Continuum percolation theory for saturation dependence of air permeability

Continuum percolation theory has recently been used to find the saturation, S, dependence of the hydraulic conductivity, K(S), of probabilistic fractal porous media. Analysis of K(S) in conjunction with solute diffusion revealed the presence of a critical volume fraction, theta(t), for percolation in natural porous media. For moisture contents within a few percent of theta(t), K(S) depends on the moisture content as a power of theta - theta(t). At higher moisture contents, K(S) is determined through critical path analysis, which uses continuum percolation theory to find the dependence of a bottleneck (flow-limiting) pore radius on S. The physics near theta(t) is thus dominated by connectivity and tortuosity issues, but far from theta(t) by the variations in the radius of a bottleneck pore. Here it is demonstrated that the bottleneck pore radius for air permeability, k(a), does not change as a function of saturation. Using the same scaling for the air permeability in the vicinity of the percolation of the air phase as proposed for the hydraulic conductivity in the vicinity of the percolation of the water phase yields results for k(a) in accordance with experimental data.