Multiscale percolation properties of a fractal pore network

Network modelling and percolation theory now occupy a firm niche in soils research, aiding in the simulation and prediction of flow and transport processes. In this study we examine the connectivity properties of a simple parameterized 2D fractal network model by direct numerical simulation and theoretically, drawing on upscaling functions from renormalization theory. We demonstrate good agreement between the two approaches and extrapolate to systems inaccessible to direct numerical simulation. We examine the relationship between porosity, the pore-size range and the connectivity of the network. We show that for fixed porosity, the connectivity is a nonlinear function of the range of scales accommodated in the fractal model. We investigate the implications of distributing a fixed porosity over different ranges of pore size and demonstrate a general impairment of pore connectivity and improvement of solid phase continuity as this range is extended.