## 2 Modelling Tools
### ATS Models Calibration  
Table 4 summarises the chemical parameters in the DOC model, both for Arrhenius kinetic terms (Equation (17)) and inhibition terms (Equation (18)) [42]. \[k_{r}=P_{f,r}e^{-\frac{E_{g,r}}{KT_{in}}} \tag{17}\]  
\[G_{ox}=T_{w}\left(1+K_{1}X_{CO,avc}+K_{2}X_{HC,ucc}\right)^{2}\left(1+K_{3}X_{ CO,avc}^{2}X_{HC,ucc}^{2}\right)\left(1+K_{4}X_{NO,avc}^{0.7}\right) \tag{18}\]  
This set of parameters was obtained from specific tests in steady-state and transient conditions. Figure 3 shows the comparison between experimental and modelling results for DOC outlet gas temperature and pollutants conversion efficiencies. The tests covered three engine speeds (1500 rpm, 2000 rpm and 2500 rpm) and an engine load variation from 5% to 40%. The combination of these engine speeds and loads contributed to vary the mass flow and the gas temperature at the DOC so that the low to high conversion efficiency range was tested accounting for chemical kinetics, i.e., \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multicolumn{3}{c}{**Kinetic Constants**} & \multicolumn{3}{c}{**Inhibition Term**} \\  & \(\mathbf{P_{f}}\) [s\({}^{-1}\)] & \(\mathbf{E_{a}}\) [J/mol] & \multicolumn{3}{c}{\(\mathbf{P_{f}}\) [-] & \(\mathbf{E_{a}}\) [J/mol]} \\ \hline HC adsorption & 2.7 & 0 & K\({}_{1}\) & 555 & \(-\)7990 \\ HC desorption & 100 & 65,000 & K\({}_{2}\) & \(1.58\times 10^{3}\) & \(-\)3000 \\ HC oxidation & \(1.7\times 10^{17}\) & 90,000 & K\({}_{3}\) & 2.98 & \(-\)96,534 \\ CO oxidation & \(3.3\times 10^{17}\) & 85,000 & K\({}_{4}\) & \(4.79\times 10^{5}\) & 31,036 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Kinetic parameters of the DOC model. temperature controlled and dwell time, i.e., mass flow controlled, effects. The tests were performed in different series corresponding to each engine speed with increasing load. Each operating condition was maintained for 300 s to ensure thermal stabilisation before the measurement and transitioning to the following load step. Thus, Figure 3a shows the modelled DOC outlet gas temperature compared to the experimental data. The high accuracy to predict this temperature, with an absolute error ranging \(\pm 5\)\({}^{\circ}\)C, is critical since it is one of the most important parameters to evaluate the effects of the fuel late post-injection on the DPF regeneration. In turn, this good agreement results from an accurate prediction of the pollutants conversion efficiency, which is shown in plots (b) and (c) of Figure 3 for CO and HC respectively together with the absolute error. It is possible to observe that the CO conversion efficiency is below 90% for the points with a lower inlet temperature due to chemical kinetic limitations. The only exception to this behaviour corresponds to the point at 1500 rpm and 5% in engine load, where the conversion efficiency is higher thanks to the longer residence time. For the rest of the operating points, characterised by higher exhaust temperature (over 200 \({}^{\circ}\)C), the conversion efficiency is higher than 95%. Similarly, the operating points with the lowest inlet temperature have HC conversion efficiency below 90%. In these points, the obtained conversion efficiency is due to two different phenomena. On the one hand, the temperature is not enough to ensure a complete oxidation of the HC in the exhaust gas. On the other hand, this low temperature promotes the HC adsorption on the zeolite washcoat. Moreover, it has to be considered that the zeolite is partially saturated due to the HC cumulated during the thermal stabilisation. Again, once the temperature reaches 200 \({}^{\circ}\)C the conversion efficiency increases over 90%. The variations of the efficiency observed in this area are due to differences in temperature and pollutants concentration, affecting the catalyst inhibition processes. However, the model well captures the experimental trends observed. The performance of the DOC model was also evaluated against highly transient operation during a complete Worldwide harmonized Light duty Test Cycle (WLTC).