Universal Equation for Gas Diffusivity in Structure-Less and Fractured, Unsaturated Soil: Use for Description, Prediction, and Risk Assessment.

The soil-gas diffusion coefficient (Dp) and its dependency on soil-air content and soil structure govern gaseous phase diffusion, uptake and emissions of e.g. climate gases and volatile organic chemicals in soils. We assume that soil-gas diffusivity contributions from soil fractures (or continuous macropores) and soil matrix are additive. Based on this, we suggest an universal equation for the relative gas diffusivity (Dp/Do, where Do is the gas diffusion coefficient in free air) as a function of soil-air content, total porosity, volumetric content of fractures, and a fracture geometry factor (H). Two additional parameters account for the pore connectivity of the dry soil matrix (Xd), and for water blockage effects (Nw) on gas diffusion inside the soil matrix (excluding fractures and continuous macropores). The new gas diffusivity equation with given parameter values is shown to unify a most of the existing, predictive Dp/Do models. The new Dp/Do equation is applied to gas diffusivity measurements for a soil profile below a building including layers with fractured soil, and to a database for gas diffusivity in undisturbed or differently-compacted soils representing around 50 differently-textured soils and 1200 measurements. For descriptive purposes, the new Dp/Do equation can easily be fitted to detailed data sets for Dp/Do as functions of soil-air content. For predictive purposes in structure-less soils, values of Xd = Nw = 1.5 are recommended but are not universal (dependent on soil type). For fractured soils, the fracture or continuous macropore volume needs to be quantified before the new equation can be applied to predict Dp/Do. For risk assessment purposes, it should be assumed that fractures or continuous macropores are always drained (air-filled) and accessible to gas transport, and that the dry soil matrix pore connectivity is high (Xd = 4/3). For risk assessment in regard to soil contribution to fluxes of volatile organic chemicals into buildings (indoor air) at polluted soil sites, we recommend five risk levels (RL) as follows. RL-I: Fractured soils (e.g. limestone or fractured silt or clay) with straight fractures (H = 1), RL-II: Fractured soils with tortuous fractures (H = 2/3), RL-III: Structure-less soils with low water blockage effects on gas diffusion (e.g. high-clay soils) represented by Nw = 0.5, RL-IV: Structure-less soils with medium water blockage effects (Nw = 1),  and RL-V: Structure-less soils with high water blockage effects (e.g. uniform, coarse sand) represented by Nw = 2. The Dp/Do equation presently used in the indoor air risk assessment models recommended by the environmental protection agencies in the US and Denmark is a risk level V equation, suggesting that estimated gas diffusivities and soil-gas fluxes are not on the safe side. Instead, we recommend that the new Dp/Do equation with individual choice of RL-I to RL-V for each identified soil layer between building foundation and chemical source be implemented in the risk assessment models.