Ind. Eng. Chem. Res. 1991,30, 1469-1478
1469
Survey of Recent Cyclohexane Pyrolysis Literature and Stoichiometric Analysis of Cyclohexane Decomposition Francis Billaud,* Marc Duret, Khalid Elyahyaoui, and Frangois Baronnet Departement de Chimie-Physique des Rbactions, URA 328 CNRS, ENSIC-INPL, 1, rue Grandville BP 451, F 54001 Nancy Ceder, France
This paper describes the present knowledge on cyclohexane pyrolysis since the literature on the pyrolysis of cycloalkanes is rather scarce compared to that published on alkane pyrolysis. The present paper summarizes the principal papers published on the subject; we mention, for each analyzed paper, the operating conditions, the type of reactor, and the main results (reaction order, temperature influence, reactions accounting for the reaction products, etc.). After this review of the significant papers, we discuss the corresponding resulb and their limits; we also give a synthetic view of the effect of additives on cyclohexane cracking, and we propose a synthetic mechanism and a stoichiometric analysis of the thermal decomposition of cyclohexane.
Introduction The thermal cracking of naphthenes and high molecular weight paraffins is of prime significance in petrochemical processes. Because cyclohexane is one of the c y c l d a n e s present in appreciable amounts in naphtha or gas oil, it is the most frequently chosen model feedstock in the naphthene pyrolysis investigations. Different experimental studies have been achieved in the past 20 years, but it is difficult to find reviews that lay out a comprehensive synthesis of all the reported data and results. Therefore this review will try to compile cyclohexane pyrolysis data for those who are interested in this area. The review is based on literature published in technical journals. Attention is given to literature published after 1960, since surveys of earlier works are available. The different techniques used in various investigations in the steady or dynamic state use, besides conventional tubular cracking reactor, other techniques such as singlepulse shock tube, fluidized quartz bed, etc. The leading research projecta since 1960 are summed up and presented in Table I. This table gives the operating conditions, the principal results, and the kinetic constants of elementary proceases or overall reactions. In this review, mechanisms of cyclohexane pyrolysis are presented first, followed by a review of the principal results obtained and a synthesis of the effects of additives. Mechanisms The main difference met in the literature concerning the cyclohexane cracking mechanism is obviously the ringopening isomerization leading to open-chain alkenes. Assumptions are made about mono- and biradical and molecular mechanisms. Kalinenko et al. (1976) presented several ways of ringopening: through an open-chain biradical or through a monoradical that leads to a l-hexene monoradical. The mechanism for the primary step is given in Scheme I. Tsang (1978) and Brown et al. (1986) suggested that the main initial processes of cyclohexane pyrolysis involve isomerization of cyclohexane to l-hexene, followed by decomposition of l-hexene (Scheme 11). From comparative rate experiments the following rate expressions have been derived: kl = 1016-7exp(-44400/RT) 5-1 kz = 1016-8exp(-35600/RT) s-l k3 = 1012.6exp(-28900/RT) s-l
* To whom correspondence should be addressed.
Scheme I
f.\
R
+()A( ) ' + R H
Scheme 11. Initiation
C3Hs'-
C3H4
+ H'
In fact, with respect to a more detailed mechanism, Ill& et al. (1969) assumed that intermediates involving biradicals would appear to be the most likely candidates. The steps are cyclohexane n-hexyl diradical- l-hexene The l-hexene bond-breaking reactions lead to an allylic resonance energy of 42.7 kJ mol-' and a heat of formation of allyl radicals of 176.6 k J mol-' (300 K). There appear to be general relations relating the rate expression for the
-
0888-5885/91/2630-1469$02.50/0 Q 1991 American Chemical Society
1470 Ind. Eng. Chem. Res., Vol. 30,No. 7, 1991
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1474 Ind. Eng. Chem. Res., Vol. 30, No. 7, 1991 decomposition of alkynes, alkanes, and alkenes. On the same basis, Korzun et al. (1979) drew the conclusion that since the formation of monoradicals is difficult, the reaction proceeds as follows during the initial period:
Scheme 111
0-0 0-C
c.-
n+=
The rate constant for this reaction is of the order of magnitude of 10" exp(-75000/RT) s-l, where 75 kcal mol-' is the energy of the C-C bond in the cyclohexane molecule. As the olefins accumulate, chain initiation via reactions of the following types become possible: C4H8 C3H5' + CH3' -+
Scheme IV
0
Since the reactions of active radicals with a C-H bond conjugated with a K bond in olefin molecules are faster than the reaction with cyclohexane (the bond strengths rate respectively 77 and 95 kcal mol-'), alkylic radicals are mainly formed subsequently: C4HB + CH3' CH4 + CH24HCHCH3
-
A
Then cyclohexane decomposes:
CHZ=CH-dH-CH3+
0+
CJI*+
0'
. When allylic radicals recombine, chain termination takes place; for example CH2=CHCHCH3 chain termination
-
Virk et al. (1979) detailed the existence of a cyclohexyl radical in the propagation sequence. This radical leads by 8 scission and ring-opening to the isomeric 1-hexen-6-yl radical, with decomposition continuing as shown to yield ethylene, 1,3-butadiene, and a hydrogen atom that is the chain carrier. This is the rather well-established primary pathway for cyclohexane, which can be subject to branching, leading to stable intermediate radicals; these stable molecules then undergo further pyrolysis reactions to yield a spectrum of pyrolysis products, e.g., methane and propylene, which are seen in smaller amounts during cyclohexane pyrolysis. The overall pathway is therefore as shown in Scheme 111. Arabike et al. (1981) proposed for the cyclohexane pyrolysis a detailed free-radical mechanism on the basis of Rice-Kossiakoff free-radical theory (Kossiakoff, A,; Rice, F. 0. J. Am. Chem. SOC.1943,65,590). They studied all the cases of cleavage of the C-C bond at the p position relative to the unsaturated valence bond, and Scheme IV resulted.
i
A
Principal Results Obtained Reaction Order. Nearly all the studies concerning cyclohexane cracking agree with the fact that the overall decomposition reaction is a first-order kinetic. Arabike et al. (1988) emphasized that over 820-860 "C, the reaction was governed by second-order kinetics. The actual mechanism for the autocatalytic conversion of cyclohexane at lower temperature (700-800 "C) may be attributed to the participation of allyl radical in a new bimolecular propagation sequence. This autocatalytic decomposition was described before by Susu (1982). It is quite possible that the initial reaction is first order. The reaction may be accelerated in a second-order process involving the participation of unsaturated free radicals generated in the initiation propagation. The second-order reaction would then occur with a lower activation energy. It appears that the new chain-propagating step may involve methyl allyl radical formed in a new initiation step as follows: H' + C4Hs C4H7. This is suggested by the presence of relatively high concentrations of hydrogen and the large drop in 1,3-butadiene selectivity. Influence of Temperature and Conversion on the Decomposition Products. The product distribution of cyclohexane pyrolysis under given reaction conditions depends on the temperature and conversion. Arabike et al. (1981) concluded that the yields of gaseous products increase with increasing conversion and the differences in the amounts of products at the same conversion level but different cracking temperature are insignificant (Figure
-
1).
Levush et al. (1969) and Arabike et al. (1981) agreed that the product distribution of cyclohexane decomposition consists of a considerable amount of ethylene, butadiene,
Ind. Eng. Chem. Res., Vol. 30, No. 7,1991 1475 ""
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Cyclohexane conversion (YO) Figure 1. Gas production as a function of cyclohexane conversion at different temperatures (Arabike et al., 1981).
propylene, methane, and hydrogen. Small quantities of ethane, propane, and butenes are also produced. The liquid is predominantly cyclohexane, with traces of benzene, cyclohexene, and toluene; this is an indication that some deshydrogenation reactions are occurring to a slight extent. Selectivities of ethene, butadiene, ethyne, ethane, and l-butene generally increased with increasing cracking temperature; those of propene and methane appear to be slightly independent of temperature. Ethene selectivity tends to pass through a maximum and minimum with increasing residence time at higher pyrolysis temperatures; it increases with residence time at lower temperatures. However, l,&butadiene selectivity behavior exhibits opposite trends. Synthesis of the Effects of Additives Dilution by Inert Gases o r Decrease of Initial Pressure. It induces the absence of self-inhibition effects of some of the pyrolysis products. The presence of excess diluent reduces the partial pressure of reacting components. This reduction in partial pressure in turn considerably reduces the progress of secondary reactions. Gerg et al. (1945) investigated the use of a diluent by cracking hydrocarbon in the presence of steam. Little difference in results was observed between the runs with or without steam. A small increase in the optimum amount of butadiene from cyclohexane was noted. The advantage of using a diluent appeared to be principally as a means of attaining the high temperature quickly and the required short contact time. Dilution by Hydrogen. The effect of diluting hydrogen in the hydrocarbon charge was analyzed by Korzun et al. (1979). The conclusion of this work is that hydrogen accelerates significantly the decomposition of cyclohexane, and the reaction in the presence of hydrogen is first order with respect to both cyclohexane and hydrogen. The effective rate constant for the decomposition of cyclohexane exp(-576OO/RZ') c'. in an atmosphere of hydrogen is The composition of the cyclohexane decomposition products changes significantly: the yields of l-butene, ethane, and methane increase, those of butadiene and ethylene decrease, and the yield of propene remains constant. According to Korzun et al. (1979) the acceleration by hydrogen of the decomposition of cyclohexane can be ex-
plained by the fact that the reactions of active radicals CH;, CzH6*, and CH2=CHCH2CH2' with hydrogen are faster than those with hydrocarbons, and the reactions of the atomic hydrogen, formed in this process, with hydrocarbons are many times faster than the reaction of the hydrocarbons radicals. The occurrence of the fast reactions of the CH3', CzH;, and CHz=CHCH2CH2'radicals with Hz explains the observed increase of the yields of methane, ethane, and butene and the decrease of the yields of ethylene and butadiene. Effects of l-Hexene. The thermal decomposition of cyclohexane studied by Korzun et al. (1979) showed that in agreement with Kuchler's study (1939) the cracking is proceeding with an induction period during which the rate of reaction is extremely low. The marked self-acceleration of the cracking of cyclohexane can be accounted for either by the accumulation of a product whose decomposition sharply facilitates chain initiation or by the accumulation of hydrogen formed on decomposition in considerable amounts. In mixtures with l-hexene the pyrolysis of cyclohexane takes place without an induction period, the reaction is appreciably accelerated, and the decomposition is first order with respect to cyclohexane and order l/z with respect to l-hexene. The activation energy in the presence of l-hexene is equal to that found without added olefin within experimental error (56.9 kcal mol-'). It is established that the kinetics of the decomposition of l-hexene are not influenced by cyclohexane within the limits of experimental error. Surface Effects. Coke deposition on the reactor wall is a serious problem that makes the study of the kinetics and mechanism of thermal cracking of hydrocarbons difficult. There is a continuous change in the surface properties of the reactor as coke is mainly deposited on the reactor wall. This causes a continuous change in the composition of the product distribution. The reproducibility of the measurements, which requires constant reactor conditions, can be improved by decreasing the partial pressure of the compounds involved in the reaction by addition of an inert diluent. Another possibility is the passivation of the inner reactor surface with surface-active agents. Discussion and Proposal of a Mechanism. Stoichiometric Analysis of Cyclohexane Decomposition at Time Zero Many hypotheses were made concerning mono- and biradical and molecular mechanisms. According to Brown et al. (1986) ring-opening isomerization of cyclohexane via a biradical mechanism leads to only one primary chain of alkene formation, namely, l-hexene: C-CgH12 = 1-C6Hiz
In fact after an induction period, the cyclohexane pyrolysis becomes l-hexene pyrolysis. Our experimental results permit us to show that the only pathway leading to the methane formation is the pathway c-C6HlZ l'C6H12 (Figure 2). We can obtain five stoichiometric equations by combination of the elementary radical steps: C6H12 = 2-C3H6 (1) C6H12 = CH4 + C6H8 (11) C6Hiz = 1,3-C4H6 + C2H4 + H2 (111) C6H12 = 3-C&4 (IV) (VIII) C6H12 = C4HB + C2H4
-
(2)
0 scission
Let us now consider the transformations of the 'C4H7 radical: Hydrogen abstraction from a cyclohexane molecule to give 1-butene: CH2~CH.CH2.CH2.CH2.Cnz[.)
c
'
4
CZM
J.0- 9+0*
P.C4H7(.)
/I
1-C4H8
Figure 2. Mechanism for 1-hexene decomposition.
From literature data [Levush et al. (1969); Arabike et al. (198l)l and by taking into account the results of our former experiments, it becomes possible to define the main primary products of the thermal decomposition of cyclohexane: H2, CHI, C2H2,C2H4, C2H6, C&, C4H6, C&, CBHB,and c-C6HIo. To explain the formation of the other products, we propose as Arabike et al. (1981) a more complete mechanism including all the rapid isomerizations of the biradical 'C6H1; that induce by hydrogen transfer for any biradical the hexyl radical, for example
0- c.+O c. 0' +
I O - c- J ("I hexene 1
The cyclohexyl radical could lead to the stoichiometric equation (VI) by abstraction of a hydrogen atom.
0'0
tH.
(R .) I
>- >
I
Formation of l,&butadiene by H' abstraction: I
I
I
I
cydohexene
0
The cyclohexyl radical can decompose by scission of C-0 bond in the 6 position by reference to the carbon bearing the unpaired electron:
0-9 According to the usual rules of free radical chemistry, we can write the following elementary steps: (1) Hydrogen abstraction
The radical
can also isomerize: I
I
I
I
1,5 hexadiene
+He
Ind. Eng. Chem. Res., Vol. 30, No. 7, 1991 1477
This isomerization leads to the following stoichiometries:
.
H.+
0- 0
+H2
. +
CZY
All these elementary steps lead to a satisfactory account of the thermal decomposition of cyclohexane by 10 main primary stoichiometric equations: C6Hlz = 2’C3H6 (1) C6H12 = CH4 + C& (11) C6H12 = 1,3-C4H6 + CzH4 + Hz (111) CeH1.2 = 3-CzH4 (IV) C6H12 = l’C6H12 C6H12 = C-CsHlo + H2 C6Hiz = 1,5-C6H10+ Hz C6Hlz = l-C4H8+ CzH4 CeHlz 2-CzH4 + CzH2 + Hz C6H12 = 1,3’c&10 + Hz C6H12 = 1,3-C4H6 + C&
(VI (VI) (VII) (VIII)
(1x1 (XI (XI)
Stoichiometric Analysis of Cyclohexane Decomposition at Zero Time In general, a substance such as cyclohexane undergoes several simultaneous reactions. It is then necessary to introduce the notion of independent constituents. Consider a reactor containing n constituents, among which none is chemically inert under the experimental conditions. All are formed from m elements and are liable to appear in s stoichiometric independent equations. (In complex systems, one can check that the equations written are indeed independent, using the Jouguet criterion (1921).) For a given system, the exact nature of these independent constituents is not determined in an absolute way, for if several noninert substances are linked by a chemical reaction, any of them can be obtained from the others, inside the system itself. Conversely, the number of independent constituents is rigorously determined, and it is characteristic of the considered system. The same conclusion holds for the number s = n - c of independent stoichiometric equations, but as for independent constituents, the choice of stoichiometric equations is not fixed in an absolute way, for a linear combination of stoichiometric equations is also a stoichiometric equation. This
emphasizes that the equation thus written in no way represents the mechanisms of the reactions actually occurring in the reactor. Thus, the stoichiometric descriptions of a chemical system requires that n constituents that are thought to be needed to describe the system be fixed (for instance, those that have been experimentally detected). Then, a group of s stoichiometric equations are written. There will be c = n - s independent constituents. If the system further includes chemically inert constituents, these will be a priori independent constituents. This is the case of purely physical systems, in which chemical reactions are excluded by definition. For simple chemical systems, the choice of stoichiometries and independent constituents presents no difficulties. Conversely, for complex systems, some reaction may be easily forgotten. Thus, it is important to have a criterion that allows one to fix a priori the number s of independent stoichiometries existing between the n considered constituents without writing any of them. Brinkley’s criterion (1946) allows one to determine the number c of independent constituents. Brinkley’sCriterion. The number c of independent constituents of a chemical system is equal to the rank of the matrix of the indexes of the elements in the formula of the constituents. Inert constituents are considered as independent. For cyclohexane, the constituents are (apart from cyclohexane) hydrogen, methane, ethane, ethylene, acetylene, propene, l-butene, 1,3-butadiene, l,Cpentadiene, and cyclohexene. Thus, n = 11 constituents, denoted in the following matrices by the symbols Hz, C1, Cz, C2=, C p , Cs, C4, C41.3,C6, c6=, and c6 for cyclohexane. The two elements are H and C. The indexes of elements in the formula of constituents are given in matrix I (Table 11). The maximum order extracted of any nonzero determinant extracted from the matrix I is 2. Thus, from Brinkley’s criterion, there are c = 2 independent constituents. Hence, s = n - c = 11 - 2 = 9 independent stoichiometric equations. Kinetic considerations have led us to write 11 stoichiometric equations. It must be checked by Jouguet’s criterion (1946) that these 11stoichiometric equations are independent. Jouguet’s Criterion. s stoichiometric equations are independent if the rank of the matrix of coefficients is equal to s. In the case of cyclohexane, only the eight stoichiometric equations (I)-(IV), (VI), (VIII), (IX), and (XI) are independent. Since the system must be described by nine independent stoichiometric equations, a ninth stoichiometric equation is necessary to describe the thermal decomposition of this cycloalkane: CsHlz = C3H6 + CH4 + C2Hz (0) The (9,9) determinant of matrix I1 (Table 111) is different from 0 and is of order 9. Thus the nine stoichiometric equations are independent and describe the decomposition of cyclohexane: C6H12 C3H6 + CH4 + CzHz (0) CeH12 = 2-CsH6 (1) C6H12 = CH4 + C5H8 (11) C ~ H =~ 1,3-C4& Z + CzH4 + H2 (111) CsHl2 = 3-CzH4 (IV) CeH12 = C-CeHlo + Hz (VI) C6H12 = l-C4H8+ C2H, (VIII) C6Hl2 2-CzH4 + CzH2 + Hz (1x1
Ind. Eng. Chem. Res. 1991,30, 1478-1485
1478
CeH12 = 1,3-CdH*+ C&
(XI)
Regirtry No. Cyclohexane, 110-82-7.
Literature Cited Aribike, D. S.; Susu, A. A. Kinetics of the pyrolysis of cyclohexane using the pulse technique. Znd. Eng. Chem. Res. 1988, 27, 915-920.
Aribike, D. S.; Susu, A. A,; Ogunye, A. F. Mechanistic and mathematical modeling of the thermal decomposition of cyclohexane. Thermochim. Acta 1981,51,113-127. Berg, L.; Summer, G. L., Jr.; Montgomery, C. W.; C o d , J. Naphtene pyrolysis for butadiene. Znd. Eng. Chem. 1946,37,352-365. Brinkley, S . R. CriGre de Brinkley. J. Chem. Phys. 1946, 14, 563-586.
Brown, T. C.; King, K. D.; Nguyen, T. T. Kinetics of primary proceesee in the pyroly~iaof cyclopentanes and cyclohexane. J.Phys. Chem. 1986,90,419-424. F a b w , B. M.; Kafesjian, R.; Smith, J. 0.; Satterfeld, C. N. Thermal decomposition rates of saturated cyclic hydrocarbons. Znd. Eng. Chem. Process Des. Dev. 1964,3,248-254. Ill&, V.;Pleszkats, I. Pyrolysis of liquid hydrocarbons, Kinetics of thermal decomposition of binary and ternary mixtures of n-Heptane, Isooctane and Cyclohexane. Acta Chim. Acad. Sci. Hung. 1974,80(3), 247-266.
Jouguet, E.Thermodynamique Chimique. J. Ec. Polytech. (Paris) 1921, 21, 61.
Kalinenko, €3. A.; Nametkin, I. S. Lee concentrations des radicaux dans la zone de pyrolyee des hydrocarbures CBde structure div-
e m . Neftekhimija 1981,21,391-398. Kalinenko, R.A.; Shevel’kova, L. V.;Titov, V. B.; Bakh, G.; Novak, Z.Kinetics relations of pyrolysis of cyclohexane mixed with pardin hydrocarbons. Neftekhimija 1976,16,100-106. Korzun, N. V.; Magaril, R. Z.; Malzarenko, I. S.; Trushkova, L. V. Sur le mecanisme de 1’ aubacc616ration de la disaociation thermique de certain8 Hydrocarbures. Neftekhimija 1979, 19, 541-547.
Korzun, N. V.; Magaril, R. Z.; Plyusnina, G. N.; Semukhina, T. I. Influence of hydrogen and hex-l-ene on the thermal decompoeition of cyclohexane. Rws. J. Phys. Chem. 1979, 53, 631-634. Kiichler, L. Homogeneous Thermal Decomposition of some cyclic Hydrocarbons. Trans. Faraday SOC.1939,35,874. Levush, S. S.; Abadzkev, S. S.; Shevchuk, V. U.Pyrolysis of cyclohexane. Neftekhimija 1969, 9, 716-721. Susu, A. A. Autocatalytic decomposition of n-eicosane in alkali-catalyzed CO-H,O systems. Niger. J . Eng. Technol. 1982,5,11-19. Tsang, W . Thermal stability of cyclohexane and 1-hexene. Znt. J. Chem. Kinet. 1978,10, 111%1138. Virk, P. S.; Korosi, A.; Woebcke, H. N. Pyrolysis of unsubstituted mono-, di-, and tricycloalkanes. Thermal Hydrocarbon Chemistry. Adu. Chem. Ser. 1979,67-76. Zimmerman, G.;Zychlinski,W.; Bach, G.; Rennecke, D. Zur Pyrolyse unsubstituierter Cyclane-Produktbildungsselektivitiiten,kine&he Parameter, mechanistische Interpretation. J.R a k t . Chem. 1985,327, 10-20.
Receiued for review July 6 , 1990 Revised manwcript received December 26, 1990 Accepted January 6,1991
Mechanism and Kinetics of the Acid-Catalyzed Formation of Ethene and Diethyl Ether from Ethanol in Supercritical Water Xiaodong Xu, Carlos
P.De Almeida, a n d Michael Jerry Antal, Jr.*
Department of Mechanical Engineering and the Hawaii Natural Energy Institute, Uniuersity of Hawaii at Manoa, 2540 Dole Street, Holmes Hall 305, Honolulu, Hawaii 96822
Ethene and diethyl ether are the only reaction products of the acid-catalyzed decomwition of ethanol in water a t 386 O C (T,= 1.02) and 34.5 MPa (P,= 1.56). The speed and high selectivity of this reaction create possibilities for farmers to convert fermentation beer directly to ethene at high pressure without prior distillation of the beer. This paper presents a kinetic model of the dehydration chemistry, which can be used for reactor design and scaleup. Ethene formation is kinetically consistent with E2 mechanisms involving protonated ethanol and protonated diethyl ether. Diethyl ether formation is kinetically consistent with an S Nmechanism ~ involving ethanol and protonated ethanol, operating simultaneously with an AdE3 mechanism involving ethanol, ethene, and acid. Introduction Over 300 million gal of ethanol are produced annually in the USA, and its use aa a fuel or chemical feedstock continues to excite the imaginations of farmers, engineers, and policy makers worldwide. Unfortunately, the concentration of ethanol in the “beernproduct of a fermenter rarely exceeds 4 mol-dm-a; consequently the cost of separating and producing fuel-grade ethanol is high. To obtain a more valuable product, some researchers (Winter and Eng, 1976;Pearson et al., 1980;Bijlani et al., 1981)have begun to explore the potential of novel processes for manufacturing ethene from ethanol. The production of poly(viny1 chloride) from ethene appears to be a particularly profitable activity for ethanol producers (Halvorsen, 1990). Early work (De Almeida, 1986; Antal et al., 1987)in this laboratory demonstrated the rapid and highly selective formation of ethene from ethanol in supercritical water at 386 OC and 34.5 MPa with very low (0.001-0.03mol.dm+) concentrations of sulfuric acid catalyst. This discovery suggested the possibility of feeding acidified fermentation
beer (without prior distillation) directly into a supercritical flow reactor. Phase separation of ethene from water at the reactor exit would reduce the cost of product separation, and the ethene would be available at high pressure. Further work (Ramayya et al., 1987)showed that when the concentration of the feed ethanol was kept below 0.5 m ~ l - d m -only ~ , ethene was detected as a product in the effluent of the flow reactor. At higher reactant concentrations, diethyl ether waa also detected as a reaction product. To optimize the design of a commercial supercritical flow reactor, a model is needed that can predict the product composition exiting the reactor. The goal of this paper is to detail such a model. Because simple engineering models (De Almeida, 1986) were unable to describe the dependence of product yields on reactant concentrations and reaction conditione, we found it neceesary to consider a complex reaction network comprising a detailed knowledge of the elementary steps involved in the dehydration reactions. In spite of the fact that a popular undergraduate text (Morrison and Boyd, 1978) uses an E l mechanism to describe the acid-cata-
0888-5885/91/2630-1478$02.50/00 1991 American Chemical Society
