictions with the available model and the existing experimental data. The present results show that the effective radial permeability and radial porosity decrease with the increase of radial distance. The parametrical effects on the radial permeability are also studied. It is found that the relative permeability for spherical seepage of wetting phase increases with the increase of wetting phase saturation, and the relative permeability of the non-wetting phase decreases with the increase of the wetting phase saturation. The contributions for permeability and relative permeability for spherical/radial seepage from capillary pressure can be negligible when pc,av/pm < 0.01, otherwise, the effect of capillary pressure on the seepage in porous media should be taken into account.