ie2015526_desproporcion de tolueno con mordenita

8/18/2019 Ie2015526_desproporcion de Tolueno Con Mordenita

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Published: November 07, 2011

r 2011 American Chemical Society 171 dx.doi.org/10.1021/ie2015526 | Ind. Eng. Chem. Res. 2012, 51, 171–183

ARTICLE

pubs.acs.org/IECR

Kinetics of Toluene Disproportionation: Modeling and Experiments

Marcos W. N. Lob~ao,†

Andre L. Alberton,‡

Sílvio A. B. V. Melo,†

Marcelo Embiruc-u,†

Jose L. F. Monteiro,§

and Jose Carlos Pinto* ,§

†Programa de Engenharia Industrial, Escola Politecnica, Universidade Federal da Bahia, Rua Aristides Novis, no 2, Federac-~ao,Salvador, 40210-630 BA, Brasil

‡Pontifícia Universidade Catolica do Rio de Janeiro, Rua Marquês de S~ao Vicente 225-371 L, Rio de Janeiro, 22451-900 RJ, Brasil§Programa de Engenharia Química/COPPE, Universidade Federal do Rio de Janeiro, Cidade Universitaria, CP: 68502,Rio de Janeiro, 21941-972 RJ, Brasil

ABSTRACT: This work presents modeling and experimental studies on the kinetics of toluene disproportionation in operationranges that include real industrial operation conditions. The inuence of reaction temperature, reactor pressure, feed composition,and residence time on conversion of reactants and product selectivity was investigated. Experiments were performed according to asequential experimental design strategy, in order to provide maximum accuracy for model predictions. Statistical treatment of parameter estimates and model adequacy was performed with the help of maximum likelihood principles. Excellent agreement

between model predictions and available experimental data was obtained in the full ranges of investigated experimental conditions.

1. INTRODUCTION

Toluene disproportionation is an important chemical trans-formation for most reneries and chemical complexes, con-stituting the heart of economically relevant commercialprocesses used for direct production of aromatic productsand indirect manufacture of polymer resins, synthetic bers,and plasticizers.1 The toluene disproportionation reaction can be represented as

2T a B þ X ðR1Þ

where T is toluene, B is benzene, and X is xylenes. Toluenedisproportionation is performed commercially with the help of heterogeneous catalysts.1,2 One of the most important pro-cesses is the Tatoray process, where typical industrial condi-tions include temperatures of 350530 C, pressures of 1050 bar, and H2/aromatic ratios between 5 and 12/1.

1,2

The high hydrogen to aromatic ratio is necessary to avoid thecatalyst deactivation.3

Reliable kinetic studies are very important for design, analysis,and control of the industrial process. Although most toluenedisproportionation technologies are mature, kinetics of toluenedisproportionation over heterogeneous catalysts is not com-pletely understood even in ranges of experimental conditions

normally employed by industrial processes. Table 1 presents asummarized review about the kinetic models proposed in theliterature, including the experimental conditions and the conversion ranges investigated by the authors.

Diff erent kinetic models have been used so far to describethe catalytic disproportionation of toluene. Many authorsproposed a pseudohomogeneous kinetics of rst order4,5

or second order610 with respect to the toluene partial pre-ssure in order to describe the reaction rates. Good ts have been reported for LangmuirHinshelwood-Hougen-Watson(LHHW) kinetic rate expressions, derived from mechanismsthat consider surface reactions1118 as the rate determiningstep (RDS), and Eley Rideal (ER) kinetic rate expressions,

derived from mechanisms that consider toluene adsorption3,6,19

or surface reaction3,20 as the RDS. In all these studies, the catalystsused to promote toluene disproportionation were based on Y-zeolites,3,15,20 ZSM-5 zeolites,4,5,10,12 and more commonly H-mordenite.68,10,11,13,14,1618

As brie y reviewed above, although the kinetics of toluenedisproportionation has been investigated by several researches,distinct reaction mechanisms have been proposed and distinctkinetic models have been derived. Discrepancies can possibly beascribed to the diff erent analyzed catalyst types, operating

conditions, conversion levels, and coking of catalysts; never-theless, it is certain that agreement has yet to be reachedregarding the kinetics of toluene disproportionation over hetero-geneous catalysts.

It is important to emphasize that many works published inthe literature were performed at low pressures and not atthe relatively high pressures practiced in real industrialenvironments.47,12,15,19,20 When the operation conditionsresembled the actual industrial operation conditions, simpli-ed models based on pseudohomogeneous approach wereproposed, specially for the study of catalyst deactivation.810

However, the use of simplied kinetic models leads to apoorer ts, when compared to the LHHW and ER ex-pressions.19 Besides, as one can observe in Table 1, many

studies were performed at low toluene conversions, reducingthe reliability of the models for prediction of real industrialoperation conditions.

Based on the previous paragraphs, the use of LHHW modelsto t experimental data obtained at operation conditions thatresemble the actual industrial conditions seems appealing. Forthis reason, the main objective of the present work is to

Received: July 17, 2011 Accepted: November 7, 2011Revised: October 11, 2011


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172 dx.doi.org/10.1021/ie2015526 |Ind. Eng. Chem. Res. 2012, 51, 171–183

Industrial & Engineering Chemistry Research ARTICLE

investigate the kinetics of toluene disproportionation over acommercial H-mordenite catalyst in a broader range of experimental conditions, including the conditions normally employed to perform the reaction in industrial sites. Theobtained experimental data are then used to build a kineticmodel in order to represent reaction rates in a wider range of experimental conditions. A sequential experimental design

technique is used to select the experiments, to accelerate themodel building process, and to provide maximum accuracy for model predictions.

2. PARAMETER ESTIMATION AND EXPERIMENTALDESIGN

Let us assume that a set of experiments has been performed.The set of independent experimental conditions dened by theanalyst is represented here by x and named as the set of designvariables (reactor design, mass of catalyst, feed ow rates, reactortemperature, and reactor pressure). The set of dependentexperimental conditions obtained by the analyst as the experi-mental results is represented here by y and named as the set of response variables (outlet compositions). Variables x and y arerelated to each other through the mass balance equations and thekinetic model.

In order to analyze the available experimental data, the follow-ing hypotheses are assumed to be valid: (i) experimentalmeasurements are subject to random experimental errors, whichfollow the normal distribution; (ii) experiments are well done, sothat gross andpersistent errorsare notpresent;(iii) theproposedmathematical model is perfect, so that experimental measure-ments uctuate around model predictions; (iv) design variablesare well controlled and are not subject to signicant experimentalerrors; and (v) experimental errors are not correlated to eachother. In this case, the set of kinetic parameters θ can be

estimated through minimization of the following objectivefunction (F )21,22

F ¼ ∑ N exp

i ¼ 1∑ Ny

j ¼ 1

yðiÞexp

j ðxðiÞ , θÞ y

ðiÞ pred j ðx

ðiÞ , θÞ

σ ðiÞ

y , j

0B@

1CA

2

ð1Þ

where Nexp represents the number of experiments, Ny is thenumber of response variables, y j

(i) is the response variable j forexperiment i , σ y , j

(i) is the standard deviation of variable y j(i) , and x(i)

is the set of experimental design variables for experiment i. Thesuperscripts exp and pred represent the experimental value andthe value calculated with the model, respectively.

After minimization of the objective function and estimation of the model parameters, it is possible to infer the uncertainties of the parameter estimates. If the experimental errors are suffi-ciently small, the covariance matrix of parameter uncertainties,V θ , can be calculated

21,22

V θ ¼ ∑

Nexp

i ¼ 1

∂ yðiÞ

∂θ !T

3 V ðiÞ

y 1

3

∂ yðiÞ

∂θ !24 35

1

ð2Þ

where the matrix V y(i) is the covariance matrix of experimental

uncertainties for experiment i. As it was assumed that experi-mental errors are independent

V ðiÞ y ¼

ðσ ðiÞ y1 Þ

2 0 3 3 3 0

0 ðσ ðiÞ y2 Þ

23 3 3 0

l l ⋱ l

0 0 3 3 3 ðσ ðiÞ yNyÞ

2

2666664

3777775 ð3Þ

Table 1. Kinetic Studies of Toluene Disproportionation over Zeolites Catalyst (Adapted from Marques17)

year ref catalyst P (bar) T (C) X T (%) kinetic modelsa

1979 (3) HY/AlF3/Cu 211.1 400500 e22 E-R reaction surface or toluene adsorption as rds

1981 (7) modied mordenite 1 350450


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The diagonal elements of V θ represent the parameter uncertain-ties, while the nondiagonal elements of V θ represent the param-eter correlations. Finally, the parameter uncertainties are trans-formed into uncertainties of model predictions as21,22

V y

pred ¼ ∂ y

∂θ 3 V

θ 3

∂ y

∂θ T ð

4Þ

Sequential experimental design strategies are used to selectexperimental conditions that allow for discrimination of rivalmodels and/or estimation of model parameters with maximumaccuracy.21,2326 In short, experimental design techniques makeuse of the available models to predict future experimental dataand infer the experimental conditions that can lead to the mostprecise set of parameter estimates, avoiding the costs of perform-ing experiments in regions where the information content islow.2123 After selection of the experimental conditions, theexperiment must be performed and the model parameters must be re-estimated. The procedure must be repeated iteratively untilattainment of the desired parameter precision or selection of the

best model candidate.Several criteria can be used for design of experiments for

estimation of precise model parameters. The y-trace criterionproposed by Pinto et al.27 is used in the present work. Accordingto this criterion, the optimal experimental condition is the onethat allows for minimization of the trace of matrix V y

pred

presented in eq 4. As explained by Pinto et al.,27 this criterionis focused on the model performance and does not necessarily leads to the most precise set of model parameters but to thelowest prediction uncertainties. As the trace of V y

pred must becalculated through model simulations, the efficiency of theexperimental design technique depends strongly on the ability of the model to predict the experimental data.

3. METHODOLOGY

3.1. Experimental Setup and Procedure. The acidity, pore volume, surface area, and chemical composition of the catalystare presented in Table 2. The catalyst used in the present work isa commercial H-mordenite grade presenting low concentrationsof Ca, K, and Na, which indicate that hydrogen constitutes theonly compensation cation in the catalytic system. The catalystpresents a low atomic Si/Al ratio of 0.62. Additional details onthe catalyst properties are described elsewhere.13

Reaction experiments were carried out in a laboratory unit, asillustrated in Figure 1A. Aromatic compounds(toluene,benzene, xylenes) kept in the liquid phase in a storage reservoir were fed

into the reactor with the help of a metering pump (Whitey 1/3HP), with ow rates in the range between 0 and 10 mL 3 min

1.The liquid stream was vaporized with the help of externalelectrical resistances and mixed with the hydrogen stream. Thehydrogen/aromatic ratio (RHC) was set to 6 (in molar basis) inall experiments.

A xed bed reactor was used to perform the reactions, asillustrated in Figure 1B. The reactor was lled with three distinctparticle layers. The catalyst bed was placed between two beds of silica of similar length. Silica particles presented the same averagediameter of catalyst particles. Experiments performed withoutthe catalyst (blank experiments) never led to any signicantconversion of the reactants. The internal reactor temperature wasmonitored and controlled with 3 type-J thermocouples placed atthe three solid layers, as shown in Figure 1B. The reactor wasplaced in a vessel containing uidized alumina pellets andelectrical resistances for improved control of the reactor tem-perature. Additional details about the experimental apparatuscan be found elsewhere.13

Table 2. Properties of the H-Mordenite Catalyst

parameter value

acidity ( μmol NH3 3 g1) 0.225

density (g3cm3) 1.33

pores volume (cm33g1) 0.66

surface area (m2/g) 330

Chemical composition

Si 18

Al 28

Fe, Zn, Ni, and Cu


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The outlet stream was condensed, and samples of the liquidstream were analyzed with the help of a CG-25 gas chromato-graph equipped with a thermal conductivity detector (TCD).Hydrogen was used as the carrier gas. The chromatographcolumns were made outof bentona 34 on chromosorb P, suitablefor separation of aromatic compounds.28

A reference experiment was performed every three experi-

ments in order to guarantee that no signi

cant deactivation of thecatalyst had occurred. Whenever observed conversion deviations were larger than 5% for the reference experimental condition, thecatalyst bed was replaced and the previous three experiments were discarded. Experiments performed with catalysts of diff er-ent sizes and with diff erent ow-rates13,29 indicated that theexternal and internal resistance to mass transfer were notsignicant at the analyzed operation conditions.

3.2. Modeling. The starting point of this work was the study developed by Krahl,13 who investigated the gas phase dispro-portionation of toluene on a commercial H-mordenite catalystand proposed LHHW kinetic rate expressions to fit the obtainedexperimental data. As observed experimentally, the productdistribution could be described very well by the kinetic model

derived from the following reaction mechanism2T a B þ X ðR1Þ

2 X a T þ TMB ðR2Þ

where TMB is a pool of trimethylbenzenes. The author proposedseveral reaction mechanisms and derived a number of LHHW and ER kinetic models to explain the available data, but the bestresults were obtained with the following reaction scheme

T þ s a Ts

2Ts a Bs þ Xs ðRDSÞ

Bs a B þ s

Xs a

X þ s2 Xs a Ts þ TMBs ðRDSÞ

TMBs a TMB þ s

ðR3Þ

where s represents a catalyst site and RDS indicates the ratedetermining steps. According to the mechanism presented in R3,the following rate expressions could be derived for toluene and xylenes disproportionation reactions

r 1 ¼ k 1 3 K

2T 3 ð P

2T P B 3 P X = K ET Þ

ð1 þ K T 3 P T þ K X P X þ K B 3 P B þ K TMB 3 P TMBÞ2

ð5Þ

r 2 ¼ k 2 3 K

2 X 3 ð P

2 X P T 3 P TMB= K EX Þ

ð1 þ K T 3 P T þ K X 3 P X þ K B 3 P B þ K TMB 3 P TMBÞ2

ð6Þ

where r 1 and r 2 are the reaction rates for toluene and xylenes,respectively; k 1 and k 2 are kinetic rate parameters; K j is theadsorption equilibrium parameter for component j; P j is thepartial pressure of component j ( j = T, X, B, TMB); and K ET and K EX are the reaction equilibrium constants for toluene and

xylenesdisproportionation, respectively.30

The kinetic rate param-eters (k 1 and k 2) and adsorption equilibrium parameters ( K j) can be described as function of the reactor temperature

k i ¼ PF i 3 e Ei=R 3 T K , i ¼ 1, 2 ð7Þ

K j

bar 1 ¼ eðΔS j=R ΔH j=R 3 T K Þ , j ¼ T , X , B , TMB ð8Þ

where PF i is the pre-exponential factor, and Ei is the activationenergy for reaction i;ΔS j is the entropy andΔH j is the enthalpy of adsorption for component j , and T K is the reactor tempera-

ture. Correlation between pre-exponential factors and activa-tion energies can be minimized if the rate expressions arereparameterized as3133

r 1

mol

g cat 3 h 3 bar 2

! ¼ e A1 þ B1 3

T K T r T K

3 ð P

2T P B 3 P X = K ET Þ

1 þ e

AT þ BT 3

T K T r T K

bar 3 P T þ

e A X þ B X 3

T K T r T K

bar 3 P X þ

e A B þ B B 3

T K T r T K

bar 3 P B þ

e ATMB þ BTMB 3

T K T r T K

bar 3 P TMB

0BBBB@

1CCCCA

2

ð9Þ

r 2

mol

g cat 3 h 3 bar 2

! ¼ e A2 þ B2 3

T K T r T K

3 ð P

2 X P T 3 P TMB= K EX Þ

1 þ e

AT þ BT 3

T K T r T K

bar 3 P T þ

e A X þ B X 3

T K T r T K

bar P X þ

e A B þ B B 3

T K T r T K

bar 3 P B þ

e ATMB þ BTMB 3

T K T r T K

bar 3 P TMB

0BBBB@

1CCCCA

2

ð10Þ

where A1 , B1 , A2 , B2 , AT , BT , A X , B X , A B , B B , ATMB , and BTMB arethe parameters that must be estimated and T r is a reference

temperature, made equal to 666.9 K in order to minimize thecorrelation between the parameter estimates.3133 The values of


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thekinetic parameters presentedin eqs9 and10 can be recoveredfrom the estimated parameter values as

PF 1 ¼ eð A1 2 3 AT þ B1 2 3 BT Þ ð11aÞ

E1 ¼ ð B1 2 3 BT Þ 3 R 3 T r ð11bÞ

PF 2 ¼ eð A2 2 3 A X þ B2 2 3 B X Þ ð11cÞ

E2 ¼ ð B2 2 3 B X Þ 3 R 3 T r ð11dÞ

ΔS j ¼ R 3 ð A j þ B jÞ , j ¼ T , X , B , TMB ð11eÞ

ΔH j ¼ B j 3 R 3 T r , j ¼ T , X , B , TMB ð11f Þ

The reactor was described as a standard plug ow reactor(PFR), which was supported by the high Peclet number (above80) and the large ratio between the reactor diameter and thecatalyst pellet diameter (higher than 20).34 Thus, the indivi-dual mass balance equations could be written as

1

M 3dyT

d τ ¼ r 1 þ

r 2

2 ð12Þ

1 M 3

dy X d τ

¼ r 2 þ r 12

ð12bÞ

y B ¼ 3 3 y

0 B þ 2 3 y

0T þ y

0 X

2 3 yT y X

3 ð12cÞ

yTMB ¼ 1 y B yT y X ð12dÞ

where yT , y X , y B , and yTMB are the molar fractions of species T , X , B , and TMB , respectively, considering only the aromaticsspecies; τ is the spatial time (in gcat 3 h/garomatic); and M is themean molecular weight of the aromatic feed. The terms yT

0 , y X 0 ,

and y B0 represent the feed conditions of yT , y X and y B.

3.3. Numerical Procedures. The set of ordinary eqs 12a-12d was solved numerically with a fourth-order RungeKuttamethod.35 The relative precision of the integration was always better than 1.0 105. Model parameters were estimated asdescribed in Section 2, using the well-known GaussNewtonmethod.21,22 Distinct initial guesses were used in order to avoidlocal minima. The relative precision of the estimation step wasalways better than 1.0 104. All numerical procedures wereimplemented in Fortran.36

3.4. Experimental Design. As the number of model param-

eters to be estimated was high, it was convenient to group themodel parameters in terms of the reactor temperature. Analyzedreaction temperatures were equal to 360, 380, 404, and 431 C, based on the work of Krahl.13 For the temperature level of 360 C, sixteen experiments were carried out, including the datareported by Krahl,13 which were generated without the proposi-tion of statistical experimental designs. For temperatures of 380,404, and 431 C, the following experimental design procedure was adopted:

(i) a set of initial experiments was selected, including datareported by Krahl;13

(ii) the set of experiments was performed;(iii) model parameters were estimated and the results evaluated;(iv) for a given temperature, the experimental design proce-

dure was interrupted when sufficiently low predictionerrors had been obtained;

(v) otherwise, a new experiment was designed, as described inSection 2, before returning to step (ii).

Some experiments were also performed for feeds containingmixtures of toluene and benzene, in order to estimate theparameters K B and K X independently. Experimental conditionsare presented in Tables 36.

In order to perform step (iv), it was assumed that reactionconditions could be manipulated in the following ranges:

• the total pressure ( P ) could assume the values of 5, 10, and30 bar, which are typical values of real industrial op-erations;1,2

Table 3. Sequence of Designed Experiments in the Temperature of 360 C, with y-Trace Criterion

aromatic molar fractions in the feed aromatic molar fractions outlet

P (bar) τ (gcat 3 h/garomatic) yT y B y X RHC yT y X

31.19 0.0563 1 0 0 7.06 0.9749 0.0117

30.54 0.1000 1 0 0 6.43 0.9524 0.0228

30.82 0.2300 1 0 0 6.15 0.8991 0.051930.93 0.3630 1 0 0 6.21 0.8697 0.0685

30.87 0.3900 1 0 0 6.53 0.8587 0.0671

30.14 0.1497 1 0 1 6.16 0.0797 0.8422

30.22 0.2500 0 0 1 6.03 0.1211 0.7616

30.22 0.0970 0 0 1 5.98 0.0574 0.8863

10.18 0.1496 0 0 1 6.03 0.024 0.9519

10.18 0.2503 0 0 1 5.94 0.0314 0.9375

5.30 0.1994 0 0 1 5.94 0.0128 0.9736

5.20 0.2989 0 0 1 5.97 0.0199 0.9603

5.30 0.4000 0 0 1 6.07 0.0264 0.9469

30.22 0.0996 0.6081 0.3919 0 6.12 0.5968 0.0050

30.12 0.1991 0.6081 0.3919 0 5.98 0.5840 0.0113

30.12 0.2988 0.6081 0.3919 0 6.05 0.5733 0.0165


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• the spatial time (τ ) could assume the values of 0.05, 0.1,0.15, 0.2, and 0.25 gcat 3 h 3 garomatic

1 , in order to allow for wide variation of conversions;

• feed could be composed of pure toluene or xylenes or mixedcharges of toluene/benzene with molar ratios of 9/1, 8/2, 7/3, 6/4, 5/5 and toluene/xylenes with molar ratios of 7/3, 5/5 in order to allow for estimation of parameters associated

with the adsorption constants of chemical speciesindependently.

Only new experimental conditions could be designed in step(iv), which means that selection of replicates was forbidden. It isalso important to emphasize that experiments performed with apure xylenes feed can allow for improved estimation of theparameters associated to the products.




Initial Set of Experiments

30.14 0.4060 1 0 0 6.56 0.6216 0.1713

31.05 0.3590 1 0 0 5.90 0.6379 0.1693

30.93 0.2350 1 0 0 6.49 0.7074 0.1410

30.90 0.0977 1 0 0 5.99 0.8354 0.0820

31.54 0.0512 1 0 0 6.20 0.9013 0.0499

30.14 0.1008 0.6046 0.3954 0 6.09 0.5449 0.0343

30.24 0.2608 0.6092 0.3908 0 6.35 0.5015 0.0586

5.50 0.3992 1 0 0 6.24 0.9442 0.0289

5.40 0.1995 1 0 0 6.08 0.9688 0.0152

10.28 0.2961 1 0 0 5.96 0.9077 0.0464

10.28 0.1009 1 0 0 6.14 0.9575 0.0212

Designed Experiments

30.14 0.2514 0 0 1 6.06 0.2493 0.4790

30.24 0.1499 0 0 1 6.13 0.2309 0.5298

30.14 0.0988 0 0 1 6.07 0.1880 0.6224

10.78 0.1494 0 0 1 6.07 0.1378 0.7301

30.22 0.0499 0 0 1 6.06 0.1282 0.7477





30.55 0.3590 1 0 0 5.82 0.7472 0.1182

30.68 0.1900 1 0 0 5.91 0.8369 0.0802

30.42 0.1070 1 0 0 6.51 0.8954 0.0509

30.97 0.0516 1 0 0 6.61 0.9496 0.0236

30.97 0.0475 1 0 0 5.96 0.9468 0.0258

30.24 0.2667 0.6041 0.3959 0 6.61 0.5516 0.0361

30.14 0.1005 0.6041 0.3959 0 6.66 0.5795 0.0169

5.399 0.3992 1 0 0 6.25 0.9685 0.0167

5.399 0.1999 1 0 0 6.10 0.9810 0.0099

10.28 0.2975 1 0 0 5.89 0.9562 0.0219

10.28 0.1051 1 0 0 6.53 0.9796 0.0104


30.14 0.2574 0 0 1 6.09 0.2215 0.5558

30.14 0.0998 0 0 1 6.09 0.1308 0.742930.24 0.1497 0 0 1 6.09 0.1599 0.6833

10.38 0.1497 0 0 1 6.02 0.0756 0.8525

30.12 0.0500 0 0 1 6.04 0.0624 0.8775


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4. RESULTS

First, replicated experiments were performed in order todetermine the experimental uncertainty of response variables(conversions of toluene and xylenes). For all experimental runs,three samples were collected for chromatographic analysis. Be-sides, for one predened standard condition of τ = 0.08 gcat 3 h 3garomatic

1 , T = 431 C, P = 30 bar and pure feed of toluene,replicates of the whole experiment were performed. Based on theprevious steps, it was observed that a suitable value for thestandard deviations for toluene and xylenes molar fractions wereapproximately equal to σ T ≈ σ X ≈ 1 10

2. It must beemphasized that the experimental error is of fundamental

importance for evaluating model adequacy and parameter sig-nicance, as described in Section 2. It is true that experimentalerrors may depend on the experimental conditions;37 however,the determination of experimental uncertainties in all investi-gated conditions is notpossiblein most kinetic studies.38 Besides,as shown below, the excellent agreement between predicted andobserved values strongly suggests that the hypothesis of constantexperimental variability is appropriate.

Tables 36 present the experimental results for each analyzedtemperature level, including the initial set of experiments and thesequentially designed experiments. Although the main focus of the present work was the analysis of the toluene disproportiona-tion, the xylenes disproportionation was also investigated

because the y-trace criterion indicated that feeding of pure xylenes could lead to improved estimation of model parameters(such as the adsorption constants K X and K TMB). As one can alsosee in Tables 36, sequentially designed experiments led toexperimentation at distinct pressure, residence time, and feedcomposition levels, allowing for good exploration of the experi-mental region.

Although experiments were grouped in terms of the reactortemperatures, obtained model parameters and experiments wereused afterward for more involving estimation of parameters forthe nonisothermal case. Parameter values and their respectivestandard deviations are presented in Tables 79. Table 7 shows

the parameter values obtained at each particular temperaturelevel after the end of the sequential design procedure.

The trajectories of model parameters for the designed experi-ments are presented in Figure 2. It can be observed that thedeterminants of the covariance matrix of parameter uncertaintiestend to decrease as additional experimental results are accumu-lated, indicating the improved precision of parameter estimates.The oscillatory behavior of the determinant values can beassociated with signicant changes of the parameter estimates,as diff erent experimental conditions are inserted into the experi-mental set. Figure 2 also indicate that parameter uncertaintiesapproach minimum limiting asymptotic values, justifying theinterruption of the sequential experimental design.





30.88 0.0911 1 0 0 5.94 0.7164 0.1361

20.61 0.1650 1 0 0 6.23 0.6978 0.1410

15.27 0.3990 1 0 0 6.10 0.6058 0.1783

31.30 0.0298 1 0 0 5.77 0.8709 0.0612

30.76 0.2500 1 0 0 5.96 0.5676 0.1943

20.86 0.0387 1 0 0 5.60 0.8939 0.0507

20.57 0.2860 1 0 0 6.27 0.6078 0.1772

5.59 0.0590 1 0 0 6.35 0.9691 0.0149

5.63 0.3790 1 0 0 5.62 0.8216 0.0886

15.35 0.0490 1 0 0 6.01 0.8943 0.0515

15.21 0.2320 1 0 0 5.64 0.6910 0.1485

10.69 0.0540 1 0 0 6.27 0.9288 0.0365

5.67 0.2200 1 0 0 6.11 0.8930 0.0533

10.36 0.3770 1 0 0 6.51 0.6964 0.147910.53 0.1950 1 0 0 5.46 0.7946 0.0968

30.14 0.1518 0.5 0.5 0 6.12 0.4187 0.0485

30.14 0.2328 0.5 0.5 0 6.14 0.3985 0.0602

30.14 0.2007 0.6011 0.3989 0 6.06 0.4597 0.0770


30.12 0.1000 0 0 1 6.05 0.2476 0.4883

30.12 0.1495 0 0 1 6.03 0.2546 0.4675

10.18 0.0998 0 0 1 6.07 0.1692 0.6653

30.22 0.0499 0 0 1 6.09 0.2051 0.5872

5.20 0.0996 0 0 1 5.96 0.0991 0.8086

10.18 0.1505 0 0 1 6.03 0.2095 0.5843

5.20 0.1497 0 0 1 5.96 0.1265 0.7538


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As one can see in Table 7, all parameters could be obtained with good precision (except K T at 360 C). Precision of modelparameters was better at higher temperatures, probably as aconsequence of the higher sensibility of response variables withrespect to the experimental conditions presented in Tables 36.Besides, the number of experimental runs was higher at 431 C.

Table 8 presents the values and precisions of parametersestimated with all available experimental data. As one canobserve, most parameters could be estimated with very good

precision. Good estimation was obtained for parameters A1 and B1 , related to k 1 3 K T

2; A2 and B2 , related to k 2 3 K X 2; AT and BT ,

related to K T ; and ATMB and BTMB , related to K TMB , whosecoefficients of variation fell between 1.18% to 21.40%. Goodestimation was obtained for parameter A B , but B B was estimated with coefficient of variation of 45%. Parameter A X was estimatedprecisely, but parameter B X could not be estimated with goodprecision. Figure 3 presents the ratio between the kineticand adsorption constants at temperatures of 431 and 360 C.One can observe the much larger variations of the kinetic rateconstants, showing the higher sensitivity of kinetic rate constantsto temperature (and the highest precision as a consequence) ascompared to the adsorption constants. On the other hand, the

parameter K B was not very sensitive to the experimental condi-tions, which explains the large uncertainty of B X . Since theparameter K X did not vary signicantly in the analyzed experi-mental range, a single constant value could be adopted for thisparameter in the temperature range investigated here.

Table 9 presents the parameters PF i , Ei (i = 1,2),ΔS j , andΔH j( j = T,B,X,TMB) that correspond to the values presented inTable 8. It can be observed in Table 9 that there are some

apparent thermodynamic inconsistencies in the estimated en-tropy and enthalpy of adsorption for several compounds. Ac-cording to the literature,39 spontaneous adsorption must beexothermic (ΔH < 0) as the entropy of adsorption is negative(ΔS < 0). Apparent thermodynamic inconsistencies have beenreported in other kinetic studies40,41 and used to discard theinvestigated models.4246 It must be pointed out, however, thatconstraints can be imposed on the estimation problems in orderto avoid such thermodynamic inconsistencies,18 which meansthat numerical procedures canbe used to force theproposed modelsto obey the imposed constraints. Nevertheless, as extensively discussed by Pinto et al.,38 there may be no fundamental theoretical basis for implementation of similar procedures, since the kinetic

Table 7. Estimated Kinetics Parameters for IndividualTemperatures

parameter mean standard value coefficient of variation (%)a

Temperature of 360 C

k 1 K T 2 3.359 104 2.907 104 86.54

K T 9.094 103 1.150 101 1265

k 2 K X 2 2.675 103 2.191 104 8.191

K X 2.379 101 2.909 102 12.23

K B 3.167 101 2.374 101 74.96

K TMB 4.555 101 2.654 101 58.27


k 1 K T 2 1.154 103 1.996 104 17.30

K T 6.438 102 3.025 102 46.99

k 2 K X 2 1.422 102 1.781 103 12.53

K X 4.751 101 5.192 102 10.93

K B 2.044 101 6.993 102 34.21

K TMB 4.466 101 1.329 101 29.77


k 1 K T 2 2.80 103 2.68 104 9.60

K T 1.08 101 2.15 102 19.90

k 2 K X 2 2.64 102 2.40 103 9.09

K X 3.75 101 3.98 102 10.63

K B 1.45 101 4.01 102 27.56

K TMB 9.42 101 1.34 101 14.24


k 1 K T 2 1.358 102 6.140 104 0.05

K T 2.983 101 1.959 102 0.07

k 2 K X 2 6.248 102 3.774 103 0.06

K X 2.963 101 5.865 102 0.20

K B 4.484 101 4.113 102 0.09

K TMB 1.324 1.745 101 0.13a Coefficient of variation is calculated as the standard deviation divided

by the mean value 100.

Table 8. Estimated Kinetic Parameters and Respective Stan-dard Deviations and Coefficients of Variation

parameter mean standard deviation coefficient of variation (%)a

A1 5.980 0.071 1.18

B1 30.700 1.450 4.72

AT 1.960 0.132 6.73

BT 12.900 2.760 21.40 A2 4.160 0.057 1.37

B2 27.200 1.180 4.34

A B 1.290 0.151 11.71

B B 7.410 3.350 45.21

A X 1.130 0.075 6.67

B X 0.021 1.470 7067.31

ATMB 0.584 0.176 30.14

BTMB 17.800 3.010 16.91a Coefficient of variation is calculated as the standard deviation divided

by the mean value multiplied by 100.

Table 9. Pre-Exponential Factors, Activation Energies, andEntropies of Adsorption and Enthalpies of Adsorption Re-covered from the Parameter Estimates Presented in Table 5

parameter mean

PF1 (mol 3 gcat1

3h1

3 bar2) 17.12

E1 (J 3 mol1) 27.17 103

ΔST (J 3 K 1

3mol1) 90.96

ΔH T (J 3 mol1) 71.53 103

PF2 (mol 3 gcat1

3h1

3 bar2) 101.33 109

E2 (J 3 mol1) 151.04 103

ΔSB (J 3 K 1

3mol1) 50.88

ΔH B (J 3 mol1) 41.09 103

ΔS X (J 3 K 1

3 mol1

) 9.57ΔH X (J 3 mol

1) 115.33

ΔSTMB (J 3 K 1

3mol1) 143.13

ΔH TMB (J 3 mol1) 98.69 103


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model is a necessary simplication of reality. Thus, the proposi-tion of kinetic models is almost always the result of arbitrary assumptions, so that thermodynamic consistency can eventually constitute a numerical trick of the kinetic formalism, especially when it can be corrected with the help of numerical techniques attheexpense of thequality of themodelt.Inthissense,onecouldalways argue that the quality of model tting is more importantthan the thermodynamic consistency of estimated parameters if the extensive investigation of the experimental region has beencarried out. This point of view is adopted in this work. Therefore,the proposed modeling procedure privileges the model t andthe regression analysis of the model parameters. In fact, excellentagreement is reached between model predictions and the experi-mental data, as shown in Figure 4 in wide ranges of toluene and

xylenes conversions. One can also observe that systematicdeviations and outliers cannot be identied in Figure 4, asassumed in Section 2.

It must be clear, though, that thermodynamic consistency should be expected in exact phenomenological kinetic models, which are rarely available, especially when the reaction mechan-isms are complex. If thermodynamic consistency is not obtainedfor a given kinetics, either the model hypotheses are not adequate(reaction network, choice of the rate determining step, etc.) or theadopted adsorption theory is not the most appropriate. In suchcase, other models might be tested by the analyst, if the analyst isnot satised with the obtained model performance, although itcannot be guaranteed that thermodynamic consistency will be

eventually obtained for all estimated model parameters whensimple reaction mechanisms and usual adsorption models areproposed.

The results presented so far illustrate typical problems of

kinetic studies related to the precise estimation of the modelparameters. Moreover, obtained results suggest that the evalua-tion of phenomenological aspects based solely on the parameter values of modelstted to available data should be performed very carefully. Thermodynamic inconsistency strongly suggests thatthe proposed model is likely to be incorrect, from the phenom-enological point of view; nonetheless, even if all parameters arethermodynamic consistent, this does not guarantee that theproposed model is phenomenologically correct. Actually, if oneis notinterested in the fundamental phenomenological aspects of the proposed model, it seems reasonable to focus primarily onthe predictive capacity of the proposed models.

It can be observed in Table 10 that activation energies reportedin the literature lie in the range between 43 and 118 kJ/mol, while

the value obtained in the present work is close to 27 kJ/mol.However, for complex models, such as the LHHW model usedhere, parameter estimates are correlated to each other, makingcomparison with previously published material questionable, asextensively discussed by Pinto et al.38 Even when very simplemodels are compared to each other, diff erent parameter values can be found, depending on the analyzed experimental range andoperation conditions. For example, Gnep and Guisnet11 foundthat the kinetics of disproportionation depended strongly on thecatalyst type and on its pretreatment. Particularly,it was found thatthe reaction order decreased with the wet-air or dry-air pretreat-mentof the mordenite catalyst prepared from uorinated alumina,making the interpretation of kinetic orders doubtful.

Figure 3. Ratio between model parameters at the maximum tempera-ture of 431 C and the minimum temperature of 360 C.

Figure 4. Experimental output molar fractions for (A) toluene feed and(B) xylenes feed.

Figure 2. Determinant of covariance matrix of parameter uncertaintiesas function of the number of designed experiments (for T = 431 C, therst design experiment was 18).

http://pubs.acs.org/action/showImage?doi=10.1021/ie2015526&iName=master.img-003.jpg&w=178&h=123http://pubs.acs.org/action/showImage?doi=10.1021/ie2015526&iName=master.img-002.png&w=171&h=285http://pubs.acs.org/action/showImage?doi=10.1021/ie2015526&iName=master.img-001.png&w=168&h=143


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It is important to emphasize that reparametrization makes theestimation of model parameters easier, since the correlations between parameters can be signicantly reduced (andsometimesremoved). However, reparameterization does not lead to im-provement of model predictions, as the model remains essen-tially the same. Despite that, reparameterization is appealing fornumerical and statistical reasons.3133 In fact, in some cases

accurate matrix inversions demanded by the parameter estima-tion procedure is feasible only when the reparametrization isperformed. Particularly, pre-exponential factors and activationsenergies of the Arrhenius equation are correlated strongly,demanding reparametrization for achievement of good param-eter estimation.3133 In the present problem, the estimationof model parameters without reprarametrization was not possible, so that it was not possible to determine the standarddeviation of the original model parameters, such as the activationenergy and pre-exponential factors presented in Table 9. Thealternative technique of error propagation could be used but

Table 10. Activation Energies for TolueneDisproportionation

ref activation energy (kJ/mol)

this work 27.17

(3) 88.00

(4) 118.71

(5) 64.79(7) 60.61

(8) 104.50

(9) 102.00

(10) 54.22

(12) 84.85

(13) 117.04

(14) 43.47

(19) 99.00

(20) 87.78

Figure 5. Experimental (symbols) and simulated (line) toluene conversions with feed of toluene+H2 at (A) 30 bar as a function of spatial

time τ for several temperatures.

Figure 6. Experimental (symbols) and simulated (line) toluene conversions with feed of toluene+benzene+H2 at 30 bar as a function of spatial time τ for several temperatures. (For T = 431, yT = 0.5, and y BZ =0.5 and for other temperatures yT = 0.6 and y BZ = 0.4).

Figure 7. Experimental (symbols) and simulated (line) toluene conversions with feed of toluene+H2 at 10 bar as a function of spatial time τ for several temperatures.

Figure 8. Experimental (symbols) and simulated (line) toluene conversions with feed of toluene+H2 at 5 bar as a function of spatial time τ for several temperatures.

Figure 9. Experimental (symbols) and simulated (line) conversions at

431

C with feed of toluene+H2 at several pressures.

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would lead to unrealistic estimation of parameter uncertainties,since the original nonlinear transformations in eq 11 must belinearized when error propagation is performed. For this reason,it is difficult to compare the data presented in Table 10 based onrigorous statistical grounds.

Figures 58 show toluene conversions as functions of thespatial time at diff erent temperatures and pressures. As shown inFigures 58, the increase of temperature signicantly increasestoluene conversions in all the investigated experimental condi-tions. A comparison between Figures 5 and6 forsimilar pressuresand temperatures reveals that the presence of benzene reducesthe conversion of toluene very signicantly. According to eq 9,the increase of the partial benzene pressure leads to reduction of the reaction rates because of both the adsorption term in the

denominator and the thermodynamic equilibrium term in thenumerator. According to Figure 6, theinuence of temperature ismuch less pronounced when benzene is present in the feed.Particularly, when temperatures are in the range between 404and 431 C, toluene conversions are essentially constant becauseof the higher amounts of benzene in the feed in the experimentperformed at 431 C.

The inuence of pressure on toluene conversions can be visualized in Figure 9, where the toluene conversions at 431 Care presented as functions of the spatial time at diff erentpressures. Figure 9 clearly shows that the increase of the pressureleads to signicant increase of toluene conversions. As observedin Figure 9, with the increase of reaction pressure, the sensitivity

of toluene conversions with respect to pressure decreases. Thiscan be explained in terms of eqs 9 and 10, as reaction ratesincrease with the square of the system pressure when the partial

pressures are close to zero and are insensitive to pressure changes when the partial pressures grow to innity. Similar results areobserved in Figures 58.

Similarly, Figures 1012 present xylenes conversions forexperiments carried out with pure xylenes in the feed. As onecanobserve in Figures 1012,theeff ectsof operation conditionson xylenes disproportionation are very similar to the eff ectsobserved for toluene disproportionation over H-mordenite. Thecomparison between Figures 5 and 10, Figures 7 and 11, andFigures 8 and 12 indicates that the rates of xylenes disproportio-nation are always higher than the rates of toluene disproportio-nation for similar experimental conditions. This can only beexplained in terms of the parameter values in the investigatedexperimental ranges, given the relative complexity of the kinetic

rate expressions and the thermodynamic reversibility of thereactions. A possible mechanistic explanation can be related toa simple statistical eff ect, as xylene molecules present two methylgroups available for disproportionation, while toluene moleculespresent only one methyl group. A second eff ect can be related tothe well-known electron-donor eff ect of methyl groups, whichcan lead to more eff ective adsorption of xylene molecules ontothe catalyst.

Based on the available experimental results, it is possible toperform sensitivity analyses regarding the inuence of theanalyzed experimental conditions on the conversion of tolueneand/or xylenes in specied experimental regions. For instance, when Figures 5 and 9 are compared, an increase of 10 bar hasapproximately the same impact on toluene conversion as an

increase of 50 C, at the contact time of 0.3 (h 3 gcat/g Aromatic).However, it is important to emphasize that the sensitivity toexperimental conditions change in the analyzed experimentalrange. Forthis reason, thekinetic rate expressions obtained in thepresent work can be used in the near future for more involvingoptimization and sensitivity analysis studies.

As shown in Figures 412, excellent model ts to experi-mental data can be obtained in all cases. Therefore, the modelpresented here can be used successfully for representation of obtained experimental data in the investigated operation range.Therefore, the model can be used with condence for simulation,process design, process control, and interpretation of industrialand laboratorial reactors.

Figure 10. Experimental (symbols) and simulated (line) conversions asa function of spatial time τ forseveral temperaturesat 30 bar with feed of

xylenes+H2.

Figure 11. Experimental (symbols) and simulated (line) conversions asa function of spatial time τ forseveral temperaturesat 10 bar with feed of

xylenes+H2.

Figure 12. Experimental (symbols) and simulated (line)conversions asa function of spatial time τ for several temperatures at 5 bar with feed of

xylenes+H2.

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4. CONCLUSIONS

The kinetics of toluene and xylenes disproportionation over acommercial H-mordenite catalyst has been investigated with thehelp of sequential experimental design procedures in a widerange of operation conditions. The inuence of reaction tem-perature, reactor pressure, feed composition, and residence timeon conversion of reactants and product selectivity was investi-

gated. Experiments were performed according to a sequentialexperimental design strategy, in order to provide maximumaccuracy for model predictions. Statistical treatment of param-eter estimates and model adequacy was performed with thehelp of maximum likelihood principles. Excellent agreement between model predictions and available experimental data wasobtained in the full ranges of investigated experimental condi-tions, although thermodynamic consistency of parameter esti-mates was not observed in some cases.

’AUTHOR INFORMATION

Corresponding Author

*Phone: 55-21-25628337. Fax: 55-21-25628300. E-mail: [email protected].

’ACKNOWLEDGMENT

The authors thank CNPq Conselho Nacional de Desen- volvimento Cientíco e Tecnologico, CAPES Coordenac-~ao de Aperfeic-oamento de Pessoal de Nível Superior, and FAPERJ Fundac-~ao Carlos Chagas Filho de Apoio a Pesquisa do Estado doRiode Janeiro, forprovidingscholarships andsupporting this work.

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