Ind. Eng. Chem. Res. 1994,33,3086-3093
3086
Mathematical Modeling of Electrically Heated Monolith Converters: Analysis of Design Aspects and Heating Strategy Se H. Oh*** and Edward J. Bissett General Motors NAO Research & Development Center, Warren, Michigan 48090-9055
The design aspects and heating strategy of a n electrically heated converter have been analyzed using the transient monolith model developed and verified in our previous studies. The results of model calculations presented here quantify the beneficial effects on cold-start emission performance of increasing the power level and heating time, decreasing the volume of the resistively heated element, and preheating the converter prior to engine start. It is also shown that a feedback controller based on converter-bed temperature measurements provides a convenient means of modulating power supply during actual operation of electrically heated converters. Just as in conventional unheated monolith converters, catalyst deactivation is predicted to cause significant deterioration of heated converter performance; increasing the maximum power level for the controller appears to be a n effective way of compensating for performance deterioration due to catalyst deactivation.
Introduction The recent adoption of the California emission standards for low-emission vehicles (LEVs) and ultralowemission vehicles (ULEVs)necessitates the development of advanced emission control technologies that can further reduce exhaust emissions. As pointed out previously (Hellman et al., 1989; Whittenberger and Kubsh, 19901, the first two minutes after a cold start contribute up to 75% of the total hydrocarbon (HC) and CO tailpipe emissions collected over the Federal Test Procedure (FTP) driving schedule for late-model gasoline vehicles, and thus it is crucial to drastically reduce cold-start exhaust emissions in order to meet the stringent future emission standards. Recent studies have demonstrated that electrically heating the catalyst substrate of a metal monolith is an effective means of shortening the time to converter lightoff and thus of reducing cold-start HC and CO emissions (Whittenberger and Kubsh, 1990, 1991; Heimrich et al., 1991; Kubsh and Lissiuk, 1991; Brunson et al., 1993). In view of the significant cold-start emission reduction potential of this technology demonstrated in these studies (generally '50% reduction compared to unheated cases), it is of practical interest to analyze in detail and optimize the design aspects and heating strategy of an electrically heated monolith converter. In this paper, the second part in a series of our heated converter modeling studies, the monolith warmup model developed and verified previously (Oh et al., 1993) is used to investigate how the cold-start emission performance of an electrically heated converter is affected by its key design and operating parameters. Specific topics covered in this paper include the role of an electrically heated element in cold-start emission reduction, parametric sensitivity analysis for the case of time-based post-crank heating (i.e., effects of heated volume, power level, and heating time), impact of catalyst deactivation in the heated element, effect of converter preheating, and heating strategies utilizing a temperature-based feedback control algorithm. Results of such analysis provide useful guidance in the design and operation of electrically heated monoliths by identifylng important system parameters and quantifylng the sensitivity of E-mail:
[email protected].
converter warmup performance to changes in each of these parameters.
Heated Converter Model A detailed description of the heated converter model and numerical technique used to solve the equations is given in our earlier paper (Oh et al., 1993). The model employed here is a transient one-dimensional (in the axial direction) model for a catalytic monolith derived from fundamental principles of heat and mass conservation. Salient features included in the model are (1) convective heat and mass transport, (2)interphase (gasto-solid) heat and mass transfer, (3) catalytic reactions and the attendant heat release in the solid phase (monolith substrate deposited with catalyzed washcoat), (4)heat accumulation in the solid phase, ( 5 ) heat conduction through the substrate, and (6) resistive heating of the solid phase due to electrical power supply. The major assumptions invoked in the model formulation are a uniform flow distribution at the monolith face and adiabatic operation of the converter (i.e., no heat loss to the surroundings). Under these assumptions, all the monolith channels would behave the same, thus allowing channel-to-channel variations or interactions to be ignored in the calculations (i.e., single-channel monolith model). These assumptions have been shown to be reasonable for the purpose of calculating converter warmup performance of interest here (Chen et al., 1988). The Pt-catalyzed oxidation reactions of CO, hydrocarbons (C3H6 and CHd, and H2 are considered. Given time-varying exhaust gas conditions specified at the converter inlet (typically at l-s intervals), the model is capable of predicting, among other quantities, both the cumulative mass emissions and the axial temperature profiles in the gas and solid phases as a function of time. It has been shown previously (Oh et al., 1993) that despite the various simplifying assumptions invoked in the development, our model describes the essential features of an electrically heated monolith well enough to provide the quantitative prediction of its thermal response and conversion performance during the cold-start portion of actual vehicle emission tests. (Measured and calculated HC emissions during the coldstart period generally agreed to within lo%.) Thus, the
0888-5885/94/2633-3086$04.50/00 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 3087
- 0
5
400
g
200
I
I-
I./
- 0
g
6
20
Y
m
L
m
E
10
G 0
0
50 100 FTP Time (s)
Figure 1. HC concentration (as C 3 ) , temperature, and mass flow rate of the exhaust gas entering converter during the first 125 s (Le., cycle 1) of the FTP.
model can be used with confidence to quickly evaluate various options for heated converter design and operation. For the simulation results reported here, we used as model input engine-out exhaust data (species concentrations, temperature, and flow rate) from a 2.3-L engine measured during the first 125 s of the Federal Test Procedure (FTP) driving schedule (see Figure 1). This portion of the government-prescribed driving schedule used for vehicle emission measurements (referred to as cycle 1)is composed of various driving modes such as idle, cruise, acceleration, and deceleration. This causes a multitude of highly transient converter inlet conditions, as illustrated in Figure 1. These converter inlet conditions (as well as CO, NO, and 0 2 concentrations not shown in Figure 1)were measured at Every 1s, and their values within each of the 1-s intervals were approximated by linear interpolation for model calculations. For this particular vehicle system, cold-start fuel enrichment lasted for about 20 s and the exhaust temperature at the converter inlet reached a typical catalyst lightoff temperature (say, 600 K or 330 "C) at -25 s into the FTP. It is assumed that a resistively heated element (10" herringbone corrugated metalsubstrate monolith with 33 channels/cm2) is placed upstream of two conventional ceramic monolith bricks (62 square channels/cm2), all housed in the same converter shell (87 cm2 frontal area by 30 cm length).
Since the total converter volume is fxed, this configuration requires shortening the front ceramic brick to accommodate the heated metallic element. The electrically heated portion of the monolith is assumed to be physically separated from the unheated portion, allowing no axial heat conduction across the interface. The characteristics of the metal (heated) and ceramic (unheated) monoliths are listed in Table 1. The presence of the washcoat on the substrate is taken into account in calculating the total heat capacity of the solid phase. The catalytic (i.e., active metal) surface area per unit converter volume was estimated by matching calculated CO and HC tailpipe emissions with those actually measured with a production converter that had been vehicle-aged for approximately 12000 miles. The active metal surface area of 150 cm-l listed in Table 1 corresponds to -6% metal dispersion, which is in general agreement with the chemisorption data previously reported for various vehicle-aged samples of a commercial three-way catalyst (Oh et al., 1993). In this study we focus on the first 125 s (Le., cycle 1) of the FTP. Consideration of this cold-transient segment is adequate for the purpose of examining the impact of electrical heating, because for the inlet exhaust gas conditions of interest here, fully warmedup converter temperatures (-550 "C) are reached in the last portion of cycle 1, making electrical heating unnecessary beyond cycle 1. Also, all the simulations reported here were carried out for a total converter length of 15 cm comprising a metallic heated element and a shortened front ceramic brick, neglecting the presence of the downstream ceramic brick. This does not limit the generality of our results, because the downstream portion of a monolith is not heated up fast enough to contribute significantly to the converter lightoff process with or without electrical heating (Oh and Cavendish, 1983; Oh et al., 1993). This argument was further supported by the results of preliminary calculations with variable converter lengths, which show that the predicted cold-start emissions are not significantly affected by the addition of the downstream ceramic brick.
Results and Discussion Converter Warmup Behavior with and without Electrical Heating. Figure 2a shows the solid temperature profiles along the monolith length with and without electrical heating at 30 s into the FTP. The temperature profile within the unheated monolith (ceramic only; 87 cm2 x 15 cm) is a decreasing function of axial distance because the incoming engine exhaust is the only heat source for the catalyst warmup process.
Table 1. Characteristics of Heated Catalytic Converter metal (heated) frontal area (cm2) length (cm) hydraulic radius of channel (cm) solid fraction of substrate solid fraction of washcoat density of substrate (g/cm3) density of washcoat (g/cm3) specific heat of substrate (J/gK) specific heat of washcoat (J/gK) substrate thermal conductivity (J/cmwK) asymptotic Nusselt number catalytic surface areakonverter volume (cm2/crn3) a
T,represents solid temperature in kelvin.
ceramic (unheated)
87 X
0.077 0.06 0.06 7.22 1.3 0.46 1.005 6.84 x 5.2 150
87 30-x 0.0565 0.22 0.12 2.5 1.3 1.071 1.56 x 10-4T, - 3.435 x lO4/TS2a 1.005 0.02
+
+ 1.571 x 10-4T,
a
3.608 150
3088 Ind. Eng. Chem. Res., Vol. 33, No. 12,1994 1.6r
-- Converter -In -Convetter-Out
/ / /
.-
-
1000
Unhealed
-
E 0.4 Heated
0
'0
\
$zoo/
0
0
120
+
Figure 3. Cumulative HC (C3He CH4) emissions into and out of converter with and without electrical heating.
I 0.8 0.2 0.4 0.6 0.8 1.0
0
Normalized Axial Distance Figure 2. Solid temperature (a, top) and gas-phase C3H6 concentration (b, bottom) profiles along the monolith length a t 30 s into the FTP with and without electrical heating.
For the heated case, an electrical power of 3000 W is assumed to be supplied t o a relatively small metalsubstrate monolith section (87 cm2 x 3 cm) placed upstream of the shortened ceramic brick (87 cm2 x 12 cm) for 60 s following the cold start. In addition to providing higher solid temperature levels, electrical heating leads to the development of a temperature peak within the monolith somewhat downstream of the metal-ceramic zone interface located at a normalized axial distance of 0.2. It is also interesting to note that the temperature rise due t o electrical heating is not confined to the resistively heated portion (front 20%) of the monolith. This prediction can be attributed to the fact that the heat supplied t o and generated (by reaction) within the electrically heated element is constantly carried downstream by the exhaust flow. The corresponding gas-phase C3H6 concentration profiles are shown in Figure 2b. Without electrical heating, the solid temperature at 30 s following the cold start is still too low for catalytic reaction to occur, as evidenced by the flat C3H6 concentration profile over the entire monolith length. Upon electrical heating, on the other hand, a substantial fraction of the monolith near the inlet exceeds typical catalyst lightoff temperature (-40% of the monolith above 600 K, see Figure 2a) and the gas-phase C3H6 concentration in that region decreases rapidly with axial distance as a result of the HC oxidation reaction occurring there. Figure 3 shows the impact of the electrical heating on the cumulative tailpipe mass emissions of total HC (Le., C3H6 CH4) during the first 125 s of the FTP for the same cases considered in Figure 2. Also included in Figure 3 for reference is the cumulative HC emission entering the converter (dashed curve) as a function of time. Comparison of the converter-in and converterout HC emissions shows that for the unheated case no significant reaction occurs until -35 s into the FTP. Upon electrical heating, however, the time to converter lightoff is predicted to be reduced to -10 s, resulting in a drastic (-75%) reduction in the total HC emissions produced during the first 125 s of the FTP. Under all operating conditions considered here, the methane conversion during cycle 1 (first 125 s of the
+
40 80 FTP Time (s)
-2
0.6
2500W '0
3000W
u 6 7.5 1.5
3
4.5
Length of Heated Section (crn) Figure 4. Cycle 1 HC emission as a function of heated volume (frontal area = 87 cm2) for various power levels.
FTP) was predicted to be negligible. The cumulative mass emission of non-methane HC (i.e., a t the end of cycle 1 can be calculated simply by subtracting 0.0618 g from the total HC emission numbers given throughout the paper. Time-Based Post-Crank Heating. We first consider simple heating strategies where a constant electrical power is supplied to the converter for a predetermined period of time after engine start (i.e., no preheating). In this case, key design and operating parameters are the size and the location of the heated element, heating time, and power level. Preliminary calculations confirm our intuition that the external heat supplied to the converter is best utilized by placing the heated element near the monolith inlet. Therefore, we restrict our attention to such a converter configuration in this paper. Figure 4 shows the effects of heated volume on the predicted tailpipe HC emission during cycle 1for various power levels. Here the heated volume varied by changing the length of the heated element (frontal area = 87 cm2) while keeping the total (i.e., heated plus unheated) converter length constant at 15 cm. All the results presented in Figure 4 were obtained by computer simulations with a heating time of 60 s. (Such a long heating time, although not necessary in practice as will be shown later, was chosen here to examine a maximum emission reduction potential for each combination of heated volume and power level.) The curve for 0 W (i.e., metallic heated element in place but no electrical power supplied) is shown in Figure 4 for comparison purposes. The prediction that the cycle 1HC emission decreases
Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 3089 1000 r
--
o.8
m
1
1.5 cm
“\,Post-Heater Element \
750
E 0.4
u
OO
1
2
Length of Heated Section (cm)
3
Figure 5. Dependence of cycle 1 HC emission on heated volume (frontal area = 87 cm2) for 2000 W i n the regime of small heated volumes.
somewhat with increasing heated volume in the unheated case can be attributed to the fact that the metalsubstrate monolith located upstream lights off faster than the conventional ceramic monolith it replaces. The same conclusion carries over to cases with relatively low power levels (e.g., 500 W). For power levels of practical interest (> 1500 W), however, the model predicts the opposite trend that decreased heated volumes lead to lower emissions. The cold-start emission performance at 2000 W is particularly sensitive to the volume of the heated section in the converter. Increasing the power level beyond 2000 W further reduces the cold-start emissions, and at the same time makes the performance of the electrically heated converter less sensitive to variations in the heated volume. In view of the greater emission reduction potential of small heated volumes predicted in Figure 4 for power levels of L 1500 W, it is of interest to examine the extent to which the performance of an electrically heated converter improves as the heated volume approaches zero. The computational results presented in Figure 5 over the range of small heated volumes (2000 W for 60 s in all cases) show that as the length of the heated element decreases from 3 to 1.5 cm, the cold-start tailpipe HC emission (solid curve) decreases rapidly and then declines gradually to a limiting level with a further decrease in the heated volume. The predicted emission for the limiting case of zero heated volume was calculated assuming that all the supplemental heat supplied to the converter has been used to directly raise the inlet exhaust gas temperature above its normal level. [This approximates a situation which occurs in a catalytic converter heated by an upstream fuel burner (Bissett, E. J.; Oh, S. H. General Motors Research & Development Center, Warren, MI, unpublished results, 1991).1 This assumption is reasonable because as the heated volume approaches zero, both the accumulation of energy and heat generation due to reaction within the resistively heated element would become negligible. The solid curve in Figure 5 shows that decreasing the length of the heated section below 1.5 cm tends to give a relatively small reduction in cold-start tailpipe emission. This suggests that the use of extremely small heated volumes in practice is undesirable, especially when
Normalized Axial Distance Figure 6. Solid temperature profiles along the monolith length at 20 s into the FTP for various lengths of the heated section (frontal area = 87 cm2). The electrical power level is 2000 W in all cases.
taking the poisoning and mechanical integrity of the heated element into consideration. The impact of poison accumulation in the heated element on heated converter performance will be discussed later in the paper. Also included in Figure 5 are predicted cycle 1 HC emissions leaving the resistively heated element as a function of its volume (dashed curve). As expected, the post-heater HC emission increases with decreasing heated volume as a result of the decreased residence time of gas within the heated element. It is interesting to note, however, that the conversion performance of the unheated ceramic monolith (as given by the difference between the dashed and solid curves in Figure 5) improves as the heated volume decreases. This compensation effect can be attributed to the fact that a small heated element is more effective at heating the downstream ceramic monolith up to the required reaction temperatures, as will be explained below. The prediction of Figures 4 and 5 that electrically heated converters with small heated volumes are effective in reducing cold-start tailpipe emissions can be explained by comparing the solid temperature profiles shown in Figure 6 for various heated volumes at a fured power level of 2000 W. With the length of the heated section as small as 1.5 cm, nearly 20% of the monolith near the inlet (total converter length = 15 cm) is well above a typical catalyst lightoff temperature of 600 K at 20 s into the FTP, leading t o complete conversion of the reactants within the monolith. As the jength of the heated section is increased to 4.5 cm, a larger converter volume near the inlet is heated above its initial temperature of 300 K, however, only a small portion of the converter (0.2 to 0.3 in the normalized axial coordinate) marginally exceeds the required reaction temperature, resulting in relatively low HC conversion (40%)at this time. For the case of a 7.5-cm-longheated section, the entire converter remains below the catalyst lightoff temperature at 20 s into the FTP and thus no significant reaction occurs within the monolithic converter. These results point to the benefit of supplying a given amount of power over a small heated volume to shorten the time t o converter lightoff. This beneficial effect of small heated volume is consistent with the solid-phase energy balance equation (eq 4 in Oh et al. (1993)),which states that the rate of heatup of the solid phase depends on the quantity, P N H ,where P = power and VH = heated volume.
3090 Ind. Eng. Chem. Res., Vol. 33, No. 12, 1994 Table 2. Cycle 1 HC Emissions for Various Channel Geometries and Lengths of Resistively Heated Element channel geometry
asymptotic Nusselt number
cycle 1HC emissions (g) 1.5 cm 3 cm
3.61
0.208
0.435
herringbone (base case)
5.2
0.205
0.439
a
8.2
0.200
0.438
(b:a= 1 )
b
(b:a=-)
r5L\ Oh
200
2000w
3000 W 4b0
sbo
*bo
lobo
Active Metal Surface Area (cm2/cm3 Converter)
Figure 8. Effect of active metal surface area on cycle 1 HC emission for both heated and unheated converters.
1OO’kJ
o 0 2 0 4 0 6 6 . . 1 2 5
Heating Time (s) Figure 7. Effect of heating time on cycle 1HC emission for three different power levels. The dimensions of the heated element are 87 cm2 x 3 cm.
As discussed earlier, convective transport of the external energy input as well as the reaction exotherm from the resistively heated element to the downstream (unheated) section of the monolith is an important mechanism by which heat is distributed within electrically heated monoliths during the cold-start period. Rapid heating of the monolith converter by this mechanism requires that the heat transfer rate between the resistively heated substrate and the exhaust gas be sufficiently high. Since the gas-solid heat transfer coefficient depends on the shape of monolith channels (Shah and London, 19711, we carried out cold-start emission calculations for various channel geometries of the metallic heated element (but without perturbing the channel size. and shape of the ceramic monolith). The results of such calculations are summarized in Table 2 for two different lengths of the heated section (2000 W power supply for 60 s; total converter length = 15 cm). It can be seen that the wide variations in the Nusselt number (and thus the gas-solid heat transfer coefficient in the heated element) lead to very little change in the predicted emission performance of the heated converter system, indicating that the rate of heat transfer between the metallic substrate and the exhaust gas is sufficiently fast for the channel geometries of practical interest. The effect of heating time on cycle 1HC emission is shown in Figure 7 for three different power levels. In this case, the electrically heated converter is assumed to have a 3-cm-long metallic heated element placed upstream of a 12-cm-long ceramic brick. For each of the power levels considered, electrically heating for less than 10 s provides no significant reduction in cold-start HC emissions from those for the same converter operating without electrical heating, presumably because the
premature termination of the electrical heating would allow the substrate to be cooled down by the incoming engine exhaust before the catalyst lightoff occurs. As the heating time is increased beyond 10 s, however, a substantial reduction in cycle 1 HC emission occurs before approaching an asymptotic emission level at heating times longer than 40-45 s. Notice that the HC emission level predicted for a heating time of 60 s is virtually the same as that for 125 s heating time (i.e., electrical heating throughout cycle 1). Thus, as mentioned earlier, the computational results presented in Figures 4 and 5 for 60-s heating should be interpreted as maximum emission reduction potentials predicted for various combinations of electrical power and heated volume. Also shown in Figure 7 are the contour lines of constant energy consumption (dashed lines). It is clear that for a given energy consumption the lowest coldstart emission occurs a t the highest power level considered, indicating a better utilization of the external heat with higher power levels. The results of Figure 7 also demonstrate the importance of using sufficiently high power levels t o achieve adequate emission reductions; the power level chosen determines an upper limit on the system’s emission reduction performance that cannot be overcome simply by increasing the heating time (and thus the energy consumption). Effects of Catalyst Deactivation. The mechanical, electrical, and catalytic durability characteristics of a metallic heated element are important factors in the design of electrically heated catalytic converters. The mechanical and electrical durability issues are beyond the scope of this study; however, our model allows us to assess the impact of catalyst deactivation on the emission reduction potential of an electrically heated converter. Two major modes of automotive catalyst deactivation are sintering (loss of active sites due to high-temperature exposure) and poisoning (deposition of poisons, such as P or Pb, onto the catalytically active surface). In our calculations, it is assumed that sintering occurs uniformly over the entire converter volume, whereas poisoning selectively deactivates the upstream section of the monolith as a result of preferential poison accumulation in that region (Shelef et al., 1978; Taylor, 1984). Figure 8 shows how cycle 1 HC emissions are affected by a variation in active metal surface area for both conventional (15-cm-long ceramic only, unheated) and electrically heated (60-s post-crank heating at 2000 and 3000 W; 3-cm-long metal 12-cm-long ceramic) converters. The effect of active metal surface area loss due to sintering can be seen by moving along the curves from
+
Ind. Eng. Chem. Res., Vol. 33, No. 12,1994 3091
50.2
I
I
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F i m e 9. e n h o n for three difflrent lengths of the heated element (frontal area = 87 cm2).“he total converter length (poisoned + unpoisoned) was held constant at 15 cm, and 60-s post-crank heating at 2000 W is considered.
right to left. (The active metal surface area per unit converter volume for typical fresh converters is, assuming 50%metal dispersion, on the order of 1000 to 1500 cm-l.) Over the range of active metal surface area values characteristic of fresh or moderately sintered converters, the cold-start emission level increases only gradually with decreasing active metal surface area. However, the model predicts that after being severely sintered (active metal surface area
