# Parametric Analysis for 3D Modeling of Consolidation-Induced Solute Transport Using OpenFOAM
## 4 Results and Discussion
### Effect of the Partitioning Coefficient on Solute Transport
As shown in Figure 35a,b, over a short period (e.g., \(t=3\) years), the center concentration in **Case 12** and **Case 13** is slightly lower than that in **Case 1**, decreasing from 0.53 to 0.52, a reduction of only 2%. This small reduction highlights that vertical diffusion dominates solute transport in the top layer, with horizontal diffusion playing a minor role. As time progresses (e.g., \(t=20\) years), the center concentrations across all three cases converge, and the differences nearly vanish. Meanwhile, the edge concentration remains consistently low (\(<\)0.05) with minimal variation, further confirming the limited influence of horizontal diffusion. This trend persists in **Case 14** (Figure 36), where \(K_{y}>K_{x}\), showing that the asymmetry in horizontal hydraulic conductivity does not significantly affect solute redistribution. Figure 37 shows the concentration contours in the centre region in the \(x\)-\(y\) plane during the tenth year under different anisotropy ratios of hydraulic conductivity. Compared to the isotropic condition (**Case 1**), both **Case 12** and **Case 14** exhibit a significantly expanded horizontal diffusion range and notable changes in the concentration of the center. However, the differences in concentration distribution between **Case 12** and **Case 14** are relatively minor, and their overall patterns remain similar. This suggests that while increasing the anisotropy ratio beyond a certain point (e.g., from **Case 12** to **Case 14**) continues to enhance diffusion, the additional effect on the concentration distribution diminishes. In the middle and bottom layers, the increase in horizontal hydraulic conductivity significantly affects solute transport and accumulation behavior, but the specific effects vary with time and the anisotropy ratio. In the short term (1-3 years), the center concentrations in the middle layer for **Case 12** and **Case 13** exceed those in **Case 1**, reflecting the cumulative effect of enhanced horizontal diffusion. Notably, **Case 13** exhibits a \"high at both ends, low in the middle\" pattern, where an excessively high \(K_{x}/K_{z}\) ratio (e.g., 10) accelerates solute diffusion toward the edges, limiting center accumulation. In contrast, **Case 12** (\(K_{x}/K_{z}=5\)) achieves a balance, with moderate horizontal diffusion leading to higher center concentrations. Over time, this \"high at both ends\" pattern in **Case 13** disappears as the system approaches equilibrium, and the solute redistrib  
Figure 34: Concentration contour plots in the \(x\)-\(y\) plane at \(z=3\) m under varying partitioning coefficient over 10 years. the center region. As shown in Figure 36, this pattern also appears in the \(y\)-direction, confirming that the asymmetry in **Case 14** does not significantly alter solute transport in the middle layer. In the bottom layer, solute transport shows even greater sensitivity to horizontal diffusion. Here, the center concentration in **Case 12** is the highest, followed by **Case 13** and **Case 1**. This indicates that a moderate ratio significantly enhances center accumulation, while excessively high ratios drive solutes toward the edges, reducing center concentrations. This increased sensitivity stems from the bottom layer's greater reliance on horizontal diffusion due to weaker vertical transport. **Case 14** supports these findings, with consistent solute distributions observed in both the \(x\)- and \(y\)-directions. In the long term (5-20 years), the concentrations in the middle and bottom layers for **Case 12** and **Case 13** gradually converge and slightly exceed those in **Case 1**. At \(t=20\) years, the center concentration in the middle layer increases from 0.42 in **Case 1** to 0.44 in **Case 12** and **Case 13**, representing an increase of approximately 5%. Similarly, at the bottom layer, the center concentration rises from 0.29 in **Case 1** to 0.32 in **Case 12** and **Case 13**, an increase of 8%. This phenomenon indicates that the marginal effect of horizontal diffusion weakens over time.