The relationship between fractal properties of solid matrix and pore space in porous media

Abstract

Measuring fractal dimensions has become a common practice for describing structural properties of porous media. Depending on the object of interest, different features of the structure can be measured: solid matrix, pores, and the interface between them. However, when measuring the fractal dimension of all these features, the question arises whether these dimensions are independent from each other or whether they can be related to an underlying property of the structure or image, respectively. For a variety of porous media we measured the fractal dimension of the matrix, the pore space, and the interface between them simultaneously using the box counting method. Analyzed images were obtained from soil thin sections and a void system in a clayey soil. Measured fractal dimensions were compared with fractal dimensions estimated by the pore-solid fractal (PSF) model, which derives the fractal properties of the matrix and the pore space completely as a function of the porosity, the size of the initiator and the fractal dimension of the interface. Measured results agree well with values obtained from the PSF model. A clear relationship between the fractal dimensions of the two phases (solid matrix and pore space) of a porous medium and their interface was observed. For all images the smallest fractal dimension was found for the interface between matrix and pores. Values for the fractal dimension of the two phases were between those for the interface and the Euclidian space with the phase with the lower mass fraction always having the smaller dimension. Porosity was found to act as weighing factor linking the dimension of the phases to those of the interface and Euclidian space. Model results also predict a dependency of the dimension of the phases on the spatial resolution of the analyzed image. For images having a high resolution (compared to the size of the initiator) phase dimensions are expected to be greater than for images having a low resolution.