# Technological Aspects of Sintering Low-Quality Wolframite Concentrate with Potassium Carbonate
## 2 Materials and Methods
During the simulation, the thermodynamic properties of gases--N\({}_{2}\), CO\({}_{2}\), O\({}_{2}\), SO\({}_{2}\), oxides--MnWO\({}_{4}\), FeWO\({}_{4}\), FeO, Fe\({}_{2}\)O\({}_{3}\), Fe\({}_{2}\)O\({}_{3}\), MnO\({}_{2}\)O\({}_{3}\), Mn\({}_{3}\)O\({}_{4}\), MnMoO\({}_{4}\), Fe\({}_{2}\) were taken into account, along with MnO\({}_{4}\), MoO\({}_{3}\), FeMoO\({}_{4}\), Al\({}_{2}\)(MoO\({}_{4}\))\({}_{3}\), SiO\({}_{2}\), Al\({}_{2}\)O\({}_{3}\), Al\({}_{2}\)SiO\({}_{5}\), CuFeO\({}_{2}\), CuMn\({}_{2}\)O\({}_{4}\), CuMoO\({}_{4}\), CuO, CuGe\({}_{2}\)O\({}_{3}\), Na\({}_{2}\)CO\({}_{3}\), Na\({}_{2}\)WO\({}_{4}\), NaAlO\({}_{2}\), NaAlSiO\({}_{4}\), NaFeO\({}_{2}\), Na\({}_{2}\)MoO\({}_{4}\), NaSiO\({}_{3}\), K\({}_{2}\)CO\({}_{3}\), K\({}_{2}\)WO\({}_{4}\), KAlO\({}_{2}\), KAlSiO\({}_{4}\), KFeO\({}_{2}\), K\({}_{2}\)MoO\({}_{4}\), K\({}_{2}\)SiO\({}_{3}\), sulfates--K\({}_{2}\)SO\({}_{4}\), MnSO\({}_{4}\), CuSO\({}_{4}\), Cu\({}_{2}\)SO\({}_{4}\), CuO\(\times\)CuSO\({}_{4}\), FeSO\({}_{4}\), Fe\({}_{2}\)(SO\({}_{4}\))\({}_{3}\), Na\({}_{2}\)SO\({}_{4}\), and sulfides--CuS, Cu\({}_{2}\)S, FeS\({}_{2}\). The simulation was carried out at 0.1 MPa in the temperature range of 298-1273 K when cooled in increments of 50\({}^{\circ}\). The graphical representation of the data is performed using Spline approximation (Microsoft Excel 2016 v.16.0.4266.1001). The degrees of transition of elements (\(\alpha\), %) from the initial working fluid to the target interaction products were calculated with the following equation:  
\[\alpha=100\times m_{prod}/m_{orig}, \tag{1}\]  
where \(m_{prod}\) and \(m_{orig}\)--the amount of the element in the target phase and the initial working medium, kg. Optimization of the sintering process of low-quality tungsten concentrate with sodium or potassium carbonates was carried out using a probabilistically deterministic experimental planning method based on M.M. Protodiakonov equation with the general form represented by the following dependence [19; 20]:  
\[\gamma_{\alpha}=\frac{\Sigma_{i=1}^{m}\gamma_{i}}{\gamma_{\alpha\text{p}}^{n- 1}} \tag{2}\]  
where \(\gamma_{\alpha}\) is a generalized function of the degree of tungsten extraction, \(\gamma_{i}\) is a partial function of a certain factor, \(\Sigma_{i=1}^{m}\gamma_{i}\) is the product of all partial functions, and \(\gamma_{\alpha\text{p}}^{n-1}\) is the average value of all functions raised to a power less than the number of partial functions by one. The proposed method allows us to take into account the physical meaning of the process in particular dependencies and adequately predict the process beyond changing arguments. The literature analysis using this method [21; 22; 23; 24; 25; 26] shows that empirical data are adequately described by the Protodiakonov M.M. equation. In addition, the method was used for both roasting [21] and hydrochemical [22; 23; 24; 25; 26] processes. For comparative analysis and finding the optimal parameters of the sintering process of low-quality wolframite concentrate with sodium or potassium carbonates, a three-factor matrix of experimental planning was used at five levels, with the following parameters varying accordingly: process temperature (T), duration (\(\tau\)), and reagent consumption (Q), which, according to literature data [1; 5; 6], have the main influence on the tungsten extraction rates in solution. The number of experiments (\(n\)) was determined by the number of varying levels (\(p\)) from the equality: \(n=p^{2}\). The influence of five levels of factors was taken into account (Table 2), and the matrix of the three-factor experiment included 25 experiments for systems containing Na\({}_{2}\)CO and K\({}_{2}\)CO\({}_{3}\). The determining parameter, the response function (\(\gamma_{\alpha}\)), of the efficiency of the sintering process of wolframite concentrate with alkali metal carbonates is the degree of extraction of tungsten into solution after leaching of sintering products depending on the a.m. coefficients (T, \(\tau\), Q). The model experiments were carried out as follows.