Ind. Eng. Chem. Res. 1993, 32, 34-42
34
V/Ti02 = titanium oxide-supported vanadium oxide percentage by weight
wt % =
Literature Cited Behrens, R.; Umland, F. Phase Transformation of Titanium Dioxide in the Preparation of Titanium Oxide-Vanadium Oxide Electrodes for Complexometric Titration. J . Less-Common Met. 1988, 137, 353-365. Gasior, M.; Gasior, I.; Grzybowska, B. O-Xylene Oxidation on the V205-Ti02Oxide System. I. Dependence of Catalytic Properties on the Modification of TiOz. A p p l . Catal. 1984, 10, 87-100. Machej, T.; Ruiz, P.; Delmon, B. Studies on the V2O5-TiOZsystem. Part 3.-Monolayers of V205. J. Chem. SOC.,Faraday Trans. 1990, 86 (4), 731-738. Paulik, F. E. Recent Developments in Hydroformylation Catalysis. Catal. Reu. 1972, 6, 49-84. Roozeboom, F.; Mittelmeijer-Hazeleger, M. C.; Moulljn, J. A.; Medema, J.; de Beer, V. H. J.; Gellings, P. J. Vanadium Oxide
Monolayer Catalysts. 3. A Raman Spectroscopic and Temperature-Programmed Reduction Study of Monolayer and CrystalType Vanadia on Various Sumorta. J. Phvs. Chem. 1980, 84. 2783-2791. Saleh, R. Y.; Waches, I. E.; Chan, S. S.; Chersich, C. The Interaction of V205with TiOz(Anatase): Catalyst Evolution with Calcination Temperature and o-Xylene Oxidation. J. Catal. 1986, 98, 102-114. Van Hengstum, A. J.; Van Ommen, J. G.; Bosch, H.; Gellings, P. J. Selective Gas Phase Oxidation of Toluene by Vanadium Oxide/ Ti02Catalysts. Appl. Catal. 1983, 8, 369-382. Wang, F.; Lee, W. Catalytic Synthesis of Isobutyraldehyde from Methanol and Ethanol over Titanium Oxide-supported Vanadium Oxide Catalysts. J . Chem. SOC.,Chem. Commun. 1991, 24, 1760-1761.
__
Receiued for review May 7, 1992 Revised manuscript received September 24, 1992 Accepted October 19, 1992
Kinetics of Toluene Hydrogenation on a Supported Ni Catalyst Lars Peter Lindfors Neste Oy, Oil Research, Technology Centre, P.O.B. 310, SF-06101 Borgci, Finland
Tapio Salmi* Laboratory of Industrial Chemistry, Abo Akademi, SF-20500 Abo, Finland
The gas-phase hydrogenation of toluene to methylcyclohexane was studied on a noncommercial supported nickel catalyst. The reaction kinetics was investigated in a differential reactor operating a t atmospheric pressure and temperatures between 120 and 200 "C. The results revealed that the hydrogenation kinetics is of the order 0.5-2 with respect to hydrogen and that the reaction order increases with temperature. The reaction order with respect to toluene increases from slightly negative values to zero order over the temperature domain studied. The kinetics was modeled with an empirical power-law rate expression and with two mechanistic rate models. The latter models were based on the assumption of rapid competitive adsorption steps of toluene and hydrogen and rate-determining surface reaction steps involving addition of hydrogen atom pairs to adsorbed toluene and partially hydrogenated intermediate molecules. The surface coverages, the activation energy, and the optimal reaction temperature giving the maximum reaction rate were estimated using parameter values obtained from one of the mechanistic models.
Introduction Hydrogenation of aromatic hydrocarbons to cyclic products is of current interest due to both environmental aspects and the wide range of industrial processes involving such reactions. Benzene hydrogenation has been used as a model system in several studies, and the hydrogenation kinetics as well as the benzene adsorption on heterogeneous catalysts has been widely studied (Canjar and Manning, 1962; Erkelens and Eggink-Du Burck, 1969; Franco and Phillips, 1980; Germain et al., 1963a,b;Hartog et al., 1965; Jiracek et al., 1968; Kehoe and Butt, 1972; Kishi et al., 1979; Marecot et al., 1991; Marangozis et al., 1979; Minot and Gallezot, 1990; Mirodatos et al., 1987; Motard et al., 1957; Nicolai et al., 1948; Orozco and Webb, 1983; Roethe et al., 1970; Rooney, 1963; Selwood, 1957,1962;Shopov et al., 1968; Snagovskii et al., 1966; Tetenyi and Babernics, 1967; Tetenyi et al., 1969; van Meerten and Coenen, 1975, 1977; van Meerten et al., 1976, 1977; Zlotina and Kiperman, 1967). However, controversial results are found in the literature regarding the reaction mechanism. For example, the nature of the active sites and the role of hydrogen and the aromatic compounds in adsorption and reaction kinetics are still somewhat uncertain. The experimental data available on toluene hydrogenation kinetics as well as the reported adsorption studies of toluene on heterogeneous catalysts are very sparse and
contradictory (Baiker and Bergougnan, 1985a,b; Klvana et al., 1988; Minot and Gallezot, 1990; Orozco and Webb, 1983; Rahaman and Vannice, 1991a,b). Rahaman and Vannice studied the hydrogenation of toluene on Pd powder and dispersed Pd on metal oxides. They detected a maximum reaction rate at 197 O C for a Pd/MgO catalyst, and reaction orders of zero and one were observed for toluene and hydrogen, respectively. They proposed a kinetic model with noncompetitive adsorption of hydrogen and toluene. Adsorption on separate sites was also proposed by Klvana et al. (1988), who studied toluene hydrogenation on a silica-supported nickel catalyst at atmospheric pressure and 363-423 K. They found that the reaction might be of zero order with respect to both reactants, and they proposed a Langmuir-Hinshelwood kinetic model, where the surface reaction between the reactants was assumed to be rate determining. Orozco and Webb (1983) studied the adsorption and hydrogenation of benzene and toluene on alumina- and silica-supported palladium and platinum catalyta at temperatures between 378 and 608 K. They found that the activity of all catalysts passed through a maximum as the temperature was increased and that toluene was more readily hydrogenated on both metals. The sites for the adsorption and hydrogenation of benzene and toluene were suggested to be different. Lindfors and Salmi (1992) studied the kinetics
Q888-5885/93/2632-OQ34$04.OO/Q 0 1993 American Chemical Society
Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 35 of toluene hydrogenation on a commercial Ni/A1,03 catalyst. The hydrogenation kinetics was of the order 1-3 with respect to hydrogen and of slightly negative order with respect to toluene. Rate models based on the assumptions of rapid competitive adsorption steps of toluene and hydrogen and rate-determining surface reaction steps involving addition of hydrogen atoms to adsorbed toluene and partially hydrogenated intermediate molecules provided the best fit to the experimental data. In this work a new noncommercial nickel catalyst will be studied in toluene hydrogenation.
Experimental Section Chemicals. In the present work gas-phase hydrogenation of toluene to methylcyclohexane was studied on a noncommercial laboratory-scale Ni/A1203 catalyst prepared from the vapor phase. Toluene of analytical grade was obtained from the J. T. Baker Co. Hydrogen and nitrogen (99.999%) were supplied by AGA. Reactor and Experimental Setup. The experimental setup was the same as in our study of toluene hydrogenation on a commercial Ni catalyst (Lindfors and Salmi, 1992). The crushed catalyst particles were placed in a laboratory-scale fixed bed reactor operating at atmospheric pressure and differential conversions of toluene and hydrogen. The toluene and methylcyclohexane contents of the product gas were analyzed by a gas chromatograph equipped with a flame ionization detector. Experimental Procedure. The experiments were carried out at a constant total molar flow of 0.61 mol/h, at atmospheric pressure, and at temperatures ranging from 120 to 200 "C. In order to avoid heat- and mass-transfer limitations as well as to suppress the effect of the reverse reaction on the kinetics, differential conditions were used, the conversion of toluene being less than 6%. The kinetic runs were carried out at 120,135,150,170,185, and 200 "C. The partial pressures of toluene and hydrogen were varied between 0.12-0.32 and 0 . 4 0 . 8 1 atm, respectively. Seven experimental observations were obtained at each temperature. The reproducibility of the measurements was checked by making two separate experiments for each data point. The average experimental error in the reaction rates was approximately 5 % . The absence of mass-transport limitations was checked by the Weisz-Prater criterion (Fogler, 1986). The catalyst was reduced in situ at ambient pressure by flowing hydrogen as the temperature was increased to 510 "C. The hydrogen flow was continued at 510 "C for 2 h at a flow rate of 0.5 m o l / h. Then, the reactor was cooled to the temperature of the kinetic run under the same hydrogen flow. As the temperature was stabilized, the flow rates of hydrogen, toluene, and nitrogen were adjusted to their values and the gases were fed to the reactor. After 30 min the steady-state conditions were achieved and the exit gas stream was analyzed. After the experiment, the toluene flow was interrupted and the catalyst was flushed with hydrogen at 400 "C for 2 hours, after which the temperature was adjusted to the temperature of the kinetic run. Thus, the same catalyst loading was used in all experiments. In this way, the possible deviations in the kinetic results caused by catalyst packing were eliminated. It was found that reproducible results were obtained in the kinetic runs and that no deactivation occurred. Therefore, we believe that the catalyst was studied at a similar state throughout the kinetic study, due to the hydrogen flushing between the experiments. Analytical Methods used in the Catalyst Characterization. The bulk concentration of nickel in the catalyst was determined by X-ray fluorescence (XRF). Very
Table I. Catalyst Characteristics nickel surface area total pore vol av pore (crn3/g) diam (A) (wt 70) (m2/g) noncommercial 9.5 144 0.44 123 supported Ni catalyst alumina carrier 152 0.47 125
small amounts of Si and Fe were detected ( 6 0 0ppm) in the support. No further impurities were found on the prepared catalysts. Prior to the XRF analysis, standards were made for the Ni/A1,03 system using commercial nickel compounds and the alumina used in the preparation of the catalysts. The comparison between experimental and calculated results for the standards proved that the method was reliable for nickel concentrations covering the nickel content in the studied catalyst. Physical properties were studied by means of nitrogen adsorption and condensation. The surface area (BET), the average pore radius, as well as the pore volume and pore size distribution were determined. The size of the nickel species was studied by X-ray diffraction (XRD). The particle size of XRD crystalline compounds was calculated using the Scherrer formula from peaks showing high intensity. The surface composition and the binding states of the surface species were characterized by X-ray photoelectron spectroscopy (XPS)using a spot size of 300 pm. By embedding the catalyst particles in an epoxy resin and then cutting the samples, the nickel penetration into the center of the particles was investigated. First, the surface containing the randomly cut particles was studied by scanning electron microscopy. This was done in order to verify that the characterized particles were properly cut in order to study the penetration of nickel into the alumina particles. Thereafter, the sample was analyzed by X-ray mapping with scanning electron microscopy-energy dispersive spectroscopy (SEM-EDS) and electron backscattering. The accelerating voltage used was 20 keV.
Results and Discussion Physical Properties of the Catalyst. In Table I the characteristics of the catalyst are shown. The physical properties of the catalyst as compared to the alumina used in the preparation of the catalyst are presented. XRD and XPS studies were also carried out on the catalyst before and after the kinetic runs. The nickel species were found to be XRD amorphous, and the nickel content detected on the surface of the catalyst by means of XPS correlated well with the bulk content on both the fresh and used catalyst. These results, indicating highly dispersed nickel species well distributed throughout the catalyst particles, agreed well with the X-ray mapping along with the electron backscattering, showing that the intensity for nickel was evenly distributed throughout the randomly cut particles. Hydrogenation Kinetics. Methylcyclohexanewas the only product detected; no partially hydrogenated intermediates could be observed. The reaction rate increased with an increasing partial pressure of hydrogen, whereas the reaction rate decreased slightly with an increasing partial pressure of toluene. The observed reaction rates as a function of the partial pressures of the reactants are shown in Figures 1and 2. The qualitative behavior of the reaction rate was similar throughout the temperature domain studied, and it correlated to some extent with our previous study on a commercial Ni/A1203 catalyst. A maximum in the reaction rate was observed at -175 "C, and at temperatures of 170 and 185 "C approximately equal reaction rates were observed. At temperatures below
36 Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993
.s
P A
j
2: 26
Table 11. Comparison of the Rates of Toluene Hydrogenation on a Commercial and a Noncommercial Catalyst rrxp
catalyst commercial supported nickel catalyst, Ni content -60 wt %
24 22 2
noncommercial supported nickel catalyst, Ni content -10 wt 5%
18
15 l A
(mol/kNi 5.4 X 6.4 X 5.2 X 13.0 X 21.4 X 19.6 X
8))
T ("c) P'T 150 171
192 150 170 186
0.20 0.20 0.19 0.18 0.18 0.18
PH
0.68 0.68 0.69 0.61 0.61 0.61
1 2
OS
06 0 4
0 2
1
I
03
05
09
0 7
pH/atm
Figure 1. Effect of hydrogen partial pressure on the reaction rate (pT= 0.12) a t 120 (VI, 135 ( X ) , 150 (A),170 (e),185 (+),and 200 " C (m). 2
*
-
*
* i
I 1
0 4
,
02
c
'2
,
, 0 16
,
I
0 20
,
, 0 24
0
ze
i
0 32
PT/atm
Figure 2. Effect of toluene partial pressure on the reaction rate (PH = 0.60) a t 120 (V),135 (X), 150 (A),170 (e),185 (+), and 200 O C
(W.
170 and above 185 "C, the rate of reaction decreased. This behavior was not caused by thermodynamic limitations; for the minimum molar ratio of hydrogen and toluene used in this study, Le., 1.75, the equilibrium conversion of toluene to methylcyclohexane at 200 "C is above 40%. A maximum turnover frequency has been reported by Orozco and Webb (1983) over alumina- and silica-supported platinum and palladium catalysts and by M a m a n and Vannice over palladium (1991a). In the hydrogenation of benzene on nickel a similar behavior has been reported by several authors (Franc0 and Phillips, 1979; Germain et al., 1963a,b; Herbo, 1941; Motard et al., 1957; Nicolai et al., 1948; van Meerten and Coenen, 1975). The maximum in the observed reaction rate as a function of temperature can-if it is not real-be due to thermodynamic limitations or catalyst deactivation. Referring to our calculations and testing procedure, we believe that our rate data are reliable over the temperature range studied. The observed rate maximum is obviously due to the opposite effects of the rate constant and the adsorption equilibrium constant included in an overall rate expression. Despite the similarities in the qualitative observations of the kinetics on the noncommercial and the commercial catalysts previously studied by us, it is interesting to notice the differences in their activities. In Table 11, the experimental reaction rate (redcalculated per gram of nickel on the catalyst is shown at various temperatures and partial pressures of hydrogen and toluene.
Table 111. Parameters for the Power-Law Rate Toluene Hydrogenation" T ( " C ) i05k' rn n WSRS 0.208 0.577 -0.430 120 0.0068 0.461 135 0.347 -0.333 0.0565 151 1.113 0.306 -0.152 0.0693 2.758 -0.061 171 0.943 0.2315 -0.006 186 4.378 1.715 0.2022 -0 3.502 1.887 0.2073 200
Model of
MRS 0.00062 0.00513 0.00630 0.02105 0.01838 0.018 85
Or = k'pHmpTn.k'= [ ] atrn+"") mol/(g s) X lo5. MRS = mean residual square. WSRS = weighted sum of residual squares.
As can be seen from the table, the activity of the noncommercial catalyst is approximately 4 times higher than that for the commercial catalyst when the rate of reaction is defined on the basis of the nickel content. The observed higher activity is probably due to a more efficient usage of the nickel species, since it contains approximately one-sixth of the nickel present on the commercial catalyst. In a study by Marecot et al. (1991), benzene hydrogenation on nickel catalysts prepared by various methods was studied. Their conclusion was that benzene adsorption and hydrogenation activity depends on the method used for catalyst preparation and more particularly on the nature of the nickel precursor. Power-Law Model for Hydrogenation Kinetics. The modeling of the reaction kinetics was started by fitting an empirical power-law rate model to the experimental data,
r = kbHmpTn
(1)
where k' denotes the apparent rate constant and m and n are the empirical exponents of hydrogen and toluene, respectively. The parameters of the model (k', m,and n) were determined at 120, 135, 151, 171, 186, and 200 "C using the nonlinear regression program package Reproche (Vajda and Valko, 1985). The Levenberg-Marquardt method was used to minimize the weighted sum of residual squarea between the observed and estimated reaction rates. The values of the exponents for hydrogen and toluene partial pressures are shown in Table I11 along with the value of the apparent rate constant and the mean residual square and weighted sum of residual squares. The relative deviation of the calculated reaction rates from the experimental was -5% for most data points. In contrast to our results in toluene hydrogenation the inhibitory effect of the aromatic compound has not been observed in benzene hydrogenation; only positive rate exponents of benzene are reported in the literature. One possible explanation is that the methyl group attached to the aromatic ring influences the adsorption strength and hydrogenation rate. Indeed, Minot and Gallezot (1990), in their study of the competitive adsorption and hydrogenation of benzene and toluene on ruthenium, rhodium, and palladium, concluded that toluene is more easily adsorbed than benzene. The distortions allow the methyl substituent to stand away from the surface. The adsorption energy barrier is lower and the adsorption well is deeper. Orozco and Webb (1983) also studied the adsorption and hydrogenation of these aromatic compounds
Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 37 on alumina- and silica-supported palladium and platinum catalysts. They found that both dissociative and associative adsorption of the aromatics takes place. In other studies similar proposals have been made for the adsorption of benzene (Marecot, 1991; Tetenyi and Babernics, 1967; van Meerten et al., 1976). Orozco and Webb (1983) suggest that the dissociative adsorption leads to the formation of retained species, while the species active in hydrogenation are associatively adsorbed. In the hydrogenation of mixtures of benzene and toluene, toluene was found to be more readily hydrogenated over both metals. They propose that the sites for adsorption and hydrogenation of benzene are different from those for toluene. The rate exponent of benzene is claimed to increase from low values (-0) at temperatures below 100 "C to approximately 0.5 at temperatures between 150 and 250 "C in several studies. The observed toluene hydrogenation kinetics as well as the exponents of the empirical rate law (1)indicate that toluene and hydrogen adsorb competitively on the same type of active sites on the Ni catalyst and that the adsorption of toluene is quite constant throughout the temperature range, whereas hydrogen adsorption decreases with increasing temperatures, especially at the highest experimental temperatures. It should be emphasized that competitive adsorption of the aromatic molecule and hydrogen has been presumed by some previous investigators in benzene hydrogenation (Germain et al., 1963; Motard et al., 1957). In our study of the commercial catalyst (Lindfors and Salmi, 1992), the empirical exponent of hydrogen increased from -1.3 to -3.3 and the exponent of toluene decreased from -0.7 to -1.6 as the temperature was increased from 150 "C to 210 "C. When these results are compared with the values for the noncommercial catalyst shown in Table 111, the behavior regarding hydrogen is similar. However, the exponent increases from a lower value of -0.3 to -1.9 when the temperature increases from 150 to 200 "C. For toluene the negative value of the exponent changes from -0.3 to 0 in the same temperature interval. These values of the exponents indicate that toluene forms weaker bonds with the noncommercial catalyst than with the commercial catalyst studied previously. Thus, the value of the hydrogen exponent is more moderate and the rate of reaction higher. Probably a surface reaction step between adsorbed hydrogen and toluene-or an adsorbed partially hydrogenated intermediate molecule-is rate determining. Approximation of the Activation Energy Based on the Apparent Rate Constant. In Figure 3, the Arrhenius plot based on the apparent rate constant is shown for the temperatures ranging from 120 to 170 "C, i.e., in the region where the reaction rate increases steadily. From the slope of the four data points corresponding to 120,135,151, and 171 "C, the apparent activation energy can be approximated to be 75 kJ/mol. In the literature, the data available on activation energies in the gas-phase hydrogenation of toluene on supported nickel catalysts are very sparse. Roas et al. (1975) reported activation energies of approximately 60 kJ/mol on silica-supported nickel catalysts at 90 "C. Klvana et al. (1988) reported an activation energy for the hydrogenation over a nickel/silica aerogel catalyst in integral flow conditions at temperatures between 90 and 150 "C to be -47 kJ/mol, whereas an activation energy of -57 kJ/mol was reported by Volter (1964) in the hydrogenation over a Ni/MgO catalyst at temperatures ranging from 90 to 200 "C. Models Based on Reaction Mechanisms. Basic Assumptions. In order to obtain mechanistic models, the
-
-
-
-
12
-
02
-
-04
-
-06
-08 -1
-12 -1 4
-16
loo00 J/mol/(RT)
Figure 3. Arrhenius plot based on the apparent rate constant derived from the power-rate law model r = k ' p ~ " ' p ~ " .
following basic assumptions are applied concerning the reaction mechanism: toluene and hydrogen adsorb competitively on similar types of sites; adsorption of hydrogen is dissociative and rapid; adsorption of toluene is nondissociative and rapid; equal numbers of adsorption sites are needed for toluene and hydrogen; the surface reaction steps are rate determining; desorption of methylcyclohexane is rapid. Detailed reaction mechanisms and corresponding rate equations require further assumptions concerning the surface reaction steps. In this study, two basic alternatives for the surface reactions are proposed: a simultaneous model and a sequential model. In the simultaneous model, the addition of hydrogen atom pairs to an adsorbed toluene molecule is presumed to occur simultaneously. In the sequential model, the surface reaction is supposed to proceed through stepwiae addition of hydrogen atom pairs to adsorbed toluene and to the partially hydrogenated intermediates. All addition steps are assumed to proceed with equal rates, thus contributing to the overall kinetics. Rate Equutions for the Simultaneom Model. When the hydrogen atoms are added simultaneously to an adsorbed toluene molecule, the reaction steps can be written as follows: Hz + 2* + 2H* (2) T+**T* (3) (4) T* YH* P* Y*
+
-
+
P* + (6 - Y)H* MCH + (7 - Y)* (5) where T, P, and MCH denote toluene, a surface intermediate, and methylcyclohexane, respectively. In eqs 2-5 Y denotes the number of hydrogen atoms reacting in the +
rate-determining surface reaction step. P* denotes adsorbed methylcyclohexane in this case. Toluene and hydrogen are assumed to be the most abundant surface intermediates. For the adsorption steps (2) and (3) the quasi-equilibrium approximation implies that the surface coverages of hydrogen (0,) and toluene (0,) are expressed with the fraction of vacant site (ev):
KH e H 2 / ( p H e v 2 ) KT = ~ T / @ T W
(6) (7) The reaction rate (r) is determined by the surface reaction step (4):
38 Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993
r = keTeHY
(8)
The site balance for the system is given by eT + O H + 8,= 1
(9)
By expressing the surface coverages e T and e H with 8, using eqs 6 and 7 and then inserting these expressions in eq 8, the rate equation is expressed by means of 8,. An analytical solution for 0, is obtained by inserting the expressions for the surface coverages of hydrogen and toluene into eq 9. By combining these expressions for e,, the final rate equation for Y = 6 becomes
r = (kKTKH3P'$H3)/(KTPT
+ (K@H)'" +
(10)
The derivation was based on dissociative adsorption of hydrogen. A similar form of rate equation is obtained if the adsorption of hydrogen were supposed to be nondissociative. A rate equation analogous to (10) is obtained, the only difference appearing in the denominator; the exponent gets the value 4, and the term (K@H)":' is replaced by K@H. Rate Equations for the Sequential Model. If the addition of hydrogen atom pairs is assumed to occur sequentially, we arrive at the following reaction mechanism: H2 + 2* == 2H* (2) T+*=T*
(3)
+ 2H* + TH2* + 2* TH2* + 2H* TH4* + 2* TH4* + 2H* + TH6* + 2* TH6* MCH + *
(11)
T*
-
(12) (13)
(14)
where TH2*, TH4*, and TH6* denote the hydrogenated surface intermediates. The adsorption quasi-equilibria of hydrogen and toluene, eqs 6 and 7,are assumed to be valid also here. Each of the surface reaction steps 11-14 proceeds with an equal velocity ( r ) ,and steps 11-13 are assumed to have equal rate constants. The rates of steps 11-14 are thus given by:
r = k + 8 T 8 H 2 - k-eTH2ev2
(15)
r = k + 8 T H 2 0 H 2 - k-eTH4ev2
(16)
r = k + 8 T H 4 0 H 2 - k-eTH6e:
(17)
For desorption of methylcyclohexane from the catalyst surface holds
r = kdeTH6
(18)
After using the site balance and eliminating the fractional coverages of the intermediates by setting eqs 15-18 equal and assuming the desorption of methylcyclohexane to be rapid, the final rate equation is obtained:
r = (k+(k+/k-)2KTKH3pTpH3)/ [((kJH/k-)2pH2+ (k+KH/k-)pH + 1)(KTPTo + (K@H)":' + iI3i (19) where ( ) represents
0 = [(I + 2(kaH/k-)pH + 3 ( k J ~ p ~ / k - ) ~ ) / (+1 (k&H/k-)PH
(~JI$H/~-)~)I
(20)
Depending on the magnitude of parameter k+KH/k-,further simplifications of eq 19 can be made. If the parameter value is small-which is expected at high temperatures,
Table IV. Parameters for the Simultaneous Model-Simultaneous Addition of Hydrogen to Toluene" T ( O C ) KH KT ~ K T K H ~ 105k WSRS MRS 22.8 0.0096 O.OOO9 120 31.79 7.41 0.54 X 10' 28.3 0.1013 0.0092 135 95.48 10.72 0.26 X lo4 52.2 0.0407 0.0037 151 81.29 8.30 0.23 X lo4 0.0738 0.0067 474 171 5.72 2.68 0.24 X lo-' 0.2469 0.0224 0.59 1.34 0.34 X lo-' 12500 186 0.1153 0.0105 200 0.30 1.14 0.11 X 10.' 34400
kKTKHY12= [ ] atm'-"Y/2) mol/(g atm-'. k = [ ] mol/(g s) X IO5. Table V. Addition T ("C) 120 135 151 171 186 200
9).
KH = [ ] atm-I. KT = [ ]
Parameters for the Sequential Model-Sequential of Hydrogen to Toluene" Ku K , (k+/k.)Kw k+(k+lk.)'KrKu3 WSRS MRS 0.0075 0.0007 80.2 0.913 X 10' 1.26 3.11 104 0.145 X lo3 0.0820 0.0082 8.60 4.80 4.64 0.567 X 10' 0.0383 0.0038 338 19.9 0.0782 0.0078 13.4 5.82 1.58 0.300 0.2294 0.0229 1.56 0.435 X 10.' -0 1.33 1.06 -0 1.41 0.216 x 0.1259 0.0126
ok+(k+/k.)2KH3KT= [ I atm-' mol/(g s). KH = [ I atm-I. KT = [ atm-'. ( k + / k . ) K , = [ ] atm-I.
since KH and probably also k + / k - decrease with an in creasing temperature-it is discarded from eq 19 and the rate equation becomes
r = (k+(k+/k-)2K'rKH3pTpH3)/(KTPT + (KGH)":'
+ (21)
On the other hand, if parameter k+KH/k- is large-which is obviously true for low temperatures, where the adsorption of hydrogen is noticeable and the effect of the reverse surface reactions are negligible-the term (20) approaches the value 3 and the rate equation is simplified to = (k+KTK@TPH)/(QKTPT+ (K@H)":'
+
(22)
If nondissociative adsorption of hydrogen were assumed, the exponent in the denominators of eqs 19, 21, and 22 would be 2 and the term (K@H)0'5would be replaced by KgH. Thus the character of hydrogen adsorption has only a minor effect on the rate equation, and it would be an impossible task to base the conclusions of the true form of hydrogen adsorption on the experimentally measured hydrogenation kinetics solely. Parameter Estimation. In the kinetic models presented above the rate and equilibrium parameters were determined by parameter estimation. The parameters to be estimated in the simultaneous model were KH,KT and kKTKH3. In the sequential model the estimated parameters were KH, KT, (k+/k-)K~, and k+(k+/k_)'KH3KT,The number of experiments (N) was 14 at all temperatures. The estimation of the rate and equilibrium parameters was performed by minimization of the sum of residual squares. The minimization of the residuals in the rate data was carried out separately at each temperature using the object function: WSRS = c[w,(rI,exp- rr,ca,J2I
(23)
where WSRS denotes the weighted sum of residual squares. An equal weight (w,)was given to every experiment in the estimation. The minimization was carried out numerically using the Marquardt-Levenberg method adopted to the kinetic nonlinear regression program package Reproche (Vajda and Valko, 1985). The algebraic model option of the program was used; the hydrogen and toluene partial pressures were the independent variables and the experimental reaction rate was the dependent variable.
Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 39
0.8
a)
I
\
0.75
0.7
0.65
0.6
0.55
o
1.1 s
0.56
7 ~
,
I
I
0.6
I
0.64
I
I
0.68
I
I
,
0.72
,
0.76
I
1
0.8
I
-2 21
2 2
2 3
2 4
;t
IOW K l l
Figure 5. Temperature dependence of the adsorption parameters (KH, W; KT, 0 ) and the rate constant (k, * ) according to the simultaneous model.
0.45
0.2
0.15 0.1
0.1
0.2
0.3
0.4
0.5
0.26
0.25 0.24 0.23 0.22 0.21 0.2
0.19 0.18
0.17 0.16 0.15 0.14
0.13
0.12
rob8
Figure 4. Experimental and calculated reaction rates according to the simultaneous (w) and sequential model ( 0 )at 135 (a), 170 (b), and 200 O C (c).
Fits of the Simultaneous and Sequential Models. The results of the regression analysis are summarized in Tablea IV and V, which give the parameter values included in the simultaneous and the sequential models, respectively. In the regression analysis the value Y = 6 (eq 4) showed to give the best fit to the data in the simultaneous model; therefore only the case Y = 6 is considered here. From Table IV some unexpected behavior can be seen for the parameter KH at the lower temperatures. The fluctuation in the parameter values is due to a correlation between the parameters KH and kKTKH3. For the sequential model, a stronger correlation between the parameters is expected, because of the mathematical struc-
ture of the model. Indeed, as can be seen from Table V, the behavior of especially the parameters KH and (k+/ k-)KH in the model seem quite uncertain at the three lowest temperatures. The estimation of four parameters from the current data is reflected in large standard deviations of the parameters and high correlation coefficienb between them. However, the overall behavior for the parameters is reasonable. The experimental vs calculated reaction rates at 135, 171, and 200 "C for the two models are shown in Figure 4. In a mathematical sense, the models give an almost equally good description of the data; the deviations between rdc and rexpare mainly caused by experimental uncertainty. Similar plots were obtained when the observed vs calculated rates were studied at the temperatures 120, 151, and 186 "C. Comparison between the Empirical and the Mechanistic Models. A statistical comparison of the mechanistic models with the empirical power-low model reveals that the mechanistic models well describe the experimental data, as can be seen from Figure 4. At 120 and 136 "C, the empirical model gives a slightly smaller s u m of residual squares than the mechanistic models, whereas the mechanistic models give a better fit at the temperatures close to the rate maximum, i.e., between 150 and 700 "C. Temperature Dependence of the Adsorption Parameters and Rate Constants in the Simultaneous Model. Since the two mechanistic models showed an equally good representation of the experimental rate data, as can be seen in Figure 4 and Tables IV and V, the temperature dependence of the parameters of the simultaneous model were studied because of its more friendly mathematical structure, involving one parameter less than the sequential model and thus having less strongly correlated parameters. As can be seen from Table IV, the behavior of the adsorption parameters KH and KT and the rate constant k is thermodynamically consistent at temperatures between 135 and 200 O C . In Figure 5, the logarithms of the constants are plotted against the reciprocal temperatures between 135 and 200 "C. The adsorption constants for both hydrogen (KH) and toluene (KT) decrease with an increasing temperature, whereas the rate constant k increases with temperature. Temperature Dependence of the Adsorption Parameters KHand KT.In order to obtain a mathematical expression for the temperature dependence for the adsorption parameters between 135 and 200 "C, nonlinear
40 Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 Table VI. Comparison of the Observed and Estimated Adsorption Constants
T ("C) 135 151 171 186 200
In
KH,obs
4.559 4.398 1.744 -0.527 -1.186
To,, 'C
In K H , ~ ~ ln ~K T , ~ ~In K T . ~ ~ ~ 4.689 3.016 1.093 -0.239 -1.406
2.372 2.116 0.986 0.294 0.130
2.462 1.781 0,998 0.456 -0.019
regression was used. By inserting the parameter values shown in Table IV into eq 24, the temperature dependence of the adsorption parameters was obtained: KH,T = A ' exp(-AH/RT) (24) where A'is exp(AS/R). The obtained correlations for KH and KT can be expressed as follows: KT = exp(-15.597 + 7368.3/T) (25) KH = exp(-39.666 + 18057/7? (26) Using expressions 25 and 26, the adsorption constants were estimated (KH,T,=t)and compared with the values observed in Tables IV and V (KH,T,obs).The comparison is shown in Table VI. The agreement between experimental and estimated values is reasonable. Determination of the Activation Energy. In order to determine the true activation energy of gas-phase toluene hydrogenation, the parameter kKTKH3in the simultaneous model was used along with the expressions for the temperature dependence of the adsorption constants presented in the previous section. The lumped parameters can be expressed as follows: KT = eXp(AST/R) eXp(-AffT/RT) = KT' exp(-hH,/RT) (27) KH = eXp(ASH/R) eXp(-AHH/RT) = KH' exP(-mH/RT) (28) k = A exp(-E,/Rn (29) Combination of eqs 27-29 gives ~ K T K H=' AKT'KH'~exp(-E, - 3bJI,)/RT (30) Nonlinear regression gives the values for the exponential expressions in eqs 27,28, and 30. By inserting the obtained values for -AHT and -AHH into the exponent of the lumped parameter kKTKH3,the activation energy was determined to be 177 kJ/mol. When compared to the activation energies, discussed earlier in this study, given in the literature, this value is 2-3 times higher. However, one must remember that most of the activation energies reported in the literature are apparent; the values of E, include the effects from both rate and adsorption parameters. Estimation of the Maximal Reaction Rate. By inserting the expressions 27, 28, and 30 for parameters KT, KH, and k&KH3, respectively, into the rate equation of the simultaneous model, eq 31 is obtained. If the rate r = [AKT'KH'~eXp(-((E,,, + A& + ~ ~ H ) / R ' I I ) P T P/ H [KT' ~ I exp((-mT/RT)PT + KHf0.5~ X P ( - ~ H / ~ R T ) P+H " ~ (31) expression is differentiated with respect to temperature, and the derivative is set equal to zero, the optimal temperature giving the maximum reaction rate is obtained. The differentiation of eq 31 with respect to temperature is shown in eq 32, which gives the optimal conditions. T' + [(E,,, + MT ~ ~ H ) ( KexP(-mT/RT)pT K H " ~ X P ( - ~ H / ~ R T ) Pt'HI)] " ~[~(KT'PT exP(-mT/RT)mT + (KH~H)'"e x p ( - ~ ~ / % r ) ~ ' ~ h H ~=/ 02 )(32) ]
1
7
c
5"
PH alin
Figure 6. Optimal reaction temperature vs hydrogen partial pressure. 0
'
i
,
05 i
I 110
150
170
190
T/.C
Figure 7. Surface coverages of toluene and hydrogen at the reaction temperatures according to the simultaneous model at various partial 6.5; (+) T,, PH/PT 6.5; ( 0 )H,, preasure ratios. (@ HmVP H / P T PH/PT 3.4; (A)T ,, P H / P T 3.4; ( X I Hcov PHIPT 1.9;(v),Tcov
PHIPT
* 1.9.
--
--
In Figure 6, the temperature of the optimal reaction rate is shown as a function of hydrogen partial pressure, having and ptot= 1 atm
(34) As can be seen from the figure, the simultaneous model predicts an optimal reaction temperature between 170 and 175 O C for the set of partial pressures given by eqs 33 and 34. Surface Coverages of Hydrogen and Toluene. Using the estimated parameters of the simultaneous model and the experimental partial pressures of hydrogen and toluene, the coverages of the surface intermediates can be calculated using eqs 6 and 7; the fraction of vacant sites (e,)needed in eqs 6 and 7 is obtained from eq 9. In Figure 7, the surface coverages of toluene and hydrogen calculated using the simultaneousmodel are shown at three different partial pressure ratios as a function of temperature. The hydrogen coverage was higher on the noncommercial catalyst compared to the commercial catalyst studied by Lindfors and Salmi (1992). For toluene, the coverage was similar. At the lowest temperatures considerable amounts of hydrogen were adsorbed on the catalyst surface. The surface was not completely covered with toluene and hydrogen at the reaction temperatures. The reaction rate is proportional to both the rate and adsorption constants and inversely proportional to the adsorption term of the rate equation. The increase of the rate constant with
Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993 41 temperature is obviously overcompensated by the decrease of the hydrogen adsorption constant causing a decrease of the surface coverage of hydrogen and a decrease of the reaction rate above the temperature of the rate maximum. Since the decrease of hydrogen surface coverage was less pronounced on the noncommercial catalyst, the decrease of the hydrogen adsorption constant reached a critical value at a higher temperature than on the commercial catalyst, thus shifting the rate maximum to a higher temperature. Our results are in good qualitative accordance with previous investigations of the hydrogenation of aromatics. Several authors report rate maxima in the hydrogenation of benzene and toluene at temperatures between 150 and 200 "C (Franco and Phillips, 1979; Germain et al., 1963a,b; Herbo, 1941: Nicolai et al., 1948; Orozco and Webb, 1983; Rahaman and Vannice, 1991; van Meerten and Coenen, 19753. Conclusions A statistical comparison of the best mechanistic models with the empirical power-law model reveals that the mechanistic models should be preferred in the description of the experimental data. When the best mechanistic models were compared, the best fit, in a strictly mathematical sense, was obtained by the model assuming a simultaneous addition of three hydrogen atom pairs. The model based on a sequential addition of atom pairs gave an almost equally good fit. From a chemical point of view, the sequential addition seems more probable. The more complex mathematical structure of the Sequential model, including four parameters instead of three as was the case for the model implying a simultaneous addition of hydrogen, resulted in strong correlations between the parameters. Thus, we cannot draw conclusions on the exact mechanism of the surface reaction steps. The experimental data are too restricted, and even with a larger experimental base, the surface reactions might require not only a steady-state study, but a combination of, e.g., steady state and isotopic transient kinetics. However, the rate models for toluene hydrogenation developed in this work are able to predict the observed reaction orders with respect to toluene and hydrogen as well as the maxinium reaction rate at temperatures around 175 "C. The characteristic features of the models are competitive and rapid adsorption of hydrogen and toluene on the Ni surface, slow surface reaction involving hydrogen addition to adsorbed toluene, and rapid desorption of methylcyclohexane from the surface. Although the observed kinetics was similar on both catalysts, the activity of the laboratory-scale catalyst was on a higher level than that for the commercial catalyst studied by Lindfors and Salmi (1992). The weaker adsorption of toluene and stronger adsorption of hydrogen observed on the noncommercial catalyst results in a lower reaction order with respect to hydrogen, a less negative order with respect to toluene, and a higher temperature for the rate maximum. Acknowledgment We thank Dr. A. 0. I. Krause for initiating this work and Mr. 0. Jylha, Mr. S. Hornytzkyj, and Mr. J. Vilhunen for their contribution concerning the characterization of the catalyst. Nomenclature A = frequency factor A' = exp(AS/R) E , = activation energy AH = enthalpy of adsorption
K = adsorption equilibrium constant K' = lumped parameter k = rate constant k' = apparent rate constant k , = forward rate constant in the sequential model k- = backward rate constant in the sequential model kd = desorption rate constant in the sequential model rn = exponent of hydrogen partial pressure in the power-law model M = number of parameters MRS = mean residual square, MRS = WSRS/(N - M) n = exponent of toluene partial pressure in the power-law model N = number of experiments p = partial pressure R = gas constant r = reaction rate AS = entropy of adsorption T = temperature w, = weight factor in regression WSRS = weighted sum of residual squares Y = parameter in the simultaneous model, number of hydrogen atoms in the rate-determining step 8 = surface coverage 0, = fraction of vacant sites * = vacant adsorption site Subscripts and Superscripts cov = coverage
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Received for review April 28,1992 Revised manuscript received September 10, 1992 Accepted October 5,1992
Simplified Treatment of the Rates of Gas-Solid Reactions Involving Multicomponent Diffusion Eric G.Eddingst Department of Chemical Engineering, University of U t a h , Salt L a k e City, U t a h 84112
Hong Yong Sohn* Departments of Metallurgical Engineering and Chemical Engineering, University of U t a h , Salt L a k e City, U t a h 84112
An approximate analytical solution is presented which describes the rate of a gas-solid reaction involving multicomponent diffusion in the gas phase. The model obviates the numerical solution of the nonlinear Stefan-Maxwell equations by defining pseudobinary diffusivities a t the diffusion boundaries which take into consideration the Stefan-Maxwell dependence of the binary diffusivities. A linear dependence on mole fraction is subsequently assumed for the pseudobinary diffusivities across the control volume. The model has been generalized to account for reversible reactions and bulk flow effects due to volume change of the gas. The approximate solution is compared with the rigorous numerical solution over a variety of conditions, and the resulting comparisons show that, even for very large differences in binary diffusivity values, good agreement is obtained between the two solutions. Introduction The theoretical analysis of gas-solid reaction systems is important in a variety of engineering applications such *To whom all correspondence should be addressed. Current address: Reaction Engineering International, Salt Lake City, Utah. +
as the removal of sulfur oxides from flue gases by injection of a solid sorbent or the reduction of metal oxides by gaseous compounds. In general, systems that involve more than two gaseous species will require solution of the nonlinear system of Stefan-Maxwell equations coupled with the applicable form of the equation of continuity (Ramachandran and Doraiswamy, 1982). The exact numerical
Q888-5885/93/2632-QQ42$Q4.QO/Q 0 1993 American Chemical Society
