## 3 Results and Discussion
### Automated Column Sorption System
#### 3.2.5 Breakthrough Curve, Capacity and Usage Rate Analysis
The overall column performance efficiency and its relationship between breakthrough capacity (C\({}_{\text{BP}}\)) and exhaustion capacity (C\({}_{\text{EP}}\)) of each sorption column are unique to the individual HMIs selected. As observed in the data displayed Table 6 and the trends visualized in Figure 3, the EP is only attained by Ni\({}^{2+}\); the remaining four HMIs have yet to reach this point due to the constraints of the 3-h analysis period. Evidently, the optimization of future works would be to prolong the service time in order to quantify the overall columns' performance efficiency. Qualitatively speaking, for both columns' effluent and total waste (TW), the Pb\({}^{2+}\) ion is completely removed throughout the analysis period, demonstrating the utmost efficiency; neither BP nor EP are attained. On the opposite end of the spectrum, the Ni\({}^{2+}\) ion reaches exhaustion quite rapidly. The volume of the effluent treated at breakthrough (V\({}_{\text{BP}}\)) is determined with the use of the mean flow rates of 8.18 mL/min (Q\({}_{\text{C1}}\)) and 5.39 mL/min (Q\({}_{\text{C2}}\)) for the sorption columns C1 and C2, respectively. These flow rates are applied to the time data of Table 4, at which BP (approximately 95% removal or 5% of the 2.0 meq/L influent concentration per HMI) is observed; as indicated by the superscript in Table 6. The 2:26 mins time required for inlet priming to the base of C1 as well as the 24:08 min:s time observed for solute contact to the base of C2 are deducted from these BP times. As summarized in Table 7, the approximate effluent volumes treated at BP (V\({}_{\text{BP}}\)) are provided for both sorption columns and each HMI selected; based on the zeolite mass in each bed (m) of 152.10 g, Equations (2) and (5) are employed to determine the corresponding breakthrough capacity (C\({}_{\text{BP}}\)) and usage rate (v\({}_{\text{U}}\)), respectively. The Pb\({}^{2+}\) and Fe\({}^{3+}\) ions are completely removed in sorption column C2, which essentially transforms the influent stock of a five HMI multi-component solution to a triple-component solution \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**HMI**} & \multicolumn{3}{c}{**Sorption Column 1**} & \multicolumn{3}{c}{**Sorption Column 2**} \\ \cline{2-7}  & **V\({}_{\text{BP,1}}\) (L)** & **C\({}_{\text{BP,1}}\) (meq/g)** & **v\({}_{\text{U,1}}\) (g/L)** & **V\({}_{\text{BP,2}}\) (L)** & **C\({}_{\text{BP,2}}\) (meq/g)** & **v\({}_{\text{U,2}}\) (g/L)** \\ \hline Cu\({}^{2+}\) & 0.3295 & 0.00433 & 461.67 & 0.7257 & 0.00954 & 209.59 \\ Fe\({}^{3+}\) & 0.9926 & 0.01305 & 153.24 & - & - & - \\ Ni\({}^{2+}\) & 0.1342 & 0.00176 & 1133.54 & 0.3547 & 0.00466 & 428.80 \\ Pb\({}^{2+}\) & - & - & - & - & - & - \\ Zn\({}^{2+}\) & 0.1342 & 0.00176 & 1133.54 & 0.5380 & 0.00707 & 282.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: System breakthrough point performance. containing Cu\({}^{2+}\), Ni\({}^{2+}\), and Zn\({}^{2+}\) ions within the 3-h analysis period. The zeolite does not have to address the competition of the two preferred HMIs, which provides greater sorption site availability for the three HMIs remaining in solution. It is important to develop a relationship between the EBCT and usage rate. The time that the fluid element is in contact with the zeolite bed in sorption column C2 is ten minutes greater than the detention time in C1. This thereby demonstrates a stronger overall treatment availability in C2; reflected in the average 195.2% increase of bed capacity at breakthrough and the average 63.94% decrease in usage rate of the zeolite between the columns; based on the trends observed for the Cu\({}^{2+}\), Ni\({}^{2+}\) and Zn\({}^{2+}\) ions detected in solution. Evidently, the columns' usage rate provides significant insight into the operation and management required for this unique sorption system.