310
Ind. Eng. Chem. Res. 1997, 36, 310-316
Kinetics of the Heterogeneously Catalyzed Formation of tert-Amyl Ethyl Ether Juha A. Linnekoski* and A. Outi Krause Laboratory of Industrial Chemistry, Helsinki University of Technology, Kemistintie 1, FIN-02150 Espoo, Finland
Liisa K. Rihko† Technology Center, Neste Oy, P.O. Box 310, FIN-06101 Porvoo, Finland
In this work, the kinetics and equilibrium of the heterogeneously catalyzed liquid-phase formation of tert-amyl ethyl ether (TAEE) were studied. The catalyst used was a commercial sulfonic acid ion-exchange resin (Amberlyst 16W). The experiments were carried out in a continuous stirred-tank reactor, measuring stationary reaction rates. The measured reaction rates were fitted to three kinetic models; homogeneous, Eley-Rideal type, and Langmuir-Hinshelwood type. Of these, the Langmuir-Hinshelwood type model described the experimental results best. This model is based on single-site adsorption of every component, with the surface reaction being the rate-limiting step. The activation energies for the formation of tert-amyl ethyl ether from 2-methyl-1-butene were 90 and from 2-methyl-2-butene 108 kJ‚mol-1. For the isomerization of 2-methyl-1-butene to 2-methyl-2-butene, an activation energy of 82 kJ‚mol-1 was obtained. Introduction Oxygenates (alcohols and tertiary ethers) have become important additives in gasoline over the last decade. At first, oxygenates were used as octaneenhancing components in gasoline, but during the 1980s it was noticed that they also improve the combustion of gasoline and reduce emissions. This has resulted in the growing use of oxygenates in the reduction of automotive exhaust emissions (Seddon, 1992). In addition to methyl tert-butyl ether (MTBE; 2-methoxy-2-methylpropane), which has been the predominant oxygenate, the octane boosters of interest are the ethers tert-amyl methyl ether (TAME; 2-methoxy-2-methylbutane), ethyl tert-butyl ether (ETBE; 2-ethoxy-2-methylpropane), and tert-amyl ethyl ether (TAEE; 2-ethoxy-2-methylbutane) (Simpson and Hibbs, 1995). The leading country in the use of oxygenates has been the United States, where the Clean Air Act Amendments of 1990, and the 1992 revisions to it, have tightened the emission limits of vehicles. These amendments will result in a growing demand for oxygenates and higher ethers in the coming years (Peaff, 1994). Higher ethers (TAME and TAEE) can be used to meet the amendments of the blend Reid vapor pressure (bRvp) levels, and the limits for the olefin content of the reformulated gasoline. TAME and TAEE have lower bRvP values than the olefins from which they are made (Pescarollo et al., 1993; Piel, 1992). Their production utilizes isoamylenes and thus reduces the olefin content of the light FCC (fluid catalyst cracking) gasoline. One advantage of TAEE is that ethanol, the other reagent, can be produced by fermentation from renewable resources, such as molasses, sugarcane, sugar, corn, or potatoes (Lynd et al., 1991). Mechanistic assumptions for the synthesis of tertiary ethers with ion-exchange resin Amberlyst 15 have been presented by Ancilotti et al. (1977, 1978). They stated * Author to whom correspondence is addressed. Fax: 3589-451 2622. Tel: 358-9-451 2666. e-mail: Linnekoski@polte. hut.fi. † e-mail:
[email protected]. S0888-5885(96)00251-5 CCC: $14.00
that the initial rate of the reaction depended on the ratio of the reactants. At stoichiometric or higher alcohol/ isobutene ratios, the initial rates showed a zero order for the alcohol and first order for the olefin. The ionic mechanism predominates, and the protonation of the olefin by the solvated proton was proposed to be the rate-determining step. At lower than stoichiometric alcohol/olefin ratios the mechanism is a concerted one, and active centers are on the associated network of sulfonic acid groups. Gicquel and Torck (1983) stated that the protons can be more or less solvated and that the proton activity can be variable depending on the methanol concentration. Kinetic studies on the liquid-phase formation of ethanol-based ethers have been presented by Jayadeokar and Sharma (1993), Fite´ et al. (1994), and Zhang and Datta (1995a,b). Jayadeokar and Sharma (1993) studied the simultaneous hydration and etherification of isoamylene (2-methyl-1-butene or 2-methyl2-butene) with 80% aqueous ethanol. They obtained a best fit with the Eley-Rideal type model, in which the controlling step was a single-site surface reaction. According to Jayadeokar and Sharma (1992), the same mechanism also controls the simultaneous hydration and etherification of isobutene with aqueous ethanol. Fite´ et al. (1994) presented an Eley-Rideal type model for the formation of ETBE. According to them, ethanol adsorbed on one center reacts with the isobutene from solution, to give the ether adsorbed on one center also. The surface reaction was the rate-limiting step, and two additional centers take part in this step. Despite the growing interest in higher ethers and ethanol-based ethers, few studies have been published regarding the formation of TAEE. Rihko and Krause (1993) published a report of the reactivity of isoamylenes with ethanol. The reaction equilibrium in the synthesis of TAEE has been studied by Rihko et al. (1994) and Kitchaiya and Datta (1995). So far, no detailed kinetic model for the formation of TAEE has been published. Therefore, in this work three kinetic models are tested: the pseudohomogeneous model, the Eley-Rideal type model, and the Langmuir-Hinshelwood type model. © 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997 311 Table 1. Repeated Experiments: Temperature (T) and Feed and Product Molar Flows feed (mol‚h-1)
product (mol‚h-1)
T (K)
ETOH
I-PEN
2M1B
2M2B
CYHE
n-OCT
ETOH
2M1B
2M2B
TAOH
TAEE
353 353 343 343 343 343 333 333 333 333
0.251 0.250 0.411 0.410 0.689 0.689 0.414 0.689 0.690 0.411
0 0 0.039 0.045 0 0 0.040 0 0 0.045
0.059 0.060 0.016 0.016 0.049 0.049 0.016 0.049 0.050 0.016
0.697 0.697 0.182 0.181 0.592 0.592 0.183 0.592 0.591 0.181
0 0 0.166 0.167 0 0 0.169 0 0 0.167
0 0 0.125 0.125 0 0 0.126 0 0 0.125
0.130 0.131 0.395 0.397 0.618 0.619 0.404 0.656 0.659 0.403
0.055 0.055 0.015 0.015 0.042 0.043 0.015 0.045 0.046 0.015
0.580 0.582 0.169 0.170 0.531 0.530 0.168 0.564 0.562 0.175
0 0 0 0 0.016 0.016 0 0.012 0.008 0
0.121 0.118 0.015 0.013 0.069 0.069 0.009 0.032 0.032 0.008
The same types of models have earlier been tested for the TAME splitting reaction (Rihko and Krause, 1995). Experimental Section Reactor. The experiments were carried out in a continuous stirred-tank reactor (CSTR, 55.6 mL stainless steel). The reaction mixture was stirred magnetically. The catalyst was placed in a metal gauze basket (60 mesh, 2 cm3), which also worked as a mixing baffle in the reactor. The temperature (323-363 K) was controlled within (0.2 K by immersing the reactor in a thermostated water bath. The pressure was kept constant at 0.7-0.8 MPa, with an accuracy of 0.03 MPa, to guarantee a liquid-phase operation at all temperatures. The feed and the reactor effluent were analyzed on-line with a gas chromatograph using an automated liquid sample valve. In order to guarantee a pulse-free flow, the reaction mixture was fed from a pressurized tank to the reactor with a pressure difference of 0.20.4 MPa over the liquid mass flow controller. The state of the system (flow, pressure, and temperature) was kept constant for 3-4 h, and repeated analyses were made of the reactor outlet to ensure that the steady state was reached. A Mettler PM 6000 balance was used to calculate the actual flow at the outlet of the reactor system. Preliminary experiments were carried out at 353 K in order to ensure that the rates were generated free of mass-transfer effects. Runs without catalyst showed that no reaction occurs in the absence of the catalyst. The effect of internal and external mass transfer on the rate of formation of TAEE was studied by varying the speed of mixing and by measuring the reaction rate with progressively smaller catalyst particle sizes. Analytical Methods. A Hewlett-Packard gas chromatograph 5890 Series II, equipped with a flame ionization detector, was used for the analysis. The compounds were separated in a 60 m × 0.258 mm glass capillary column DB-1, with a film thickness of 1.0 µm (J & W Scientific). All compounds were calibrated in order to obtain quantitative results. In order to test the reliability of the analysis, some of the kinetic experiments were repeated. These experiments are presented in Table 1. According to Table 1, the reproducibility of the experiments is (2%, calculated from the obtained ether molar flow. Catalyst. The catalyst used was a commercial, strong cation-exchange resin, Amberlyst 16W (Rohm & Haas). The exchange capacity of the ion-exchange resin was 4.4 mequiv/g of dry catalyst, and the cross-linking level was 12 wt %. The water present in the system strongly affects the etherification rate (Linnekoski et al., 1996; Cunill et al., 1993). Therefore, the catalyst particles were treated with ethanol at room temperature before experiments in order to remove water from the
catalyst pores. Iborra et al. (1993) have shown that although this is an effective method some water remains in the catalyst particles. One indication of the water amount in the system is the amount of tert-amyl alcohol, formed from isoamylenes (2M1B and 2M2B) and water, in the outlet. In this work the maximum amount of TAOH formed was 0.6 mol %. In prior alcohol treatment the catalyst was sieved, and a particle size of 0.3-0.6 mm was used in the experiments. The catalyst was replaced after several runs. After the runs, the catalyst was dried and weighed. All rate calculations are based on the amount of dry catalyst. The amount of dry catalyst used in the experiments varied between 0.5 and 1.0 g. Reactants and Solvents. The reagents used were ethanol (ETOH; Alko Oy, >99.5 wt %), 2-methyl-1butene (2M1B; Aldrich, 99 wt %), and a mixture of 2-methyl-2-butene and 2-methyl-1-butene (2M2B; Fluka Chemie, 90.7 wt %). In some experiments, the reagents were diluted with a mixture of unreactive hydrocarbons, 10 wt % isopentane (I-Pen; Fluka Chemie, p.a.), 45 wt % cyclohexane (CYHE; Merck, p.a.), and 45 wt % n-octane (n-OCT; Fluka Chemie, p.a.). The solvent hydrocarbons were chosen to represent the typical hydrocarbons present in an FCC gasoline fraction. Reaction Rate. The reaction rate (mol‚h-1‚g-1 cat) for the formation of TAEE was calculated using eq 1.
rTAEE ) (FTAEE,out - FTAEE,in)/mcat
(1)
Results External Mass Transfer. The effect of external mass transfer on the formation rate of TAEE was studied by varying the speed of mixing between 0 and 17 s-1. The temperature was 353 K and the pressure 0.7 MPa, and the feed compositions were xETOH ) 0.317, xOLEF ) 0.305, and xSOLVENT ) 0.378. The rate of formation of TAEE as a function of the mixing speed is presented in Figure 1. The results showed that, at mixing speeds >5.0 s-1, the reaction rate is unaffected by the mixing speed. In all the kinetic experiments the mixing speed was set to 17 s-1. Internal Mass Transfer. The influence of internal mass transfer on the reaction rate was studied by performing experiments with different particle sizes, while maintaining the same flow rate, mixing speed (17 s-1), catalyst amount, and feed composition xETOH ) 0.292, xOLEF ) 0.290, and xSOLVENT ) 0.418. The average particle sizes were 0.35, 0.45, 0.55, 0.65, and 0.85 mm. The results indicate that the reaction rate maintains a steady value (40 ( 5 mmol‚h-1‚g-1) with average particle sizes of 0.35-0.65 mm and has a smaller value (∼20%) with particle sizes >0.65 mm. The temperature was 353 K and the pressure 0.7 MPa.
312 Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997
In the following, we present the kinetic equations for the etherification of isoamylenes with ethanol. In the case of the homogeneous reaction model, eq 2 gives a simple power-law rate model for the formation of TAEE (eq 5).
rTAEE ) k1aETOHa2M1B - k2aTAEE + k3aETOHa2M2B - k4aTAEE (5)
Figure 1. Effect of mixing speed on the formation rate of tertamyl ethyl ether. Temperature 353 K, pressure 7 bar. The feed compositions were xETOH ) 0.317, xOLEF ) 0.305, and xSOLVENT ) 0.378.
Kinetic Experiments. Kinetic experiments were carried out at five different ethanol/isoamylene mole ratios of 0.3, 0.7, 1, 3, and 5 at three temperatures 333, 343, and 353 K. Most of the experiments were made using ethanol and a mixture of 2M1B and 2M2B as reagents. However, in this mixture the isoamylenes were so close to equilibrium that the modeling of the isomerization reaction from these data was not possible, and some experiments with pure 2M1B and ethanol as reagents were made. In the conditions used in this work the only ether detected was TAEE (2-ethoxy-2-methylbutane). This agrees with the work of Krause and Hammarstro¨m (1987), who concluded that in the etherification of isoamylenes only olefins with a double bond attached to the tertiary carbon atom react with methanol to yield ethers. In addition to the etherification reaction, some tert-amyl alcohol was formed from the residual water remaining in the catalyst after drying.
Instead of concentrations, we use activities (ai) in the models. This is because of the nonideality of the liquid phase, as Oost and Hoffmann (1996), Panneman and Beenackers (1995a,b), Parra et al. (1994), Rehfinger and Hoffman (1990), and Rihko et al. (1994) have stated for the etherification of the alkenes with an alcohol. UNIFAC estimates of the activity coefficients were used to calculate the activities (Fredeslund, 1977). By combining terms and using the equilibrium constants for the reactions, we obtain the rate equation for the formation of TAEE in the case of the homogeneous system,
rTAEE ) k1(aETOHa2M1B - aTAEE/Ke1) + k3(aETOHa2M2B - aTAEE/Ke2) (6) where the equilibrium constants are defined in this model as Ke1 ) k1/k2 and Ke2 ) k3/k4. In the case of models B and C, we made the following assumptions. All adsorption sites (S) on the catalyst are energetically equivalent, and the adsorption of the molecules is fast compared to the surface reaction. In the case of the model B only, ethanol adsorbs:
ETOH + S / SETOH
(7)
The rate-limiting step is the surface reaction between the adsorbed alcohol and isoamylenes from the liquid phase.
Kinetic Models For this work, we developed three models based on different mechanistic assumptions and tested the validity of these models by fitting the proposed rate equations to the experimental rate data. The models chosen were the most common models proposed in the literature for the etherification reactions: a pseudohomogeneous model (A), an Eley-Rideal type model (B), and a Langmuir-Hinshelwood type model (C). In the formation of TAEE, the following reactions take place. The reversible formation of TAEE from ethanol and isoamylenes: k1
ETOH + 2M1B {\ } TAEE k 2
k3
ETOH + 2M2B \ {k } TAEE 4
(2)
An important side reaction is the reversible isomerization of the isoamylenes. k5
2M1B {\ } 2M2B k 6
(3)
Another side reaction is the formation of tert-amyl alcohol, in the presence of water.
2M1B + H2O f TAOH 2M2B + H2O f TAOH
(4)
SETOH + 2M1B / STAEE
(8)
SETOH + 2M2B / STAEE
(9)
In the case of model C, all reagents adsorb:
ETOH + S / SETOH
(10)
2M1B + S / S2M1B
(11)
2M2B + S / S2M2B
(12)
The rate-limiting step is the surface reaction between the adsorbed alcohol and adsorbed isoamylene.
SETOH + S2M1B / STAEE + S
(13)
SETOH + S2M2B / STAEE + S
(14)
Combining terms and using the equilibrium constants for the reactions, we obtain the rate equations for models B (eq 15) and C (eq 16).
rTAEE ) k1ΘETOHa2M1B - k2ΘTAEE + k3ΘETOHa2M2B - k4ΘTAEE (15) rTAEE ) k1ΘETOHΘ2M1B - k2ΘTAEEΘ + k3ΘETOHΘ2M2B - k4ΘTAEEΘ (16) The surface concentrations of the species Θi can be described with the Langmuir isotherm, where Ki is the
Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997 313 Table 2. Kinetic Equations Based on the Proposed Mechanisms A, B, and C rate equations formation of TAEE
mechanism A
mechanism B
mechanism C
k1′(a2M1BaETOH - aTAEE/Ke1) rT ) + 1 + KETOHaETOH
rT ) k1(a2M1BaETOH - aTAEE/Ke1) + k3(a2M2BaETOH - aTAEE/Ke2)
rT )
k1′(a2M1BaETOH - aTAEE/Ke1)
k3′(a2M2BaETOH - aTAEE/Ke2) 1 + KETOHaETOH formation of 2M1B
r21 )
adsorption of alcohol and ether
adsorption equilibrium constant and ai is the activity of component i.
Θi )
Kiai 1+
∑KiAi
(17)
(1 + KETOHaETOH)2 -k1′(a2M1BaETOH - aTAEE/Ke1) (1 + KETOHaETOH)2
-
k5′(a2M1B - a2M2B/Ke3)
k5(a2M1B - a2M2B/Ke3) homogeneous reaction
+
k3′(a2M2BaETOH - aTAEE/Ke2)
-k1′(a2M1BaETOH - aTAEE/Ke1) r21 ) 1 + KETOHaETOH
r21 ) -k1(a2M1BaETOH - aTAEE/Ke1) k5(a2M1B - a2M2B/Ke3)
(1 + KETOHaETOH)2
(1 + KETOHaETOH) adsorption of all reactants
The apparent reaction rate coefficients (ki′) are determined as k1′ ) k1KETOH and k3′ ) k3KETOH in eq 20 and k1′ ) k1KOLEFKETOH and k3′ ) k3KOLEFKETOH in eq 21. The complete set of equations used in the estimation procedure are shown in Table 2. Equilibrium Constants
Using eq 17 in eqs 15 and 16, we obtain the equations for the formation of TAEE according to model B (eq 18) and model C (eq 19). rTAEE )
rTAEE )
k1KETOH(aETOHa2M1B - aTAEE/Ke1) + 1 + KETOHaETOH + KTAEEaTAEE k3KETOH(aETOHa2M2B - aTAEE/Ke2) (18) 1 + KETOHaETOH + KTAEEaTAEE k1KETOHKOLEF(aETOHa2M1B - aTAEE/Ke1)
(1 + KETOHaETOH + KTAEEaTAEE + KOLEF(a2M1B + a2M2B))2 k3KETOHKOLEF(aETOHa2M2B - aTAEE/Ke2) (1 + KETOHaETOH + KTAEEaTAEE + KOLEF(a2M1B + a2M2B))2
(1 + KETOHaETOH) rTAEE )
(1 + KETOHaETOH)2
(22)
Ke2 )
aTAEE a2M2BaETOH
(23)
a2M1B a2M2B
(24)
(19)
(20)
k1′(aETOHa2M1B - aTAEE/Ke1) + (1 + KETOHaETOH)2 k3′(aETOHa2M2B - aTAEE/Ke2)
aTAEE a2M1BaETOH
Ke3 )
k1′(aETOHa2M1B - aTAEE/Ke1) + (1 + KETOHaETOH) k3′(aETOHa2M2B - aTAEE/Ke2)
Ke1 )
+
In model B, the equilibrium constants are in the form Ke1 ) k1KETOH/k2KTAEE and Ke2 ) k3KETOH/k4KTAEE. For model C, the equilibrium constants are in the form Ke1 ) k1KETOHK2M1B/k2KTAEE and Ke2 ) k3KETOHK2M2B/ k4KTAEE. In model C, we also assume that K2M1B ) K2M2B ) KOLEF; i.e., the adsorption of the olefins is equally strong. According to Helfferich (1962) and Zhang and Datta (1995a,b), the adsorption of the strongly polar component (alcohol) is much stronger than the adsorption of the less polar components (isoamylenes and ether). Considering this, we assume that the terms KTAEEaTAEE and KOLEF(a2M1B + a2M2B) are much smaller than the term 1 + KETOHaETOH and omit them, which was also proven by the estimation results. Thus, we obtain the simplified reaction rates for models B (eq 20) and C (eq 21).
rTAEE )
The equilibrium constants (Ke1, Ke2, Ke3) for the etherification and isomerization reactions (eqs 2 and 3) can be calculated from eqs 22-24 (Smith and Van Ness, 1975, p 385).
(21)
The equilibrium compositions have been published by Rihko et al. (1994). In the present work, the UNIFAC estimates of activity coefficients were used to calculate the activities (Fredeslund, 1977). The temperature dependence of the equilibrium constants can be expressed with eq 25 (Castellan, 1983, p 239).
ln Kei )
-∆rH° ∆rS° + RT R
(25)
A plot of ln Kei versus 1/T produces a straight line. The standard heats of the reactions (∆rH°) can be obtained from the slopes of these lines. From the intercept, we obtain the values for the standard entropy change of the reactions (∆rS°). The standard heat of the reaction of TAEE from 2M1B was 34.5 kJ‚mol-1, and from 2M2B, 27.0 kJ‚mol-1. The standard entropy changes of the reactions were 80.1 and 76.5 J‚mol-1‚K-1, respectively. The values are very close to those obtained by Rihko et al. (1994) using the UNIQUAC method to calculate the activity coefficients. Parameter Estimation The temperature dependence of the reaction rate parameters was correlated using the Arrhenius equation. In order to reduce the correlation between the preexponential factor A0 and activation energy E, the equation was written in the form
k ) Ameane-zE
(26)
314 Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997 Table 3. Results of the Kinetic Estimations model
WSRS
explained %
STD
A B C
0.043 0.030 0.020
96.1 97.3 98.2
0.021 0.018 0.012
where Amean is defined as A0e-E/RTmean and z as 1/8.314‚ (1/T - 1/Tmean). The temperature dependence of the adsorption coefficient of ethanol was correlated also with eq 26, only the activation energy was replaced with ethanol’s liquid-phase adsorption enthalpy (-∆HETOH). The rate equations for the different mechanisms were fitted to the experimentally measured rates of reaction of etherification and isomerization. The estimated parameters were the mean preexponential factors, activation energies, and ethanol’s adsorption enthalpy. The estimation was carried out with the nonlinear MODel ESTimation program (MODEST) (Haario, 1994) by minimizing with the Lewenberg-Marquardt method the weighted sum of residual squares (SRS) between the experimental and calculated rates of reaction (27). The weight factor wi was set to 1 in all experiments.
WSRS )
∑(rexp - rest)2wi
(27)
All the models predicted the Amean quite well, having only a 10-20% standard error of estimates. Homogeneous models had the smallest standard error of estimates for the apparent activation energies from 10 to 15%, and Eley-Rideal type models had the largest from 130 to 160%. The standard errors of estimates for the apparent activation energies in the Langmuir-Hinshelwood type model were from 75 to 130%. For -∆HETOH models B and C predicted values -33.5 and -19.7 kJ‚mol-1 with high standard errors 338 and 435%. Both values are high compared to the literature values of -3.0 (Sola et al., 1995) and -3.4 kJ‚mol-1 (Fite´ et al., 1994). One explanation to this is the high standard error of estimates. The correlation matrix was similar for all the models. Significant correlations were between the activation energies E1′ and E3′ (0.997), E1′ and E5′ (0.994), and E3′ and E5′ (0.910). Correlations were also found between the activation energies and the adsorption enthalpy. They were for E1′ and -∆HETOH (0.999), E3′ and -∆HETOH (0.999), and E5′ and -∆HETOH (0.996). Statistical parameters describing the goodness of the fit for each of the models are presented in Table 3. The statistics show that the Langmuir-Hinshelwood type model has a smaller standard error of estimate, a bigger explained value, and a smaller sum of residual squares than the homogeneous or Eley-Rideal type models. Figure 2 shows that the fit between the experimental and estimated etherification rates, according to the Langmuir-Hinshelwood type model, is good until at low ethanol mole fractions, which could be an indication that the mechanism changes with decreasing alcohol mole fraction. As a result, we can conclude that the Langmuir-Hinshelwood type model describes the whole data range better than the homogeneous or Eley-Rideal type models. The values of the estimated parameters for the Langmuir-Hinshelwood type model (C) are shown in Table 4. The assumption that the terms KTAEEaTAEE and KOLEF(a2M1B + a2M2B) are smaller than the term 1 + KETOHaETOH was checked by including the terms in the Langmuir-Hinshelwood type model and carrying out the estimation procedure. The sum of squares and
Figure 2. Experimental (0) and estimated (9) etherification rates (mol‚h-1‚g-1) versus ethanol mole fraction. Table 4. Estimated Parameter Values for the Proposed Mechanism C
k1 k3 k5 KETOH
Amean (mol‚h-1‚g-1)
Ei (kJ‚mol-1)
7.74 2.27 1.78 3.75
76.8 95.9 72.9
∆HETOH (kJ‚mol-1)
STD (%)
19.7
137 114 74.3 338
Table 5. Activation Energies for the Etherification and Isomerization of the Isoamylenes model
E1 (kJ‚mol-1)
E3 (kJ‚mol-1)
E5 (kJ‚mol-1)
A B C
47 79 90
69 98 108
59 58 82
standard error of estimate increased to 0.0209 and 0.0153, respectively, and the explained value decreased to 98.1%, which shows that the terms does not increase the fit between the experimental and estimated reaction rates. Activation Energies. The activation energies obtained for the three models are presented at Table 5. The estimation procedure gives apparent activation energies, and the true activation energies, E, can be computed from the apparent ones and from the liquidphase adsorption enthalpies of isoamylenes and ethanol using eq 28. Because of the high standard error of
E1 ) E3 ) E1′ - ∆HOLEF - ∆HETOH; E5 ) E5′ - ∆HOLEF (28) estimate of the ethanol adsorption enthalpy obtained in this work, we use the values obtained by Fite´ et al. (1994). For the ethanol adsorption enthalpy Fite´ et al. (1994) obtained a value -3.4 kJ‚mol-1. The liquidphase adsorption enthalpy of isobutene can be calculated from the vapor-phase adsorption enthalpy -30 kJ‚mol-1 (Iborra et al., 1992) and from the enthalpy of vaporization 20.6 kJ‚mol-1 (Daubert and Danner, 1992) to be -9.4 kJ‚mol-1. The values for the isoamylenes can be expected to be at the same range. The results in Table 5 support the conclusion that the Langmuir-Hinshelwood type model describes the whole data range best of the three models. It predicts activation energies, which are within the range of typical values for the etherification. The activation energy for the isomerization reaction agrees with the value (76.6 kJ‚mol-1) obtained by Pavlova et al. (1986) for the isomerization of 2M1B to 2M2B in the formation of TAME. No literature values were found for the activation energies for the formation of TAEE. So, the obtained values were compared with the values obtained
Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997 315 Table 6. Pseudo-Reaction Rate Coefficients (mol‚h-1‚g-1) in the Synthesis of TAEE (This Work) and THEE (Zhang and Datta, 1995b) at 333 K reaction rate coefficients (mol‚h-1‚g-1) TAEE 2M1B 2M2B 2M1P 2M2P
THEE
3.40 0.81 0.96 0.34
Conclusions
Figure 3. Two-dimensional profiles of the maximum likelihood function: (a) E3′ versus E1′, (b) E5′ versus E1′, (c) ∆HETOH versus E1′ (d) E5′ versus E3′.
by Zhang and Datta (1995a,b) in the tert-hexyl ethyl ether synthesis. They obtained an activation energy of 92.8 kJ‚mol-1 for the etherification of R-olefin (2-methyl1-pentene) with ethanol and an activation energy of 108.7 kJ‚mol-1 for the etherification of β-olefin (2methyl-2-pentene) with ethanol. The values obtained in this work for corresponding C5 olefins are 90 and 108 kJ‚mol-1. As a conclusion the Langmuir-Hinshelwood type model predicts activation energies that are close to the literature values. Based on the above, we propose a Langmuir-Hinshelwood type model for the formation of tert-amyl ethyl ether (eq 21), where the ratedetermining step is the surface reaction between the adsorbed reactants (ethanol and isoamylenes).
The diffusion free rate of the formation of TAEE from isoamylenes was measured, and three reaction mechanisms were tested. It was found that, of the three reaction mechanisms, the Langmuir-Hinshelwood type model best describes the experimental measurements. The rate-determining step, in the model, is the surface reaction between adsorbed alcohol and isoamylene. Activation energies were determined for the three reactions using the Langmuir-Hinshelwood type model. The value for the formation of TAEE from 2M1B was 90 kJ‚mol-1 and from 2M2B 108 kJ‚mol-1. For the isomerization of 2M1B to 2M2B an activation energy of 82 kJ‚mol-1 was obtained. Apparent rate constants calculated from eq 26 and from parameter values in Table 4 were compared to those in the tert-hexyl ethyl ether (THEE; Zhang and Datta, 1995b) synthesis. Results at Table 6 shows that the values obtained in this work are, as expected, higher than those of the terthexyl ethyl ether synthesis. Acknowledgment The financial support for this work from the Nordic Minister Council and from the research foundation of the Neste Corp. is gratefully acknowledged.
Sensitivity Analysis
Notation
The identifiability of the model parameters can be studied using the maximum likelihood function (eq 29).
ai ) activity Amean ) A0eE/RTmean, mol‚h-1‚g-1 A0 ) preexponential factor, mol‚h-1‚g-1 E ) activation energy, kJ‚mol-1 E′ ) apparent activation energy, kJ‚mol-1 Fi ) molar flow of component i, mol‚h-1 ∆rH° ) standard heat of the reaction, kJ‚mol-1 ∆HETOH ) adsorption enthalpy for ethanol, kJ‚mol-1 ki ) rate constant, mol‚h-1‚g-1 Kei ) equilibrium constant of reaction i Ki ) adsorption equilibrium constant for component i m ) catalyst mass, g R ) 8.314, J‚mol-1‚K1 ri ) rate of reaction for component i, mol‚h-1‚g-1 Si ) vacant adsorption site ∆rS° ) standard entropy change of the reaction, J‚mol-1‚K-1 T ) temperature, K Tmean ) mean temperature, 347 K wi ) weight factor xi ) mole fraction of component i
(
p(θ) ) exp -
)
1 l(θ) 2σ2
(29)
In eq 29, σ is the pure experimental error. By plotting one- or two-dimensional contour lines of function p, we can study the identifiability of the problem. The maximum of p is obtained at the minimum of l(θ), i.e., at the solution point of the least-squares problem. The forms of the model equations (models B and C; Table 2) produce easily high standard errors for the parameters. In order to study the identifiability of the estimated parameters in the Langmuir-Hinshelwood type model, we plot two-dimensional profiles of the maximum likelihood function. The plots are presented in parts a-d of Figure 3 for the E1′, E3′ E5′, and ∆HETOH, respectively. From figures we can see that the parameters are determined quite well. Contour lines with a p value of 0.8 produce confidence regions where the average change from the optimum value is ( 3.2% for E1′, ( 3.4% for E3′, and ( 3.6% for E5′. The correlation between the adsorption enthalpy and activation energies can be seen clearly from Figure 3c. The shape of the contour lines changes, and the average change for E1′ grows to (5.3%. As a result, we can conclude that, although the form of model equations produces correlation problems, the identifiability of the parameters is adequate.
Abbreviations FCC ) fluid catalytic cracking MEOH ) methanol ETOH ) ethanol 2M1B ) 2-methyl-1-butene 2M2B ) 2-methyl-2-butene 2M1P ) 2-methyl-1-pentene 2M2P ) 2-methyl-2-pentene I-PEN ) isopentane n-OCT ) n-octane
316 Ind. Eng. Chem. Res., Vol. 36, No. 2, 1997 ETBE ) ethyl tert-butyl ether (2-ethoxy-2-methylpropane) TAEE ) tert-amyl ethyl ether (2-ethoxy-2-methylbutane) THEE ) tert-hexyl ethyl ether (2-ethoxy-2-methylpentane) TAOH ) tert-amyl alcohol CYHE ) cyclohexane cat ) catalyst, g STD ) standard error of estimate, % SRS ) sum of residual squares (corrected for means) OLEF ) olefins (2M1B and 2M2B) SOLVENT ) mixture of isopentane, cyclohexane, and n-octane Greek Letters Θ ) fraction of surface covered by component i σ ) error level in the sensitivity analysis
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Received for review May 3, 1996 Revised manuscript received November 4, 1996 Accepted November 8, 1996X IE960251+ X Abstract published in Advance ACS Abstracts, January 1, 1997.
