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Catalytic oxidation in wall-flow reactors with zoned coating
Chemical Engineering Science 63 (2008) 1142 – 1153 www.elsevier.com/locate/ces
Catalytic oxidation in wall-flow reactors with zoned coating Christos K. Dardiotis, Onoufrios A. Haralampous, Grigorios C. Koltsakis ∗ Laboratory of Applied Thermodynamics, Aristotle University Thessaloniki, 541 24 Thessaloniki, Greece Received 24 January 2007; received in revised form 16 October 2007; accepted 5 November 2007 Available online 17 November 2007
Abstract Modern diesel engine technology has recently adopted the wall-flow particulate filter technology. Most commercial filters are also catalyst coated, which gives the potential option to combine oxidation and filtration functionalities in a single reactor. Due to high precious metal costs, it is desirable to make optimal usage of the catalytic coating by applying catalyst zoning. The present study presents and applies a mathematical model that is able to describe the governing heat, mass transfer and chemical reaction phenomena occurring in a wall-flow monolithic reactor with axially variable catalytic activity. The results show that a zoning scheme with more catalysts in the frontal part is beneficial for CO and HC conversion in cold-start transients. The trends are inversed in the case of a simulated cool-down scenario. The effect of different zoning schemes is investigated in a fully transient legislated driving cycle corresponding to a passenger car application. The reactors’ performances are analyzed by examining the transient temperature and species profiles in the inlet and outlet channels. It was shown that the conversion efficiency is a complex function of combined thermal, species transport and reaction phenomena. The results highlight the increased engineering flexibility provided by the catalyst zoning technology and the challenges faced in applications where transient operating conditions prevail. 䉷 2007 Elsevier Ltd. All rights reserved. Keywords: Chemical reactors; Particulate filter; Catalysis; Mathematical modelling; Diesel engine; Pollution
1. Introduction The diesel particulate filter (DPF) technology is nowadays recognized as a technically feasible solution for the emission control of diesel engines (Johnson, 2003). The wall-flow ceramic honeycomb particulate filter, already introduced more than 20 years ago (Howitt and Montierth, 1981; Abthoff et al., 1985), is currently the most mature filter type. This type of filters exhibits excellent filtration efficiency (typically higher than 95%). Most commercial diesel particulate filters (DPFs) are currently installed downstream an oxidation catalyst. The presence of the oxidation catalyst upstream the DPF ensures the efficient reduction in CO and hydrocarbons during normal operation, as well as during forced regeneration with post-injection (Banno et al., 2004). In the latter case, the exothermy of the reactions
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in the oxidation catalyst is subsequently transferred to the DPF through the exhaust gas enthalpy. Most DPFs are today coated with a Precious metal catalyst. The purpose of this catalyst is to facilitate regeneration and to minimize CO emissions during regeneration. Therefore, since catalyzed filters are efficient in oxidizing CO and hydrocarbons, it could be possible to completely remove the oxidation catalyst (Mizutani et al., 2004; Maly et al., 2004). In the case of a system with a single coated DPF, oxidation of CO and HC could take place in the filter. During postinjection the increased concentrations of these species could lead to a temperature increase directly in the catalyzed filter walls, thereby increasing the wall temperature for regeneration. It has been suggested (Punke et al., 2006) that an axially non-uniform catalyst distribution could improve the cold-start behavior for CO and HC conversion in legislated driving cycles. This technology, usually termed “catalyst zoning”, typically employs putting higher amounts of Precious Metal in the front part of the filter, which is more relevant during the critical warm-up phase.
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Obviously, catalyst zoning offers additional degrees of freedom in designing cost-effective catalytic DPF systems, especially taking into account the high cost of Precious metals. In this respect, it is very important to support the design optimization with mathematical modeling in order to minimize the required demanding experimental testing. Only a few research works in the literature deal with the catalyzed DPF as a reactor for catalytic oxidation. In a previous paper (Haralampous and Koltsakis, 2004a), a mathematical model that couples the wall reaction phenomena with the species transfer between gas and wall phases at isothermal conditions was presented. This model was extended to account for transient non-isothermal conditions in Haralampous et al. (2004a,b). This kind of modeling offers the opportunity to study the effect of this coupling on the regeneration performance of the catalyzed DPF, as shown by Koltsakis et al. (2005a). This model is also able to account for intra-layer species diffusion phenomena, some of them being relevant for the operation of catalyzed DPFs, i.e. NO2 “back-diffusion”. Moreover, this model was used to compare wall-flow with flow-through type of substrates taking into account mass-transfer and transient thermal response phenomena (Dardiotis et al., 2006). Modeling of the combined mass-transfer/reaction phenomena in a catalyzed DPF has been presented by Knoth et al. (2005) using steady-state computational fluid dynamics. This work also presents performance comparisons with flow-through substrates. To simplify the model and reduce the computational load, the authors do not include the species-transfer effects from the inlet channel to the wall in their comparisons. In a more recent work of the same group it is recognized that the above simplification is valid only at high flow velocities (Votsmeier et al., 2007). In the present paper, we employ the transient model developed in our previous paper (Dardiotis et al., 2006) to simulate the performance of the Zoned Coated Diesel Particulate Filter (zCDPF) as an oxidation catalyst in order to make direct comparisons under transient conditions simulating cold-start engine start and a cool-down phase, which are most relevant for automotive emissions control. Finally, comparisons will be presented based on transient simulations of complete legislated driving cycles. 2. Catalyzed wall-flow filter model The equations of the catalyzed wall-flow monolith model have been presented for the first time by Haralampous and sKoltsakis (2004a). This model is an extension of the classical single channel regeneration model introduced originally by Bissett (1984) with the inclusion of an additional dimension through the wall. This feature allows for the computation of intra-layer reaction processes and coupling with species diffusion phenomena in the wall and the bulk gas flow. These phenomena are important for the prediction of NO2 -assisted regeneration especially in catalyzed filters (Muntean et al., 2003), as well as O2 diffusion phenomena in the case of high soot loading regenerations (Haralampous and Koltsakis, 2004b; Haralampous et al., 2004a).
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Fig. 1. Schematic of channel model: (a) front view, (b) side view.
A full 3-dimensional filter model based on the single channel approach has also been presented aiming at reliable regeneration predictions (Koltsakis et al., 2005b). Three-dimensional modeling is interesting in the case of high temperature regenerations, where the overall process is affected by non-uniformities in the inlet flow and thermal field, heat losses and channel-tochannel heat exchange. For the purpose of this study, it is sufficient to work with the single channel version of the model, in order to exclude any influence from a radial temperature profile and flow nonuniformities on monolith scale. Moreover, the model will be used only for the case of a completely clean filter, since this paper focuses only on the oxidation of the gaseous species. A schematic of the side and front view of a channel model is given in Fig. 1. The model presented here is able to account for axial variations in the catalyst. The governing equations for the conservation of mass, momentum and energy are given as follows: Conservation of mass of channel gas: j 2 (d vi ) = (−1)i 4dw vw . jz i i
(1)
Conservation of momentum of channel gas: jpi j + (i vi2 ) − 1 vi /di2 . jz jz
(2)
Conservation of energy of channel gas: Inlet channel: Cp,g 1 v1 |z
jT1 4 = h1 (Ts − T1 ). jz d1
(3)
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Outlet channel: Cp,g 2 v2 |z
jT2 4 = (h2 + Cp,g w vw ) (Ts − T2 ). jz d2
(4)
Pressure drop across the ceramic wall: The pressure difference across the inlet and exit channels at a fixed z is the pressure loss due to the flow through the wall, described by the Darcy law: vw ws . (5) p1 − p2 = ks A set of boundary conditions is necessary to solve the system of differential equations (1)–(5). The mass flow rate and the gas temperature are required at the entrance of the inlet channel and additionally the pressure at the outlet channel exit. The solution of the system yields the channel flow field (vw , v1 , v2 ), the pressure field (p1 , p2 ) and the gas temperature field (T1 , T2 ). Energy balance of the solid phase: The temperature field in the filter is described by the equation of transient heat conduction with heat sources in cartesian co-ordinates: s · Cp,s
jTs j2 Ts = s,z 2 + S. jt jz
(6)
The values of s , Cp,s , s,z take into account the respective material properties as functions of temperature. The source term S includes the contribution of the convective heat transfer of the gas flow in the channels and through the wall and the exothermic heat release: S = Hconv + Hwall + Hreact .
(7)
2.1. Heat sources Reaction exotherm: ws Hreact = sF Rk (z)Hk dx. 0
(8)
k
In addition to previous models, the present model is able to account for axial variations in catalytic activity. In Eq. (8) the reaction rate of reaction k is a function of axial distance “z”. Convection of heat due to flow through the wall: The convection of heat due to flow through the wall can be expressed as Hwall = w · vw · sF · Cp,g · (T1 − Ts ).
(9)
Convection of heat due to flow along the channels: The conversion of heat due to flow along the channels can be expressed as Hconv = h1 · sF · (T1 − Ts ) + h2 · sF · (T2 − Ts ).
(10)
2.2. Reaction scheme For the purpose of this study, we will confine our interest to CO and hydrocarbon oxidation reactions, which are the most relevant for catalyzed wall-flow diesel particulate filter applications. A representative hydrocarbon molecule for diesel exhaust has 7 carbon atoms. Moreover, the molecular ratio H/C in
Constant
Adsorption heat Ha,j
Adsorption factor Ka0,j
K1 K2 K3
−7990 −3 × 103 −96534
65.5 2.08 × 103 3.98
Table 2 Geometric properties of the CDPFs Substrate material
Cordierite
Filter diameter Filter length Plug length Channel density Wall thickness Substrate density Substrate permeability
0.144 m 0.1508 m 0.005 m 300 cells/in2 3.048 × 10−4 m 1250 kg/m3 5 × 10−13 m2
diesel exhaust is around 1.8. Therefore, the following reaction scheme considers a single representative hydrocarbon molecule C7 H13 : 1. CO + 1/2O2 −→ CO2 ,
(11)
C7 H13 + 10.25O2 −→ 7CO2 + 6.5H2 O.
(12)
2.
The rate expressions employed in the above reactions follow the traditional L-H approach introduced for Pt-based catalysts by Voltz et al. (1973) and reformulated by Oh and Cavendish (1982): R1 (z) = −
A1 (z) · e−E1 /RT · yCO · yO2 , G1
(13)
R2 (z) = −
A2 (z) · e−E2 /RT · yC7 H13 yO2 G1
(14)
with the following expression accounting for the inhibition term: 2 G1 = T (1 + K1 yCO + K2 yC7 H13 )2 (1 + K3 yCO yC2 7 H13 ),
(15)
Kj = K0,j e−H,j /R·Ts ,
(16)
j = 1 to 3.
The values of the adsorption equilibrium constants are presented in Table 1. The present model does not account for HC storage on zeolite, since the main purpose is to compare the fundamental features of the catalyst zoning concept. Introduction of HC storage is important for the case of real-world system simulation and is discussed in another publication (Koltsakis et al., 2008).
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For the purpose of this study, we will confine our interest to systems of equal external dimensions, namely 5.66 in diameter and 6 in length. The cell density is 300 cells per square inch and the wall thickness is 3.048 × 10−4 m. The geometric properties are summarized in Table 2. Moreover, both systems are assumed to contain exactly the same amount of catalytic material. 2.3. Coupling with species diffusion The governing equation for the mass conservation of any species in the soot layer and wall is jyj jyj j w vw cj,k Rk (z) (17) − w Dj = Mg jx jx jx k
with the following boundary condition for the inlet jyj w vw y1s,j − w Dj jx 1s = w vw y1,j − 1 k1,j · (y1s,j − y1,j ). And for the outlet channel jyj −w Dj = 2 k2,j · (y2s,j − y2,j ). jx 2s
(18)
(19)
The boundary conditions couple the wall with the channel concentrations given in the following mass balances for the inlet and outlet channels (Danckwerts, 1953): d
j ( v1 y1,j ) = −w vw y1,j + 1 k1,j (y1s,j − y1,j ), jz 1
(20)
d
j ( v2 y2,j ) = w vw y2s,j + 2 k2,j (y2s,j − y2,j ). jz 2
(21)
In the above equations, the mass transfer coefficients kij between the gas and the wall in the inlet and outlet channels are calculated based on the Sh number for laminar flow in square channels. kij =
Sh · Dmol,j . di
(22)
Compared with previous publications (Haralampous and Koltsakis, 2004a; Haralampous et al., 2004b), gas density has been included in the mass transfer balances to account for the differences between inlet channel density 1 , outlet channel density 2 and gas density inside wall w . The latter is assumed to be uniform across x as temperature and pressure variation in the wall is negligible (less than 0.5% variation for the flow conditions studied here).
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The effective diffusivity is calculated based on the mixed diffusion model: 1 1 1 (23) = + Dj p Dmol,j Dknud,j with the Knudsen diffusivity dp 8RT Dknud,j = . 3 Mj
(24)
The values of porosity p , tortuosity and mean pore size dp are based on the microstructural properties of the filter wall. 3. Transient warm-up performance In Eqs. (13) and (14) the pre-exponential terms A1 (z) and A2 (z) depend on the local amount of Precious metal loading. As a first approximation, it is assumed that the pre-exponential terms depend linearly on the local PM loading, an assumption commonly used in the literature. The correlation between PM loading and pre-exponential factor in reality may be more complicated; however, this falls outside the scope of this study. For real applications, it is important to study the system behavior during the cold-start, which typically governs the emission performance of a vehicle. In this section, the CDPF model will be used to analyze two systems as regards their gaseous species oxidation performance. The reaction kinetics of the two systems are presented in Table 3. The zCDPF is 1.8 times more active than the CDPF at its first half and 5 times less active than the CDPF at its last half. The performance is calculated at steady exhaust gas composition at inlet, which is summarized in Table 4. To simplify the method and facilitate a better understanding, we assume a simplified test condition, where the reactor is initially at room temperature and is subjected to exhaust gas with constant temperature, flow rate and composition at inlet (200 ◦ C, 0.02 kg/s) resembling diesel exhaust. Fig. 2 shows the substrate temperature profiles calculated for both systems at different times during the warm-up phase. The two systems have the same thermal properties, whereas any differences in reaction exotherm have negligible effect. Thus, the thermal behavior is identical, as shown in the figure. Table 4 Exhaust gas concentrations used for the simulations O2 concentration CO concentration HC concentration
10% 100 ppm 90 ppm
Table 3 Reaction kinetics in the wall-flow filter modeling Reaction
Activation energy
Frequency factor CDPF
Frequency factor zCDPF front
Frequency factor zCDPF rear
1 2
100000 100000
3.5 × 1019 1.0 × 1019
6.3 × 1019 1.8 × 1019
7.0 × 1018 2.0 × 1018
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Fig. 2. Wall temperature profiles during the warm-up test case. The calculated temperature profiles are identical for both CDPF and zCDPF.
Fig. 3. CO concentration profiles at time = 15 s during the warm-up test case along CDPF and zCDPF.
Fig. 3 presents the computed CO concentration profiles at time = 15 s. The CO conversion efficiency in the zCDPF is higher, as evidenced by comparing the CO concentrations of both systems at the exit. It has to be noted that the coupling of convective and diffusive mass-transfer modeling with wall reactions is essential in order to predict the axial distribution of gaseous species along the inlet and outlet channels, as shown by Dardiotis et al. (2006). It can be realized, from the formulation of the model equations, that the convective mass transfer between the gas-phase and the wall is coupled with the calculation of intra-wall diffusion phenomena and thus the intra-layer discretization cannot be avoided. Although this model extension increases the numerical cost by approximately one order of magnitude, it is absolutely necessary to account for the oxidation catalytic performance in catalyzed wall-flow reactors, especially in the case of catalyst zoning. The reader may easily
recognize that in the simplified case in which species diffusion phenomena are ignored, the species concentration profile along the inlet channel would have been constant, which is apparently far from being a realistic assumption. At this point, we should bear in mind that the specific rate expressions used in the simulations produce very low reaction rates at temperatures below 150 ◦ C. Therefore, based on Fig. 2, we could identify that the “active length” of the two systems is the same for both, approximately 27 mm. Despite the same “active length”, the zCDPF is more effective, because CO oxidation is faster at this first half of the reactor. At a time instant corresponding to 55 s, both reactors are sufficiently warm, as already shown in Fig. 2. Fig. 4 presents the CO concentration profiles at this operating condition. Due to high reaction rates at this high temperature, the concentration of CO is almost zero as the flow exits the wall, even at the
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Fig. 4. CO concentration profiles at time = 55 s during the warm-up test case along CDPF and zCDPF.
Fig. 5. CO and HC conversion efficiency vs time during the warm-up test case.
Fig. 6. HC concentration profiles at time = 55 s during the warm-up test case along CDPF and zCDPF.
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Fig. 7. Wall temperature profiles during the cool-down test case. The calculated temperature profiles are identical for both CDPF and zCDPF.
Fig. 8. CO concentration profiles at time = 15 s during the cool-down test case along CDPF and zCDPF.
entrance of the exit channel, so the advantage of the zCDPF is eliminated. The conversion efficiency in both cases is above 95%. The temporal evolution of the CO conversion efficiency is presented in Fig. 5. As explained above, the zCDPF exhibits a superior performance in the initial warm-up period until 100% efficiency is reached for both systems. The situation is somewhat different in the case of C7 H13 , which represents the diesel exhaust hydrocarbons (HCs). HCs are oxidized at slightly higher temperatures compared with CO and have lower diffusivity. The zCDPF oxidizes HCs more efficiently during the initial warm-up phase due to its higher local catalytic activity in the relevant frontal part. However, after the complete reactor becomes sufficiently warm (time = 55 s), the zCDPF shows lower efficiency. This can be explained by observing the HC concentration profiles in Fig. 6.
In the front part of the reactor and up to its mid-length, the conversion is higher in the zCDPF, in which the HC concentration in the exit channel is diminished. However, due to the relatively poor mass-transfer rate in the inlet channel, there is still a significant amount of unburned HCs entering the rear part of the reactor with lower catalytic activity. This was not the case for CO, due to its higher diffusion coefficient as discussed in Fig. 4. In the rear part, the flow passes from the inlet to the outlet channel, being incompletely oxidized and mixes with the originally HC free stream of the outlet channel. On the other hand, the uniformly coated cDPF is more reactive in the rear part, resulting in a final lower HC concentration at the exit of the reactor. 4. Transient cool down performance In this section we assume a simplified test condition, where the reactor is initially at 200 ◦ C and is subjected to exhaust gas
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Fig. 9. CO concentration profiles at time = 35 s during the cool-down test case along CDPF and zCDPF.
Fig. 10. Flow profiles at time = 35 s along the CDPF and zCDPF during the cool-down test case.
with constant temperature, flow rate and composition at inlet (100 ◦ C, 0.02 kg/s) corresponding to diesel exhaust. This protocol resembles a transient operating condition, where the engine shifts from medium to low load, e.g. due to vehicle deceleration. The exhaust gas composition and the characteristics of the filter are the same as the previous section. Fig. 7 shows the substrate temperature profiles calculated for both systems as a function of time during the cool-down test case. As discussed in Fig. 2, the thermal behavior is identical in both systems. Fig. 8 presents the computed CO concentration profiles at time = 15 s. At this instant, the temperature close to the filter inlet is already too low for CO oxidation in both systems. Due to the increasing temperature downstream, the CO conversion efficiency increases and reaches 50% at z = 48 mm of the outlet channel of the CDPF. The respective distance for the zCDPF
is approximately 5 mm shorter, obviously due to the higher catalytic activity in the frontal part. Fig. 9 presents the computed CO concentration profiles at time = 35 s. At this specific instant, the front half part of the filters is below 150 ◦ C. Although the zCDPF is more active in this area, both systems are practically inactive in the first 75 mm. The conversion increases significantly in the rear part of the CDPF, approaching almost 90% at the exit. On the other hand, the activity of the zCDPF in the warmer rear part is much lower, resulting in a substantially lower conversion at the filter exit. Close to the exit of the monoliths, the CO concentration at the outlet channel is higher compared with the respective concentration of the inlet channel in the same axial position. This “paradox” is due to the fact that the outlet channel concentration is actually a result of mixing of two flows, as it is shown in
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Fig. 11. CO and HC conversion efficiency vs time during the cool-down test case.
Fig. 12. Inlet temperature, CO and HC concentrations at inlet during the legislated driving cycle.
Fig. 10: the flow along the outlet channel and the flow coming through the wall from the inlet channel. Near the exit of the filter, the flow entering the wall from the inlet channel has a low axial velocity component which favors the local mass-transfer from the inlet channel to the wall with subsequent decrease in the local CO concentration. The resulting low concentration is further reduced as the flow passes through the catalyzed wall. However, the relative magnitude of this wall-flow is not significant compared with the axial flow along the outlet channel, flowing with a higher local CO concentration. Therefore, the mixing of the two flows results in a concentration which is governed by the locally higher concentration of the outlet channel. The temporal evolution of the CO and HC conversion efficiency during the cool-down test case is presented in Fig. 11. It is obvious that for both CO and HC, the CDPF retains its higher conversion for a longer period compared with the zCDPF, as
a result of the combined thermal, transport and reaction phenomena explained above. 5. Driving cycle performance The results presented in the previous sections showed that the catalyst zoning is beneficial in the case of a warm-up scenario; however, its transient performance during a cool-down phase may be significantly inferior compared with a uniformly coated filter. In practical automotive applications, both situations are of interest. A typical engineering target is the system optimization over a specific legislated transient driving cycle. In this section, we present simulation results for the legislated European Driving Cycle for a typical passenger car application. The input data are taken from a 2.0 l engine conforming to Euro III legislation limits. The inlet temperature of the exhaust
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Fig. 13. Cumulative CO mass during the NEDC performance for four different zoned arrangements.
Fig. 14. Cumulative HC mass during the NEDC performance for four different zoned arrangements.
gas corresponds to a position immediately after the turbine exit. Fig. 12 presents in addition the CO and HC concentrations at filter inlet as functions of time. A parametric analysis is performed covering different zoning schemes. In all cases, the total catalytic activity is the same, which resembles equal Precious Metal usage. The two design parameters are: (a) the zoning intensity, i.e. the percentage of total catalytic activity assigned to the frontal zone and (b) the zoning length, i.e. the length of the frontal zone. Each zoning scheme is thus characterized by two percentile figures. Thus, the zoning scheme 90-50 corresponds to a reactor where 90% of the Precious Metals is located in the frontal 50% of the total reactor length. In total, 21 combinations were performed combining three different zoning lengths and seven different zoning intensities.
Fig. 13 presents the calculated cumulative CO emissions during the driving cycle for three zoned CDPFs and for the uniform one (CDPF). Although the differences are less than 10%, it is evidenced that all the examined zoned systems exhibit superior performance compared with the uniformly coated CDPF. The best CO emissions performance was obtained with a system having 70% of the total Precious Metals in the first 25% of the reactor length. By examination of Fig. 13, it is obvious that the main differences come from the first 200 s of the cycle, which is actually the warm-up phase. In the analysis presented above, it was shown that a zoning scheme with more catalyst in the front part is advantageous in such operating conditions. Similar results for the case of hydrocarbons are presented in Fig. 14. Contrary to CO, the best performance is obtained by an inverse zoning scheme, where only 30% of the total
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Fig. 15. CO and HC iso-efficiency plots in the driving cycle as function of zoning length and intensity.
Precious Metals are placed in the frontal 75% of the total length. Fig. 14 shows that in the early cold-start part of the driving cycle (time < 100 s) the zoning scheme 90-50 seems superior for the reasons explained above. However, the situation is reversed later in the driving cycle, where HC slip occurs primarily during engine cool-down modes. As shown in the previous section, a system with more catalysts in the frontal area will suffer from lower efficiency in a cool-down mode. In the case of hydrocarbons, the net effect is that the cold-start advantage of the zoning scheme 90-50 is lost and the final cumulative result is in favor of the zoning scheme 30-75. Fig. 15 presents in contour plot format the results in terms of overall conversion efficiency in the driving cycle for the 21 zoning schemes simulated. It is interesting to note that there is no single optimum scheme that fulfills both CO and HC conversion efficiency maximization under the specific constraints used here. 6. Conclusions The present study compared the transient performance characteristics of catalyzed wall-flow diesel particulate filter with different zoning schemes. The comparison was based on a pure computational basis, using a mathematical model previously published and experimentally validated. A zoning scheme with more catalyst in the frontal part was shown to be beneficial for CO conversion in a simulated coldstart transient. In the same test case, hydrocarbon conversion was shown to be affected by mass-transfer limitations in the frontal part, which results in a lower conversion of the zoned systems at full-warmed conditions. In a simulated cool-down
transient, the same zoned system performance was consistently inferior for both CO and HC. The reactor performance was analyzed by examining the transient temperature and species profiles in the inlet and outlet channels. It was shown that the conversion efficiency is a complex function of combined thermal, species transport and reaction phenomena. Finally, transient simulations with input data from a legislated driving cycle were performed for different zoning schemes. The conclusions are in line with the simplified transient analysis, showing that a preferential coating of the frontal part reduces the cold-start emissions. However, this advantage may be negated during cool-down modes occurring later in the cycle, which was especially the case for hydrocarbons. The results presented in this paper highlight the increased engineering flexibility provided by the catalyst zoning technology and the challenges faced in applications where transient operating conditions prevail. Modeling tools are expected to provide substantial help toward optimizing system design for each specific application. Notation A cj,k Cp D d di dp E G
reaction rate frequency factor, mol K/m3 s stoichiometric coefficient of species j in reaction k specific heat capacity, J/kg K mass diffusivity, m2 /s hydraulic diameter, m hydraulic diameter of channel i, m mean pore size, m activation energy, J/mol inhibition term, K
C.K. Dardiotis et al. / Chemical Engineering Science 63 (2008) 1142 – 1153
H h ki,j Kp ks Mg p R R Sh sf T v ws x yj z
heat transfer per filter volume, W/m3 convection coefficient, W/m2 K mass transfer coefficient of species j in channel i, m/s chemical equilibrium constant, dimensionless permeability of ceramic substrate, m2 molecular weight, kg/mol pressure, Pa universal gas constant, J/mol K reaction rate, mol/(m3 s) sherwood number, dimensionless specific surface area per reactor volume, m−1 temperature, K velocity, m/s channel wall thickness, m space variable perpendicular to wall surface, m mole fraction of species j, dimensionless axial distance, m
Greek letters 1 constant in channel pressure drop correlation, dimensionless H reaction heat, J/mol p porosity, dimensionless thermal conductivity, W/m K exhaust gas viscosity, kg/m s density, kg/m3 tortuosity, dimensionless Subscripts 1s inlet channel–soot surface interface (x = −w) 2s outlet channel—wall surface interface (x = ws ) g exhaust gas i channel index (1=inlet channel, 2=outlet channel) j species index k reaction index s solid, ceramic substrate w wall-outlet channel interface z axial direction References Abthoff, J., Schuster, H.-D., Langer, H.-.J., Loose G., 1985. The regenerable trap oxidizer—an emission control technique for diesel engines. SAE paper 850015. Banno, Y., Tanak, Y., Hihara, T., Nagata, M., 2004. Pre-filter diesel oxidation catalyst development for DOC-CSF system. SAE paper 2004-01-1430. Bissett, E.J., 1984. Mathematical model of the thermal regeneration of a wall-flow monolith diesel particulate filter. Chemical Engineering Science 39, 1233–1244.
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Danckwerts, P.V., 1953. Continuous flow systems: distribution of residence times. Chemical Engineering Science 2, 1–13. Dardiotis, C.K., Haralampous, O.A., Koltsakis, G.C., 2006. Catalytic oxidation performance of wall-flow vs flow-through monoliths for diesel emissions control. Industrial & Engineering Chemistry Research 45, 3520–3530. Haralampous, O.A., Koltsakis, G.C., 2004a. Back-diffusion modeling of NO2 in catalyzed particulate filters. Industrial & Engineering Chemistry Research 43, 875–883. Haralampous, O.A., Koltsakis, G.C., 2004b. Oxygen diffusion modeling in diesel particulate filter regeneration. A.I.Ch.E. Journal 50, 2008–2019. Haralampous, O.A., Dardiotis, C.K., Koltsakis, G.C., Samaras, Z.C., 2004a. Study of catalytic regeneration mechanisms in diesel particulate filters using coupled reaction-diffusion modeling. SAE 2004-01-1941. Haralampous, O.A., Koltsakis, G.C., Samaras, Z.C., Vogt, C.D., Ohara, E., Watanabe, Y., Mizutani, T., 2004b. Reaction and diffusion phenomena in catalyzed diesel particulate filters. SAE paper 2004-01-0696. Howitt, J.S. Montierth, M.R., 1981. Cellular ceramic diesel particulate filter. SAE paper 810114. Johnson, V.T., 2003. Diesel emission control in review—the last 12 months. SAE paper 2003-01-0039. Knoth, J.F., Drochner, A., Vogel, J., Gieshoff, J., Kögel, M., Pfeifer, M., Votsmeier, M., 2005. Transport and reaction in catalytic wall-flow filters. Catalysis Today 105, 598–604. Koltsakis, G.C., Haralampous, O.A., Dardiotis, C.K., Samaras, Z.C. Vogt C.D., Ohara, E., Watanabe, Y., Mizutani, T., 2005a. Performance of catalyzed particulate filters without upstream oxidation catalyst. SAE paper 200501-0952. Koltsakis, G.C., Haralampous, O.A., Margaritis, N., Samaras, Z.C., Vogt, C.D., Ohara, E., Watanabe, Y., Mizutani, T., 2005b. 3-Dimensional modeling of the regeneration in SiC particulate filters. SAE paper 2005-01-0953. Koltsakis, G.C., Dardiotis, C.K., Samaras, Z.C., Frey, M., Wenninger, G., Krutsch, B., Haralampous, O., 2008. Model-based optimization of catalyst zoning in diesel particulate filters. SAE International, submitted for publication. Maly, M., Claussen, M., Carlowitz, O., Kroner, P., Ranalli, M., Schmidt, S., 2004. Influence of the nitrogen dioxide based regeneration on soot distribution. SAE paper 2004-01-0823. Mizutani, T., Watanabe, Y., Yuuki, K., Hashimoto, S., Hamanaka, T., Kawashima, J., 2004. Soot regeneration model for SiC-DPF system design. SAE paper 2004-01-0159. Muntean, G., Rector, D., Herling, D., Lessor, D., Khaleel, M., 2003. LatticeBoltzmann diesel particulate filter sub-grid modeling—a progress report. SAE paper 2003-01-0835. Oh, S.H., Cavendish, J.C., 1982. Transients of monolithic catalytic converters: response to step changes in feedstream temperature as related to controlling automobile emissions. Industrial Engineering Chemistry Production Research and Development 21, 29–37. Punke, A., Grubert, G., Li, Y., Dettling, J., Neubauer, T., 2006. Catalyzed soot filters in close coupled position for passengers vehicles. SAE paper 2006-01-1091. Voltz, S.E., Morgan, C.R., Liederman, D., Jacob, S.M., 1973. Kinetic study of carbon monoxide and propylene oxidation on platinum catalysts. Industrial Engineering Chemistry Production Research and Development 12, 294–301. Votsmeier, M., Gieshoff, J., Kögel, M., Pfeifer, M., Knoth, J.F., Drochner, A., Vogel, H., 2007. Wall-flow filters with wall-integrated oxidation catalyst a simulation study. Applied Catalysis B: Environmental 70, 233–240.
Catalytic oxidation in wall-flow reactors with zoned coating Christos K. Dardiotis, Onoufrios A. Haralampous, Grigorios C. Koltsakis ∗ Laboratory of Applied Thermodynamics, Aristotle University Thessaloniki, 541 24 Thessaloniki, Greece Received 24 January 2007; received in revised form 16 October 2007; accepted 5 November 2007 Available online 17 November 2007
Abstract Modern diesel engine technology has recently adopted the wall-flow particulate filter technology. Most commercial filters are also catalyst coated, which gives the potential option to combine oxidation and filtration functionalities in a single reactor. Due to high precious metal costs, it is desirable to make optimal usage of the catalytic coating by applying catalyst zoning. The present study presents and applies a mathematical model that is able to describe the governing heat, mass transfer and chemical reaction phenomena occurring in a wall-flow monolithic reactor with axially variable catalytic activity. The results show that a zoning scheme with more catalysts in the frontal part is beneficial for CO and HC conversion in cold-start transients. The trends are inversed in the case of a simulated cool-down scenario. The effect of different zoning schemes is investigated in a fully transient legislated driving cycle corresponding to a passenger car application. The reactors’ performances are analyzed by examining the transient temperature and species profiles in the inlet and outlet channels. It was shown that the conversion efficiency is a complex function of combined thermal, species transport and reaction phenomena. The results highlight the increased engineering flexibility provided by the catalyst zoning technology and the challenges faced in applications where transient operating conditions prevail. 䉷 2007 Elsevier Ltd. All rights reserved. Keywords: Chemical reactors; Particulate filter; Catalysis; Mathematical modelling; Diesel engine; Pollution
1. Introduction The diesel particulate filter (DPF) technology is nowadays recognized as a technically feasible solution for the emission control of diesel engines (Johnson, 2003). The wall-flow ceramic honeycomb particulate filter, already introduced more than 20 years ago (Howitt and Montierth, 1981; Abthoff et al., 1985), is currently the most mature filter type. This type of filters exhibits excellent filtration efficiency (typically higher than 95%). Most commercial diesel particulate filters (DPFs) are currently installed downstream an oxidation catalyst. The presence of the oxidation catalyst upstream the DPF ensures the efficient reduction in CO and hydrocarbons during normal operation, as well as during forced regeneration with post-injection (Banno et al., 2004). In the latter case, the exothermy of the reactions
∗ Corresponding author. Tel.: +30 2310 995870; fax: +30 2310 996019.
E-mail address: [email protected] (G.C. Koltsakis). 0009-2509/$ - see front matter 䉷 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2007.11.012
in the oxidation catalyst is subsequently transferred to the DPF through the exhaust gas enthalpy. Most DPFs are today coated with a Precious metal catalyst. The purpose of this catalyst is to facilitate regeneration and to minimize CO emissions during regeneration. Therefore, since catalyzed filters are efficient in oxidizing CO and hydrocarbons, it could be possible to completely remove the oxidation catalyst (Mizutani et al., 2004; Maly et al., 2004). In the case of a system with a single coated DPF, oxidation of CO and HC could take place in the filter. During postinjection the increased concentrations of these species could lead to a temperature increase directly in the catalyzed filter walls, thereby increasing the wall temperature for regeneration. It has been suggested (Punke et al., 2006) that an axially non-uniform catalyst distribution could improve the cold-start behavior for CO and HC conversion in legislated driving cycles. This technology, usually termed “catalyst zoning”, typically employs putting higher amounts of Precious Metal in the front part of the filter, which is more relevant during the critical warm-up phase.
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Obviously, catalyst zoning offers additional degrees of freedom in designing cost-effective catalytic DPF systems, especially taking into account the high cost of Precious metals. In this respect, it is very important to support the design optimization with mathematical modeling in order to minimize the required demanding experimental testing. Only a few research works in the literature deal with the catalyzed DPF as a reactor for catalytic oxidation. In a previous paper (Haralampous and Koltsakis, 2004a), a mathematical model that couples the wall reaction phenomena with the species transfer between gas and wall phases at isothermal conditions was presented. This model was extended to account for transient non-isothermal conditions in Haralampous et al. (2004a,b). This kind of modeling offers the opportunity to study the effect of this coupling on the regeneration performance of the catalyzed DPF, as shown by Koltsakis et al. (2005a). This model is also able to account for intra-layer species diffusion phenomena, some of them being relevant for the operation of catalyzed DPFs, i.e. NO2 “back-diffusion”. Moreover, this model was used to compare wall-flow with flow-through type of substrates taking into account mass-transfer and transient thermal response phenomena (Dardiotis et al., 2006). Modeling of the combined mass-transfer/reaction phenomena in a catalyzed DPF has been presented by Knoth et al. (2005) using steady-state computational fluid dynamics. This work also presents performance comparisons with flow-through substrates. To simplify the model and reduce the computational load, the authors do not include the species-transfer effects from the inlet channel to the wall in their comparisons. In a more recent work of the same group it is recognized that the above simplification is valid only at high flow velocities (Votsmeier et al., 2007). In the present paper, we employ the transient model developed in our previous paper (Dardiotis et al., 2006) to simulate the performance of the Zoned Coated Diesel Particulate Filter (zCDPF) as an oxidation catalyst in order to make direct comparisons under transient conditions simulating cold-start engine start and a cool-down phase, which are most relevant for automotive emissions control. Finally, comparisons will be presented based on transient simulations of complete legislated driving cycles. 2. Catalyzed wall-flow filter model The equations of the catalyzed wall-flow monolith model have been presented for the first time by Haralampous and sKoltsakis (2004a). This model is an extension of the classical single channel regeneration model introduced originally by Bissett (1984) with the inclusion of an additional dimension through the wall. This feature allows for the computation of intra-layer reaction processes and coupling with species diffusion phenomena in the wall and the bulk gas flow. These phenomena are important for the prediction of NO2 -assisted regeneration especially in catalyzed filters (Muntean et al., 2003), as well as O2 diffusion phenomena in the case of high soot loading regenerations (Haralampous and Koltsakis, 2004b; Haralampous et al., 2004a).
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Fig. 1. Schematic of channel model: (a) front view, (b) side view.
A full 3-dimensional filter model based on the single channel approach has also been presented aiming at reliable regeneration predictions (Koltsakis et al., 2005b). Three-dimensional modeling is interesting in the case of high temperature regenerations, where the overall process is affected by non-uniformities in the inlet flow and thermal field, heat losses and channel-tochannel heat exchange. For the purpose of this study, it is sufficient to work with the single channel version of the model, in order to exclude any influence from a radial temperature profile and flow nonuniformities on monolith scale. Moreover, the model will be used only for the case of a completely clean filter, since this paper focuses only on the oxidation of the gaseous species. A schematic of the side and front view of a channel model is given in Fig. 1. The model presented here is able to account for axial variations in the catalyst. The governing equations for the conservation of mass, momentum and energy are given as follows: Conservation of mass of channel gas: j 2 (d vi ) = (−1)i 4dw vw . jz i i
(1)
Conservation of momentum of channel gas: jpi j + (i vi2 ) − 1 vi /di2 . jz jz
(2)
Conservation of energy of channel gas: Inlet channel: Cp,g 1 v1 |z
jT1 4 = h1 (Ts − T1 ). jz d1
(3)
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Outlet channel: Cp,g 2 v2 |z
jT2 4 = (h2 + Cp,g w vw ) (Ts − T2 ). jz d2
(4)
Pressure drop across the ceramic wall: The pressure difference across the inlet and exit channels at a fixed z is the pressure loss due to the flow through the wall, described by the Darcy law: vw ws . (5) p1 − p2 = ks A set of boundary conditions is necessary to solve the system of differential equations (1)–(5). The mass flow rate and the gas temperature are required at the entrance of the inlet channel and additionally the pressure at the outlet channel exit. The solution of the system yields the channel flow field (vw , v1 , v2 ), the pressure field (p1 , p2 ) and the gas temperature field (T1 , T2 ). Energy balance of the solid phase: The temperature field in the filter is described by the equation of transient heat conduction with heat sources in cartesian co-ordinates: s · Cp,s
jTs j2 Ts = s,z 2 + S. jt jz
(6)
The values of s , Cp,s , s,z take into account the respective material properties as functions of temperature. The source term S includes the contribution of the convective heat transfer of the gas flow in the channels and through the wall and the exothermic heat release: S = Hconv + Hwall + Hreact .
(7)
2.1. Heat sources Reaction exotherm: ws Hreact = sF Rk (z)Hk dx. 0
(8)
k
In addition to previous models, the present model is able to account for axial variations in catalytic activity. In Eq. (8) the reaction rate of reaction k is a function of axial distance “z”. Convection of heat due to flow through the wall: The convection of heat due to flow through the wall can be expressed as Hwall = w · vw · sF · Cp,g · (T1 − Ts ).
(9)
Convection of heat due to flow along the channels: The conversion of heat due to flow along the channels can be expressed as Hconv = h1 · sF · (T1 − Ts ) + h2 · sF · (T2 − Ts ).
(10)
2.2. Reaction scheme For the purpose of this study, we will confine our interest to CO and hydrocarbon oxidation reactions, which are the most relevant for catalyzed wall-flow diesel particulate filter applications. A representative hydrocarbon molecule for diesel exhaust has 7 carbon atoms. Moreover, the molecular ratio H/C in
Constant
Adsorption heat Ha,j
Adsorption factor Ka0,j
K1 K2 K3
−7990 −3 × 103 −96534
65.5 2.08 × 103 3.98
Table 2 Geometric properties of the CDPFs Substrate material
Cordierite
Filter diameter Filter length Plug length Channel density Wall thickness Substrate density Substrate permeability
0.144 m 0.1508 m 0.005 m 300 cells/in2 3.048 × 10−4 m 1250 kg/m3 5 × 10−13 m2
diesel exhaust is around 1.8. Therefore, the following reaction scheme considers a single representative hydrocarbon molecule C7 H13 : 1. CO + 1/2O2 −→ CO2 ,
(11)
C7 H13 + 10.25O2 −→ 7CO2 + 6.5H2 O.
(12)
2.
The rate expressions employed in the above reactions follow the traditional L-H approach introduced for Pt-based catalysts by Voltz et al. (1973) and reformulated by Oh and Cavendish (1982): R1 (z) = −
A1 (z) · e−E1 /RT · yCO · yO2 , G1
(13)
R2 (z) = −
A2 (z) · e−E2 /RT · yC7 H13 yO2 G1
(14)
with the following expression accounting for the inhibition term: 2 G1 = T (1 + K1 yCO + K2 yC7 H13 )2 (1 + K3 yCO yC2 7 H13 ),
(15)
Kj = K0,j e−H,j /R·Ts ,
(16)
j = 1 to 3.
The values of the adsorption equilibrium constants are presented in Table 1. The present model does not account for HC storage on zeolite, since the main purpose is to compare the fundamental features of the catalyst zoning concept. Introduction of HC storage is important for the case of real-world system simulation and is discussed in another publication (Koltsakis et al., 2008).
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For the purpose of this study, we will confine our interest to systems of equal external dimensions, namely 5.66 in diameter and 6 in length. The cell density is 300 cells per square inch and the wall thickness is 3.048 × 10−4 m. The geometric properties are summarized in Table 2. Moreover, both systems are assumed to contain exactly the same amount of catalytic material. 2.3. Coupling with species diffusion The governing equation for the mass conservation of any species in the soot layer and wall is jyj jyj j w vw cj,k Rk (z) (17) − w Dj = Mg jx jx jx k
with the following boundary condition for the inlet jyj w vw y1s,j − w Dj jx 1s = w vw y1,j − 1 k1,j · (y1s,j − y1,j ). And for the outlet channel jyj −w Dj = 2 k2,j · (y2s,j − y2,j ). jx 2s
(18)
(19)
The boundary conditions couple the wall with the channel concentrations given in the following mass balances for the inlet and outlet channels (Danckwerts, 1953): d
j ( v1 y1,j ) = −w vw y1,j + 1 k1,j (y1s,j − y1,j ), jz 1
(20)
d
j ( v2 y2,j ) = w vw y2s,j + 2 k2,j (y2s,j − y2,j ). jz 2
(21)
In the above equations, the mass transfer coefficients kij between the gas and the wall in the inlet and outlet channels are calculated based on the Sh number for laminar flow in square channels. kij =
Sh · Dmol,j . di
(22)
Compared with previous publications (Haralampous and Koltsakis, 2004a; Haralampous et al., 2004b), gas density has been included in the mass transfer balances to account for the differences between inlet channel density 1 , outlet channel density 2 and gas density inside wall w . The latter is assumed to be uniform across x as temperature and pressure variation in the wall is negligible (less than 0.5% variation for the flow conditions studied here).
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The effective diffusivity is calculated based on the mixed diffusion model: 1 1 1 (23) = + Dj p Dmol,j Dknud,j with the Knudsen diffusivity dp 8RT Dknud,j = . 3 Mj
(24)
The values of porosity p , tortuosity and mean pore size dp are based on the microstructural properties of the filter wall. 3. Transient warm-up performance In Eqs. (13) and (14) the pre-exponential terms A1 (z) and A2 (z) depend on the local amount of Precious metal loading. As a first approximation, it is assumed that the pre-exponential terms depend linearly on the local PM loading, an assumption commonly used in the literature. The correlation between PM loading and pre-exponential factor in reality may be more complicated; however, this falls outside the scope of this study. For real applications, it is important to study the system behavior during the cold-start, which typically governs the emission performance of a vehicle. In this section, the CDPF model will be used to analyze two systems as regards their gaseous species oxidation performance. The reaction kinetics of the two systems are presented in Table 3. The zCDPF is 1.8 times more active than the CDPF at its first half and 5 times less active than the CDPF at its last half. The performance is calculated at steady exhaust gas composition at inlet, which is summarized in Table 4. To simplify the method and facilitate a better understanding, we assume a simplified test condition, where the reactor is initially at room temperature and is subjected to exhaust gas with constant temperature, flow rate and composition at inlet (200 ◦ C, 0.02 kg/s) resembling diesel exhaust. Fig. 2 shows the substrate temperature profiles calculated for both systems at different times during the warm-up phase. The two systems have the same thermal properties, whereas any differences in reaction exotherm have negligible effect. Thus, the thermal behavior is identical, as shown in the figure. Table 4 Exhaust gas concentrations used for the simulations O2 concentration CO concentration HC concentration
10% 100 ppm 90 ppm
Table 3 Reaction kinetics in the wall-flow filter modeling Reaction
Activation energy
Frequency factor CDPF
Frequency factor zCDPF front
Frequency factor zCDPF rear
1 2
100000 100000
3.5 × 1019 1.0 × 1019
6.3 × 1019 1.8 × 1019
7.0 × 1018 2.0 × 1018
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Fig. 2. Wall temperature profiles during the warm-up test case. The calculated temperature profiles are identical for both CDPF and zCDPF.
Fig. 3. CO concentration profiles at time = 15 s during the warm-up test case along CDPF and zCDPF.
Fig. 3 presents the computed CO concentration profiles at time = 15 s. The CO conversion efficiency in the zCDPF is higher, as evidenced by comparing the CO concentrations of both systems at the exit. It has to be noted that the coupling of convective and diffusive mass-transfer modeling with wall reactions is essential in order to predict the axial distribution of gaseous species along the inlet and outlet channels, as shown by Dardiotis et al. (2006). It can be realized, from the formulation of the model equations, that the convective mass transfer between the gas-phase and the wall is coupled with the calculation of intra-wall diffusion phenomena and thus the intra-layer discretization cannot be avoided. Although this model extension increases the numerical cost by approximately one order of magnitude, it is absolutely necessary to account for the oxidation catalytic performance in catalyzed wall-flow reactors, especially in the case of catalyst zoning. The reader may easily
recognize that in the simplified case in which species diffusion phenomena are ignored, the species concentration profile along the inlet channel would have been constant, which is apparently far from being a realistic assumption. At this point, we should bear in mind that the specific rate expressions used in the simulations produce very low reaction rates at temperatures below 150 ◦ C. Therefore, based on Fig. 2, we could identify that the “active length” of the two systems is the same for both, approximately 27 mm. Despite the same “active length”, the zCDPF is more effective, because CO oxidation is faster at this first half of the reactor. At a time instant corresponding to 55 s, both reactors are sufficiently warm, as already shown in Fig. 2. Fig. 4 presents the CO concentration profiles at this operating condition. Due to high reaction rates at this high temperature, the concentration of CO is almost zero as the flow exits the wall, even at the
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Fig. 4. CO concentration profiles at time = 55 s during the warm-up test case along CDPF and zCDPF.
Fig. 5. CO and HC conversion efficiency vs time during the warm-up test case.
Fig. 6. HC concentration profiles at time = 55 s during the warm-up test case along CDPF and zCDPF.
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Fig. 7. Wall temperature profiles during the cool-down test case. The calculated temperature profiles are identical for both CDPF and zCDPF.
Fig. 8. CO concentration profiles at time = 15 s during the cool-down test case along CDPF and zCDPF.
entrance of the exit channel, so the advantage of the zCDPF is eliminated. The conversion efficiency in both cases is above 95%. The temporal evolution of the CO conversion efficiency is presented in Fig. 5. As explained above, the zCDPF exhibits a superior performance in the initial warm-up period until 100% efficiency is reached for both systems. The situation is somewhat different in the case of C7 H13 , which represents the diesel exhaust hydrocarbons (HCs). HCs are oxidized at slightly higher temperatures compared with CO and have lower diffusivity. The zCDPF oxidizes HCs more efficiently during the initial warm-up phase due to its higher local catalytic activity in the relevant frontal part. However, after the complete reactor becomes sufficiently warm (time = 55 s), the zCDPF shows lower efficiency. This can be explained by observing the HC concentration profiles in Fig. 6.
In the front part of the reactor and up to its mid-length, the conversion is higher in the zCDPF, in which the HC concentration in the exit channel is diminished. However, due to the relatively poor mass-transfer rate in the inlet channel, there is still a significant amount of unburned HCs entering the rear part of the reactor with lower catalytic activity. This was not the case for CO, due to its higher diffusion coefficient as discussed in Fig. 4. In the rear part, the flow passes from the inlet to the outlet channel, being incompletely oxidized and mixes with the originally HC free stream of the outlet channel. On the other hand, the uniformly coated cDPF is more reactive in the rear part, resulting in a final lower HC concentration at the exit of the reactor. 4. Transient cool down performance In this section we assume a simplified test condition, where the reactor is initially at 200 ◦ C and is subjected to exhaust gas
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Fig. 9. CO concentration profiles at time = 35 s during the cool-down test case along CDPF and zCDPF.
Fig. 10. Flow profiles at time = 35 s along the CDPF and zCDPF during the cool-down test case.
with constant temperature, flow rate and composition at inlet (100 ◦ C, 0.02 kg/s) corresponding to diesel exhaust. This protocol resembles a transient operating condition, where the engine shifts from medium to low load, e.g. due to vehicle deceleration. The exhaust gas composition and the characteristics of the filter are the same as the previous section. Fig. 7 shows the substrate temperature profiles calculated for both systems as a function of time during the cool-down test case. As discussed in Fig. 2, the thermal behavior is identical in both systems. Fig. 8 presents the computed CO concentration profiles at time = 15 s. At this instant, the temperature close to the filter inlet is already too low for CO oxidation in both systems. Due to the increasing temperature downstream, the CO conversion efficiency increases and reaches 50% at z = 48 mm of the outlet channel of the CDPF. The respective distance for the zCDPF
is approximately 5 mm shorter, obviously due to the higher catalytic activity in the frontal part. Fig. 9 presents the computed CO concentration profiles at time = 35 s. At this specific instant, the front half part of the filters is below 150 ◦ C. Although the zCDPF is more active in this area, both systems are practically inactive in the first 75 mm. The conversion increases significantly in the rear part of the CDPF, approaching almost 90% at the exit. On the other hand, the activity of the zCDPF in the warmer rear part is much lower, resulting in a substantially lower conversion at the filter exit. Close to the exit of the monoliths, the CO concentration at the outlet channel is higher compared with the respective concentration of the inlet channel in the same axial position. This “paradox” is due to the fact that the outlet channel concentration is actually a result of mixing of two flows, as it is shown in
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Fig. 11. CO and HC conversion efficiency vs time during the cool-down test case.
Fig. 12. Inlet temperature, CO and HC concentrations at inlet during the legislated driving cycle.
Fig. 10: the flow along the outlet channel and the flow coming through the wall from the inlet channel. Near the exit of the filter, the flow entering the wall from the inlet channel has a low axial velocity component which favors the local mass-transfer from the inlet channel to the wall with subsequent decrease in the local CO concentration. The resulting low concentration is further reduced as the flow passes through the catalyzed wall. However, the relative magnitude of this wall-flow is not significant compared with the axial flow along the outlet channel, flowing with a higher local CO concentration. Therefore, the mixing of the two flows results in a concentration which is governed by the locally higher concentration of the outlet channel. The temporal evolution of the CO and HC conversion efficiency during the cool-down test case is presented in Fig. 11. It is obvious that for both CO and HC, the CDPF retains its higher conversion for a longer period compared with the zCDPF, as
a result of the combined thermal, transport and reaction phenomena explained above. 5. Driving cycle performance The results presented in the previous sections showed that the catalyst zoning is beneficial in the case of a warm-up scenario; however, its transient performance during a cool-down phase may be significantly inferior compared with a uniformly coated filter. In practical automotive applications, both situations are of interest. A typical engineering target is the system optimization over a specific legislated transient driving cycle. In this section, we present simulation results for the legislated European Driving Cycle for a typical passenger car application. The input data are taken from a 2.0 l engine conforming to Euro III legislation limits. The inlet temperature of the exhaust
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Fig. 13. Cumulative CO mass during the NEDC performance for four different zoned arrangements.
Fig. 14. Cumulative HC mass during the NEDC performance for four different zoned arrangements.
gas corresponds to a position immediately after the turbine exit. Fig. 12 presents in addition the CO and HC concentrations at filter inlet as functions of time. A parametric analysis is performed covering different zoning schemes. In all cases, the total catalytic activity is the same, which resembles equal Precious Metal usage. The two design parameters are: (a) the zoning intensity, i.e. the percentage of total catalytic activity assigned to the frontal zone and (b) the zoning length, i.e. the length of the frontal zone. Each zoning scheme is thus characterized by two percentile figures. Thus, the zoning scheme 90-50 corresponds to a reactor where 90% of the Precious Metals is located in the frontal 50% of the total reactor length. In total, 21 combinations were performed combining three different zoning lengths and seven different zoning intensities.
Fig. 13 presents the calculated cumulative CO emissions during the driving cycle for three zoned CDPFs and for the uniform one (CDPF). Although the differences are less than 10%, it is evidenced that all the examined zoned systems exhibit superior performance compared with the uniformly coated CDPF. The best CO emissions performance was obtained with a system having 70% of the total Precious Metals in the first 25% of the reactor length. By examination of Fig. 13, it is obvious that the main differences come from the first 200 s of the cycle, which is actually the warm-up phase. In the analysis presented above, it was shown that a zoning scheme with more catalyst in the front part is advantageous in such operating conditions. Similar results for the case of hydrocarbons are presented in Fig. 14. Contrary to CO, the best performance is obtained by an inverse zoning scheme, where only 30% of the total
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Fig. 15. CO and HC iso-efficiency plots in the driving cycle as function of zoning length and intensity.
Precious Metals are placed in the frontal 75% of the total length. Fig. 14 shows that in the early cold-start part of the driving cycle (time < 100 s) the zoning scheme 90-50 seems superior for the reasons explained above. However, the situation is reversed later in the driving cycle, where HC slip occurs primarily during engine cool-down modes. As shown in the previous section, a system with more catalysts in the frontal area will suffer from lower efficiency in a cool-down mode. In the case of hydrocarbons, the net effect is that the cold-start advantage of the zoning scheme 90-50 is lost and the final cumulative result is in favor of the zoning scheme 30-75. Fig. 15 presents in contour plot format the results in terms of overall conversion efficiency in the driving cycle for the 21 zoning schemes simulated. It is interesting to note that there is no single optimum scheme that fulfills both CO and HC conversion efficiency maximization under the specific constraints used here. 6. Conclusions The present study compared the transient performance characteristics of catalyzed wall-flow diesel particulate filter with different zoning schemes. The comparison was based on a pure computational basis, using a mathematical model previously published and experimentally validated. A zoning scheme with more catalyst in the frontal part was shown to be beneficial for CO conversion in a simulated coldstart transient. In the same test case, hydrocarbon conversion was shown to be affected by mass-transfer limitations in the frontal part, which results in a lower conversion of the zoned systems at full-warmed conditions. In a simulated cool-down
transient, the same zoned system performance was consistently inferior for both CO and HC. The reactor performance was analyzed by examining the transient temperature and species profiles in the inlet and outlet channels. It was shown that the conversion efficiency is a complex function of combined thermal, species transport and reaction phenomena. Finally, transient simulations with input data from a legislated driving cycle were performed for different zoning schemes. The conclusions are in line with the simplified transient analysis, showing that a preferential coating of the frontal part reduces the cold-start emissions. However, this advantage may be negated during cool-down modes occurring later in the cycle, which was especially the case for hydrocarbons. The results presented in this paper highlight the increased engineering flexibility provided by the catalyst zoning technology and the challenges faced in applications where transient operating conditions prevail. Modeling tools are expected to provide substantial help toward optimizing system design for each specific application. Notation A cj,k Cp D d di dp E G
reaction rate frequency factor, mol K/m3 s stoichiometric coefficient of species j in reaction k specific heat capacity, J/kg K mass diffusivity, m2 /s hydraulic diameter, m hydraulic diameter of channel i, m mean pore size, m activation energy, J/mol inhibition term, K
C.K. Dardiotis et al. / Chemical Engineering Science 63 (2008) 1142 – 1153
H h ki,j Kp ks Mg p R R Sh sf T v ws x yj z
heat transfer per filter volume, W/m3 convection coefficient, W/m2 K mass transfer coefficient of species j in channel i, m/s chemical equilibrium constant, dimensionless permeability of ceramic substrate, m2 molecular weight, kg/mol pressure, Pa universal gas constant, J/mol K reaction rate, mol/(m3 s) sherwood number, dimensionless specific surface area per reactor volume, m−1 temperature, K velocity, m/s channel wall thickness, m space variable perpendicular to wall surface, m mole fraction of species j, dimensionless axial distance, m
Greek letters 1 constant in channel pressure drop correlation, dimensionless H reaction heat, J/mol p porosity, dimensionless thermal conductivity, W/m K exhaust gas viscosity, kg/m s density, kg/m3 tortuosity, dimensionless Subscripts 1s inlet channel–soot surface interface (x = −w) 2s outlet channel—wall surface interface (x = ws ) g exhaust gas i channel index (1=inlet channel, 2=outlet channel) j species index k reaction index s solid, ceramic substrate w wall-outlet channel interface z axial direction References Abthoff, J., Schuster, H.-D., Langer, H.-.J., Loose G., 1985. The regenerable trap oxidizer—an emission control technique for diesel engines. SAE paper 850015. Banno, Y., Tanak, Y., Hihara, T., Nagata, M., 2004. Pre-filter diesel oxidation catalyst development for DOC-CSF system. SAE paper 2004-01-1430. Bissett, E.J., 1984. Mathematical model of the thermal regeneration of a wall-flow monolith diesel particulate filter. Chemical Engineering Science 39, 1233–1244.
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