Universal scaling of gas diffusion in porous media

Gas diffusion modeling in percolation clusters provides a theoretical framework to address gas transport in porous materials and soils. Applying this methodology, above the percolation threshold the air-filled porosity dependence of the gas diffusion in porous media follows universal scaling, a power law in the air-filled porosity (less a threshold value) with an exponent of 2.0. We evaluated our hypothesis using 71 experiments (632 data points) including repacked, undisturbed, and field measurements available in the literature. For this purpose, we digitized D-p/D-0 (where D-p and D-0 are gas diffusion coefficients in porous medium and free space, respectively) and epsilon (air-filled porosity) values from graphs presented in seven published papers. We found that 66 experiments out of 71 followed universal scaling with the exponent 2, evidence that our percolation-based approach is robust. Integrating percolation and effective medium theories produced a numerical prefactor whose value depends on the air-filled porosity threshold and the air-filled porosity value above which the behavior of gas diffusion crosses over from percolation to effective medium.