## 4 Results and Discussion
The values of the air flow rate and bubble diameters corresponding to the relative rate of bubble rise and the specific aeration intensity in laboratory experiments were established. The obtained values were taken as the initial values for calculating the component of the dependence of the flotation rate constant on the air flow rate. Based on the systematization of the obtained data, the values of the general flotation rate constants for different conditions were calculated. The values of constants for pyrite are summarized in Table 6.  
The values of constants for arsenopyrite are summarized in Table 7. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{\(Q_{A}\), m\({}^{3}\cdot\)min\({}^{-1}\)} & \multicolumn{4}{c}{**Flatation Rate Constants for the Collectors Used**} \\ \cline{2-5}  & **Collectorless** & **PNBX** & **PNBX + SBDTP** & **P BX + SBDTP** \\  & **Flatation** & **(I)** & **(II)** \\ \hline
1.97 & 8.14 & 56.33 & 94.07 & 96.89 \\
3.09 & 14.57 & 100.86 & 168.43 & 173.48 \\
3.95 & 19.79 & 136.94 & 228.69 & 235.55 \\
5.92 & 24.10 & 166.77 & 278.51 & 286.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Established flotation rate constants for pyrite. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Flatation Machine Chamber** \\ **Volume, m\({}^{3}\)** \\ \end{tabular} } & \begin{tabular}{c} **Height of the Working Area** \\ **of the Flotation Machine** \\ **Chamber, m** \\ \end{tabular} & \
\begin{tabular}{c} **Maximum Air Volume** \\ **Supplied to the Aerator,** \\ **m\({}^{3}\)/min** \\ \end{tabular} &
\begin{tabular}{c} **Cross-Sectional Area of the** \\ **Flatation Machine** \\ **Chamber, m\({}^{2}\)** \\ \end{tabular} \\ \hline
25.0 & 3.8 & 13.0 & 6.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulated flotation cell’s parameters. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{3}{c}{**Parameters of the Laboratory Flotation Machine**} \\ \hline \(Q_{A}\), m\({}^{3}\cdot\)min\({}^{-1}\) & \(A_{cell}\), m\({}^{2}\) & \(d_{32}\), m & \(Sb\) \\ \hline
0.008 & 0.017 & 0.009 & 315.58 \\ \hline \hline \multicolumn{3}{c}{Operating parameters of an industrial plant for an identical value of bubble rise rate} \\ \hline
3.09 & 6.58 & 0.0089 & 315.58 \\ \hline \multicolumn{3}{c}{Industrial plant parameters for various air flow rates and bubble diameters} \\ \hline
2.4 & 6.58 & 0.0123 & 177.28 \\
4.8 & 6.58 & 0.0138 & 317.42 \\
7.2 & 6.58 & 0.0152 & 430.99 \\
9.6 & 6.58 & 0.0167 & 524.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameters for modeling of gas distribution in flotation cell. the foam and its destruction. However, after the stage of the sharp decline, there is a stabilization of the foam layer and a gradual increase in the content and yield of the froth product. After the air supply, the flotation process reaches the stationary mode in 26.1 min of simulation time. In the second stage, the effect of changes in the productivity of the flotation operation on the feed and air flow rate was evaluated. In addition, the foam height and concentrate productivity were investigated. In the simulation mode, we simulated changes in the power supply performance one by one and then simulated changes in the air flow rate. The values of changes for the supply and air flow rate were 10% of the initial values. A graphical interpretation of the obtained results is shown in Figures 11-16. Figure 11: Concentrate mass flow rate values in the simulation. Figure 12: Froth height values in the simulation. Figure 14: FeS\({}_{2}\) concentrate grade values in the simulation. Figure 13: FeS\({}_{2}\) concentrate recovery values in the simulation. Figure 15: FeAsS concentrate recovery values in the simulation. Through the results of the simulation, it is established that, at an interval from 0 min till 4.5 min, the difference in the responses on the change in parameters is insignificant.