Computer model of a porous medium

Abstract

A computer model has been set up to represent a porous medium. The basis for this model is a two-dimensional square network (100×100) of channels that have randomly assigned widths between the value of zero (closed) and the value of one (open, unrestricted flow). The channel width assignments have been made by a random selection from five different distributions:f(q)=q, f(q)=sinq, f(q)=erf(q),f(q)=1−sinq, andf(q)=1 −erf(q). Diffusion of particles in the network has been studied by a random-walk procedure for each realization of the channel width assignments. The diffusivity is quite sensitive to the distribution of channel widths. The percolation properties of the networks obtained from the three most restrictive distributions have been investigated and the independent, linked clusters within the network have been determined. For cluster sizes that are less than the full width of the network, the network does not percolate and either the flow is not diffusive or the diffusivity is severely reduced. An approximate value for the percolation threshold has been determined in each case and the fractal dimension has been calculated also.