T h e several isothermal examples treated in this paper should be sufficient illustration of both the power and relative simplicity of the recycle model as a device whereby complex, yield-sensitive, reaction networks may be profitably analyzed as regards the influence of backmixing upon yield. Other systems of interest-e.g., equilibrium reactions, LangmuirHinshelwood, Hougen-Watson rate equations-may also be treated in the fashion outlined here. For the adiabatic reactor, the recycle concept extends the Douglas-Eagleton adiabatic P F R analytical solution to a domain free of the plugflow restriction. Backmixing is not, per se, always deleterious to yield ( 7 7 ) ) nor does conversion necessarily suffer under its influence, as the adiabatic reactor analyses presented here demonstrate. T h e recycle model does reduce to the nonsegregated, micromixedness condition for nonlinear reaction kinetics, as R is increased to values above 20. As Eagleton notes, since the PFR ( R = 0) is totally segregated, it is likely that intermediate values of R physically describe a partially segregated system. For linear kinetics, this is of no consequence, while in cases involving nonlinearity the distinction is of import. Thus the results set forth here are qualitatively sound for nonlinear kinetics and quantitatively sound for linear systems. Application of the model is now being extended to adiabatic yield sensitive schemes as well as to emulsion phase mixing in fluidized bed reactors in which the pumping action of the bubble phase might be a suspected agent in promoting actual emulsion phase recycle. Acknowledgment
We are indebted to L. C. Eagleton for his invaluable review of the manuscript and, particularly, for bringing the work of G. R. Worrell to our a?te:ntion. Nomenclature
A , B, C,
c,
D
= molecular species, or concentration
= heat capacity
D,
= axial mixing coefficient = activation energy
rexp F
= exponential
E
g -AH K
k L
= reduced concentration, A / A , = total flow rate to PFR = Q = functiona1,ity
+q
= reaction enthalpy change = rate constant ratio = rate constant = reactor length
n
P
Q
q
= = = =
R
=
RT.
= = = = = = = = = = = =
U
V x
X,Y , Z C R
a Po
e
Y 7
P
x
number of CSTR’s functionality volumetric flow rate to recycle system recycle flow rate recycle ratio, q / Q gas constant temperature velocity in reactor reactor volume distance along reactor defined by Equation 26 rate of reaction
4-K
defined by Equation 24 holding time, V / Q defined by Equation 26 holding time, V / Q q = density = axial thermal conductivity
+
SUBSCRIPTS initial or system feed condition
0
=
1
= feed condition to P F R
literature Cited
(1) Almasy, G., Acta Chim. Acad. Sci. Hung. 24, 197 (1960). ( 2 ) Zbid., 25, 243 (1960). (3) Benson, Sidney, “Foundations of Chemical Kinetics,” p. 43,
McGraw-Hill, New York. 1960. (4) Carberry, J.’J., A . Z. Ch: E . J . 4, 13 M (1958). (5) Carberry, J. J., Can. J . Chem. Eng. 36,207 (1958). (6) Carberry, J. J., Wendel, M. M., A . Z. Ch. E. J . 9, 129 (1963). (7) Cholette, A., Can. J . Chem. Eng. 39, 192 (1961). (8) Coste, J., Amundson, N. R., Rudd, D., Zbid., 39, 149 (1961). (9) de Maria, F., Longfield, J. E., Butler, G., Znd. Eng. Chem. 53, 259 (1961). (10) Douglas, J. M., Eagleton, L. C., IND.ENG.CHEM.FUNDAMENTALS 1, 116 (1962). (11) Gillespie, B. M., Carberry, J. J., Chem. Eng. Sci., 21, No. 5, (May 1966). (12) Kramers, H., Westerterp, K. R., “Chemical Reactor Design and Operation,” Academic Press, New York, 1963. (13) Levenspiel, O., “Chemical Reactor Engineering,” Wiley, New York, 1964. (14) Parts, A. G., Australian J . Chem. 11, 251 (1958). (15) Smith, J. M., “Chemical Engineering Kinetics,” p. 128, McGraw-Hill, New York, 1956. (16) Wehner, J. F., Wilhelm, R. H., Chem. Eng. Sci. 6,89 (1956). (17) Worrell, G. R., Ph.D. thesis, University of Pennsylvania, 1963. (18) Worrell, G. R., Eagleton, L. C., Can. J . Chem. Eng. 42, 254 (1964). (19) Zwietering, T. N., Chem. Eng. Sci. 11, l(1959). RECEIVED for review July 6, 1965 ACCEPTED February 3, 1966 Work supported in part by a grant from the National Science Foundation.
HETEROGENEOUS CATALYSIS IN A CONTINUOUS STIRRED TANK REACTOR D. G. T A J B L , ’ J .
B. SIMONS, A N D JAMES J. CARBERRY
Department of Chemical Engineering, University of Notre Dame, Notre Dame, Znd.
THE procurement of precise kinetic data for solid-catalyzed gaseous reactions poses a number of problems in that transport phenomena (interparticle and inter-intraphase) often intrude upon the surface reaction, tending to falsify the data and thus frustrate both the physical chemist seeking surface 1
Present address, Institute of Gas Technology, Chicago, 111.
rate laws and the chemical engineer who seeks surface rate models which become bases for reactor scale-up. T h e often employed integral catalytic reactor can rarely be operated isothermally and differentiation of integral reactor data further complicates analysis. T h e differential reactor, operating a t extremely small conversion levels, does provide point rate data : However, extremely precise analytical VOL. 5
NO. 2
MAY 1966
171
A continuous stirred tank catalytic reactor has been designed, evaluated as a perfect mixer, and employed to determine the kinetics of CO oxidation with oxygen as catalyzed by 0.5 weight % Pd on a-alumina pellets. The rate is found to be proportional to the Oz/CO ratio and the apparent activation energy is 28.5 kcal. per mole in the temperature range of 205” to 234” C. at a total pressure of 1 atm.
methods are then required if precise rate laws or models are to be derived from the raw data. Clearly, the ideal laboratory catalytic reactor is one which operates isothermally (negligible interparticle, interphase, and intraparticle gradients of heat and mass) while delivering integral reactor conversions. T h e continuous recycle reactor (8) and its equivalent, the continuous stirred tank catalytic reactor (CSTCR) provide, in principle, the transport-gradient-free character of the differential reactor and, a t the same time, permit operation a t finite (integral reactor) conversion levels ( 3 ) . Trotter and Wilhelm (72) employed a reactor capable of utilizing fluidizable catalysts, while Ford and Perlmutter (6) designed one in which the reactor wall itself served as the catalytic surface. O u r concern is directed toward a reactor which will accommodate commercial size pellets and extruded catalysts ( 3 ) . The design, construction, and operation of such a catalytic C S T R are described in this paper. The region of operation (r.p.m. and flow rate) in which “perfect mixing” prevails was specified by pulse testing and kinetics of palladium-catalyzed oxidation of CO with 0 2 determined over a temperature range of from 200” to 234’ C. Catalysis by other transition metals was also studied and will be reported later (77).
Figure 4. The cross-hatched zone designates the apparant transition boundary between the perfectly mixed regime of operation (above the boundary) and that region (below the boundary) wherein the pulse response data deviated from the theoretical prediction. Based upon this information, the CSTCR is always operated a t an agitator speed above 1600 r.p.m., thus permitting the maximum variation in flow rate (contact time). Kinetic Study
To demonstrate the operability of the CSTCR, the palladium-catalyzed oxidation of C O with 0 2 was selected as a worthy test system because the reaction is highly exothermic, the system is of interest per se, and C O oxidation merits attention in view of apprehensions regarding smog and its abatement by oxidation of automotive exhaust fumes. The fact that product analysis poses no major difficulties also inspired selection of this oxidation. Prior Work
Surprisingly little systematic research has been focused upon
CO oxidation as catalyzed by palladium. A recent review ( 4 ) Details of Reactor
The continuous stirred tank catalytic reactor, constructed of stainless steel, is a cylindrical vessel, 3 inches in i.d. and 3 inches high, provided with inlet and effluent ports and a cooled agitator shaft and seal as detailed in Figure 1. Four vertical baffles are placed 90” apart on the inner wall. The catalyst pellets are contained in a single layer, in four thin baskets constructed of low mesh stainless steel screen, as shown in Figure 2. The four-basket unit (each basket set a t a right angle to the other) is affixed to the agitator shaft. Two single propellers, one above and the other below the catalyst basket unit, are also secured to the shaft. In operation, the feed gas enters beneath the rotating shaft and leaves, above the swirling catalyst, a t the top of the reactor just off-center from the shaft seal. A thermocouple well is situated within the reactor. In operation, the catalyst pellets are swept through the continuously fed reacting gas stream.
,&&E--
Pul l e y S h e a v e
Glycerol
Sea -Bearing
Coolant
Teflon Bearing ,Product
Mixing Characteristics of Reactor
T o exploit the lumped parameter advantage of the CSTCR, it must be demonstrated that the reactor behaves as a perfect mixer. T h e mixing characteristics of the reactor described above were determined by measuring the response of the nonreacting system to a pulse input of helium injected into a steadily flowing air stream a t various volumetric flow rates and agitation speeds. O u r interest was confined to a determination of the operating region (agitator speed, r.p.m., and feed rate) in which apparent perfect mixing prevailed as judged by obedience of the effluent pulse concentration to the theoretical response predictable for a single CSTR. In Figure 3 are shown sample data points secured in the pulse testing study. The solid line is the theoretical response for perfect mixing. The term “perfect mixing” is used here in the phenomenological sense, as no attempt was made to investigate the micro scale character of mixing within the reactor. T h e results of the mixing study for a wide range of agitation and feed rates are presented in a n operating diagram for our particular reactor in 172
I&EC FUNDAMENTALS
Prope I I o r
I Figure 1 .
- 1
Continuous stirred tank catalytic reactor
Agitator Shaft
A%
Figure 2. basket unit
Detail of
catalyst
gas
cites the work of Schwab ( 9 ) in which kinetics were formulated for CO oxidized by 0 2 over a palladium wire. Schwab found
which model might suggest that the rate-controlling step is oxygen chemisorption. More formally
- dCO __ ,it
kOz
(1
+ kCO)
(2)
which, for high adsorption of CO, reduces to Equation 1. Schwab‘s observed rate law may also suggest surface reaction between oxygen and CO as rate-controlling. For if CO is far more strongly absorbed than 0 2 , then
- dCO
kOz.CO - __ (1
c’t
+K C 0 7
(3)
which obviously reduces to Equation 1 a t high values of KCO (KCO>>l). I n another study, Modell (7) measured the oxidation kinetics over Pd and found a rate law similar to Schwab’s. I n conflict with Schwab’s results, Eley and Daglish ( 5 )found, for the reaction catalyzed by pure Pd (lOOyo), the rate equation
dCO - k dt
0 2
p
(4)
which might suggest the dissociative chemisorption of 0 2 as rate controlling. Pertinent to these kinetic studies is the recent work of Stephens (70), who studied the CO-Oesystem in the presence of Pd metal film. T h e very high absorptivity of CO on Pd was established in this work, in conformity with the general implications of Equations 1, 2, 3, and 4. Chemisorption rates of 0 2 on Pd in the presence of CO are not to be found, as reaction is then inevitable, thus frustrating measurements of adsorption per se. O n the other hand, 0 2 adsorption rates in the absence of C O would be of questionable value, as the Pd surface is clearly affected, with respect to its adsorptive characteristics, by the presence or absence of adsorbed C O . Thus while prior studies shed light upon C O oxidation kinetics on wires and films, no data exist on Pd deposited upon a commercial support. Aside from the practical interest associated with supported catalysts, a reasoned interest exists among catalytic chemists in the relation, if any, which may exist in the catalytic activity (kinetics) of a given metal as used in diverse forms, such as a film, wire, and a deposited entity. Description of Catalyst
In this particular phase of the work we employed 0.5 weight 70 of Pd deposited upon 0-alumina in the form of 3/16-inch cylinders, as freely supplied by M. Arnold, The Girdler Catalyst Corp. The method of Pd deposition \\as such that the Pd is superficially deposited upon the shell of the 3j16-inch alumina pellet. The actual depth of Pd penetration into the cylinder is less than 1 mm. The reported BET surface area of the catalyst pellet here employed is 7 to 10 sq. meters per gram and the pore volume is 0.04 cc. per gram. Preparations and Procedure
l
I
R l
!
Figure 3. T3ypical pulse-testing data in mixing study l2
w
I
I
I
I
1
I
Perfect Mixing
\
/
”\
Reactants C O and 0 2 are each metered individually using soap-bubble meters and then mixed, dried, and passed into the CSTCR. An effluent bypass permits sampling of the stream for analysis in a Fisher partitioner (Model 25V). The partitioner resolves 0 2 , N2, CO, and CO?. The reactor (Figure 1) is heated by electrical heating tape, temperature control being maintained within 1’ C . by a Thermolyne stepless input control. Flowmeters were calibrated on a frequent basis, as was the partitioner, using known mixtures. A run was initiated by simply admitting the reactant mixture to the CSTCR, allowing time for both flow and catalyst equilibration, and then sampling the effluent for CO? determination. Temperature, a function of extent of reaction and feed and effluent heat capacities as well as heater input, was adjusted to a constant and knonn value prior to sampling for rate determination. For the CSTCR the rate is simply equal to the difference between input and exit mole quantities (of COz) divided by holding time determined by total flow rate and reactor volume. For a solid-catalyzed reaction, rates are more appropriately expressed in terms of moles per time, grams of catalyst, and are so reported here. Analysis of Data
For the reaction
0
400
12oo
800
1600
A g i t a t o r S p e e d , RPM.
Figure 4. Operating diagram for continuous stirred tank catalytic reactor Regime in which perfect mixing occurs
CIS
the rate of COZformation in a well stirred, continuously fed reactor is
inferred from mixing srwdier
VOL. 5
NO. 2 M A Y 1 9 6 6
173
for no C O Zin the feed, where Q is the effluent flow rate, Vis the free reactor volume, (CO,) is concentration, and p is grams of catalyst per unit volume of reactor. Q is clearly a simple function of reactor temperature, pressure, and extent of conversion. Analysis of partitioner samples provided C O Z concentration (found to be linear in peak height) which, since C O and 0 2 analyses were also provided, agreed with reactant consumption data within i l % . For a given temperature, r, the rate as determined by Equation 6 was measured as a function of effluent and, therefore, reactor concentrations of C O , 0 2 , and CO,; these species variations were realized by contact time and/or feed composition variation for a given temperature. In this study conversion varied from 2 to 1570, in the temperature range 200' to 234OC. The amount of catalyst used was 10 grams (100 pellets). In a few runs agitation rate was purposely reduced to zero and the reaction rate was then observed to drop, suggesting reactant bypassing-Le., nonideal mixing.
I 3 / I
m
0 X
L
Results
As shown in Figure 5, a t several temperature levels of operation, the measured rate proved to be linear in the O2jCO ratio. This arithmetic plot represents rate of reaction as a function of 0 2 / C O ; thus the slopes provide the rate constant, k. In Figure 6, an Arrhenius plot of log k us. 1 / T is displayed, from which a n apparent activation energy of 28.5 kcal. per mole is derived. The results are compared with those of other investigations in Table I.
Figure
Table 1.
Results
T:mP., Investigator Catalyst C. E, Kcal. Schwab ( 9 ) Pd wire 250-320 22,2" Eley and Daglish ( 5 ) Pd wire 95-130 28.3b Model1 (7) Pd wire 140-150 28.7" This work Pd on a-alumina 200-234 28.5" zk 2 . 7 Based upon rate model, k.On/ a Based upon rate model, k.Oz/CO. (Coy.
l&EC FUNDAMENTALS
5.
Reaction rate as a function of
0 2 /
CO ratio at various temperature levels 0.
NC6
I t is impossible to suggest a n unambiguous surface rate model o n the basis of the kinetic equation found to fit C O oxidation by 0 , as catalyzed by supported Pd. Clearly the same kinetic form prevails for Pd fashioned as a wire filament and as a metal deposited (and dispersed) upon a support. Small differences in activation energy are apparent as a function of the form assumed by the catalyst. Diffusional influences were apparently absent from our study. Specifically, intraparticle mass and thermal diffusional gradients would be determined by a modified Thiele modulus in which the actual catalyst "thickness" is less than 1 mm., although the support is "16 inch in diameter (and length). Calculations demonstrate that the appropriate Thiele modulus for the highest rate encountered is less than unity, assuring an effectiveness of virtually unity a t the highest rate of reaction (2). Interphase gradients are subject to firmer assessment, for the CSTR operates a t a uniform flux of mass and heat. I n consequence, if interphase heat and mass transport coefficients can be calculated, interphase concentration and temperature differences may be directly calculated ( 7 ) . Values of h and k, can be estimated, since the position and agitator speed allow an estimate of particle velocity through the gas. Precise deter-
174
02/20
+
Discussion
I
0
Y
I
\
E=,
28.5 kcal.
3 1
0.0
0.001~
L 2.05
Figure 6. Specific rate constant, oxidation over Pd on a-alumina
k
2.1
2
15
vs. 1 / T o K., in CO
mination of this velocity is not possible, as the pellets are not swept through a "still" gas, but rather a gas environment in unknown motion. Nevertheless, a minimum interphase AT can be computed a firiori and, as shown in Figure 6 for two of the 234' C. runs, finite temperature differences were calculated to exist between particle surface and the gas, thus accounting for the nonlinearity of these higher rate data secured a t 234OC. Given the high activation energy of nearly 30 kcal., even small interphase A T ' S can significantly enhance the rate over the values anticipated on the basis of fluid phase temperature measurements. Conclusions
A continuous stirred tank catalytic reactor (CSTCR) has been designed, constructed, evaluated as a perfect mixer, and
demonstrated to be an effective device for the procurement of catalytic rate data. Specifically, the oxidation kinetics of CO as catalyzed by supported Pd in the presence of 0 2 has been studied and the rate equation and apparent activation energy have been determined. Because of the uniform flux resulting from the perfect mixing realized in thc CSTCR, interphase temperature and concentration gradients can tle readily estimated a priori for a given reaction rate, enthalpy change, and agitator-catalyst r.p.m. Nomenclature C = concentration h = interphase heat transfer coefficient = rate constant k K = adsorption coefficient = interphase mass transport coefficient k, Q = volumetric flow rate r.p.m. = agitator speed, revolutions per minute r = rate of reaction AT = interphase temperature difference V = reactor volume = grams of catalyst/volume of reactor P
literature Cited (1) Carberry, J. J., A . Z . Ch. E. J . 6,460(1960). (2) Ibid., 7 , 350 (1961). (3) Carberry, J. J., Znd. Eng. Chem. 56, No. 11, 39 (1964). ( 4 ) Dixon. J. K.. Longfield. J. E.. Catalysis 7 . 281 (1960). (5) Eley, ,D. D.,‘ Dadish, A. G.,‘ 2nd ‘Interkational Congress on Catalysis, Vol. 11, pp. 1615-24, 1961. (6) Ford, F. E., Perlmutter, D. D., Chem. Eng. Sci. 19, 371 (1964). (7) Modell, M., D. Sc. thesis, Massachusetts Institute of Technology, 1964. (8) Perkins, T. K., Rase, H. P., A . I. Ch. E. J . 4, 351 (1958). (9) . . Schwab, G. M., Gossner,. K.,. Z. Physik. Chem. Neue Folge - 16, . 39 (1958): (10) Stephens, S. J., J . Phys. Chem. 63, 188 (1959). (11) Tajbl, D. G., Ph.D. thesis, University of Notre Dame, 1966. (12) Trotter, Ide, Wilhelm, R. H., forthcoming publication.
RECEIVED for review July 16, 1965 ACCEPTED February 1, 1966 Work supported by a Grant from the Petroleum Research Fund of the American Chemical Society. Grateful acknowledgment is made to the donors of the fund. The kinetic studies are a part of the dissertation of D. G. Tajbl submitted to the Graduate School, University of Notre Dame, in partial fulfillment of the requirements for the degree of doctor of philosophy.
RATE AND MECHANISM OF GAS-PHASE
0x1DATION 0F
PARTSPER-M I LLlO N
CONCENTRATIONS OF NITRIC OXIDE M I L T O N E . MIORRISON,l R O B E R T G. R I N K E R , * A N D W I L L I A M
H . CORCORAN
California Institute of Technology, Pasadena, Calif. Rdtes of the air oxidation of parts-per-million concentrations of nitric oxide were studied homogeneously a t atmospheric pressure and ambient temperatures in a constant-volume batch reactor. The initial concentration of nitric oxide was varied from 2 to 75 p.p.m., while the oxygen concentration ranged from 3 to The initial order of the oxidation reaction in the absence of nitrogen dioxide was deter2 5 volume mined to b e ;!.OO =k 0.09 for nitric oxide and 0.97 f 0.1 1 for oxygen. From initial rate data a t 26.5” C., a third-order rate constant of (1.297 0.051) X 1 O4 (liter)2/(g. mole)2(sec.) was obtained. The addition of nitrogen dioxide increased the initial oxidation rate, and that compound showed an autocatalytic effect throughout the course of the reaction. A nonlinear least-squares analysis was used to develop a mechc nism involving six reactions, with NO$,Nz03, and NzOs as intermediates. Use of that mechanism gave a minimum standard deviation of 1.6 p.p.m. for the predicted concentrations of nitric oxide relative to the experimental data.
9;.
*
of the air in metropolitan areas is a n increasing problem. Nitric oxide and unburned hydrocarbons, formed by high-compre.ssion, internal-combustion engines and industrial plants, are of major concern in air pollution. Nitric oxide reacts in the atmosphere with molecular oxygen to form nitrogen dioxide, which oxidizes hydrocarbons photochemically to ketones, aldehydes, and alcohols. These compounds, nitrogen oxides and oxidized hydrocarbons, are the constituents of so-called “smog” and are detrimental to the health of both the human and plant population. T h e basic chemical reactions OLLUTION
Present address, E. I. du Pont de Nemours & Co., Inc., Chattanooga, Tenn. Present address, University of California, Santa Barbara, Calif.
which occur in these atmospheres, however, are not well understood. Because of the small amount of quantitative work which has been carried out on the air oxidation of nitric oxide in parts-per-million concentrations (p.p.m., defined as mole fraction X 106), rates of reaction of nitric oxide with oxygen were measured, and a mechanism is proposed. T h e mechanism of the oxidation of nitric oxide to nitrogen dioxide has been a subject of controversy ever since Raschig (20) found that the reaction was third order. He reported that the oxidation of nitric oxide was second order in nitric oxide and first order in oxygen. A number of other investigators (3-5, 76,24,28, 33) after Raschig also studied the system. Although they generally agreed that a t total pressures below 50 mm. of mercury the reaction was second order in nitric oxide VOL. 5
NO. 2
MAY 1966
175
