## 2 Migration Modelling and Numerical Simulation of Contaminated Fields
### Numerical Simulation of the Migration Characteristics of the Contaminated Site
The resistivity changes were obtained for migration times of 10, 100, 200, 300, 400, and 500 days, respectively, as shown in Figure 2.  
As shown in Figure 2, the migration of Cr pollutants within 10-100 days in the pulverized clay area is mainly influenced by gravity. The apparent resistivity of the pollutants is uniformly distributed in a step-like manner. The contaminated area did not undergo significant lateral migration due to the poor water permeability of the pulverized clay and the insignificant effect of convective dispersion. The ground pollutant has completely disappeared in 100 days, and the depth of pollution reaches 4.7 m, at this time, the polluted area is about 265 m\({}^{2}\). As well, 100 days after the pollutant enters into the fine sand layer, it starts to spread obviously along the lateral direction, and the scope of the polluted area varies greatly in 100-200 days. The center of the pollutant migrates in the lateral direction from 50-100 to 122-127 m. The pollutant field spreads to the inner part of the aquifer, and the bottom edge has come to 9.8 m. Which indicates that the high permeability coefficient of the fine sand and the aquifer have a great influence on the migration of the pollution field. From the 200 th day onwards, Cr pollutants take the pollution center (dark blue area) as the radiation source and keep the whole pollution field spreading downward and to the right at the same time spreading to the surrounding area in the form of a ladder. At this time, the pollution field has already radiated a new semi-ellipsoidal contamination area. The top of it is again approaching to the ground vertically, and its height is even more than that of the original contaminated field. On the 300 th day, the heavily contaminated area had completely left the fine sand area. The whole contaminated area was between \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter Names** & **Pulverized Clay** & **Fine Sand** & **Medium Sand** & **All Areas** & **Unit** \\ \hline Permeability & \(10^{-8}\) & \(5\times 10^{-5}\) & \(2\times 10^{-4}\) & None & m/s \\ coefficient (\(K\)) & & & & & \\ Porosity & 0.20 & 0.30 & 0.35 & None & \(\times\) \\ Resistivity & None & None & None & 390 & \(\Omega\cdot\)m \\ Mass water & 0.15 & 0.20 & 0.12 & None & \(\times\) \\ content & & & & & \\ Vertical diffusivity & None & None & None & 0.5 & m \\ Horizontal & None & None & None & 0.005 & m \\ diffusivity & & & & & \\ Density & 1700 & 1600 & 1500 & None & kg/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model parameters (”None” means that it is replaced by another setting). the fine sand and the medium sand area, with a tendency to continue to penetrate into the medium sand area. At this moment, the contaminated area had already reached 746 m\({}^{2}\), which was 12 times as much as that on the 10 th day. After 400 days of migration time, the upper right part of the pollution field has moved laterally into the middle sand area and spread laterally over a large area in the middle sand area. Meanwhile, the rest of the field continues to migrate downward in the aquifer. Then, 500 days later, the middle sand area and its vicinity had encompassed nearly half of the polluted area, which indicates that the permeable layer with a high permeability coefficient has a very good adsorption effect on the pollutants. At this juncture, the pollution field has already migrated out of the model range and spreads to a deeper and wider area. Therefore, it is very necessary to control the migration of pollution sources as early as possible. In Figure 2, the overall contaminated area gradually increases with time, but the dark blue heavily contaminated area is gradually decreasing. Which is due to the continuous diffusion of Cr-contaminated solutes to the surrounding area, resulting in a slight decrease in the concentration of the center of the contamination.