Number of Actives Sites in TAME Synthesis: Mechanism and Kinetic

number of active sites involved in TAME synthesis was also investigated by using a ... mechanism is the most adequate for the description of the TAME ...
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Ind. Eng. Chem. Res. 2004, 43, 5156-5165

Number of Actives Sites in TAME Synthesis: Mechanism and Kinetic Modeling Manuela V. Ferreira† and Jose´ M. Loureiro* Laboratory of Separation and Reaction Engineering, Department of Chemical Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

The kinetics and thermodynamic equilibrium of tert-amyl methyl ether (TAME) liquid-phase synthesis from the reactions between methanol and the isoamylenes 2-methyl-1-butene (2M1B) and 2-methyl-2-butene (2M2B) were studied in a batch reactor in the temperature range 324362 K at 10 bar using Amberlyst 15Wet as catalyst. A kinetic model based on a LangmuirHinshelwood-type mechanism was developed assuming methanol as the most abundant surface species. To ensure model applicability for a large range of species activities, the fraction of vacant sites was not neglected. The reaction rates were written in terms of activities, and the liquidphase activity coefficients were calculated by the modified UNIFAC method of Dortmund. The number of active sites involved in TAME synthesis was also investigated by using a partially deactivated catalyst. The results showed that the etherification reaction rates are proportional to the square of the concentration of active sites of the catalyst, i.e., there are two active sites involved in each etherification reaction, which indicates that a two-site Langmuir-Hinshelwood mechanism is the most adequate for the description of the TAME catalytic synthesis in the liquid phase. 1. Introduction To reduce hydrocarbon (HC), carbon monoxide (CO), and nitrogen oxide (NOx) emissions, catalytic converters were introduced into automobile exhaust systems, and a new type of gasoline, without lead, was needed. A new challenge was faced by refineries: remove lead, reduce the aromatics content, and respond to the growing demands for higher-octane gasoline. Oxygenated additives, such as MTBE (methyl tert-butyl ether), ETBE (ethyl tert-butyl ether), and TAME (tert-amyl methyl ether), were found to be good substitutes for the aromatics, both in accomplishing the desired octane levels and in reducing the HC and CO emissions. Up to a few years ago, the oxygenate market was dominated by MTBE, but the increasing constraints on gasoline volatility led to the introduction of less volatile branched ethers, such as TAME.1 The recent problems related to MTBE detection in groundwater, which led to a ban on MTBE in California and other states in the U.S., contributed also to the growing interest in TAME production as it is less water-soluble than MTBE. TAME is catalytically produced in the liquid phase by the reaction of methanol (MeOH) with the isoamylenes 2-methyl-1-butene (2M1B) and 2-methyl-2-butene (2M2B) over an acidic macroreticular ion-exchange resin. Its synthesis involves three simultaneous reversible reactions - two etherifications and the isomerization between the isoamylenes

2M1B + MeOH h TAME

(1)

2M2B + MeOH h TAME

(2)

2M1B h 2M2B

(3)

In the establishment of the mechanism for catalytic synthesis, one key issue is the number of active sites * To whom correspondence should be addressed. Fax: +351 225081674. E-mail: [email protected]. † Present address: ESTG-IPVC, Av. do Atla ˆ ntico, Apartado 574, 4900 Viana do Castelo, Portugal.

involved in the reactions. Because it is known that, for an ion-exchange resin, the adsorption of polar compounds is considerably stronger than the adsorption of less polar compounds,2 in TAME synthesis, methanol is much more adsorbed than the others relatively nonpolar components, and each methanol molecule will occupy an active site of the catalyst. Thus, there seem to be essentially two options for TAME synthesis mechanisms: (i) the involvement of only one active site in each etherification reaction, i.e., an adsorbed methanol molecule reacts with an isoamylene molecule from the liquid-bulk phase, following a Rideal-Eley (RE) type of mechanism, or (ii) the involvement of two active sites in each etherification reaction, i.e., both methanol and isoamylenes molecules are adsorbed, following a Langmuir-Hinshelwood (LH) type of mechanism. In both mechanisms, TAME is also adsorbed. The different steps of each mechanism are represented in Scheme 1. Several works have been published regarding the liquid-phase synthesis of TAME and other tertiary ethers. In some of them, RE-type mechanisms are proposed;3-5 in others, the choice is the LH mechanism.6-10 So far, in most of the works published, the mechanism proposed (i) is based on some assumptions (e.g., adsorption of all or only some components), (ii) is based on literature information (e.g., adsorption studies11,12), or (iii) is the one that provides the reaction rate expressions that give the best fit to the experimental data. The major objective of the present work was to obtain some experimental evidence for the most probable mechanism for TAME catalytic synthesis. Experimental results with a partially deactivated catalyst were used to clarify the number of active sites involved in each etherification reaction and, thereby, to discriminate between the RE and LH mechanisms. No similar reaction data, i.e., obtained in heterogeneous catalysis with the same catalyst, were found in the open literature.

10.1021/ie0308801 CCC: $27.50 © 2004 American Chemical Society Published on Web 07/22/2004

Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5157 Scheme 1. Reaction Steps in TAME Synthesis for Rideal-Eley and Langmuir-Hinshelwood Mechanismsa

a S represents a catalyst vacant site and 2M1B‚S , 2M2B‚S , a a a MeOH‚Sa, and TAME‚Sa represent 2M1B, 2M2B, methanol, and TAME molecules adsorbed on one active site of the catalyst.

Figure 1. Experimental setup. BR, batch reactor; M, motor; TT, thermocouple; PT, pressure transducer; TB, thermostatic bath; V1, sampling valve; V2, injection valve (loop filling position); WT, vacuum vent; GC, gas chromatograph; FID, flame ionization detector.

2. Experimental Section The influence on the TAME synthesis reaction kinetics of several operating variablessstirring speed (400 and 600 rpm), particle diameter (0.125-1.180 mm, wet form), mass of dry catalyst (3.0-9.5 g), initial molar ratio of reactants (0.5, 1.0 and 2.0), temperature (324362 K), and pressure (8.05-10.58 bar)swas studied. Experiments to determine the equilibrium were performed in the same temperature range for different initial molar ratio of reactants (0.5, 1.0, and 2.0) at 10 bar. A particular experiment with a 20% deactivated catalyst was also performed. It was carried out at 353.6 K and 10 bar with an initial molar methanol/isoamylenes ratio of 1.0 and with 7.1 g of dry catalyst. In all experiments, a reaction volume of 600 mL was used. Apparatus. The experiments were carried out in an experimental setup with a batch reactor and automatic, on-line acquisition of concentrations, pressure, and temperature13 (Figure 1). The reactor was a glassjacketed 1-dm3 autoclave (Bu¨chi BEP280, Uster, Swit-

zerland), mechanically stirred and equipped with temperature and pressure sensors. The temperature was controlled by thermostated water (Lauda Ecoline RE104, Ko¨nigshofen, Germany) that flows through the reactor’s cover and jacket. To maintain the reaction mixture in the liquid phase over the whole temperature range, the reactor was pressurized with helium. The stirrer shaft was set in motion by a three-phase motor. The catalyst was placed in a basket at the top of that stirrer shaft, and at the beginning of the agitation, the basket fell into the reaction mixture, and the experiment started (time zero). One of the reactor’s outlets was directly connected to the three-way sampling valve (Valco C3WE, Houston, TX), and when the six-way injection valve (Valco CI4WE.1) was in the injection position, 0.1 µL of pressurized sample was injected into the gas chromatograph. Analysis. The samples were analyzed on a gas chromatograph (Chrompack CP9003, Middelburg, The Netherlands) equipped with a flame ionization detector. The compounds were separated in a nonpolar capillary column with 50-m length, 0.20-mm inner diameter, and 0.5-µm film thickness (Hewlett-Packard HP-PONA, Palo Alto, CA). Helium was used as the carrier gas (1 mL/ min) and the column, injector, and detector temperatures were set at 35, 150, and 200 °C, respectively. Response factors were determined with calibration solutions. Chemicals. The reactor was fed with methanol (>99.8 wt %, Riedel-de-Hae¨n, Seelze, Germany) and a C5 cut obtained by the distillation of cracking gasoline (Sines Refinery, Petrogal S.A., Sines, Portugal). Its composition was determined by GC analysis: 10.43 wt % of 2M1B, 17.66 wt % of 2M2B, 39.24 wt % of isopentane, and 32.67 wt % of other inert C5 compounds. For calibration solutions, 2M1B (>97 wt %, Fluka), 2M2B for synthesis (85 wt % 2M2B and 15 wt % 2M1B, Merck), methanol (>99.8 wt %, Riedel-de-Hae¨n), TAME (>97 wt %, Fluka), and isopentane (>99 wt %, Riedelde-Hae¨n) were used. Catalyst. A commercial macroreticular strong cation ion-exchange resin in hydrogen form (Amberlyst 15 Wet, Rohm & Haas) was used as the catalyst. According to the supplier, the ion-exchange capacity is g4.7 mequiv/g of dry resin, and its surface area is 45 m2/g. The catalyst was sieved in four size groups: 0.707-1.180, 0.6000.707, 0.500-0.600, and 0.125-0.500 mm (wet form). Prior to the experiments, it was treated with methanol and then dried at 60 °C. Partially Deactivated Catalyst Experiment. The concentration of active sites of the catalyst was first determined by titration with a standard 0.5 M sodium hydroxide solution until complete neutralization of all active sites. Then, 20% of the active sites of a fresh sample were neutralized by addition of the corresponding volume of 0.5 M NaOH solution on the basis of the concentration of active sites determined previously. Part of that catalyst was again titrated until complete neutralization, and the degree of deactivation was confirmed. 3. Results and Discussion Thermodynamic Equilibrium. The high difference in polarity between methanol and the other components makes the reaction mixture highly nonideal, so the equilibrium constants must be evaluated in terms of activities and not concentrations. This nonideality is

5158 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 Table 1. Experimental Equilibrium Data and Calculated Activity Coefficients and Equilibrium Constants Based on Molar Fractions and Activities for TAME Liquid-Phase Synthesis equilibrium molar fractions

modified UNIFAC

modified UNIFAC

RM/IA

T (K)

1B

2B

M

T

γ1B

γ2B

γM

γT

Kx1

Kx2

Kx3

Keq1

Keq2

Keq3

1.0 0.5 1.0 0.5 2.0 1.0 1.0 0.5 1.0 2.0 0.5

324.6 325.2 343.4 344.2 344.6 352.6 352.6 353.2 358.6 362.2 363.0

0.004 0.009 0.007 0.012 0.004 0.009 0.008 0.014 0.009 0.006 0.017

0.070 0.147 0.096 0.155 0.056 0.111 0.105 0.163 0.111 0.076 0.169

0.062 0.010 0.084 0.021 0.261 0.090 0.102 0.028 0.109 0.280 0.037

0.198 0.129 0.163 0.115 0.155 0.148 0.146 0.104 0.138 0.127 0.093

1.076 1.038 1.082 1.039 1.298 1.081 1.090 1.040 1.093 1.302 1.042

1.059 1.020 1.066 1.022 1.283 1.065 1.074 1.023 1.077 1.287 1.025

7.223 11.524 6.196 9.627 3.026 5.918 5.620 8.910 5.369 2.839 8.149

1.083 1.203 1.060 1.172 0.983 1.054 1.044 1.159 1.037 0.975 1.141

720.34 1305.20 271.89 435.25 142.41 174.33 169.24 271.68 135.25 72.30 148.70

45.76 83.59 20.09 34.75 10.63 14.66 13.70 22.72 11.34 6.00 14.78

15.74 15.61 13.54 12.53 13.40 11.89 12.35 11.96 11.93 12.04 10.06

82.28 76.26 37.67 34.33 38.44 25.65 26.32 24.37 22.20 20.61 15.37

5.19 4.88 2.76 2.73 2.83 2.14 2.11 2.03 1.84 1.69 1.52

15.84 15.61 13.65 12.56 13.57 12.00 12.47 12.00 12.05 12.22 10.11

shown by the values of the equilibrium constants based on molar fractions, Kx, and the values of the liquid-phase activity coefficients, γ, that largely differ from unity for methanol (Table 1). The thermodynamic equilibrium constant for reaction j based on activities, Keqj, is defined as N

Keqj )

(xei γi) ∏ i)1

νij

) KxjKγj

(4)

where xei is the equilibrium molar fraction of component i, N is the number of components, νji is the stoichiometric coefficient of component i in reaction j, and Kγj is the equilibrium constant based on activity coefficients. Table 1 shows the experimental conditionss the initial molar ratio of reactants, RM/IA; the temperature, T; and the average equilibrium composition at each temperaturesthe liquid-phase activity coefficients calculated by the modified UNIFAC method of Dortmund,14 and the equilibrium constants based on molar fractions and activities. All inert compounds present in the reaction mixture were grouped as a pseudocompound, represented by isopentane because it comprises 55% of the inerts. The values in Table 1 show that TAME synthesis from 2M2B is less favorable than its synthesis from 2M1B, as Keq2 is lower than Keq1. This fact might be related to the thermodynamic stabilities of the isoamylenes. The relative stability of an olefin is determined by the number of alkyl groups bonded to the carbon atoms with double bonds, with olefins being more stable as that number increases.15 As 2M2B has three alkyl groups bonded to carbon atoms with double bonds whereas 2M1B has only two, 2M2B should be more stable than its reactive isomer. Another conclusion that can be taken from the values of Table 1 is concerned with the isomerization reaction equilibrium constant: it is almost independent of temperature. The temperature dependence of the equilibrium constants can be expressed by the following equation16

ln Keqj )

∆S0j ∆H0j 1 R R T

(5)

A plot of ln Keqj versus 1/T should give a straight line (Figure 2). The liquid-phase standard enthalpy change of reaction, ∆H0j , and standard entropy change of reaction, ∆S0j , are obtained from the slope and intercept, respectively (Table 2). The values obtained in this work agree with others published in the literature.17-21

Figure 2. ln Keq versus 1/T and linear fitting (0, reaction 1; 4, reaction 2; O, reaction 3). Table 2. Liquid-Phase Standard Enthalpy Changes of Reaction and Standard Entropy Changes of Reaction Obtained from Experimental Data (95% Confidence Intervals) reaction 1 reaction 2 reaction 3

∆H0 (kJ‚mol-1)

∆S0 (J‚mol-1‚K-1)

-38.5 ( 4.0 -29.7 ( 1.6 -8.8 ( 2.7

-82.1 ( 11.6 -78.0 ( 4.7 -4.1 ( 7.8

The following equations were thus obtained for the two etherification reactions (for isomerization, ln Keq3 ) ln Keq1 - ln Keq2)

ln Keq1 )

4.63 × 103 - 9.875 T(K)

(6)

ln Keq2 )

3.57 × 103 - 9.382 T(K)

(7)

The temperature dependence of Keq can be predicted from thermodynamic data by integration of the van’t Hoff equation.16 It is known that the accuracy of equilibrium constants calculated from thermodynamic information is highly sensitive to the quality of data, especially for reactions with moderate standard Gibbs free energy changes, as is the case for reversible reactions. As a result of the lack of information on thermodynamic formation properties for TAME (and the lack of agreement between sources), the experimental data obtained in this work were used to determine the standard enthalpy and Gibbs free energy changes of reaction at 298.15 K, as described elsewhere,21 and along with heat capacity data, expressions 8 and 9 were obtained for the thermodynamic prediction of the etherification equilibrium constants. A good agreement was

Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5159

Figure 3. Effect of initial molar ratio of reactants and temperature on the initial rate of TAME formation (4, 323 K; 0, 343 K; O, 353 K; ×, 363 K).

obtained between the thermodynamic prediction and the experimental data.

ln Keq1 ) 1.190 × 103 - 25.801 ln[T(K)] + T(K) 7.599 × 10-2T(K) - 4.377 × 10-5[T(K)]2 (8)

1.299 × 102 +

ln Keq2 ) 2.916 × 102 - 24.942 ln[T(K)] + T(K) 7.356 × 10-2T(K) - 4.192 × 10-5[T(K)]2 (9)

1.255 × 102 +

Effect of Operating Variables on Reaction Kinetics. Preliminary experiments were performed to study the effect of external diffusion of reactants to the catalyst surface by varying the stirring speed. Two experiments were performed, one at 400 rpm and another at 600 rpm. Although a stirring speed of 400 rpm seemed sufficient to eliminate the external resistance, 600 rpm were used in all further experiments. The next step was the investigation of internal diffusion. Experiments were performed under the same conditions, varying only the particle size fraction used. Because no significant effect was observed, the catalyst seems to work in the chemical regime for particles with diameters lower than 1.180 mm, so it can be used unsieved. Another variable studied was the initial molar ratio of reactants, RM/IA, along with temperature. Sets of experiments were performed by keeping constant, in each set, temperature, pressure and mass of catalyst and using three different values of RM/IA: 0.5, 1.0, and 2.0 (values lower than 0.5 and larger than 2.0 were not used because of the detection limitations in the GC analysis for methanol and 2M1B). The temperatures tested were 323, 343, 353, and 363 K. No experiment with RM/IA ) 2.0 at 323 K was performed because it would have been extremely long. As an example, Figure 3 shows the effect of initial molar ratio of reactants and temperature on the initial rate (conversion < 5%), r0, of TAME formation: it decreases as RM/IA increases from 0.5 to 2.0. Whereas a similar behavior was observed for the initial rate of 2M1B disappearance, for 2M2B, the opposite happened: its initial rate of disappearance showed an increasing tendency as RM/IA increased. It is also important to notice that the initial rates of 2M2B

Figure 4. Effect of temperature and initial molar ratio of reactants on the TAME mass fraction at equilibrium (0, RM/IA ) 0.5; O, RM/IA ) 1.0; 4, RM/IA ) 2.0).

disappearance were the lowest, approximately 1 order of magnitude lower than those of the other components. The higher reactivity of 2M1B relative to its reactive isomer can be explained by the localization of the double bonds.15 As shown in Figure 3, the initial reaction rate of TAME formation increases with temperature, but because of the exothermic nature of the reactions, as equilibrium is reached, the conversion of reactants and the production of TAME decrease (Figure 4), so a compromise exists between reaction rates and TAME production. TAME production increases with RM/IA, as shown in Figure 4, but because the TAME mass fractions at equilibrium for RM/IA values of 1.0 and 2.0 are almost the same, it seems that, from the TAME production point of view, the optimum methanol/isoamylenes ratio in the feed should be close to stoichiometric. In addition to limiting the side products formation favored by methanol high concentrations (e.g., dimethyl ether), a stoichiometric ratio also decreases the recovery and recycling costs of unreacted methanol. For the experiments with RM/IA ) 0.5, a different behavior was observed for concentration histories: they followed an almost linear tendency until equilibrium was reached (similar to the observed with a zeroth-order kinetics), and then, the reactions stopped, and no further concentration changes were observed. This behavior is more evident for low temperatures (Figure 5). No side products were detected in the ranges of feed conditions and temperature tested in this work. Pressure was varied between 8 and 10.6 bar, keeping all other operating conditions, and no variations were observed in the reaction kinetics. Once a sufficient pressure that guarantees liquid phase is used, this variable does not affect the reaction rates. Kinetic Modeling. The model developed is based on a Langmuir-Hinshelwood mechanism, shown in Scheme 1, with competitive adsorption on the same active sites. Surface reactions are assumed to be the controlling steps, with the other steps remaining in equilibrium. Because the reaction mixture is highly nonideal, rate expressions must be written in terms of activities of components, ai. Multicomponent Langmuir adsorption isotherms, also written in terms of activities,22 are assumed for the description of the adsorption equilibrium. Assuming that inert species present in the reac-

5160 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004

Figure 5. Influence of initial molar ratio of reactants on the shape of the TAME concentration history (0, RM/IA ) 0.5; O, RM/IA ) 1.0).

tion mixture are not adsorbed on the catalyst, the following rate expressions are obtained

(

B k 1KMK1B r1 )

(1 + K1Ba1B + K2Ba2B + KMaM + KTaT)2

(

B k 3KMK2B aMa2B r2 )

)

aT aMa1B Keq1

)

aT Keq2

(1 + K1Ba1B + K2Ba2B + KMaM + KTaT)2

(

)

a2B Keq3 r3 ) 1 + K1Ba1B + K2Ba2B + KMaM + KTaT B k 5K1B a1B -

(10)

(11)

(12)

where KM, K1B, K2B, and KT are the adsorption equilibrium constants of methanol, 2M1B, 2M2B, and TAME, k3, and B k5 are the kinetic constants respectively, and B k1, B for the etherification and isomerization surface reactions in the forward direction. Considering an Arrhenius-type expression for the temperature dependence of the kinetic and adsorption equilibrium constants, as presented in eqs 10-12, the model has 14 parameters: 6 due to kinetics (3 preexponential factors, k0,j, and 3 activation energies, Eact,j) and 8 due to adsorption (4 preexponential factors, K0,i, and 4 heats of adsorption, ∆Hads i ). Because it is not possible to determine the parameters independently with the experimental kinetic data available (reaction and adsorption occur simultaneously) and because there are many combinations for the 14 parameters that lead to objective function local minima, the step-by-step procedure described below was adopted to simplify the model. The rate equations and parameter and objective function values obtained in each step are summarized in Table 3. Step 1. Methanol adsorption was assumed to be much stronger than that of the other components, and the fraction of vacant sites was taken as negligible. These assumptions led to model 1. Lumping kinetic and adsorption equilibrium constants into apparent kinetic constants, kap,j, the number of model parameters was reduced to six. Step 2. Values of kap,j were first estimated directly from the experimental data on the initial rates of

reactions, using the results of 10 experiments at different temperatures (323-361 K) and the initial molar ratio of reactants (0.5-2.0). Apparent preexponential factors, k0ap,j, and activation energies, Eap,j, were obtained by fitting these values to an Arrhenius-type law. Several experiments were simulated with these parameters values, and the calculated curves followed the experimental points reasonably well. Step 3. To improve the fitting, new parameters values were obtained by minimizing the sum of the squared differences between the calculated and experimental mass fraction values for each component, fobj (eq 13), using a multivariable optimization technique with adaptive random search.23 Eleven experiments (371 experimental points) were used, restricted search intervals were imposed, and the initial estimates were the values obtained in step 2.

fobj )

2 exp ∑j ∑i ∑k [xcalc m (j,i,k) - xm (j,i,k)]

(13)

Although model 1 is able to describe TAME synthesis very reasonably, at least for the experimental conditions studied, it has an inconsistency: when the methanol activity is zero, or very close to zero, the initial etherification reaction rates tend to infinity (see eqs 14-16 in Table 3) and not to zero as they should. This is due to one of the assumptions behind model 1: that the fraction of vacant sites is negligible. Thus, to have a kinetic model that is valid for a wider range of conditions, a new step was taken: Step 4. Keep the assumption of stronger methanol adsorption, but do not neglect the fraction of vacant sites. This led to model 2. Step 5. Using the (kinetic) parameters values obtained in step 3, there is only one variable to determine: KM. As for the apparent kinetic constants, KM was first estimated from the experimental initial rates of TAME formation. The methanol heat of adsorption, ∆Hads M , and the preexponential factor of its adsorption equilibrium constant, K0,M, were obtained by fitting these values to an Arrhenius-type law. Simulating the same 11 experiments with model 2, the value obtained for fobj was higher than the one obtained for model 1 after optimization (step 3). Step 6. Fixing the kinetic parameter values obtained in step 3, a two-parameter optimization was performed in order to obtain better estimates for ∆Hads M and K0,M. In this optimization, the values obtained in step 5 were used as initial estimates and restricted search intervals were imposed. Step 7: Final Step. To improve the fitting with model 2, an eight-parameter optimization (three apparent activation energies, three apparent kinetic preexponential factors, methanol heat of adsorption, and preexponential factor of its adsorption equilibrium constant) was performed imposing a search interval of only (10% for each parameter and using as initial estimates the values previously obtained in the optimizations with models 1 and 2. A comparison between simulations using models 1 and 2 is made in Figure 6. As shown, and as expected given that the values of the objective function are very close, the results obtained with the two models are very similar and equally satisfactory. As mentioned before, the advantage of model 2 over model 1 is the fact that the first is applicable for a wider

Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5161 Table 3. Rate Equations for Models 1 and 2 and Parameter and Objective Function Values Obtained in Each Step of the Approach Adopted in the Kinetic Modeling Rate Equations

r1 ) kap,1

r2 ) kap,2

r3 ) kap,3

( (

model 1

a1B 1 aT aM K a2 eq1 M a2B 1 aT aM K a2 eq2 M

(

) )

)

a1B 1 a2B aM Keq3 aM

model 2 2

(14)

r1 )

(15)

r2 )

(16)

r3 )

kap,1KM

2

(1 + KMaM) kap,2KM2

2

(1 + KMaM)

( (

aMa1B -

aT Keq1

aMa2B -

aT Keq2

(

kap,3KM a2B a 1 + KMaM 1B Keq3

) )

)

(17)

(18)

(19)

Parameters k0ap,1b (mol‚g-1‚h-1) k0ap,2c (mol‚g-1‚h-1) k0ap,3d (mol‚g-1‚h-1) Eap,1 (kJ‚mol-1) Eap,2 (kJ‚mol-1) Eap,3 (kJ‚mol-1) -1 ∆Hads M (kJ‚mol ) K0,M fobj a

step 2

step 3

step 5a

step 6a

step 7

4.68 × 1017 2.02 × 1012 3.38 × 1011 123.90 87.60 81.14 nae na 5.02 × 10-2

2.35 × 1015 1.02 × 1013 4.93 × 1011 106.76 92.72 82.17 na na 2.18 × 10-2

-31.4 6.21 × 10-4 3.24 × 10-2

-18.87 9.01 × 10-2 2.47 × 10-2

2.53 × 1015 9.50 × 1012 5.42× 1011 106.47 92.45 82.43 -17.00 8.34 × 10-2 2.14 × 10-2

k0ap,j and Eap,j fixed at the values obtained in step 3. b kap,1 ) B k1K1B/KM. c kap,2 ) B k3K2B/KM.

d

kap,3 ) B k5 K1B/KM. e na ) not applicable.

Figure 6. Experimental and simulated results according to model 1 (a, b, c) and to model 2 (a′, b′, c′) using optimized parameters. Experimental conditions: (a, a′) T ) 323 K, RM/IA ) 1.0; (b, b′) T ) 343 K, RM/IA ) 0.5; (c, c′) T ) 353 K, RM/IA ) 2.0.

range of conditions, namely, when the methanol activity is very low. The adequacy of the model in all ranges of concentrations assumes a very important role when

considering TAME production in units where the methanol/isoamylenes ratio in the liquid phase in contact with the catalyst can take many values, as is the case in

5162 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004

Figure 7. Initial rates of etherification predicted by models 1 and 2 as a function of methanol molar fraction, for a feed of pure methanol, 2M1B, and 2M2B, with the isoamylenes in equal quantities.

Figure 8. Methanol activity in the liquid phase as a function of the methanol molar fraction in a mixture of pure methanol, 2M1B, and 2M2B, with the isoamylenes in equal quantities.

reactive distillation units. Figure 7 shows the initial rates of etherification predicted by the two models, for reaction temperatures of 333 and 353 K, as a function of the methanol molar fraction. In this simulation, a feed of pure methanol, 2M1B, and 2M2B was considered, being the isoamylenes in equal quantities. The predictions of the two models are practically coincident for almost all of the concentration range, starting to differ when the methanol molar fraction reaches very low values: whereas the initial rate of etherification for model 2 starts to decrease in that region until it is zero when there is no methanol in the reaction mixture, for model 1, the initial rate approaches infinity and not zero as it should for the sake of consistency given that there is no etherification without methanol. The models differ only for very low methanol molar fractions because, even for that situation, the methanol activity remains very high, as shown in Figure 8. To assess whether the obtained kinetic and adsorption parameters calculated in step 7 are within the range of published results, a comparison is made in the following discussion. The value obtained for the heat of adsorption of methanol (∆Hads M ) -17 kJ/mol, Table 3) is relatively close to the value of -10 kJ/mol estimated by Rehfinger and Hoffmann6 over the commercial resin A15. The apparent activation energies obtained are related to the “true” activation energies by the following expressions

ads Eap,1 ) Eact,1 + ∆Hads 1B - ∆HM

(20)

ads Eap,2 ) Eact,3 + ∆Hads 2B - ∆HM

(21)

ads Eap,3 ) Eact,5 + ∆Hads 1B - ∆HM

(22)

To determine the true activation energy values, it is also necessary to know the heat of adsorption of each isoamylene. Oktar et al.11 obtained the values of -37.2 and -26.8 kJ/mol for the heats of adsorption of 2M1B and 2M2B, respectively, in the gas phase. Applying phase-equilibrium thermodynamic principles to adsorption and supposing that the adsorbed phase can be treated as a different phase from the thermodynamic point of view,24 it is possible to determine the heats of adsorption in liquid phase from the gas-phase values and the enthalpies of vaporization of the isoamylenes (25.51 kJ/mol for 2M1B and 26.32 kJ/mol for 2M2B25). Using these data, values of -11.69 and -0.48 kJ/mol ads are obtained for ∆Hads 1B and ∆H2B , respectively, in the liquid phase. Using eqs 20-22 and the values in Table 3, the following values were obtained for the true activation energies: 101.16 kJ/mol for reaction 1, 75.93 kJ/mol for reaction 2, and 77.12 kJ/mol for reaction 3. These values are comparable to the ones published in the literature: Piccoli and Lovisi17 report values of 85.6 and 92.5 kJ/mol for the etherifications of 2M1B and 2M2B, respectively. Kiviranta-Pa¨a¨kko¨nen et al.26 published values of 76.8, 99.7, and 81.7 kJ/mol for reactions 1-3, respectively. In works where the isoamylenes were not treated individually but grouped into a “pseudoisoamylene”, the values of 89.5 kJ/mol (Oost and Hoffmann8) and 81.09 kJ/mol (Randriamahefa et al.27) were reported for the energy of activation of the etherification reaction. More recently, Kiviranta-Pa¨a¨kko¨nen and Krause10 published the values of 101.98, 101.09, and 97.21 kJ/mol for the etherifications of 2M1B and 2M2B and for their isomerization, respectively. Experiment with a Partially Deactivated Catalyst. As previously mentioned, one key step in kinetic modeling is the establishment of the mechanism. The determination of the number of active sites involved in each etherification reaction in TAME synthesis will help in establishing the correct mechanism. Although a mechanism based on the Langmuir-Hinshelwood formalism seems to be the most adequate for TAME synthesis, as the isomerization cannot occur in the absence of catalyst, kinetic models based on a RidealEley mechanism giving good results have also been published. To determine which of these two mechanisms is the most appropriate for TAME synthesis, we decided to determine the number of active sites that are involved in the etherification reactions. For the Rideal-Eley and Langmuir-Hinshelwood mechanisms (see Scheme 1), considering that the surface reactions are the controlling step in both cases, a Hougen-Watson treatment leads to the etherification and isomerization reaction rates listed in Table 4.28 As shown by eqs 23-28, whereas the etherification reaction rates are proportional to the concentration of active sites of the catalyst, L, for the Rideal-Eley mechanism, for the Langmuir-Hinshelwood mechanism, they are proportional to its square. As for the isomerization reaction rate, it does not depend on the concentration of active sites if the Rideal-Eley mechanism is considered, but it is proportional to L in the case of the Langmuir-Hinshelwood mechanism.

Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5163 Table 4. Rate Equations for TAME Synthesis for Rideal-Eley- and Langmuir-Hinshelwood-type Mechanisms mechanism

(

Rideal-Eley

aT k1KM a1BaM Keq1 r1 ) L 1 + KMaM + KTaT

(

aT Keq2 r2 ) L 1 + KMaM + KTaT k2KM a2BaM -

(

r3 ) k3 a1B -

a2B Keq3

)

) )

Langmuir-Hinshelwood (23)

(24)

(25)

(

aT Keq1

)

(

aT Keq2

)

k1K1BKM a1BaM -

r1 ) L2 (1 + K1Ba1B + K2Ba2B + KMaM + KTaT)2 k2K2BKM a2BaM -

r2 ) L2 (1 + K1Ba1B + K2Ba2B + KMaM + KTaT)2

(

)

a2B Keq3 r3 ) L 1 + K1Ba1B + K2Ba2B + KMaM + KTaT k3K1B a1B -

(26)

(27)

(28)

Then, if a partially deactivated catalyst, with a degree of deactivation R, is used and a Rideal-Eley mechanism is considered, the etherification reaction rates should decrease by a factor (1 - R), and the isomerization reaction rate should not be affected. If a LangmuirHinshelwood mechanism is considered, the etherification reaction rates should decrease by (1 - R)2, and the isomerization reaction rate should decrease by (1 - R). This fact can then be used as a way of discriminating between the mechanisms and determining the number of active sites involved in the reactions. An experiment with a 20% deactivated catalyst was performed (see Experimental Section). In the simulation of this experiment, two kinetic models were used. One of the models is based on the Rideal-Eley mechanism and was developed by Kiviranta-Pa¨a¨kko¨nen et al.;26 the

other model is model 2 developed in this work, based on the Langmuir-Hinshelwood mechanism. The model developed by Kiviranta-Pa¨a¨kko¨nen et al.26 is also activity-based, considers the surface reactions as the controlling step, and assumes that the fraction of vacant sites is negligible. Figure 9 shows the results of an experiment where the catalyst used was 100% active and the curves calculated according to the model proposed by KivirantaPa¨a¨kko¨nen et al.26 and model 2. As shown, both models are capable of representing with reasonable accuracy the experimental results when the catalyst is fully active. For the experiment with the 20% deactivated catalyst, according to the Hougen-Watson treatment, in the calculation of the simulated curves the etherification reaction rates (r1 and r2) have to be multiplied by a factor of 0.8 for the case of the model proposed by

Figure 9. Experimental results for TAME mass fraction history using 100% active catalyst and calculated curves: (a) model proposed by Kiviranta-Pa¨a¨kko¨nen et al.,26 (b) model 2 (this work).

Figure 10. Experimental results for TAME mass fraction history using a 20% deactivated catalyst and calculated curves: (a) model proposed by Kiviranta-Pa¨a¨kko¨nen et al.,26 (b) model 2 (this work).

5164 Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004

Kiviranta-Pa¨a¨kko¨nen et al.26 and by a factor of 0.64 when model 2 is used. The isomerization rate remains unchanged for the Kiviranta-Pa¨a¨kko¨nen et al.26 model, but it has to be multiplied by 0.8 for model 2. The experimental results and the simulated curves calculated in this manner are represented in Figure 10. Whereas the curve calculated using model 2 is still able to follow the experimental points with reasonable accuracy, the curve calculated with the KivirantaPa¨a¨kko¨nen et al.26 model is not. This result seems to indicate that there are, in fact, two active sites involved in each etherification reaction and that a LangmuirHinshelwood-type mechanism is the most adequate for TAME synthesis. Moreover, because we verified in our studies that the isomerization reaction takes place only in the presence of catalyst, one of the two catalytic sites involved in the etherifications reactions is certainly due to the adsorption of the isoamylenes. Kogelbauer et al.,29 when studying the homogeneous acid catalytic synthesis of MTBE, attributed the two active sites to the alcohol (methanol), which cannot be the case in the heterogeneous catalytic synthesis of TAME, as then three sites should be involved in the etherifications, contradicting the experimental evidence shown here. 4. Conclusions The values obtained for the thermodynamic equilibrium constants showed that TAME synthesis from 2M1B is more favorable than that from 2M2B, because Keq1 is larger than Keq2, which is related to the higher thermodynamic stability of 2M2B. It was also verified that the isomerization thermodynamic equilibrium constant is almost independent of temperature. From the experimental results and using the modified UNIFAC method of Dortmund14 for predicting the activity coefficients, the values of -38.5, -29.7, and -8.8 kJ/mol were obtained for the enthalpies of the etherification reactions of 2M1B and 2M2B and for the isomerization reaction, respectively. In the kinetic study of the reactions involved in TAME synthesis, temperature and feed composition were found to be the most important variables. Whereas the initial rates of disappearance of 2M1B and methanol and the initial rate of formation of TAME are higher when there is an excess of isoamylenes in the feed, the opposite is verified for 2M2B. As concluded from the equilibrium study, the kinetic experimental results showed that 2M2B is the less reactive isoamylene. Its initial rates of disappearance are about 1 order of magnitude lower than those of 2M1B. From the point of view of TAME production, it is important to balance two variables: the initial rate of formation and production. Whereas the first is favored by feeds with excess of isoamylenes, the TAME equilibrium fraction that is obtained under such conditions is much lower than that obtained with an equimolar feed or with excess methanol in the feed. The optimum feed molar ratio of methanol/isoamylenes seems to be close to stoichiometric. In respect to temperature, it is important to find a compromise between the rates of reaction and conversion: the rates of reactions increase with temperature, but the reactant equilibrium conversion decreases. A temperature between 343 and 353 K seemed to provide a good compromise solution. For modeling TAME synthesis, a mechanism based on the Langmuir-Hinshelwood was chosen.

A step-by-step approach was adopted in the kinetic modeling: the parameter values were first obtained directly from the experimental initial rate data and only then was an optimization performed, using restricted search intervals. The first model developed, based on the assumptions of stronger methanol adsorption and a negligible fraction of vacant sites, was able to simulate satisfactorily experiments with different feed conditions in the temperature range of 323-363 K. The use of the kinetic model in TAME production units where the methanol/isoamylenes ratio in the liquid phase in contact with the catalyst can take many values, as is the case in reactive distillation units, make it very important to have a model that is valid in all ranges of concentrations. Despite the fact that the first model developed is adequate for the conditions of temperature and feed analyzed, it fails for methanol activities close to zero. To obtain a model valid over a wider range of conditions, namely, when the methanol fraction is very low, a new model was developed from the first. In this second model, the assumption of stronger methanol adsorption was kept, but the fraction of vacant sites was not neglected. With this model, the apparent activation energies obtained were 106.47 kJ/ mol (etherification of 2M1B), 92.45 kJ/mol (etherification of 2M1B), and 82.43 kJ/mol (isomerization). A value of -17.00 kJ/mol was obtained for the methanol heat of adsorption. The second model developed was also able to simulate with reasonable accuracy an experiment in which a partially deactivated catalyst was used. With this experiment, it was possible to demonstrate that there are two active sites of the catalyst involved in each etherification reaction, showing that the LangmuirHinshelwood mechanism, with the surface reaction between one adsorbed methanol and one adsorbed isoamylene molecules as the controlling step, is the most adequate for TAME synthesis. This experiment showed also that, although the Rideal-Eley mechanism is able to simulate experiments with 100% active catalysts, it is not adequate for TAME synthesis, as pointed out before based on the fact that this mechanism implies a noncatalytic isomerization reaction. Acknowledgment The authors thank Fundac¸ a˜o para a Cieˆncia e a Tecnologia (FCT) of Portugal for sponsoring M.V.F.’s Ph.D. grant (PRAXIS XXI/BD/18433/98), FEDER for the financial support of this project (POCTI/EQU/41406/ 2001), the Portuguese Petroleum Company (Petrogal, S.A.) for offering cracking gasoline and allowing the use of its facilities to distill it, and Professor Romualdo Salcedo from FEUP for the optimization code. Nomenclature ai ) liquid-phase activity of component i Eact,j ) activation energy of reaction j, J‚mol-1 Eap,j ) apparent activation energy of reaction j, J‚mol-1 fobj ) objective function Keqj ) thermodynamic equilibrium constant of reaction j Kx ) equilibrium constant based on molar fractions Kγj ) equilibrium constant based on activity coefficients Ki ) adsorption equilibrium constant of component i B k ) kinetic constant for reaction in the forward direction, mol‚g-1‚h-1 kap,j ) apparent kinetic constant of reaction j, mol‚g-1‚h-1 k0,j ) kinetic preexponential factor of reaction j, mol‚g-1‚h-1

Ind. Eng. Chem. Res., Vol. 43, No. 17, 2004 5165 k0ap,j ) kinetic apparent preexponential factor of reaction j, mol‚g-1‚h-1 K0,i ) adsorption preexponential factor of component i L ) concentration of active sites on the catalyst, equiv‚g-1 N ) number of components R ) ideal gas constant, J‚mol-1‚K-1 RM/IA ) initial molar ratio of reactants r0 ) initial rate, mol‚g-1‚h-1 rj ) rate of reaction j, mol‚g-1‚h-1 Sa ) catalyst vacant site T ) temperature, K xei ) equilibrium molar fraction of component i Abbreviations 2M1B or 1B ) 2-methyl-1-butene 2M2B or 2B ) 2-methyl-2-butene ETBE ) ethyl tert-butyl ether LH ) Langmuir-Hinshelwood mechanism MeOH or M ) methanol MTBE ) methyl tert-butyl ether RE ) Rideal-Eley mechanism TAME or T ) tert-amyl methyl ether Greek Letters γi ) liquid-phase activity coefficient of component i ∆H0j ) standard enthalpy change of reaction j, J‚mol-1 ∆Hads ) heat of adsorption of component i, J‚mol-1 i 0 ∆Sj ) standard entropy change of reaction j, J‚mol-1‚K-1 νji ) stoichiometric coefficient of component i in reaction j

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Received for review December 30, 2003 Revised manuscript received April 28, 2004 Accepted April 28, 2004 IE0308801