Water retention of prefractal porous media generated with the homogeneous and heterogeneous algorithms

Fractal models of porous media are of interest in numerous scientific disciplines, including hydrology and soil science. This interest arises in part from the ability of these models to parsimoniously produce highly complex and richly structured geometries. Examination of the soil hydrology literature suggests that there are at least two different ways these models are being constructed. We review the two primary algorithms and compare the computed water retention behavior of the different media. Water retention is computed using a method that explicitly considers the connections between pores and to the atmosphere. The distributions of simulated water saturations (for 1000 realizations) around their median values as a function of applied tension were complex and multimodal for both homogeneous and heterogeneous prefractals. The range between the first and third quartiles for the water retention in heterogeneous prefractal structures was, on average, more than twice as large as that for the homogeneous prefractals. This suggests that relations between fractal parameters used to construct the porous media and the water retention behavior of the media can be more readily determined for homogeneous prefractals.