## 4 Active Regeneration Analysis
On the other hand, Figure 10 shows that higher temperature is reached at the inlet of the DPF as the post-injected fuel mass rate increases. However, this condition is not enough to accelerate the regeneration. As observed in Figure 12, points #A and #B reach the fastest regeneration with 6 and 4 mg/cc respectively. The regeneration is not even able to be completed when post-injecting 8 mg/cc in the case of point #B. The reason behind this limitation for post-injected fuel mass rate is the reduction in O\({}_{2}\) concentration at the DPF inlet as the fuel mass increases, as observed in Figure 9. Very low O\({}_{2}\) concentration causes limitations to the chemical kinetics of the soot oxidation process [22]. These effects are more critical once the highest reactivity stage has finished, as observed in Figure 12.  
With the aim of better understanding the boundaries defining the best post-injection settings, Figure 13 shows the DPF pressure drop, soot mass, outlet temperature and outlet O\({}_{2}\) concentration during the fastest active regeneration for both operating points: 6 mg/cc and 60 CAD aTDC in point #A and 4 mg/cc and 60 CAD aTDC in point #B. Plots (a) and (b) in Figure 13, which are related to the pressure drop and soot mass change along the regeneration, also include the duration of each of the regeneration stages for this fastest strategy. Additionally, two extreme regeneration strategies are plotted for each operating point: one with a post-injection timing of 30 CAD aTDC but maintaining the post-injected fuel mass rate and another one with a fuel mass of 8 mg/cc but maintaining the timing at 60 CAD aTDC. Figure 13: DPF pressure drop, soot mass, outlet temperature and outlet O\({}_{2}\) concentration during the fastest active regeneration, advancing the post-injection and increasing the post-injected fuel mass rate. Point #A is characterised by fast pre-heating and maximum reactivity stages due to its high DPF inlet temperature before triggering the active regeneration. Nevertheless, moving the post-injection settings to an early timing (30 CAD aTDC) gives as a result the minimum temperature at the DPF outlet (600 \({}^{\circ}\)C), as observed in Figure 13c. It is still high enough to promote the soot oxidation. In fact, the O\({}_{2}\) outlet concentration is very similar to that in the fastest strategy during the pre-heating and maximum reactivity stages (Figure 13e). However, the soot mass in the DPF decreases very slowly converging to the equilibrium condition (steady soot mass). As previously discussed, this is due to the increase in soot emission that is taking place for these post-injection settings (Figure 8c). The same behaviour is observed for point #B when the post-injection is advanced. In this case, the lower DPF inlet temperature and, as a consequence, the longer thermal transient, produces longer pre-heating and maximum reactivity stages. In this case, the earliest post-injection case presents just slightly lower temperature than the fastest strategy and the O\({}_{2}\) consumption is almost identical. This fact points out a very similar soot depletion rate. However, more soot mass is again found for the earliest post-injection case due to its higher raw soot emission rate (Figure 8d). The representation of the highest post-injected fuel mass rate cases in Figure 13 makes evident the importance of the O\({}_{2}\) availability on the oxidation rate. The highest DPF outlet temperature (750 \({}^{\circ}\)C) is obtained when the post-injected fuel mass rate is increased to 8 mg/cc both in points #A and #B. However, the regeneration dynamics is not the fastest. In point #A, the regeneration is almost as the fastest one (6 mg/cc) but the decrease in O\({}_{2}\) concentration (below 3% at the DPF outlet) makes the regeneration slower. In point #B, the O\({}_{2}\) concentration falls below 1% and slows the regeneration down significantly.