1172
Znd. Eng. Chem. Res. 1995,34,1172-1180
Kinetics of Heterogeneously Catalyzed tert-Amyl Methyl Ether Reactions in the Liquid Phase Liisa K. Rihkot and A. Outi I. Krause" Laboratory of Industrial Chemistry, Helsinki University of Technology, FIN-02150 ESPOO, Finland
The kinetics of tert-amyl methyl ether (TAME, 2-methoxy-2-methylbutane) reactions was investigated using a commercial ion exchange resin (Amberlyst 16) a s catalyst at temperatures between 324 and 354 K. The rates of reaction were determined experimentally in the liquid phase in a continuous stirred tank reactor at a pressure of 0.8 MPa. Kinetic equations derived for three different mechanisms were compared. In the forward reaction the adsorbed methanol reacted with isoamylene (2-methyl-1-butene or 2-methyl-2-butene) striking from the bulk liquid phase, and in the splitting reaction the adsorbed ether split to alcohol and isoamylene. The kinetic equations were written in terms of activities, and the activity coefficients were calculated by the UNIQUAC method. The activation energy was determined to be 95 kJ/mol for the splitting reaction of TAME to 2-methyl-1-butene and methanol and 100 kJ/mol for the splitting reaction of TAME to 2-methyl-2-butene and methanol.
Introduction
.
cy1
The production of tertiary ethers, especially methyl tert-butyl ether (MTBE), has increased in the last decade. The superior properties of tertiary ethers as gasoline componentshave been the major reason for the growth (Brockwell et al., 1991). Aside from the production of MTBE, the interest in the production of higher tertiary ethers, especially tert-amyl methyl ether (TAME), has steadily increased in recent years (Rock, 1992; Pescarollo et al., 1993). However, in spite of the growing commercial interest, only a few papers have been published describing experimental investigations of TAME reactions (Pavlova et al., 1986; Muja et al., 1986; Krause and Hammarstrom, 1987; Randriamahefa and Gallo, 1988; Safronov et al. 1989; Fleitas et al., 1991). TAME is made by the liquid phase reaction of isoamylenes (2-methyl-l-butene,2M1B, or 2-methyl-2butene, 2M2B) and methanol (MeOH). In the formation and splitting (i.e., the backward reaction of ether to isoamylenes and alcohol) of TAME there are three equilibrium reactions proceeding simultaneously. The reaction network is presented in Figure 1. The reaction pairs (rl and r2), (7-3 and r4), and (r5 and 7-61 presented in Figure 1 establish reaction equilibria. Krause and Hammarstrom (1987) observed in their experiments that at temperatures above 333 K the formation of TAME was limited by the thermodynamic equilibrium. The reaction equilibrium constants in liquid phase have been experimentally measured by Safronov et al. (1989) and more recently by authors using commercial ion exchange resin as catalyst (Rihko et al., 1994). The etherification reaction of the isoamylenes with alcohol and the isomerization of the isoamylenes are both catalyzed by acids. Because of a relatively low reaction temperature (below 363 K), a strong acidic macroreticular ion exchange resin is usually used as catalyst in the liquid phase etherification. In a comparison of several commercial ion exchange resins Randriamahefa and Gallo (1988) found differences in
* Author t o whom correspondence should be addressed. E-mail:
[email protected]. Present address: Neste Oy, Technology Center, P.0.B 310, FIN-06101 PORVOO, Finland. E-mail:
[email protected].
CH, = C - CH,- CHI '2 - methyl - 1 - butme
15
.
CHI CH,- C = CH - CHI 2 - methyl - 2 - butene
?6
4/
\\
cy, CHI-
7 9
-CH,- CHI
CH,
ferf- amyl methyl ether
Figure 1. The reaction network in the formation and splitting of TAME.
the activity of the resins in the liquid phase etherification of isoamylenes with methanol. These results are in contradiction with the earlier studies of Colombo and Dalloro (19831, where equal activity of resins was found in the MTBE formation reaction. Fleitas et al. (1991) found the bentonites to have a better selectivity to TAME than commercial ion exchange resin (Amberlyst 15) in the liquid phase. Kinetic studies on the formation or splitting of TAME appear to be limited to very few publications. Pavlova et al. (1986) propose a kinetic model of TAME reactions, which is written in terms of the activities of the components and is based on the Langmuir mechanism. Randriamahefa and Gallo (1988) report some kinetic data on the synthesis of TAME. Nevertheless, they did not take into account the strong nonideality of the liquid phase, which had been discussed in the studies of TAME (Pavlova et al., 1986; Krause and Hammarstrom, 1987) and in the studies of MTBE (Rehfinger and Hoffmann, 1990; Colombo et al., 1983). Randriamahefa and Gallo (1988) proposed an electrophilic addition reaction mechanism with a carbocationic intermediate where the rate-determining step was the protonation of the alkene. Because there appear to be very few literature references to kinetic investigations of TAME formation, we briefly refer here to the kinetics of the formation of MTBE and ETBE (ethyl tert-butyl ether) in the liquid
0888-588519512634-1172$09.00/0 0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1173 phase, where the reaction conditions are in many ways comparable to those for TAME formation. The first kinetic data for the formation of MTBE were published by Ancillotti et al. (19781, who observed the negative reaction order for the methanol in the formation of MTBE. Rehfinger (1988) made a comprehensive literature survey of the kinetics of MTBE synthesis but found serious deficiencies in most. Subsequent t o this, Rehfinger and Hoffmann (1990)proposed a three-parameter kinetic model for the formation of MTBE based on a Langmuir-Hinshelwood rate expression concluding that the rate of forward reaction was proportional to the activity ratio of isobutene to methanol and the splitting reaction (the reverse reaction of MTBE to methanol and isobutene) was first order for MTBE and negative second order for methanol activity. Recently, Francoisse and Thyrion (1991) published kinetics and mechanistic data for the formation of ETBE in the liquid phase. They present a complicated kinetic equation for the formation of ETBE which was based on the Langmuir mechanism. In the present work we interpret the kinetics of TAME reactions on the basis of new experimental data, used in conjunction with the chemical equilibrium data (Rihko et al., 1994).
Experimental Section In the experiments the effect of various process variables (pressure, temperature, reagent concentration, and space time) on the rate of the splitting of TAME was measured. Apparatus. The rate of reaction was measured in a continuous stirred tank reactor (CSTR) (V = 55.6 mL, stainless steel), where the reaction mixture was magnetically stirred. The catalyst (0.04-4.00 g) was placed in a metal gauze basket (60 mesh). The temperature (323-353 K)was regulated by immersing the reactor in a thermally controlled water bath. The pressure was kept constant at 0.8 MPa in order to guarantee a liquidphase operation at all temperatures. The pulse-free flow rate (25-75 g h ) of the feed was controlled by a liquid mass flow controller. The feed and the reactor eMuent were analyzed on-line with a gas chromatograph using an automated liquid sample valve. Analytical Methods. A Hewlett-Packard gas chromatograph 5990 Series I1 equipped with a flame ionization detector (FID) was used for the analysis. The compounds were separated with a 60-mglass capillary column DB-1 (J &W Scientific). For quantitative analysis the gas chromatograph was calibrated with an external standard. Chemicals and Catalyst. A commercial strong ion exchange resin, Amberlyst 16 (Rohm & Haas), was used as catalyst. The exchange capacity of the resin was 5.2 mequiv/g dry catalyst and the cross-linking level 12 wt %. The resin was treated with methanol at room temperature before the experiments in order to remove the water from the catalyst pores. After about five experiments the catalyst was removed from the reactor and dried at 353 K overnight. The rate of reaction was calculated on the basis of the amount of the dried catalyst. The rate of reaction was measured at four TAME mole fraction levels (XT = 0.96, 0.46, 0.33, and 0.16). A mixture of isopentane (10 wt %), cyclohexane (45 wt %), and isooctane (45 wt %I was used as solvent in runs where the mole fraction of TAME was 0.46,0.33, or 0.16.
Table 1. Effect of the Stirrer Speed on the Rate of Splitting of TAME at an 0.4, ZM * 0.05, ~j 0.01, and XZB * 0.04. Temperature, 354 K; Pressure, 0.8 MPa stirrer speecUrpm 0 80
500
rate of reactiodmol g-1 h-1 0.115 0.172 0.250
stirrer speecUrpm
rate of reactiodmol g-1 h-1
750 950
0.245 0.257
TAME was supplied by Yarsintez, Russia, and the purity was 298.5 wt %. The purities and the suppliers of solvents were isopentane, >99.0 wt % (Fluka Chemie); cyclohexane, >99.5 wt % (Merck);isooctane, '99.5 wt % (Merck).
Results and Discussion External and Internal Diffusion. First, we investigated the effects of internal and external diffusion on the rate of reaction. To study the effect of the external diffusion of the reactants to the catalyst surface, the speed of the magnetic stirrer was varied. The results of these experiments are presented in Table 1. The influence of the stirrer speed on the splitting of TAME was independent of the speed above 500 rpm, and the speed was therefore set a t 950 rpm in all further experiments. In the examination of internal diffusion, the commercial resin was sieved into five size fractions, as listed in Table 2. The effect of internal diffusion on the rate of reaction was then investigated by measuring the rate of reaction with three catalyst fractions (see Table 2). The average rate of reaction was slightly higher for fraction I1 than for fraction 111. However, the difference was insignificant when the rates for the different fractions were compared with an F-test. In the experiments with fraction IV the rate of reaction was considerably lower than with the other fractions. In this case the rate of reaction was affected by significant diffusion resistance. However, because the percentage of fractions IV and V was only 1.5 wt %, we decided to use the unsieved resin in the experiments. When the pressure was varied from 0.7to 1.14 MPa, we noticed no variations in the reaction rate. This agreed well with the earlier observations about the liquid phase etherification (Rehfinger and Hoffmann, 1990). kssumptions of the Models and the Derivation of Equations. Since the liquid phase is highly nonideal in the etherification of alkenes with alcohols (Pavlova et al., 1986; Rihko et al., 1994; Rehfinger and Hoffmann, 1990), we decided to use in our kinetic equations the activities instead of the concentrations. From the reaction network introduced in Figure 1, the net rates of each component can be written
+ r2 - r3 + r4 rIB= - r1 + r2 - r5 + r6 rzB= - r3 + r4 + r5 - r6 rT = + rl - r2 + r3 - r4 rM = - r1
(1) (2) (3)
(4)
The subscript numbers in eqs 1-4 denote the respective reactions in Figure 1. We now develop three kinetic models based on different mechanistic assumptions about the reactions of
1174 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 Table 2. Effect of the Particle Size of the Catalyst on the Rate of Reaction and the Standard Deviation (SD)of the Measured Rate at ZT = 0.9, zm = 0.06, ZIB * 0.01,and Z2B 0.06. Temperature, 354 K Pressure, 0.8 MPa particle fraction of the average SD of group sizdmm catalystht % rate/mol g-l h-' the rate I 0.0 < d, < 0.3 0.0 I1 0.3 < d, < 0.5 27.2 0.595 0.039 I11 0.5 d, < 0.8 71.3 0.542 0.048 IV 0.8< d, < 1.0 1.1 0.380 0.008 v 1.0 -=z d, 0.4
TAME. The validity of these models is then tested by fitting the proposed rate equations to the experimental rate of TAME splitting. Assuming the homogeneous reaction mechanism, we obtain the following net rate for TAME: rT
= - '&T
+ 'Ala@1B
-
+ 'ACia@2B
(5)
TAME TAMES, TAMES,
+ Saz=
2 2
MeOHS,
TAMES,
MeOHS,
(9)
+ 2M1B
+ 2M2B MeOH + Sa
MeOHS, Fir.
2M2B
(loa) (lob)
2M1B
(12)
where S a is a vacant adsorption site. Equation 9 describes the adsorption of ether, and eq 11 the desorption of alcohol. Reaction 12 describes the isomerization of the isoamylenes. With the assumptions noted above, the adsorption equilibrium constants for TAME and MeOH can be derived from eqs 9 and 11as follows:
Combining the terms of the forward and splitting reactions for both 2M1B and 2M2B with the reaction equilibrium constants K1 and Kz,we get
where the reaction equilibrium constants K1 and K 2 are expressed as 'A1 K -l-k,
(7)
(13)
Because the solvents were nonpolar, their adsorption is weak, and we therefore also assume that they do not compete on the adsorption of active sites. The adsorption of isoamylenes is also assumed to be so small compared to the adsorption of alcohol and ether that it can be neglected in the site balance. The site balance for the system can then be expressed as
kA3
K-- 'A4
The equilibrium constants K1 and K2 for the formation of TAME are those published by Rihko et al. (1994).The rate equations of each component based on this mechanism are presented in Table 3 (Mechanism A). In addition t o the homogeneous mechanism we developed two further mechanisms, B and C, where the surface reaction is the rate-determining step. In the derivation of mechanisms B and C we assumed that all adsorption sites on the catalyst were energetically equivalent and that the adsorption of the molecules was competitive on the same active sites. The adsorption of the molecules was assumed to be fast. The adsorption of a polar component (alcohol) to the ion exchange resin from a solvent mixure has been found t o be considerably stronger than the adsorption of the less polar components (Helfferich, 1962). We assumed in mechanism B that only aZcoho2 and ether are adsorbed to a considerable extent on the active sites of the catalyst. So, in mechanism B the forward reaction was assumed to proceed between an adsorbed alcohol molecule and a striking isoamylene molecule impacting directly from the liquid bulk phase. The adsorption of the isoamylenes is assumed to be very small, so the fraction of the sites occupied by the isoamylenes is minimal but still enough the give a finite isomerization rate. Mechanism B can be seen as a modification of the Eley-Rideal mechanism, which has widely been proposed for gas phase reactions (Satterfield, 1991). With these assumptions we can write the following reaction steps for mechanism B:
(11)
=1
@M+@T+@s
(15)
Using eqs 13-15, we can write expressions for the surface coverages:
0, = K + T @ s a
(16) (17)
os,=
1
K+T +K@M + 1
(18)
where Oi describes the fraction of surface covered by component i, and OS, presents the fraction of vacant sites. As an example, we write here the equation for the net rate for TAME in mechanism B: f~ =
-k
+
~ 2 @ k~B i @ @ i B
- kB4@T
+
k~,@@2~
(19) Consequently, combiningeqs 16-18 with eq 19, the net rate of TAME can be written as rT
=
- kB&$T
+ kBIK@@lB
(1+ K + T
- k B 4 K f l T + kB&@@ZB
+ K@M)
(20)
By combining reaction steps 9, loa, and 11for 2M1B and 9, lob, and 11 for 2M2B, we can write the overall reaction equilibria for the formation of TAME. For the
Ind. Eng. Chem. Res., Vol. 34,No. 4, 1995 1175
1176 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995
reaction equilibrium constants K1 and KZfor mechanism B we get the expressions
(29)
(21)
Combining eqs (13, 14, 27-29) with eq 27 we get the following rate equation for TAME:
The equilibrium constants K I and KZfor the formation of TAME are known from the earlier publication (Rihko et al., 1994). We express the equilibrium for the isomerization in a similar way:
For the reaction equilibrium constants K1 and KZ we get the expressions
(31)
'B5
K3 = -
(23)
kB6
K2 =
The rate equation for TAME, eq 20, can then be written
r, =
'C&MK2B
(32)
kC4KT
Combining eqs 31 and 32 with eq 30 and dividing the rate equation by KM and assuming 1/KM to be insignificant relative to the other factors in the denominator we get the final form of the rate equation of TAME in mechanism C:
Dividing the rate equation by KMand assuming l/KM to be insignificant relative to the other factors in the denominator, we can write the net rate of TAME by mechanism B in final form as
rm= - k BzKM QT KT
(1- K)-:
KT - kB4=(l
- K2-
(ST (25)
For mechanism C we assumed the competitive adsorption of all reagents, methanol, isoamylenes, and ether. As in B, the adsorption of solvents was assumed to be weak, and solvents were excluded from the competitive adsorption on active sites. Because of the balance of the active sites, in this mechanism an active site occupied by TAME must be accompanied by one unoccupied site for the reaction to proceed. Based on these assumptions we get the following net rate of TAME:
+ kC1oMolB kC4@T@Sa
+ kcS@M@,B (26)
For the mechanism C the site balance for the system is 0,
+ 0, + 0 1 , +
02,
+ @sa=
KM
1- K )-:
'(
KT - k4-T( KM
1 - K2-
(33)
+ .M)
rT = - kCzO@S,
KT - k,---a
1
(27)
In addition to the adsorption equilibrium constants for TAME and MeOH in eqs 13 and 14 the adsorption equilibrium constants for 2M1B and 2M2B can be written:
Table 3 shows the final rate equations for each component according to the three different mechanisms. The number of parameters to be estimated in each model a t a constant temperature is shown in Table 3. For the equations describing mechanism A, the parameters to be fitted are km, k ~ 4 and , k ~ 5 .In the case of mechanism B, there are four parameters to fit: kB&d KM,ksdiT/KM,12135, and KT/KM; while for mechanism c the corresponding parameters are kc&dK2, kc&dKM2, kc&$&, K ~ K MK ,~ $ K Mand , Kz$KM. In the fitting of the kinetic parameters according to mechanism C, we further assumed that the adsorption of 2M1B and 2M2B on the catalyst active site was equal, i.e., K ~ = B
KZB. Parameter Estimation and Comparison of Mechanisms. The parameters of the kinetic rate equations for the different mechanisms were fitted to the experimentally measured rates of reaction of each component. The kinetic equations are expressed in terms of activities (a, = yixl). In the estimation of activity coefficients (yl) we used the UNIQUAC method. The parameters for the UNIQUAC method were taken from the literature (Gmehling and Onken,1977). A two-stage optimization procedure was followed in the parameter estimation. First we derive an initial value for the ratio kdkz. Initially, the number of parameters to be fitted was reduced by analyzing more closely the ratio of isoamylenes produced in the splitting of TAME. Figure 2 shows the mole ratio of the formed isoamylenes as a function of space time. We derive here the ratio kdkz for mechanism B, but it can be derived in a similar way for the other mechanisms. In the beginning of the splitting reaction, when neither the
Ind. Eng. Chem. Res., Vol. 34,No. 4, 1995 1177
2 s
3 i
I
I
I
I
I
I
I
I
I
I
I
21 I t
I I
I
I
1
oJ
I
I
!
!
I
i
0.01
0 02
0 03 space time AI
0.04
0.05
0 06
0
Figure 2. The ratio of XZ$XIB as a function of space time, r. Temperature, 354 K, pressure, 0.8 MPa; catalyst, Amberlyst 16.
forward nor isomerization reaction yet proceeds, i.e., XlB, and XM FZ 0, the mole balance can be written
XZB,
K,
Dividing eq 35 by by 34 we get
- - - -_ -‘2B
‘ZB
‘1B
‘1B
- ‘4
(36)
‘2
We then estimated the initial splitting ratio of TAME to 2M1B and 2M2B by expressing the mole fraction of 2M2B as a function of 2MlB. A third-order polynomial equation fitted best to the data in Figure 2. Initially (space time t = 01, when X ~ BE;: 0, we got 5.35 as the value of the derivative. 16.35 was used as a starting value in the parameter estimation for the ratio kdk4. In the final estimation we used the optimization routine to find the best values for the ratio k d k 4 . The estimation of the parameters was carried out by minimizing the weighted sum of residual squares (WSRS) between the experimental and calculated rates of reaction: (37) where the weighting factor Wj was 1 for every experiment. The nonlinear regression program package Reproche (Vadja and Valko, 1985)that uses the LevenbergMarquardt method was used in the calculation. The results of the regression analysis are summarized in Table 4. The values of the parameters at 354 K, their standard deviations, the mean residual square (MRS), and weighted sum of residual squares (WSRS) are listed in the table. The discrimination of the models was done by comparing the weighted sum of residual squares. From the results of the regression analysis (Table 4) it is clear that the rate equations for mechanisms A and B describe better than the rate equations for mechanism C the experimental data. The weighted sum of residual square (WSRS) is much higher for mechanism C than for the other mechanisms, so mechanism C is the least
probable. For comparison of the different mechanisms, the experimental and calculated rates of reaction (TAME splitting) at 354 K are presented in Figure 3a-c. For a model to represent the experimental measurements adequately, the deviation between the measured and calculated rates of reaction should be random and not follow a trend with respect to an independent variable. If we compare parts a and b of Figure 3, we can see a difference in the quality of the fit. Although mathematically the WSRS is slightly smaller for kinetic model A than B, the deviation of the calculated rate from the experimental rate is not random in the case of mechanism A. As experimentally observed, the rate of the splitting of TAME increased rapidly as MeOH content decreased in the reaction mixture. This kind of increase can be seen in the calculated rates based on mechanism B but not in the rates based on mechanism A. The experimental data are thus more accurately described by the rate equations for mechanism B, which correctly describe the negative reaction order for methanol activity. An example of the fit is given in Figure 4a-c, where the experimental rate of reaction vs the values calculated according to the different mechanisms are given at 354 K. The points are marked according to the various TAME mole fractions in the feed ( X T = 0.96, 0.46, 0.33, and 0.16). For mechanism A or C, the calculated rate deviates systematically from the experimental one. The calculated rate according to mechanism B deviates more randomly. However, in Figure 4b there could be seen few points where the calculated rates differ from the experimental rates considerably. At these experiments the mole fraction of methanol was very small ( ~ 0 . 0 2in ) the reactor outlet. Due to the form of the equations the calculated rate of reaction increases very strongly when the methanol mole fraction is small. Therefore it shoud be pointed out that the validity of the equations is limited in conditions where the mole fraction of methanol is very small. Evaluation of Mechanism B. Figure 3 shows the experimental and calculated rates of reaction for the splitting of TAME over the whole composition range of TAME. The rate of reaction was studied at four TAME mole fraction levels in the feed (XT = 0.96, 0.46, 0.33, and 0.16), as can be seen in the figure. In the parameter estimation procedure, the parameter kB&/KM was identified without difficulty; the standard deviation was only 7% of the parameter. The determination of the other parameters, k ~ d k ~ k4 ~, 5 and , KdKM, was more difficult; the standard deviations of the parameters were larger, 20%, 45%, and 22%) respectively. However, compared to the other mechanisms the parameter estimation for the model based on mechanism B was considerably more precise than for the other models. In the cases A and C we got standard deviations which were several orders of magnitude higher than the parameters. The ratio of the adsorption equilibrium constants of TAME and MeOH, K T / K M , is relatively small (0.1301, a result which suggests that TAME adsorbs more weakly than methanol on the active sites of the catalyst. This is in good agreement with the known selective adsorption of polar components into ion exchange resins, e.g., the adsorption of alcohol into resin in a solvent mixture (Helfferich, 1962). The results also show our initial assumption of 1IKM = 0 to be acceptable. There could not be seen any severe correlation between the parameters in the model based on mechanism B. The highest correlation coefficients between the
1178 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 Table 4. Values of Parameters and the Standard Deviation of the Parameters (SD),the Mean Residual Square (MRS) and the Weighted Sum of Residual Square (WSRS) for the Kinetic Equations Based on the Mechanisms A, B, and C mechanism parameter unit value SD (%) MRS WSRS A k~dk~4 0.1918 28 0.001 762 0.4105 0.4462 4 k~4 mol h-I g-' k~5 mol h-' g-l 1.077 x very large .B k~dk~4 0.2437 20 0.002 566 0.5953 0.1615 7 kB&& mol h-' g-l mol h-I g-' 3.1767 45 ks5 C
kcdkc4 kcdWh2 kc&id& KTIK~~ Kid& Kzdh
mol h-I g-' mol h-' g-'
0.1283 0.4532 0.0270 4.6403 0.0636 3.1540 x lo-* 3.1540 x lo-@ 0.70 I
parameters were calculated between kB&T/KM and KTI KM,which was 0.83. Temperature Dependence of Parameters. The temperature dependences of the reaction equilibrium constants K1, Kz, and K3 were calculated from the reaction equilibrium data of Rihko et al. (1994). The temperature dependence of K1, K2, and K3 can be expressed as
+ 4041.2/T) K, = e x p ( 4 . 2 4 7 3 + 3225.31T) K3 = exp(-0.1880 + 833.3/T) Kl = exp(43.3881
22 33 19 29 48 very large very large
0.013 091
3.0239
I
I
I
I
I
I
I
I
I
I
010
020
030
040
OS0
060
070
080
090
100
070
080
090
100
(38) 000
TAME actinty I -
(39) 0 70
(40)
060
0 50
Most of the experiments were carried out at temperatures of 334 or 354 K. Initially, we estimated the parameters at both 334 and 354 K. Assuming the kinetic parameters k ~ and 4 k ~ t2o be of Arrhenius type we obtained for the activation energy of the surface reaction of TAME splitting to 2M1B and methanol, eq loa, an estimated value of 100.0 kJ/mol. For the activation energy of the surface reaction of TAME splitting to 2M2B and methanol, eq lob, we got an estimated value of 95.1 kJ/mol. In a similar way we obtained an activation energy E , of 39.1 kJ/mol for the isomerization of 2M1B to 2M2B, eq 12. The ratio of adsorption equilibrium constants KT/KMwas estimated to be 0.1283 at 354 K and 0.1405 at 334 K. Finally, 0 the activathe pre-exponential factors k ~ 2 oand k ~ 4 and tion energies for the reactions with all the experimental data at temperatures between 324 and 354 K were estimated with the optimization routine. The preexponential factors kBzo and kB40 were 1.7054 x loi4 and 1.3282 x 1014with standard deviations of 29% and 6%, respectively. The E , values for the surface reactions of TAME splitting, eqs 10a and lob, did not change, the standard deviations for the parameters were 39% and 9%, respectively. These values are comparable t o the value published by Randriamahefa and Gallo (1988) who found E , for the splitting reaction of TAME to be 114.95 kJImol. Furthermore, the obtained activation energy for TAME splitting is in the range of a typical activation energy of a chemical reaction. For the isomerization reaction, we got an activation energy of 39.1 kJ/mol with a standard deviation of 74.4 kJ1mol. The objective function was considerably less sensitive for this parameter compared to the other parameters indicating that the estimation is not very accurate. This value deviates from the values found in literature: 76.6 kJ/mol (Pavlova et al., 1986) or 46.4 kJ/mol (Muja et al., 1986). A probable reason is that the ratio of the isomers
*m Z 040
3
030
Y
0 20
0 IO
OW
OW
010
020
030
040
050
060
TAME actinty / 0.70
1
~
I
I
I
1
I
I
I
I
I
020
030
040
050
Ob0
070
080
090
100
0.60
-'m 0.50 k 0.40
! +
0.30
0.20 0.10 0.00 000
010
TAME lcttvity /
-
Figure 3. The rate of the splitting of TAME as a function of U T : (m) the experimental and (0)calculated rates of reaction according to mechanisms (a, top) A, (b, middle), and (c, bottom). Temperature, 354 K, pressure, 0.8 MPa; catalyst, hnberlyst 16.
was in every measurement relatively near to the chemical equilibrium. Conclusions The effects of process variables-pressure, temperature, reagent concentration, and space time-on the rate of the splitting and formation of TAME were measured. In a comparison of three reaction mechanisms, the experimental results were found to be best described
Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1179
" 0.50
a 0.40 0.30 0.20
0.10 0.00 0.00
0 10
020
030
0.40
050
0.60
070
qw 0.70
Abbreviations
0.60
MRS = mean residual square SD = standard deviation WSRS = weighted sum of residual square 2M1B = 2-methyl-1-butene 2M2B = 2-methyl-2-butene TAME = tert-amyl methyl ether, 2-methoxy-2-methylbutane MeOH = methanol MTBE = methyl tert-butyl ether, 2-methoxy-2-methylpropane ETBE = ethyl tert-butyl ether, 2-ethoxy-2-methylpropane
0.50
4 0.40
'
Ki = adsorption equilibrium constant for component i kio = pre-exponential factor, mol g-' h-' Kj = reaction equilibrium constant for a reactionj,j = 1-3 ni = amount of a component i, mol ri = rate of reaction for component i, mol g-' h-' r,dC= rate of reaction calculated by a model, mol g-1 h-l rex,= rate of reaction measured experimentally, mol g-1 h-I Sa = vacant adsorption site T = temperature, K t = time, h V = volume of the reactor, mL wi = weight factor xi = mole fraction of component i
0.30 0.20 0.10
0.00 0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
qnp
Greek Letters 0.70
yi = activity coefficient for component i Oi = fraction of surface covered by component i z = space time, h
0.60 0.50
Subscripts and Superscripts
tl 0.40 'f
1B = 2-methyl-1-butene 2B = 2-methyl-2-butene M = methanol T = tert-amyl methyl ether
0.30
0.20 0.10
0.00 000
0.10
020
030
040
050
060
070
w
Figure 4. The experimental vs calculated rate of the splitting of TAME according to mechanisms (a, top) A, (b, middle) B, and (c, bottom) C. Mole fraction of TAME in the feed XT = (0)0.16, (A), 0.33, ( 0 )0.46, (A)0.96; temperature, 354 K pressure, 0.8 MPa.
by the kinetic equations for a mechanism, in which the ether and alcohol adsorb on the catalyst active site. The rate-determining step was the surface reaction. The kinetic equations were written in the terms of the activities of the components. When, additionally, the reaction equilibrium data were known for the reactions the experimental results of the splitting of TAME and the isomerization of isoamylenes were best described by a four-parameter model.
Acknowledgment The financial support for this work from the Technology Development Centre of Finland and Neste Oil is gratefully acknowledged.
Nomenclature ai = activity of a component i = yixi ci = concentration of a component i d, = particle diameter, mm E , = activation energy, kJ mol-'
k,,
= rate constant for mechanism n, n = A, B, or C, mol and for reaction m in Figure 1.
g-' h-'
Literature Cited Ancillotti, F.; Massi Mauri, M.; Pescarollo, E.; Romagnoni, L. Mechanism in the Reaction between Olefins and Alcohols Catalyzed by Ion Exchange Resins. J.Mol. Catal. 1978,4,3748. Brockwell, H. L.;Sarathy, P. R.; Trotta, R. Synthesize ethers. Hydrocarbon Process. 1991,70 (9), 133-141. Colombo, F.; Dalloro, L. MTBE Synthesis: Activity of Different Catalysts and Kinetics. In Proceedings of Vth International Symposium on Heterogeneous Catalysis,Varna, Part 11, 1983, 407-412. Colombo, F.; Corl, L.; Dalloro, L.; Delogu, P. Equilibrium Constant for the Methyl tert-Butyl Ether Liquid-Phase Synthesis by Use of UNIFAC. Znd. Eng. Chem. Fundam. 1983a,22,219-223. Fleitas, D. H.; Macanio, H. R.; PBrez, C. F.; Orio, 0. A. Selective Production of t-Amyl Methyl Ether Using Sheet Silicates. React. Kinet. Catal. Lett. 1991,43,183-188. Francoisse, 0.; Thyrion, F. C. Kinetics and Mechanism of Ethyl tert-Butyl Ether Liquid-phase Synthesis. Chem. Eng. Process. 1991,30,141-149. Gmehling, J.;Onken, U. Vapor-liquid Equilibrium Data Collection; Chemistry Data Series; Dechema: Frankfurt, 1977; Vol. 1. Helfferich, F. Zon Exchange; McGraw-Hill Book Company Inc.: New York, 1962; pp 511-512. Krause, A. 0.I.; Hammarstrom, L. G. Etherification of Isoamylenes with Methanol. Appl. Catal. 1987,30,313-324. Muja, I.; Goidea, D.; Marculescu, N.; Andreescu, G.; Curca, C.; Antonescu, I. Aditia metanolului la izoamilene pe cationiti macroporosi. Rev. Chim. 1986,37,1047-1054. Pavlova, I. P.; Caplic, D. N.; Isuk, I. V.; Basner, M. E. Issledovanie i razrabotka technologii proizvodstna monomerov i sinteticeskick kaucukov. CNZIE - Neftechim 1986,103-112. Pescarollo, E.;Trotta, R.; Sarathy, P. R. Etherify light gasolines. Hydrocarbon Process. 1993,72 (21, 53-60.
1180 Ind. Eng. Chem. Res., Vol. 34, No.4,1995 Randriamahefa, S.;Gallo, R. Synthhse de l'ether methyl teramylique (TAME) en catalyse acide: cinbtiques et equilibres de la methoxylation du methyl-2 butene-2. J . Mol. Catul. 1988, 49, 85-102. ReMnger, A. Reaktionstechnische Untersuchungen zur Fliissigphasesynthese von Methyl-tert-butylether (MTBE) an einem starksauren makroporosen Ionenaustauscherharz als Katalysator. Ph. D. Disseratation, Technische Universitiit Clausthal, 1988. Rehfinger, A.; Hoffmann, U. Kinetics of Methyl Tertiary Butyl Ether Liquid Phase Synthesis Catalyzed by Ion Exchange Resin - I. Intrinsic Rate Expression in Liquid Phase Activities. C k m . Eng. Sei. 1990,45,1605-1617. Rihko, L. K.; Linnekoski, J. A.; Krause, A. 0. I. Reaction Equilibria in the Synthesis of tert-Amyl Methyl Ether and tert-Amyl Ethyl Ether in Liquid Phase. J. Chem. Eng. Data 1994 39,700-704. Rock, K.TAME: technology merits. Hydrocarbon Process. 1992, 71 (5), 86-88.
Satterfield, C. N. Heterogeneous Catalysis in Industrial Practice, 2nd ed.; McGraw-Hill, Inc.: New York, 1991; pp 65-66. Safronov, V. V.; Sharonov, K. G.; Rozhnav, A. M.; Alenin, V. I.; Sidorov, S. A. Thermodynamics of the Synthesis of t e r t - b y 1 Methyl Ether (TAME).Appl. Chem. USSR Engl. Transl. 1989, 62 (4),Part 1, 763-767. Vadja, S.; Valkd, P. Reprock, Regression Program for Chemical Engineers; Eureca: Budapest, 1986. Received for review March 15,1994 Revised manuscript received November 4,1994 Accepted November 21, 1994"
IE9401519 Abstract published in Advance ACS Abstracts, February
15, 1995.
