Applied Catalysis A: General 349 (2008) 29–39

Assessment of dominant factors affecting liquid phase hydroisomerizationon bifunctional zeolites

A. Funez a, J.W. Thybaut b,*, G.B. Marin b, P. Sanchez a, A. De Lucas a, J.L. Valverde a

a Departamento de Ingenierıa Quımica, Facultad de Ciencias Quımicas, Universidad de Castilla-La Mancha, Avd. Camilo Jose Cela s/n, 13071 Ciudad Real, Spainb Ghent University, Laboratory for Chemical Technology, Krijgslaan, 281-S5, B-9000 Ghent, Belgium

A R T I C L E I N F O

Article history:

Received 17 January 2008

Received in revised form 14 June 2008

Accepted 10 July 2008

Available online 19 July 2008

Keywords:

n-Octane

Hydroisomerization

Liquid phase conditions

Experimental investigation

Kinetic model

Zeolite

USY

Beta

Mordenite

A B S T R A C T

The hydroisomerization of n-octane in the liquid phase was investigated over beta, USY and mordenite

zeolites loaded with 1 wt% Pt in a stirred semi-batch microautoclave. The total pressure ranged form 5 to

9 MPa and the temperature from 523 to 563 K with an initial catalyst/n-octane ratio of 7 gcatalyst=moln-C8.

PtBETA was the most active catalyst at all operating conditions, followed by PtMOR and PtUSY. The

isomer yields on PtMOR were somewhat lower than on PtBETA and PtUSY. Increasing the total pressure

always resulted in a decrease in the n-octane conversion, which is indicative of so-called ideal

hydroisomerization. The n-octane hydroisomerization experiments were simulated with a kinetic model

based on a parallel/consecutive reaction scheme involving reversible mono- and multibranching and

irreversible cracking from mono- as well as multibranched isomers. The model fitted adequately the

experimental data on PtBETA and PtUSY. However, more dispersion was observed with catalyst PtMOR.

The ratio of the composite rate coefficients for cracking to that for monobranching was significantly

higher on PtMOR than on PtUSY and PtBETA. The composite activation energy for monobranching was

20 kJ mol�1 higher on USY if compared to that of mordenite and beta. These modelling results were

related to pore sizes and geometry and average acid strength.

� 2008 Elsevier B.V. All rights reserved.

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Applied Catalysis A: General

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1. Introduction

Environmental regulations place strong restrictions on thearomatic content of fuels in general and unleaded gasoline inparticular. As a result, there has been an urgent need to developefficient technologies for octane number enhancement processesin order to meet the demand for high octane number unleadedgasoline with low total aromatics content. Boosting the octanenumber of a gasoline fraction by increasing the content ofbranched alkanes is an environmentally acceptable alternativecompared to other technologies, such as blending with oxygenatesand aromatics [1,2]. Hence, the hydroisomerization of normalparaffins to branched paraffins is of considerable interest and hasbeen studied intensively [3–7].

Hydroisomerization is a bifunctional process requiring metal aswell as acid sites. Saturated hydrocarbons are dehydrogenated onthe metal sites producing unsaturated hydrocarbons which in turnundergo protonation on the acid sites of the zeolite with formationof carbenium ions as reaction intermediates. These carbenium ions

* Corresponding author. Tel.: +32 9 264 45 19; fax: +32 9 264 49 99.

E-mail address: Joris.Thybaut@UGent.be (J.W. Thybaut).

0926-860X/$ – see front matter � 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.apcata.2008.07.009

undergo skeletal rearrangements and b-scission reactions fol-lowed by deprotonation and hydrogenation of the resulting olefins[8]. Prior to these chemical steps, physisorption occurs in themicropores of the catalyst [9,10]. The balance between the numberand the activity or strength of the metal and the acid sites plays akey role in the product selectivities [11–14].

Bifunctional zeolite catalysts exhibit high activity in thehydroisomerization of alkanes [15–17]. The zeolite provides theacid function where the isomerization reaction occurs, whereas ametal provides the hydrogenation–dehydrogenation capability.Noble metal-zeolite catalysts, in particular Pt or Pd loaded beta,mordenite and Y possess a high activity and selectivity forhydroisomerization of n-alkanes [18].

A large number of studies on n-alkane hydroisomerization overbifunctional zeolite catalysts have been reported in the literature,some of them studying the effect of the reaction conditions on thehydroisomerization process. Chao et al. [19], for example, studiedthe effect of the reaction pressure on the n-heptane hydroconver-sion on platinum-loaded mordenite and beta zeolites. de Lucaset al. [20] reported the effect of key reaction conditions, such as thetemperature and the pressure, the hydrogen/n-octane molar ratio,the space time and the time on stream on the hydroisomerizationof n-octane over beta zeolite. As expected, an increase in the

Nomenclature

A pre-exponential factor (kgcat (mol s)�1)

b parameter vector

Ci concentration of component i ðmol kg�1catÞ

Ctot total concentration of acid sites ðmol kg�1catÞ

Eact activation energy (J mol�1)

F statistical value

fi fugacity for component i (MPa)

H Henry’s coefficient ðmol kg�1cat MPa�1Þ

DH8 standard reaction enthalpy (J mol�1)

j index

k index

k rate coefficient (kgcat (mol s)�1)

Kdeh equilibrium coefficient for dehydrogenation (MPa)

Ki partition coefficient for component i between the

vapor and the liquid phase

KLan,i Langmuir physisorption coefficient for component

i (MPa�1)

Kprot equilibrium coefficient for protonation

(kgcat mol�1)

N number of moles

nob number of observations

nresp number of responses

p pressure (MPa)

R ideal gas constant (J (mol K)�1)

ri reaction rate for component i (mol (kg s)�1)

S selectivity (mol/mol)

SSQ sum of squares

t statistical t-value

t time (s)

T temperature (K)

V(b)i,i ith diagonal element of the variance matrix of the

parameter estimates

W catalyst weight (kg)

wiweighing factor for component i

X conversion (mol/mol)

xi liquid phase mole fraction for component i

Y yield (mol/mol)

yi vapor phase mole fraction for component i

zi global mole fraction for component i

Greek lettersF vapor phase fugacity coefficient for component i

w ratio of the number of moles in the vapor phase and

the liquid phase

mi chemical potential for component i (MPa)

n0i pure liquid phase fugacity coefficient

Superscripts^ calculated

app apparent

comp composite

Subscript0 initial

ave average

cr cracked products

deh dehydrogenation

G gas phase

i component index

j component index

k component index

L liquid phase

mo monobranched

mu multibranched

n normal alkane

ncomp number of components

nob number of observations

npar number of parameters

nresp number of responses

phys physisorption

prot protonation

sat saturation

tot total

A. Funez et al. / Applied Catalysis A: General 349 (2008) 29–3930

conversion with increasing reaction temperature and space timewas observed. The opposite effect was noted with increasingreaction pressure and H2/n-C8 molar ratio. No considerablechanges in conversion were appreciated for different values oftime on stream, indicating that catalyst deactivation was notoccurring to a measurable extent. Wang et al. [21] also reported theeffect of these parameters on the hydroisomerization of n-heptaneover Pt-loaded beta zeolite, obtaining similar trends.

Most experimental work on hydroisomerization and hydro-cracking has been performed at vapor phase conditions. Scarceliterature about these processes in the liquid phase exists [22].Nevertheless, industrially three-phase conditions have been used[23]. Working at vapor phase conditions is, however, easier than atliquid phase conditions from the analytical and setup constructionpoint of view.

Different kinetic models for n-alkanes hydrocracking andisomerization reactions have been reported [24–27]. These modelsrange from a priori lumped models over a posteriori lumpedmodels to microkinetic models. In addition, the number ofpotentially quasi-equilibrated steps can be different. de Lucaset al. [16] simulated the n-octane hydroisomerization using alumped kinetic model. Martens et al. [26] used a relumped kineticmodel to describe hydrocracking on non-shape selective Pt-HUSY.Thybaut et al. [28] developed a microkinetic model for alkanehydrocracking based on experimental data on three Pt/USYzeolites with varying Si/Al ratio. Recently, Thybaut et al. [29]have reported a kinetic model for non-ideal hydrocracking.

Concerning the modelling of liquid phase hydroisomerization,Denayer et al. [22] analyzed the competitive hydroconversion ofheptane and nonane in liquid phase over Pt/HY zeolite catalystwith an adsorption-reaction model based on intrinsic kineticparameters obtained from vapor-phase experiments. Narasimhanet al. [30] have recently reported a methodology which enables toaccount for dense phase aggregation states, i.e., high pressurevapor phase or liquid phase, starting from a microkinetic modeldeveloped based on experiments performed low-pressure vaporphase conditions. Only two parameters, i.e., the excess physisorp-tion coefficient and the excess standard protonation enthalpy haveto be estimated from experimental data to apply a single-eventmicrokinetic model based on vapor phase n-alkane hydroconver-sion data to liquid phase conditions.

A. Funez et al. / Applied Catalysis A: General 349 (2008) 29–39 31

The aim of this work is to compare the hydroisomerizationkinetics at liquid phase conditions on a series of three Pt-loadedzeolites, i.e., beta, USY and mordenite. These are 12-membered ringzeolites, beta and USY with a three-dimensional pore structure andmordenite with a one-dimensional pore structure. The latterzeolite has the smallest pore size. The catalyst behaviour has beeninterpreted in terms of pore sizes and geometry and average acidstrength. Kinetic modelling using a lumped reaction networkcontributed to the understanding of the catalyst effect on theobserved kinetics.

2. Procedures

2.1. Experimental

2.1.1. Catalyst preparation

The parent zeolites, i.e., USY (Si/Al = 13.0), mordenite (Si/Al = 10.4) and beta (Si/Al = 13.0) were supplied in the ammoniumform by Zeolyst International. The acid form of the zeolites (HUSY,HMOR and HBETA) was obtained by calcination at 550 8C for 15 h.

Metal incorporation was carried out by impregnation. Firstly, acatalyst sample was placed in a glass vessel and kept undervacuum at room temperature for 2 h in order to remove water andother compounds adsorbed on the zeolite. A known volume of anaqueous metal precursor solution (H2PtCl6) was then poured overthe zeolite. Next, the solvent was removed by evaporation undervacuum. The metal concentration of the impregnating solutionwas calculated to yield a final Pt content in the catalysts of 1 wt%.

After metal incorporation, the sample was calcined at 400 8C for4 h, and reduced in a fixed-bed reactor under a hydrogen flow,leading to the catalysts PtUSY, PtMOR and PtBETA.

2.1.2. Catalyst characterization

Surface area, micro and mesopore volume, total acid sitedensity, acid strength distribution and metal dispersion measure-ments were performed in order to characterize the catalysts.Below follows a brief description of the apparatus and techniquesused.

Pores size distribution and BET surface area were determinedon a Micromeritics ASAP 2010 adsorptive and desorptiveapparatus. The samples were evacuated under vacuum of5 � 10�3 Torr at 350 8C for 15 h. Specific total surface areas werecalculated using the BET equation, whereas specific total porevolumes were evaluated from N2 uptake at a relative pressure (P/P0) of N2 equal to 0.99. The Horvath–Kawazoe method was used todetermine the microporous surface area and micropore volume.The Barret, Johner and Halenda (BJH) method was used todetermine the distribution of the mesopores. Surface areameasurements had an error of 3%.

The concentration of the acid sites was measured bytemperature programmed desorption of ammonia (TPDA) usinga Micromeritics TPD/TPR 2900 analyzer. The sample was firstlyheated from room temperature to the calcination temperature at15 8C min�1 under a flow of helium, holding this temperatureduring 30 min. After reducing the catalyst under a hydrogen flow,the system was cooled to 180 8C. After saturating the sample withammonia, it was first purged and consequently the temperaturewas ramped at 15 8C min�1 from 180 to 560 8C. Weak and strongacid site concentrations are obtained by peak integration at thelowest and the highest temperatures, respectively. The averagerelative error in the acidity determination was lower than 3%.

The platinum dispersion was determined from chemisorptionmeasurements in the same Micromeritics TPD/TPR 2900 analyzer.The experiments were carried out using the dynamic pulsetechnique with an argon flow of 50 ml min�1 and pulses of

hydrogen. An adsorption stoichiometry of Pt/H = 1 was assumed.The sample was pre-treated by heating at 15 8C min�1 in flowinghelium up to 250 8C and kept constant at this temperature for20 min. After in situ reduction of the sample, it was flushed with aninert gas for 30 min and cooled down 60 8C, the temperature atwhich the dispersion was measured to avoid the spill overphenomenon. The dispersion measurements with H2 pulses hadan error of 5%.

2.1.3. Kinetics measurements

The n-octane hydroisomerization runs were carried out in a50 ml semi-batch microreactor (Autoclave Engineers). Firstly, thecatalyst was reduced in a fixed-bed reactor under a hydrogen flowof 0:0565 mol H2 s�1 kg�1

cat at 410 8C for 4 h.Next, the semi-batch microreactor was filled with 0.105 mol of n-

octane and the catalytic basket with the desired quantity of catalyst,typically 0.75 g. Afterwards, it was pressurized with hydrogen till apressure 1 MPa below the final pressure. Then, it was heatedgradually at the desired temperature. Once this temperature wasreached, the total pressure was finally set. The heating of the reactortypically takes 10–15 min. The octane conversion in this period wasalways lower than 5% of the conversion measured at the differentbatch times. It was experimentally verified that a stirring rate over370 rpm was sufficient to establish complete mixing in the reactor.The same test indicates the absence of external mass transportlimitations. In zeolites internal mass transfer limitations could occurin the intercrystalline pores or the intracrystalline pores. Theabsence of internal mass transport limitations in the intercrystallinepores was verified by performing experiments on catalyst sampleswith a varying particle size. Intracrystalline diffusion was assessedthrough calculation of the Weisz modulus for the various zeolitesconsidered. Even if literature reported values for diffusion coeffi-cients in zeolites might not exactly apply to the case considered here,an order of magnitude calculation of the Weisz-modulus can bemade and the relative values obtained are expected to be valid. Sincereported diffusion coefficients for alkanes in mordenite are two tothree orders of magnitude lower than for beta and USY, intracrystal-line diffusion limitations are most likely to occur on mordenite[31,32]. For a diffusion coefficient of 10�13 m2 s�1 and a crystallitesize of 10�5 m, a Weisz modulus in the order of 10�2 is obtained formordenite. As a result, the onset of intracrystalline diffusionlimitations can be expected in the data obtained on mordenite,while the data on beta and USY can be considered free from any kindof diffusion limitations.

Blank runs demonstrated that non-catalytic n-octane conver-sion was negligible. The reaction was generally carried out for 24 h.Samples of liquid products were taken at regular intervals. 20 ml ofliquid was taken through a six-way valve, the reactor pressurebeing sufficient to fill the loop, which was purged afterwards withnitrogen. Vapor samples were collected through a 200 ml loop, thecontent of which was expanded into a larger recipient, prior totaking a sample through a septum. Because the gas phase is mainlyconstituted by hydrogen, liquid phase mole fractions were used inthe regression, cfr. infra, and vapor samples were collected lessfrequently. Gas products were analyzed in a gas chromatograph,HP 5890 Series II, equipped with a flame ionization detector and acapillary column, SUPELCO Petrocol DH 50.2, 0.2 mm i.d. and 50 mlength. Liquid products were analyzed in a gas chromatograph, GC-17A SHIMADZU, coupled to a mass spectrometer, QP-5000SHIMADZU. A capillary column, SUPELCO Petrocol DH, 100-mlength with a 0.25 mm i.d., was used in this GC.

The n-octane conversion was defined as:

Xn-C8¼

Nn-C8;0� Nn-C8

Nn-C8;0

(1)

A. Funez et al. / Applied Catalysis A: General 349 (2008) 29–3932

The n-octane mono- and multibranched isomers selectivity wascalculated as:

Smo ¼Nmo

Nn-C8;0� Nn-C8

(2)

Smu ¼Nmu

Nn-C8;0� Nn-C8

(3)

The n-octane mono- and multibranched isomers yield wasdefined as:

Ymo ¼Nmo

Nn-C8;0

(4)

Ymu ¼Nmu

Nn-C8;0

(5)

n-Octane conversion and isomer selectivities could typically bereproduced within 3%.

2.2. Modelling

2.2.1. Parameter estimation

Parameter estimations were performed using a combination ofa Rosenbrock [33] and a Marquardt [34] algorithm. An in-housewritten code was used for the Rosenbrock method, while for theMarquardt algorithm the ordinary least squares (OLS) option of theODRPACK-package version 2.01 was used [35]. Some additionalsource code was added to ODRPACK in order to retrieve additionalstatistical information.

The weighted sum of the squared differences between theobserved and the calculated molar fractions was minimized byadjusting the model parameter vector b, which is expected toapproach the real parameter vector b when the optimum isreached,

SSQ ¼Xnob

i¼1

Xnresp

j¼1

w jðXi; j � Xi; jÞ2�!b Min (6)

The weighting factors wP jare the diagonal elements of the

inverse of the covariance matrix of the experimental errors of theresponses determined from replicated experiments.

The regression results are assessed through the F-value for theglobal significance of the regression as well as the t-values for theindividual significance of the parameters and the correspondingconfidence intervals. The F-value is calculated as the ratio of theregression and the residual sum of squares divided by theirrespective degrees of freedom:

F ¼Pnob

i¼1

Pnrespj¼1 w jðXi; jÞ

2=nparPnob

i¼1

Pnrespj¼1 w jðXi; j � Xi; jÞ

2=nob ncomp� npar

The individual confidence intervals for the parameters arecalculated as

bi � tnob nresp�npar

ffiffiffiffiffiffiffiffiffiffiffiffiffiVðbÞi;i

q< bi < bi þ tnob nresp�npar

ffiffiffiffiffiffiffiffiffiffiffiffiffiVðbÞi;i

qWith tnob nresp � npar the tabulated t-value and V(b)i,i is the ith

diagonal element of the variance matrix of the parameterestimates.

2.2.2. Reactor model

The reactor was modelled as perfectly mixed semi-batchreactor. Isothermal conditions and a constant total pressure wereassumed. As a result, the following expression for the reactor

content of alkanes Pi can be used:

dNi

dt¼ riW (7)

The integration of the set of ordinary differential equations(ODE’s) was performed with DVODE-subroutine. The rate expres-sion, ri, used in Eq. (7) is explained in more detail in Section 3.5.

2.2.3. Vapor liquid equilibrium

At a given temperature T and pressure p, equilibrium isestablished between a gas and a liquid phase when the chemicalpotentials of each of the components in the vapor phase are equalto the chemical potentials of the corresponding components in theliquid phase. When these chemical potentials mi(T) are expressedin terms of fugacities, the equilibrium condition for eachcomponent i reduces to:

f iGðT; p; y1; . . . ; yNÞ ¼ f iLðT; p; x1; . . . ; xNÞ (8)

Using the definition of the fugacity coefficient, which relates thefugacities of each component in both liquid and vapor phase to itsmole fraction xi and yi, the so called K-factor, i.e., the ratio of themole fractions of each component in vapor and liquid phase, can beobtained as follows:

yi

xi¼ Ki ¼

FiLðT; p; x1; . . . ; xncompÞFiGðT; p; y1; . . . ; yncompÞ

(9)

with values for the fugacity coefficients FiL and FiG obtained froman equation of state, such as Peng–Robinson’s. Performing a flashcalculation for a mixture consisting of n species with a totalnumber of moles N and composition zi requires the solution of a setof 2n + 2 algebraic equations. In addition to n equations [9] for eachcomponent i, also a molar balance for each component i over thephases present in the reaction mixture have to be made:

Nzi ¼ NLxi þ NGyi (10)

Complemented with the trivial conditions:Xi

xi � 1 ¼ 0Xi

yi � 1 ¼ 0(11)

this results in 2n + 2 equations that have to be solved to obtain xi, yi,NL and NG.

This set of 2n + 2 equations has to be solved in an iterative waysince all Ki’s in equation [9] are a function [3] of the liquid and gasphase composition. Initial estimates for the values of the variousKi’s are found using the assumption of ideality in both vapor andliquid phase, i.e., FiG = 1 and with FiL ¼ n0

i ;n0i being the fugacity

coefficient for the pure liquid component i at the mixture pressureand temperature calculated using the correlation originallyproposed by Chao and Seader [36]. Values for the critical propertiesof each component are obtained from literature or estimated usingFedors’ group contribution method [37] for Tc,i and Joback’smethod for Pc,i.

Using these initial values of Ki, initial estimates for thecomposition of both the liquid and vapor phase result fromcombining Eqs. (9) and (10):

xi ¼zi

1� ’þ Ki’

yi ¼Kizi

1� ’þ Ki’

(12)

with w = NG/NL.At the operating conditions used, the vapor phase is for more

than 99% constituted by hydrogen, the rest being cracked products.

A. Funez et al. / Applied Catalysis A: General 349 (2008) 29–39 33

The vaporization of the cracked products is always below 5%,whereas the vaporization of the reactant and its isomers isnegligible.

3. Kinetic model construction

3.1. Reaction network

A lumped reaction network for the main reactions of n-octanehydroisomerization is depicted in Fig. 1. The hydroisomerizationmechanism, as has been explained in the introduction, comprisesseveral steps that have to be accounted for in the kinetic model, i.e.,physisorption, (de)-hydrogenation, (de)-protonation and skeletalrearrangement and cracking. The linear, secondary, carbeniumions formed from n-octane rearrange into branched, tertiary,carbenium ions which can deprotonate and restore the Bronstedacid site while being released as an isomerized alkene or which cancrack via b-scission yielding a lighter alkene and carbenium ion[20]. Hydrogenolysis and oligomerization, as evidenced by theformation of C1, C2, C6, C7 and C8+ alkanes, did not significantlycontribute to the product distribution at the investigated operatingconditions and, hence, were not accounted for in the reactionnetwork considered.

3.2. Physisorption of alkanes

The first step in the reaction mechanism is the physisorption ofalkanes into the pores of the zeolite. A Langmuir isotherm candescribe the physisorption process in a satisfactory way [26–28,38].

Ci ¼CsatKLan;iCi

1þPncomp

j¼1 KLan; jC j

(13)

In our case, liquid phase concentrations rather than partialpressures have been used. These concentrations have beenobtained from the vapor–liquid equilibrium calculations discussedin Section 2.2.3.

The Langmuir physisorption coefficient for an alkane on azeolite can be determined from its Henry coefficient and saturationconcentration

KLan;i ¼Hi

Csat;i(14)

Fig. 1. Lumped hydroisomerization reaction scheme considering one reactant lump,

two isomer lumps (mono and multibranched products), and one cracked products

lump.

Values for the Henry coefficients and saturation concentrationswere taken from the literature [9]. An average value was calculatedfor the Langmuir coefficients for monobranched and multi-branched octane isomers while the physisorption of crackedproducts was assumed to be negligible compared to that of theparent octane molecules [9].

3.3. (De)hydrogenation equilibrium

Hydrogenation/dehydrogenation equilibrium expressionsallowed us to relate the alkene j concentration to the alkane i

concentration,

C j ¼KdehCi

pH2

(15)

An average (de)hydrogenation equilibrium coefficient wascalculated for n-octane and its isomers from literature reportedvalues for standard enthalpies of formation and absolute entropies(TRC tables).

3.4. Alkene protonation

Alkenes j are protonated on the acid sites of the catalyst yieldinga carbenium ion k. This protonation is described using a Langmuirrelationship:

Ck ¼CtotKprotC j

1þPncomp

i¼1 KprotCi

(16)

However, since alkylcarbenium ion concentrations have beenfound to be small, especially at higher total pressures [38,39], thedenominator in this equation is approximately equal to one and,hence, carbenium ion concentrations can be calculated from:

Ck ¼ CtotKprotC j (17)

The (de)protonation equilibrium coefficient is a catalystdependent property that cannot be calculated a priori and, hence,has to be estimated by regression.

3.5. Rate expressions

The rate of an acid catalyzed elementary step is obtained usingthe law of mass action:

r ¼ CtotkreactionCk (18)

using the above derived relations, the carbenium ion concentra-tions can be related to the liquid phase concentrations and thereaction rate expressed in terms of observable quantities. Forwardas well as reverse reactions are considered for mono andmultibranching, while cracking is supposed only to occur in theforward direction:

rmono ¼CsatCtotKdehKprotkmoðKLan;nCn � ðKLan;moCmo=KmoÞ=CH2

Þ1þ

Pncompi¼1 KLan;iCi

(19)

rmu ¼CsatCtotKdehKprotkmuðKLan;moCmo � ðKLan;muCmu=KmuÞ=CH2

Þ1þ

Pncompi¼1 KLan;iCi

(20)

rcr-mo ¼CsatCtotKdehKprotKLan;mokcr-moCmo=CH2

1þPncomp

i¼1 KLan;iCi

(21)

rcr-mu ¼CsatCtotKdehKprotKLan;mukcr-muCmu=CH2

1þPncomp

i¼1 KLan;iCi

(22)

Table 1Surface area, pore volume and platinum dispersion measurements

Catalyst Surface area

ðm2 g�1catÞ

DH2Pore volume ðml g�1

catÞ

Micropores Mesopores and macropores

PtUSY 799 69 273 164

PtMOR 556 92 193 56

PtBETA 614 65 159 409

A. Funez et al. / Applied Catalysis A: General 349 (2008) 29–3934

Note that these rate equations correspond to so-called ‘‘ideal’’hydrocracking behaviour because a quasi-equilibrium relationshipis used for the (de)-hydrogenation reactions. The ideal character ofthe observations can be most easily assessed via the total pressureeffect, because lower conversions are observed at higher totalpressures [29]. This can be easily observed from Eqs. (19) to (22).The total pressure significantly affects the concentration ofhydrogen dissolved in the liquid, whereas the hydrocarbonconcentrations are barely affected. As a result, higher totalpressures result in lower concentrations of reactive intermediatesand, hence, lower reaction rates. The presence of the hydrogenconcentration in the denominator of Eqs. (19)–(22) is specific forideal hydrocracking. For non-ideal hydrocracking, i.e., when the(de)-hydrogenation reactions are not quasi-equilibrated, thereaction rate increases with the total pressure [29].

The rate coefficients, kmo, kmu, kcr-mo and kcr-mu are to beestimated from experimental data. Note that these coefficientsalways appear in the rate equations simultaneously with the(de)protonation equilibrium coefficient. As a result, parameterestimations based on these equations lead to composite parametersthat consist of a protonation part and a contribution from theisomerization or cracking step:

kcompreaction ¼ Kprotkreaction (23)

and, consequently, also composite pre-exponential factors andactivation energies will be obtained which represent the product ofthe pre-exponential factor of the protonation coefficient and thereaction rate coefficient or the sum of the protonation enthalpyand the real activation energy:

Acompreaction ¼ AprotAreaction (24)

and:

Ecompact;reaction ¼ DH�prot þ Eact;reaction (25)

The composite activation energy compares the energy level ofthe transition state and the acid site with that of the physisorbedalkene and the acid site. The overall temperature dependence ofthe reaction rate is determined by the apparent activation energy.The apparent activation energy depends on the strength of thephysisorption, i.e., on the magnitude of the denominator inEqs. (19)–(22). If physisorption is relatively weak, such as on USYwith a physisorption enthalpy of �60 kJ mol�1 [40,41], thedenominator will not be significantly different from one. Hence,the apparent activation energy includes, apart from the realactivation energy and the standard protonation enthalpy, also thestandard physisorption enthalpy and the standard dehydrogena-tion enthalpy:

Eappact ¼ DH�phys þDH�deh þDH�prot þ Eact (26)

If physisorption is strong, however, such as on BETA and MORwith physisorption enthalpies amounting to �90 kJ mol�1 [40,41],the denominator is significantly larger than one and thephysisorption enthalpy is eliminated from the apparent activationenergy:

Eappact ¼ DH�deh þDH�prot þ Eact (27)

In order to avoid high correlation between the pre-exponentialfactors and the corresponding activation energies, the compositerate coefficients were entered into the rate equations in theirreparameterized form:

kcompreaction ¼ kcomp

reaction;Taveexp �

Ecompact;reaction

R

1

T� 1

Tave

� � !(27)

4. Results and discussion

Surface area and platinum dispersion data for the threecatalysts used are shown in Table 1. The highest metal dispersionwas obtained for PtMOR. This is due to the lower meso andmacropore volumes observed for this catalyst. According to Gilleet al. [42] a macro- or mesoporous material allows a better metalgrowth than a microporous one. Hence, it will generally exhibit alower metallic dispersion than materials with a proportionallyhigher micropore volume. USY and beta zeolites showed a highervolume of mesopores, for that reason, they showed a lowermetallic dispersion in comparison to mordenite sample.

Acidity data of the different catalysts are summarized inTable 2. All the samples showed two peaks corresponding to weakand medium to strong acidity [16]. Samples based on mordeniteshowed the highest acid site density; additionally, the peak in thetemperature programmed desorption spectra of NH3 related tostrong acid sites was obtained at higher temperatures [16].

4.1. n-Octane hydroisomerization on PtBETA, PtMOR and PtUSY

The effect of the temperature and the total pressure on thehydroisomerization of n-octane over USY, mordenite and betazeolite using platinum as the hydrogenating–dehydrogenatingfunction was studied. Previously reported hydroisomerization datafor n-octane on the same catalysts [16] were limited to a singletemperature and total pressure, i.e., 543 K and 9 MPa. According tothat work, the catalytic activity decreased in the following order:beta > mordenite > USY. Furthermore, USY and beta zeolitesshowed a higher n-C8 isomers selectivity at the same level of n-octane conversion in comparison with mordenite zeolite. Themaximum n-octane isomers yield obtained ranged from 70% onmordenite to 80% on beta.

The isomer selectivity at comparable n-octane conversion in thevicinity of 40% and 70% is shown in Table 3. USY and beta zeolites,due to their relatively large pore sizes, have a lower tendencytowards cracking at the same level of n-octane conversion incomparison with mordenite based catalyst as evidenced by thehigher total isomerization selectivities observed for these cata-lysts. Within the isomers formed, the higher selectivities tomultibranched isomers are obtained on mordenite. These differ-ences in isomerization-cracking selectivity can be explained on thebasis of differences in not only the pore size but also the acidity.The pore geometry of mordenite is such that branched alkanediffusion inside it is more difficult to occur than n-alkane diffusion.As a result, monobranched alkanes have a higher probability toundergo a secondary reaction, such as isomerization or cracking onmordenite compared to beta or USY. In addition, because of thehigher average acid strength of the mordenite, non-ideal hydro-cracking resulting in an enhancement of secondary reactions ismore likely to occur on this zeolite [29].

Compared to vapor phase hydroisomerization, higher yields areobtained for monobranched as well as for multibranched isomersat liquid phase conditions [20,43]. A maximum isomers yield of65 mol% in the n-octane hydroisomerization at vapor phaseconditions over beta zeolite agglomerated with bentonite was

Table 2Acid properties of the catalysts used

Catalyst Total acidity ðmol NH3 kg�1catÞ Weak acidity ðmol NH3 kg�1

catÞ Td (K) Strong acidity ðmol NH3 kg�1catÞ Td (K)

PtUSY 0.449 0.050 548 0.399 663

PtMOR 0.918 0.123 573 0.795 753

PtBETA 0.799 0.187 550 0.612 660

Table 3Isomers selectivity over the three catalysts at approximately 40 and 70 mol% conversiona

Catalyst Temperature (8C) Conversiona �40% Conversiona �70%

Conversion

(mol%)

Time

(h)

S mono

(mol%)b

S multi

(mol%)c

S total

(mol%)d

Conversion

(mol%)

Time

(h)

S mono

(mol%)b

S multi

(mol%)c

S total

(mol%)d

PtUSY 250 32.1 11 90.2 9.8 100 – – – – –

270 41.5 5.5 84.8 14.3 99.1 62.0 9.8 72.3 25.7 98.0

290 35.2 1 86.8 13.2 100 74 4.3 60.6 35.9 96.5

PtMOR 250 38.2 24 74.7 23.3 98 – – – – –

270 28.0 4.5 67.3 26.2 93.5 77.4 10.5 55.7 36.6 92.3

290 43.4 1 65.2 28.6 93.8 72.2 3.5 59.5 34.3 93.8

PtBETA 250 43.7 4 82.9 16.9 99.8 67.5 6 67.7 30.2 97.9

270 44.8 2 80.2 18.5 98.6 60.8 3.6 72.9 25.6 98.5

290 – – – – – 72.5 1.5 64.5 31.7 96.2

a Reaction conditions: Pressure, 9 MPa; W/M, 7 gzeolite=moln-C8 .b Monobranched isomers selectivity.c Multibranched isomers selectivity.d Total isomers selectivity.

Fig. 2. n-Octane conversion as a function of the batch time on PtBETA (^), PtUSY

(&) and PtMOR (~) at 543 K (a) and 563 K (b). Reaction conditions: Pressure,

9 MPa; initial catalyst/n-C8 ratio (gzeolite=moln-C8), 7.

A. Funez et al. / Applied Catalysis A: General 349 (2008) 29–39 35

reported at a temperature of 603 K [20] compared to the 80 mol%observed in this work at liquid phase conditions. Mono- andmultibranched isomer selectivities obtained at the maximum totalisomer yield at vapor phase conditions are similar to thoseobtained at liquid phase conditions, i.e., 65% monobranchedisomers versus 35% multibranched isomers. Apart from thepresence of the binder, which has a minimal effect on theselectivity observed on PtBETA catalysts [43], this lower maximumisomerization yield can be attributed to the significantly highertemperature used and the lower total pressure, that may lead to anon-ideal behaviour [29]. Similar observations were made byDenayer et al. [22].

4.1.1. Effect of the reaction temperature on the hydroisomerization

behaviour

The effect of the reaction temperature in the range of 523–563 K was investigated, keeping the other operating conditions,i.e., the reaction pressure and the catalyst/n-C8 ratio constant. Fig. 2shows a comparison between the activity of the three catalysts at(a) 523 and (b) 563 K. In a previous work [16], the comparison at atemperature of 543 K was reported. Regardless the temperature,the highest activity was shown by the catalyst PtBETA, followed bymordenite and USY, except for a temperature of 523 K, at which thecatalytic activity for USY was higher than that for mordenite, cfr.Section 4.2.2.

Fig. 3 shows for the sample PtUSY, the isomers yield versus n-octane conversion at the three different temperatures. Isomer yieldpassed through a maximum, which is consistent with the existenceof consecutive reactions [21,44]. The higher the temperature, theshorter batch time needed to reach this maximum isomer yield.The maximum isomer yield amounts to 80 mol% and is obtained ata total n-octane conversion of 80%, irrespective of the operatingtemperature.

Fig. 4 shows the monobranched and multibranched isomerselectivity for PtBETA versus n-octane conversion. At low n-octaneconversions monobranched isomers are predominant. Withincreasing n-octane conversion monobranched isomers are con-secutively isomerized into multibranched isomers. Only at high

Fig. 3. Total isomers yield as a function of the n-octane conversion on PtUSY at 523 K

(^), 543 K (&) and 563 K (~). Reactions conditions: Reaction pressure, 9 MPa;

initial catalyst/n-C8 ratio (gzeolite=moln-C8), 7.

Fig. 5. n-Octane conversion as a function of the batch time on PtBETA at 5 MPa (^),

7 MPa (&) and 9 MPa (~). Reaction conditions: Temperature, 543 K; initial

catalyst/n-C8 ratio (gzeolite=moln-C8), 7.

A. Funez et al. / Applied Catalysis A: General 349 (2008) 29–3936

conversions the latter are cracked into shorter hydrocarbonfragments [7,45,46]. Similar observations were made on PtUSYand PtMOR.

4.1.2. Effect of the reaction pressure on the hydroisomerization

behaviour

The effect of the reaction pressure was investigated in the rangefrom 5 to 9 MPa, at 543 K and with a catalyst/n-octane ratio of7 gcatalyst=moln-C8

.Fig. 5 shows the evolution of the n-octane conversion with

batch time for PtBETA, at the three different pressures. At eachbatch time, the n-octane conversion decreased when the pressurewas increased. A combination of physisorption and dehydrogena-tion effects in the formation of the reactive intermediates from thereactant alkane is responsible for this peculiar, negative totalpressure effect [19–21]. The dissolution of hydrogen in the liquidphase is moderating the total pressure effect on the hydroisome-rization kinetics. As a result, longer batch times are required inorder to observe a pronounced total pressure effect, as indicated inFig. 5.

The n-octane isomer yield as a function of the n-octaneconversion over PtBETA is shown in Fig. 6. Again, a maximum in theisomers yield was observed, which indicated the consumption ofthe isomerized products in consecutive cracking reactions. The

Fig. 4. Mono (closed symbols) and multibranched (open symbols) isomers

selectivity as a function of the n-octane conversion on PtBETA at 523 K (^),

543 K (&) and 563 K (~). Reaction conditions: Total pressure, 9 MPa; initial

catalyst/n-C8 ratio (gzeolite=moln-C8), 7.

maximum isomer yield obtained amounted to 80 mol% irrespec-tive of the pressure used. The lower the pressure, the shorter batchtime needed to reach this maximum yield.

Fig. 7 shows the selectivity to mono and multibranched isomersversus n-octane conversion for the catalyst PtBETA at differentpressures. At low n-octane conversion the monobranched isomerswere always produced in larger excess and also the formation ofcracked products was practically negligible. When the n-octaneconversion increased, monobranched isomers further reacted intomultibranched isomers. A decrease in the reaction pressure led to afaster formation of mono and multibranched products. Only whena sufficient amount of multibranched isomers was formed,cracking became an important reaction.

The rather strictly consecutive character of the formation ofmonobranched, multibranched and cracked products as primary,secondary and tertiary products, is an indication of the well-behaved bifunctional character of the catalyst, i.e., so-called ‘‘ideal’’hydroisomerization is observed. Because the metal component ispresent in sufficient excess for the (de)-hydrogenation reactions tobe quasi-equilibrated and the reactions on the acid sites to be rate-determining, cfr. Section 3.5 [29].

Fig. 6. Total isomers yield as a function of the n-octane conversion on PtBETA at

5 MPa (^), 7 MPa (&) and 9 MPa (~). Reaction conditions: Temperature, 543 K;

initial catalyst/n-C8 ratio (gzeolite=moln-C8), 7.

Fig. 7. Mono (closed symbols) and multibranched (open symbols) isomers

selectivity as a function of the n-octane conversion on PtBETA at 5 MPa (^),

7 MPa (&) and 9 MPa (~). Reaction conditions: Temperature, 543 K; initial

catalyst/n-C8 ratio (gzeolite=moln-C8), 7.

A. Funez et al. / Applied Catalysis A: General 349 (2008) 29–39 37

A qualitatively similar behaviour with the total reactionpressure was observed on PtMOR and PtUSY, indicating that theinterpretation of the reaction selectivities and the correspondingconclusions with respect to the ideal character of the hydrocrack-ing data can be extended to these catalysts.

4.2. Kinetic modelling

4.2.1. Isothermal regression at 543 K

The estimated composite rate coefficients at 543 K are reportedin Table 4. All coefficients were estimated significantly, except thatfor cracking from multibranched n-octane isomers on PtBETA. Forall zeolites, the composite rate coefficients for monobranching wasestimated most significantly. This can be easily understood,because these parameters determined the overall n-octaneconversion on the various zeolites. The multibranching compositerate coefficients had individual 95% confidence intervals whichwere somewhat wider than those for monobranching. This can beexplained as follows: the former coefficients corresponded to asecondary reaction in the mechanism and covered much moreelementary steps than the latter. Moreover, multibranched molefractions were generally somewhat lower than monobranchedmole fractions. Although almost all of them were estimatedsignificantly, the composite rate coefficients for cracking frommonobranched as well as from multibranched hydrocarbons hadthe widest individual 95% confidence intervals. These coefficientscorrespond to secondary and even tertiary reactions in the reactionmechanism and were important only at relatively high conver-sions. Typically, also the experimental scatter was most pro-nounced on the cracked products.

The values of the rate coefficients do not reflect the differencesin NH3 desorption temperature. The acid site concentration asdetermined from NH3-TPD, cfr. Table 4, is explicitly accounted for

Table 4Estimated composite rate coefficients (s�1) at 543 K

PtUSY PtMOR PtBETA

kcompmono;270 �C 8.483 � 0.001 3.868 � <0.001 20.016 � <0.001

kcompmulti;270 �C 7.278 � 0.035 7.739 � 0.001 7.690 � 0.002

kcompcr-mono;270 �C 0.675 � 0.016 1.028 � 0.16 1.506 � 0.499

kcompcr-multi;270 �C 0.846 � 0.160 2.472 � 0.002 0.315 � 1.212

in the rate equations. Hence, the reported rate coefficientsrepresent the activity per active site and not the total catalystactivity. The following discussion is made for the monobranchingrate coefficient because it is the most representative for the n-octane conversion. The highest NH3 desorption temperatures wereobtained with mordenite. If representative for the interaction ofalkenes with these acid sites, the highest monobranching ratecoefficients should be obtained on PtMOR. However, PtMOR wasthe catalyst for which the lowest monobranching rate coefficientwas obtained. Moreover, despite the similar NH3 desorptiontemperatures on PtBETA and PtUSY, leading to expected similarmonobranching rate coefficients on these two catalysts, thecomposite monobranching rate coefficient on PtBETA is morethan twice higher than that on PtUSY. Both observations illustratethat, for the zeolites considered in this work, the interaction of NH3

with the zeolite acid sites was not representative for theinteraction of the alkenes with these active sites, cfr. Section 4.2.2.

The highest composite rate coefficient for monobranching wasobtained on PtBETA, which was also the zeolite that exhibited thehighest hydroisomerization rate. The composite monobranchingrate coefficient for PtUSY was approximately double of that forPtMOR. The total acid site concentration on MOR, however, wasabout twice that on USY. As a result, the overall activity of bothcatalysts was comparable.

A striking difference was that the ratio of the multibranchingcomposite rate coefficient and the monobranching composite ratecoefficient was much higher on PtMOR than on PtBETA or PtUSY.The same holds for the ratio of the cracking composite ratecoefficients and the monobranching composite rate coefficient,especially for the cracking from multibranched components. Thisindicates that the monobranched components formed on PtMORwere highly susceptible to further isomerization and crackingcompared to the monobranched species on PtBETA and PtUSYzeolites. This high susceptibility to secondary reactions most likelyresults from internal diffusion phenomena which were notexplicitly accounted for in the current model and, hence, becameapparent in the estimated rate coefficients. The lack of accountingfor diffusion phenomena in the case of PtMOR was reflected in theF-value obtained for the global significance of the regression. Thelatter amounts to 414 for PtMOR while for Pt and Pt it amounts to770 and even to 1240. The parity diagrams for the n-octane molefraction on the three zeolites used are presented in Fig. 8 and are inline with the above reported F-values for the significance of theregression. The parity diagram for Pt/mordenite exhibits muchmore scatter than the parity diagrams for n-octane on Pt/BETA andPt/USY. Typical parity diagrams for monobranched, multibranchedand cracked product mole fractions obtained by using beta zeoliteas the catalyst, are shown in Fig. 9 and illustrate the adequacy ofthe model used.

4.2.2. Non-isothermal regression

The estimates for the composite activation energies arereported in Table 5. Composite activation energies can be negativebecause they are the sum of the protonation enthalpy and the realactivation energy, i.e., a negative and a positive quantity, videEq. (25). If the absolute value of the protonation enthalpy exceedsthat of the real activation energy the resulting compositeactivation energy becomes negative. The reactions involving morestable, tertiary carbenium ions and with lower real activationenergies, such as multibranching, are the most likely to havenegative composite activation energies, vide Table 5, second row.However, if the acid sites are sufficiently strong, also reactionsinvolving less stable, secondary carbenium ions and with higherreal activation energies can have a negative composite activationenergy, vide Table 5, first row, last two columns.

Fig. 8. Parity diagrams for the liquid phase n-octane molar fraction obtained in the

hydroisomerization on PtUSY (a), PtMOR (b) and PtBETA (c). Calculated mole

fractions were obtained from the solution of reactor model Eq. (7) with the rate

expressions, Eqs. (19)–(22), after accounting for the vapor liquid equilibrium,

Eqs. (9)–(11).

Fig. 9. Parity diagrams for the liquid phase mole fraction of monobranched (a),

multibranched (b) and cracked products (c) obtained in n-octane hydroisomerization

on PtBETA. Calculated mole fractions were obtained from the solution of reactor

model Eq. (7) with the rate expressions, Eqs. (19)–(22), after accounting for the vapor

liquid equilibrium, Eqs. (9)–(11).

Table 5Estimated composite activation energies (J mol�1)

PtUSY PtMOR PtBETA

Ecompact;mono 17,300 � <10 �3010 � <10 �3070 � <10

Ecompact;multi �5760 � 2340 �5880 � 570 �5520 � 4340

Ecompact;cr-mono 1580 � >100,000 �22,340 � 8290 4790 � 12,740

Ecompact;cr-multi 1111 � >100,000 8000 � 36,000 341,920 � 574,470

A. Funez et al. / Applied Catalysis A: General 349 (2008) 29–3938

Similar to the individual 95% confidence intervals for thecomposite rate coefficients, the intervals for the activation energieswere the narrowest for monobranching, somewhat wider formultibranching and the widest for cracking. An analogous inter-pretation as that for the composite rate coefficients can be made. Inparticular, the monobranching activation energy was very accu-rately determined because it is directly related to the n-octaneconversion. The cracking activation energies could hardly beestimated significantly because cracking became only importantat the highest temperatures. At these temperatures, the experi-mental data contained insufficient information to significantlyestimate the temperature dependence of the cracking coefficients,especially the one for cracking from multibranched components.Assuming that the real activation energies for isomerization andcracking were independent of the zeolite considered [27,28,30]differences in protonation enthalpies can be assessed among thezeolites considered in this work. The composite activation energy for

monobranching on Pt/USY is 20 kJ mol�1 higher than on PtBETA andPtMOR. The composite activation energies for multibranching hadvery similar values, but the corresponding individual 95% confidenceintervals were wider. This indicates that PtUSY had weaker acid sitesthan PtBETA and PtMOR. Relationships between these differences instandard protonation enthalpy and the acidity data reported inTable 2 cannot be established, i.e., the interaction of a base, such asNH3 with the zeolite’s acid sites is not representative for alkeneinteractions with the same acid sites, e.g., due to differences inaccessibility to the acid sites for the considered bases, also denotedas confinement effects.

A. Funez et al. / Applied Catalysis A: General 349 (2008) 29–39 39

The composite activation energy for cracking from mono-branched components was much lower on mordenite than on betaand USY. A similar explanation as that formulated for the ratio ofthe composite rate coefficient for cracking from monobranchedcomponents to that for monobranching can be given, i.e., notaccounting in the model for diffusion phenomena results inparameter values which enhanced the secondary reactions.

When accounting for the n-octane physisorption enthalpies onthe various zeolites and the n-octane dehydrogenation enthalpythe composite activation energies can be converted into apparent

activation energies, vide Eq. (25) on the one hand and Eqs. (26) and(27) on the other hand. In Eqs. (26) and (27), the dehydrogenationenthalpy is zeolite independent. Because monobranching was thefirst acid catalyzed step considered in the reaction mechanism,apparent activation energies for n-octane hydroisomerizationwere calculated from the composite activation energy formonobranching. Accounting for a dehydrogenation enthalpy of125 kJ mol�1, the apparent activation energies for n-octanehydroisomerization amounts to 82 kJ mol�1 on PtUSY, and122 kJ mol�1 on PtBETA and PtMOR. Hence, the n-octane hydro-isomerization rates depended more strongly on the temperatureon PtBETA and PtMOR than on PtUSY. This explains the comparablen-octane hydroisomerization rates on PtMOR and PtUSY at 523 K,while at higher temperatures, higher rates were observed onPtMOR compared to PtUSY.

5. Conclusions

Within the series of investigated zeolites in this work, PtBETAwas the one presenting the highest activity as well as total isomeryield. The smaller pore size of PtMOR and its higher acid strengthenhanced consecutive reactions, such as multibranching andcracking, resulting in lower total isomer yields. The decreasinghydroisomerization activity with increasing total pressure indi-cated the ideal character of the hydroisomerization observed andconfirmed the appropriate balance of metal and acid sites on thecatalysts investigated in this work.

A kinetic model based on a parallel/consecutive reaction schemeallowed interpreting the dominant factors affecting the liquid phasehydroisomerization on the bifunctional zeolites catalysts used inthis work: (i) the number and the strength of the acid sites, (ii) thephysisorption properties of the catalyst, (iii) he pore geometry of thecatalyst, including the corresponding hydrocarbon diffusion proper-ties, and (iv) the ideality of the hydroisomerization behaviour asdetermined by the operating conditions, such as temperature andtotal pressure on the one hand and the acid metal balance of thecatalyst on the other hand. As a result of these factors, PtBETA wasfound to have the acid sites with the highest activity, whileconsecutive reactions were most prominent on PtMOR. PtUSY wasthe zeolite with the weakest acid sites but still allows obtaining totalisomer yields comparable to PtBETA. On all zeolites, the accuracy ofthe composite rate coefficients and activation energies for primaryreactions, i.e., monobranching, was higher than those for secondaryand tertiary reactions, such as multibranching and cracking.Diffusional effects were present in the results obtained on PtMORand should be accounted for in the model to obtain a more accuratedescription of the data.

Acknowledgments

Part of this research was carried out within the framework ofthe Interuniversity Attraction Poles Programme funded by theBelgian Science Policy.

Financial support from Ministerio de Ciencia y Tecnologıa ofSpain (ProjectCTQ-2004-07350-C02-O) and Consejerıa de Ciencia yTecnologıa de la Junta de Comunidades de Castilla-La Mancha(Proyect PBI-05-038) are gratefully acknowledged.

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