Znd. Eng. Chern. Res. 1993,32,1555-1559
1555
Performance of a Monolithic Catalytic Converter Used in Automotive Emission Control: The Effect of a Longitudinal Parabolic Active Metal Distribution Apostolos Psyllos and Constantine Philippopoulos' Department of Chemical Engineering, Laboratory of Chemical Process Engineering, National Technical University of Athens, 9 Heroon Polytechniou Street, GR 157 80 Athens, Greece
The effect of a longitudinal parabolic active metal distribution on the performance of a monolithic converter is reported. On the basis of the results of numerical calculations, the improvement in the performance of the catalytic converter with parabolic axial active material distribution compared with the respective uniform distribution is verified. In addition, in cases where operating conditions fail t o light-off (or ignite) the catalytic system with uniform material distribution, high conversions can be achieved by catalysts with parabolic distribution of the active material, for the same quantity of precious metal.
Introduction The improvement of catalysts used in automotive emission control requires interdisciplinary efforts. Mathematical models developed in chemical reaction engineering research can be used in the identification and evaluation of key process variables which can be exploited in the design of the catalytic converters. Typical catalyst design parameters include descriptors of the structure and composition of the surface, the pore structure, the activity distribution in the catalyst body, and the shape and size of the catalyst (Hegedus, 1990;Pereira, 1988). In the case of the design of a monolithic catalyst converter the effect of the transient operating conditions on the catalyst startup and the processes of heat transfer, mass transfer and chemical reaction should also be taken into consideration (Heck, 1976;Finlayson, 1974;Votruba, 1975a,b;Sinkule, 1978). Transient, heat-up models have been used to determine the effects of monolith geometry, noble metal loading, inlet exhaust conditions, and physical properties on monolith light-off (or ignition) (Oh, 1982). In practical applications, monolithic catalytic converters are operated at non-isothermal conditions. In this case, the active metal distribution along the length of the converter may influence its performance. Indeed, better conversionscan be achieved by controlling the distribution of the same quantity of active material. In the present work, the effect of a longitudinal noble metal distribution on the performance of a monolith catalytic converter is investigated. Namely, a parabolic axial noble metal distribution is combined with the rate expression for carbon monoxide oxidation and the reactor operating Conditions.
Model Used The model takes account of heat and mass balances over a differential control volume of the monolithic structure and takes account of the heat and mass transfer by convection and an exothermic catalytic reaction occurring on the catalyst surface associated to a single tube of a monolith matrix (Figure 1). The governing equations are based on the following assumptions:
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Figure 1. Diagram of asinglemonolithicchannelwith its geometrical characteristics.
(a) The whole monolith matrix is described by a single channel. We neglect interactions between adjacent monolith channels since temperature and concentration profiles in all channels of the monolith are nearly the same so that analysis and modeling of one channel suffice. (b) The catalytic reaction taking place is
-
co + (1/2)0, co, The CO oxidation is the most exothermic reaction in the exhaust gas purification process which causes the system to light-off. The basic implications from the use of a catalytic material distribution could be seen even with a single catalytic reaction. (c) Ideal tubular reactor behavior is assumed in a single channel since the length to diameter ratio for the channel is large enough (over 100). (d) We have assumed an insulated monolith channel operating a t adiabatic conditions. That is true for ceramic monoliths with low thermal conductivity. (e) One-dimensional heat and mass transfer by conduction is considered. (f) Heat transfer and mass transfer by axial and radical diffusion are ignored in comparison to the convection of heat and mass. (g) Intrinsic kinetics has been taken into account, neglecting internal heat- and mass-transfer phenomena since the catalytic layer in the monolithicstructure is very thin and a very fast surface catalytic reaction occurs. (h) Steady state model equations are consideredas they are lead to a simple mathematical model. The mass balance equations in the gas and the gassolid interphase are 0 1993 American Chemical Society
1556 Ind. Eng. Chem. Res., Vol. 32, No. 8, 1993
dCf + Uk,(Cf - C*) = 0 sp dx
(a) The mass of active material m(c) must remain nonnegative throughout the reactor length, thus
ak,(Cf- C*) + UUR(C*,T,) = 0 (2) The heat balances in the gas phase and on the wall are respectively
m(5) I0, 0 I5 I1 (13) (b) The total catalyst mass must be equal to that considered in the uniform catalyst mass distribution case (UCMD), which implies that if mo is the total catalyst mass in both cases, m(f‘)satisfies the following equation:
(3)
ah(Tw- Tf)- aa(-AH)R(C*,T,) = 0 (4) The intrinsic reaction rate, R , for CO oxidation is given by Koberstein and Wannamacher (1987). Their kinetic model, which is valid for Pt\Rh monolithic catalyst (support: cordierite monolith 400 cells in-2, 100 g of washcoat per liter of catalyst containing y-alumina, nonprecious metals, oxide additives, and 1.3 g of Pt\Rh precious metals at a ratio 5:l) over the temperature range 190-350 O C and reactant (CO, 02)concentrations ranging between 0.1 and 2.0%,is E ko exp( cco,wco*,w RgTw R(C*,Tw)= (5) 11 + k,Cco,w12 Initial and boundary conditions for concentration of reactants and temperature of the solid and fluid phases are
Jolm(E) d5 = mo
(14)
In the present work, a family of parabolas of the general form
+
m(5) = at2 b[ + mo
(15)
has been chosen, where mo stands for the total catalyst mass. From the constraint described in eq 13 and eqs 14 and 15 parameters a and b can be expressed by
-)
Cf(0) = Cco,in at x = 0 Tf(0) = Tin at x = 0
(6)
The model equations are rendered dimensionless in order to achieve a more tractable solution. The following transformations are applied:
where 5, is the point where the function m(5)is minimized. The ACMD is inserted in the model equations via the Damkohler number (Da),which is a function of catalyst mass. In the case of the uniform mass catalyst distribution, Da is proportional to mo. In the case of axial mass catalyst distribution, Da is a linear function of catalyst mass distribution m(5).
Numerical Solution The set of equations (7)-(11) represents a system of two first-order nonlinear differential equations and two algebraic equations constrained by two boundary conditions. By applying appropriate transformation (subtraction and substitution), the system can be reduced to a simpler one made up of two differential and two algebraic equations: dyldx = jD@* - Y)
- Y) = (Da)r@*,Ow) dOf/dx = jH(Ow - of)
j,@*
By substitution of these parameters to the model equations the following dimensionless equations are deduced: dyldx = jD(Y* - Y)
(7)
j,@* - Y ) = (Da)r@*,d,)
(8)
d8f/dx = jH(ew - 6,) j H ( e w - 8,) + B(Da)r(y*,Ow)= 0 and the reaction rate expression is
(9) (10)
The dimensionless boundary and initial conditions read y - 0 at [ = O , O , = 1 at 5 = 0 (12) In addition, the axial catalyst mass distribution (ACMD) of the active components should satisfy the following constraints:
Ow = 1 + BO’D/jH) cy* - y) + By These equations are integrated by means of the implicit method of Gear (Gear, 1971) and a nonlinear algebraic equation solver based on the Newton-Raphson method.
Results and Discussion Calculations were based on the following design parameters: (a) The reactor space-time, 7-l (GHSV, h-l), is proportional to the inlet gas volumetric rate per unit reactor volume and determines the time required by the chemical species to react. This variable affects the Da,jD, and j~ numbers and through them the integration of the model. (b)The gas inlet temperature, TdK),is a very important variable since it determines the ignition temperature for the catalytic reaction via the y number, the Da number, and the kinetic term. (c) The carbon monoxide inlet concentration Cc0,in (% v/v) exerts a major influence on the reaction rate. (d) The air/fuel ratio dimensionless ratio, AFR = Coz/ (~CCO), determines the maximum attainable carbon monoxide conversion.
Ind. Eng. Chem. Res., Vol. 32, No. 8,1993 1857 Table I. Base Case Operating Conditions GHSV 56 OOO h-1 Ti. 550 K ccosn 1.0% v/v 0.90 AFR parabolic eq consts m~= 3 and Ern = 1 Table 11. Monolithic Honeycomb Characteristics geometry monolith cell density 400 cells4n.-2 wall thickness 0.02cm void fraction 0.75 GSA 24 cm2.cma length 15 cm outer diameter 10 cm physical properties reactor (solid phase) Pw 2.5 g c m a Cp,, 0.256 kcal*kgl-K-1 exhaust gases 0.57 gL-' a t 600 K, 1bar Pf CPC 0.232 cal-mol-1.K-1 mass-transfer coefficient Sh = 0.71 ((Re)D/L)04Sco.M (Votruba, 1975a) Nu = 0.57((Re)D/L)O.67 heat-transfer coefficient (Votruba, 1975a) JZO = 1.0 X 1015 cm2.s-1.gmt-1 kinetics for CO oxidation kl = 1.0 X 108 cm*.mo1-1 E = 17 kcalamol-1
In order to compare the performance of monolithic converter with ACMD to that of UCMD, as described above, the following runs were performed: (a) A base case is considered where operating conditions remain fixed at the values given in Table I. In the same of ACMD with a distribution the values of parameters are rno = 3.0 and Em = 1.0, and hence the parabola equation is
m([)= 3t2- 6( + 2 (b) Independent variations of r l ,Ti,,, CCO,~, and AFR from the base run were carried out. (c) For a given set of operating conditions (the base case), various catalyst parabolic distributions were considered and an optimum parabolic distribution to that set of operating conditions was searched. In Table I1the values for the geometrical characteristics and transport properties of the monolithic catalyst converter are given. Gas velocity, reactor wall properties, and gas physical properties are functions of temperature. The values of these parameters were substituted in the appropriate expression valid for the dimensionless numbers, and subsequently the model was solved using the method stated above. Effect of Inlet Gas Temperature, Ti,. As shown in Figure 2,for the base case a decrease of 40 "C in the lightoff temperature can be achieved when the parabolic distribution is used. For a variation of the inlet gas between 500and 550K,the improvement temperature, Ti,,, in the performance of the converter with axial mass catalyst distribution is clearly confiimed. Model predictions indicate that, at temperatures greater than 550K, catalytic converters with and without active metal distribution show a similar behavior (not shown in Figure 2). Effect of the Residence Time, rl.For Ti,= 600 K, the results of the catalytic converter simulation are illustrated in Figure 3. A conversion of 80 % is achieved in the case of ACMD compared with 5 % conversion in the uniform catalyst situation, although the inlet gas temperature is sufficient for the uniform catalytic converter start-up.
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510 K
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515 K
~~~~~~~~,1',,~,,,,,,,,,1,,,,,,,,,1,,,,,,,,,
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Figure 2. Effect of inlet gas temperature, Ti.,for GHSV = 70 OOO h-l, Cc0,i. = 1%,AFR 0.9. 1 .o
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Normalized Reactor Length Figure 3. Effect of residence time, for Ti.= 600 K, Ccob = 1%, AFR = 0.9.
At values of the gas hourly space velocity (GHSV)greater than 220000 h-l both systems fail to light-off. By decreasing GHSV from 200 000to 70 000h-l the converter with ACMD enters first the light-off region. For values of GHSV lower than 70 OOO h-' both systems give the same conversion at the reactor exit. Effect of Initial CO Concentration, As CO input becomes lower than 0.4% and the inlet gas temperature is kept lower than or equal to 600 K, neither the converter with ACMD nor that with UCMD can operate. When the initial CO concentration increases above the 0.4% limit, the system with ACMD lights off first. At the value of inlet CO concentration equal to 0.55%, the maximum difference in reactor outlet CO concentration between the converter systems with and without distribution of the active metal is evident. For inlet CO concentrations greater the above value, a similar conversion difference is confirmed. Figure 4 is a complete pictorial presentation of the observed performance differences of two categories of converters. An additional important observation is that the exit pollutant concentration is lower for greater values
1558 Ind. Eng. Chem. Res., Vol. 32, No. 8, 1993 3.00
Distribution --- Uniform Parabolic Distribution
.
1
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3
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C
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8
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Figure 4. Effect of initial CO concentration, for Ti.= 600 K, GHSV = 70 OOO h-l, AFR = 0.9.
0.2
0.4 0.6 0.8 Norrnolized Reactor Length
1 .o
Figure 6. The family of parabolic shapes tested. 1 .o
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0.6 0.8 Normalized Reactor Length
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Figure 8. Effect of air/fuel ratio.
of CO inlet concentrations. Thus for exhaust gases with high pollutant concentration the catalytic converter operates at a higher efficiency. At high carbon monoxide inlet concentration both systems indicate a similar response. Effect of Air/Fuel Ratio, AFR (Dimensionless). In Figure 5 the effect of AFR value on the exit carbon monoxide conversion is presented. At high AFR values (>0.70), there is no any improvement in the performance of the converter when the active material is longitudinally distributed. At AFR values lower than 0.70 the converter with ACMD gives a better performance compared with the UCMD system. Effect of the Shape of the Parabolic Distribution. The family of the parabolic shapes tested is illustrated in Figure 6. In comparison with the uniform distribution, the quantity of the active material is enhanced in the front section of the catalytic converter and controlled to be higher or lower at the end converter exit section. The results of the converter simulation for the base-case values of parameters are presented in Figure 7,in terms of exit carbon monoxide concentration achieved for the certain parabolic distribution.
0.4 0.6 0.8 Normalized Reactor Length
0.2
1 I
Figure 7. Effect of shape of the parabolic distribution. Exit CO concentration v8 normalized reactor length. (Ti. = 550 K, GHSV = 70 OOO h-l, AFR = 0.9, Ccojn 1 % ).
In each one of the cases considered, the catalytic converters with ACMD are more efficient than those with a uniform distribution of the active material. The temperature profiles for the family of parabolas and the uniform distribution are illustrated in Figure 8. It is evident that the allocation of the catalytic material in the front end of the converter gives rise to converter operation at higher temperatures. This benefit is more pronounced for low inlet gas temperatures. The constraint concerning the catalytic converter maximum operated temperature (
