1092
Ind. Eng. Chem. Res. 1996,34, 1092-1101
Ethers from Ethanol. 2. Reaction Equilibria of Simultaneous tert-Amyl Ethyl Ether Synthesis and Isoamylene Isomerization Prakob Kitchaiya and Ravindra Datta* Department of Chemical and Biochemical Engineering, The University of Iowa, Iowa City, Iowa 52242-1219
The recent requirements for blending oxygenates with gasoline for pollution abatement and octane improvement have opened up huge markets for ethers, synthesized by catalytically reacting a n isoolefin with a n alcohol. Consequently, alternatives to isobutylene-derived methyl tert-butyl ether (MTBE) obtained from methanol and ethyl tert-butyl ether (ETBE) obtained from ethanol are being explored. This paper provides a thermodynamic analysis of the liquidphase etherification of ethanol with 2-methyl-l-butene (2MlB) and 2-methyl-2-butene (2M2B), the two reactive isoamylene isomers. Both these isomers produce tert-amyl ethyl ether (TAEE) but also undergo isomerization. Theoretical and experimental results are provided here for the simultaneous TAEE synthesis and isoamylene isomerization. Expressions for the three thermodynamic equilibrium constants as a function of temperature are developed. Gibbs free energy and the enthalpy of formation of TAEE are also obtained. The equilibrium constants' correlations are utilized to compute the effect of the feed mole ratio of the isoamylenes and the inert solvent to ethanol as well as the reaction temperature on the equilibrium conversions and selectivities. Conditions t h a t maximize etherification conversion and selectivity are explored.
Introduction With the phaseout of leaded octane enhancers in gasoline, oxygenates such as alcohols and ethers have been used effectively as substitutes. In addition, oxygenates reduce tailpipe CO emissions and are, consequently, now required in a large fraction of the gasoline consumed in the United States under the programs of the Clean Air Act Amendments of 1990. Ethers are, in general, better than alcohols for blending with gasoline. Blending of alcohols results in higher Reid vapor pressure (RVP)and phase separation in the presence of water. Major members of the ether oxygenate family are methyl tert-butyl ether (MTBE), tert-amyl methyl ether (TAME),ethyl tert-butyl ether (ETBE),tert-amyl ethyl ether (TAEE),and other ethers resulting from the combination of the higher isoolefins (e.g., C g ) with methanol or ethanol (Zhang and Datta, 1995b). Liquidphase ether synthesis reactions involving the combination of an alcohol (methanol or ethanol) with an isoolefin occur readily over a protonated cation exchange resin catalyst such as Amberlyst 15 but are limited by equilibrium conversion, particularly at the higher temperatures desirable for higher reaction rates. Thermodynamic studies of the first three fuel oxygenates listed above have been published (Colombo et al., 1983; Safronov et al., 1989; Rehfinger and Hoffman, 1990; Izquierdo et al., 1992;Vila et al., 1993; Zhang and Datta, 1995a; Jensen and Datta, 1994). For TAEE, there is one published report on the reactivity of isoamylenes with ethanol (Rihko and Krause, 1993). An advantage of TAEE is that it is partially produced from a renewable resource, i.e., ethanol. This is significant due to the increasing emphasis on renewable oxygenates by the US. EnvironmentalProtection Agency (EPA). Further, with the accelerating demand for MTBE and ETBE, the isobutylene supply is likely to become limiting (Haggin, 1993). Thus, alternate isoolefins produced from fossil or natural resources are being explored. In particular, isoamylenespresent in the fluid catalytic cracking gasoline fraction, which have a blend-
* Author t o whom correspondence should be addressed.
ing RVP of 19 and 15 psig, respectively, for its two isomers, 2-methyl-l-butene (2MlB) and 2-methyl-2butene (2M2B)(Brockwell et al., 19911,can alternatively be used to produce TAEE, which has a reported RVP of only 1 psig (Kivi et al., 1991). TAEE is also a good octane enhancer. Thus, the motor octane number (MON) of TAEE is 112 (Hirao and Pefley, 19881, while the research octane number (RON) is 105 (Kivi et al., 1991). TAEE, thus, appears to be an attractive alternative oxygenate candidate. Colombo et al. (1983) first studied MTBE reaction thermodynamics and demonstrated that the activities required for the determination of the chemical equilibrium constant can be calculated by the UNIFAC method for the liquid-phase MTBE reaction mixture, even though the UNIFAC parameters were originally developed for predicting phase equilibrium. Izquierdo et al. (1992) also confirmed the validity of the UNIFAC activity coefficients for MTBE synthesis and further took into account the effect of the temperature dependence of the heat capacities of the components involved. Zhang and Datta (1995a) provide a further discussion of the MTBE reaction. Vila et al. (1993) conducted a study of the equilibrium constant for ETBE liquid-phase synthesis. Jensen and Datta (1995)further investigated the thermodynamics of ETBE and obtained equivalent results by following alternate thermodynamicpathways, due to the state function property of the enthalpy and Gibbs free energy of reaction. Rihko and Krause (1993) reported the reactivity of isoamylenes with ethanol at a low flow rate (WHSV = 1.9 h-l) in a packed-bed reactor. They found that, at temperatures above 60 "C, the conversions obtained for both 2M1B and 2M2B etherification and isomerization were limited by equilibrium at this WHSV. Isomerization, not etherification, however, was found to be the main reaction for both the isoamylene feeds. It will later be shown that this result is a consequence of the feed composition used by these authors, which was 3.8 wt % isoamylene and 2.5 wt % ethanol, with the balance being inert solvent. Equilibrium data are thus required at different feed compositions and temperatures for the synthesis of TAEE and are provided here in the form of expressions for the
0888-5885/95/2634-1092$09.00/0 0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34,No. 4,1995 1093 2-methyl-I-butene (6)
HsC-CHz-OH
11
-k
ethanol (A)
2-methyl-2-butene (C)
Figure 1. Reaction network of TAEE synthesis and isoamylene isomerization.
thermodynamic equilibrium constants as a function of temperature. These results are then used to compute the equilibrium conversion and selectivity for etherification and isomerization under different conditions of temperature and feed compositions.
derived from the thermodynamic relationship, d(AGfd RT)IdT = -AHiJRP, which when combined with eq 5 results in the van't Hoff equation
Thermodynamic Analysis There are primarily three reversible reactions that occur simultaneously in TAEE production from ethanol and isoamylene as shown in Figure 1 and in eqs 1-3 below, namely, etherification of 2M1B to TAEE (reaction 11, etherification of 2M2B to TAEE (reaction 2), and isomerization between 2M1B and 2M2B (reaction 3):
+ 2M1B (B)==TAEE (D) ethanol (A) + 2M2B ( C ) TAEE (D) ethanol (A)
--L
2M1B (B) = 2M2B ( C )
(1) (2) (3)
In addition, trace amounts of tert-amyl alcohol (TAA) are also formed from the hydration of isoamylenesif any water is present. There were no other significant sideproducts detected in this study. It may be noted that only two of the above three reactions are stoichiometrically independent. For instance, addition of reactions 2 and 3 provides reaction 1. In general, the equilibrium constant, K,,for the ith = 0, among the n species liquid-phase reaction, CnJ=1vYAJ AJ is (Jensen and Datta, 1995) n
n
where AH~T is the standard enthalpy of reaction i at the temperature T. The standard enthalpy of reaction i at the temperature T may be written in terms of the enthalpy of reaction i at T = T", m p , and the difference between the molar heat capacities of the products and reactants of reaction i, ACfp, i.e.,
m:T= m:T+ $ A c g
dT
i = 1,2,..., q
(7)
where the molar heat capacity of speciesj , Cjj, is usually written as a cubic polynomial in temperature (Reid et al., 1987), i.e., CFj = aj bjT C j T 2 djP. Use of eq 7 in eq 6, followed by integration from the standard temperature, T",to the reaction temperature of interest, T,provides the following expression for the equilibrium constant (Jensen and Datta, 1995):
+
+
Abi IiH Aai InK, = IiK - - -1n T + -T 2R RT R
+
-F Ad , 12R
+
Aci + -F + 6R
i = 1,2, ..., q (8)
where
n
j=1
i = 1, 2, ...,q (4) Here, the activity of species j in the liquid phase, uj = y ~ j is , calculated from its mole fraction, xj, and the activity coefficient, yj, estimated by an appropriate correlation, such as the UNIFAC method (Reid et al., 1987). The equilibrium constant, in turn, is related to the standard Gibbs free energy of reaction i at the temperature T, AG&, by i = 1,2,...,q
(5)
The effect of temperature on the standard Gibbs free energy change of reaction i at constant pressure is
and
where Kill" is related to AG&, by eq 5. The above predictive approach is based on a knowledge of the appropriate standard thermochemical data for all the species involved. If the required data are not all available, as is frequently the case including this study, then chemical reaction equilibrium conversion
1094 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995
data may, in turn, be used to calculate the lacking thermodynamic data. For this purpose, eqs 8-10 may be combined and rearranged into the form
z = 1 , 2 , ..., q (11) where the function
Abi -)T"1 + Aai ln-T"T + $T
-
Aci
T")+ -[p - (T")']+ 6
Thus, from eq 11,plotting (In Ki - 4JR) versus ( 1 / T 1/27 should result in a straight line that could be used t o calculate K p , and hence AG+, as well as AH+, at 298.15 K separately from the y-intercept and the slope upon linear regression, provided that the species heat capacity data are available, or can be estimated reliably, for calculating &. Alternatively, AG+, may be directly determined by performing equilibrium experiments at 298.15 K and using eq 5. Then AH~Tcould be calculated by nonlinear regression of eq 8.
Experimental Section Amberlyst 15, a sulfonic acid macroreticular cation exchange resin catalyst manufactured by Rohm and Haas Co. and obtained from Sigma Chemical Co., was first washed with ethanol to remove any organic residue, then converted into the acid form by washing with 1M HNO3 acid, and finally rinsed with deionized water until the wash water was free of acid. The ion exchange capacity of the catalyst was checked according to the method of Fisher and Kunin (1955) and confirmed to be 4.8 f 0.1 mequivlg of dry resin. Amberlyst 15 resin (0.05 g), dried under vacuum, was loaded into a V4 in. stainless steel reaction tube, 4 in. long, with both ends sealed with Swagelok fittings. A liquid mixture of 2-methyl-2-butene (99%purity, obtained from Aldrich) and ethanol (200 proof, obtained from Pharmco Products, Inc.), dried by molecular sieve 3A, was charged into this batch reaction tube. The tube was then immersed in a water circulation bath (Fisher Scientific, Model 9005, with a stipulated temperature variation of f0.25 "C) set at the desired temperature. Experiments at each temperature were performed at different feed molar ratios. After at least 4 days and after longer periods for the lower temperature experiments, the reaction tube was removed from the water bath and chilled immediately in an ice-water bath to quench the reaction. The cap was opened for liquid sampling, and the composition analysis was done by gas chromatography using the AutoSystem from Perkin-Elmer equipped with a Supelco capillary column (SPB-1,0.25mm i.d., 1.0 pm film thickness, 60 m length) along with FID at 250 "C. Helium (Air Products) at 30 psig was used as the carrier gas, and an injection split ratio of 200:l was employed. Hydrogen and compressed air supplied to the FID were also obtained from Air Products. The temperature program began with a temperature of 35 "C for 9 min, which was then ramped at the rate of 20 "C/min to 135 "C and finally maintained at this temperature for 3 min.
Under these conditions, the retention times of ethanol, 2MlB, 2M2B, and TAEE were 5.7, 7.1, 7.9, and 15.6 min, respectively. The maximum error in the mole fraction determination was estimated to be less than 2.5%. This error in composition propagates into an error in the calculated equilibrium constants of up to 3.5%. The tube was then returned to the water bath and checked for any detectable composition change on the next day to ensure that chemical equilibrium had indeed been reached. Experiments were also conducted at 25 "C to directly determine the standard Gibbs free energy of the reactions at 298.15 K from eq 5. This was compared with the standard Gibbs free energy of reactions determined as described above from the experimental results at different temperatures and by making use of eq 11. In addition to ethanol, 2MlB, 2M2B, and TAEE, 0.30.8 mol % of tert-amyl alcohol (TAA) was also usually detected (retention time, 12.6 min) in the final liquid product as a result of the reaction between isoamylene and trace amounts of water present in the resin or the liquid feed mixture. This hydration reaction occurs readily due t o the strong adsorption of water on the catalyst. There were no other detectable side products. The presence of the small amount of TAA was taken into account in the activity coefficients calculations. The activitiy coefficient of each component at equilibrium was computed from the equilibrium mole fractions by the UNIFAC method using parameters obtained from Reid et al. (1987).
Results and Discussion Equilibrium Constants. The experimental equilibrium constants for the three reactions were calculated by using eq 4 from the experimental equilibrium compositions and the corresponding activity coefficients obtained by the UNIFAC method. The results for the case of the equimolar feed ratio of 2M2B to ethanol, Oc = 1, are summarized in Table 1, which lists the equilibrium species mole fraction data obtained at the different temperatures and the corresponding Kxi, K,,, and Ki calculated from these data. It may be noted that, for rough calculations, the following appoximations suffice: K,3 = 1and Kyl FZ K,'. The results for the other values of OCare tabulated in Table 2 and are also shown in Figures 2-4. The fact that the different feed compositions at a given temperature all provide thermodynamic equilibrium constants, Ki, that are quite close to each other provides confidence in the reliabilty of the activity coefficients computed by the UNIFAC method. Error bars in Figures 2-4 show the magnitude of two standard deviations, which vary from 0.5 to 3.8% from the mean value. All three thermodynamic equilibrium constants decrease monotonically with temperature, as is characteristic of exothermic reactions. In order to determine the standard enthalpy and standard Gibbs free energy of reaction i at 298.15 K, the enthalpy and Gibbs free energy of formation of all species are required. Alternately, these may be determined from eq 11,provided the species liquid molar heat capacities as a function of temperature are available. Experimental data on the liquid-phase heat capacity and the standard enthalpy and Gibbs free energy of formation of ethanol, 2MlB, and 2M2B at 298.15 K are available and are listed in Table 3. There is thermodynamic information on TAEE available in the TRC Thermodynamic Tables (1992). However, the reported
Ind. Eng. Chem. Res., Vol. 34, NO. 4, 1995 1096 Table 1. Experimental Equilibrium Mole Fractions Ed,E#, and Et at Different Temperatures for 8 c = la
T("C) 25 40 50 60 70 a
XAe
XBe
XCe
XTAAe
XDe
0.167 0.243 0.266 0.292 0.322
0.011 0.017 0.021 0.026 0.030
0.184 0.219 0.248 0.280 0.302
0.005 0.004 0.003 0.003 0.007
0.618 0.515 0.461 0.397 0.332
&l
321.5 126.6 83.21 52.40 33.98
Kxz 20.04 9.660 6.969 4.847 3.415
Kx3 16.04 13.11 11.94 10.81 9.950
Ky1 0.281 0.352 0.374 0.398 0.428
K~z 0.281 0.351 0.373 0.396 0.425
Ky3 1.002 1.003 1.004 1.005 1.006
KI 90.50 44.63 31.14 20.86 14.54
KZ 5.631 3.393 2.597 1.919 1.453
K3
16.07 13.15 11.99 10.87 10.01
"he balance of the mole fraction is a mixture of pentenes and is represented by 1-pentene in the activity calculation.
80 -
*-
60
-
......... Klb
~
I
40
M ... ..... .
I I
r
2o
F
0
290
300
310
320
330
340
350
Figure 2. Equilibrium constant of reaction 1 versus temperature. For the correlation methods of K I , and &b, see the explanation in the text. Table 2. Experimental Equilibrium Constants at Different Temperatures and Feed Mole Ratios of 2M2B to Ethanol, 8 c Ki with different QC mean reaction temperature 1 ("C) 1.111 1.000 0.909 0.769 0.667 Ki u 1 25 90.50 90.01 90.07 87.22 89.45 1.50 40 45.19 44.63 46.92 43.92 45.36 45.20 1.11 50 30.92 31.14 28.69 32.07 30.31 30.63 1.25 60 21.06 20.86 20.40 20.94 20.78 20.81 0.25 70 14.65 14.54 14.32 14.27 15.67 14.68 0.56 2 25 5.63 5.52 5.44 5.30 5.47 0.14 40 3.48 3.39 3.57 3.34 3.43 3.44 0.09 50 2.62 2.60 2.43 2.65 2.54 2.57 0.09 60 1.95 1.92 1.88 1.92 1.90 1.91 0.03 1.47 1.45 1.44 1.43 1.55 1.47 0.05 70 ' 3 25 16.07 16.31 16.56 16.46 16.35 0.21 40 12.99 13.15 13.12 13.14 13.20 13.12 0.08 50 11.80 11.99 11.83 12.12 11.95 11.94 0.13 60 10.81 10.87 10.85 10.92 10.91 10.87 0.04 70 9.95 10.01 9.95 10.01 10.13 10.01 0.07
values in it were not obtained experimentally but were estimated instead. Therefore, these values for TAEE are not listed in Table 3 and are not used here to justify the experimental equilibrium constants, but rather, the experimental chemical reaction equilibrium results obtained are used to calculate these thermodynamic data for the formation of TAEE. The heat capacity coefficients of TAEE listed in Table 3 were estimated by the commonly utilized Rowlinson method, which generally gives an error of less than 5% (Reid et al., 1987). The thus-estimated heat capacity of TAEE at 25 "C is 240 J/mol K, as compared with the 244 J/mol K estimate provided by the TRC Thermodynamic Tables (1992). This error in the estimation of heat capacity is acceptable for our purposes since calculations indicate that an error in the value of heat
Figure 3. Equilibrium constant of reaction 2 versus temperature. For the correlation methods of K h and &b, see the explanation in the text.
K,exp.
o
- - - K3 a 5 -
I
......... K3b
o""'""'"'"'"'""'""'' 290
300
310
320
330
340
350
T (K) Figure 4. Equilibrium constant of reaction 3 versus temperature. For the correlation methods of K& and K 3 6 , see the explanation in the text.
capacity of 10 J/(mol K) introduces an error of less than 1.5%into the calculated equilibrium constants for TAEE synthesis. On the other hand, a 1 kJ/mol difference in the standard Gibbs free energy of formation leads to a 50% difference in the equilibrium constant, thus requiring precise data. Equation 11 is plotted in Figure 5 in order to determine the standard enthalpy and Gibbs free energy of the three reactions a t 298.15 K from the slope and
1096 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 Table 3. Liquid-Phase Thermochemical Data and Liquid-Phase Heat Capacity Equation Coefficients, Ckj = ai biT ciTL d ; F (J/(mol K)) heat capacity coefficients component AGgr AH& 1 a, b, C, d, (kJ/mol) (kJ/mol) ethanola 29.01 0.2697 -5.6583-4 2.0793-6 -174.8 -277.7 65.0 -62.47 2M1Bb 126.5 -0.0609 5.0843-4 1.6923-7 58.4 -69.91 132.9 -0.1475 7.5113-4 -8.81734 2M2Bb NA 107.1 0.5065 -3.7643-4 5.8033-7 NA TAEE'
+
+
+
a Heat capacity coefficients from Jensen and Datta (1995); AG$p and AH$p from CRC Handbook of Chemistry and Physics (1992). Heat capacity coefficients from Yaws (1992); AG$p and AH$y from Stull et al. (1969). Heat capacity coefficients estimated by the Rowlinson method (Reid et al., 1987). NA = experimental data not available.
i'
"
'
"
' "
"
' '
"
' ' I
"
"
"
"
"
Table 5. Calculated Liquid-Phase Thermodynamic Data of TAEE at 298.15 K from reaction
AG$P" (kJ/mol)
(kJ/mol)
1 2 average
-120.90 -120.62 -120.81
-373.56 -371.90 -372.73
MIHFJp"
AH$+
AG8T.b (kJ/mol)
(kJ/mol)
-119.90
-372.90
"Calculated in this work. bFrom TRC Thermodynamics Tables (1992).
standard enthalpy and the Gibbs free energy change of the reactions at 298.15 K. As described above, these thermodynamic values were determined by either (a) eq 11or (b)the standard Gibbs free energy of reactions determined directly from experiments at 298.15 K, coupled with the standard enthalpy of reactions at 298.15 K determined from a nonlinear regression of eq 8. The thermodynamic parameters from these two different methods were used to correlate theory and experiments, as shown in Figures 2-4. The data obtained from eq 11(method a) gave the best overall fit to the experimental results as shown in Figures 2-4 and were chosen to obtain the following equilibrium constant correlations: In Kl = 22.809
3 + 3136 - 5.8227 In T + 0.0179T T
6.395 x 1OP6T2 - 1.672 x lO-'P (13) 2078 6
In K2 = 26.779 + -- 6.5925 In T T
+ 0,02312' -
1.126 x 1 0 - 5 p - 1.414 x 1O-*P(14) -1
0
1
2
3
4
5
In K3 = -3.97
( I/TO - I / T ) ( x io4 ), I / K Figure 5. Plot of eq 11 for the determination of the standard enthalpy and Gibbs free energy of reactions at 298.15 K.
+
~
T
+ 0.7698 In T - 0.0052T +
4.865 x 10-6?i3 - 2.58 x
i
AGfy a (kJ/mol)
AHrpa (kJ/mol)
AGry (kJ/mol)
AHryC (kJ/mol)
1 2 3
-11.10 -4.22 -6.88
-33.39 -24.29 -9.10
-11.14 -4.21 -6.93
-33.62 -24.19 -9.16
a Determined by eq 11. From experiments at 298.15 K and eq 5. From nonlinear regression of eq 8.
intercept of the resulting straight lines. The calculated values are listed in Table 4. Gibbs free energies of the reactions and equilibrium constants determined directly from the equilibrium experiments a t 298.15 K are also listed in Table 4. It is seen that these values are quite close to those determined by eq 11 and Figure 5 . Assuming that the Gibbs free energy changes of the reactions calculated directly from the experiments at 298.15 K are accurate, the enthalpy changes for the reactions were also computed by the nonlinear regression of eq 8 by using the computer program SYSTAT 5.2 (SYSTAT, Inc., 19921, as shown in the last column of Table 4. The Gibbs free energy change of reaction 3 thus obtained is different by about 4.5% from that calculated from the literature values of the Gibbs free energy of formation of 2M1B and 2M2B listed in Table 3. Expressions for equilibrium constants as a function of temperature in the form of eq 8 require both the
(15)
It may be noted from Table 5 and eqs 13-15 that (16)
Table 4. Calculated Standard Enthalpy and Gibbs Free Enerev of Reactions at 298.15 K reaction
iO-'1"1
(17) and thus
lnKl = lnK,
+ lnK3
(18)
i.e., the Gibbs free energy change and enthalpy change for reactions 2 and 3 add up to the corresponding values for reaction 1, as they should, since the three reactions (eqs 1-3) are not all stoichiometrically independent. The only exceptions are the values obtained by the nonlinear regression method. It may further be checked that eqs 13-15 conform to eq 18. Thermodynamic Data for TAEE. To calculate the standard enthalpy and Gibbs free energy of formation of TAEE at 298.15 K from the standard enthalpy and Gibbs free energy changes of the reactions at 298.15 K obtained from eq 11,the thermodynamic data of ethanol, 2MlB, and 2M2B listed in Table 3 were used. The values of liquid-phase standard enthalpy and Gibbs free energy of formation of TAEE a t 298.15 K were thus calculated and are compared to the estimates provided by the TRC Thermodynamic Tables (1992) in Table 5. It may be noted that the difference is less than 1%. However, this difference can be very significant in chemical reaction equilibrium calculations. Equilibrium Conversion and Selectivity. In order to calculate the equilibrium conversions and selec-
Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1097 tivities for this reaction network (Figure 1)for a given temperature and feed compositon by making use of eqs 13-15 along with eq 4, the following stoichiometric relationship that relates the mole fraction of species j in a reacting mixture involving R independent reactions, from a total of q reactions, to the extent of each reaction may be used.
oj + x.= J
n
R
_i = l R
j = 1,2, ...,n
(19)
where Oj is the molar feed ratio o f j with respect to the key component (here ethanol), i.e., Oj, NjdN~o,while the dimensionless extent of reaction z,
