Ind. Eng. Chem. Prod. Res. Dev. 1983, 22, 509-518
509
CATALYST SECTION Design Aspects of Poison-Resistant Automobile Monolithic Catalysts Se H. Oh* Physical Chemistry Department, General Motors Research Laboratories, Warren, Michigan 48090
James C. Cavendlsh Mathematics Department, General Motors Research Laboratories, Warren, Michigan 48090
The poison resistance of automobile exhaust catalysts is an important factor in the design of catalytic converters. A mathematical model was developed which is capable of describing both the position penetration profile (along the length as well as across the washcoat) and conversion performance of a monolith as a function of its exposure time to the poison. Results of parametric calculations using the model indicate that the warmup performance of a monolith under poisoning conditions can be improved by increasing the washcoat thickness, by increasing its BET surface area, by decreasing the wall thickness, by increasing the noble metal loading, or by optimizing the monolith volume. Graphs are presented that quantify the parametric sensitivity of these individual effects. Since simultaneous variations of washcoat thickness and monolith volume offer the greatest potential for improving converter performance when using currently available monolith substrates and washcoat material, a “design chart” was developed which illustrates the combined effects of these two design parameters on the warmup performance and pressure drop across a poisoned monolith.
Introduction Deactivation of automobile exhaust catalysb is a rather complex event involving various chemical and physical processes. Extensive discussion of this subject is given in recent review articles by Shelef et al. (1978) and by Hegedus and McCabe (1981). One important mode of catalyst deactivation in automobile exhaust is the deposition of poisons (e.g., P b or P) onto the catalytically active surface. Commercial lead-free gasoline currently used in the U.S.contains only small traces of lead (1to 2 mg/L) and phosphorus (-0.05 mg/L). However, motor oil contains significant quantities of phosphorus (typically 1.2 g P/L) and thus phosphorus derived from oil consumption is the major source of catalyst poisoning (Weaver et al., 1976; Kummer, 1980; Hegedus and McCabe, 1981). The detailed mechanism of phosphorus poisoning of automotive catalysts is not yet completely understood. However, there is strong experimental evidence to suggest that the poisoning process involves the simultaneous pore diffusion of the phosphorus-containing poison precursor (presumably P205or H3P04)and its irreversible reaction with the catalyst surface (active sites as well as support) to form catalytically inactive deposits (Hegedus and Summers, 1977; Hegedus and Baron, 1978; Shelef et al., 1978; Angele and Kirchner, 1980a). This diffusion-reaction interaction causes the poison to concentrate near the pore entrance of the catalyst, as was confirmed by electron microprobe analysis (Bomback et al., 1975; Hegedus and Baron, 1978). Such preferential poison accumulation in the pore-mouth region deactivates the catalyst as a result of the combined effect of the attendant removal of catalytic sites in the poisoned zone and decreased accessibility of the reactants to the unpoisoned inner portion of the catalyst. The poison resistance of automotive catalysts is an important factor in the design of catalytic converters. Since converter performance under poisoning conditions is a complex function of converter design parameters (catalyst properties and converter geometries) and operating conditions, mathematical modeling promises to be helpful in developing catalytic converters with improved durability 0196-432 118311222-0509$01 .SO10
characteristics. The poisoning of packed-bed catalytic converters has been analyzed rather extensively (e.g., Hegedus and McCabe, 1981, and references therein). In contrast, most of the monolith models previously reported in the literature (e.g., Heck et al., 1976; Young and Finlayson, 1976; Lee and Aris, 1977; Oh and Cavendish, 1982) do not account for the effect of poison accumulation on reactor performance, with the exception of recent studies by Lee and Aris (1978) and by Lester and Marinangeli (1980). This study was undertaken to provide guidance in the design of poison-resistant monoliths by analyzing, using a transient mathematical model, the behavior of monolithic converters under conditions of phosphorus poisoning. The model is capable of predicting both the poison penetration profiles (along the reactor length and across the washcoat) and the attendant deterioration in conversion performance as a function of exposure time to the poison. The Ptcatalyzed oxidation of CO, hydrocarbon (C,H,), and H, is considered as the main reactions. The performance of a monolithic converter after a given poisoning time was examined by simulating the transient response of the monolith (initially cold) to a step increase in the exhaust temperature. Consideration of such dynamic behavior of a catalytic monolith allows one to examine simultaneously two important factors influencing overall converter performance: (1) warmup time (Le., time required for the converter to become operational following a cold start), and (2) steady-state conversions (i.e., conversion levels after the converter is fully warmed up). Since it is required that the vehicle emission standards be met after 80 000 km of use (or 1000 h driving at 80 km/h), emphasis will be given here to the effects of various converter design parameters on the warmup performance of a 1000 h-poisoned monolithic converter. Basic Equations and Assumptions In this paper, we deal with two transient processes: poison accumulation in a monolith and warmup performance of a poisoned monolith. The time scale for the poisoning process is, however, much longer than that for the warmup process, so that the poison penetration profile
0 1983 American
Chemical Society
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Ind. Eng. Chem. Prod. Res. Dev., Vol. 22, No. 4, 1983
can be assumed to remain unchanged during the measurements of monolith warmup performance. A single-passage monolith model is used for the analysis (that is, channel-to-channel variations or interactions are ignored), assuming that the flow distribution at the face of the monolith is uniform. The model neglects the transverse variations of the gas-phase temperature, velocity, and concentrations of the reactants and poison precursor within the individual channels, so that these variables are to be interpreted as cross-sectional averages. Axial diffusion of mass and heat is also assumed to be negligible in the gas phase. It is assumed that the wall of the individual channel is coated with a porous, Catalytically active layer (Le., washcoat) of uniform thickness. The washcoat is sufficiently thin (typically -50 pm or less) that its curvature is unimportant; however, diffusion resistances in this porous layer are considered for both the poison precursor and main reactants. The poisoning reaction is assumed to be a first-order reaction with respect to both the poison precursor concentration and the unpoisoned fraction of adsorption sites (Lee and Aris, 1978; Angele and Kirchner, 1980b). Also, the rate constant for the poisoning reaction was found to be practically independent of temperature (Angele and Kirchner, 1980b); thus, the model assumes that the poisoning occurs under isothermal conditions. However, the thermal effects associated with the main reactions are included in the model. It is assumed that temperature gradients in the solid phase in the transverse direction are negligible and that the washcoat layer is at the same temperature as the monolith substrate. However, since the longitudinal temperature gradients can be very large under reaction conditions (Oh and Cavendish, 19821, the axial heat conduction in the solid phase is considered. Radiative heat transfer in the monolith is assumed to be negligible. Hegedus et al. (1979) have shown that the poison accumulation process in automotive catalysts is affected only slightly by the stoichiometry of the exhaust. Furthermore, recent phosphorus poisoning experiments on an engine dynamometer system (Oh, 1982) showed that the phosphorus penetration rate is virtually independent of the type and loading of the noble metals. Therefore, it is assumed in this study that the phosphorus accumulation process is not affected by the presence of the reactants or active metal components (i.e., nonselective poisoning). Poison Accumulation Model. The conservation of the poison precursor in the gas phase of the channel is described by %P
e-
=
at --UP
a%,, dX
-
k,,,S[c,,,(t,x) - c,,,(t,x,H)I
(0
< x < L) (1)
where c,,,(t,x,H) is the concentration of the poison precursor at the outer edge of the washcoat (i.e., at z = H) at time t and axial position x. In the solid phase (i.e., washcoat layer), an irreversible poisoning reaction occurs between the poison precursor (P) and unpoisoned adsorption sites (a)to form catalytically inactive deposit (W). That is kP
P+u-w
(2)
where rate is given by
R,
= kpCs,,(l - 0,)
(3)
Here c,,, is the concentration of the poison precursor in
the pores of the washcoat and Ow is the fraction of the adsorption sites covered with W (i.e., poison coverage). The balance equations for the washcoat are
and
do, = R, (for all x and z ) dt Equation 4 describes the diffusion-reaction interaction for the poison precursor within the pores of the washcoat, and the rate of poison deposition on the catalyst surface is goverened by eq 5 . Notice that the axial diffusion term d2cs,,/dx2 is not included in eq 4; when the spatial variables is found are made dimensionless, its coefficient (to be negligibly small compared to that for the transverse diffusion term (-1) considered in eq 4. For our calculations, the accumulationterms in eq 1and 4 were neglected because the poison deposition described by eq 5 occurs much more slowly and consequently dominates the time scale of the poisoning process. With this quasi-static approximation, we adopt the following boundary and initial conditions c,,--
(7)
=0
e,(o,x,z)
(9)
For all the results reported here, we assume that the monolith is initially fresh, as indicated by eq 9. As mentioned earlier, the poisoning is assumed to occur under isothermal conditions; thus, the energy balance equations are not included for the analysis of poison accumulation. Warmup Performance Model. The conversion performance of a monolithic converter after a given poisoning time [i.e., for a given poison coverage profile O,(t,x,z)] was examined by simulating the transient response of the monolith, initially at room temperature, following a step flow of stabilized exhaust gas at an elevated temperature. In this case, the thermal response of the monolith plays an important role in determining the reactor performance, and thus the energy balance equations are included in the model. The Pt-catalyzed oxidation reactions of CO, C3Hs, and H2 are considered. The rate expressions for these reactions are taken from Oh and Cavendish (1981). The material and energy balances for the gas phase in the channel are dcg,i t-
at
a(ucg,i)
= - -- k,,$S[C,i(t,X)
ax
- c&x,H)]
(i = 1, ..., 4) (10)
a T,
€pgCpg-
at
= -up
g
aT g cpg + hS[T, - T,] ax
(11)
The subscript i in eq 10 refers to the reactive species of interest: i = 1, CO; i = 2, C&,; i = 3, H,; and i = 4, 02. The inlet boundary conditions for eq 10 and 11 are C,,i(t,O)
=
Cg,ii"
T,(t,O) = Tgi"
(12) (13)
Ind. Eng. Chem. Prod. Res. Dev., Vol. 22, No. 4, 1983 511
The correspondingmodel equations for the solid phase are
a(*,T,) - A$,-at
a2T,
+ hS(T, - T,) -!-
ax2
uSt(-AH)i( i=l sHRi(l 0 -
dz) (15)
The quantity *a in eq 15 represents the heat capacity of the solid phase (substrate plus washcoat). That is
c
where the physical properties of the washcoat ( p , and ) are allowed to be different from those of the substrate and CPJ. I t is assumed in eq 15 that the axial heat conduction occurs in the substrate only because the thermal conductivity of the substrate (cordierite), A,, is typically ten times higher than that of the washcoat (y-alumina). Notice in eq 14 and 15 that the rates of the main reactions decrease with (1- e,)2 as the poisoning progresses. This coverage dependence of the reaction rates is adopted under the assumption that the dual-site Langmuir-Hinshelwood mechanism predominates under conditions of interest here (see Lee and Aris, 1978, for derivation). A similar nonlinear relationship between reaction rate and poison coverage was observed during CO oxidation over lead-poisoned Pt films (Baron, 1978). The boundary conditions for eq 14 and 15 are
p"p,
ac,i
-(t,x,O)
az
=0
Again, the accumulation of mass and heat in the gas phase and mass in the solid phase was neglected for the calculations (that is, acg,i/at= aT,/& = ac,,i/at = 0 in eq 10, 11,and 14, because their time constants are typically much smaller than that of the thermal response of the solid phase. With the quasi-static approximation, we need to specify the initial condition only for the solid temperature
Ta(0,X)= Tso(d (20) For all the computations reported here, Ts0(x)= 300 K. Numerical Solution of the Equations The purpose of this section is to provide a brief description of the numerical methods used to approximate the poison accumulation model (eq 1,4, and 5) and the warmup performance model (eq 10, 11,14, and 15) subject to the associated boundary and initial conditions. In these methods, the time variable, t , was left continuous while discrete approximations to the spatial variables were provided by a combination of finite difference and Galerkin methods. The resulting ordinary matrix differential equation in the time domain was then integrated by use of a banded version of the GEAR codes (Hindmarsh, 1976). A more detailed description of the numerical methods developed is reserved for the Appendix. Model Parameter Values Table I shows a standard set of parameter values used for the computations. The monolith properties listed in Table I are similar to those of a ceramic monolithic converter (cordierite substrate coated with y-alumina) used
Table I. Standard Set of Parameter Values monolith substrate frontal area = 100 cm* length = 15 cm cell density = 46.5 square channels/cm' wall thickness = 0.0254 cm density = 2.5 g/cm3 J/cm.s.K thermal conductivity = 1.675 x specific heat = 1.071 + 1.56 x 10-4T,- 3.435 x 104/Ts2 J/g.K washcoat thickness = 50 km BET surface area = 96.5m2/g density = 0.823 g/cm3 specific heat = 0.8374 J/g.K noble metal content = 0.311 g active Pt (0.01 toz) per converter I CO = 0.348 cm2/s C,H, = 0.220 cm2/s effective diffusivities ( a t 838 K) H. = 1.344 cm2/s Of= 0.349 cmZ)s H,PO, = 0.138 cm2/s saturation concentration of poison = 3.65 X mol/cm2 BET rate constant for poisoning reaction = 0.1 cm/s
1
exhaust gas pressure = 101.3 Wa flow rate = 30 g/s specific heat = 1.089 J/g.K ( a ) poisoning (b) warmup performance temperature = 838 K temperature = 300 K + (isothermal) 700 K poison concn = 1 x 2% CO, 450 ppm C,H,, mol P/cm3 0.667% H,, 5% 0,, 500 ppm NO
on some 1980 General Motors vehicles sold in California. The poisoning is assumed to occur isothermally at 838 K (typical of fully warmed-up converter temperatures) because catalytic converters usually spend a large fraction of their poison exposure time under such high temperature conditions. The exhaust gas temperature and composition used for the warmup performance calculations are similar to the test conditions used in an engine dynamometer system developed for the evaluation of converter lightoff (Herod et al., 1973). The methods used for parameter estimation will be discussed briefly in the following paragraphs. The poison precursor was assumed to be H,PO,. The effective diffusivities of the poison precursor and reactants in the washcoat were calculated from the random pore model of Wakao and Smith (Smith, 1970) using the pore size distribution data of the washcoat scraped from the commercial ceramic monolith. The effective diffusivities were assumed to increase with the 1.4th power of temperature. The phosphorus concentration in the exhaust entering the monolith was calculated based on an oil consumption rate of 0.95 L/8000 km and its phosphorus content of 1.2 g/L. The saturation concentration of the phosphorus, cW,=, on the catalyst surface was taken from the work of Hegedus and Baron (1978). The rate constant, k,, for the poisoning reaction was estimated by fitting model predictions to the phosphorus penetration profile (measured by electron microprobe) across the washcoat of a ceramic monolith aged on an engine dynamometer system under well-controlled conditions (Monroe, 1982). This approach was used because preliminary calculations showed that the poison penetration profile across the washcoat (rather than the posion accumulationprofile along the reactor length) was sensitive to variations in k,.
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Ind. Eng. Chem. Prod. Res. Dev., Vol. 22, No. 4, 1983 1.0 I
/
1
/
/
/
I l'O
fl
0.8
W
I \
z
1
0.6
0.2i. 0
I
0 2
0
04
Figure 1. Poison coverage contours within the washcoat layer after lo00 h poisoning. Parameter values are listed in Table I. 6, = poison coverage; r / L = normalized axial distance measured from the monolith inlet; z / H = normalized depth within the washcoat, measured from the washcoat-cordierite interface.
km,i = ShmDi/(2Rh) (i = 1, ..., 4) km,, = ShmDp/(2Rh)
10
Figure 2. Poison accumulation profile along the monolith length at various poisoning times. Parameter values are listed in Table I. (6,) is the average poison coverage across the washcoat thickness, defined by eq 24.
900
(21) (22) (23)
where the molecular diffusivitiesof the reactive species and poison precursor, Diand D,,were estimated by using the Slattery-Bird formula (Bird et al., 19601, and the thermal conductivity of the reaction mixture, A,, was approximated by that of N2, The temperature dependence of these physical properties (and thus the heat and mass transfer coefficients) wm accounted for in the warmup performance calculations. Also, we remark that the effect of the hydrodynamic entrance region near the monolith inlet (where the heat and mass transfer coefficients are higher) was neglected in the calculations because its length is only a small fraction of the total monolith length under typical converter operating conditions (Sherony and Solbrig, 1970).
Analysis of the Standard Case In this section we examine the standard case (Table I) in some detail in order to gain insight into the mode of poison accumulation in a monolith and its attendant activity deterioration. Mode of Poison Accumulation. Figure 1 shows the calculated poison coverage contours within the washcoat layer (0 Iz I50 pm; 0 Ix d 15 cm) after 1000 h poisoning. (This poisoning time is equivalent to 80000 km of driving a t 80 km/h.) I t is clear from Figure 1 that at a given axial position, the poison coverage increases as we move toward the outer edge of the washcoat (i.e., z / H = 1). Furthermore, the poison coverage at a given depth into the washcoat is seen to increase with decreasing axial distance. The prediction of such preferential poison accumulation near the external surface of the washcoat and near the monolith inlet is in qualitative agreement with actual measurements [e.g., Bomback et al., 1975; Weaver et al., 1976; Shelef et al., 1978). Figure 2 shows how the poison accumulation profile along the monolith length varies with poisoning time. The quantity (6,) is the integral-averaged poison coverage at time t and axial position x , defined as
n
iioor
The gas-solid heat and mass transfer coefficients were estimated based on the Nusselt and Sherwood numbers obtained from analytical solutions for fully developed laminar flow with constant wall heat flux (Shah and London, 1971). That is
h = NumA,/(2Rh)
08
06 x/L
x/L
L +
500 300
-
5s
1.0 I
12s
o'2t\ 0
0
0.2
I
0.4
!25s!
0.6
0.8
, 1.0
x/L Figure 3. Time variation of the solid temperature (top) and gasphase CO concentration (bottom) profiles along the reactor length during the warmup period of a fresh monolith. Parameter values are listed in Table I.
Notice that the poison profile at each time is a decreasing function of axial distance (i.e., heavier accumulation in the front) and that the poison front progresses deeper into the reactor with increasing poison exposure time. In contrast to this preferential accumulation of poison in monoliths, the poison content in a packed-bed converter is found to be virtually uniform over the entire converter volume (Hegedus and McCabe, 1981), presumably as a result of pellet migration during vehicle use. Influence of Poisoning on Warmup Behavior. In order to understand how the poison accumulation influences the performance of a monolithic converter, it is instructive to compare the warmup behavior of a fresh monolith with that of its poisoned counterpart. Figure 3 shows the time variation of the solid temperature and gas-phase CO concentration profiles along the reactor length after a fresh (cold; 300 K) monolith has been subjected to a step flow of hot exhaust gas (700 K). A t early times (see t = 5 s), the upstream portion of the monolith is heated up primarily by the convective gas-solid heat transfer. (Note that virtually no reaction occurs at this time because the solid temperature is still too low.) As time elapses further (see t = 12 s and 15 s), however, the upstream section eventually reaches high enough temperatures for significant reactions to occur (i.e., reaction
Ind. Eng. Chem. Prod. Res. Dev., Vol. 22, No. 4, 1983 513
l 1900 O0L
E201
/ 20
0
50 s
40 Time
80
60 (6)
Figure 5. Comparison of the CO conversion performance of fresh and poisoned monoliths during the warmup period. Parameter values are listed in Table I.
Cg, Coin 0.4
0.2
I
0 0
0.2
175sL 0.4
0.6
0.8
1000 h Poisoning
1.0
x/ L
Figure 4. Time variation of the solid temperature (top) and gasphase CO concentration (bottom) profiles along the reactor length during the warmup period of a lo00 h-poisoned monolith. Parameter values are listed in Table I.
temperature), and the gas-phase CO concentration in that region decreases with increasing axial distance as a result of catalytic reactions occurring there. At 25 s into the warmup process, the conversion of CO in the reactor is nearly complete and the attendant reaction exotherm leads to a solid temperature exceeding the inlet exhaust temperature (700 K) in the upstream portion of the monolith. Notice that for the fresh monolith considered here, the reaction is confined to a small fraction (about 15%) of the monolith near the inlet throughout the warmup period. This interesting observation is useful in understanding some of the results of parametric calculations to be discussed later. It should be noted, however, that the rear portion of the monolith plays an increasingly important role in determining the converter performance as the poison accumulates in the monolith. Shown in Figure 4 is the warmup behavior of the same monolith after lo00 h poisoning. Just as we saw for the fresh monolith, the hot exhaust gas heats up the upstream portion of the poisoned monolith at the early stages of the warmup process (note the similarity between the temperature profiles at t = 5 s in Figures 3 and 4). At t = 20 s, the monolith inlet reaches a solid temperature of about 700 K; however, the monolith still remains inactive because of complete poisoning near the inlet (see Figure 2). This condition persists until t = 65 s, when the leading edge of the catalytically active portion of the monolith ( x / L > -0.5; see Figure 2) reaches the reaction temperatures. The rapid decrease in the gasphase CO concentration predicted at t = 70 s and 75 s is a direct consequence of vigorous reactions occurring in the downstream section of the monolith. The resulting reaction exotherm, then, causes a temperature peak in the solid phase well above the inlet exhaust temperature, as illustrated by the temperature profile at t = 75 s. We see from the results discussed above that during the warmup period, the poisoned zone located near the monolith inlet acts as a heat sink, thereby increasing the time required for the reactor to become operational (that is, delaying the converter lightoff). This aspect is clearly illustrated in Figure 5, where comparison is made of the conversion performance of the monolith before and after poisoning. Notice, however, that the converter perform-
;t 40
t
o b
I
'
I
'
'
'
80 40 60 Washcoat Thickness (pm)
I
100
Figure 6. Effects of washcoat thickness (standard value = 50 pm) on the warmup time of fresh and poisoned monoliths. Other parameter values were held constant at those listed in Table I.
ance after lightoff (i.e,, the steady-state warmed-up performance) corresponds to nearly complete conversion of the reactant for both the fresh and poisoned monoliths. In fact, our parametric calculations show that for all cases of practical interest, the monolith exhibits sufficiently high warmed-up activity even after 1000 h poisoning. This indicates that steady-state warmed-up performance is not a limiting factor in the design of poison-resistant monolithic converters, at least for the oxidizing conditions considered here. In light of this observation, we chose as a design criterion the time required to achieve 50% CO conversion (hereafter referred to as the warmup time) following a step increase in the inlet exhaust temperature.
Results of Parametric Calculations This section describes the results of parametric calculations obtained using our monolith model. The effects of key design parameters on the warmup performance of a monolithic converter are investigated by systematically perturbing them around the standard values listed in Table I. Although the monolith performance after 1000 h poisoning is the item of practical importance, the warmup performance of fresh monoliths will also be examined in order to improve our understanding of the system's behavior. Effects of Washcoat Properties. Figure 6 shows how the warmup time of a monolith is affected by the washcoat thickness before and after poisoning. When the monolith is fresh, converter warmup time increases moderately with increasing washcoat thickness, primarily due to the attendant increase in the heat capacity of the monolith (see eq 16). After lo00 h poisoning, however, the monolith with
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Ind. Eng. Chem. Prod. Res. Dev., Vol. 22, No. 4, 1983
\ 0 0.2
0
0.4
0.6
0.8
x/L
50 I
1 .o
Figure 7. Poison accumulation profile along the monolith length after lo00 h poisoning for two different washcoat thicknesses. Other parameter values were held constant at those listed in Table I. (8), is the average poison coverage across the washcoat thickness, defined by eq 24.
I
I
1.o 1.6 Noble Metal Content ig Pt per converter)
20
Figure 9. Effects of Pt content (standard value = 0.311 g) on the warmup time of a lo00 h-poisoned monolith at two different inlet exhaust temperatures. Other parameter values were held constant at those listed in Table I.
'"rt u /
\',
loo,
I
I
0 5
0
80 -
1000 h Poisoning
;60
,
1000 h Poisoning-
-
0 0
50
100
150
BET Surface Area (m2/cm3 washcoat) Figure 8. Effects of BET surface area of the washcoat (standard value = 79.4 mz/cm3) on the warmup time of fresh and poisoned monoliths. Other parameter values were held constant at those listed in Table I.
a thick washcoat is predicted to outperform the one with a thin washcoat. This can be explained based on the results of Figure 7, which show that a substantially larger fraction of the monolith remains unpoisoned after 1000 h poisoning when the washcoat thickness is increased from 30 pm to 100 pm. This improvement in poison resistance predicted for a thick washcoat can be attributed to its increased poison retention capacity, which in turn decreases the rate of poison propagation along the reactor length. The poison retention capacity can also be increased by increasing the total (BET) surface area of the washcoat. Figure 8 shows the expected results that the warmup performance of the poisoned monolith is improved as the BET surface area of the washcoat increases. Similar beneficial effects of increasing the support surface area on the poison resistance of pelleted automotive catalysts have been demonstrated experimentally by Hegedus and Summers (1977). It should be noted that our model prediction of the performance of a fresh monolith is independent of the BET surface area of the washcoat. This is reasonable because the BET surface area of catalyst supports is usually high enough to maintain the noble metal well dispersed. Figure 9 shows how the warmup time of a poisoned monolith (1000 h) changes with noble metal content (i.e., total amount of active Pt per converter) for two different
0
t 0
5
10
15
Length of Inert Zone ( c m )
Figure 10. Effects of the length of the inert zone (standard value = 0 cm) on the warmup time of fresh and poisoned monoliths. Other parameter values were held constant at those listed in Table I.
inlet exhaust temperatures. As expected, a longer warmup time is required when the noble metal content is decreased. More interesting is the prediction that converter lightoff becomes less sensitive to a variation in the amount of Pt as the Pt content is increased. This indicates that increasing the noble metal content beyond a certain value would give only small benefit. This prediction has important economic implications in the design of monolithic converters because the noble metals account for a large fraction of total converter cost. The Pt content corresponding to the rapidly increasing portion of the curves is related to the minimum amount of active noble metal required to maintain adequate converter warmup performance. Notice that the value of this critical Pt content depends on the temperature level of the inlet exhaust gas, as illustrated in Figure 9. (The amount of active noble metal in the converter generally decreases with time as a result of sintering, so this factor should be accounted for in actual converter design.) In view of the observation that the poison tends to deposit preferentially near the monolith inlet, one would be tempted to leave the washcoat in the upstream portion of the monolith unimpregnated, so that the amount of noble metal deactivated by the poison accumulation can be minimized. The effects of this design strategy on converter warmup performance are presented in Figure 10, where the warmup time of a monolith is plotted against the length of the inert zone located near the monolith inlet.
Ind. Eng. Chem. Prod. Res. Dev., Vol. 22, No. 4, 1983 515
Table II. Effects of Noble Metal Impregnation Profile on Warmup Time for Various Poisoning Times
1oor
I
Pt impregnation profile
fresh
linearly increasing 31.6s [ a = 10420x/L] uniform (standard) 13.6 s [ a = 52101 linearly decreasing 11.7 s [ a = 10420(1- x / L ) ]
500h
1OOOh
1500h
47.7 s
67.3 s
88.3 s
41.9 s
68.6 s
93.9 s
38.2s
70.1 s
129.3 s
Here both the Pt content per converter and the total (Le., inert plus active) length of the monolith were held constant at the standard values listed in Table I. Interestingly, the warmup time of a poisoned monolith is predicted to be shortest at an intermediate value of the length of the inert zone. If the length of the inert zone is smaller than the optimum value, converter warmup performance deteriorates as a result of insufficient protection of the noble metal from poisoning in the upstream portion of the monolith. If the length of the inert zone is too long, on the other hand, the benefit of protecting the nobel metal is overshadowed by the additional time required before the active zone located downstream reaches the reaction temperatures (see Figure 4), resulting in an increase in the converter warmup time. Because of the latter negative effect, the warmup time for the fresh monolith increases monotonically with the length of the inert zone, as illustrated in Figure 10. We see from Figure 10 that the design strategy of leaving the upstream portion of the monolith unimpregnated can generally provide only small improvement in converter performance after 1000 h poisoning, thus limiting the practicality of this approach in monolith design. Notice that the case discussed in Figure 10 is a special case of general design strategies involving nonuniform distribution of the noble metal along the reactor length. We also investigated how the warmup performance of a monolith changes with poisoning time when the Pt concentration (cm2Pt/cm3 washcoat) profile is either a linearly increasing or a linearly decreasing function of axial distance (see Table 11). Results for the standard case of uniform Pt concentration profile are also included in the same table for direct comparisons. We remark that the total Pt surface area (and thus the total amount of active Pt) in the monolith is the same for the three cases considered here. In accord with the results of our previous study (Oh and Cavendish, 1982), Table I1 shows that the warmup performance of a fresh monolith can be improved by concentrating the noble metal in the upstream section of the monolith. The warmup performance of the monolith after 500 h poisoning is similarly affected by the variations in the noble metal impregnation profile. After 1000 h poisoning, however, the beneficial effect of concentrating the noble metal in the upstream section disappears because it is counterbalanced by the preferential poison accumulation in that region. For longer poison exposure times, this detrimental effect dominates the warmup behavior of the monolith, so it is preferable to concentrate the noble metal in the downstream (instead of the upstream) portion of the monolith (compare the warmup times after 1500 h poisoning). It is clear from Table I1 that the proper noble metal impregnation profile generally depends on the length of the reactor operation time. For automobile emission control applications, a poisoning time of 1000 h is of interest; our calculations show that the warmup performance of a monolithic converter after 1000 h poisoning is relatively insensitive to variations in the noble metal impregnation profile along the reactor length.
ug 6 0 t 0
ff
0 401 0
c.
t -
0
0
20 40 Monolith Length (cm)
60
Figure 11. Effects of reactor length (standard value = 15 cm) on the warmup time of fresh and poisoned monoliths. Other parameter values were held constant at those listed in Table I.
The model also predicts that twofold variations (both increase and decrease) in the effective diffusivities around the standard values do not significantly change the performance of a poisoned monolith during the warmup period. This implies that the effective diffusivities in the washcoat of currently used monoliths are sufficiently large, so that attempts at a further increase in their values are not warranted. Effects of Substrate Properties. Analysis of the model equations and numerical calculations show that the simultaneous variation of the frontal area and length of a monolith while keeping their product (i.e., converter volume) constant does not significantly change the poison accumulation and warmup characteristics of the monolith. This indicates that the warmup behavior of a monolith under poisoning conditions depends primarily on its total volume and not on the individual values of the frontal area and length. Figure 11shows how the warmup performance of fresh and poisoned monoliths is influenced by converter volume. Here the converter volume was perturbed by varying the length of the monolith while keeping its frontal area constant (100 cm2). In addition, the total amount of Pt per converter was held constant in the calculations. As shown in Figure 11, the warmup time of a fresh monolith increases when a given amount of Pt is distributed over a larger converter volume (thereby decreasing the local Pt concentration in the converter). This can be explained based on the findings of Figure 3, which suggest that the warmup behavior of a fresh monolith depends primarily on the Pt concentration in the upstream portion of the converter (and not on the total amount of Pt in the converter). Figure 11 also shows that the same trend carries over to the poisoned monolith when its length exceeds 9 cm. For monolith lengths shorter than 9 cm, however, the opposite trend is predicted; that is, the converter warmup performance deteriorates drastically upon decreasing its length. This can be attributed to the fact that as the converter length is decreased below 9 cm, the abovementioned beneficial effect of the increased local Pt concentration is dominated by the detrimental effect of the increased fraction of the monolith deactivated as a result of the poison accumulation. The wall thickness of the substrate (cordierite) is an important design parameter in developing monolithic converters with improved warmup performance. As Figure 12 shows, the warmup time for both fresh and poisoned
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Ind. Eng. Chem. Prod. Res. Dev., Vol. 22, No. 4, 1983 100
80
.-E
1000 h 60 x c
V
c
L
5
40
U
40,
.c, 20 \
2 kPa 0
-
0 0.01 0.02 0.03 Wall Thickness (cm)
0
0.04
Figure 12. Effects of wall thickness (standard value = 0.0254 cm) on the warmup time of fresh and poisoned monoliths. Other parameter values were held constant at those listed in Table I. 100
-
-
-Z 80 C
.-
1000 h Poisoning
-
e
$ 600
0
-
O
L
'
I
I
I
0.04 0.06 Channel Radius (cm)
1
0.08
Figure 13. Effects of channel size (standard value = 0.05562 cm) on the warmup time of fresh and poisoned monoliths. Other parameter values were held constant at those listed in Table I.
monoliths is shortened as the wall thickness is decreased (with the channel radius fixed at the standard value of 0.05562 cm). (The wall thickness for commercial ceramic monoliths typically varies from 0.015 cm to 0.03cm.) This improved lightoff behavior predicted for a monolith having thinner walls (and thus the reduced thermal capacity) is a direct consequence of faster heating of the monolith substrate by the hot exhaust gas. Notice that the warmup performance becomes much more sensitive to a variation in wall thickness after 1000 h poisoning. The effect of channel size variation (with the wall thickness fixed at the standard value of 0.0254 cm) on the warmup time of a monolith is depicted in Figure 13. It can be seen that the warmup performance is weakly dependent upon the channel size over the realistic range of channel radii considered here, for both fresh and poisoned monoliths. This prediction is perhaps not surprising, because a tradeoff exists between improving the gas-solid heat transfer characteristics and increasing the heat capacity of the monolith, as the channel size decreases (Oh and Cavendish, 1982).
Practical Design Considerations In the previous section, we examined the independent effects of the variation of individual design parameters on
20
40 Monolith Length (cm)
4 kPa
I 60
Figure 14. Effects of washcoat thickness and monolith length (frontal area fixed at 100 cm2) on the warmup time and pressure drop of a 1000 h-poisoned monolith. Other parameter values were held constant at those listed in Table I.
the warmup performance of a monolithic converter. The results of such parametric calculations are useful because they identify important parameters associated with monolith design and point ways toward possible improvements in converter performance. In general, monolith performance is goverened by complex interactions of various design parameters. Therefore, in order to find an optimum monolith configuration, we need to take such interactions into consideration in design calculations. In practice, however, some of the design parameters can be varied only over relatively narrow ranges. For example, the variation of the cell density and wall thickness of a monolith is usually limited by manufacturing constraints and also by the requirements for mechanical strength and thermal shock resistance of the unit (Howitt, 1980). As a result, only several monolith substrates of differing geometrical properties are commercially available for use in automobile emission control applications (Howitt, 1980). Also, some of the washcoat properties (e.g., stable BET surface area) can be varied only to a limited degree at this time. In view of such practical limitations on the variability of some of the design parameters, we decided to focus on the combined effects of two monolith design parameters that can be conveniently manipulated, instead of mounting a full-scale optimization on all the design variables. For the illustrative example to be discussed here, the washcoat thickness and monolith length are chosen as the design variables of interest, with all other properties of the substrate and the washcoat held constant at the standard values listed in Table I. The results of design calculations are summarized in Figure 14, where both the contour lines of constant warmup time (after lo00 h poisoning; solid lines) and those of constant pressure drop (dotted lines) are shown in the domain of the washcoat thickness and the monolith length. The pressure drop across the monolith was calculated by using the formula given in Shah and London (1972) and is included here in view of its importance in converter design. One convenient feature of Figure 14 is that it allows one to visualize the effects of simultaneous variations in the two design parameters chosen here on the warmup performance and pressure drop of poisoned monolithic converters. The utility of Figure 14 in monolith design can perhaps be best illustrated by comparing a monolith (A) and its improved counterpart (B). Compared to monolith A, monolith B has a thicker washcoat (80 pm vs. 30 pm) and
Ind. Eng. Chem. Prod. Res. Dev., Vol. 22, No. 4, 1983 517
a shorter length (15 cm vs. 50 cm). Figure 14 indicates that by making such changes in the design parameters, we can significantly shorten the warmup time (by about 45 s) and reduce the pressure drop (by more than a factor of 2), with the added advantage of decreasing the total monolith volume (by more than a factor of 3). However, a further design change to monolith C (3 cm long, 100 pm thick washcoat) is not desirable because the warmup performance would become too sensitive to variations in the design parameters. Concluding Remarks A mathematical model has been developed which is capable of describing both the poison penetration profile (along the length as well as across the washcoat) and conversion performance of a monolith as a function of its exposure time to the poison. The model was used to analyze the effects of various design parameters on the warmup performance of a platinum-impregnated monolithic converter undergoing phosphorus poisoning. The model suggests that the key parameters associated with the design of poison-resistant monolithic converters are washcoat thickness, BET surface area of the washcoat, wall thickness of the substrate, noble metal loading, and monolith volume. The results of our parametric calculations indicate that converter warmup performance under poisoning conditions can be improved by increasing the washcoat thickness, by increasing its BET surface area, by decreasing the wall thickness, or by increasing the noble metal loading. The graphs presented in this paper quantify the parametric sensitivity of these effects. The model predictions also suggest that a proper choice of the monolith volume is crucial in the design of poison-resistant monolithic converters. The optimum monolith volume is, in general, a complex function of other design and operating parameters; however, contour plots such as those shown in Figure 14 would aid in the determination of the optimum value. Although the results of our parametric calculations are generally in qualitative agreement with experimental observations previously reported in the literature, the quantitative prediction of optimum monolith properties requires a further evaluation of the validity of the model. Studies are underway for experimental verification of the monolith model developed here, and the results will be reported later. Appendix Poison Accumulation Model. Before developing numerical methods for integrating the poison accumulation model, the spatial variables and the dependent concentration variables are made dimensionless. Replacement of x by X l L , z by ZlH, cg,? by cg,p/cg,pin and c,,p by cs,p/cg,pin gives the following quasi-static model
(A-2) (A-3) where x and z are defined on the unit square fl = [0,1] X [0,1]and t > 0. The boundary and initial conditions become c,,(t,O) = 1 (-4-4) (A-5a)
Ow(0,x,z)= 0
(A-6)
The quantities wl, w2, w3, and w4 appearing in the above equations are defined in the Nomenclature section. To provide numerical approximationsfor this model, the spatial domain 0 < x < 1is first partitioned into a network of uniformly spaced lines, II,: 0 = xl < x 2 < ... < X N = 1 with xi - xi-l = Ax. Our strategy is to numerically integrate eq A-1 to A-6 at each mesh line x i proceeding from x i to xi+l. To that end, suppose that approximations have been developed for the lines ( t ,x l l z), ( t ,x2, z ) , ..., ( t ,x i , z ) and we now seek an approximation along ( t ,xi+l, z ) where 0 < z < 1. The interval 0 < z < 1is first partitioned by II,: 0 = z1 < z2 < ... < ZM = 1. Defining the vectors F,,p
= (cs,p(t, x i + l , z1), cs,p ( t ,xi+l, 221,
.e*,
c,,p(t, xi+1, ZM))
z1),Ow(t, xi+l, z2), ..., Ow(t, x i + l , ZM)) Equation A-3 is discretized by the vector-differential equation 8w(t) =
(Ow(t, xi+1,
(A-7) where F,(t,
8,) = ~ , , , ( t ,x,+1, z,)(l - Ow@, x , + ~ ,2,))
(1 5 j 5 M)
Equation A-7 is integrated in t using a banded version of the GEAR computer codes (Hindmarsh, 1976). Evaluation of F in eq A-7 for given t and 8, requires evaluation of Cs,y The vector is evaluated by coupling a two-step modified Euler approximation (Isaacson and Keller, 1966) to eq A-1 to estimate cg,p( t ,x,+J from available data a t xL,with a piecewise linear Galerkin approximation (Cavendish and Oh, 1976) to eq A-2 and A-5 to approximate Fs,p. In effect, we integrate eq A-1 to A-6 from the inlet of the monolith (x = 0) to the outlet (x = 1). In our calculations, it was adequate to use N = M = 20. With this scheme the GEAR methods are used to control time trun ition errors to a user-specified level. Spatial truncatio srrors are of the order O(Ax2)and O(Az2). Warmbp Performance Model. The warmup performance model is integrated after a poison coverage function, Ow(t,x, z ) has been calculated from the poison accumulation model. Before integrating the warmup performance model, we again nondimensionalize x and z with division by L and H, respectively. The dependent variables c , and cs4are made dimensionless with division by cg,y, w k e T , and Tg are made dimensionless with division by T P . Our approach to solving the quasi-static warmup performance model is similar to that used to integrate the poison accumulation model with T, playing the role of Ow, c , playing the role of c and c,,, playing the role of c,,~. I-fowever, it is not p o s s g e to integrate the warmup performance model “a line at a time” because of the presence of the conductivity term in eq 15. As was the case for the poison accumulation model, the time variable t is left continuous while the spatial variables are made discrete using the partitions II, and n,. We begin by forming a piecewise linear approximation to the solid temperature T,using the partition II, N
T,(t,x)= C T;(t)@,b)
(A-8)
,=1
where [ @ , ( x ) ] ~ ,is= the ~ basis of “hat functions” spanning
518
Ind. Eng. Chem. Prod. Res. Dev., Vol. 22, No. 4, 1983
the space of piecewise linear functions associated with II, (Cavendish and Oh, 1979). Next, a Galerkin formulation (Oh and Cavendish, 1982) is developed for the dimensionless form of eq 15 to produce an ordinary matrix differential equation d Ts A -d t = E(Tg)T9 G(T,, F,, E,) (A-9) In eq A-9, A and B(Tg)are N X N tridiagonal matrices and T,, Tg,Fg are vectors of solid temperatures, gas-phase temperatures, and gas-phase concentrations, respectively, evaluated a t the partition points, xi,of II,. We integrate eq A-9 using the banded version of the GEAR code (Hindmarsh, 1976). The right-hand side of eq A-9 is an implicit function of T, whose evaluation requires evaluation of Tg,cg, and E,. The vector Tg is evaluated by solving a two-step backward Euler finite difference approximation to eq 11. With the calculation of T,, the gas-solid heat and mass transfer coefficients are updated. Evaluation of F, and Fs requires numerical integrations of the coupled eq 10 and 14. Equation 10 is discretized on the mesh II, using a first-order backward difference formulation relating E, ( t ,xi+J to known F,(t, xi), and ~ , ( t , xi,1). With this approximation to F g ( t , xi+l), eq 14 and 17 are discretized using piecewise linear Galerkin representations of c,,~ on the mesh II,. This discretization yields a system of nonlinear algebraic equations which are solved by Newton's method. To complete the passage from x ito xi+l,a second pass is made through the discrete versions of eq 10 and 14. In summary, our approach is to develop a continuous time/discrete space approximation to the quasi-static warmup performance model. The resulting ordinary matrix differential eq A-9 is integrated using the GEAR computer code, and evaluation of the right-hand side of eq A-9 is carried out by solving discrete finite difference approximations to eq 10 and 11, coupled with Galerkin approximations to eq 14. The approach permits optimal time step strategies with accurate control over accumulated time truncation errors. As with the integration of the poison accumulation model, spatial truncation errors remain second order. Nomenclature a = catalytic surface area per unit washcoat volume, cm2/cm3 c = species molar concentration, mol/cm3 C,, = specific heat of gas, J / g K Cps = specific heat of substrate, J / g K C,, = specific heat of washcoat, J / g K cw,, = saturation poison concentration, mol of P/cm2 BET D = molecular diffusivity in the reactive mixture, cm2/s De = effective diffusivity in the washcoat, cm2/s = fraction of the face area occupied by the substrate f, = fraction of the face area occupied by the washcoat H = washcoat thickness, cm h = gas-solid heat transfer coefficient, J/cm2.s-K = heat of combustion of species i , J/mol k , = gas-solid mass transfer coefficient, cm/s k , = rate constant for poisoning reaction, cm/s L = length of monolith, cm Nu, = limiting Nusselt number Rh = hydraulic radius of channel, 2(flow area/wetted perimeter), cm = specific reaction rate for species i , mol/cmz Pt.s R, = specific rate for poisoning reaction, mol/cm2 BET-s S = geometric surface area per unit reactor volume, cm2/cm3 Sh, = limiting Sherwood number t = time, s T = temperature, K
+
(-mi
Bi
Tso= initial temperature in the solid phase, K
u = linear superficial velocity of exhaust gas, cm/s x = axial coordinate, cm z = coordinate for depth within the washcoat, cm
Greek Letters a = BET surface area per unit washcoat volume, cm2/cm3 t = void fraction of the monolith, 1 - f, - fa t,
= void fraction of the washcoat
Ow = poisoned fraction of adsorptionsites (i.e., poison coverage) (Ow) = integral-averaged poison coverage defined by eq 24 X, = thermal conductivity of gas, J/cms.K X, = thermal conductivity of substrate, J/cm.s.K pg = density of gas, g/cm3 p, = density of substrate, g/cm3
0, = density of washcoat, g/cm3 \ka = quantity defined by eq 16 w1 = k , SL/u w2 = k,/D,,
tfi
Subscripts
g = gas phase in the channel g,i = reactant i in the gas phase g,p = poison precursor in the gas phase i = main reactant p = poison precursor s = solid phase s,i = reactant i in the washcoat s,p = poison precursor in the washcoat Superscript in = reactor inlet Registry No. P, 7723-14-0.
Literature Cited Angeie, B.; Kirchner, K. Chem. Eng. Sci. 1980a, 35, 2089. Angeie, B.; Kirchner, K. Chem. Eng. Sci. I980b, 35, 2093. Baron, K. Thln SolM Films 1978, 55, 449. Bird, R. B.; Stewart, W. E.: Lightfoot, E. N. "Transport Phenomena"; Wiley: New Yo&, 1960; p 505. Bomback, J. L.; Wheeler, M. A.; Tabock, J.; Janowski, J. D. Environ. S d . Techno/. 1975, 9, 139. Cavendish, J. C.; Oh, S. H. Chem. Eng. J. 1979, 17,41. Heck. R. H.; Wei, J.; Katzer, J. R. AIChE J. 1978, 22,477. Hegedus, L. L.; Baron, K. J. Catel. 1978, 54, 115. Hegedus, L. L.; McCabe, R. W. Carai. Rev. Sci. Eng. 1981, 23, 377. Hegedus, L. L.; Summers, J. C. J. Catel. 1977, 48, 345. Hegedus, L. L.; Summers, J. C.; Schiatter, J. C.; Baron, K. J. Caral. 1979, 56,321. Herod, D. M.; Nelson, M. V.; Wang, W. M. Society of Automotive Engineers, Detroit, MI, March 1973; Paper No. 730557. Hindmarsh, A. C. "GEARIB, Solutlon of Implicit Systems of.Ordinary Differential Equations with Banded Jacobian"; Lawrence Livermore Laboratory Report UCID 30130, Feb 1976. Howitt, J. S. Society of Automotive Engineers, Detroit, MI, February 1980; Paper No. 800082. Isaacson, E.; Keiler, H. B. "Analysis of Numerical Methods"; Wiiey: New York, 1966; p 384. Kummer, J. T. frog. Energy Combust. Sci. 1980, 6, 177. Lee, S. T.; Aris, R. Chem. Eng. Sci. 1977, 32,827. Lee, S. T.; Aris, R. ACS Symp. Ser. 1978, No, 65, 110. Lester, G. R.; Marinangeli, R. E. Society of Automotive Engineers, Detroit, MI, Feb 1980; Paper No. 800844. Monroe, D. R. General Motors Research Laboratories, Warren, M I , personal communication, 1982. Oh, S. H. General Motors Research Laboratories. Warren. MI. unoublished results, 1982. Oh, S. H.; Cavendish, J. C. AIChE Fall Annual Meeting, Los Angeles, CA, Nov 1982. oh,S. H.; Cavendish, J. C. Ind. Eng. Chem. Prod. Res. Dev. 1962, 21,29. Shah, R. K.; London, A. L. Technical Report No. 75, Department of Mechanical Engineerlng, Stanford University, Stanford, CA, 1971. Sheief, M.; Otto, K.; Otto, N. C. A&. Catel. 1978, 27, 31 1. Sherony, D. F.; Solbrig, C. W. Int. J. Heat Mass Transfer 1970, 13, 145. Smith, J. M. "Chemical Engineering Kinetics", 2nd ed.; McGraw-Hill: New York, 1970; p 414. Weaver, E. E.; Shiiier, J. W.; Piken. A. G. AIChESymp. Ser. 1976, 72(156), 369. Young, L. C.; Finlayson. 8. A. AIChE J. 1978, 22,331.
Received f o r review April 18, Accepted August 8,
1983 1983
