A Model Development for Evaluating Soot-NO - American

Article pubs.acs.org/IECR

A Model Development for Evaluating Soot-NOx Interactions in a Blended 2‑Way Diesel Particulate Filter/Selective Catalytic Reduction Soo-Youl Park,†,⊥,* Kushal Narayanaswamy,‡ Steven J. Schmieg,‡ and Christopher J. Rutland† †

Engine Research Center, University of Wisconsin-Madison, 1500 Engineering Drive, Madison, Wisconsin 53706, United States General Motors Global Research and Development, 30500 Mound Road, Warren, Michigan 48092, United States

‡

S Supporting Information *

ABSTRACT: The 2-way diesel particulate filter/selective catalytic reduction (DPF/SCR) emission reduction system has been considered as a potential candidate for future emission standards owing to its advantages in cost savings and packaging flexibility. For the 2-way device, Cu−zeolite is coated inside the DPF substrate as nitrogen oxide (NOx) reducing (DeNOx) catalytic material. Therefore, when exhaust gas passes through the 2-way device, NOx reduction and soot filtration occur simultaneously. However, the operating characteristics of the combinatorial device might be different from individual DPF and SCR devices. In this work, a previously developed model was improved to include soot filtration and oxidation. The model has been tested and validated with experimental data from a reactor flow bench in a systematic manner and applied to capture the effect of soot deposits on NOx reduction performance in a 2-way DPF/SCR device. Accordingly, the soot oxidation characteristics of a 2-way device are investigated with various feed gas compositions. Then the effect of soot deposit on the SCR reaction is investigated in terms of deterioration of DeNOx performance and the interaction between soot oxidation reactions and DeNOx SCR reactions.

1. INTRODUCTION As carbon dioxide (CO2) emissions regulation become more stringent, automakers are increasing their attention on technologies that decrease fuel consumption. For powertrain development, the hybridization of the power source and increasing efficiency in the internal combustion engine itself are viable technologies. Consequently, interest in diesel engines has increased because they have better fuel efficiency than gasoline engines. Heterogeneous combustion is one feature of diesel combustion. This makes locally favorable conditions for the formation of NOx and PM (particulate matter) inside the combustion chamber. Under stringent emission regulations, automakers are forced to decrease tailpipe emissions, and a viable solution is the use of emission aftertreatment systems. Representative technologies for emissions aftertreatment are (1) oxidation of carbon monoxide (CO), hydrocarbon (HC), and nitric oxide (NO) in a diesel oxidation catalyst (DOC), (2) NOx reduction in a lean NOx trap (LNT) or urea/ammonia selective catalytic reduction (SCR) catalyst, and (3) PM reduction by filtration in a diesel particulate filter (DPF). SCR is generally accepted as one of most promising alternative NOx reduction technologies. It has wider operating temperature range and higher conversion efficiency than other NOx reduction technologies. However, a disadvantage of SCR is it requires a storage tank of ammonia or urea and an injection system. Thus, it results in larger packaging requirements. A typical diesel aftertreatment system is composed of DOC, NOx reduction catalyst, and DPF placed in series in the exhaust system. In recent years, catalyst suppliers are introducing multifunctional devices for minimizing packaging problems. In particular, both soot filtration and NOx reduction by SCR are implemented in a 2-way DPF/SCR device by coating SCR © 2012 American Chemical Society

catalyst on a DPF substrate. Figure 1 shows the schematic diagram for a blended 2-way DPF/SCR device. Integration of DPF and SCR functionalities into a single device might cause other problems which do not appear in separate devices. The operation of the 2-way device might be different from that of conventional DPF and SCR in accordance with different performance characteristics. He et al.1 tested 2-way DPF/SCR by installing it in a pickup truck. Cu-zeolite was used as catalytic material and test conditions were the US city (FTP) and highway (US06) drive cycles. NOx conversion efficiency across the 2-way DPF/SCR device was 75% for FTP and 83% for US06 mode with 60 000 miles of engine aging. Also they compared filter regeneration performance between the 2-way DPF/SCR and a conventional catalyzed DPF, and the results show that regeneration performance in the 2-way device is almost the same as that of a catalyzed DPF. However, CO release during the regeneration is much higher with the 2-way device. Lee et al.2 showed how NOx reduction performance is affected by filter regeneration over a 120 000 mile aged 2-way DPF/Cu−zeolite SCR catalyst device. They suggested that more ammonia should be injected to compensate for the amount of ammonia oxidation at filter regeneration temperatures. However, no quantified results for this effect were presented. Fuel penalty during filter regeneration is another important aspect. To improve low temperature soot oxidation for minimizing fuel penalty, oxidation catalysts are coated on DPF substrates. Usually, noble metals are used as a catalytic Received: Revised: Accepted: Published: 15582

August 3, 2012 October 7, 2012 November 12, 2012 November 12, 2012 dx.doi.org/10.1021/ie3020796 | Ind. Eng. Chem. Res. 2012, 51, 15582−15592

Industrial & Engineering Chemistry Research

Article

Figure 1. Schematic diagram of blended 2-way DPF/SCR.

The coordinate system and computational domain for equations 1−6 are shown in Figure 2.

material for soot oxidation and numerous studies have been conducted to examine this effect. Song et al.3 measured soot oxidation with a Pt/CeO2 catalyst, and they showed that the oxidation temperature decreases by 130 °C compared to that of an uncatalyzed device. In this work, Cu−zeolite is used as a SCR catalytic material for NOx reduction. Moreover, limited studies have shown that copper is also a catalytic material for soot oxidation. Levin et al.4 studied how copper fuel additives affect soot oxidation. They showed that it expands vehicle operability by reducing particulate mass loading and related external energy consumption required during regeneration. Murphy et al.5 added metal chlorides dissolved in methanol to diesel soot and showed that the copper decreased the ignition temperature by about 100 °C. The objective of this study is to develop a model to understand the soot-NOx interaction in a 2-way DPF/SCR device. A previously developed model describing the transport and reaction phenomena inside a wall flow type substrate (Park et al.6) forms the basis of this study. This model incorporated SCR kinetics and was validated under temperature programmed desorption tests and steady state NOx conversion tests. For soot filtration and oxidation, mathematical formulations based on previous research work by Bisset7 and Konstandopoulos8 is incorporated. In this paper the existing 2way DPF/SCR model is expanded to include soot filtration and oxidation. For this purpose, a soot cake layer model is added and both NO2- and O2-based soot oxidation reactions are included. The model has been validated in a systematic manner with available experimental data to capture the effect of soot deposits on NOx reduction performance of the 2-way DPF/ SCR device.

4k I ∂ I I 4 (u C b, i ) + (u w C b, i I) + c (C b, i I − Cwf, i|y = 0 ) = 0 ∂x a a (1)

∂ 2Cwf, i ∂ (u w Cwf, i) − Dw + k wSw(Cwf, i − Cws, i) = 0 ∂y ∂y 2

(2)

k wSw(Cwf, i − Cws, i) = RR i

(3)

C b, i Iu w + kcI(C b, i I − Cwf, i|y = 0 ) = Cwf, i|y = 0 ·u w − Dw

∂Cwf, i ∂y

(4)

y=0

4k O ∂ O O 4 (u C b, i ) − (u w Cwf, i|y = w ) + c (C b, i O − Cwf, i|y = w ) ∂x a a (5)

=0

kcO(Cwf, i|y = 0 − C b, i O) = −Dw

∂Cwf, i ∂y

y=w

(6)

The symbols Cb,iI Cwf,i Cws,i nd Cb,iO represent the concentration of species i measured at the inlet channel, gas stream inside the wall, solid surface inside the wall and outlet

2. MATHEMATICAL FORMULATION FOR 2-WAY DPF/SCR 2.1. Species Transport Equations. The basic foundations for building a model for an aftertreatment device are transport equations for species, energy, and momentum. The governing equations for flow and temperature of a wall flow-type device are based on Bisset.7 They are composed of conservation of mass, momentum, and energy for the inlet and outlet channel. Darcy’s law for pressure drop across the porous media is used to relate the inlet and outlet channel pressures. Only single inlet and outlet channel are solved under the assumption that all channels are identical. The species transport equations for each species under a wall flow substrate were introduced by Park et al.6 These are shown in eqs 1−6, and they are applied to inlet channel (eqs 1 and 4), outlet channel (eq 5 and 6) and porous filter wall (eqs 2 and 3).

Figure 2. Discretization of computational domain and coordinate system. 15583

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channel, respectively. In eq 1 and 5, kc is a mass transfer coefficient between the fluid in the channel and walls (or cake layer) in the inlet and outlet channel, respectively. The filter wall and soot cake layer are porous media, so the flow in the inlet channel has a suction flow as well. Hwang et al.9 studied how the heat transfer coefficient changes with the intensity of suction or blowing flow in a rectangular duct with porous wall and suggested an experimental correlation as presented in eq 7. This experimental correlation is directly used to get the mass transfer coefficient under the assumption of Lewis (Le) number of ∼1. However, eq 7 is derived when only one of four walls is porous but each DPF channel has four porous walls. Nevertheless, in the case of engineering application, several studies6,10 used eq 7 and they showed acceptable correlation with experimental results both for species and energy transport. Most recently, Kostoglou et al. derived the Nu−Re w correlations based on an analytical approach for a wall flow monolithic catalytic reactor.11 Comparisons of transport coefficient between single and four porous walls will be studied further and updated to the simulation code.

there are 6n unknowns and 6n equations. A solver for the equation is designed by discretizing the differential equations of eq 1, 2, and 5. Equations 1 and 5 do not include the diffusion term because it is so slow as compared to the convective transport along the channel axial direction, but eq 2 includes the diffusion. Thus, eqs 1−6 should be solved simultaneously at a given location of x, and then the solution marches to the next channel axial position. As seen in the rate expression of “NO oxidation” and “Fast SCR reaction” in Supporting Information, Table S2, the nonlinear terms are included, so the finally discretized algebraic equations are nonlinear system equations. The solver was programmed by Fortran using an internal nonlinear system equation subroutine which is available in the International Math and Static Library (IMSL). 2.2. Model for Soot Filtration and Oxidation. To describe the soot mass conservation inside the 2-way device, models for soot filtration and soot oxidation are needed. Soot filtration occurs in two different modes.8,13−16 First, at the initial stage of the filtration process, soot is deposited inside the filter wall, and this is called deep bed filtration. After filling up the substrate, soot deposition starts to occur on the filter wall and forms a soot cake layer. Konstandopoulos et al.8 contributed much on the development of a model for soot filtration and oxidation. The model for soot filtration used in this study is based on their work and additional implementation details can be found in refs 8 and 17. The mathematical expression of soot mass conservation is described depending on the form of the deposit. Equation 9 represents a mass conservation equation for the soot deposited inside the filter wall. It is applied to each wall element.

Nu = 2.712 − 0.367Re w + 0.0212Re w 2 − 0.000443Rew 3 0 < Re w < 20

(7)

Equation 3 represents species balance between mass transfer and surface reaction. However, in eq 3, the surface area per unit volume (S) has a very large value so Cwf,i and Cws,i are almost equal. It represents that the overall reaction in a porous media is mostly limited by reaction kinetics. The mass transfer coefficient from gas stream to solid surface inside the soot cake layer or filter wall which is denoted by kw can be calculated by experimental correlation suggested by Dwivedi12 as seen in eq 8. εp

0.765 0.365 Sh = + 0.82 Re w Re w0.386 Sc Re w 1/3

Vj

∂Cw,soot ∂t

cat = −RR O − RR NO2 + R f,w 2

(9)

In this equation, the soot concentration changes in time due to oxidation and filtration processes. The symbol Rf,w is the soot filtration rate by deep-bed filtration and is calculated using the incoming flux of soot particles and filtration efficiency.8 The first term on the right-hand side represents the catalytic soot oxidation rate, and it is expressed by eq 10.

(8)

where Sh and Sc represent Sherwood number and Schmidt number, respectively. Depending on the y-location, the domain should be classified as soot cake layer or catalytic filter wall. The mass transfer coefficient (kw) diffusivity (Dw) and surface area (S) are porous wall properties and determined depending on their position. The reaction rate for species i which is denoted by RRi is also determined depending on its y-location. While the soot cake layer involves only the soot oxidation reactions, the catalytic filter wall includes SCR related reactions as well as soot oxidation reactions. An additional assumption included in this study is that the soot deposit inside the filter wall also undergoes catalytic oxidation in the presence of Cu−zeolite catalyst. The reaction mechanisms are summarized in Supporting Information, Table S1 and their rate expressions are presented in Table S2. For ammonia desorption, the activation energy which is denoted by EA,2 is dependent on the ammonia surface coverage. According to Park et al.,6 the exponential formulation for dependency of the activation energy on the ammonia surface coverage works much better than linear formulation so this exponential formulation is still used in this research. The validation of eq 1−6 and rate expressions for SCR are well described in their study.6 The reaction rate term, RRi can include a product of concentrations of two or more species and it also couples eqs 1−6 through all trace species. The unknowns in eqs 1−6 are Cb,iI, Cwf,i, Cws,i, Cwf,i|y=0 Cwf,i|y=w and Cb,io for n trace species, so

cat RR O = Sw,soot kcat[O2 ] 2

(10)

Here kcat is a reaction constant for the soot oxidation reaction which occurs on the surface of soot particles and it has units of [m/s]. kcat is modeled by a modified Arrhenius equation which includes a linear dependency of the pre-exponential factor on temperature. The activation energy for each soot oxidation pathway is summarized in Supporting Information, Table S6. Sw,soot is surface area per unit volume [m2/m3]. For the soot deposited inside the filter wall, Sw,soot can be estimated by the following equation. Sw,soot = A sCw,soot MWC × 1000

(11) 2

Here As is a surface area per unit mass of soot particles [m /kg] and MWC is the molecular weight of carbon. The soot deposited in the cake layer is assumed to behave like a shrinking or inflating layer.18 Under this assumption, the density or concentration of soot cake layer denoted by Ccake stays constant. The soot mass conservation equation is represented in eq 12. A jCcake 15584

∂wcake = −RR Oth2 − RR NO2 + R f,cake ∂t

(12)



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Here, wcake is a thickness of soot cake layer. The superscript “th” represents thermal oxidation. For the soot cake layer, thermal oxidation is a main reaction pathway for soot oxidation because most of the catalytic material is coated inside the filter wall.

Figure 3 shows the NO to NO2 formation by oxidation as a function of temperature. The feed gas does not contain NO2, so

3. EXPERIMENTAL SETUP AND TEST PROCEDURE Experimental data from 2-way DPF/SCR catalyst core samples (sample size ≈ 0.95 in. diameter by 2.38 in. length) provided by a catalyst supplier was used for model validation. The washcoat containing the catalyst powder was supported on 300 CPSI/12 mil cordierite wall flow monolith substrate and aged prior to testing. Supporting Information, Table S3 lists the hydrothermal aging conditions and the dimensions of the catalyst samples used in the experiments. The aging was meant to simulate approximately 120 000 miles of vehicle operation. The catalyst sample cores were tested in a fixed-bed flow reactor system and FTIR (Fourier transform infrared) spectroscopy was used for measuring the concentration of each gas species. Additional details on the experimental setup and tests can be found.19 The aged core samples were then loaded with soot particles by amounts of 1.0 to 3.0 g/L using a Euro-4 V6 diesel engine operating on diesel certified fuel (cetane number 42) and with a DOC mounted upstream of the filter carrier. The catalyst samples were preheated to 500 °C in N2 gas in order to eliminate volatile organics and any adsorbed ammonia or NOx from the catalyst. Then the catalyst samples were cooled to 200 °C before testing. The experimental work is focused on elucidating both the soot oxidation characteristics for the 2-way device and the difference in SCR performance between clean and soot loaded samples. Data from the following set of controlled reactor experiments were used to validate the model in a systematic manner. NO oxidation and NO2 dissociation experiments: As a precursor to soot oxidation inside the 2-way device, NO2 formation is examined because it is an active soot oxidizer. NO2 dissociation is examined to be able to differentiate its impact with and without the presence of soot. Soot oxidation experiments attributed only to O2 in the inlet feed stream: The experimental data provided information on thermal soot oxidation and low temperature soot oxidation in the presence of Cu−zeolite catalytic material. Soot oxidation experiments in the presence of O2 and NO2 in the feed stream: Both NO2 and O2 work as a soot oxidizer. The soot oxidation rate by NO2 can be quantified in this step. Experiments comparing SCR performance between clean and soot loaded 2-way DPF/SCR cores: Both clean catalyst and soot loaded catalyst samples are examined in terms of DeNOx performance under temperature programmed conditions to isolate soot-NOx interactions.

Figure 3. NO to NO2 conversion efficiency with respect to temperature. Conversion efficiency is calculated by 1 − Ci,IN/Ci,OUT.

the NO2 in the outlet gases is the result of NO oxidation by O2. As expected, greater NO oxidation occurs with 10% O2 compared to 5% O2. The results from the experiment and model agree within 2%. The NO conversion becomes higher as temperature goes up but it is still less than 7%. This is low compared to the NO oxidation over a DOC. One study shows the conversion of NO by oxidation to NO2 within a DOC is up to 40% over a fresh catalyst at 35 000 1/h space velocity.20 The 1% difference between experiment and simulation at 200 °C is due to drift of experimental measurement because, in general, 200 °C is too low to cause a meaningful NO oxidation reaction. In Figure 4, NO2 dissociation under the programmed temperature condition is plotted. The inlet feed gas does not

Figure 4. Concentration of NO and NO2 in the outlet of 2-way blended DPF/SCR during NO2 dissociation test using the temperature programmed oxidation (TPO) procedure.

4. RESULTS 4.1. NO Oxidation and NO2 Dissociation. As NO2 is an active soot oxidizer, the model should capture the concentration of NO2 inside the 2-way device for better prediction of soot oxidation characteristics. The NO2 can exist in exhaust gases and it also can be formed from NO oxidation over the Cu−zeolite catalyst. The purpose of the first test is to investigate the NO oxidation characteristics to NO2 over Cu−zeolite catalyst using experimental results and to calibrate the model using the experimental data. The test conditions are listed in Supporting Information, Table S4.

include NO. Hence, the entire NO in the outlet feed gas is from NO2 dissociation. Significant NO2 dissociation is observed over 400 °C. It is observed that the NO2 dissociation is much higher than NO oxidation which is shown in Figure 3. At 600 °C, the NO2 dissociation is almost 77%, whereas the NO oxidation is only 7%. This implies that NO oxidation is significantly limited by NO2 dissociation at high temperature due to thermodynamic equilibrium. The NO oxidation and NO2 dissociation 15585



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tests confirm that the model can capture the NO2 conversion with good accuracy. 4.2. Soot Oxidation. The NO oxidation and NO 2 dissociation test were conducted with soot-free 2-way DPF/ SCR samples. For the soot oxidation tests, the samples were prepared with an initial loading of soot. Two test cases are examined for the soot oxidation study, and they are summarized in Supporting Information, Table S5 under labels “test 1” and “test 2”. The feed gas composition in test 1 contains 500 ppm of NO and 5% O2, which is a soot oxidizer at temperatures above 550 °C. For test 2, the feed gas includes 5% O2 and 100 ppm of NO2, which is known to oxidize soot at temperatures below 550 °C. Figure 5 represents the COx (carbon monoxide and carbon dioxide) release rate due to soot oxidation for test 1. The Figure 6. Comparison of CO2 release with and without catalytic soot oxidation for test 1.

400 °C. Therefore, it can be inferred that most of the low temperature soot oxidation reaction in test 1 is caused by catalytic oxidation. Figure 7 shows the COx release rate due to soot oxidation for test 2 described in Supporting Information, Table S5. For this

Figure 5. Concentration of COx in the outlet of 2-way blended DPF/ SCR during the soot oxidation test 1.

simulation result overestimates the soot oxidation rate. However, based on the integration of the COx release curve from the experiment, the estimated weight of the soot-loaded 2way DPF sample is less than the actual measured weight of the soot-loaded 2-way DPF-SCR sample by approximately 21%. This could be one of the reasons for discrepancy in comparing experimental and simulation results. It is also observed that there is some soot oxidation for test 1 at lower temperatures (300−400 °C). Possible mechanisms for this low-temperature soot oxidation are NO2-assisted soot oxidation and catalytic soot oxidation by the Cu−zeolite SCR catalyst. The nature of low temperature soot oxidation observed during test 1 is investigated further by using the model. The calibrated values of activation energy for soot oxidation are listed in Supporting Information, Table S6 and are consistent with previous research work.21−25 To investigate low temperature oxidation, test 1 was recalculated by the validated model with the catalytic soot oxidation option turned off (RRcat O2 = 0 in eq 9). In Figure 6, the results with and without catalytic oxidation of soot are compared. Without catalytic oxidation, the low temperature soot oxidation rate underpredicts the actual oxidation rate. The difference between the two curves in Figure 6 implies soot oxidation occurs by catalytic reaction. As such there is no NO2 in the inlet feed gas and consistent with steady state results on NO oxidation (Figure 3), a small amount of NO2 is formed by the NO oxidation reaction between 300 and

Figure 7. COx concentration in the outlet of 2-way blended DPF/SCR during soot oxidation test 2.

test, the inlet feed gas consists of NO2 only as the NOx constituent. The soot oxidation reaction starts at 300 °C because of both catalytic and NO2-assisted oxidation. Figure 8 shows the NO2 and NO concentrations in the outlet feed stream. It should be noted that in the absence of ammonia in the inlet feed stream, there is no DeNOx reaction and the total amount of NOx is unchanged. The relative concentrations of NO2 and NO change due to NO2-assisted soot oxidation and NO2 dissociation. Good agreement between simulation and experiment in Figure 8 represents that soot oxidation by NO2 is well captured by simulation with the activation energy in Supporting Information, Table S6. The transient results from the NO2 dissociation test (clean 2way DPF/SCR sample) and test 2 (soot-loaded 2-way DPF/ SCR sample) are plotted in terms of NO2 conversion efficiency with respect to temperature in Figure 9. This plot shows how much NO2 is decomposed to NO for each test case. More NO2 15586



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the inner surface of the porous wall and a deposit layer grows to form pore bridging. In the case of a clean porous wall, an exhaust gas stream can directly contact the catalyst which is coated inside the porous wall so the mass transfer mechanism from the exhaust gas stream to the inner catalyst washcoat is a boundary layer diffusion as represented in the left-hand side of eq 3. However, in the soot deposited case, the exhaust gas stream tries to find its pathway to minimize flow resistance inside the filter wall so there is little chance for the exhaust gas stream to contact directly the inner catalyst washcoat. Hence, the diffusion through the soot deposit to the catalyst washcoat is added to the mass transfer mechanism. This soot deposit layer has very small inner length scale so diffusion mechanism might be Knudsen diffusion and it might significantly limit the overall reaction rate as compared with a clean case as summarized in Supporting Information, Table S7. Thus, the actual concentration on the catalyst washcoat (Cws,i) becomes lower as compared to the clean case, and the reaction rate denoted by RRi(Cws,i) will decrease. A schematic diagram for this case is presented in Figure 10.

Figure 8. The NOx concentration in the outlet of 2-way blended DPF/SCR during soot oxidation test 2.

Figure 10. Schematic diagram for soot deposit as a deep bed filtration and related variables for eqs 13 to 15.

Figure 9. Comparison of NO2 to NO conversion for the soot-loaded case (test 2) and clean case (NO2 dissociation test).

The concept of effectiveness factor and a parameter called the Thiele modulus has been used to model the effect of diffusion inside the catalyst washcoat. This idea can be extended to the soot loaded filter wall to capture the reaction mechanism between the exhaust gas stream and the catalyst washcoat inside the porous filter wall. As discussed, diffusion through the soot deposit layer is a deterministic mass transfer mechanism for the soot deposit case. Therefore, the diffusionreaction equation can be used to model the balance between mass transfer and reaction for the soot deposited case as it is expressed by eq 3 for the clean case. On the basis of the coordinate system shown in Figure 10, the diffusion reaction equations are

is converted to NO for test 2 than for the NO2 dissociation test. This is because NO2 is also consumed by the soot oxidation reaction in test 2. The difference in NO2 conversion efficiency between the two tests implies the consumption of NO2 due to the soot oxidation reaction. At 400 °C, the difference is at its maximum and further decreases with an increase in temperature. At 600 °C, it is observed that all the NO2 to NO conversion is from dissociation as opposed to NO formation from soot oxidation. 4.3. Effect of Soot Deposit on SCR Reaction. 4.3.1. Effect of Soot Deposit Inside the Filter Wall. Deterioration of catalyst performance by coking is very common in a device which uses hydrocarbon fuel. This performance deterioration can be recovered to the original state if the soot particles are removed. This is different from catalyst deactivation by sintering or poisoning. Several empirical relations have been suggested to model the impact of coking.26,27 In this study, an analytical approach was developed to model the effect of soot deposits inside the filter wall and the impact on SCR reactions. The assumption is that soot deposits inside the filter wall work as a barrier for mass transfer from the gas stream to the catalytic sites, and this reduces the overall catalytic reaction rate for the SCR reactions facilitating NOx reduction. Usually, during a deep bed filtration process, soot particles deposit on

∂ 2C̅ ∂ξ ̅

2

∂ 2C̅ ∂ξ ̅

2

− Φ2C̅ = 0

=0

for 0 ≤ ξ ̅ ≤ δw

for 0 ≤ ξ ̅ ≤ δs

(13a)

(13b)

where C̅ s a nondimensional concentration and defined as C̅ = C/CI and ξ̅ is a nondimensional length scale and defined as ξ̅ = ξ/δw. The symbol CI is the concentration at the interface of the soot deposit and the washcoat. The thickness of the soot deposit layer, δs − δw can be estimated using the unit collector model8 which is incorporated in the deep-bed filtration model. 15587



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The symbol Φw represents the Thiele Modulus which is defined as

RR ideal = −kR,wCws

kR,wδw 2

Φw =

ηs =

Deff,w

(14)

(20)

Deff,s ⎛ 1 − C I/Cws ⎞ RR act = ⎜ ⎟ RR ideal kR,wδw ⎝ δs − δw ⎠

(21)

where Cws/CI can be acquired from eq 17. Equation 21 can be rearranged to eq 22 by replacing Cws/CI with eq 17.

This represents the ratio of diffusion and reaction inside the washcoat. The symbol kR,w is a representative first-order reaction constant. The boundary conditions for eqs 13a and 13b are

ηs =

⎛ ⎞ Deff,w kR,w tanh(Φw ) ⎟ × ⎜⎜ kR,wδw ⎝ (δs − δw ) Deff,w kR,w tanh(Φw ) + Deff,s ⎟⎠ Deff,s

atξ ̅ = 0,

∂C̅ =0 ∂ξ ̅

(15a)

(22)

atξ ̅ = 1,

C̅ = 1

(15b)

Equation 22 shows that if δs approaches δw (e.g., the soot layer thickness goes to zero), the effectiveness factor converges to that of a soot-free catalyst as given by eq 23.

atξ ̅ =

δw , δs

C̅ =

Cws CI

(15c)

lim ηs =

The solutions for the eqs 13a are sinh(Φw ξ ̅ ) C(̅ ξ ̅ ) = sinh(Φw ) C̅(ξ ̅ ) =

for 0 ≤ ξ ̅ ≤ δw

(16b)

RR act = ηs RR clean

The value of CI can be determined by the condition that the molar flux is continuous at this interface and expressed by eq 17. The molar fluxes at the interface can be calculated from the derivatives of eq 16a and 16b. Equation 17 is obtained by equating the derivatives of eqs 16a and 16b and rearranging for CI Deff,s

Cws

(δs − δw )

(17)

In eq 17, CI has two asymptotic values with respect to the Thiele modulus. When the Thiele modulus is very large, that is, the reaction rate is very fast, CI has a minimum as given in eq 18a. In contrast, when the Thiele modulus has a very small value, CI is its maximum equal to Cws Deff,s

C I,min =

(δs − δw )

Deff,w δw +

Deff,s

Cws

(δs − δw )

C I,max = Cws

(18a) (18b)

Using eq 16, an effectiveness factor that modifies the reaction rate can be derived for the soot loaded condition. The actual reaction rate inside the washcoat is equal to the influx rate to the washcoat so the reaction rate can be expressed as shown in eq 19. RR act =

⎛ ∂C 1⎜ −Deff,s ⎜ δw ⎝ ∂ξ

⎞ ⎟ = −Deff,s(Cws − C I) ⎟ δw(δs − δw ) ξ = δw ⎠

tanh(Φw ) = ηc Φw

(23)

(24)

Even though this effectiveness factor is derived based on the assumption of a first order reaction, it can be applied to the SCR reactions, since most of the SCR reactions used in this study are of first order. Equations 22 and 24 are implemented into the 2-way DPF/ SCR solver and the model is applied to simulate a numerical exercise. Test conditions are listed in Supporting Information, Table S8, and the simulations are conducted for a clean and soot loaded 2-way DPF/SCR. The catalyst is initially free from adsorbed ammonia until time t = 0 min. In Figure 15, it is observed that NOx conversion is significantly decreased in the case of a soot-loaded filter at 200 and 300 °C. There is also no significant soot oxidation in this temperature range. However, at 400 °C or higher, DeNOx performance for the soot-loaded filter is recovered to the clean case performance because these temperatures are high enough to burn out the soot deposited inside the filter wall. Figure 12 shows the variation of the amount of soot deposited inside the filter wall and the thickness of the soot cake layer. Around 50 min into the test, indicated by “(A)” in Figure 11, there is still soot remaining inside the filter wall. Inhibition by soot present inside the filter wall contributes to poor NOx conversion compared to the clean sample. At around 200 min into the test, the soot deposited inside the filter wall is burned out, but soot still remains in the cake layer as shown in Figure 12. At this moment, the filter is in a partially regenerated status as indicated by “(B)” in Figure 11. The SCR performance at this point is recovered to its clean status. Variation of the effectiveness factor during the test is shown in Figure 13. The effectiveness factor is dependent on the amount of soot deposited inside the filter wall and the reaction rate. At 50 min, the effectiveness factor is 0.54 for the standard SCR reaction and 0.22 for the ammonia adsorption reaction. It means that the ammonia adsorption rate and SCR rate

Deff,s (δs − δw )

=

In the case of a wall-flow-type SCR, the washcoat layer is much thinner than that of a flow-through type SCR. Hence, the ηc is close to unity as seen in Figure 13 and RRclean is almost equal to RRideal. Finally, the apparent reaction rate for the soot-loaded case can be adjusted using the effectiveness factor giving the following expression:

(16a)

δc(Cws − CI) C δ − Cwsδw ξ̅ + I s CI(δs − δw ) CI(δs − δw )

Deff,w kR,w tanh(Φw ) +

kR,wδw

δs → δw

for δw < ξ ̅ ≤ δs

CI =

Deff,w kR,w tanh(Φw )

(19)

The ideal reaction rate is given in eq 20, and the effectiveness factor for the soot-loaded condition can be derived as in eq 21. Here, the ideal reaction rate means a maximum reaction rate under infinitely fast diffusion conditions. 15588



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wall is totally burned out, the effectiveness factor returns to the clean filter case values. Steady state NOx conversion efficiencies for the numerical exercise shown in Figure 11 is compared with experimental data in Figure 14. The experimental results also show that the NOx

Figure 11. Comparison of SCR performance between clean and sootloaded 2-way blended DPF/SCR under programmed temperature conditions. The “-SL” and the “-C” in the legend represent “sootloaded case” and “clean case”, respectively.

Figure 14. Comparison of simulated and experimental NO x conversion efficiency between clean and soot loaded case.

conversion efficiency for the soot-loaded filter is lower at low temperatures but returns to the clean filter efficiencies at temperatures greater than 400 °C, a trend which is captured in the simulations using the effectiveness factor. 4.3.2. Effect of Soot Oxidation on SCR Reaction. In this section, the interaction between the soot oxidation reactions and the SCR reactions are examined using the model. Test conditions are listed in Supporting Information, Table S9. A temperature of 400 °C for soot oxidation is chosen because at this temperature meaningful filter regeneration starts to occur by NO2-assisted soot oxidation. To exclude the effect of soot deposited inside the filter wall, soot is initialized in the cake layer. This condition can occur in partially regenerated filters as shown with the label “(B)” in Figure 11. In Figure 15 a comparison of the NOx conversion efficiency is made between the clean and partially regenerated 2-way device. As a reference the NOx conversion efficiency at 200 °C from a clean 2-way DPF/SCR sample is shown. The NO2 composition in the engine exhaust gas is very small under normal operating conditions. However, the DOC which is

Figure 12. Variation of soot molar density inside the filter wall and thickness of soot cake layer for the soot-loaded filter in Figure 11. These results are for the axial midpoint of the channel.

Figure 13. Variation of effectiveness factor for ammonia adsorption and standard SCR reaction corresponding to the results in Figure 11.

decreases by 0.54 and 0.22 times due to soot deposit inside the filter wall. At 200 min, when the soot deposited inside the filter

Figure 15. Comparison of NOx conversion rate with respect to NO2/ NOx ratio. 15589



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In the middle of the channel, as shown in Figure 18, the ammonia adsorption rate is very low for the ammonia

usually located in front of the DPF or SCR converts much NO to NO2 around 300 to 400 °C. Hence the concentration NO2 is varied for a fixed inlet concentration of NOx. The maximum NOx conversion rate for the clean case can be achieved at a NO2/NOx ratio of 0.5 for 200 °C and at about 0.4 for 400 °C as shown in Figure 15. However, the NOx conversion rate is almost the same regardless of the NO2 to NOx ratio for the partially regenerated 2-way device because all of the NO2 is consumed inside the soot cake layer before the SCR reaction inside the catalytic filter wall. Figure 16 shows the concentration distributions of NO2 and NO along the inlet channel axial length for a NO2 to NOx ratio

Figure 18. Concentration distribution of NOx through the wall and soot cake layer for a NO2/NOx ratio of 0.75 measured at the axial midpoint. The center line represents the center of the inlet channel.

underdosing condition (NH3/NOx ratio α = 0.9), so the SCR reaction is less active than at the front end of the inlet channel. For the soot-loaded case, the creation of NO by NO2 soot oxidation inside the cake layer and the reduction of NO by SCR inside the catalytic filter wall are almost balanced as shown in Figure 18. Therefore it looks like that there is no concentration gradient of NO in the wall direction. In the rear side of the channel, the creation of NO inside the cake layer is larger than the reduction inside the catalytic filter wall so NO is diffused back into the inlet channel. This is the why the NO concentration increases at the rear side of the channel as shown in Figure 16.

Figure 16. Concentration distribution of NOx inside the inlet for NO2/NOx ratio of 0.75.

of 0.75 at which the difference in NOx conversion rate between the clean and soot-loaded case is largest. Figure 16 shows that NO2 is consumed and converted more for the soot loaded device due to both SCR reaction and soot oxidation. However, NO conversion is very poor. The NO concentration first decreases and then increases again along the channel axial length because of NO formation from NO2 soot oxidation reaction. At the front end of the channel, ammonia is fully adsorbed to its saturated state. From Figure 17, the NO2 conversion rate at this end is 53% for the soot loaded case and 45% for the sootfree case. Soot oxidation increases NO2 conversion by 8%. The NO conversion rates at the front end are 99% and 96%, respectively for the clean and soot-loaded cases.

5. CONCLUSION The 2-way DPF/SCR is characterized by simultaneous reduction of soot by filtration and oxidation and reduction of NOx by SCR reactions. Hence, the interactions between soot and the DeNOx reactions are important phenomena. In this study, a model that can capture this interaction is described and validated using lab-scale flow bench experiments. The soot oxidation characteristics in the 2-way DPF/SCR are examined when the oxidizer is O2 only. The results from the temperature programmed soot oxidation test show that soot oxidation starts to occur at 300 °C. This is much lower than normal thermal soot oxidation temperatures, and it is concluded that the copper zeolite used as a catalytic material for the SCR reactions could potentially work as a catalytic material for soot oxidation. The soot deposited in the form of deep-bed filtration contacts the catalytic material directly and it starts to oxidize first as temperature increases. The soot deposited in the 2-way DPF/SCR affects the DeNOx reaction in two ways. First, the soot deposited in the form of deep-bed filtration inhibits the DeNOx reaction because it acts as a resistance for mass transfer from the exhaust gas stream to the catalytic sites. A mathematical model for changes of reaction rate due to soot deposits was introduced and implemented in the 2-way DPF/SCR model. The predicted DeNOx performance under programmed temperature conditions with the soot loaded 2-way DPF/SCR sample agrees well with the measured DeNOx performance. Second, the soot oxidation reaction consumes significant amounts of

Figure 17. Concentration distribution of NOx through the wall and soot cake layer for NO2/NOx ratio of 0.75 measured at the front end. The center line represents the center of the inlet channel. 15590



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S = active catalytic site Sw = surface area per unit volume of catalytic filter wall [1/ m] Sw,soot = surface area of soot deposit per unit volume [1/m] u = gas flow velocity in the inlet channel [m/s] uw = wall flow velocity [m/s] Vj = volume of jth wall element [m3] w = catalytic filter wall thickness [m] wcake = thickness of soot cake layer [m]

NO2 in the soot cake layer. Under soot-free conditions, the DeNOx performance becomes poor as the NO2/NOx ratio becomes higher than 0.5. However, when soot is fully loaded in the 2-way device and exhaust gas temperature is high enough to cause NO2-assisted soot oxidation (e.g., 400 °C), the DeNOx performance is almost independent of the NO2/NOx ratio.

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ASSOCIATED CONTENT

S Supporting Information *

Tables as described throughout the text. This material is available free of charge via the Internet at http://pubs.acs.org.

■

Subscript and Superscripts

i = ith species act = actual IN = inlet I = inlet channel O = outlet channel OUT = outlet

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address ⊥

Greek

Sloan Automotive Laboratory 31-158, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was sponsored by General Motors as an agreement of UW-GM Collaborative Research Laboratory.

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NOMENCLATURE a = channel width [m] Aj = cross sectional area of jth wall element [m2] As surface area of soot deposit per unit mass [m2] C concentration [mol/m3] Cb concentration in channel [mol/m3] Cwf concentration of gas stream inside the filter wall [mol/ m3] Cws concentration of gas species on solid surface inside the filter wall [mol/m3] Cw,soot = molar density of soot deposited inside the filter wall [mol/m3] Ccake = molar density of soot cake layer [mol/m3] CI = concentration of gas species on the interface of washcoat and soot deposit layer [mol/m3] Dw = effective bulk diffusivity inside the DPF substrate [m2/ s] Deff,w = effective diffusivity inside the washcoat [m2/s] Deff,s = effective diffusivity inside the soot deposit layer [m2/ s] f CO = CO selectivity f CO,cat = CO selectivity for catalytic soot oxidation gCO = CO selectivity for NO2 born soot oxidation kc = mass transfer coefficient in the channel [m/s] kw = mass transfer coefficient inside the catalytic filter wall [m/s] kR,w = representative first order reaction rate constant [1/s] MWC = Molecular weight of carbon RR = reaction rate for a gas species [mol/s] RRcat O2 = soot oxidation rate by O2 due to catalytic reaction [mol/s] RRth O2 = soot oxidation rate by O2 due to thermal reaction [mol/s] RRNO2 = soot oxidation rate by NO2 [mol/s] Rf,w = soot filtration rate as a deep bed filtration [mol/s] Rf,cake = soot filtration rate by soot cake layer [mol/s]

δw = washcoat thickness [m] δs = washcoat thickness plus soot deposit layer inside the filter wall [m] εp = porosity Φw = Thiele modulus ηs = effectiveness factor for soot loaded case ηc = effectiveness factor for clean filter case ξ = coordinate system for deriving the effectiveness factor

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A Model Development for Evaluating Soot-NO - American

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