Liquid-Phase Synthesis of Ethanol-Derived Mixed Tertiary AlkylEthyl Ethers in an Isothermal Integral Packed-Bed Reactor

Tiejun Zhang, Kyle Jensen, Prakob Kitchaiya, Cory Phillips, and Ravindra Datta*

Department of Chemical and Biochemical Engineering, The University of Iowa, Iowa City, Iowa 52242-1219

Industrial production of mixed tertiary ethers by reacting methanol or ethanol with a mixedtertiary olefin stream is a distinct possibility. Consequently, the synthesis of mixed ethyl tertiaryalkyl ethers from ethanol and mixtures of reactive iso-olefins in an isothermal integral packed-bed reactor is studied. The rate expressions in terms of activities for the individual reactionrates in this family of ethers are taken from related work. These kinetic expressions are utilizedhere for comparison with experimental data obtained in a packed-bed reactor containingAmberlyst 15 ion-exchange resin catalyst for a mixed iso-C6 olefin feed stream as well as for amixed C4, C5, and C6 iso-olefin stream. Etherification and isomerization conversions increasewith space time at the lower temperatures; however, at the higher temperatures equilibriumlimitations are approached. As a function of temperature, the conversions first increase andthen decline due to thermodynamic limitations for these exothermic reactions. Good agreementis obtained between predictions and experiments.

Introduction

Oxygenated fuels have shown a steady growth duringthe nineties. Methyl tert-butyl ether (MTBE), producedby reacting a C4 stream containing isobutylene withmethanol over an ion-exchange resin catalyst, is cur-rently the dominant gasoline additive. Industrial syn-thesis of ethyl tert-butyl ether (ETBE), produced bysubstituting ethanol for methanol, has also commenced.Due to the immense growth of these oxygenates, how-ever, the isobutylene supply may become limiting in thefuture. Consequently, higher tertiary ethers producedfrom a combination of methanol or ethanol with C5 andC6 tertiary olefins are of interest. There are substantialquantities of C5 and C6 olefins present (∼10.5 and 6.5%,respectively) in the fluid catalytic cracking (FCC) lightgasoline stream (Ignatius et al., 1995), which could beutilized to form these ethers. Owing to the high olefinvolatility, their conversion into the corresponding ethersinstead of blending the olefins directly with gasoline isattractive. Furthermore, there is little reason to pro-duce pure ethers from separated olefins, since a mixtureof ethers resulting from the FCC light gasoline streamwithout separating the individual olefins should beequally effective for blending purposes. This paper is,hence, concerned with the synthesis of mixed ethersfrom ethanol and mixed olefin streams in an integralpacked-bed reactor.As shown in Table 1, ethanol and isobutylene form

ETBE, while tert-amyl ethyl ether (TAEE) is formedwith ethanol from either of reactive C5 isomer, namely2-methyl-1-butene (2M1B), or 2-methyl-2-butene (2M2B).There are three possible isomers of tertiary hexyl ethylethers (THEE) formed from ethanol, i.e., THEE1 fromeither 2-methyl-1-pentene or 2-methyl-2-pentene (2M1Por 2M2P), THEE2 from 2,3-dimethyl-1-butene or 2,3-dimethyl-2-butene (2,3DM1B or 2,3DM2B), and THEE3from cis- or trans-3-methyl-2-pentene (C3M2P or T3M2P)or 2-ethyl-1-butene (2E1B). These higher ethers alsohave desirable gasoline-blending properties. Thus,TAEE has a motor octane number (MON) of 112 and aresearch octane number (RON) of 105. The threeisomers of the tertiary hexyl ethyl ether have RON )

105.9 and MON ) 93.1 for THEE1, RON ) 104.9 andMON ) 91.9 for THEE2, and RON ) 101.4 and MON) 91.5 for THEE3 (Milne, 1996).The etherification reaction occurs according to the

Markownikoff addition; that is, the hydrogen fromethanol adds to the less-substituted carbon atom of thedouble bond. Furthermore, except, of course, for isobu-tylene, each iso-olefin also undergoes isomerization onthe catalyst. Thus, ETBE, TAEE, THEE1, and THEE2are synthesized as shown in Figure 1a, with either theR-olefin or the â-olefin reacting with ethanol. Theisomerization of 2M1B and 2M2B follows pathwaynumber 3 of Figure 1a, as do the olefins that formTHEE1 and THEE2. Three conformational isomeriza-tion reactions are possible for the C6 olefins (i.e., 2E1B,C3M2P, and T3M2P) that form THEE3 as shown inFigure 1b. These etherification reactions are denotedby numbers 1, 2, and 3, whereas the isomerizationreactions are labeled as 4, 5, and 6 in Figure 1b. Due

* Author to whom correspondence may be addressed. E-mail: radatta@icaen.uiowa.edu.

Figure 1. Ether synthesis reaction network. (a) ETBE, TAEE,THEE1, and THEE2 systems from the corresponding olefins (Band C), except isobutylene (B) which has no conformational isomer(C). (b) THEE3 (D) reaction system, including isomerization amongC3M2P (B2), T3M2P (B3), and 2E1B (B1).

4586 Ind. Eng. Chem. Res. 1997, 36, 4586-4594

S0888-5885(97)00099-7 CCC: $14.00 © 1997 American Chemical Society

to the structural similarities of the olefins and acommon alcohol involved, it seems reasonable to assumethat there may be some systematicity in the mechanism,rate expressions, and the kinetics.

Reaction Kinetics and Thermodynamics

A recently published series of papers provides expres-sions for the equilibrium constants for ETBE (Jensenand Datta, 1995), TAEE (Kitchaiya and Datta, 1995),and the THEEs (Zhang and Datta, 1995b, 1996).Furthermore, kinetic expressions have been developedfor liquid-phase synthesis of ETBE (Jensen and Datta,1997), TAEE (Kitchaiya and Datta, 1997a), and THEEs(Zhang and Datta, 1995c, 1996) in terms of activities.Zhang and Datta (1995c, 1996) provided Langmuir-Hinshelwood-Hougen-Watson (LHHW) mechanism-based rate expressions for THEE synthesis, assumingthat two active catalyst sites are involved in the rate-determining step (rds) of etherification (A + B a D) andone site in the rds of isomerization (B a C). Morerecently, Jensen and Datta (1997) and Kitchaiya andDatta (1997b), through the use of partially deactivatedcatalysts to vary the total number of active catalystsites, determined that a total of three sites are involvedin the surface reaction rate-determining step of theetherification reaction, with two adsorbed ethanol sitesreacting with one adsorbed tertiary olefin, while a totalof two sites are involved in the surface rate-determiningstep of the olefin isomerization, with an adsorbed olefinreacting with a vacant site. Thus, the previous dataare reanalyzed here to conform to the revised form ofthe rate expressions. These are then utilized in theanalysis of the mixed ether systems.Based on the above, the overall mechanism, thus, is

Applying the thermodynamic transition-state theory(TTST) (Connors, 1990) to each of the above elementarysteps, i.e., assuming each step to possess a uniquetransition state, along with the assumption of pseu-doequilibrium for the adsorption and desorption steps,and surface reaction as the rds, with the most abundantsurface species assumption (MASSA) for ethanol (Kit-chaiya and Datta, 1997a), yields the following rateexpressions (Jensen and Datta, 1997; Kitchaiya andDatta, 1997a)

and

for etherification and isomerization, respectively, whereksE ≡ kEKA

2KBCt3, ksI ) kIKBCt

2, KE ) KAKBkE/KDk-E,and KI ) kIKB/KCk-I. The ethanol adsorption equilib-rium constant for ethanol on Amberlyst 15 was deter-mined by independent adsorption experiments by Kit-chaiya and Datta (1997a) as

Kitchaiya and Datta (1997a) have further shown thatdue to the strong adsorption of ethanol, except for xA e0.04, the vacant sites fraction may also be neglected.For this case eqs 2 and 3 reduce to the power-law forms

and

where krE ) ksE/KA3 and krI ) ksI/KA

2. The activitycoefficients in the above rate expressions are calculatedby the UNIFAC method (Reid et al., 1987).The thermodynamic equilibrium constants,KE and KI,

in the above rate expressions were determined previ-ously (Jensen and Datta, 1995; Kitchaiya and Datta,1995; Zhang and Datta, 1995b, 1996) and are given forreaction i as

where the coefficients, λi, for the different reactions aregiven in Table 2. The Arrhenius parameters (Ai, Ei) forthe rate constants of etherification (eq 2) and isomer-ization (eq 3) reaction are given in Tables 3 and 4,respectively, while those for the power-law forms, eqs5 and 6, are also provided in these tables.

Experimental Section

Catalyst. Amberlyst 15, a cation-exchange macrore-ticular resin catalyst, was obtained from Sigma Chemi-cal Co. and has the following properties: averageparticle diameter ) 0.74 mm, surface area ) 50 m2/g,porosity ) 30%, and exchange capacity ) 4.8 mequiv/g.The catalyst was first washed and then converted intothe acid form by contacting with 1 N HNO3. The acid-exchanged catalyst particles were washed with ethanolprior to drying overnight in a vacuum oven. Groundand sieved to obtain a granulometric fraction in the sizerange of 0.125-0.25 mm (average diameter ) 0.188mm), the catalyst was mixed with cleaned and driedsilicon carbide diluent to prevent temperature variationsin the reactor bed. With this particle size, the internaldiffusional limitations were judged to be eliminatedunder all the experimental conditions investigated(Zhang and Datta, 1995a).Materials. For the THEEs synthesis, the individual

C6 olefins, 2E1B (purity > 97%), 2M1P (purity ) 98%),and 2,3DM2B (purity ) 98%) were obtained from TCIAmerica. Isobutylene (Matheson, cp grade) and 2M2B

A + S \kA

k-AA•S (1a)

B + S \kB

k-BB•S (1b)

2A•S + B•S \kE

k-ED•S + A•S + S (1c)

B•S + S \kI

k-IC•S + S (1d)

D•S \k-D

kDD + S (1e)

C•S \k-C

kCC + S (1f)

rE )ksEaA

2[aB - aD/(KEaA)]

(1 + KAaA)3

(2)

rI )ksI(aB - aC/KI)

(1 + KAaA)2

(3)

KA ) 27 exp[11 000R (1T - 1303)] (4)

rE ≈ krE(aBaA -aD

KEaA2) (5)

rI ≈ krI( aBaA2 -aC

KIaA2) (6)

ln Ki ) λi1 + λi2/T + λi3 ln T + λi4T + λi5T2 + λi6T

3

(7)

Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4587

(TCI > 95%), and a C6 olefin, were the feed olefins forthe mixed ether synthesis. Other materials used were

ethanol (Pharmco, dehydrated, 200 proof) and siliconcarbide (McMaster-Carr, size ) 0.25-0.45 mm).

Table 1. Reactive C4-C6 Olefins and Ethers Formed with Ethanola

a Only iso-olefins with the double bond attached to a tertiary carbon are reactive in etherification.

Table 2. Coefficients of Liquid-Phase Etherification and Isomerization Reaction Equilibrium Constant Correlations,ln Ki ) λi1 + λi2/T + λi3ln T + λi4T + λi5T2 + λi6T3, T in K

reaction, i λi1 λi2 λi3 λi4 λi5 × 105 λi6× 108

EtOH + IB a ETBE 10.387 4060.59 -2.8906 -0.019 15 5.2859 -5.3298EtOH + 2M1B a TAEE 22.809 3136.3 -5.8227 0.0179 -0.6395 -1.672EtOH + 2M2B a TAEE 26.779 2078.6 -6.5925 0.0231 -1.126 -1.4142M1B a 2M2B -3.970 1057.7 0.7698 0.0052 0.4865 -0.258EtOH + 2M1P a THEE1 -71.4519 7149.74 11.0547 -0.040 06 3.8979 -3.6812EtOH + 2M2P a THEE1 -84.4308 6870.67 13.0318 -0.037 83 3.3181 -3.26022M1P a 2M2P 12.9789 279.07 -1.9771 -0.002 23 0.5798 -0.0421EtOH + 2,3DM1B a THEE2 -76.2082 6000.86 12.5825 -0.047 62 4.7885 -4.0210EtOH + 2,3DM2B a THEE2 -61.4243 4660.20 9.4324 -0.027 28 2.7866 -2.96842,3DM1B a 2,3DM2B -14.7839 1340.66 3.1501 -0.020 34 2.0019 -1.0526EtOH + 2E1B a THEE3 -75.2419 6296.29 12.2972 -0.041 53 3.7941 -3.5474EtOH + C3M2P a THEE3 -72.1147 5433.52 11.4115 -0.034 62 3.1287 -3.2044EtOH + T3M2P a THEE3 -85.5225 5730.14 13.6057 -0.038 08 3.2520 -3.19022E1B a C3M2P -3.1272 862.77 0.8857 -0.006 91 0.6654 -0.34302E1B a T3M2P 10.2806 566.15 -1.3085 -0.003 45 0.5421 -0.3572C3M2P a T3M2P 13.4078 -296.62 -2.1942 -0.003 46 -0.1233 -0.0142

4588 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997

Reaction Kinetics Experiments. The liquid-phasereaction kinetics were studied in a stainless steeltubular packed-bed reactor (12 in. length, 3/8 in. diam-eter) system, similar to the reaction system describedby Zhang and Datta (1995c). The temperature of thejacketed reactor was controlled by an external waterbath (Fisher, model 9101). The pressure was main-tained at 100 psig to ensure a liquid phase in thereactor. Depending upon the reaction temperature andthe mode of operation, a varying amount (0.155-0.66g) of the catalyst, uniformly diluted with inert siliconcarbide grains, was carefully packed into the tubularreactor. The temperature variation along the packedbed of catalyst was thus maintained to be less than 1 Kto simulate isothermal conditions. The reactor endswere filled with glass wool to prevent any catalyst lossfrom the reactor.The reactor was operated in the integral mode, i.e.,

the WHSV employed were such that at the reactionconditions high conversions (up to equilibrium values)were obtained. The olefin conversions at the reactoroutlet were experimentally determined at differenttemperatures and WHSV and were utilized to test thepredictions based on the rate expressions and kineticsparameters determined from operation in the dif-ferential mode, i.e., at low conversions. Steady statewas monitored by periodical on-line analyses by meansof an internal liquid sampling injector (Valco, CI4WE,size ) 0.2 µL) of the product composition in a gaschromatograph (GC) as described below. When nochange was observed in the product composition, typi-cally after about 2 h of start-up, steady state wasdeemed to have been achieved. Thereafter, an averageof at least three measurements was taken to determinethe steady-state product composition. Some of the runswere replicated to check the reproducibility of theresults under a given set of experimental conditions. Themaximum deviation in the conversions found in suchruns was 5%. No discernible deactivation of the catalystwas observed under extended operation. The selectivityof the reactions studied under the reaction conditions

was very high, with 99.5% of the mass being accountedfor by the detected species.For the mixed C6 feed experiments, the reactant feed

consisted of ethanol and three C6 olefins isomers (2M1P,2,3DM2B, and 2E1B) without any solvent. The molarratio of ethanol to each olefin was in the range of Ω )1.05-1.5. For the mixed C4, C5, and C6 olefin feedexperiments, a mixture of 2M2B, C6 olefin, ethanol, andn-pentene diluent was fed independently to the reactorsystem described above by a positive displacement pump(Gilson Medical Electronics, Inc., model 302). In addi-tion, isobutylene (Matheson, cp grade) was introducedto the system by a ice-cooled pump head in a mannerdescribed previously by Zhang and Datta (1995a). Eachfeed vessel was placed on a top-loading balance forgravimetric measurement (Zhang and Datta, 1995c).Analysis. The liquid mixture composition was de-

termined by using a Perkin-Elmer AutoSystem GCequipped with a flame ionization detector (FID) and He(99.999%) as the carrier gas. Ethanol, olefins, ethers,and the solvent were separated using a Supelco capillarycolumn (SPB-1, 0.25 mm i.d. × 60 m). The column wastemperature programmed with a 10 min initial hold at65 °C, followed by a 20 °C/min ramp up to 160 °C, andit was finally held at 160 °C for 5 min. Analysis withthe column being held at 160 °C for longer periodsindicated no elution of any dimerization products. TheGC was calibrated for all the species, and the error inmole fraction was estimated to be 2%.

Results and Discussion

Single C6 Olefin Feed. In earlier work, Zhang andDatta (1995c) had utilized a rate expression based on atwo-site model for the THEE synthesis along with anethanol adsorption constant, KA ) 2.75. As discussedabove, subsequent work (Jensen and Datta, 1997; Kit-chaiya and Datta, 1997a) determined the number ofsites to be three for etherification and two for isomer-ization. Furthermore, the adsorption equilibrium con-stant for ethanol was determined to be given by eq 4(Kitchaiya and Datta, 1997a). For consistency, it wasdecided to check the new rate expressions for the THEEsystem. As shown in Figure 2, for THEE2 synthesis,the new expression, eq 2, fits the experimental dataadequately for the etherification reaction. Similarresults were found for isomerization.Mixed C6 Olefin Feed. A feed of mixed C6 olefins,

namely 2M1P, 2,3DM2B, and 2E1B, in the absence of

Table 3. Arrhenius Kinetics Parameters for EtherSynthesis from Ethanol

kri (eq 5) ksi (eq 2)

reactiveolefin

Ari × 10-12

(mol/(h‚g))Eri

(kJ/mol)Asi × 10-11

(mol/(h‚g))Esi

(kJ/mol)

isobutylene 15.78 87.2 74.18 60.42M1B 2.75 85.6 3.12 54.92M2B 3.89 89.5 4.4 58.82M1P 2.62 86.9 2.97 56.12M2P 119.0 100.9 134.85 70.12,3DM1B 12.5 93.3 14.17 62.52,3DM2B 8.87 96.2 10.05 65.42E1B 6.54 89.9 7.41 59.2C3M2P 1.66 89.6 1.88 58.9T3M2P 3.03 90.9 3.43 60.1

Table 4. Arrhenius Kinetics Parameters for OlefinIsomerization

kri (eq 6) ksi (eq 3)

reactionAri × 10-12

(mol/(h‚g))Eri

(kJ/mol)Asi × 10-11

(mol/(h‚g))Esi

(kJ/mol)

2M1B f 2M2B 2.15 85.0 5.02 64.52M2B f 2M1B 0.8 89.1 1.86 68.62M1P f 2M2P 1.25 87.1 2.08 66.62,3DM1B f 2,3DM2B 3.63 91.3 6.06 70.82,3DM2B f 2,3DM1B 16.6 102.7 27.4 82.22E1B f C3M2P 3.05 91.9 7.15 71.42E1B f T3M2P 4.32 90.2 10.1 69.7C3M2P f T3M2P 1.38 89.9 3.22 69.4

Figure 2. Comparison of experimental THEE2 synthesis ratedata from Zhang and Datta (1995c) and the three-site etherifica-tion rate expression, eq 2, with Arrhenius parameters from Table3.

Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4589

any solvent, and ethanol were fed to the reactor. Sinceall the three isomers of THEE are simultaneouslyformed in parallel from this mixed C6 olefin feedsteam,the following olefin conversions were calculated for theTHEE system k from the experimentally measuredmolar composition of the product at the reactor outlet.

The symbols for the various conversions given above areexplained in the Nomenclature section. Furthermore,the individual molar ratios of ethanol to 2M1P, 2,3DM2B,and 2E1B are defined as Ω1, Ω2, and Ω3, respectively.The overall molar ratio of ethanol to all three olefins isthen calculated from

Material Balance Equations. The etherification andisomerization conversions may be determined from thefollowing sets of mass balance equations of the products:

where (Rk) is the rate of production vector for the THEEsystem k, [ν]k is the stoichiometric coefficient matrix ofthe THEE system k, and (r)k is the reaction rate vectorfor the THEE system k. The rates of product formationmay be written in terms of the rates of reactionsaccording to the reaction stoichiometry in each indi-vidual ether system, i.e.,

Thus, the rate of production vectors (Rk) are respectivelydefined for the three THEE systems (k ) 1, 2, 3) by

where the individual rates refer to the reactions inFigure 1 and the corresponding etherification and

isomerization rate expressions are provided above alongwith the equilibrium and rate constants in Tables 2-4.The space time for the mixed C6 system is defined on

the basis of the total feed rate of the three reactiveolefins, τ ≡ W/Folefins ) W/(F2M1P + F2,3DM2B + F2E1B).Then, the mass balance equation from eq 12 may bewritten in the form

subject to the intial conditions

The conversion vectors (Xk) are defined for the threeTHEE systems as

The ethanol mole fraction is related to the above-definedconversions by

For the feed olefins, the mole fractions are

Figure 3. Effect of temperature. Experimental and predicted: (a)etherification and (b) isomerization conversions with Ω1 ) Ω2 )Ω3 ) 3.15 (Ω ) 1.05) in the absence of any solvent. Open markersand dashed curves are for those at a space time τ ) 5.8 g‚h/moland solid markers and curves are for those at τ ) 15.2 g‚h/mol.

For THEE1 system (k ) 1):

X1,E ) xTHEE1/(x2M1P + x2M2P + xTHEE1)X1,I ) x2M2P/(x2M1P + x2M2P + xTHEE1) (8)

For THEE2 system (k ) 2):

X2,E ) xTHEE2/(x2,3DM1B + x2,3DM2B + xTHEE2)X2,I ) x2,3DM1B/(x2,3DM1B + x2,3DM2B + xTHEE2)

(9)

For THEE3 system (k ) 3):

X3,E ) xTHEE3/(x2E1B + xC3M2P + xT3M2P + xTHEE3)X3,IC ) xC3M2P/(x2E1B + xC3M2P + xT3M2P + xTHEE3)X3,IT ) xT3M2P/(x2E1B + xC3M2P + xT3M2P + xTHEE3)

(10)

1

Ω) ∑

j)1

3 1

Ωj

(11)

(dFk

dW) ) (Rk) ) [ν]k(r)k (k ) 1, 2, 3) (12)

(Rj)k ) (∑i)1

q

νijri)k (k ) 1, 2, 3) (13)

(R1) ≡ (RTHEE1R2M2P

)1

) (r1 + r2-r2 + r3 )

1(14)

(R2) ≡ (RTHEE2R2,3DM1B

)2

) (r1 + r2-r1 - r3 )

2(15)

(R3) ≡ (RTHEE3RC3M2PRT3M2P

)3

) (r1 + r2 + r3-r2 + r4 - r6-r + r5 + r6

)3

(16)

(dXk

dτ ) )Ωk

Ω(Rk) )

Ωk

Ω[ν]k(r)k (k ) 1, 2, 3) (17)

(Xk) ) 0 at τ ) 0 (k ) 1, 2, 3) (18)

(X1) ≡ (X1,E

X1,I), (X2) ≡ (X2,E

X2,I), (X3) ≡ (X3,E

X3,IC

X3,IT) (19)

xEtOH ) (1 - ∑k)1

3 Xk,E

Ωk)/Y (20)

4590 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997

For the olefins formed by THEE decomposition andisomerization

and the product THEEs mole fractions

while for any inert compounds in the feed stream

where

The molar ratio of ethanol to inert solvent, ΩI, may beexpressed in terms of the mole fraction of the reactiveolefins in the olefin stream (before being mixed with

alcohol), Q, and the molar ratio of ethanol to the olefins,Ω, i.e.,

If a pure olefin stream without any inert solvent isused to react with alcohol, then Q ) 1 and ΩI f ∞.The above mole fractions were utilized in the UNIFAC

method for estimating the activity coefficients, and theactivities were then used to compute each individualreaction rate from the rate constants with the pre-exponential factors and activation energies given inTables 3 and 4. Differential equations represented byeq 17 were numerically solved by the Runge-Kuttamethod for the initial conditions represented by eq 18.Effect of Temperature. With a feed consisting of an

equal fraction of 2M1P, 2,3DM2B, and 2E1B withoutany solvent, integral reactor experiments were con-ducted at space times τ ) 5.8 and 15.2 g‚h/mol,respectively. The molar ratio of ethanol to each of thethree C6 olefins, thus, was 3.15, leading to an overallmolar ethanol to olefins ratio of Ω ) 1.05. Theoreticalpredictions were also made as described above for theseconditions. The results are plotted in Figure 3a foretherification and in Figure 3b for isomerization conver-sions as a function of temperature. It is seen that theetherification conversions are in the following decreas-ing order: 2M1P > 2E1B > 2,3DM2B, a result expectedfrom the olefin stability and the order of variation oftheir reaction rate constants. Etherification and isomer-ization conversions are higher at higher space times atlow temperatures, but approach the same thermody-namic conversions when the temperature is increased.

Figure 4. Effect of space time at a temperature of 333 K.Experimental and predicted: (a) etherification and (b) isomeriza-tion conversions with Ω1 ) Ω2 ) Ω3 ) 3.15 (Ω ) 1.05) in theabsence of any solvent.

Figure 5. Effect of space time at 343 K. Experimental andpredicted: (a) etherification and (b) isomerization conversions withΩ1 ) Ω2 ) Ω3 ) 3.15 (Ω ) 1.05) in the absence of any solvent.

x2M1P ) (1 - X1,E - X1,I)/(Ω1Y)

x2,3DM2B ) (1 - X2,E - X2,I)/(Ω2Y) (21)

x2E1B ) (1 - X3,E - X3,IC - X3,IT)/(Ω3Y)

x2M2P ) X1,I/(Ω1Y)

x2,3DM1B ) X2,I/(Ω2Y) (22)

xC3M2P ) X3,IC/(Ω3Y)

xT3M2P ) X3,IT/(Ω3Y)

xTHEEk ) Xk,E/(ΩkY) (23)

xI ) 1/(ΩIY) (24)

Y ≡ 1 +1

Ω+

1

ΩΙ

- ∑k)1

3 Xk,E

Ωk

(25)

ΩI ) Ω( Q1 - Q) (26)

Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4591

The agreement between the experimental data andpredictions is very good.Effect of Space Time. The effect of reactor space time

was experimentally investigated at two different tem-peratures, 333 and 343 K, respectively. The feed molarratio of ethanol to each individual C6 olefin was alsoequal to 3.15, leading to an overall molar ethanol toolefins ratio of Ω ) 1.05. No solvent was present in thefeed. The experimental data are compared with thepredictions as shown in Figure 4 at 333 K and in Figure5 at 343 K, indicating very good agreement in each case.The conversions increase with space time, eventuallyapproaching the equilibrium conversions at higher spacetimes.Predicted Effect of Inert Solvent. In industry, the

stream containing reactive olefins usually containssubstantial amounts of other inert substances as well.Such inert species are not directly involved in theetherification or isomerization reactions, but will retardthese reactions by diluting the reactants. Two differentmole fractions of reactive olefins, i.e., Q ) 0.1 and 0.5(ΩI ) 0.1167 and 1.05, corresponding to Ω ) 1.05), wereused in calculations to simulate the effect of inertsolvent on the etherification conversion of reactiveolefins. Normal heptane was assumed to be the inertsolvent in the calculations, and the molar ratio ofethanol to C6 olefins (2M1P, 2,3DM2B, and 2E1B) wasassumed to be equal to 1.05. The etherification conver-sions are compared in Figure 6 as compared with theresults for Q ) 1 (i.e., no inert solvent) at the temper-ature of 333 K. The presence of an inert solventevidently decreases the etherification conversions ofolefins at a given space time.

Mixed C4, C5, and C6 Olefin Feed. A similarprocedure as above was followed in the analysis of theexperiments with a mixed C4, C5, and C6 olefin feed.Effect of Temperature. For these mixed ethers syn-

thesis experiments, a feed of isobutylene, 2M2B, and2M1P was fed to the upflow reactor without any solventin the feed stream for the simultaneous production ofETBE, TAEE, and THEE1. Integral experiments wereconducted at a space time τ of 6.1 g‚h/mol and anequimolar olefin feed with the overall ethanol to olefinmolar ratio of Ω ) 1.05. Using the procedure describedabove, the olefin conversions predicted agree reasonablywell with experiments, as shown in Figure 7. Conver-sions of olefins to ethers, shown in Figure 7a, increasewith increasing temperature until the conversion be-comes equilibrium-limited and then decline for theseexothermic reactions. It may be noted that the conver-sion of isobutylene to ETBE is substantially higher thanthat of other olefins to the corresponding ethers, fol-lowed by THEE1 and then TAEE. This order is inaccord with the order of the corresponding equilibriumconversions as shown by Zhang and Datta (1996) intheir Figure 5. Isomerization conversion of 2M2B and2M1P, shown in Figure 7b, increases with increasingtemperature.Effect of Space Time. Space time effects of the mixed

olefin feed with Ω ) 1.05 at a temperature of 333 K areshown in Figure 8. The predicted conversions shownby the solid lines are in good agreement for both theetherification and the isomerization conversions of thefeed olefins and approach equilibrium conversions at thehigher space times.

Figure 6. Effect of inert solvent. Predicted etherification conver-sions as a function of space time at 333 K with Ω1 ) Ω2 ) Ω3 )3.15 (Ω ) 1.05) as compared (a) between 50% and 100% and (b)between 10% and 100% olefins in stream. Solvent assumed isn-heptane.

Figure 7. Mixed ether production of ETBE, TAEE, and THEE1at different temperatures. Predicted and experimental conver-sions: (a) etherification and (b) isomerization for equimolar olefinfeed of isobutylene, 2M2B, and 2M1P (Ω ) 1.05).

4592 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997

Conclusions

It is shown here that the developed rate expressionsbased on LHHW formalism, with kinetic parametersseparately evaluated from experiments in differentialreactors, are reliable in predicting the integral behaviorof isothermal mixed ether systems, for example, for asystem of simultaneous THEE1, THEE2, and THEE3syntheses using a mixed C6 olefin feed stream. Theeffects of temperature and space time were experimen-tally investigated and theoretically simulated with goodagreement. Feed mixtures of C4, C5, and C6 olefins werealso studied for the simultaneous synthesis of ETBE,TAEE, and THEE and showed good agreement betweenpredictions and experiments. Etherification and isomer-ization conversions increase with space time at lowertemperatures; however, at higher temperatures equi-librium limitations are approached.It is thus concluded that a consistent set of expres-

sions based on the same mechanism are applicable tothe entire set of etherification and isomerization reac-tions for this family of reactions. The results of thispaper are of interest since commercial production ofmixed ethers for blending with gasoline is possible. Pureethers are, of course, not necessary for blending pur-poses, and mixed ethers should suffice so long as theblend requirements of octane number, oxygen content,and RVP are met.

AcknowledgmentThe funding provided for this work by the National

Renewable Energy Laboratories and the Iowa CornPromotion Board is gratefully acknowledged.

NomenclatureA, B, C, D ) ethanol, R-olefin, â-olefin, ether, respectivelyAi ) pre-exponential factor of reaction i, mol/(h‚g)

aj ) activity of species j, ≡ γjxj ) γjCCjCj ) concentration of species j, mol/dm3

Ct ) total acid site concentration of Amberlyst 15, mequiv/gkB ) Boltzmann’s constant, 1.38 × 10-23 J/KEi ) activation energy of reaction i, kJ/molFj ) molar flow rate of species j, mol/hh ) Planck’s constant, 6.626 × 10-34 J‚ski ) rate constant of surface reaction (rds) of reaction i,mol/(h‚g)

kri, ksi) effective rate constant of reaction i, mol/(h‚g)Ki ) liquid-phase thermodynamic equilibrium constant ofreaction i

KA ) adsorption equilibrium constant of A )27 exp[11 000(1/T - 1/303)/R]

ri ) rate of reaction i, mol/(h‚g)(r)k ) reaction rate vector for the ether system kR ) gas constant, 8.314 J/(mol‚K)Rj ) rate of production of species j(Rk) ) rate of production vector for the THEE system kT ) temperatureW ) weight of catalyst, gxj ) mole fraction of species jX1,E ) etherification conversion of 2M1P to form THEE1X1,I ) isomerization conversion of 2M1P to form 2M2PX2,E ) etherification conversion of 2,3DM2B to form THEE2X2,I ) isomerization conversion of 2,3DM2B to form2,3DM1B

X3,E ) etherification conversion of 2E1B to form THEE3X3,IC ) isomerization conversion of 2E1B to form C3M2PX3,IT ) isomerization conversion of 2E1B to form T3M2P(Xk) ) conversion vector for the THEE system k

Greek Letters

κ ) transmission coefficientνij ) stoichiometric coefficient of species j in reaction i[ν]k ) stoichiometric coefficient matrix of the ether systemk

ν ) universal frequencyτ ) space time of olefin, h‚g/molΩj ) molar ratio of ethanol to olefin jΩI ) molar ratio of ethanol to inert I

Subscripts

1, 2, 3 ) reactions 1, 2, 3, respectivelyA, B, C, D ) ethanol, R-olefin, â-olefin, ether, respectivelyi ) of reaction ij ) of species jk ) THEE system k. k ) 1 (THEE1); k ) 2 (THEE2); k )3 (THEE3)

Abbreviations

2M1B ) 2-methyl-1-butene2M2B ) 2-methyl-2-butene2M1P ) 2-methyl-1-pentene2M2P ) 2-methyl-2-pentene2,3DM1B ) 2,3-dimethyl-1-butene2,3DM2B ) 2,3-dimethyl-2-butene2E1B ) 2-ethyl-1-buteneC3M2P ) cis-3-methyl-2-penteneT3M2P ) trans-3-methyl-2-penteneETBE ) ethyl tert-butyl etherIB ) isobutyleneLHHW ) Langmuir-Hinshelwood-Hougen-WatsonMASSA ) the most abundant surface species assumptionMON ) motor octane numberMTBE ) methyl tert-butyl etherrds ) rate-determining stepRFG ) reformulated gasolineRON ) research octane numberTAEE ) tert-amyl ethyl etherTSC ) transition-state complexTTST ) thermodynamic interpretation of the transition-state theory

Figure 8. Effect of space time on the olefin conversion. Predictedand experimental conversions: (a) etherification and (b) isomer-ization for equimolar olefin feed of isobutylene, 2M2B, and 2M1P(Ω ) 1.05).

Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997 4593

THEE ) tert-hexyl ethyl etherVOC ) volatile organic compoundsWHSV ) weight hourly space velocity, h-1

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Received for review February 4, 1997Revised manuscript received August 14, 1997

Accepted August 24, 1997X

IE970099R

X Abstract published in Advance ACS Abstracts,October 15,1997.

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