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.