570
Ind. Eng.
Chem. Process Des. Dev. 1981, 20, 570-575
they increase with decreasing droplet size. Photographic evidence for this system and supporting studies with charged water droplets in n-heptane have confirmed that there is a similar trend in oscillation frequency with droplet size (Thornton, 1976; Bailes, 1977). It would seem therefore that the electric field enhances the rate of extraction appreciably during droplet motion by virtue of its effect on turbulence levels and hence eddy diffusion. This finding can only be regarded as specific to the extraction system studied and there may well be other field induced effects with, for example, metals systems where there is a chemical interaction with the extractant. One such case is the removal of copper from acidified sulfate media by hydroxyoxime extractants in a hydrocarbon diluent. Here it appears that the sign of the charge imparted to the aqueous-organic interface may have a distinct influence on the overall extraction mechanism (Bailes and Wade, 1980). Conclusion
Several solvent extraction systems of commercial significance have electrical properties which allow the sustained application of high-voltage electric fields. Work with single charged droplets in a parallel electrode geometry has shown that an applied field can be used to substantially modify the size, velocity, and coalescence characteristics of droplets. Such droplets are of practical interest in liquid-liquid extraction because when small they remain turbulent and high rates of mass transfer are therefore possible. Nomenclature
de = equivalent spherical droplet diameter, d , droplet diam-
eter in the absence of an electric field
DN = nozzle diameter
E,, = nominal applied field strength Eo = field acting on the droplet E T = fractional approach to equilibrium g = acceleration due to gravity k d = dispersed phase film mass transfer coefficient Q = detached droplet charge
U = charged droplet velocity V = detached droplet volume Greek Symbols y = interfacial tension e = dielectric constant to = permittivity of free space (8.854 X pc = density of continuous phase Ap = density difference
F/m)
Note: Primed symbols refer to properties of the pendant droplet before detachment. Literature Cited Agaev. A. A. et al. Izv. Vyssh. Ucheb. Zaved. 1989, 72(3), 53. BaHes, P. J. Roc. Int. Solvent Extr. Conf. 1977, 7, 233 (CIM Special VoC ume 21, 1979). Balles, P. J.; Guymer, P. U.K. Patent Application No. 1737176. Bailes, P. J.; Kalbasl, M. Proc. 4th Int. Conf. Electrostatics, The Hague, May 1981 (to be published In Journal of Electrostatlcs; Elsevier: Amsterdam). Bailes, P. J.; Thornton, J. D. Roc. Int. Solvent Extr. Conf. 1971, 2 , 1431. Bailes, P. J.; Wade, I. R o c . Int. Solvent Exh. Conf. 1980, 7 , Session 28, 80-196. Brown, B. A. Ph.D. Thesls. Universtty of Newcastle, U.K., 1970. Grace, J. R.; Wairegi, T.; Nguyen, T. H. Trans. Inst. Chem. Eng. 1978, 54(3), 167. Harkins, W. D.; Brown, F. E. J. Am. Chem. SOC., 1919, 4 7 , 499. Hendricks, C. D.; Sadek, S. I€€€ Trans. Appl. Ind. 1977, IA- 73, No. 5 , 489. Mehner, W.; Mueller, E.; Hoehfeld, G. Proc. Int. Solvent Extr. Conf. 1971, 2 , 1265. Murray, D. J. J. Chem. Tech. BiOtechno/. 1979. 29, 367. Pear-, C. A. R. Bm. J. Appl. phys. Apll 1954, 136. Prestridge, F. L. U.S. Patent 3772 180, Nov 1973. Prestridge, F. L. U.S. Patent 4 120769, Oct 1978. Richards, K. J.; Clark, D. R. US. Patent 4 039 404, Aug 1977. Stewart, G. Ph.D. Thesis, University of Newcastle, U.K., 1970. Stewart, G.; Thornton, J. D. I . Chem. E . Symp. Ser. No. 26, 1967, 29, 37. Sumner, C. G. Clayton’s “The Theory of Emulsions and Theh Technlcal Treatment”, 5th Ed.; Churchill: 1954. Thornton, J. D. Bkmingham Unlv. Chem. Eng. 1978, 27(1), 6. Thornton, J. D.; Brown, B. A. U.K. Patent 1205562. June 1966. Warren, K. W.; Prestridge, F. L. U.S. Patent 4 161 439, July 1979. Warren, K. W.; Prestridge, F. L.; Sinclair, B. A. Min. Eng. Aprll, 1978. Waterman, L. C. Chem. Eng. Prog., 1985, 61(10) 51. Whitehead, J. 6 . ; Marvin, R. H. Trans. Am. Inst. Nec. Eng. 1990, 49(2), 847.
Received for review July 10, 1980 Accepted February 23, 1981
Calculation of Kinetic Parameters for the Deactivation of Heterogeneous Catalyst A. Romero, J. Bflbao, and J. R. GonzSlez-Velasco’ Departamento de admica T&nica, Universkiad del Pais Vasco, Apdo. 644, B/Ibao, Spain
Two procedures are shown for the calculation of kinetic parameters for the deactivation of a Cu supported on SiOp catalyst. Procedure A is based on the analysis of the conversion data vs. time, resulting in the equation -da/dt = [11.87 exp(5044.33/T) x 2.73 x exp(7063.2/~)pA]/[1 4- [8.3 x exp(3048.4/ T ) 42.73 x io-5 exp(7063.2/ T ) ] ~ A 2.88 x io-’ eXp(l1506.6/ - PA)/^)]
q(n
Procedure B studies the temperature-time sequences experimentally followed to keep constant different conversion values at the reactor outlet. The equation for the deactivation is -da’/dt = 503 exp(-5178.66/ T)pA0,79a’
Introduction
For the design, operation, and optimization of catalytic reactors a knowledge of the kinetic equation representing the deactivation of the catalyst is necessary. Although a standard method, universally accepted, to determine the 0196-4305/81/1120-0570$01.25/0
kinetics of the deactivation has not been established yet, remarkable advances in this field have been obtained. The studies carried out until 1970 contemplate the catalyst activity as dependent only on the reaction time, linearly (Mated, 1951), exponentially (Eley and Rideal, 0 1981 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 3, 1981 571
1941; Herington and Rideal, 1945), hyperbolically (Pozzi and Rase, 1958; Maat and MOSCOU, 19651, potentially (Voorhies, 1945; Blanding, 1953; Prater and Lago, 1956) or according to the Elovich equation (Parravano, 1953). But none of those equations gives information about the mechanism of the deactivation or on the influence of the operating conditions: temperature, concentration of reactants and products, catalyst conditions, etc. Sz6pe and Levenspiel (1971) propose the use of two kinetic equations to describe the reaction system. In the case of deactivation in parallel -FA = (-rA)o*a (1) -da/dt = kdpAnad (2) Levenspiel (1972) proposes a method to determine kd and d. Chu (1968) developed a theoretical model for the study of the series deactivation of the catalyst for a reaction A e R, establishing
0.8r
Figure 1. Conversion at time zero against space time. Table I. Values of the Kinetic Constants at the Studied Temperatures
T,"C
For the same reaction and parallel deactivation Froment (1976) establishes
The work of Jodra et al. (1976) to determine the kinetic equation at zero time of the Yang-Hougen type and parallel deactivation, has been expanded by Romero et d. (1979) and Corella et al. (1980), extending the method of data analysis to integral reactors. Two different procedures of data analysis are shown and applied here with experimental data to determine the kinetic equation of the deactivation of a Cu supported on SiOz catalyst for the dehydrogenation of benzyl alcohol to benzaldehyde. Experimental Equipment and Catalyst Employed The experimental equipment employed to carry out the kinetic experiments has been described in detail in a previous work (Romero et al., 1979). The reactor was of the fixed bed, isothermal and plug flow type, 13 mm inside diameter. The conversion of benzyl alcohol to benzaldehyde was determined continuously by measuring the hydrogen given off from the reaction and at regular intervals measuring the concentration of aldehyde in the liquid product by means of gas chromatography (column: 2.5% SE 30 over Chromosorb GAW-DMCS; injector temperature, 250 "C; column temperature, 180 OC; detector temperature, 250 "C; flow of gas carrier, 30 cm3/min). The catalyst employed, 20% Cu on SO2,was prepared by impregnating, a t reduced pressure, silica gel with an aqueous solution of C U ( N O ~ ) ~ - ~ H The ~ Osilica . gel was prepared by the precipitation of NazSi03in an aqueous solution with 3 N HzS04. The precipitate was extruded to homogenize its structure and give it mechanical strength. Details of the method of preparation were given in a previous work (Gonzdez-Velasco, 1979). These are some of the physical properties of the catalyst: particle density, 1.03 g/cm3; chemical density, 2.03 g/cm3; particle porosity, 0.49; specific surface; 180 m2/g; prevalent form of pore, "ink bottle". Kinetic Equation at Operation Time Zero The kinetic experiments lasted 7 h and were carried out in an integral reactor for different values of contact time and with the following operating conditions: percentage
240 270 290 310 330
k 0.92 1.45 1.90 2.45 3.06
KA
KB
3.12 2.39 1.92 1.33 1.42
14.36 5.16 2.29 1.09 0.54
of alcohol in the feed, 100%; temperature range, 240-330 "C; granulometry of catalyst, -2 +1.19 mm; linear velocity of gases, 6 cm/s. Figure 1shows the conversion data at time zero against space time, for all the temperatures under consideration. The values of rate of reaction of time zero, (-rJ0, obtained by the graphic derivation of the curves in Figure 1,conform to the kinetic equation
k@A - PR2/K) (5) 1 + KAPA+ KRPR The values of the kinetic constants k , KA, and KR are shown in Table I. The following relation between the kinetic constant and the temperature has been determined k = 2960 exp(-4140.59/T) (6) (-rA)D =
KA = 8.3 X exp(3048.4/T) (7) KR = 2.88 X exp(ll506.6/T) (8) Thus, the kinetic equation for the dehydrogenation a t time zero (eq 5) will be (-rA)O [2960@~- p R 2 / K ) exp(-4140.59/T)]/[l + 8.3 X 10-3pAexp(3048.4/T) + 2.88 X p~ exp(ll506.6/T)] (9) Kinetic Equation of the Deactivation Reaction Romero et al. (1980) studied the effect of the time, partial pressure of the reactant, space time, and temperature on the catalyst deactivation. They determined that the origin of deactivation is the alcohol benzyl polymerization; its product, polybenzyl (Jodra et al., 1974), is degraded into a carbonaceous matter, coke, deactivating progressively the catalyst. In simple form, this parallel deactivation is represented by A*R+S +mA
A-Pi (10) Procedure A. The validity of this procedure, when deactivation takes place in parallel with the main reaction,
572
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 3, 1981 0.81
Table 11. Values of -rA (mol/(g of cat. h)) for Different Reaction Times
1
XAS
T = 240°C XA 0.61 0.5
c
0.10
0.15
0.20
0.25
t, h
0.818
0.739
0.667
0.600
0 0.5 1 2 4 7
0.147 0.143 0.141 0.138 0.129 0.119
0.117 0.116 0.113 0.111 0.104 0.095
0.083 0.082 0.081 0.081 0.076 0.070
0.061 0.060 0.059 0.058 0.056 0.051
PA, atm
o,41 0.3
I
t ime
o.l r r 0
0.5
0
I
I
1.0
1.5
+
0.5
0
1
0
4
x
7
T = 270°C XA
Figure 2. Conversion against space time for different times of operation at 270 "C.
a
Pressure @ ,
330'C
082 at 067
+ 0
x 0
0.10
0.15
0.20
0.25
0.30
t, h
0.818
0.739
0.667
0.600
0.538
0 0.5 1 2 4 7
0.343 0.329 0.324 0.309 0.285 0.243
0.293 0.284 0.278 0.267 0.243 0.211
0.246 0.239 0.236 0.225 0.207 0.180
0.206 0.202 0.198 0.189 0.174 0.150
0.164 0.261 0.157 0.150 0.139 0.121
2.5
2.0
0 54 043 0 33
T = 290°C XA 0.10
0.20
t, h
0.818
0.667
0.538
0.429
0 0.5
0.559 0.537 0.523 0.492 0.430 0.361
0.444 0.428 0.417 0.392 0.346 0.291
0.338 0.328 0.319 0.301 0.270 0.228
0.230 0.225 0.219 0.207 0.186 0.159
0.7
0.30
PA, 06
'+. I
t 0.5 0
1 2 4 7
\
I
4
I
I
I
I
I
1
2
3
4
5
6
7
t (hi
Figure 3. Activity against time of operation for different values of the partial pressure of reactant at 270 "C.
has been shown in previous works (Jodra et al., 1976; Corella et al., 1980). The necessary deactivation data to apply this procedure are plotted in Figure 2. The deactivation data from experiments carried out in an integral reactor are shown as conversion against space time, for different catalyst utilization times and at one of the temperatures under considerations, 330 "C. By graphic derivation of the curves in Figure 2 and the homonym for other working temperatures the values of the rate of reaction (+A) for different times have been obtained and are shown in Table 11together with the rate of reaction a t time zero. With these values for (-rA) and (-?-do the corresponding activity values have been calculated for each value of the partial pressure of the reactant, conforming to a=-
+A
(-rA)O
(11)
values which have been plotted in Figure 3 against time. The fact that the graphs of the data for all the temperatures under consideration are linear shows that the activity follows with time the equation a =
exp
S, - 1 + KAPA+ KA*PA+ KRPRdt (12) t
k&A*PAm+l
general expression already deduced and applied by Chu (1968) and Froment (1976) when the deactivation takes
0.40
atm
T = 310°C XA 0.10
0.20
t, h
0.818
0.667
0 0.5 1 2 4 7
0.890 0.874 0.846 0.782 0.662 0.515
0.716 0.687 0.666 0.616 0.523 0.422
0.30
0.40
0.50
0.538
0.429
0.333
0.581 0.561 0.546 0.505 0.436 0.349
0.433 0.420 0.409 0.381 0.329 0.264
0.280 0.274 0.269 0.249 0.217 0.182
0.40
0.50
PA,
atm
T = 330°C
XA 0.10
0.20
0.30
t, h
0.818
0.667
0.538
0.429
0.333
0
1.008 0.947 0.917 0.842 0.706 0.549
0.924 0.878 0.850 0.785 0.661 0.508
0.760 0.726 0.707 0.654 0.562 0.445
0.544 0.522 0.511 0.473 0.411 0.332
0.416 0.403 0.395 0.366 0.318 0.258
PA, atm
0.5 1 2 4 7
place in parallel with the main reaction, see reaction 10. Equation 12 can be written
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 3, 1981 573
Table 111. $ (T,p*) Experimental Values X A p ~ , a t m~ O ° C p 2 7 0 0 C 290°C 0.10 0.818 0.520 0.788 1.050 0.15 0.739 0.517 0.758 0.20 0.667 0.483 0.728 1.041 0.25 0.600 0.472 0.714 0.30 0.538 0.694 0.897 0.40 0.429 - 0.884 0.50 0.333 -
310°C 330°C 1.402 1.487 1.223
1.426
1.210 1.197 0.985
1.280 1.194 1.121
Table IV. Values of the Kinetic Constants of the Deactivation Reaction T , "C 310 330 290 240 270 hd X KA*
lo3
0.64 26.92
pn
1.05 12.11
1.60 7.00
2.10 5.30
where deactivation depends on the partial pressure of reactant. It is particularly interesting to determine a deactivation equation which can be easily handled to calculate the temperaturetime sequences in order to keep the conversion at reactor outlet constant -da '/dt = kdpAna
The dependence of the rate constants of the main and the deactivation reactions on the temperature is given by k = A. exp(-E/RT) (19) kd
2.70 3.38
Temperature x 2CO'C 0 270
($-i)])
(1-exp[
The slope of the linear graphs obtained when plotting
In a against time (Figure 3) is the function of deactivation, $(T,PA), which values are shown in Table 111. Rearranging eq 13, where pR= (IIwe deduce p ~ -~1 + +K ~ ~n / 2+ KA + KA* - K R / ~ -PA (14) #(T,PA) kdKA* kdKA* On the graph of this equation when m = 0, we obtain good accuracy (Figure 4). With the values of the ordinate in the origin and the slope in Figure 4, and the homonym for other temperatures and with the kinetic constants KA and KR (Table I), we have obtained the values of the kinetic constants of deactivation kd and KA* shown in Table IV. The relation between the constants of the deactivation equation and the temperature is given by the equations k d = 11.87 eXp(-5044.33/T) (15) exp(7063.2/T)
(20)
Isolating a'in eq 22 and taking it to eq 23 we arrive a t the equation for the temperature-time sequence exp ( E d /R To) X t= AdPAn((Ed/E) - d + 1)
Figure 4. Plots of PA/J.(T,pA)vs. P A .
X
= Ad exp(-Ed/Rr)
In order to keep the conversion constant in a fixed bed reactor subjected to the deactivation of the catalyst we must follow a sequence of increasing temperature, so that the effective rate constant given by alz(T) is kept constant aWT) = MTo) (21) The relation between the activity and the temperature is obtained from eq 19 and 21 -1= - lRn a f + - 1 T E TO Substituting eq 20 and 22 in eq 18 and integrating, for each value of the conversion (when t = 0, a' = 1)we arrive at
p,latl
KA* = 2.73
(18)
(16)
The deactivation equation will be -da/dt = [11.87 exp(-5044.33/T) X 2.73 X lo-' eXp(7063.2/T)p~]/[l+ [8.3 x lo5 exp(3048.4/T) + 2.73 X 10" eXp(7063.2/T)]p~ 2.88 X lo-' exp(ll506.6/T)((II - PA)/^)] (17) The kinetics of the dehydrogenation equation for any time of operation will be described by the eq 5, 11, and 17. Procedure B. This procedure is based on a mathematical model proposed by Krishnaswamy and Kittrell (1979) which has been extended to the more complex case
(24)
The kinetic parameters of the deactivation, E d , Ad, n, and d have been calculated by making the temperature-time sequences, which experimentally keep constant different conversion values, satisfy eq 24. In Figure 5, a, b, c, and d show the temperature-time sequences experimentally followed with the conversion values obtained. Each figure is for a conversion value. The data of these sequences have been adjusted to satisfy eq 24, which written in a simpler form is t = M ( 1 - eNY)
(25)
where
N =
Dd-dE+E R
To calculate the M and N parameters we can use besides the nonlinear regression, a method of approximate calculation of great simplicity (Krishnaswamy and Kittrell, 1979). If t vs. 1/T is plotted and the reciprocal temperature axis is subdivided into four equal segments, namely (l/Tn, l/Tn+Jwith n = 0, 1,2, and 3, it can be shown that
M =
tlt4
- t2t3
(tl + t4) - (tz + t3)
574
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 3, 1981 0.3 0 XA
XA
0.30 0.2 0 0.2 0
oj0 0.1 0 .A.‘ ‘3 A O
Temperature C onv e r s ion
0
a
0
16
8
24
32
40
Temperature
.A*
P.oAo Conversion
0
48
24
16
32
40
t (h)
t (h)
T (OC
T (OC
0
c
48
0
10
20
30
Conversion
P U A O
Conversion
260
d
o
I
I
10
20
I 30 t!h)
t (h)
0
Figure 5. Temperature-time sequences and conversions obtained with different values of space time: a, X A = 0.23; b, X A = 0.30; c, X A = 0.37; d, X A = 0.42. Table V. Values of l / { A d q [~( E~d / E )- d + 11 } at Different Values of the Partial Pressure of Reactant
0.63 0.54 0.46 0.41
2.35 2.62 2.94 3.27
where t, are the times corresponding to the reciprocal temperatures l/T,. Once an estimate of the constant M has been obtained, the values of In M are plotted against l/To for the four values of the conversion in Figure 6. From the fact that the corresponding data for the four conversion values are on the linear graphs we infer that eq 26 is valid for all cases. From their slopes (approximately equal for the four conversion) we deduce an approximate value Ed = 10290 Cal/mOl (29) The values of the ordinates in the origin of the different graphs are shown in Table V. On the other hand, eq 25 can be written In (1 - t / M ) = NY (30) The experimental values of In (1 - t / M )against the values of Y for four conversion values are shown in Figure 7. The slope N of the graphs for the different conversion values has the same value. E,j-dE+E = -5170.85 (31) R
‘01
a //’
x
0 37 0 42
i /
1 ‘ 1
8
1 7
I
18
,
1
,
‘9
1103 P K - ~I TO
Figure 6. Plots of In M vs. l/To for different conversion values.
Hence’d E 1. Once we know E , Ed, and d, the values of A@A” are calculated with the values on Table I. Figure 8 shows these values against P A . The slope of that graph is n = 0.79 and the ordinate in the o r e , Ad = 503. Thus,the deactivation equation is -da ’ / d t = 503 exp(-5178.66/ T)pAO”IQa ’ (32)
which together with eq 5 and 21 describe the kinetics of the system for any time of operation.
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 3, 1981 575
The expression for the rate of deactivation is similar in both cases
523
02
o
A
553
x
5L3
8
L
12
16
20
ze
ZL
i ;-f11o5
iw'i
Figure 7. Plots of In (1- t / M ) w. Y for different conversion values.
1
J
I
1 /" 03
04
05
06
07
0 8 09
Also, the values of the deactivation energy are very near each other: procedure A, E d = 10023 cal/mol; procedure B, Ed = 10 290 cal/mol. Nomenclature A, R, S = benzyl alcohol, benzaldehyde, and hydrogen, respectively Ad = preexponential factor of the Arrhenius equation for the deactivation reaction (h-l atm-") A. = as above, for the dehydrogenation reaction, mol/(g of cat. h atm) a, a' = catalyst activity, defined in eq 11 d, n = deactivation factors, defined in eq 18 E = energy of activation for the dehydrogenation reaction, cal/mol E d = energy of activation for the deactivationreaction, cal/mol FA^ = molar flow of feed, mol/h K = equilibrium constant of the main reaction, atm-' KA,KR = equilibrium adsorption constants of A and R, atm-' KA*= equilibrium adsorption constant of A to give coke, atm-' k = rate constant of the main reaction, mol/(g of cat. h atm) kd = rate constant of the deactivation reaction, h-' atm-" M = parameter defined in eq 26 N = parameter defined in eq 27 PA,PR = partial preasurea of reactant and product respectively, atm (-rA) = rate of reaction referred to benzyl alcohol, mol/(g of cat. h) (-rJo = rate of reaction referred to benzyl alcohol at time zero of operation, mol/(g of cat. h) T = temperature, K To= initial temperature for each temperaturetime sequence, K t = time, h W = weight of catalyst, g X A = conversion referred to benzyl alcohol Y = parameter defined in eq 28
P,(ati
Figure 8. Plots of log Ad PAnvs. log p k
Discussion of Results Both procedures used practically require the same number of kinetic experiments. We can apply procedure A to obtain an empirical kinetic equation with separable variables and/or a mechanistical equation, both with the same difficulty. In this work we have obtained by procedure A a mechanistic rate equation. The application of procedure B to obtain mechanistic equations should be very complex, however, due to the difficulty in integrating eq 17. Thus, an empirical rate equation has been obtained by procedure B. Now, for reactions subjected to catalyst deactivation to be continuous, it is convenient to keep conversion at the reactor outlet constant, although we can act on any of the variables which influence the rate of the main and the deactivation reactions (temperature, space time, partial pressure of the reactants, etc...). In industry the conversion reactor outlet is kept constant generally by programming increasing sequences of temperature-time. Procedure B is more practical to calculate these sequences because its deactivation equation fits this objective better.
Greek Letters
+(T,pA)= function of deactivation, defined in eq 13 ll = total pressure, atm Literature Cited Blanding, F. H. I d . Eng. Chem. 1953, 45, 1186. Chu, Ch. Ind. Eng. Chem. Fundam. 1988, 7 , 509. Corella, J.; Bilbao, J.; Asua, J. M. Chem. Eng. Scl. 1980, 35, 1447. Eley, D. D.; R i l , E. K. Roc. R . SOC. London, Ser. A 1941, 178, 429. Froment, G. F. Roc. Int. Congr. Catal. 6th. 1976, 10. Gonzilez-Velasco, J. R. Ph.D. Thesis, Bllbao University, 1979. Herington, E. F. K.; RMeal, E. J. Roc. R . SOC.London, Ser. A. 1945, 184, 434. Jodra, L. G.; Corella, J.: Romero, A. An. Qulm. 1974, 9 , 10. Jodra, L. G.; Romero, A.; Corella, J. An. Qulm. 1976. 72, 823. Krishnaswamy, S.; Klttrell, J. R. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 399. Levenspiel, 0. J . Catal. 1972, 25, 265. Maat, H. J.; Moscou. L. Roc. Int. Cong. Catal. 3rd 1965, 1277. Maxted, E. B. Adv. Catal..l951, 3, 129. Parravano, 0. J. Am. Chem. SOC.1953, 75, 1448. Pozzl, A. L.; Rase. H. I. Ind. Eng. Chem. 1958, 50, 1075. Prater, C. D.; Lago, R. M. Adv. Catal. 1958, 8 , 293. Romero. A,; Bilbao, J.; Gonzilez-Velasco, J. R. Aflnldad 1979, 384, 472. Romero, A.; Bilbao, J.; Gondlez-Velasco, J. R. Afhldad 1980, 365. 21. SzBpe, S.; Levenspiel, 0. "Proceedings, 4th European Symposium on Chem lcal Reaction Engineering"; Pergamon: London, 1971;, p 265. Voorhies, A. rnd. Eng. hem. 1945, 37, 318.
Received for reuiew June 16, 1980 Accepted March 31,1981
