Assisted Regeneration of Diesel Particulate Filters - American

developed show quite high filtration efficiencies, fre- quently in ... oxygen with noticeable reaction rates at temperatures .... oxidation catalyst i...
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Ind. Eng. Chem. Res. 2002, 41, 2115-2123

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NO2-Assisted Regeneration of Diesel Particulate Filters: A Modeling Study Ioannis P. Kandylas and Grigorios C. Koltsakis* Laboratory of Applied Thermodynamics, Mechanical Engineering Department, Aristotle University Thessaloniki, 540 06 Thessaloniki, Greece

The reduction of particulate emissions from diesel engines is of major interest, considering the strict emission standards posed by the legislation worldwide. Although the technology of particulate filters has been under development for more than 20 years, considerable technological challenges remain regarding effectiveness and durability. The emergence of the continuous regenerating trap (CRT) in conjunction with the availability of low-sulfur diesel fuel represents a promising solution, especially for heavy-duty engines. In the present paper, a modeling approach for the combined catalyst and diesel particulate filter system is presented. The model is used to understand the main behavior trends of the oxidation catalyst and the NO2 regenerated trap individually and as a system. Illustrative model applications are also presented for the case of a modern heavy-duty engine and operating conditions corresponding to the European testing procedures. Although the model is based on global reaction schemes, it is useful in explaining the parameters affecting the CRT system behavior in the real world. Such engineering models are expected to support the selection and design of CRT systems, minimizing the testing effort. Introduction Particulate filtration in the exhaust system of diesel engines is increasingly gaining in importance for both light-duty and heavy-duty applications. Passenger cars equipped with diesel particulate filters (DPFs) already appeared in the market as a means to achieve the low particulate emission standards in Europe.1 The particulate filter technology is also considered the most promising solution toward attaining the emission standards of heavy-duty vehicles.2-5 Some of the diesel filter materials which have been developed show quite high filtration efficiencies, frequently in excess of 90%, as well as acceptable mechanical and thermal durability. The most important issue with diesel traps is filter regeneration. Because of the fuel penalty resulting from the increased backpressure of the loaded DPF, it is necessary that the filter be regenerated, either periodically or continuously, during the regular engine operation. The Continuously Regenerating Trap (CRT) is the trade name for a two-stage catalytic, passive particulate filter system capable of regeneration at temperatures of below 300 °C on a suitable application and with the use of ultralow-sulfur diesel fuel. The principle of CRT regeneration is based on the finding that diesel particulate matter (PM) is easily oxidized by nitrogen dioxide (NO2). Carbon in the form of soot is oxidized by oxygen with noticeable reaction rates at temperatures above 550 °C. With NO2, the process begins to occur already at 250 °C, a temperature which can be encountered in diesel exhaust during normal driving cycles. The CRT is composed of a diesel oxidation catalyst (DOC) installed upstream of a typically ceramic wallflow diesel filter. Apart from converting CO and HC, a * To whom correspondence should be addressed. Tel: +30-310-996066. Fax: +30-310-996019. E-mail greg@ antiopi.meng.auth.gr.

main role of the DOC is to oxidize NO to NO2.6 Engineout NOx emissions from diesel engines are typically composed of NO (only 5% of the total NOx emissions is NO2). At temperatures of 300-350 °C, the catalyst part of the CRT oxidizes a proportion of the NO in the exhaust stream to form NO2, increasing the NO2 fraction to about 50% of the total NOx. A successful CRT application requires that raw engine emissions meet several conditions and limitations. As is the case with all other totally passive filter systems, the CRT behavior depends on the vehicle’s duty cycle. Therefore, it is important to design application-specific optimized systems. This design optimization can be substantially supported by numerical modeling in terms of time-to-market and development cost.7 The CRT regeneration is affected by the NOx/soot ratio in the engine-out emissions. This ratio is typically defined as the ratio of the engine-out NOx mass emissions (calculated with the molecular weight of NO2) to the engine-out soot mass emissions. Higher NOx/soot ratios result in higher NO2 concentrations and better filter regeneration. The NOx/soot ratio of the exhaust emitted by a diesel engine varies considerably with engine type (DI, IDI, and turbocharged), injection pressure, exhaust gas recirculation (EGR) rate, and engine operation point (speed and load and exhaust temperature).8 The main obstacle, however, to the widespread introduction of the CRT is that its performance is impaired by sulfur. The sulfur sensitivity can be attributed to the fact that sulfur dioxide (SO2) adsorption inhibits adsorption of NO2 on the catalytically active sites in the catalyst element of the CRT. This competitive adsorption is blocking the active sites, lowers the formation of a sufficient amount of NO2 in the catalyst, and is characterized by long-term storage effects. As a result, the trap requires higher exhaust temperatures to regenerate and clogging of the filter is more likely to occur.6

10.1021/ie010842m CCC: $22.00 © 2002 American Chemical Society Published on Web 03/26/2002

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Table 1. Reaction Scheme and Rate Expressions Employed in the CRT Oxidation Catalyst

1. CO +

1/

2O2

R1 )

f CO2

A1e-E1/RTcCOcO2 G2(Ts,cj) A2e-E2/RTcCxHycO2

2. CxHy + (x + y/4)O2 f xCO2 + (y/2)H2O

R2 )

3. NO + 1/2O2 f NO2

R3 )

A3e-E3/RTcNOcO2 Eq3 G4(Ts,cj)

4. NO2 f NO + 1/2O2

R4 )

A4e-E4/RTcNO2 Eq4 G4(Ts,cj)

G1(Ts,cj) G3(Ts,cj)

inhibition terms G1 ) Ts(1 + Ka1cCO + Ka2cHC)2(1 + Ka3cCO2cHC2)(1 + Ka4cNO0.7) G2 ) Ts(1 + Ka5cCO + Ka6cHC)2(1 + Ka7cCO2cHC2)(1 + Ka8cNO0.7) G3 ) (1 + Ka9cO2)1.5 G4 ) Ts(1 + Ka10cCO + Ka11cHC)2(1 + Ka12cCO2cHC2)(1 + Ka13cNO0.7)

Another reason for using ultralow-sulfur fuels with the CRT system is catalytic oxidation of SO2. To maximize the NO/NO2 conversion, a very active oxidation catalyst formulation is used in the CRT. That catalyst is also effective in oxidizing SO2 to SO3 and, thus, in producing sulfate particulates. The nucleation of sulfate particulates occurs after gases leave the filter, leading to an observed decrease in the PM filtration efficiency. The effects of the fuel sulfur level on the performance of a continuously regenerating DPF have been experimentally investigated in ref 9 using fuels with various sulfur contents. In this paper we present a modeling approach aiming at the prediction of the combined catalyst + DPF system behavior. In a first step, the reaction scheme of a previously developed oxidation catalyst model10 is extended in order to match the case of the CRT catalyst. Next, we present a mathematical model of the wall-flow DPF. This model is based on a previously presented onedimensional model,11 which has been equipped with an extended reaction scheme in order to include the phenomena involved in the soot reaction with NO2. These two models are used to simulate the behavior of the CRT system. The regeneration behavior of the system at different exhaust gas conditions is discussed. It should be noted that, because of the high commercial interest, very few experimental data on the performance of CRT systems are available in the open literature. In this paper, our primary target is to highlight the areas of modeling application in the design of CRT systems rather than attempting a thorough validation of the model versus experiments. Oxidation Catalyst Model The diesel oxidation catalytic converter code models the transient behavior of DOC in any mode of engine operation. A detailed description of the basic model can be found in a previous authors’ work.10 Although the referenced model is two-dimensional, for our purposes, the radial temperature profiles can be neglected and the problem is simplified to one-dimensional. The onedimensional approach is valid in the case of low heat losses as well as a negligible velocity profile at the catalyst inlet face. The basic features of the “quasisteady” mathematical model can be summarized as follows:

(i) Computation of the convective heat and mass transfer from the exhaust gas to the catalytic surface. A “film approach” is adopted employing mean bulk values for the gas-phase species concentrations and solid-gas interface values for the solid-phase species concentrations. (ii) Computation of the heterogeneous chemical reactions taking place on the catalytic surface based on Langmuir-Hinshelwood-based rate expressions. “Lumping” of surface adsorption/desorption and pore diffusion phenomena in the kinetic rate expressions. (iii) The one-dimensional transient temperature field in the cylindrical converter is computed by taking into account the heat conduction in the substrate using the reaction exothermy and the convective heat transfer with the exhaust gas as source terms. Detailed formulation of the energy and mass balance equations as well as the solution procedure followed is described in detail in ref 12. As with all “quasi-steady” models, the computation of the species concentrations and the reaction rates is based on the equation of the diffusion and reaction rates for each species j:

n˘ i,j(cg,i,j,cs,i,j) ) Ri,j(cjs,i,Ts,i)

(1)

The left-hand side of the equation concerns the mass diffusion rate resulting from the concentration gradient between the gas bulk phase and the wall. The reaction rates Rj (right-hand side) are nonlinear functions of the local temperature and composition at the gas-solid interface. The reaction of interest in the case of the CRT system oxidation catalyst is NO oxidation to NO2. However, additional oxidation reactions of CO, H2, and hydrocarbons present in the diesel exhaust produce heat that may affect the performance of the catalyst. Therefore, a comprehensive reaction scheme including the respective rate expressions is presented in Table 1. At low temperatures and as long as the conditions of chemical equilibrium favor the NO oxidation reaction, the rate of the reverse reaction (NO2 dissociation to NO) is assumed to be zero. Moreover, the reaction rate of the NO oxidation reaction should approach zero as we reach the conditions of chemical equilibrium. At higher temperatures, where chemical equilibrium favors the NO2 dissociation, the situation is exactly reversed.

Ind. Eng. Chem. Res., Vol. 41, No. 9, 2002 2117 Table 2. Adsorption Equilibrium Constants in Oxidation Catalyst Modeling constant

adsorption heat (J/mol)

adsorption factor ka0j

-7990 -3 × 105 -96534 31036 -7990 -3000 -96534 31036 0 20 100 3.98 2 × 105

Ka1 Ka2 Ka3 Ka4 Ka5 Ka6 Ka7 Ka8 Ka9 Ka10 Ka11 Ka12 Ka13

655 2.08 × 103 3.98 4.79 × 105 655 2.08 × 103 3.98 4.79 × 105 0 -7990 -3000 -96534 31036

Figure 1. Computed and measured NO2 fraction in NOx (6% O2 in N2) and effect of O2 concentration on the NO2 fraction in NOx after a 50 g/ft3 Pt oxidation catalyst (270 vppm NO, 10% H2O in N2).

Table 3. Geometric and Thermophysical Properties of the Oxidation Catalyst washcoat loading catalyst diameter catalyst length channel density wall thickness substrate density washcoat density monolith conductivity monolith specific thermal capacity

50 g/ft3 Pt 26.67 cm (10.5 in.) 15.24 cm (10.5 in.) 400 cells/in.2 0.15 mm (0.006 in.) 1687 kg/m3 1500 kg/m3 1.5 W/m‚K 1020 J/kg‚K

Table 4. Kinetics Employed in the Oxidation Catalyst Modeling reaction

activation energy Ei (J/mol)

activity factor Ai (mol‚K/m2‚s)

1 2 3 4

80 000 100 000 70 000 70 000

1 × 1017 4 × 1020 4.5 × 1014 1 × 1014

Figure 2. Effect of NO concentration on the NO2 fraction in NOx after a 50 g/ft3 Pt oxidation catalyst (6% O2, 10% H2O in N2).

To account for these phenomena in the mathematical model, the following factors are applied in the rates of the NO oxidation and NO2 dissociation reactions:

Eq3 ) 1 -

cNO2 cNOcO20.5Kp3(T)

Eq4 ) 1 -

cNO2cO20.5 cNOKp4(T)

(2)

(3)

The adsorption equilibrium constants have the following form:

Kaj ) ka0j exp(-∆Haj)/RTs, j ) 1-4

(4)

The values used for the adsorption equilibrium constants are given in Table 2: As was already mentioned, the role of the oxidation catalyst is to increase the NO2 fraction in the NOx up to the maximum given by the thermodynamic equilibrium between NO and NO2. A series of experiments allowing the study of this behavior was conducted by Gieshoff et al. in ref 13. Selected data from the results of these experiments were used to assess the kinetic constants of the rate expressions. These experiments involved model gas tests using gas-mixing equipment and bottled gases to generate the desired feed stream. The model gas composition was 270 ppm NO, 6% O2, and 10% H2O in N2, and the space velocity of the catalyst was 50 000 h. Table 3 gives the catalyst’s geometric data used for these experiments.

Table 4 presents the kinetics employed in the model to describe the reactions in the oxidation catalyst. The reactions, kinetic expressions, and kinetic constants used in the present model are described in detail in ref 14. Figure 1 shows the measured NO2 fraction in NOx after the oxidation catalyst as a function of temperature for the case of 6% O2. When the rate constants are fitted for this reaction, it is possible to predict with sufficient accuracy the behavior of the oxidation catalyst as a function of temperature in this case. At temperatures below 150 °C, the catalyst is not active enough to oxidize NO to NO2 at space velocities typical for diesel exhaust. For gas temperatures in the region between 150 and 280 °C, the activity of the catalyst is not sufficient to convert enough NO to reach thermodynamic equilibrium and the NO2 reaction is kinetically controlled. At higher temperatures, the oxidation rate is sufficiently high, but the conversion efficiency is limited by chemical equilibrium (thermodynamically controlled). Figure 1 also presents the computed NO to NO2 conversion in the same oxidation catalyst for four different O2 concentrations. The NO2 formation in the oxidation catalyst is of main interest because the NO2 concentration is the main agent for soot oxidation. When operating at low temperatures, in the kinetically controlled regime, the conversion rate increases with the O2 concentration. Moreover, the thermodynamical equilibrium shifts higher, favoring a better catalytic activity. The effect of the inlet NO concentration on the conversion efficiency is presented in Figure 2. It is interesting to note that, according to the simulation model, higher NO concentrations lead to lower efficiencies. This is explained by the effect of NO self-inhibition which typically occurs in precious metal catalysts. This effect is taken into account in our model through the inhibition term appearing in the reaction rate expression.

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where subscript i identifies regions 1 (inlet channel) and 2 (outlet channel). Conservation of Momentum of Channel Gas. The momentum balance of theexhaust gas in inlet and outlet channels can be formulated as follows:

∂pi ∂ + (Fivi2) ) -R1µvi/D2 ∂z ∂z

Figure 3. Effect of catalyst space velocity on the NO2 fraction in NOx after a 50 g/ft3 Pt oxidation catalyst (270 vppm NO, 6% O2, 10% H2O in N2).

The space velocity seems to affect strongly the efficiency of the NO oxidation as presented in Figure 3. Relatively low space velocities are needed to attain high efficiencies in the low-temperature regime. This is particularly important for the correct sizing of the oxidation catalyst. The dimensions of the oxidation catalyst should be carefully and cost-effectively selected for each application, based on the expected flow rates and the conversion efficiency requirements. Mathematical modeling plays an important role in this respect. Particulate Filter Model Because research on the application of trap systems started more than 15 years ago, there already exists a fairly large number of computer models for thermal regeneration of cellular ceramic filters.15-19 Here one must mention first the classical work of Bisset and Shadman20 with a zero-dimensional model. In ref 21, Koltsakis and Stamatelos presented a zero-dimensional catalytic regeneration model (flow conditions and filter temperature were assumed to be uniform along the filter channels), which was validated for certain high flow rate applications. The need for higher accuracy in the prediction of the filter regeneration has prompted the development of a more complicated one-dimensional model, which computes the flow distribution, heat transfer, and reactions across the channels of a wallflow particulate filter.11 This model offers the possibility of computing localized temperature peaks, as well as axial temperature gradients along the filter, which are important for filter safety under uncontrolled regenerations. One-dimensional modeling is sufficient in the case where all filter channels behave in the same way. This is true in the case of negligible heat losses to ambient and uniform radial flow distribution at the filter inlet. These conditions are met in the case of the CRT filter, and therefore we employ the equations of the onedimensional model. In the present work, we based our model on the model previously presented in ref 11 and we extend the reaction scheme to include the effect of carbon reaction with NO2. The governing equations for the conservation of mass, momentum, and energy in the flowing exhaust gas are given below: Conservation of Mass of Channel Gas. In the balance equation for mass conservation, the mass flowing in inlet and outlet channels should be taken into account:

∂ (F v ) ) (-1)i(4/D)Fwvw ∂z i i

(5)

(6)

The right-hand-side term of eq 6 represents the pressure losses in the axial flow direction z, caused by the viscous drag forces. Because the mass flow passing through the wall is only a small fraction of the axial flow, the velocity profile should be close to that observed in flow in close channels. Thus, the relation used to compute the pressure loss is the one used for laminar flows in square ducts. Conservation of Energy of Channel Gas. In the formulation of the energy balance of the channel gas, the convective heat exchange with the channel wall, as well as the enthalpy flowing into or from the elementary control volume through the filter wall, is taken into account. For the inlet channel the gas leaves the control volume at temperature T1:

Cp,gD2F1v1T1|z+∆z - D2F1v1T1|z + 4D∆zFwvwT1|z ) h1 × 4D∆z(Tw - T1) (7) On the other hand, for the outlet channel, the gas enters the control volume at temperature Tw:

Cp,gD2F2v2T2|z+∆z - D2F2v2T2|z - 4D∆zFwvwTw|z ) h1 × 4D∆z(Tw - T2) (8) Soot Combustion. The reaction scheme which takes into account carbon oxidation by exhaust gas oxygen is

C + R1O2 f 2(R1 - 0.5)CO2 + 2(1 - R1)CO

(9)

where R1 is an index of the completeness of the reaction taking values from 0.55 to 0.9, depending on the reactor temperature levels. It must be mentioned that estimation of the value of index R1 can be performed with good accuracy based on the analysis of routine regeneration tests with simple temperature recordings, according to the methodology reported in refs 22 and 23. Additionally, the oxidation of the soot by the NO2 can be described by the following reaction scheme:

C + R2NO2 f R2NO + (2 - R2)CO + (R2 - 1)CO2 (10) where R2 is an index of the completeness of the reaction taking values here from 1.2 to 1.8. The rates of the above reactions are assumed to be Arrhenius-type functions of temperature, and the following rate expression is used for these reactions:

k1,k ) kkTe-Ek/RT

(11)

where subscript k identifies the gaseous reactants 1 (O2) and 2 (NO2). For the apparent activation energies E appearing in the above equations, experimental evidence21,23-25 implies that a value of 125 000 J/mol for the O2/soot reaction and 95 000 J/mol for the NO2/soot reaction satisfactorily represent regeneration reaction behavior.

Ind. Eng. Chem. Res., Vol. 41, No. 9, 2002 2119

Having adopted the values for the apparent activation energy, the factor k can be accordingly tuned to obtain good agreement between calculations and measurements. Considering the stoichiometry of the reactions, the mass balance equation for the deposit layer, assuming that the deposit is consumed in a shrinking mode, gives26

Fp

dw dt

2

-

Figure 4. Comparison of computed onset temperatures for the combustion of soot using nitrogen dioxide and oxygen.

)

∑

k)1

{( ) Mc

[ (

)]}

Spk1(Tw) w Fwvwyk 1 - exp Rk , Mk Rk vw k ) 1 and 2 (12) 1

Energy Balance in the Wall. The energy balance equation for the wall should take into account the contribution of convective heat transfer from the channel flow and from the flow through the wall, the heat released by exothermic soot combustion, and the conductive heat transfer along the channel wall:

∂ (F C T + FsCp,sTw) ) h1(T1 - Tw) + ∂t p p,p w h2(T2 - Tw) + FwvwCp,g(T1 - Tw) + Hreact + Hcond (13) From the equation for the consumption rate of the deposit (eq 12), the heat released by the overall reaction expressed per unit time is computed: 2

Hreact )

( ) [ (

∑k)1

∆Hk Mk

)]

Spk1(Tw) w 1 Fwvwy 1 - exp , Rk vw k ) 1 and 2 (14)

∆Hk indicates a combined reaction enthalpy resulting from the complete and incomplete oxidation of carbon in the two cases of soot/O2 and soot/NO2 reactions, which is linked to R according to the relations

∆H1 ) 2(R1 - 0.5)∆HCO2 + 2(1 - R1)∆HCO (15) ∆H2 ) (1 - R2)∆HCO2 + (R2 - 0.5)∆HCO - R2∆HNO (16) The contribution of heat conduction is

Hcond ) -λp

(

)

∂Tw ∂2 Tw ∂ w - λsws ∂z ∂z ∂z2

(17)

Pressure Drop. A simple pressure drop model is employed, accounting for the flow resistance through the soot layer and the filter wall, based on Darcy’s law.27 It has been shown that the following expression approximates well the total pressure drop through the loaded filter:

∆p )

µ µ v w + v w ws kp w ks

(18)

Initial and Boundary Conditions. The initial temperature and soot loading along the channel wall are provided as initial conditions for the model which may be axially nonuniform. The boundary conditions, which need to be defined, include the exhaust gas

Table 5. Reaction Scheme and Kinetics Parameters Employed in the Soot Oxidation reaction

rate law

activation energy Ei/R (K)

frequency factor Ai (mol‚K/m2‚s)

C/O2 C/NO2

k1 ) A1Te-E1/RT k2 ) A2Te-E3/RT

1.25 × 105 9.00 × 104

2.8 × 10-2 5.0 × 10-1

temperature, flow rate, and oxygen content as functions of time. The governing equations presented above are solved numerically with finite difference techniques using an iterative procedure in the spatial direction controlled by the requirement of zero axial velocity at the end of the inlet channel and atmospheric pressure at the end of the exit channel. Time marching was effected with a fourth-order Runge-Kutta technique. Model Tuning. As was already mentioned, the operating principle of the CRT is based on the fact that NO2 combusts soot at much lower temperatures than does O2. Figure 4 shows the model-predicted “light-off” curves for the reactions of soot with O2 and NO2. These results were obtained by fitting the kinetic constants of the respective reactions to match the behavior reported in the related literature.28 In this test, the temperature was increased at a rate of 1 °C/min and the selected gas was composed of either 1% NO2 in He or 5% O2 in He for the two cases. It can be seen that, although 500 °C is required to combust soot using O2, the onset of combustion occurs at approximately 200 °C when NO2 is used. Table 5 presents the kinetics employed in the model to describe the soot oxidation reactions in the trap. Results and Discussion Based on the above-described model, a study of continuous regeneration of diesel filters under a variety of operating conditions will be presented in this section. The engine-out emissions data used for our computational study were based on a modern six-cylinder, 9-L EGR turbocharged DI diesel engine as presented in ref 29. This engine is calibrated to attain the very low NOx standards compliant with EURO IV requirements. This is mainly supported by a cooled EGR system, which reduces drastically the engine-out NOx levels. The geometrical data for the oxidation catalyst and the particulate filter of the CRT system were selected based on the rough sizing guidelines that are given in the literature.28 These data together with the thermophysical properties of the materials of the catalyst and filter are given in Tables 3 and 6, respectively. A typical regeneration of a CRT filter is presented in Figure 5 in terms of soot mass evolution vs time. In this simulation, we assume an initial filter loading of 30 g of soot (1.77 g/L), which is considered as a modest filter loading. The exhaust gas conditions are assumed to correspond to particularly favorable conditions for regeneration (NOx/soot ) 40, flow rate ) 0.11 kg/s, inlet

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Table 6. Geometrical Data and Thermophysical Properties of the CRT Trap filter material cell density wall thickness diameter length plug length substrate permeability substrate density

Cordierite 100 cells/in.2 0.43 mm (0.017 in.) 266.7 mm (10.5 in.) 304.8 mm (12 in.) 10 mm 4 × 10-3 m2 1300 kg/m3

Figure 7. Soot regeneration behavior for different NOx/soot ratios and exhaust gas temperatures (soot emission ) 40 g/h, flow rate ) 0.15 kg/s).

Figure 5. Computed deposit mass during the regeneration (initial soot loading ) 30 g, NOx/soot ) 40, flow rate ) 0.11 kg/s, inlet gas temperature ) 300 °C).

Figure 8. European stationary cycle (ESC).6

Figure 6. Evolution of soot deposit thickness along the filter during the regeneration (initial soot loading ) 30 g, NOx/soot ) 40, flow rate ) 0.11 kg/s, inlet gas temperature ) 300 °C).

gas temperature ) 300 °C). Although this operation point is characterized by high NOx emissions and the efficiency of the oxidation catalyst in this temperature region is over 90%, the simulation indicates a rather slow rate of soot oxidation and the filter regeneration lasts more than 2 h. The evolution of the regeneration in the form of soot deposit thickness along the filter for different moments is represented in Figure 6. The regeneration starts in the front of the filter because of the local higher temperature and proceeds backward, as shown in this figure, in the form of deposit thickness. To clarify the combined effect of the temperature and NOx/soot ratio on the regeneration behavior, a series of simulations were carried out, as presented in Figure 7. The simulations refer to operation at different exhaust gas temperatures (250-500 °C) and stepwise modifications of the NOx/soot ratio. According to the stoichiometry of the soot reaction, this ratio should be greater than 7.2 (assuming the ratio of the completeness of the reaction, as defined in eq 10, is R2 ≈ 1.8). Because the rate of soot conversion depends on the NO2 concentration, a certain excess in NO2 is always needed to avoid soot accumulation and backpressure increase. Moreover, assuming that the NO2-assisted soot oxidation is first order with respect to nitrogen dioxide, the reaction rate

will increase linearly with increasing NO2 concentration.30 At 200 °C the trap is continuously loading irrespective of the NOx/soot ratio because the gas temperature is too low to initiate the soot/NO2 reaction. At 250 °C the NO2 production in the catalyst becomes significant, and at the same time the NO2 reaction with soot is activated. However, the reaction rates are kinetically limited, and the regeneration rate is higher than the accumulation rate only for very high NOx/soot ratios. At 300 °C the NO2 production exhibits a maximum (see also Figure 1). At the same time the rate of the NO2/soot reaction is sufficiently high to favor the regeneration even for a modest NOx/soot ratio. A further temperature increase to 350 °C leads to lower NO2 production in the oxidation catalyst (thermodynamic limitations; Figure 1). The higher soot/NO2 reaction rate cannot compensate for this effect, and the regeneration is always lower compared to 300 °C. The same trends are observed at 400 and 450 °C. When the temperature is further increased to 500 °C, the soot oxidation with O2 becomes important and compensates for the very low NO2 formation rate. In the following we study the trap behavior in real world conditions, as defined by the European legislative procedures for heavy-duty diesel engines. According to the European stationary cycle (ESC; also known as the OICA/ACEA cycle), the engine is tested on an engine dynamometer over a sequence of 13 steady-state modes. These modes are depicted in Figure 8. According to the legislative procedure, the emissions are measured dur-

Ind. Eng. Chem. Res., Vol. 41, No. 9, 2002 2121 Table 7. Equilibrium Loaded Soot Mass [g/L of Trap] for ESC-OICA Test Modes (Fresh and Aged Oxidation Catalyst)

mode

engine speed (rpm)

2 3 4 5 6 7 8 9 10 11 12 13

1330 1700 1700 1330 1330 1330 1700 1700 2070 2070 2070 2070

a

load (N)

exhaust temp (°C)

1067 519 779 534 800 267 1038 260 845 211 634 423

505 375 430 400 480 290 465 315 415 305 380 330

NOx/soot

equilibrium mass with fresh catalyst (g/L of trap)

equilibrium mass with aged catalyst (g/L of trap)

17.5 9.8 8.3 9.8 9.0 14.0 7.9 15.0 5.3 5.8 5.9 6.0

1.17 8.26 13.09 6.17 2.49 0.54 11.60 0.31 a a a a

1.31 22.46 15.32 7.45 2.60 0.89 12.79 0.56 a a a a

Equilibrium is not attained.

Figure 9. Computed deposit mass (mode 6 in the ESC test).

ing each mode and averaged over the cycle using a set of weighting factors. Table 7 presents the engine and exhaust gas conditions corresponding to each of these modes (modes 2-13) including exhaust temperatures and NOx/soot ratios. From this table, it is obvious that the exhaust gas temperature for all modes is in the range of 280-500 °C and the highest exhaust temperatures are experienced at engine speeds below peaktorque speed and at full-load conditions. The exhaust gas data for these points were assessed based on the data reported in ref 29. The CRT system behavior was simulated for all of the operating points of the ESC test cycle. An initially clean filter was assumed in all cases. The filter was continuously loaded with soot according to the engine-out emissions, assuming a 100% filter collection efficiency. At the same time the NO2 produced in the oxidation catalyst reacted with the collected soot. Typically, the two phenomena resulted in equilibrium conditions, where the soot loading rate is equal to the carbon reaction rate with NO2 (and/or O2 at higher temperatures). As an example Figure 9 presents the evolution of the soot mass in the filter for the engine-operating mode 6. For the high-speed operating points with a low NOx/ soot ratio, the equilibrium cannot be attained. The filter loading at equilibrium conditions for all of the ESC operating points is presented in Table 7. From these data it can be concluded that the NOx/ soot ratio is much more important for continuous trap regeneration behavior than the exhaust temperature level. At the low-load, high-speed operation points, represented by this test, the higher soot, lower NOx emissions may lead to a more or less loaded filter. As a result, some strategies should be adopted to prevent such undesired trap behavior from too low NOx/soot ratio. Such measures are reducing the EGR rate or

Figure 10. Comparison of the computed NO2 fraction in NOx of fresh and aged oxidation catalyst (270 vppm NO, 6% O2, 10% H2O in N2).

improving the combustion to reduce soot formation, thus increasing NOx emissions in the critical areas, or modifying the oxidation catalyst’s coating toward higher NO2 formation. It is well-known that the oxidation catalyst is poisoned by several exhaust gas species that are nonreversibly accumulated on the catalytic surface. These deposits reduce the catalytically active surface area, and therefore the catalytic activity is deteriorated. For the case of a CRT system, this may progressively lead to a reduction of the oxidation catalyst capacity to produce sufficient NO2 for the filter regeneration. The effect of this catalyst aging may be computationally studied by simulating an oxidation catalyst with lower active surface area. This is typically done by reducing the preexponential factors of the reactions in the oxidation catalyst. Figure 10 presents the simulated efficiency curves for a fresh and aged catalyst, assuming that the aged catalyst has 10% of the fresh catalyst’s active sites. It is obvious that not only is the maximum conversion efficiency remarkably lower but also it occurs at higher temperatures. The effect of catalyst aging on the complete CRT system performance, in terms of equilibrium filter loading, is shown in Table 7. Interestingly, although the effect is negligible in some operating modes, it can be very important in some marginal operating conditions with low NOx/soot ratio and medium temperatures (see mode 3). Taking into account the above conditions, the design of CRT systems with respect to catalyst aging could be supported by models able to predict the performance of the aged oxidation catalyst. Concluding Remarks CRTs are extensively studied as a means to achieve the oncoming strict diesel emissions standards. In

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response to the need for computational tools supporting the development of CRT systems, a mathematical model of the NO2-based regeneration process has been developed. This model is comprised of a combination of previously individually developed models of the oxidation catalyst and particulate filter, which is enhanced by the inclusion of the NO2/soot reaction mechanism. The current state of knowledge of the reaction mechanisms of soot oxidation by NO2 was considered toward the selection of a simplified reaction mechanism. However, the results provide at least indications on the conversion and temperature profiles along the system during actual operation, which can be used to assess the system design. Our initial results are consistent with the published experimental data and are able to provide better insight in the physical and chemical phenomena involved. Focusing on the oxidation catalyst, the model is able to predict the light-off as well as the high-temperature, thermodynamically limited NO2 production trends. A very simple kinetics fitting procedure is needed to characterize the activity of a specific catalyst formulation. Regarding the chemistry of the NO2/soot reaction in the particulate filter, the published kinetic data are not sufficient to support mathematical modeling. For our purpose, we employed a relatively simplified reaction scheme, consistent with literature results, regarding the dependency of the reaction rate on temperature. The computational study validated that the dominant factor for the efficiency of a CRT system is the NOx/ soot ratio in the exhaust gas, which is consistent with the previously reported experience. However, the system efficiency may considerably vary as a function of temperature, exhaust flow rate, and the aging status of the oxidation catalyst. This proves the need of careful design of such systems, which can be supported by engineering models. Future work in this area should verify the validity of the proposed modeling methodology in predicting CRT behavior during random transient driving conditions. This would allow the assessment of the engine/CRT system in terms of attaining the legislated emission standards.

ka0 ) adsorption equilibrium coefficient K ) rate coefficient for the reaction in the oxidation catalyst, m/s kp ) permeability of particulate deposit layer, m2 ks ) permeability of ceramic substrate, m2 Ka ) adsorption equilibrium constant Kp ) chemical equilibrium constant M ) molecular weight, kg/mol n˘ ) molecular flux, mol/m3‚s NOx/soot ) weight ratio of NOx to carbon in raw exhaust gas p ) pressure, bar PM ) particulate matter ∆p ) trap backpressure, bar R ) reaction rate (mol/m2‚s) or gas constant (J/mol‚K) sp ) specific area of the deposit layer, m-1 t ) time, s T ) temperature, K v ) velocity, m/s w ) thickness of the deposit layer, m ws ) channel wall thickness, m x ) carbon atoms in the hydrocarbon molecule or distance, m y ) hydrogen atoms in the hydrocarbon molecule yk ) species concentration (mole fraction) z ) axial distance, m

Notation

Literature Cited

Variables A ) frequency factor, mol‚K/m2‚s cj ) vector of species concentrations, mole fraction c ) species concentration, mole fraction Cp ) specific heat capacity, J/kg‚K CRT ) continuous regenerating trap D ) hydraulic diameter of channel, m DI ) direct injection diesel engine DOC ) diesel oxidation catalyst DPF ) diesel particulate filter E ) apparent activation energy, J/mol EGR ) exhaust gas recirculation Eq ) chemical equilibrium rate expression G ) inhibition factor H ) heat convection coefficient, W/m2‚K Hcond ) conductive heat flux, W/m2 Hreact ) reaction heat release, W/m2 ∆Ha ) heat of adsorption, J/mol ∆Hk ) enthalpy of reaction, J/mol HC ) hydrocarbon IDI ) indirect injection diesel engine K ) collisions frequency factor, m/s‚K

Greek Letters R1 ) index of the completeness of thermal soot oxidation R2 ) index of the completeness of NO2/soot reaction R1 ) constant in channel pressure drop correlation λ ) thermal conductivity, W/m‚K µ ) exhaust gas viscosity F ) exhaust gas density, kg/m3 Subscripts c ) carbon g ) exhaust gas i ) space node index, region j ) indication of exhaust species or region k ) indication of reaction k (equations) or gaseous reactants p ) particulate layer, pressure s ) solid, ceramic substrate w ) environmental conditions

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Received for review October 10, 2001 Revised manuscript received January 24, 2002 Accepted January 25, 2002 IE010842M