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

Abstract

The air permeability (k a ) and soil gas diffusion coefficients (D p ) are controlling factors for gas transport and fate in variably saturated soils. We developed a unified model for k a and D 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 H 2 O 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 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 k a and D were fitted to the measured data. For both structureless and structured porous media, Archie's saturation exponent (n) was higher for D p than for k a , indicating higher water blockage effects on gas diffusion. For structured soils, the saturation exponent for the large-pore region (n 1 ) was lower than for the small-pore region (n 2 ). Generally, n 1 values of ∼1 for k a and 2 for D p and n 2 values of 4/3 for k a and 7/3 for D described the data well. Two reference-point expressions for k a at pF 2 were also developed and tested together with existing models for D at pF 2 against independent data across soil types. The best-performing reference-point models were a k a model based on the classical Kozeny equation and the Moldrup D p model.