To validat e th e model, all 44 expe rimenta lly tes ted operat ing point s ha ve bee n simu lat ed an d th e res ults were compar ed to th e measur ed ones。 The res ults ar e summar ized in Figur e 6。 The bar chart s prese nt th e compar ison betwee n th e “app ar ent” an d comput ed soot accumu lat ion or consum ption rat e in th e filter, which is th e ma in res ult of engineering int eres t in such kinds of modeling applicat ions。 The “app ar ent” rat e is indi- rectly inferr ed  based on  th e  measur ement of  NO an d

Figu re 5。  Comparison betwee n expe riment an d simulation: (a) filter outlet temperatur e; (b) backpr ess ur e; (c) NO2 filter outlet emissions;

(d) NOx/soot an d  NO2/soot rat ios。

CO production in th e filter, using eq 4。 Four bar chart s ar e give n for reasons of clar ity, with each corr esponding to sep arat e temperatur e level s。 In each bar chart , th e sort ing ha s bee n done in ascending order of app ar ent soot accumu lat ion rat e。 The operat ing conditions for each steady-stat e point can  be foun d in Table   4。

For operat ing temperatur es un der 275 °C, th ere is always net soot accumu lat ion becau se th e reaction rat e of NO2 with car bon is very slow。 The model res ults follow th e expe rimenta lly obse rved tr ends for a lar ge ran ge of conditions。 In th e second chart , corr esponding to temperatur es in th e ran ge of 275-332 °C,  net soot con sum ption is expe rimenta lly obse rved at two operat - ing point s。 The model is able  to predict corr ectly th ese

conditions, an d th e quant itat ive agreement with th e measur ed results is sat isfactory for th e res t of th e cases。 At th e higher temperatur e ran ge shown in th e th ird chart , already 3 out of 11 operat ing point s res ult in net soot ma ss decrease, an d th e sam e is tru e for th e highest temperatur e  point s  shown  in  th e  last  gra ph。  It is int eres ting to note that th e model is  able  to predict corr ectly in all cases wheth er soot will be accumu lat ed or consum ed in th e filter。 The quant itat ive agreement is quite sat isfactory for engineering pur poses, tak ing into account th e relat ively lar ge num ber of modeling ass um ptions an d th e difficulty in assess ing th e expe ri- menta lly  obse rved  soot  accumu lat ion/consum ption rat es。

Figu re 6。  Summar y of app ar ent  an d comput ed  res ults in term s of soot  accumu lat ion/consum ption rat e:  (a) T < 275 °C; (b) 275 °C <  T

< 332 °C; (c) 334 °C < T < 387 °C; (d) 387 °C < T < 440 °C。

Not sur prisingly, all operat ing conditions with net soot consum ption ar e associat ed with high rat ios of NOx/ soot ma ss emissions。 The most favora ble temperatur e ran ge is 330-400 °C, although cont inuous regenerat ion is also obse rved once even at 275 °C。 Mostly, net soot consum ption is obse rved at low-flow-rat e conditions。 Howeve r, th e effect of flow rat e cann ot be assessed from th ese measur ement s only becau se  it was not possible to obta in high NOx/soot rat es at high-flow-rat e condi- tions becau se of th e specific engine operat ing chara c- teristics。 A computat iona l param etr ic ana lysis on th e

effect of different operat ing conditions is prese nt ed  in a  previous work。17

The corr elat ion betwee n app ar ent an d model-pre- dicted soot accumu lat ion rat es for all 44 tes ted operat ing point s is ill ustrat ed in Figur e 7。 The corr elat ion coef- ficient R2 is 0。98, indicat ing a very good model perfor- man ce for th e lar ge  ran ge of th e tes t conditions。

As a next step, it is int eres ting to investigat e th e sensitivity of th e model res ults on th e reaction kinetic con stant s (activat ion energy an d preexponent ial factor) used for th e car bon + NO2  reaction。 To this end, we have