The Role of Fractal Quantities, as Specific Surface and Tortuosities, for physical properties of porous media

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Abstract
Besides the knowledge of material constants of the homogeneous phases of a disperse system, a good understanding of its geometrical properties is necessary for describing physical processes. In order to characterize the shape of the interface between solids and pore space with respect to the irregularities in all orders of magnitude, the fractal dimension has proved to be an informative parameter. By this study the theory of fractal dimensions, in three‐dimensional space originally limited to topological curves, surfaces and volumes, is extended into physical properties like specific surface, tortuosity, porosity and formation factor with “physical” dimensions −1 or 0 as an exponent of the unit of length. The typical properties of the true fractals are transferable to some of these derived parameters. This leads to power laws describing the dependence of the particular measure on the resolution length. With special models, which seem to be of widespread validity in nature, petrophysical considerations lead to further power laws for the rest of the physical parameters, dependent on discrete length parameters such as grain radius and pore radius. By determination of the exponents of such independent power laws, a better particle characterization is possible, as the fractal dimension of the surface alone may be misleading, especially when the grain size of the particles is not uniform.