## 3 Results
Figure 3a-c shows that the acid concentration increases and the amount of cobalt in the composition increases, the conversion of the benzothiophene increases. This may be due to the substitution of magnesium ion by hydrogen ion, as well as an increase in the acid centers of the support. Literature analysis showed that there is no data on the effect of acid concentration on chrysotile activity during benzothiophene hydrogenation. Figure 3: Dot plots and approximation curves. Dependence of the yield of benzothiophene hydrogenation products on: (a)—HCl concentration, mol/L; (b) is the ratio of HCl concentration to nickel concentration; (c)—ratio of HCl concentration to cobalt concentration. After the selection of partial dependencies, their calculated values at matrix levels were combined into the separate table (Table 6). Having determined the significance of particular functions, the generalized Protodyakonov equation was used for each optimization parameter:  
\[Y_{p}=\frac{\prod\limits_{i=1}^{n}Y_{i}}{Y_{av.}^{n-1}} \tag{3}\]  
where \(Y_{p}\)--generalized function, \(Y_{i}\)--private function, \(\prod\limits_{i=1}^{n}\)--product of all private functions, \(Y_{av. }\)--total average of all considered values. Using the generalized Protodyakonov Equation (4), the theoretical data were calculated, which were checked for significance by comparing the calculated results with the experimental data:  
\[Y_{p}=\frac{0.98e^{0.06222X_{2}}X_{2}^{-0.6524}\cdot\left(0.7928X_{1}^{2}-0.809 X_{1}+0.5725\right)\cdot 0.5369e^{0.04074X_{3}}X_{3}^{-0.2822}}{0.2033} \tag{4}\]  
Table 7 shows the comparison of the calculated hydrogenate yield values with the actual experimental values. According to the data captured in Table 7, the correlation coefficient R = 0.9849 and the significance \(\mathrm{t_{R}}\) = 73.48 were found using Formulas (1) and (2). From Equation (4), the optimal catalyst preparation parameters for the highest catalyst activity were calculated:  
- the hydrochloric acid concentration equal to 1 M;  
- the ratio of HCl concentration to nickel concentration (\(\mathrm{C_{HCl}}/\mathrm{C_{N\! {}^{2+}}}\))--20 (nickel weight (in terms of pure nickel) equal to 21.96% of the support weight);  
- the ratio of HCl concentration to cobalt concentration (\(\mathrm{C_{HCl}}/\mathrm{C_{C\! {}^{3+}}}\))--20 (cobalt weight (in terms of pure cobalt) equal to 29.47% of the support weight). The results of the reaction of the hydrogenation of benzothiophene with the catalyst prepared according to the above conditions are as follows: \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Function**} & \multicolumn{3}{c}{**Levels**} & \multirow{2}{*}{**R**} & \multirow{2}{*}{**t\({}_{\text{R}}\)**} \\ \cline{2-2} \cline{4-6}  & **1** & & & **2** & **3** \\ \hline Y = 0.7928\(X_{1}^{2}-0.809X_{1}+0.5725\) & 0.4424 & 0.3725 & 0.5563 & R = 1.0000 & t\({}_{\text{R}}\) = 100 \\ Y = 0.98e\({}^{0.06222X_{2}}X_{2}^{-0.6524}\) & 0.4681 & 0.4065 & 0.4818 & R = 1.0000 & t\({}_{\text{R}}\) = 100 \\ Y = 0.5369e\({}^{0.04074X_{3}}X_{3}^{-0.2822}\) & 0.4179 & 0.4213 & 0.5207 & R = 1.0000 & t\({}_{\text{R}}\) = 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Calculated values of the partial functions for Y\({}_{\text{P}}\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Experience No.** & **Experimental Values (Y\({}_{e}\))** & **Calculated Values (Y\({}_{\text{P}}\))** \\ \hline
1 & 0.4218 & 0.4333 \\
2 & 0.3746 & 0.3692 \\
3 & 0.5480 & 0.5205 \\
4 & 0.3843 & 0.3717 \\
5 & 0.3733 & 0.3878 \\
6 & 0.3604 & 0.3541 \\
7 & 0.6901 & 0.6864 \\
8 & 0.4802 & 0.4638 \\
9 & 0.5194 & 0.5341 \\ \hline \hline \end{tabular} Note: Y\({}_{\text{P}}\)—[PERSON] calculated hydrogenate yield.  
\end{table} 
Table 7: Experimental and design values of hydrogenate yield. - & hydrogenate yield (benzothiophene conversion)--69.01%;
- & 2,3-dihydrobenzothiophene yield--3.52%;
- & ethylbenzene yield--63.52%. An increase in temperature above 400 \({}^{\circ}\)C led to an increase in the yield of by-products (mercaptan, diphenyl)] [12].