## 5 Conclusions  
A study of the late fuel post-injection impact on the DPF active regeneration dynamics was presented. In particular, the engine fuel consumption, the flow properties at the DPF inlet and the regeneration duration were analysed with a modelling approach. The engine, DOC and DPF models were validated against experimental data corresponding to steady-state and transient operating conditions. The most efficient way to increase the DPF inlet temperature was demonstrated to be the use of high delays in the post-injection since it reduces the amount of post-injected fuel burned out within the combustion chamber and, hence, generates useful work. This trend is particularly significant at high load and as the EGR rate gets reduced. In addition, delaying the post-injection avoids the increase of the soot emission that might lead the DPF to an incomplete regeneration when combined with small increase in DPF inlet temperature. Increasing the post-injected fuel mass rate also contributes to obtaining higher DPF inlet temperature but at the expense of lower post-injection efficiency and the reduction of the O\({}_{2}\) concentration. This can become a critical parameter slowing down the soot depletion rate dramatically and avoiding the regeneration completeness. In fact, the fastest regeneration events were shown to be those with low post-injected fuel mass rate, in particular around 20% of the fuel mass rate of the main injection. However, when the post-injected fuel consumption is also considered, the optimum post-injection strategy in terms of post-injected fuel mass rate is to set it to increase the DPF inlet temperature until 600 \({}^{\circ}\)C during the pre-heating and maximum reactivity stages. Although the soot depletion rate is not the maximum in these conditions, it is kept high due to high O\({}_{2}\) concentration. The duration of the first two stages of the regeneration is not highly damaged and the fuel consumption is minimised in agreement with the maximum post-injection efficiency condition. Finally, to accelerate the late oxidation stage is positive. This stage is one order of magnitude longer than the previous ones due to the low soot depletion rate. To improve it, the post-injected fuel mass rate can be incremented if the O\({}_{2}\) availability is a non-limiting factor. In these cases, higher gas temperature increases exponentially the depletion rate. As a consequence, the duration of the late oxidation stage is reduced and compensates the increase in the post-injected fuel mass rate. Conceptualization, J.R.S. ; Formal analysis, P.P. and E.J.S. ; Funding acquisition, J.R.S. and P.P. ; Investigation, J.R.S., P.P., J.D.I.M. and E.J.S. ; Methodology, J.D.I.M. ; Project administration, J.R.S. and P.P. ; Software, P.P. and E.J.S. ; Supervision, P.P. ; Writing--original draft, P.P., J.D.I.M. and E.J.S. ; Writing--review & editing, J.R.S., P.P., J.D.I.M. and E.J.S. This work has been partially supported by FEDER and the Ministerio de Ciencia, Innovacion y Universidades of the Government of Spain through Grant No. TRA2016-79185-R. The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results. The following abbreviations are used in this manuscript: \begin{tabular}{l l} \(c_{p}\) & specific heat \\ \(C\) & thermal capacity \\ \(E_{PI}\) & post-injection efficiency \\ \(E_{a}\) & activation energy \\ \(G_{ox}\) & inhibition term for oxidation reactions \\ \(k_{m}\) & mass transfer coefficient \\ \(k_{r}\) & kinetic constant of reaction \(r\) \\ \(K_{ij}\) & inhibition term coefficient \\ \end{tabular}