Fluid permeability and DC conductivity of networks with a broad distribution of bond resistances: comparison of the critical path approximation with 3-D Monte Carlo simulations

Todd Skaggs

George E. Brown jr. Salinity Laboratory

Viscous fluid flow and electrical conduction in porous media has been studied in the past using a random resistor network model with a wide distribution of bond conductances. Calculations of fluid permeability and DC conductivity for these systems can be made using the critical path method. The basic idea of the critical path method is that in strongly inhomogeneous media flow occurs primarily on a few pathways that have significantly lower resistance than all other possible pathways, and that the biggest resistors on those low resistance pathways control the overall resistance of the system. Percolation theory is used in critical path analysis to quantify the expected number of low resistance pathways and to calculate the system conductivity. Monte Carlo computations of the conductivity for two-dimensional systems are in agreement with the critical path calculation, but three-dimensional computations have consistently deviated from the critical path prediction. It has been speculated that the discrepancy in 3D is due finite-size effects on the percolation correlation length. The present work evaluates the 3D critical path approximation using Monte Carlo data that are more extensive than previously available, and includes an analysis of finite-size effects.