392
I n d . Eng. Chem. Res. 1995,34,392-399
Ethers from Ethanol. 1. Equilibrium Thermodynamic Analysis of the Liquid-Phase Ethyl tert-Butyl Ether Reaction+ Kyle L. Jensen and Ravindra Datta’ Department of Chemical and Biochemical Engineering, The University of Iowa, Iowa City, Iowa 52242
The equilibrium-limited liquid-phase synthesis of ethyl tert-butyl ether (ETBE) from the combination of ethanol and isobutylene over an ion-exchange resin catalyst, typically Amberlyst 15, is a reaction of considerable industrial importance now. An equilibrium constant relationship is developed here for the liquid-phase ETBE reaction by following three alternative thermodynamic pathways and critically evaluating the resulting expressions. The final theoretical expression is compared against experimental data obtained in this study from the decomposition of ETBE over Amberlyst 15,as well as that reported in the literature for ETBE synthesis. It can thus be used with reasonable confidence for the calculation of the equilibrium constant, despite a dearth of thermodynamic data yet available in the literature for ETBE. I n addition, a n expression is derived for the gas-phase equilibrium constant and compared to experimental data from the literature. The thermodynamic approach utilized here should also be useful for other liquid-phase reaction systems.
Introduction Oxygenated compounds (those containing oxygen) have now replaced lead compounds as gasoline additives in the United States and are gradually gaining acceptance worldwide. The two main classes of competing oxygenates at present are alcohols and ethers, both possessing the desired characteristics of octane enhancement and CO emissions reduction. In general, however, ethers are preferred over alcohols because of their fungibility, or blending characteristics, as they are more like conventional gasoline hydrocarbon constituents. Alcohols are substantially more polar than ethers and other gasoline hydrocarbons and, consequently, can result in phase separation in the presence of any water in the gasoline distribution system. Further, in spite of their low individual vapor pressure, alcohols tend to produce a higher blending Reid vapor pressure (RVP) and, thus, more volatile organic compounds (VOC) emissions. The predominant oxygenate used at present is methyl tert-butyl ether (MTBE, or 2-methoxy-2-methylpropanej, synthesized commercially by the exothermic liquidphase reaction of methanol and isobutylene over an acid ion-exchange resin catalyst (Voloch et al., 1987; Rehfinger and Hoffman, 1990), although other catalysts have been suggested (Pien and Hatcher, 1990; Hutchings et al., 1992). In fact, spurred by the passage of the Clean Air Act Amendments of 1990, MTBE is now the second largest volume organic chemical produced in the U.S., behind only ethylene (Reisch, 19941. This is remarkable since its commercial production began barely two decades ago. Although MTBE is currently the industry standard, the Environmental Protection Agency has proposed an increased role of renewable oxygenates, aimed primarily at reducing the dependence on the finite fossil fuel resources. Furthermore, this would alleviate concerns about the buildup of carbon dioxide in the atmosphere, the major “greenhouse”gas. As a result, ethyl tert-butyl ether (ETBE, or 2-ethyoxy2-methylpropane), derived from renewable ethanol and isobutylene, has emerged as a promising new oxygenate.
* Author to whom correspondence may be addressed. Presented at the ACS Meeting, Washington, DC, August, 1994. +
ETBE has a somewhat lower blending RVP and a higher octane number than MTBE, both of which are attractive properties for improved automotive performance and reduced VOC emissions. The commercial production of ETBE, by the equilibrium-limited exothermic reaction of ethanol and isobutylene over an acid ion-exchange resin catalyst, has now begun (Oxy-Fuel News, 1992). Although little published information is available on the process, it is known that ETBE synthesis is quite like that of MTBE. In fact, commercial MTBE plants can be retrofitted easily to produce ETBE. The MTBE reaction is conducted at a temperature of around 50-60 “C and a pressure of around 200-250 psig required to maintain isobutylene in the condensed phase. Under these conditions, the equilibrium conversion of MTBE is roughly 96% but drops substantially at higher temperatures, desirable from the kinetics standpoint, due to the considerable exothermic heat of the reaction. In order to overcome the thermodynamic constraints, the MTBE reaction is, thus, conducted either in two sequential packed-bed reactors with interstage cooling or in a reactive-distillation column. Since ETBE conversion is also equilibrium limited, in fact even more so than the MTBE synthesis, roughly being 94% under the above cited conditions, accurate information on the reaction equilibrium constant is needed. In spite of its anticipated industrial importance, only limited information on the thermodynamics of the liquid-phase formation of ETBE is available in the literature. The objective of this paper, thus, is to provide a detailed thermodynamic analysis of the liquid-phase ETBE synthesis. Unlike the case of ETBE, a number of correlations for the equilibrium constant of the MTBE reaction are available in the literature. Thus, Colombo et al. (1983) developed an expression for the equilibrium constant for the liquid-phase MTBE synthesis based on gas-phase thermodynamic data available in the literature and by assuming constant molar heat capacities. They first used the UNIFAC method for determining the activity coefficients to account for the liquid-phase nonideality. Izquierdo et al.(1992)developed an alternate expression for the liquid-phase equilibrium constant of MTBE as a function of temperature, using estimated polynomial expressions for the liquid molar heat capacities. Reh-
0888-588519512634-0392$09.00/0 0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 393 finger and Hoffman (19901, and Zhang and Datta (1994), have proposed still other correlations, which appear to be more accurate. For ETBE synthesis, Iborra et al. (1989) proposed an expression for the equilibrium constant for reaction in the gas phase. However, since commerciallythe reaction occurs in the liquid phase, it is the thermodynamics of the liquid-phase reaction that is of the principal interest. Vila et al. (1993) have recently reported an expression for the liquid-phase ETBE equilibrium constant; however, the constants of integration in it were used as fitted parameters. Consequently, a careful thermodynamic analysis is warranted, which is provided here along with experimental data over a range of temperatures of practical interest. It is well-known that the accuracy of the reaction equilibrium constants calculated from literature data can be highly sensitive to the accuracy of the reported thermodynamic data, particularly for reactions with a moderate standard Gibbs energy change of reaction, i.e., reversible reactions (e.g., Resnick, 1981). It is important to be mindful of this fact here, since there is as yet a paucity in the literature of reported thermodynamic data for ETBE. Although a number of estimation methods are available (Reid et al., 1987),these can only introduce additional uncertainty in the calculated results. Furthermore, while the gas-phase standard state thermodynamic data are available for a large number of species (e.g., Reid et al., 19871, liquid-phase data are not routinely available. Even though the required liquid-phase data can be estimated from the thermodynamic gas-phase data (e.g., Colombo et al., 19831,the alternate procedures for such calculations are apparently not widely appreciated. For the above cited reasons, we first provide thermodynamic relationships for the alternate pathways possible, owing to the fact that Gibbs energy is a state function, to obtain the equilibrium constant for a liquid-phase reaction as a function of temperature. This allows a critical analysis of the calculated results and sources of errors. The approach provided here is, in fact, general. It is, indeed, surprising that although the problem of determination of liquid-phase reaction equilibria from gas-phase thermodynamic data is common, it is not the stuff of textbooks yet. Due to the large polarity difference among alcohols, isobutylene, and ethers, both the MTBE and the ETBE reaction systems are very nonideal. Thus, activities coefficients are required for calculation of the equilibrium constant from equilibrium conversion data, and vice versa. The UNIFAC method for prediction of activity coefficients is utilized in this study. Izquierdo et al. (1992) and Vila et al. (1993) have, respectively, demonstrated that for the MTBE and ETBE reaction systems, this method provides reliable predictions of the activity coefficients, since the equilibrium constants calculated from the experimental data were found to be independent of the feed composition.
Thermodynamic Analysis Thermodynamic Equilibrium Constant. The equilibrium constant for the liquid-phase reaction, XT=ivfiJ = 0, among the species Aj is
aj 3 y g j , when the pressure correction term is negligible.
Upon relating the activity coefficients, yj, to the mole fraction, xj, through an appropriate relation, such as the UNIFAC correlation, the equilibrium composition may be determined for a given K(l), or alternately, K(1) may be calculated from experimental equilibrium composition. The equilibrium constant, in turn, is related to the thermodynamic properties of the mixture through
for a reaction occurring in a phase a at the reaction temperature T. The standard Gibbs energy change for the reaction is calculated from n
AGo&a)= Z v j A W G d a )
(3)
j=l
where AG"Gt(a) is the Gibbs energy of formation of speciesj in the phase a at the reaction temperature, T. The standard enthalpy change for the reaction at the temperature T may be obtained from
The standard Gibbs energy, enthalpy, and entropy change for the reaction at the temperature T are, of course, interrelated by AG"T(a) = AWT(a)- TA,S"T(a), where AS"T(a)3 &=,~jS"ja). Literature data on the Gibbs energy and enthalpy of formation are, however, normally available only at the standard state (ideal gas; P" = 1bar) and a t T = T" = 298.15 K, rather than at the reaction conditions of interest (e.g., condensed phase; P f Po,T f T"). While the effect of pressure is usually small, AG'da) at other temperatures is obtained from the integrated form of the van't Hoff equation
where the standard enthalpy change of reaction as a function of temperature is obtained from the Kirchoff equation
where for the reaction n
ACo,(a)
ZvjACo,(a)
(7)
j=1
The molar heat capacities of species are generally expressed as a polynomial in temperature of the form (Reid et al., 1987)
+
C",(a) = uj(a) bj(a)T+ c j ( a ) p+ d j ( a ) p (8) The second equality stems from the definition of activity,
Upon using eqs 7 and 8 and carrying out the integration in eq 6, there results
394 Ind. Eng. Chem. Res., Vol. 34,No. 1, 1995
AGo,&l) = AGo,&g)
. + R T In P2 + T(l)(Po- Pvj) Po
(15)
where I d a ) is the constant of integration, obtainable in terms of A H O Y from eq 9 by using T = T",and n
n
n
n
Ac(a) = zv,cj(a); A d ( a ) = zvJdj(a) (10) j=l
where P,,, is the vapor pressure of speciesj a t T and q{l) is the liquid-phase molar volume of j a t T. The above relation is based on the assumption of ideal vapor phase and a substantially incompressible liquid phase and further requires knowledge of Puj as a function of temperature. An alternative expression in terms of AH+pmay be developed by neglecting the last term on the right hand side of eq 15, which is usually small in magnitude, and utilizing the Clausius-Claperyon equation for the second term (with AZ,,= l)
j=l
The use of eq 9 in eq 5 results in
where I d a ) is the constant of integration that can be obtained in terms of AGOy by using T = T" in eq 11. Finally, using eq 11in eq 2 yields
Thus, the enthalpy (eq 9) and the Gibbs energy (eq 11)change, as well as the equilibrium constant K (eq 121, may be determined for the reaction in the phase a (gas or liquid) a t a temperature T. In addition, the entropy change may also be calculated. However, this procedure presupposes availability of the required thermochemical data for the phase of interest. In practice, while gas-phase data may be found, complete liquidphase data are frequently not available. Thus, prediction of the liquid-phase thermochemical data is discussed below. Estimation of Liquid-Phase Thermodynamic Properties from Gas-Phase Data. Different corresponding states correlations are available that relate the liquid-phase heat capacity to the gas-phase heat capacity (Reid et al., 1987), such as the Sternling and Brown correlation (Perry and Green, 1984)
C"pj(1)- CO,(g) R
+ 2.2w)[3.67 + 11.64(1 - TJ4 + 0.634(1 - Tr)-l] (13) = (0.51
Equation 13 is purportedly accurate to within 8%, except for T, > 0.95 and quite polar compounds, such as ethanol. If c"pj(Z) is determined in this manner, it is useful to recast the result in the form of eq 8 in order to obtain K(Z) of the same algebraic form as eq 12. The enthalpy of formation of j in the liquid phase is related to that in the gas phase by AHO,&l) = M O , & g )
- AHoVJ T
(14)
where M ' v j T is the standard enthalpy of vaporization of speciesj at the temperature T. The liquid-phase Gibbs energy of formation of j may be related to that in the gas-phase by (Denbigh, 1981)
The lower limit of integration results from the fact that a t the normal boiling point, Puj= 1atm Po (1.01325 bar). In fact, eq 16 may alternatively be directly obtained by the application of the van't Hoff equation, eq 5 , and is precise. The enthalpy of vaporization as a function of temperature required in eqs 14 and 16 may be estimated by the Kirchoff equation, eq 6. Thus, for a vaporization process viewed as a reaction (Yeremin, 19811, i.e., Aj(1) *Aj(g), the enthalpy of vaporization can be written as
where, in accord to eq 7, along with vj(g) = 1and vJ{l) =
-1,
AC",
E
c"&)
- c"&)
(18)
The above relations are approximate to the extent that, more rigorously, the heat capacities employed should not be at constant pressure. Using eq 8 in the above two equations results in AHOvjT = IHj
Abj Ac. Adj + AajT + --?a + A P + T P 2 3
(19)
where in view of eq 10
Auj E aj(g) - ~ ~ ( 1 Abj );
bj(g) - bj(1);
Acj E cj(g)- ~j(1); Adj
dj(g) - dj(l)
(20)
with the constant of integration, Zw,obtainable from eq 19 with T = T". An alternative procedure would be to estimate the enthalpy of vaporization of j as a function of temperature directly from the Watson relation (Watson, 1943)
However, upon estimation of M,,,T in this manner, it would be prudent to correlate the result with an expression of the form of eq 19, in order that the resulting K(1) remains in the algebraic form of eq 12. Furthermore, if A H v j T is estimated fist from the Watson relation, or experimentally, the liquid-phase heat capacity o f j may alternatively be calculated from the differential form of the Kirchoff equation, i.e.,
Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 395
Finally, using eq 16 in eq 3, and eq 14 in eq 4, the estimated liquid-phase Gibbs energy and enthalpy change for the reaction in terms of the corresponding gas-phase quantities are Step I
AG"@
RT -
AG'Ag) RT
1
Equation23
T mvjT
n
+ Rj=l -xvj(
Step IV
Equation 23
J
T
dT) (23) ~
~
f and Step II j=l
Alternate Pathways for Computation of the
Equilibrium Constant. The use of the above relations allows the computation of AG"dl), and consequently K(1) (eq 21, for a given liquid-phase reaction at a temperature, T. However, as illustrated in Figure 1,since Gibbs energy is a state function, independent of path, different pathways are possible for calculating AG"T(1). Thus, if the standard-state thermodynamic data were available for the liquid phase, only step 11, involving the use of eq 5 is required. We denote this as method 1. On the other hand, if standard-state data were available for the gas phase, two alternate pathways are possible: one (method 2) involving steps I (eq 23) plus I1 (eq 51, and the other (method 3) comprising steps I11 (eq 5) plus IV (eq 23). Although, in principze, the final result should be independent of the pathway chosen, in practice the results should be expected to vary somewhat owing t o the uncertainties involved in the data obtained from the various sources or the property estimation methods utilized. In fact, this procedure could be used to check the internal consistency of the thermodynamic data reported by different sources. Keeping in view the dearth of data available for ETBE, we utilize all three methods here for the ETBE reaction system, before selecting the one that best represents the experimental data.
Experimental Section Experimental results for the thermodynamic equilibrium constant were obtained from the decomposition of ETBE (obtained from Aldrich Chemical, 99% purity) with Amberlyst 15 ion-exchange resin as the catalyst, in a 6 cm stainless steel reactor tube (diameter 1/4 in.). The catalyst (obtained from Sigma Chemical Co.) was prepared by washing the resin first with distilled water, followed by 0.1 M nitric acid. The resin was dried overnight in a vacuum oven a t 110 "C. After filling the stainless steel reactor tube with liquid ETBE, approximately 10-20 grains (particle size, 16-50 mesh) of Amberylst 15 were added and the tube was sealed. The reactor was immersed into a temperature controlled (to within f0.25 "C)water bath (Fischer Scientific, model no. 9001). The experiments were performed over the range of temperatures 20-60 "C. The reactor system was allowed to equilibrate for at least 24 h before sampling and substantially longer periods for temperatures under 35 "C. At least three liquid samples were taken by a syringe through a septum and analyzed by gas chromatography. A Perkin Elmer AutoSystem Gas Chromatograph with helium as the carrier gas (25 mL/
,
II
AG3ri u
Figure 1. Different thermodynamic pathways for calculating the liquid-phase standard Gibbs energy change for a reaction at temperature 2'. Method 1 comprises step 11, method 2 comprises steps I and 11, while method 3 involves steps I11 and lV.
min) using a P O W A K R column (6 ft x 1/8 in.) a t an oven temperature of 170 "C was used for sample analysis. The GC was calibrated for ETBE over a wide range of compositions for accurate analysis, and consequently, the maximum error in the measurement of its mole fraction was estimated to be f0.005. At the lowest temperatures (largest K ) , however, even this small error could result in substantial maximum errors in K (f13%). Thus, highly accurate data are required at high conversions. However, the accuracy increases at the higher temperatures, where K and the conversion are smaller, with the maximum error estimated as f 7 % a t the highest temperatures. The corresponding error bars are shown later. As mentioned before, calculation of the activity coefficients for K, was done by the UNIFAC method, with parameters obtained from Skjold-Jorgensen et al. (1979), Gmehling et al. (19871, and Smith and Van Ness (1987).
Results and Discussion As noted above, values of the calculated thermodynamic equilibrium constant for the ETBE reaction are highly sensitive to the errors in the thermodynamic data used. Cognizant of the variability of the data for ethanol and isobutylene from different sources and the lack of availability of all the required data for ETBE, it was, thus, decided to select the data carefully and preferably from a single source to maintain consistency and, where possible, to test the values against experimental data. The TRC Thermodynamics Tables (1986) were, thus, selected as the preferred source of data for this system. In fact, this is one of the few sources of thermodynamic data available for ETBE. Further, we utilized all three alternate methods outlined above based on gas-phase and liquid-phase data, before selecting the expression that best represents the experimental data. Table 1 provides the values for the gas-phase thermochemical data as obtained from the TRC Thermodynamics Tables (1986). In addition, Table 1contains the coefficients of the equation for molar heat capacity of the components in the vapor phase. The coefficients for the third-order polynomial in temperature, eq 8, were fitted to the experimental data for ethanol and isobutylene taken from Gallant (1968) and are slightly different from those given in Reid et al. (1987).AS shown in Figures 2 and 3, the expressions agree quite well with the gas-phase heat capacity data. Also included in
396 Ind. Eng. Chem. Res., Vol. 34,No. 1, 1995 Table 1. Gas-Phase Thermochemical Dataa and Fitted Coefpicienta of the Gas-Phase Heat Capacity Equation
component isobutylene ethanol ETBE a
heat capacity coefficients of eq 8 bj Cj 0.2804 -1.010 10-4 0.2040 -8.450 x 0.6293 -3.690 x
ai
14.55 19.80 7.505
4
AG"fip, kJ/mol
A H o f i ~kJ/mol ,
9.098 x 1.373 x low9 7.072x
58.2 -167.73 -121.15'
-17.1 -234.95 -316.5
From TRC Thermodynamics Tables (1986). From eq 16.
300 350 400 Temperature, K Figure 2. Comparison of ethanol heat capacities for the gas and liquid phases from eq 8,with coefficients given in Tables 1 and 2, and experimental data (Gallant, 1968). 250
140
3
130
2 2
120
.g
110
agreement with the literature values at the standard conditions cited above and are given in Table 2. The other thermochemical data for the liquid phase obtained from the TRC Thermodynamics Tables (1986) are also listed in Table 2. However, the liquid-phase Gibbs energy of formation for isobutylene was not found in the literature and was, therefore, calculated making use of eq 16. Initially, the literature value of the standard liquid-phase enthalpy of formation of ETBE was taken from the TRC Thermodynamics Tables (1986) as -351.5 kJ/mol but was subsequently adjusted to -357.5 kJ/mol, or by about 1.7%, for reasons discussed later. If the standard gas-phase enthalpy of formation of ETBE of -316.5 kJ/mol given in Table 1 is assumed to be correct, the resulting enthalpy of vaporization from eq 14,consequently, becomes 41 kJ/mol, as compared to the reported value of 35 kJ/mol (TRC Thermodynamic Tables, 1986). However, the adjusted value seems to be within a reasonable range of values, when compared to other standard heats of vaporization of similar compounds of like molecular weight. Further, as given by eq 16,this necessitates a slight change in the gasphase Gibbs energy of formation of ETBE, which must be adjusted accordingly from the original literature value of 121.7 kJ/mol (TRC Thermodynamic Tables, 1986)to 121.15kJ/mol, or by 0.5%. Figure 4 shows the liquid-phase thermodynamic equilibrium constant as a function of temperature calculated using method 1 (Figure l), with the adjusted and nonadjusted values for the standard enthalpy of formation of ETBE. The expression resulting from the adjusted value is
59 + 4060 A - 2.89055In T T 1.91544 x T + 5.28586 x 10-5p-
In KO) = 10.387 70 250
" " "
'
"
300
"
'
" "
'
"
350
1 J
400
5.32977 x
Temperature, K
lO-*P(25)
Figure 3. Comparison of isobutylene heat capacities for the gas and liquid phases from eq 8,with coefficients given in Tables 1 and 2,and experimental data (Gallant, 1968).
whereas that resulting from the nonadjusted value is
Figures 2 and 3 are the results of fitted equations for the liquid-phase heat capacity data for ethanol and isobutylene, also obtained from Gallant (1968). The coefficients of the fitted expressions for the liquid-phase heat capacity are given in Table 2. Unfortunately, data for the heat capacity of ETBE are reported in the literature only at the standard conditions for both the gas and liquid phases, as 161.7 J/mol*K and 219.3 J/mol*K,respectively, and are not available as a function of temperature. Therefore, the coefficients of the expression for the molar heat capacity of ETBE in the gas phase were first estimated by the Rihani and Doraiswamy method (Reid et al., 1987) but were, subsequently, adjusted to some extent for better agreement with the literature values noted above at the standard conditions. Then, making use of eq 13 t o estimate c"pj(l), the coefficients of liquid-phase heat capacity for ETBE were determined by fitting the result to eq 8. The resulting coefficients for the liquid-phase heat capacity were slightly adjusted further for better
In K(1) = 12.767
3350 84 +T - 2.89055In T -
+
1.91544 x 10-2T 5.28586 x 5.32977 x 10-8P (26)
As expected, by adjusting the standard enthalpy, the slope of the plotted expression is altered. However, the equilibrium constant values near the standard conditions remain quite similar. This is important since the value of the equilibrium constant at the standard temperature (298.15 K), which can be independently calculated from the standard Gibbs energy of formation of the various species given in Table 2,agrees well with the experimental data. Further, as shown in Figure 4, eq 25 agrees very well with the experimental data throughout the range of temperatures of experiments, while predictions of eq 26 lie outside the error range associated with the data. This, hence, justifies the altered value of the standard enthalpy of formation of ETBE employed in obtaining eq 25.
Ind. Eng. Chem. Res., Vol. 34,No. 1, 1995 397 Table 2. Liquid-Phase Thermochemical Dataa and Liquid-Phase Heat Capacity Equation Coefficients heat capacity coefficients of eq 8 bj cj
component
aj
isobutylene ethanol ETBE
35.44 29.01 40.418
-3.124 x -5.658 x -1.053 x
0.802 0.2697 0.7532
4
5.045 x 2.079 x 1.8066 x
hG"o~, kJ/mol
AH'fip, kJ/mol
AHO.p, kJ/mol
60.672* -174.Bd -126.8
-37.7 -277.51 -357.5e
20.6c 42.56 41.W
TRC Thermodynamics Tables (1986). Not given in the literature, calculated by eq 16. From A P I Project 44 (1953). From CRC Handbook (1992). e Adjusted Value. I
"
'
L
1
t 6:
Method 1 adjusted
2
.
-Method 1 unadjusted :
-,'
- i
Experimental
1
'
'
0.0028
~
'
"
'
'
'
'
'
0.003 0.0032 0.0034 1 /Temperature, 1 /K
'
'
~
'
~
+ 4060*49- 2.89055 In T + 1.91544 x 10-2T+ 5.28586 x 10-5p -
lO-'P
(27)
which is remarkably similar to eq 25 obtained by following method 1. The expression obtained by following method 3 is
+ 5345'01 - 3.56724 In T + 3.65829 x 10-2T - 6.02157 x 1 0 - 5 p +
In K(1) = 0.558036
5.32295 x lO-'P (28)
As evident from Figure 5 , while the equilibrium constant expressions resulting from both methods 2 (eq 27) and 3 (eq 29) provide reasonable agreement with the experimental data, and are certainly within the error range associated with the data, eq 25 obtained from method 1appears to be the best. Further, the good agreement among the various expressions from the different methods provides confidence in the approach as well as in the internal consistency of the data given in Tables 1and 2. For the purpose of comparison, the expression provided by Vila et al. (1993) is also shown in Figure 5, but its agreement is poor. Their expression is reproduced here:
1.0872' - 1.114 x 1 0 - 3 p
, I , ,,
Experimental ,
,
,
,
,
,
,
I
Ii
l/Temperature, 1/K
In K(1) = 10.6162
T
, , ,
0.00288 0.00304 0.0032 0.00336 0.00352
Next, employing method 2 (Figure 11, along with the data in Tables 1and 2, the following alternate expression results
lnK(1) = 1140 - 14580 - 232.9 In T
0 E' % ,
r
0.0036
Figure 4. Equilibrium constant using method 1 (Figure 1) with a nonadjusted (eq 26) and an adjusted (eq 25) standard liquidphase enthalpy of formation for ETBE as compared with experimental data.
5.32977 x
'
+
+ 5.538 x lO-'P (29)
in which IH and IK (eq 12) were used as fitted param-
Figure 5. Equilibrium constant expressions from methods 1 (eq 25), 2 (eq 27), and 3 (eq 281, along with the expression (eq 29) of Vila et al. (19931, as compared with experimental data.
eters, obtained from the slope and intercept of a plot of {In K(1) AT)} versus 11T of the experimental equilibrium constant, where AT) collectively denotes all the terms on the right hand side of eq 11, except the two involving IH and ZK. Finally, as shown in Figure 6,eq 25 agrees quite well with experimental data from not only this work but also those reported by Vila et al. (1993) and by Frangoisse and Thyrion (1991) and is, consequently, the recommended expression. Further confidence in the methodology used here is provided by a comparison with experiments of the expression for the gas-phase equilibrium constant obtained from using step I11 of method 3 (Figure 1). The resulting expression is
+
lnK(g) = -9.998
+ 7539*18 - 2.12834 In T + T - 3.68856 x 1 0 - 6 p 9.7865 x lO-"P (30)
6.97017 x
As shown in Figure 7, this expression agrees quite well with the experimental results reported in the literature for the gas phase equilibrium constant (Iborra et al., 1989). These authors also provide an expression for the gas-phase equilibrium constant with fitted parameters 7223 +T - 3.102 In T + 8.432x T - 3.155 x 1 0 - 6 p + 2.332 x lO-'P
In K(g)= -4.10
~
(31)
which is also included in Figure 7. Although not the focus of this study, it is significant that our theoretical expression compares very well with the gas-phase data and, thus, provides credence to both the approach employed here as well as the thermodynamic data values.
398 Ind. Eng. Chem. Res., Vol. 34,No. 1, 1995
K. The thermodynamic analysis approach utilized herein should also be useful for other liquid-phase systems. 5 r
-iz A
Acknowledgment 4 r
The funding provided for this work by the Iowa Corn Promotion Board and the National Renewable Energy Laboratories is gratefully acknowledged.
.5
0
2 ~
Francoisse&Thyrion,(1991) Method1
0.00288 0.00304 0.0032 0.00336 0.00352 1/Temperature, 1 / K
Figure 6. Experimental and literature data compared with predicted values of the liquid-phase equilibrium constant from method 1 (eq 25).
K(g) from from Step I11 Iborra et. al. (1989)
0 0.0027 0.00276 0.00282 0.00288 0.00294 0.003 1/Temperature, 1/K
Figure 7. Gas-phase equilibrium constant expression (eq 30) compared with data and the expression (eq 31) of Iborra et al. ( 1989).
Conclusions A detailed thermodynamic analysis of the ETBE reaction is performed to obtain an expression for the liquid-phase equilibrium constant (eq 25) that agrees well with experimental data. The result is of practical significance in view of the imminent prominence of ETBE as an oxygenate gasoline additive. The analysis is based on the thermodynamic data reported in the literature, with the exception of ETBE, for which complete data are not yet available. Consequently, the standard enthalpy of formation of ETBE was adjusted to -357.5 kJ/mol, as compared with a reported value of -351.6 kJ/mol, in order to obtain a better agreement with data over the range of temperatures. However, the gas-phase standard enthalpy of formation of ETBE was not adjusted from its literature value. Equilibrium constant expressions were obtained following three different thermodynamic pathways and yielded similar results, thus providing confidence in the approach as well as the final result. The resulting expressions for the gas-and liquid-phase equilibrium constants agree well with experimental data reported in the literature and that obtained in this study over a range of temperatures, including the standard temperature (298.15 K), which provides independent confirmation of the standard Gibbs energy change for the reaction at 298.15
Nomenclature aj,b,,c,,dj= coefficients of molar heat capacity expression, eq 8 a, = activity of speciesj , y 9 . C"pj(a)= molar heat capacity of species j in phase a, J/mol-K g = gas phase ZH = constant of integration in Kirchoff s equation, eq 9 Z H ~= constant of integration in eq 19 ZK = constant of integration in van't Hoff equation, eqs 11 and 12 K(1) = liquid-phase thermodynamic equilibrium constant K(g) = gas-phase thermodynamic equilibrium constant K(a)= thermodynamic equilibrium constant for phase a Ky = equilibrium constant in terms of activities, eq 1 K, = equilibrium constant in terms of mole fractions, eq 1 1 = liquid phase n = total number of species P = pressure, bar Po = standard pressure, 1 bar Pd = vapor pressure of speciesj , bar R = gas constant, 8.3143J/mol.K S " ~= T standard entropy of speciesj at the temperature T , J/mol*K T = temperature, K T" = standard temperature, 298.15K T,= critical temperature, K T , = reduced temperature, = T / T , T",= reduced standard temperature, T " / T , q(1)= liquid molar volume of speciesj , mum01 xj= mole fraction of speciesj 2 = compressibility factor Greek letters
a = phase (g or 1) yj = activity coefficient of speciesj AC"w = heat capacity difference between gas and liquid phases, eq 18,J/mol.K AG"Cda)= standard Gibbs energy of formation of species j in phase a at temperature T , kJ/mol AG"da)= standard Gibbs energy change for reaction in phase a at temperature T, eq 3,kJ/mol AH'Cda) = standard enthalpy of formation of speciesj in phase a at temperature T , kJ/mol A P d a ) = standard enthalpy change for reaction in phase a at temperature T , eq 4,kJ/mol A€P~= T standard heat of vaporization of species j at temperature T, kJ/mol hs"~ = standard entropy change for reaction at temperature T , Jimo1.K vj = stoichiometric coefficient of speciesj in reaction w = acentric factor Subscripts
e = at equilibrium f = of formation j = of speciesj T = at temperature T 2" = at standard temperature
Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 399 Superscripts O
= at standard state (1 bar; also ideal gas for gas phase)
Abbreviations
ETBE = ethyl tert-butyl ether MTBE = methyl tert-butyl ether VOC = volatile organic compound RVP = Reid vapor pressure
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Received for review May 25, 1994 Accepted September 23, 1994" IE940335N
Abstract published in Advance ACS Abstracts, December 15,1994.
