An Experimental Investigation into the Effect of NO₂ and Temperature on the Passive Oxidation and Active Regeneration of Particulate Matter in a Diesel Particulate Filter

Abstract

The kinetics of particulate matter (PM) oxidation in a catalyzed particulate filter (CPF) under different exhaust temperature and NO₂ conditions is presented along with a literature review of the related PM kinetic studies. The study was conducted with a 2013 heavy-duty engine that had NO₂ levels significantly higher than engines that met the earlier 2007/2010 EPA standards, and the results show a significant increase in PM oxidation rate that is possible under normal vehicle operating conditions, to diminish the need to actively regenerate the DPF. The detailed procedure for determining the PM oxidized during the experiments is described. Two types of tests were conducted to determine the NO₂ assisted as well as the thermal oxidation kinetics. Passive Oxidation (PO) tests were conducted for selected engine conditions that would cover the range of exhaust NO₂ concentrations (137 to 1013 ppm tested) and temperatures (299 to 388 °C tested) during regular engine operation. Active regeneration (AR) tests were conducted to determine the thermal oxidation kinetics at exhaust temperatures from 498 to 575 °C which was induced by post fueling. The CPF was first loaded with PM to a target loading, and then the PM was oxidized under specific exhaust temperature and NO₂/O₂ concentration conditions. The data obtained in this study can also be used to calibrate a CPF model. The activation energies and pre-exponential factors for NO₂ assisted and thermal oxidation were developed from the PO and AR data. It was also found that PM reactivity during PM loading was greater than for the passive oxidation tests.

Appendices

Appendix 1. Mass Balance

The PM mass balance for stage 2 loading, passive oxidation and active regeneration stages are given in this section in Tables 15 and 16. “PM retained” is the amount of PM in the CPF at the end of the stage. “PM available” is the sum of the PM retained at the beginning of the stage (end of previous stage) and the PM that entered the CPF during the stage (“PM in”), which represents the total PM available for oxidation. “Percent oxidized” is the percent of PM available that was oxidized (PM oxidized). “Loading” is the g/L of PM retained at the end of the stage. PM oxidized is estimated by the difference between “PM in” and the sum of “PM out” and the change in PM retained before and after the stage, or “PM added.” The procedures for determining the PM retained at the beginning and end of the oxidation stage are given in Appendices 3 and 4.

Table 15 PM balance for S2

Table 16 PM balance for oxidation stages

Appendix 2. CPF Thermocouple Arrangement and Temperatures

The thermocouple arrangement used for the CPF is as given in Fig. 3.

Fig. 3

Thermocouple arrangement for the CPF [4]

To estimate the average CPF temperature based on the individual thermocouple readings, first, the radial weighted temperatures for each axial section l_j (T_l,j, j = 1,…,4), based on the radial temperatures in that axial section (T_d,i, i = 1,..,4) were estimated. Here, “l” is the axial position and “d” is the diametric position of the thermocouple given by radial position “i” and axial position “j.” To estimate the radially weighted average temperatures for each axial position, the following formula was used:

$$ {T}_{l,j}=\sum_1^3\frac{\left({T}_{d,i}+{T}_{d,i+1}\right)}{2}\frac{\left({d}_{i+1}-d\right)}{d_4-{d}_1}\kern0.75em $$

(6)

T_l,j which is the radial weighted average temperature at each axial location ‘j’, was first estimated for each j. Then a similar approach was followed to estimate the weighted average temperature over the length of the CPF based on each T_l,j and l_j:

$$ {T}_{avg}=\sum_1^3\frac{\left({T}_{l,j}+{T}_{l,i+1}\right)}{2}\frac{\left({l}_{j+1}-{l}_j\right)}{l_4-{l}_1}\kern0.75em $$

(7)

where T_avg is the weighted average CPF temperature [°C].

Here, l1 = 25 mm, …, l4 = 225 mm, r1 = 0 mm,…, r4 = 215 mm as shown in Fig. 3. If a thermocouple was broken or otherwise reading incorrectly, which was considered as being the case if the reading was beyond ± 150 °C of the CPF inlet temperature reading, the next thermocouple in the sequence was considered for estimating the weighted average.

Appendix 3. Reaction Rate Estimation

This appendix discusses the procedure used to estimate the reaction rate for S2 and oxidation stages of each run.

To calculate the reaction rate, the following equation was used (Eq. 8), which is based on integrating the PM balance equation (Eq. 2) over the duration of interest. Filtration efficiency, CPF inlet PM concentration, and reaction rate are considered constant:

$$ {m}_2={\upeta}_{\mathrm{f}}{C}_{in}\frac{Q_{std}}{R{R}_o\ast 1000}\left(1-\exp \left(-R{R}_o\mathrm{t}\right)\right)+{m}_1\exp \left(-R{R}_o\mathrm{t}\right) $$

(8)

where

m₂ :

is the PM mass retained in the CPF at the end of the time step [g]

m₁ :

is the PM mass retained in the CPF at the beginning of the time step [g]

η_f :

is the filtration efficiency of the CPF [−] (constant, determined during S2)

C_in :

is the PM conc. into CPF [mg/scm] (constant, stage average value)

RR_o, :

is the rate of reaction of PM [1/s] (constant)

“t”:

is the duration of the time step [s]

Q_std :

is the standard volumetric flow rate [scm/s] which is calculated as

$$ {\mathrm{Q}}_{\mathrm{s}\mathrm{td}}\left[\frac{\mathrm{s}\mathrm{cm}}{\mathrm{s}}\right]=\frac{\mathrm{MF}{\mathrm{R}}_{\mathrm{exh}}\left[\frac{\mathrm{kg}}{\min}\right]}{1.18\ {\left[\frac{\mathrm{kg}}{{\mathrm{m}}^3}\right]}^{\ast }\ 60\left[\frac{\mathrm{s}}{\min}\right]} $$

(9)

where

MFRexh:

is the exhaust mass flowrate [kg/min]

1.18 kg/min:

is the standard density of exhaust (at 298 K and 1 atm)

60:

is the conversion from minutes to seconds.

Beginning with m₁ = m_start (PM retained at the beginning of the duration of interest) and an initial RR_o value of zero (or close to zero can be used if infinity cannot be handled by the software/solver), m₂ was found for the time step. Then, m₁ for the next time step was set equal to m₂ from the previous time step and m₂ was obtained for the next time step. This was continued till the final time step, and the value of m₂ at the final time step was compared to the experimental m_stop (PM retained at the end of the duration of interest) ± 0.05 g. If the final m₂ value is less than experimental m_stop − 0.05 g, the value of RR_o is incremented by a small value (in this case, 10⁻⁷/s). If the value of m₂ at the final time step is greater than the experimental m_stop + 0.05 g, RR_o is decreased by 10⁻⁷/s and the iteration run again. The computational tolerance of ± 0.05 g has been kept low enough to not have significant impact on the kinetics, at the cost of some increase in computation time. At this level of tolerance, the maximum deviation between experimental and computational PM retained would be ± 0.1 g during stages. This iteration is done until the final value of m_stop is within the tolerance limit from the experimental value and the value of RR_o obtained in the final iteration is taken to be the reaction rate for that run.

Alternatively, the MS Excel® solver was used to optimize RR_o (kept constant) to minimize the error between m₂ and m_stop in Eq. 8. In this case, filtration efficiency, CPF inlet PM concentration reaction rate, the standard volumetric flow rate was also considered constant (the time average value for the stage). This method was used for calculating the reaction rate for the oxidation stages.

Appendix 4. Methodology and Uncertainty Analysis to Determine PM Oxidation Kinetics

Figure 4 shows the variation of PM retained at various stages of the experiment as described in Sect. 4. PM weight measurements are done at the end of S1, S2, S3, and S4 and using these values, the PM retained at the beginning and end of the oxidation (Ox.) stage are determined as described in this section. The criteria for the PM oxidation stage was to have between 40 and 70% of the mass oxidized to have a sufficient delta PM mass to measure and also so that the PM retained at the end of oxidation stage is sufficient to weigh the PM.

Fig. 4

Schematic of PM retained vs. time for a typical run

1.1 CPF Weighing Procedure

A similar procedure was followed for weighing the CPF as in reference [22]. First, the engine was brought to idle and shutdown, the exhaust diverted through the bypass line during this process. The CPF inlet exhaust temperatures were around 270–290 °C at the beginning of this step. Simultaneously, the clamps fastening the DPF to the aftertreatment system were loosened to remove the DPF from the trapline. The exhaust fans were turned off as soon as the engine shutdown to prevent air currents from cooling the DPF further. Once the CPF was dismantled, it was carried over to the weighing scale. Before weighing the CPF, a dummy known weight (15 kg) was weighed thrice and the readings averaged and compared to the previous weights during the experiment to ensure that the scale was accurate. After this was done, the temperatures of the CPF for each of the thermocouples as shown in Fig. 3. were recorded. The CPF was weighed hot when a majority of the thermocouples were above 150 °C, and the average thermocouple temperature reading was greater than 200 °C. The target variation between the temperature measurements of the same thermocouple for different weights during the experiment was ± 15 °C to ensure that thermal effects did not significantly affect the weight measurement. Then, the CPF was weighed thrice and the three readings recorded and averaged to determine the weight of the CPF + PM for that stage. The weighing arrangement is shown in Fig. 5 and the CPF weight measurements are shown in Table 17. ‘m_ret’ refers to the PM retained in the CPF at the end of stage. The time between diverting the exhaust through the bypass to the time taken to weigh the CPF at the end of the various loading stages was around 10 min.

Fig. 5

CPF and weighing scale for weighing at S1, S2, S3, and S4 [4]

Buoyancy of the air trapped in the substrate, viscosity due to air currents, and moisture could affect the weight measurement of the DPF which are in turn effects of temperature although it is noted that moisture is not expected to significantly affect the weight measurement at higher temperatures (reference [23]). Reference [23] concluded that the consistency of the procedure used and similar temperatures during each weighting was important to get consistent weights. The overall thermocouple measurement data prior to weighing for some test conditions is shown in Table 18. Other runs for which data is unavailable is expected to have similar variation due to similar procedure.

1.2 Stage 2 Kinetics

Knowing the NO₂ concentrations, O₂ concentrations, and temperatures of exhaust entering the CPF during S2, it was possible to estimate kinetics for the loading stages like the oxidation stages. Due to the relatively low exhaust temperatures during S2 (< 300 °C), the PM oxidation during this stage was considered NO₂ assisted.

Based on the initial values for S2 kinetics obtained based on an Arrhenius fit, the reaction rates for L-RU and S3 stages were computed and in turn, the PM retained at the beginning and end of oxidation were computed (“PM retained at the beginning and end of oxidation stage” section of this appendix). Then, the reaction rate for the oxidation stage was calculated by minimizing the absolute difference between the experimental and calculated PM retained at the end of the oxidation stage, for each run (as given in Appendix 3).

Using these values of reaction rates, the PM oxidation kinetics obtained under a range of NO₂ and temperature conditions (Sects. 5 and 6) were calculated. Then, the activation energy for PM oxidation during S2 was assumed to be the same as that of the NO₂-assisted kinetics obtained (Table 11). Thus, the NO₂-assisted pre-exponential factor was obtained for S2 by minimizing the error between the estimated S2 reaction rates and the S2 kinetics obtained thus were A_S2 = 57.2[10⁶/s] and E_a,S2 = 87.5 [kJ/gmol].

When this kinetics were used again to calculate the PM retained at the beginning and end of the oxidation stage, the PM retained at the end of oxidation was not found to vary from the previous calculation. Hence, this value of S2 kinetics was considered to represent the data.

Table 17 CPF weight measurement for S1 and S2 of the various runs during loading

Table 18 CPF temperature data prior to weighing

1.3 PM Retained at Beginning and End of Oxidation Stage

The PM retained at the end of Loading-RU (beginning of the oxidation stage) and the end of oxidation (beginning of S3) was estimated by applying Eq. 8 to the ramp up and oxidation portions to estimate the PM retained at the end of ramp up and oxidation stages, respectively. To do this, the reaction rate (RR_o) during the Loading RU and S3 portions was first determined using the kinetics of S2 (Table 13) which was then used with Eq. 8 to obtain Eqs. 10 and 11.

The results of this analysis for the Loading Ramp Up (L-RU) and Stage 3 (S3) stages are shown in Table 19. Here, “RU” represents the Loading-RU stage, “Ox” represents the end of oxidation stage. The temperatures and NO₂ are the CPF inlet values for Loading-RU and S3, respectively. The target oxidation percentage was between 40 and 70% to have sufficient PM oxidized while also having sufficient PM in the DPF to obtain accurate measurement of the PM oxidized during the oxidation stage. Table 20 shows these results for the oxidation stage in the context of the oxidation rates and kinetic parameters:

$$ {m}_{ret, RU}={\upeta}_{\mathrm{f}}{C}_{in, RU}\frac{Q_{std, RU}}{R{R_{o,\kern0.5em RU}}^{\ast }1000}\left(1-\exp \left(-R{R}_{o, RU}{\mathrm{t}}_{\mathrm{RU}}\right)\right)+{m}_{ret,S2}\exp \left(-R{R}_{o, RU}{\mathrm{t}}_{\mathrm{RU}}\right) $$

(10)

where

m_ret,RU :

is the PM mass retained in the CPF at the end of the L-RU [g],

m_ret,S2 :

is the PM mass retained in the CPF at the beginning of the L-RU [g],

η_f :

is the filtration efficiency of the CPF [−]

C_in,RU :

is the PM conc. into CPF during L-RU (assumed the same as S2) [mg/scm]

RR_o,RU :

is the rate of reaction of PM during the L-RU stage [1/s]

“t_RU”:

is the duration of the RU stage [s]

Q_std,RU :

is the standard volumetric flow rate during the L-RU stage [scm/s] (Eq. 9)

Rearranging Eq. 10 for the S3 stage we get Eq. 11 (correspondingly similar notations as Eq. 10)

$$ {m}_{ret, Ox}=\frac{{\mathrm{m}}_{\mathrm{ret},\mathrm{S}3}-{\upeta}_{\mathrm{f}}{C}_{in,S3}\kern0.2em \frac{Q_{std,S3}}{R{R_{o,S3}}^{\ast }1000}\left(1-\exp \left(-R{R}_{o,S3}{\mathrm{t}}_{\mathrm{S}3}\right)\right)}{\exp \left(-R{R}_{o,S3}{\mathrm{t}}_{\mathrm{S}3}\right)}\kern0.5em $$

(11)

m_ret,Ox :

is the PM mass retained in the CPF at the end of the oxidation stage [g]

m_ret,S3 :

is the PM mass retained in the CPF at the end of S3 [g]

C_in,S3 :

is the PM conc. into CPF during S3 [mg/scm]

RR_o,S3, :

is the rate of reaction of PM during the S3 stage [1/s]

“t_S3”:

is the duration of the S3 stage [s]

Q_std,S3 :

is the standard volumetric flow rate during the S3 stage [scm/s] (Eq. 9)

1.4 Error Analysis

The error in PM retained at the end of L-RU (beginning of oxidation) and at the beginning of S3 (end of oxidation stage) was estimated. This was done using Eqs. 12–14 which are obtained by applying error propagation using partial derivatives (reference [24]) to Eqs. 10, 11, and 5.

Equation 14 is applicable to both L-RU and S3 stages. Errors in m_ret,S3 and m_ret,S2 were considered to be ± 0.2 g in accordance with the scale accuracy (± 0.1 g) and considering that these values are obtained by subtracting the clean weight from the CPF weights at the end of the stages. Error in NO₂ was 2% of the reading in accordance with the MS specifications and error in O₂ not considered an important factor at these temperatures. The error in thermocouple measurement was ± 2.2 °C according to the thermocouple specifications (but an error of ± 4.0 °C was considered in this analysis).

Table 19 PM retained at the beginning and end of oxidation stages for each experiment

Table 20 PO and AR calculations to determine the RR_o and ln(k)

$$ err\left({m}_{ret, RU}\right)=\sqrt{\begin{array}{c}{\left({\eta}_f\frac{Q_{std, RU}}{R{R_{o,\kern0.5em RU}}^{\ast }1000}\left(1-\mathit{\exp}\left(-R{R}_{o, RU}{t}_{RU}\right)\right) err\left({C}_{in, RU}\right)\right)}^2\\ {}+{\left(\mathit{\exp}\left(-R{R}_{o, RU}{t}_{RU}\right) err\left({m}_{ret,S2}\right)\right)}^2\ \\ {}+{\left({\eta}_f\frac{Q_{std, RU}}{R{R}_{o,\kern0.5em RU}1000}{C}_{in, RU}\left({t}_{RU}\mathit{\exp}\left(-R{R}_{o, RU}{t}_{RU}\right)-\left(\frac{1-\mathit{\exp}\left(-R{R}_{o, RU}{t}_{RU}\right)}{R{R}_{o, RU}}\right)\right) err\left(R{R}_{o, RU}\right)\right)}^2\end{array}} $$

(12)

$$ err\left({m}_{ret, Ox}\right)=\sqrt{{\left(\frac{err\left({m}_{ret,S3}\right)}{\mathit{\exp}\left(-R{R}_{o,S3}{t}_{S3}\right)}\right)}^2+{\begin{array}{c}\left({\eta}_f\frac{Q_{std,S3}}{R{R}_{o,\kern0.5em S3}\ast 1000}\left(1-\mathit{\exp}\left(-R{R}_{o,S3}{t}_{S3}\right)\right) err\left({C}_{in,S3}\right)\right)\\ {}+{\left(-{\eta}_f\frac{Q_{std,S3}}{R{R}_{o,S3}\ast 1000}{C}_{in,S3}\left({t}_{S3}\mathit{\exp}\left(R{R}_{o, S3}{t}_{S3}\right)-\left(\frac{1-\mathit{\exp}\left(-R{R}_{o, S3}{t}_{S3}\right)}{R{R}_{o, S3}}\right)\right) err\left(R{R}_{o, S3}\right)\right)}^2\end{array}}^2} $$

(13)

$$ \mathrm{err}\left({\mathrm{RR}}_{\mathrm{o}}\right)=\sqrt{\begin{array}{c}{\left({A}_{NO2}\mathit{\exp}\left(\frac{-{E}_{a, NO2}}{R^{\ast }T}\right) err\left(N{O}_2\right)\right)}^2\\ {}+{\left({A}_{O2}\mathit{\exp}\left(\frac{-{E}_{a,O2}}{R^{\ast }T}\right) err\left({O}_2\right)\right)}^2\\ {}+{\left(\left({A}_{NO2}N{O}_2\mathit{\exp}{\left(\frac{-{E}_{a, NO2}}{R^{\ast }T}\right)}^{\ast}\frac{-{E}_{a, NO2}}{R^{\ast }T}\left(\frac{-1}{T^2}\right)+{A}_{O2}{O}_2\mathit{\exp}{\left(\frac{-{E}_{a,O2}}{R^{\ast }T}\right)}^{\ast}\frac{-{E}_{a,O2}}{R^{\ast }T}\left(\frac{-1}{T^2}\right)\right) err(T)\right)}^2\end{array}} $$

(14)

Thus, the minimum value of error, err(m_ret,RU), obtained using Eqs. 12–14 was 0.2 g and the maximum value of error, err(m_ret,Ox), was 0.4 g. To account for other possible uncertainties, a total error of ± 1 g was considered. After applying this correction, the kinetics based on the maximum reaction rate (+ 1 g for m_ret,RU and − 1 g for m_ret,Ox) and minimum reaction rates (− 1 g for m_ret,RU and + 1 g for m_ret,Ox) were calculated. The values are shown in Table 21.

Table 21 Kinetics considering error in PM retained at beginning and end of oxidation respectively

The difference in ln(k) for the repeat runs is shown in Table 22. It is seen that the difference between the ln(k) values for repeat runs is minimal (not more than 0.35) indicating the repeatability of the experiment.

Table 22 “k” for Repeat runs

Fig. 6

PM Oxidized during the oxidation stages (est. vs. experimental). Error bars are ± 1 g

Fig. 7

Variation of NO₂, RR_o, and temperature with each run (RR_o logarithmic—base 10 scale)

Figure 6 shows the estimated vs. measured PM oxidized during the oxidation stages for the various runs.

A plot of NO₂, temperature, and RR_o for various runs is shown in Fig. 7. It is seen that a range of NO₂, temperature, and reaction rates are covered with values divided across the range for each parameter.

Thus, we have determined the kinetics of the reacting species related to PM oxidation based on the measurements and analysis methodology.