PREDICTIVE-DESCRIPTIVE MODELS FOR GAS AND SOLUTE DIFFUSION COEFFICIENTS IN VARIABLY SATURATED POROUS MEDIA COUPLED TO PORE-SIZE DISTRIBUTION

Abstract

Accurate description of the soil-gas diffusion coefficient (DP) as a function of air-filled (ε) and total (Φ) porosities is required for studies of gas transport and fate processes. After presenting predictive models for DP 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, εin. Three model-based interpretations of εin 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 εin term (= 0.1 m3 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 (εth) to a maximum at ε = Φ, (3) a power-law model (VIPS) assuming variable εin that linearly decreases from a maximum at ε = εth to zero at ε = Φ. Assuming εth = 0.1 m3 m−3, all three models satisfactorily predicted DP in 18 repacked soils. The difference between the three models is mainly pronounced for higher-Φ 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 εin with ±0.03 m3 m−3 and is applicable for stochastic gas transport simulations at field scale. The mathematically flexible VIPS model highly accurately fitted DP(ε) data for undisturbed soil, illustrating the large possible variations in εth 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.