## 3 Results and Discussions  
The mathematical equations describing the evolution of the washing process using chitosan solution, which were obtained as a result of the proposed algorithm, are shown in Table 3 as a function of the metal removed from the soil and the two concentrations of the chitosan-containing washing solutions that were investigated: 2% and 5%, respectively. For each mathematical model, the values of the R-squared (R2) and adjusted R-squared coefficients (R2 adj) were calculated and included in Table 3.  
By analyzing the four equations of the second-degree polynomial mathematical models, it can be observed that the coefficients of the \({X_{2}}^{2}\) variables have very small values. Therefore, in order to simplify the models, they can be considered as equal to zero. In this case, the \({b_{22}}{X_{2}}^{2}\) terms will disappear from the model equations. This approach is also supported by the fact that when the adjusted R-squared coefficients (R2 adj) were calculated for the new models (in which the \({X_{2}}^{2}\) terms no longer appear), the values of these coefficients compared to the initial ones indicate that the influence of the \({X_{2}}^{2}\) terms was insignificant. This is because the new coefficients R2 adj have higher values than the initial ones. The graphical representation of the obtained mathematical relationships that describe the evolution of the washing process using chitosan solution are indicated in Figures 1 and 2. Figure 1: Cu removal efficiency using chitosan for (**a**) C = 2% and (**b**) C = 5%. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Metal**} & \multirow{2}{*}{
\begin{tabular}{c} **The Chitosan Concentration in** \\ **Washing Solution** \\ \end{tabular} } & \multicolumn{2}{c}{**Mathematical Equation**} \\ \hline \multirow{4}{*}{**Cu**} & \multirow{2}{*}{2\%} & \(Y=23.703+93.403{X_{1}}+0.958{X_{2}}-1.509\)\({X_{1}}{X_{2}}-505.425{X_{1}}^{2}-0.006{X_{2}}^{2}\) \\  & & \(\text{R}^{2}=0.472\) & \(\text{R}^{2}\text{adj}=0.578\) \\  & & \(\text{Y}=33.389-54.511{X_{1}}+2.264{X_{2}}-0.471{X_{1}}{X_{2}}+76.708{X_{1}}^{ 2}-0.037{X_{2}}^{2}\) \\  & & \(\text{R}^{2}=0.694\) & \(\text{R}^{2}\text{adj}=0.335\) \\  & & \(\text{Y}=19.531+190.82{X_{1}}+2.313{X_{2}}-1.109{X_{1}}{X_{2}}-546.364{X_{1}}^{ 2}-0.03{X_{2}}^{2}\) \\  & & \(\text{R}^{2}=0.887\) & \(\text{R}^{2}\text{adj}=0.124\) \\  & & \(\text{Y}=30.606+86.089{X_{1}}+1.809{X_{2}}-0.547{X_{1}}{X_{2}}-357.542{X_{1}}^{ 2}-0.023{X_{2}}^{2}\) \\  & & \(\text{R}^{2}=0.875\) & \(\text{R}^{2}\text{adj}=0.136\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mathematical relationships that describe the evolution of the depollution process by washing the soil with chitosan solution. Thus, the graphical representation of the dependence of copper removal efficiency on the two variables of the washing process (stirring time and S/L ratios) indicates that the efficiency of copper removal from the soil gradually increases with an increase of the stirring time of the contaminated soil with washing solution containing chitosan (Figure 1). By increasing the chitosan concentration in washing solution from 2% to 5%, a great improvement of the copper removal efficiency could be observed, in agreement with experimental data and the results reported by other researchers [6]. A previously published work [46] reported that high concentrations of washing solution containing chitosan or other chelating agents could provide more binding sites for metals, resulting in an increase in the efficiency of heavy metal removal from the soil. Furthermore, the highest copper removal efficiencies (52.51% and 62.59% in the case of the 2% and 5% washing solution concentrations, respectively) are obtained at a S/L ratio of 0.0625 dec.fr. Therefore, the removal efficiency of copper increases as the stirring time of the contaminated soil as the washing solution containing 2% chitosan increases, and the S/L ratio decreases from 0.2 to 0.0625 dec.fr.