Fractal Analysis Of Permeability Of Porous Media After The Capillary Pressure Is Taken Into Account

Porous media widely exist in nature, engineering materials, organs, oil and water reservoirs etc. Due to the complexity of porous media, the traditional analytical theory about the seepage in porous media is based on the continuum hypothesis. The permeability is the hydraulic conductivity for flow through porous media, and it can be found, in general, by experimental measurements and numerical solutions. In this thesis, the author analyzes the permeability by taking into accounting the effect of capillary pressure. Base on the fact that porous media can be approximated as statistically self-similar fractal media, and according to Hagen-Poiseulle equation and Darcy's law, the permeability of porous media consisting of tortuous parallel capillaries is derived and a fractal permeability model is obtained which accounts for the capillary pressure.This thesis also studies the fractal relative permeability for unsaturated porous media. The proposed fractal relative permeability model also accounts for the capillary pressure. Last part of this thesis devoted to the simulation of the relative permeability of unsaturated porous media by Monte Carlo method. The theoretical predictions are all compared to the available experimental data, and good agreement between the proposed models and experimental data is found and the validity of the proposed models is thus verified.