Predictive-descriptive models for gas and solute diffusion coefficients in variably saturated porous media coupled to pore-size distribution: III. Inactive pore space interpretations of gas diffusivity

Accurate description of the soil-gas diffusion coefficient (D-P) as a function of air-filled (epsilon) and total (Phi) porosities is required for studies of gas transport and fate processes. After presenting predictive models for D-P in repacked and undisturbed soils (Part I and II), this third paper takes a more descriptive approach allowing for the inclusion of inactive air-filled pore space, Fin. Three model-based interpretations of E.. are presented: (1) a simple power-law model (labeled Millington-Call) with the exponent (V) taken from Millington (1959; Science 130:100-102), and expanded with a constant epsilon(in) term (= 0.1 m(3) m(-3)), (2) a model (SOLA) based on analogy with solute diffusion and assuming a linear increase in pore continuity from zero at the threshold air-filled porosity where gas diffusion ceases (epsilon(th)) to a maximum at F = 0, (3) a power-law model (VIPS) assuming variable F-in that linearly decreases from a maximum at epsilon = epsilon(th) to zero at epsilon = Phi. Assuming epsilon(th) = 0.1 m(3) m(-3), all three models satisfactorily predicted D-p in 18 repacked soils. The difference between the three models is mainly pronounced for higher-Phi soils, and each model has its own advantage. The SOLA model together with similar models for solute diffusivity allows a direct comparison of pore continuity in the soil gaseous and liquid phases, suggesting large differences in tortuosity and inactive fluid-phase between the two phases. The low-parameter Millington-Call model could account for variability in measured Dp along a field transect (Yolo, California) by varying epsilon(in) with +/- 0.03 m(3) m(-3) and is applicable for stochastic gas transport simulations at field scale. The mathematically flexible VIPS model highly accurately fitted Dp(epsilon) data for undisturbed soil, illustrating the large possible variations in Eh and V. The VIPS model is coupled with the van Genuchten (vG) soil-water characteristic model, yielding a closed-form expression for Dp as a function of soil-water matric potential. The VIPS-vG model is useful to illustrate the combined effects of pore size distribution and inactive pore space on soil-gas diffusivity.