Ind. Eng. Chem. Res. 1989,28, 899-910 of C 0 2 formation and the final product distributions for both mono- and bifunctional compounds.
Acknowledgment This work was partly supported by a Grant-in-Aid for Scientific Research (No. 61030017) from the Ministry of Education, Science and Culture, Japan. Registry No. CH30H, 67-56-1; CH3CH20H,64-17-5; CH,(CH2)20H, 71-23-8; CH,(CH,),OH, 71-36-3; HCOZH, 64-18-6; CH,C02H, 64-19-7; CH,CHZC02H, 79-09-4; CH3(CH2)&02H, 107-92-6 CH3NH2, 74-89-5;CH,CHZNH2,75-04-7; CH3(CHZ),NH2, 107-10-8; CH,(CH2)3NH2, 109-73-5; CH,CHO,75-07-0; CHSCN, 75-05-8; CH3CONH2, 60-35-5; HO(CHp)ZOH, 107-21-1; HO(CH2)3OH, 504-63-2; HO(CH2)40H, 110-63-4; HO(CH2)2NH2, 14143-5; HO(CH2)3NHZ, 156-87-6; HzN(CH2)2NHz, 107-15-3; N2N(CHZ),NH,, 109-76-2; H,NCHZC02H, 56-40-6; H2N(CH2)&02H, 107-95-9; (COZH),, 144-62-7; CH2(C02H)2, 141-82-2; HO&(CH2),C02H, 110-15-6; C 0 2 0 3 , 1308-04-9; COz, 124-38-9; NH,, 7664-41-7.
Literature Cited Baldi, G.; Goto, S.; Chow, C.-K.; Smith, J. M. Catalytic Oxidation of Formic Acid in Water. Intraparticle Diffusion in Liquid-Filled Pores. Ind. Eng. Chem. Process Des. Deu. 1974, 13, 447-452. Imamura, S.; Hirano, A.; Kawabata, N. Oxidation of Acetic Acid Catalyzed by Co-Bi Complex Oxides. Ind. Eng. Chem. Process Des. Deu. 1982a, 22, 570-575. Imamura, S.; Kinunaka, H.; Kawabata, N. The Wet Oxidation of Organic Compounds Catalyzed by Co-Bi Complex Oxide. Bull. Chem. SOC.Jpn. 1982b,55, 3679-3680.
899
Imamura, S.; Doi, A,; Ishida, S. Wet Oxidation of Ammonia Catalyzed by Cerium-Based Composite Oxides. Ind. Eng. Chem. Prod. Res. Deu. 1985, 24, 75-80. Imamura, S.; Nakamura, M.; Kawabata, N.; Yoshida, J.; Ishida, S. Wet Oxidation of Poly(ethy1ene glycol) Catalyzed by Manganese-Cerium Composite Oxide. Ind. Eng. Chem. Prod. Res. Deu. 1986, 25, 34-37. Lebedev, N. N.; Manakov, M. N.; Litovka, A. P. Kinetics of the Liquid-Phase Oxidation of Butyraldehyde by Oxygen in the Case of Catalysis by Cobalt and Copper Salts. Kinet. Katal. 1974,15, 791-793. Levec, J.; Smith, J. M. Oxidation of Acetic Acid Solutions in a Trickle-Bed Reactor. AIChE J . 1976, 22, 159-168. Nakagawa, T.; Oyanagi, Y. Program System SALS for Nonlinear Least-Square Fitting in Experimental Sciences. In Recent Developments in Statistical Inference and Data Analysis; Matusita, K., Ed.; North Holland Publishing Co.: 1980; pp 221-225. Sadana, A.; Katzer, J. R. Catalytic Oxidation of Phenol in Aqueous Solution over Copper Oxide. Ind. Eng. Chem. Fundam. 1974,13, 127-134. Shogenji, T. Wet Combustion Process. Kagaku Kogaku 1968, 32, 514-523. Tanaka, H.; Komiyama, H.; Inoue, H. Behavior of Urea in Wet Oxidation Treatment. Kagaku Kogaku Ronbunshu 1981,7,324-325. Tanaka, H.; Komiyama, H.; Inoue, H. Selective Oxidation of Dissolved Ammonia to Nitrogen by Co203Catalysts. Kagaku Kogaku Ronbunshu 1982,8,699-703. Tanaka, H.; Komiyama, H.; Inoue, H. Oxidation of Dissolved Ammonia Using Various Metal Oxide Catalysts. Kagaku Kogaku Ronbunshu 1986,22, 222-224. Zimmermann, F. J. New Waste Disposal Process. Chem. Eng. 1958, 65(Aug 25), 117-120.
Received for reoiew September 6, 1988 Accepted March 10, 1989
Fundamental Kinetic Modeling of Hydroisomerization and Hydrocracking on Noble-Metal-Loaded Faujasites. 1. Rate Parameters for Hydroisomerization Miguel A. Baltanas,+Kristiaan K. Van Raemdonck, Gilbert F. Froment,* and Sergio R. Mohedad Laboratorium uoor Petrochemische Techniek, Rijksuniuersiteit Gent, B-9000 Gent, Belgium
The hydroisomerization and hydrocracking of paraffins on zeolites is modeled in terms of fundamental reaction steps involving carbenium ions. This fundamental kinetic modeling is discussed in detail and applied to the hydroisomerization of n-octane into monomethylheptanes on a Pt/US-Y zeolite. T h e reaction network, involving more than 100 reactions written in terms of elementary steps, was generated by computer, and the kinetic parameters were estimated by Marquardt's minimization procedure, accounting for thermodynamic constraints. T h e model fits the experimental data over a wide range of operating conditions. T h e kinetic parameters are in agreement with bifunctional catalytic behavior and carbenium ion chemistry.
Introduction Hydroisomerizationand HydrocrackingOf Paraffins. Bifunctional hydroisomerization and hydrocracking of paraffins on noble-metal-loaded acid zeolites are well established industrial processes. Fundamental aspects have been reported by Choudhq and (1975)7
* T o whom correspondence should be addressed. t presentaddress: INTEC, Universidad ~ ~del Litoral, ~ Guemes 3450, 3000 Santa Fe, Argentina. Present address: INIQUI, Universidad Nacional d e Salta, Buenos Aires 177, 4400 Salta, Argentina.
*
0888-5885/89/2628-0899$01.50/0
(1976).and Guisnet and Perot (1984). A svstematic effort to unveil the catalytic chemistry behind"the observable reaction kinetics and product distribution arising from the processing of n-paraffins and branched paraffins, from c6 to Cl7,has been undertaken by several groups (Steijnset 1981; Steijns and Froment, 1981; Jacobs et 1981; Weitkamp, 1978, 1982; Baltanas et al., 1983; Vansina et al., 1983; Martens et al., 1985; Martens and Jacobs, 1986a,b). From this body of work, the general qualitative that~ hydroisomerization and hydroi picture~ indicates ~ l cracking on Pt- or Pd-loaded faujasites follow the trends encountered already with superacids (Brouwer, 1980); Le., whenever it is possible to have an abundant supply of
0 1989 American Chemical Society
900 Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989
- -
somewhat stable carbenium ions, a sequence of isomerization and cracking reactions such as linear
monobranched
=dbranched
multibranched
cracked prcducts
is taking place. By use of adequate loadings (0.1-0.5% w/w) of welldispersed noble metals, the "ideal bifunctional hydroisomerization and hydrocracking" can be achieved (Weitkamp, 1978): in the presence of a dehydrogenation/hydrogenation function, the alkanes can form alkenes, which are readily protonated to give alkylcarbenium ions, which can further isomerize or crack through several pathways. Among other findings for noble-metal-loaded faujasites, the following should be mentioned: linear and monobranched isomers do not crack easily; dibranched isomers are formed by isomerization of monobranched isomers and undergo further isomerization to tribranched isomers or crack; tetrabranched isomers are never found; secondary cracking is negligible. Coonradt and Garwood (1964) and Weitkamp et al. (1983) have observed that, due to competitive adsorption on the acid sites, the probability of secondary isomerization increases with increasing carbon number of the cracked products, at a given carbon number of the feed. The higher the carbon number of the feed, the more effectively the cracked products are prevented from undergoing secondary branching reactions. F u n d a m e n t a l versus Lumped Models. So far, the description of hydroisomerization and hydrocracking of even single hydrocarbons has been based upon simplified reaction networks, involving drastic lumping of intermediates (Steijns and Froment, 1981; Baltanas et al., 1983) or drastically simplifying heuristic assumptions with regard to the reaction kinetics (Weitkamp, 1982; Martens and Jacobs, 1986b). Yet, even then the number of kinetic and adsorption parameters is large. In the case of n-octane, e.g., the scheme used by Baltanas et al. (1983) contained seven parameters. The problem with those lumped schemes and lumped kinetic parameters is their specificity: for each different hydrocarbon feed, even within the same homologous series, another set of lumped parameters has to be determined. This means that in complex mixtures, as dealt with in industrial practice, the number of parameters becomes overwhelming. In other words, lumping, leading to more or less empirical parameters, is not the approach to be followed, since it cannot achieve the goal for which it was primarily introduced. Moreover, because of the existence of so many different routes, it seems an almost impossible task to extend the lumped reaction schemes to account for the full complexity. In the present paper, on the contrary, a detailed and fundamental network is developed, accounting for the carbenium ions involved in the reactions on acid sites. Since a detailed model should consider individual reaction steps, the number of elementary kinetic and adsorption parameters largely exceeds the number of parameters associated with a lumped reaction network, if only a single pure alkane feed is processed. When feedstocks with increasing chain lengths are taken, however, the number of elementary kinetic parameters is not very significantly increased, since the same parameters are encountered again in the same elementary steps. I t may seem like a paradox, but the full benefit and superiority of the fundamental approach is most strongly felt with complex
Table I. Enthalpies of Formation of Activated Complexes and Reaction Rate Constants (Extrapolated to 453 K ) of Different Carbenium Ion Reactions in Superacid Solutions. Data Taken from Brouwer and Hogeveen (1972) and Brouwer (1980) reaction type A H o ' , lo3 kJ/kmol k (453 K), s-' hydride shift 1010-10'1 tert-tert 12.5- 5.0 10" sec-sec €12.5 2.0 sec-tert tert-sec 56.5 methyl shift 10'0-10" tert-tert 12.5- 5.0 (6-9) X 10" sec-sec 8.5 10'2 sec-tert tert-sec 56.5 PCP branching 70.0-72.5 (2-4) x 104 tert-tert 22.0 2.5 X 1OO ' sec-sec 134.0 tert-prim 75.5 sec-prim cracking 62.0 5.5 x 105 tert-tert 1.3 x 103 84.5 tert-sec hydrogen transfer 15.0 3.9 x 1050 tert-tert 54.5-58.5 1.3 X lo2" tert-sec 8.5 2.5 x ioga sec-tert In L.(mol.s)-'.
feedstocks, those for which it has been standard practice to resort to extreme lumping. The hydroisomerization of rz-octane into monomethylheptanes on a Pt/US-Y zeolite is used to demonstrate the benefits of this approach. The approach requires detailed insight into the chemistry of the reactions, more particularly of carbenium ion reactions. Carbenium Ion Chemistry i n Zeolites Most of what is presently known about carbenium ion catalytic chemistry originated from early studies of their stability in the gas phase (Franklin, 1968), followed by NMR and calorimetric determinations using superacids in the liquid phase. The major part of our knowledge about carbenium ion stability and reactivity in superacid solutions was provided by Brouwer and Hogeveen (1972) and Hogeveen (1973) and was reviewed by Brouwer (1980). The stability of carbenium ions (R+)decreases in the order R3C+ >> R2CH+>> RCH2+>> CH3+. The stabilizing effect of alkyl groups results mainly from a combination of hyperconjugation and inductive effects. There seem to be no significant differences in stabilizing effects between methyl, ethyl, isopropyl, tert-butyl, etc., groups. The differences in stability between primary and secondary and between secondary and tertiary carbenium ions are around 105 and 54 kJ/mol, respectively. Carbenium ions rearrange or crack according to wellestablished routes: intramolecular reactions type-A rearrangements hydride shift alkyl shift type-B rearrangements PCP branching cracking by a-scission
intermolecular reactions hydrogen transfer
The sequence of relative reactivities in the liquid phase is alkyl shift > tert-tert R+ cracking > PCP branching > sec-tert R+ cracking > sec-sec R+ cracking, where PCP stands for protonated cyclopropane. According to Brouwer (1980), it has been found consistently that A S " * for the intramolecular rearrangements is practically zero. Hence,
Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989 901
A G O * = A H o * - T I S ” * is nearly independent of temperature, which facilitates comparison of reactions that have been studied a t widely different temperatures. The use of AH O * also makes it easier to quantify the relations between reaction rates and the relative stabilities of reactant, intermediate, and product ions. Table I lists the known information about reactivities. The reaction rate constants have been extrapolated to temperatures typical for bifunctional hydroisomerization processes. Additional work extending these liquid-phase results to solid acid carbenium chemistry has been reviewed by several authors (Poutsma, 1976; Rabo, 1981; Barthomeuf, 1984). More recently, Kramer and McVicker (1986), Kramer et al. (1985), and Corma et al. (1982, 1985a,b) have devoted much attention to the subject of carbenium ion reactivity on solid acids. On US-Y zeolites, the sequence of relative reactivities appears to be (Martens and Jacobs, 1986a) tert-tert R+ cracking > alkyl shift > PCP branching > sec-tert R+ cracking, tert-sec R+ cracking > sec-sec R+ cracking. Bifunctional catalysts, which inhibit secondary reactions, are the best tool for obtaining a more detailed knowledge of the relative isomerization and cracking rates (Poutsma, 1976). Besides of the monomolecular carbenium ion reactions considered so far, faujasites also enhance bimolecular hydrogen-transfer reactions of the type R+ + R’H + RH
+ R’+
This has been recognized by different reviewers of catalytic cracking (Bolton, 1976; Poutsma, 1976; Rabo, 1981) or reforming (Gates e t al., 1978) processes. Bimolecular hydrogen-transfer reactions between carbenium ions in liquid-phase superacid environments are known to proceed very rapidly a t low temperatures, with a low activation energy (Brouwer, 1980; Kramer and McVicker, 1986). At higher temperatures, these processes become slower than other carbenium ion reactions (Table I), as corroborated by Corma et al. (1982) in their work on chromium-exchanged Y zeolites. At 673 K, these authors found hydrogen transfer to be up to lo4 times slower than carbenium ion rearrangement reactions. If cage effects are invoked to bring about a high concentration of hydrocarbons inside the faujasites, that concentration is of the order of 1 gmol/L, so that the pseudo-first-order constants also turn out to be rather low (Table I). So far, the only studies at moderate temperatures which invoke bimolecular reactions in the isomerization of alkanes using noble-metal-loaded zeolites are those of Bolton and Lanewala (1970). Other authors disregard the hydrogen-transfer reactions altogether for hydroisomerization and hydrocracking at moderate temperature (Poutsma, 1976; Martens and Jacobs, 1986a). Most workers have found hydroisomerization and hydrocracking processes to be of first order with respect to the hydrocarbon reactants, i.e., monomolecular.
Development of a Fundamental Kinetic Model for Hydroisomerization and Hydrocracking The different types of reactions are listed in Table 11. In addition, it was necessary to account explicitly for the physical adsorption of the hydrocarbons in the zeolite cages. Usually the number of elementary steps, even after several simplifying assumptions, is so large that the reaction network has to be generated by computer. Baltanas and Froment (1985) generated the detailed reaction network, describing the structure of hydrocarbons and carbenium ions with binary relation matrices, a concept al-
Table 11. Steps Involved in Bifunctional Hydroisomerization and Hydrocracking of Alkanes reaction type description“
-
+ zeolite 3 L P(ads)
physical adsorption of paraffin in the zeolite pores
P(g)
dehydrogenation of paraffin on metal sites protonation of olefin on acid sites isomerization of R+, on acid sites
E L O(ads) + H2 P(ads) --O(ads)
+ H+
kp,(O;mI
R+m
k~s(m;d
hydride shift
R+nl
= ’ R+q
methyl shift PCP branching cracking of R+, on acid sites
R+,
kc,(m;v,Ol kDslh;O”)
R+h deprotonation of RCh from acid sites h = m, q, r, u, v 0” = isoolefin (io) or cracking product olefin (0’) hydrogenation of isoolefins iO(ads) on metal sites hydrogenation of cracking O”(ads) product olefins physical desorption of isoparaffins iP(ads) physical desorption of cracking paraffins
P”(ads)
+ R’, O”(ads) + Ht O’(ads)
-
+ H, 2L iP(ads) + H, 5 P”(ads)
s + sP”(g) + iP(g)
zeolite zeolite
EQ denotes quasi-equilibrium.
ready applied earlier by Clymans and Froment (1984) in the development of reaction networks in thermal cracking. Since primary carbenium ions are much less stable than secondary and tertiary ions, reactions in which primary carbenium ions are formed, are excluded in the generation of the reaction network, except for cracking reactions. Also, since hardly any methane or ethane is found among the products of hydrocracking, cracking reactions leading to either methyl or primary carbenium ions are expected to be very slow. Parameters of the Fundamental Kinetic Model. For the physical adsorption in the zeolite pores and for the (de)hydrogenation on the metal sites, quasi-equilibrium is reached (Steijns and Froment, 1981; Baltanas et al., 1983). Consequently, rate coefficients have to be defined only for the reactions on the acid sites, viz., protonation of olefins and isomerization and cracking and deprotonation of carbenium ions. These rate coefficients are determined by the type of reaction, on one hand, and by the character of the carbenium ions and olefins, on the other hand. In Table 11, the subscripts of the rate coefficients indicate the type of reaction. The character of the carbenium ions, indicated between parentheses in the rate coefficients and as a subscript in the notation for the carbenium ions, is determined by the nature of the charge-bearing carbon atom. The number of alkyl groups on the charge-bearing carbon atom can be 3,2,1, or 0, corresponding with tertiary (t),secondary (s), primary (p), or methyl (Me) carbenium ions, respectively. This restriction to four basic energy levels for the carbenium ions is necessary to limit the number of parameters but is only justified if the influence of differences in inductive, mesomeric, hyperconjugative, or other effects between the alkyl groups stabilizing the charge-bearing carbon atom is negligible with respect to
902 Ind. Eng. Chem. Res., Vol. 28, No. 7 , 1989 Table 111. Elementary Rate Coefficients Involved in a Detailed Fundamental Kinetic Model for Hydroisomerization and Hydrocracking of Hydrocarbons on a Noble-Metal-Loaded Zeolite Catalysto elementary rate coeff reaction
UI
A S O *symm = R In u*
(2)
*
where the subscripts r and refer to the reactant and activated complex, respectively. In the rate constant, this standard entropy difference is comprised as the factor exp(AS o*,,,/R 1, which is identified with the number of single events, ne, so that the latter follows from ne = exp(ASo*,,,/R)
= u,/u*
(3)
whereby eq 2 was used. Factoring out the number of single events, the rate constant can be written as
k = ne&
(4)
where & represents the single-event rate constant. When optically active species are involved, the symmetry contribution to the standard entropy has to be augmented with the contribution due to the mixing of the different enantiomers. For racemic mixtures, this contribution is given by the influence of the number of stabilizing groups. In heterogeneous catalysis, this seems to be true, a t least in the first approximation (Brouwer, 1980). Table I11 gives a survey of the rate coefficients of the different elementary carbenium ion reactions proceeding on the acid function of a noble-metal-loaded faujasite catalyst during hydroisomerization and hydrocracking of a hydrocarbon. There are 18 isomerization rate coefficients, and these are universal, i.e., independent of the type of feed, be it light or heavy, single or complex. The number of protonation and deprotonation rate coefficients, on the other hand, strongly depends on the type of feed, because the nature of the involved olefin has been accounted for in the definition of the rate coefficient. When reactions involving methyl or primary carbenium ions are excluded, the reaction network for the hydroisomerization and hydrocracking of n-octane contains 58 olefinic species and requires the introduction of 75 protonation and 85 deprotonation rate coefficients. Accounting for thermodynamic constraints reduces these numbers to a much smaller set of independent rate coefficients, as will be shown in a subsequent section. For cracking too, the nature of the produced olefin has been accounted for in the definition of the rate coefficient, in addition to the character of the reacting and produced carbenium ions. Again constraints have to be introduced to reduce the number of rate coefficients to a set of independent ones. This is a problem that will be dealt with in more detail in a following paper. Each rate coefficient in Table I11 refers to a truly single event. If an elementary step occurs several times through identical single events, the rate coefficient has to be multiplied by the number of single events to come to the rate coefficient of the elementary step. How to calculate the number of single events is explained in the next section. Number of Single Events. The occurrence of identical single events in an elementary reaction is related to the symmetry changes involved in the formation of the activated complex out of the reactant(s). The contribution to the standard entropy resulting from the symmetry of a molecule is given by Sosymm = -R In u (1) where u is the symmetry number of the molecule. Hence, the change in standard entropy due to the symmetry changes involved in the formation of the activated complex out of the reactant(s) is given by
S
Ochlr
= R In 2“
(5)
where n is the number of chiral centers in the species. Adding the chirality and symmetry contributions, given by eq 5 and 1, respectively, yields
S OSymm
+S
= -R In (u/2”)
Ochlr
(6)
This expression suggests the introduction of a global symmetry contribution to the standard entropy ‘sy”,glob
= -R In
uglob
(7)
with an associated global symmetry number: uglob
= u/2n
(8)
Since eq 7 is formally the same as eq 1,eq 3 remains valid, provided that global symmetry numbers are used. The above method for the determination of the number of single events is not easily implemented into a computer algorithm. Therefore, a second method was devised, based upon the “statistical factor” concept. Bishop and Laidler (1965, 1969) showed that gr/u* =
S*f/S*,
(9)
where slf and s*, are statistical factors for the forward step and reverse step, respectively, of the equilibrium reaction between reactant(s) and activated complex. A precise definition of these statistical factors can be found in Pollak and Pechukas (1978). Combining eq 3 and 9 yields an alternative expression for the number of single events: ne = s * ~ / s * ,
110)
The two methods for determining the number of single events are illustrated by means of an example. Consider the following 1,2-hydride shift reaction:
The method that makes use of the statistical factors s t f and s * implies ~ the counting of physically distinct configurations of the reactant and activated complex, in which identical atoms have been labeled. For this purpose, the
Ind. Eng. Chem. Res., Vol. 28, No. 7 , 1989 903 Table IV. Determination of the Number of Single Events for a Hydride Shift Reaction type of shift reactant activated complex
Table V. Number of Single Events for Different Types of Elementary Reactions reaction type no. of single events protonation 1 deprotonation nolH hydride shift 2nd methyl shift 24Me PCP branching /3-cleavage 2 &-cleavage 2nbHlnc+-n
-
axis ( d ) , cri = 33 X 2 ; no external axes; no chiral centers; so ur = 33 x 2 H
activated complex
H
H2
7
H2
n Bu
H1
e2 Bu
H1
MeH a
!
Bue
three internal %fold axes, ui = 33; no external axes; one chiral center (the bondlength of the two hydrogen atoms is different, since one of them is in a bridging position); so u* = 33/2. Applying eq 3, the number of single events now becomes hydrocarbon structure is represented in Table IV by the Newman projection. If the Newman circle is placed perpendicularly on the bond between the carbon atoms that exchange the hydride ion, only identical atoms (or groups) on those two carbon atoms have to be labeled. The planar structure of the electron-deficient carbon atom permits a hydride ion to shift on either side of the plane. For the case considered here, there are two candidate hydrogen atoms, each of which has the possibility of shifting as a hydride ion in two different ways. In the resulting four single events, represented in Table IV, the semibonds between the shifting hydride ion and the two carbon atoms are indicated by means of dotted lines. The definition of S I f requires that the labeled reactant structures represent only one physically distinct configuration, whereas the configurations of the labeled activated complex, on the contrary, have to be all physically distinguishable. These conditions are satisfied, since in the reactant structure free rotation is possible, whereas in the activated complex this is prevented by the bridged hydrogen atom. Consequently, the statistical factor for the forward reaction, SIf, amounts to 4. For the determination of the statistical factor for the reverse reaction, S I , , any one of the four labeled activated complex structures of Table IV may be chosen as a starting point. It is clear that, whichever is chosen, only one physically distinct labeled reactant configuration can be reached from the given labeled activated complex configuration. Hence, sir equals one so that eq 10 yields
ne = s*f/s*r= 4 / 1 = 4
This result is identical with the one obtained with the method based on the statistical factors, slf and S I , . For hydride shift, it follows from Table IV, i.e., from the method based upon statistical factors, that the number of single events equals twice the number of hydrogen atoms on the carbon atom in the position a with respect to the charge-bearing carbon atom in the reacting carbenium ion: ne = 2naH. This is a formula that is easily implemented into a computer algorithm. For the other types of elementary reactions, an analogous procedure has been followed. The results are summarized in Table V and have been verified for each type of reaction, using the method based on symmetry numbers. Thermodynamic Constraints on the Rate Coefficients. (a) Constraints on the Rate Coefficients for Protonation and Deprotonation. For any arbitrary pair of olefin isomers appearing in the reaction network, a reversible reaction pathway can be found which connects both olefins via a series of carbenium ions. The existence of such reversible pathways gives rise to relations between the involved rate coefficients, since the equilibrium constant for the isomerization between the olefins does not depend on how this isomerization is achieved. Consider, by way of example, two olefin isomers that can be connected via one single carbenium ion, e.g.,
(11)
The global symmetry numbers for the reactant and the activated complex are calculated as follows: reactant
\
Tb
\
three internal 3-fold axes (a, b, c ) and one internal 2-fold
The equilibrium constant for the isomerization between these two olefins can be expressed as the product of the equilibrium constants for the reactions in their respective isomerization pathways via the common carbenium ion. With obvious notations, this yields 0,) = KPr/De(Ol + R ~ + ) K D ~ / P ~+ ( R0,) ~+ Kisom(O1 (13) For an elementary reaction, the equilibrium constant can
904
Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989
be equated to the ratio of the forward to the backward rate coefficient. By use of this property, together with the observation that R1+ is a secondary ion, eq 13 becomes
Applying the above treatment leads to
-*
Equation 14 can be simplified if it is assumed that the activated complex in a (de)protonation reaction has a planar structure resembling the olefin structure but with the double bond not completely broken (formed) yet. This assumption, which was also used in determining the number of single events for protonation and deprotonation, is analogous to the one made by Willems and Froment (1988) in relation to the decomposition of radicals in the thermal cracking of light hydrocarbons. Pursuing this line of thought, it seems reasonable to assume that the differences in stability between the olefin isomers are maintained in the corresponding activated complexes or, in other words, that the activation enthalpy and entropy, associated with the protonation of an olefin, are independent of the nature of the reacting olefin. Consequently, the nature of the reacting olefin is not accounted for in the definition of the rate coefficient for protonation, only the nature of the carbenium ion, so that kp,(O,;m) reduces to kp,(m). It is clear that in this way the number of rate coefficients for protonation no longer depends on the type of feed and amounts to two only: kpr(s)and kpr(t). Equation 14 then becomes
In order to rewrite eq 15 in terms of single-event constants, the number of single events is factored out of each of the rate coefficients, using the definition based on symmetry numbers (eq 3). It is thereby assumed that the activated complex has the same symmetry number as the related olefin, as suggested by the structural analogy between both species. Further, the symmetry numbers of the olefins are factored out of the isomerization equilibrium constant in the same way as was done for the rate constants (eq 1-4). Equation 15 then becomes
%?isom(ol 0,) = Un
u 2
(gR1+/GO2)iDe(S;02) (16) (flR,+/uO1)LDe(S;01) (g02/a02)hPr(S) (gO,/gO1)hPr(S)
All the symmetry numbers cancel one another, as well as the rate coefficients for protonation, so that eq 16 reduces to RIsom(O1 e 0 2 ) = hDe(s;o2)/hDe(s;o1) (17) This expression can be generalized for any pair of olefins for which an isomerization pathway via one and the same carbenium ion of type m exists, Le., for each of two olefins with a common skeletal structure and adjacent double bonds: R,,,,(O, + 0,) = KDe(m;O,)/KDe(m;O,) (18)
( g R 2 + / g*)hMS(s;s) (OR3+/ u04)~De(s;04) (go3/ uO,)hPr(s) (gR,+/'JO3)hDe(S;03j( g R B + / g t ) L M S ( S ; S ) ( g 0 4 / g 0 4 ) ~ P r ( s ) (19)
Once more, all the symmetry numbers cancel one another, as well as the rate coefficients for protonation and methyl shift. The reduced equation is then Risom(O3
e 0 4 ) = hDe(s;o4)/RDe(s;o,)
(20)
which is analogous to eq 18. It can be shown that eq 18 holds for any pair of olefin isomers, no matter what the number of carbenium ions involved in the reaction pathway connecting the two olefins may be. The only obvious condition that must be satisfied is that the carbenium ions on both ends of the connecting pathway are of the same type. The importance of the general validity of eq 18 becomes clear when the equation is rewritten as follows: RDe(m;Ojj= be(m;Or)Ei8nm(Or 0,)
(21)
0, represents a reference olefin isomer with the double bond preferably in such a position that both a secondary and a tertiary carbenium ion can be formed by protonation. Equation 21 shows that for a fraction with a given carbon number, further represented by CN fraction, the number of independent rate coefficients for deprotonation is determined solely by the number of different types of reactant carbenium ions, despite the fact that the rate coefficient assigned to each deprotonation reaction not only depends on the type of reacting carbenium ion but also on the identity of the product olefin. If only reactions involving secondary and tertiary carbenium ions are considered, there are only two independent rate constants for deprotonation per CN fraction. For the hydroisomerization and hydrocracking of n-octane, involving 4 CN fractions (C8, C5, C4, C&, the above implies that from the 85 (Le., 75 6 3 + 1) deprotonation coefficients only 7 are independent. Equation 21 can only be applied when the olefin isomerization equilibrium constants are available. For individual olefin isomers with more than six carbon atoms, experimental data for the thermodynamic state functions cannot be found in the literature, but estimates can be obtained from Benson's group contribution method (Benson et al., 1969). (b) Constraints on the Rate Coefficients for Isomerization. Unless the double bond is in the terminal position, olefin protonation always produces two carbenium ions which can be interconverted through a single 1,2-hydride shift. If the double bond is located between a secondary and a tertiary carbon atom, the product carbenium ions are of different types, namely, tertiary and secondary, as illustrated in the following example:
+ +
For the more general case of two olefins with a different skeletal structure, the isomerization pathway implies at least two carbenium ions, e.g., 2:
-\,p\ 'Z
5
_t
- 1
4,-
Y
R i
Since the equilibrium constant for the isomerization between the two carbenium ions does not depend on the reaction pathway, the following equation can be written:
Ind. Eng. Chem. Res., Vol. 28, No. 7, 1989 905
Proceeding through the same steps as in the previous section leads to the following relation between the single-event rate coefficients:
This is automatically satisified for two olefins within the same CN fraction, since eq 18 comprises in fact two relations when both olefin isomers can produce secondary and tertiary carbenium ions: Risom(0,
e
01) =
~De(s;o])/iDe(S~o~) = kDe(t;01)/iDe(t;0~)
This equation can be easily generalized for any olefin 0, with a double bond located between a secondary and a tertiary carbon atom: iHs(t;s) -iHS(s;t)
-_
&pr(s)hDe(t;o,)
kp,(t) hDe(s;oj)
(24)
For an isomerization reaction between secondary and tertiary carbenium ions, which consists of a methyl shift or P C P branching, the two corresponding olefin isomers have to be included in the reaction scheme, e.g., (061
& -
(Si 1
t H t
L
-
~
Ht
The latter equation directly leads to eq 29. For olefins with different carbon numbers, eq 29 is not automatically satisfied, so it can be used to further reduce the number of independent rate coefficients for deprotonation. For the hydroisomerization and hydrocracking of n-octane, this means that from the 85 deproto_nation coefficients only 5 y e truly indepsndent ones, e.g., kp,(s;Or(Cs)),k&;Or(C4)), kDe(s;or(c5)),kD&;Or(c8)), and kQe(t;Or(Cg)). Via eq 29, the coefficients kDe(t;0,(C5))and kDe(t;Or(C4))can be expressed in terms of the 5 previous ones, whereas the 78 remaining deprotonation coefficients in turn can be expressed in terms of the 7 previous ones, via eq 21. Concentrations of Paraffins, Olefins, and Carbenium Ions and Rate Equations. On the basis of the preceding sections, the rate equations for observable and intermediate species can now be constructed. Paraffins disappear by dehydrogenation and are formed by hydrogenation of olefins on the metal sites:
P, + O,, -
v+
The relationship between the single-event rate coefficients, derived from this scheme, is
Both olefins 0 6 and O7 can produce a secondary carbenium ion by protonation so that eq 18 can be applied: zisom(O6
F=
0,) = iDe(s;o7)/iDe(s;o6)
(26)
Combining eq 25 and 26 and rearranging leads to the following expression, which is of the same type as eq 24: iMS(t;s) -gMS(S;t)
-_
hPr(s) i D e ( t ; o 6 ) kPr(t) hDe(s;o6)
(27)
iHS(t;S)
iMs(t;s) kMS(S;t)
bHS(S;t)
hpCp(t;S) kpCp(S;t)
&pr(s)i D e ( t ; o j ) kpr(t) hDe(s;oj)
+ H2
(31)
The subscript j in the product olefin denotes that one paraffin can produce several olefins which are double-bond isomers with respect to one another. The distinction between these double-bond isomers is essential, for the position of the double bond determines which carbenium ions can be formed from the olefin. In other words, different elementary reactions are associated with different double-bond isomers. From the same point of view, it is not necessary to distinguish between geometric isomers, so cis and trans isomers can be lumped. This was explicitly taken into account in the determination of the “number of single events” and the calculation of the equilibrium constants for olefin isomerization and paraffin dehydrogenation. The net rate of formation of a paraffin is then represented by RpL= C [ ~ H ( ~ ~ ) C O-, ,~PDHH~ ( ~ ~ ) C P , ](32)
and which is easily generalized. A similar expression can be derived for P C P branching. It then becomes possible to write a general expression for the three types of isomerizations between secondary and tertiary carbenium ions: -=-=-=-r.i---
(30)
(28)
The three equalities which are summarized in eq 28 are thermodynamically based relations between rate constants, which are-used to exprejs the isomerization rate constants kHS(t;s), IzMs(t;s), and kpCp(t;s), respectively, in terms of the rate constants for the respective reverse reactions and a group consisting of rate constants for protonation and deprotonation. Clearly, eq 28 is a direct consequence from the assumption that differences in stability between isomeric carbenium ions are determined by the character of the charge-bearing carbon atom only. For eq 28 to be independent of the olefin appearing in the deprotonation rate coefficient, the following relation should be valid for any arbitrary pair of olefins:
I
The olefins formed on the metal function are protonated on the acid sites. Per olefin, two carbenium ions can be formed: 0,
+ H+
(33)
The subscripts m, and m2 refer to the type of carbenium ion. Only protonation reactions producing the more stable secondary and tertiary carbenium ions are considered. If the olefin has a terminal double bond, one of the carbenium ions in (33) is primary and the corresponding protonation reaction is excluded from the reaction network. On account of the well-accepted phenomenon of competitive sorption on the acid sites (Weitkamp, 1978), protonation reactions of light olefins (e.g., with five or less carbon atoms) are excluded from the reaction network as well. The formation of olefin Oij as a result of carbenium ion cracking should be taken into account for the general network: R+,
-
Oij
+ R+,
(34)
906 Ind. Eng. Chem. Res., Vol. 28, No. 7 , 1989
The general expression for the net rate of formation of an olefin then becomes
Rot, =
~ H ( ~ ~ ) C O+ ~ P H , kDe(ml;Oy)CR+,, ml + kDe(m2;O~~)CR+,, z, [kp,(mJ + k p , ( m z ) l C ~ , C ~ ++kCr(V;W,Oy)CRt, (35) kDH(ij)cPt -
The pseudo-steady-state approximation, applied to the olefin intermediates, sets the net rates of formation of the olefins equal to zero: Ro,, = 0
(36)
If the rate-determining step is on the acid function, combination of eq 32,35, and 36 yields the following expression for the net rate of formation of a paraffin: Rp, = ClkDe(ml;O,,)CRC,j,l+ kDe(m2;Oi])CRC,,zI
[kp,(mi) + kp,(m,)]Co,,C~++ ~c~(V;W,OI,)CR+,! (37) In this expression, as well as in the rate expressions for the carbenium ions which will be derived below, each rate constant should be interpreted as the product of the single-event rate constant, k , and the number of single events, ne, The reactions through which carbenium ions are formed and disappear have been described in a previous section. The general expression for the rate of formation of a caibenium ion is RR+, = (Ckp,(m)CoCH++ CkHs(q;m)CR+q+ 0
q
CkMs(r;m)CR+,+ CkpCp(u;m)CR+,+ I
U
Ckc,(v;m,O’ )CR+,]- ICkDe(m;O) + C k d m ; q ) + 0
V
q
CkMs(m;r) + Ckpcp(m;u) + CkC,(m;Z,O” )VR+,(38) r
z
U
Since the various carbenium ions and olefins may have different structures, the corresponding subscripts (ij)are omitted; only the subscripts referring to the character of the carbenium ions are retained. To calculate the concentrations of the carbenium ions, the pseudo-steady-state approximation is applied so that RR+, = 0
(39)
Equation 38 still contains the unknown concentration of free active sites, however. Since the active sites are either free or occupied by carbenium ions, the following equation has to be satisfied:
c, = CH+ + CCRt, m
(40)
where C, is the total concentration of active sites. Introducing relative concentrations, defined as C*H+ = CH+/Ct C*R+, = CR+,/Ct (41) into eq 40 leads to C*H+ = 1 - CC*R+, m
(42)
The total concentration of active sites is inserted into the rate constants:
k* = kCt (43) Together with the relative concentration of free active sites, (eq 42), these modified rate constants are substituted into the rate expressions for the carbenium ions (eq 38). Setting the latter equal to zero (eq 39) and rearranging into a set of linear equations permits the relative concentrations of the carbenium ions to be calculated in terms of the olefin
concentrations. Subsequently, the relative concentration of free active sites is calculated from eq 42. The relative concentrations of carbenium ions and free active sites obtained in this way are substituted into the rate expressions for the paraffins (eq 37), rewritten to account for eq 41 and 43. This results in equations that express the net rates of formation of the paraffins in terms of the physisorbed olefin concentrations. The latter can be calculated in terms of the physisorbed paraffin concentrations, since quasi-equilibrium was assumed for the (de)hydrogenation step: (44) The equilibrium constants for dehydrogenation, KDH,l,, are calculated by means of the thermodynamic state functions. For the paraffins and hydrogen, these can be found in the literature, but for the olefins, estimates based upon Benson’s group contribution method were used (Benson et al., 1969). Physical adsorption is also assumed to be in quasiequilibrium. It is described by using a Langmuir-type isotherm, as was found in previous lumped kinetic studies (Steijns and Froment, 1981; Baltanas et al., 1983): (45) The unknown saturation concentration of physisorbed hydrocarbons, Csat, is lumped into the rate constant which multiplies the olefin concentration, i.e., the protonation rate constant. Since a light hydrocarbon is further from its saturation pressure than a heavier one, the adsorption of all compounds lighter than C6 may be disregarded above 450 K (Gates et al., 1978). Equations 44 and 45 can be combined to give
The olefin concentrations are now expressed in terms of partial pressures of hydrocarbons and hydrogen, which are experimentally accessible, so that substitution in the rate expressions for the paraffins finally leads to the equations for the net rates of formation of the paraffins in terms of observable quantities.
Kinetic and Adsorption Parameters for the Hydroisomerization of n -Octane on a Pt/US-Y Zeolite The hydroisomerization and hydrocracking of n-octane on an ultrastable Y zeolite, containing 0.5 wt % Pt, was studied over a wide range of temperatures (180-240 “C) and pressures (10-100 bar) in a Berty-type reactor with complete mixing of the gas phase. The US-Y faujasite had a very low acidity, as shown by IR, DTA, TG, and T P D of NH3. The details of the equipment, materials, procedures, and results were published before (Vansina et al., 1983). The primary products of the reaction of rz-octane are monobranched methylheptanes. Multibranched feed isomers and cracked products are formed in consecutive reactions. In a first attempt to derive the parameters of a fundamental model for hydroisomerization and hydrocracking, the problem is partitioned, so as to limit the number of reactions and parameters. A t low conversions (
