Hierarchical, Bimodal Model for Gas Diffusivity in Aggregated, Unsaturated Soils

The soil gas diffusion coefficient (Dp) and its dependency on soil air content, epsilon, and tortuosity–connectivity of the air-filled pore networks control the transport and fate of gaseous-phase contaminants in variably saturated soil. The bimodality in pore size distribution of structured soil often yields a variation of Dp with epsilon in the intraaggregate pore region that is distinctly different from that in the interaggregate region. Data imply a highly nonlinear behavior of soil gas diffusivity, Dp(epsilon)/Do (where Do is the gas diffusion coefficient in free air), in the interaggregate region of aggregated soils similar to that of structureless soils with a unimodal pore size distribution, probably due to diffusion-limiting effects by connected water films at low epsilon. In contrast, for the intraaggregate region, we show that the impedance factor F* (= Dp/epsilonDo) and tortuosity factor T [= (1/F*)1/2] are approximately constant for most soil media. We suggest a typically well-defined separation between the two pore regions at the minimum for the pore connectivity factor X* [= log(Dp/Do)/log(epsilon)], at which point the interaggregate pores are devoid of water while the intraaggregate pore region is water saturated. Based on this, a hierarchical two independent region (TIR) Dp/Do model was developed by applying a cumulative series of Buckingham–Currie power-law functions, FepsilonX. A nonlinear, water-content-dependent expression for F best described the measured Dp/Do in the interaggregate region, while constant F (around 0.5) and X (around 1) generally sufficed for the intraaggregate region. The TIR model better predicted gas diffusivities for both aggregate fractions and highly structured soils across the entire range of moisture conditions with RMSE reduced by two to five times compared with traditional predictive Dp(epsilon)/Do models.