## 4 Model
### Adsorption Phase: Effect of the Operating Parameters  
In order to study the effect of the parameters on the performances of the adsorption phase, we computed the CO and CO\({}_{2}\) outlet concentrations by varying the contact time and the CO inlet concentration. In Figure 7, the CO and CO\({}_{2}\) outlet concentrations are shown as a function of time as computed at different values of the residence time of the reactor, R.  
As expected, when increasing the residence time, CO outlet concentration decreases at any given time and the time length at which CO outlet concentration is lower than 100 ppm increases. The CO\({}_{2}\) outlet concentration increases even more than expected due to the non-linear behavior of residence time with respect to CO\({}_{2}\)/CO ratio observed and explained in [48]. In Figure 8, the time at which CO outlet concentration is equal to 100 ppm is plotted versus the residence time of reactor R.  
When increasing the residence time, the duration of the adsorption phase may potentially increase up to more than 1 min for a residence time of 300 s. Nevertheless, the figure also shows clear changes of the slope by increasing the residence time, due to non-linear behavior of the reactive adsorption on the CuO/CeO\({}_{2}\) catalyst [48]. In Figure 9, the CO and CO\({}_{2}\) outlet concentrations are plotted versus time as calculated at different values of CO inlet concentration. When increasing the CO content in the feed mixture, the time at 100 ppm significantly decreases, as expected. Nevertheless, the same does not occur for CO\({}_{2}\) at high values of CO inlet concentration. The amount of CO\({}_{2}\) released at 5000 ppm CO approaches that released for 7000 ppm. This effect can be considered opposite to that produced by the increase of residence time observed in [1] and highlights the limiting step of CO\({}_{2}\) oxidation and desorption. In other words, transfer of CO\({}_{2}\) from \(\theta_{2}\) to \(\theta_{3}\) sites with subsequent CO\({}_{2}\) desorption and reduction of \(\theta_{1}\) sites into \(\theta_{4}\) sites has a plateau value likely related to vicinity of Cu\({}^{2+}\)-O\({}^{2-}\)-Ce\({}^{4+}\) sites and Ce\({}^{4+}\)-O\({}^{2-}\)-Ce\({}^{4+}\) sites, which is a measure of copper dispersion. On the other hand, CO adsorption can still continue on copper/ceria sites not able to oxidize CO and transfer CO\({}_{2}\). In Figure 10, the time at which the CO outlet concentration is equal to 100 ppm is plotted versus the CO inlet concentration, showing that upon increasing the CO inlet concentration, the time duration of the adsorption phase should be lower and lower. It is worth noting that due to the non-linear \begin{table}
\begin{tabular}{c c c} \hline \hline
**Step** & **Kinetic Constant (k\({}_{i}\), (m\({}^{3}\)/mol)\({}^{0.5}\) s)** & **Activation Energy (E\({}_{i}\), J/K mol)** \\ \hline
5 & 50 & 21,000 \\
6 & 5 & 22,000 \\ \hline \multicolumn{3}{c}{SRMSE = 0.35} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Kinetic parameters of steps 5 and 6.  
behavior of the CO reactive adsorption on the CuO/CeO\({}_{2}\) catalyst, the adsorption time is significantly higher than expected in absence of CO reaction and CO\({}_{2}\) release (dashed line in Figure 10). In Figure 11, the site concentrations are plotted as calculated for all the CO\({}^{\text{in}}\) concentrations. It appears that at the highest values of CO\({}^{\text{in}}\) (5000 and 7000 ppm), the sites distribution almost overlaps, suggesting a saturation of the catalyst sites. Figure 7: CO (**a**) and CO\({}_{2}\) (**b**) outlet concentrations versus time at different values of the residence time (model results). CO\({}^{\text{in}}\) = 5000 ppm; \(T\) = 55 \({}^{\circ}\)C.  
Figure 8: Time at which CO outlet concentration is equal to 100 ppm as a function of the reactor residence time, \(\tau_{1}\). \(CO^{in}=5000\) ppm; \(T=55\)\({}^{\circ}\)C.  
Figure 9: CO (**a**) and CO\({}_{2}\) (**b**) outlet concentrations versus time at different values of the CO inlet concentration (model results).