Ind. Eng. Chem. Fundam.
410
p = pressure p c = pressure scale factor defined by eq 12 p s = ambient pressure Q = volumetric flow rate r = radial coordinate R = radius of sphere Re = Reynolds number, ycu,/u =: Q/(S?rRv) s = sin 0 N sin x u = streamwise velocity component nondimensionalizedwith respect to u, u, = streamwise velocity scale factor defined by eq 10 u, = surface velocity nondimensionalized with respect to u, v = cross-streamvelocity component nondimensionaliied with
respect to L',
v , = cross-stream velocity scale factor defined by eq 11 We = Weber number y/pycu,2 = [y3(2?rR)5v/(Q5p3g)11/3 x = re, streamwise coordinate nondimensionalized with respect
to x , x, = R y = r - R , cross-streamcoordinate nondimensionalized with respect to y c y c = cross-stream length scale defined by eq 14
1983,22, 410-420
Greek Letters y = surface tension 6 = y,/R = [ v Q / ( 2 ~ R ~ g ) ] ~ / ~
8 = angle in radians measured from pole at which flow ori-
ginates
= shear viscosity u = kinematic viscosity p = density $ = stream function nondimensionalized with respect to uyyP
Literature Cited Danckwerts, P. V. "Gas-LiquM Reactions"; McGraw-Hill: New York, 1970; pp 82-84, 179. DavMson, J. F.; Cullen, E. J. Trans. Znst. Chem. €ng. 1957, 35, 51. Lynn, S.;Straaterneler, J. R.; Kramers, H. Chem. Eng. Sci. 1955a. 4, 49. Lynn, S.; Straatemeier, J. R.; Kramers, H. Chem. Eng. Sci. 1855b, 4 , 58. Lynn, S.: Straatemeier, J. R.; Kramers, H. Chem. Eng. Sc/. 1855c, 4 , 63. Zollars, R. L.; Krantz, W. B. 11%'.Eng. Chem. Fundam. 1878, 75, 91. Zollars, R. L.; Krantz, W. B. J. NuMMech. 1980, 96, Part 3, 585.
Received for review May 26, 1982 Revised manuscript received May 16, 1983 Accepted July 8, 1983
Dynamic Behavior of a Single Catalyst Pellet. 1. Symmetric Concentration Cycling during CO Oxidation over Pt/AI2O3 Byong K. Cho Physical Chemlstty Department, General Motors Research Laboratories, Warren, MIchigan 48090
The transient response of a single R/AI,O, catalyst pellet to feed composition cycling during CO oxidation has been investigated by means of a nonequilibrium adsorptin-desorptkn model. The time-average reactivity of the pellet was examined in connection with evolution patterns of the surface coverage profile of reactants in the pellet. Results showed that cyclic operation may give better conversion performance than steady-feed operation under certain condltions. The effect of cyclic operation on the time-average rate of CO oxidation was more pronounced when the alumina pellet was impregnated with R in a shallow band near the external surface than when the pellet was uniformly impregnated. The enhanced or deteriorated reactivity of the catalyst during cyclic operation is discussed in light of the chromatographic and antichromatographic effects.
Introduction In recent years, considerable attention has been focused on the effects of feed composition cycling on reactor performance. The potential benefits of cyclic operation of chemical reactors include enhanced separation between reaction mixtures (Cho et al., 1980), improved selectivity and/or conversion (Unni et al., 1973; Lee and Bailey, 1974; Cutlip, 1979; Abdul-Kareem et al., 1980a,b,c),improved stability and reduced parametric sensitivity (Fjeld, 1974; Codell and Engel, 1971), and complete conversion of an equilibrium-limited reaction (Cho et al., 1980). Extensive reviews of recent developments in this area can be found elsewhere (Bailey, 1973, 1977). In a recent study, Cutlip (1979) alternately introduced oxygen and carbon monoxide to a fixed-bed reactor containing a supported platinum catalyst and observed enhanced carbon monoxide conversion performance compared with a steady flow of the thoroughly mixed gases. Mihail and Paul (1979) attempted to model, with some error as was pointed out by Jain et al. (1981), the effect of composition cycling on the SO2oxidation rate but could not predict the resonance effects observed by Unni et al. (1973) and later by Abdul-Kareem
et al. (1980b,c). The possibility of unusual dynamic phenomena during forced periodic operation of a CSTR has been suggested by SinEiE and Bailey (1977). Introduction of concentration pulses of reactants into a fixed-bed reactor may lead to complex interactions between catalytic and chromatographic effects. This concept has been applied to a continuous chromatographic reactor (Cho et al., 1980), which is a different version of a cyclic reactor. Feed composition fluctuations as occur in automobile three-way catalytic converters represent a practical application of unintentional periodic operation. These fluctuations occur with a frequency on the order of 1Hz (Canale et al., 1978). Gandhi et al. (1976) pointed out that including an "oxygen storage" component in the catalyst moderates the effects of rapid changes between rich and lean exhaust stoichiometries. Recently cerium has received much attention as a base metal additve for three-way catalyst formulations. Schlatter and Mitchell (1980) investigated the transient response of a Rh-Ce three-way catalyst under cyclic operating conditions and observed enhanced conversion compared with steady-state operating conditions. More recently, Taylor and Sinkevitch (1983)
0196-4313/83/lO22-O410$01.5OlO 0 1983 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 22, No. 4, 1983
used both symmetric and asymmetric air-fuel ratio cycles in their laboratory experiments of cyclic operation of automobile three-way catalysts. In this work, we have developed a transient mathematical model which describes the behavior of a single catalyst pellet under conditions of feed composition cycling. The model accounts for the kinetics of various catalytic surface processes (i.e., adsorption, desorption, and surface reaction) and extra- and intrapellet diffusion resistances. Surface processes were included in our model because, as we will see later, variations in surface concentrations of reactants play an important role in determining catalyst activity during feed composition cycling. Numerical simulations were then carried out using the model in order to gain insight into the dynamic behavior of a catalyst under cyclic operating conditions and to investigate how cycling characteristics and catalyst properties influence catalyst activity. This paper w i l l focus on the case of symmetric feed composition cycling during CO oxidation over Pt/A1203.
Two-Phase Nonequilibrium-Adsorption Model A single catalyst pellet surrounded by a uniform gaseous environment can be considered a basic element of a three-way catalytic converter. In this paper, we develop a two-phase nonequilibrium-absorption model which describes the catalyst's behavior during feed composition cycling. Simplifying assumptions invoked in developing the model are listed below. (1) The reactor is isothermal. (2) Oxygen and carbon monoxide adsorb competitively. (3) Oxygen adsorbs atomically and carbon monoxide adsorbs molecularly. (4) adsorption-desorption processes follow Langmuir kinetics. ( 5 ) Surface reaction follows Langmuh-Hinshelwood kinetics. (6) Feed composition cycling is symmetric about the stoichiometric point in sinusoidal wave forms. (7) Cycling frequency is the same for both oxygen and carbon monoxide. The mass balance for the intrapellet gas phase gives
SP
T[ka,ici(N- nl - nz)' - kd,ini'] 1
(i = 1,2)
The feed conditions are cif(t) =
if + ciA sin (2rft + +J
(7)
Recognizing the following characteristic time scales of our system 7f
l/f;
7~
= l/NkR;
7 ~ ,= i
$R2/D,,i; and
7,
= VE,/Q (8a
we introduce the following dimensionless variables 7 =
t / 7 ~ ;f r/R; Ui = C i / E A U t = ni/N, U? = C?/C'if; Uif = cif/Eif; UiA = CiA/C'i'; @i = (7Dli/7R)l/,; = TS/7R; w = 2r7~/7fq ; = kd,i/kRW-'; Bi = KiEif; pi = NSp/cpEif;CY, = &i/i; Ki = k,i/kd,i; pi = 4rR2km,i/Q;Bi = Rk,,i/D, (8b Note in eq 8b that Bi can also be expressed as
4 = u'i,e/(I - ~ ' 1 -, ~~ ' 2 , ~ )
(84
here u ~is ~the, surface ~ coverage of species i at adsorption-desorption equilibrium. Equations 1 through 7 reduce to
(1)
The subscript i refers to the species of interest: in the gas phase i = 1 for CO and i = 2 for 0,;on the surface i = 1 for adsorbed CO and i = 2 for adsorbed oxygen atoms. The mass balance for the catalytic surface becomes ani _ - k,iCi(N - nl - nJi - kd,i?$ - k~nln2 (2) at The mass balance for the bulk gas phase of the reactor yields
The initial conditions are ci(r,O) = ci,o
(44
ni(r,O) = ni,o
(4b)
Ct(0) = q0b
(44
The appropriate boundary condtions are aci -(O,t) = 0 ar
411
uif(7) = 1 + uiAsin
(w7
+ qi)
(15)
In eq 8a, Tf is the period of the feed composition fluctuation. TR, T ~and , T ~ are , ~the characteristic response time of the surface reaction, the space time, and the response time of the intrapellet diffusion process, respectively. Under the typical converter operating conditions, 7 R s, T~ s, T ~ , 1~ s, 7f 1 s. The feed-stream oscillation (73 and the intrapellet diffusion processes (Q) are on the same time scale. Also, the response time of intrapellet diffusion (7D,i) is much slower than that of surface reaction (7d which is in turn slower than that of the bulk gas phase (7'). The bulk gas phase concentration can therefore be safely approximated by the pseudosteady-state hypothesis (PSSH)
-
-
-
-
This approximation, which presumes an instantaneous steady-state relationship between the state of the system and the feed fluctuation, is valid only when the ratio of 7t/7, is sufficiently large. Bailey (1972) showed in his
412
Ind. Eng. Chem. Fundam., Vol. 22, No. 4, 1983
Table I. Standard Conditions Used for the Model Simulation Feed and Reactor Operating Conditions c I A= 6.307 x low8mol/cm3 (0.4vol %) mol/cm3 (0.05vol %) c A = 0.788 x $f= 9.46 x lo-*mol/cm3(0.6vol %) = 4.73 x mol/cm3 (0.3 vol %) f = 1 Hz km,l = 20.5 cm/s hm,z = 20.0 cm/s P = 101.3 kPa (1atm) Q = 11.12 cm3/s (at 773 K, 101.3 kPa) T = 773 K V = 0.032 cm3 E B = 0.36 (I, = TI (lean initial half-cycle)
df
$,=O
Initial Conditions u.,= 0 u k , , = (clean surface) u j,,= 0
o
Adsorption, Desorption, and Reaction Kinetics 6.2658 X lo4 s-' (Fairand Madix, 1980) 1.2887 X lo9 (mol/cm2Pt)-' s-' (Wilf and Dawson, 1977) h~ = 5.0 X 10'O (mol/cmz Pt)-'s-' (Bonzel and Burton, 1975;Oh et al., 1978) K, = 1.2790 X lo9 (mol/cm3gas)-' (Hegedus e t al., 1977) K, = 6.9368x 10" (mol/cm3 gas)-' (calculated from ha,, and hd.2) Catalyst Properties d = 80% De,' = 0.0468 cmz/s De,z = 0.0450 cm2/s m = 0.05 wt % N = 2x mol/cm2 Pt r, = 0 (uniform impregnation) R = 0.17cm S, = 814 cm2 R / c m 3 pellet E,, = 0.4 p p = 0.783 g/cm3 pellet kd,l = kd =
example that the PSSH is valid when this ratio is greater than 100. In model eq 9 through 15, we identify the system parameters, u, p, 6, p, @, and B for each component, which govern the behavior of our system. The parameter u represents the ratio of the desorption rate to the surface reaction rate; /3 represents the ratio of the storage capacity of the surface to the storage capacity of the gas-phase; 6 represents the ratio of the number of occupied sites to the number of vacant sites a t adsorption equilibrium; p represents the ratio of the external mass transfer rate to the gas flow rate; @ represents the modified Thiele modulus, and B represents the ratio of the external mass transfer rate to the intrapellet diffusion rate. The important feed control parameters are w , the dimensionless frequency of oscillation, and $, the phase lag. Parameter Estimation Table I shows the standard set of parameter values used in the numerical simulations. Because we are interested in the behavior of a single catalyst pellet in an automobile catalytic converter, the reactor volume V and the gas flow rate Q listed in Table I are the values associated with the single pellet under typical operating conditions of a Type-260 GM production converter. Feed composition cycling with a phase difference ?r between CO and O2concentration fluctuations was taken as the standard condition because typical feed composition fluctuation in a three-way catalytic converter is such that the O2 concentration decreases (increases) when the CO
concentration increases (decreases). This type of feed composition cycling is referred to here as "180-degree out-of-phase" cycling. Cycling with no phase lag between the concentration fluctuations of CO and O2is designated as "in-phase" cycling. The stoichiometric number is defined here as the ratio of (u2/u1);a stoichiometric number greater than 1designates lean conditions and smaller than 1designates rich conditions. The values of cf and c t in Table I approximate periodic composition cycling of the feedstream between a stoichiometric number of 0.5 and 3.5 for 180-degree out-of-phase cycling, and between 0.7 and 2.5 for in-phase cycling. Adsorption-desorption parameters for CO were obtained from the literature as shown in Table I. The desorption rate constant of CO reported by Fair and Madix (1980) is in good agreement with that reported by Bonzel and Burton (1975). Though Ertl et al. (1977) observed a small variation of desorption activation energy for CO with CO coverage, we used lumped data by Fair and Madix (1980). The adsorption rate constant of oxygen was estimated using the kinetic theory of adsorption for a perfect gas
where so is the initial sticking coefficient of oxygen on platinum. The reported value of so varies widely from 7 X lo-' to 4 X 10-1 (Weinberg et al., 1972; Bonzel and Ku, 1973; Schwaha and Bethtold, 1977; Wilf and Dawaon, 1977; Gland, 1980), and so depends on the type of platinum surface. However, a reasonable consensus appears to be that the value of so lies between 0.004 and 0.1. Wilf and Dawson (1977) showed that s is an approximately linear which is consistent with dissociative function of (1- u2e)2 adsorption, while Bonzel and Ku (1973) obtained an exponential dependence of the oxygen sticking coefficient on coverage. In this study the value of so was assumed to be 0.01, which is consistent with data by Gland (1980) and estimated values of Herz and Marin (1980). Our model eq 2 assumes a linear dependence of s on (1- uls - uzs)2 in accordance with Langmuir kinetics for competitive multicomponent adsorption. Gland et al. (1980) reported a desorption activation energy of oxygen varying from 160 to 500 kJ/mol depending on the coverage, while Schwaha and Bethtold (1977) obtained a value between 172 and 206 kJ/mol. In this study, the oxygen desorption data were taken from Wilf and Dawson (1977),neglecting the dependence of the activation energy on the coverage. The stoichiometry of carbon monoxide chemisorption on platinum-alumina catalysts is reasonably constant on small platinum crystallites and approximately equal to the stoichiometry of hydrogen chemisorption (Freel, 1972). The stoichiometry of oxygen chemisorption on platinumalumina catalysts is more complex and related to, for example, the thermal history of the sample (Wilson and Hall, 1972; Freel, 1972). After a long high-temperature treatment in hydrogen, the catalyst surface behaves like that of platinum black, adsorbing approximately equal quantities of hydrogen and oxygen (Freel, 1972). More recently, Kobayashi et al. (1980) observed that at 25 "C that ratio of O/Pt was unity for a platinum dispersion less than 45%, and this ratio fell progressively below unity at higher dispersions of platinum. They also found. that at 300 "C and approximately 803'% dispersion of platinum, determined by Hz chemisorption, the ratio of O/Pt was approximately unity and increased with increasing temperature of oxygen chemisorption. In view of the current
Ind. Eng. Chem. Fundam., Vol. 22, No. 4, 1983 b
a
1'5s
--I
=4.3s
-,-\I,,
0.2
0.0
1.0
,' ' 0.8
t=10s
I \
I
08
0.6
Dimensionless Radial Position
I I
10.6
I,, I , J , Il,-> T,, where 7, is the characteristic response times of the system like T D , ~ ,T ~ and , 7R in eq 8a) and relaxed-steady periodic operation ( T ~
