## 4 Model
### Trap Simulation
The above results suggest that by a proper choice of the regeneration (oxidation) time, the CO trap system could work with only two reactors operated under adsorption/oxidation conditions, as shown in Figure 1.  
Figure 15: CO\({}_{2}\) (**a**) and CO (**b**) concentrations and site concentrations (Cu-containing (**c**) and ceria (**d**) sites) as functions of time, complete trap simulation. \(\tau_{1}\) = 95 s. Adsorption phase: CO\({}^{in}\) = 5000 ppm and O\({}_{2}\)\({}^{in}\) = 0. Oxidation phase: CO\({}^{in}\) = 0; O\({}_{2}\)\({}^{in}\) = 5 vol %. Time duration of the oxidation phase = 200 s.  
From the above results, it appears that the time required to reach 100 ppm is quite high (about 400 s) and that after about 200 s, CO fast reaches 85 ppm, then increasing very slowly up to 100 ppm. We then simulated the trap by fixing the time duration of both the adsorption and the oxidation phase at t = 200 s.  
In Figure 16, the CO and CO\({}_{2}\) concentrations are shown as functions of time as obtained by assuming the first cycle is stopped when CO reaches 100 ppm (about 85 s) and then by switching the feed composition every 200 s.  
After a transient phase lasting about 1000 s (corresponding to three adsorption/oxidation cycles), a periodic stable (forced) regime is attained. CO concentration is oscillating between 10 and 85 ppm. The site concentrations are plotted in Figure 16 as well. It is worth noting that the catalyst is stabilized in the oxidized form, \(\theta_{4}\) and \(\theta_{6}\) (reduced sites containing both copper and cerium and only cerium, respectively) being nearly zero. The high oxidation degree of ceria sites (\(\theta_{5}\)), oscillating between 0.8 and 0.95, thus behave as an oxygen reservoir for copper sites during the adsorption phase, promoting both CO adsorption and oxidation to CO\({}_{2}\). Figure 16: CO\({}_{2}\) (**a**) and CO (**b**) concentrations and site concentrations (Cu-containing (**c**) and ceria (**d**) sites) as functions of time, complete trap simulation. \(\tau_{1}\) = 95 s. Adsorption phase: CO\({}^{in}\) = 5000 ppm and \(O_{2}{}^{in}\) = 0. Oxidation phase: CO\({}^{in}\) = 0; \(O_{2}{}^{in}\) = 5 vol %. Time duration of both the adsorption and oxidation phases = 200 s (first adsorption excluded). It should also be noted that, during the oxidation phase, a complete desorption of CO\({}_{2}\) occurs (\(\theta_{3}\approx 0\) in the oxidation phase). Conversely, CO is not completely oxidized, since \(\theta_{2}\) is always higher than zero, even in the oxidation phase. From these results, we may conclude that the key step of the reaction mechanism at these operating conditions is the oxygen transfer from the Ce sites to the Cu sites (step 4). It is worth noting that according to this trap operation, the valves switching time is 200 s for both phases, which is compatible with the process operation. When switching from one feed to the other, unavoidable mixing can occur. In particular, when switching from the CO adsorption to the CO oxidation phase, hydrogen still present in the reactor may be mixed with the oxygen-containing stream generating a H\({}_{2}\)/O\({}_{2}\)/N\({}_{2}\) mixture. This mixture represents a loss of H\({}_{2}\) and it could in principle be flammable. Likewise, when switching from the CO oxidation phase to the CO adsorption phase, a mixture of H\({}_{2}\)/O\({}_{2}\)/N\({}_{2}\)/CO is generated which cannot be fed to the fuel cell and represents a loss of H\({}_{2}\). In order to avoid incorrect feeding and H\({}_{2}\) loss, it is crucial to optimize the delay time between the switch of the inlet/outlet valves of the two reactors of the process. It should be said that immediately after switching, a H\({}_{2}\)/O\({}_{2}\)/N\({}_{2}\)/CO could be formed. In the chosen operating conditions (oxidizing stream containing 5% O\({}_{2}\)), this mixture is not flammable, the oxygen content being lower than the H\({}_{2}\) minimum oxide concentration (MOC = 5%).