A more rat iona l app roach would be to use a mecha- nistic math emat ical model that describe s both th e momentum an d heat tran sfer as well as th e reaction phenomena in th e filter, tak ing into account th e geo- metr ical an d th ermophysical propert ies of th e specific reactor。 In th is case, th e fitt ing param eters will concern th e rat e of th e NO2-car bon reaction only。 Once th ese param eters ar e fitt ed, it will be, in principle,  possible to apply th e model at different operat ing conditions, filter designs, etc。 Moreover, if such a model conta ins also time-depe ndent term s for filter temperatur e, soot loading, etc。, it will be possible to apply it in real driving conditions, which ar e typically  highly tran sient 。 Such a  model is prese nt ed in th e next  section。

Mode li ng

Start ing from th e fun dam enta l work of Bisse tt an d Sha dman  with  a  zero-dimensiona l  model,21   th ere al-

ready exis ts a  fairly  lar ge  num ber  of  models  in  th e li teratur e for th erma l regenerat ion of cellular ceram ic

filters。22-24   One-dimensiona l  modeling  is  sufficie nt  in

th e case in which all filter chann els beha ve in th e sam e way。 This is tru e in th e case of negligible  heat losses  to

Applying th e formu la (4) to all of th e measur ed data an d plott ing th e rat e of reaction as a function of th e filter temperatur e, we obta in th e gra ph prese nt ed in Figur e 4。

am bient an d un iform ra dial flow distr ibut ion at th e filter inlet。 These conditions ar e met in th e case of our expe rimenta l con ditions, an d th erefore th e equat ions of th e one-dimensiona l  model ar e employed。 The prese nt

work is based on th e previously prese nt ed model,17 which includes an extended reaction scheme tak ing into account th e car bon reaction with NO2。 The ma in equa- tions of th is model ar e briefly prese nt ed below。 More- over, in th e prese nt paper, we additiona lly describe in detail th e press ur e drop model used in th is stu dy, which is necess ar y for th e int erpretat ion of th e expe rimenta l

The process of ident ifying th e kinetic param eters will be describe d lat er。

Following th e solut ion method of Bisse tt an d Sha d- man 22 an d tak ing into account th e incomple te oxidat ion term s above, th e oxidant concentrat ion as it exits th e soot layer is exp ressed  by  th e followi ng equat ion:

res ults。

Conse rvation  of Mass  of the  Channe l  Gas 。

yk  ) yin,k  exp-

sp k1,k(Tw)

v

wRk k ) 1, 2   (11)

 ∂ (F v ) ) (-1)i(4/D)F  v

(5)

w

Considering th e stoichiometry of th e reactions an d th e

∂z   i   i w   w

where subscript i identifies regions 1 (inlet chann el) an d 2 (out le t chann el)。

Conse rvation  of Momentum   of the Channe l Gas。

oxidant consum ption using eq 11, th e ma ss balance equat ion for th e deposit layer, assuming that th e deposit is consum ed in a shr inking mode, give s

d w 2   Mc 1

∂pi

+  ∂

(F v 2) ) -Rµv /D2

(6)

Fp ) -

dt k)1

Fwvwyk

Mk

1 -

Rk

∂z ∂z