Sept., 1955
KINETICS OF
THE
CATALYTIC DEHYDROGENATION OF CYCLOHEXANE
823
EFFECT OF INTRA-PARTICLE DIFFUSION ON THE KINETICS OF CATALYTIC DEHYDROGENATION OF CYCLOHEXANE BY P. B. WEISZAND E. W. SWEGLER Contribution from Socony-Vacuum Laboratories, A Division of Socony-Vacuum oil Research and Development Departmentl Pau~sboro,N . J .
co.,
Inc.
Received February 66, 1066
The effect of intra-particle diffusion rates on the product distribution and reaction rates during catalytic conversion by consecutive reaction steps in a porous catalyst particle is demonstrated. The reaction c clohexane + cyclohexene 4benzene on chromia-alumina catalyst was studied in a differential reactor. The ratio of cyc%hexene to benzene is shown to depend on catalyst particle size. Derivation of the ratio of the two successive reaction velocity constants must include the effect of finite diffusive residence time. When this is done, consistent results are obtained for all particle sizes. Criteria for the detectability of reaction intermediates are also given.
Introduction Diffusion transport rates of reactants within porous catalyst particles can markedly affect the kinetic interpretation of observed reaction rates and product distribution when more than a single one-step reaction proceeds. Wheeler’ has mathematically examined a number of such cases. For the case of successive reactions via an intermediate compound, we will discuss simple criteria which allowestimatestobemadewhether diffusion phenomena will influence the observed product distribution, and for the detectability of reaction intermediates. For the dehydrogenation of cyclohexane to benzene over chromia-alumina catalyst, Herington and Ridea12have presented evidence for the successive dehydrogenation via cyclohexene. For this reaction an experimental study demonstrates the dependence of detected cyclohexene concentration on intra-particle diffusion parameters (particle size and diffusivity), which is found to be in excellent agreement with theoretical prediction. Theoretical Principles Competition of Reaction Velocity and Diffusive Escape of Reaction Intermediate.-When, in a porous catalyst particle, a reaction A + C proceeds by way of an intermediary product B, the over-all kinetics may be influenced by diffusion transport rates of A into, and B and C out, of the particle
With these concepts it becomes clear that (a) no effect of diffusive transport on the observed concentration of B and C will exist when T D > TR. Detectability of an Existing Intermediate.-For the case where T D > TR, the ratio of the external concentration of the intermediate, B, to that of the product C, will be
-
When for B/C the analytical limits of detection for the species B relative to C are used, this equation defines the magnitude of the rate constant IC2 above which the existence of the intermediate cannot be experimentally established. Relation of Observed Production Rate of Intermediate Species, Rate Constants and Diffusion Parameters.-Assuming the two reaction steps in the scheme (1) above to follow first-order laws, we find
- CdB _I A--
Bo
{m+-&\
- -
coth ( ~ 6 1 ) pcothp- 1
wherew --t D symbolizes the rate of diffusive transport in the catalyst solid. Molecules within the catalyst particle have a finite diffusive residence time whose magnitude is T D = R2/D,e, where X is a length parameter and Des the effective diffusivity in the pore structure. Assuming catalyst particles to be near spherical, with radius R, X = l / 5 R, since one-half of the molecules will be within a depth equal to 0.207 R. The reaction rate decay constant T R has the magnitude of the reciprocal first-order rate constant, l/k (referred to unit volume-strictly speaking of pore volume-of catalyst).
The solution relates the ratio dB/dA of the rate of emanation from the catalyst particle of product B to the total rate of reaction, the ratio of the concentrations Bo/Ao of intermediate and primary reactant at the particle boundary, the ratio of the rate constants m = k2/k1, and the diffusion modulus (o which characterizes the degree of the diffusion effect of the primary reaction velocity (-dA/dt). The manner of derivation has already been discussed by Wheeler’ for the case of cylindrical geometry. The above formula applies to spherical particles3a and neglects gas flow effects resulting from molar volume change during reaction. Although molar volume increase accompanies the dehydrogenation of cyclohexane the assumption is justified in the following work since the pore structure of the catalyst used is such that all diffusion is of the Knudsen type.3
(1) A. Wheeler, Aduances i n Catalysis, 3, 250 (1951). (2) E. F. G. Herington and E. K.Rideal, Proc. Royal Soc. (London),
(3) P. B. Weisz and C. D. Prater, Advances in Catalysis, 6, (1954): (a) p. 176 (erratum: in formula (30) “cosh” should read “coth.”)
ki kz A + B + C
AlQO, 289 (1947).
(b) p. 154-157.
P. B. WEISZAND E. W. SWEGLER
824
Experimental Materials.-Phillips Pure Grade cyclohexane was further purified by passing through silica gel. The product was compared mass spectrometrically with a Bureau of Stand’ pure. It had less if ards sample stated to be 99.96 mole % any benzene, 0.04 mole % CBHlowith respect to the standard, and better than 99.9% purity. The catalyst was a sample of eo-gelled chromia-alumina spherical bead catalyst, containing 20% Crz03 by weight, having a surface area of 180 m2/g. (BET), and a particle density of 1.56 g./cc. Three sizes were selected: beads of 0.310 em. and 0.184 em. radius, and particles of approximately 0.050 em. radius, obtained by crushing and sizing through #I6 on #20 screens. Apparatus.-The apparatus was identical t o that described by Weisz and Prater.sb A special reactor chamber design was used and is shown in Fig. 1. Differential reactor conditions were used, i . e . , very low conversion (about 1%or less), and the reactor chamber design was intended to result in highly turbulent flow to achieve “stirring” in the small reaction zone. I n this way, the concentrations of reactant and products at the boundaries of all catalyst particles within the contact zone could be expected t o be the same and known from the analysis of the product samples.
Vol. 59
cyclohexene. Ultraviolet spectrophotometer analysis showed traces of other material. The latter material imparted fluorescence t o the liquid samples. Since it was not detected by the mass spectrometer, a high molecular weight, greater than 200, was indicated. I t was removable by silica gel, indicating unsaturation. A sample of liquid roduct was subjected to an azeotropic distillation to remove Eenzene. The ultraviolet absorption spectrum of the remaining sample indicated the presence of a polynuclear aromatic.
Results Rates of reaction of cyclohexane (-dA/dt) were determined from the rates of formation of all products. Total hydrogen production rate was determined from the pressure-rise data by the relation n = .
PSPS+BV B
( ~s P~+B)RTB
where rate of production of Hz in moles/unit time rate of pressure rise in system PS+B= rate of pressure rise in system with calibrated bulb included VB = volume of bulb Tg = temperature of bulb
Ps
= =
Production rates of benzene and cyclohexene were obtained by direct observation of these products. Of the total cyclohexane rate, that part corresponding to the formation of the unknown aromatic and of the solid polymer remaining on the Fig. 1.-Reactor tube, with catalyst chamber. catalyst was determined from the additional Catalyst was introduced into the chamber B through the hydrogen production rate not accounted for by thermocouple well opening A. The well was then put in cyclohesene and benzene production. For this place and the ring seal made a t A. The spacing between purpose, a C/H ratio of unity was assumed for the the rim of the glass plate D and the chamber walls was sufficiently small to retain the catalyst. The glass beads C unknown aromatic and the polymer. This is a fair assumption for a high-boiling aromatic, as were used t o insure adequate preheating of the reactant. Besides the thermocouple in the well, touching the cata- well as the type of carbonaceous deposit observed. lyst, two others were attached to the outside of the catalyst Only 7-15% of the total hydrogen rate is accounted chamber at opposite sides. All three couples (iron-co2stantan, #30 wire) gave the same temperature, within 0.5 , for by these products. Therefore, an error in C/H during all runs. Temperature variation was held within ratio of as much as 25% would cause only a 2-5Oj, f 0 . 2 ” by use of a low heat capacity, cylindrical furnace, error in the total cyclohexane rate. controlled by a thermel operated, high-sensitivity electronic Rates of Cyclohexene and Benzene Formation.relay. The controlling thermel junctions were located next These rates were obtained directly from the mass to the furnace windings. Starting Procedure.-Initial studies of the catalyst had spectrometer values for the liquid sample concentrashown that, for the dehydrogenation of cyclohexane, a re- tions and the rates of sample accumulation in each producible activity, virtually constant for over one hour, case. could be obtained by evacuating the catalyst for three hours The Ratio Bo/Ao.-The ratio of the gas phase or more a t 510”, 10-5 mm. Thus, with this constant activity, and with the fixed reactant concentration, the effect concentrations of cyclohexene and cyclohexane of variation in catalyst, bead diameter on total reaction rate was obtained directly from the liquid sample could be determined reliably. Therefore, prior to each run, analyses, with a small correction for the dilution by after installing the catalyst sample, the above catalyst treathydrogen which occurs in the reactor. ment was used. The rest of the apparatus was evacuated Summary of Measurements.-Complete results a t the same time. The system was then closed off from the pumps and argon admitted to the apparatus to a pressure for one run are shown in Table I to indicate the slight,ly greater than one atmosphere. With all parts of the level of conversion obtained (approximately 1%) system at operating temperatures, cyclohexane was admitted from the reservoir after opening the system to the and to demonstrate the near-constancy of the rates. atmosphere. Circulation of reactant began immediately. Rate Measurements.-The rate of hydrogen production was measured by closing the system off from the atmosphere and observing the rate of pressure rise with and without a calibrated volume in the system. Periodically, weighed samples, accumulated over a short, measured time interval, of the condensed reactant and product vapors were taken. Measurements were continued over a 60;70 minute run time. The reaction temperature wa3 478.5 . Analysis of Products.-Mass spectrometer analyses of samples of the gas stream showed the gas produced to be essentially 100% hydrogen. The liquid samples were analyzed by the mass spectrometer. The only observed products were benzene and
TABLE I Run D-6, Rs = 0.310 em., 1.434 g. catalyst
9.7 1.16 0.32 0.63 20.8 10.4 1.11 .31 .66 39.0 1.11 10.6 .31 .68 50.3 10.8 1.11 .32 .68 60.7 1.11 .31 10.8 .68 70.2 a Rate units are mole/min./g. X lo5.
2.29 2.37 2.44 2.36 2.43
4.0 4.2 4.3 4.3 4.3
c
KINETICS OF THE
Sept., 1955
825
CATALYTIC D E H T D R O G E N A T I O N O F CYCLOHEXANE
Table I1 gives total rates of reaction of cyclohexane (-dA/dt) vs. time for the other two runs. Table 111 shows average total rate of reaction of cyclohexane (-dA/dt), average rates of formation of cyclohexene (dB/dt) and benzene (dC/dt), Bo/Ao, and the ratios dB/dA and dB/dC, all us. bead size.
1
.0
l
l
l
I
1
1
1
-.k2
1
-
.7 -
20 30 40 50 60 4
-
D-7 (Rz = 0.184 crn.)" D-8 ( R I = 0.050 cm.)a 5 , 6 (1.579 g. catalyst) 9 . 2 (0.740 g. catalyst) 5.7 8.9 5.7 8.8 5.8 8.7 5.8 8.7 dA/dt (mole/min./g. X 105).
TABLE I11
--Aa d z dt dt
E
dB
dt
2
dB
Ao
50 .I -
I
'51
100
y2= 2.5 -
.4
Ra = 0.310cm. 4 . 2 1.11 2 . 4 0 . 4 6 0.0032 0 . 2 6 R2 = 0.184 cm. 5 . 7 1.81 3 . 1 .58 ,0054 .32 ,0082 .61 R1 = 0,050 cm. 8 . 8 5 . 4 2 . 8 1 . 9 a All rates in mole/min./g. X lo5.
The probable percentage error in total rate of reaction of cyclohexane is estimated to be about *4%. That for &/Ao is *5%, and for dB/dA, about *6%, due primarily to the probable errorsin the mass spectrometer results. Discussion Observed Rate of Production of Cyclohexene Intermediate, Particle Size Dependence.-The results concerning the observed ratio of the rate of production of the intermediate cyclohexene to that of benzene (column 4,Table 111) show a clear dependence on particle size. For the smallest particles nearly twice as much net production of the intermediate was achieved as compared to the normal end product. Determination of Kinetic Constants and Agreement with Theory.-The experimental procedure allowed the measurement of the over-all rate of reaction and of production of each component, and of the concentration ra?io of Bo/Aoat the boundary of the catalyst particles. Therefore, for the use of formula 3, Bo/Ao and -dB/dA are obtained from measurem.ent, while m = kz/kl and p are unknown. 0.8
-
-
0.5
1.0
2.0
5.0
10.0
(0.
Fig. 2.-Functional relationship between 9 and (0, with method of obtaining (0% from measured q and 9 ratios for different catalyst bead sizes.
10 15
20
TABLE I1 Time (min.)
kl
IO IS
20
50 *4
t
Lp3
4.2 IO
15
20 .I
-
.005 BO/Ao
Fig. 3.-Graphical
50 IO 0 .OlO
solutions of equation 3 for the measured values of p.
The dBusion modulus cp is obtained from the variation of the over-all reaction rate for a known change in particle size, by the "triangle method" described by Weisz and Praters3 Use is made of the known functional relationship of the utilization factor q, defined by the first-order relationship of the primary reaction rate
%
--=
Mo?
(4)
and the diffusion modulus cp for spherical particles, as shown by the drawn out curve in Fig. 2. For the two measurements in which the particle sizes Rz and R3 were used, (p2/cp3 = R2/R3;and the ratio qz/q3 is found from the rate measurements as 0 2 / 0 3 = (dA2/dt)/(dA3/dt) (in view of (4)). Fitting the values of (pz/cp3 = 0.59 and q2/q3 = 1.36 on the double logarithmic plot in Fig. 2, cpz and cp3 become determined. cpl is accordingly found from these by multiplication by the size ratio c p l / ( ~ a = Ri/R3 = 0.16. Accordingly, we find cp3 = 4.2, cpz = 2.5, cp1 = 0.68. The rate constants ratio kz/kl can now be found from the equation 3, with the measured values of BO/&, -dB/dA, and cp for any one particle size. We can test the adequacy of the theoretical treatment by comparing the results of all three particle sizes. I n Fig. 3 are plotted the functional rela-
P. B. WEISZAND E. W. SWEGLER
826
tionships for -dB/dA os. B,/A, for the three pvalues (particle sizes) used, with kz/kl as the independent parameter. The measured values (dotted lines) yield the solutions From particle size
kdk1
R1 = 0.05 Rz = 0 . 1 8 Rs = 0 . 3 1
16 13 14
The results of all three experiments are seen to give consistent solutions. The values of experimental errors lead us to estimate the probable error of each kz/kl to be about f 3 . From the three measurements, we conclude that kz/kl = 14 f 2. In contrast to the above complete solution, a determination of the ratio of the kinetic constants without regard to the intra-particle diffusion effect, according to the simple solution
Vol. 59
dA/dt = 8.8 X 10-6 m./min./g., and the particle density of 1.56 g./cc., we obtain for the primary rate constant referred to unit catalyst volume kl = 0.15 sec.-l; kz = 2.1 sec.-l
The latter follows from the previously determined ratio. The catalyst particle diffusivity, de^, can now be obtained from any of the three (particle size) sets of data. PI =
0.7 = R 4 Z = 0.504;
0.15
gives D e s = 0.8 X cm.2/sec. Diffusive Residence Time and Detectability of Intermediate.-The average diffusive residence time of a molecule within a catalyst particle of the medium size Rz = 0.18 cm. calculates to T D = 1/25 (RZ/D,a) = 1.6 see. Comparison with the - -dB - 1 - -ki -Bo 2 l/kz M 0.48 reaction rate decay constant 7 ~ = dA ki Ao sec. demonstrates how the above-described criteria would have resulted in k2/kI = 50, 125, 230, re- predict a heavy diffusion effect on the rate of prospectively, for the three experiments in order of duction of intermediate. increasing particle size, Le., in values which are Using the criterion, formula (2), with the minimuch too large and inconsistent among the three mum detectable concentration of an unknown cases. intermediate c,-such as cyclohexadiene-taken as The rate constants ICl and ICz are obtained from (4). )/50 of that of benzene cc, we find, with T D M The smallest particle size gives the simplest solu- 1/25 (R2/Des)= 0.13 see., for the smallest particle m./cc. size Rs,that it would not have been detected if its tion, since r] = 1.0. With A0 = 1.55 X (atmospheric pressure, T = 478.5", cyclohexane) reaction rate constant was k , 2 30.
r
