Analysis of seepage characters in fractal porous media

In this paper, the plane-radial and plane-parallel flows for Newtonian fluid in fractal porous media are analyzed. Based on the assumption that the porous medium consists of a bundle/set of tortuous streamlines/capillaries and on the fractal characteristics of pore size distribution in porous media, the expressions for porosity, flow rate, velocity and permeability for both radial and parallel flows are developed. The obtained expressions are the functions of tortuosity, fractal dimension, maximum and minimum pore diameters, and there are no empirical constant and every parameter has clear physical meaning in the expressions. The pressure distribution equations for plane-radial and plane-parallel flows in fractal porous media are also derived. The pressure and velocity distributions in plane-radial reservoirs are calculated and discussed.