Evaluation of a Percolation-Based Air Permeability Calculation in Porous Media.

Estimation of a soil’s relative (unsaturated) air and water permeability is an area of active research.  In this study, we evaluate the universal scaling of the saturation-dependence of air permeability, which should in theory be a power law in the air-filled porosity (less a threshold value) with exponent  2.00. For this purpose, a large database including 33 experiments is used. The proposed percolation threshold-dependent model was fitted well to the measured air permeability data, with correlation coefficient (R²) value greater than 0.87 in each individual case.  Relative air permeability fitted as a function of normalized effective air-filled porosity had a prefactor of 0.923, an exponent of 1.998, and correlation coefficient R²=0.97, confirming the universal behavior. We compared the proposed model with three other methods: Millington and Quirk, Burdine-Brooks-Corey, and Kawamoto et al. The universal scaling approach estimated air permeability more accurately than the other three methods as evidenced by RMSE and AIC_c values.