## 3 Materials and Methods
### Campaigns with Industrial Iron Precipitation Residues
Test data considered are mass loss and chemical analysis of the final material. Considering the chemical analyses of the used iron precipitation residues in the mixture and the solid residues of each experiment, the calculation of extraction rates \(\mathrm{e_{EI}}\) for the elements of interest in percent was performed according to Equation (1):  
\[\mathrm{e_{EI}}=\left(1-\frac{\mathrm{x_{EI(Fin)}*m_{Fin}}}{\mathrm{x_{EI(Res)}* m_{Start}*f_{R}}}\right)*100\% \tag{1}\]  
where \(\mathrm{m_{Start}}\) is the mass of the mixture (g), \(f_{\mathrm{R}}\) is the respective share of precipitation residue in the mixture, and \(\mathrm{m_{Fin}}\) represents the mass of final solid residue from the chlorination treatment (g). Furthermore, \(\mathrm{x_{EI(Res)}}\) represents the concentration of element El in the iron precipitation residue (wt %), and \(\mathrm{x_{EI(Fin)}}\) represents the concentration of element El in the final solid residue (wt %). Due to the high number of calculated extraction rates in trials with residues for the zinc industry and the resulting difficulty in evaluating the overall process performance, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Concentration** & & & & & & \\
**[wt \%]** & & & & & & \\ \hline \multicolumn{8}{c}{Structural Elements} \\ \hline Fe & 25.6 \(\pm\) 1.8 & 29.1 \(\pm\) 1.9 & 36.6 \(\pm\) 0.3 & 39.9 \(\pm\) 1.7 & 36.6 \(\pm\) 1.3 & 61.9 \(\pm\) 2.3 \\ S & 13.83 \(\pm\) 0.24 & 7.16 \(\pm\) 0.33 & 6.38 \(\pm\) 0.08 & 7.86 \(\pm\) 0.04 & 6.61 \(\pm\) 0.02 & 0.19 \(\pm\) 0 \\ K & 2.77 \(\pm\) 0.05 & 0.2 \(\pm\) 0 & 0.08 \(\pm\) 0.01 & 4.03 \(\pm\) 0.05 & 0.23 \(\pm\) 0.05 & 0.12 \(\pm\) 0 \\ Na & 1.46 \(\pm\) 0.06 & \textless{}0.05 & 0.01 \(\pm\) 0 & 2.24 \(\pm\) 0.15 & 0.06 \(\pm\) 0.01 & 0.15 \(\pm\) 0.01 \\ Ca & 0.53 \(\pm\) 0.02 & 4.78 \(\pm\) 0.24 & 0.01 \(\pm\) 0 & 0.78 \(\pm\) 0.01 & 6.08 \(\pm\) 0.03 & 0.01 \(\pm\) 0 \\ As & 0.42 \(\pm\) 0.01 & 0.19 \(\pm\) 0.01 & 0.26 \(\pm\) 0 & 0.63 \(\pm\) 0.01 & 0.23 \(\pm\) 0 & 0.45 \(\pm\) 0.01 \\ Mg & 0.19 \(\pm\) 0 & 0.15 \(\pm\) 0 & \textless{}0.01 & 0.30 \(\pm\) 0 & 0.18 \(\pm\) 0 & \textless{}0.01 \\ Al & 0.37 \(\pm\) 0 & 0.89 \(\pm\) 0.03 & 0.19 \(\pm\) 0.02 & 0.56 \(\pm\) 0 & 1.10 \(\pm\) 0 & 0.26 \(\pm\) 0 \\ \hline \multicolumn{8}{c}{Valuable Elements} \\ \hline Zn & 3.57 \(\pm\) 0.07 & 9.60 \(\pm\) 0.21 & 0 & 5.37 \(\pm\) 0.05 & 11.90 \(\pm\) 0.08 & 0 \\ Pb & 1.26 \(\pm\) 0 & 0.68 \(\pm\) 0 & 0.06 \(\pm\) 0 & 1.9 \(\pm\) 0 & 0.84 \(\pm\) 0 & 0.08 \(\pm\) 0 \\ Ni & & & 3.08 \(\pm\) 0.04 & & & 5.43 \(\pm\) 0.26 \\ \hline \multicolumn{8}{c}{[ppm]} \\ \hline In & 591 \(\pm\) 3 & 410 \(\pm\) 9 & 0 & 882 \(\pm\) 11 & 495 \(\pm\) 9 & 0 \\ Ag & 282 \(\pm\) 40 & 136 \(\pm\) 32 & 0 & 403 \(\pm\) 79 & 194 \(\pm\) 26 & 0 \\ Cu & 2713 \(\pm\) 25 & 9113 \(\pm\) 67 & 47 \(\pm\) 2 & 4053 \(\pm\) 5 & 11,000 & 68 \(\pm\) 2 \\ Sn & 1703 \(\pm\) 26 & 308 \(\pm\) 6 & \textless{}20 & 2617 \(\pm\) 52 & 376 \(\pm\) 5 & \textless{}20 \\ Bi & 941 \(\pm\) 8 & 181 \(\pm\) 2 & 17 \(\pm\) 1 & 1440 \(\pm\) 20 & 224 \(\pm\) 3 & 28 \(\pm\) 0 \\ \hline \multicolumn{8}{c}{[ppb]} \\ \hline Au & 367 \(\pm\) 9 & 264 \(\pm\) 13 & 73 \(\pm\) 10 & 547 \(\pm\) 18 & 333 \(\pm\) 103 & 114 \(\pm\) 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Chemical analysis of the investigated original and calcined iron precipitation residues. an evaluation factor was calculated that summarizes the respective extraction rates as a function of the element concentration and the current market price of the metals. The factor (Equation (2)) is referred to as valex (value extraction) and enables the evaluation of the tests in monetary terms with regard to the simultaneous recovery of all considered valuable metals. The elements considered in calculating the valex values were In, Ag, Zn, Pb, Cu, Sn, Au, and Bi. The calculated valex factor ranges from 0 to 1 whereby it has to be stated that the amount of residue in the mixture is not considered, therefore giving only information of the extraction itself but not on the actual economic performance.