# Parametric Analysis for 3D Modeling of Consolidation-Induced Solute Transport Using OpenFOAM
## 4 Results and Discussion
### Effect of the Partitioning Coefficient on Solute Transport
When the anisotropy ratio reaches a threshold (e.g., 5 or 10), the differences in solute accumulation effects between cases stabilize, indicating diminishing returns from further increases. This stabilization is also observed in **Case 14**, reinforcing the notion that horizontal anisotropy beyond a threshold value has minimal impact on solute redistribution. Furthermore, in both the middle and bottom layers, the edge concentrations remain consistently low, likely because horizontal diffusion primarily enhances solute transport closer to the center region. This low edge concentration is attributed to weak concentration gradients near the boundaries, limiting lateral transport. While short-term effects in **Case 13** suggest enhanced edge diffusion, the edge concentration in all cases remains close to zero over the long term, indicating minimal lateral migration. This confirms that horizontal diffusion predominantly affects the center region, with limited impact on the edges. Despite the significant difference in anisotropy ratios between **Case 12** and **Case 13**, their solute concentration profiles are remarkably similar. At the top layer, after 20 years, edge concentrations differ by less than 0.05 between these cases, and center concentrations plateau at approximately 0.65. This similarity indicates that the effect of increasing the anisotropy ratio diminishes beyond a threshold value of \(\frac{K_{x}}{K_{x}}=\frac{K_{y}}{K_{x}}\approx 5\). The diminishing returns can be attributed to minimal changes in concentration gradients across different anisotropy ratios. Beyond the threshold, horizontal transport is increasingly limited by low concentration gradients, diffusion constraints, and boundary conditions. As the system approaches a dynamic equilibrium, further increases in \(\frac{K_{x}}{K_{x}}\) and \(\frac{K_{y}}{K_{x}}\) have a negligible impact on solute redistribution. Synthesizing the analysis of the middle and bottom layers reveals that the effects of increasing horizontal hydraulic conductivity vary with depth and time. In the middle and bottom layers, increasing \(K_{x}\) and \(K_{y}\) significantly enhances solute accumulation in the short term, with **Case 12** achieving optimal results. In the long term, the differences between **Case 12** and **Case 13** diminish as the system reaches equilibrium and the marginal effect of \(K_{x}\) stabilizes. Similarly, the inclusion of **Case 14**, where \(K_{x}\) and \(K_{y}\) exhibit asymmetry, demonstrates that horizontal anisotropy does not significantly alter the solute redistribution trends observed in symmetric cases. The findings suggest that optimizing horizontal hydraulic conductivity to \(\frac{K_{x}}{K_{x}}\approx 5\) can balance diffusion enhancement and cost-effectiveness, providing practical guidance for soil engineering and contaminant management. Figure 35: Distributions of concentration in the \(x\)-direction along (**a,b**) the top horizontal cut line at \(z=3\) m; (**c,d**) the middle horizontal cut line at \(z=1.5\) m; (**e,f**) the bottom horizontal cut line at \(z=0\) m for varying anisotropy ratio. Solid lines represent **Case 1**; squares represent **Case 12**; triangles represent **Case 13**. Figure 36: Distributions of concentration in the \(y\)-direction along (**a,b**) the top horizontal cut line at \(z=3\) m; (**c,d**) the middle horizontal cut line at \(z=1.5\) m; (**e,f**) the bottom horizontal cut line at \(z=0\) m for varying anisotropy ratio. Solid lines represent **Case 1**; squares represent **Case 12**; triangles represent **Case 14**.