TORTUOSITY–POROSITY RELATIONSHIP IN TWO-DIMENSIONAL FRACTAL MODEL OF POROUS MEDIA

Abstract

Tortuosity (τ) of two-dimensional fractal model of porous media is investigated to study their relationship with porosity. Square full-walk technique is applied to obtain τ in a two-dimensional fractal model of porous substance constructed by Randomized Sierspinski Carpets. The numerical result is in good agreement with previous results and empirical relation between tortuosity and porosity given by τ ~ p(1 - ϕ) + 1 that was found by other using Lattice Gas Automata method for solving flow equation on two-dimensional porous substance constructed by randomly placed rectangles of equal size and with unrestricted overlap. Average tortuosity of the flow path decreases linearly as fractal dimension of pore increases at each fractal iteration. Both fractal dimension and iteration give almost the same linearly tortuosity–porosity relation. The type of random algorithm for constructing Randomized Sierspinski Carpets has no significant influence on the tortuosity–porosity relation.