# Parametric Analysis for 3D Modeling of Consolidation-Induced Solute Transport Using OpenFOAM
## 4 Results and Discussion
### Effect of the Partitioning Coefficient on Solute Transport
Under conditions of a larger distribution coefficient (**Case 11**), the adsorption effect is significantly enhanced, leading to substantial retention of solutes on solid surfaces. This strong adsorption effect may localise the solute concentration gradient in the pore water, resulting in irregularities in the concentration distribution. Simultaneously, the migration rate and extent of the solute increase significantly, further highlighting the critical role of adsorption in regulating solute migration. The physical mechanism behind these phenomena can be attributed to the obstructive effect of the partition coefficient, which greatly enhances the binding between the solute and the solid phase, thereby significantly reducing the effective migration rate of the solute in the liquid phase. Moreover, the lower lateral diffusion rate further restricts the solute's spread toward the peripheral region, leading to a distribution pattern characterized by higher concentrations in the center region and lower concentrations at the edges. In summary, the sensitivity analysis underscores the significant impact of the partition coefficient (\(K_{d}\)) on solute transport behavior. As \(K_{d}\) increases, solute migration slows due to enhanced adsorption, resulting in lower concentrations across both spatial and temporal scales. The effects are most pronounced in the center region, where advection dominates and solute migration is more concentrated. At the edges, diffusion and retardation combine to further hinder solute transport, leading to sharper concentration declines. Vertical variations reveal that adsorption effects significantly reduce solute migration into deeper layers, particularly for larger \(K_{d}\) values. These findings highlight the critical role of adsorption in modulating solute transport, emphasizing the need to consider partition effects when modeling contaminant migration in porous media. Figure 31: Distributions of concentration over time at the center (\(x=y=20\) m, \(z=1.5\) m/3 m) and on the edge (\(x=y=30\) m, \(z=1.5\) m/3 m) for varying partitioning coefficient. Solid lines represent **Case 1**, squares represent **Case 10**, and triangles represent **Case 11**: (**a**) \(c_{f}\) vs. \(t\) at the center; (**b**) \(c_{f}\) vs. \(t\) on the edge. Figure 34: _Cont._  
Figure 33: Distributions of concentration along (**a,b**) the top horizontal cut line at \(z=3\) m for varying partitioning coefficient. Solid lines represent **Case 1**; squares represent **Case 10**; triangles represent **Case 11**. Figure 32: Distributions of concentration over depth at the center (\(x=y=20\) m, \(z=3\) m) and on the edge (\(x=y=30\) m, \(z=3\) m) for varying partitioning coefficient. Solid lines represent **Case 1**, squares represent **Case 10**, and triangles represent **Case 11**: (**a**) \(c_{f}\) vs. \(z\) at the center for different years; (**b**) \(c_{f}\) vs. \(z\) on the edge for different years. Effects of the Anisotropy Ratio (\(\frac{K_{x}}{K_{z}}\) and \(\frac{K_{y}}{K_{z}}\)) on Solute Transport  
Figure 35 illustrates the solute concentration distributions along the horizontal direction for varying anisotropy ratios of horizontal to vertical hydraulic conductivity (\(\frac{K_{x}}{K_{z}}\)). The analysis considers four cases: **Case 1** (\(\frac{K_{x}}{K_{z}}=\frac{K_{y}}{K_{z}}=1\)), **Case 12** (\(\frac{K_{x}}{K_{z}}=\frac{K_{y}}{K_{z}}=5\)), **Case 13** (\(\frac{K_{x}}{K_{z}}=\frac{K_{y}}{K_{z}}=10\)), and **Case 14** (\(\frac{K_{x}}{K_{z}}=5\), \(\frac{K_{y}}{K_{z}}=10\)) over different timescales. Notably, **Case 14** introduces non-symmetric horizontal anisotropy, allowing a direct comparison of solute transport in the \(x\)- and \(y\)-directions. Such scenarios mimic real-world conditions in heterogeneous soils, where deposition history can result in different \(K_{x}\) and \(K_{y}\) values. In the top layer, increasing the horizontal hydraulic conductivity (\(K_{x}\)) has a relatively limited and time-dependent effect on the center concentration.