Quantifying the Impact of 3D Pore Space Morphology on Soil Gas Diffusion in Loam and Sand

Effective diffusion is an important macroscopic property for assessing transport in porous media. Numerical computations on segmented 3D CT images yield precise estimates for diffusive properties. On the other hand, geometrical descriptors of pore space such as porosity, specific surface area and further transport-related descriptors can be easily computed from 3D CT images and are closely linked to diffusion processes. However, the investigation of quantitative relationships between these descriptors and diffusive properties for a diverse range of porous structures is still ongoing. In the present paper, we consider three different soil samples of each loam and sand for a total of six samples, whose 3D microstructure is quantitatively investigated using univariate as well as bivariate probability distributions of geometrical pore space descriptors. This information is used for investigating microstructure-property relationships by means of empirically derived regression formulas, where a particular focus is put on the differences between loam and sand samples. Due to the analytical nature of these formulas, it is possible to obtain a deeper understanding for the relationship between the 3D pore space morphology and the resulting diffusive properties. In particular, it is shown that formulas existing so far in the literature for predicting soil gas diffusion can be significantly improved by incorporating further geometrical descriptors such as geodesic tortuosity, chord lengths, or constrictivity of the pore space. The robustness of these formulas is investigated by fitting the regression parameters on different data sets as well as by applying the empirically derived regression formulas to data that is not used for model fitting. Among others, it turns out that a formula based on porosity as well as mean and standard deviation of geodesic tortuosity performs best with regard to the coefficient of determination and the mean absolute percentage error. Moreover, it is shown that regarding the prediction of diffusive properties the concept of geodesic tortuosity is superior to geometric tortuosity, where the latter is based on the creation of a skeleton of the pore space.