# Green Production of Glycerol Ketals with a Clay-Based Heterogeneous Acid Catalyst
## 3 Results and Discussion
### Glycerol Ketalization Kinetic Studies
#### 3.3.4 Kinetic Model Fitting
It seems that the activation energies depend notably on the ketone statistical parameters, changing between 60 and 80 kJ/mol for the ketalization and hydrolysis reactions in systems 1 and 3, and being in excess of 100 kJ/mol for the less active system 2 (MEK or butanone). These results are, in any case, within the range of values observed in literature for the solketal system (system 1), which are between 56 and 127 kJ/mol [17; 41]. In any case, temperature affects more deeply the reaction rate in the less active system than in the other two. If considering the activity remaining at infinitum time (\(\beta\)), as observed also in Section 3.3.3, acetone and solketal affect the catalyst activity in a lower degree than the other ketones and ketals, remaining almost 43% of the original activity after the progressive deactivation process. For MEK and cyclohexanone only 12-13% of the initial activity remains. A possible blockage due to the ketal and/or the ketone can be suggested in this case. It must be considered that higher amounts of isopropanol (almost twice as much as in system 1) were needed for system 2 and 3 to get a homogeneous system, indicating a more hydrophobic nature of MEK and cyclohexanone. A relatively hydrophobic solid could strongly adsorb such ketones (and even their ketals) with the subsequent blockage deactivation. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameter** & **System 1** & **System 2** & **System 3** \\ \hline Ln k\({}_{\text{d1}}\) & 12.61 \(\pm\) 0.25 & 27.61 \(\pm\) 0.8 & 12.88 \(\pm\) 0.13 \\ E\({}_{\text{a}}\)/R (k\({}_{1}\)) & 7869 \(\pm\) 77 & 12,665 \(\pm\) 25 & 8477 \(\pm\) 43 \\ Ln k\({}_{\text{d2}}\) & 15.65 \(\pm\) 0.72 & 36.70 \(\pm\) 0.68 & 20.12 \(\pm\) 0.19 \\ E\({}_{\text{a}}\)/R (k\({}_{2}\)) & 8497 \(\pm\) 214 & 15,487 \(\pm\) 223 & 10,446 \(\pm\) 61 \\ Ln k\({}_{\text{dd}}\) & 24.88 \(\pm\) 2.24 & 19.76 \(\pm\) 0.18 & 19.74 \(\pm\) 0.30 \\ E\({}_{\text{a}}\)/R (k\({}_{\text{d}}\)) & 9944 \(\pm\) 687 & 8360 \(\pm\) 57 & 10,446 \(\pm\) 61 \\ \(\beta\) & 0.425 \(\pm\) 0.09 & 0.117 \(\pm\) 0.07 & 0.134 \(\pm\) 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Kinetic parameters for the model fitted to all data from acetone (system 1), MEK (system 2) and cyclohexanone (system 3) ketalization reactions with glycerol. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameter** & **System 1** & **System 2** & **System 3** \\ \hline N & 1869 & 2880 & 2404 \\ K & 7 & 7 & 7 \\ DF & 1862 & 2873 & 2397 \\ SSR & 1.53 & 0.904 & 1.533 \\ RMSE & 0.0292 & 0.0198 & 0.0175 \\ F-value & 138,148 & 423,794 & 323,899 \\ VE (\%) & 98.86 & 98.26 & 99.41 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Goodness-of-fit parameters for the kinetic model for acetone (system 1), MEK or butanone (system 2) and cyclohexanone (system 3) ketalization reactions with glycerol. Figure 16: Fit of the proposed kinetic model to all data from system 1 (acetone+glycerol). Points correspond to the experimental data while lines show the fit of the model to such data. Figure 17: Fit of the proposed kinetic model to all data from system 2 (MEK+glycerol). Points correspond to the experimental data while lines show the fit of the model to such data. Figure 18: Fit of the proposed kinetic model to all data from system 3 (cyclohexanone+glycerol). Points correspond to the experimental data while lines show the fit of the model to such data. All kinetic parameters have narrow error intervals (low standard errors) at 95% confidence, regardless of the reaction system being considered. Therefore, considering all physical and statistical criteria, the kinetic model here proposed, in spite of its simplicity, can be fitted adequately to a wide experimental range for the three systems. Finally, Table 5 shows the estimated values of the kinetic constants and parameters from the minimal and maximal temperature values of the range studied here.