## 3 Engine and DOC Response  
Firstly, the effects of the late fuel post-injection on the engine performance and the gas properties in the exhaust are analysed varying the post-injected fuel mass rate and its timing. These results were achieved by using the gas dynamics engine model. Later on, the modelled flow properties at the turbine outlet, i.e., mass flow, pressure, temperature and composition, were imposed as boundary conditions to describe the response of the DOC. Two engine operating points, which are defined in Table 6, are evaluated. A medium-high load operating point without EGR (#A) is compared with a low load operating point with high HP-EGR rate (#B). Both points share a similar raw O\({}_{2}\) concentration but represent different boundaries for good pollutants abatement. To consider closed EGR in point #A is an extreme case that is to evidence how the resulting DPF inlet temperature increases its sensitivity to the post-injection timing. It is representative of high in-cylinder temperature leading to the need to properly manage the late fuel post-injection timing. At the same time, low EGR rate engine operating conditions improve the dynamics of the soot oxidation in the DPF because of the high O\({}_{2}\) concentration and mass availability after the DOC. It contrasts with the case of the same raw O\({}_{2}\) concentration (DOC inlet, point #B in Table 6) but high HP-EGR rate. This is representative of an operating condition which limits the available O\({}_{2}\) mass across the DPF while at the same time providing high dwell time. The O\({}_{2}\) availability makes the definition of the active regeneration strategy more dependent on the post-injected fuel mass rate. Figure 7 shows the effect of the post-injection timing and the post-injected fuel mass rate on the brake specific fuel consumption (BSFC) and the torque. Figure 7 shows in plots (a) and (b) how the increase of the fuel mass in the post-injection leads to an increase of the BSFC for both operating points and over the complete range of the study. As described by [PERSON] et al. (2016) for high load and no-EGR conditions, point #A shows higher sensitivity to the post-injection timing on BSFC. This happens because of the increase of the engine torque, which is especially relevant when the post-injection delay with respect to the main injection is small ([PERSON] et al., 2017), as observed in Figure 7c and to a lesser extent in \begin{table}
\begin{tabular}{l c c} \hline Point ID & \#A & \#B \\ Engine speed [rpm] & 1250 & 1500 \\ Torque [Nm] & 168.7 & 74.5 \\ Engine load [\%] & 75 & 25 \\ EGR rate [\%] & 0 & 40.2 \\ Exhaust mass flow [kg/s] & 0.0307 & 0.0171 \\ Raw O\({}_{2}\) concentration [\%] & 6.7 & 6.6 \\ DOC inlet temperature [\({}^{\circ}\)C] & 459 & 354 \\ DOC dwell time [ms] & 20.7 & 39.6 \\ DPF dwell time [ms] & 24.5 & 44.5 \\ \hline \end{tabular}
\end{table} 
Table 6: Operating points for DPF active regeneration analysis. Figure 6: Comparison of experimental and modelled results during DPF passive regeneration under WLTC conditions of (**a**) DPF gas temperature and (**b**) DPF filtrated and cumulated soot. Figure 7d, in which the iso-torque lines evidence a lower slope. Thus, the torque increase becomes negligible as the post-injection is delayed, giving rise to a more evident penalty in BSFC, which gains dependence on the post-injected fuel mass rate for all points. The impact of the late fuel post-injection on the raw HC and soot emissions is shown in Figure 8. Plot (a) in Figure 8 points out that point #A is characterised by increasing raw HC concentration as the post-injection is delayed and as the post-injected fuel mass rate increases at high delays. This behaviour agrees with the high torque increase as the post-injected fuel mass rate is done at reduced delays and the loss of dependence with mass as the post-injection is further delayed.