# Impact of Pore Geometry and Water Saturation on Gas Effective Diffusion Coefficient in Soil
## 3 Results and Discussions
### Impact of Saturation on Effective Diffusion Coefficient  
We first simulated carbon dioxide diffusion in soil as shown in Figure 1. Since gas diffusion is dependent on temperature and pressure [52], a temperature 300 K and pressure 1 bar and a bulk diffusion coefficient \(d=0.16\) cm\({}^{2}\)/s were used in the simulations. For each image, we calculated its effective bulk diffusion coefficient (\(D_{b}\)), omitting the Knudsen diffusion, the effective Knudsen diffusion coefficient (\(D_{bn}\)), omitting the bulk diffusion and the overall effective diffusion coefficient (\(D_{\mathit{eff}}\)) considering both the bulk and Knudsen diffusions. For convenient analysis, we normalized all the effective diffusion coefficients by the bulk diffusion coefficient \(d\).  
Figure 8 shows the changes of effective diffusion coefficient (\(D_{\mathit{eff}}\)/\(d\)) with mean pore diameter in comparison with the effective bulk diffusion coefficient (\(D_{b}\)/\(d\)) and the effective Knudsen diffusion coefficient (\(D_{bn}\)/\(d\)), under saturations 0, 0.267 and 0.825. For all three water saturations, the patterns of the effective diffusion coefficient changes with pore diameter were similar, the effective diffusion coefficient increased with mean pore diameter as the effective Knudsen diffusion coefficient in the Knudsen regime, and asymptotically approached the value of the effective bulk diffusion coefficient in the continuum regime. As shown in Figure 8, the effective diffusion coefficient decreased with increasing water saturation. This is mainly because the swelling of water saturation decreases the porosity and mean pore diameter of soil as illustrated before, and hence, the soil becomes less diffusible.  
To prove the above impact of water saturation on the gas diffusion coefficient is a general principle, we simulated oxygen diffusion in the two soil samples with bulk diffusion coefficient \(d=0.20\) cm\({}^{2}\)/s [43]. The simulated results are shown in Figure 9. The curves of effective diffusion coefficient with pore diameter are similar to those of carbon dioxide, and the effective diffusion coefficients also decrease with water saturation increasing.  
Under certain water saturation, the values of the effective diffusion coefficients (\(D_{\mathit{eff}}\)) of carbon dioxide and oxygen, as well as their changes with mean pore diameter differ considerably (not presented). However, after normalization, the values of \(D_{\mathit{eff}}\)/\(d\) were approximately equal, particularly when the mean pore diameter was relatively large, as shown in Figures 8 and 9, indicating that \(D_{\mathit{eff}}\)/\(d\) depends only on the pore geometry and not on the molecular mass of gas. To prove this, we simulated the effective diffusion coefficient of methane and hydrogen in the soil in Figure 1; and the results also show that the normalized effective diffusion coefficient is independent of the molecular mass of gas as shown in Figure 9,d.  
Figure 8: Changes of effective diffusion coefficient \(D_{\mathit{eff}}\)/\(d\) (solid line) of carbon dioxide under three saturations (0.825, 0.267 and 0) with mean pore diameter, compared with those of effective bulk diffusion coefficient \(D_{b}\)/\(d\) (dotted) and effective Knudsen diffusion coefficient \(D_{bn}\)/\(d\) (short dash). The dark green, dark blue and dark red colors represent the saturation of 0, 0.267 and 0.825, respectively.