## 4 Model
### Model Validation  
In order to derive the kinetic parameter values. we preliminary fitted the experimental curves of the adsorption phase, in the absence of O\({}_{2}\) in the feed on the basis of data reported in [48] that were obtained at different temperatures and contact times. The values of kinetic parameters obtained are given in Table 3, together with the value of the regression factor, SRMSE. The SRMSE value suggests that the agreement between the two curves is quite satisfactory being \(\leq\)0.045 [53]. In Figure 5a, the comparison between the experimental and the model outlet CO and CO\({}_{2}\) concentrations during the adsorption are shown as a function of time. In Figure 5b, the reaction rate of CO consumption is compared with the experimental rate. Both figures show a very good agreement between experimental and model results. Trends of the site concentrations were also computed from the model. In Figure 5c the temporal evolution of the site concentrations is shown. It is found that at the end of the reaction, Cu sites in the oxidized form are completely consumed (\(\theta_{1}=0\)). Parts of them are covered by CO (\(\theta_{2}\)) and parts of them are simply reduced (\(\theta_{4}\)). It is worth noting that CO\({}_{2}\) is still present over the Ce sites (\(\theta_{3}\)) and the Ce sites are only partially reduced, since the concentration of oxidized sites is higher than zero (\(\theta_{5}\)). Furthermore, from the trend of \(\theta_{5}\), it is possible to follow the O transfer from Ce sites to Cu sites, which allows for CO adsorption. \(\theta_{5}\) (\(\sigma\)'-O) first decreases, driving the CO\({}_{2}\) formation through step 2 and then it increases, since it is restored by CO\({}_{2}\) desorption (step 3). The O transfer is then facilitated by the CO-CO\({}_{2}\) cycle occurring over the catalyst surface and by step 5, which eventually allows for the reduction of Ce based sites (\(\theta_{5}\rightarrow\theta_{6}\)). At the end of the run (\(\sim\)400 s), CO\({}_{2}\) is almost completely desorbed (\(\theta_{3}\approx 0\)). From these results, it turns out that the controlling parameter is O availability/mobility. After the adsorption phase, O\({}_{2}\) is fed to the reactor in order to re-oxidize the catalyst sites. According to our trap experiment (Figure 3), the adsorption step is stopped at about 45 s (CO \(\approx\) 100 ppm). To quantify the kinetic parameters of the oxidation reactions of the mechanism (steps 6 and 7), we fitted the experimental curves. It is worth noting that in the experiments there is a time delay between the adsorption phase and the oxidation phase in which the catalyst is under CO/CO\({}_{2}\)/N\({}_{2}\) atmosphere at isothermal conditions. In Figure 6, the comparison between the experimental and the model curves during the oxidation are shown. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Step** & **Kinetic Constant (ki\({}_{i}\), 1/s)** & **Activation Energy (Ei\({}_{i}\), J/K mol)** \\ \hline \(1\) & 120 & 30,000 \\ \(-1\) & 60,000 & 33,000 \\ \(2\) & 10,000 & 32,000 \\ \(3\) & 6000 & 32,000 \\ \(4\) & 50 & 25,000 \\ \hline \hline \end{tabular} Root mean square error (SRMSE) = 0.021  
\end{table} 
Table 3: Kinetic parameters of steps 1–4. Figure 5: Experimental (dashed lines) and model (solid lines) CO and CO\({}_{2}\) concentrations (**a**) and CO reaction rate (**b**) as a function of time during the adsorption. Site concentrations (**c**) as a function of time during the adsorption. \(T=55\)\({}^{\circ}\)C, CO\({}^{in}=5000\) ppm (\(\theta_{1}\) = fraction of site i). Figure 6: Experimental (solid lines) and model (dashed lines) CO and CO\({}_{2}\) concentrations as a function of time during the oxidation. \(T=55\)\({}^{\circ}\)C, CO\({}^{in}=0\) ppm, O\({}_{2}\)\({}^{in}=5\) vol.%. The agreement between the experimental and the model curves is poor. This deviation could be explained on the basis of the model of the reactor we used.