n-Hexadecane Mixture on

Jun 15, 1997 - sConn., Columbia, Maryland 21044. A mechanism-derived lumping strategy for modeling the acid-cracking kinetics of hydrocarbon mixtures ...
0 downloads 0 Views 441KB Size
Download PDF
2954

Ind. Eng. Chem. Res. 1997, 36, 2954-2963

Mechanistic Modeling of a 1-Phenyloctane/n-Hexadecane Mixture on Rare Earth Y Zeolite Beth A. Watson and Michael T. Klein* Center for Catalytic Science and Technology, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716

Robert H. Harding W. R. Grace & Co.sConn., Columbia, Maryland 21044

A mechanism-derived lumping strategy for modeling the acid-cracking kinetics of hydrocarbon mixtures based on a limited set of pure component experimental data was tested in terms of its ability to predict the kinetics and product spectra from the reaction of a 1-phenyloctane/nhexadecane mixture. The modeling approach has two main components. First, reactant and product molecules are organized into compound classes, e.g., paraffins, olefins, and aromatics. Second, the elementary steps of the acid cracking of each member of a compound class are constrained by quantitative structure-reactivity relationships (QSRRs) determined from pure component experiments only. This two-dimensional, mechanism-derived lumping approach provided a significant reduction in the number of parameters required to model the cracking reaction. Application of this lumping strategy to the acid cracking of the phenyloctane/ hexadecane reacting mixture provided good agreement between experimental data and a kinetic model containing only 14 parameters obtained from separate pure component experiments. The model revealed the applicability of the QSRR-based lumping approach to the cracking kinetics of hydrocarbon mixtures. Introduction Lumping is an important part of the history of chemical reaction engineering modeling because of two traditional concerns. First, the statistical significance and ease of use of reaction models provide motivation for the formulation of simple, lumped kinetic descriptions. Second, historical limitations on the available analytical chemistry provided, as the initial conditions for models, only groups or aggregates of molecules with similar boiling points or solubility classes. Recent advances in analytical chemistry now provide modelers with very fine-grained reactant lumps; indeed, for up to gas oil boiling range material, it is reasonable to view the lumps as molecular isomers. This newly available structural information has motivated the formulation of a new class of molecularly explicit models. These “delumped” models capture the detail and complexity of multicomponent hydrocarbon mixtures. These notions have been developed for pyrolysis (Clymans and Froment, 1984; Hillewaert et al., 1988) and catalytic (Feng et al., 1993) conversion models. Mobil’s SOL (Quann and Jaffe, 1992) lumping approach is an insightful treatment of catalytic hydroprocessing modeling along these lines. Liguras and Allen (1989a,b) have treated fluid catalytic cracking (FCC) reaction chemistry well in this manner. Several advantages of these structure-explicit models are compelling. First, the molecular formulation allows the introduction of fundamental physical/organic chemistry to chemical reaction engineering models. Second, the derived molecular product slate provides a connection to both performance and environmental properties of the product. These molecule-based models introduce a new obstacle to be overcome, however: the required set of rate * To whom correspondence should be addressed. FAX: (302) 831-1810. E-mail: [email protected]. S0888-5885(96)00508-8 CCC: $14.00

constants can appear daunting. Realistic model or pure component experimental programs cannot be expected to provide all of the possible thousands of molecular species’ rate constants. Direct parameter estimation from complex mixture data is difficult and statistically questionable. That is, the direct estimation of order 105 kinetic parameters via optimization to experimental data suffers from the statistical degrees of freedom. Moreover, these structure-explicit models carry a statistical and computational burden. Overall, the direct mechanistic simulation of the reactions of hydrocarbon mixtures is difficult because of the large number of species, reactions, and associated rate constants. The sheer size of this and similar problems suggests that the search for simplifying approximations would be useful. This motivated the development of a twodimensional lumping scheme that organizes the reacting mixture components and reduces the number of (adjustable) reaction parameters without significantly sacrificing the advantages of the structure-explicit models noted above. The essential guiding hypothesis was that a limited database of pure component experiments could provide kinetic parameters of a sufficiently fundamental nature that for a given catalyst, at least, they would be independent of the reactant structure and could thus be used to predict the behavior of hydrocarbon mixtures. Solid acid-catalyzed cracking reactions of hydrocarbons were chosen to help develop this modeling strategy because of their profound significance in refining, e.g., FCC, hydrocracking, alkylation, and reforming, as well as other chemical conversions. The complexity of a hydrocarbon mixture diminishes when the molecules are viewed as belonging to compound classes. That is, molecules can be lumped into one of paraffin, isoparaffin, olefin, alkylbenzene, alkylnaphthene, or alkylhydroaromatic compound classes. The literal complexity of the mixture derives from the sheer number and statistical arrangements of substit© 1997 American Chemical Society

Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 2955

uents, ring sizes, and other structural attributes of these compound classes. The complexity of acid-cracking chemistry diminishes when the elementary steps of reaction are lumped into the classic protonation, hydride transfer, β-scission, isomerization, etc., families. These observations suggested that a two-dimensional, mechanism-derived lumping scheme that recognizes the similarities in compound types and associated cracking reaction families would be fruitful. This report begins to develop this lumping approach, as follows. First, experimental cracking data for a mixture of 1-phenyloctane and n-hexadecane on a rare earth Y (REY) catalyst are described to provide a qualitative basis for model development and the experimental reality for the ultimate model assessment. The kinetic model is then developed in terms of reaction families for the elementary steps of acid cracking. This model provided an elementary step description of the time evolution of reactant conversion and product evolution. The kinetics of each reaction family were summarized in terms of a quantitative structurereactivity relationship (QSRR), the parameters of which being obtained from separate pure component experiments. The favorable agreement between the experimental data and this a priori model allowed further scrutiny of the key reactions underlying the conversion of the mixture. Experimental Section The 1-phenyloctane and n-hexadecane (Aldrich, 99%+ purity) reactants were obtained commercially and used as received. The reacting mixture was composed of 61.2% 1-phenyloctane (PO), 37.5% n-hexadecane (HD), and 1.3% hydrocarbon impurity by weight, as determined by gas chromatography. The activity and selectivity measurements were taken at W.R. Grace & Co.-Conn. using an isothermal fixed bed reactor. The reactor vessel was a quartz tube approximately 50 cm in length and 2 cm in diameter. The catalyst was pressed to 40/80 mesh size, positioned in the center of the reaction tube, and preheated for 30 min at 500 °C under 10 cm3/min nitrogen flow. The quartz tube was heated with a three-zone furnace, and the actual catalyst temperature was measured with a type-K thermocouple in the center of the bed. The mixture was pumped into the reaction chamber with a syringe infusion pump at the rate of 0.6 g/min. Nitrogen was cofed with the mixture at the rate of 10 cm3/min (at STP) set by a mass flow controller. The cracking reactions were run for 3 min time on stream at 500 °C and 101.3 kPa. The reactant partial pressures were 58.7 kPa for phenyloctane and 30.2 kPa for hexadecane. The weight hourly space velocity (WHSV) was varied by changing the amount of catalyst in the reactor tube. The space velocities spanned the range of 72-360 h-1. To maintain a constant thermal mass, the catalyst was diluted with alundum (a low surface area alumina) to a constant bed volume of 4 cm3. Alundum by itself converted less than 1% of the mixture at all space velocities reported in this work. Liquid products were collected in an ice bath and then analyzed by gas chromatography. The volume of the gas products was determined by water displacement. The gas products were analyzed by flame ionization detector and thermal conductivity detector. Coke levels were determined by mass difference between the catalyst after 100 °C calcination and 540 °C calcination for 1 h. Only experiments with mass balances above 97%

Figure 1. Phenyloctane (PO)/hexadecane (HD) cracking kinetics at 500 °C with REY: conversion versus space time.

are reported in this study. Typical mass balances were 100 ( 3 wt %. The catalyst was a rare earth Y (REY) zeolite with a bulk Si/Al ratio of 2.7. The zeolite was ammoniumexchanged and calcined to its acidic form. The zeolite was spray-dried with kaolin clay and a silica binder. The catalyst was composed of 40% rare earth Y zeolite, 40% clay, and 20% silica binder. The clay and binder materials were tested separately and showed less than 1% conversion of the reactants. The surface area and pore volume of the catalyst were 103 m2/g and 0.11 cm3/ g, respectively, as determined by nitrogen porosimetry. The mean particle size of the catalyst was 40.0 µm as determined with a Malvern particle size analyzer. Prior to the cracking experiments, the catalyst was steamdeactivated for 4 h at 816 °C (95% steam). The unit cell size of the steam-deactivated catalyst was 24.39 Å as determined by X-ray diffraction. Experimental Results Figure 1 summarizes the conversion kinetics of the mixture and its reactant components. Additionally, the results from pure component experiments (Watson et al., 1996a,b) are included in Figure 1 to facilitate comparison. The mixture conversion (xmix ) 1 - (NPO + NHD)/(NPO0 + NHD0)) ranged from 0.281 at a WHSV-1 of 0.0028 h to 0.587 at a WHSV-1 of 0.014 h. The individual conversion of phenyloctane in the mixture ranged from 0.333 to 0.673, whereas that for hexadecane ranged from 0.180 to 0.420. The rate of phenyloctane cracking was approximately the same in the mixture as in the pure component study. In contrast, the conversion of hexadecane was distinctly lower in the mixture than in the pure component case. The rate of pure component hexadecane cracking was similar to the rate of phenyloctane cracking; however, the rate of hexadecane cracking in the mixture was approximately half the rate of phenyloctane cracking. Clearly, phenyloctane inhibited the cracking of hexadecane. Previous studies (Jacob et al., 1976; Guerzoni and Abbot, 1993) have shown that aromatics competitively adsorb on the catalyst and retard the reaction rate of paraffins in the cracking of mixtures. The product identities, product selectivities, and reaction pathways probe the kinetics of the reaction mechanism. The cracking products and their molar selectivities (si ) yi/xmix; yi ) Ni/(NPO0 + NHD0)) over the

2956 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 Table 1. 1-Phenyloctane/n-Hexadecane Mixture Cracking Product Distributions: Selectivities at 500 °C with REY WHSV-1, h mixture conversion 1-phenyloctane conversion n-hexadecane conversion

0.0028 0.281 0.333 0.180

0.0056 0.387 0.454 0.256

0.0083 0.512 0.592 0.356

0.014 0.587 0.673 0.420

methane ethane ethene propane propene n-butane isobutane butenes n-pentane isopentane pentenes n-hexane branched hexanes hexenes n-heptane branched heptanes heptenes n-octane branched octanes octenes n-nonane branched nonanes nonenes n-decane branched decanes n-undecane branched undecanes n-dodecane branched dodecanes n-tridecane n-tetradecane benzene toluene C2 benzenes C3 benzenes C4 benzenes C5 benzenes hydrogen

0.022 0.021 0.040 0.047 0.230 0.050 0.128 0.253 0.025 0.142 0.138 0.016 0.088 0.073 0.014 0.038 0.087 0.023 0.094 0.031 0.003 0.018 0.006 0.003 0.010 0.002 0.003 0.001 0.005 0.001 0.001 0.282 0.047 0.042 0.020 0.078 0.062 0.003

0.019 0.017 0.035 0.058 0.228 0.062 0.146 0.226 0.026 0.168 0.105 0.015 0.111 0.068 0.014 0.045 0.086 0.020 0.099 0.022 0.003 0.021 0.002 0.003 0.009 0.002 0.005 0.001 0.004 0.001 0.001 0.249 0.049 0.046 0.024 0.079 0.079 0.003

0.018 0.017 0.036 0.070 0.261 0.073 0.173 0.241 0.029 0.193 0.103 0.016 0.121 0.060 0.013 0.045 0.078 0.018 0.091 0.016 0.003 0.022 0.002 0.003 0.008 0.002 0.005 0.001 0.004 0.001 0.000 0.234 0.048 0.044 0.023 0.073 0.079 0.003

0.013 0.013 0.027 0.074 0.230 0.079 0.178 0.208 0.029 0.205 0.086 0.016 0.135 0.040 0.013 0.109 0.025 0.018 0.106 0.012 0.003 0.026 0.002 0.003 0.013 0.002 0.005 0.001 0.003 0.000 0.001 0.226 0.048 0.044 0.025 0.081 0.089 0.003

coke, wt % yield product recovery index, %

0.050 95.5

0.102 94.2

0.194 92.5

0.404 92.2

REY-based FCC catalyst at 500 °C are listed in Table 1 for the mixture. This compilation also includes the coke yield (wt %) and the product recovery index, defined as the total weight of identified products divided by the amount of reactant fed. Product Spectra and Selectivities. The products of phenyloctane/hexadecane cracking included normal paraffins, isoparaffins, olefins, benzene, toluene, C2C5-substituted benzenes, hydrogen, and coke. The product recovery indices ranged from 92% to 96% over all conditions studied. Benzene, propene, and butenes were observed in highest selectivity. Other products observed in high selectivity included propane, n-butane, isobutane, isopentane, pentenes, branched hexanes, hexenes, heptenes, branched octanes, toluene, C4substituted benzenes and C5-substituted benzenes. These products were the same as those observed from the pure component cracking of phenyloctane and hexadecane (Watson et al., 1996a,b). Benzene, propene, butenes, and branched octanes were observed in highest selectivity for phenyloctane cracking, and propene, butenes, and pentenes were the dominant products of hexadecane cracking. Figure 2 summarizes the conversion dependence of the product class spectra for phenyloctane/hexadecane cracking as plots of molar selectivity versus mixture

Figure 2. Product distributions for phenyloctane/hexadecane cracking at 500 °C with REY: selectivities to compound classes.

conversion. The selectivity to normal paraffins was relatively constant with conversion. The selectivity to isoparaffins increased with conversion such that at high conversion isoparaffins were the dominant product class. The selectivity to olefins decreased with conversion and mirrored the increase in selectivity to isoparaffins, which indicated that olefins are being converted to isoparaffins via hydrogen transfer reactions. The selectivity to aromatics was relatively constant with conversion. Reaction Pathways. The foregoing results indicate that the reaction pathways of the mixture were qualitatively similar to the pathways of the pure components. The paraffins and olefins were produced via dealkylation and cracking in the alkyl side chain of phenyloctane and by cracking of hexadecane. Isomerization was also apparent. Dealkylation of phenyloctane produced benzene, whereas cracking in the side chain evidently led to toluene and the C2-C5-substituted benzenes. Trace levels of bicyclic aromatic compounds were observed and were likely formed from self-alkylation of phenyloctane’s aromatic ring by its alkyl side chain. Hydrogen was likely formed through protolytic cracking. The likely coke precursors were olefins and the bicyclic compounds. More quantitative information about the pathways in the mixture can be obtained through comparisons of the product selectivities in the mixture with the selectivities which would be expected based on the pure component data. Figures 3-6 illustrate these comparisons for the major n-paraffinic, isoparaffinic, olefinic, and aromatic products of the mixture, respectively. In these plots, the pure component data were used to predict the product selectivities in a hypothetical independent mixture at equivalent conversions of phenyloctane and hexadecane. These predictions were compared with the actual mixture data to determine any differences in product selectivities due to mixture effects. Figures 3 and 4 indicate that the mixture had higher selectivities to the paraffinic products than those predicted by the pure component data. Hydrogen transfer was likely enhanced in the mixture, which resulted in higher selectivities to paraffinic products. A possible explanation for this enhancement effect is that hydrogen transfer was faster with the benzylic-position-containing phenyloctane than with hexadecane. Thus, the species produced from hexadecane cracking underwent more rapid hydrogen transfer with phenyloctane in the

Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 2957

Figure 3. Comparison of product selectivities to normal paraffins in the mixture and as predicted from pure component data for phenyloctane/hexadecane cracking at 500 °C with REY.

Figure 4. Comparison of product selectivities to isoparaffins in the mixture and as predicted from pure component data for phenyloctane/hexadecane cracking at 500 °C with REY.

Figure 6. Comparison of product selectivities to aromatics in the mixture and as predicted from pure component data for phenyloctane/hexadecane cracking at 500 °C with REY.

tivities expected based on pure component results. Figure 6 illustrates that the selectivities to the aromatic products were lower in the mixture than was expected. In particular, the selectivity to benzene was approximately 20% lower in the mixture than that predicted by the pure component data. An explanation for this result is that the reaction pathway contributions to the conversion of phenyloctane were different in the mixture those in the pure component. As just noted, hydrogen transfer was enhanced in the mixture. Evidently the contribution of hydrogen transfer to phenyloctane conversion, relative to the contributions from the dealkylation and protolysis pathways, was greater in the mixture than in the pure component experiments. Thus, at equivalent phenyloctane conversion, the selectivities to the aromatic products were lower in the mixture than expected. These experimental results suggest that the kinetic interactions in a mixture can lead to rate enhancement or suppression. Mechanistic modeling of these interactions would lead to a better understanding of catalytic cracking of complex systems and would improve the translation of pure component data to the modeling of mixtures. Model Development

Figure 5. Comparison of product selectivities to olefins in the mixture and as predicted from pure component data for phenyloctane/hexadecane cracking at 500 °C with REY.

mixture than they did with hexadecane in the pure component study. Figure 5 indicates that the mixture selectivities to the major olefinic products were comparable to the selec

Mechanistic models have previously been developed to describe the catalytic cracking of phenyloctane and hexadecane as pure components (Watson et al., 1996a,b). Both models reproduced the experimentally observed kinetics well. The models were based on the elementary steps for acid-catalyzed cracking reactions which involve carbenium and carbonium ion intermediates. The 15 classes of elementary steps with the associated atomic rearrangements summarized in the reaction matrices of Table 2 were used to construct the individual models. These 15 elementary steps are (1) protonation, (2) paraffin adsorption, (3) β-scission, (4) carbonium ion cracking, (5) hydride shift, (6) methyl shift, (7) isomerization, (8) reverse isomerization, (9) ring closure, (10) ring opening, (11) ring contraction, (12) ring expansion, (13) hydride transfer, (14) deprotonation, and (15) paraffin desorption. In terms of a catalytic cycle, protonation and paraffin adsorption are the initiation reactions that create carbocations. The primary cracking mechanisms are β-scission and carbonium ion

2958 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 Table 2. Reaction Matrices for the Phenyloctane/Hexadecane Cracking Model

cracking. Hydride shift, methyl shift, and isomerization/reverse isomerization are rearrangement reactions that produce β-scission precursors. Ring closure/opening and ring contraction/expansion are rearrangement reactions for alkylaromatic species that produce coke precursors. Hydride transfer is the bimolecular reaction of a carbenium ion with a saturated molecule that leads to a net exchange of saturation. Deprotonation and paraffin desorption terminate the catalytic cycle. Reaction Bond-Ion Matrices. A unifying property of each of these reactions is that the connectivity of only

a few (three to four) of the atoms in the involved molecules changes. Thus, the bond breakage and formation resulting from each of these reaction families can be summarized succinctly in terms of the formal reaction matrix (Broadbelt et al., 1994) for each. Mathematical addition of the reaction matrix to the reactant submatrix constituting the few involved atoms yields the product submatrix. Table 2 illustrates the reaction matrices for the ionic chemistry reaction families. Note that for the cases of isomerization and reverse isomerization, two reaction matrices are needed for each family

Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 2959 Table 3. Rules for the Application of the Elementary Step Reaction Matrices of Table 2 in the Construction of the Phenyloctane/Hexadecane Cracking Model reaction family protonation paraffin adsorption β-scission carbonium ion cracking hydride shift methyl shift isomerization reverse isomerization ring closure ring opening ring contraction ring expansion hydride transfer

deprotonation paraffin desorption

reaction rules require aromatic ring or double bond allow proton attack on C-C and C-H bonds in alkyl side chain of phenyloctane and on C-C bonds in hexadecane require at least three consecutive carbons adjacent to charged carbon to prohibit methyl ion formation prohibit methyl ion and proton formation allow all carbenium ions to react, permit branched alkyl ions with more than eight carbons to only react between tertiary carbon, R-carbon to branch and β-carbon to branch require methyl-branched carbenium ion prohibit change in degree of branching require linear carbenium ion with at least four carbons require formation of methyl-branched ion require methyl-branched carbenium ion require alkylphenyl carbenium ion with charge in γ-position or δ-position allow reverse of ring closure reaction for bicyclic R9- and R10-based carbenium ions require bicyclic r10 carbenium ion require bicyclic R9 carbenium ion with an alkyl group in the R-position require abstracting carbenium ion to be an alkyl ion with 12 or less carbons, a linear alkylphenyl ion with the charge in a secondary position, or a branched alkylphenyl ion with the charge in the tertiary or benzylic position allow hydride abstraction from secondary positions in phenyloctane side chain and secondary positions in hexadecane require carbenium ion require alkyl ions to have less than ten carbons allow reverse reaction of paraffin adsorption

to represent the two different products which can be formed during reaction owing to the nature and options of the protonated-cyclopropane intermediate (Gates et al., 1979). Reaction Rules. Formally, the construction of the pure component models amounted to application of the reaction family matrices to the phenyloctane, hexadecane, and REY reactants and subsequent product species. Application of these reaction family matrices in the mechanistic modeling of the mixture is conceptually straightforward since the same steps are operative. However, in the mixture, the cross reactions, which involve interaction of ions from one reactant with the other reactant and derived products, must also be included. Several logical chemical “reaction rules” were invoked to guide the construction of the pure component models. These same rules were also used to construct the mixture model and are shown in Table 3. The rules in Table 3 also account for the cross reactions in the mixture. The initial reactants were phenyloctane, hexadecane, and the REY catalyst, which was represented by the protons or acidic sites. The number of Brønsted acid sites on the catalyst was set equal to the number of aluminum cations in the zeolite. Phenyloctane was permitted to undergo protonation of the aromatic ring. Reaction products, including alkylbenzenes, bicyclic aromatics, and olefins, were also allowed to undergo protonation. Phenyloctane was permitted to undergo paraffin adsorption to form carbonium ions by protons attacking either C-C or C-H bonds in the alkyl side chain. Proton attack was also allowed on the C-C bonds in hexadecane. Carbenium ions formed during reaction were permitted to crack via β-scission. The smallest ion formed from cracking was the ethyl ion; β-scission to methyl ions was not permitted. Carbonium ions formed from proton attack on C-H bonds decomposed to produce hydrogen and a carbenium ion. Carbonium ions formed from proton attack on C-C bonds decomposed to a paraffinic molecule and the corresponding carbenium ion. Decomposition which formed the energetically unfavorable methyl ion or proton was not permitted.

All carbenium ions were permitted to undergo rearrangement via hydride shift. For branched alkyl ions with more than eight carbons, hydride shift was only permitted between the tertiary carbon, the carbon in the R-position to the branch, and the carbon in the β-position to the branch. These alkyl ions would encompass the large branched ions in highest concentration since they are the most stable ions or would produce the most stable ions via β-scission. Carbenium ions with methyl branches could undergo methyl shift as long as no change in the degree of branching occurred. Linear alkyl and alkylphenyl carbenium ions could react via isomerization to form methyl-branched ions. Only linear ions were permitted to react to singly branched ions; singly branched ions were not permitted to form multibranched ions. Reverse isomerization was permitted for ions with methyl branches. Alkylphenyl carbenium ions with the charge located in the γ-position or δ-position were permitted to undergo ring closure reactions to form bicyclic R9 or R10 carbenium ions (where Ri indicates i carbons in rings). The reverse reaction, ring opening, was also permitted. Bicyclic R10 carbenium ions were allowed to undergo ring contraction to form bicyclic R9 carbenium ions. Bicyclic R9 carbenium ions with an alkyl group in the R-position were permitted to undergo ring expansion to form bicyclic R10 carbenium ions. Linear and branched alkyl ions with 12 or fewer carbons were allowed to react via hydride transfer. Linear alkylphenyl ions with the charge in a secondary position and branched alkylphenyl ions with the charge in the tertiary or benzylic position were also allowed to react via hydride transfer. Protons were not permitted to participate in hydride transfer. Hydride abstraction was permitted from the secondary positions in the alkyl side chain of phenyloctane and from the secondary positions in hexadecane since these positions yield more stable ions and phenyloctane and hexadecane are the species present in highest concentrations. All carbenium ions were permitted to undergo deprotonation with the exception of alkyl ions containing more than nine carbons, which was consistent with the olefinic

2960 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997

products observed experimentally. All carbonium ions could desorb to reform phenyloctane or hexadecane. Reaction Network and Associated Equations. Application of the reaction matrices in Table 2, with the associated rules of Table 3, generated a mechanistic model totaling 5717 reactions which could be organized into reaction families as follows: 280 protonation reactions, 24 paraffin adsorption reactions, 644 β-scission reactions, 37 carbonium ion cracking reactions, 804 hydride shift reactions, 102 methyl shift reactions, 247 isomerization reactions, 247 reverse isomerization reactions, 49 ring closure reactions, 49 ring opening reactions, 23 ring contraction reactions, 23 ring expansion reactions, 2884 hydride transfer reactions, 280 deprotonation reactions, and 24 paraffin desorption reactions. In addition to these reactions, two molecular level pathways were incorporated into the model to account for the appearance of coke. The tendency of olefins and polynuclear aromatics to form coke (Wojciechowski and Corma, 1986) was represented in the model by the following reactions: kOC

olefins 98 coke kBC

bicyclic aromatics 98 coke

(1)

EA ) E0 + R∆Hrxn

(4)

Equation 5 thus shows how the Polanyi relationship and the Arrhenius expression combined to represent the rate constant, kij, where i denotes the reaction family and j denotes the specific reaction in the family:

(2)

Molecular level pathways rather than mechanistic pathways were used since the mechanism of coking and the structure of coke are not well established. These pathways were able to account for coking in the pure component models successfully. Coke formation leads to catalyst deactivation, and a standard deactivation function (Froment and Bischoff, 1990) was incorporated into the model to link coke content to catalyst activity:

φ ) exp(-ωCc)

each family. Previous work has shown the ability of LFERs, such as the Polanyi relationship, to correlate rate constants to the standard enthalpy change of reaction (Semenov, 1958; LaMarca, 1992; Dumesic et al., 1993). More specifically, Dumesic and co-workers (Dumesic et al., 1993) have demonstrated the use of the Polanyi formalism for acid-catalyzed carbenium ion chemistry reactions. A recent application to n-heptane cracking (Watson et al., 1996c) validated the approach further. This same approach was also used successfully in the development of the pure component cracking models for phenyloctane and hexadecane (Watson et al., 1996a,b). For the present purposes, the rate constants within each reaction family were described in terms of a familyspecific Arrhenius A factor and the Polanyi relationship parameters that related the activation energy to the enthalpy change of reaction, as shown below in eq 4:

(3)

In eq 3, Cc represents the coke content of the catalyst and ω is a constant. With the inclusion of coking, a total of 5719 reactions and 825 different species (230 molecules, 24 carbonium ions, 569 carbenium ions, 1 proton, and coke) were present in the model. It should be noted that reaction path degeneracy was accounted for in the kinetics of the model. Also, catalytic site conservation was assured by the stoichiometry of the reaction network. The change in concentration for each species in the model was represented by an ordinary differential equation. It is worth noting that this numerical model has the same conceptual basis as a conventional Langmuir-Hinshelwood-Hougen-Watson (LHHW) model. The elementary steps would be the same, and only the solution method would differ. In the LHHW formalism, a ratedetermining step (e.g., adsorption, surface reaction, desorption) will frequently be identified so that a closed form, analytical rate law can be obtained. The numerical solution of the same elementary steps does not require the identification of a rate-determining step but reduces to the LHHW limiting case when appropriate. Thus the full set of 825 ordinary differential equations constituted the phenyloctane/hexadecane mixture cracking model. Solution of this set of 825 equations required estimates of the rate constants for each elementary reaction step. Reaction Kinetics. The reaction family concept provided an approach to estimate the rate constants for each elementary step. In short, a linear free energy relationship (LFER) kinetic correlation was used for

kij ) Ai exp(-(E0,i + Ri∆Hrxn,j )/RT)

(5)

In short, each reaction family could be described with a maximum of three parameters (A, E0, and R). Procurement of a rate constant from these parameters required only an estimate of the enthalpy change of reaction for each elementary step. In principle, this enthalpy change of reaction estimate amounted to the simple calculation of the difference between the heats of formation of the products and reactants. However, since many model species, particularly the ionic intermediates, were without experimental values, an estimation method was required. Thus attention was focused on the use of computational quantum chemistry to estimate heats of formation. For the present work, MOPAC calculations based on the MNDO-PM3 method were used to estimate the heats of formation. The MOPAC calculations provided gas-phase heats of formation. To account for the influence of the catalyst surface on the ionic surface species, this gas-phase heat of formation was modified following the approach of Dumesic and co-workers (Dumesic et al., 1993). This approach introduces one catalyst-dependent parameter denoted as ∆H+. This parameter represents the heat of stabilization of the proton relative to the carbonium or carbenium ion in the catalyst (Dumesic et al., 1993). Qualitatively, ∆H+ reflects the acid strength of the catalyst such that the more acidic the catalyst, the lower the value of ∆H+. It should be noted that ∆H+ was applied only to the ions because they are surface species; the molecules are gas-phase species. Quantitatively, ∆H+ was only important in the protonation/deprotonation and paraffin adsorption/desorption reactions, where ions are created or consumed; for the other elementary steps, ∆H+ canceled out since there is no net change in the number of ionic species during reaction. Model Parameters. The phenyloctane/hexadecane cracking model as described thus far contains three LFER parameters per reaction family, A, R, and E0, one catalyst-dependent parameter, ∆H+, two coking rate constants, kOC and kBC, and the deactivation constant ω. Values for these parameters were taken from the literature or were estimated from the pure component

Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 2961 Table 4. A Factors for the Phenyloctane/Hexadecane Cracking Reaction Families (Dumesic et al., 1993) reaction family

Table 5. Polanyi Relationship Parameters for the Phenyloctane/Hexadecane Cracking Model

log10 A (Pa1-n s-1)

protonation paraffin adsorption β-scission dealkylation of alkylaromatic ions cracking of alkyl ions and alkylphenyl ions carbonium ion cracking decomposition of phenyloctane C-C ions decomposition of Cbenzylic-C ion decomposition of other C-C ions decomposition of phenyloctane C-H ions decomposition of Cbenzylic-H ion decomposition of other C-H ions decomposition of hexadecane C-C ions hydride shift methyl shift isomerization reverse isomerization ring closure ring opening ring contraction ring expansion hydride transfer abstraction from phenyloctane abstraction from benzylic position abstraction from secondary positions abstraction from hexadecane deprotonation paraffin desorption

3.0 3.0

protonation/deprotonation paraffin adsorption/desorption β-scission dealkylation of alkylaromatic ions cracking of alkyl ions and alkylphenyl ions carbonium ion cracking decomposition of phenyloctane C-C ions decomposition of Cbenzylic-C ion decomposition of other C-C ions decomposition of phenyloctane C-H ions decomposition of Cbenzylic-H ion decomposition of other C-H ions decomposition of hexadecane C-C ion hydride shift methyl shift isomerization/reverse isomerization ring closure/opening ring contraction/expansion hydride transfer abstraction from phenyloctane abstraction from benzylic position abstraction from secondary positions abstraction from hexadecane

16.0 16.0 16.0 16.0 16.0 16.0 16.0 13.2 13.2 12.4 12.4 11.8 16.0 12.4 12.4 3.0 3.0 3.0 17.8 16.4

E0 (kcal/mol) 0.0 0.0 21.8 19.3 22.7 9.5 29.6 17.0 23.2 0.0 0.0 0.0 0.0 0.0 25.6 13.0 24.5

additional model parameters ∆H+ ) 172.3 kcal/mol kOC ) 2.19 × 10-9 mol/(g Pa s) kBC ) 9.98 × 10-8 mol/(g Pa s) ω ) 3.36 × 10-5 Pa-1

cracking experiments. The A factor values were taken from literature estimates that used transition state theory arguments (Dumesic et al., 1993). The values used herein are summarized in Table 4. The values of R were set at 0.5 for all reaction families based on the pure component modeling results, which revealed a lack of sensitivity to the precise values of R. The values of E0, ∆H+, kOC, kBC, and ω, were obtained from the phenyloctane and hexadecane pure component models as described previously (Watson et al., 1996a,b). These pure component model parameters had been determined through regression of the model predictions to the experimental data. These values are summarized in Table 5 and represent a priori input to the mixture model. Three parameters which were common to the phenyloctane and hexadecane pure component models, E0 for β-scission of alkyl ions, kOC and ω, had slightly different optimized values between the individual models. The values which were used for these parameters in the mixture model were the weighted averages of the pure component values based on the mixture feed composition. It should be noted that reaction families that are the reverse of each other, such as protonation and deprotonation, have the same E0 value for thermodynamic consistency such that

EA, forward rxn-EA, reverse rxn ) ∆Hrxn

reaction family

(6)

The pure component results indicated that the protonation/deprotonation, paraffin adsorption/desorption, hydride shift, methyl shift, isomerization/reverse isomerization, ring closure/opening, and ring contraction/ expansion reactions were all insensitive to their E0 values. These reactions were fast and not kinetically controlled. As a result, the E0 values were set equal to zero for these seven families in the pure component models. For the mixture model, the assumption was made that these same reactions would be fast, and so their E0 values were again set equal to zero.

Tables 4 and 5 introduce 10 subfamilies of the reaction families discussed previously. These subfamilies represented kinetically independent reactions within a general reaction family. These subfamilies were consistent with those used in the pure component models. β-Scission had two subfamilies which distinguished between dealkylation reactions of alkylaromatic ions and cracking reactions of alkyl ions or alkylphenyl ions. The first subdivision of carbonium ion cracking was made to discriminate between phenyloctane and hexadecane and between the two different types of carbonium ions, those formed from proton attack on a C-C bond and those formed from proton attack on a C-H bond. Within the phenyloctane subfamilies, another division was made for cracking reactions involving carbonium ions with a protonated Cbenzylic-C bond on the alkyl side chain or with a protonated Cbenzylic-H bond on the alkyl side chain. These reactions were put in separate families due to the distinct nature of these carbonium ions. Hydride transfer had three subfamilies to distinguish between abstraction from the benzylic position in phenyloctane, abstraction from all other secondary positions in the alkyl side chain of phenyloctane, and abstraction from hexadecane. Model Results and Discussion Figure 7 summarizes the quantitative match between the mixture model predictions and the experimental data using only parameters based on pure component data. This plot compares the predicted with the experimentally determined molar yields of phenyloctane, hexadecane, and their cracking product classes. The line in Figure 7 represents parity. The model predictions were good, as the overall parity between experimental and model values was yModel ) 0.00889 + 0.895yexpt with a correlation coefficient of 0.935. The model tended to overpredict the conversion of phenyl

2962 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997

The reaction family for abstraction from the secondary positions in phenyloctane had an E0 value of 13.0 kcal/ mol, which contrasts with that for the reaction family for abstraction from hexadecane, which had an E0 value of 24.5 kcal/mol. Recall that these values were based on pure component experimental data. These values, in combination with the (R ∆Hrxn) term in the Polanyi relationship, resulted in lower activation energies and faster rates for hydride transfer reactions with phenyloctane than with hexadecane. Thus, the ions generated from hexadecane cracking reacted more quickly with phenyloctane in the mixture than they did with hexadecane in the pure component study. The result was enhanced hydrogen transfer in the mixture. Summary and Conclusions

Figure 7. Parity between mechanistic model predictions and experimental results for phenyloctane, hexadecane, and their cracking product classes at 500 °C with REY.

Figure 8. Parity between mechanistic model predictions and experimental results for phenyloctane, hexadecane, and their major cracking products at 500 °C with REY.

octane. Thus, the model also tended to overpredict the product yields of normal paraffins and aromatics. Figure 8 compares the predicted with the experimentally determined molar yields of phenyloctane, hexadecane, and their major cracking products. The model underpredicted the yield of isobutane; this was also the case for the pure component models. The model tended to overpredict secondary cracking, as illustrated by the high yields of propene and pentenes and low yields of heptenes shown in Figure 8. At high mixture conversion, however, the model underpredicted the yields of olefins, which was due to consumption of olefins in the coking reaction. The model overpredicted the yields of benzene and C4 benzenes. The good agreement between model and experimental results shown in Figures 7 and 8 invites use of the mixture cracking model to provide insight into the dominant reaction pathways and underlying reaction mechanisms. The model correctly captured the enhancement of hydrogen transfer in the mixture which had been observed in the experimental data. The mixture data had shown higher yields of isoparaffinic products than had been expected based on the pure component data. The model was able to correctly predict the yields of isoparaffins in the mixture. The enhancement of hydrogen transfer in the mixture can be explained through examination of the input model parameters for hydride transfer, specifically the E0 values, and their impact on the activation energies.

Experimental studies were conducted to determine the kinetics, reaction pathways, and mechanisms of the catalytic cracking of a mixture of 1-phenyloctane and n-hexadecane on REY. The mixture results were compared to experimental results from pure component studies. The rate of phenyloctane cracking was approximately the same in the mixture as in the pure component study. In contrast, the conversion of hexadecane was distinctly lower in the mixture than in the pure component case. Phenyloctane clearly inhibited the cracking of hexadecane in the mixture via competitive adsorption on the catalyst. The products, reaction pathways, and mechanisms determined from the cracking of the mixture were the same as those found from the pure component studies. The highest selectivities were to benzene, propene, and butenes. The selectivities to paraffins in the mixture were greater than expected based on the pure component data, whereas the selectivities to aromatics were lower than expected. These differences in selectivities resulted because the contribution of the hydrogen transfer reaction pathway to phenyloctane conversion was greater in the mixture than in the pure component study. In contrast, the contributions of the dealkylation and protolysis pathways were smaller in the mixture. A detailed mechanistic model was developed to describe the cracking of the mixture. Phenyloctane and hexadecane pure component models which were developed previously were used to guide the construction of the mixture model. The model was based on the concept of reaction families and associated LFERs for rate constant evaluation. The reaction families were summarized mathematically by reaction matrices and a set of associated rules. The cracking model was constructed through the formal application of these matrices and rules to the reactants (phenyloctane, hexadecane, and REY) and derived products. Two molecular level coking pathways as well as catalyst deactivation were incorporated into the model. The mixture model rate constants were organized into structure-reactivity relationships, whose parameters were obtained from the literature and from pure component experiments. The parameters optimized to the pure component data provided a good prediction of the mixture reaction kinetics, as the overall parity between model and experimental values was ymodel ) 0.00889 + 0.895yexp with a correlation coefficient of 0.935. The optimized set of structure-reactivity parameters shown in Table 5 summarized the entire model compound database and provided for reasonable extrapolation in terms of just a few parameters. It is important to note that these parameters ultimately accommodated the uncertainty in the model and experimental data.

Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 2963

That is, the approach outlined here extracted the structure-reactivity parameters from overall rate constants. The overall rate constant is a combination of several mechanistic steps and is generally a more easily measured quantity than elementary rate parameters. Thus, uncertainties in the measurements, in the mechanistic steps, in reaction by reaction variation in A factors and in assumptions inherent in the structure-reactivity relationships, ultimately appeared in the values of the QSRR parameters. Clearly, the model and perhaps the approach will still require refinement before use in exacting quantitative design or scale-up procedures. Such is the case with all lumped reaction model approaches. The approach should be viewed as a thermochemically reasonable strategy for summarizing a large model compound database in terms of a relatively few fitted parameters. It is a two-dimensional lumping strategy where the similarity of the elementary steps of a few reaction families was recognized. The imposed structure-reactivity relationships resulted in a drastic reduction of parameter space. The implications to hydrocarbon reaction modeling are realized in the reduction of potential parameters from an order of 105 to an order of 10. The small number of structure-reactivity parameters was easily extracted from the model compound database and may be refined with improvements in the database. Acknowledgment The authors thank W. R. Grace & Co.-Conn. and the National Science Foundation for financial support. Nomenclature A ) Arrhenius preexponential factor Ai ) Arrhenius preexponential factor for reaction family i Cc ) coke content of the catalyst EA ) activation energy E0 ) Polanyi parameter in eq 4 E0,i ) Polanyi parameter for reaction family i ∆Hrxn ) enthalpy change of reaction ∆Hrxn,j ) enthalpy change of reaction j ∆H+ ) catalyst parameter kOC ) rate constant for the reaction of olefins to coke kBC ) rate constant for the reaction of bicyclic aromatics to coke kij ) rate constant for reaction j in reaction family i LFER ) linear free energy relationship Ni ) moles of product i NHD0 ) initial moles of hexadecane NHD ) moles of hexadecane NPO0 ) initial moles of phenyloctane NPO ) moles of phenyloctane n ) order of reaction in Table 4 QSRR ) quantitative structure-reactivity relationship R ) gas constant si ) selectivity to product i T ) temperature WHSV ) weight hourly space velocity xmix ) fractional conversion of the mixture

yi ) molar yield of product i R ) Polanyi parameter in eq 4 Ri ) Polanyi parameter for reaction family i φ ) deactivation function ω ) deactivation constant

Literature Cited Broadbelt, L. J.; Stark, S. M.; Klein, M. T. Computer Generated Pyrolysis Modeling: On-the-Fly Generation of Species, Reactions, and Rates. Ind. Eng. Chem. Res. 1994, 33, 790-799. Clymans, P. J.; Froment, G. F. Computer-Generation of Reaction Paths and Rate Equations in the Thermal Cracking of Normal and Branched Paraffins. Comput. Chem. Eng. 1984, 8, 137142. Dumesic, J. A.; Rudd, D. F.; Aparicio, L. M.; Rekoske, J. E.; Trevino, A. A. The Microkinetics of Heterogeneous Catalysis; American Chemical Society: Washington, DC, 1993. Feng, W.; Vynckier, E.; Froment, G. F. Single-Event Kinetics of Catalytic Cracking. Ind. Eng. Chem. Res. 1993, 32, 2997-3005. Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and Design, 2nd ed.; John Wiley & Sons: New York, 1990. Gates, B. C.; Katzer, J. R.; Schuit, G. C. A. Chemistry of Catalytic Processes; McGraw-Hill: New York, 1979. Guerzoni, F. N.; Abbot, J. Catalytic Cracking of a Binary Mixture on Zeolite Catalysts. Appl. Catal. A 1993, 103, 243-258. Hillewaert, L. P.; Dierickx, J. L.; Froment, G. F. Computer Generation of Reaction Schemes and Rate Equations for Thermal Cracking. AIChE J. 1988, 34, 17-24. Jacob, S. M.; Gross, B.; Voltz, S. E.; Weekman, V. W. A Lumping and Reaction Scheme for Catalytic Cracking. AIChE J. 1976, 22, 701-713. LaMarca, C. Kinetic Coupling in Multicomponent Pyrolysis Systems. Ph.D. Dissertation, University of Delaware, 1992. Liguras, D. K.; Allen, D. T. Structural Models for Catalytic Cracking. 1. Model Compound Reactions. Ind. Eng. Chem. Res. 1989a, 28, 665-673. Liguras, D. K.; Allen, D. T. Structural Models for Catalytic Cracking. 2. Reactions of Simulated Oil Mixtures. Ind. Eng. Chem. Res. 1989b, 28, 674-683. Quann, R. J.; Jaffe, S. B. Structure-Oriented Lumping: Describing the Chemistry of Complex Hydrocarbon Mixtures. Ind. Eng. Chem. Res. 1992, 31, 2483-2497. Semenov, N. N. Some Problems in Chemical Kinetics and Reactivity; Princeton University: Princeton, NJ, 1958. Stark, S. M. An Investigation of the Applicability of Parallel Computation to Demanding Chemical Engineering Problems. Ph.D. Dissertation, University of Delaware, 1993. Watson, B. A.; Klein, M. T.; Harding, R. H. Catalytic Cracking of Alkylbenzenes: Modeling the Reaction Pathways and Mechanisms. 1996a (in preparation). Watson, B. A.; Klein, M. T.; Harding, R. H. Mechanistic Modeling of n-Hexadecane Cracking on REY. 1996b (in preparation). Watson, B. A.; Klein, M. T.; Harding, R. H. Mechanistic Modeling of n-Heptane Cracking on HZSM-5. Ind. Eng. Chem. Res. 1996c, in press. Wojciechowski, B. W.; Corma, A. Catalytic Cracking; Marcel Dekker: New York, 1986.

Received for review August 15, 1996 Revised manuscript received January 15, 1997 Accepted January 20, 1997X IE9605084

X Abstract published in Advance ACS Abstracts, June 15, 1997.