## 3 Results and Discussion
### Kinetic Modelling
#### 3.5.4 Stability and Deactivation  
Glycerol and ethylene carbonate are hygroscopic, and this is also evident in the smectite. Therefore, water tends to accumulate in the pores and the inner surface of the clay, and hydrolytic reactions are also possible at these moderate temperatures, competing with the transcarbonation process. Moreover, though all alkaline catalysts are active in this process, their progressive neutralization in the presence of carbon dioxide (in the air) reduces their activity. In this case, carbonate sites become bicarbonate sites, with a notable reduction in their pK\({}_{\text{b}}\). To further study the deactivation phenomenon, we have applied the proposed kinetic model to datasets at diverse operation temperature for several cycles. In this case, the equation also include a first-order total deactivation of the catalyst [44; 49]. Here, k\({}_{\text{d}}\) is the first-order deactivation kinetic constant. Therefore, the kinetic Equation (8) is modified to include k decreasing in the following form:  
\[\frac{dx}{dt}=k\cdot\frac{C_{cat}\cdot exp(-k_{d}\cdot t)}{K_{cat}+C_{cat}}\cdot C _{Gly0}\cdot(1-X)\cdot(M-X) \tag{10}\]  
Figure 17 shows the variation of the kinetic constant k and the deactivation constant k\({}_{\text{d}}\) with the number of cycles at different temperatures from 80 to 110 \({}^{\circ}\)C. We can observe  
Figure 16: Glycerol conversion (X\({}_{Gly}\)) in the transesterification reaction of glycerol with ethylene carbonate catalyzed by Tunisian smectite at different temperatures (\(\blacksquare\): 80 \({}^{\circ}\)C; \(\bullet\): 90 \({}^{\circ}\)C; \(\blacktriangle\): 100 \({}^{\circ}\)C and \(\blacktriangledown\): 110 \({}^{\circ}\)C).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{k_{0}}\) & \(\mathbf{E_{g}/R}\) & \(\mathbf{RSS}\) & \(\mathbf{S_{e}}\) & \(\mathbf{VE\ \%}\) & \(\mathbf{F}\) \\ \hline
18.09 \(\pm\) 0.68 & 9077 \(\pm\) 251 & 0.0697 & 3.47\% & 98.62 & 7444 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Statistical parameters calculated by fitting the sigmoidal model to different sets of experimental data at varying temperatures. Residual sum of squares (RSS), standard error of estimate (Se), percentage of variation explained (VE %) and Fisher’s F value (F).  
that there is an activation from the first to the second cycle at all temperatures, but this is more evident at the highest temperature (a notable increase in the k value). The constant k decreases in the third and fourth cycles until it reaches its original value at all operation temperatures. For example, at 110 \({}^{\circ}\)C, which is chosen as the best temperature for this system, the rate constant k increases from 3.7\(\cdot\)10\({}^{-3}\) min\({}^{-1}\) after the first cycle to 1.1\(\cdot\)10\({}^{-2}\) min\({}^{-1}\) with the end of the second cycle, however it decreases to 3.8\(\cdot\)10\({}^{-3}\) min\({}^{-1}\) after the fourth cycle. If we consider the deactivation constant k\({}_{\rm d}\), it shows a significant decrease from 4.1\(\cdot\)10\({}^{-2}\) min\({}^{-1}\) in the second cycle to 1.6\(\cdot\)10\({}^{-2}\) min\({}^{-1}\) in the fourth cycle at 100 \({}^{\circ}\)C, while it increases at all other operation temperatures from one cycle to the next one. Again, as expected, the catalyst activation and deactivation is much more evident at the highest temperature, but it is interesting to observe that the deactivation rapidly decreases from one cycle to the other, suggesting a progressive stabilization of the remaining activity of the smectite. This is in agreement with the stabilization of the yield to glycerol carbonate and ethylene glycol at 4 h at 75-80%.