Chemical Equilibrium Conversion of the tert-Amyl-methyl-ether

Apr 8, 2010 - The chemical equilibrium conversion of the reversible liquid-phase etherification of isoamylene with methanol to tert-amyl-methyl-ether ...
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Ind. Eng. Chem. Res. 2010, 49, 4412–4419

Chemical Equilibrium Conversion of the tert-Amyl-methyl-ether Synthesis in the Presence of n-Pentane, Tetrahydrofuran, or Benzene Vincent Liebert, Torben Hector, and Ju¨rgen Gmehling* Department of Industrial Chemistry, UniVersity of Oldenburg, D-26111 Oldenburg, Germany

The chemical equilibrium conversion of the reversible liquid-phase etherification of isoamylene with methanol to tert-amyl-methyl-ether using Amberlyst 36 as catalyst was investigated in a temperature range from 312.15 to 354.15 K. The experiments were also carried out in the presence of n-pentane, tetrahydrofuran, or benzene to investigate the influence of different inert solvents on the equilibrium conversion. From the results the standard enthalpy and standard Gibbs energy of reaction have been determined. The experimental conversions have been compared with the predicted conversions assuming ideal and nonideal behavior. For the predictions, tabulated standard thermodynamic properties at 298.15 K in the ideal gas state (∆Hf0, ∆Gf0), vapor pressures Pis, and standard molar heat capacities cp0 in the liquid phase have been used. The required activity coefficients were calculated with the help of the Wilson model or predicted using the group-contribution method modified UNIFAC (Dortmund). 1. Introduction With the usage of catalysts in automobile exhaust systems for the removal of environmental harming emissions there was a need for lead-free gasoline.1 To improve the burning efficiency of gasoline and to reduce the exhaust gas emission, oxygenates can be added. Since the early 1990s methyl-tert-butyl-ether (MTBE) has become the major gasoline blending oxygenate.2 However due to groundwater contamination, MTBE has been banished in the United States and in the future will be replaced around the world by other oxygenates.3 An alternative oxygenate to MTBE is the heavier tertiary ether tert-amyl-methyl-ether (TAME), which has an octane number similar to MTBE but is less water-soluble and less volatile and therefore more environmentally friendly. The reversible, equilibrium-limited formation of TAME by the reaction of isoamylene with methanol is readily carried out in the liquid phase, catalyzed by acid cation-exchange resins such as Amberlyst 36. Since there are two reactive isoamylenes (2-methyl-1-butene (2M1B), 2-methyl-2-butene (2M2B)), in total three simultaneous reversible reactions have to be consideredsbesides two etherification reactions the isomerization reaction of 2M1B to 2M2B. The reaction network is presented in Figure 1. Additionally a few side reactions can take place. One possible side reaction is the dehydration reaction of methanol to dimethyl ether (DME) and water, whereby water, in a consecutive reaction can react with isoamylene to isoamyl alcohol. Another possible reaction is the dimerization of the isoamylenes. For the considered system a few equilibrium studies have already been published.3-9,21 In two publications1,7 the C5-cut was used instead of the pure isoamylenes as reactants. Oost et al.8 used a mixture of isoamylenes and n-pentane to simulate the C5-cut. But it was not possible to compare their results with ours since the initial mole numbers of the reactants were missing. In our work also the influence of different amounts of n-pentane on the chemical equilibrium conversion was investigated. Additionally tetrahydrofuran and benzene were used as inert solvents for the reversible etherification reaction, to show * To whom correspondence should be addressed. Tel.: +49 441 7983831. Fax: +49 441 7983330. E-mail: [email protected].

how the equilibrium conversion can be influenced by varying the real behavior (activity coefficients) of the system. For the calculation of the equilibrium constants, activities instead of mole fractions were used. The required activity coefficients were calculated using the group-contribution method modified UNIFAC (Dortmund)10 or the Wilson model.11 2. Experimental Section Chemicals and Purities. TAME and the isoamylenes were obtained from Ineos Ko¨ln GmbH, methanol from VWR Prolabo, n-pentane from Normapur, THF from Bu¨fa, and benzene from Roth. TAME was purified as described by Kra¨henbu¨hl and Gmehling.12 Methanol, THF, and benzene were dried over molecular sieves while the other components were used as delivered by the supplier. The water content for every compound was checked by Karl Fischer titration.13 In all cases the water concentration determined was less than 100 ppm. Furthermore the purity of the compounds was checked by GC analysis. The supplier of the chemicals and the purities are summarized in Table 1. Catalyst. All reactions were catalyzed by Amberlyst 36, a macroreticular, sulfonic acid ion-exchange resin from Rohm and Haas. The catalyst has a surface of 33 m2 g-1 and an average pore diameter of 24 nm, and its beads have a harmonic mean size between 0.6 and 0.85 mm.

Figure 1. Reaction network of the etherification reaction of isoamylene with methanol to TAME.

10.1021/ie901850b  2010 American Chemical Society Published on Web 04/08/2010

Ind. Eng. Chem. Res., Vol. 49, No. 9, 2010

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Table 1. Supplier and Purities of the Chemicals Used compound

supplier

purity (%)

methanol tert-amyl-methyl-ether isoamylene n-pentane tetrahydrofuran benzene

VWR Prolabo Ineos Ineos Normapur Bu¨fa Roth

99.9 99.8 99.3 (13.9% 2M1B/86.1% 2M2B) 99.1 99.9 99.7

The catalyst was prepared by washing with distilled methanol to remove impurities until the supernatant liquid was colorless. Afterward the catalyst was dried for 2 days at 333.15 K and then at 353.15 K under vacuum conditions for about 3 days until mass constancy was reached. Apparatus and Procedure. The cleavage and synthesis of TAME with and without solvent were carried out in an autoclave tank reactor from Bu¨chi Glas Uster (model 0618). The experimental setup is shown in Figure 2. The tank reactor has a volume of 1 L and can be used up to pressures of 6 MPa. Intensive agitation is achieved with a classical stirrer, causing less abrasion of the catalyst compared to a magnetic stirrer. The autoclave is equipped with a temperature and a pressure sensor. An external controller is used to read off the agitation speed and the temperature. First the vacuum-dried catalyst was placed into the autoclave. After the reactor and the reactants were brought to the desired temperature using a thermostat (Julabo 12 from Ju¨rgens), the reactants were charged into the evacuated tank reactor via a Teflon tube. The operating pressure was set to approximately 1 MPa using argon to enable the sampling at the bottom of the autoclave with the help of capillary tube. This capillary tube was kept at 263.15 K avoiding evaporation of the volatile components of the reaction mixture. Furthermore a metallic frit was installed inside of the autoclave to prevent the discharge of the catalyst. The samples taken were stored in a freezer until they were analyzed by gas chromatography (HP model 6890, TCD). Before the GC analysis the sample vials were cooled down to 283.15 K using a cryostat (RC 6 Lauda from Ju¨rgens) to avoid

Figure 3. Experimental results for the cleavage of TAME with n-pentane (mole TAME/mole n-pentane ) 1:1) at 315.95 K and 10.8 g of catalyst: (×) n-pentane; (b) tert-amyl-methyl-ether; (O) methanol; (2) 2-methyl-2butene; (4) 2-methyl-1-butene.

evaporation of the volatile components from the reaction mixture. Exemplary in Figure 3 the compositions as function of time are shown for the cleavage of TAME in the presence of n-pentane (mole TAME/mole n-pentane ) 1:1) at 315.95 K and 10.8 g of catalyst. The determination of the kinetic parameters will be discussed in an upcoming paper.14 3. Results and Discussion Chemical Equilibrium. Chemical equilibrium was assumed, when the mole fractions did not change with time. This was checked by repeated sampling. If other side reactions are excluded the etherification of isoamylenes with methanol to TAME consists of three reversible, equilibrium limited reactions as shown in Figure 1. This means that three equilibrium constants Ka have to be taken into account. They are given in eqs 1 to 3: Ka,1 )

Ka,2 )

aTAME xTAME γTAME ) ) Kx,1Kγ,1 a2M1BaMeOH x2M1BxMeOH γ2M1BγMeOH (1) aTAME xTAME γTAME ) ) Kx,2Kγ,2 a2M2BaMeOH x2M2BxMeOH γ2M2BγMeOH (2) Ka,3 )

Figure 2. Scheme of the autoclave with sampling device: (A) autoclave; (B) motor; (C) stirrer; (D) metallic frit; (E) sampling device; (F) feed; (G) argon; (H) vacuum pump; (I) thermostat; (J) cryostat.

a2M2B x2M2B γ2M2B ) ) Kx,3Kγ,3 a2M1B x2M1B γ2M1B

(3)

where ai stands for the activity, xi for the mole fraction and γi for the activity coefficient of component i. The required activity coefficients were predicted with the group-contribution method modified UNIFAC (Dortmund).10,15 In this group-contribution method the size and the form of the components are taken into account via the relative van der Waals volumes Rk and the relative van der Waals surface areas Qk of the subgroups k. The required van der Waals properties and group interaction parameters anm, bnm, and cnm between the main groups have been published elsewhere.15 The activity coefficients were also calculated with the Wilson model.11 In the case of the Wilson model, the binary interaction parameters for all components were fitted with the help of the program package Recval/3 using the Simplex-Nelder-Mead algorithm.16 Recval/3 was developed for the simultaneous regression of gE-model parameters using vapor-liquid equilibria (VLE), azeotropic data (AZD), activity coefficients at infinite dilution (ACT), liquid-liquid

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Table 2. Interaction Parameters of the Wilson Equation for Different Binary Systems component

interaction parameters

1

2

∆λ12 (cal mol-1)

∆λ21 (cal mol-1)

methanol methanol methanol methanol methanol methanol TAME TAME TAME TAME TAME 2M2B 2M2B 2M2B 2M2B 2M1B 2M1B 2M1B

TAME 2M2B 2M1B n-pentane THF benzene 2M2B 2M1B n-pentane THF benzene 2M1B n-pentane THF benzene n-pentane THF benzene

1467.13 2090.97 1766.31 2027.39 681.51 1756.12 -280.62 300.80 91.02 -545.23 213.25 434.97 -115.94 -75.32 205.76 147.30 96.01 218.21

-354.79 287.62 430.44 616.61 -79.75 157.62 408.06 -171.69 85.82 653.59 44.80 -310.57 285.64 325.55 88.89 -54.05 120.77 68.44

Table 3. Molar Volumes and Second Virial Coefficients of the Pure Compounds at 298.15 K16 component

Bii (cm3 mol-1)

V (cm3 mol-1)

methanol TAME 2M1B 2M2B n-pentane THF Benzene

-2677 -2418 -1060 -1272 not required not required not required

40.73 133.45 107.84 105.90 116.11 81.55 89.41

equilibria (LLE), solid-liquid equilibria of eutectic systems (SLE), excess enthalpies (HE), and excess heat capacities (CPE). The required experimental data for the different binary systems for fitting the parameters were taken from the Dortmund Data Bank (DDB).16 However, for fitting the parameters used in this work only a part of the data were available. The fitted temperature-independent Wilson interaction parameters are given in Table 2. Additionally the required pure component molar volumes are listed in Table 3. Figures 4 and 5 show all equilibrium constants Ka obtained by the synthesis and cleavage reaction with and without an inert solvent. The equilibrium constants were obtained from the experimental mole fractions in chemical equilibrium, that is, at t f ∞ taking into account the activity coefficients predicted by the modified UNIFAC (Dortmund)10,15 and the Wilson model.11 As can be seen nearly the same results are obtained. From the equilibrium constants as function of temperature the standard enthalpy of reaction ∆Hr0 and the standard Gibbs energy of

Figure 5. Equilibrium constants Ka1 (9), Ka2 ((), and Ka3 (2) for TAMEsynthesis and the cleavage reaction together with the best fit of the data (s) using activity coefficients calculated with the help of the Wilson model.

reaction ∆Gr0 for the liquid state at 298.15 K can be obtained by linear regression from the slope and the intercept of the data, assuming a temperature-independent standard enthalpy of reaction ∆Hr0 in the temperature range covered, using the van’t Hoff equation:17 ln Ka(T0) ) -

ln Ka ) ln Ka(T0) -

ln Ka )

0 ∆Gr,l RT0

(4)

(

0 ∆Hr,l 1 1 R T T0

)

(5)

0 0 0 ∆Hr,l ∆Hr,l - ∆Gr,l 1 RT0 R T

(6)

To compare the standard thermodynamic properties of reaction (standard state: liquid phase l at 1 atm) obtained with the already available data for the ideal gas phase, the differences of the thermodynamic properties between the liquid and the ideal gas state have to be taken into account. The difference of the standard enthalpy of formation is approximately identical with the enthalpy of vaporization at T0 (298.15 K), so that the standard enthalpy of reaction for the reaction in the ideal gas phase can be calculated by the following equation: N

0 0 ∆Hr298,g ≈ ∆Hr,298,l +

∑ ν ∆H i

0 V,298

(7)

i)1

The standard Gibbs energy of formation for the liquid phase can be calculated from the standard Gibbs energy of formation in the ideal gas phase by 0 0 ∆Gf,298,l ) ∆Gf,298,g + RT ln

(

φsi Psi Poyi 1 atm

)

(8)

where φis is the fugacity coefficient, Pis is the saturation pressure, and Poyi is the Poynting factor, which shows a value of approximately 1 for low pressure differences. φis can be calculated with the help of the following virial equation: ln φsi ) Figure 4. Equilibrium constants Ka1 (9), Ka2 ((), and Ka3 (2) for the TAMEsynthesis and the cleavage reaction together with the best fit of the data (s) using activity coefficients calculated with the help of the modified UNIFAC (Dortmund) group-contribution method.

BiiPsi RT

(9)

The second virial coefficients Bii at 298.15 K were taken from the DDB.16 The values used for Bii are listed in Table 3. The saturation pressure Pis can be determined using the Antoine equation:

Ind. Eng. Chem. Res., Vol. 49, No. 9, 2010

log Psi ) A -

B ϑ+C

(10)

Table 5. Standard Thermodynamic Data of the Compounds Investigated quantity

The Antoine parameters A, B, and C used are listed in Table 4. In Table 5 the standard thermodynamic data used to calculate the standard enthalpy of reaction and the standard Gibbs energy of reaction are given. In ref 20, for the standard Gibbs energy of formation for TAME in the gas phase, a value of -104.00 kJ/mol is given. However Thiel and Hoffmann,18 Syed et al.,5 and Rhiko et al.19 showed that this value is about 4-5 kJ/mol too high. Therefore in this work a value of -113.8 kJ/mol (standard state: liquid phase) recommended by Syed was used.5 Using eqs 8-10 and a value of -113.8 kJ/mol (standard state: liquid phase) a standard Gibbs energy of formation for TAME in the gas phase of -108.05 kJ/mol is obtained. A comparison of the calculated and experimental thermodynamic standard values is given in Table 6. It can be seen that the enthalpies of reaction (standard state, liquid phase) derived from the equilibrium constants Ka (see Table 6) differ only by about 3 kJ/mol from the calculated values using eq 7. In addition our values are in good agreement with the experimental findings by Heintz et al.21 For the reaction of 2M2B with methanol they obtained a value of -28.4 ( 1.5 kJ/mol for the enthalpy of reaction (standard state, liquid phase) and a value of -7.1 ( 0.3 kJ/mol for the isomerization. The derived standard Gibbs energies of reaction (standard state, liquid phase) are also in agreement with the values calculated using the tabulated Gibbs energies of formation (see Table 5) considering eq 8-10. Equilibrium Conversion. The equilibrium conversion for the limiting reactant can be calculated from the number of moles at the beginning of a reaction and the number of moles at t ) ∞. The conversion of any reactant i is defined as Xi )

ni,0 - ni,e ni,0

(11)

where ni,0 is the initial number of moles and ni,e is the number of moles of component i in chemical equilibrium (t f ∞). In the previous chapter the standard enthalpy of reaction was determined. Since the synthesis of TAME is exothermic the equilibrium constant and the maximum equilibrium conversion should decrease with increasing temperature. The opposite is true for an endothermic reaction, for example, the cleavage of TAME. The following equations for the equilibrium conversion of methanol are derived. In the case of the synthesis of TAME in the presence of an inert solvent, the following expression is obtained for the equilibrium conversion of methanol XMeOH, when only reaction (2) in Figure 1 is considered: XMeOH ) xMeOH,e(nMeOH,0 + nisoamylene,0 + nsolvent,0) - nMeOH,0 ) ∆n xMeOH,e - 1 (12) where ∆n is the number of moles of TAME formed during the reaction. This value is identical to the decreasing number of

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0

∆Hf,298,g 0 ∆Gf,298,g 0 ∆Hv,298

unit

MeOH

2M1B

kJ/mol kJ/mol kJ/mol

-201.16 -162.5017 37.528 17

2M2B

-36.34 65.658 26.008

8

TAME

-42.58 59.708 27.008

-298.708 -108.055 35.308

8

moles of the reactants methanol and isoamylene. The number of moles of the inert solvent will not change during the reaction. For the synthesis of TAME without solvent the term nsolvent,0 can be eliminated in eq 12. The calculation of the equilibrium conversion for the cleavage reaction of TAME with a solvent can be carried out in a similar way. The following results are obtained: XMeOH )

xMeOH,e(nTAME,0 + nsolvent,0) ) ∆n 1 - xMeOH,e

(13)

For a cleavage reaction without any solvent the term nsolvent,0 can be eliminated in eq 13. To be able to compare the equilibrium conversions both for the synthesis and the cleavage of TAME, the results will be referred to the synthesis of TAME. Therefore eq 13 will be rearranged: XMeOH ) 1 - ∆n

(14)

In Figures 6-9 the experimental and calculated equilibrium conversions XMeOH are shown as a function of temperature for different initial mole ratios of the components obtained for the cleavage and synthesis of TAME with and without the presence of n-pentane, THF, or benzene. Up to now the equilibrium conversions with THF (mole TAME/mole THF ) 1:4) were measured in a smaller temperature range. The number of moles of each component at the beginning of the reaction and the mole fraction of methanol in equilibrium are given in Tables 7-9. For the mole fraction of methanol in equilibrium, the mean value of the last three experimental data points was used. To simplify the comparison of the synthesis and cleavage reaction all equilibrium conversions XMeOH in Tables 7-9 and in the figures are given for the forward reaction (synthesis of TAME). Figure 6 shows that our conversion results for the synthesis of TAME without an inert solvent are in good agreement with values taken from literature ensuring the reproducibility of our measurement technique. The conversions shown in Figures 6-9 were calculated with a Mathcad program22 assuming ideal and nonideal behavior of the liquid phase. For the calculation, tabulated standard thermodynamic properties for the ideal gas state (∆H0f,298,g, ∆G0f,298,g) listed in Table 5 and saturation vapor pressures Pis of the pure components are used. The vapor pressures Pis were calculated using eq 10 and the Antoine parameters listed in Table 4. Furthermore the temperature dependency of the standard enthalpy of reaction was considered using Kirchhoff’s equation: ∆Hr0(T) ) ∆Hr0(T0) +

∫ ∑νc T

T0

0 i p,i

dT

(15)

The required standard molar heat capacities are listed in Table 10.

Table 4. Antoine Parameters A, B and C16 for the Investigated Compoundsa

a

Antoine parameter (-)

MeOH

2M2B

2M1B

TAME

pentane

THF

benzene

A B C

8.081 1582.300 239.700

6.923 1099.100 233.317

6.864 1048.900 232.194

6.851 1208.400 217.907

6.879 1061.700 229.313

6.99515 1202.290 226.254

6.870 1196.800 219.161

Units in eq 10: Pis [mmHg]; ϑ [°C].

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Table 6. Experimental and Calculated Values of the Standard Enthalpy of Reaction and Standard Gibbs Energy of Reaction (Liquid Phase)a reaction MeOH + 2M1B hTAME MeOH + 2M2B h TAME 2M1B h 2M2B a

0 ∆Hr,exp,W (kJ/mol)

0 ∆Hr,exp,U (kJ/mol)

0 b ∆Hr,calc (kJ/mol)

0 ∆Gr,exp,W (kJ/mol)

0 ∆Gr,exp,U (kJ/mol)

0 c ∆Gr,calc (kJ/mol)

-34.53 -28.50 -6.16

-36.41 -29.73 -6.61

-32.98 -25.74 -7.24

-13.15 -6.32 -6.91

-13.11 -6.35 -6.82

-11.84 -5.23 -6.61

U, modified UNIFAC; W, Wilson model. b Calculated with eq 7. c Calculated with eq 8.

Figure 6. Equilibrium conversion of methanol for the synthesis and cleavage of TAME as a function of temperature: (b) experimental (cleavage); (2) experimental (synthesis); (O) Rihko et al.6 (cleavage); (∆) Rihko et al.6 (synthesis); (×) Syed et al.5 (cleavage); (---) ideal; (- · · -) Wilson; (s) modified UNIFAC.

Figure 8. Equilibrium conversion of methanol for the cleavage of TAME in the presence of n-pentane or THF (mole TAME/mole n-pentane/THF ) 1:4) as a function of temperature: (b) experimental (cleavage); (9) experimental (cleavage, THF); (---) ideal; (- · · -) Wilson; (s) modified UNIFAC.

Figure 7. Equilibrium conversion of methanol for the synthesis and cleavage of TAME in the presence of n-pentane or THF (mole methanol (mole TAME)/mole n-pentane/THF ) 1:1) as a function of temperature: (b) experimental (cleavage, n-pentane); (2) experimental (synthesis, n-pentane); (9) experimental (cleavage, THF); (---) ideal; (- · · -) Wilson; (s) modified UNIFAC.

Figure 9. Equilibrium conversion of methanol for the cleavage of TAME in the presence of benzene (mole TAME/mole benzene ) 1:1/1:4) as a function of temperature: (×) experimental (cleavage, 1:1); (O) experimental (cleavage, 1:4); (---) ideal; (- · · -) Wilson; (s) modified UNIFAC (the lower values of both prediction methods belong to the molar ratio 1:4).

Since the number of moles decrease during the synthesis reaction, following the LeChatelier principle the methanol conversion decrease with an increasing amount of an inert solvent in the reacting mixture, as calculated assuming ideal behavior of the liquid phase (compare Figures 6-9). But that is not the case when looking at the experimental conversions shown in Figures 6-9. Looking at the conversions in the presence of n-pentane, it can be seen that the conversions measured stay nearly the same with and without the presence of n-pentane. The reason is the positive deviation from Raoult’s law of this system. In particular the activity coefficient of methanol strongly increases at higher n-pentane concentrations. This leads to a decrease of Kγ and an increase of Kx with increasing n-pentane concentrations and a compensation of the dilution effect by the nonideal behavior. Similar behavior is observed in the presence of benzene as shown in Figure 9. The cleavage of TAME in the presence of different amounts of

benzene (mole TAME/mole benzene ) 1:1/1:4) lead to nearly the same methanol equilibrium conversions, which again can be explained by the strong positive deviation from Raoult’s law. Using THF as inert solvent, smaller methanol conversions are observed than in the presence of n-pentane or benzene, as shown in Figures 7 and 8. The reason is, that the activity coefficient of methanol shows smaller values in the presence of THF than in the presence of n-pentane or benzene. This results in larger Kγ-values and smaller values of Kx. From this it follows that lower equilibrium conversions are obtained in the presence of THF in comparison to n-pentane or benzene. In Tables 11-14 the experimental and predicted conversions, activity coefficients, and equilibrium compositions are listed for the solvent-free as well as the solvent-containing systems (mole TAME/mole n-pentane/THF/benzene ) 1:1) for a temperature range from 312.54 to 316.05 K. From Tables 12 and 14 it can be seen, that the activity coefficient of methanol shows almost the same value in the presence of n-pentane and benzene at a given temperature.

Ind. Eng. Chem. Res., Vol. 49, No. 9, 2010 Table 10. Standard Molar Heat Capacities in the Liquid Phase

Table 7. Experimental Values for the Determination of the Equilibrium Conversion of Methanol for the Synthesis and Cleavage of TAME without Solvent at Different Temperatures

cleavage

synthesis

T (K)

xMeOH,e

∆n

XMeOH (1 - ∆n)

313.15 323.15 323.15 333.15 333.15 343.15 343.15 353.15 353.15

0.1676 0.1741 0.1932 0.2085 0.2243 0.2433 0.2410 0.2732 0.2743

0.2013 0.2108 0.2395 0.2634 0.2892 0.3215 0.3175 0.3759 0.3780

0.7987 0.7892 0.7605 0.7366 0.7108 0.6785 0.6825 0.6241 0.6220

cp0 (J mol-1 K-1)a

MeOH23

2M1B24

2M2B24

TAME16

a b c d

7.696 0.162 2.058 × 10-4 2.874 × 10-7

126.5 -0.061 5.084 × 10-4 1.692 × 10-7

132.9 -0.148 7.511 × 10-4 -8.817 × 10-8

576.8 -3.416 0.010 -8.385 × 10-6

a

T (K)

xMeOH,e

nMeOH,0

nisoamylene,0

∆n

XMeOH (∆n)

316.25 335.05 353.55

0.1569 0.2071 0.2477

1.0000 1.0000 1.0000

1.0000 1.0000 1.0000

0.8139 0.7388 0.6707

0.8139 0.7388 0.6707

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Polynomial temperature dependency:17 cp ) a + bT + cT2 + dT3.

amounts of n-pentane do the experimental results show larger deviations to the predicted results, as can be recognized from Figure 8. From Figure 6 it can be seen that for the solvent-free system the conversions measured are also in good agreement with the results of other authors.5,6 Unfortunately no published results are available with varying amounts of THF or benzene. The influence of inert solvents on the equilibrium conversion of an etherification reaction has to be taken into account in practice. Solvent effects of C5-alkanes are a matter of particular interest, since these alkanes together with the isoamylenes are present in the C5-raffinate stream, which is used for the etherification reaction.

Measurement inaccuracies are caused by the initial weight of educts and solvents, inaccuracy of the temperature, evaporation effects during the sampling process, and the quality of the gas-chromatographic analysis including calibration. All the effects result in an absolute error of about (1% for the methanol conversion. In all cases the experimental findings are in good agreement with the predictions using the Wilson model11 or modified UNIFAC (Dortmund).10,15 Only at higher temperature and large

4. Conclusions The equilibrium conversions for the reversible liquid-phase synthesis of TAME catalyzed by Amberlyst 36 in a temperature

Table 8. Experimental Values for the Determination of the Equilibrium Conversion of Methanol for the Synthesis and Cleavage of TAME in the Presence of n-Pentane, THF, or Benzene (mole Methanol (mole TAME)/mole n-Pentane/THF/Benzene ) 1:1) at Different Temperatures

cleavage

synthesis

xMeOH,e

nTAME,0

npentane,0

∆n

XMeOH (1 - ∆n)

316.05 326.15 335.65 345.15 354.15

0.1039 0.1236 0.1473 0.1624 0.1756

1.0000 1.0000 1.0000 1.0000 1.0000

0.9989 0.9989 0.9989 0.9989 0.9989

0.2318 0.2819 0.3453 0.3876 0.4258

0.7682 0.7181 0.6547 0.6124 0.5742

T (K)

xMeOH,e

nMeOH,0

nisoamylene,0

npentane,0

∆n

XMeOH (∆n)

312.15 321.05 328.75 346.45

0.0869 0.0963 0.1166 0.1279

1.0000 1.0000 1.0000 1.0000

0.9812 0.9812 0.9812 0.9812

0.9811 0.9811 0.9811 0.9811

0.8132 0.7909 0.7410 0.7122

0.8132 0.7909 0.7410 0.7122

cleavage

cleavage

T (K)

T (K)

xMeOH,e

nTAME,0

nTHF,0

∆n

XMeOH (1 - ∆n)

312.54 322.04 332.04 342.03

0.1194 0.1397 0.1583 0.1748

1.0000 1.0000 1.0000 1.0000

0.9999 0.9999 0.9999 0.9999

0.2713 0.3248 0.3762 0.4237

0.7287 0.6752 0.6238 0.5763

T (K)

xMeOH,e

nMeOH,0

nisoamylene,0

nbenzene,0

∆n

XMeOH (1 - ∆n)

312.71 321.94 331.65 341.53 351.34

0.0882 0.1045 0.1283 0.1477 0.1688

1.0000 1.0000 1.0000 1.0000 1.0000

1.0000 1.0000 1.0000 1.0000 1.0000

1.0017 1.0017 1.0017 1.0017 1.0017

0.1935 0.2336 0.2946 0.3470 0.4064

0.8065 0.7664 0.7054 0.6530 0.5936

Table 9. Experimental Values for the Determination of the Equilibrium Conversion of Methanol for the Cleavage Reaction of TAME in the Presence of n-Pentane, THF, or Benzene (mole TAME/mole n-Pentane/THF/Benzene ) 1:4) at Different Temperatures

cleavage

T (K)

xMeOH,e

nTAME,0

npentane,0

316.05 325.45 335.55 345.25 354.88 312.42 322.24 312.07 321.91 331.72 341.45 351.35

0.0482 0.0586 0.0697 0.0846 0.0987 0.0727 0.0819 0.0376 0.0461 0.0558 0.0655 0.0766

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

3.9927 3.9927 3.9927 3.9927 3.9927

nTHF,0

nbenzene,0

∆n

XMeOH (1 - ∆n)

4.0249 4.0249 4.0249 4.0249 4.0249

0.2528 0.3108 0.3741 0.4614 0.5467 0.3919 0.4459 0.1964 0.2430 0.2970 0.3525 0.4168

0.7472 0.6892 0.6259 0.5386 0.4533 0.6081 0.5541 0.8036 0.7570 0.7030 0.6475 0.5832

3.9996 3.9996

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Ind. Eng. Chem. Res., Vol. 49, No. 9, 2010

Table 11. Experimental and Predicted Conversions, Equilibrium Compositions, Activity Coefficients, and Kγ for the Cleavage of TAME without Solvent at 313.15 K experimental XMeOH (1 - ∆n) xMeOH,e xisoamylene,e xTAME,e γMeOH γisoamylenea γTAME Kγ

0.7987 0.1676 0.1742 0.6582 2.865b 1.224b 1.025b 0.292

ideal 0.6067 0.2823 0.2823 0.4354 1.000 1.000 1.000 1.000

Wilson 0.7810 0.1796 0.1796 0.6408 2.850 1.339 1.050 0.275

modified UNIFAC (Dortmund) 0.7716 0.1859 0.1859 0.6281 2.739 1.252 1.031 0.301

a Activity coefficients calculated for 2M2B. b Activity coefficients for the given composition calculated with modified UNIFAC (Dortmund).

Table 12. Experimental and Predicted Conversions, Equilibrium Compositions, Activity Coefficients, and Kγ for the Cleavage of TAME in the Presence of n-Pentane (mole TAME/mole n-Pentane ) 1:1) at 316.05 K

XMeOH (1 - ∆n) xMeOH,e xisoamylene,e xTAME,e xpentane,e γMeOH γisoamylenea γTAME γpentane Kγ

experimental

ideal

Wilson

modified UNIFAC (Dortmund)

0.7682 0.1039 0.1008 0.3492 0.4461 5.161b 1.088b 0.978b 1.163b 0.174

0.5010 0.1997 0.1997 0.2005 0.4001 1.000 1.000 1.000 1.000 1.000

0.7484 0.1118 0.1118 0.3323 0.4441 4.834 1.134 1.036 1.157 0.189

0.7565 0.1086 0.1086 0.3372 0.4457 5.085 1.093 0.977 1.167 0.176

a Activity coefficients calculated for 2M2B. b Activity Coefficients for the given composition calculated with modified UNIFAC (Dortmund).

Table 13. Experimental and Predicted Conversions, Equilibrium Compositions, Activity Coefficients, and Kγ for the Cleavage of TAME in the Presence of THF (mole TAME: mole THF ) 1:1) at 312.54 K

XMeOH (1 - ∆n) xMeOH,e xisoamylene,e xTAME,e xTHF,e γMeOH γisoamylenea γTAME γTHF Kγ

experimental

ideal

Wilson

modified UNIFAC (Dortmund)

0.7287 0.1194 0.1104 0.3216 0.4485 2.400b 1.372b 1.018b 1.007b 0.309

0.5188 0.1939 0.1939 0.2091 0.4031 1.000 1.000 1.000 1.000 1.000

0.7017 0.1298 0.1298 0.3053 0.4351 2.452 1.425 1.072 0.990 0.307

0.7022 0.1296 0.1296 0.3056 0.4352 2.400 1.382 1.014 1.008 0.306

a

Activity coefficients calculated for 2M2B. b Activity coefficients for the given composition calculated with modified UNIFAC (Dortmund).

range from 312.15 to 353.55 K have been investigated with and without the presence of n-pentane, benzene, and THF. Experimental equilibrium constants Ka were obtained by carrying out both the cleavage and the synthesis of TAME in a batch reactor taking into account the activity coefficients using the group-contribution method modified UNIFAC (Dortmund) and the Wilson model. The derived standard enthalpies of reaction and the standard Gibbs energies of reaction are in good agreement with the values calculated from tabulated standard enthalpies of formation, standard Gibbs energies of formation, and standard molar heat capacities. The experimental results for the equilibrium conversion of the etherification reaction with and without n-pentane, benzene, or THF as inert solvents are in good agreement with the predicted results using the Wilson model and modified UNIFAC

Table 14. Experimental and Predicted Conversions, Equilibrium Compositions, Activity Coefficients, and Kγ for the Cleavage of TAME in the Presence of Benzene (mole TAME/mole Benzene ) 1:1) at 312.71 K experimental

ideal

Wilson

modified UNIFAC (Dortmund)

0.8065 0.0882 0.0894 0.3570 0.4654 4.897b 1.286b 0.938b 1.101b 0.149

0.5180 0.1942 0.1942 0.2087 0.4029 1.000 1.000 1.000 1.000 1.000

0.7619 0.1064 0.1064 0.3404 0.4468 4.297 1.302 1.029 1.158 0.184

0.7790 0.0995 0.0995 0.3507 0.4502 4.629 1.294 0.936 1.115 0.156

XMeOH (1 - ∆n) xMeOH,e xisoamylene,e xTAME,e xbenzene,e γMeOH γisoamylenea γTAME γbenzene Kγ

a Activity coefficients calculated for 2M2B. b Activity coefficients for the given composition calculated with mod. UNIFAC (Do).

(Dortmund) method, while the negligence of the nonideal behavior leads to poor results. Since it is possible to influence the equilibrium conversion of any reversible reaction by the addition of a solvent, the selection of the “best” solvent is an important step to increase the equilibrium conversion and therewith reduce the total costs of a chemical plant at least for reversible reactions carried out in an inert solvent or solvent mixture. Of course the costs for the separation step have also to be considered. From the results obtained in this paper it can be recognized that for the etherification reaction in the presence of benzene and n-pentane nearly the same equilibrium conversions are obtained. The equilibrium conversion decreases in the presence of THF, since THF leads, for example, to smaller activity coefficients of methanol. From the predicted results presented in this work it can be concluded that the group-contribution method modified UNIFAC allows the reliable selection of the most suitable solvent. Acknowledgment The authors thank both the Adam-Haker-Fonds and the MaxBuchner-Stiftung (No. 2771) for the financial support of this work. The authors also thank Ineos Ko¨ln GmbH for the supply of TAME and isoamylene free of charge. Nomenclature Roman Letters a ) activity anm,bnm, cnm ) interaction parameters Bii ) second virial coefficient of the pure component i [cm3 mol-1] cp ) molar heat capacity [J mol-1 K-1] f ) fugacity [kPa] ∆Gf0 ) standard Gibbs energy of formation [kJ mol-1] ∆Gr0 ) standard Gibbs energy of reaction [kJ mol-1] ∆Hf0 ) standard enthalpy of formation [kJ mol-1] ∆Hr0 ) standard enthalpy of reaction [kJ mol-1] ∆Hv0 ) standard enthalpy of vaporization [kJ mol-1] Ka ) equilibrium constant in terms of activities Kx ) equilibrium constant in terms of mole fractions Kγ ) equilibrium constant in terms of activity coefficients n ) number of moles Poy ) Poynting factor ps ) saturation pressure [kPa] Qk ) relative van der Waals surface area of subgroup k R ) general gas constant, 8.31433 [J mol-1 K-1] Rk ) relative van der Waals volume of subgroup k

Ind. Eng. Chem. Res., Vol. 49, No. 9, 2010 T ) absolute temperature [K] V ) molar volume [cm3 mol-1] x ) mole fraction X ) conversion Greek Letters γ ) activity coefficient φ ) fugacity coefficient ϑ ) temperature [°C] ν ) stoichiometric coefficient Superscripts 0 ) at standard condition Subscripts 0 ) at the start of a reaction calc ) calculated value e ) at equilibrium exp ) experimental value g ) ideal gas state i,j ) component i, j l ) liquid phase

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ReceiVed for reView April 20, 2009 ReVised manuscript receiVed March 12, 2010 Accepted March 25, 2010 IE901850B