3718
Ind. Eng. Chem. Res. 1996,34,3718-3725
Thermodynamic and Kinetic Studies of the Liquid Phase Synthesis of tert-Butyl Ethyl Ether Using a Reaction Calorimeter Lluis Sola and Miquel A. Perkas* Departament de Quimica Orghnica, Facultat de Quimica, Universitat de Barcelona, Marti i Franquds, 1, 08028 Barcelona, Spain
Fidel Cunill* and Javier Tejero Departament d%nginyeria Quimica, Facultat de Quimica, Universitat de Barcelona, Marti i Franquds, 1, 08028 Barcelona, Spain
The liquid-phase addition of ethanol to isobutene to give tert-butyl ethyl ether (ETBE) on the ion-exchange resin Lewatit K2631 has been studied in a calorimetric reactor. The heat capacity of ETBE and the enthalpy change of the ETBE synthesis reaction in the temperature range 312-333 K have been determined. ETBE heat capacity in the liquid phase has been found t o follow the equation C, (J-mol-l0K-l) = 486.73 - 2.253 (TK) 0.00479 At 298 K the standard molar reaction enthalpy is AHo = -32.0 kJ-mol-l. A determination of the apparent activation energy of 86.5-89.2 kJ-mol-l has been performed graphically from the plots of heat flow rate versus time. An Eley-Rideal mechanism, with two active sites involved in the rate determining step, has been proved to be correct. From this model a n apparent activation energy of 80.6 kJ-mol-' is deduced. A -3.0 kJ-mol-l value has been found for the adsorption enthalpy of ethanol. This allows the estimation of the actual gel-phase activation energy of 77.6 kJ-mol-l.
+
Introduction The addition of oxygenated organic compounds to gasoline allows the removal of lead additives, raises combustion temperatures, and improves engine efficiencies (Corbett, 1991). The results are lower levels of carbon monoxide and unburned hydrocarbons in auto exhaust. Emission standards imposed by governments are expected t o require, depending on the maximal allowed CO emission level, the use of either reformulated or oxygenated gasoline, with oxygen contents of 2 and 2.7 w t %, respectively. Refiners can use either lighter alcohols or tertiary ethers as the oxygen source. However, ethers are preferred t o lighter alcohols as blending components of gasoline because of their more similar behavior to conventional hydrocarbons. Alcohols (methanol and ethanol) lead to phase separation during storage and transport, and they possess a too high blending vapor pressure, particularly in summertime. To date, practically the only tertiary ether used as additive in gasolines has been tert-butyl methyl ether (MTBE), because it is cheaper and its properties are well-known to refiners. Nevertheless, the risks associated with a high dependence on MTBE and its rather high blending vapor pressure have led to consideration of the use of other ethers such as tert-amyl methyl ether (TAME) and tert-butyl ethyl ether (ETBE). There are some advantages in adding ETBE instead of MTBE to gasoline. ETBE has a Reid blending vapor pressure between 3 and 5 psi as opposed to 8-10 psi for MTBE. This fact is very important in order to reduce evaporative emissions of cars. ETBE also has a slightly higher octane number than MTBE, 110 vs 109. In addition, ETBE has a lower weight percent of oxygen, which means that more ether can be blended t o the reformulated gasoline to achieve the allowed oxygen level. In this way, ETBE blends allow the greatest reduction (dilution effect) on the concentration of aromatics, sulfur, and benzene, which is an aim t o be reached in clean gasolines. Finally, it is worth noting that ETBE is produced from renewable ethanol, while 0888-588519512634-3718$09.00/0
MTBE is obtained from methanol produced from natural gas via synthesis gas. In this context the US. Enviromental Protection Agency has proposed that 30%of the oxygen required in the federal reformulated gasoline program is to be produced from renewable sources. This implies that ETBE will account for about 10% of the overall reformulated gasoline. ETBE is obtained by the addition reaction of ethanol to isobutene. The reaction is reversible, moderately exothermic, and usually catalyzed by macroporous sulfonic acid resins. The selectivity is very high, but some byproducts such as diisobutene and diethyl ether can appear if the temperature is high enough and the ethanollisobutene molar ratio is far from the stoichiometric one. It is worth noting that MTBE plants can be easily adapted to ETBE production by introducing slight modifications (Forestierre et al., 1990; Cima et al., 1993). Such flexibility would allow one t o change the production from one ether to another, depending on the alcohol availability. In recent years, bench scale calorimetry has risen as a powerful tool for a detailed study of chemical processes (Regenass, 1985,1987; Hoffmann, 1989; Shatynski and Hanesian, 1993). Computer controlled reactors allow the study of chemical reactions, easily monitoring useful chemical parameters: reaction temperature, reactor jacket temperature, stirring rate, pH, pressure, dosing rate, etc. In this way the exact reaction conditions are known, and the experiments show a very high reproducibility. Since the heat flow rate measured by a calorimetric reactor is directly related to the reaction rate, a study of the reaction kinetics and thermodynamics is possible without interfering with the process (Regenass, 1983). Up to now, several calorimetric reactors have been designed following different measuring principles (Karlsen and Villadsen, 1987a,b). Among them, those working on the heat flow rate principle are the most useful since they ensure a rapid and efficient reactor temperature control and allow the easy performance of calorimetric calculations. Their geometrical characteristics, type and
0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34,No. 11, 1995 3719 form of inserts, resemble those of an industrial reactor, so a reliable scale-up of chemical parameters is possible. In spite of the increasing interest in ETBE, one finds little information available in the open literature regarding the catalytic reaction kinetics (Ancillotti et al., 1977;Kaitale et al., 1988;Frangoisse and Thyrion, 1991; Fit6 et al., 1994) and thermodynamics (Frangoisse and Thyrion, 1991; Rock, 1992;Vila et al., 1993). We report, in the present paper, a complete thermodynamic and kinetic study of the liquid phase synthesis of tert-butyl ethyl ether (ETBE) from 2-methylpropene and ethanol using reaction calorimetric techniques.
of the reaction temperature, since heat transfer is very efficient and suppresses the need for reactor thermal insulation. The heat flow rates produced as a consequence of a chemical reaction or physical change are calculated on the basis of heat flow rate and mass balances for the reactor. The mass balance needs to consider dosing or withdrawal of any reactant or product. The heat flow rate balance has to consider all possible heat flow rates between the reaction mass and its surroundings. When a reaction is carried out a t temperatures below the boiling point of the reaction mixture, the overall heat flow rate balance is qr = q e x + q a c c + qdos + qloss - q c a l
Experimental Section (i) Materials. Ethanol HPLC (99.8% pure) was supplied by Romil Chemicals Ltd. (Shepshed, U.R) and was dried over 3-81 molecular sieves (Fluka, Buchs, Switzerland). Isobutene (99% pure) was obtained from Carburos Metdicos (Barcelona, Spain) and used without further purifications. The main impurities of isobutene were isobutane and linear butenes which do not react under the explored reaction conditions. ETBE was obtained from the reaction of ethanol and isobutene, as will be thoroughly described further in the paper. It was purified first by extraction of ethanol with water followed by distillation of isobutene and dried over MgS04. ETBE ('99.5% GC) was obtained. It was kept under 3-81 molecular sieves prior to use. The catalyst was the ion-exchange resin Lewatit K2631, formerly SPC 118, from Bayer AG (Leverkusen, FRG). The commercial resin was ground and sieved, and the fraction with diameter between 0.063 and 0.16 mm was used in the experiments. Immediately before use, catalyst samples were dried at 110 "C under vacuum (1 mmHg) for 3 h. The residual amount of water in the resin seems to be negligible since no tertbutyl alcohol could be detected along the experiments which is easily formed in the presence of water (Cunill et al., 1993). (ii) Apparatus. A commercially available (Mettler RC 1)computer controlled reaction calorimeter was used throughout the study. The reaction vessel was a l-L jacket cooled stirred tank (Mettler MPlO reactor) suitable for work under pressure ( ~ 1 . MPa). 0 The calorimetric reactor is designed to work in three different temperature control modes. In the isoperibolic mode the temperature of the jacket is kept constant or ramped. In the adiabatic mode the temperature of the jacket is controlled so that any heat emmited due to the reaction is used t o heat the reaction mass. Finally, in the isothermal mode the temperature of the jacket is controlled so that a constant or ramped temperature of the reaction mass is obtained. The last mode was used in all the experiments described in this article. The RC1 reactor calorimeter works according to the heat flow rate principle (Karlsen and Villadsen, 1987a). Following this principle the heat flow exchanged with the jacket fluid, which can be written as eq 1,depends
only on the difference between T, and Tj (Hoffmann, 1989). Tj remains essentially constant between the input and the output of the reactor jacket through a high speed circulation of the heat transfer fluid. UA is the overall heat transfer coeficient, specific to each reactor and reaction mass, and can be easily calculated at different stages of the reaction by a simple calibration. This type of reaction calorimeter ensures rapid control
(2)
Heat losses can only take place through the reactor lid, the only part of the reactor vessel which is not jacketed. In order to minimize these losses the reactor lid is externally thermostated 1 "C over the reaction temperature. Since no dosing takes place during the experiments (batch operation), the energy balance reduces to
where
(4) The experiments in our study were essentially performed in an isothermal way. Under these conditions, q e x is the most relevant term in eq 3 and qacc accounts only for the heat flow rate due t o changes in heat capacity of the reaction mixture. The heat release due t o the reaction is calculated by numerical integration of the heat flow rate during the reaction period, according to
where a proper definition of base line and initial and final reaction times are chosen. (iii)Analysis. A 0.2-pL aliquot of pressurized liquid was injected by a liquid sampling valve (VALCO 4-CL4WE) into a HP 5890 GLC apparatus equipped with TCD. A 6 m x 3.2 mm od GLC column packed with Chromosorb 101 (SO/lOO mesh) separated ETBE, ethanol, isobutene, water, and possible reaction byproducts (diisobutene, diethyl ether, and tert-butyl alcohol). The column was temperature programmed with a 4 min initial hold at 130 "C followed by a 25 "C/min ramp up t o 200 "C and held at that temperature for 12 min. Helium (SEO, Barcelona, Spain) with a minimum purity of 99.998% was used as a carrier gas (flow rate 30 cm3/ min). (iv) Procedure. (a)ETBE Heat Capacity Determination. The reactor was charged with a known amount of pure ETBE (0.6-0.8 L). The system was then heated to the desired temperature where a calibration cycle (calibration heater, 15 min; 10-min delay; temperature ramp, 5 "C/lO min; 10-min delay; calibration heater, 15 min) was performed. Evaluation of the heat flow rate balance along this cycle directly provided the heat capacity a t the specified temperature. (b)ETBE Synthesis. The reactor was charged with ethanol (203 g, 4.40 mol) and the catalyst (21.5 g, 5 wt %). The mixture was cooled t o -18 "C, and isobutene (227 g, 4.06 mol) was then added. The reactor was pressurized with Nz at about 0.4 MPa in order to ensure
3720 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 liquid phase reaction, and stirring (250 rpm) was set up. The mixture was rapidly brought to the desired temperature (3.5 "C/min), and the pressure was set at 0.8 MPa. When the mixture reached the desired reaction temperature, an aliquot was withdrawn and analyzed by GLC as described above in order to determine if ETBE formation had occurred to some extent during the interval of the temperature rise. The progress of the reaction was monitored by the direct measure of T, - Tj and/or through the variation of the internal pressure, which depends on liquid composition. When the equilibrium composition was nearly reached, which was easily seen by the achievement of a constant value of the gradient T, - T j and/or internal pressure, another aliquot was withdrawn and analyzed by GLC to determine the final composition. Data of the following variables were stored in a computer every 6 s: T,, Tj, dT,ldt, Qc, R. After each experiment was finished, calculation of &r was performed. For those experiments where ETBE could be detected and measured in the chromatographic analysis when the temperature first reached the desired reaction temperature (experiment at 60 "C), ti was defined as the point when the reaction temperature was reached and the mixture composition measured at this point was taken as the initial composition. For the other experiments (39, 46, and 53 "C) ti was established as the time when heat flow rate due to the reaction was initially detected. In all the experiments tf was established as the time when the heat flow rate due to the reaction returned t o the base line value. In all cases a base line proportional to T, was used. The methodology used ensures that all experiments were run in an isothermal mode. In this context, it is interesting to point out here that, under the most critical conditions used in this study, i.e., the initial stages of the reactions performed a t 60 "C, the derivation with respect to isothermal behavior (T, - Tj) is only of 1.9 "C. ( c ) Ethanol Heat Adsorption Calculation. The reactor was charged with a known amount of ethanol (800 g, 17.37 mol) which was kept a t room temperature (24 "C) in order to minimize heat losses through the reactor lid. The reactor was stirred at 250 rpm. Catalyst (25 g) was manually added at the same temperature as the ethanol of the reactor. The progress of the ethanol adsorption was monitored by measurement of Tr - Tj and ended when a constant value of T, - Tj was achieved. In order to evaluate the amount of ethanol adsorbed on the resin, a thermogravimetric analysis was performed. An amount of wet resin (0.127 g) from the previous experiment was loaded in a thermobalance (SETAFUM TG DTA 92) at 25 "C. A temperature ramp of 1 "C/min was set up to 110 "C where it was held for 120 min. Clear differentiation of adsorbed and wetting ethanol could be made. The adsorbed ethanol was calculated and extrapolated to the overall amount charged into the reactor.
Results and Discussion (i) Specific Heat Capacity. Surprisingly, t o the best of our knowledge, no ETBE heat capacity experimental values are available in the open literature. Specific heat capacity of ETBE in the temperature range 298-328 K with 5 "C intervals was determined with the RC1 reaction calorimeter. Results are shown in Table 1 along with those estimated by Rowlinson and Bondi (Reid, 1987). A very good agreement is found between both sets of values. Interesting to recall is that our experimental values are slighly higher and more
Table 1. Specific Heat Capacity (Jsmol-l.K-l) for ETBE from 298 to 333 K 298K 303K 308K 313K 318K 323K Rowlinson-Bondi this work
218.7 220.9 226.6 225.8
223.1 225.4 227.7 230.0 228.1 232.9 237.0 240.1
Table 2. Specific Heat Capacity (J-mol-l.K-l)Coefficients for ETBE Rowlinson-Bondi this work
a1
a.
83.158 468.73
0.5894 -2.253
a3
10-2
-8.641 47.9
a4
10-4
1.386
Table 3. Standard Molar Enthalpy (kJ.mol-l) of ETBE Formation from Isobutene and Ethanol 298K 312K 319K 326K 333K -27.6 Francoisse and Thyrion (1991) -44.3 Vila et al. (1993) -34.8 -35.2 -35.4 -35.7 -35.9 this work -32.6 -34.1 -34.5 -35.8 Rock (1992)
temperature dependent. It is important to notice that the values reported by Rowlinson and Bondi correspond to estimates, not t o experimental values. The molar heat capacity of ETBE can be given by a second order polynomial, eq 6, whose coefficients are shown in Table 2. 3
cp= &T-'
(6)
1=1
(ii) Heats of Reaction. Experiments were run a t four different temperatures (312,319,326, and 333 K). The overall heat of the ETBE formation process was calculated as described in the Experimental Section. Since the experiments were performed in the liquid phase under pressure, considering products and reactants in their standard states at the same temperature, the measured Q, can be assimilated to AHO. Table 3 shows the standard enthalpy change values at the different temperatures. At the present time very few values reported in the open literature referred t o the molar enthalpy change of the ETBE synthesis, and they are quite divergent. Rock (1992) reported a value of -27.6 kJ*mol-l, but nothing is said about how and under which conditions it was obtained. Franqoisse and Thyrion (1991) deduced a value of -44.3 kJ-mol-l and Vila et al. (1993) a value of -34.8 kJ-mol-l, both calculated from equilibrium constants. None of these values is directly obtained from experimental results. Very good agreement is found between values in this work and those of Vila et al. (1993). It is interesting to note that values reported by Vila et al. (1993) are less temperature dependent than ours, mainly due to a smaller variation with temperature of the estimated specific heat capacity used for the calculations. Extrapolation at 298 K provided a value of AHO298 = -32.0 kJ mol-l. As we already reported for the study of MTBE synthesis (Solii et al., 1994) the Q, value measured at a constant pressure of 0.8 MPa differed only in 1.1%from the corresponding experiment with pressure decay (from 0.8 to 0.4 MPa). We may conclude that if the mixture is kept in the liquid phase, no substantial influence of pressure can be detected. In order to test the reproducibility of the values obtained with the reaction calorimeter, the experiments at 312 and 323 K were performed twice. The difference between the molar enthalpies was 2.5% for the experiment at 312 K and 1.5% for the experiment at 323 K. The greater of the two values (2.5%) was assumed to
Ind. Eng. Chem. Res., Vol. 34,No. 11, 1995 3721
The reaction rate can be related to the heat flow rate in the following way:
r=------+--=d(%m dt
1
1
I
1
1
.I
0
2axx)
Qxx)
am0
dOOOO
1
&I
dt V
dVn1 dt
v2
n1drIep -
V
Qr
t(S)
Figure 1. Heat flow rate released in the synthesis of ETBE vs time a t 312, 319,326, and 333 K.
be a correct margin of experimental error in our determinations. This experimental error is consistent with that recorded in analogous studies of similar systems. Figure 1 shows a plot of heat flow rate against time for the experiments performed at the four different temperatures (312,319,326, and 333 K). Values were saved every 6 s, so, in the time scale used, the plot appears as a continuous set of data. It is to be noted that the reaction is highly temperature sensitive. The time required for equilibrium to be reached doubled when the reaction temperature was decreased by 15 "C, while the maximum heat flow rate doubled when the reaction temperature increased by 7 "C. (iii) Kinetic Parameters. For a reaction taking place t o completion or to an equilibrium composition the heat flow rate represents an indirect measurement of the reaction rate (Regenass, 1983). If no secondary reactions nor reaction intermediates accumulation occurs, the heat flow rate can easily be assimilated t o the reaction rate provided that the final composition is known. In the reaction studied, and under the experimental conditions used, ETBE is the only product formed. According t o the chromatographic analysis, no secondary reactions are observed and we may conclude that the heat flow rate data obtained are due solely to the ETBE formation reaction from ethanol and isobutene. Conversion of the limiting reactant (isobutene) referred to equilibrium composition is related with qr and Q r in the following way:
dx, = XIe-41. dt
(8)
Qr
where XI/XI, is the relative reaction conversion of isobutene, XI,is the final isobutene conversion, and XI is the isobutene conversion given by
n, = n1& - XI)
(9)
Reaction volume has a variation, during the reaction time, proportional t o conversion, given by
Apparent activation energy of a chemical reaction can be easily deduced. Assuming a general reaction rate equation of the type 7.
(14)
= k(T)f(Cj)
where k, the rate coefficient, depends only on temperature according to the Arrhenius equation, and combining it with eq 13 for the initial conditions, eq 15 can be obtained.
Taking the natural logarithm of eq 15 gives In ro = In A
+ l n ~ c j o )-l E-a -1 RT
(16)
Considering that the preexponential factor A is independent of temperature, a plot of In ro as a function of 1lT should be a straight line with a slope of -E,IR. Thus, apparent activation energy is obtained by measuring qro at several temperatures, plotting In ro vs 1/T, and calculating Ea from the slope. A plot of q r and XI/XI, for a typical experiment at 53 "C is shown in Figure 2. In this way, as mentioned earlier, the application of eq 13 to data obtained in the calorimetric reactor can give rise t o an almost continuous set of reaction rate data in a highly reliable form. Reaction rate had a form similar to that described for the MTBE formation reaction (Sola et al., 1994). It was maximum at the beginning, after a very short induction period, then it decreased with increasing reaction progress, and finally it tended t o zero as chemical equilibrium was reached. The maximum heat flow rate for the synthesis reaction of ETBE was smaller than that of MTBE at all temperatures, and hence MTBE reached equilibrium composition faster than ETBE (See Table 4). The graphical determination of qro, which allows the obtention of initial reaction rates, has already been described and applied to the study of the MTBE synthesis kinetics. Initial heat flow rates can be estimated in two different ways, first, by extrapolation at t = 0 of the linear decay zone of the curves and, second, by taking as initial heat flow rates the maximum value of qr. A straight line is obtained for the plots
3722 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 Table 4. ComDarison of MTBE and ETBE S.ynthesis Reaction ~~
max heat flow rate (W) max heat flow rate (W) equilib time equilib time
MTBE ETBE MTBE ETBE
312 K 6.125 5.60 14 h 16 min 16 h 10 min
319 K 11.7 11.5 6h8min 10 h 37 min
326 K 26.8 25.5 3 h 38 min 4 h 31 min
333 K 61.5 50.0 2 h 15 min 2 h 44 min
1.28
1.0
-
0.6
-
8 8
8 8 8 8 8 8 8 8
8
Q r
8
0.6-
8 8
X L
8
.
8
04-
0.2
8 8 8
-
8 8 '
8
8
8 8
8
PO4
.
l
0.0
.
l
0.2
.
l
.
l
0.6
0.4
.
l
0.8
.
i
1.2
1.0
t(s) Figure 2. Heat flow rate released and isobutene conversion vs time for ETBE synthesis a t 326 K.
of In ro against 1IT at the different temperatures, for both sets of estimates (Figure 5 ) . The values of 86.5 and 89.2 kJ*mol-l are found for E,. In accordance with what is known for the MTBE (Rehfinger and Hoffmann, 1990; Gicquel and Torck, 1983) and ETBE (Francoisse and Thyrion, 1991; Fit6 et al., 1994) synthesis reaction, we assumed as a start point kinetic model an Eley-Rideal (ER) mechanism (for a description of the Eley-Rideal mechanism, see Fit6 et al. (1994))in which adsorbed ethanol reacts with isobutene from the solution to afford adsorbed product. One or more supplementary active sites are involved in the surface reaction step, which is considered to be rate determining. k J E t ( aIBaEt
r=
-
2)
128
8
8
I:
8
10-
8 8
8 8 8
8 8
8
B r X
8
a 8
a a
L
(1 ,-.7)
(1+ K E & t + K E a E ) " As was deduced by Fit6 et al. (1994) for the ETBE synthesis reaction, the model reduces to the reaction rate expressed as I
k('H3aEt
-
r=
2)
where = kJ.Q-1)
4
8 . -
, 02
.
, 04
.
, 06
.
, 08
.
1
.
10
,
. 1.2
1
. 14
1
, 16
(18)
(aEtY
k
001
(19) This means ultimately that ethanol presents a very preferential adsorption compared to ETBE, and, due to the high ratio of EtOWactive sites, an insignificant fraction of unoccupied sites exist. It has been reported that up to seven active sites take place in the rate determining step (Wesley and Gates,
Figure 3. Reaction rate vs eq 21 in the conversion range 2099% for n = 2 (top) and 3 (bottom) at 326 K.
1974). Quite recently Fit6 et al. (1994) have shown that either two or three active sites are more likely involved in the reaction. In order to provide more definite evidence on this controversial issue, we have studied the fitting of our almost continuous sets of data t o models with n ranging from 2 to 7. Since alcohol-olefin liquid mixtures behave nonideally, the analysis of the EtOH-isobutene-ETBE system
Ind. Eng. Chem. Res., Vol. 34,No. 11, 1995 3723 14
1.4-
1.2
1 .o
.
0.8
...
-
1.0
-
0.8
a?
. .
B
r; 0.6 L
.
'ri s ~
0.6-
L
*
04
.
1.2-
0.4
-
0.2
-
.
0.0-
1 t . l . 0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.2
14-
1.0-
:
Oi
-
*
0.8
1.0
.
2.4
l . l . l . l . l . l
2.6
2.8
3.0
3.2
3.4
36
1
1.4
12-
**
.
1
:. .
0.6
I 0.2
0.0
L
.. . . .*
0.4
-
0.2
-
.
-
0.0
Figure 4. Reaction rate vs eq 21 in the conversion range 20-99% for n = 4 (top, left), 5 (top, right), 6 (bottom, left), 7 (bottom, right) at 326 K.
has been described as a function of activities instead of concentrations of involved species. The activities are related to its molar fractions by means of
(20) a E. = x.y. E L where the activity coeficients (yi) are estimated from the UNIFAC prediction method. The parameters needed for the use of UNIFAC were taken from the tables published by Fredeslund et al. (19771,Skjold-Jorgensen et al. (19791,Almeida et al. (19831,and Tiegs et al. (1987). At each temperature, a discrete set of representative and uniformly distributed conversion values XIwere
obtained from heat flow rate data as shown in eq 7. Since initial and final composition were known, the corresponding molar fractions were calculated which, in turn, were used to calculate the activity coefficients (yi) and the corresponding activities (aj) as described above. For each selected point the term
was calculated with n ranging from 2 to 7 and using values of K, reported by Vila et al. (1993). Plots of eq 21 against reaction rate (see eq 13)at the
3724 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995
"1 Y C
\\\
"1
Ink = 22.66 -98841TT
\ \
-7.51
\
\ 1-
6.5
-.-
.
, 3.00
.
3.03 -
3.b
1
.
3.10
3.b
'
3.b
~
Figure 5. Logarithm of initial reaction rate determined graphically vs 1/T W, using as qmthe value of maximum dqddt; 0 , using as qfi the extrapolation of the linear decay zone of dq,ldt at t = 0.
experimental temperatures were drawn in the conversion range from 20 to 99%) as shown in Figures 3 and 4 for the experiment a t 53 "C. With n = 4, 5, 6, 7 as exponential values, the graphs shown in Figure 4 were obtained and their fitting to a straigth line was impossible. With n = 2 a straight line was obtained with an excellent fitting. From our data we can definitely discriminate exponent 2 compared to 3 as a much better fit. From this result we may conclude that the reaction between EtOH and isobutene to give ETBE occurs through a mechanism where two active sites are involved in the rate determining step. From the slope of the straight line a value of K was obtained for each temperature, which allowed estimation of an apparent activation energy of 80.6 kJ-molv1 through an Arrhenius plot, as can be seen in Figure 6. According to eq 19, and using n = 2, the overall rate constant K was (22)
Using Arrhenius law for temperature variation of the rate constants and Van't Hoff law for temperature variation of the adsorption equilibrium constants, an activation energy in the gel phase of the resin, E,can be computed from the apparent activation energy (E,) and the liquid-phase adsorption enthalpy of ethanol as
E =E,
+
ASHE,
3.10
1lT (1lK) x
l/T (VK) x 103
k = k+&,
3.05
(23)
An experimental determination of A&Et was performed using reaction calorimetry and thermogravimetry techniques, as described in the Experimental Section. A value of -(3.0-3.1) kJ*mol-l was obtained; thus, according to eq 23, a value of 77.6 kJmol-' for the gelphase activation energy is deduced. The experimental value of A&Et deduced in this work is in very good agreement with estimated values from vaporization and gas-phase adsorption enthalpies (AJ& = -3.4 kJmol-l, Fit6 et al. (1994)). It is interesting to note that the
3.15
3.20
lo3
Figure 6. Logarithm of reaction coefficient K vs 1/T at 312, 319, 326, and 333 k. The slope of the straight line gives the value of the apparent activation energy (Ea).
values obtained for the activation energy in the liquid phase for ETBE are similar to literature values: 81.2 f 6.7 kJ*mol-l (Franqoisse and Thyrion, 1991) and 79.3 kJ-mol-l (Fite et al., 1994). The activation energy is slightly smaller than that reported for the synthesis of MTBE.
Conclusions Values of heat capacity and reaction enthalpy have been deduced for the liquid-phase addition of ethanol t o isobutene to give tert-butyl ethyl ether (ETBE) by using reaction calorimetry techniques in good agreement with literature values. The system has been found to follow an Eley-Rideal kinetic model with two active sites involved in the rate determining step. The apparent activation energy of the ETBE synthesis has been deduced both by graphical means, from the initial heat flow rates, and from the kinetic model. In summary reaction calorimetry has been found to be a very useful tool for the study of this kind of system. Extension of this methodology to the study of related systems is in progress in our laboratories and will be reported in due course.
Acknowledgment We thank Dr. Carles de las Cuevas and Lourdes Miralles from the Laboratori d'Investigacions en Formacions Salines, Facultat de Geologia, Universitat de Barcelona, for their help in using the SETTG DTA 92 thermoanalyzer. We also thank Drs. Albert Moyano and Antoni Riera for helpful discussions and the Universitat of Barcelona for financial support.
Nomenclature A = reactor area for heat transfer (m2) ai = parameter of eq 6 (J.mol-l.K-l) aj = activity of compound j (dimensionless) cj = molar concentration of compound j (mo1.L-l)
Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 3725
C,,
= specific heat capacity of the reacting mixture (J*Kg-'*K-') dTAdt = reaction temperature variation rate (K-s-l) E = activation energy (kJ-mol-l) E , = apparent activation energy (kJ-mol-') f = general function I = isobutene k = rate coefficient (mol.(L.s)-l) K, = thermodynamic equilibrium constant for the reaction (dimensionless) I$ = adsorption equilibrium constant of compound j (dimensionless) n10 = initial number of moles of isobutene nIf = final number of moles of isobutene n~= number of moles of isobutene nj = number of moles of compound j m, = mass of the reacting mixture (kg) q = heat flow rate (W) qacc= accumulated heat flow rate (W) qcal = calibration heat flow rate (W) qdos = heat flow rate due to dispensing (W) qex= heat flow rate through the reactor jacket (W) qloss= lost heat flow rate (W) qr = heat flow rate due to chemical reaction (W) Q, = overall heat transferred to the cooling jacket (kJ) r = intensive reaction rate (mol.(s.L)-') R = stirring speed (rpm) t = time (s) T = temperature (K) T, =jacket reactor temperature ("C) T, = reacting mixture temperature ("C) U = overall heat transfer coefficient (W.m-2*"C-1) V = reaction mass volume (L) Vo = initial reaction mass volume (L) Vf = final reaction mass volume (L) X, = conversion of reactant j (dimensionless) A W = standard enthalpy change of reaction (kJ.mol-l) A& = adsorption enthalpy of compoundj (kJmol-l)
Subscripts a = apparent e = equilibrium I = isobutene Et = ethanol ETBE = tert-butyl ethyl ether o = initial
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IE940760G
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Abstract published in Advance ACS Abstracts, September
15, 1995.
