3784
Ind. Eng. Chem. Res. 1995,34, 3784-3792
Homogeneous Catalysis of Ethyl tert-Butyl Ether Formation from tert-Butyl Alcohol in Hot, Compressed Liquid Ethanol Christine Habenicht, Lance Cameron Kam, Maarten Jan Wilschut, and Michael Jerry Antal, Jr.* Hawaii Natural Energy Institute and the Department of Mechanical Engineering, University of Hawaii at Manoa, Honolulu, Hawaii 96822
Ethyl tert-butyl ether (ETBE) and isobutene are the only significant products of the sulfuric acid ( ~ 0 . 0 0 1M) catalyzed reactions of tert-butyl alcohol in watedethanol mixtures at 3 MPa and 170 "C. Equilibrium is established after a few minutes or less. A 10 parameter kinetic model which embodies a first order elimination reaction and a first order nucleophilic substitution reaction adequately describes the influences of reactant (ethanol, water, and tert-butyl alcohol) concentrations, acid concentration, and residence time on product yields. The fit of the model t o the data improves when the influence of water on the solvent's dielectric constant is included by the addition of two more parameters. One finding of the simulation effort is that protonated isobutene (the key ingredient in ETBE formation) forms only from tert-butyl alcohol (not isobutene) under the conditions employed in this work. Thus tert-butyl alcohol should be preferred over isobutene as a reactant for ETBE synthesis a t elevated pressures and temperatures.
Introduction As a result of the U.S. Clean Air Act Amendments of 1990, which mandated the addition of oxygenate fuels to reformulated gasoline in CO and ozone nonattainment areas, there has been an explosion of interest in the synthesis of methyl tert-butyl ether (MTBE) and ethyl tert-butyl ether (ETBE). Relative to other oxygenates (e.g., methanol and ethanol), these ethers possess many attractive properties, including their low heat of vaporization, low blending Reid vapor pressure, and insensitivity to water (Garibaldi et al., 1978; Iborra et al., 1988; Pie1 and Thomas, 1990). MTBE is currently the most favored ether from an economic standpoint. Nevertheless, use of ETBE is expected to grow as a result of its high blending motor octane number and research octane number, as well as its dilution potential and fungibility (Schiblom et al., 1990). In the future these technical advantages may seem unworthy of mention in light of the opportunities ETBE presents (via its bioethanol component)to increase farm employment and mitigate the greenhouse effect. Moreover, anticipated cost breakthroughs in the production of bioethanol from cellulosic biomass (Lynd et al., 1991) soon may make it the alcohol of choice for ether production. Both MTBE (Tejero et al., 1988, 1989; Brockwell et al., 1991) and ETBE (Iborra et al., 1992; Vila et al., 1993; Fite et al., 1994) are manufactured commercially by the addition of the alcohol to isobutene (IB) over a strongly acidic ion exchange resin. As practiced by industry, the etherification reaction is highly specific: the conversion of IB is typically 95%, but can be as high as 99%, and the selectivity of IB to MTBE is 99% (Chang et al., 1992). However, the ion exchange resin catalyst cannot tolerate temperatures above about 100 "C. Consequently, hours are required for the etherification reaction to reach equilibrium (Cunill et al., 1993). In addition, the catalytic activity of the resin is strongly inhibited by even small amounts of water (Cunill et al., 1993). Since the ethanol-water azeotrope contains about 11% water (by mole) and further drying of bioethanol is costly, the resin's inability to accommodate water is an important drawback. Other heterogeneous catalysts have been studied (Le Vanmao et al., 1993),
but reaction rates were low and diethyl ether was a significant byproduct. ETBE was first synthesized over 60 years ago from ethanol and tert-butyl alcohol using concentrated sulfuric acid as a catalyst (Norris and Rigby, 1932; Evans and Edlund, 1936). Nevertheless, little attention has been given to homogeneous catalysis of the etherification reaction in the liquid phase. This approach can utilize both higher temperatures and pressures t o enhance the reaction rate by about 2 orders of magnitude above that realized commercially (see below). Another advantage of homogeneous catalysis is its relative insensitivity to the presence of water in the reactant feed. For example, earlier work in this laboratory revealed the facile dehydration of ethanol to ethene (Antal et al., 1987; Xu et al., 1990, 19911, l-propanol (Narayan and Antal, 1989, 1990) and 2-propanol (Ramayya et al., 1987)to propene, tert-butyl alcohol (BuOH) t o IB (Xu and Antal, 1994), fructose t o &(hydroxymethyl)-2-furaldehyde (Antal et al., 19901, and xylose to furfural (Antal et al., 19911, all in supercritical or hot compressed liquid water with sulfuric acid catalyst. Similarly, organic acids catalyze their own dehydration in supercritical and hot compressed liquid water. Thus, acrylic acid is a major product of the reactions of lactic acid (Mok et al., 1989),and methacrylic acid is the major product of citric acid decomposition (Carlsson et al., 1994),in both near-critical and supercritical water. The goal of this research was to gain insight into the chemistry of ETBE synthesis from tert-butyl alcohol in hot, compressed liquid ethanol with sulfuric acid catalyst. Following earlier work, we also hoped to develop a kinetic model of the observed reaction chemistry that would embody the detailed mechanism of ETBE formation. Finally, since tert-butyl alcohol is a major byproduct of propylene oxide production and can be less costly than IB, we employed it instead of IB as a reactant. This had the effect of enriching the water content of our feed relative t o a reactant containing IB and alcohol alone.
Apparatus and Experimental Procedures All the experimental results presented in this paper were obtained by use of a 80 cm long, annular flow
0888-5885/95/2634-3784$09.0QI0 0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 3786 Table 1. Typical Nondimensional Numbers Which Characterize the Annular Flow Reactor nondimensional no. value ~~
Re Pr sc Pesd Petd
7.OE+01 6.9E+00 7.4E-01 5.2E+01 4.93+02 2.93-03
Da reactor fabricated from Hastelloy 276 tubes with 6.351 4.57 mm o.d.1i.d. (outer annulus) and 1.59/0.0635 mm o.d.1i.d. (inner annulus). A Waters 6000A HPLC pump provided reactant flow rates of 1.0-2.0 mumin at standard temperature and pressure (STP), which resulted in residence times of 120-240 s at 170 "C and 3.0 MPa. The reactor was housed in a 30 cm long cylindrical furnace. Both the entrance and the exit of the reactor were cooled by 13 cm long water jackets. A separately controlled, 1 cm long entry heater located immediately before the furnace was set at a temperature typically 10-20 "C above the operating temperature of the furnace (170 "C). This entry heater caused the reactant flow to reach 170 "C prior to the flow's entry into the section of the reactor surrounded by the furnace. Thus the furnace was only responsible for preventing heat loss from the reactor: it provided almost no heat to the reactant flow. An exit heater located immediately after the furnace pinned the temperature of the reactor outlet to that of the furnace and isolated the isothermal section of the reactor (within the furnace) from the exit cooling jacket. Seven type K thermocouples located at evenly spaced intervals and held tightly t o the outer wall of the reactor, and one movable type K thermocouple which was able to traverse the centerline of the reactor down the inner annulus, enabled measurements of both axial and radial temperature gradients during the course of an experiment. Centerline temperature measurements indicated that the reactor typically enjoyed an isothermal functional length of about 30 cm, with a 5 cm length required for heatup of the reactant flow from 120 t o 170 "C and a 3 cm length for quench to 25 "C. Measured radial temperature gradients within the isothermal zone of the reactor never exceeded 3 "C; however a 15 "C overshoot of temperature (above 170 "C)was occasionally observed over a 1.5 cm length in the heatup zone of the reactor during high flow (short residence time) experiments. Other details concerning product sampling procedures and general operation of the reactor have been described in earlier publications (Xu et al., 1991; Xu and Antal, 1994). Table 1 lists characteristic nondimensional numbers (see Cutler et al. (1988) for nomenclature) for the reactor during a typical experiment. Although the reactor plainly functions with a laminar flow within its annulus, various criteria (Cutler et al., 1988) which account for the role of species diffusion indicate that kinetic analysis of the results can be safely accomplished using the plug flow idealization (Ramayya and Antal, 1989). Ethanol (100 and 95 vol %) from U.S. Industrial Chemicals Co., tert-butyl alcohol from Mallinckrodt Specialty Chemicals Co., and ETBE from Aldrich Chemical Co. were employed as reactants. No significant impurities were detected in these reagents by gas chromatography-mass spectrometry. HPLC grade deionized water was added to 100 vol % ethanol to obtain 90 vol % ethanol. Water was also introduced into the feed during addition of sulfuric acid from 0.1, 1.0, and 5.0 M stock solutions. In this case the mass added
(typically 0.2-1 g per 700 g of reactant) was treated as pure water. At each operating condition multiple samples of the reactor e f i e n t were collected and analyzed by duplicate injections. Qualitative analysis of the liquid and gaseous products was accomplished using a Hewlett Packard Model 5790A gas chromatograph (GC) coupled to a Hewlett Packard Model 5970A mass selective detector. Quantitative analysis of both the liquid and gaseous products, and the reactant (as a calibrant), was carried out on a Hewlett Packard Model 5890 Series I1 GC equipped with a flame ionization detector. A J&W DB-1 Megabore column (30 m x 0.53 mm i.d. with 5.0 pm film thickness) separated the products ethene, IB, ETBE, and diethyl ether (deteded only in trace amounts), as well as unreacted tert-butyl alcohol. We employed a temperature program of 8 min initial hold at 40 "C followed by a 30 "C1min temperature ramp with a final hold for 5 min a t 120 "C t o secure the needed separations. The injection port was heated t o 250 "C. The carrier gas was 8%hydrogen in helium flowing at 5 mL1 min. The same reagents listed above were used as external standards for calibration purposes, as well as a 1%isobutene in nitrogen standard gas mixture from Scott Specialty Gases. Product IB was almost completely dissolved in the reactor's liquid effluent. Consequently, no measurable gaseous products were detected in the sampling system (other than the background vapor pressure of ethanol and a trace amount of IB). Thus, the concentration of IB was determined by GC analysis of the sample's liquid phase after the experiment was completed, but these analyses took time t o accomplish, during which some of the IB entered the vapor phase and was lost from the analysis. Carbon balance data indicate that this loss was small; nevertheless it may have affected the measured yield of IB in a few of the experiments (see below). Measured weights of all species present in the reactant mixture were used to calculate the mole fractions and density at STP of the reactant feeds studied in this work (see Table 2). Employing these data, we estimated the density and other thermodynamic properties of the feed at reaction temperature and pressure (RTP) using a UNIFAC correlation available in the HYSIM (1992) software from Hyprotech. As a check on the UNIFAC density calculation, the density of various reactant feeds was estimated using the Hankinson-Brobst-Thomson (HBT) equation for saturated liquids, and Thornson's generalization of the HBT method for compressed liquids, together with appropriate mixing rules (Reid et al., 1987). Accord to three significant figures was usually obtained between the three methods, but occasionally a disagreement as large as 4% was observed. Both the reactant density a t RTP and the effective isothermal length of the reactor (as well as the mass flow rate, which was measured gravimetrically and continuously recorded) are needed to calculate the reactant residence time at RTP. The foregoing results indicate that errors in the estimate of reactant density at RTP make an insignificant contribution t o errors in the residence time calculation relative to errors in the estimate of the reactor's effective isothermal length.
Results and Discussion Because no information was available concerning ETBE formation from tert-butyl alcohol in compressed liquid ethanol a t temperatures above 100 "C, this
3786 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 Table 2. Mole Fractions of Reactant Mixtures and Densities (p) at Standard (STP) and Reaction (RTP)Conditions EtOH expt t-BuOH (STP),moUL (RTP),m o m ETBE Hz0 HzS04 1.413-01 5.323-05 1.88Ef01 1.513+01 8.323-01 0.003+00 1 2.703-02 1.443-01 5.223-05 1.93ES01 1.553+01 2 2.993-03 8.533-01 0.003+00 1.543+01 1.453-01 2.083-05 1.92ES01 0.003+00 3 3.063-03 8.523-01 2.353-05 1.70ES01 1.363+01 1.303-03 0.003+00 4 2.963-03 9.963-01 1.36Ef01 6.523-04 5.873-05 1.70ES01 0.003+00 9.973-01 5 2.823-03 6.653-04 5.993-05 1.67ES01 1.323+01 9.653-01 0.003+00 6 3.393-02 1.373+01 1.303-02 2.333-05 1.72ES01 0.003+00 9.843-01 7 3.083-03 5.963-05 1.68ES01 1.333+01 3.313-03 9.683-01 0.003+00 8 2.873-02 1.743+01 2.643-01 4.733-05 2.11ES01 7.343-01 9 2.383-03 0.003+00 2.07ES01 1.703+01 2.583-01 4.843-05 10 2.573-02 7.173-01 0.003+00 9.443-06 2.133+01 1.74Ef01 2.663-0 1 7.323-01 11 2.423-03 0.00Ef00 9.663-06 2.073+01 1.69Ef01 2.603-01 7.153-01 12 2.553-02 0.00Ef00 1,173-05 1.713+01 1.37Ef01 6.513-03 13 3.143-03 0.003+00 9.903-01 1.33Ef01 1.68Ef01 9.613-01 0.003+00 6.633-03 1.193-05 14 3.223-02 2.083+01 1.69Ef01 0.00Ef00 2,603-0 1 9.643-06 7.153-01 15 2.533-02 2.073+01 1.69Ef01 7.183-01 0.00Ef00 2.583-0 1 4.833-05 16 2.443-02. 1.34Ef01 1.683+01 0.003+00 6.623-03 1.19E-05 9.653-01 17 2.943-02 1.68E+01 1.333+01 5.953-05 3.313-03 9.683-01 0.003+00 18 2.893-02 1.33Ef01 1.693+01 0.003+00 3.303-03 5.953-05 9.673-01 19 2.943-02 1.513+01 2.653-05 1.893+01 1.423-01 8.333-01 0.003+00 20 2.683-02 1.893+01 1.513+01 0.003+00 1.433-01 5.303-05 8.303-01 21 2.713-02 1.54E+01 1.943+01 1.483-01 1.033-05 0.003+00 8.473-01 5.213-03 22 1.89Ef00 1.513+01 O.OOE+OO 1.433-01 5.313-05 8.313-01 23 2.563-02 1.69Ef01 2.07Ef01 2.583 -01 4.843-05 7.20E-0 1 0.003+00 24 2.403-02 2. lOE+Ol 1.743+01 7.343-01 0.003+00 2.643 -01 4.763-05 25 2.803-03 1.743+01 2.113+01 2.643 -01 4.733-05 7.343-01 0.003+00 26 2.653-03 1.71Ef01 1.363+01 3.243-03 5.843-05 9.933-01 0.003+00 27 3.333-03
e
Table 3. Critical and Reduced Properties at RTP for Species Present in Reaction Mixture
To K EtOH t-BuOH water IB
513.90 506.20 647.30 417.90
T, 0.8623 0.8754 0.6846 1.0604
P,,MPa
P,
6.14 3.97 22.1
0.4886 0.7557 0.1356 0.7500
4.00
research was initiated with a survey of the influence of temperature and the presence of water on ETBE yields (yield = moles of product/mole of tert-butyl alcohol fed) from tert-butyl alcohol in ethanol at high pressure (34.5 MPa), which assured liquid phase reactions. Although increasing temperature a t this pressure favored the formation of IB over ETBE, the apparent equilibrium yield of ETBE and the ETBE to IB ratio did not change greatly between 140 and 170 "C, but began to fall noticeably above 170 "C. The presence of water also reduced the ETBE yield, particularly at higher temperatures. These preliminary results led us to select reaction conditions of 170 "C with 10%by volume water in ethanol (180 proof) to pure (200 proof) ethanol reactant as the focus of this work. This temperature seemed to be near the upper limit for attractive ETBE yields, and was sufficiently above the values employed by industry to reveal whatever advantages might accrue to the process due to its enhanced reaction rates and its ability to accept water in the feed. The operating pressure at this temperature was selected empirically with the goal of ensuring liquid phase conditions under all circumstances of interest to this work. Experimental data showed that modest decreases of pressure below 3.0 MPa and significant increases above it had no measurable effect on product yields. Since 3.0 MPa is much greater than the saturation pressure of pure ethanol at 170 "C(about 0.7 MPa), it was selected as a conservative value for use in this work. Table 3 lists the critical (Reid et al., 1987)and reduced temperatures and pressures of ethanol, tert-butyl alcohol, isobutene and water at these conditions. Both alcohols and water behave as compressed liquids, but isobutene is gaseous. Nevertheless, all evidence indicates that product IB is
e
fully dissolved in the liquid phase within the reactor, and that only one phase exists within the reactor. One goal of this work was to develop a kinetic model of the reaction chemistry that embodied the important elementary steps involved in the formation of products ETBE and IB. This goal offers the dual benefits of giving insight into mechanistic chemistry and providing a model which could be useful to industry. Experience indicates that experimental data which lie at extremes of reaction conditions are most useful for model development; consequently the core of the experimental plan used in this work included measurements of product yields at high (0.5 M) and low (0.05 M)tert-butyl alcohol concentrations in ethanol with high (10% by volume water; 180 proof) and low (100%by volume ethanol; 200 proof) water concentrations, as well as high (0.001 M) and low (0.0002 M) sulfuric acid concentrations. Industrial practice would probably employ higher concentrations of tert-butyl alcohol in the reactant, but for us this choice would result in a variation in the density of the reactant mixture down the length of the reactor, thereby severely complicating an estimate of the reactant residence time. Similarly, industry might choose to employ higher concentrations of acid with a concomitant reduction in residence time requirements, but we could not reliably obtain residence times significantly below 120 s at 170 "C in the existing reactor system. Residence times were selected to secure both low and high (near equilibrium) conversions of tert-butyl alcohol. In addition, one experiment with no acid, one with ETBE as a reactant, and some experiments with intermediate water and acid concentrations, and residence times, were included in the experimental matrix. No conversion of tert-butyl alcohol was observed in the experiment without acid, plainly indicating the importance of homogeneous catalysis in the reaction chemistry. Table 4 summarizes the experimental results. Yields of ETBE as high as 0.36, and IB as high as 0.25, were achieved with a high conversion (65%) of tert-butyl alcohol (see experiment 27). Illustrating the strong effect of water on the reaction chemistry, these yields dropped to 0.2 and 0.13 (respectively)in 90% (180 proof")
Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 3787 Table 4. List of ExDeriments BuOH, expt M 1 5.1E-1 2 5.73-2 3 5.93-2 4 5.OE-2 5 4.83-2 6 5.7E-1 7 5.33-2 8 4.8E-1 9 5.OE-2 10 5.3E-1 11 5.1E-2 12 5.3E-1 13 5.43-2 14 5.4E-1 15 5.2E-1 16 5.1E-1 17 5.OE-1 18 4.9E-1 19 5.OE-1 20 5.OE-1 21 5.1E-1 22 1.OE-1' 23 4.8E-1 24 5.OE-1 25 5.93-2 26 5.63-2 27 5.73-2 a
H20lEtOH, HzS04, % (vlv) M 5 1.OE-03 5 1.OE-03 5 4.OE-04 0 4.OE-04 0 1.OE-03 0 1.OE-03 0 4.OE-04 0 1.OE-03 10 1.OE-03 10 1.OE-03 10 2.OE-04 10 2.OE-04 0 2.OE-04 0 2.OE-04 10 2.OE-04 10 1.OE-03 0 2.OE-04 0 1.OE-03 0 1.OE-03 5 5.OE-04 5 1.OE-03 5 2.OE-04 5 1.OE-03 10 1.OE-03 10 1.OE-03 10 1.OE-03 0 1.OE-03
res time, s 209 209 118 118 118 118 121 120 119 120 116 115 108 105 217 213 207 107 230 244 125 125 227 227 103 194 187
BuOH expt mod 5.8E-1 5.7E-1 5.6E-1 5.7E-1 8.7E-1 8.7E-1 8.OE-1 7.8E-1 6.OE-1 6.2E-1 6.3E-1 6.4E-1 8.OE-1 8.OE-1 6.OE-1 5.9E-1 7.OE-1 7.4E-1 7.3E-1 7.4E-1 9.OE-1 9.4E-1 9.5E-1 9.4E-1 8.8E-1 8.9E-1 9.1E-1 9.OE-1 9.1E-1 8.9E-1 5.9E-1 6.OE-1 8.2E-1 8.1E-1 6.1E-1 6.2E-1 3.8E-1 4.OE-1 6.5E-1 7.1E-1 6.6E-1 7.1E-1 3.33-2 3.33-2 5.4E-1 5.5E-1 5.6E-1 5.9E-1 7.4E-1 7.7E-1 6.3E-1 6.3E-1 3.5E-1 3.4E-1
yield ETBE expt mod 2.4E-1 2.4E-1 2.8E-1 2.5E-1 8.OE-2 8.53-2 1.5E-1 1.5E-1 2.4E-1 2.5E-1 2.2E-1 2.3E-1 1.2E-1 1.3E-1 2.3E-1 2.6E-1 1.7E-1 1.6E-1 1.6E-1 1.6E-1 3.93-2 3.93-2 3.83-2 3.83-2 8.33-2 7.53-2 7.33-2 6.63-2 5.83-2 6.83-2 2.4E-1 2.2E-1 1.3E-1 1.2E-1 2.4E-1 2.4E-1 3.5E-1 3.4E-1 2.1E-1 1.8E-1 1.8E-1 1.8E-1 9.2E-1 9.5E-1 2.6E-1 2.5E-1 2.3E-1 2.3E-1 1.4E-1 1.4E-1 2.OE-1 2.2E-1. 3.6E-1 4.OE-1
IB expt 1.5E-1 1.7E-1 4.OE-2 7.OE-2 1.5E-1 1.3E-1 6.43-2 1.5E-1 1.OE-1 1.OE-1 2.1E-2 2.OE-2 4.33-2 2.23-2 3.33-2 1.8E-1 7.33-2 1.7E-1 2.7E-1 1.5E-1 1.3E-1 2.33-2 1.4E-1 1.6E-1 8.83-2 1.3E-1 2.5E-1
mod 1.8E-1 1.8E-1 4.43-2 7.23-2 1.3E-1 1.3E-1 6.73-2 1.6E-1 1.OE-1 1.OE-1 2.OE-2 2.1E-2 3.63-2 3.33-2 3.93-2 1.8E-1 6.43-2 1.4E-1 2.6E-1 1.1E-1 1.1E-1 2.23-2 2.OE-1 1.9E-1 8.83-2 1.6E-1 2.6E-1
ETBEIIB 1.6 1.6 2.0 2.1 1.6 1.7 1.9 1.5 1.7 1.6 1.9 1.9 1.9 3.3 1.8 1.3 1.7 1.4 1.3 1.4 1.4 40.0 1.9 1.4 1.6 1.5 1.4
c4 bal date 96.6 2/1/94 100 2/1/94 99.6 2/8/94 99.5 2/8/94 100.1 2/8/94 101.5 2/8/94 95.5 3/1/94 99.5 3/1/94 98.8 3/1/94 96.8 3/1/94 98 3/8/94 95.9 3/8/94 99.8 3/8/94 100.6 3/8/94 101.7 3/15/94 101.3 3/15/94 98.4 3/15/94 98.1 3/15/94 100 3/29/94 97.8 3/29/94 94.7 3/29/94 100 3/29/94 99.2 4/12/94 100.9 4/12/94 96.6 5/16/94 96.5 5/16/94 95.9 5/16/94
ETBE substituted for BuOH as the reactant. -t-+.-
0.00
0.05
t-hon. iao isoprooi Proof
0.10 0.15 0.20 (Residence Time) [H~SOI]
0.25
Figure 1. Yields of tert-butyl alcohol and ETBE as a function of (residence time) x [HzS041 and water content of the ethanol feed.
ethanol (see experiment 26). Figure 1displays in more generality the influence of water concentration on the yields of tert-butyl alcohol and ETBE as a function of residence time and acid concentration. The dependence of the yields on the initial concentration of tert-butyl alcohol is not included in this figure, and the lines serve only to indicate trends in the data. Addition of water significantly reduces the conversion of tert-butyl alcohol, but has a lesser impact on the yield of ETBE. Other features of the data given in Table 4 are discussed below. One indicator of the reliability of the experimental results is the C4 carbon balance, which is the sum of the yields of ETBE, IB, and unreacted tert-butyl alcohol. The mean value of the C4 balances given in Table 4 is 0.986 with a sample standard deviation of 0.019. Also, the scatter of the C4 balance about 1.0 appears to be random: no systematic deviations (i.e., as functions of tert-butyl alcohol, acid, or water concentrations) were detected. For example, the mean values of the C4
balance for experiments employing loo%, 95%,and 90% by volume ethanol were 0.990, 0.983, and 0.985 with sample standard deviations of 0.019, 0.022, and 0.023 (respectively). These results are consistent with our finding that ETBE and IB (accompanied by nonquantifiable traces of diethyl ether) are the only significant reaction products. Another figure of merit for the reliability of the experimental data is their reproducibility. Table 4 displays numerous reproductions (for example, see experiments 1 and 2 3 , 4 and 7, 6 and 8, 16 and 24) which were conducted on different days. In all cases, the results enjoyed a good accord. We estimate the fractional sample standard deviations associated with measurements of the yields of tert-butyl alcohol, ETBE, and IB t o be 0.04, 0.05, and 0.13 (respectively). In other words, the sample standard deviation associated with a measured tert-butyl alcohol yield of 0.1 is 0.004, whereas that associated with a measured IB yield of 0.1 is 0.013. The first step in the formation of ETBE from tert-butyl alcohol and ethanol is anticipated t o be protonation of the tertiary alcohol (not ethanol) by a strong acid, such as sulfuric acid or the hydronium ion (Loudon, 1988). Nucleophilic substitutions of protonated alcohols proceed by either first order (SN1) or second order (SN2) mechanisms (Gleave et al., 1935). However, the bulky CH3 groups surrounding the tertiary carbon atom provide a steric hindrance that effectively precludes a direct attack by ethanol on tert-butyl alcohol. Such an attack would manifest second order kinetics. Instead, the reaction chemistry is expected to be governed by the first order s N 1 mechanism, wherein a slow heterolysis of the protonated alcohol is followed by a rapid coordination between the resulting carbocation and the substituting agent (Ingold, 1969). The rate-determining step of such unimolecular, nucleophilic substitutions involves electron transfer without any compensating gain of electrons by the alkyl group of the substrate.
3788 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 H2S04
t
H20
&
H S 0 4 t H30+
A *4
H20 + B u O H p
H30+
t
BuOH
H30+
t
ETBE
h2
H20
t
ETBEHt
k6
H20 + C4Hgt
H3O++ C4Hg k8
C4Hg+ + H 2 0
BuOHqt kio
C4Hgt
t
EtOH
k12
ETBEH’
Figure 2. Base kinetic model for ETBE formation
Substitution products are often accompanied by elimination products, which are formed by loss of a ,&proton from the carbocation. In our case the sN1/E1branching ratio is represented by the ETBEAB ratio (see Table 41, which varies from 1.3 t o 3.3. Figure 2 displays the elementary reactions which together represent the expected mechanism for ETBE and IB formation from tert-butyl alcohol. These elementary reactions serve as a basis for a kinetic model (‘%base”model) which achieves a good fit to the data listed in Table 4. As will be discussed later, this sN1/E1 base model was augmented by many other elementary reactions and exotic intermediates during the course of this research, but these embellishments did not result in a better fit of the more complex model to the data. The base model displayed in Figure 2 involves protonated water (hydronium ion), protonated tert-butyl alcohol, protonated ETBE, and the tertiary carbocation CdHs+ as intermediates. Step 9 is the accepted, rate-determining step of the s N 1 mechanism, which results in the formation of carbocation and water from protonated tert-butyl alcohol. Branching occurs via reactions 11 and 8, which lead t o the formation of ETBE and IB (respectively). The presence of water in the reactant mixture exerts the familiar “leveling))effect which causes hydronium ion (not sulfuric acid) to be the catalytic agent for the reaction. Note that even when 200 proof ethanol was used as the solvent, water was still greatly in excess of sulfuric acid in the reactant mixture (see Table 2). Water is also a key ingredient in reaction 8, which is the sole source of IB. The other reactions displayed in Figure 2 represent proton transfers between charged intermediates and water, the conjugate base of acid H30+. The time dependent behavior of the concentrations of each of the 11 species displayed in Figure 2 is described by a set of 11 coupled, nonlinear, stiff, ordinary differential equations (ODE’S). By employing algebraic expressions which define the charge balance, C2 conservation, oxygen conservation, and sulfur conservation, only seven ODE’Smust be integrated numerically t o describe product evolution down the length of the reactor. A FORTRAN subroutine which represents these algebraic expressions and ODE’S is included as supporting information t o this paper (see paragraph at the end of the paper regarding availability of supporting information). The time dependent behavior of the species in the reactor also depends upon the initial reactant concentrations (listed in Table 21, the assumed disposition of the intermediates at the exit of the reactor, and the 12 rate constants indicated in Figure 2. These rate constants are parameters whose values are chosen to give a best fit (in the least squares sense) of the model to the experimental data. The quality of this fit is measured by the value of x,,~,where
m
R
j=1 k = l
and the residual ej,k = (yj,keXP - yj,kmod), where yj,k is the yield of each of the three species (tert-butyl alcohol, ETBE, and IB corresponding t o k =1, 2, 3) included in the model at reaction conditions j = 1, ..., m, as measured experimentally (exp) or calculated by the model (mod). Also, Uk is the sample standard deviation associated with the yield measurement of each species (Bevington, 19691, and v is the number of degrees of freedom. As discussed in detail elsewhere (Xu et al., 1991;Xu and Antal, 1994),we employ proven minimization methods (Antal and Anderson, 1994) t o identify values of the rate constants ki which minimize the value of xv2. If a good fit is realized, the kinetic model is said to be “consistentnwith the experimental data, whereas a poor fit indicates that the reaction mechanism (from which the model is derived) does not describe the observed kinetics. Typically, values of xu2 < 1represent a good fit, and past experience with systems of this kind (Narayan and Antal, 1989; Antal et al., 1991; Xu et al., 1991, Xu and Antal, 1994) with similar systems indicates that values of xV2ranging from 0.2 to 0.7 characterize models which are manifestly consistent with the data. Of course, it is not always possible to find a kinetic model which is consistent with an experimental data set, but when such a model is discovered, it is natural to inquire if other models (mechanisms) exist which fit the data comparably well. Again, experience (Narayan and Antal, 1989; Antal et al., 1991; Xu et al., 1991;Xu and Antal, 1994)teaches that usually only one kinetic model (representing a meaningful chemical mechanism) can succeed in fitting a high quality data set which spans a wide range of reactant and product concentrations. In other words, kinetic models of the type described in this paper are useful in discriminating between various potential reaction mechanisms when a high quality data set is available. A more thorough discussion of this interesting, open-ended subject is beyond the scope of this paper, but is addressed in more detail in a series of recent papers and theses (Xu, 1992; Xu and Antal, 1994; Kam, 1994). Table 5 lists values for the rate constants of the base model which result in a best fit (xV2= 2.90) of that model to the experimental data. Two of the rate constants in the model could not be distinguished from zero, leading to a model with only 10 active pathways (see Figure 3). The idea that sulfuric acid dissociates irreversibly (k2 = 0) in ethanol at these conditions may disturb some readers. To understand this result, it is important to recall that the acid concentrations employed in this work were very low ( ~ 0 . 0 0 1M), and that all acids completely dissociate at sufficiently low concentrations. Furthermore, the modeling effort does not assert that the value of k2 is identically zero. The only conclusion is that a nonzero value of the parameter does not improve the ability of the model to fit the data. The significance of the finding k7 = 0 is discussed below. The alert reader will have already remarked that the value xu2 = 2.90 associated with the fit of the base model to the experimental data is not good, especially in light of earlier work with similar systems. The following summarizes attempts to augment the sN1/E1 base model with additional reaction pathways and intermediate species t o improve its fit to the experimental data. (i) Pathways were added to permit the direct formation of ETBE and IB from protonated tert-butyl alcohol
Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 3789 Table 5. Elementary Rate Constants
H2°
H
base model entire data set xu2 = 2.90
12 param model entire data set xv2 = 1.76
12 param model omitting 2 outliers x> = 1.44
6.063+00 0.0 6.553+00 6.653+00 5.643+00 2.41Ef03 0.0 2.693+02 3.943+02 1.06E+04 2.983+04 1.60E+06
1.23E+00 0.0 1.183+01 7.543+02 5.233+00 4.303+03 0.0 6.893+02 1.853+02 2.183+03 4.023+04 1.50E+06 2.983-01 2.463-01
1.19E+OO 0.0 1.213+01 9.55Ef02 5.09E+00 3.903+03 0.0 7.343+02 2.333+02 2.353+03 4.713+04 1.573+06 3.00E-01 2.553-01
SO
\2”:04.
C4H8 Figure 3.
sN1
ETBE
scheme for ETBE formation.
via sN2 and E2 reaction mechanisms. As expected, these additional pathways did not improve the ability of the model to fit the data. (ii) The intermediate species s042-was added, together with reaction pathways that enabled both sulfuric acid and the bisulfate anion to mimic the hydronium ion as the potent acid catalyst. In addition, more pathways were added to enable both the bisulfate anion and the sulfate anion to mimic water as the conjugate base of each added acid catalyst. No improvement in the fit of the model to the data resulted from these additions. We also examined the influence of the amount of dissociation of sulfuric acid at the entrance of the reactor on the ability of the model t o fit the data. Unfortunately, this modification of the initial condition realized no improvement in the model’s ability to fit the data. (iii) Protonated ethanol was added as a reaction intermediate, together with a large number of pathways to account for all its potential interactions with the other species present in the model. This gross increase in the model’s complexity did not achieve a better fit to the data. Subsequently, both diethyl ether and protonated diethyl ether were also added to the model, but the fit did not improve. (iv) Protonated and unprotonated di-tert-butyl ether were added as potential intermediates, together with pathways accounting for their formation and subsequent decomposition to both IB and tert-butyl alcohol (see Xu and Antal (1994) for a discussion of this rather complex chemistry). No improvement in the fit was obtained. (v) The diisobutene carbocation and diisobutene were added to the model as undetected products, but the fit did not improve.
12 param model omitting 6 outliers xu2 = 1.08 1.21E+01 0.0 1.173+01 1.293+03 5.233+00 3.933+03 0.0 7.023+02 3.443+02 2.16Ef03 5.803+04 2.023+06 2.893-01 1.91E-01
(vi) The inorganic esters (C4HdHS04 and (C4H&S04 were added to the model as potential intermediates in the formation of IB from tert-butyl alcohol (and vice versa), but no improvement in the fit was realized. (vii) Pathways were added to account for the uncatalyzed decomposition of ETBE t o ethanol and isobutene, and the uncatalyzed hydrolysis of ETBE by water. These additional pathways did not improve the ability of the model t o fit the data. (viii) Various combinations of the above embellishments were also examined, but no improvement in the fit was obtained. It is well-known (Laidler, 1987) that the solvent dielectric constant can exert a strong influence on elementary rate constants. For example, Narayan and Antal (1990) reported a 3-fold increase in the acidcatalyzed rate constant for l-propanol dehydration in supercritical water as the dielectric constant decreased from 12 to 3.6. Although the dielectric constant of compressed liquid ethanol at 170 “C is not known, it is certain that the dielectric constant of compressed liquid water a t this temperature is much larger. Consequently, we might anticipate a change in the magnitudes of the elementary rate constants as water is added t o the reactant mixture. To examine this possibility, the ability of the base model to fit three subsets of the experimental data containing 0%, 5%, and 10% by volume water in ethanol was evaluated. Confirming our expectations, the fits improved considerably, as evidenced by values xv2 = 1.0, 2.9, and 1.8 for the 0%, 5%, and 10%water in ethanol experimental results. On the other hand, no improvements in the fit were realized with random subsets of the entire data set. Theory predicts (Laidler, 1987) that the logarithm of an elementary rate constant should be linearly dependent on the reciprocal of the solvent dielectric constant, and an examination of the experimental data of Moriyoshi et al. (1990)reveals that the dielectric constant of water in ethanol mixtures (at 298 K) is linear in water concentration within the range of interest to this work. Consequently, we attempted to model the data by including two adjustable parameters in each elementary rate constant to account for its functional dependence on the solvent’s dielectric constant:
hi = ho,iexp(l/a, - 14%
+ &[H201))
where ko,i is the rate constant for pathway i in pure ethanol, [HzOI is the concentration of water in the reactant mixture a t RTP, and the and pL are adjustable parameters associated with the influence of the solvent’s dielectric constant on each rate constant.
3790 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995
Surprisingly, only elementary rate constant k g evidenced a sensitivity to the solvent’s dielectric constant, but this sensitivity was significant. The inclusion of two additional parameters (a9and P g ) to the 10 parameter model reduced the value of xy2 from 2.90 to 1.76. Why should pathway 9 be so sensitive to the solvent’s dielectric constant? Note that pathway 9 liberates two quite different species: a strongly acidic carbocation and water. The carbocation is evidently a strong acid because the hydronium ion is unable to protonate isobutene under these conditions ( l t 7 = 0, see Table 5); hence the carbocation is a much stronger acid than the hydronium ion. Perhaps the presence of water stabi: 1 lizes the formation of protonated isobutene by increasing the solvent’s dielectric constant, thereby increasing the value of k g . Not all the experimental measurements contribute equally to the value of xv2. As mentioned earlier, the sampling and analytic techniques employed in this work may not have detected all the IB exiting the reactor. Although the carbon balance data suggest that this loss was quite small, it could still impact on isolated experimental results. An analysis of residuals reveals that the IB yields of experiments 14 and 23 are significantly lower than the model predictions. In the case of experiment 14, the experimental value of the yield is very low (2.2%);hence the difference between this value and the model value (3.2%)has no significant impact on the carbon balance (101%). Also, note that the ETBEAB ratio of this experiment is abnormally large, as would be expected from an erroneously small measurement of the yield of IB. In the case of experiment 23, the difference between the experimental value (14%)and the model value (20%)would account for the poor carbon balance (94%)associated with this experiment. If the yields of IB in experiments 14 and 23 are treated as outliers and deleted from the data set, the value of xy2 is reduced t o 1.44. This change in the data set results in only small changes in the best fitting rate constants (see Table 5). Residuals associated with the ETBE yields of experiments 15 and 20 also make an abnormally large contribution to xy2. Both these experiments possess good carbon balances (100%and 101%, respectively); consequently it is more difficult to treat these results as outliers. Nevertheless, in experiment 15 the conversion of tert-butyl alcohol is low (9.1%)and the experimental value of the yield of ETBE is very low (5.8%),resulting in a very low concentration of ETBE in the product mixture. The difference between the experimental value of the ETBE yield and the model value (6.8%)may be attributed to difficulties in analyzing products present in very low concentrations in the liquid effluent. In the case of experiment 20, the experimental value of tert-butyl alcohol conversion (35%) is high relative to the model value (29%), and the experimental values of both the yields of ETBE and IB (21% and 15%, respectively) are high relative to the model values (18% and 11%, respectively). These results suggest that the reactor may have been operating at a slightly higher temperature than the desired 170 “ C . If we consider the ETBE yield of experiment 15, and all three yields associated with experiment 20 to be outliers (in addition to the two potential outliers mentioned previously), the value of xv2 becomes 1.08. In most cases, the best fitting rate constants associated with this subset of the entire data set do not differ greatly from those associated with the entire data set (see Table 5). Figures 4-6 display parity plots of the
Tj
i:
-4
-0
08-
070 6 -
0 00 0
0 1
02
0 3
0 4
05
06
07
08
09
10
Experimental Fractional Yield
Figure 4. Parity plot of tert-butyl alcohol yields.
09
2 i: -3 C
0
0 8 -
0 7 i
0 6 -
Experimental Fractional Yield
Figure 5. Parity plot of ETBE yields.
00 00
08 03 Experimental Fractional Yield
0 1
04
Figure 6. Parity plot of isobutene yields.
accord between the best fitting model values (using the parameters associated with fit xv2 = 1.08) and the experimental values for the yields of tert-butyl alcohol, ETBE, and IB. These figures display a satisfylng agreement between the model and the experimental data, since in almost all cases the model values lie within the 95%confidence interval of the experimental result. A pointed outcome of the modeling results given above is that product ETBE forms from reactant carbocation (protonated isobutene), which is produced from protonated tert-butyl alcohol via the El elimination step 9 in Figure 2. The carbocation is not produced at a significant rate by protonation of isobutene. Thus IB is not a productive reactant in the formation of ETBE (see Figure 3). This finding reflects the fact that protonated
Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 3791 isobutene is a very strong acid (as discussed above), and concomitantly IB is a weak base. This is not to say that rate constant k7 is identically zero. Evidently, the rate of reaction 7 is immeasurably small a t the conditions employed in this work relative to the rate of reaction 8. Thus, we do not dispute the commercial use of isobutene to produce ETBE at lower temperatures and pressures in the presence of a heterogeneous acid catalyst. We simply conclude that, under conditions similar to those employed in this study, tert-butyl alcohol should be favored over isobutene as a feedstock for the sulfuric acid-catalyzed synthesis of ETBE.
Heineken and Dr. Maria Burka of NSF for their interest in this work, and Dr. Helena Chum, Dr. Ralph Overend, and Dr. David Johnson of NREL for the loan of a HPLC pump. We also thank Karen Ikeda (UH) for assistance with data reduction, Magnus Carlsson (TPS Termiska Processer AB)for advice concerning analytic techniques, Professor Maitland Jones, Jr. (Princeton University), for a critique of our conclusions regarding the reaction chemistry, Professor Donald G. M. Anderson (Harvard University) for contributions to the numerical methods employed in this work, and two anonymous reviewers for their constructive comments.
Conclusions 1. In liquid ethanol ( P = 3 MPa) at 170 "C with up to 10%by volume water and a trace ( ~ 0 . 0 0M) 1 amount of sulfuric acid catalyst, tert-butyl alcohol reacts quickly to form ETBE and isobutene. Depending on the amount of acid catalyst present, equilibrium is established after a few minutes or less. 2. The reaction chemistry is extremely selective: ETBE and isobutene are the only significant products. 3. The presence of water in the reactant mixture significantly reduces the conversion of tert-butyl alcohol, but has a lesser effect on the yield of product ETBE. 4. A kinetic model based on acid-catalyzed s N 1 and E l reaction mechanisms offers an adequate fit to experimental data. This model employs protonated tertbutyl alcohol, protonated ETBE, and tertiary carbocation (protonated isobutene) as key intermediates in the formation of products ETBE (via nucleophilic substitution) and isobutene (via elimination). Ten nonzero parameters (rate constants) are required to fit the experimental data. 5. The addition of a wide variety of elementary reactions and exotic intermediates to the base model described above does not improve the ability of the augmented model t o fit the experimental data. 6 . The fit of the 10 parameter model is considerably improved when the effect of water on the dielectric constant of the reacting mixture is incorporated into the rate constant associated with the formation of carbocation from protonated tert-butyl alcohol. Two additional parameters are involved in this model, which realizes a good fit to the entire data set and an effectively perfect fit t o a subset of the experimental data that excludes a few questionable measurements. 7. Conclusion 6 suggests that future fundamental studies of this system may offer significant new insights into the effects of the solvent's dielectric constant on the rates of elementary reactions occuring within the solvent. 8. Kinetic simulations indicate that the protonated isobutene carbocation is a very strong acid, and that isobutene is a relatively weak base under the conditions of interest in this work. Consequently, the carbocation is formed via an E l elimination from protonated tertbutyl alcohol, and not by protonation of isobutene. Since the carbocation is the key ingredient in the formation of ETBE, the kinetic simulations indicate that tert-butyl alcohol should be strongly favored over isobutene as a feed for ETBE synthesis under the conditions examined in this work.
Supporting Information Available: FORTRAN subroutine specifying the set of ODE'S associated with the mechanism for ETBE formation given in Figure 2 (4 pages). Ordering information is given on any current masthead page.
Acknowledgment This research was supported by the National Science Foundation (NSF) under Grant BCS 91-11743, and the Coral Industries Endowment. We thank Dr. Fred
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Abstract published in Advance ACS Abstracts, August 1, 1995. @
