2830
Ind. Eng. Chem. Res. 1994,33, 2830-2835
Equilibrium Constants for Methyl tert-Butyl Ether and Ethyl tert-Butyl Ether Liquid-Phase Syntheses Using Cq Olefinic Cut Jose F. Izquierdo, Fidel Cunill,' Meritxell Vila, Montserrat Jhorra, and Javier Tejero Chemical Engineering Department, University of Barcelona, Marti i Franqubs, 1, 08028 Barcelona, Spain Equilibrium constants for the liquid-phase syntheses of methyl tert-butyl ether (MTBE) and ethyl tert-butyl ether (ETBE) were determined experimentally in the temperature range 313353 K and at 1.6 MPa, using as source of 2-methylpropene (isobutylene) a C4 olefinic cut proceeding from a steam cracking unit. To reach etherification equilibrium, the macroporous sulfonic acid resin K-2631 (Bayer) was used as the catalyst. The thermodynamic equilibrium constants and the enthalpy, free energy, and entropy changes of reactions were given as a temperature function. At 298 K, the standard molar reaction enthalpy A,Hm0(298K, 1.6 MPa) for MTBE and ETBE are -(37.3 f 2) and -(34.8 f 1.3)kJ-mol-l, respectively, and are compared with literature data. A comparison of the equilibrium constant values with those obtained using pure reactants with and without small initial amounts of water ('5 wt 96) is also included. The UNIFAC estimates of activity coefficients were used to describe the liquid-phase nonideality. The standard molar enthalpies of formation A$-Imo(l, 298.2 K) of MTBE and ETBE are -313.5 and -349.9 kJ-mol-l, respectively.
Introduction Environmental legislation around the world has forced the use of oxygenates (alcohols and tertiary ethers) for gasoline blending to phase out the lead additives and to reduce reactive evaporative and exhaust emissions. The U.S. Clean Air Act Amendments of 1990 (EPA, 1992) set forth the basic guidelines for future transportation fuel composition and require the manufacture of oxygenated and reformulated gasolines (Peeples, 1991; Hadder, 1992; Unzelman, 1993). The oxygenated gasoline requires that, beginning Nov 1, 1992, gasoline with a minimum oxygen content of 2.7 wt % must be sold during winter months in U.S. cities not in compliance with carbon monoxide standards. The reformulated gasolines (RFG) with a minimum of 2 wt % oxygen are required by J a n 1, 1995, in nine areas with extreme or severe ozone pollution problems. In conclusion, the presence of oxygen in gasoline is unquestioned. Now, attention within the petroleum refining industry is focused on the question of which ether (tertiary) or alcohol (methanol, ethanol, tert-butyl alcohol (TBA))or their mixings or combinations of ethers can do the best job of handling RFG blending within the refinery complex and a t lowest cost. Tertiary ethers, such as methyl tert-butyl ether (MTBE), ethyl tert-butyl ether (ETBE), and tert-amyl methyl ether (TAME), are preferred by refiners to the lighter alcohols, among others reasons, because of their lower blending Reid vapor pressure (bRvp), lower vaporization latent heats, and because they avoid phase separation in the presence of water, which accounts for their full compatibility in the petroleum refining and distribution systems. However, alcohols will be used as needed during critical supply periods of ethers, particularly the next few years when RFG come into force. For a variety of reasons, mainly economical, MTBE has overwhelmingly become the oxygenate of choice. Thus, global MTBE production and use will achieve the highest growth rate of all major chemicals during the 1990s. MTBE demand is forecasted to be tripled (29 million metric tons) by the year 2000 (Hunt, 1993). Nevertheless, the risks associated with high dependence on MTBE have led to use of other ethers (TAME and 0888-5885/94/2633-2830$04.50/0
ETBE) and research into the production and use of others, such as diisopropyl ether (DIPE) and dimethyl carbonate (DMC). The olefinic C4 cut is the main source of inexpensive isobutylene feedstock, and is becoming scarcer. This is why ETBE is a true rival of MTBE, but ETBE competitiveness depends on ethanol price. ETBE production costs (U.S. basis) including subsidies for ethanol are slightly higher than those for MTBE (from C4) and TAME but less than those of MTBE (via isomerization and deshidrogenation of butane), DIPE, and DMC (Hunt, 1993). From a technical point of view, ETBE outranks MTBE as an octane enhancer and is more attractive than MTBE and ethanol for low bRvp blends less than 8 psi required in some places during summer as its bRvp is only 4 psi. Furthermore, ETBE has a lower oxygen content (15.7 wt %I than does MTBE (18.2) and ethanol (34.701, which means that it can provide the greatest dilution effect. ETBE can be blended at 17.3 vol % to achieve a n oxygen level of 2.7 wt %, a level reached by MTBE a t 15 vol % and by ethanol at only 7.7 ~ 0 1 %In . this manner, ETBE blends allow the greatest reduction in concentration of aromatics, sulfur, and benzene, which is an objective to be reach in clean gasolines. It is noteworthy to mention that EPA (Environmental Protection Agency) proposed December 1993 that 30% of the oxygen required in the federal RFG program was to be produced from renewable sources (Oxy-Fuels News, 1993a). In this context, it is estimated that in U.S. MTBE will remain the most popular oxygenate, commanding about two-thirds of the total oxygen market. Ethanol blends, used primarily during winter because of volatility concerns, will have about 20% of the RFG market, and ETBE will provide about 10%. TAME would account for the remainder (Oxy-Fuel News, 1993b). Therefore, these oxygenated compounds will have a very important role in RFG. MTBE and ETBE are obtained by the addition reaction of methanol or ethanol to isobutene, respectively. The reactions are reversible, moderately exothermic, and usually catalyzed by macroporous sulfonic acid resins. The selectivity of both reactions is very high, 0 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2831 but some byproducts such as dimethyl ether and methyl sec-butyl ether (Kaitale et al., 1988; Sarathy and Suffridge, 1993) (by addition of methanol to linear butenes) for MTBE synthesis, and diisobutenes can appear if the temperature is high enough and the molar methanol/ isobutene ratio is far from the stoichiometric one. For ETBE synthesis diethyl ether and diisobutylene are the main byproducts. The presence of tert-butyl alcohol in both reactions is also possible if the reactor feed contains water and/or dialkyl ether is formed. Despite the fact that more than 1000 papers about MTBE can be found in the literature, relatively few experimental thermodynamic quantities for the ether are available. Much more scarce is literature about ETBE. This work was undertaken to determine experimental values of the equilibrium constant for both etherification reactions by direct measurement of the mixture compositions at several temperatures using as source of isobutylene a Cq olefinic cut proceeding from a steam cracking unit, including the range 313-323 K, for which there is really a shortage of experimental data. Then the equilibrium constants were compared with those obtained for pure reactants with and without an initial amount of water less than 5 wt %. Standard enthalpy change of the MTBE and ETBE syntheses were calculated and compared with those found in the literature. Finally, the standard enthalpy of formation of both compounds is derived.
Experimental Section (i)Materials. Methanol, ethanol, and MTBE HPLC (ROMIL Chemicals Ltd., Shepshed, England), with a minimum purity of 99.8% were dried over 3& . molecular sieve before use. ETBE was prepared in our laboratory by reacting ethanol and isobutene and was purified by extraction with water and distillation up t o 99% pure (GC). Isobutene was obtained from the C4-hydrocarbon stream of a steam cracking (SC) unit. The composition of the Cq fraction was typically isobutene, 40-50 wt %; 1-butene, 20-30 wt %; n-butane, 5-10 wt %; trans-2butene, 5-10 wt %; cis-2-butene, 3-7 wt %; isobutane, 1-5 w t %; and other hydrocarbons < lwt %. Nitrogen supplied by SEO, Barcelona, with a minimum purity of 99.998% was used to achieve the suitable pressure to maintain the reacting mixture in the liquid phase a t every temperature. The commercial acidic resin used was K-2631 produced by Bayer. The particle size range was (0.25-1.6) x m (effective bead size 0.73 x m) and the concentration of exchangeable hydrogen ions determined by titration was 4.7 (mequiv of HS03Hg-l of dry resin). (ii) Apparatus. The experiments were carried out m3 in a stainless steel jacketed autoclave of 3 x capacity (Autoclave Engineers, USA) in batch operation. The reaction medium was agitated at 500 rpm by a magnetic-drive turbine. Temperature was controlled to within f 0 . 2 K by thermostatic water that flowed through the jacket. For more detailed information of the apparatus see Izquierdo et al. (1992). (iii) Analysis. The reactor was connected directly to the liquid sampling valve (VALCO 4-CL4WE), which injected 0.2 p L of pressurized liquid to a gas chromatograph (HP5890A) equipped with a flame ionization detector. A 50 m x 0.2 mm x 0.5 pm of methyl silicone capillary column (PONA-HP 190915-001) was used to separate and determine methanol; MTBE and byproducts; and ETBE, ethanol, and their byproducts. The
PONA column was temperature programmed with a 1-min initial hold a t 273 K followed by a 2 Kmin-l ramp up t o 283 K, and held for 2 min. Then, a 20 K-min-l second ramp was used t o reach 433 K. The Cq mixture resolution was done on a 50 m x 0.32 mm x 5 pm A1203 fused silica capillary column (PLOT-HP 19091P-AL5). The PLOT column was temperature programmed with a 4-min initial hold at 338 K followed by a 9 K-min-l ramp up to 463 K. In both cases helium (SEO, Barcelona) with a minimum purity of 99.998% was used as a carrier gas. The carrier gas flow rate was 30 mL-min-I. (iv) Procedure. A calculated amount of methanol and about 10 g of resin dried at 378 K for at least 24 h was charged into the open reactor. The residual water amount in the dried resin, titrated by the Karl-Fisher method, was less than 3 wt %. After the reactor was checked for leaks, a C4 quantity, given by the planned methanollisobutene ratio, was measured a t 0.8 MPa in a calibrated buret and charged into the reactor by shifting with nitrogen. After a few minutes the pressure was controlled a t 1.6 MPa and then a sample was withdrawn to calculate the initial composition. At the desired temperature, the reaction was allowed t o reach equilibrium, which was checked by taking out several samples at successive times until a stationary composition was obtained. Equilibrium was assumed to be attained based on the results of some experiments of previous works (Izquierdo et al., 1992; Vila et al. 1993) in which equilibrium was approached from both directions. To do this, the mixture at equilibrium at the lowest temperature, 313 K (high ether equilibrium conversion), was used t o attain to the equilibrium at the highest temperature, 353 K, which leads to ether decomposition. Equilibrium constant obtained a t that temperature was in excellent agreement with that calculated by obtaining a constancy of composition in one direction. As at lower temperatures it took many hours (24 h as a minimum) to reach equilibrium, an initial amount of the respective ether was used to achieve equilibrium faster. For more detailed information of the procedure see Izquierdo et al. (1992).
Results and Discussion (i) MTBE Equilibrium Synthesis. A set of six experiments was carried out in the temperature range 313.5-353 K with an initial methanol-isobutene molar ratio, m,rangingfrom 0.92 to 1.14. In all experiments, tert-butyl alcohol was detected as a result of the presence of traces of water introduced in the system by the resin and methanol. In some experiments diisobutylene was also detected. Table 1 shows the experimental conditions and results. It was computed from analytical data that the experimental error of molar fractions, x , is about f0.002 (but for diisobutene that was something greater), which allowed one to express the molar fractions to three decimal places. The activity coefficients of compounds, y , were calculated by the UNIFAC method (SkoldJorgensen et al., 1979; Gmehling et al., 1982; Almeida et al., 1983; Tiegs et al., 1987), whose validity for this system was already checked (Colombo et al., 1983; Izquierdo et al., 1992; Vila et al., 1993). Besides methanol (Mt), isobutene (I), MTBE, tert-butyl alcohol (TBA),and, in some cases, diisobutene (DIB),the actual components of the system, which are inert in our operation conditions, are 1-butene, n-butane, trans- and cis-2-butene, and other minor components, such as isobutane. Considering that the predicted activity
2832 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 Table 1. Experimental Conditions and Obtained Equilibrium Constants for MTBE Synthesis from Cr Cut expt 5°K rMVI XMt XI XME XTBA XDIB Xi-b
K, YMt
YI YME YTBA YDIB Y1-b
Ky K
1 313.7 0.92
2 323.5 1.10
3 333.4 1.10
4 333.4 1.14
5 343.3 1.10
6 353.2 1.10
0.022 0.070 0.782 0.004 0.008 0.113 508 3.727 1.145 1.001 2.590 1.308 1.116 0.235 119
0.068 0.027 0.632 0.003 0.000 0.271 347 3.488 1.173 0.992 2.306 0.000 1.144 0.242 84
0.070 0.046 0.586 0.004 0.001 0.294 182 3.521 1.160 0.995 2.273 1.237 1.132 0.244 44
0.091 0.033 0.582 0.006 0.000 0.288 191 3.224 1.189 0.993 2.119 0.000 1.160 0.259 50
0.091 0.054 0.574 0.017 0.000 0.265 118 3.072 1.186 0.994 2.024 0.000 1.160 0.273 32
0.100 0.060 0.570 0.004 0.005 0.262 97 3.049 1.178 0.993 2.012 1.258 1.153 0.277 27
Table 2. Comparison of MTBE Eauilibrium Constants
T/K
pure reactives
in the presence of water
isobutene from Cq cut
average value
313 323 333 343 353
121 72 50 33 23
111 87 57 39 27
119 84 47 32 27
117 f 20 8 1 f 19 53 11 36 f 8 26 f 5
*
coefficients of all inert hydrocarbons of the C4 cut are very similar and close to unity (Colombo et al., 19831, 1-butene is assumed t o be the representative compound of all the inert hydrocarbons. Therefore, only the six components showed in Table 1 were considered in the UNIFAC predictions for the reacting system; i.e., all the species present in solution, both reacting and inert, were considered. The values of K, calculated by the relation
Ky = Y M T B ~ Y M Y I
(1)
showed the nonideal behavior of the system, the methanol being the most nonideal, showing activity coefficients greater than 3. MTBE behaved ideally and hydrocarbons were slightly nonideal. The thermodynamic equilibrium constant for a liquidphase reaction of a nonideal system is given by S
Table 3. Constants for the Equation cJ(J mol-' K-l) = a + b(T/K)+ C(T/KP+ d(T/K)3 compound methanola isobutene" MTBEb
a,
b,
lo%,
105d,
1391.6 596.89 53.176
-12.364 -4.6387 0.7173
3.781 1.440 -0.1533
-3.719 -1.372 0.20241
a Calculated from Gallant (1970) by fitting of a third-order equation. Estimated by the Rowlinson-Bondi method (Reid et al., 1987).
librium constant by considering that all the equilibrium constant values are included in the confidence interval for a 95% probability level for the average equilibrium constant at each temperature. The comparison of the obtained values with those obtained by other authors was done in a previous paper (Izquierdo et al., 1992). The dependence of K on temperature can be estimated by integration of the van't Hoff equation. In this context, taking into consideration previous results (Izquierdo et al., 1992; Vila et al., 19931, it is better to accept the fact that reaction enthalpy change is a function of temperature (Kirchoff equation). Assuming that the molar heat capacities of the species are given by the third-degree polynomials shown in Table 3, the integration of Kirchoff equation yields the well-known expression U b C d In K - -In T - -T - -p - -p = R 2R 6R 1% lnK+f(T)=IH--
IK
(3)
RT where
with ai, bi, ci , and di values of Table 3. The constants ZK and ZH can be calculated from the temperature dependence relationship for the experimental equilibrium constant of MTBE reaction. By fitting eq 3 to data of Table 3 for pure reactants, we obtain ZK from the slope and IHfrom the intercept. Thus, the expression for the temperature dependence of K values of Table 2 is
In K = 1145.0257 - 14714.411T1 232.7593 In T + 1.065597T - 1.0775 x
S
~ o - +~5.30525 P
S i=l
The effect of the pressure on the equilibrium constant was neglected due to the pressure being less than 2 MPa (Colombo et al., 1983). Using the liquid molar volumes reported by these authors and the conditions of the present work, the Poynting correction factor introduced an error in the calculation of K less than 1%,which is less than the experimental one. Therefore, we assume that K is only a function of temperature. It is worth noting that the K values obtained followed the general trend of lowering when temperature increased, as expected for an exothermic reaction. Table 2 shows a comparison of the obtained K values with those obtained in previous work using pure reactants with (Cunill et al., 1993) and without (Izquierdo et al., 1992) a small initial amount of water. As can be seen, the presence of initial amount of water or TBA formed and inert hydrocarbons did not affect the equi-
10-~T3(5)
The average K values of Table 2 are well correlated by the following relation, which is more manageable for engineering calculations.
K = 1.65 x
exp[4224.34/Tl
(6)
By considering the following well-known thermodynamic relations
AS" = R In K
+M"/T
(8)
and AGO = -RTIn K = A W - ThS"
(9)
we can obtain the standard molar changes of the reaction ArHmo, A,Sm0, and A,.G," as a function of temperature:
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2833
+
hamo = 122341.5 - 1935.2541T 8.8598P 1.7915 x 1Ow2p 1.3234 x 1 0 - 5 p (10)
+
A$,'
+
= 7584.9478 - 1935.254 In T 17.7196T 2.6874 x 1 0 - 2 p 1.7645 x 1 0 - 5 p (11)
+
+
ArGmo= 122341.5 - 9520.2019T 1935.254T In T - 8 . 8 5 9 8 p 8.9590 x 1 0 - 3 p 4.411 x 1 0 - 6 p (12)
+
At 298.15 K we have the following values, A$Imo(1)= -(37.3 f 2.0) kJ-mol-I A+Sm0(l)= -(79.5 f 1.0) J-mo1-l-K-l A,Gmo(l)= -(13.6 f 2.0) kJ*mol-' Table 4 shows a comparison of the standard molar enthalpy change of the reaction determinated in this work with those theoretical and experimental values deduced in other works using different methodologies, namely, theoretical estimations (Rehfinger and Hoffmann, 19901, reaction calorimetry (Arntz and Gottlieb, 1985; Sola et al., 19941, and similar methods, i.e., equilibrium data (Gicquel and Torck, 1983; Colombo et al., 1983). It may be seen that the value found in this work has fallen in the center of the distribution of the literature data, which accounts for the validity of the methodology used. A comparison of the standard molar free energy change with that reported by Rehfinger and Hoffmann (19901, ArGmo(1,298.2K) = -(14.0) kJ*mol-l reveals excellent agreement. Furthermore, from the and the formation enthalpies (Pedexperimental ArHmo ley et al., 1986) AfHmo{(CH3)2C=CH2, 1, 298.2 K} = -37.5 kJ-mol-l and AfHmo(CH30H,1,298.2 K) = -239.1 kJ-mol-l, the molar formation enthalpy AfHmo{(CH3)3COCH3, 1, 298.2 K} = -313.9 kJ*mol-l is obtained. Comparison with the result from Fenwick et al. (19751, AfHmo((CH3)30CH3,1, 298.2 K} = -(313.56 f 1.29) kJ*mol-' and registered by Pedley et al. (1986) (-313.6 kJ-mol-l), shows a good agreement, which backs up again the methodology used in this work. (ii) ETBE Equilibrium Synthesis. A set of nine experiments was performed in the temperature range 313.5-353 K with an initial ethanol-isobutene ratio, ~ f i ranging , from 1.0 t o 1.3. In all the experiments, no diisobutylene was detected. Diethyl ether formation could only be detected at the highest temperature. TBA was also detected as a result of the addition of traces of water to isobutene. The amounts detected were so minute that they did not alter ETBE equilibrium and the estimation of activity coefficients. Table 5 shows the experimental conditions, the equilibrium molar fractions, the activity coefficients, the equilibrium constants based on molar fractions, and the thermodynamic equilibrium constants. The activity coefficients were estimated by the UNIFAC method mentioned earlier. As data suggest, as for the MTBE equilibrium system, the system was clearly nonideal, with ethanol behavior being the most nonideal. The same as for MTBE-C4,l-butene was assumed to be the representative compound of all the inert hydrocarbons. The values of K y and K were calculated by eqs 1and 2, respectively, and we assume the same hypothesis about the pressure effect on the equilibrium constant. As expected, we can observe that the K values lowered
Table 4. Standard Molar Enthalpy of MTBE Synthesis in the Liquid Phase at 298 I( reference
h,H,"/(kJ~nol-~)
this study Rehfinger and Hoffmann (1990) Arntz and Gottlieb (1985) Sola et al. (1994) Gicquel and Torck (1983) Colombo et al. (1983) Obenaus (1980) Gupta and Prakash (1980) Brockwell et al. (1991)
-37.3 f 2.0 -37.7 -39.2 f 0.4 -34 f 2 -39.8 f 2 -34.0 -37.0 -36.8 -40
when temperature increased. It is to be mentioned that duplicate runs at 343.3 K and triplicate runs at 353.2 K showed that the reproducibility was very good and, a t the same time, showed that the thermodynamic equilibrium constant was independent of composition, as expected. Table 6 shows a comparison of the obtained K values with those obtained in our previous work using pure reactants with (Cunill et al.,1993) and without (Vila et al., 1993) a small initial amount of water and those of the literature (Franqoisse and Thyrion, 1991). As can be seen, similar to the MTBE system, the presence of initial amount of water or TBA formed did not affect significantly the equilibrium constants. Practically, the K values found by Franqoisse and Thyrion (1991) are included in the confidence interval for a 95% probability level a t each temperature over 313 K. Using eqs 3,4, 7,8, and 9 for the ETBE system with the heat capacities of Table 7, we deduced the following expressions for the temperature dependence of K
In K = 1140.876 - 1483.2T' - 232.873 In T 1.086489T
- 1.11385 x
+
+
10-3p 5.53858 x 1 0 - 7 p (13)
To do equilibrium calculations, the following relation can be used for the average equilibrium constant:
K = 7.40
x
exp[4262.21/Tl
(14)
For the standard molar changes of reaction AJImo, A$,,,", and ArGmowe obtain
+ + Ag," = 7549.5 - 1936.2 In T + 18.0669T 2.7785 x 10-2p+ 1.8419 x 1 0 - 5 p (16) ArGmo= 121248.9 - 9485.7T + 1936.2T In T 9.0335p + 9.261 x 10-3p - 4.605 x 10-6T' (17) A q m 0 = 121248.9 - 1936.2T 9.0335P 1.8524 x 1 0 - 2 p 1.3814 x 1 0 - 5 p (15)
At 298.15 K we obtain the following values:
hamo = -(34.8 f 1.3)kJ-mol-' = -(77.3
* 0.6)J.rno1-l.K-l
ArGmo= -(11.8 f 1.3)kJ-mol-' Unfortunately, there are few values in the literature of the standard enthalpy change of ETBE synthesis to do reliable comparison. Rock (1992)mentions the value of -27.6 kJ-mol-l, but nothing is said about how and under which conditions it was obtained. Anyway, it
2834 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 Table 5. Experimental Conditions and Obtained Equilibrium Constant for EWE Synthesis from Cq Cut 3 expt 1 2 4 5 6 7 8 TAX 313.7 323.5 333.4 333.4 343.3 343.3 353.2 353.2 1.06 1.06 1.31 1.10 1.28 1.10 1.28 rEt? 1.02 0.038 0.058 0.081 0.136 0.081 0.140 0.108 0.163 XEt 0.064 0.070 0.036 0.066 0.047 0.066 0.074 0.051 XI 0.527 0.412 0.409 0.596 0.554 0.397 0.374 0.368 XE 0.000 0.005 0.004 0.003 0.002 0.002 0.003 0.003 XTBA 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.002 XDEE 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 XDIB 0.301 0.320 0.318 0.413 0.442 0.415 0.438 0.413 Xinerts 241.8 150.3 92.6 83.2 76.9 60.8 44.3 46.6 K, 4.214 3.390 3.209 3.771 2.977 3.603 2.905 2.667 YEt 1.084 1.113 1.073 1.096 1.136 1.084 1.099 1.148 YI 0.997 0.994 0.993 0.993 0.986 0.991 1.099 0.993 YE 0.000 2.662 2.407 2.096 2.500 2.050 2.240 1.893 YTBA 0.000 0.000 0.000 0.000 0.000 0.000 0.828 0.836 YDEE 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 YDIB 1.045 1.057 0.1071 1.111 1.061 1.110 1.078 1.127 Yinerts 0.220 0.243 0.267 0.253 0.301 0.279 0.294 0.324 KY 53.3 36.6 24.8 19.4 K 24.4 18.3 13.0 14.4 Table 6. Comparison of ETBE Equilibrium Constants in the
pure presence isobutene average literature T/K reactives of water from C4 cut value data 313.5 323.5 333.4 343.2 353.2
58.9 42.1 26.4 18.4 12.8
60.8 41.5 26.8 18.1 12.6
53.3 36.6 24.6 18.8 13.9
5 8 f 10 41 f 7 26 f 3 18 f 1 13 f 2
46.0 26.3 16.2 11.5
Table 7. Constants for the Equation cd(J mol-' K-l) = a b(T/K) c(T/K)2 d(T/K)S
+
+
product
ethanola
isobutene" ETBEb
+
ai
bi
l0ZCi
105di
1422.5 596.89 83.158
-12.839 -4.6387 0.5894
4.031 1.440 -0.08641
-4.016 -1.372 0.1383
a Calculated from Gallant (1970) by fitting of a third-order equation. Estimated by the Rowlinson-Bondi method (Reid et al., 1987).
seems it is a small value if we take into consideration the value of MTBE synthesis. Frangoisse and Thyrion (1991) quoted the value of -35 kJ-mol-l; however, they obtained a constant value of -44.3 kJ*mol-l. Values, not yet published (Sola, 19941, obtained at 323 K by reaction calorimetry are 32.1-34.4 kJ-mol-l, which are close to that estimated by eq 14 at that temperature (-35.5 kJ*mol-'1. From all these, we consider that our value of -34.8 kJ*mol-l is a reliable value and much more if we bear in mind that the methodology used gave excellent results for MTBE. From the experimental A,Hmo and the formation enthalpies (Pedley et al., 1986) AfH," {(CH3)2C=CH2, 1,298.2K} = -37.5 kJ-mol-l and (Slayden and Liebman, 1993) AfH," (CH~CHZOH, 1,298.2 K) = -277.6 kJ.mol-l, the molar formation enthalpy AfH," { (CH3)3COCH2CH3), 1, 298.2 K) = -349.9 kJ.mol-l is obtained. This value, which is not found in the main data banks and handbooks, falls in the range of values for similar monoethers (CsH1401, such as di-n-propyl ether (-328.8 kJ.mol-l), TAME (-340.1 kJ.mol-l), and diisopropyl ether (-351.5 kJ-mol-l) (Slayden and Liebman, 1993).
0.172 0.049 0.368 0.003 0.000 0.000 0.407 43.2 2.595 1.156 0.996 1.847 0.000 0.000 1.136 0.332 14.3
perform calculations. In this way, the compositions of the outlet stream of the reactor, which are designed to reach the equilibrium, can be calculated. The heat released by the reactions in the reactor can be also calculated as a function of the temperature. This allows design of the cooling system.
Acknowledgment The authors wish to express thanks for financial support to CIRIT (Catalonia Government) and t o the refining company REPSOL PETROLEO S.A.
Nomenclature a , b, c , d = changes of molar heat capacity coefficients with chemical reaction a,, b,, c,, d, = coefficients in the equation for molar heat capacity of component i a', = activity of component z, dimensionless bRvp = blending Reid vapor pressure, psi cp, = molar heat capacity of component z, J-mol-l.K-l AT) = function of a, b, c, d and T defined in eq 2 G o = standard free energy, J-mol-I H" = standard enthalpy, J.mo1-l IH = integration constant in van't Hoff equation, dimensionless IK = integration constant in Kirchoff equation, J-mol-l K = thermodynamic equilibrium constant Ky = ratio of activity coefficients K, = experimental equilibrium constant based on molar fractions r = initial molar ratio R = gas constant, J.mo1-l.K-l So = standard entropy, Jemol-l-K-l T = temperature, K x , = molar fraction of component i, dimensionless ArGmo= standard molar free energy change of reaction, kJ-mol-l ArHm" = standard molar enthalpy change of reaction, kJ-mol-l A S m ' = standard molar entropy change of reaction, J-mol-1.K-1 Greek Symbols
Conclusions Conversion and, therefore, concentration at equilibrium for MTBE and ETBE syntheses can be predicted from the respective equilibrium constant in the presence of inert hydrocarbons of the C4 cut. As the systems behave nonideally, the use of activities is necessary to
9 353.2 1.31
y , = activity
coefficient of component i v, = stoichiometric coefficient of component i
Subscripts
b = butene DIB = diisobutene DEE = diethyl ether
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2835
E = ethyl tert-butyl ether E t = ethanol I = isobutene M t = methanol M E = methyl tert-butyl ether
T = tert-butyl alcohol Abbreviations 1-b = 1-butene b R v p = blending Reid vapour pressure ETBE = ethyl tert-butyl ether DIB = diisobutylene MTBE = methyl tert-butyl ether TBA = tert-butyl alcohol TAME = methyl tert-amyl ether
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Received for review March 1, 1994 Revised manuscript received July 14, 1994 Accepted July 25, 1994@ Abstract published i n Advance ACS Abstracts, October 1, 1994. @
