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Received for review February 25,1991 Revised manuscript received March 13, 1992 Accepted May 5, 1992
KINETICS AND CATALYSIS Application of the Response Surface Methodology to the Kinetic Study of the Gas-Phase Addition of Ethanol to Isobutene on a Sulfonated Styrene-Divinylbenzene Resin Montserrat Iborra,* Jose F. Izquierdo, Fidel Cunill, and Javier Tejero Chemical Engineering Department, Faculty of Chemistry, University of Barcelona, Mart; i FranquBs, 1, 08028 Barcelona, Spain
The kinetics of vapor-phase addition of ethanol to isobutene to give ethyl tert-butyl ether (ETBE) on the ion exchange resin Amberlyst 15 has been studied. Rate data were obtained in a continuous differential reactor operated a t atmospheric pressure and 53-78.5 "C. The most probable Langmuir-Hinshelwood-Hougen-Watson (LHHW) rate models stem from two quite similar reaction mechanisms. Four active centers take part in the rate-determining step of the two mechanisms. The first one suggests the reaction between the ethanol and the isobutene, both adsorbed molecularly on one center, and the second mechanism proposes the reaction between the ethanol adsorbed molecularly on one center and the isobutene adsorbed on two centers without cleavage. Both mechanisms are physicochemically coherent.
Introduction To find the most suitable function to correlate rate data and independent variables is the main problem in kinetics. The reaction rate equation must be detailed enough to describe minor influences, but it should not be too complex to be useful in reactor design. Empirically developed models, despite their simplicity, are of limited value in extrapolation. Therefore, theoretically founded models are more desirable. The response surface procedures appear to be useful for finding empirical models for a given reaction. They allow an adequate fit, giving an empirical rate equation in the form of a power series sometimes useful for preliminary designs, and an indication of possible mechanistic rate expressions, as shown by Pinchbeck (1957)in the vaporphase oxidation of naphthalene to phthalic anhydride, Kittrell and Erjavec (1968)in the re-examination of vapor-phase isomerization of n-pentane to 2-methylbutane data obtained by Carr (19601,Pirard and Kalitventzeff (1978) in the hydrogenation of ethylene on coppermagnesia catalysts, and Tejero et al. (1989)in the vaporphase addition of methanol to isobutene on Amberlyst 15. The response surface methodology used as a preliminary approach to the identification of the kinetic equation is more rational than the direct fit of nonlinear equations
because it introduces into the regression only the significant variables on a statistical basis. This is the basis of the Hofmann method (Hofmann, 1972)for determining the best kinetic equation for reactions from which little or nothing is known. The method consists of the following stages. (a) With factorial, simplex, or central composite designed experiments as the starting point, the response surface of the reaction rate is explored by linear regression of the data and transformation of the regression equation into its canonical form to visualize it. At this stage significant variables can be selected. (b) The information thus obtained and any additional information about the type of reaction should be used to establish some mechanietic reaction schemes, leading to several possible model equations. Selection between these rival models is possible using the classical discrimination techniques. (c) For the most suitable model equation, the parameter values should be determined by nonlinear regression. Now then, when experimental setups have a low experimental error, a quadratic function does not often fit the rate surface in a statistically significant fashion and so a higher order function should be fitted (Himmelblau, 1970). As a result, interpretation of the influence of the
0888-5885/92/2631-1840$03.00/00 1992 American Chemical Society
Ind. Eng. Chem. Res., Vol. 31, No. 8, 1992 1841 independent variables on the reaction rate is more difficult. On the other hand, in reacting systems with a complex rate surface, it is not always possible to explore the whole surface of interest using orthogonal and rotatory experimental designs. So, other designs of lower statistical properties, such as lattices, should be used in the exploration of the response surface. Despite these difficulties, we think that the Hofmann scheme is useful. So, this work is devoted to checking the suitability of the response surface methodology for deriving Langmuir-Hinshelwood-Hougen-Watson (LHHW) kinetic models. For this purpose, addition of ethanol to isobutene to give ethyl tert-butyl ether (ETBE) on Amberlyst 15 has been selected as the reaction model. ETBE is a good octane booster (Garibaldi et al., 1978; Marceglia and Oriani, 1982; Farhat and Mazhar, 1984; Prezelj, 1987; Iborra et al., 1988). Besides, ETBE synthesis, the same as the methyl tert-butyl ether (MTBE) one, could also have interest as a means for the quantitative separation of isobutene from l-butene of C4 cuts following a similar reaction scheme. ETBE is formed by addition of ethanol to iaobutene on acid catalysts. The reaction is reversible and fairly exothermic. In industry, it could be performed in liquid phase on sulfonated resins (Amberlyst 15, Lewatit SPC llS), at 2-40 atm, 45-120 "C, and an isobutene/ethanol molar ratio of about 1:1, with good yield and a selectivity of about 99% in ether (Leum et al., 1949; Macho et al., 1982; Baratella et al., 1983; Childs, 1984). In vapor phase the chemical equilibrium is not favorable at temperatures higher than 100 "C (Iborra et al., 1989), but selectivity and yield in ether are rather good on sulfonated resins at 85-100 "C and atmospheric pressure (Setinek et al., 1977). In spite of that no kinetic study has been found in open literature. So, we have studied the vapor-phase addition of ethanol to isobutene on Amberlyst 15 at atmospheric pressure and 53-78.5 OC. A three-stage procedure, similar to the Hofmann method, has been followed. The procedure was outlined by Tejero et al. (1989) in the study of the reaction of addition of methanol to isobutene. In that work more than 60 possible LHHW-type models up to third order were proposed. Screening between them showed that only three models correlate data in a statistically significant fashion. Moreover, authors showed also that analysis of the rate surface had already suggested the main features of these three models. Thus, this method leads to a few models that can represent appropriately rate data saving the effort of fitting all the possible LHHW kinetic models. The method consists of the following. (a) A study of the rate surface based on an experimental design which allowed exploration of as wide an interval of the independent variables (pressure of reactants) as possible. The influence of the independent variables is analyzed at this stage. (b) From this analysis and some additional information available, some reaction mechanisms are proposed, giving rise to not too many kinetic models. Between them, only those in agreement with conclusions drawn from the response surface are selected. (c) Finally, the parameters of kinetic models are fitted by a nonlinear least-squares method, and the physicochemical coherence of the models are checked. Discrimination between models is made by applying statistical and thermodynamic criteria.
Experimental Section Materials. Ethanol ( 36.2 f 0.5 10 < -(-22.7 f 1.0) < 24.3 f 0.5 2 0 < -(-63.4 f 3.0) < 73.07 0 < -(-51.8 f 0.4) < 69.5 10 < -(-51.8 f 0.4) > 41.0 f 0.2 10 < 4-63.4 f 3.0) > 45.4 f 1.3 3 0 < -(-11.3 f 7.4) < 73.07 0 < -(-23.8 f 0.5) < 69.5 10 < -(-11.3 f 7.4) < 18.0 f 3.5 10 < -(-23.8 f 0.5) < 26.2 f 0.2 4 0 < -(-19.0 f 1.2) < 73.07 0 < 4-23.2 f 0.4) < 69.5 10 < 4-19.0 f 1.2) < 22.21 f 0.05 10 < -(-23.2 f 0.4) < 26.1 f 0.2
Ind. Eng. Chem. Res., Vol. 31, No. 8, 1992 1847 Table XI. (A) Comparison of Adsorption Constant of Ethanol and Isobutene with Literature Data. (B) Comparison of Standard Adsorption Enthalpy and Entropy of Ethanol and Isobutene with Literature Data ref Tejero (1986)" Tejero (1986)b Setinek (1987) Hejtmankova et al. (1990) Kabel and Johanson (1962)
K,,atm-' K,,atm-' KI,atm-' Kl, atm-' K,,atm-'
Part A 53.1 "C 0.85 1.60
___
61.8 OC 0.52 0.90
70.5 "C 0.33 0.52
78.5 "C 0.22 0.32
85 "C
0.50 0.74 57.2
37.5
25.1
17.6
Part B ref Tejero (1986)" Tejero (1986)* Kabel and Johanson (1962) ''
Isobutene adsorbed on one center.
kcal/mol -12.2 1.2 -14.5 i 1.5
A&",
A&,', call(mo1.K) -37.8 i 4 -43.5 i 5
fin.", kcal/mol
A&-". cal/(mol.K)
-10.50
-24.3
Isobutene adsorbed on two centers without cleavage.
obtained in this work, except for model 2. Unfortunately, standard adsorption enthalpy and entropy values of isobutene are not comparable. Still, provided that K , values are more reliable than those of K,, we conclude than models 3 and 4 are probably the best models for the reaction. Both adsorption models proposed for isobutene are possible from a physical standpoint at the working temperatures and even could take part simultaneously. Nonetheless, isobutene adsorbs weakly on resins. This fact hinders the screening of an only model for the reaction. Both mechanisms, which only differ in the adsorption model for isobutene, are very similar and agree with the conclusions of Tejero et al. (1989), Setinek (1987), and Hejmankova et al. (1990) on the homologous reaction for obtaining MTBE. The former studied the reaction at 41-61.8 "C and 0.02-0.3 atm of pressure of reactants and proposed a mechanism whose rate-determining step was the surface reaction between the methanol adsorbed on one center with isobutene adsorbed on two sites. The two latter studied it at 70-100 "C and 0.15-0.85 atm of pressure of reactants and proposed a mechanism whose rate-determining step was the surface reaction between methanol and isobutene adsorbed on one site with a third site being necessary. The discrepancy between these authors is probably due to the different ranges of temperature and pressure explored. With regard to the reaction of the addition of ethanol to isobutene a fourth center is probably needed in the rate-determining step owing to the fact that the molecular size of ethanol is higher than that methanol.
Conclusions Vapor-phase addition of ethanol to isobutene has been studied at atmospheric pressure and 53-78.5 "C on the ion-exchange resin Amberlyst 15. Rate data show that ethanol inhibits the reaction, whereas isobutene enhances it. Analysis of the response surface of the reaction rate as a function of the partial pressures of ethanol and isobutene suggests that the best LHHW rate equation can be deduced from a reaction mechanism in which three or four active sites take part in the rate-determining step. Two LHHW models, physicochemically coherent, represent rate data in a statistically significant fashion. The first one stems from a mechanism whose rate-determining step is the surface reaction between the ethanol and the isobutene, both adsorbed on one center. The second model is based on a mechanism whose rate-determining step is the surface reaction between the ethanol adsorbed on one center and the isobutene adsorbed on two centers. In both mechanisms four sites take part in the rate-determining step. It was not possible to distinguish between the two
models because isobutene adsorbs slightly on Amberlyst 15.
Acknowledgment We thank the donors of the Interdepartamental Commission of Research and Technological Innovation of the Goverment of Catalonia for partial support of this work.
Nomenclature bk = parameter relative to the k term of a polynomial E = ETBE Et = ethanol F = variances ratio Fi = flow molar rate of compound i, mo1.h-l I = isobutene Kj = adsorption equilibrium constant of the substancej , atm-' k = rate coefficient, mol-(h-g)-' 1 = active center p , = partial pressure of the substance j , atm = intensive reaction rate, mol.(h.g)-' So = absolute entropy, cal.(mol.K)-' Sd = sum of squares of lack of fit W = mass of the catalyst, g Xi= degree of conversion of reactant i x i = molar fraction of sustance i in exhaust gases a t significance level AHa"= standard adsorption enthalpy, kcabmol-' ASao = standard adsorption entropy, cal-(mol-K)-' ASd = increment of the sum of squares due to the removal of parameter bk Subscripts E = ethyl tert-butyl ether g = vapor phase I = isobutene e = ethanol W = water Registry No. ETBE, 637-92-3; EtOH, 64-17-5; Amberlyst 15, 9037-24-5;isobutene, 115-11-7.
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