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over a wide range of experimental conditions. This implies that the reactions approximately have the same activation energy. Exclusive cracking of monomethyl isomers of the feed component is unlikely. Many multibranched feed isomers are formed and these may crack according to energetically favored routes. Acknowledgment This work was undertaken thanks to a “Center of Excellence” Grant awarded by the Belgian Ministry of Scientific Affairs within the framework of the “Concerted Actions on Catalysis”. P. A. Jacobs acknowledges a permanent research position as “Bevoegdverklaard Navorser” from N.F.W.O. (Belgium). Literature Cited Beecher, R.; Voorhies, A.; Eberly, P. Ind. fng. Chem. Prod. Res. Dev. 1968, 7 , 203. Berty, J. M. Chem. Eng. frog. 1974, 70(5), 76. Boiton, A. P. ACSMonogr. 1976, No. 171, 714. Brouwer, D. M.; Hogeveen, H. Rec. Trav. Chim. Pays-Bas 1970, 89, 211. Chen, N. Y. 011 Gas J . 1968, 66, 151. Chevalier, F.; Guisnet, M.; Maurel, R. Roc. 6th Int. Congr. Catal. 1977; 1 , 476. Choudhary, N.; Saraf, D.N. Ind. Eng. Chem. frd.Res. Dev. 1975, 14, 74. Clapetta, F. G.; Hunter, J. B. Ind. Eng. Chem. 1953, 45, 147. Condon, F.E. “Catalysis”; Emmett, P. M., Ed.; Reinhold New York, 1956; Vol. 11, Chapter 2. Engler, B. Ph.D. Thesis, Technical University Aachen, Aachen, Federal Republic of Germany, 1976.
Gol’dfarb, Yu. Ya.; Katsobashvlli, Ya. R.; Rozental’, A. L. Kinet. Catal. 1977, 18. 364. Jacobs,-P. A. “Carboniogenic Activity of Zeolites”; Elsevier Scientific Publ. Co.: Amsterdam. Oxford. New York. 1977. Jaffe, S. B. Ind. Eng. Chem. frocessbes. Dev. 1974, 13, 34. Kelley, A. E.; Peralta, 6.; Reeg, C. P. Chem. Eng. Monogr. 1979, 10, 171. Matukuma, A. “Gas Chromatography”; Harbourn, C. L. A., Ed.; The Institute of Petroleum: London, 1969; p 55. Mavity, V. T.; Ward, J. W.; Whitebread, K. E. Hydrocarbon h o c . 1978, 7 1 , 157. McDaniel, C. V.; Maher, P. K. “Molecular Sieves”; Society of the Chemical Industry: London, 1968. Meot-Ner, M.; FleM, F. H. J. fhys. Chem. 1976, 80, 2865. Olah, G. A.; von R. Schleyer, P. “Carbonium Ions”; Wiley: New York, 19661973; Vol. 1-4. Poutsma. M. L. ACSMonogr. 1976, No. 171, 513. Steijns, M.; Froment. G. F.; Jacobs, P. A.; Uytterhoeven, J. B.; Weitkamp, J. Erctil, Kohle, Erdgas, Petrochem. 1978, 31, 561. Stull, R. D.; Westrum, E. F.; Slnke. G. C. “The Thermodynamics of Organic Compounds”; Wiley: New York, 1969. Voge, H. H. “Catalysis”; Emmett, P. H., Ed.; Reinhold: New York, 1956; Vol. 11, Chapter 5. Ward, J. W.; Hansford, R. C.; Reichle, A. D.; Sosnowski, J. Oil Gss J . 1973, 5, 69. Weltkamp, J. Ph.D. Thesis, University of Karlsruhe, Karisruhe, Federal Republic of Germany, 1971. Weitkamp, J. ACS Symp. Ser. 1975, No. 20. 1. Weitkamp, J.; Farag, H. “Compendium 76/77 ErdoI, Kohle, Erdgas, Petrochem.”; Industrie-verlag von Hernhaussen: Leinfelden-Echterdingen, 1976; Vol. 1, p 276. Weitkamp. J. Erdjl, Kohle, Erdgas, Petrochem. 1978, 31, 13. Weitkamp, J.; Farag, H. Act. fhys. Chem. 1978, 24, 327.
Received for reuiew February 23, 1981 Accepted July 6 , 1981
Hydroisomerization and Hydrocracking. 3. Kinetic Analysis of Rate Data for n-Decane and n-Dodecane Matt Steijns and Gilbert F. Froment Laboratorium voor Petrochemische Techniek, Rljksuniversiteit Gent, Krijgslaan 27 1, B-9000 Gent, Belgium
n-Decane and ndodecane were isomerized and hydrocracked on a 0.5 wt % phtinum/ultrastabb Y zeolite catalyst in a CSTR (Berty type) at T = 130-250 OC and P = 5-100 bar. A first screening of rival models was based on data on the global hydroisomerizationrate of ndecane. The most adequate models were those explicitly accounting for a concentration effect in the zeolite cages by a physical adsorption process. Similar conclusions were arrived at from the modeling of both hydrocracking and hydroisomerization kinetics of n-decane and n-dodecane. The most adequate form of reaction network considers the cracking from the dibranched isomers to be the preferential cracking route. This is in complete agreement with carbenium ion chemistry as outlined in the preceding paper.
Introduction A previous paper reported on the product distributions obtained in hydroisomerization and hydrocracking of ndecane and n-dodecane on a Pt/US-Y zeolite catalyst and discussed the mechanism of such reactions (Steijns et al., 1981). The present paper deals with the kinetics of these processes. Even with simple feedstocks the reaction scheme is very complicated. Simplification which involves the lumping of reaction steps and products is required. Beecher et al. (1968) studied the hydrocracking of model components: n-decane, decalin, and the binary mixture n-decaneldecalin for hydrocracking studies on mordenite catalysts. The cracked products were grouped into one pseudo-component, despite the fact that extensive secondary cracking did take place. Hydroisomerization was not considered for the kinetic modeling. Flock et al. (1976) divide the products of hydroisomerization and hydrocracking into three groups: nonbranched cracked products,
branched cracked products, and feed isomers. The assumption that only cracking of nonbranched alkanes takes place is unrealistic, as pointed out before (Steijns et al., 1981). Moreover, the assumption of first-order kinetics for these zeolite-catalyzed reactions is highly questionable. Gol’dfarb et al. (1977) studied the kinetics of n-decane hydrocracking on alumina-nickel-molybdenum oxide catalysts. It was shown that the distributions of methylnonanes and dimethyloctanes approach thermodynamic equilibrium over the experimental range. They therefore lumped the products as follows: methylnonanes, dimethyloctanes, and cracked products. The aim of this work is dual: on one hand to develop kinetic models which reflect as much as possible the true physicochemical nature of the process, and on the other hand to provide a better insight into carbenium ion reactions and bifunctional catalysis. For this purpose ndecane and n-dodecane were isomerized and cracked on
0196-4321/81/1220-0660$01.25/00 1981 American Chemical Society
Ind. Eng. Chem. Prod. Res. Dev., Vol. 20, No. 4, 1981 661
a Pt/US-Y zeolite catalyst in a Berty-type reactor with complete mixing. Details on the catalyst preparation, purity of the feed, high-pressure equipment, and experimental procedure were given in the previous paper (Steijns et al., 1981). The use of a CSTR allowed net rates of formation for any product to be obtained directly from a simple mole balance over the reactor. Since the equipment was free of leaks and no deactivation by coke formation was observed, a 100% carbon balance was assumed. It should be mentioned also that hydroisomerization and hydrocracking do not give rise to any volume change. Procedure for Parameter Estimation and Model Discrimination The methodology of kinetic analysis, outlined by Froment (1975,1976), was applied. An objective function for the multi-response case was defined, which contained the weighted sum of the squares of the residuals (observed response - calculated response) and their cross products. In matrix notation this function is simply represented as S = trace[& M(k)] (1) where Q is an m X m weighting matrix, m is the number of responses, and M ( k ) is the moment matrix of the residuals for a vector of parameter estimates k. A weighting matrix was constructed from a preliminary parameter estimation without weighting. A second weighting matrix, which differed slightly from the first matrix was determined from the first regression with weighting. This second matrix was used in the final regression. For the special case of a single response the sum of squares of the residuals was taken as an objective function. Reparameterization as proposed by Kittrell (1970)
k = ko exp(-
&)
20 P, = 2 L
R ~ 3 2
pI
pI -102 R
0 100
(E T
)
(2)
where T is the average temperature of the data set, was used to accelerate the convergence to the minimum of the objective function. A nonlinear regression computer program, incorporating the algorithm of Marquardt (1963), was used in the iterative search for this minimum. Initial parameter estimates for a given model and a data set covering the whole range of experimental conditions were obtained in various ways: (1)from a simpler model containing one parameter less; (2) from the modeling of several isothermal data sets; (3) from the modeling of isothermal data at low conversion (no hydrocracking yet, only isomerization); these data were also used for a preliminary discrimination among rival models. The choice of the initial parameter estimates is not critical when reparameterization is applied. The significance of the overall regression was tested by calculation of the F statistic. The significance of the individual estimates for the model parameters was expressed by their t values. To obtain information on the adequacy of the model an analysis of the residuals was made. The statistical testing of the results formed the basis for the discrimination among the various rival models. Discussion of the Results Modeling the Global Kinetics of Hydroisomerization of n -Decane. The kinetic analysis was started with a set of data from experiments at one temperature and at low conversion (
