Analytical tortuosity-porosity correlations for Sierpinski carpet fractal geometries

Naturally-occurring porous media, such as sedimentary rock, rarely consist of mono sized particles, but rather tend to consist of distributions of particle sizes (poorly-sorted porous media). In this study, deterministic fractal geometries including a Sierpinski carpet and a slightly altered version of the Sierpinski carpet with a generator that has a circular inclusion were used to provide insight into the poorly-sorted porous media found in sedimentary rock. The relationships between tortuosity and porosity within these fractal geometries were investigated by presenting and applying a novel mathematical approach. We found a new correlation between the tortuosity, tau, and porosity, phi, within the Sierpinski carpet (tau = 3/2 - phi/2), which agrees well with previous empirical observations reported in the literature. We also found an analytical tortuosity-porosity correlation within the circular-based Sierpinski carpet (tau = (1 - 4/pi)phi + 4/pi), which is to the best of the authors' knowledge, the first tortuosity-porosity relationship proposed for such fractal geometry. (C) 2015 Elsevier Ltd. All rights reserved.