Ethers from Ethanol. 4. Kinetics of Liquid-Phase Synthesis of Two tert-Hexyl Ethyl Ethers

Ind. Eng. Chem. Res. 1995,34, 2247-2257 2247

Ethers from Ethanol. 4. Kinetics of the Liquid-Phase Synthesis of Two tert-Hexyl Ethyl Ethers

Tiejun Zhang and Ravindra Datta* Department of Chemical and Biochemical Engineering, The University of Iowa, Iowa City, Iowa 52242-1219

Tertiary ethers produced from reactive C5 and c6 olefins and ethanol or methanol are being investigated as oxygenate gasoline additives in addition to isobutylene-derived methyl tert-butyl ether and ethyl tert-butyl ether. The kinetics of liquid-phase etherification and accompanying isomerization of four reactive c6 olefin isomers with ethanol catalyzed by the ion-exchange resin catalyst Amberlyst 15 were determined at temperatures from 313 to 353 K and a pressure of 0.69 MPa in a differential packed-bed reactor. Rate expressions in terms of species activities, with the activity coefficients determined by the UNIFAC method, were developed to correlate the experimental data over a wide range of compositions. The rate expressions are based on the Langmuir-Hinshelwood-Hougen-Watson formalism involving a dual-site surface etherification reaction and a single-site surface isomerization reaction as the rate-limiting steps, along with the assumption of ethanol as the most abundant surface species. The negligibility of olefins and ether adsorption terms, but the nonnegligibility of vacant sites, was confirmed by independent liquid-phase adsorption experiments. The developed rate expressions were finally tested in an integral reactor and found to be accurate.

Introduction

Just as tertiary methyl ethers (MTBE, TAME) are produced from the addition reactions of reactive C4 (isobutylene) and C5 (isoamylene) olefins to methanol, tertiary ethyl ethers (ETBE, TAEE, and THEE) can also be readily synthesized from the reactive C4, C5 and c6 olefins and ethanol over a protonated cation-exchange resin catalyst such as Amberlyst 15. Although ETBE is slated for growth (Peaff, 1994), MTBE is currently the only major commercial ether oxygenate, and its demand is expanding owing to the Clean Air Act Amendments (Reisch, 1994). However, since the production of MTBE or ETBE is potentially limited by the supply of isobutylene (Haggin, 19931, higher tertiary ethers mentioned above are also being explored as potential supplemental oxygenates for gasoline (Igna- tius et al., 1995). This paper is, thus, concerned with the kinetics of the etherification of c6 olefins with ethanol.

There are seven noncyclic tertiary c6 olefins (those with the double bond attached to a tertiary carbon) that can react with ethanol to produce three isomers of tert- hexyl ethyl ether (THEE), namely, 2-methyl-2-ethoxypentane (THEEl) from 2-methyl-l-pentene (2MlP) and 2-methyl-2-pentene (2M2P), 2,3-dimethyl-2-ethoxybutane (THEE2) from 2,3-dimethyl-l-butene (2,3DMlB) and 2,3-dimethyl-2-butene (2,3DM2B), and 3-methyl- 3-ethoxypentane (THEE3) from 2-ethyl-l-butene and cis- and truns-3-methyl-2-pentene (Zhang and Datta, 1995b). Based on Markovnikov’s rule, the general scheme of etherification reaction of ethanol with a tertiary olefin is

* Author to whom correspondence should be addressed. E-mail address: [email protected].

while the accompanying isomerization reaction between the tertiary a-olefin and the corresponding tertiary ,!3-olefin may be represented by

H R1’ R3‘ H R1’ Rz’ I l l

H

H+ I l l

I H

H-C=C-C-R2’ = H-C-C=C--Rp’ (2) I

a- olefin p-olefin

where R1, Rz, R; and are alkyl groups, while R3, R4, and could be either alkyl groups or hydrogen atoms. It may be noted that the p-olefin is structurally more stable than the a-olefin and is, consequently, less reactive in etherification.

Despite the potential importance of these ethers, however, the kinetics and thermodynamics of C6 tertiary olefin etherification reactions have barely been investigated (Krause et al., 1984). Part 1 (Jensen and Datta, 1995) and part 2 (Kitchaiya and Datta, 1995) of this series of papers dealt, respectively, with the thermodynamics of ETBE and TAEE, while part 3 (Zhang and Datta, 1995b) reported on the reaction equilibria for THEEl and THEE2 syntheses. Correlations of equilibrium constants were developed as a function of temperature. It was found that the equilibrium constant of the etherification reaction of an a-olefin with an alcohol is larger than that of the corresponding ,&olefin with the same alcohol, owing to the higher stability, or lower potential energy, of the ,&olefin as compared with the a-olefin (Zhang and Datta, 1995b). In this paper (part 41, the kinetics of etherification and simultaneous isomerization reactions of THEE 1 and THEE2 systems are reported. The temperature covered in this kinetic study ranges from 313 to 353 K, while the pressure was held constant at 0.69 MPa. Simpli- fication of the proposed rate expressions in terms of component activities based on the use of the most abundant surface species assumption for alcohol was confirmed by independent liquid-phase adsorption experiments. The developed rate expressions were successfully used to correlate the experimental data obtained in a differential packed-bed reactor, and were

0888-588519512634-2247$09.00/0 0 1995 American Chemical Society

2248 Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995

also finally utilized to study the performance of an integral packed-bed reactor.

Experimental Section Apparatus and Method. The reaction apparatus

utilized for a previous MTBE study was modified and used in this investigation. Its details are provided by Zhang and Datta (1995a). The feed consisted of ethanol and a single reactive c6 olefin at a time with or without solvent (n-heptane). Contained in a bottle placed on a top-loading balance for gravimetric measurement, the feed was introduced first into a preheater tube and then into a 318 in. stainless steel tubular packed-bed reactor. Both the preheater and the reactor were maintained at a constant temperature by circulating water a t the temperature from a bath through a jacket. The catalyst bed temperature was measured by two type-K thermo- couples, one placed in the middle of catalyst bed and the other located 1 in. into the catalyst bed inlet.

The reactor was operated differentially for kinetics measurements; i.e., weight-hourly space velocities em- ployed were such that a sufficiently low conversion (15- 10%) was obtained. As a result, the composition within the reactor could be assumed to be uniform and the reaction rates were calculated directly from the difference between inlet and outlet compositions. The at- tainment of a steady state was monitored by periodical on-line analyses by means of an internal liquid sampling injector (Valco, CMWE, size 0.2 pL) of the product composition in a gas chromatograph as described below.

Liquid-phase adsorption experiments were also conducted utilizing the conventional procedure (Kipling, 19651, with n-heptane used as the solvent. Thus, dry catalyst was immersed in the solution of interest and was allowed to equilibrate a t the selected temperature. The resulting equilibrium solution was analyzed in the gas chromatogaph (GC) as described below. The amount of solute adsorbed was calculated from the difference between the initial and final solute concentrations in the solution and a knowledge of the volume of solution and weight of catalyst.

Materials. Ethanol used was obtained from Pharm- co (dehydrated, 200 proof). 2M1P (purity 98%) and 2M2P (purity 95%) were obtained from TCI America, while 2,3DMlB (purity 97%) and 2,3DM2B (purity 98%) were obtained from Aldrich. The impurities contained in these olefins are a mixture of nonreactive c13 Olefins, which were represented by 1-hexene in the calculation of activity coefficients by the UNIFAC method. n- Heptane was obtained from Fisher (HPLC grade). All these chemicals were used without further purification. THEEl and THEE2 used for GC calibration were synthesized in the laboratory by reacting the appropri- ate (26 olefin with ethanol, and were purified by distillation to a minimum purity of 97%.

Amberlyst 15 ion-exchange resin (manufactured by Rohm and Haas and obtained from Sigma Chemical Co.) was used as the catalyst in this study, since it is the catalyst of choice in MTBE manufacture. Its properties are listed by Zhang and Datta (1995a). Before use, the catalyst was washed first with an aqueous solution of 6 vol % nitric acid, and then with ethanol, and finally dried overnight in a vacuum oven a t 378 K. The cooled catalyst was then ground and sieved to obtain a granu- lometric fraction in the size range of 0.125-0.25 mm (average diameter 0.188 mm), and was dried again immediately prior to use. In our earlier investigation of MTBE synthesis (Zhang and Datta, 1995a), it was

determined that both the internal and external transport limitations of reaction are negligible with this particle size for temperatures up to 353 K. Thus, even though for THEE synthesis system the species size is larger and the diffusion coefficients, consequently, are somewhat smaller, it is believed that the transport limitations would also be negligible for this case because the reaction rates are at least an order of magnitude lower than those of MTBE.

Depending upon the reaction temperature, an amount varying between 0.1 and 1 g of the conditioned catalyst was uniformly diluted with inert silicon carbide grains (McMaster-Carr, size 0.25-0.45 mm) to maintain iso- thermality and then carefully packed into the tubular reactor. Placed between two 10-pm stainless steel frits, the reactor ends were filled with glass wool to prevent any catalyst loss from the reactor. The dilution weight ratio varied from 30 to 100 to ensure that the temperature variation along the packed bed of catalyst was less than 1 K under all the conditions investigated. The inertness of silicon carbide had previously been confirmed for the case of MTBE synthesis (Zhang and Datta, 1995a).

Analysis. The liquid mixture composition from both kinetics and adsorption experiments was determined by using a Perkin-Elmer Autosystem gas chromatograph equipped with a Supelco capillary column (SPB-1,0.25 mm i.d., 1.0 pm film thickness, and 60 m length) along with the flame ionization detector (at 250 "C) to separate ethanol, c6 olefin isomers, ethers, and solvent. The column was temperature programmed with a 10-min initial hold at 65 "C, followed by a 20 "C/min ramp up to 160 "C, and finally a hold at 160 "C for 5 min. A negligible amount of tertiary alcohol, Le., 2-methyl-2- pentanol or 2,3-dimethyl-2-butanol, was detected as the side product via hydration of 2M1P and 2M2P or 2,3DMlB and 2,3DM2B. However, GC analyses with the column being held at 160 "C for a longer period of time did not result in the elution of any dimerization products. The GC was calibrated over a wide range of compositions, and the experimental error in the measurement of mole fraction was estimated to be less than 2%.

Calculation of Reaction Rate. The overall net- work of simultaneous etherification and isomerization reactions for THEEl as well as THEE2 system is (Zhang and Datta, 1995b)

a-olefin (B)\

ethanol (A) + @) (3)

p-olefin (C)

The rate of formation of species j can be related to the rates of individual reactions ri by

4

Rj = vliri (4) i = l

where ri =E - Fi and q is the total number of reactions. In differential kinetics experiments, when the feed

contained only the tertiary a-olefin (B) and no ether, the initial rate of THEE (D) formation, RDO, and the initial rate of olefin isomer (C) formation, Reo, were computed from the experimental product composition a t steady state by using

Ind. Eng. Chem. Res., Vol. 34, No. 7, 1995 2249

rl = klKAKB(aAUB - aD/K,)/(l + q U j ) 2 ( 8 ) n

j = 1

Further, from eq 4, the initial rates of formation are RDO = r10 + 7-20 % r1o and Rco = r30 - r20 = n o . These simplifications are possible since the reactor was operated differentially so that XC - 0 and thus rzo - 0. Similarly, when a ,&olefin was the single feed olefin,

(7)

and from eq 4, RDO = r10 + r20 r1o this feed.

r20 and RBO = -r30 - since r1o - 0 in the differential reactor for

Results and Discussion Correlation with Rate Expressions. The earlier

rate expressions for MTBE and ETBE syntheses were proposed in terms of species concentrations, as is the universal custom in the kinetics literature. Examples are those proposed by Ancillotti et al. (1977), Gicquel and Torck (1983), Subramaniam and Bhatia (19871, and Al-Jarallah et al. (1988) for MTBE synthesis, and that by Francoisse and Thyrion (1991) for ETBE synthesis. However, because of the dissimilar polarities of species involved in the tertiary ether synthesis, the liquid-phase reaction mixture is quite nonideal. Thus, Columbo et al. (1983) first used activities in the correlation of the MTBE equilibrium constant, while ReMnger and Hoff- mann (1990) utilized activities in their reaction rate expression for MTBE. Further, irreversible thermodynamics teaches that a reaction is driven by its affinity, which is related to the species activities. For reversible reactions, a rate expression in terms of species activities is also internally consistent with the requirements of reaction equilibrium. Thus, it appears to be apt to develop rate expressions in terms of activities. The activity coefficients may, for instance, be calculated by the UNIFAC method (Reid et al., 1987).

On the basis of the Langmuir-Hinshelwood-Hou- gen-Watson (LHHW) formalism of adsorption of reactants, surface reaction, and eventual desorption of products, and assuming the surface reaction between the adsorbed reactants as the rate-determining step (rds), i.e.,

reaction 1 rds: A*S + B*S DS + S

k2 reaction 2 rds: A*S + C*S D-S + S

k3 reaction 3 rds: B*S C*S

where S represents a catalytic site, with all adsorption/ desorption steps assumed to be at pseudo-equilibrium, the rates of the three reactions may be written as

r3 = k&B(aB - ac/K,)/(1 + q U j ) (10) j=1

wherej includes reactants, products, as well as any other "inert" species. The thermodynamic equilibrium constants of the three overall reactions are KI = klKAK$(k;KD), K2 k&AKc/(kzD), and K3 k&$ (It&).

Since there is no isomerization reaction in the case of MTBE synthesis, eq 8 alone is needed and was simplified by ReMnger and Hof iann (1990) as follows:

rl = k r l k - - 1 aD -) Ki a i

which further reduces to

r10 krl(aB/aA) (12)

for the initial rate in the absence of product D in the feed. Equation 11 was obtained by invoking the most abundant surface species assumption for ethanol, i.e., by neglecting the adsorption terms of all species other than alcohol as well as unity representing the vacant sites term in the denominator of eq 8. Equation 12 was used successfully by Rehfinger and Hoffmann (1990) to correlate the experimental initial rates obtained in a CSTR in the range of aA = 0.6-0.85 and a$aA = 0.05- 0.6. Equation 11 was also experimentally examined in an integral packed-bed reactor for liquid-phase MTBE synthesis by Zhang and Datta (1995a), and they found that the isobutylene conversion could be adequately predicted over the range of conditions investigated.

Upon utilizing similar assumptions, eqs 9 and 10 may also be simplified to

r 2 x k,, - -- (:: - i2 :;) and

(13)

which in turn reduce to the following initial rate expressions:

~ 2 0 kr2(ac/a,) (15)

and

depending upon the feed olefin utilized. In the above expressions, the pseudo-rate constants are related to the rate constants of the individual steps and the species adsorption equilibrium constants by kr1 = klK$KA, kr2 = k z K c / K A , kr3 = k&$KA, and ki3 E k j K c / K A = kdK3.


100

0.01' ' " " "

I I/

0.03 0.1 1 2 Activity Ratio, a,/aA or aJaA

Figure 1. Regression analyses of experimental initial rate data of etherification (open symbols) and isomerization (solid symbols) reactions according to the simplified rate expressions eqs 12, 15, and 16.

Equations 12,15, and 16 were found to be satisfadory in correlating the experimental initial rates of etherification and isomerization reactions of the four CS olefins with ethanol over a limited range of compositions. As shown in Figure 1 for the temperature of 333 K, linear relationships were obtained between the initial rates and the corresponding activity ratios as predicted by eqs 12,15, and 16. The slopes of the straight lines in Figure 1 are equal to unity and the y-intercepts at a$aA or ad aA = 1 are equal to the corresponding pseudo-rate constants a t the temperature. Similar satisfactory linearity was also observed at other temperatures. It may be noted that the upper limit value of the activity ratio, a$aA or adaA = 1, in Figure 1 roughly corresponds to a composition with a molar ethanol to olefin ratio, Q, of 1.5 in the absence of any solvent. Experimentally, the activity ratio was decreased through addition of n-heptane as the solvent to the mixture while maintain- ing Q = 1-1.5.

More recently, Fite et al. (1994) concluded that a rate expression similar to eq 11 was not the most satisfadory one in describing their experimental data for ETBE obtained in a differential packed-bed reactor. Rather, the best fit was obtained with

(17)

where kfl k1K$KA2. A mechanistic interpretation of eq 17 requires three active sites involved in the rate- determining step. It was, thus, decided to empirically determine the number of active sites providing a rate expression yielding the best fit to the experimental data. For this purpose, an initial rate expression of the form

was used to correlate the experimental initial rates of etherification of 2M1P with ethanol at 333 K, with m = 1,2, and 3. As shown in Figure 2, the regression looks equally satisfactory in the upper-right corner of the plot for m = 1, 2, and 3. Over the entire range, however, the use of m = 2 provides a fit that is superior to that obtained with either m = 1 or m = 3. Therefore, the more plausible dual-site LHHW mechanism was adopted here for the etherification reactions. Figure 2 also suggests that an erroneous number of active sites can result in this manner if the experiments are not conducted over a sufficiently wide range of conditions.

As discussed earlier, eqs 8,9, and 10 were reduced to eqs 11, 13 and 14 based on two assumptions: (1) that the surface concentrations of species other than alcohol

Figure 2. Regression plot to determine the number of active sites involved in the etherification reaction of 2M1P with ethanol a t 333 K according to eq 18.

. 2 0.01 8 0.008

2 0.006 71 2 0.004 1 g 0.002 e

Equilibrium Activity

I ' ....* 1 M 0.03 7-F. , , , . , . , , , , , , , , , , , , , ,

Equilibrium Concentration, mol/l

Figure 3. Liquid-phase equilibrium adsorption isotherms. (a) Ethanol a t 313, 323, and 333 K. (b) s, single solute of 2,3DM2B at 295 K, ethanol and dibutyl ether a t 313 K, bl , binary solutes of ethanol and 2,3DM2B in equimolar concentration at 313 K, b2, binary solutes of ethanol and dibutyl ether in equimolar concentration at 313 K.

are negligible as compared that of alcohol and (2) that the fraction of vacant sites is also negligible. While the first assumption appears to be plausible because alcohol molecules are preferentially adsorbed on the ion- exchange catalyst as compared to the relatively non- polar olefins and ethers, there is little evidence regard- ing the validity of the neglect of the vacant site term, except that the resulting rate expressions are adequate over the limited range of activities studied based on regression analyses of the experimental data as shown in Figure 1 and by Rehfinger and Hoffmann (1990) and Fite et al. (1994). Therefore, doubts about the validity of the above assumptions were addressed by conducting independent liquid-phase adsorption experiments and carrying out additional kinetics experiments over a wider range of conditions, as described below.

Liquid-Phase Adsorption. Liquid-phase equilibrium adsorption experiments were first conducted for ethanol in n-heptane as solvent. The adsorption isotherms at 313, 323, and 333 K are provided in Figure 3a. Langmuir isotherm expression in terms of activity, qA/qA,m = KAaA/(1 -k KAaA), Was used to Correlate the data and the adsorption equilibrium constant, KA, was obtained to be 1.6, 1.41, and 1.81 at 313, 323, and 333 K, respectively. However, such values of KA do not


justify the neglect of unity representing the vacant sites in the denominator of eqs 8-10 even a t a A = 1, the highest possible ethanol activity.

Liquid-phase adsorption experiments were also conducted for (26 olefins and ethers, and the adsorption isotherms are plotted in Figure 3b. 2,3DM2B was chosen as the representative of the c6 olefins because it is the most stable tertiary c6 olefin. It was found that the isomerization reaction of 2,3DM2B proceeded to a very limited extent and also no significant dimerization product was detected a t the temperature (295 K) investigated. Since any tertiary ether would decompose in the presence of Amberlyst 15 catalyst, dibutyl ether, which has the same molecular weight as THEE but does not decompose, was selected as an analog of THEE in the adsorption experiments. In experiments involving binary adsorption of ethanol and 2,3DM2B, a correction was made to account for the small extent of etherification reaction, by taking advantage of the fact that ethers do not adsorb significantly on Amberlyst 15. From Figure 3b, it can be seen that (1) adsorption of dibutyl ether is very small even in the absence of ethanol, and is even smaller in the presence of ethanol; (2) adsorption of 2,3DM2B in the absence of ethanol is significant, but is largely eliminated by the presence of ethanol; and (3) the adsorption of ethanol is also significant and is only imperceptibly affeded by the presence of either 2,3DM2B or dibutyl ether, apparently because ethanol, being much more polar than 2,3DM2B or dibutyl ether, is preferentially adsorbed.

The above observation is significant because it provides direct experimental evidence validating the most abundant surface species assumption for ethanol and the neglect of the olefin and ether adsorption terms in the rate expressions eqs 8- 10, without substantially sacrificing data fitting accuracy. Retaining the vacant site term, however, as reasoned above, eqs 8-10 may be simplified to

rl ~ , , (uAuB - aD/K,)/(l + KA~A)2 (19)

and

while for the initial rates, these reduce to

(22)

and

~ 3 0 x k,,uB/(l + KAuA) or r30 -kL3uc/(l + KAuA)

(24)

depending upon the feed olefin utilized. In the above, k,1 = k1K&B, k,2 = k&&c, ks3 = k& and ki3 = k F c = kdK3.

It may be pointed out that the saturation amount of ethanol adsorbed on Amberlyst 15 shown in Figure 3 is higher than the amount required for 1 monolayer coverage calculated by assuming that 1 equivalent exchange capacity corresponds to 1 mol of adsorption sites. This is different from the observation of Kabel and Johanson (1962), who found that a monolayer of

100 , I I , , , . , I , , , . , , I I I .;, I , , , ,

g [ 40

z- 2o 0

0 0.5 1 1.5 2 2.5 Activity Ratio, a,/ aA

Figure 4. Comparison of experimental initial rates of 2,3DM2B etherification reaction with predictions of the simplified rate expression eq 15 and the proposed rate expression eq 23.

ethanol is achieved in the vapor-phase adsorption of ethanol. While solids adsorb gases chemically even a t low temperatures, chemisorption is known to be ac- companied by physical adsorption when a liquid solution is involved (Kipling, 1965). Besides, the liquid-phase adsorption on ion-exchange resin organic catalysts such as Amberlyst 15 is complicated by other factors such as catalyst swelling (Harland, 1994).

Kinetics over a Wider Composition Range. Ki- netics experiments with one of the CS olefins, namely 2,3DM2B (a tertiary p-olefin), were extended to cover a wider range of activity ratios than that shown in Figure 1. The activities of ethanol and 2,3DM2B were varied respectively from 0.42 to 0.82 and from 0.03 to 0.92. This was accomplished by diluting the reactants in n-heptane or by reducing 8. The corresponding activity ratio, ad a A , covers a range from 0.06 to 2, in comparison to the previously investigated ranges of 0.05-0.6 for MTBE synthesis (Rehfinger and Hoffiann, 1990) and 0.8-1.4 for ETBE synthesis (Fite et al., 1994) in the literature. The experimental initial rates of 2,3DM2B etherification with ethanol at the three temperatures of 333,343, and 353 K are plotted in Figure 4. The'experimental data fall well below the dashed lines predicted by eq 15 for adaA > 1, indicating the inadequacy of the assumption of the negligibility of vacant sites, but agree well with the solid curves predicted by eq 23, to be discussed shortly. Similar, but less deviant, results were obtained for the isomerization reaction. Equations 12, 15, and 16 are evidently erroneous in the extreme case when alcohol activity a A approaches zero, or when the ratio a$aA or U ~ U A approaches infinity, as may occur in a reactor if 8 *: 1. In such a case, infinite initial rates of reactions would be predicted by eqs 12, 15, and 16.

Since it may be reasoned that the number of vacant active sites increases as the ethanol activity decreases, eq 23 was rearranged into the following form to obtain a linear relation between UA and $J defined by

in order to determine the value of KA from the kinetics data of 2,3DM2B etherification. A regression plot of 4 versus a A is provided in Figure 5. The straight lines imply that the data can be adequately represented by eq 23. The adsorption equilibrium constants computed from the division of the slope by the intercept are equal to 2.74,2.11, and 3.38 respectively at 333,343, and 353 K. As observed in the adsorption experiments described above, KA obtained from the kinetics experiments is also rather insensitive to the temperature in the range investigated. Thus, the average KA = 2.75 was adopted in the subsequent data analyses according to eqs 19- 24. With this value, eq 23 was successfully applied to


10

8

4

2 0.4 0.5 0.6 0.7 0.8 0.9

a A

Figure 5. Regression plot of experimental initial rates of 2,3DM2B etherification reaction to determine the equilibrium adsorption constant of ethanol at three different temperatures.

70 , , , , , I , , I I , , , , , ,rr/ , , ,

JR 0 0.02 0.04 0.06 0.08 0.1

aAac I(1 + KAaA)'

Figure 6. Regression plot of experimental initial rate of 2,3DM2B etherification with ethanol according to the proposed rate expression eq 23.

Table 1. Pseudo-Rate Constants (moY(hs)) Obtained from Regression of the Experimental Initial Rates According to Eqs 22-24 with KA = 2.75

THEE1 system THEE2 system

T, K ks1 k.52 ks3 ksl k s ~ ks3 4 3

313 0.130 0.0302 0.0182 0.0523 0.0106 323 0.364 0.102 0.0506 0.162 0.039 0.0314 0.00208 333 0.975 0.335 0.136 0.473 0.115 0.0891 0.00656 343 2.438 0.962 0.340 1.222 0.315 0.228 0.0200 353 0.812 0.0581

fit the experimental initial rates of 2,3DM2B etherification as shown in Figure 4.

Reaction Rate Constants, Activation Energies, and Extrathermodynamic Correlations. With the adoption of KA = 2.75, the experimental data were analyzed according to the initial rate forms of the proposed rate expressions, eqs 22-24. An example is provided in Figure 6 for the etherification of 2,3DM2B with ethanol plotted according to eq 23. The slopes of the straight lines are the pseudo-rate constants, ks2, and are equal to (39.0 f 3.21, (115 f 5.81, (315 f 12.7) and (812 & 25.4) mmol/(h*g) a t 323, 333, 343, and 353 K, respectively. The intervals of the slopes are estimated to be less than 10% of the slopes at a 95% confidence level by the t-test. The resulting pseudo-rate constants for 2,3DM2B as well as for the other tertiary olefins studied are summarized in Table 1. These data can be satisfactorily correlated with the Arrhenius equation, and the resulting preexponential factors and apparent activation energies are provided in Table 2. The intervals of E at a 95% confidence level listed in Table 2 were also estimated by the t-test. For comparison purposes, Table 2 also provides the apparent activation energies of the pseudo-rate constants k,. obtained from a regression of the simplified rate expressions eqs 12, 15, and 16.

It is seen from Table 1 that the pseudo-rate constants k,i of the etherification reactions of tertiary a-olefins

with ethanol are higher than those of the corresponding tertiary B-olefins. In fact, these data for all four reactive olefins were found to conform to the linear free-energy relation, i.e., the log of the rate constant of etherification reactions is in a linear proportion to the log of the reaction equilibrium constant, In k,, = a In Ki + c, as shown in Figure 7, where a and c are constants. The reaction equilibrium constants used in the figure were obtained from Zhang and Datta (1995b) and are given below from eq 29 to eq 32. The usual forms of such linear relationships are the familiar Hammett equation for many reactions of compounds containing phenyl and substituted phenyl groups or the Bronsted relation for the acid- and base-catalyzed reactions, where K, is the acid or base dissociation constant (Rase, 1977). It is further noted in Figure 7 that the slope of about 0.57 is constant at the different temperatures while the intercept increases with the temperature. It is noteworthy that a similar (Bronsted) plot for acid-catalyzed dehydration of acetaldehyde hydrate provided a slope of 0.54 (Gates, 1992). At any rate, these correlations may be useful for prediction of etherification reaction kinetics of other reactive C g olefins with ethanol.

A general trend of compensation effect between the preexponential factors and the activation energies is also observed for both the etherification and isomerization reactions, as shown in Figure 8. Further, for the isomerization reaction, 2,3DMlB * 2,3DM2B (reaction 3 in THEE2 system), the data in Tables 1 and 2 allow an examination of the requirements for thermodynamic consistency, Le., RT" ln(Ah3/Ao3) = AG",,. - m3,., E3 - E; = m 3 T O (Dumesic et al., 19931, and kSdkL3 = K3. These criteria are indeed satisfied based on the standard enthalpy and Gibbs free energy of the isomerization reaction, m3,. = -11.6 kJ/mol and AG& = -7.7 kJ/ mol, respectively, at T" = 298 K (Zhang and Datta, 1995b1, if an experimental uncertainty of f l kJ/mol is allowed, and with K3 = K1/K2 obtained from eq 31 and eq 32 given below for the THEE2 system.

It may further be noticed in Table 2 that the two values of the apparent activation energy for each reaction are very close to each other even though the pseudo-rate constants are defined differently according to eqs 11-16 and eqs 19-24. For instance, the pseudo- rate constant for reaction 1 is defined as k,1 = k1KdKA based on eq 11, and is defined as k,l = klK&B according to eq 19. As a result, E1 = E,I f AHA - AHB = Esl - AHA - A& and AHA = 0.5[E51 - E,J Thus, the close values of E, and E, suggest a small enthalpy of ethanol adsorption on Amberlyst 15 in the liquid phase. This agrees with the earlier reported adsorption enthalpies of -3.8 kJ/mol for methanol (Sola et al., 1994) and -3.4 kJ/mol for ethanol (Fite et al., 1994) on ion-exchange resin catalysts in the liquid phase.

The adsorption enthalpy of olefin is also included in the apparent activation energy. The liquid-phase adsorption enthalpy of olefin was not found in the literature, but may be estimated from the vapor-phase adsorption data and the enthalpy of vaporization. For instance, from the kinetics data of ETBE synthesis in the vapor phase over Amberlyst 15 (Iborra et al., 1990), Fite et al. (1994) estimated the vapor-phase adsorption enthalpy to be -72.6 kJ/mol for isobutylene. This unusually high value was found to be erroneously calculated, and thus a new value of -22.7 kJ/mol was recalculated. Along with the enthalpy of vaporization of 20.6 kJ/mol (API Project 44, 1953), an adsorption enthalpy of -2.1 kJ/mol was, thus, calculated for liquid


Table 2. Preexponential Factor and Activation Energy in Arrhenius Equation k = A0 exp(-E/RT), Ao in moY(hg), E in kJ/mol, and T in K

(a) According to Eqs 12, 15, and 16, the Simplified Rate Expressions THEEl synthesis THEE2 synthesis

krl krz kr3 k r l krz kr3 k:3

Ao 2.62 x 10l2 1.19 1014 1.56 x 10l2 1.25 1013 8.87 x 10l2 4.54 x 1012 2.07 1013 Eri 86.9 100.9 87.1 93.3 96.2 91.3 102.7 CI” 10 .8 f 3 . 7 1 1 . 1 h3.1 f 2 . 6 f 1 . 8 f 1 . 3

(b) According to Eqs 22-24, the Proposed Rate Expressions THEEl synthesis THEE2 synthesis

ksl ks2 ks3 k s l ksz k s3 k:3 Ao 4.81 1013 5.14 x 10l6 6.69 x 10l2 2.59 1014 1.28 1014 2.05 1013 2.22 1014 Em 87.3 103.2 87.3 94.0 95.9 91.6 105.3 CI” 10 .7 f 2 . 5 f 1 . 2 f 3 . 0 f 0 . 8 11.8 12 .6 E,b 92.8 108.7 89.4 99.5 101.4 93.7 107.4

a CI = 95% confidence interval in E estimated by the t-test, kJ/mol. b “True” activation energies calculated according to eq 26.

10 - 1 10 100

Equilibrium Constant

Figure 7. Linear free-energy correlation for etherification reactions of CS olefins with ethanol over Amberlyst 15 catalyst.

ap

5i E

. . . . . . . . . . . . . .

1 0 1 5 1

90 95 100 105 E - - P 85

Activation Energy, E, kJ/mol

Figure 8. Compensation effect separately exhibited by etherification reactions and isomerization reactions of c6 olefins.

isobutylene. Similar values may be expected for c6 olefins. These adsorption enthalpies of liquid-phase ethanol (-3.4 kJ/mol) and olefins (-2.1 kJ/mol) are both close to the 95% confidence intervals of the apparent activation energy as seen in Table 2. Thus, the “true” activation energies may be computed from

E , = E,, - A H A - A H B ; E , = E,, - A H A - AHc; E, = E,, - AH*; E: = Ei3 - A H C (26)

and the results are provided in Table 2. It is seen that Ei are not substantially different from E,i due to the small values of adsorption enthalpies.

The superiority of the proposed rate expressions, eqs 19-24, over the simplified expressions, eqs 11-16, has already been illustrated in Figure 4. This can further be seen in Figure 9a, which shows the fit of the experimental initial rates of 2,3DM2B etherification versus ethanol mole fraction XA in the absence of solvent. As is evident from Figure ga, over a range O f xA = 0.3-

f 2o 0

0.0 0.2 0.4 0.6 0.8 1.0

50

40

30

20

10

0 0.0 0.2 0.4 0.6 0.8 1.0

Mole Fraction of Ethanol, xA

Figure 9. Comparison of experimental initial rates of 2,3DM2B with predictions of the simplified rate expressions eqs 15 and 16 and the proposed rate expressions eqs 23 and 24 for (a) etherification and (b) isomerization reactions in the absence of solvent.

1.0, both the relations are equivalently satisfactory. However, whenxA is lower, eq 15 overpredicts the initial rate, which erroneously approaches infinity as XA approaches zero. On the other hand, eq 23 adequately predicts the initial rate experimentally observed. A maximum in the initial rate of etherification is, thus, predicted at XA 0.05. Further, the rate goes to zero, as it should, as XA goes to zero. A similar comparison is shown in Figure 9b for the initial rates of 2,3DM2B isomerization. The initial rate of isomerization reaches a maximum at XA = 0 as observed experimentally and predicted by eq 24. On the other hand, eq 16 predicts the rate to approach infinity as XA - 0. The reaction rate decreases monotonically with XA, indicating that the isomerization reaction is inhibited in the presence of ethanol due to its strong competitive adsorption, which is evident from the denominator of eq 21 or eq 24.

The proposed rate expression, eq 22, was also used to correlate the available literature data for MTBE and ETBE syntheses. KA = 2.75 for ethanol as obtained above was used, while KA = 10.5 for methanol was obtained through a regression analysis of the experimental data for MTBE synthesis at 333 K (Rehfinger and Hoffmann, 1990) by using an equation similar to


0.0 0.2 0.4 0.6 0.8 1.0

Mole Fraction of Alcohol, xA

Figure 10. Comparison of various model predictions with experimental data of MTBE and ETBE syntheses obtained from Fkhfinger and H o f i a n n (1990) for MTBE synthesis and from Fite et al. (1994) for ETBE synthesis.

eq 25. Methanol is more polar than ethanol and, therefore, arguably has a higher adsorption equilibrium constant than ethanol. As shown in Figure 10, the present rate expression, eq 22, can describe the experimental data of MTBE synthesis as well as its simplified form, eq 12, proposed by Reffiger and Hoffmann (1990) in most of the range of alcohol mole fraction. For ETBE synthesis, the three-site rate expression, eq 17, proposed by Fite et al. (1994) provides a somewhat better fit in the limited range of mole fraction over which their experiments were conducted. However, the major difference between the present rate expression and the literature models is the predicted maximum in the initial rate of the etherification reaction a t a rather low mole fraction of alcohol. This sharp peak was also experimentally observed by Ancillotti et al. (1977,1978) in the liquid-phase MTBE synthesis, and cannot be explained by either the Rehfinger and Hoffmann (1990) rate model or the Fite et al. (1994) model. The reaction rate peak predicted for ETBE synthesis is less sharp due to the lower value of the adsorption equilibrium constant of ethanol as compared with methanol.

Reaction Mechanism. The rate expressions eqs 19-21 suggest a LHHW mechanism with a dual-site rate-determining step for the etherification and a single- site rate determining step for the isomerization reactions. On the basis of this observation, a mechanism and the corresponding potential energy profiles are proposed in Figure 11, where the example is given of 2M1P that either isomerizes to 2M2P or reacts with ethanol to form THEEl in the presence of acidic catalysts such as Amberlyst 15. Of course, similar mechanistic schemes may be developed when other reactive olefins or methanol are involved.

It is known that olefins, owing to their mild basicity, react with strong acids (e.g., polymer-bound S03-H+, or Pn-S03-H+) to yield carbenium ions. The tertiary carbenium ion, thus formed and considered to be a common intermediate, goes on to react further in isomerization or the etherification reactions, which are postulated to have different rate-determining steps. Thus, the rate of the isomerization reaction is assumed to be limited by the migration of the attached Pn-S03- H+ from the primary carbon atom (C1) to the secondary carbon atom ((33). This is supported by the demonstra- tion that -S03-H+ groups are strong proton donors as well as acceptors (Zundel, 1969). This characteristic of -SO3-H+ groups has also been utilized by Gates et al. (1972) in proposing a concerted mechanism involving four -S03-H+ groups in the dehydration of tert-butyl alcohol. In addition, it is assumed here that ethanol is protonated by a second Pn-S03-H+ group to form an

ethyloxonium ion. The combination of this oxonium ion with the carbenium ion, resulting in the release of a P n - SO3-H+, is assumed to be the rate-determining step for the etherification reaction.

The potential energy diagram in Figure 11 explains the higher activation energy (Ei3) required for the isomerization reaction of an ,!?-olefin (C) as compared with that (Es3) of the corresponding a-ole& (B), because the ,!?-olefin has a lower potential energy level than the a-olefin. Similarly, the activation energy (ELl) required for an ,!?-olefin etherification reaction is higher than that (E,I) for the etherification reaction of the corresponding a-olefin.

Integral Analysis of THEE Synthesis Kinetics. The rate expressions developed from the differential experiments as described above were eventually tested in an integral packed-bed reactor with a feed consisting of ethanol and a single c6 reactive olefin (2MlP or 2,3DM2B) in the absence of solvent. The integral reactor experiments and kinetic analysis are similar to those done for MTBE synthesis (Zhang and Datta, 1995a). Catalyst of average particle size 0.1875 mm was used to ensure the elimination of mass transport resistance, and the catalyst was diluted with inert silicon carbide grains to obtain uniform temperature throughout the catalyst bed. The experimental olefin conversions at the reactor outlet were compared with those predicted from the following integral reactor performance equations, which can be formulated from the mass balances of the product ether or the olefin isomer:

for a-olefin feed:

for ,!?-olefin feed:

where from eq 4, RD = rl + r2 , RB = -r3 - rl, and Rc = r3 - 1-2, where rl, r2, and r3 are given by eqs 19-21 along with the pseudo-rate constants listed in Table 1. The equilibrium constants in eqs 19-21 for the THEEl system are (Zhang and Datta, 1995b)

In Kl = -71.4519 + 7149.74/T + 11.0547 In T - 0.04006 T +

3.8979 x T2 - 3.6812 x (29)

In K2 = -84.4308 + 6870.67/T + 13.0318 In T - 0.03783 T +

3.3181 x - 3.2602 x lo-' p (30)

while those for THEE2 system are

In Kl = -76.2082 + 6000.86lT + 12.5825 In T - 0.04762 T + 4.7885 x

In K, = -61.4243 + 4660.2lT + F - 4.021 x lo-* p (31)

9.4324 In T -0.02728 T + 2.7866 x F - 2.9684 x p (32)

Further, K3 = Kl/K2 for either system (Zhang and Datta, 1995b). At a given value of space time, WlFm or WIFco, the etherification and isomerization conversions of an


(1) (2M2P) 7 7 slow r H

( N I P ) - CHS-C=CHCHzCH3 + Pn-SO;Ht H-F-f=y-CHzCH3 a I

H-C= C-CHzCH2CH3+Pn-SO;Ht l+f=f-?-CH2CH3 I 1 H CH3 H CHjH H CH3H CH3

Ethanol

Potential Energy Profile lor ( I )

FHZCH3 A T- CH3-F-CHzCHZCHj +

CH3

2-methyl-Z-ethoxy pentane (THEE1)

Pn- SO;H+

Potential Energy Profile lor (E) Pn-SO;H+

Figure 11. Reaction mechanisms and potential energy profiles for (E) etherification of 2M1P with ethanol and (I) double-bond isomerization between 2M1P and 2M2P.

1

4 0.8 B

0.6

0 0.4 8 6 2 0.2 $ 6

c

u o 300 310 320 330 340 350 360

Temperature, K 1 , , , . . . , , . , , . , , , , . . . , . . , , . . , . . ,

0 50 100 150 W E B o or W/Fco, g.h/mol

Figure 12. Experimental olefin etherification conversions obtained in an integral reactor: (a) as a function of temperature at two values of WIFBO or WIFco; (b) as a function of WIFBO or WIFco a t 333 K with those predicted from the proposed rate expressions and the parameters as determined from the differential kinetics experiments.

olefin a t the reactor outlet were determined to satisfy eq 27 or eq 28, which were numerically solved, with the activity coefficients estimated by the TJNIFAC method.

Figure 12a shows the etherification conversions of olefins to tertiary ethers as a function of temperature a t WIFBo or WIFco = 15.8 and 61.4 ghlmol and at $2 = 1.05 in the absence of any solvent. The experimental and predicted results for 2M1P and 2,3DM2B yield good agreement, thus confirming the rate expressions obtained from the differential experiments. It is seen that the conversion rapidly increases with temperature to the corresponding equilibrium value, beyond which the

conversion obtained is totally limited by the thermodynamic equilibrium. At w/FBo = 15.8 ghlmol, the maximum conversion is about 70% a t 343 K for 2MlP. For 2,3DM2B, this maximum conversion is only 36% at 353 K a t WIFco = 15.8 ghlmol, and increases to 43% a t 343 K a t the higher WIFco of 61.4 ghlmol. In the literature, a conversion level of 40% is cited for one- step etherification of c6 olefins with methanol (Pesca- rollo et al., 1993). However, parameters such as temperature and space velocity were not provided, and as a result, further analysis could not be carried out. Nevertheless, it is evident that the equilibrium conversions in THEE syntheses are much lower than those in MTBE or ETBE syntheses. Thus, schemes designed to enhance conversion such as catalytic distillation or multiple-step etherification should be even more useful.

Figure 12b shows the predicted etherification conversions of the four c6 olefins as a function of WIFBO or WIFco at 333 K and a t B = 1.05 in the absence of any solvent. Some limited experimental data are also plotted. At low values of W&o or WIFco, the conversion of a-olefm (2MlP or 2,3DMlB) is much higher than that of the corresponding ,&olefin (2M2P or 2,3DM2B). This is expected because the etherification reaction rate constant of the a-olefin is higher than that of the corresponding p-olefin (Table 1). The difference in conversion between a- and /%olefins decreases at higher w/FBo or WIFco, and eventually disappears when the equilibrium is approached. Similar results were experimentally observed by Krause et al. (1984) for the etherification of 2M1P and 2M2P with methanol at 353 K.

Conclusions

The kinetics of simultaneous etherification and isomerization reactions of four reactive c6 olefins with ethanol over Amberlyst 15 catalyst have been investigated, and the developed rate expressions based on the LHHW formulation have been used to successfully correlate the


experimental data. While their simplified forms are adequate over a limited range of species activities, it was found that the proposed rate expressions including the vacant catalyst site terms correlate the kinetics data better over a wider range of compositions. The adsorption equilibrium constant of ethanol estimated from the kinetics data agrees reasonably with the values determined from independent liquid-phase ethanol adsorption experiments. Adsorption experiments also confirmed the negligibility of the adsorption terms of olefins and ether, but it was found that the neglect of the vacant sites is erroneous. Apparent activation energies determined accordingly are in the range of 87-105 kJ/ mol depending on the olefin and the reaction, and are close to the “true” activation energies due to the negligible adsorption enthalpies of olefins and ethanol in the liquid phase. Integral behavior of the packed- bed reactors is well predicted based on the proposed rate expressions.

Acknowledgment The funding provided by the National Renewable

Energy Laboratories for this study is gratefully acknowl- edged, as are the helpful comments of Kyle Jensen, Prakob Kitchaiya, Bahman Rejai, and Marvin Klotz.

Nomenclature A, B, C, D = ethanol or methanol, a-olefin or isobutylene,

@-olefin, tertiary ether (MTBE, ETBE, THEE1, or THEEP), respectively

a, = activity of species j = X,Y, A0 = preexponential factor, mol4h-g) E = “true” activation energy, kJ/mol E,, E , = apparent activation energy, kJ/mol F,o = flow rate of species j at the reactor inlet, mom AG:To = standard Gibbs free energy of reaction i at T”,

wy = standard enthalpy of reaction i in the liquid

A€€‘, = adsorption enthalpy of species j in the liquid phase,

k , = true rate constant of surface reaction i, moV(h-g) k f , k,, k, , k , = pseudo-rate constants, mol/(h-g) K, = equilibrium constant of reaction i I$ = adsorption equilibrium constant of species j on catalyst m = number of active sites involved in rds n = total number of species q = total number of reactions q, = amount of species j adsorbed on catalyst, moVg R = gas constant, 8.314 J/(mol*K) r, = rate of reaction i, r, = 7, - F,, mol4h.g) RJ = rate of formation of species j , moV(hg) S = catalytic site T = temperature, K, To = 298.15 K W = catalyst weight, g xJ = mole fraction of species j X E , X I = etherification and isomerization conversions of an

Greek Letters yJ = activity coefficient of species j vIJ = stoichiometric coefficient of species j in reaction i s2 = molar feed ratio of ethanol to reactive olefin, FAdFBo

$J = function defined by eq 25 Subscripts 0 = initial rate of reaction 1, 2, 3 = reactions 1, 2, and 3, respectively, eq 3

liquid phase, kJ/mol

phase at T“, kJ/mol

kJ/mol

olefin, respectively

or FAdFco

A, B, C, D = alcohol, a-olefin (or isobutylene), P-olefin, ether, respectively

E, I = etherification, isomerization, respectively i = of reaction i (1, 2, 3) j = of speciesj (A, B, C, D) out = at the reactor outlet Superscripts ’ = of reverse reaction Abbreviations 2,3DMlB = 2,3-dimethyl-l-butene 2,3DM2B = 2,3-dimethyl-2-butene ETBE = ethyl tert-butyl ether (2-methyl-2-ethoxypropane) 2M1P = 2-methyl-1-pentene 2M2P = 2-methyl-2-pentene MTBE = methyl tert-butyl ether (2-methyl-2-methoxy-

rds = rate-determining step TAEE = tert-amyl ethyl ether (2-methyl-2-ethoxybutane) TAME = tert-amyl methyl ether (2-methyl-2-methoxy-

THEE = tert-hexyl ethyl ether (=El, THEE2, or THEE31 THEE 1 = 2-methyl-2-ethoxypentane THEE2 = 2,3-dimethyl-2-ethoxybutane THEE3 = 3-methyl-3-ethoxypentane

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Received for review December 29, 1994 Accepted May 10, 1995 @

IE940777Z

@ Abstract published in Advance ACS Abstracts, June 15, 1995.

Ethers from Ethanol. 4. Kinetics of Liquid-Phase Synthesis of Two tert-Hexyl Ethyl Ethers

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