# Impact of Pore Geometry and Water Saturation on Gas Effective Diffusion Coefficient in Soil
## 3 Results and Discussions  
### Impact of Saturation on Pore Structure  
Figure 3 shows the changes of porosities for total, connected and unconnected pores with water saturation. As water saturation increased, the porosity of the total pores and connected pores decreased, while the unconnected pores increased. When water saturation was less than 0.4, the connected pore porosity was approximately equal to the total pore porosity, indicating that under low water saturations, a smaller fraction of the pores is occupied by water. This is in stark contrast to when saturation is higher than 0.5.  
As mentioned before, each pore voxel is associated with a pore diameter. The volume of pores for each diameter under different saturations is shown in Figure 4. The curve shapes for total and connected pores were similar, and the volume of pores decreased with increasing water saturation except for small pores (diameter \(<2\) voxels), which increased with water saturation in the initial stage and decreased later. This is because water entering pores in the hydrophobic soil reduced the diameters of the large pores. The mean pore diameters decreased with water saturation. If \(S\) is water saturation, then (\(1-S\)) denote gas saturation, and the normalized mean pore diameter increases with gas saturation, as shown in Figure 5. The increase can be fitted into a power law, \(\delta^{\prime}=\alpha(1-S)^{\beta}\), where \(\delta^{\prime}\) is the normalized mean pore diameter. As an illustration, Figure 5 shows the comparison between the calculated mean pore diameter and that estimated by \(\delta^{\prime}=\alpha(1-S)^{\beta}\). To test that the formula was valid for other soils, we calculated the normalized mean pore diameter under different saturations in another soil sample with contrasting pore geometrical shape and pore size distribution, as shown in Figure 6. The results (not presented) show that the relationship between average pore diameter and gas saturation can be fitted into a power-law.  
Figure 4: Volume of pores for different diameters under various saturations: (a) Total pores. (b) Connected pores.  
Figure 3: Changes of porosity (\(V_{\text{gas}}/V\)) with water saturation. Here, porosity is the volume ratio of void voxels to the whole soil sample in Figure 1b.  
As most biogeochemical processes in soil occur at the interface of water, air and solid [51], we calculated the interface areas of gas-water, gas-solid and water-solid under different water saturations. For convenient analysis, we normalized all the interface areas by \(A_{0}\), where \(A_{0}\) is the interface area of gas-solid when water saturation is 0. Figure 7 shows the changes of interface areas \(A/A_{0}\) with water saturation. Swelling of water saturation decreased the interface area of gas-solid exponentially, concurrent with exponentially increasing the interface area of water-solid, and the interface area of gas-water increased with water saturation in early stages and decreased with an increasing rate in later stages.  
Figure 5: Comparison between calculated mean pore diameter \(\delta^{\prime}\) and that estimated by \(\delta^{\prime}=\alpha(1-S)^{\beta}\). Here, \(\delta^{\prime}\) is normalized by \(\delta_{0}\) which is the mean pore diameter when water saturation is 0.  
Figure 6: The soil (sample 2) used for testing (**a**); the spatial distribution of soil pores (**b**); pore-size distribution (**c**).  
Figure 7: Changes of interface areas \(A/A_{0}\) for water–solid, gas–water and gas–solid with water saturation.