Kinetic Model Discrimination for Toluene Hydrogenation over Noble

Aug 22, 2007 - Idoia Hita , Andrés T. Aguayo , Martin Olazar , Miren J. Azkoiti , Javier Bilbao , José M. Arandes , and Pedro Castaño. Energy & Fue...
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Ind. Eng. Chem. Res. 2007, 46, 7417-7425

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Kinetic Model Discrimination for Toluene Hydrogenation over Noble-Metal-Supported Catalysts Pedro Castan˜ o,*,† Jose´ Marı´a Arandes,† Ba´ rbara Pawelec,‡ Jose Luis G. Fierro,‡ Alazne Gutie´ rrez,† and Javier Bilbao† Departamento de Ingenierı´a Quı´mica, UniVersidad del Paı´s Vasco, Apartado, 644. 48080 Bilbao, Spain, and Institute of Catalysis and Petrochemistry, CSIC, C/ Marie Curie, 2, Cantoblanco, 28049 Madrid, Spain

The hydrogenation of toluene has been studied using an integral fixed-bed reactor with a Pt/γ-Al2O3 commercial catalyst over a wide range of experimental conditions: temperature ) 100-250 °C, H2 inlet pressure ) 0.3-1.9 bar, toluene inlet pressure ) 0.04-0.15 bar, and space time ) (2-10) × 10-2 gcat h gtol-1. Hydrocarbon molecules block the active sites at elevated temperature and toluene partial pressure, and, as a consequence, three reaction-controlled regimes occur: (i) kinetic, (ii) surface coverage, and (iii) thermodynamic. The experimental data have been fitted to 23 kinetic models proposed in the literature (empirical and mechanistical), and their parameters have been estimated. The model discrimination has been performed based on statistical F-test and mechanistical aspects. A simplified kinetics model is proposed by introducing the thermodynamical equilibrium constant. Finally, that kinetic model is used for reactor simulation. 1. Introduction The actual environmental concern has brought about severe clean-fuel legislation, in which the reduction of aromatic compounds is one of the most challenging issues.1-3 The problem can be even more serious, because of the following simultaneous aspects: (i) The growing demand of light alkenes and hydrogen has caused an increase in the light aromatic supply, especially the benzene, toluene, and xylenes (BTX) fraction; and (ii) Additionally, a constant demand is forecasted for the following years.4-7 Initially, aromatic hydrocracking has been revealed as an interesting valorization route to solve the gap between the market supply-demand. From this reaction, a highquality steam cracker synthetic feedstock can be obtained, mainly formed by C2+ n-alkanes. Furthermore, this process can be performed either by direct hydroprocessing or via a twostage route, known as the ARINO process,8 where, after the aromatic is saturated over a hydrogenation catalyst, it is cracked using an acid shape-selective zeolite.9 The hydrogenation of aromatics is an important stage of the hydrocracking process. In this paper, toluene has been chosen as a test molecule, because of (i) its difficulty for being hydrogenated compared to benzene;10 (ii) the high probability of market saturation of this product, because its demand is the lowest in the BTX fraction;9 and (iii) according to Raichle et al.,11 the results obtained in the hydrogenation of toluene are comparable to those obtained using a real refinery feedstock, such as pyrolysis gasoline. The kinetic modeling of the hydrogenation of aromatic compounds has been widely studied in the literature, focusing particular emphasis on the catalyst and limiting the experimental range to work in a univocal regime. Several metals and metal combinations (such as nickel, platinum, or palladium) have been used so far. Noble-metal-supported catalysts are appropriate for the hydrotreatment of low-sulfur gasoline if the right balance * To whom correspondence should be addressed. Tel. +34 94 6012511. Fax: +34 94 6013500. E-mail: [email protected]. † Departamento de Ingenierı´a Quı´mica, Universidad del Paı´s Vasco. ‡ Institute of Catalysis and Petrochemistry, CSIC.

is struck between activity, selectivity, and economic aspects,12 because such catalysts are stable under appropriate conditions.13 Toluene hydrogenation kinetic models can be classified as follows: (i) empirical power-rate models and (ii) mechanistical models. The latter, in turn, can be subdivided into two groups: (a) models with two different adsorption sites or noncompetitive models, and (b) models with only one adsorption site or competitive model. Noncompetitive models consider that the adsorption of the aromatic molecule occurs simultaneously on the metal surface and on the acidic support,14-16 assuming the existence of the well-known spill-over phenomenon.17 Competitive models contemplate the metal as the only site for aromatic and hydrogen adsorption.18-21 According to the latter type of models, the hydrogenation activity enhancement of the acidity is due to metal-support interactions (MSIs). The source of the dissimilarities among the kinetic models proposed is the unconnected experimental conditions used. Thus, the principal objective of the present work is the kinetic model discrimination of the hydrogenation of aromatics over a wide range of experimental conditions. This model will be useful for the design of the reactor and catalyst and for process simulation and optimization. The discrimination has been performed based on integral-type reactor experiments, which, in turn, can faithfully simulate the industrial operating conditions. 2. Summary of Kinetic Models The proposed kinetic models for toluene hydrogenation described in the literature are summarized next. 2.1. Empirical Models. The most extended kinetic model in the hydrogenation of toluene is the power rate, based on the empirical estimation of activation energies and reaction orders:

-rT ) kPtTPHh 2

(1)

It has been demonstrated that the experimental conditions determine the toluene hydrogenation mechanism, in regard to the way that they modify the rate-determining step (RDS). Therefore, operational variables influence the estimated values of reaction orders and activation energies. For this reason, a large divergence of the kinetic results can be found between

10.1021/ie070094m CCC: $37.00 © 2007 American Chemical Society Published on Web 08/22/2007

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authors: e.g., Lin and Vannice22 reported values of t ≈ 0 and h ) 0.7-1.0, whereas Thybaut et al.21 account values of t ) (-0.2)-(+0.3) and h ) 0.6-1.8. Generally, the hydrogen reaction order is 1,16 whereas toluene reaction order is 0 when PT is high enough. Consequently, the surface coverage of the aromatic species is near saturation under these conditions, because the heat of adsorption toluene of is greater than that of hydrogen. The increase in the hydrogen order with temperature is due to surface dehydrogenation reactions, which occur in parallel with the hydrogenation reactions of the aromatics and give way to hydrogen-deficient species or intermediates.23,24 This can also be attributed to the stabilization of the hydrogen species suffering spill-over when the temperature is increased. Moreover, the inconsistent values of kinetic constants for this model found in literature are due to the ignorance of the deficient adsorption of reaction intermediates, focusing on the kinetic regime only, i.e., transport limitation phenomena occurred at high surface coverage. Gaidai and co-workers25,26 have proposed three semiempirical models taking into account the dissociative (K′H2) and nondissociative (KH2) adsorption of hydrogen, being the latter the one reacting with toluene:

-rT )

kKTKHi 2PHi 2PT

aromatic reactant is the most abundant surface intermediate, i.e., surface coverage of all other reaction intermediates is negligible. These models usually consider the addition of the first or second hydrogen atom as the RDS. The desorption of the products from both active sites occurs easily and rapidly.23,24 According to these assumptions, Rahaman and Vannice16 proposed a mechanism for the reaction of intermediate compounds and hydrogen atoms adsorbed on different sites in the metallic function, in which the RDS is the addition of the second hydrogen atom. According to the postulates of the Langmuir and Hinshelwood (LH) equation, the adsorption, reaction, and desorption steps are given as follows: KH

2

H2(g) + 2l 798 2H-l KT

T(g) + s 798 T-s KM 1

T-s + H-l 798 TH-s + l k

TH-s + H-l T TH2-s + l K3

TH2-s + H-l 798 TH3-s + l K4

(2)

TH3-s + H-l 798 TH4-s + l

This model assumes RDS as the addition of the first (i ) 1), second (i ) 2) or third (i ) 3) hydrogen molecule. 2.2. Noncompetitive Models with Two Active Sites. The models with two active sites, known as noncompetitive models, suggest that the aromatic molecule and the hydrogen adsorb on different types of active sites. According to some authors, increasing the catalyst reduction temperature has a negative effect on the activity.27 Bearing in mind that sintering of the metal is negligible,16 one must assume that aromatic molecule adsorption occurs on active sites that are diiferent from those of hydrogen. Noncompetitive models consider that increasing the acidity of the support has a positive effect on the overall activity, as a result of enlarging the number of active sites for aromatic adsorption. In the 1990s, Vannice and co-workers14,16,22 suggested that the site where the toluene is adsorbed is located on the acidic support (γA), whereas hydrogen dissociate adsorption occurs on the metal sites (γM).28 Hydrogen migrates to the support via spill-over and the hydrogenation total rate is the sum of the hydrogenation rate on the metal and on the support:

TH4-s + H-l 798 TH5-s + l

[(K′H2PH2)1/2 + KTPT + KH2PH2]2

A -rT ) (-rM T ) + (-rT )

(3)

According to Rahaman and Vannice,16 the active sites of the support (γA) are surface hydroxyl groups (Brønsted sites), which can be created by the abstraction of spill-over hydrogen species on the Lewis acidic sites.29 The adsorption of aromatics molecules on Brønsted sites is a well-known fact30-33 that is associated with the formation of carbonium ions. In fact, metalfree zeolites with high Brønsted acidity have the ability to hydrogenate aromatics,30 because toluene adsorption strength with the active site is higher when the electronic deficiency of the latter is higher.31 From this belief, the aromatic is more favorably chemisorbed on the acidic support.16 The spilled-over hydrogen is a highly mobile species and is quasi-equilibrated with the molecular gas-phase hydrogen present in the reactor.23,24 It is also assumed that the adsorbed

(RDS)

K5

K6

TH5-s + H-l 798 MCH-s + l K7

MCH-s 798 MCH(g) + s where l and s are the sites for hydrogen and toluene adsorption on the metallic phase in the catalyst and THi are the intermediate compounds obtained subsequent to the addition of i hydrogens. For the previous mechanism, a standard derivation corresponding to Langmuir-Hinshelwood-Hougen-Watson (LHHW)-type equations yields

(

M M -rM T ) k K1

KH2PH2

1 + xKH2PH2

)(

KM T PT

1 + KM T PT

)

(4)

Rahaman and Vannice16 considered the possible contribution of an additional mechanism to that occurring on the metallic sites, which is a consequence of the hydrogenation of the aromatic compound adsorbed on the metal-support interphase by the H atoms migrating from the metallic phase. A similar development to the previous one provides the following expression for the kinetic equation for this additional step:

(-rT)AT

)

(

k1KA1 KH2PH2

KAT PT

1 + KAT PT

)

(5)

Consequently, the overall reaction rate is the sum of eqs 4 and 5. Lin and Vannice22 recently proposed the inclusion of a concurrent dehydrogenation reaction that involved the aromatic reactant molecule to produce hydrogen-deficient species on the metal surface. These species adsorb irreversibly and block the active sites.34,35 One of the proposed models suggested the RDS to be the addition of the second H atom and that the dehydro-

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genation reaction happens on the metal site. The other model proposed that the dehydrogenation steps occur in parallel on the metal and on the acidic support, with the RDS being the addition of the first H atom.22 In these models, it is further assumed that one of the possible hydrogen-deficient surface species dominates, which is usually assumed to be the one formed via the first dehydrogenation of toluene. Keane and Patterson proposed a noncompetitive model, assuming the adsorption of both reactants to happen in different active sites (γM) and in the acidic support (γA).20 Their model is based on the existence of a surface-activated complex, which represents a transition state and is in equilibrium with the adsorbed reactants. This equilibrium can be characterized by the constant (KTH) and it is supposed to be the same for the formation of the activated complex on the acidic sites or on the metal. Although they suggested considering a third type of active site, for the sake of simplicity, it is not taken into account and KTH is considered to be a global equilibrium constant, because a single activated complex exists. According to these authors, the hydrogenation occurs by means of the sequential addition of H atoms, with the RDS being the addition of the first one. Therefore, the hydrogenation rate follows immediately from the surface concentration of the activated complex:

-rT ) kKTHKTPT xKH2PH2

(6)

Based on the temperature range used, this equation can be fitted independently (i) for temperatures in the range of 100-200 °C, where the apparent activation energy is positive, as a result of the kinetic regime, and (ii) for temperatures in the range of 200250 °C, where the apparent activation energy is negative, as a result of the surface coverage regime. 2.3. Competitive Models with One Active Site. The competitive adsorption models are based on the existence of only one type of active site on the metal particle (γM), where the adsorption of hydrogen and the aromatic molecule competitively occur, i.e., a competitive adsorption between toluene and hydrogen.18,19 This hypothesis is based (i) on the higher strength of toluene adsorption, compared to hydrogen, especially at high temperature, and (ii) on the decrease in the reaction rate when the hydrogen partial pressure is increased. Lindfors et al.18 established the basic assumptions for the single-active-site models, where the effects caused by the surface heterogeneity are negligible and, thus, the Langmuir adsorption theory can be applied. Hydrogen adsorption is assumed to be dissociative, whereas toluene adsorption is reactive; both of them are fast enough to be considered to be equilibrated. The desorption of MCH is assumed to be irreversible and rapid. According to these authors, the hydrogenation reaction occurs through surface reaction steps in which H atoms are added to the adsorbed aromatic intermediate compounds, where one of these steps is the RDS. The addition of hydrogen to toluene can occur via several routes: (a) Simultaneous addition of H atoms (simultaneous model):

-rT )

kKTKH2i/2PH2i/2PT (1 + KTPT + KH21/2PH21/2)i+1

(7)

where the RDS can be the addition of the first (i ) 1), second (i ) 2), third (i ) 3), fourth (i ) 4), fifth (i ) 5), and sixth (i ) 6) H atom to the adsorbed aromatic molecule. (b) Sequential addition of H atom pairs (sequential model). The RDS is assumed to be the addition of the first, second, and third hydrogen molecule.18,19

(c) Surface reaction steps with equal velocity. Consequently, the quasi-equilibrium model can be applied (quasi-equilibrium sequential models). These models are applied at low and high temperatures.18 The rate equation for the low-temperature model is

-rT )

kKTKH2PTPH2 (1 + 3KTPT + KH21/2PH21/2)3

(8)

Thybaut et al. proposed the following quasi-equilibrium sequential model:21

-rT ) kB3KTPTKH21/2PH21/2(B3 + B2 + B + 1) × [(B3 + B2 + B + 1)(1 + KH21/2PH21/2) + KTPT(4B3 + 3B2 + 2B + 1)]-2 (9) where B is

B ) KsupKH21/2PH21/2

(10)

3. Experimental Section 3.1. Catalyst. The catalyst used for the hydrogenation experiments was a commercial catalyst: 0.5 wt % platinum supported on γ-Al2O3. The original solid was crushed and pelletized to obtain a particle size of 0.01-0.1 mm for optimal diffusion control. The absence of mass-transport limitations in the catalyst was verified by calculating the Weisz-Prater moduli,36 with values in the range of 0.1-0.4. The characterization of this catalyst has been performed by means of N2 adsorption isotherm, CO chemisorption, NH3 adsorptiondifferential scanning calorimetry (DSC), and NH3-temperatureprogrammed desorption (TPD). The main properties of the catalyst are as follows: BET surface area ) 118 m2/gcat, total pore volume ) 0.26 cm3/gcat, metal dispersion ) 84.6%, and platinum area ) 1.04 m2/gcat. Prior to the activity tests, the catalyst was mixed with 1 g of inert R-Al2O3 (Merck) with a particle size of 0.3 mm, to improve the fluidodynamic properties, and then was activated in situ by heating to a reduction temperature of 400 °C under a 90 cm3/min flow of a H2/N2 mixture (volume ratio of 1:2) at atmospheric pressure, followed by isothermal reduction at this temperature for 2 h. 3.2. Kinetic Experiments. Kinetic experiments of toluene (Panreac, 99.5%) hydrogenation have been performed in a fixedbed reactor. The operating conditions have been as follows: total pressure, 2 bar; temperature range, 100-250 °C; H2 inlet pressure, 0.3-1.9 bar; toluene inlet pressure, 0.04-0.15 bar; and space time, (2-10) × 10-2 gcat h/gtol. During the experimental runs, the catalytic activity remained constant (i.e., there was no significant catalyst deactivation). The reproducibility of the measurements has been examined by making duplicate or triplicate experiments for each data point. The total number of runs was 277, conducted under 111 different conditions, for statistical application. 3.3. Methodology for Parameter Estimation and Model Discrimination. Parametric estimation has been performed using the lsqcurvefit function of Matlab R14, which solves nonlinear data-fitting problems by minimizing the sum of squared residuals (SSR) between experimental data (yi) and calculated data (F(k,xi)). The extent of toluene hydrogenation rate (given in terms of molT/min (ξ), which has been described elsewhere,37 has been used as the fitting variable. The lsqcurvefit function finds the coefficients k that best-fit the following equation:

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Ind. Eng. Chem. Res., Vol. 46, No. 23, 2007 Nexp

SSR )

(F(k,xi) - yi)2 ∑ i)1

(11)

where x and y are vectors of length equal to the number of experiments (Nexp). F(k,x) is the value(s) calculated for the x vector and k, for the fitting variable/s by means of the integrated rate equations. The functions ode45, ode23s, ode15s, and ode113 of Matlab R14 have been used to solve the differential equations of mass conservation (i.e., rate equations). The fitting quality of each kinetic model was evaluated using the analysis of variability, based on the assumption that the SSR is a stochastic variable with a specific distribution function. The significance of the kinetic constants and the variability of each model have been calculated using methods that have been described elsewhere.38 The statistical significance of the global regression is expressed by means of the so-called F-test, which weights the lack of fit of one postulated model with the experimental error. The value of the F-statistics is computed as the ratio of mean square terms:

F)

V12

(12)

V22

These mean square terms correspond to the lack of fit and to pure experimental error. Furthermore, the sum of squares of the residuals (SSR) is defined as

SSR ) SSEPE + SSELF

(13)

where SSEPE is the sum of the squares corresponding to the pure error (PE) and SSELF is the sum of squares corresponding to the lack of fit of the model, which is calculated from the values of SSR and SSEPE by means of eq 13. The mean squares required in eq 12 are calculated from the corresponding sum of squares and degrees of freedom: p

V12 )

SSELF p - nk

)

ni[(yj)i - F(k,xi)]2 ∑ i)1 p - nk p

V22 )

SSEPE (Nexp - 1) - p

)

(14)

nj

[yij - (yj)i]2 ∑ ∑ i)1 j)1 (Nexp - 1) - p

(15)

where p is the number of points of the independent variable at which there are experimental (observed) values of the dependent variable, and nk is the number of parameters being estimated or number of parameters that contain vector k. The term ni represents the number of replications or repeated experiments at each point of the independent variable, and yi is the mean value of each group of repeated experiments. 4. Results 4.1. Evaluation of Kinetic Data. The hydrogenation of toluene yielded his saturated naphthene, i.e., methylcyclohexane (MCH), as the only identified product; no partially hydrogenated or dehydrogenated intermediate compounds were detected in the reactor outlet stream, nor coke deposited on the catalyst. As can be found in previous papers, the reaction rate typically has a maximum as a function of temperature.14,15,20,27 Our

Figure 1. Toluene-hydrogenation-controlled turnover frequency (TOF), as a function of reaction temperature. WHSV ) 50 h-1, PH2 ) 0.9 bar, PT ) 0.1 bar, and P ) 2 bar.

experimental results, shown in Figure 1, confirm this behavior: The turnover frequency (TOF) first increases, and, for temperatures of >200 °C, the TOF decreases. According to the Arrhenius expression, the hydrogenation rate should increase with temperature; thus, this phenomenon can be attributed to a reduction in the reaction intermediate’s surface coverage.20,21 Other factors for this behavior can be neglected: 18,20 (i) transport limitations, according to the low value of the Weisz-Prater moduli (section 3.1); (ii) catalyst poisoning, no sulfur in the feed; and (iii) metallic sintering. Figure 2 displays, as an example, the evolution of toluene conversion along the reactor space time (τ). The reaction rate is constant and independent of toluene conversion only at τ values in the range of 0-0.02 h, under the conditions represented in Figure 2. From the experimental results displayed so far, three regimes should be considered in the best kinetic model: (i) that controlled by Arrhenius kinetics, (ii) that controlled by the surface coverage of actives sites by adsorbed toluene, and (iii) that controlled by the thermodynamics. According to Figure 2, the latter case is present at temperatures and space time values higher than 175 °C and 0.16 h, respectively. Figure 3 recapitulates all the information regarding the experimental areas of control previously explained. The effect of inlet partial pressures of reactants on the toluene hydrogenation rate is shown in Figure 4, under quasi-differential reactor conditions (i.e., space time ) 0.02 h). These experimental results can be fitted to the power-rate model (eq 1) with the purpose to calculate the reaction orders of both reactants and, also, the activation energies. The reaction rate increases correspondingly with the hydrogen partial pressure in the temperature range of 100-250 °C, which means that the hydrogen adsorption favors the metallic and acidic site accessibility. The explanation to this phenomenon can be attributed to the high mobility of the chemisorbed hydrogen species under these conditions. In contrast, increasing the toluene partial pressure resulted in two different reaction performances. For temperatures in the range of 100-150 °C, the toluene reaction order has a very low value (close to zero). For higher temperatures, Figure 4 displays two different areas: (i) When the toluene partial pressure is 0.09 bar, this behavior reverses and the reaction order becomes zero or even negative.

According to this, it can be concluded that, at low temperature, the hydrogenation rate is slow enough to make the activity almost independent of toluene partial pressure and avoid the saturation of the active sites; while at high temperature, the reaction rate is higher; thus, the toluene adsorption can be either (i) nonsaturated, at PT < 0.09 bar, where the toluene reaction order is positive, or (ii) saturated, at PT > 0.09 bar, where the toluene reaction order is negative. Consequently, the stability of hydrocarbon intermediates adsorbed on the catalytic surface depends on temperature and when the aromatic concentration is elevated (PT > 0.09 bar), such intermediates can block the active sites. Figure 5 represents the areas in terms of the experimental conditions, where the saturation of active sites is significant for the adsorption of toluene. When this occurs, the competitive mechanism is considered conventionally. Nevertheless, the information indicated up to this point is not sufficient to prove that there is only one type of active site: it happens when the toluene partial pressure increases. 4.2. Parameter Estimation and Model Discrimination. Table 1 summarizes the aforementioned kinetic models found in the literature for toluene hydrogenation and used in this paper. Each model has been numbered with a superscripted reference for easier identification. The agreement between the calculated and experimental extent of reaction (ξ) for each kinetic model is shown in Figure

Figure 4. Toluene hydrogenation rate versus partial pressure of reactants. WHSV ) 50 h-1 and P ) 2 bar.

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Ind. Eng. Chem. Res., Vol. 46, No. 23, 2007 Table 2. Fitting of the Kinetic Models Summarized in Table 1a

Figure 5. Effect of temperature and toluene partial pressure over the conversion (over the lines, in %), and the zones with different adsorption mechanism. WHSV ) 50 h-1, PH2 ) 0.9 bar, and P ) 2 bar.

6, which gives an idea of the suitability of each model. The values of the statistical parameters obtained for each model are summarized in Table 2. The majority of the models have significant kinetic constants. Power-rate models 1 and 8 do not fit properly, because they consider the existence of the Arrhenius regime. Thus, the calculated kinetic constants are not continuous over the entire set of experimental conditions, because of the variability of the activation energy (Figure 1) and reaction orders (Figure 4). The empirical models proposed by Gaiday et al.25 fit properly, especially model 3, which assumed the addition of the second hydrogen molecule to be the RDS, as is deduced by its low F-value. Focusing on the models proposed by Vannice and coworkers16,22 (models 5-7), and according to the high SSR values

model

description

SSR (× 10-7)

MSR (× 10-10)

F-test

significance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

power-rate empirical empirical empirical 2 sites 2 sites (deh.) 2 sites (deh.) 2 sites 2 sites 1 site (sim.) 1 site (sim.) 1 site (sim.) 1 site (sim.) 1 site (sim.) 1 site (sim.) 1 site (seq.) 1 site (seq.) 1 site (seq.) 1 site (quad-eq.) 1 site (quad-eq.) 1 site (quad-eq.) 1 site (seq.) 1 site (seq.)

51.88 13.00 6.74 17.90 5.72 51.60 22.62 51.74 5.36 8.46 8.82 7.32 7.46 16.96 11.88 7.12 6.34 27.08 7.40 95.14 5.84 8.32 21.50

9.50 2.42 1.25 3.33 1.07 9.81 4.27 9.51 0.98 1.58 1.63 1.35 1.38 3.13 2.19 1.34 1.20 5.11 1.36 17.55 1.09 1.54 3.97

650 170 88 235 75 712 307 655 66 112 109 91 94 212 150 96 84 368 93 1236 74 102 278

yes yes yes yes yes yes yes no yes no yes yes yes yes yes yes yes yes yes yes yes yes yes

a Abbreviations: deh. ) dehydrogenation; sim. ) simultaneous; seq. ) sequential; qua-eq. ) quasi-equilibrium.

obtained for models 6 and 7, the dehydrogenation reactions on both the metallic surface or the support acid sites, at least under our experimental conditions, are highly improbable; therefore, they have been dismissed. Model 5, which suggests that the hydrogenation should occur in two different types of active sites, gives an excellent fitting. Concerning the models proposed by Keane and Patterson,20 a substantial improvement is shown by model 9, in comparison to its equivalent for a single temperature range (model 8). Although, according to the statistical analysis, model 9 seems to be the most suitable one, it has been rejected, based on mechanistic terms, because it has a discontinuity, because of the division performed for the estimation of the kinetic and adsorptive parameters. However, this model can be used to estimate the value of the apparent activation energy (100-175 °C) and the apparent adsorption enthalpy (200-250 °C).

Table 1. Summary of the Kinetic Models in the Literature for Toluene Hydrogenation modelref 1 225 325 425 516 622 722 820 920 1019 1119 1219 1319 1419 1519 1618 1718 1818 1918 2018 2121 2221 2321

equation

number of constants

eq 1 eq 2, with i ) 1 eq 2, with i ) 2 eq 2, with i ) 3 eqs 4 + eq 5 dehydrogenation over γM. RDS: second H- atom addition dehydrogenation over γM and γA. RDS: first H-atom addition eq 6 eq 6 for two temperature ranges: 100-200 and 200-250 °C eq 7, with i ) 1 eq 7, with i ) 2 eq 7, with i ) 3 eq 7, with i ) 4 eq 7, with i ) 5 eq 7, with i ) 6 sequential, RDS: first H2-molecule addition sequential, RDS: second H2-molecule addition sequential, RDS: third H2-molecule addition eq 8 quasi-equilibrium sequential model for high temperatures eqs 8, 9, and 10 sequential, RDS: third H-atom addition sequential, RDS: fourth H-atom addition

4 8 8 8 10 14 14 2 4 6 6 6 6 6 6 12 12 12 6 6 8 6 6

Ind. Eng. Chem. Res., Vol. 46, No. 23, 2007 7423 Table 3. Fitting for the Proposed Kinetic Model 24 (using eq 16) parameter

value 10-7

SSR variability F-test significance

5.64 × 1.04 × 10-10 71 yes

k′130 °C ′ (Ea)kapp

(3.98 ( 0.10) × 10-2 molT gcat-1 h-1 bar-2 (53.97 ( 0.32) kJ/mol

°

C KH130 2 -∆HH2 (adsorption) °C K130 T -∆HT (adsorption)

(3.07 ( 0.47) × 10-4 bar-1 (196.3 ( 1.9) kJ/mol (3.58 ( 0.64) × 10-7 bar-1 (279.7 ( 2.2) kJ/mol

Table 4. Fitting of Kinetic Model 25 (using eq 17) parameter

value

SSR MSR F-test significance

5.58 × 10-7 1.01 × 10-10 69 yes

k′130 °C ′ (Ea)kapp

(4.05 ( 0.11) × 10-2 molT gcat-1 h-1 bar-2 (57.26 ( 0.50) kJ/mol

°

C KH130 2 -∆HH2 (adsorption) °C K130 T -∆HT (adsorption)

(1.08 ( 0.15) × 10-3 bar-1 (181.0 ( 1.6) kJ/mol (3.92 ( 0.89) × 10-7 bar-1 (281.5 ( 2.4) kJ/mol

The simultaneous models 10-15 indicate that the addition of the third H atom is most likely RDS (model 12). According to the fitting of the sequential models 16-18, the addition of the second hydrogen molecule should be considered as the RDS, as a result of the best fitting achieved for model 17. Based on the physicochemical calculations,39 and according to the small improvement shown by the fitting results considering one or another hydrogen addition step as the rate-determining one (models 10-15), particular emphasis should be placed on quasi-equilibrium models 19 and 21, which fit the experimental data quite accurately. Among these models, model 21, proposed by Thybaut et al.,21 which considers no RDS, significantly improves the fitting obtained over the other two quasiequilibrium models proposed by Lindfors and Salmi (models 9 and 20).19 Thus, there is no clear difference between the fitting shown by the models assuming an RDS or the same hydrogenation rate for all the hydrogen addition steps (quasi-equilibrium models). However, in the event of considering an RDS, the addition of the second hydrogen molecule or the addition of the third H atom seems to be the most suitable one, in view of the obtained results. 4.3. Proposed Kinetic Model. Based on the statistical results, models 5, 9, and 21 are appropriate to describe our kinetic data. However, as has been previously mentioned, model 9 cannot be accepted, as a result of the discontinuity shown in the range of temperature studied in this work. Furthermore, a new rate equation can be obtained for model 21, because some of the kinetics parameters are negligible and the hydrogenation rate over the acidic support is insignificant. Under these considerations, eq 4 can be simplified:

-rT )

k′PH2PT 1 + KTPT + xKH2PH2

Figure 6. Comparison of the conversion predicted by model 24 (lines) with experimental data (points): (a) effect of temperature and (b) effect of space time.

tions are not important, because of its simplicity and statistical (F-test ) 71) and mechanistical aspects. The parameters calculated for this model are shown in Table 3 and, as can be observed, substantial improvement has been achieved because of the simplification done. The suitability of model 24 for the simulation of the reactor has been studied using a simulation programmed in Matlab R14. The experimental data have been compared with those predicted by the model data and, furthermore, the model is able to forecast hydrogenation results under conditions different from those used in this kinetic study. The results shown in Figure 6 are an example of the fitting. The effect of temperature and space time is accurately described by model 24. Nevertheless, in a particular region (high values of temperature and space time), the model seems to diverge from the experimental data, as a consequence of ignoring the thermodynamic limitation in the kinetic expression (eq 16). The experimental conditions studied in the literature are within the kinetic regime, because low conversions are achieved by working in differential reactors. However, in this work, the experimental data fall into the three different regimes, discussed in section 4.1. Adding a new term to eq 16 to consider the thermodynamic effect on the toluene hydrogenation rate, the following expression is obtained:

-rT ) (16)

This new kinetic model (derived from model 21), numbered as model 24, describes the hydrogenation of toluene over a noblemetal-based catalyst, but only when the thermodynamic limita-

k′PH2PT 1 + KTPT + xKH2PH2

(

1-

PMCH KPH23PT

)

(17)

The parameters estimated for this model, numbered as model 25, are shown in Table 4, and Figure 7 shows the parity diagram for this model. The inclusion of the equilibrium control regime is an advisable target for industrial purposes, because, in this

7424

Ind. Eng. Chem. Res., Vol. 46, No. 23, 2007

conditions. The great difference between this model and those previously suggested is the versatility of the rate equation, because it is applicable not only in the kinetic regime (i.e., for low conversions) but also when high temperatures or space times are used, which is especially relevant in industrial applications. 5. Conclusions Toluene hydrogenation kinetics has been studied over a wide range of experimental conditions on a commercial Pt/γ-Al2O3 catalyst. Among the vast literature found, kinetic model discrimination was performed using statistical tools and mechanistical considerations, pretending to obtain a simplified model. The experimental results show that the kinetics can be controlled by several regimes, which restricts the majority of the proposed kinetic models, up to certain conditions. Using an extensive number of experiments (277), we propose two simple kinetic models formally useful in the kinetic controlled regime (model 24, eq 16) and for thermodynamically controlled regime (model 25, eq 17). The simulation results, the parity diagrams, and the F-test show that model 25 is satisfactory for describing toluene hydrogenation over a wide range of experimental conditions. This model is also suitable under conditions in which the kinetics is limited by hydrogenation irreversibility. Although the objective of this paper has not been the study of reaction mechanisms, the results obtained show the limitations of the empirical kinetic models. Moreover, although the simplicity of the kinetic equation proposed does not allow for adopting a clear position on the more-suitable mechanism proposed in the literature, the results are consistent with a mechanism on two active sites, without competition in the adsorption of toluene and hydrogen, and where the ratedetermining step is the reaction of toluene adsorbed on the metallic sites.

Figure 7. Parity diagram for proposed kinetic model 25.

Nomenclature

Figure 8. Comparison of the conversion predicted by model 25 (lines) with the experimental data (points): (a) effect of temperature and (b) effect of space time.

case, very high space times are used. The value of the equilibrium constant has been taken from the literature:40

K ) 2.78 × 10-10 exp

[205R (T1 - 6501 )]

(18)

Based on the aforementioned discussion, the statistical results (the SSE and the F-value) for model 25 are highly satisfactory. Nevertheless, the differences between the results of this model and model 24 are not important, because of the fact that most experimental data used in the kinetic modeling correspond to the kinetic regime. The simulation of the reactor using this model has allowed conversion results at the reactor outlet to be obtained, which are shown in Figure 8, together with the experimental results. A significant improvement is clearly observed for model 25 in the region of thermodynamic control (T > 200 °C and τ > 0.16 h), because of the effect of not only temperature but also space time. Thus, the model proposed in this paper accurately describes the hydrogenation of toluene under a high range of experimental

F ) statistics of Fischer distribution, eq 12 P ) total pressure (bar) PT ) toluene partial pressure (bar) PH2 ) hydrogen partial pressure (bar) -rT ) toluene hydrogenation rate (molT gcat-1 h-1) K ) equilibrium constant (kPa-3) Ki ) equilibrium constants for hydrogen atom incorporation steps in the hydrogenation mechanism KT ) adsorption equilibrium constants of the toluene intermediate compound KH ) adsorption equilibrium constant of the hydrogen intermediate compound KTH ) adsorption equilibrium constant of the hydrocarbon intermediate compound k ) kinetic constant h ) reaction order of H2 t ) reaction order of toluene MSR ) mean square of the residuals Nexp ) number of experiments ni ) number of repeated runs at each point nk ) number of parameters that contain vector k p ) number of points of the independent variable R ) constant of gases; R ) 8.314 × 10-3 kJ mol-1 K-1 SSEPE ) sum of squares of pure error SSLF ) sum of squares of the lack of fit SSR ) sum of squares of the residuals s ) active sites for toluene adsorption

Ind. Eng. Chem. Res., Vol. 46, No. 23, 2007 7425

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ReceiVed for reView January 15, 2007 ReVised manuscript receiVed April 27, 2007 Accepted May 2, 2007 IE070094M