# Impact of Pore Geometry and Water Saturation on Gas Effective Diffusion Coefficient in Soil
## 1 Introduction  
Understanding the movement of gas in soil is of great importance in many fields, such as estimating the environmental effect of gas spills [1; 2; 3], designing engineering projects to inject and store CO\({}_{2}\)[4; 5; 6; 7; 8], treatments of volatile constituents of hazardous wastes in landfills and disposal sites [9; 10; 11]. Owing to the intrinsic complexity of soil structure, the practical study of gas transport in soil is generally based on macroscopic approaches, wherein the microscopic features are volumetrically averaged by omitting the pore geometry [12; 11; 13]. Because only the void space allows gas to diffuse, gas diffusive flow in soil mainly depends on pore geometry and water saturation [14; 15; 16].  
In the literature, the gas effective diffusion coefficient (\(D_{\mathit{eff}}\)) in soil is usually assumed to be proportional to their bulk diffusion coefficient (\(d\)) in free air. For example, [PERSON] [17] andMillington [18], respectively, proposed a power-law, \(D_{\mathit{eff}}/d=\varepsilon^{n}\), with \(n\) being a fitting parameter. Considering the connectivity of pores, [PERSON] [19; 20] proposed an improved model, \(D_{\mathit{eff}}/d=(1/k)\varepsilon\), with \(k\) being the tortuosity factor. Several similar models have been proposed [21; 22; 23; 24], but these models are inadequate for calculating the impact of pore geometry and water saturation on the effective diffusion coefficient. Furthermore, in small pores when the Knudsen effect has to be considered, the diffusion will be much more complicated [14; 15; 25].  
Soils are usually aggregated with a hierarchical structure in which the pores inside the aggregates are much smaller than that between the aggregates. Several methods can be employed to measure the porosity of soil, such as water saturation method [26], water evaporation method [26], mercury intrusion [27; 28] and gas absorption [28; 29]. All the above methods can achieve a precise porosity and mercury intrusion, and gas absorption can also get the pore size distribution, but these methods cannot acquire the pore structure features, including pore space distribution, pore shape, isolated pores, and also they cannot rebuild 3D pore structure [30; 31]. The evolution of tomography, particularly the X-ray tomography technique and focused ion beam/scanning electron microscopy (FIB/SEM), has revealed the interior microstructure of porous media visible at resolutions less than 1 \(\upmu\)m [32; 33; 34]. This, together with pore-scale modelling method, could substantially improve our understanding of certain fundamental processes occurring in porous media [35; 36; 37; 38].  
In this paper, we calculated the void structure and the effective diffusion coefficient of soils under different saturations using pore-scale modelling and computed tomography, and to investigate the impact of pore geometry and water saturation on gas effective diffusion coefficient in soil. Firstly, we calculated water distribution by a morphological model [38; 39], and to extrapolate the impact of saturation on void structure, i.e., pore geometry including porosity, pore diameter, connectivity and interfacial area. The pore geometry varies with saturation; therefore, we simulated gas diffusion under different saturation conditions to explore the influence of pore geometry on gas diffusion. Secondly, we directly calculated the effective diffusion coefficient by a pore-scale model [15], and to deduce the impact of pore diameter and saturation on effective diffusion coefficient. As studies on how the effective Knudsen diffusion coefficient changes with mean pore diameter and water saturation in porous media is limited in the literature, we attempted to address this using the pore-scale model.