Ind. Eng. Chem. Prod.
Res. D ~ v 1981, . 20, 457-466
Topp, N. E. “The Chemistry of the Rare Earth Elements”; Eisevier: London, 1985. Wangl W.-M.“Air-Fuel Control to Reduce Emissions, 11. Engine-Catalyst Characterization Under Cyclic Conditions”, SAE Paper No. 800052, 1980. Yao, H. C.; Sieg, M.;Plummer, H. K., Jr. J. &la/. 1979, 59, 365. Yao, H. C.; Shelef, M., Paper A21-1, Preprints, 7th International Congress on Catalysis, Tokyo, July 1980. Yao, Y.-F. Y. ”Oxygen Storage capacity of CeOp Containing cataiysts”. Ford Motor Company Technical Report SR-79-36, presented at 6th North Am-
457
erican Meeting Catalysis Society, Chicago, Iii., March 1979.
Received for review October 23, 1980 Accepted April 29, 1981
This work w8s at the SecondChemicalcongress of the North American Continent, Las V e g a NV, Aug 1980, ACS Division of Colloid and Surface Chemistry.
Kinetics of the Metathesis of Propene over Re2O7/yAl2O3 Freek Kapteijn, Hubert L. G. Bredt, Ernst Homburg, and Johannes C. Mol’ Institute for Chemical Technology, University of Amsterdam, Plantage Muidergracht 30, 10 18 TV Amsterdam, The Netherlands
On the basis of a statistical analysis of initial-rate data, obtained with both pure and mixed reactant feed, and the application of physicochemical constraints, a kinetic model is selected for the heterogeneously catalyzed metathesis of propene over a Re2O7/yAI2O3catalyst. In this model, which is based on present ideas about the reaction mechanism, surface complexes, viz. metal carbenes, are the active centers for the metathesis. The LangmuirHinshelwood model, which is frequently used as a kinetic description for this reaction, is rejected as an adequate model. In spite of the high catalytic activity, less than 1% of the rhenium atoms were found to be active for metathesis. This implies a maximum site density of 10’o-1012cm-2. The earlier observed exponential increase in activity as a function of the rhenium content of the catalyst is ascribed to surface heterogeneity.
Introduction Since the metathesis of alkenes was first reported in the open literature by Banks and Bailey in 1964, much work has been done in the field of this catalytic reaction. Highly active and selective catalysts were developed for both homogeneous and heterogeneous reaction systems, and many investigations were set up for the elucidation of the reaction mechanism. (See reviews of Mol and Moulijn, 1975; Haines and Leigh, 1975; Rooney and Stewart, 1977; Grubbs, 1978.) Investigations into the mechanism of complex chemical reactions commonly require detailed kinetic studies. Such studies invariably include the development of realistic kinetic models based on relevant elementary steps pertaining to the model under consideration and the evaluation of acceptable values for the parameters contained in these models. In many cases, however, experimentally observed kinetics can be explained equally well by different mechanisms. Therefore, one cannot expect that kinetic experiments by themselves would suffice to fully establish the reaction mechanism, but, on the other hand, they can be used to eliminate mechanisms or to support others. With regard to the metathesis of alkenes, most of the kinetic studies have been concerned with the metathesis of propene (eq 1)over several solid catalysts (Lewis and Wills, 1969 and 1971; Moffat and Clark, 1970; Mol, 1971; Davie et al., 1972; Luckner et al., 1973; Hattikudur and Thodos, 1974; Lin et al., 1976). 2CH2=CHCH3 + CH2=CH2 + CH3CH=CHCH3 (1)
catalyzed metathesis of propene. A reaction rate expression derived from this model gave also a good correlation of the experimental data. Since the metathesis was recognized as a transalkylidenation reaction, several more detailed descriptions of possible reaction mechanisms have been published (Calderon et al., 1976). Initially, mechanistic schemes were presented involving a pairwise interchange of alkylidene groups between two alkenes complexed to the active center (Figure 1). Herisson and Chauvin (1971) were the first to suggest a nonpairwise chain mechanism, in which the reaction proceeds through a carbene-metal complex (Figure 2). Furthermore, it follows from several investigations that the metathesis catalyst becomes active only after being brought into contact with alkenes (Luckner and Wills, 1973; Olsthoorn and Boelhouwer, 1976). This may support the idea of surface complexes being the active centers. From the mechanistic studies presented in the literature so far, hardly any support can be obtained for a dual-site mechanism. Therefore, Van Rijn and Mol (1977) presented some other kinetic models, based on alkene and alkylidene surface complexes as the active centers for the reaction. They tested the derived rate expressions with the experimental data available from the literature and showed that their models describe these data at least equally as well as the Langmuir-Hinshelwood model. In order to establish whether rate expressions derived from models which are compatible with present results of mechanistic studies give a better description of the experimental data than the originally developed ones, we made a systematic study of the kinetics of the metathesis of propene over a Re207/y-A1203catalyst by initial-rate measurements, using either pure propene or mixed reactant feed. Experimental Section The catalyst used for the model selection contained a calculated amount of 5.8% Re2O7by weight. To investigate the influence of the rhenium content on the kinetic
These studies indicate that the heterogeneously catalyzed metathesis of propene can be kinetically well interpreted by the Langmuir-Hinshelwood model, viz. a dual-site mechanism, with the surface reaction as the rate-controlling process. Hughes (1970) used for the homogeneously catalyzed metathesis of 2-pentene a model in which the reaction takes place between two alkene molecules complexed successively to the same active center. Mol (1971) applied this scheme to the heterogeneously 0196-4321/81/1220-0457$01.25/0
0
1981 American Chemical Society
458
Ind. Eng. Chem. Prod. Res. Dev., Vol.
20,No. 3, 1981 C2H4 C3H6 'C4H8 He
\
R1'
R2
Figure 1. Pairwise exchange mechanism. M9
2
+
c
/+ R2
R
F
R
FFLOW SENSORS
2
PRESSURE
i """"""
GAUGE POP
/=\ R1
R1
"""-
DATA PROCESSING VENT
Figure 2. Nonpairwiee chain mechanism.
behavior of the catalyst, some experiments were conducted with catalysts containing a calculated amount of 3.0, 5.7, 8.3, or 10.7 w t 90Re207,respectively. All catalysts were prepared by impregnation of y-alumina (Ketjen CK-300) with an aqueous solution of ammonium perrhenate, followed by drying at 390 K and calcining in dry oxygen at 830 K. The catalyst had a surface area of 180 m2/g (BET, nitrogen). All catalyst samples were activated in situ by heating a t 830 K in a stream of dry air for 4 h, followed by heating in helium at the same temperature for 2 h (Kapteijn et al., 1977). This standard activation procedure gave a fairly constant and reproducible activity for the metathesis of propene. The experiments were carried out in a microcatalytic fixed-bed flow reactor system designed for precise kinetic experiments under steady-state conditions, in which the setting variables (pressure, flow rate and temperature) could be accurately controlled (Kapteijn, 1980). Figure 3 shows a flow diagram of the reactor system. Before entering the reactor, the feed gases were passed through a purification section to remove water, oxygen, and traces of sulfur compounds. The reactor itself was a stainless steel tube (id. 7 X m) placed in an electric oven. The total pressure in the reactor was kept constant during an experimental run; different partial pressures of the reactants were obtained by diluting with helium. The flow rates were measured with thermal mass flow sensors (Brooks); the pressure was measured with pressure transducers (Kuppers). The accuracy of the flow- and pressure control was within 0.5%. A constant temperature profile in the catalyst bed was obtained by means of three independently controlled oven sections. The temperature in the reactor was measured by calibrated chromel-alumel thermo-elements just under and above the catalyst bed. The product stream was analyzed by an on-line gas chromatograph, operated at room temperature, on a 3.3 m X 1/4 in. column packed with 30% bis(2-(2-methoxyethoxy)ethyl) ether on Chromosorb P (0.18-0.25 mm), using nitrogen as carrier gas and a flame ionization detector. The gas chromatographic signal was real-time processed by a PDP 11/10 computer system, provided with a GC-signal integrating program (Woerlee and Mol, 1980). The further data processing was performed on a CDC-7300 computer system. Polymerization grade propene was used; it contained 0.1% propane and 0.01% ethane. The ethene (CP grade)
11/10
i
RESULTS
Figure 3. Flow diagram of reactor setup.
contained 0.05% ethane. 2-Butene (CP grade) was a cis/trans mixture (cktrans ratio 1:1.6) and contained 0.1% n-butane and isobutane, and 0.03% 1-butene.
Kinetic Measurements The initial reaction rate, ro, was measured directly by the differential method, according to eq 2, where x represents the conversion corrected for the backward reaction. (It has been demonstrated that neglecting this correction can lead to systematic errors that strongly influence the parameter estimation (Kapteijn, 1980).) The conversion was always less than 5%. xF ro =
w
The experiments were carried out at temperatures of 313, 323, 343, 373, and 403 K, over a pressure range of 0.01-0.35 MPa with catalyst samples of 0.25-0.9 g (particle size 0.18-0.25 mm). To establish a uniform flow pattern in the reactor, the smaller amounts of catalyst were mixed with inert glass beads of the same dimensions. The selectivity of our catalyst for the metathesis of propene was very high at all temperatures: only ethene and 2-butene (cis and trans) and sometimes a minor amount of 1-butene (less than 0.5% of the total butenes) were formed. At steady-state conditions ethene:Zbutene ratio did not deviate more than 1% from 1:l. The "break-in" period, often observed in heterogeneous metathesis (Luckner and Wills, 1973), in which the activity gradually increases to its steady-state value, lasted 30 min or less. It was both calculated and experimentally verified that mass transfer limitations (pore and film diffusion, capillary condensation) were absent (Kapteijn, 1980). The very low reaction enthalpy excludes any heat transfer limitation in advance. Data Correlation The parameters of the different rate expressions were estimated by nonlinear regression techniques minimizing the sum of squares of residuals (SSR), the differences between the calculated and the observed reaction rates. The main computer program uses a CERN package of subroutines, MINUITS, for minimizing functions (James
Ind. Eng. Chem. Prod. Res. Dev., Vol. 20, No. 3, 1981 459 elementary process
model
rdP (a-11
I
I1
1
P + *
2
2 P*
f
E* + B*
3
E*
f
E
4
B*
L
B
1
P + *
2 3
P+P* P2*
4
* +
(b-21
P* P 2* EB*
EB*
*
B*
+
E
5
EB*
f
E*
+
B
6
B*
f
B
+ * +*
3
7
E*
f
E
1
P+P*
f
P * 2 EB*
*
* *
2
+ * +*
f
2 IIIa
P*
4+5 r
=
k Kp Pp
r
=
+
(
K,
Ppl
P,’
k lp ( P,’
P,
+
K, Ppl
- P, P, +
KE
- P, +
1
P,
xes
+
P, /
KE P,
xes +
)
E, P,
1
’,P,
(e31 +
,E ,
P, P,
+
XPE P, PE
+
K,,
Pp PE
+
Kp,
+
K,,
Pp
P,
2
3
P 2 EB*
4
EB*
*
E* + B
5
P+B*
f
P*+B
6
P+E*
*
P*+E
B*
(C.11
+
E
K
3+4
K,
(
PPI
r =
P,
+
Kp Ppl
- PE p, +
/ de
ZE PE
+
I
’,P,
(c-41
P,
P,
Figure 5. Reaction-rate expressions for the metathesis of propene.
These kinetic models represent a sequence of elementary processes through which the reactant must go to yield the p2* products. From the reaction-rate expressions, initial-rate 2 2 P2* EB* expressions can be obtained by neglecting the terms con3 EB* B* + E taining the partial pressures of the products. 3+4 4 EB* E* + B Figure 4 shows the models considered. In this figure E, IIIb 5 P + B* PB* P, and B represent ethene, propene and 2-butene, re6 P + E* PE* spectively, e is a =CH2 group (methylidene) and b is a 7 PB* * P* + B =CHCH3 group (ethylidene), while * represents an active 8 PE* + P* + E site. The Langmuir-Hinshelwood model (I) will be compared with some other kinetic models. Model I1 represents a consecutive adsorption of two propene molecules on one 1 P + e* + Pe* active center, followed by a surface reaction and desorption 2+5 2 Per * Eb* of the products. The active center in models IIIa and IIIb 3+6 3 Eb* * b* + E is an alkene surface complex. This complexes with a IV 4 P + b* * Pb* propene molecule, reacts, and then the products desorb 5 Pb* * Be* or exchange with an incoming new propene molecule. I t 6 Be* + e* + B is noted that the models I, 11, and 111are all based on the Figure 4. Kinetic models for the metathesis of propene. pairwise exchange mechanism. Model IV is based on alkylidene surface complexes as active centers (carbene and Roos, 1975). Two minimizing techniques were used mechanism). In this reaction sequence ethene and 2in series, the first according to the simplex method of butene are successively formed by reaction of propene with Nelder and Mead (1965) and the second according to the a methylidene complex (e*) and an ethylidene complex variable metric method of Fletcher (1970). From the (b*). It is assumed that the surface complexes in models variance-covariance matrix of the parameter estimates, 111and IV are initially formed during the break-in period, used by the latter routine, 95% confidence limits of the the number of these complexes being independent of the parameter estimates were calculated alkene pressure in the steady state. The relevant rate expressions derived from these models, bi f tv,0.025[u(bi)I”2 (3) with the rate-determining processes (rdp) as indicated in Figure 4, are given in Figure 5. The indices of the various Since the confidence intervals are approximations of the ICs merely indicate their position in the rate expression; nonlinear situation, and do not take into account a possible the composition of the relevant ICs will be discussed below. correlation between the parameters, we also constructed Three initial-rate expressions remain when propene is the exact contours at approximate 95 and 99% significance only reactant (Figure 6): (a-1) reduces to (a), (b-1) and level of constant (SSR) value (b-2) to (b), and (c-1) - (c-4) to (c). P Expressions based on other elementary processes being (SSR)0.96 = (SSR),;, + (SSR)min~_p J’(P,N- ~ ~ 0 . 9 5 ) rate determining yield initial-rate expressions of the form (4) ro = constant or ro = constant.pp. These are not further considered because of incompatibility with the experiKinetic Models mental initial-rate data, as can be seen from Figure 7, Reaction-rate expressions for the metathesis of propene where the experimental initial-rate data are given as a were derived from several kinetic models, using the function of the propene partial pressure. steady-state approximation, assuming surface uniformity, Regression Analysis one or two elementary processes not in (quasi-) equilibIn order to select a proper rate expression, several asrium, and also assuming the total number of active sites pects of regression analysis must be considered (Draper being independent of the partial pressure of the reactants. 1
P+P*
f f
f
f f f
460
Ind. Eng. Chem. Prod. Res. Dev., Vol. 20, No. 3, 1981
2
2
KP P P
2
r
0
K1 K 2 P P
= 1
+ KIPP
+
2 5 5 P p
1
r
=
0
KP P P
Table I. Constraints for Thermodynamic Properties for Adsorption and Unimolecular Surface Reaction
unimolecular surface reaction: rules: I I1 I11 guidelines: I I1
Kads = exp( 4 S0ds/R)
exp(-A H",,/RT) h = A exp(-E,/RT)
< - A s o a d s < so, AH',^^ > o E, > 0 -iSIads > 40 (J/mol K ) - A S ads < 51.0 - 0 . 0 0 1 4 A H o , ~ 0
-
(J/mol K )
and Smith, 1967; Kittrel, 1970; Froment, 1976). Lack-of-Fit Test. The kinetic parameters in the rate expression under consideration are estimated by minimizing the s u m of squares of residuals (SSR). This (SSR) is composed of a pure-error s u m of squares (SSE),due to the errors in the experimental data, and a lack-of-fit sum of squares (SSL), the incapability of the rate expression to correlate the experimental data. The (SSE) can be estimated from replicated data at the same settings of the partial pressures of the reactants. The adequacy of the rate expression is tested by comparing the mean (SSE)and (SSL) (i.e., the sum of squares divided by its number of degrees of freedom) in a lack-of-fit test. An expression adequately describes the data if mean (SSL) < F(~,,~z,0.95) (5) mean (SSE) Residual Analysis. The distribution of the residual reaction rate (observed reaction rate minus the calculated reaction rate) a function of an independent variable (e.g., partial pressure of a reactant) should be random with zero mean in case of a proper model. Trending effects in this Table 11. Mean (SSR) Values (x Degrees of Freedom ( N - p ) reactant(s) propene
+ ethene propene + 2-butene ethene + 2-butene propene
02
04
03
Pp
Figure 6. Initial-rate expressions for the metathesis of propene; pp represents the initial propene pressure.
adsorption :
01
(MPa)
-
Figure 7. Initial reaction rate vs. propene pressure for several temperatures. The drawn lines are the reaction rates calculated with expression (e).
residual distribution indicate the incompatibility of the rate expression with the experimental data. Parameter Limits. If the 95% confidence interval (eq 3) or 95% confidence region (eq 4) includes zero value for one of the parameters, it is doubtful whether this parameter is necessary in the rate expression. Physicochemical Constraints. For a rate expression to be of fundamental significance, the temperature dependency of the parameter estimates must follow the laws of thermodynamics with respect to the enthalpy and entropy changes of the relevant elementary processes as well as to the activation entropy and energy. The activation energy of the rate-determining process must be positive. For the standard entropy and enthalpy of adsorption, dissociative as well as nondissociative, Boudart et al. (1967), Boudart (1972), and Vannice et al. (1979) derived certain rules and guidelines. The rules and guidelines which must be satisfied are presented in Table I. In some kinetic studies of the metathesis of propene (Luckner et al., 1973; Hattikudur and Thodos, 1974) the adsorption enthalpy of propene turned out to be positive for the selected Langmuir-Hinshelwood model, a physically meaningless result. Statistical Analysis of the Experimental Data Propene Feed. For the experiments with pure propene feed the results of the minimization procedure applied to expressions (a), (b), and (c) (Table 11) point out a better correlation of these data by expressions (b) and (c) over (a), the Langmuir-Hinshelwood model. The mean (SSR) values, (SSR)/(N- p ) , for expressions (b) and (c) appear to be the same. This can be explained by the fact that parameter K 1in expression (b) approaches infinity, so mathematically expression (b) reduces to expression ( c ) . Physically this would mean that in the steady state tF e
l o 8 )for Initial Rate Expressions. Numbers in Parentheses Are the Numbers of
expression (a) (b), ( c ) (6) (7) (7Y (9)
313 K 0.83 0.64 0.45 0.41
(27) (27) (17) (16)
323 K 2.30 0.96 1.3 1.1 0.14 0.10 3.4 1.9
(89) (89) (98) (97) (16) (15) (16) (15)
temperature 343 K 3.00 0.71 2.6 1.5 0.38 0.24 10.5 2.0
(66) (66) (58) (57) (16) (15) (16) (15)
373 K 9.0 2.2 1.6 0.65 1.2 0.63 19 1.4
(79) (79) (53) (52) (16) (15) (16) (15)
403 K 15 3.6 32 9.7 2.6 2.6 43 6.1
(10) In these minimizations parameter k was kept fixed at the value obtained from the regressions of the experiments with propene and propene + ethene feed in order t o obtain realistic parameter estimates. a
Ind. Eng. Chem. Prod. Res. Dev., Vol. 20, No. 3, 1981 481 Table 111. Lack-of-Fit Test for Expressions (a) and (c)
T,K
expression
a
107(SSR) d.f.'
18.3 (a) 323 16.2 (a) 343 66.3 373 (a) 8.19 (c) 3 23 3.98 (c) 343 15.6 (c) 373 Number of degrees of freedom.
67 44 62 67 44 62
10'(SSE)
d.f.
6.30 2.82 14.3 6.30 2.82 14.3
58 37 52 58 37 52
'8
t -1
12.0 13.4 52.0 1.89 1.16 1.35
9 7 10 9 7 10
12.3 25.0 18.9 1.93 2.17 0.49
significant lack-of-fit
2.04 2.25 2.04 2.04 2.25 2.04
t
+ + -
-
Table IV. Estimates of Diagnostic Parameter h and Its 95% Confidence Limits feed
'1 I
mean (SSL) 107(SSL) d.f. mean (SSE) F(v,,v,,0.95)
0 0
T,K
propene and ethene
propeneand 2-butene
313 3 23 343 373 4 03
0.45 f 0.47 * 0.54 f 0.49 f 0.42 f
0.51 * 0.54 * 0.53 * 0.39 i
0
0
8:
i,
:I
0
0
0
I
0
0
I
0
a
!
I
i
0
0.2
0.4 pp
1 MPal
0.58 0.53 0.31 0.21 0.43
0.79 0.63 0.52 2.3
terms. This means that (c-1) and (12-2)reduce to eq 6 and (c-3) and (c-4) to eq 7.
+
kKPPP2
ro (= r2) = PP
(7)
+ K P P P+ ~ KE(B)PE(B) + KPE(B)PPPE(B)
For a selection of one of these two rate expressions, another quantitative method of discriminating between rival models was applied. This method is based on the use of a nonintrinsic diagnostic parameter X (Mezaki and Kittrel, 1966). For the case of two rival models, this parameter is defined through eq 8 r = (X + f/z)r2- (A - Y2)r1 (8) where r is a newly defined reaction rate, while rl and r2 are reaction rates calculated with the nonlinear leastsquares estimates of the parameters in the two expressions under consideration. The value of X is estimated by linear least-squares minimization. If r1 is the correct expression, then h should be -lI2, while if r2 were adequate, X should be +1/2. If the confidence interval for X contains both these values, no decision can be made about the most adequate model. Table IV summarizes the linear least-squares estimates of X at each temperature studied, together with their 95% confidence limits, applied to the minimization results of eq 6 and 7. Except for the highest temperature studied in the case of mixed propene/2-butene feed, all results indicate a significant preference for eq 7. Trending effects can be noticed in the residual distribution as a function of the partial pressures of propene and ethene for eq 6 (Figure 9A), whereas the residuals for eq 7 are evenly distributed around the zero axis over the whole pressure range (Figure 9B). The examination of the residuals of the minimizations for the experiments with mixed propene/2-butene feed needs some caution. Owing to the low vapor pressure of 2-butene, the experiments could only be carried out over a small pressure range. Therefore, trending effects may be ascribed partly to a lack of sufficient data (Figure 10A and B). It can be concluded that for both ethene/propene and 2-butene/propene feed from a statistical point of view eq 7 correlates our experimental data better than eq 6 does. This indicates that the pressure terms p p p ~and p p p ~
' I
-1
0
0.2
0.4
Figure 8. Plot of the residual initial reaction rate vs. propene pressure for expression (a) (top), and for expression (c) (bottom). Temperature, 373 K; feed, propene.
are no unoccupied active sites at the catalyst surface; Le., model I1 passes into model 111. A lack-of-fit test was applied to the results of the experiments at 323,343, and 373 K which contain sufficient replicated data points over several kinetic runs. The (SSR) values given in Table I11 are somewhat lower than those given in Table 11, because these values only contain the contributions of at-least-three-times replicated settings of the partial propene pressure. It is clear that expression (a) shows a significant lack-of-fit, which cannot be concluded for expression (c). Representative plots of the residual initial reaction rate vs. the partial propene pressure at 373 K exhibit a large trending effect in case of expression (a). This trending is absent in case of expression (c) (Figure 8). These results lead to the conclusion that only expression (c) gives an adequate description,of the experimental data (Figure 7). On the basis of this statistical analysis the Langmuil-Hinshelwood model turns out to be an improper model for the metathesis of propene over our catalyst. Mixed Feed. The results of the initial-rate experiments with mixed feed (propene + ethene or propene + 2-butene) were correlated with the rate expressions obtained from expressions (c-1) to (c-4) by neglecting the proper pressure
I
1-
- ro
ro
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ro - ro
1
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.
md/s kg
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t
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e
t
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