## 4 Model Validation  
The present paragraph briefly describes the procedure adopted to validate the kinetic conversion model of main gaseous pollutants and the oxygen storage phenomena. First of all, a default kinetic mechanism with a reaction scheme from [17] was the starting reference model. This mechanism, already implemented in a default model in GT-Suite and comprising 13 chemical species and 21 reactions, was specifically developed to summarize the most relevant reaction paths taking place in a TWC for exhaust streams from a gasoline engine. The governing equations are reported in the software manual and are also contained in [17].  
Applying this initial model to simulations of an NG engine, it was not possible to obtain a correct prediction of the main pollutant species' concentrations at the tailpipe, even though the injection mode was similar to a traditional gasoline SI engine.  
As an example, Figure 5 shows engine-out and tailpipe concentrations of some of the main converted species obtained through the default kinetic scheme [17]. For the sake of brevity, only the results of the most favorable conditions at high loads in SS were proposed. The wide deviations between the pink curve and the green curve are significant, demonstrating the inaccuracy of the starting model.  
The following section describes the protocol adopted to perform TWC model calibrations, both in SS conditions and during lambda scans.  
To this aim, a sensitivity analysis was performed for the pre-exponential factor \(\mathbf{A}\) and the activation energy \(\mathbf{E_{a}}\), which characterize the rate expression of each reaction. The global reaction rates are generally expressed in this form [17]:  
\[\omega=k\prod_{k}X_{k}^{\alpha_{k}}\prod_{m}\Gamma_{l}\theta_{m}^{\beta_{m}}/ \prod_{k}F_{j}, \tag{4}\]  
with the Arrhenius terms:  
\[k\left(kmol/m^{3}\right)=AT_{s}^{\beta}\ \exp[-E_{a}/RT_{s}]. \tag{5}\]  
The calibration procedure began with steady-state cases, monitoring the rate of each reaction. The starting point was the deactivation of all reactions in order to obtain the same compositions in  
Figure 4: \(H_{2}\)/\(CO\) ratio. Empirical correlation from [PERSON] et al. [17].  
engine-out and in tailpipe conditions. Then, an algorithm based on the order of activation of each reaction, dictated by the species that had higher concentrations in the exhaust, of the kinetic scheme were implemented. The platinum group metals (PGM) chemical reaction calibration procedure can be summarized in the following steps:  
1. Deactivation of all reactions;
2. Activation of reactions with CO and CO\({}_{2}\) in reagents and products;
3. Run simulation and monitor reaction rates;
4. Further deactivation of all reactions except the one with the higher rate;
5. Parameterization of this reaction to get the result as close as possible to experiments;
6. Activation and calibration of each reaction based on the highest rate;
7. Repeat steps 2 to 6 for reactions with CH\({}_{4}\);
8. Check and recalibrate reactions with CO and CO\({}_{2}\);
9. Repeat steps 2 to 6 for reactions with NO; and
10. Check and recalibrate reactions with CO, CO\({}_{2}\), and CH\({}_{4}\).  
Calibration of the kinetic scheme was carried out under the operating conditions 1900 RPM (100%) both in steady-state and transient conditions. The reaction model was then verified also at partial loads in order to validate its consistency.