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Fundamental Kinetic Modeling of Catalytic Reforming

Rogelio Sotelo-Boyas and Gilbert F. Froment*

Artie McFerrin Department of Chemical Engineering, Texas A&M UniVersity, College Station, Texas 77843-3122

A fundamental kinetic model for the catalytic reforming process has been developed. The complex network

of elementary steps and molecular reactions occurring in catalytic reforming was generated through a computeralgorithm characterizing the various species by means of vectors and Boolean relation matrices. The algorithmis based on the fundamental chemistry occurring on both acid and metal sites of a Pt-Sn/Al2O3 catalyst. Thenumber of rate coefficients for the transformations occurring on the metal sites was reduced by relating themto the nature of the involved carbon atoms. The single event concept was applied in the development of rateexpressions for the elementary steps on the acid sites. This approach allows obtaining rate coefficients thatare independent of the feedstock, owing to their fundamental chemical nature. The Levenberg -Marquardtalgorithm was used to estimate the rate coefficients. The estimation was based on data reported from a previousnaphtha reforming study in a fixed bed reactor with Pt -Sn/Al2O3 as a catalyst. The agreement between theexperimental and estimated yields is excellent. The statistical tests were also satisfied. The kinetic model wasused in pseudo-homogeneous and heterogeneous reactor models simulating an industrial three-bed adiabaticcatalytic reformer with centripetal radial flow.

1. Introduction

Recent environmental legislations established by the CleanAir Act1 and the Federal Reformulated Gasoline Programdemand the reduction in emissions of volatile, toxic, andpolluting components in gasoline, such as sulfur, benzene, andolefins. One of the most affected refining units by thisreformulation is the catalytic reformer. The main objective ofcatalytic reforming is the transformation of low-octane straightrun naphtha consisting of C5 to C12 hydrocarbons with a researchoctane number of 50-60 into gasoline with an octane numberof 90-105. This is achieved by transforming paraffins andnaphthenes into the corresponding isoparaffins and aromatics.The reformer contributes for about 50 vol % to the gasoline

pool in a refinery. The process is typically carried out in threeor four adiabatic catalytic beds in which reactions such asdehydrogenation, isomerization, hydrocracking, dehydrocycliza-tion, hydrogenolysis, and coking are taking place. It is carriedout over bifunctional catalysts (metal/acid) with platinum aloneor platinum combined with rhenium, iridium, or tin, dispersedon acidic alumina. The Pt-Sn/Al2O3 catalyst used in the presentstudy is less subject to coking than Pt- and Pt-Re catalystsand permits operation at a lower pressure, which is beneficialfor the yield of aromatics and, consequently, for the octanenumber.

Advanced optimization of such a complex process requiresa detailed mathematical model capable of accurately predictingthe reformate composition, the product quality, and the catalyst

life cycle over a wide range of operating conditions. Thecatalytic reforming process has been modeled until now bylumping the spectrum of naphtha components ((200 hydro-carbons at a reasonable concentration level) into a small numberof pseudocomponents.2-9 With such an approach the kineticmodeling is simple and the estimation of the kinetic parametersis a relatively easy task. The drawback is that these parametersdepend on the composition of the feedstock, so that for adifferent feed the kinetic parameters have to be re-estimated

on the basis of a new experimental program. Quann and Jaffe10

have addressed this problem by developing structure orientedlumping. A large number of key molecules are generated byassembling 22 structural groups in various ways. This syntheticfeed has to satisfy the observable characteristics, both chemicaland physical. Klein and co-workers11 reduced the complexityof the feed by introducing a number of representative pseudocom-ponents by Monte-Carlo simulation and generated the reactionnetwork of this synthetic feed by computer using graph theory.The approach was applied to catalytic reforming.12 The draw-back of the two approaches mentioned here is the use oflumpssbe they called pseudo- or key-componentssthat inevi-tably lead to rate coefficients depending on the feedstockcomposition.

In the present paper the kinetic modeling is based upon adetailed description of the fundamental chemistry of thetransformation of each individual hydrocarbon. The rates of thereactions on the metal sites are systematized by relating themto the nature of the C-atoms linked to a double bond in theproduct or to the single bond to be broken in the reactant. Therates of the transformations on the acid sites are described interms of the elementary steps of carbenium ion chemistry. Bydoing so the number of elementary steps definitely becomeshuge, but they belong to a limited number of types. It is possibleto formulate their rates using only a reasonable number ofindependent kinetic parameters by applying the single eventconcept introduced by Froment et al.13-19 The single-event

concept has been applied previously to the kinetic modeling ofthermal cracking,14,20 catalytic cracking,17,21,22 hydrocracking,23

alkylation,24 hydroisomerization, 13,25,26 and the methanol-to-olefins27,28 process. The single-event rate parameters are trulyinvariant with respect to the feedstock composition, and theprediction of the reformate composition is much more accurateand reliable, even for a wide range of operating conditions.

2. Chemistry of the Process

Catalytic reforming requires a bifunctional catalyst containinga metal and an acid function.29 The metal function is responsiblefor the dehydrogenation of paraffins and naphthenes, thehydrogenation of olefins and aromatics, and the hydrogenolysis

* To whom correspondence should be addressed. E-mail:[email protected].

Present address: Instituto Politecnico Nacional, ESIQIE, MexicoD.F. 07738, Mexico.

Ind. Eng. Chem. Res. 2009, 48, 11071119 1107

10.1021/ie800607e CCC: $40.75 2009 American Chemical SocietyPublished on Web 09/10/2008


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of paraffins, that is, the demethylation (DEM) and deethylation(DET) producing methane and ethane. The transformations onthe metal sites are considered at a molecular level; the moleculeis considered as a whole.

The transformations on the acid alumina sites are describedin terms of elementary steps of carbenium ion chemistry. Theparaffins are first dehydrogenated on the metal sites into olefins,which are then protonated on the acid sites of the catalyst toproduce carbenium ions. These isomerize through hydride shift

(HS), methyl and ethyl shift (MS and ES) and branching (PCP-isomerization), but also undergo cyclization and -scission. Theions thus generated (also the cyclic ones) are deprotonated intothe corresponding olefins, which are then hydrogenated on themetal sites, thus producing new paraffins and naphthenes.

The reforming of naphthenes involves dehydrogenation,isomerization, and cracking steps. First, the naphthenes aredehydrogenated into cyclic olefins, which are protonated intocyclic carbenium ions. Four types of isomerization steps wereconsidered for these cyclic ions. The first is an intraring alkylshift (IRAS) and leads to ring contraction or ring expansionwithout altering the degree of branching. The ring expansion istypical for naphthene isomerization. The conversion of methyl

cyclopentane (MCP) into benzene, for example, first proceedsthrough ring expansion into cyclohexane, which is then dehy-drogenated into benzene. The second type is the formation of aprotonated cyclic propane ionsa cyclic PCP stepsleading toring contraction or ring expansion while altering the degree ofbranching. The third type is an IRAS in which the relativepositions of the substituents on the ring are changed withoutaltering the degree of branching. The fourth is an acyclic PCPisomerization, in the alkyl side chain. The cracking of the cyclicions proceeds through endo- and exocyclic -scissions. Hydro-genolysis on the side chain of cycloalkanes is also accountedfor, but not their ring opening on the metal sites. This reactionis difficult under reforming conditions and does not significantly

affect the product distribution.

30

The aromatics are produced by dehydrocyclization of paraffinsor by dehydrogenation of naphthenes. As in the dehydroisomer-ization of naphthenes, there are intermediate steps between theparaffin and the aromatic, involving both metal and acid sitesof the catalyst. Direct dehydrocyclization of paraffins intoaromatics is not included in this work. Instead, as shown inFigure 1, the paraffins dehydrogenate into olefins which undergoan additional dehydrogenation producing diolefins. These areprotonated into olefinic carbenium ions that are transformed intocyclic carbenium ions and subsequently into naphthenes, whichare dehydrogenated to produce aromatics. For cyclization tooccur, a paraffin with at least a six-carbon straight chain isneeded.

Alkyl aromatics may undergo dehydrogenation and hy-drodealkylation in their side chain to produce aromatic olefinsand smaller aromatics, respectively. A previous study31 hasshown that dealkylation of propylbenzene can proceed on bothacid and metal sites. In this work hydrodealkylation of aromaticsfollows a bifunctional mechanism. On the acid sites, thedealkylation of aromatics occurs via exocyclic -scission ofaromatic carbenium ions. Although a naphtha feedstock maycontain hydrocarbons up to C12, dicyclic components were notincluded in the network, based upon conclusions by Davis30

according to whom the use of a Pt/Sn catalyst drastically reducesthe extent of a second cyclization producing a dicyclic aromatic.

Figures 1, 2, and 3 illustrate molecular reactions and

elementary steps in the reforming of paraffins, naphthenes, andaromatics, respectively.

3. Computer Algorithm for the Generation of the

Reaction Network

The network of molecular reactions and elementary steps forparaffins, naphthenes, aromatics, and all types of olefins andcarbenium ions was generated by computer. Some simplifica-tions and rules were imposed:

1. The maximum carbon number in the network is C12.2. Methyl and primary carbenium ions are very unstable so

that their contribution to the process can be neglected.3. The acid-active sites of the catalyst are of the Bronstedtype.

4. There is no direct transformation of paraffins into aromatics.5. Hydrogenolysis of naphthenes and aromatics occurs only

on the side chain.6. Bimolecular reactions do not occur.7. Dicyclic components are not generated.8. The maximum number of double bonds in a molecule is

two. Only conjugated diolefins are considered.

Starting from these rules the network involving all possibletransformations was generated by means of a computer programfollowing the sequence described in Figure 4. The program isbased on the algorithm developed by Clymans and Froment14

and Baltanas and Froment.13,26 Boolean relation matrices areused to describe the structure of each species and generate the

Figure 1. Molecular reactions and elementary step of carbenium ions inthe catalytic reforming of paraffins.

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molecular reactions and elementary steps. Although the Boolean

matrices are rather sparse they occupy a lot of memory.

Therefore, they are stored in the form of vectors and recon-

structed from these to generate a transformation of a molecule

or ion in the network.

In the reforming of C10 hydrocarbons, the total number of

components (P, O, N, A) generated amounts to 4748 and the

total number of carbenium ions to 6202 (Table 1). Figure 5

shows how the number of components and carbenium ions

increases with the carbon number for three types of hydrocar-

bons. For C11 hydrocarbons the number of components and ions

is much higher than for C10 hydrocarbons so that the time

required for generating the network for C11 hydrocarbons isabout three times that for C10.

4. Single Event Kinetic Modeling

Figure 5 illustrates that the catalytic reforming of naphthainvolves thousands of species and thousands of individual elemen-tary steps. Fortunately, in catalytic reforming as in other acid-catalyzed hydrocarbon processes, the elementary steps belong toonly a few types: protonation, deprotonation, alkyl shifts, branchingreactions, cyclization, and -scission. Nevertheless, the influenceof the structure of the members of a given homologous seriesundergoing a certain type of elementary step still leads to a hugenumber of parameters. The only way to reduce the number ofrate coefficients is to model them. Froment et al.15,26 have madeuse of the transition state theory for this purpose:

k)kBT

hexp(S

o

R ) exp(-H

o

RT ) (1)The effect of structure on the rate coefficient is related to theratio of the global symmetry numbers of the reactant andactivated complex, gl

r and gl . This ratio, called the number of

single events, ne, is factored out of the rate coefficient

k)

(

glr

gl

)(kBT

h

) exp(So

R

) exp(-Ho

RT

) (2)

The remaining part ofkis called the single event rate coefficientand is represented by k. The rate coefficient of the elementarystep, k, is a multiple of k:

k) nek (3)

Equation 2 also reveals that it is possible to define a singleevent frequency factor that does not depend upon the structureof the reactant and activated complex and is unique for a giventype of elementary step:19

A )kBT

h

exp(So

R

) (4)By factoring out the number of single events from the ratecoefficient or frequency factor of an elementary step, the effectof structure on the change of entropy is explicited. To calculatethe number of single events, it is necessary to know theconfiguration of the reactant and the activated complex.Quantum chemical packages (Gaussian, Gamess, Mopac, etc.)yield reliable results for this. Because of the extremely largenumber of intermediates the determination of the transitionstructure for each of them is an overwhelming task. Therefore,on the basis of previous experience in quantum chemicalcalculations, formal rules have been established for the deter-mination of the single event numbers.13

Recently, in their work on the hydrocracking of a mixture ofparaffins, Kumar and Froment32 used the linear free-energy-type relationship of Evans-Polanyi to obtain the activationenergy of each elementary step belonging to a given type,starting from two parameters related to a reference step for thattype. For a very complex mixture like vacuum gas oil, however,they considered only four activation energies per type, definedby the nature (secondary, tertiary) of both the reacting andproduced carbenium ions and independent of the chain lengthand other structural aspects.32 Calculations of Park and Fro-ment33 about methylation, oligomerization, and -scission inthe methanol to olefins process (MTO) indicated this to be themain determining factor for E. As a consequence and given theunique value of A only a maximum of four single event rate

coefficients have to be considered per type of elementary step:k(s,s), k(s,t), k(t,s), and k(t,t).

Figure 2. Molecular reactions and elementary steps of carbenium ions inthe catalytic reforming of naphthenes.

Figure 3. Molecular reactions and elementary steps of carbenium ions inthe catalytic reforming of aromatics.

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5. Rate Equations for the Elementary Steps on the Acid

Sites

5.1. Derivation. Rates have been formulated for the elemen-tary steps of paraffins, naphthenes, aromatics, and olefins. Theolefins are adsorbed on the acid sites and are converted afterprotonation into carbenium ions. Taking into account the stepsin which the olefins participate (protonation/deprotonation andcracking), their net rates of formation on the acid sites can bewritten as

ROij)

k

(ne)depk

dep(mik, Oij)CRik+ -k

(ne)prk

pr(mik)CH+POij+

l o (ne)crk

cr(mlo, mik, Oij)CRlo+(5)

The concentrations of the carbenium ions on the surface of thecatalyst are not directly accessible, but by applying the pseu-dosteady state approximation the net rate of formation ofcarbenium ions can be written as

RRik+)

j

(ne)prk

pr(mik)CH+POij-j

(ne)depk

dep(mik, Oij)CRik+ -

l

o

(ne)isomk

isom(mik, mlo))CRik+ +

l

o

(ne)isomk

isom(mlo, mik)CRlo+ -

l o (ne)crk

cr(mik, mlo, OuV)CRik+

+

l

o

(ne)crk

cr(mlo, mik, OuV)CRlo+ ) 0 (6)

The isomerization term involves all types of isomerizations thatthe acyclic carbenium ions can undergo: ethyl-, methyl-, hydrideshift, and PCP-branching.

(De)protonation steps are known to be extremely rapid andto reach equilibrium.16 Equating the rates of deprotonation andprotonation and solving for CRik

+ leads to:

C Rik+*

)

j

(ne)prk

pr(mik)CH+*

POij

j

(ne)depk

dep(mik, Oij)(7)

with

Figure 4. General sequence followed in the network generation for naphtha reforming: (---) (de)hydrogenation reactions on metal sites; (s) elementary stepson acid sites.

Table 1. Number of Molecular Components and Carbenium Ions inthe Network for C10 Hydrocarbons Reforming

component no.

Hydrocarbons

paraffins 125naphthenes 165aromatics 36olefins 584diolefins 1085cyclic olefins 963cyclic diolefins 1757aromatic olefins 33total HCs: 4748

Carbenium Ions

paraffinic carbenium ions 454cyclic carbenium ions 801aromatic carbenium ions 32olefinic carbenium ions 1835cyclic olefinic carbenium ions 3080total ions: 6202

Figure 5. Number of paraffins, naphthenes and aromatics in the networkup to C11 hydrocarbons.



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CRi+*

)

CRi+

Ctand CH+

*)

CH+

Ct(8)

CH+* represents the concentrations of free acid sites relative to

the total concentration of acid sites. They relate to CRi+* by the

following equation:

CH+*

+i

k

CRik+*

) 1 (9)

The use of relative concentrations avoids the estimation of thetotal acid sites concentration, Ct.

5.2. Thermodynamic Constraints. The single event ratecoefficients for deprotonation depend on the nature of thecarbenium ion and of the olefin. This leads to an overwhelmingnumber of deprotonation coefficients. Baltanas et al.26 were ableto reduce the number of required deprotonation parameters byusing the following thermodynamic constraint:

Kisom(Oj, Oref) )kdep(m, Oref)

kdep(m, Oj)(10)

or

kdep(m, Oj) )kdep(m, Oref)

Kisom(Oj, Oref)(11)

where Oref is a reference olefin, and Kisom(Oj,Oref) is theequilibrium constant for the isomerization of the olefin j intothe reference olefin. This leads to the selection of one referenceolefin per carbon-number so that only two independent depro-tonation rate coefficients per carbon number are left, kdep(s,Oj)and kdep(t,Oj). These two coefficients are then included by meansof a reference protonation equilibrium constant, Kpr. Forinstance, for a secondary (s) carbenium ion R1

+ that deprotonatesinto an olefin Oj, the concentration is given by Kisom(Oj,Oref):

CR1+*

)j (n

e)prkpr(s)CH+* POj

j

(ne)depk

dep(s, Oj)(12)

Equation 12 is further simplified by introducing the thermody-namic constraint for the deprotonation step (eq 11):

CR1+*

)j

((ne)pr

(ne)dep)Kpr(Oref, s)Kisom(Oj, Oref)CH+* POj (13)

Equation 13 is the concentration of carbenium ions producedby protonation of olefins. By application of the pseudosteadystate approximation to the net rates of formation for each type

of ion, similar equations can be obtained for calculating theconcentration of other types of carbenium ions, such as thoseproduced from diolefins, cyclic olefins, and aromatic olefins.These equations, together with eq 9, form a set of nonlinearequations that can be easily solved to obtain CRik

+* and CH+* .

5.3. Composite Single Event Parameters. The substitutionof the relative concentrations of the carbenium ions into eq 5requires the inclusion of the total concentration of active acidsites, Ct, into the single-event rate coefficients k so that newsingle-event rate coefficients have to be defined. Moreover,because of the equilibrium of the (de)protonation steps, thesingle-event rate coefficients and the single-event protonationequilibrium constant cannot be determined separately, so thatthey appear in a composite parameter. For these reasons, the

relative concentrations of the carbenium ions are replaced bythe relative concentrations divided by Kpr, that is:

CR1+*

) ( CR1+*

Kpr(Oref, m)) )

j(

(ne)pr

(ne)dep)Kisom(Oj, Oref)CH+* POj

(14)

In the rate equations the single-event rate coefficients, k, arereplaced by the corresponding composite rate coefficients, k*:

k*

) CtK

pr(Oref, m)k (15)

These composite single event parameters are then used in thefinal formulation of the rates of the elementary steps on theacid sites. For example, the rate equation for the elementarystep PCP-isomerization of a secondary carbenium ion R1

+(s) intoanother secondary carbenium R2

+(s) is written

Rpcp(s, s) ) (ne)pcpCtk

pcp* (s, s)CR1+(s)

* (16)

The rate coefficients are considered to depend only on the natureof the reacting and produced carbenium ions and not on theproduced olefin.15 The composite parameters are the ones thatare estimated from experimental data.

5.4. Accounting for Incomplete Analysis of Feed and

Products. For a complex feedstock like the naphtha used in

catalytic reforming, a gas chromatographic analysis that quanti-fies all the individual isomers is not available. The process modelhas to account for this. That is why groups of isomers (GOI) ofhomologous hydrocarbons with a same degree of branching wereintroduced. This also reduces the number of continuity equationsto be integrated along the reactor in the kinetic analysis ofintegral reactor data and in design simulations. If the composi-tion of the GOI of the feedstock is unknown, it is safe to assumethat the isomers are in equilibrium. Their evolution through thereactor is, of course, accounted for through the networkgeneration and kinetic equations.

Paraffins were subdivided into normal paraffins (nP), single-branched paraffins (SBP), double-branched paraffins (DBP), and

triple-branched paraffins (TBP). The same was done with theolefins. Naphthenes were subdivided into cyclopentanes (5Ni)and cyclohexanes (6Ni), while aromatics were grouped accord-ing to their number of carbon atoms. A naphtha containinghydrocarbons up to C10 then contains 27 paraffinic, 25 olefinic,11 naphthenic, and 5 aromatic components and GOI. Includinghydrogen, the kinetic model contains 69 components and GOI.

The rate coefficients in such a model can be constructed fromthe single event rate coefficients, accounting for the full networkof elementary steps. It should be stressed that for the rate of

Figure 6. LC for PCP(s,s) isomerization of normal olefins at 733 K.



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transformation of GOI1 into GOI2, all possible transformationsof the components of GOI1 into the components of GOI2 areconsidered. Hence, the reaction rate is the sum of the rates ofall the elementary steps that convert all the carbenium ions andmolecules of GOI1 into carbenium ions and molecules of GOI2.For instance, the rate of reaction for the PCP isomerization ofGOI1 into GOI2 can be written as

RpcpL1TL2)

k

(ne)pcpk

pcp* (m1, m2)CRik+,m1

*-

k

(ne)pcpk

pcp* (m2, m1)CRik+,m2

* (17)

The relative carbenium ion concentrations are calculated asdescribed by eq 14. Substitution into the first term of eq 17leads to

RpcpL1fL2) ((LC)pcp(s, s)k

pcp* (s, s) + (LC)pcp(s, t)k

pcp* (s, t) +

(LC)pcp(t, s)k

pcp* (t, s) + (LC)pcp(t, t)k

pcp* (t, t))CH+

*POj

(18)

where POj are the partial pressures of the olefinic GOIj and LCare the so-called lumping coefficients. They are defined by thefollowing equation:

(LC)pcp(m1, m2) ) m1,m2

((ne)pr

(ne)dep)nepcpyi,LjKisom(Oj, Oref) (19)

where yi,Lj is the mole fraction of the component i in the GOIj.5.5. Calculation of the LC-Coefficients. The LC are

functions of temperature only and do not depend on thefeedstock composition. Their values, calculated for temper-ature intervals of 5 K and stored in the computer memory,are utilized in the integration of the ODEs in the adiabaticreactor simulations. The LC do not contain the rate coef-ficient. They vary with the number of carbon atoms andslightly with temperature. To calculate the equilibriumconstants that appear in the LC requires the thermodynamicproperties cp, Hf, and Sf of the saturated and unsaturatedspecies. These properties were calculated using groupcontribution methods developed by Benson et al.34

Figure 6 shows the LC for PCP(s,s) isomerization of n-olefinsat 733 K as a function of the carbon number. The increase inthe value of LC with respect to the carbon number results fromthe increase in the number of isomerization steps with increasingcarbon number.

6. Rate Expressions for Reactions on Metal Sites

The main types of molecular reactions that occur on the metalsites under reforming conditions are dehydrogenation of paraf-

fins and naphthenes and hydrogenolysis of paraffins, as well asthe reversible reactions involved, that is, hydrogenations ofolefins, cyclic olefins, and aromatics.

6.1. Dehydrogenation of Paraffins and Hydrogenation

of Olefins. In the present work, a dehydrogenation mechanismsimilar to that proposed by Dumez and Froment35 was used(Scheme 1).

When the surface reaction is the rate determining step (rds),the following rate equation is derived:

rP-O )

kP-OK1 (pP -pOpH

Keq(P-O))

(1 + K1pP + K3pO + K4pH)2

(20)

The rate coefficient kP-O and the adsorption constants K1, K3,K4 depend on the nature and molecular weight of the paraffin

and the olefin. The mole fractions of the components of theGOI are determined from ratios of isomerization equilibriumconstants calculated by the group contribution method of Bensonet al.34

6.2. Hydrogenolysis of Paraffins: Demethylation and

De-ethylation. The hydrogenolysis of paraffins on the metalsites involves a C-C bond scission with formation of methaneand ethane. Several authors36-40 have studied the hydrogenolysisof paraffins. A generally accepted mechanism for hydrogenolysison metals assumes that a paraffin must lose several H atomsprior to the C-C bond scission. That requires the formation ofmultiple carbonsmetal bonds.41,42

H2 chemisorption: KHH2 + 2L h 2HL (I)

paraffin dehydrogenation: KpCmHn + (n + 1 - x)L h CmHxL + (n - x)HL (II)

scission of the dehydrogenated species (rds) k1CmHxL + HL f CpHyL + Cm-pHx-y+1L (III)

hydrogenation and desorption of products: kjCpHyL + (2p + 2 - y)HL f CpH2p+2 + (2p + 3 - y)L (IV)

where n ) m + 2. It is the number of hydrogen atoms in thereacting paraffin; x is the number of H atoms remaining on thehydrocarbon species; x < n + 1, y < x + 1.

With step III as the rate determining step, the rate equationtakes the form

rhls )k1Kppp(KHpH)

(n+1-x) 2

(Kppp + (KHpH)(n-x) 2

+ (KHpH)(n+1-x) 2)2

(21)

From the four parameters (k1, Kp, KH, and x), the mostsignificant is Kp, which is the one that controls the concentra-tion of the reacting paraffin. Because the dehydrogenationis endothermic Kp increases with temperature. Bond et al.

42-44

have shown that the value of x does not significantly affectthe rate. A similar behavior was found in this work andtherefore a constant value for each paraffinic GOI was setfor x. This implies that whatever the paraffin and hydrogenpressures there is only one reactive intermediate for eachparaffinic GOI.

6.3. Dehydrogenation of Alkyl Cyclohexanes and Hydro-

genation of Aromatics. The dehydrogenation of cyclohexaneshas been extensively studied45-48 over different types of catalyst.Van Trimpont et al.48 studied this reaction on a Pt-Re/Al2O3catalyst. They found that a model based on a single sitemechanism reproduced the observed data better than a modelwith a dual site mechanism. Verstraete and Froment47 have alsostudied this reaction over a Pt-Sn/Al2O3 catalyst. After

discrimination between three different mechanisms they retaineda single site mechanism:

Scheme 1



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N + LhNLNLhCNL + H2

CNLhCDNL + H2 (rds)

CDNLhAL + H2ALhA + L

where CNL ) cyclic olefin, CDNL ) cyclic diolefin. Whenthe surface reaction is the rate determining step the rate equationbecomes

rN-A )kN-A (pN - pApH

3 KN-A)

pH(1 + KNpN + KApA)(22)

The equilibrium constant for the dehydrogenation, KN-A, iscalculated from Bensons group contribution method.

6.4. Modeling of the Metal Site Parameters. 6.4.1. Kinetic

Parameters for the Dehydrogenation of Paraffins. The kineticparameters of equations (20) are valid for the dehydrogenationof a particular paraffin. The large number of paraffins in naphthaleads to a very large number of rate parameters. Only asystematic approach can reduce that number. The energyrequired to remove a hydrogen atom depends on the nature ofthe parent carbon atom: primary, secondary, or tertiary.49 The

activation energies for the dehydrogenation of paraffins thendepend on the location of the double bond in the product olefin,that is, on the nature of the carbon atoms linked to the doublebond.32 As a result, all the rate coefficients, kP-O in eq 21, belongto one of the following five types: kdeh_p(p-s), kdeh_p(p-t),kdeh_p(s-s), kdeh_p(s-t) and kdeh_p(t-t). The first one, for example,indicates that the dehydrogenation of a given paraffin producesan olefin with a double bond between primary and secondarycarbon atoms.

6.4.2. Kinetic Parameters for the Hydrogenolysis of

Paraffins. In this case no olefin is formed so that the nature ofthe C-atoms linked to the bond where the scission occurs istaken to be determining. Consequently, for both types of

hydrogenolysis considered in this work, the modeling is basedonly on three types of kinetic parameters, k(s-p), k(t-p),k(q-p), for demethylation, and k(s-s), k(t-s), k(q-s), for de-ethylation. For example, k(q-p) is the rate constant for thescission of a bond between quaternary and primary carbonatoms.

6.4.3. Kinetic Parameters for the Dehydrogenation of

Naphthenes. In this case only one kinetic constant is used foreach type of aromatic produced, that is, one for benzene, onefor toluene, one for xylenes, etc., up to C10.

6.4.4. Adsorption Constants of the Hydrocarbons. In theirstudy of the adsorption of alkanes on zeolites, Denayer et al.50,51

showed that the physisorption enthalpy and entropy vary linearlywith the carbon number of the physisorbed alkane.

ln Ki ) aCNi + b (23)

The a and b parameters account for the contribution of thephysisorption entropy and enthalpy, and are considered to bedependent on the type of hydrocarbon. By relating the adsorptionconstant of a given hydrocarbon, Ki, with that of a referencehydrocarbon, K0, of the same type (same value for b), thefollowing equation is derived:

Ki ) K0 ea(CNi-CN0) (24)

Therefore, only one independent adsorption constant (K0) foreach type of hydrocarbon (P, O, N, A) is included in the model.Denayer et al.50,51 showed that the parameters a and b in eq 23

strongly depend on the catalyst type and pore size. In the presentworka is assumed to have a unique value at a given temperature.

7. Reduction of the Number of Parameters

The formulation of the rate equations for the elementary stepsand molecular reactions leads to a kinetic model containing forisothermal conditions 56 parameters, belonging to the typeslisted in Table 2.

In Table 2 the parameters for the elementary steps on theacid sites are the true single-event rate parameters. The use ofthe composite parameters, together with the application ofthermodynamic constraints, allows a reduction in the numberof parameters. The thermodynamic constraint is applied to theisomerization steps, as first derived by Baltanas et al.26 in termsof the single-event protonation equilibrium constants:

kisom(t, s)

kisom(s, t))

Kpr(OrefTRs

+)

Kpr(OrefTRt+)

(25)

By substituting one of the rate coefficients into eq 25, it is readilyfound that

kisom* (t, s) ) kisom

* (s, t) (26)

Because the thermodynamic constraint applies to each type ofisomerization, the number of parameters for PCP-branching,

intraring alkyl shift, and ring contraction/expansion is reducedfrom four to three for each of them. A second reduction stemsfrom the similarity between acyclic -scission and exocyclic-scission on the side chain.

Further reduction is possible by observing that cyclization isthe reverse of endocyclic -scission, so that only one set ofparameters and the thermodynamic equilibrium constant arerequired. The cyclization of 1-heptene into methyl cyclohexaneis given here as an example:

The overall equilibrium constant for the cyclization of the olefininto the naphthene can be expressed as the product of theequilibrium constants of the steps involved in that reactionsequence:

KcycOihNj

) KdehOihDOjKprde

DOjhORim+(kcycOifNj

kendoNjfOi)(KprdeCOjhCRim+ KdehNjhCOi)-1

(27)

so that

kendoNjfOi

)Kdeh

OihDOjKprdeDOjhORim+

KprdeCOjhCRim+ Kdeh

NjhCOiKcycOihNj

kcycOifNj (28)

The protonation/deprotonation equilibrium constants cancel outwhen the rate coefficients are written in terms of the compositesingle-event rate coefficients. The dehydrogenation and cycliza-tion equilibrium constants are calculated from the thermody-namic properties of the corresponding species by means ofBensons group contribution method.34

Summarizing, the number of parameters has been reduced

by 11 so that for isothermal conditions the model contains 45independent parameters: 21 composite single-event rate coef-



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ficients for the elementary steps on acid sites and 24 parametersfor the reactions on the metal sites. These 45 parameters wereestimated from the experimental data.

8. Experimental Data and Their Simulation

The present modeling work was based on data collected in acomprehensive experimental study of Verstraete and Froment.47

Their data were obtained from experimentation in a fixed-bedintegral reactor loaded with a Pt-Sn/Al2O3 catalyst. The reactorwas divided into eight beds, with sampling in between them sothat values of the yields of each response were obtained at eightdifferent space times. To eliminate internal mass transferlimitations, the catalyst was crushed to a size between 0.5 and0.7 mm. To avoid catalyst deactivation by coke deposition, theexperiments were carried out at temperatures not exceeding 733K and higher partial pressures of hydrogen than the one appliedin industrial operation. Three different temperatures and threetotal pressures were investigated in the experimental program.A summary of the operating conditions is given in Table 3.

For a plug flow reactor the fluid field continuity equationsfor the various species can be written as

dFi

dWcat) Ri (29)

Because of the very fast dehydrogenation of paraffins andnaphthenes, the set of differential equations can be very stiff,especially at the entrance of the first reactor. Gears method52

was used to solve the set of the coupled nonlinear continuityequations for the components and GOI.

The optimal set of parameters was estimated by minimizingan objective function based upon the weighted sum of squares

of residuals which are the differences between experimental andcalculated yields of the responses:

SSQ )j)1

nresp

l)1

nresp

wjli)1

nexp

(yij - yij)(yil - yil) (30)

The weighting factors used in the estimation were calculatedfrom the elements of the main diagonal of the inverse of theerror covariance matrix (nrespectively nrespectively).

wjj ) jj-

1 )

(i)1

nexp

yij)-m

k)1

nresp

(i)1

nexp

yik)-m (31)

The power m expresses the relative importance of the responses.For m ) 1, the real weight of each response is used in theminimization, while for m ) 0, all the responses are equallyweighted. Previously, Feng53 and Park54 have found valuesbetween 0.1 and 0.3 to be adequate. In this work, values of mranging from 0.3 to 0.6 were chosen. A value of m equal to 0.6is used for olefins, which are present in very low concentrations.

The Marquardt55-Levenberg56 algorithm was used to mini-mize the objective function. Parameter estimates were firstdetermined per temperature. Then, using appropriate reparam-etrization57 and considering the complete set of experimentaldata, the parameters (Ea and Ao, or H and S) weresimultaneously estimated at the three experimental temperatures.All parameters were significant and showed narrow confidenceintervals and high t-values. The F-tests were consistently highat the three temperatures.

The rate coefficients of the molecular reactions on the metalsites generate trends observed in industrial reforming. Forexample, the rate coefficient of naphthene dehydrogenationincreases with the C-number and the number of substituents inthe ring and largely exceeds that of paraffin dehydrogenation.In the latter, k(s-s) is favored. Combined with the relevantconcentrations it becomes clear that intrinsically these rates on

the metal sites are much higher than those on the acid sites, asituation aimed for in catalytic reforming. The rate coefficientsfor de-ethylation exceed those for demethylation. In the formerthe (q-s) type is the fastest, in the latter the (q-p) type is.

The values for the single-event rate coefficients follow a trendtypical for carbenium ion chemistry. In PCP steps k*(s,s) >k*(s,t) > k*(t,t). In acyclic and exocycyclic -scission k*(t,t)largely exceed the others. The same trend is observed inendocyclic -scission, but the k* values are lower. In ring

Table 2. Types and Numbers of Parameters in the Kinetic Model

parameter description no.

kpcp PCP isomerization of acyclic R+ 4k -scission of acyclic R+ 4kiras intraring alkyl shift of cyclic R+ 4krce ring contraction/expansion of cyclic R+ 4kcyc cyclization of olefinic R+ 4kendo endocyclic -scission of cyclic R+ 4kexo exocyclic -scission type I (on side chain of cyclic R+) 4kexo exocyclic -scission type II (of cyclic R+) 4

kdehp dehydrogenation of paraffins 5kdem demethylation of paraffins 3kdeet de-ethylation of paraffins 3kdehN dehydrogenation of naphthenes 5KP-deh adsorption of paraffins for dehydrogenation 1KP-hyls adsorption of paraffins for hydrogenolysis 1KO adsorption of olefins 1KN adsorption of naphthenes 1KA adsorption of aromatics 1KH2deh adsorption of hydrogen 1KH2hyls adsorption of hydrogen in hydrogenolysis 1a parameter in eq 24 1

total 56

Table 3. Experimental Conditions (Verstraete and Froment47)

conditions 673 K 713 K 733 K

total pressure, bar 7 5, 7, and 9 5, 7, and 9molar ratios H2/HC 10 10 10, 15.4space time interval,

(gcat h mol-1 HC fed)

0-103 0-92 0-92

number of experiments 8 8 8number of responses 15 40 56

Figure 7. Calculated (s) and experimental ((,2,b) yields for normal, single-branched, and multibranched paraffins at 733 K and 7 bar.



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contraction and expansion k*(t,t) > k*(s,t) > k*(s,s). The LCfor PCP are two or three orders larger than those for -scission.It may be safely concluded that the rate of PCP-branchingisomerization is larger than that of-scission, as also observedin hydrocracking16 and MTO.58

In Figures 7-10 the values of the yields calculated by themodel at 733 K are compared with the experimental data forthe various types of hydrocarbons. The model also predictsvalues of the individual members of the different types, ofcourse, as evidenced by Figure 10.

9. Simulation of a Multibed Adiabatic Reformer with

Radial Flow

A reforming unit consisting of three adiabatic beds with radialcentripetal flow was simulated using the detailed kinetic modeldescribed above. The reactor model contained continuity equa-tions for 69 components and GOI, an energy equation, and anequation for the pressure drop. The diffusional limitations insidethe catalyst particles were accounted for either through theStefan-Maxwell or Wilke equations. The naphtha feed amountedto 120 000 kg h-1. Its composition was that used in theexperimental program discussed above. The hydrogen recycleratio was maintained at 5.0 mol H2 mol

-1 HC, and the total

pressure was 7 bar. The three beds operate at equal inlettemperatures of 510 C (783.15) K. The catalyst particles were

spheres with a diameter of 3.18 mm, and the reactor loadingdensity was 1211 kgcat m

3r-1. In what follows the results of the

simulations based upon a heterogeneous model are comparedwith those obtained by a pseudohomogeneous model.59 Theheterogeneous reactor model explicitly accounts for diffusionlimitations inside the catalyst particle by additional transportequations, to be integrated in each increment used for theintegration of the fluid field conservation equations. Interparticletransport limitations are negligible in industrial catalytic reform-ers because of the high flow rates. The homogeneous reactormodel ignores these transfer limitations and considers only thefluid field continuity-, energy-, and pressure drop-equations.

Figure 11 shows the temperature profiles in each catalyst bed.A steep temperature drop is observed in the inlet zone of thefirst bed, caused by the very rapid naphthene dehydrogenations.For the heterogeneous model, the total temperature drop in the

first bed amounts to 60 K. In the second bed additionaldehydrogenation of naphthenes and paraffins occur, causing atemperature drop of about 55 K. In the third bed dehydrocy-clization and the exothermic hydrocracking occur. The temper-ature drop in the third bed is 33 K. The total space time waslimited to 56.1 Kgcat h K mol

-1 HC fed to avoid excessivehydrocracking and the resulting loss in reformate yield, whichis defined as the summation of yields of C5

+ hydrocarbons.Figure 12 shows the composition profiles of the PINA

fractions, that is, C5+ n- and i-paraffins, naphthenes, and

aromatics, and again the difference between the two modelpredictions is pronounced. The diffusion limitations inside thecatalyst particle cannot be neglected.

The yield of the nP and naphthene fractions predicted bythe heterogeneous model is lower than that predicted bythe homogeneous model. The components of these fractions arereactants and in the presence of diffusion limitations theconcentration of reactants is lower in the center of a particlethan at the surface so that the rate at which they react is lower.It is the other way around with the aromatic fraction that ismade up to a large extent of products. The difference in the iPyields of both models reflects the production of iP componentsin the first bed and their conversion at higher space times, thatis, in beds 2 and 3. At the end of the second bed, the paraffinisomers are almost at equilibrium among themselves. In the thirdbed dehydrocyclization of paraffins into aromatics takes place,along with hydrocracking by -scission on the acid sites and

hydrogenolysis on the metal sites, so that the concentration ofi-paraffins keeps decreasing.

Figure 8. Calculated (s) and experimental (b, 9) yields for single-branchedand multibranched C7 paraffins at 733 K and 7 bar.

Figure 9. Calculated (s) and experimental (() yields for naphthenes at733 K and 7 bar.

Figure 10. Caculated (s) and experimental (b, 9, 2) yields for the BTXaromatics at 733 K and 7 bar.



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Figure 13 shows the low effectiveness factors for thedehydrogenation of n-octane resulting from the steep internalconcentration profiles. These factors are even lower for the veryfast naphthene dehydrogenations: they evolve from 0.15 to 0.30.The -values increase toward the end of each bed where thelower temperature slows down the reaction rate. Figure 13 also

illustrates that the detailed kinetic model used here obviouslyallows the prediction of the compositions of the various fractionsin great detail, that is, up to the individual components.

The hydrogen yield profile through the catalyst beds is shownin Figure 14. The highest rate of production of hydrogen isobserved in the first bed, due to the fast dehydrogenation ofnaphthenes. Because hydrogen is a product its yield predictedby the pseudohomogeneous model is too high.

Olefins are undesirable in the reformate because of theirtendency to produce gums. Figure 16 illustrates that for thechosen operating conditions the total olefin (C2

) to C10)) yield

at the reactor exit is not negligible. The olefins are mainlyproduced by the dehydrogenations on the metal function of thecatalyst. Their yield rises very sharply at the high inlet

temperature of the three beds and then decreases as they areconsumed by the acid catalyzed steps.

Figure 16 shows the evolution of the RON and reformate

yield. The RON was determined by using the correlationobtained by Petroff et al.60

Figure 11. Comparison of the simulated temperature profiles through the catalytic beds for the pseudohomogeneous and heterogeneous models. Inlet conditions:783.15 K, 5.0 mol H2/mol HC, and 7 bar total pressure. The difference between the two model predictions is significant.

Figure 12. Comparison of the simulated PINA yield profiles through thecatalyst beds.

Figure 13. Evolution of the effectiveness factor for the dehydrogenationof n-octane: solution by the Wilke-type approximation with three collocationpoints.

Figure 14. Hydrogen yield profiles.



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10. Conclusions

The very detailed model for the catalytic reforming of naphthadeveloped from its fundamental chemistry provides a thorough

insight into the process and a wide predictive potential but itcontains a huge number of parameters. The application of thesingle-event approach to the modeling of the rate constants andthermodynamic constraints allowed the reduction of the numberof independent parameters for the steps on the acid sites to only21.

Current reforming models impose equilibrium for the hydro-genations and dehydrogenations. This is not the case in thepresent model. By focusing on moieties in the molecules, inthis case the C-atoms on the produced double bonds or thoselinked to the bond where the scission occurs, it was possible toreduce the number of rate and adsorption parameters for thereactions on the metal function to 24. The total number of

parameters of the kinetic model then amounts to 45. These canbe estimated from a well-designed experimental program.Because of their fundamental nature the parameters are invariantwith respect to the feedstock.

For the commercial catalyst used in this investigation thevalues of the rate parameters of the dehydrogenation reactionson the metal function were found to be very large comparedwith those of the single-event rate coefficients, so that the rate-determining steps for the reforming reactions occur on the acidalumina function. That leads to a reformate with optimalcomposition. Because of its fundamental nature the model isalso applicable to other reforming catalysts, like those of thePt/Re type, provided that the appropriate rate parameters are

available.Despite the size of the kinetic model, the application to the

simulation of industrial reformers with radial flow was straight-forward and smooth. The reactor model contains 69 continuityequations for the external fluid field and the correspondingnumber of equations for diffusion and reaction inside the pores.The results proved the reliability of the model and illustratedits performance as a tool for the prediction of the reformerbehavior and the optimization of the product yields. In this way,the model significantly reduces the amount of pilot plantexperimentation. It can also be used in the investigation of newcatalysts.

The simulations have shown in an unambiguous way that

diffusion limitations are important in catalytic reforming andhave to be accounted for. There is no way to compensate the

absence of these in the reactor model by expressing the kineticmodel in terms of so-called effective rate parameters.

Acknowledgment

Rogelio Sotelo-Boyas acknowledges the National Council ofScience and Technology of Mexico, CONACYT, for thefinancial support in the development of this work. The authorsalso address special acknowledgments to Dr. Jan Verstraete forproviding the experimental data, as well as to Dr. RayfordAnthony for stimulating discussions.

Appendix

List of Symbols

A ) aromatic

a ) first contribution parameter of physisorption H and S

b ) second contribution parameter of physisorption H and S

Ct ) surface concentration of total acid active sites, mol sites g cat-1

CR+

) surface concentration of carbenium ions, mol R+ gcat-1

CH ) surface concentration of free acid sites, mol sites gcat-1

CR+*

) relative concentration of acid sites with R+ on the surface

CR+*

) composite relative concentration of acid sites with R+ on

the surface

CH+*

) relative concentration of free acid sites on the surface

deh ) dehydrogenation

dep ) deprotonation

Fi ) flow rate of component i, mol h-1

GOI ) group of isomers

H+ ) free or vacant acid sites

h ) Planks constant, 6.626068 10-34 m2 kg h-1

hyd)

hydrogenationK ) equilibrium adsorption constant

Kisom ) equilibrium single-event isomerization constant, dimension-

less

Kpr ) equilibrium single-event protonation constant, bar

Keq ) equilibrium constant, dimensionless

KDH ) equilibrium dehydrogenation constant, bar

kcr ) single-event rate coefficient for cracking, h-1

kdep ) single-event rate coefficient for deprotonation, h-1

kpr ) single-event rate coefficient for protonation, bar h-1

k*dep ) composite deprotonation single-event rate coefficient, mol

gcat-1 h

k*pr ) composite protonation single-event rate coefficient, mol gcat-1

bar h

k*pcp ) composite single-event rate coefficient for PCP, mol gcat-1

bar h

Figure 15. Simulated total olefins yield profiles, from C2) to C10

).Figure 16. Simulated profiles of the reformate yield and research octanenumber.



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k*cr ) composite single-event rate for cracking, mol gcat-1 bar h

kN-A ) rate constant for the dehydrogenation of naphthenes

L ) active site

Li ) lump i

LC ) lumping coefficient, dimensionless

N ) naphthene

n ) chiral centers

ne ) single-event number in an elementary step

nexp ) number of experiments

nrespectively ) number of responsesO ) olefin

P ) paraffin

pro ) protonation

rds ) rate determining step

T ) absolute temperature, K

W ) weight of catalyst, Kg

wjl ) elements of the inverse of the covariance matrix

Y ) response in terms of yields, g of i/100 g HC fed

Greek Letters

) refers to -scission step

i ) symmetry number of component i

Superscripts

m ) power relative to the weight factor of responses

+ ) indicates charge of carbenium ion

* ) used to describe a composite single-event rate coefficient, i.e.,

k*

^ ) calculated value, e.g., y is the calculated yield

o ) initial, e.g., initial flow: Fo

Subscripts

A ) aromatic

cr ) cracking

dep ) deprotonation

deh ) dehydrogenation

hyd ) hydrogenation

hls ) hydrogenolysis

iras ) intraring alkyl shift

M ) general notation for type of carbenium ion: s or tN ) naphthene, also naphtha in xNO ) olefin

P ) paraffin

pro ) protonation

pcp ) isomerization via a protonated cyclopropane intermediate

Q ) quaternary carbon atom

Ri+

) carbenium ion

rce ) ring contraction o expansion

ref ) reference, e.g., reference olefin: Orefs ) secondary carbenium ion

t ) tertiary carbenium ion

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ReceiVed for reView April 15, 2008ReVised manuscript receiVed June 30, 2008

Accepted July 2, 2008

IE800607E


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