# Technological Aspects of Sintering Low-Quality Wolframite Concentrate with Potassium Carbonate
## 3 The Results and Discussion
### Thermodynamic Assessment of the Main Reactions
As a result of the approximation of experimental data (Figure 3), mathematical expressions for each particular function linking the degree of extraction of tungsten into solution with the coefficients considered were obtained. Special functions for systems containing Na2 CO3:  
\[\gamma_{T}=-418.4+1.08\cdot 10^{6}/\mathrm{T}-5.80\cdot 10^{8}/\mathrm{T}^{2}, \tag{6}\]  
\[\gamma_{\tau}=57.47+0.128\cdot\tau-5.49\cdot 10^{-4}\cdot\tau^{2}, \tag{7}\]  
\[\gamma_{Q}=1454-36.55\cdot Q+0.312\cdot Q^{2}-8.67\cdot 10^{-4}\cdot Q^{3}. \tag{8}\]  
Partial functions for K2 CO3 functions:  
\[\gamma_{T}=-224.2+4.94\cdot 10^{-4}\cdot\mathrm{T}^{2}-1.945\cdot 10^{-10}\cdot \mathrm{T}^{4}, \tag{9}\]  
\[\gamma_{\tau}=45.79+0.221\cdot\tau-5.39\cdot 10^{-4}\cdot\tau^{2}, \tag{10}\]  
\[\gamma_{Q}=142.3-2.1\cdot 10^{-2}\cdot Q^{2}+1.537\cdot 10^{-6}\cdot Q^{4}-3.40 1\cdot 10^{-11}\cdot Q^{6}. \tag{11}\]  
The generalized Protodiakonov equations (Equations (10) and (11)) included all partial functions to describe the dependence of the degree of tungsten transition into solution during sintering with Na2 CO3 (\(\gamma_{\alpha 1}\)) and K2 CO3 (\(\gamma_{\alpha 2}\)). \[\gamma_{\alpha 1}=\gamma_{T}\cdot\gamma_{\tau}\cdot\gamma_{Q}/62.5^{2}, \tag{12}\]  
\[\gamma_{\alpha 2}=\gamma_{T}\cdot\gamma_{\tau}\cdot\gamma_{Q}/56.5^{2} \tag{13}\]  
To verify the adequacy of the obtained partial dependencies and generalized equations, correlation coefficients (R) were calculated, and their significance was assessed by Student's criterion (tR). The R values of the Protodiakonov equations are 0.89 and 0.92, respectively, with their significance tR = 19.6 and 26.5, which indicates the adequacy of the description of the experimental data by Equations (12) and (13) (Table 4). The results obtained are consistent with the literature [26] on molybdenum roast and the conversion of molybdenum into solution. To select the reagent mode and sintering parameters based on the data obtained, graphical dependences of the degree of tungsten extraction on the main factors during sintering of wolframite concentrate with Na2 CO3 and K2 CO3 are also presented (Figure 4). The analysis of the results showed the advantages of using K2 CO3 at temperatures of \(-1073\)-\(1123\) K: High tungsten recovery rates (more than 95%) were achieved with an amount of K2 CO3 equal to 105-110% according to stoichiometric requirements and sintering duration of 100-120 min. When sintering a concentrate with Na2 CO3 under the same conditions, the extraction of tungsten does not exceed 70%. High extraction of tungsten (more than 95%) during sintering with Na2 CO3 was achieved with the introduction of \begin{table}
\begin{tabular}{c c c} \hline \hline
**Function** & **R** & **tR** \\ \hline \multicolumn{3}{c}{Experiment with Na2 CO3} \\ \(\gamma_{\mathrm{T}}\) & 0.97 & 24.5 \\ \(\gamma_{\mathrm{T}}\) & 0.73 & 2.69 \\ \(\gamma_{\mathrm{Q}}\) & 0.83 & 4.63 \\ \(\gamma_{\alpha 1}\) & 0.89 & 19.6 \\ \multicolumn{3}{c}{Experiment with K2 CO3} \\ \(\gamma_{\mathrm{T}}\) & 0.97 & 33.8 \\ \(\gamma_{\mathrm{T}}\) & 0.98 & 34.8 \\ \(\gamma_{\mathrm{Q}}\) & 0.84 & 4.92 \\ \(\gamma_{\alpha 2}\) & 0.92 & 26.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Correlation coefficients (R) and significance (tR) for equations of partial (6)–(11) and generalized (12) and (13) functions. carbonate in an amount of 130-140% according to stoichiometric requirements for the formation of Na\({}_{2}\)WO\({}_{4}\), Na\({}_{2}\)MoO\({}_{4}\), and Na\({}_{2}\)SO\({}_{4}\). Industrial Testing of Laboratory Data on Sintering of Wolframite Concentrate with Sodium and Potassium Carbonates  
Based on research analysis as well as thermodynamic modeling data, the basic parameters of sintering low-quality wolframite concentrate with reagents for pilot tests are proposed.