## 3 Results and Discussion
### Modeling \(H_{2}\) Effect under Altitude and Sea Level Conditions
Notably, the model accurately predicted the dominance of zeolite adsorption at lower temperatures [16]. Additionally, it captured the dependence of the conversion efficiency on both temperature and mass flow rate for oxidation reactions. However, the model exhibited lower sensitivity than the experiments to these factors. The calibrated reactions allowed CO and HC elimination prediction across diverse conditions under CDC operation, emphasizing the O\({}_{2}\) oxidation pathway for lean combustion scenarios and accounting for HC accumulation. Nonetheless, these reactions cannot account for the influence of H\({}_{2}\) present in exhaust gases, as elaborated in Section 2.1. Figure 2: Modeled results for CO and HC conversion efficiency as a function of exhaust mass flow and catalyst inlet temperature: **(a)** CO conversion efficiency at 0 m & 20 \({}^{\circ}\)C; **(b)** HC conversion efficiency at 0 m & 20 \({}^{\circ}\)C; **(c)** CO conversion efficiency at 2500 m & \(-7^{\circ}\)C; and, **(d)** HC conversion efficiency at 2500 m & \(-7^{\circ}\)C.  
To address this gap, a targeted calibration of reactions that occur in the presence of H2 was needed. Therefore, the next phase of calibration focused on fine-tuning the reactions involving H2 within the catalyst, specifically targeting reactions \(R_{7}\) to \(R_{12}\) listed in Table 4. The goal was to refine the predictive capability of the model regarding the catalytic processes influenced by H2. A new objective function for this calibration phase was added to reflect the selectivities (\(S_{p,R_{k}}\)) of CO and HC to reactions involving H2 and O2 pathways. These selectivities were detailed in a preceding investigation by [PERSON] et al. [28], which examined the reactivity of an OC across different H2 concentrations in standard conditions. The objective of this calibration step was to ensure that the removal of CO and HC occurred in the presence of H2. Selectivity, defined in Equation (7), accounts for the contribution of each reaction (\(\Lambda_{p,R_{e}}\)) to the conversion of the individual species, calculated as the proportion of a change in concentration of a species due to a specific reaction to its total concentration change, which is the sum of all reaction contributions. \[S_{i,R_{k}}=\frac{\Lambda_{i,R_{k}}}{\sum\limits_{r}\Lambda_{i,R_{r}}} \tag{7}\]  
A new error function was formulated based on the selectivities of each reaction for both the simulation and the reference case, as described in Equation (8):  
\[\varepsilon_{S_{i,R_{k}}}^{t}=\sum\limits_{test}\left|S_{i,R_{OC_{reference}}}^ {t}-S_{i,R_{OC_{semilatism}}}\right| \tag{8}\]  
Equation (9) shows the objective function to calibrate the model when H2 is present in the exhaust gases. The second term of this equation refers to the selectivity of CO to the oxidation with O2 (\(R_{3}\)) and the oxidation with \(\cdot\)OH (\(R_{11}\)). Complementary, it also accounts for the selectivity of HC to the oxidation with O2 (\(R_{4}\)) and the oxidation with \(\cdot\)OH (\(R_{12}\)). \[ \begin{split}\Phi_{OC_{H_{2}}}=\sum\limits_{\text{test}}\omega_{ \text{test}}\left(\sum\limits_{t}\varepsilon_{CO}^{t}+\sum\limits_{t} \varepsilon_{HC}^{t}\right)\\ +\sum\limits_{\text{test}}\omega_{\text{test}}\left(\sum\limits _{\text{test}}\varepsilon_{SC,R_{3}}^{t}+\sum\limits_{\text{test}}\varepsilon_ {SC,R_{11}}^{t}+\sum\limits_{\text{test}}\varepsilon_{S_{HC,R_{4}}}^{t}+\sum \limits_{\text{test}}\varepsilon_{S_{HC,R_{12}}}^{t}\right)\end{split}  \tag{9}\]  
The results corresponding to the OC operation with H2 are shown in Figure 3, which compares the selectivities for CO and HC oxidation via O2 or \(\cdot\)OH with those reported by [PERSON] et al. [28]. As observed, to account for the presence of H2 in the exhaust gases for the studied OC, closely aligned with the reference. With respect to CO reactivity, which is depicted in Figure 3a,c, the model exhibited a high degree of consistency with the reference data in terms of selectivity.