V
= volume, cc.
MATHEMATICAL SYMBOLS
X
= spatial coordinate, cm. = volume fraction of designated particles, dimension-
A
Y
less = volume fraction of designated fluid, dimensionless
x
GREEKSYMBOLS drag coefficient in Langevin Equation 1, dimensions depending on exponent n friction coefficient in particle stochastic Equation 16, set.? friction coefficient in fluid stochastic Equation 45, set.? friction coefficient for macroscopic disturbances of stochastic Equation 59, sec.-l void fraction, dimensionless viscosity, poises fixed time interval in Equation 7 , sec. intensity of macroscopic disturbances, sq. cm./ sec.2 particle energy, g. sq. cm./sec.2 X) (u?(a?). = parameter, dimensionless (1 q / p , kinematic viscosity, sq. cm./sec. variable of integration, sec. 3.1416 density, g./cc. interstitial fluid velocity, cm./sec. transition probability in configuration space, dimensionless coefficient of virtual mass, dimensionless transition probability in velocity space, dimensionless angular frequency of particle-fluid oscillations, rad./sec.
+
= = = = = = =
n
P 0
1 2, 3 m
2
fluidized bed point of incipient fluidization fluid or continuous phase running indices corresponding to coordinates 1, 2, 3 exponent in drag law of Equation 1 particle or discontinuous phase initial condition vertical coordinate horizontal coordinates single particle in a n infinite fluid total for all spatial directions
SUPERSCRIPT = marked particles or fluid
*
n
=
finite difference
= product or pi function = !sum
-
=
I
= prime or fluctuating quantity = ememble average
=
bar or time average defined by Equation 7 derivative, d/dt
Literature Cited
(1) Batchelor, G. K., “Homogeneous Turbulence,” Cambridge UniLrersity Press, Cambridge, 1953. (2) Chandrasekhar, S., Reu. .2lod. Phys. 15, 1 (1943). (3) Doob. J. L., Ann. .Math. 43, 351 (1942). (4) Doob, J. L., “Stochastic Processes,” Chapman and Hall, London. 1952. (5) Einstein, A , , Ann. Phvcnk. 1 7 . 549 (190$) (6) Eyring, H., J . Chr‘m. Phys. 4, 283 (1936). (7:I Furukawa. J., Ohmae, T., Ind Eng. Chem. 50, 821 (1958). (8) Hanratty, T. J., Latinen, G., LVilhelm. R. H., A . I . Ch. E . J . 2, 372 11956’). (9) .Hinze, J. 0.: “Turbulence,” McGraw-Hill, New York, 1959. (10) Houghton, G., J . Chem. Phys. 40, 1628 (1964). (11) Ibid., 41, 2208 (1964). (12) Houghton, G., Proc. Roy. Soc. A272, 33 (1963). (13) Houghton, G., unpublished. (14) Kirkwood, J. G., J . Chem. Phys. 14, 180 (1946). (15) Kramers, H., it’estermann, M. D., Groot, J. H., Dupont, F. A. A., Proceedings of Symposium on Interaction between Fluids and Particles (London), June 20-22, 1962, Third Congress of European Federation of Chemical Engineering. (16) Lapple, C. E.: Shepherd, C. B., Ind. Eng. Chem. 32, 605 (1940). (17) Levy, P., “Theorie de l’addition des variables aleatoires,” Gauthier-Villars, Paris, 1937. (18) Lewis, i V . K., Gilliland, E. R., Bauer, \V. C., 2nd. Eng. Chem. 41, 1104 (1949). (19) Longuet-Higgins, H. C., Pople, J. A., J . Chem. Phys. 25, 884 (1956). (20) Massimilla, L., Tt’estwater, J. T.V., A . I . Ch. E. J . 6 , 134 (1960). (21) Ottar, B., Acta Chem. Scand. 9, 344 (1935). (22) Pigford, R. L., Baron, T., IND.EXG. CHEM.FUNDAMENTALS 4, 81 (1965). (23) Poisson, S. D., M i m . Inst. (Paris) 11, 521, 566 (1832). (24) Ruckenstein, E., IND. END. CHEM.FUNDAMENTALS 3, 260 (1964). (25) Stokes, G. G., Proc. Cam6ridge Phil. Soc. 9,8 (1850). (26) Sutherland, K. S., Trans. Brit. Inst. Chem. Engrs. 39, 188 (1961). (27) Taylor, G. I., Proc. London Math. Soc. 20, 196 (1921). (28) Taylor, G. I., Proc. Roy. Sac. A219, 186 (1953). (29) Uhlenbeck, G. E., Ornstein, L. S., Phys. Reu. 36, 823 (1930). (30) Lt’ilhelm, R. H., Kwauk, M., Chem. Eng. Progr. 44,201 (1948). RECEIVED for review May 21, 1965 ACCEPTEDSeptember 20, 1965
INFLUENCE OF MIXING ON ISOTHERMAL REACTOR YIELD AND ADIABATIC REACTOR CONVERSION B E R N A R D G I L L E S P I E I A N D J A M E S J. C A R B E R R Y
Department of Chemical Engineering, University of Notre Dame, Notre Dame, Ind.
the fact that backmixing of reacting fluid elements and yield (selectivity) for all but simple isothermal reaction networks, a precise quantitative assessment of finite mixing effects is lacking. Effective comparison of conversion and/or yield is readily established for the plug flow reactor (PFR) and continuously fed stirred tank IVEN
G affects conversion
1 Present
164
address, Socony-Mobil Oil Co., Paulsboro, N. J
l&EC FUNDAMENTALS
reactor (CSTR) for given holding time or, as Levenspiel (73) demonstrates, the ratio of volume requirements for these isothermal limiting reactor types can be determined as a function of conversion. Rather complex systems involving nonlinear kinetics may be so analyzed with the understanding that either segregated (macromixed) or nonsegregated (micromixed) flow must be assumed in fashioning the CSTR model (79). Intermediate levels of mixing are more commonly encountered
For a number of linear and nonlinear yield sensitive isothermal reaction schemes, the influence upon selectivity of mixing levels intermediate between plug flow (PFR) and well stirred (CSTR) conditions i s evaluated in terms of CI plug flow reactor with effluent recycle. As the mixing parameter (recycle ratio) enters the problem as IY boundary condition, systems which heretofore escaped analysis can now be easily assessed. Yield-conversion results are presented for a variety of isothermal networks. Further, the Douglas-Eagleton adiabatic PFR analytical solution i s extended to include the effects of finite mixing upon adiabatic conversion, suggesting that optimal performance may be realized under conditions of finite mixing in a thermally sensitive adiabatic system.
than limiting levels associated with the PFR and CSTR. I n such cases a series of CSTR's or series combination of P F R and CSTR (7) or the plug flow-axial diffusion model (5, 6, 8, 9, 72, 73, 76) may be gainfully employed to establish the influence of mixing upon reactor performance. Linearity must exist to permit analytical solution of the axial diffusion model and though the series CSTR-PFR networks are not so limited, tedious computations and cumbersome expressions are often involved for even modestly complex kinetics. Of far greater importance than conversion is yield or selectivity and one is often called upon to predict yield trends for complex nonlinear reactions in real reactors which may display backmixing behavior intermediate between the ideal limits of the PFR and CSTR. Various models invoked to describe the finite mixing-conversion problem can, in some simple cases, be extended to treat the yield situation as illustrated by Kramers and Westerterp (72). Effective yet simple treatment of complex nonlinear reaction yield-backmixing behavior would seem to be desirable. Yield prediction under conditions of finite mixing would certainly be of value for a reaction network such as k4
kl
A-.B-.D
c a linear version of which has been analyzed by de Maria et al. (9) in terms of the plug flow-diffusion model. Other networks such as
Recycle Reactor Model
Consider the system in Figure 1, consisting of a PFR, some portion of the effluent of which is recycled and perfectly mixed with fresh feed a t the PFR inlet. Essential features of this model are illustrated with reference to a simple first-order reaction. Then dC - = -kC dr where
dr =
(5)
dV -
F
and Vis reactor volume and F = Q ance
FCi = QC,
+ q.
By a material bal-
+ qC
(6)
or
+ C, R+1
RC
c1 =
where R = q/Q. PFR inlet concentration, C1, thus depends upon recycle ratio, R, and conversion level. Equation 5 is integrated for the PFR between the limits C1 and C with the result
(7) where
ki
A
+
B
(2nd order)
f
\-4
k2
C
(1st order)
B
(1st order)
4 .
+ C -. D ki kt
+B4.C
-
0 ~
R + 1
and 0 = V/Q
(2nd order) or
A + A + B
B
Q + q
(3)
k2
B
c/c,; 7 = _V_
For large values of R, the argument of the logarithm approaches unity, so that upon expanding and retaining the first term of the expansion:
ki
A
=
(both 2nd order)
1
(4)
to cite some typical selectivity-sensitive systems, are not conveniently resolved to provide yield predictions as a function of degree of mixing, since nonlinearity precludes analytical solution of the axial diffusion model, while sheer complexity marks description of thrse systems in terms of CSTR-PFR series combinations. Useful yield-mixing relationships can be fashioned, however, by visualizing the backmixing process in terms of a PFR with partial effluent recycle, this concept being applicable to any reaction rate expression for which a simple PFR or batch reactor analytical solution exists.
= [l
+ (R +
1)7k]
-~ 1 - (1 k0)
+
7
Figure 1.
Recycle reactor model VOL. 5
NO. 2
MAY 1966
165
‘I
k2/k 1 =+ K=O. I
B/Ao
k8.0.
I and I
0 I Figure 2.
5
IO
15
20
25
0
n,number o f C S T K ’ s i n s e r i e s R-n-CSTR relation for first-order kinetics
0.4
0.2
0.6
0.8
0.6
U.8
I
Conversion.1-f
which is the single CSTR result. O n the other hand, as R approaches zero, PFR performance is manifested. In the case of second-order reaction, large values of R lead to the nonsegregated micromixed CSTR result, suggesting that the recycle reactor model reduces essentially to a micromixedness rather than segregated flow limit. Given that large and zero values of R yield the CSTR and PFR extremes, it follows that intermediate, finite values of R may well describe the intermediate backmixing-reaction circumstances and thus allow simple assessments of the influence of mixing upon yield for complex nonlinear reactions. As the recycle ratio, R, enters the problem as a boundary condition, any reaction system for which a simple PFR integrated expression exists can be expressed in terms of various levels of mixing by a simple substitution of a n integration limit.
0
k!
0.2
0.4
1
Conversion,I-f
Recycle Ratio-Series CSTR Relationship
Some concrete significance can be attached to the recycle ratio R, by a performance comparison with a series of n CSTR’s, each of equal volume. Thus, for first-order reactioni n n CSTR’s:
B/Ao
1 fm
=
0.05
(9)
(1n + ) :
0
where 0 is total holding time. Equating Equation 9 to that describing the recycle system of Figure 1 we have
+t)” 1
fm = -
(1
- fR =
exp (- kB/R
0
+ 1)
0.2
0.4
Conversion, Figure 3. kl
Yield vs. conversion, 1
0.6
0.8
I
I-f
-
f, for reaction
kl
A+B+C T h e resulting n-R relationship is shown in Figure 2 for a range of k0 values. Some sensitivity to k0 is evident. For any value of k0, a value of R greater than about 20 assures single CSTR behavior. Should analysis indicate that some finite recycle ratio is optimum [as shown for the Van de Vusse kinetic scheme (77)], it is clear that since only integer values of n have real meaning, the precise n-R relationship is not of great importance. An optimum R value of, say, 1.5 would mean that a series of two or three CSTR’s would provide the required mix166
I&EC FUNDAMENTALS
ing level (alternatively, a PFR could be used and operated a t the desired recycle ratio). Application of Recycle Model-Isothermal Reactors
While no particular advantage resides with the recycle model for simple first-order reaction, the merits of the recycle model become clear when a simple consecutive reaction is considered :
ki
IO
k2
A+B+C
8
I 6
-\\
4
B/C
CSTR
To simulate yield alteration due to mixing intermediate between that of the PFR and CSTR, one might express B / A , for a series of n-CSTR's or solve the appropriate second-order differential equations employing axial diffusion as a n index of mixing (72). I n either case, even for this elementary selectivity system cumbersome relations result. By contrast, in terms of recycle ratio, the yield of B is
2
0 0.4
0.6
0.8
I-f
I which expression is obtained by substituting into Equation 12 where f e f ' .
0.8 ,1\-u.
-
I
I
R=I .5-
0.6
now f = A / A o and
0.4
B/C 0.2
Results are displayed in Figure 3, where B / A o is plotted against conversion of A for a range of recycle ratios and K values.
K = k 2 / k I AO= I 0 0.2
0.4
0.6
I
0.8
I -f
Yield or Selectivity in Complex Systems
Consider the network (first order) kr
ki
A+B+D
0* I
( 1 5)
h . l k 3
C 0 08
where B might be considered a desired product. pressed in integrated form for the PFR is
0 .06
B/A, =
Kz
~
- Ki
1
B/C .
n~
Yield ex-
uKi- f l + A, BO fK'
which is, of course, simply Equation 12, in which the first term is multiplied by K Z
0 where
K = k g / k I A,=
Ki
I0
=
ka ki ~
+ kd and K 2 = kl + kz ki + ka ~
Rephrased in terms of the recycle system (Bo = 0)
0 0
0.2
0.6
0.4
0.8
I
1-f Figure 4. Yield of 6 relative to C vs. conversion of A for the reaction
B/Ao =
( 17)
ki
A+A-+B k 2 L
c
T h e single C S T R result is for Bo = 0: VOL. 5
N O , 2 M A Y 1 9 6 6 167
Equation 26 is plotted in Figure 5 for various values of K over a range of recycle ratios. In cases in which a reactant is common to each consecutive step of the same order, such as
Selectivity in Nonlinear Kinetic Systems
For the reaction scheme
A
+A
ki
(2nd order)
+B
k h
ki
(19)
C
A+B-.C
(lstorder)
ka
the ratio of product B to by-product C is for the PFR, where K = kz kiAo'
B+C-D it is clear that the intermediate yield CIA, relation is identical to that of the simple first-order system treated above (Equations 11 et seq.) Another consecutive case of interest is that involving firstand second-order steps-Le., ki
A+B Direct substitution in terms of the recycle parameters yields (Bo = 0):
(28)
ka
A+B+C For the PFR, a solution implicit in B/Ao results ( K = kl/k2Ao)
B/Ao T h e single CSTR expression for nonsegregated flow is (Bo = 0) :
f = -
B/C
(22)
K
---I
+ 2K In [KK -- Bo/Ao B/Ao
=
-Bo
A.
-
(1
-f
)
(29)
This result was obtained by Benson ( 3 ) , who presents a tabulation of numerical values of B as a function of A/Ao for various rate constant ratios. The single CSTR result is
For a range of K values, B/C is plotted against conversion (1 - f ) in Figure 4 for various degrees of mixing as characterized by the recycle ratio, R.
B/Ao =
Nonlinear Consecutive Reactions
while the yield of B for intermediate degrees of mixing is, in terms of recycle ratio (Bo = 0) :
For the system ki
A+A+B
-B/Ao
kn
B+B+C
+ 2(R + 1 ) K l n
K - B/Ao
Results are shown in Figure 6.
T h e yield B/Ao for batch and PFR operation is
B/Ao = f
[-
-1
Nonisothermal Reactors
- f"
BO
I-CY
I+a
where
2KBo/Ao - (1 = 2KBo/Ao - ( 1
K
=
kJkl and
For the single CSTR
B/Ao =
f'
2K(1
-f)
CY
d[-
- a)
+ a) = d 1 + 2K - 11
(25)
Substituting appropriate recycle concentrations into Equation 24, there results
There is a class of nonisothermal reactor for which backmixing influence may be fruitfully assessed in terms of recycle ratio-namely, the adiabatic reactor in which radial gradients are negligible. When backmixing cannot be ignored in an adiabatic system, the plug flow-axial diffusion model can be invoked ; however, the second axial derivative in the mass and thermal energy differential equations can create difficulties in the numerical solution (6, 8, 76). Specifically, for the adiabatic reactor which exhibits mixing character intermediate between plug flow and perfect mixing, the equations demanding solution are, for mass:
dLC D, dx2
- u dC dx
=
kog(C)exp
(32)
and thermal energy
With the usual Wehner-Wilhelm boundary conditions (76), numerical solution of the above equations is realized only by 168
l & E C FUNDAMENTALS
Equation 34 is the usual PFR relation; however, Equation 35, with the lower integration limit
0.4
c1 = 0.3
B/Ao 0. I
0
0.4
.
’
0..6
’
0.8
I-f
I
K-k2/k
+ C,
’
R + l
actually describes the nonplug flow condition. Inlet temperature is, of course, also governed by the recycle ratio. T h e adiabatic catalytic oxidation of SO2 provides a concrete example where any simulation effort of the first, shallow, reactor bed must account for backmixing. I n this case, Equation 35 should prove more convenient in solution than simultaneous solution of Equations 32 and 33. T o be sure, exit concentration and temperature are found in the inlet boundary condition ; however, in reactor design effluent values are usually specified while reactor dimension is to be determined by appropriate computation. Extension of Adiabatic PFR Analytical Solution to Regime of Finite Backmixing of Heat and Mass. Parts (74) and Almasy (7, 2) have discussed the solutions to the constant volume, constant pressure adiabatic, PFR unit; these solutions can be obtained in terms of exponential integrals. They have been extended and summarized by Douglas and Eagleton (70). T h e recycle notion set forth in this paper permits a logical extension of these solutions to the general case free of the plug flow restriction. Specifically. we illustrate the application of the recycle model for two adiabatic cases:
0.2
0.2
RC
0.3
0.2 B/A,
0. I
CASE1. An example, originally provided by amith (75) and solved analytically by Douglas and Eagleton (70) :
0
E/R, = 5580’ K., A = exp (16.87), min.-l, first-order reaction where k = A exp(-E/R,T). CASE2. T h e same system as Case 1 except that E / R , = 20,000’ K. T h e adiabatic temperature rise for 70% conversion is 11.4’ C. in each case.
I -f 0.4
0.3
0.2 B/A, 0. I
0
O.i!
0.4
0.6
0.8
. I
I-f Figure 5. Yield of 6 vs. conversion for the reaction ki
.4+A+B kn
6+B-+C implicit techniques (6). T h e same physical situation may be described by
or
(35) Temperature being uniquely related to conversion in a n adiabatic system, then
Results obtained by use of exponential integrals with recycle integration limits are expressed in terms of k,B, (proportional to reactor volume) as a function of conversion, 1 - f,for PFR, C S T R , and recycle ratios of 0.1, 1.5, and 20 in Case 1 (Figure 7) and for PFR, CSTR, and R = 1.5 in Case 2 (Figure 8). T h e two cases treated illustrate rather clearly that for the specified thermal properties of the system, in the instance of small activational energy (Case l ) , the expected superiority of the PFR over a mixed reactor is found, while in Case 2, characterized by a much higher activational energy, the CSTR commands the advantage over the PFR up to about 85% conversion, but the intermediate mixing case (R = 1.5, equivalent to about two CSTR’s in series) reveals an advantage over the PFR u p to a conversion level of about 96y0’,.Below a conversion of about 7oy0the C S T R holds a slight advantage over both the P F R and partially mixed reactor. [Design may then specify a CSTR followed by a partially mixed (recycle) reactor.] By “advantage” we mean, of course, a lower reactor volume requirement for a given feed rate and conversion. While it is not our purpose to optimize the system considered, it is evident that analysis phrased in terms of finite recycle (mixing) establishes a basis upon which optimal reactor types and their deployment can be established for a given system. Unfortunately, yield-sensitive reaction schemes are not conveniently described for adiabatic conditions by the exponential integral method, as a multiplicity of reactions are necessarily involved. I n such circumstances, the usual numerical techniques must be employed, although in principle the recycle concept as found in Equation 35 applied to a complex reaction network may still prove of merit. VOL. 5
NO. 2
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169
I
6
E/Rg= 5580 0.8
5
0.6
4
3
0.4 %/Ao
kO00 0.2
2
0
I
0.2
0.4
0.6
0.8
I'
I
I-f
I
0 0
I
K=kl/k2A0=
Conversion,
kl
0.8
0.4
0.2
A-B k2 A t B-C
0.6
0..8
I-f
Figure 7. Conversion vs. k,& for adiabatic reaction of low activation energy at various mixing levels
0.6
I, .2 ___E/Rg* 2,0,000
0.4
i
11.0
B/Ao
A-B
0.2 0.8 0 I
0.2
0.4
0.6
0.8
0.6
I- ? k000
0.4
0 . IO
0.2
B/Ao 0.05
0 0
I 0
0.2
0.4
0.6
0.8
I
I -f Figure
6.
Yield of 6 vs. conversion for the reaction
0.2
0.4
0.6
0.8
I'
Conver\sion, I -? Figure 8. Conversion vs. k,6, for adiabatic reaction of high activation energy at various mixing levels
ki
A-+6 kz
A+6+C T h e concept of recycle to describe nonplug flow in a n adiabatic stirred tank loop has also been developed by Worrell (77), who presents a graphical method of solution as part of a stirred tank segregated flow-reaction study (78). Conclusions
For any reaction rate expression which is capable of being integrated for the plug flow reactor (PFR) condition, the influence of finite backmixing upon isothermal conversion and yield can be assessed in terms of effluent recycle. Bypassing 170
l&EC FUNDAMENTALS
and stagnant zone retention are excluded by the model, though these factors can be anticipated with, of course, a consequent increase in the number of parameters required to describe a given system. Bypassing, segregation, and dead zones may readily be anticipated-for example, by various series-parallel combinations of recycle m i t s including crossflow. The recycle ratio is phenomenologically related to a number of CSTR's set in series and in turn related to an apparent axial dispersion coefficient, through the well known stirred tank in tandem-dispersion coefficient relationship (4, 5, 8, 72)
n = Lu/2D, for a reactor of length L and fluid velocity u
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
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171
