Two-Region Extended Archie's Law Model for Soil Air Permeability and Gas Diffusivity

The air permeability (ka) and soil gas diffusion coefficients (Dp) are controlling factors for gas transport and fate in variably saturated soils. We developed a unified model for ka and Dp based on the classical Archie's law, extended by: (i) allowing for two-region gas transport behavior for structured soils, with the natural field moisture condition (set at −100 cm H2O matric potential [pF 2]) as the reference (spliced) point between the large-pore (drained pore diameter ≥30 μm at pF ≤ 2) and the small-pore (subsequently drained pores <30 μm at pF > 2) regions, and (ii) including a percolation threshold, set as 10% of the total porosity for structureless porous media or 10% of the porosity in the large-pore region for structured soils. The resulting extended Archie's law with reference point (EXAR) models for ka and Dp were fitted to the measured data. For both structureless and structured porous media, Archie's saturation exponent (n) was higher for Dp than for ka, indicating higher water blockage effects on gas diffusion. For structured soils, the saturation exponent for the large-pore region (n1) was lower than for the small-pore region (n2). Generally, n1 values of∼1 for ka and 2 for Dp and n2 values of 4/3 for ka and 7/3 for Dp described the data well. Two reference-point expressions for ka at pF 2 were also developed and tested together with existing models for Dp at pF 2 against independent data across soil types. The best-performing reference-point models were a ka model based on the classical Kozeny equation and the Moldrup Dp model.