The simple expressions for the fractal dimensions of multiphase fractal media are derived and are found to be a function of porosity, phase content, ratio of the maximum to minimum pore sizes. There is no any empirical constant in the proposed fractal dimensions. For the three-phase fractal porous medium or unsaturated porous medium, the fractal dimensions are found to be meaningful only in certain ranges of saturation Sw, i.e. Sw > S min for wetting phase and Sw < S max for non-wetting phase for a given porosity, based on real porous media for requirements from both fractal theory and experimental observations. The present analysis of the fractal dimensions is verified by a comparison with the existing experimental measurements. It allows for the analysis of transport properties such as permeability, thermal dispersion, and conductivities (both thermal and electrical) in multiphase fractal media by the proposed model.
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Boming Yu (2006) studied this question.
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