Variable Pore Connectivity Factor Model for Gas Diffusivity in Unsaturated, Aggregated Soil

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The soil gas diffusion coefficient (D_p) and its variations with soil air content (ε) and soil water matric potential (ψ) control vadose zone transport and emissions of volatile organic chemicals and greenhouse gases. This study revisits the 1904 Buckingham power-law model where D_p is proportional to ε^X, with X characterizing the tortuosity and connectivity of air-filled pore space. One hundred years later, most models linking D_p(ε) to soil water retention and pore size distribution still assume that the pore connectivity factor, X, is a constant for a given soil. We show that X varies strongly with both ε and matric potential [given as pF = log(−ψ, cm H₂O)] for individual soils ranging from undisturbed sand to aggregated volcanic ash soils (Andisols). For Andisols with bimodal pore size distribution, the X–pF function appears symmetrical. The minimum X value is typically around 2 and was observed close to ψ of −1000 cm H₂O (pF 3) when interaggregate voids are drained. To link D_p with bimodal pore size distribution, we coupled a two-region van Genuchten soil water retention model with the Buckingham D_p(ε) model, assuming X to vary symmetrically around a given pF. The coupled model well described D_p as a function of both ε and ψ for both repacked and undisturbed Andisols and for other soil types. By merely using average values of the three constants in the proposed symmetrical X–pF expression, predictions of D_p were better than with traditional models.