## 4 Model
### Reaction Mechanism and Kinetic Model
Thus, the kinetic constant of step (\(i\)) is:  
\[k_{i}=k^{\circ}{}_{i}\,\,exp(-E_{i}/RT) \tag{14}\]  
The unsteady balance equations on the fraction (\(\theta_{1}\), \(\theta_{2}\), \(\theta_{3}\) and \(\theta_{5}\)) read:  
\[\frac{d\theta_{1}}{dt}=-R_{1}+R_{-1}+R_{4}+R_{6} \tag{15}\]  
\[\frac{d\theta_{2}}{dt}=R_{1}-R_{-1}-R_{2} \tag{16}\]  
\[\frac{d\theta_{3}}{dt}=+R_{2}-R_{3} \tag{17}\]  
\[\frac{d\theta_{5}}{dt}=-R_{2}+R_{3}-R_{5}+R_{5} \tag{18}\]  
The total sites conservation equations complete the system:  
\[R_{3}=k_{3}\,\theta_{3} \tag{10}\]0  
\[R_{3}=k_{3}\,\theta_{3} \tag{10}\]1  
The initial conditions are:  
\[R_{3}=k_{3}\,\theta_{3} \tag{10}\]2  
\[R_{3}=k_{3}\,\theta_{3} \tag{10}\]3  
\[R_{3}=k_{3}\,\theta_{3} \tag{10}\]4  
\[R_{3}=k_{3}\,\theta_{3} \tag{10}\]5  
Regarding the balance on gas phase species, we assumed the reactor was composed by two vessels (R) and (T) (Figure 4). The vessel R is the catalytic reactor, while T is representative of the tube connecting the reactor (R) and the analyzer, whose residence time represents the delay time between gas species' exit from the reactor and their detection in the analysis system. \[R_{3}=k_{3}\,\theta_{3} \tag{10}\]6 Scheme of the reactor network. R: catalytic reactor; T: reactor-analyzer connection tube. The lab reactor used here for the tests is characterized by value of the axial Peclet (Pe) number equal to 50. This value suggests that each channel of the monolith behaves as a reactor with significant back diffusion. As a consequence, the reactor has an intermediate behavior between a plug flow reactor (PFR) and a continuous stirred tank reactor (CSTR). We used a CSTR as model reactor to simplify the fitting procedure. This choice allows a rough estimation of the kinetic parameters which can be used in the trap model to (at least qualitatively) test the idea. Further work will be focused on the development of the complete process configuration, which will take into account the real behavior of the reactor. Furthermore, transport limitations are negligible since the kinetic regime is fully maintained by keeping the operating temperature very low (55 \({}^{\circ}\)C). The CO molar balance equations in the reactor (R) and in the connecting tube (T) are the following:  
**R:**:  
\[R_{3}=k_{3}\,\theta_{3} \tag{10}\]7
**T:**:  
\[R_{3}=k_{3}\,\theta_{3} \tag{10}\]8  
The CO\({}_{2}\) molar balance equations are the following:
**R:**:  
\[R_{3}=k_{3}\,\theta_{3} \tag{10}\]9
**T:**:  
\[R_{4}=k_{4}\,\theta_{4}\,\theta_{5} \tag{11}\]0  
where \(C^{\circ}\) is the total gas concentration (mol/g) and \(\tau_{1}\) and \(\tau_{2}\) are the residence times (s) of the reactor R and the connecting tube T respectively. The O\({}_{2}\) molar balance equations are the following:
**R:**:  
\[R_{4}=k_{4}\,\theta_{4}\,\theta_{5} \tag{11}\]1
**T:**:  
\[R_{4}=k_{4}\,\theta_{4}\,\theta_{5} \tag{11}\]2  
The initial conditions of the CO, CO\({}_{2}\), and O\({}_{2}\) molar balances are the following:  
\[R_{4}=k_{4}\,\theta_{4}\,\theta_{5} \tag{11}\]3  
\[R_{4}=k_{4}\,\theta_{4}\,\theta_{5} \tag{11}\]4  
\[R_{4}=k_{4}\,\theta_{4}\,\theta_{5} \tag{11}\]5  
when simulating the oxidation phase, the initial conditions for both the site concentrations (\(\theta_{i}\)) and the gas phase molar concentration (\(C_{i}\)) are the final values corresponding to the adsorption phase simulation. The model equations with the initial conditions were solved by means of the Runge-Kutta method. To quantify the differences between the experimental and the model curves, we computed the root mean square error (SRMSE) normalized by the maximum value of the experimental curve (\(C_{max}\)) [53]:  
\[R_{4}=k_{4}\,\theta_{4}\,\theta_{5} \tag{11}\]6  
According to [PERSON] et al. [53], if SRMSE \(\leq\) 0.045 then the experimental and modeling curves may be considered in good agreement.