Ind. Eng. Chem. Res. 1988,27, 1966-1971
1966
is done in such a way that the agreement between simulated and experimental product distributions is optimal.
Conclusions It has been shown that, in reaction schemes with large numbers of mechanistically similar reactions, transitionstate theory can be successfully used to calculate frequency factors. Theoretical uncertainties have led to the introduction of parameters, which can then be used to optimize the values of the frequency factors with respect to experimental results. The above method is only advantageous if the same group of parameters can be used to calculate the frequency factors of a large group of similar reactions. In this case, the number of parameters to be optimized is reduced in a very significant way. The statistical significance of the parameters is increased by the fact that every parameter is used in many different reactions. A lack of direct experimental information for a given reaction does not necessarily result in insignificant parameter values because the same parameters are used in many other reactions. Nevertheless, experimental data on the cracking of various types of hydrocarbons over a wide range of operating conditions are an absolute necessity. Acknowledgment P. A. Willems is grateful to the Belgian “Nationaal Fonds voor Wetenschappelijk Onderzoek” for a Research Assistantship over the period 1982-1986. Literature Cited Benson, S. W. Thermochemical Kinetics, 2nd ed.; Wiley: New York, 1976. Cohen, N. “The Use of Transition State Theory to Extrapolate Rate Coefficients for Reactions of OH with Alkanes”. Int. J . Chem. Kinet. 1982, 14, 1339-1362.
Edelson, D.; Allara, D. L. “A Computational Analysis of the Alkane Pyrolysis Mechanism: Sensitivity Analysis of Individual Reaction Steps”. Int. J . Chem. Kinet. 1980,12,605-621. Eyring, H. J. Chen. Phys. 1935a, 3, 107. Eyring, H. “The Activated Complex and the Absolute Rate of Chemical Reactions”. Chem. Rev. 193513, 17, 65. Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and Design; Wiley: New York, 1979. Glasstone, S.; Laidler, K. J.; Eyring, H. The Theory of Rate Processes; McGraw-Hill: New York, 1941. Goossens, A. G.; Dente, M.; Ranzi, E. “Rigorous Prediction of Olefin Yield from Hydrocarbon Pyrolysis through Fundamental Simulation Model (SPYRO)”. Presented at the 12th European C.A. C.E. Symposium, Montreux, Switzerland, April 8-11, 1979. Hirschfelder, J. 0. ‘Simple Method for Calculating Moments of Inertia”. J . Chem. Phys. 1940, 8, 431. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids,3rd ed.; McGraw-Hill: New York, 1976. Scharfe, M.; Ederer, H. J.; Stabel, U.; Ebert, K. H. “Modeling of n-Hexane Pyrolysis: Experimental Investigation in a Flow Reactor at Normal Pressure”. Ger. Chem. Eng. (Engl. TransE.)1985, 8, 119-129. Sundaram, K. M.; Froment, G. F. “1. Thermal Cracking of Ethane, Propane and Their Mixtures”. Chem. Eng. Sci. 1977a, 32, 601. Sundaram, K. M.; Froment, G. F. “2. Cracking of I-Butane, N-Butane, and Mixtures EthanePromne-N-Butane“. Chem. Eng. Sci. 197713, 32, 609. Sundaram. K. M.: Froment. G. F. “Modeling of Thermal Cracking Kinetics. 3. Radical Mechanisms for t i e Pyrolysis of S i m p i Paraffins, Olefins and Their Mixtures”. Ind. Eng. Chem. Fundam. 1978, 17, 174-182. Sundaram, K. M.; Froment, G. F. “A Comparison of Simulation Models for Empty Tubular Reactors”. Chem. Eng. Sci. 1979,34, 117-124. Willems, P. A.; Froment, G. F. “The Calculation of the Rotational Contributions to the Standard Entropy of Hydrocarbons by Means of a Monte Carlo Simulation Technique”. Unpublished results, 1988.
Received for review April 6, 1988 Accepted July 25, 1988
Kinetic Modeling of the Thermal Cracking of Hydrocarbons. 2. Calculation of Activation Energies Paul A. Willems and Gilbert F. Froment* Laboratorium voor Petrochemische Techniek, Rijksuniversiteit Gent, B-9000 Gent, Belgium
The kinetic modeling of the thermal cracking of hydrocarbons is based upon a free-radical reaction scheme containing several hundred reactions. The most important problem to be solved hereby is to assign values to the corresponding reaction rate constants. A group contribution type of method is introduced for the calculation of activation energies. The contributions are based on an analysis of the mechanism of the reactions and on the relative stabilities of the reacting species. A thermodynamic analysis of the reaction network leads to relationships between these contributions and reduces their number. A literature data base provides numerical values for the contributions. The thermal cracking of hydrocarbons proceeds through a free-radical chain mechanism. The reactions can be classified into six groups: initiation and termination, hydrogen abstraction, radical addition and decomposition, and isomerization. Listed in this order they form four groups of reversible reactions: termination is the opposite process of initiation and addition the opposite of decomposition. The application of these mechanism to the thermal cracking of light hydrocarbons is rather straightforward, but it results in a list of some 500 reactions. Assigning values to the corresponding 500 reaction rate constants is the more difficult part of the construction of the kinetic model.
The procedure for the calculation of the frequency factors is discussed in the preceding paper in this issue (Willems and Froment, 1988). The present paper focuses on the calculation of the activation energies.
Reaction Rate Constants and Thermodynamics The thermodynamic equilibrium constant, K,, of a reversible reaction is calculated from --AGO = RT In (K,)
(1)
and can explicitly be written in terms of standard enthalpies and entropies as follows:
0888-5885/88/2627-1966$01.50/0 0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 1967
AH"
In (K,) = -RT
AS" +R
In many cases, the equilibrium constant is related to a standard state in concentration units. The relation between both constants is
K, = Kc(RfT)Au
(3)
where Av is the change in number of moles during the reaction. The equilibrium constant is also related to the reaction rate constants of forward and backward reactions. For an elementary reaction, this relation is Kc = kcf/kcb (4) Accounting for eq 2 and 3 and the Arrhenius dependence of the reaction rate constants, eq 4 becomes
AS" --AH" + - Av In ( R ' T ) = In
RT
R
(2)
- Ecf
-
RT (5)
Introducing the definitions R T 2 d In ( K c ) / d T= A U o
R T 2 d In (kcf)/dT = Ecf
(6)
R T 2 d In ( k c b ) / d T = E c b leads to the final relation between Arrhenius parameters and thermodynamic state functions: Ecf- Ecb = AH" - AvRT In (Acf/Acb) = A S o / R - Av(1 + In ( R T ) ) (7)
Calculation of Activation Energies by Means of "Structural Contributions" The calculation of thermodynamic state functions by means of group contributions is well established. Benson (1976) lists contributions for the calculation of standard enthalpies of formation and standard entropies for different types of components. The calculated thermodynamic state functions are found to be in good agreement with experimental values. For a reversible reaction, the difference in activation energy between the forward and backward reaction is equal to the change in standard enthalpy of the reaction (eq 7). From this it can be expected that the activation energies can also be calculated by means of a group contribution method. The basic principles for the calculation of activation energies by means of structural contributions were already applied by Rice and Kossiakoff (1931, 1943) in their pioneering papers on the thermal cracking of hydrocarbons. Since the bond strength of all primary H atoms and all secondary H atoms is approximately the same, they concluded that there must be a constant difference in activation energies between the abstraction of a primary and that of a secondary H atom. When this type of analysis is applied in full detail to the reaction scheme, a series of differences in activation energies is obtained. In the present paper, a simple reaction is taken as a reference in each class of reactions. The activation energy of this reaction is called the reference activation energy, Erenand the activation energy of any other reaction pertaining to this class is obtained by adding corrections to E,& These account for the structural differences between the reactants and produces of a given reaction and those of the reference reaction. This is the reason why the group contributions are called "structural contributions to the activation energy".
Before discussing the details of this method, one simplification has to be made: it is generally accepted that the activation energy for radical recombination reactions (terminations) must be equal to zero. A termination reaction is the reverse process of an initiation reaction. considering eq 7 with E c b = 0 and Av = -1 yields for the activation energy of an initiation reaction E,(initiation) = AH"(initiati0n) + RT (8) With the standard enthalpies of formation calculated from Benson's group contribution method, eq 8 yields the activation energy of initiation reactions. An average temperature T,,, = 750 "C (1023 K) is used in RT. This should give accurate results for the temperature range of interest to industrial thermal cracking (600-900 "C, 873-1173 K). The group of hydrogen abstraction reactions is used as an example to illustrate the definition of the structural contributions. In this group, the abstraction of a primary H atom in a paraffin by a hydrogen radical is the reference reaction: H' + C2HG H2 C2H5' E = Eref= EAb(Hp)(H')
-
+
The bonds between a secondary or tertiary hydrogen and carbon are weaker than those of a primary hydrogen. As a result, the activation energy for abstraction of those H atoms is lower. The corrections mAb(Hs)and u & ( H t ) take this into account. The strength of a bond in the neighborhood of a double bond is influenced by the presence of this double bond: bonds in the /3-position are weakened, those in the a-position become stronger, and this has an influence on the activation energy for abstraction of a H atom in the neighborhood of a double bond. This is accounted for by the contributions A.EAb(ff) and m A b ( / 3 ) . The bond strength of the H atoms in methane and in the hydrogen molecule are also different, leading to AEAb(H2)and MAb(CH4).The nature of the abstracting radical also has an influence on the activation energy. The abstracting radical in the reference reaction is the hydrogen radical. A difference in activation energy is introduced for all the other abstracting radicals. These are the contributions mAb(CH3*), hE~b(C2H3'),m A b (C2H5*),etc. The use of the structural contributions can be summarized in the form of a list of statements. If a certain statement is valid for a given reaction, the corresponding contribution has to be taken into account for the calculation of the activation energy. Table I shows this list of statements for the calculation of the activation energies of the hydrogen abstractions. Tables 11,111,and IV show the statements for respectively the decomposition reactions, the radical addition reactions, and the isomerization reactions. The definition of the contributions is self-explanatory from these tables and from the nomenclature. From the above it is clear that each contribution accounts for specific changes in structure during the reaction. By comparison with the group contributions for the calculation of the standard enthalpies of formation, a range can be set for the value of the structural contribution. These intervals are used to define the allowable parameter space in the parameter optimization.
Thermodynamic Restrictions on the Structural Contributions For a reversible reaction, the activation energies of the forward and backward reaction steps are related to the thermodynamic state functions of the species according to eq 7. This relation is not necessarily satisfied if the activation energies are calculated by means of structural contributions.
1968 Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 Table I. Definition and Use of the Structural Contributions for the Calculation of the Activation Energies of Hydrogen Abstraction Reactions 1. initialization E = EAb(Hp)(H*) 2. the abstracted hydrogen is primary secondary + aAb(Hs) + tertiary 3. the abstracted hydrogen is located in the neighborhood of a double bond in the a-position + mAb(a) + UAb(0) in the 6-position others 4. the molecule from which a hydrogen is abstracted is hydrogen aAb(H2) methane + aAb(CHd others 5. the abstracting radical is hydrogen methyl +~A~(CHS*) vinyl uAb(C&,') ethyl uAb(C2H6') etc. etc. Table 11. Definition and Use of the Structural Contributions for the Calculation of the Activation Energies of Radical DecomDosition Reactions 1. initialization 2. the radical carrying C atom in the dissociating radical is primary secondary tertiary double bonded part of resonance stabilization 3. the bond to be broken is located in the neighborhood of a double bond in the a-position in the /3-position others 4. the radical which is formed during decomposition is hydrogen methyl primary secondary tertiary vinyl allylic 5. the C atom in the double bond of the produced olefin is bound to (2X) 2 H atoms 1 C atom and 1 H atom 2 C atoms acetylene allene a conjugated diene Table 111. Definition and Use of the Structural Contributions for the Calculation of the Activation Energies of Radical Addition Reactions 1. initialization E = EAd(p)(H') 2. the reacting radical is hydrogen methyl UAd(CH3') vinyl MAd(C88.) ethyl + mAd(C&') etc. etc. 3. the produced radical is primary secondary + mAd(S) tertiary + mAd(t) vinyl + AEJvinyl) allylic + MAd(allY1) 4. addition on a conjugated diene + AEAd(conj. diene) 5 . a tertiary C atom is formed by the + mAd(ct) addition
Table IV. Definition and Use of the Structural Contributions for the Calculation of the Activation Energies of Radical Isomerization Reactions 1. initialization E = Eh(1-2) 2. the isomerizing radical is primary secondary +U d S ) tertiary + AEdt) 3. the produced radical is primary secondary + a, f(8) tertiary + AEI, At)
Performing a thermodynamic analysis in full detail requires the knowledge of the thermodynamic state functions of all species involved. The reliability of this type of data for free radicals is sometimes questioned. In this work it was assumed that the group contributions listed by Benson (1976) can be used with confidence both for molecules and for free radicals. However, even if certain thermodynamic data are not available, a thermodynamic analysis is still possible. To illustrate this point, all derivations will be made as if certain thermodynamic data were missing. The introduction of the thermodynamic restrictions will be illustrated by means of an example. The generalization to the complete reaction scheme will be dealth with afterwards. Initiation and termination reactions do not require any further attention if their activation energies are calculated in accordance with eq 8. Therefore, consider the following two hydrogen abstraction reactions: H' + C2Hs H2 + C2H5' (forward step)
--
C2H5*+ H2
+
C2H6 H'
(reverse step)
The activation energies for both reactions are
Ecf= EAb(Hp)(H*) The change in standard enthalpy associated with the reaction is
AH" =
AP"(H2) + AP"(C2H5') - AP"(H') - APo(C2H,3)
AH" = AfP"(C2H5')
194.4
at 750 "C (kJ/mol) (10) In eq 10 it is assumed that the standard enthalpy of formation of the ethyl radical is not accurately known. Since there is no change in the number of moles during the reaction (Av = 01, eq 7 becomes mo(C2H5*)+ hE~b(H2)+ hE~b(C2H5')= 194.4 (11) -
Equation 11 can be considered as defining AfP"(C2H5'). This unknown thermodynamic state function can then be eliminated from the equations corresponding to the other reversible reactions in which the ethyl radical is involved. Every component with unknown thermodynamic state functions is defined by an equation analogous to eq 11. When the numerical values of all the thermodynamic state functions are accurately known, eq 11 itself can be used as a thermodynamic restriction. The final thermodynamic restrictions are obtained by reducing this set of equations to a system of linearly independent equations. The mathematical generalization of this procedure makes use of vectors and matrices. The general form of the ith reversible reaction between species Aj is represented by
Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 1969 The stoichiometric coefficients, vij, are positive for reaction products and negative for reactants. The complete system of reversible reactions is
v*A = 0
(13)
The column vector of all species, A is organized in such a way that the species for which no thermodynamic data are available come in the first positions. The matrix of stoichiometriccoefficientscan be split into two submatrices v =
(VI
vs)
(14)
v I contains the stoichiometric coefficients corresponding
to the species with unknown thermodynamic state functions, and us contains the remaining coefficients. In many cases, I and S correspond to intermediates (like radicals) and stable components. AHfo contains the standard enthalpies of formation for the species, ordered in the same way as A. In turn, this vector can be split into two subvectors: AH.O = (AH?
AH^^^)^
(15)
Av is the column vector which contains the change in number of moles for every reaction. The structural contributions for the different reaction classes are also organized into a column vector E = (Ej). The activation energy for the forward and the reverse steps of the ith reversible reaction is written
Ecbi = CPbijEj i
(16)
The difference in activation energy between the forward and reverse steps is
Ecfi - Ecbi =
c(Pfij -Pbij)E, I
= CPijEj j
(17)
or for the entire reaction scheme and making use of matrix notation
E,. - Ecb = @.E The equivalent of eq 7 then becomes B.E = vI.AHIfO + vS-AHSf0- RTaAv
(18) (19)
The thermodynamic state functions AHsfo and RT-Av are evaluated at an average temperature T, of 750 "C and are grouped into a constant y y = vgAHSfo(Tm)- RTm.Av
(20)
Equation 19 reduces to
vI-AHIfO- &E
+y =0
(21)
The final set of thermodynamic restrictions is obtained from eq 21 by applying a two-stage elimination: In the first stage, the unknown thermodynamic state functions, AH?, are eliminated from a maximum number of equations. This is done by transforming vI by means of row operations to a matrix of the form
L o
_I
The rows of B and y are submitted to the same operations as those of V I .
This procedure leads to eq 11. These equations cannot be used as a thermodynamic restriction, because they still contain the unknown AH?. They are disregarded in the second stage of the procedure. After this first elimination, the set of equations that only contain the structural contributions, Ej, can be written as -@'-E+ 7' = 0 (22) Determining a set of linearly independent rows in B' yields the final thermodynamic restrictions. For further reference, these are written as
b-E = c
(23)
The final system of equations contains some 30 linearly independent thermodynamic restrictions. They must be fulfilled in order to guarantee the thermodynamic consistency of the calculated activation energies.
Assigning Values to the Structural Contributions Values for the contributions are obtained by means of regression of experimental data. In this optimization, the limitations on the parameters have to be taken into account. These limitations are allowable interval E, 5 E 5 EM thermodynamic restrictions b-E = c
(24)
An obvious way of limiting the parameter space in the optimization is to set up steep walls on the edges. As soon as a parameter takes a value outside the allowable interval, the objective function is artificially increased. To apply this method, a set of initial values for the contributions which lie inside the allowed parameter space must be available. Given the dimensionality of eq 24, this is not a trivial problem, and a trial and error approach for determining such an appropriate set of initial values is not likely to be successful. A systematic solution of the problem is possible by means of linear programming. This is a technique for the optimization of a linear objective function whose parameters are subject to linear restrictions. These restrictions can be both equalities and inequalities. More details about linear programming can be found in optimization textbooks (Hoffmann and Hofmann, 1970). Carlile and Gillet (1972) list a general, easy to use Fortran code for linear programming applications. The restrictions (eq 24) consist of a set of linear equations together with a set of inequalities. These limitations are exactly of the form used in linear programming. A general linear programming problem is usually solved in two steps: first a solution is determined which satisfies all the boundary conditions (eq 24). In the second phase, the solution is selected for which all boundary conditions are satisfied and for which the objective function reaches its optimal value. In this problem, any point which lies within the allowable parameter space is a suitable solution. In order to have some control over the location of the selected solution, the sum of all structural contributions was minimized. The activation energies of free-radical reactions listed in 27 publications on the thermal cracking of hydrocarbons were collected in a literature data base from which the values for the structural contributions were obtained (Semenov, 1958; Sagert and Laidler, 1963; Amano and Uchiyama, 1964; Lin and Back, 1966a-c; Frey and Walsh, 1969; Tsang, 1969; Camilleri et al., 1970; Leathard and Purnell, 1970; Kunugi et al., 1970; Ill&, 1971; Herriott et al., 1972; Pacey and Purnell, 1972a,b; Murata et al., 1974; Lifshitz and Frenklach, 1975; Fujii and Tetsuro, 1977; Volkan and April, 1977; Sundaram and Froment, 1978;
1970 Ind. Eng. Chem. Res., Vol. 27, No. 11, 1988 Table V. Values (kJ/mol) for t h e S t r u c t u r a l Contributions for the Calculation of Activation Energies Determined from a Literature Data Base w i t h Published Reaction Rate Constants value, value, value, Darameter kJ/mol kJ/mol parameter kJ/mol 19.9 39.5 AE&-2) 152.3 25.1 21.4 ~EI,(s) 8.0 26.5 -2.6 AE18(t) 17.5 24.6 -8.0 44.1 mIs f(S) 13.7 -17.5 f(t) 40.4 2.6 -8.0 -6.0 AEid(t). -16.0 mD(t) -1 2.0 h E A d (vinyl) -22.6 U D ol(s) -11.7 MAd(allY1) -16.5 .IrED -26.1 AEAd(conj. diene) -5.4 UDdacet) 29.1 m~d(Ct) -8.5 m D Jallene) 11.9 AED ,I(conj. diene) -11.4 ~~
w,
Table VI. Comparison of t h e Activation Energies (kJ/mol) Calculated by Means of S t r u c t u r a l Contributions with t h e Average Values Obtained from a Literature Data Base
reaction H' + C2H6 Hz + CzH,' H' + C3Hs H2 + 1-C&' H' + C3Hs Hz + 2-C3H7' CH3' + CzHe --c CH4 + CzHb' CH3' + C3H8 CH4 + 1-C H ' CH3' + C3H7 CH4 + 2-CsH77 * CZHS' CzH4 + H' 1-C&' C3Hs + H' -t -t
4
-t
-
-
, -
13-C4Hg
:.3-C&
1-C&'
H. H.
+
C3He
H' H'
+
+ CzH4 + CH3' - + C2HC
--a
+ CzH4 + C3H6
+
h'
+
13-C4H6
H'
+
1.3-CiH6
CH;
+ CpH4
C2H5'
+
C3H6
CZH,' l-C3H7* &y"
l-C3H7*
E, structural lit. contributions data base 39.9 42.5 39.9 35.5 31.9 36.9 53.9 63.5 55.2 53.9 45.9 53.8 173.7 163.3 162.0 159.5 195.5 197.4 156.6 138.4 136.2 130.9 90.0 117.6 19.9 14.1 19.9 14.8 0.0 6.7 14.5 29.2 45.0 40.2 36.5 48.5
Goossens et al., 1979; Edelson and Allara, 1980; Hautman et al., 1981; Isbarn et al., 1981; NBS, 1981; Clymans, 1982; Moens, 1982; Sankaran, 1982; Sharfe et al., 1985). These values were optimized with respect to the literature data base by means of the minimization routine of Powell (1964). The values obtained from the linear programming were used as initial values in this optimization. The limitation of parameter space was included in the procedure by setting up steep walls on the edges. The thermodynamic restrictions were taken into account in the following way. In every equation, one contribution was chosen as a dependent variable. The system of restrictions was then solved for the dependent variables. The values of the latter were then calculated by direct substitution of the values of the remaining, independent contributions. After every new estimate for the independent contributions, the values of the dependent contributions were recalculated from the restrictions. Table V shows the parameter values that were obtained from this optimization. Together with the procedures outlined in Tables I-IV, these values can be used to calculate the activation energies of the different types of free-radical reactions which occur in the thermal cracking of hydrocarbons. Table VI compares the activation energies calculated by means of the structural contributions with the arithmetic
average values from the literature data base. When comparing the figures, it should be kept in mind that the values in the literature vary over wide intervals. Conclusion The calculation of activation energies of free-radical reactions by means of structural contributions greatly simplifies the kinetic modeling of the thermal cracking of hydrocarbons. Only a limited number of parameters has to be introduced. The same parameters are used in many different reactions. This increases the statistical significance of the parameter values. The introduction of thermodynamic restrictions reduces the number of independent parameters and guarantees the thermodynamic consistency of the calculated activation energies. The parameter values that have been derived from the literature data base can be used to estimate the activation energies of free-radical reactions. The final parameter values have to be determined by optimization with respect to experimental product distributions. The values derived from the literature serve as initial values in this optimization, and this reduces the amount of computer time needed for this final optimization. Acknowledgment
P. A. Willems is grateful to the Belgian "National Fonds voor Wetenschappelijk Onderzoek" for a Research Assistantship over the years 1982-1986. Literature Cited Amano, A.; Uchiyama, M. "Mechanism of the Pyrolysis of Propylene: The Formation of Allene". J. Phys. Chem. 1964,68, 1133. Benson, S. W. Thermochemical Kinetics, 2nd ed.;Wiley: New York, 1976. Camilleri, P.; Marshall, R. M.: Purnell, J. H. "Reaction of Hydrogen Atoms with Ethane". J. Chem. SOC.,Faraday Trans. 1 1970, 70, 1434. Carlile, R. E.; Gillet, B. E. "Linear Programming Solves Gasoline Blending". Oil Gas J. 1972, J a n 17, 92-94. Clymans, P. "The Production of Olefins from Gasoils and the Rigorous Simulation of the Thermal Cracking-. Ph.D. Dissertation, Ghent State University, Belgium, 1982. Edelsen, D.; Allara, D. L. "A Computational Analysis of the Alkane Pyrolysis Mechanism: Sensitivity Analysis of Individual Reaction Steps". Int. J. Chem. Kinet. 1980, 12, 605-621. Frey, H. M.; Walsh, R. "The Thermal Unimolecular Reactions of Hydrocarbons". Chem. Reu. 1969, 69, 103-124. Fujii, N.; Tetsuro, A. "High Temperature Reaction of Benzene". J. Fac. Eng. Univ. Tokyo 1977,34, 189-224. Goossens, A. G.; Dente, M.; Ranzi, E. "Rigorous Prediction of Olefin Yield from Hydrocarbon Pyrolysis through Fundamental Simulation Model (SPYRO)". Presented at the 12th European C.A.
Ind. Eng. Chem. Res. 1988, 27, 1971-1977 C.E. Symposium, Montreux, Switzerland, April 8-11, 1979. Hautman, D. J.; Santoro, R. J.; Dryer, F. L.; Glassman, I. "An Overall and Detailed Kinetic Study of the Pyrolysis of Propane". Znt. J. Chem. Kinet. 1981,13,149-172. Herriott, G. E.; Eckert, R. E.; Albright, L. F. "Kinetics of Propane Pyrolysis". AZChEJ. 1972,18,84-89. Hoffman, T.; Hofmann, T. Einfuhrung in die Optimierung; Verlag Chemie Gmbh: Erlangen, 1970. Ill&, V. "The Pyrolysis of Gaseous Hydrocarbons, 111. Kinetics and Mechanism of the Thermal Decomposition of Propane". Acta Chin. Acad. Sci. Hung. 1971,67,41-60. Isbarn, G.; Ederer, H. J.; Ebert, K. H. Springer Series in Chemical Physics; Springer Verlag: Berlin, 1981. Kunugi, T.; Soma, K.; Sakai, T. "Thermal Reaction of Propylene: Mechanism". Znd. Eng. Chem. Fundam. 1970,9,319. Leathard, D. A.; Purnell, J. H. "Paraffin Pyrolysis". Ann. Rev. Phys. Chem. 1970,21,177. Lifshitz, A.; Frenklach, M. "Mechanism of the High Temperature Decomposition of Propane". J. Phys. Chem. 1975,79,686-692. Lin, M. C.; Back, M. H. "The Thermal Decomposition of Ethane. Part I. Initiation and Termination Steps". Can. J. Chem. 1966a, 44,505. Lin, M. C.; Back, M. H. "The Thermal Decomposition of Ethane. Part 11. The Unimolecular Decomposition of the Ethane Molecule and the Ethyl Radical". Can. J. Chem. 1966b,44,2357. Lin, M. C.; Back, M. H. "The Thermal Decomposition of Ethane. Part 111. Secondary Reactions". Can. J. Chem. 1966c,44,2369. Moens, J. "A Rigorous Kinetic Model for the Simulation of the Thermal Cracking of Light Hydrocarbons and Their Mixtures". Ph.D. Dissertation, Ghent State University, Belgium, 1982. Murata, M.; Takeda, N.; Saito, S. "Simulation of Pyrolysis of Paraffinic Hydrocarbon Binary Mixtures". J . Chem. Eng. Jpn. 1974, 7,286. NBS "Tables of Experimental Rate Constants for Chemical Reactions Occurring in Combustion (1971-1977)". Interim Report 81-2254,1981. Pacey, P. D.; Purnell, J. H. "Propylene from Paraffin Pyrolysis". Znd. Eng. Chem. Fundam. 1972a,11, 233.
1971
Pacey, P. D.; Purnell, J. H. "Arrhenius Parameters of the Reaction CH3. + C2Hs---CHI + CzH{''. J. Chem. SOC.,Faraday Trans. 1 1972b,68,1462. Powell, M. J. D. "An Efficient Method for Finding the Minimum of a Function of Several Variables without Calculating Derivatives". Comput. J . 1964,7, 155-166. Rice, F. 0."The Thermal Decomposition of Organic Compounds from the Standpoint of Free Radicals". J . Am. Chem. SOC. 1931, 53, 1959. Rice, F. 0.; Kossiakoff, A. "Thermal Cracking of Hydrocarbons, Resonance Stabilization and Isomerization of Free Radicals". J . Am. Chem. SOC.1943,65,590. Sagert, N. H.; Laidler, K. J. "Kinetics and Mechanism of the Pyrolysis of n-Butene". Can. J. Chem. 1963,41,838. Sankaran, N. "Thermal Cracking of Cyclohexane and Methylcyclopentane". Ph.D. Dissertation, Ghent State University, Belgium, 1982. Scharfe, M.; Ederer, H. J.; Stabel, U.; Ebert, K. H. "Modeling of n-Hexane Pyrolysis: Experimental Investigation in a Flow Reactor at Normal Pressure". Ger. Chem. Eng. 1985, 8, 119-129. Semenov, N. N. Some Problems in Chemical Kinetics and Reactiuity, Vol I; Princeton University Press: Princeton, NJ, 1958. Sundaram, K. M.; Froment, G. F. "Modeling of Thermal Cracking Kinetics. 3. Radical Mechanisms for the Pyrolysis of Simple Paraffins, Olefins and Their Mixtures". Ind. Eng. Chem. Fundam. 1978,17,174-182. Tsang, W. "Thermal Decomposition of 3,4-Dimethylpentene-2,3,3Trimethylpentane, 3,3-Dimethylpentane, and Isobutylbenzene in a Single Pulse Shock Tube". Znt. J . Chem. Kinet. 1969, 1, 245-278. Volkan, A. G.; April, G. C. "Survey of Propane Pyrolysis Literature". Ind. Eng. Chem. Process Des. Deu. 1977,16,4269-436. Willems, P. A.; Froment, G. F. "Kinetic Modeling of the Thermal Cracking of Hydrocarbons. 1. Calculation of Frequency Factors". Znd. Eng. Chem. Res. 1988,preceding paper in this issue. Received for review December 8, 1987 Accepted July 7, 1988
Dimerization of Ethylene to 1-Butene Catalyzed by the Titanium Alkoxide-Trialkylaluminum System S. Muthukumaru Pillai,* Gopal L. Tembe, Marayil Ravindranathan, and Swaminathan Sivaram Research Centre, Indian Petrochemicals Corporation Limited, Baroda 391 346,India
Dimerization of ethylene to 1-butene catalyzed by Ti(OC4H9-n)4-A1R3(R = CH3, C2H6,i-C4H9)was investigated a t 1-12.5 kg/cm2 of ethylene pressure and 25-45 "C in hydrocarbon solvent. The influence of reaction conditions such as Al/Ti ratio, nature of alkylaluminum, nature of alkoxy or aryloxy group around titanium, solvents, pressure, temperature, catalyst concentration, and additives on the rate, conversion of ethylene, and selectivity to 1-butene was studied. The experimental observations conform to a titanium metallacycle as intermediate in selective dimerization of ethylene to 1-butene. Selective dimerization of olefins catalyzed by transition-metal compounds has received considerable attention in the literature (Lefebvre and Chauvin, 1970; Muthukumaru Pillai et al., 1986). Recently, commercial interest in the selective conversion of ethylene to butenes has been revived (Commereuc et al., 1984; Cooper and Banks, 1985). Of the metals studied for dimerization of ethylene, titanium-based compounds have been found to be ideally suited, giving high yields of 1-butene at ambient temperature and pressure (Muthukumaru Pillai et al., 1987; Commereuc et al., 1984; Lequan et al., 1985; Knee, 1962; Ono and Yamada, 1970; Belov et al., 1975; Beach and Kissin, 1984, 1986). However, 1-butene formation is invariably accompanied by formation of higher oligomers of ethylene and polymers. Formation of these byproducts which complicate the efficacy of an industrial process is 0888-5885/88/2627-1971$01.50/0
believed to be a function of catalyst type and reaction conditions. In this paper, we wish to report the results of a systematic study of the role of catalysts and reaction parameters on the kinetics of dimerization of ethylene as well as on conversion and selectivity of the reaction.
Experimental Section Melting points (uncorrected) were determined on a Toshniwal melting point apparatus. Infrared spectra were recorded on a Perkin-Elmer 567 instrument. DSC derivatograms were run on Du Pont 990 derivatograph under nitrogen atmosphere. Gas chromatographic analyses were carried out on a Shimadzu GC-7AG gas chromatograph using a column packed with AgN03 (2%) and Carbowax 20M (15%)on Chromosorb W. GC-MS analyses were 0 1988 American Chemical Society
