Pore-scale simulation of gas diffusion in unsaturated soil aggregates: Accuracy of the dusty-gas model and the impact of saturation

Gas diffusions in soil control all physical and biogeochemical processes in terrestrial ecosystems and correctly describing them is critical to numerical modelling of these processes. The movement of gases in soil needs to overcome the resistances caused by both gas-gas collision and gas-wall collision, and the relative significance of one resistance over another depends on the size and spatial distribution of the pores. Practical models often use the empirical dusty-gas formula to estimate the effective gas diffusion coefficient, assuming that all resistances are addable even after a volumetric average. Since it is impossible to separately measure the two resistances, the accuracy and reliability of this approach remains unknown. We investigate this using pore-scale modelling and tomography. Soil aggregates are acquired using X-ray computed tomography and the size and spatial distribution of their pores are calculated using a morphological model; each pore is associated with a bulk diffusion coefficient and a Knudsen diffusion coefficient, with the latter calculated based on the pore size. We then develop pore-scale models to simulate gas diffusion, and the diffusive flux and gas concentration simulated at pore scale are volumetrically averaged to calculate i) the effective Knudsen diffusion coefficient assuming the bulk diffusion coefficient is infinite, ii) the effective bulk diffusion coefficient assuming the Knudsen diffusion coefficient is infinite, and iii) the overall effective diffusion coefficient considering both the bulk and the Knudsen diffusions. The dusty-gas model estimates the effective diffusion coefficient using the effective bulk and the Knudsen diffusion coefficients, and its accuracy is tested against the effective diffusion coefficient directly calculated from the pore-scale simulations. The results indicate that the dusty-gas model is accurate when the diffusion is dominated by either bulk diffusion or Knudsen diffusion, whereas in the transition regime it systematically overestimates the effective diffusion coefficient. We also investigate the impact of saturation on the effective diffusion coefficients when the aggregates are either hydrophobic or hydrophilic, elucidating the significance of the Knudsen diffusion as the saturation of the aggregates increases.