A Fundamental Kinetic Model for the Catalytic Cracking of Alkanes on

The kinetic parameters are estimated by regression of experimental data of 2,2,4-trimethylpentane cracking on a USY zeolite catalyst between 698 and 7...
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Ind. Eng. Chem. Res. 2001, 40, 1337-1347

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A Fundamental Kinetic Model for the Catalytic Cracking of Alkanes on a USY Zeolite in the Presence of Coke Formation Hans C. Beirnaert,† John R. Alleman, and Guy B. Marin* Laboratorium voor Petrochemische Techniek, Universiteit Gent, Krijgslaan 281, B-9000 Gent, Belgium

The catalytic cracking of alkanes in the presence of deactivation by coke formation is presented. Elementary reactions such as protonation, deprotonation, hydride transfer, isomerization, β scission, and protolytic scission are explicitly accounted for. A distinction is made between the formation of primary coke by irreversible adsorption of hydrocarbons on catalytic sites and the formation of coke by further growth on said primary coke. Termination of the coke growth occurs when the coke molecules reach the dimensions of the zeolite pores. Primary coke molecules are formed out of the reaction of an alkene with a carbenium ion on the catalyst surface. The degree of coverage of the catalyst surface with carbenium ions is obtained from the pseudo-steadystate approximation. The deactivation effect of coke on each elementary reaction is modeled with empirical exponential deactivation functions. These functions are expressed as a function of the amount of primary formed coke, this being a measure for the amount of deactivated acid sites. The kinetic parameters are estimated by regression of experimental data of 2,2,4trimethylpentane cracking on a USY zeolite catalyst between 698 and 723 K, a hydrocarbon partial pressure between 7 and 15 kPa, and catalyst coke contents between 0.48 and 3.35 wt %. The deactivation effect of coke on the various elementary reaction steps is different and increases in the order deprotonation < protonation; protonated cyclopropane isomerization < (t,t) β scission; protolytic scission < hydride transfer on alkanes < β scission in which secondary carbenium ions are involved. Introduction Catalytic cracking of heavy oil fractions toward more valuable light hydrocarbons is one of the most important conversion processes in the oil refining industry. The optimal and flexible operation of catalytic cracking units requires accurate process models. Therefore, reliable kinetic models must be available. Recently, significant progress was made in the development of fundamental kinetic models for catalytic cracking.1-11 The single-event kinetic modeling, developed by Froment and co-workers, takes into account the detailed carbenium ion chemistry occurring on the active sites of zeolite catalysts.12-15 The reaction rate expressions are based explicitly on the elementary reaction steps involved in the transformation of the intermediates. This approach leads to rate coefficients which are independent of the feedstock because of their fundamental chemical nature. They can be determined from experiments with typical key components and simple mixtures of these. This approach was developed first for hydrocracking on Pt-loaded Y zeolites14,15,17,18 and later on extended to catalytic cracking on Y zeolites.2,19 Dewachtere19 developed a single-event kinetic model for catalytic cracking of alkanes, cycloalkanes, and aromatics. A very important aspect of catalytic cracking is coke formation and its impact on the reaction kinetics. This was not yet accounted for in the single-event kinetic modeling. In the present paper, a single-event kinetic * To whom correspondence should be addressed. E-mail: [email protected]. Fax: +32 9 2644999. † Current address: UCB Chemicals, Pantserschipstraat 207, B-9000 Gent, Belgium.

model for catalytic cracking of alkanes is constructed, taking into account deactivation by coke formation. Often, the deactivation effect of coke on the reaction kinetics of catalytic cracking is taken into account by a single deactivation function, describing the effect of coke on the global catalyst activity.4,8,20 However, the effect of coke on all reaction types involved in catalytic cracking is not identical.21,22 The deactivation effect of coke on a reaction depends on several aspects, such as the amount of sites involved in the reaction, acid strength distribution, site density, and texture of the catalyst.23-26 Accounting for all of these effects on an explicit basis is very difficult because of the complexity of the resulting kinetic model and the amount of structural catalyst properties to be determined. For that reason, empirical deactivation functions are often used when modeling the deactivation effect of coke on a reaction. The resulting model is more reliable when the deactivation function is expressed as a function of a variable related to the cause of the deactivation, i.e., the coke content on the catalyst, and not as a function of time on stream.23,27 This requires, however, a kinetic model for coke formation. The present model for coke formation is innovative in the way that it reflects the fundamental carbenium ion chemistry underlying the catalytic cracking process. The coke formation is indeed considered as starting from carbenium ions on the catalyst surface. The concentration of the carbenium ions on the catalyst surface is obtained via the single-event modeling of the catalytic cracking reactions as such. Experimental Section Reactor. The reactor setup consists of a combination of an electrobalance and a recycle reactor. With the

10.1021/ie000497l CCC: $20.00 © 2001 American Chemical Society Published on Web 02/01/2001

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Ind. Eng. Chem. Res., Vol. 40, No. 5, 2001

electrobalance, the mass increase of the catalyst is measured continuously. At the end of the experiment, the catalyst is flushed at pretreatment conditions and the final amount of coke is obtained from the mass difference of the catalyst before and after the experiment. The reactor is operated gradientlessly at high conversion by external recirculation, with online gas chromatographic analysis of the effluent. A detailed description of the reactor setup is given elsewhere.21 Catalyst. The catalyst is a commercial USY zeolite, LZ-Y-20 of Union Carbide. This is a Y zeolite, dealuminated by steaming, in which the aluminum removed from the framework remains in the zeolite as extraframework aluminum (Si/Al framework ) 30 mol/ mol; total Si/Al ) 2.6 mol/mol).28 The steaming treatment results in a secondary pore structure of mesopores. For each experiment this catalyst was brought to a reproducible activity by the following pretreatment: heating in an inert flow of nitrogen at a rate of 5 K/min up to 773 K and remaining at that temperature for 1 h before establishing the reaction conditions. Conditions. Eleven experiments with 2,2,4-trimethylpentane were performed. The space time was varied between 16.5 and 81.1 kg‚s/mol, the partial pressure between 6.8 and 15 kPa, and the temperature between 698 and 748 K. At each set of conditions, the gas effluent composition was followed as a function of time. In total 64 compositions were used for the parameter estimation. The experiments were executed in the absence of diffusional limitations. Catalytic Cracking Reactions Single-Event Approach. In this section the principles of the single-event kinetic model for alkane catalytic cracking are briefly discussed. The very large number of global reactions occurring in the catalytic cracking of hydrocarbons consists of a limited number of types of elementary steps on the carbenium ion level: protonation; deprotonation; protolytic scission; hydride transfer; hydride shift, methyl shift, and protonated cyclopropane (PCP) isomerization; and β scission. The present model only includes protolytic scission of an alkane yielding a carbenium ion and a smaller alkane; protolytic dehydrogenation is not considered. In the cracking of alkanes, the initial carbenium ions feeding the catalytic cycle are formed through protolytic scission. The formation of carbenium ions through protonation reactions dominates if alkenes are present in the feed. Figure 1 shows the various types of elementary steps on the carbenium ion level involved in the catalytic cracking of alkanes. Figure 2 schematically represents the reaction network for the catalytic cracking of isooctane. It illustrates, for instance, how the global cracking reaction of isooctane into isobutane and isobutene consists of the consecutive elementary steps of (a) hydride transfer generating the isooctyl carbenium ion; (b) (t,t) β scission leading to isobutene and the isobutyl carbenium ion; and (c) desorption of the latter by hydride transfer with another carbenium ion, leading to isobutane. The first step in the reaction of hydrocarbons is the formation of carbenium ions on the Brønsted acid sites of the catalyst surface by protonation of alkenes or by protolytic scission of an alkane with the formation of a smaller alkane and a carbenium ion. The carbenium ions can undergo a limited number of elementary reactions: β scission with formation of an alkene and a

Figure 1. Types of elementary steps involved in the catalytic cracking of alkanes.

Figure 2. Schematic representation of the catalytic cracking reaction network of isooctane. The various global reactions consist of a limited number of elementary steps.

smaller carbenium ion or isomerization reactions such as hydride shift, methyl shift, or PCP isomerization. An adsorbed carbenium ion can act as a Lewis acid site and may undergo hydride transfer with an alkane, resulting in the desorption of the carbenium ion as an alkane and the formation of a carbenium ion out of the first alkane. Deprotonation of a carbenium ion leads to an alkene and the regeneration of the Brønsted acid site. The formation of primary carbenium ions is only considered for protolytic cracking. These unstable ions do not undergo any isomerization or cracking reactions but only desorb via hydride transfer or deprotonation. In all other reactions, only secondary and tertiary carbenium ions are involved. For a given feedstock, a complete reaction network can be generated via these elementary steps.11,12 The reacting hydrocarbon species are represented by Bool-

Ind. Eng. Chem. Res., Vol. 40, No. 5, 2001 1339

ean relation matrices. The elementary reaction steps can be represented by changes of these matrices. The structure of all fed and formed hydrocarbon species is stored in a more compact vector notation, from which the sparce Boolean relation matrices can always be generated.15 The reaction rate of an elementary step is given by the product of the corresponding rate coefficient and the concentration of the reacting species of either a molecule or a carbenium ion. Transition state theory can be used to show that these elementary step rate coefficients k are multiples of single-event rate coefficients, k˜ :15,17

k ) nek˜

(1)

where ne is the number of single events associated with the elementary step. The latter can be calculated from the global symmetry numbers, σgl, of the reactant and the transition state:15,17

ne ) σgl,r/σgl,*

(2)

The number of single-event rate coefficients could be significantly reduced on the basis of some simplifying assumptions and thermodynamic constraints:2,11,13-15,17,18 (a) Only one rate coefficient for hydride transfer on alkanes is considered. (b) The single-event deprotonation coefficients are assumed to be independent of the structure.19 This results in a single deprotonation rate coefficient for each type of carbenium ion. Thermodynamics then imply that the single-event protonation coefficients are dependent on the type of the formed carbenium ion and on the structure of the alkene. They can be calculated out of the protonation rate coefficient of a reference alkene. By a judicious choice of the reference alkenes, only two independent single-event protonation rate coefficients are retained, k˜ Pr(s) and k˜ Pr(t).19 (c) For the protolytic scission of alkanes, proceeding via carbonium ions as intermediates, it is assumed that the single-event rate coefficients are only dependent on the carbenium ion type formed (primary, secondary, or tertiary). (d) The single-event reaction rate coefficients for surface reactions between carbenium ions depend only on the carbenium ion type of the reactant and the product, resulting in four rate coefficients for hydride shift, methyl shift, PCP isomerization, and β scission ((s,s), (s,t), (t,s), (t,t)). With the above assumptions, the number of singleevent rate coefficients for the modeling of the catalytic cracking of alkanes could be limited to 25. Rate Equations for the Elementary Reactions. The reaction rate of an elementary step, for instance, the (s,s) β scission of a secondary carbenium ion R1+ is given by

rβ ) nek˜ β(s,s)θR1+Φβ(s,s)

(3)

where θR1+ is the fractional coverage of the Brønsted acid sites with R1+. The total concentration of the Brønsted acid sites is incorporated in the single-event rate coefficient k˜ β(s,s). The deactivation function, Φ, expresses the decrease of the reaction rate due to coke formation. The fractional coverage of the Brønsted acid sites with a carbenium ion can be derived by applying the pseudosteady-state approximation to the latter, expressing that the disappearance rate of R1+ by deprotonation and

hydride transfer with alkanes, coke, and aromatic precursors is equal to its formation rate by protonation of alkenes, protolytic cracking of alkanes, and hydride transfer of an alkane P1 with adsorbed carbenium ions:

∑j (ne)Depk˜ Dep(s)ΦDep(s) +

θR1+

par

(ne)HtfPP + Rarom ∑ Htf /θcarb) ) j)1 k˜ Pr(s)ΦPr(s)(1 - θcarb)∑(ne)PrK ˜ (OjSOref)PO + j k˜ Proto(s)ΦProto(s)(1 - θcarb)∑(ne)ProtoPP + j θR1+(k˜ HtfΦHtf

j

j

j

(ne)Htfk˜ HtfΦHtfPP1θcarb (4) This balance explicitly accounts for the formation of alkanes via hydride transfer reactions involved in the formation of aromatics and coke via the last term on the left-hand side. Below it is explained how the arom corresponding alkane formation rate, RHtf , can be obtained from eq 21. Note that the surface reactions are assumed to proceed on a much smaller time scale than the adsorption and desorption reactions, so that only the latter have to be considered in the balance. Solution of eq 4 leads to the following expression for the fractional coverage of the Brønsted acid sites with R1+: θR1+ )

∑(n )

k˜ Pr(s)ΦPr(s)(1 - θcarb)

˜ (OjSOref)POj e PrK

j

+

(ne)av,Depk˜ Dep(s)θDep(s) + k˜ HtfΦHtf

∑ )∑(n )

(ne)HtfPPj + Rarom Htf /θcarb

j

k˜ Proto(s)ΦProto(s)(1 - θcarb

e ProtoPPj

j

(ne)av,Depk˜ Dep(s)ΦDep(s) + k˜ HtfΦHtf

+

∑(n )

e HtfPPj

+

Rarom Htf /θcarb

j

k˜ HtfΦHtfθcarb(ne)HtfPP1 (ne)av,Depk˜ Dep(s)θDep(s) + k˜ HtfΦHtf

∑(n )

e HtfPPj

(5) +

Rarom Htf /θcarb

j

where (ne)av,Dep is the average number of single events of the elementary deprotonation steps of R1+. The total fractional coverage of the Brønsted acid sites, θcarb, is calculated as the sum of the fractional coverages with carbenium ions Ri+, given by equations similar to eq 5, leading to an implicit equation in θcarb:

θcarb )

∑ θR

ions

+

i

(6)

Rate Equations for the Global Reactions. Global reactions consist of a number of elementary steps, as illustrated in Figure 2. On a molecular level, the global reaction rates are calculated by summation of the reaction rates of the elementary reaction steps which transform carbenium ions formed out of the reacting molecule into carbenium ions which desorb to the product molecule. For example, the reaction rate for the β scission of an alkane P1 into an alkene O and an alkane P2 is obtained from a summation of rates of elementary β-scission reactions, which transform secondary or tertiary carbenium ions formed out of P1 into secondary or tertiary carbenium ions which desorb to P2.

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The lumping coefficients LC are independent of the value of the single-event rate coefficients. They only depend on the generated reaction network and the lump composition. They can be calculated from par LCβ(m,n) )

∑yi,L (ne)Htf(ne)β

m,n

Figure 3. Schematic representation of the relumping for the β scission of the lump of alkanes L1 into alkenes and the lump of alkanes L2. A fraction D(n) of the product carbenium ions desorbs through hydride transfer to alkanes of lump L2; the other product carbenium ions deprotonate to alkenes.

Practically, a certain degree of lumping between molecules may be necessary. For instance, the exact composition of complex feed mixtures is not always known because of the limits of chemical analysis techniques. Moreover, the solution of the continuity equations for all components in the reaction mixture can lead to excessive calculation times, especially at higher carbon numbers. Single-event modeling enables one to calculate the reaction rates between lumps in a rigorous way. The reaction rate between two lumps is found by the summation of the rates of all elementary reaction steps which transform carbenium ions, formed out of molecules of the first lump, into ions, which desorb to molecules of the second lump. This so-called relumping is illustrated in Figure 3 for the β scission of a lump of alkanes L1 into alkenes and a lump of alkanes L2. The corresponding reaction rate is calculated as19 par rβ(L1fO + L2) ) LCβ(s,s) Fβ(s,s)k˜ β(s,s)Φβ(s,s)PL1 + par Fβ(s,t)k˜ β(s,t)Φβ(s,t)PL1 + LCβ(s,t) par LCβ(t,t) Fβ(t,s)k˜ β(t,s)Φβ(t,s)PL1 + par Fβ(t,t)k˜ β(t,t)Φβ(t,t)PL1 LCβ(t,t)

(10)

The F factors are given by Fβ(m,n) ) k˜ HtfΦHtfθcarbD(n) par lumps

(ne)av,Depk˜ Dep(m)θDep(m) + k˜ HtfΦHtf

∑

LCHtfPLj + Rarom Htf /θcarb

j)1

(11)

where m and n are the carbenium ion types, either secondary or tertiary. The factor D(n), which is the fraction of carbenium ions which desorbs by hydride transfer to alkanes belonging to lump L2, is calculated from D(n) ) par lumps

k˜ HtfΦHtf

∑

LCHtfPLj + Rarom Htf /θcarb

j)1

par lumps

(ne)av,Depk˜ Dep(m)θDep(m) + k˜ HtfΦHtf

∑

LCHtfPLj + Rarom Htf /θcarb

j)1

(12)

with summations over all lumps of alkanes in the reaction mixture. The other fraction of the product ions desorbs toward alkenes by deprotonation.

1

(13)

The summation in eq 13 extends over all β-scission reactions which transform carbenium ions of type m, formed out of the lump L1, into carbenium ions of type n, which desorb to alkanes of lump L2. The factor (ne)Htf is the number of single events of the hydride transfer reaction from which the reactant ion is formed, and (ne)β the number of single events of the elementary β-scission reaction. The lumping coefficient LCHtf is calculated from

LCHtf )

∑i yi,L (ne)Htf 1

(14)

with the summation extending over all alkanes of the lump Lj. Equations which are similar to those above can be derived for the other global reactions necessary to describe the catalytic cracking of acyclic hydrocarbons. These reactions are, for the lumps of alkanes, hydride transfer/protolytic scission/PCP isomerization/β scission and, for the lumps of alkenes, protonation/PCP isomerization/β scission. Hydride transfer of lumps of alkanes results in the transformation of alkanes into alkenes by hydride transfer followed by deprotonation. Protonation of lumps of alkenes transforms alkenes into alkanes by protonation, followed by hydride transfer. Protolytic scission converts alkanes into smaller alkanes and carbenium ions, which can desorb as alkanes or as alkenes. PCP isomerization of lumps of alkanes or alkenes results in the formation of carbenium ions with a different degree of branching, desorbing as alkanes or as alkenes. Finally, β scission converts lumps of alkanes or alkenes into smaller alkenes and carbenium ions, which can desorb as alkanes or as alkenes. The net rates of formation of the different lumps, necessary for the solution of the corresponding continuity equations, are found by summation of these global reaction rates. Coke Formation Reactions. Coke formation is assumed to start from alkenes in the gas phase. Small alkenes such as isobutene readily undergo consecutive elementary reaction steps such as protonation, deprotonation, alkylation, isomerization, hydride transfer, and ring closure, leading to macromolecules, which cannot diffuse out of the supercages of the USY zeolite.22,29-31 Coke molecules are not chemically inert but interact with the cracking reactions and continue to grow until the dimensions of the growing molecules reach the dimensions of the zeolite pores. Coke growth is terminated by steric hindrance. This reaction route is modeled by two consecutive reactions: the formation of primary coke by site coverage, followed by coke growth on the primary coke molecules. The formation of primary coke by irreversible adsorption on catalyst sites is considered to start from carbenium ions on the catalyst surface. In this way, the coke formation is linked with the cracking reactions.

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This is reflected in the kinetic equations and will be discussed below. The primary coke can further grow through alkylation with an alkene from the gas phase, according to an Eley-Rideal reaction mechanism. The termination of the coke growth is also accounted for in the kinetic model. The simplified modeling by two consecutive reactions implies that the kinetic parameters for coke formation will show a certain dependence on the composition of the reaction mixture, in contrast to the single-event rate parameters. Rate Equations. The formation of a primary coke by site coverage is considered to proceed through the reaction of an alkene in the gas phase with a carbenium ion on the catalyst surface. The rate of formation of a primary coke is therefore proportional not only to the alkene partial pressure, Pol, but also to the degree of coverage of the catalyst surface with carbenium ions, θcarb, as obtained from eq 6:

dCs/dt ) RCs ) ksθcarbPolΦC

(15) s

The presence of θcarb and Pol in this equation makes a simultaneous modeling of the coke formation and the kinetics of the cracking reactions necessary. The deactivation function, Φ, accounts for the deactivation effect of coke on the reaction rate. An empirical exponential deactivation function is used:

ΦCs ) exp(-RsCs)

(16)

It is expressed as a function of the amount of coke formed by site coverage, Cs, and not as a function of the total coke content, CC. In the absence of diffusional limitations within the catalyst particles and of effects of pore blockage, Cs is proportional to the amount of deactivated acid sites.32,33 Coke growth cannot continue indefinitely. It is terminated by sterical constraints once the coke molecule has reached the dimensions of the pore volume. Analogous to work by Beyne and Froment26 and Devoldere and Froment,34 this termination is explicitly taken into account. In this respect, the kinetic model considers the amount of coke, Csg, involved in the site coverage which is still active for further growth. In agreement with the coke formation mechanism, the rate of coke growth is proportional to the alkene partial pressure and to the amount of coke still susceptible to growth, Csg:

dCg/dt ) RCg ) kgPolCsg

(17)

The termination of coke growth corresponds to the formation of nonreactive coke by reaction of a gas-phase alkene with coke which is still susceptible to growth.26 The rate of termination is therefore proportional to both the alkene partial pressure and Csg. The net production rate of coke, which is still active for further growth, follows from the difference between the formation rate of a primary coke and the termination rate due to sterical constraints:

dCsg/dt ) RCsg ) ksθcarbPolΦCs - ktCsgPol

(18)

The total amount of coke on the catalyst is given by the sum of both contributions of site coverage and coke growth, of which the respective evolutions in time are obtained by integration of eqs 15 and 17:

CC ) Cs + Cg

(19)

Correspondingly, the total coke formation rate is the sum of both site coverage and coke growth rates:

RC ) RCs + RCg

(20)

Hydride Transfer Involved in the Formation of Aromatics and Coke. The hydride transfer involved in the formation of aromatics and coke significantly enhances the formation rate of alkanes because of the fact that in these reaction paths hydride transfer with carbenium ions is frequently occurring.22 This is accounted for in the kinetic model by considering the alkane formation rate through said hydride transfer arom , such as, for instance, in the carbereactions, RHtf nium ion balance equation (4). Because of the limited selectivity for aromatics and coke formation in the reaction of acyclic hydrocarbons on a USY zeolite catalyst, no single-event approach was used to model the reaction path toward these reaction products. The arom is calculated based on the alkane formation rate RHtf observed formation rate of monoring aromatics and the calculated formation rate of coke. In the formation of a molecule with one aromatic ring out of an acyclic molecule, four hydride transfer steps are involved: one in the formation of the allylic carbenium ion out of which a cycloalkane is formed and three in the aromatization of the latter, proceeding as a sequence of hydride transfer and deprotonation steps. This is illustrated in Figure 4. To quantify the hydride transfer in the coke formation, the H/C ratio of the coke molecules must be known and a molecular mass of the coke molecules has to be assumed. Pyrene was taken to represent a typical coke molecule (H/C ) 0.625, MW ) 202 g/mol). Its properties are quite in agreement with the results of Dimon et al.,35 who found H/C ratios of the coke molecules between 0.4 and 0.8, by characterization of the coke formed out of propene at 723 K on a USY zeolite. The formation of pyrene out of acyclic molecules is accompanied by the desorption of 12 carbenium ions as alkanes. Hence, the total amount of alkanes formed by hydride transfer on aromatic and coke precursors follows from the rate of formation of monoring aromatics and coke

Rarom Htf ) 4Rarom + 12RC,mol

(21)

whereby the molar coke formation rate, RC,mol, is obtained by eq 20, considering the molecular mass of pyrene as a typical coke molecule. The choice of another coke model molecule could result in a different number of associated carbenium ion desorption steps, i.e., a different coefficient of RC,mol in eq 21, a different molar coke formation rate, and ultimately a slightly different alkane formation rate, arom . A heavier coke model molecule would result not RHtf only in a higher number of desorption steps but also in a lower molar coke formation rate, with both effects compensating for each other. The activity of all carbenium ions for hydride transfer is assumed to be identical, so that the rate of disappearance of R1+ by the hydride transfer involved in the formation of aromatics and coke is given by

θR1+Rarom Htf /θcarb

(22)

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Figure 4. Reaction scheme for the formation of a molecule with one aromatic ring out of an acyclic molecule, involving four hydride transfer reaction steps.

This carbenium ion disappearance rate is included in the carbenium ion balance equation (4), from which the degree of coverage, θR1+, is calculated. Deactivation Functions for the Cracking Reactions. The deactivation functions, Φi(Cs), in the expressions for the elementary reaction rates, for instance, eq 3, account for the decrease in the reaction rates due to the decreased number of catalyst active sites as a result of site coverage by coke molecules. Different empirical exponential deactivation functions are considered for each type of elementary reaction:

Φi(Cs) ) exp(-RiCs)

(23)

Kinetic Parameter Estimation. The optimal values of the kinetic parameters were determined by minimization of the following objective function with the Rosenbrock algorithm:36 m-1

S)

n

wj∑(Xij,exp - Xij,cal)2 + ∑ j)1 i)1 11

(CCi,exp - CCi,cal)2 ∑ i)1

wm

(24)

with m the number of responses, n the number of observations (64), Xij the responses which are the molar conversions to lump j for experiment i, and CCi the total coke content for experiment i. The experimental responses are determined at various effluent analysis times.21 Only the final coke content for each experiment is taken into account in the objective function. The final coke content is determined after flushing the catalyst with inert gas at reaction temperature. The weight factors wj were determined as19

wj )

( ) n

n

a

(25)

2 Xij,exp ∑ i)1

whereby, if a ) 1, all responses have the same contribu-

tion to the residual sum of squares, S, or, if a ) 0, all responses have the same weight, meaning that larger responses contribute to a larger extent to S. An acceptable value for a is 0.2. The weight factors wm were determined in such a way that the contribution of cokes to the residual sum of squares is about the same as the contribution of the gasphase products. To reduce the correlation between the preexponential factors and the activation energies of the rate coefficients, reparametrization was applied according to Kittrell.37 Experimentally, the composition of the isomers with an identical degree of branching was found to be independent of conversion. This implies that hydride shift and methyl shift are faster than the global 2,2,4trimethylpentane conversion, so that an equilibrium composition is measured for these isomers and the rate of interconversion between these isomers cannot be calculated. Therefore, all hydrocarbons with the same degree of branching are lumped, resulting in 38 molecular components and lumps: 19 alkane lumps, 18 alkene lumps, and coke. Because no significant amount of tribranched C8 isomers was measured, the lump composition of tribranched C8 alkanes is not the equilibrium composition but only 2,2,4-trimethylpentane. The molar conversions of the different molecular components and lumps are calculated by solution of the corresponding continuity equations valid for the perfectly mixed flow reactor:

Xi - Ri(P,T,Cs,Csg) W/F°iC8 ) 0,

i ) 1, ..., 37

(26)

with Ri the formation rate of lump i, calculated from the reaction rates between lumps, such as, for instance, that given by eq 10. Because the mean residence time is small with respect to the time at which the effluent is analyzed, the effects of accumulation are negligible. Hence, the continuity equations form a set of algebraic equations. The continuity equations (26) are coupled with the kinetics of coke formation, described by eqs 15-18. The complete set of equations is integrated progressively for time intervals [ti, ti+1]. Initially, i.e., on time zero, no coke is present on the catalyst, and the olefin partial pressure and total fractional coverage of the catalyst surface θcarb are calculated. The set of eqs 15-18 is then integrated from time zero to time t1, resulting in values for coke formed by site coverage Cs and for the amount of coke which is still susceptible to growth Csg on time t1. This allows the calculation of the olefin partial pressure and θcarb on time t1. This procedure is repeated for every time interval [ti, ti+1]. For the calculation of the responses, the reactor pressure, the temperature, the 2,2,4-trimethylpentane/ nitrogen ratio in the feed, the space time, and the times on stream for the effluent analyses are used as independent variables. The estimation of preexponential factors and activation energies for all single-event rate coefficients would lead to an excessive amount of parameters. Therefore, the temperature effect on protonation was neglected, and one single activation energy was estimated for hydride transfer, deprotonation, PCP isomerization, β scission, and protolytic scission. Because (t,t) β scission is important in the 2,2,4-trimethylpentane cracking, it was possible to estimate the temperature dependence of the related rate coefficient separately.

Ind. Eng. Chem. Res., Vol. 40, No. 5, 2001 1343 Table 1. Estimatesa for the Arrhenius Parameters of the Elementary Steps during the Catalytic Cracking of 2,2,4-Trimethylpentane, Together with the Values of the Rate Coefficient at 748 K reaction

Aa

E (kJ/mol)

k˜ (748 K)

Htf Pr(s) Pr(t) Dep(p) Dep(s) Dep(t) PCP(s,s) PCP(s,t) PCP(t,s) PCP(t,t) β(s,s) β(s,t) β(t,s) β(t,t) Proto(p) Proto(s) Proto(t)

1.11 × 100 6.38 × 100 1.11 × 103 3.04 × 1017 2.91 × 1012 1.18 × 1012 2.62 × 100 3.59 × 100 4.24 × 10-1 1.58 × 101 8.97 × 109 4.24 × 1010 1.90 × 108 9.47 × 105 2.86 × 102 1.11 × 103 1.45 × 104

47.3

5.73 × 10-4 6.38 × 100 1.11 × 103 7.77 × 107 7.43 × 102 3.02 × 102 5.94 × 10-2 8.11 × 10-2 9.61 × 10-3 3.56 × 10-1 8.33 × 101 3.92 × 102 1.76 × 100 2.27 × 101 2.60 × 10-6 1.01 × 10-5 1.32 × 10-4

137.6 137.6 137.6 23.8 23.8 23.8 23.8 115.2 115.2 115.2 66.4 115.4 115.4 115.4

a

Units: mol/(kg s) or mol/(kg s kPa) for hydride transfer, protonation, and protolytic cracking.

The number of deactivation constants was limited to 7: one for hydride transfer, one for protonation and PCP isomerization, one for deprotonation of primary and secondary carbenium ions, one for deprotonation of tertiary carbenium ions, one for (s,s), (s,t), and (t,s) β scission, one for (t,t) β scission, and one for protolytic cracking. Four parameters were necessary for the modeling of coke formation: the deactivation constant Rs, the factor kt/kg, and the rate coefficients for site coverage, ks, and coke growth, kg. The ratio kt/kg can be considered as a measure for the degree of polymerization of the coke formed by growth of a primary coke. The temperature effect on these rate coefficients could not be estimated. However, this does not mean that the calculated coking rate will be temperature-independent, because the calculated surface coverage and the alkene partial pressure depend on the reaction temperature. The total amount of kinetic parameters was 34. The optimal values are given in Tables 1-3. The values of the single-event rate coefficients at 748 K are also included in Table 1. All parameter estimates are significant, as appeared from the corresponding t values. The preexponential factors of (s,t) and (t,s) PCP isomerization were fixed at the values given in Table 1. Because these values did not influence the residual sum of squares, these rate coefficients could not be determined from experiments with 2,2,4-trimethylpentane. Parity plots for the global conversion, the coke content, and several reaction products are given in Figure 5. These plots show that the kinetic model is able to fit the experimental data very well. Assessment of the Kinetic Parameter Values. The values of the reaction rate coefficients within each reaction family can be explained by the stability of the carbenium ions involved. Table 1 clearly shows that the protonation and protolytic cracking rate coefficients increase with the stability of the formed carbenium ion: (p) < (s) < (t). In contrast, the rate coefficients for deprotonation of less stable primary and secondary carbenium ions are higher than that for the deprotonation of a tertiary carbenium ion. The rate coefficient for (s,t) β scission, whereby a more stabilized carbenium ion is formed out of a secondary carbenium ion, is higher than the rate coefficients for the other β-scission reac-

tions. The same trends were observed by Dewachtere19 for the catalytic cracking of acyclic hydrocarbons on a RE-Y zeolite. The high activation energy for deprotonation implies that the surface coverage with carbenium ions has a negative temperature dependence. This was expected because the measured initial coke formation decreases with increasing temperature. Also remarkable is the significant difference in the activation energy between the (t,t) β scission and β-scission reactions where secondary carbenium ions are involved. Table 2 reveals that the deactivation effect of coke is not identical for the different elementary reactions. The estimated deactivation constants increase in the order

RDep(p)+Dep(s) , RDep(t) < RPr+PCP , Rβ(t,t) < RProto < RHtf < Rβ Protonation reactions are found to be more deactivated than deprotonation reactions. This is in accordance with preferential coke formation on the strongest acid sites of the zeolite.30,31,38,39 The formation of rather unstable primary and secondary carbenium ions by protonation of olefins requires indeed strong acid sites and is therefore strongly deactivated by coke formation. Furthermore, β scission, protolytic scission, and hydride transfer to alkanes are more sensitive to deactivation than protonation and PCP isomerization. Also, (t,t) β scission is less deactivated by coke than the β-scission reaction, in which secondary carbenium ions are involved and which need stronger acid sites to stabilize the transition state. The selectivity changes observed during the experiments with 2,2,4-trimethylpentane are caused by a combination of two effects, viz., the different sensitivity for deactivation of the elementary reactions and the concentration changes in the continuously stirred tank reactor (CSTR). Figure 6 illustrates that the kinetic model is able to describe these selectivity changes: while the isobutane formation is strongly deactivated, the isobutene formation remains more or less unaffected. The parameters for coke formation are listed in Table 3. The high value for the deactivation constant Rs shows that in the 2,2,4-trimethylpentane conversion the coke formation by site coverage is strongly deactivated. The high value for kt/kg indicates that coke growth is limited in the USY zeolite. This is also illustrated in Figure 7. This is not very surprising because the alkylation reaction between coke molecules and the branched isobutene molecule, which is the most important alkene in the reaction mixture of 2,2,4-trimethylpentane, will be sterically hindered in the supercages of the USY zeolite. Probably, coke growth will mainly occur in the secondary mesopore structure of the zeolite. Termination of coke growth results in the increasing difference between Csg, the amount of coke formed by site coverage which is still active for growth, and Cs, the amount of coke formed by site coverage (Figure 7). Experimentally, a strong dependence between the coking rate and the 2,2,4-trimethylpentane conversion was observed. The kinetic model is not fully capable of describing this dependence, as is clearly shown in Figure 8: at low space times, the amount of coke is overestimated, while at high space times, it is underestimated. The overestimation of the coking rates at low conver-

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Figure 5. Experimental versus calculated values for the 2,2,4-trimethylpentane conversion, the coke content, and the conversions to isobutane, isobutene, propene, and isopentane. Calculated values obtained with a relumped kinetic model based upon a single-event approach for the cracking reactions, taking into account the deactivation by coke formation and a lumped kinetic model for coke formation, as represented by the continuity equations (15), (17), (18), and (26) and considering the parameter values of Tables 1-3. Experimental values obtained from 2,2,4-trimethylpentane conversion on a USY zeolite catalyst with W/F° ) 16.5-81.1 kg‚s/mol, P°iC8 ) 6.8-15 kPa, and T ) 698-748 K.

sions explains the slight deviation of the parity plot for the 2,2,4-trimethylpentane conversion in Figure 5. A more detailed kinetic modeling of the coke formation, based on the single-event approach, would probably remediate this bias. For that purpose, the formation of allylic carbenium ions, alkylation, and ring closure need to be incorporated in the single-event kinetic model. This would lead to a kinetic model for coke formation with parameters which would be independent of the

feedstock. At the same time, this approach would lead to kinetic expressions for the formation of aromatic compounds out of acyclic hydrocarbons, because the same elementary reaction steps are involved. Conclusions A kinetic model for the catalytic cracking of alkanes in the presence of coke formation was applied to 2,2,4-

Ind. Eng. Chem. Res., Vol. 40, No. 5, 2001 1345

Figure 6. Experimental and calculated conversion to isobutane (9) and to isobutene (2) as a function of time on stream in a CSTR reactor. Experimental conditions: 2,2,4-trimethylpentane conversion on a USY zeolite catalyst at T ) 723 K, P°iC8 ) 6.8 kPa, and W/F° ) 44 kg‚s/mol. Calculated lines are obtained as described in the caption of Figure 5.

Figure 7. Calculated evolution of CC, Cs, Cg, and Csg as a function of time on stream in a CSTR reactor, obtained as described in the caption of Figure 5. Experimental conditions: 2,2,4-trimethylpentane conversion on a USY zeolite catalyst at T ) 723 K, P°iC8 ) 6.8 kPa, and W/F° ) 44 kg‚s/mol.

Table 2. Estimates of the Deactivation Constants Coupled with the Elementary Steps of the Kinetic Model for Catalytic Cracking of 2,2,4-Trimethylpentane reaction

R [(wt %)-1]

Htf Pr + PCP Dep(p) + Dep(s) Dep(t) β(s,s) + β(s,t) + β(t,s) β(t,t) Proto

0.653 0.148 0.031 0.127 0.825 0.407 0.445

Table 3. Estimates for the Kinetic Model of Coke Formation Involved in the Catalytic Cracking of 2,2,4-Trimethylpentane parameter %)-1]

Rs [(wt kt/kg ks [kg (100 kg‚s‚kPa)-1] kg [(s‚kPa)-1]

value 1.951 2.573 5.23 × 10-3 7.52 × 10-5

trimethylpentane cracking on a USY zeolite catalyst. The cracking reactions were modeled by a fundamental kinetic model, taking into account elementary reactions such as protonation, deprotonation, hydride transfer, isomerization, β scission, and protolytic scission. Coke formation was described as the formation of a primary coke out of carbenium ions on the catalyst surface, followed by coke growth. Coke formation and cracking kinetics are linked with each other. The deactivation effect of coke on each elementary reaction was modeled with empirical exponential deactivation functions, expressed as a function of the amount of primary formed coke. The parameter values indicated that the deactivation effect of coke is strongly dependent on the nature of the elementary reactions. The kinetic model describes the kinetic data very well, except the strong effect of conversion on the coking rate. This shows that there is a need for a more detailed kinetic model for coke formation, based upon the single-event approach. Such an approach would also lead to kinetic expressions for coke formation with parameters which are independent of the feedstock, as is the case for the kinetics of the cracking reactions.

Figure 8. Experimental and calculated evolution of the total coke content as a function of time on stream in a CSTR reactor. Experimental conditions: 2,2,4-trimethylpentane conversion on a USY zeolite catalyst at T ) 723 K, P°iC8 ) 6.8 kPa, and W/F° ) 16.5 (b), 43.6 (9), and 89.7 ([) kg‚s/mol. Full lines are calculated as described in the caption of Figure 5.

Acknowledgment The authors are grateful to the Fonds voor Wetenschappelijk Onderzoek Vlaanderen (FWO-N) for financial support of part of the research. Nomenclature Roman Symbols A ) preexponential factor, reaction dependent CC ) total coke content, wt % Cg ) coke formed by growth, wt % Cs ) coke formed by site coverage, wt % Csg ) coke formed by site coverage which is still active for growth, wt % k˜ ) single-event rate coefficient, reaction dependent k ) elementary step rate coefficient, reaction dependent kg ) rate coefficient for coke growth, (s kPa)-1 ks ) rate coefficient for coke formation by site coverage, kg/(100 kg s kPa)-1 kt ) rate coefficient for termination of coke growth, (s kPa)-1

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K ˜ iso(O1,O2) ) modified equilibrium coefficient of the isomerization reaction between O1 and O2 (without global symmetry number) LC ) lumping coefficient ne, (ne)s ) number of single events (of elementary steps s) Pi ) partial pressure of component i, kPa Rarom ) formation rate of aromatics, mol/(kg s) RC ) coking rate, kg/(100 kg s) RC,mol ) molar coke formation rate, mol/(kg s) RCg ) formation rate of coke by growth on a primary coke, kg/(100 kg s) RCs ) formation rate of a primary coke by site coverage, kg/(100 kg s) RCsg ) formation rate of coke which is still active for growth, kg/(100 kg s) Rarom ) global desorption rate of carbenium ions to alHtf kanes due to hydride transfer with aromatics and coke formation, mol/(kg s) T ) temperature, K Xij ) molar conversion of lump j in experiment i yi,Li ) mole fraction of component i in lump Li W/F° ) space time, kg‚s/mol wi ) weight factor of response i Greek Symbols R ) deactivation constant, (wt %)-1 θ ) surface coverage σgl,r ) global symmetry number of the reactant σgl,* ) global symmetry number of the transition state Φ ) deactivation function Subscripts β ) β scission cal ) calculated carb ) carbenium ions Dep ) deprotonation exp ) experimental Htf ) hydride transfer iC8 ) 2,2,4-trimethylpentane ol ) alkenes PCP ) PCP isomerization Pr ) protonation Proto ) protolytic scission Superscripts ° ) in the feed par ) alkanes

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Received for review May 17, 2000 Revised manuscript received November 9, 2000 Accepted November 28, 2000 IE000497L