Znd. Eng. Chem. Res. 1993,32, 1297-1303
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KINETICS, CATALYSIS, AND REACTION ENGINEERING A Mechanism-Oriented Lumping Strategy for Heavy Hydrocarbon Pyrolysis: Imposition of Quantitative Structure-Reactivity Relationships for Pure Components Abhash Nigam and Michael T. Klein' Center for Catalytic Science and Technology, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
A thermochemical kinetics-based lumping strategy for modeling the pyrolysis of individual components of heavy hydrocarbon mixtures is suggested. Pyrolysis of a given feedstock is viewed from two perspectives. First, molecules are organized into compound classes, e.g., paraffins, alkylnaphthenes, and alkylaromatics. Second, the elementary steps of pyrolysis of each member of a compound class are constrained by a quantitative structure-reactivity relationship (QSRR). This two-dimensional, mechanism-oriented lumping approach provides significant reduction in the number of parameters required to model pyrolysis. Application of this lumping strategy to the pyrolysis of, individually, paraffins, alkylcyclohexanes, and alkylaromatics provided good agreement between available experimental data and the kinetics model containing only four fitted QSRR parameters over roughly 5 orders of magnitude in reactivity. Introduction Lumping, in the chemical reaction engineering context, is the aggregation of a larger set of species into a smaller set of pseudospecies. The use of lumps is motivated by at least two broad concerns. First, the statistical significance and ease of use of reaction models provide impetus for the formulation of simple, lumped kinetic descriptions. Second, and perhaps more pragmatic, analytical chemistry often provides only groups or lumps of molecules as the basis for model formulation. Irrespective of these forces, numerous classic examples of lumped models exist (Weekman, 1979;Beaton and Bertolacini, 1991). The basic idea underlying lumped models is the association of a property (e.g., reactivity) with the identity or index of a lumped species. In discrete lumped models, this will often be the association of a rate constant with boiling point or solubility classified lumps. In continuous mixture theory, an index (or two) ( h i s and Gavalas, 1966; Astarita and Ocone, 1988) such as carbon number will provide a measure of the rate constant, and integration over the limits of the mixture provides the overall behavior of the mixture. Some of the peculiarities of these lumped models and conditions for exactness have been examined (Luss and Hutchinson, 1971;Wei and Kuo, 1989;Coxson and Bischoff, 1987). Recent advances in analytical chemistry now provide modelers with very fine-grained reactant lumps: indeed, for up to gas oil boiling point range materials, it is reasonable to view the lumps as molecular isomers. This new structural information reveals the limitation of boiling point-based globally lumped models. For example, molecules with very similar boiling points can undergo different mechanisms of reactions with different global kinetics. This newly available structural information has motivated the formulation of a new class of molecularly structure explicit models. These "delumped" models 0888-588519312632-129X$O4.O0/0
capture the detail and complexity of multicomponent hydrocarbon mixtures. Mobil's structure-oriented lumping (Quann and Jaffe, 1992) approach is an insightful treatment of catalytic hydroprocessing modeling along these lines. Liguras and Allen (1989)have treated FCC reaction chemistry well in this manner. The advantages of these structure explicit models are 2-fold. First, the molecular formulation allows the introduction of fundamental physical/organic chemistry to chemical reaction engineering models. Second, the thusderived molecular product slate provides a connection to both performance and environmental properties of the product. The paradigm of product engineering seems quite reasonable in this light. The advantages of these molecule-based models are tempered when considered in the light of the required set of rate constants. Realistic model or pure component experimental programs cannot be expected to provide all of the possible thousands of molecular species' rate constants. Direct parameter estimation from complex mixture data is difficult and statistically questionable, that is, the direct estimation of O(106)kinetic parameters via optimization to experimental data suffers from the statistical degrees of freedom. Moreover, these structureexplicit models carry a statistical and computational burden. To illustrate the challenges noted above, consider the task of the mechanistic simulation of heavy hydrocarbon pyrolysis reactions. A typical complex hydrocarbon mixture may comprise of order lo6distinct molecular species. Each of these molecules, in turn, exhibits significant structural complexity: they can have up to six aromatic rings with several partially saturated hydroaromatic moieties and a large degree of alkyl substitution. The pyrolysis of each of these molecules gives rise to of order 10 radical intermediates with varying thermochemical properties. Overall, then, the direct mechanistic simulation of the pyrolysis of heavy hydrocarbon molecules 1993 American Chemical Society
1298 Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 RPD
and their mixtures is difficult because of the large number of species, reactions, and associated rate constants. The sheer size of this and similar problems suggests that the search for simplifying approximations would be useful. This is particularly true when the reaction model is only a component of a bigger process model integrating the complexity of fluid mechanics, mass, and heat transfer. This motivated the development of a two-dimensional lumping scheme that organizes the mixture components and reduces the number of (adjustable) reaction parameters without significantly sacrificing the advantages of the structure-explicit models noted above.
Lumping by Reaction Family and Mechanism The complexity of heavy hydrocarbon feedstocks diminishes when the molecules are viewed as belonging to compound classes. That is, feedstock molecules can be lumped into one of paraffin, isoparaffin, alkylbenzene, alkylnaphthene,or alkylhydroaromatic compound classes. The literal complexity of the feedstock derives from the sheer number and statistical arrangement of substituents, ring sizes and other structural attributes of these compound classes. The complexity of pyrolysis diminishes when the elementary steps of reaction are lumped into the classic bond fission, H-transfer, @-scission,and radical recombination/disproportionation families. These observations suggested that a two-dimensional, mechanismoriented lumping scheme that recognizes the similarities in compound types and associated reaction families of pyrolysis would be fruitful. To begin to develop this lumping approach, model compound data for the paraffin, alkylbenzene, and alkylnaphthene compound classes were organized in terms of the four pyrolysis reaction families noted above. The kinetics of each reaction family were summarized in terms of a quantitative structure-reactivity relationship (QSRR). The essence of this lumping approach is to use the similarity in molecular structures and the elementary steps by which they pyrolyze to reduce the apparent complexity of hydrocarbon pyrolysis to its essential component. Pyrolysis Reaction Pathways, Kinetics, and Elementary Steps Paraffins. The literature on paraffin thermal cracking is enormous. Two correlations summarize the thermal cracking kinetics well (Fabuss et al., 1964a,b). The first, due to Voge and Good (19491,correlates experimental data for n-paraffin pyrolysis with carbon number for Cd-Cls at 500 "C and 1 atm. This is shown as eq 1. The second
kapp= (n - 1)(1.57n - 3.9) X
s-l
(1)
correlation, due to Tilicheev (19391, correlates experimental data on paraffin pyrolysis for Cll-C32 at 425 "C and 150 atm. This is shown in eq 2. Typical activation kapp= (2.3n - 15.6) X 10"
5-l
(2)
energies for n-paraffin pyrolysis often fall in 60 f 5 kcal/ mol range. The product distribution for paraffin pyrolysis is quite sensitiveto pressure. At low conversionsand low pressures (-1 atm), paraffins crack selectively to form olefins, methane, and ethane. Among the olefin products, the distribution is largely weighted toward ethylene and propylene. At higher pressures, though, the distribution shifts to higher carbon numbers because of chain transfer.
6
Iogl~A
13.0
13.0
26 24 26
13
28
13
26 28
13.0
4
13
4
4
E kcaVmol
I3 I3 I3
30 2R
13.0
2RO
130
280
26
Figure 1. Elementary steps in a Rice-Herzfeld pyrolysis scheme for n-octane.
(a-PDB)
('5
(y-PDB)
'
p
(Minor)
.
(15
P'+ ..-,
L 38)
Figure 2. Elementary steps in aRice-Herzfeld pyrolysis scheme for alkylbenzenes.
For smaller alkanes it is often possible to enumerate the complete list of important elementary steps. As an illustration, n-octane pyrolysis can be modeled in terms of four Rice-Herzfeld (RH) chains (Dryer and Brezinsky, 1985),such as those shown in Figure 1. Note that only the propagation cycle involving H-transfer and @-scissionsteps is shown. Bond fission and radical recombination/ disproportionation balance to maintain the steady-state radical pool. Similar mechanistic steps are operative for pyrolysis of other paraffin molecules. Alkyl Aromatics. The pyrolysis of long-chain alkylbenzenes has been studied extensively (Blouri et al., 1985; Mushrush and Hazlett, 1984;Savage and Klein, 1989a,b). Savage and Klein (1989a,b) studied pyrolysis of pentadecylbenzene (PDB) in detail. PDB pyrolysis yields two major primary product pairs: toluene plus tetradecene and styrene plus tridecane. In addition, several minor alkylbenzenes and corresponding a-olefins were detected. The products were rationalized based on a RH mechanism. Figure 2 illustrates a RH propagation cycle and associated rate parameters (log(A/s-l), E*/kcal mol-') for an alkylbenzene pyrolysis. This free-radical mechanism includes three distinct RH chains: 1. A benzylic radical formed a to the ring (PI) undergoes @-scissionto form vinyl product (MI) and a primary alkyl radical @I). 2. The radical formed y to the ring (p2) undergoes 8-scissionto form the resonance-stabilized benzylic radical (82) and an a-olefin product (M2). 3. All other radicals are lumped into a third chain where radicals ~3 form and, upon @-scission,lead to minor products (M3) and minor primary radicals (ad. Initiation is by homolysis to form the benzylic radical (log A = 16.0, E* = 68 kcal/mol) and termination is with log A = 8.5, E* = 0.0 kcal/mol. Alkyl-Substituted Naphthenes. Pyrolysis of both alkylated and denuded naphthenes has been reported in the literature (Fabuss et al., 1964a,b; Mushrush and Hazlett, 1984; Savage and Klein, 1988; Virk et al., 1979).
Ind. Eng. Chem. Res., Vol. 32, No. 7, 1993 1299 Table 11. Quantitative StructureReactivity Relationships for the Pyrolysis of Heavy Hydrocarbon Compound Classes reaction family ~oK(A)O E* ~
bond homolysis H-abstraction
Figure 3. Elementary steps in a Rice-Herzfeld pyrolysis scheme for alkylcyclohexane. Table I. Operative Pyrolysis Pathways for Paraffin, Alkylaromatic, and Alkylcyclohexane Compound Classes comDound class reaction Daths paraffins cracking alkylaromatics dealkylation alkylcyclohexanes dealkylation,ring opening ~~
~
~
~~
The major reaction paths for alkyl-substituted alkylnaphthenes include dealkylation and ring opening. Savage and Klein (1988) studied the pyrolysis of tridecylcyclohexane (TDC) in detail. TDC pyrolysis provided two major primary product pairs: cyclohexane plus tridecene and methylene cyclohexane plus dodecane. A variety of minor products was also identified. Ring opening was important a t higher temperature and conversions. The selectivity of methylene cyclohexane to cyclohexane increased with the total concentration of TDC. Representative elementary steps for alkylnaphthene dealkylation and ring-opening paths are shown in Figure 3. Pyrolysis proceeds via four coupled RH chains. These chains engender eight free radicals, four involved in bimolecular propagation steps (8) and four involved in unimolecular propagation steps ( p ) . The tertiary radical assumes the significance that the benzylic radical held in alkylbenzene pyrolysis. Specifically,a radical on the chain 8 to the tertiary carbon forms a cyclohexyl radical and an olefin upon /?-scission. The tertiary radical on the ring leads to the methylenecyclohexane product and a primary radical upon 8-scission. Secondary radicals on the ring lead to ring-opening products. The minor radicals on the chain can be lumped. Summary. The reaction pathways shown in Table I capture the main features of paraffin, alkylbenzene, and alkynaphthene pyrolysis. The operative mechanisms are, in each case, composed of bond fission, H-transfer, @-scission,and radical recombination/termination elementary steps. Closer scrutiny of the thermochemistry of these elementary steps will reveal how a substantial reduction in kinetics parameters can be achieved via the imposition of quantitative structure-reactivity relationships.
Quantitative Structure-Reactivity Relationships for Pyrolysis Reaction Families The structurereactivity relationships sought were based on the use of thermochemial properties (AHf",Sf", Cpo) for estimating elementary step kinetic parameters (A, E*). A reaction family was defined as a set of elementary steps for which the entropy of activation and therefore A was invariant. This lumping approach is rather forgiving as often, for a reaction family, small changes in the entropy of activation will be proportional to changes in the enthalpy. Thus intrareaction family differencesin reaction family reactivity, due to substituent effects, can be correlated in terms of their effect on E*. The families of
16.0 8.5
Ad' E* = E.* - aq(exo) E* = Ea* - (1 - a)q(endo) E* = E@*- @q 0.0
@-scission 13.0 recombination 9.0 'A correction log(RPD) was added to account for multiple, energetically equivalent pathways.
bond homolysis, H-transfer, &scission, and radical recombination are considered in turn. Bond Homolysis (Initiation). For Cq+hydrocarbons, log(A/s-l) = 16 f 1 is representative but of course not literally exact for all molecules. Nevertheless, in the spirit of lumping, a constant log(A/s-') = 16.0 was imposed on the bond homolysis family. A reaction path degeneracy (RPD) correction accounted for energetically identical paths for bond homolysis as a multiplier of A. The activation energy for bond homolysis was taken as the bond strength (Ad") of the weakest C-C bond in the molecule. This is because the reverse reaction of bond homolysis (i.e., radical recombination) proceeds with practically zero activation energy. Equation 3 therefore provides the simplest structure (Ad")-reactivity (E*) relationship.
E* = Ad"
(3)
H-Abstraction (Propagation). Statistical mechanics estimates and perusal of experimental data provide log(A/L mol-l s-l) = 8.5 f 1 as a reasonable band for H-abstraction entropies. This fixed value was used for the H-abstraction reaction family, allowing for suitable corrections for RPD to account for energetically identical H-abstraction paths. An Evans-Polyani relationship (Boudart, 1968)was used to correlate E* with the structure and energetics of the molecules and radicals involved in the H-abstraction elementary step. For an exothermic step, the EvansPolanyi relationship has the form of eq 4, where q = -AH,* E* = E ,
- aq (kcal/mol)
(4)
and E , and a are the Polanyi parameters. For the reverse endothermic step, the activation energy is greater than that for the forward exothermic step by the enthalpy of reaction. Thus the functional forms of eqs 4 and 5 were
Ej* = E , - (1- a)qj
(5)
imposed on the exothermic and endothermic H-abstraction steps, respectively. The parameter valueswere determined via optimization of these QSRR relations to the available model compound data base. &Scission (Propagation). Statistical mechanics estimates of the entropy of activation and experimental data provide log(A/s-l) = 13 f 1(Benson, 1976) as a reasonable band for 8-scissionreactions. A constant log(A/s-l) = 13.0 was therefore imposed throughout the ,!I-scissionfamily. E* was correlated according to an Evans-Polyani relationship. The functional form of eq 6 was imposed on
Ej* = E, - piqj
(6)
all 8-scission reactions with parameter values being subsequently adjusted to the experimental data. Radical Recombination (Termination). This mode of termination was modeled as being collision controlled.
1300 Ind. Eng. Chem. Res., Vol. 32, No.
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A constant value of log(AIL mol-l s-l) = 9.0 = log k was uniformly imposed for the entire family.
I
Experimental Database k obs [ T,P, molecule]
Best-Fit Structure-Reactivity Parameters Table I1 summarizes the structure-reactivity relationships imposed on the various reaction families. These quantitative structure-reactivity relationships (QSRR) drastically reduced the number of potentially adjustable parameters in the kinetic models. The four Arrhenius A parameters were held constant as noted in Table 11, duly corrected for RPD's, and the activation energies E* for the bond homolysis and radical recombination families were fixed as Ado and 0, respectively. Therefore, the structure-reactivity parameters a,E,, j3, and E@of eqs 4-6 were the only adjustable parameters in the mechanistic kinetics models of the compound classes. Note, however, that, the best-fit QSRR values are subject to scrutiny as to their chemical significance (Boudart, 1968). Figure 4 summarizes the logic used to obtain the optimal set of structure-reactivity parameters from the model compound experimental data base. The experimental data available for paraffins, alkylbenzenes, and alkylcyclohexanes, taken for various molecules and a range of temperatures and pressures, were considered separately and in turn. The experimental pyrolysis kinetics for these compound classes were summarized as a set of pseudofirst-order experimental rate constants kobs by dividing
QSRR Parameters
I
Mechanistic Simulation I
Thermochemistry
dR*/dt =O =...... d N d t = - Z k R* A km = 1/A*(-dNdt)
Update QSRR Parameters I
1
e
, ,
I
Z
(kobs-kpred)
2
*
