# Study on Fluorine Pollution in a Slag Yard
## 5 Numerical Modelling Investigation
### Model Definition for Dissolved Solute Transport  
The solute component identification test showed that the concentration value of fluorine in the slag solute was approximately 0.0045 kg/m\({}^{3}\), while that of the solute on the clay surface was approximately 0.00005 kg/m\({}^{3}\). The following conditions were set for solute migration simulation. The initial value of slag solute was set to 0.0045 kg/m\({}^{3}\), while that of other solutes were set to be 0.00005 kg/m\({}^{3}\). Boundary conditions were as follows. Flux boundary was set to the upper surface of the model. The flux of the slag yard surfaces was (3.2 \(\times\) 10\({}^{-8}\)) \(\times\) 0.0045 kg m\({}^{-2}\) s\({}^{-1}\), while that of the clay surfaces was (3.2 \(\times\) 10\({}^{-8}\)) \(\times\) 0.00005 kg m\({}^{-2}\) s\({}^{-1}\). The concentration of fluorine in the water of the border surface with the higher constant hydraulic heads was set to 0.00005 kg/m\({}^{3}\). The advective flux model was set to the border surface with the lower constant hydraulic heads. The flux of the bottom surface was zero. The fluxes of the two border surfaces vertical to the x-axis were set to be zero for the 3D FEM model. The parameters of the materials used in the dispersion calculation are shown in Table 7. The molecular diffusion coefficient of material 2 was determined as D\({}_{\rm m}\) = 4.85 \(\times\) 10\({}^{-6}\) m\({}^{2}\) s\({}^{-1}\) based on the unsaturated dispersion test results shown in Table 5 and the clay saturation of survey results shown in Table 8. Other parameters, shown in Table 7, were determined according to the experience values in geotechnical engineering. Figure 7: Soil–water characteristic curve for material 2. Groundwater quality near the slag field was analyzed to evaluate the slag field effects on the surrounding groundwater. Table 9 shows the groundwater sample test results and corresponding numerical simulation results. It can be seen that the numerical simulation results and test results are nearly identical. Hence, the numerical simulation results could be used as the basis of groundwater environment evaluation. Figure 9 provides some solute migration simulation results of the 2D model. Over time, the solution with the fluorine concentration in the slag field migrated outward slowly. The dispersion velocity near the groundwater was so large that the fluorine concentration in the groundwater did not increase with time. The final fluorine concentration in the groundwater, 100 years after disposal started, did not exceed 0.001 kg m\({}^{-3}\), which is the legislative upper limit of the second-grade water of China. The concentration in the groundwater did not exceed the legislative upper limit of the second-grade water of China. The maximal pollution water range, from the slag yard to the south, 52 years after disposal started, was approximately 123 m, and was approximately 172 m 100 years after disposal started. Figure 8: Saturation contour in clay: (**a**) 2D model and (**b**) 3D model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample** & **Test Result C/(kg/m\({}^{3}\))** & **Simulation Result C/(kg/m\({}^{3}\))** \\ \hline ZKJ-1 & 0.00005 & 0.000053 \\ ZKJ-2 & 0.00006 & 0.000051 \\ ZKJ-3 & 0.00007 & 0.000054 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison between test results and simulation results. Figure 9: Simulated concentration contour of fluorine in groundwater of the situation of the neighboring slag yard of 2D model: (**a**) 1 year after disposal started, (**b**) 52 years after disposal started, and (**c**) 100 years after disposal started. Figures 10-12 provide some solute migration simulation results of the 3D model. Over time, the solution with the fluorine concentration in the slag field migrated outward slowly. The dispersion velocity near groundwater was so large that the fluorine concentration in the groundwater did not increase with time. The final fluorine concentration in the groundwater 100 years after disposal started did not exceed 0.001 kg m\({}^{-3}\).