On the Determination of Transport Properties of Disordered Systems

We describe several methods of calculating transport properties of disordered systems. These include the effective-medium approximation (EMA) and the position-space renormalization group (PSRG) method. Both methods do not yield accurate estimates of transport properties of three-dimensional disordered systems near a percolation threshold. We propose a modified EMA which is relatively simple but is significantly more accurate than EMA for three-dimensional disordered systems. We also show that a simple combination of EMA and a PSRG method provides a powerful means of estimating transport properties of such systems. We use these methods to estimate the relative permeabilities to two-phase flow through porous media, containing a strongly-wet phase and a completely nonwet phase. The agreement between the predictions and the available experimental data is very good.