PM Oxidation Kinetics

Table4.7gives a description of the PM oxidation reaction kinetic parameters that were considered to be varied to get agreement with the experimental PM mass retained and CPF pressure drop.

For calibrating the PM kinetics associated with the thermal and N O₂-assisted mechanisms in the PM cake layer and substrate wall, the following steps were followed:

1. Initial values of activation energies and pre-exponential factors for the N O2-assisted PM oxidation reaction were determined by an optimization computation with experimental data from the passive oxidation experiments, grouped according to fuel type (ULSD, B10 and B20) as shown in Table 4.8. Initial values of kinetic parameters of thermal (O2) PM oxidation were fixed at values obtained from analysis of experimental data in reference [4]. Pre-exponential factors of these reactions according to the fuel and activation energy are shown in Table4.8.

2. Since the CPF inlet PM concentrations were known to be varying from experiment to experiment, specific values of CPF inlet PM concentrations were determined for stage-1 and stage-2 for all passive oxidation and active regeneration experiments such that the original values of N O2-assisted PM oxidation kinetic parameters in the PM cake layer (A_{N O2,cake}) could be used to simulate end-of-stage-2 PM mass retained within (-1.1 / + 0.9 g) as shown in TableJ.2 in Appendix J. The specific values of CPF inlet PM concentrations used for stage-1 and stage-2 of all passive oxidation and active regeneration experiments are as shown in TableH.2 in AppendixH. The pre-exponential factors of N O2-assisted PM oxidation in the wall during loading (A_{N O2,wall}) were adjusted to simulate the slope of the loading pressure drop.

3. Using the values of N O₂-assisted PM oxidation kinetic parameters in the cake and wall, the active regeneration experiments were simulated. Specifically, the pre-exponential factors of thermal PM oxidation reaction in the PM cake layer (A_th,cake) were calibrated for all active regeneration experiments to simulate end-of-stage-3 PM mass retained in the filter (as shown in Table J.2) and the pre-exponential factors of thermal PM oxidation reaction in the wall during active regeneration (A_th,wall) were adjusted to simulate the slope of the pressure drop during active regeneration.

4. The N O2-assisted PM oxidation kinetic parameters of all passive oxidation experiments and thermal PM oxidation reaction kinetic parameters of all active regeneration experiments were analyzed using Arrhenius plots and optimized values of pre-exponential factors and activation energies were arrived at from these Arrhenius plots for all passive oxidation and active regeneration experiments.

The model calibration procedure explained in this chapter was used with the experimental data described in Tables4.3and4.4to calibrate the model. The next chapter applies this procedure to determine the parameters needed for the model calibration. The detailed results for a PO and AR case are then presented along with the differences between the experimental data and the model in AppendixJfor all eighteen experimental cases.

Table 4.5: Filtration-related input parameters considered for the CPF model calibration

Parameter Description Expt. Data Used to

Calibrate Parameter D Diameter of substrate

Geometry/specifications of CPF

L Length of substrate

w_s Thickness of substrate wall n_cell Number of inlet channels in the

substrate

ρ_s Bulk density of substrate wall cp,s

Specific heat capacity of substrate wall

λ_s Thermal conductivity of substrate wall

k_s,0 Initial permeability of substrate wall Clean pressure drop

k_trans Transition permeability of substrate

wall

Duration of deep-bed filtration

_s,0 Initial porosity of substrate wall

Deep-bed pressure drop

d_pore,0 Mean pore size of substrate wall

C_1,ρpw First constant in wall packing density calculation

C_2,ρpw

Second constant in wall wall packing density calculation

w_cat Thickness of catalyst washcoat

Catalyst specifications d_pen Depth of penetration of catalyst into

the substrate wall

α_p,0 Initial solidosity of PM cake layer Calculate according to Peclet number [72]

k_p,0 Initial permeability of PM cake layer Slope of cake filtration pressure drop

λ_p Thermal conductivity of PM cake

layer Constants

c_p,p Specific heat capacity of PM cake layer

A_η PM cake filtration efficiency parameter

Table 4.6: Catalytic reaction kinetic parameters considered for the CPF model calibration

Parameter Description Expt. Data Used to

Calibrate Parameter

Table 4.7: PM oxidation kinetic parameters considered for the CPF model calibration Location Parameter Description Expt. Data Used to

Calibrate Parameter

NO2 Cake A_{N O2,cake} Pre-exponential factor Mass of PM retained after passive oxidation

Ea_{N O2,cake} Activation energy

Wall A_{N O2,wall} Pre-exponential factor Pressure drop during passive

oxidation EaN O2,wall Activation energy

Thermal

Cake A_th,cake Pre-exponential factor Mass of PM retained after

active regeneration

Ea_th,cake Activation energy

Wall Ath,wall Pre-exponential factor Pressure drop during active

regeneration

Ea_th,wall Activation energy

Table 4.8: Initial values of kinetic parameters of PM oxidation reactions determined by optimization computation of N O2-assisted PM oxidation and from analysis of experimental data

in reference [4] used for calibration of high-fidelity CPF model Parameter ULSD B10 B20 Units

AN O2 0.21 0.06 0.015 [m/s]

Ea_{N O2} 74.1 68.3 59.4 [kJ/gmol]

A_th 0.942 1.17 1.93 [m/s]

Ea_th 139 [kJ/gmol]

5. R ESULTS AND D ISCUSSION ¹

The CPF model was calibrated using experimental data from 6 PO and 12 AR experiments. As a result of calibration of the model, all calibration parameters that need to be specified as inputs to the model were determined. The following sections of this chapter discuss the parameters obtained and the performance of the CPF simulated using these parameters compared to the experimental data obtained during PO and AR experiments. A comparison of the measured experimental CPF performance data to the model results from one PO and one AR experiment are presented in the chapter with additional comparisons from all PO and AR experiments have been given in AppendixJ.