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Compound class modeling of hydropyrolysis
Science, Chemical Enginewiny Printed in Great Britain.
Vol.
43. No.
10, pp. 2845-2857,
1988. 0
COMPOUND
CLASS RICHARD
Department (First
MODELING S. PARNAS
received
2 December
OF HYDROPYROLYSIS
and DAVID
of Chemical Engineering, UCLA, 1986, accepted
ooo%2so9/88 %3.00+0.00 1988 Pergamon Press plc
T. ALLEN’
Los Angeles, CA 90024, U.S.A. in revisedform
28 April
1988)
Abstract-The primary objective of this work is to extend the utility of compound class modeling for complex kinetic systems. Compound class modeling involves lumping the many species of a complex mixture into classes based on chemical structure and has been applied to many types of reacting systems. Each compound class represents many species, and previous compound class models have not satisfactorily addressed the problem that the chemical characteristics of the classes can change as the reactions progress. This limitation has prevented the full exploitation of compound class models. In this work we extend compound class modeling by following not only the concentration of each class but also the average carbon number and variance of the carbon number distribution for each compound class. The thermal hydropyrolysis of reacting hydrocarbon mixtures will be used as an example of a complex reaction network involving many components. For thermal hydropyrolysis, 10 compound classes were proposed and rate parameters derived from model compound studies were used to estimate the rates of interconversion among compound classes. The compound class model is in qualitative agreement with experimental observations reported in this work and with results available in the literature.
INTRODUCTION
The primary objective of this work is to extend the utility of compound class modeling for kinetic systems containing a very large number of components. Since the precise composition of such complex mixtures cannot always be determined, some type of lumping based upon measurable quantities is necessary to model chemical kinetics. Compound class modeling involves lumping the many species of a complex mixture into classes based on chemical structure. Once the compounds are lumped into classes, individual reactions can no longer be followed. Instead, the transformations that occur at specific bond locations are used to describe the chemical changes that transform material in one compound class into another class. Previous literature on modeling complex kinetic systems developed the concepts of exact and approximate lumping (Wei and Kuo, 1969; Kuo and Wei, 1969; Liu and Lapidus, 1973). However, previous models calculated only the concentrations of the compound classes. Also, most previous models used empirically derived rate constants and in general have not relied on fundamental rate parameters. Aggregate, or lumped rate constants have been used to represent the kinetic behavior of the compound classes. The model presented in this work differs in two respects from most previous lumped kinetic models. First, in addition to the total concentration of each kinetic lump, the model computes statistical quantities such as the average carbon number of each compound class. A method for computing the variance around the average carbon number is also presented. A second nove1 feature of this model is the use of fundamental +To whom correspondence should be addressed. CES
43:10-s
2845
rate parameters in describing the chemical reactions of the compound classes. This paper will focus on thermal hydropyrolysis of heavy oils as an example of a complex reacting system amenable to a compound class approach. Compound class concentrations and average carbon numbers will be computed. Rate parameters will be based on the literature described below. The pyrolysis and hydropyrolysis of relatively light hydrocarbons have been studied in great detail. Brooks (1967), and Shultz and Linden (1962) studied the effects of hydrogen pressure and tetiperature on the thermal hydropyrolysis of straight-chain paraffins. Illes et al. (1974) studied the pyrolysis of branched paraffins. Benson and Shaw (1967a, b) studied the pyrolysis of cyclic paraffins, paraffins, olefins and cycloolefins. Fabuss et al. (1965) studied the effect of sulfur on the pyrolysis of saturated hydrocarbons. Rebick (1983) summarizes these and several other studies, concluding that the free-radical mechanism first proposed by Rice (1933) and later modified by Kossiakoff and Rice (1943) is almost universally accepted as the mechanism of thermal hydrocarbon cracking. Investigations of the pyrolysis and hydropyrolysis of aromatic materials are less evident in the literature than are studies of the lighter hydrocarbons mentioned above. The thermal demethylation of toluene was studied by Zimmerman and York (1964). More recently, Davis (1983) studied the formation of toluene from ethylbenzene by thermal pyrolysis. Yamada and Amano (1983) report a study on the hydropyrolysis of toluene and conclude that the free-radical mechanism is valid for the pyrolysis of aromatic as well as saturated hydrocarbons. Pyrolysis of partially hydrogenated naphthalenes has been studied by Bredael and Rietvelde (1979) and Allen and Gavalas (1983).
2846
RICHARDS
S. PARNAS and DAVID
Analysis of the product composition from the decomposition of two ring compounds is complicated by the large number of secondary reactions that may occur with such complicated starting materials. Hydropyrolysis of two ring compounds has been investigated by Penninger and Slotboom (1973). In order to retain reasonable simplicity, they studied the reactions at very low conversions and found that free-radical mechanisms adequately explained their experimental data. Even in the presence of large excess quantities of hydrogen, a small amount of dehydrogenation to condensed material occurred. The only available work on pyrolysis of heavier aromatic materials is on the pyrolysis of anthracene (Stein, 1981). The predictions of thermochemical kinetics developed by Benson (1976) were used to differentiate plausible from implausible kinetic mechanisms. Detailed mechanistic models of the free-radical chemistry of hydropyrolysis can be proposed based on the thermochemical estimation techniques of Benson and the experimental work outlined above. Dente and Ranzi (1983) wrote such a detailed model for the thermal pyrolysis of light hydrocarbons, e.g. butane, and were very successful at predicting experimental results. Their model included I I6 reactions and 45 individual species. To model a heavy hydrocarbon mixture, detailed mechanistic modeling of every reaction and species is not possible. Dente and Ranzi lump heavy components of naphtha and gas oil feedstocks into compound classes to simplify the reaction network but still report a reaction scheme of over 2000 reactions and 100 species. Hydropyrolysis of heavy crudes or coal-derived liquids require further simplification of the reaction scheme. This work seeks to drastically simplify the reaction scheme necessary to describe hydropyrolysis and yet retain enough detail about the product composition to be useful. COMPOUND
CLASS
MODELING
Ten compound classes will be considered in this model of thermal hydropyrolysis. The classes are listed in Table I and include a variety of aliphatic, olefinic and aromatic groups. A more extensive list could be formulated; however, these classes are readily measurable and include most of the molecular classes present in heavy oils. Larger aromatic structures will be considered in future work.
Table 1. Class no.
Class name
1 2 3 4 5 6 7 8 9 10
Paraffins Olefins Cycloparaffins Cycloolefins Cyclodiolefins Benzenes Tetrahydronaphthalenes Dihydronaphthalenes Naphthalenes Diolefins
T. ALLEN
The free-radical reactions of the compound classes include initiation, termination and propagation steps. The propagation reactions are subdivided into those that have high rates (hydrogen abstraction) and four reversible unit transformations that occur at lower rates. The four types of slower propagation reactions include: (I)
/I-scission of a carbon-carbon bondtifreeradical addition to a double bond (2) H atom addition%loss of H atom (3) cleavage of aryl-R bond%radical attack on aromatic (4) cleavage of aryl-aryl bond*aryl radical attack on aromatic
Examples of these reactions are shown in Fig. 1. The pscission reaction is one in which a carbon+arbon bond in the /J-position relative to a radical breaks, producing a molecule with an alpha double bond and a smaller radical. The reverse of p-scission is a freeradical addition reaction in which a radical attacks a double bond. Cleavage of the aryl-R bond is a reaction in which the substituent on an aromatic ring is removed following an attack by an H atom, producing a less substituted aromatic and a paraffin radical. Paraffin radicals may also attack aromatic structures in the reverse reaction. Aromatic structures that are not fully condensed may break at aryl-aryl bonds following attack by hydrogen atoms, producing smaller aromatics and aromatic radicals. Several simplifying assumptions are used in the model. Substituents on single-ring compounds are assumed to be saturated straight-chain hydrocarbons. Therefore, only the paraffin and single-ring compound classes interact through unit transformation (3). Substituents on double-ring aromatic compounds are assumed to be aromatic rings. Therefore, only the single and double-ring compound cIasses interact through unit transformation (4). The total concentration of radicals is calculated using the pseudo-steady-state approximation. Also.
p Sclsslon
free
_
/ 0
addltlon
z==
/-lPL/H atom
rodvxtl
addttlon
fH’
_
it/--l_/
dehydrogenation *
-
0
Cleavage
of Aryl-X
Cleavage
of Aryl-Aryl
bond
ZII!
bond
rodeo1
_
Aryl
Fig. 1. Examples of the propagation
ctttock
radlcol
on
aromatIc
attack on oromarlc
reaction classes.
Compound class modeling of hydropyrolysis termination by disproportionation is neglected. total radical concentration is given by
CR’1= WEOCR~Y
The
(1)
where K,o is the equilibrium constant for the appropriate initiation and termination reactions, and [R] is the total concentration of molecular species. Although a more rigorous formulation of eq. (1) would include only radical-forming species in [R]. an algorithm for following just those species as their concentrations evolve over time has not yet been included in the model. To estimate Kbu, values for the Arrhenius parameters of initiation and termination reactions available in the literature (Allen and Gavalas, 1983; Dente and Ranzi, 1983) were reviewed. Activation energies for most initiation reactions lie in the range of 70-90 kcal/mol. For olefins, activation energies on the order of 30 kcal/mol are reported for initiation reactions. However, the olefin reactions are generally disproportionation reactions and although the activation energies are low, the preexponential factors are also low, resulting in overall rate constants similar to those for other compounds. A value of 60 kcal/mol for the activation energy of initiation reactions was chosen as a compromise between the low activation energies of disproportionation and the higher activation energies of other initiation reactions. The reported activation energies for termination reactions are zero as expected for radical recombination. After similar considerations, a value of 1OL6 was chosen for the preexponential factor of initiation reactions and a value of IO’” was chosen for the preexponential factor of termination reactions. The equilibrium constant K EQ is then given by K,,=:=
lo6 exp(-60,000,RT).
(2)
t The parameter
K,,
must be viewed as an adjustable
parameter in the current formulation of the model. The value of this parameter should be a function of composition. The sensitivity of the model to changes in K,, will be examined later in this work. The hydrogen abstraction reactions that occur during hydropyrolysis are assumed to be fast relative to the other propagation reactions. Therefore, each compound class i is assumed to be in equilibrium with the radicals of the species making up the compound class: R,+R’%R,‘+R
(3)
CR'liCRl
K,=
’
CRliCR'l
(4)
’
The ratio of the concentrations of any two classes of radicals, i and j, are then given by the ratios of their associated molecular compound classes and their equilibrium constants:
CR’li -=-_ CR’lj
KiCRl, Kj CRlj
(5)
The totat radical concentration defined in eq. (1) and the ratios of the radical concentrations defined in eq. (5) can be used to calculate the concentration of radicals in each compound class. The total radical concentration and the concentration of the various radical classes are allowed to change over time as the molecular class concentrations evolve. In this model, the parameter KEQ is a constant although one may expect that K,, would also change over time since it is an aggregate parameter relating total molecular and radical concentrations. In future versions of the compound class model, K EQ may depend upon the overall mixture composition. The kinetic model consists of 29 reactions interconnecting 10 compound classes. A schematic diagram of the major reaction pathways is shown in
l(7)
poroffm radlcols 4
2847
cycloparoffin radicals
I A
llll-0 ..-.
4
I
3(25)
I (IO)
l(ll)
2YEl,
2q:9,
‘I 3
I(z2)
benzenes
cycle-diolefins
cycle-OkfIns
benzene rodxols
cycio-dlolefm rodlcals
cycle-olef radicals
t
5(26) 5(29)
-
in
tetra- hydra naphthalenes
di-hydro naphtholenes
tetra- hydro naphtholene radicals
dl-hydro naphthalene radicals
4 naphthalenes naphthatene radicals
Fig. 2. Schematic-diagram of the simulated reaction network showing major reaction pathways. The numbers
that label each arrow
indicate the unit transformation and, in parentheses, defined in Table 2.
the reaction
number,
as
RICHARDS S. PARNAS and DAVID
2848
Fig. 2. Each compound class occupies a box and reaction pathways are shown by the connecting arrows. The 29 reactions and their rate constants are
Table
No. 1 2 3 4 5 6 7 8 9 IO
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27 28 29
2. Reaction
T. ALLEN
given in Table 2. The Arrhenius parameters were taken from Dente and Ranzi (1983) and Allen and Gavalas (1983).
rate parameters
Reaction J?-Scission of paraffin radical + olefin + smaller paraffin radical Loss of H atom from paraffin radical + olefin Paraffin radical + olefin --t large paraffin radical H atom + olefin - paraffin radical &Scission of olefin radical + diolefin + smaller olefin radical Olefin radical + olefin + larger olefin radical /?-Scission of cycloparaffin radical + olefin radical Loss of H atom from cycloparaffin radical + cycloolefin H atom + cycloolefin t cycloparaffin radical p-Scission of substituent from a cycloparaffin radicalparaffin radical + cycloolefin Paraffin radical tcycloolelin - cycloparafik radical Loss of H atom from cycloolefin radical + cyclodiolefin H atom + cyclodiolefin -+ cycloolefin radical /3-Scission of substituent from a cycloolefin radical paraffin radical tcyclodiolefin Paraffin radical +cyclodiolefin + cycloolefin radical Loss of H atom from cyclodiolefin + single ring aromatic H atom + single-ring aromatic - cyclodiolefin radical Loss of H atom from tetrahydronaphthalene radical+dihydronaphthalene Loss of H atom from dihydronaphthalene radical+naphthalene H atom + naphthalene - dihydronaphthalene radical H atom +dihydronaphthalene -+ tetrahydronaphthalene radical j?-Scission of tetrahydronaphthalene radical+single-ring aromatic Naphthalene radical + benzene - substituted naphthalene rddicdl Naphthalene radical + naphthalene - substituted naphthalene radical Cleavage of aryl-X bond of singlering aromatic radicalparaffin radical + single-ring aromatic Cleavage of aryl-aryl bonds to substituted naphthalene radicals+ benzene radicals + naphthalene + naphthalene radicals Loss of H atom from olefin radicals + dioletins H atom + diolefin - olefin radical Benzerle radical + naphthalene -+ substituted naphthalene radical
(s-’
A
or I mol-‘s-l)
E (cal/mol)
10’4s-’
40,000
10’4sC’
40,000
lO”lmol-Is-’
15,000
iO’“.5
1rnol-‘~-~
2000 40,000
10’4S_’ 1O”.5 lmol-‘s-’
6000
10’4sm’
40,000
10’4s-’
45,000
10’0~51mol-‘s-’
2000
10’4s~’
45,000
IO8 Imol-Is-’
15,ooo
10’4sC’
40,000
10”
lmol-‘s-’
3000
10’4s-’
40,000
IO” lmol-‘s-l
15.000
10’4s-’
30,000
IO” Imol-‘s-’
3000
10’4s-’
40.000
10’4.5 sm 1
27,000
IO”
Imol~‘s~’
3000
10’451mol-‘s-1
3000
,014 5 s-
1
30,000
10” lmol~‘s~
35,000
10” lmol-Is-’
35,000
5x 10hlmol-‘s-l
39,000
5x 1061mol-Is-’
39,000
10’3s-’
35,000
1O’o.5 1 mol- ’ s- ’ 108Jmol-‘s-’
2000 20,000
Compound
class
Tables I and 2 indicate that hydropyrolysis kinetics of heavy hydrocarbons can be formutated in a much simpler manner than a detailed mechanistic model. The most important simplification is the reduction of the number of components from several hundred in a hydrocarbon mixture to a number on the order of IO in the compound class model. The current model can be run on a mini-computer (VAX 1 l/750) while full mechanistic models would require the use of supercomputers. The question remains, can the compound class model provide adequate details of the product distribution to be useful? Each compound class represents many compounds, so, integrating the differential equations for the concentrations of each compound class in the mixture will not provide adequate detail about the product distribution. Additional quantities such as the average number of carbon atoms in each compound class, the average length of substituents, and the variance of these two quantities should provide enough detail to make the compound class model useful. Such quantities can be calculated algebraically from the reaction rates and compound class concentrations. The average number of carbon atoms in each molecule of a compound class is simply the total number of carbon atoms in the compound class divided by the number of molecules. or the concentration of the class. Each reaction transfers carbon atoms from one compound class to another. For example, reaction I creates a smaller paraffin radical and an olefin from the pscission of a paraffin radical. If it is assumed that the location of the scission is random, it can be shown that, on average, paraffin radicals break in half, transferring half their carbons to the olefin compound class and retaining half their carbons in the paraffin class. Let Mij be the number of molecules of class j transferred to another class in a small increment of time At by reaction i. Also, let CT,, be the number of carbon atoms per molecule transferred by reaction i. Then, general algebraic equations can be formulated to keep track of the movement of carbon atoms throughout the reaction network. If Cj is the number of carbon atoms in class j at time r then N-.x,
CjI,+*t= Cjl,f
c
MijCTij.
i=l
The number of molecules, or the concentration Rj, of compound class j is obtained by numerically integrating the net rate of formation of molecules of the class:
Rjlr+nr= Rilt+At
=Cjlr+ctrlRjlt
of carbons in the molecules of the compound class from which material is being drawn. For example, reaction 4, in which an H atom adds to an olefin to give a paraffin radical, transfers molecules from the olefin class to the paraffin class. The number of carbons transferred per molecule is simply the average number of carbons in each molecule of the olefin class. Another example is reaction 29, the free radical addition of naphthalene and benzene radicals which produces substituted naphthalenes. Reaction 29 does not change the concentration of the naphthalene class but it does reduce the benzene class concentration. The effect of reaction 29 on the naphthalene class is to increase the average number of carbon atoms in the molecules of the naphthalene class. Further addition of aromatic materials and ring closure reactions which are not included in the model would lead to coke precursors. Following the average number of carbons in the molecules of each compound class in addition to the concentration of the classes provides additional insight into the evolving composition of the hydropyrolysis product. Greater insight may be obtainable by following higher moments of the compound classes such as the variance of the average number of carbons of each class. In that case information on the product distribution within each compound class would become available. The usual measure of the variance of a sample is the standard deviation. However, the standard deviation involves nonlinear terms and it may be difficult to derive proper mixing rules for the calculation of the variance around the average. A simpler measure of the variance is the average deviation about the norm defined below:
D=i=l
N
+At-
(8)
The number of carbon atoms transferred by reaction i, CT,,, depends on the reaction and the average number
(9)
where N = the size of the sample, x= the sample average, and Xi=the ith value in the sample. The average deviation is used because computing the upper bound on the deviation of mixed samples is much easier with the average rather than with the standard deviation. If sample A with average R, and deviation D, is mixed with sample B, the resulting sample C average is the weighted sum of the averages of samples A and B: R,.=
N/,x,
+ N,i?,
N,fN,
N”,”
c dM,,/dt. (7) i= I More variable-step fourth-order precisely, a Runge-Kutta integration algorithm was used to integrate the concentrations as well as to obtain the individual Mij (Johnson and Riess, 1982). The average number of carbon atoms in classj is then Cjavg
2849
modeling of hydropyrolysis
The average deviation weighted sum: D,<
can be bounded
N,(D,+lK,-K,I)+N,(D,+IK,--R,I) N,+N,
(10) by a similar
(II1
For the system of chemical reactions used in hydropyrolysis the deviations of the number of carbons from the average in each compound class can be computed using the above formula.
RICHARDS
2850
S. PARNAS and
DAVID T. ALLEN Table
RESCJI.TS
The compound class model was integrated numerically under a variety of conditions to assess its ability to describe thermal hydropyrolysis. The,temperature, hydrogen concentration, and initial hydrocarbon composition (see Table 3) were varied. The numerical simulations were carried out with a VAX I l/750 computer. Most runs simulated IO s of real time but this was not feasible in all cases. At the higher temperatures, especially with high hydrogen concentrations, the system of equations became quite stiff and required large amounts of computer time. Therefore, some of the runs simulated 5 s of real time. Representative results are shown in Figs 3-9. Concentrations of the major compound classes are plotted against time as are the average number of carbon atoms in each class. Figures 335 show results using an initial mixture containing olefins and benzenes (mixture no. 3 in Table 3). These results summarize the model capabilities for handling light, reactive hydrocarbons. In Fig. 3, at 700°C with no hydrogen, the benzenes are unreacted after 10 s. The olefin concentration drops while the average length of olefin molecules increases dramatically, indicating that polymerization occurs to a great extent at those conditions. The extent of polymerization shown in Figs 3
I8
3. Initial compositions
used in the simulations
(1) [Paraffins] [Benzenes] [Naphthalenes]
0.1 mol/l 10.0 mol/l 5.0 mol/l
C,,,,= 12 carbons C,,,, = 10 carbons C,,,, = 10 carbons
(2) [Paraffins] [Benzenes] [Naphthalenes]
10.0 mol/l 0.1 mol/l 10.0 mol/l
C,,,, = 12 carbons C,,,,= 6 carbons Caavg = 16 carbons
(3) [Olefins] [Benzenes]
5.0 mol/l 10.0 mol/l
C,,,,= C,.,,=
7 carbons 6 carbons
and 4 is probably much larger than would occur in a reacting mixture because ring closure reactions are not included in the model. Figure 4, also at 7OO”C, shows the effect of adding a small amount of hydrogen to the initial hydrocarbon mixture. Again, the benzene class is virtually unaffected. However, a smatl amount of paraffin is produced by hydrogenation of olefins. In Fig. 5, substantial hydrogen is added at 6OO’C and the results are markedly different from those shown in the previous two figures. Both the olefin and benzene concentrations become very small within the first 2 s. The paraffin concentration increases rapidly due to hydrogenation. The cycloparaffin concentration increases rapidly at first due to hydrogenation, goes through a maximum, and then decreases more slowly
, Olef ins
16 14 12 IO 8-
Diolefins
0’
’ 0
I
’ 2
’ 3
1 4 Time
I
,
5
6
I
7
I
8
I
9
--
1
IO
i
(seconds)
0
ooa
1 0.005 0004 0003
_y
. 0
0
I
2
1
3
D(olefins-
4 Time
5
6
7
8
9
IO
0.002 ooo,
0
(seconds)
and the compound class average carbon number Fig. 3. Evolution of the compound class concentrations initial composition 3 (olefins and benzenes, see Table 3) with no added hydrogen at 700°C.
for
Compound
class modeling
2851
of hydropyrolysis
91 Olefins
Diolefins Paraffins
Benzenes 01 0
0.8
1 I
1 2
1 3
I 4 Time
1 I 5 6 (seconds)
I 7
I 6
I 9
IO
, 0.008
r
_1 0.003
Diolef ins _
- 0.001 r-l
-0
Fig. 4. Compound
I
2
3
4 Time
class concentrations
5 6 (seconds)
7
and average
benzenes, see Table 3) with hydrogen
as scission reactions open the ring. The sizes of paraffins in the reaction mixture change as time progresses. The average number of carbons in the olefins and paraffins classes increases initially, then decreases as cracking reactions in the paraffins dominate after 2 s. Figures 6 and 7 show aromatic chemistry using initial composition no. 1, made up predominantly of benzenes and naphthalenes. The initial average number of carbon atoms in the benzene molecules is 10, indicating that the benzenes are substituted. Figure 6, at 700°C with no hydrogen, shows the addition of naphthalene and benzene radicals as well as the breaking of substituents from the benzene rings. The increase in paraffin concentration and the decrease in the average number of carbon atoms indicates that the molecules making up the paraffin class are increasingly scission products from the benzene class. Moreover, the average number of carbon atoms in the benzene class decreases over time, indicating that the substituents are being removed. The concentration of the naphthalene class remain nearly constant but the average number of carbons increases. The source of the additional carbons in the naphthalene class is the benzene class as can be seen by observing that the
8
IO
9
carbon numbers for initial composition concentration = 0.1 mol/l at 700°C.
3 (olefins and
benzene class concentration decreases over time. Thus, benzene class radicals are undergoing addition to the naphthalenes (reactions 23 and 30 in Table 2). Figure 7 shows the result of adding hydrogen at 700°C to the same initial mixture as was used to generate Fig. 6. The benzenes rapidly hydrogenate while the naphthalenes do so more slowly. The average carbon number of the naphthalene class stays nearly constant, indicating that the combination of benzenes cant
and naphthalenes
extent.
naphthalene
The
average
molecules
does number increases
not occur
to a signifi-
of carbons very
slowly.
in the The
average number of carbons in the benzene class approaches the same value as that for the naphthalenes after a lag of about 2 s. After the initial supply of benzenes hydrogenate. the naphthalene class is a small but steady supplier of carbon to the benzene class. The average length of paraffins goes to about 10, the average number of carbons in the aromatic classes. Then, the paraffin concentration gradually increases as carbon is transferred through the cycloparaffin class from the aromatics. The rate-limiting steps of hydrogenation are the conversion of naphthalenes to benzenes. Figures 8 and 9 show the interaction between light
RICHARDS S. PARNAS and DAVID T. ALLEN
2852
Benzenes. Cycloporaffins Poraff ins Olefins
I:;/ 0
,
,
,
I
2
3
,
,
,
4 5 6 Time (seconds)
L
,
,
,
7
8
9
IO
1.0 0.9 0.8 -
Cycloporaffins
-0
I
2
3
4 5 6 7 Time (seconds)
8
9
IO
Fig. 5. Compound class concentrations and average carbon numbers for initial composition benzenes, see Table 3) with hydrogen concentration= 10 mol/l at 600°C.
and aromatics in hydropyrolysis using initial composition no. 2, mainly paraffins and naphthalenes. In both Figs 8 and 9 the paraffin concentration and average number of carbons do not change significantly. In the presence of light hydrocarbons only, as in Figs 3-5, cracking reactions were important for paraffins. In Fig. 8, at 700°C with no hydrogen, the naphthalenes condense with themselves slightly and with the small amount of benzenes present. Some paraffin cracking does occur as is evidenced by the small amount of olefins formed. Figure 9 shows the result of adding hydrogen at 700°C to the same initial hydrocarbon mixture as was shown in Fig. 8. The benzene concentration decreases to a low but constant level maintained by naphthalene hydrogenation. That the benzene concentration is maintained by naphthalene hydrogenation is readily seen by observing that the average number of carbons in the benzene class increases rapidly from its initial value of 6 to the same value as the average number of carbons in the naphthalene class, about 16. The cycloparaffin concentration rises steadily but is still quite low after 10 s. At longer times as the cycloparaffin concentration rose further, ring-opening reactions would lead to a transfer of carbon to the paraffin class. hydrocarbons
3 (olefins and
In all of these simulations a single value for the activation energy of initiation reactions was utilized in In order to test the sensitivity of the parameter K,,. the mode1 to the value of K,,, the simulation shown in Fig. 7 was rerun using two larger values for the activation energy of the initiation reactions. Figure 10 shows that the value of this parameter does not affect the shape of the concentration profiles. Rather, it merely alters the time scale of the simulation.
DISCUSSION
The results obtained from the numerical simulations generally agree with experimental results in the literature. However, previous experimental investigations have examined the pyrolysis or hydropyrolysis of pure compounds at low conversions, and most often focused on paraffins, olefins, and single-ring compounds. The compqund class model is explicitly intended to simulate the reactions of complex mixtures and therefore sacrifices detail concerning the specific composition of any single compound class. Nevertheless, several trends that have been observed in past investigations are demonstrated by the above results.
Compound
class modeling
2853
of hydropyrolysis Naphtholenes
Benzenes
2 ;
Paraffins
0.2 -
b r=OL
” I
0
” 3
2
4 Time
I
I
I
I
1
6 5 (seconds)
7
8
9
IO
0.8 0.7
t
Time
(seconds)
Fig. 6. Compound class concentrations and average carbon numbers for initial composition and naphthalenes, see Table 3) with hydrogen concentration = 0 mol/l at 700°C.
kE
1 (benzenes
1.2
2 .= 1.0 B $ 0.8
Paraffins
ZL o 0.6 $
t
gg
,
z”
,
I
0
,
,
2 Time
,
,
3 (seconds)
,
,
4
,
,
5
0.8 0.7
.I
Benzenes
Cyc’oparoffins
i&J+-
Time
[seconds)
Fig. 7. Compound class concentrations and average carbon numbers for initial composition 1 (benzenes and naphthalenes, see Table 3) with hydrogen concentration = 100 mol/l at 700°C.
2854
RICHARDS S. PARNAS and DAVID T. ALLEN
E
ij 0.5 z 0
I
I
1
2
I
3
I
4 Time
I
I
I
I
t
L
5
6
7
0
9
IO
(seconds)
0.008
0.8 0.7
-
-: 0.6 z 50.5 E
CParaff ins KNaphthalenes
i
Benzenes-
s 0.4 m $
0.3 Olef ins 4
-0
I
2
3
4
5
6
7
8
9
IO
-
0.007
-
0.006
- 0.005 -
0.004
-
0.003
-
0.002
-
0.001 ”
Time (seconds)
and average carbon numbers for initial composition 2 (parafins Fig. 8. Compound class concentrations naphthalenes, see Table 3) with hydrogen concentration =0 mol/l at 700°C.
Figures 3-5 show that increasing hydrogen concentration suppresses olefin formation and enhances paraffin cracking as the results of Brooks (1967) indicate. That result is to be expected since hydrogen rapidly converts olefins to paraffins. Figures 6-9 show that increasing hydrogen concentration accelerates the conversion of cyclic and aromatic compounds as Yamada and Amano (1983) have shown. Moreover, the initial hydrogenation of aromatic structures is the rate-determining step in their conversion. That cannot be seen from the figures because the concentrations of hydronaphthalenes and partially hydrogenated benzenes are not shown for the sake of clarity. In all cases, as benzenes are converted to cyclohexanes, the concentrations of intermediate molecular species, cyclodiolefins and cycloolefins, are very small relative to the benzene concentration. Similarly, as naphthalenes are converted to benzenes, the concentrations of dihydronaphthalenes and tetrahydronaphthalenes are very small. The compound class model also shows that naphthalenes are much more refractory than benzene compounds as was shown by Miki et al. (1983) and Hohnholt and Faust0 (1984). Most studies conducted previously focused on elucidating the rate parameters for individual reactions. Reactions were carried out at very low conversions to minimize interference from secondary reactions. That the results discussed above agree with trends found
and
previously reflects the fact that rate parameters and major reaction pathways were selected from the literature. Results not shown clearly in the literature revolve around the effects of mixtures on the individual compound classes. Shah et al. (1973) showed that in olefin-parafIin mixtures undergoing pyrolysis, the paraffins accelerate olefin cracking and the olefins inhibit parafIin cracking. Figures 4 and 5 show that the model accounts for these effects. In Fig. 4 very few paraffins are present and cracking does not occur to a significant extent in either the paraffins or olefins as can be seen from the curves of average carbon number. However, in Fig. 5 a larger concentration of paraffins is created and cracking reactions dominate the reaction sequence after 1.6 s in both the olefins and paraffins. Prior to I.4 s in Fig. 5, cracking reactions play a minor role since the paraffins concentration is low. The transition from addition reaction dominance to cracking reaction dominance is marked in Fig. 5 by the maxima in the curves of average carbon number for the olefins and paraffins. Rebick (1983) predicted that the presence of aromatics would inhibit the cracking of paraffins while, conversely, paraffins would accelerate the conversion of aromatics. A comparison of Figs 5 and 9 bears out that prediction. Paraffin cracking is clearly shown in Fig. 5 but is absent in Fig. 9. Aromatics inhibit paraffin
Compound
class
modeling
of hydropyrolysis
2855
28 2.6
Cycloparoffins
Naphthalenes
0.8
0
I
2
3
4 Time
5 6 (seconds)
7
8
9
IO
0.0
I5
0.014 0.013 0.012 0.01 I 0.010 0.009 0.008 0.007 0.006 Paraffins
0.005
Naphtholenes
0.004 0.003 0.002
Benzenes
-
* 0 Fig.
I
2
class concentrations 9. Compound naphthalenes, see Table
3
4 Time
5 6 (seconds)
8
9
IO
0
and average carbon numbers for initial composition 2 (paraffins 3) with hydrogen concentration = 100 mol/l at 700°C.
because they depress the number of paraffin radicals in the mixture due to the superior resonance stabilization of aromatic radicals. In Fig. 5, at t = 5 s, the concentration of paraffins is approximately 10 mol/l and the concentration of paraffin radicals is 6.9 x 10m5 mol/l. In Fig. 9, the paraffin concentration is about 10 mol/l but the paraffin radical concentration is only 5.4 x 10-s, three orders of magnitude less than in Fig. 5. The converse effect, paraffins accelerating aromatics conversion is not shown because reactions between paraffin radicals and naphthalenes were not included in the model. Preliminary thermal hydropyrolysis experiments were conducted in order to further test the model. The
cracking
7
0.001
and
experiments were performed in a stainless steel bomb reactor using an initial mixture of n-hexane, I-octene, benzene and naphthalene. The initial concentration of each reactant was 0.01 mol/l and the reactor was pressurized to 100 psi with hydrogen. The reaction was carried out at 450°C for periods of time up to 2 h. The liquid product remaining after the experiment was analyzed by gas chromatography using a non-polar (DB- 1) 30-m capillary column. The conversion of benzene and naphthalene after 10 min was correctly predicted by the model as 22 and O%, respectively. The model was able to predict conversions because benzene and naphthalene were the only components in the benzene and naphthalene
2856
RICHARDS S.
0
I
2
PARNAS
4
3
and DAVID
T. ALLEN
5
Time (seconds)
c)
z g 5
Time
4-
0
(seconds)
KEQ = 70K
I
2
Time
3 becondo)
4
Fig. 10. Effect of varying the assumed activation energy of initiation reactions from 60 to 70 kcal/mol. Initial composition 1 was used and the concentrations of the naphthalene (a), benzene(b), and cycloolefin (c) classes are plotted.
classes. The conversion of n-hexane and loctene could not be closely followed by the model because the model follows compound classes rather than individual compounds. Several other paraffins and olefins were present in the liquid product after 10 min. However, reasonable agreement was obtained between the model predictions of paraffin and olefin class concentrations and the experimentally determined n-hexane and I-octene concentrations. In order to follow the concentrations of individual compounds with a compound class model, both the average and the variance of the carbon number distribution function for each compound class must be calculated. These initial results highlight the importance of computing statistical quantities in lumped models in order to validate such models against experiment.
NOTATION
compound
CONCLl-JSrONS
A new type of compound class model has been formulated which computes the structural characteristics of each compound class in addition to the class concentrations. The structural characteristics are given by the average carbon number and the variance of the carbon number. This model was used to simulate thermal hydropyrolysis and adequately summarized the available literature data.
number of carbon atoms in compound class j average number of carbon atoms in the molecules of compound class j C Tij number of carbon atoms per molecule transferred from compound class j by reaction i D average deviation from the norm average deviation of data sample A DA K EQ equilibrium constant for the initiation and termination reactions equilibrium constant between radicals and molKj ecules of compound class j rate constant for initiation reactions ki rate constant for termination reactions k number of molecules transferred from class j by Mij reaction i in a small increment of time, the integrated rate of reaction i N rxn total number of chemical reactions in the simulated reaction scheme R a molecule a molecule in compound class i Ri R’ a radical R; a radical in compound class i norm of data sample A R” REFERENCES
D. T. and Gavalas, G. R., 1983, Kinetics of dialen thermolysis. Inr. J. &em. Kinetics 15, 219.
Allen,
Compound
class modeling
S. W., 1976, Thermochemical Kinetics, 2nd edition. Wiley. New York. Benson, S. W. and Shaw, R., 1967a, Kinetics and mechanism of the pyrolysis of 1,4-cyclohexadiene. Trans. Faraday Sac. 63, 985. Benson, S. W. and Shaw, R., 1967b, Kinetics and mechanism of the pyrolysis of l,3-cyclohexadiene. J. Am. them. Sot. 89, 5351. Bredael, P. and Rietvelde, D., 1979, Pyrolysis of hydronaphthalenes. 2. Pyrolysis of cis-decalin. D. Fuel 58, 215. Brooks, C. T., 1967, High pressure thermal hydrogenolysis of hydrocarbons. Ind. Engng Chem. Prod. Res. Dev. 6, 236. Davis, H. G., 1983, Rate of formation of toluene from ethylbenzene. Int. J. them. Kinetics 15. 469. Dente, M. E. and Ranzi, E. M., 1983, Mathematical modeling of hydrocarbon pyrolysis reactions. In Pyrolysis: Theory and Industrial Practice (Edited by G. R. Gavalas), p. 33. Academic Press, New York. Fabuss. B. M., Duncan, D. A., Smith, J. 0. and Satterfield, C. N., 1965, Elfect of organosulfur compounds on the rate of thermal decomposition of selected hydrocarbons. Ind. Engny Chem. Process Des. Dev. 4, I 17. Hohnholt, J. F. and Fausto, C., 1984, Residual oil upgrading utilizing fixed-bed hydroprocessing technology. Symp. on Petroleum Residual Upgrading, AlChE Annual Meeting. Illes, V., Welther. K. and Szepesy, L., 1974, Pyrolysis of liquid hydrocarbons IV. Acta chim. hung. 80, 1. Johnson, L. W. and Weiss, R. D., 1982, Numerical Analysis, p. 378. Addison-Wesley, Reading, MA. Kossiakoff, A. and Rice, F. O., 1943, Thermal decomposition of hydrocarbons, resonance stabilization and isomerization of free radicals. J. Am. them. Sac. 65, 590. Kuo, J. C. W. and Wei, J., 1969, A lumping analysis in Benson,
of hydropyroIysis
2857
monomolecular reaction systems. Ind. Engng Chem. Fundam. 8, 124. Liu, Y. A. and Lapidus, L., 1973, Observer theory for lumping analysis of monomolecular reaction systems. A.1.Ch.E. J. 19, 467. Miki,Y., Yamadaya,S., Oba, M. and Sigmoto, Y., 1983, Role of catalyst in cracking heavy oil. J. Catalysis 83, 371. Penninger, J. M. L. and Slotboom, H. W., 1973, Kinetics and mechanism of primary cracking reactions in thermal high pressure hydrogenolysis of tetralin and indan. Part I. Recueil 92, 5 13. Rebick, C., 1983. Pyrolysis of heavy hydrocarbons. In Pyrolysis: Theory and Industrial Practice (Edited by G. R. Gavalas), p. 69. Academic Press, New York. Rice, F. O., 1933, The thermal decomposition of organic compounds from the standpoint of free radicals. III. J. Am. them. Sac. 55, 3035. Shah, Y. T., Stuart, E. B. and Kunzru, D., 1973, Thermal cracking of hydrocarbon mixtures. Ind. Enyng C’hem. Process Des. Deo. 12, 344 Shultz, E. B. and Linden, H. R., 1962, Pressure hydrogenolysis of paraffins. Ind. Euyng Chem. Process Rrs. Drv. 1, 1 i 1. Stein, S. E., 1981, Thermochemical kinetics of anthraccnc pyrolysis. Carbon 19, 421. Wei, J. and Kuo, J. C. W., 1969, A lumping analysis in monomolecular reaction systems. Ind. Engng chrm. Fundam. 8. I 14. Yamada, M. and Amano, A., 1983, Pyrolysis: hydrogenolysis of toluene. In Pyrolysis: Theory and Industrial Practice (Edited by G. R. Gavalas), p. 117. Academic Press, New York. Zimmerman, C. C. and York, R., 1964, Thermal demethylation of toluene. ind. Engng Chem. Process Des. Der. 3, 254.
Vol.
43. No.
10, pp. 2845-2857,
1988. 0
COMPOUND
CLASS RICHARD
Department (First
MODELING S. PARNAS
received
2 December
OF HYDROPYROLYSIS
and DAVID
of Chemical Engineering, UCLA, 1986, accepted
ooo%2so9/88 %3.00+0.00 1988 Pergamon Press plc
T. ALLEN’
Los Angeles, CA 90024, U.S.A. in revisedform
28 April
1988)
Abstract-The primary objective of this work is to extend the utility of compound class modeling for complex kinetic systems. Compound class modeling involves lumping the many species of a complex mixture into classes based on chemical structure and has been applied to many types of reacting systems. Each compound class represents many species, and previous compound class models have not satisfactorily addressed the problem that the chemical characteristics of the classes can change as the reactions progress. This limitation has prevented the full exploitation of compound class models. In this work we extend compound class modeling by following not only the concentration of each class but also the average carbon number and variance of the carbon number distribution for each compound class. The thermal hydropyrolysis of reacting hydrocarbon mixtures will be used as an example of a complex reaction network involving many components. For thermal hydropyrolysis, 10 compound classes were proposed and rate parameters derived from model compound studies were used to estimate the rates of interconversion among compound classes. The compound class model is in qualitative agreement with experimental observations reported in this work and with results available in the literature.
INTRODUCTION
The primary objective of this work is to extend the utility of compound class modeling for kinetic systems containing a very large number of components. Since the precise composition of such complex mixtures cannot always be determined, some type of lumping based upon measurable quantities is necessary to model chemical kinetics. Compound class modeling involves lumping the many species of a complex mixture into classes based on chemical structure. Once the compounds are lumped into classes, individual reactions can no longer be followed. Instead, the transformations that occur at specific bond locations are used to describe the chemical changes that transform material in one compound class into another class. Previous literature on modeling complex kinetic systems developed the concepts of exact and approximate lumping (Wei and Kuo, 1969; Kuo and Wei, 1969; Liu and Lapidus, 1973). However, previous models calculated only the concentrations of the compound classes. Also, most previous models used empirically derived rate constants and in general have not relied on fundamental rate parameters. Aggregate, or lumped rate constants have been used to represent the kinetic behavior of the compound classes. The model presented in this work differs in two respects from most previous lumped kinetic models. First, in addition to the total concentration of each kinetic lump, the model computes statistical quantities such as the average carbon number of each compound class. A method for computing the variance around the average carbon number is also presented. A second nove1 feature of this model is the use of fundamental +To whom correspondence should be addressed. CES
43:10-s
2845
rate parameters in describing the chemical reactions of the compound classes. This paper will focus on thermal hydropyrolysis of heavy oils as an example of a complex reacting system amenable to a compound class approach. Compound class concentrations and average carbon numbers will be computed. Rate parameters will be based on the literature described below. The pyrolysis and hydropyrolysis of relatively light hydrocarbons have been studied in great detail. Brooks (1967), and Shultz and Linden (1962) studied the effects of hydrogen pressure and tetiperature on the thermal hydropyrolysis of straight-chain paraffins. Illes et al. (1974) studied the pyrolysis of branched paraffins. Benson and Shaw (1967a, b) studied the pyrolysis of cyclic paraffins, paraffins, olefins and cycloolefins. Fabuss et al. (1965) studied the effect of sulfur on the pyrolysis of saturated hydrocarbons. Rebick (1983) summarizes these and several other studies, concluding that the free-radical mechanism first proposed by Rice (1933) and later modified by Kossiakoff and Rice (1943) is almost universally accepted as the mechanism of thermal hydrocarbon cracking. Investigations of the pyrolysis and hydropyrolysis of aromatic materials are less evident in the literature than are studies of the lighter hydrocarbons mentioned above. The thermal demethylation of toluene was studied by Zimmerman and York (1964). More recently, Davis (1983) studied the formation of toluene from ethylbenzene by thermal pyrolysis. Yamada and Amano (1983) report a study on the hydropyrolysis of toluene and conclude that the free-radical mechanism is valid for the pyrolysis of aromatic as well as saturated hydrocarbons. Pyrolysis of partially hydrogenated naphthalenes has been studied by Bredael and Rietvelde (1979) and Allen and Gavalas (1983).
2846
RICHARDS
S. PARNAS and DAVID
Analysis of the product composition from the decomposition of two ring compounds is complicated by the large number of secondary reactions that may occur with such complicated starting materials. Hydropyrolysis of two ring compounds has been investigated by Penninger and Slotboom (1973). In order to retain reasonable simplicity, they studied the reactions at very low conversions and found that free-radical mechanisms adequately explained their experimental data. Even in the presence of large excess quantities of hydrogen, a small amount of dehydrogenation to condensed material occurred. The only available work on pyrolysis of heavier aromatic materials is on the pyrolysis of anthracene (Stein, 1981). The predictions of thermochemical kinetics developed by Benson (1976) were used to differentiate plausible from implausible kinetic mechanisms. Detailed mechanistic models of the free-radical chemistry of hydropyrolysis can be proposed based on the thermochemical estimation techniques of Benson and the experimental work outlined above. Dente and Ranzi (1983) wrote such a detailed model for the thermal pyrolysis of light hydrocarbons, e.g. butane, and were very successful at predicting experimental results. Their model included I I6 reactions and 45 individual species. To model a heavy hydrocarbon mixture, detailed mechanistic modeling of every reaction and species is not possible. Dente and Ranzi lump heavy components of naphtha and gas oil feedstocks into compound classes to simplify the reaction network but still report a reaction scheme of over 2000 reactions and 100 species. Hydropyrolysis of heavy crudes or coal-derived liquids require further simplification of the reaction scheme. This work seeks to drastically simplify the reaction scheme necessary to describe hydropyrolysis and yet retain enough detail about the product composition to be useful. COMPOUND
CLASS
MODELING
Ten compound classes will be considered in this model of thermal hydropyrolysis. The classes are listed in Table I and include a variety of aliphatic, olefinic and aromatic groups. A more extensive list could be formulated; however, these classes are readily measurable and include most of the molecular classes present in heavy oils. Larger aromatic structures will be considered in future work.
Table 1. Class no.
Class name
1 2 3 4 5 6 7 8 9 10
Paraffins Olefins Cycloparaffins Cycloolefins Cyclodiolefins Benzenes Tetrahydronaphthalenes Dihydronaphthalenes Naphthalenes Diolefins
T. ALLEN
The free-radical reactions of the compound classes include initiation, termination and propagation steps. The propagation reactions are subdivided into those that have high rates (hydrogen abstraction) and four reversible unit transformations that occur at lower rates. The four types of slower propagation reactions include: (I)
/I-scission of a carbon-carbon bondtifreeradical addition to a double bond (2) H atom addition%loss of H atom (3) cleavage of aryl-R bond%radical attack on aromatic (4) cleavage of aryl-aryl bond*aryl radical attack on aromatic
Examples of these reactions are shown in Fig. 1. The pscission reaction is one in which a carbon+arbon bond in the /J-position relative to a radical breaks, producing a molecule with an alpha double bond and a smaller radical. The reverse of p-scission is a freeradical addition reaction in which a radical attacks a double bond. Cleavage of the aryl-R bond is a reaction in which the substituent on an aromatic ring is removed following an attack by an H atom, producing a less substituted aromatic and a paraffin radical. Paraffin radicals may also attack aromatic structures in the reverse reaction. Aromatic structures that are not fully condensed may break at aryl-aryl bonds following attack by hydrogen atoms, producing smaller aromatics and aromatic radicals. Several simplifying assumptions are used in the model. Substituents on single-ring compounds are assumed to be saturated straight-chain hydrocarbons. Therefore, only the paraffin and single-ring compound classes interact through unit transformation (3). Substituents on double-ring aromatic compounds are assumed to be aromatic rings. Therefore, only the single and double-ring compound cIasses interact through unit transformation (4). The total concentration of radicals is calculated using the pseudo-steady-state approximation. Also.
p Sclsslon
free
_
/ 0
addltlon
z==
/-lPL/H atom
rodvxtl
addttlon
fH’
_
it/--l_/
dehydrogenation *
-
0
Cleavage
of Aryl-X
Cleavage
of Aryl-Aryl
bond
ZII!
bond
rodeo1
_
Aryl
Fig. 1. Examples of the propagation
ctttock
radlcol
on
aromatIc
attack on oromarlc
reaction classes.
Compound class modeling of hydropyrolysis termination by disproportionation is neglected. total radical concentration is given by
CR’1= WEOCR~Y
The
(1)
where K,o is the equilibrium constant for the appropriate initiation and termination reactions, and [R] is the total concentration of molecular species. Although a more rigorous formulation of eq. (1) would include only radical-forming species in [R]. an algorithm for following just those species as their concentrations evolve over time has not yet been included in the model. To estimate Kbu, values for the Arrhenius parameters of initiation and termination reactions available in the literature (Allen and Gavalas, 1983; Dente and Ranzi, 1983) were reviewed. Activation energies for most initiation reactions lie in the range of 70-90 kcal/mol. For olefins, activation energies on the order of 30 kcal/mol are reported for initiation reactions. However, the olefin reactions are generally disproportionation reactions and although the activation energies are low, the preexponential factors are also low, resulting in overall rate constants similar to those for other compounds. A value of 60 kcal/mol for the activation energy of initiation reactions was chosen as a compromise between the low activation energies of disproportionation and the higher activation energies of other initiation reactions. The reported activation energies for termination reactions are zero as expected for radical recombination. After similar considerations, a value of 1OL6 was chosen for the preexponential factor of initiation reactions and a value of IO’” was chosen for the preexponential factor of termination reactions. The equilibrium constant K EQ is then given by K,,=:=
lo6 exp(-60,000,RT).
(2)
t The parameter
K,,
must be viewed as an adjustable
parameter in the current formulation of the model. The value of this parameter should be a function of composition. The sensitivity of the model to changes in K,, will be examined later in this work. The hydrogen abstraction reactions that occur during hydropyrolysis are assumed to be fast relative to the other propagation reactions. Therefore, each compound class i is assumed to be in equilibrium with the radicals of the species making up the compound class: R,+R’%R,‘+R
(3)
CR'liCRl
K,=
’
CRliCR'l
(4)
’
The ratio of the concentrations of any two classes of radicals, i and j, are then given by the ratios of their associated molecular compound classes and their equilibrium constants:
CR’li -=-_ CR’lj
KiCRl, Kj CRlj
(5)
The totat radical concentration defined in eq. (1) and the ratios of the radical concentrations defined in eq. (5) can be used to calculate the concentration of radicals in each compound class. The total radical concentration and the concentration of the various radical classes are allowed to change over time as the molecular class concentrations evolve. In this model, the parameter KEQ is a constant although one may expect that K,, would also change over time since it is an aggregate parameter relating total molecular and radical concentrations. In future versions of the compound class model, K EQ may depend upon the overall mixture composition. The kinetic model consists of 29 reactions interconnecting 10 compound classes. A schematic diagram of the major reaction pathways is shown in
l(7)
poroffm radlcols 4
2847
cycloparoffin radicals
I A
llll-0 ..-.
4
I
3(25)
I (IO)
l(ll)
2YEl,
2q:9,
‘I 3
I(z2)
benzenes
cycle-diolefins
cycle-OkfIns
benzene rodxols
cycio-dlolefm rodlcals
cycle-olef radicals
t
5(26) 5(29)
-
in
tetra- hydra naphthalenes
di-hydro naphtholenes
tetra- hydro naphtholene radicals
dl-hydro naphthalene radicals
4 naphthalenes naphthatene radicals
Fig. 2. Schematic-diagram of the simulated reaction network showing major reaction pathways. The numbers
that label each arrow
indicate the unit transformation and, in parentheses, defined in Table 2.
the reaction
number,
as
RICHARDS S. PARNAS and DAVID
2848
Fig. 2. Each compound class occupies a box and reaction pathways are shown by the connecting arrows. The 29 reactions and their rate constants are
Table
No. 1 2 3 4 5 6 7 8 9 IO
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27 28 29
2. Reaction
T. ALLEN
given in Table 2. The Arrhenius parameters were taken from Dente and Ranzi (1983) and Allen and Gavalas (1983).
rate parameters
Reaction J?-Scission of paraffin radical + olefin + smaller paraffin radical Loss of H atom from paraffin radical + olefin Paraffin radical + olefin --t large paraffin radical H atom + olefin - paraffin radical &Scission of olefin radical + diolefin + smaller olefin radical Olefin radical + olefin + larger olefin radical /?-Scission of cycloparaffin radical + olefin radical Loss of H atom from cycloparaffin radical + cycloolefin H atom + cycloolefin t cycloparaffin radical p-Scission of substituent from a cycloparaffin radicalparaffin radical + cycloolefin Paraffin radical tcycloolelin - cycloparafik radical Loss of H atom from cycloolefin radical + cyclodiolefin H atom + cyclodiolefin -+ cycloolefin radical /3-Scission of substituent from a cycloolefin radical paraffin radical tcyclodiolefin Paraffin radical +cyclodiolefin + cycloolefin radical Loss of H atom from cyclodiolefin + single ring aromatic H atom + single-ring aromatic - cyclodiolefin radical Loss of H atom from tetrahydronaphthalene radical+dihydronaphthalene Loss of H atom from dihydronaphthalene radical+naphthalene H atom + naphthalene - dihydronaphthalene radical H atom +dihydronaphthalene -+ tetrahydronaphthalene radical j?-Scission of tetrahydronaphthalene radical+single-ring aromatic Naphthalene radical + benzene - substituted naphthalene rddicdl Naphthalene radical + naphthalene - substituted naphthalene radical Cleavage of aryl-X bond of singlering aromatic radicalparaffin radical + single-ring aromatic Cleavage of aryl-aryl bonds to substituted naphthalene radicals+ benzene radicals + naphthalene + naphthalene radicals Loss of H atom from olefin radicals + dioletins H atom + diolefin - olefin radical Benzerle radical + naphthalene -+ substituted naphthalene radical
(s-’
A
or I mol-‘s-l)
E (cal/mol)
10’4s-’
40,000
10’4sC’
40,000
lO”lmol-Is-’
15,000
iO’“.5
1rnol-‘~-~
2000 40,000
10’4S_’ 1O”.5 lmol-‘s-’
6000
10’4sm’
40,000
10’4s-’
45,000
10’0~51mol-‘s-’
2000
10’4s~’
45,000
IO8 Imol-Is-’
15,ooo
10’4sC’
40,000
10”
lmol-‘s-’
3000
10’4s-’
40,000
IO” lmol-‘s-l
15.000
10’4s-’
30,000
IO” Imol-‘s-’
3000
10’4s-’
40.000
10’4.5 sm 1
27,000
IO”
Imol~‘s~’
3000
10’451mol-‘s-1
3000
,014 5 s-
1
30,000
10” lmol~‘s~
35,000
10” lmol-Is-’
35,000
5x 10hlmol-‘s-l
39,000
5x 1061mol-Is-’
39,000
10’3s-’
35,000
1O’o.5 1 mol- ’ s- ’ 108Jmol-‘s-’
2000 20,000
Compound
class
Tables I and 2 indicate that hydropyrolysis kinetics of heavy hydrocarbons can be formutated in a much simpler manner than a detailed mechanistic model. The most important simplification is the reduction of the number of components from several hundred in a hydrocarbon mixture to a number on the order of IO in the compound class model. The current model can be run on a mini-computer (VAX 1 l/750) while full mechanistic models would require the use of supercomputers. The question remains, can the compound class model provide adequate details of the product distribution to be useful? Each compound class represents many compounds, so, integrating the differential equations for the concentrations of each compound class in the mixture will not provide adequate detail about the product distribution. Additional quantities such as the average number of carbon atoms in each compound class, the average length of substituents, and the variance of these two quantities should provide enough detail to make the compound class model useful. Such quantities can be calculated algebraically from the reaction rates and compound class concentrations. The average number of carbon atoms in each molecule of a compound class is simply the total number of carbon atoms in the compound class divided by the number of molecules. or the concentration of the class. Each reaction transfers carbon atoms from one compound class to another. For example, reaction I creates a smaller paraffin radical and an olefin from the pscission of a paraffin radical. If it is assumed that the location of the scission is random, it can be shown that, on average, paraffin radicals break in half, transferring half their carbons to the olefin compound class and retaining half their carbons in the paraffin class. Let Mij be the number of molecules of class j transferred to another class in a small increment of time At by reaction i. Also, let CT,, be the number of carbon atoms per molecule transferred by reaction i. Then, general algebraic equations can be formulated to keep track of the movement of carbon atoms throughout the reaction network. If Cj is the number of carbon atoms in class j at time r then N-.x,
CjI,+*t= Cjl,f
c
MijCTij.
i=l
The number of molecules, or the concentration Rj, of compound class j is obtained by numerically integrating the net rate of formation of molecules of the class:
Rjlr+nr= Rilt+At
=Cjlr+ctrlRjlt
of carbons in the molecules of the compound class from which material is being drawn. For example, reaction 4, in which an H atom adds to an olefin to give a paraffin radical, transfers molecules from the olefin class to the paraffin class. The number of carbons transferred per molecule is simply the average number of carbons in each molecule of the olefin class. Another example is reaction 29, the free radical addition of naphthalene and benzene radicals which produces substituted naphthalenes. Reaction 29 does not change the concentration of the naphthalene class but it does reduce the benzene class concentration. The effect of reaction 29 on the naphthalene class is to increase the average number of carbon atoms in the molecules of the naphthalene class. Further addition of aromatic materials and ring closure reactions which are not included in the model would lead to coke precursors. Following the average number of carbons in the molecules of each compound class in addition to the concentration of the classes provides additional insight into the evolving composition of the hydropyrolysis product. Greater insight may be obtainable by following higher moments of the compound classes such as the variance of the average number of carbons of each class. In that case information on the product distribution within each compound class would become available. The usual measure of the variance of a sample is the standard deviation. However, the standard deviation involves nonlinear terms and it may be difficult to derive proper mixing rules for the calculation of the variance around the average. A simpler measure of the variance is the average deviation about the norm defined below:
D=i=l
N
+At-
(8)
The number of carbon atoms transferred by reaction i, CT,,, depends on the reaction and the average number
(9)
where N = the size of the sample, x= the sample average, and Xi=the ith value in the sample. The average deviation is used because computing the upper bound on the deviation of mixed samples is much easier with the average rather than with the standard deviation. If sample A with average R, and deviation D, is mixed with sample B, the resulting sample C average is the weighted sum of the averages of samples A and B: R,.=
N/,x,
+ N,i?,
N,fN,
N”,”
c dM,,/dt. (7) i= I More variable-step fourth-order precisely, a Runge-Kutta integration algorithm was used to integrate the concentrations as well as to obtain the individual Mij (Johnson and Riess, 1982). The average number of carbon atoms in classj is then Cjavg
2849
modeling of hydropyrolysis
The average deviation weighted sum: D,<
can be bounded
N,(D,+lK,-K,I)+N,(D,+IK,--R,I) N,+N,
(10) by a similar
(II1
For the system of chemical reactions used in hydropyrolysis the deviations of the number of carbons from the average in each compound class can be computed using the above formula.
RICHARDS
2850
S. PARNAS and
DAVID T. ALLEN Table
RESCJI.TS
The compound class model was integrated numerically under a variety of conditions to assess its ability to describe thermal hydropyrolysis. The,temperature, hydrogen concentration, and initial hydrocarbon composition (see Table 3) were varied. The numerical simulations were carried out with a VAX I l/750 computer. Most runs simulated IO s of real time but this was not feasible in all cases. At the higher temperatures, especially with high hydrogen concentrations, the system of equations became quite stiff and required large amounts of computer time. Therefore, some of the runs simulated 5 s of real time. Representative results are shown in Figs 3-9. Concentrations of the major compound classes are plotted against time as are the average number of carbon atoms in each class. Figures 335 show results using an initial mixture containing olefins and benzenes (mixture no. 3 in Table 3). These results summarize the model capabilities for handling light, reactive hydrocarbons. In Fig. 3, at 700°C with no hydrogen, the benzenes are unreacted after 10 s. The olefin concentration drops while the average length of olefin molecules increases dramatically, indicating that polymerization occurs to a great extent at those conditions. The extent of polymerization shown in Figs 3
I8
3. Initial compositions
used in the simulations
(1) [Paraffins] [Benzenes] [Naphthalenes]
0.1 mol/l 10.0 mol/l 5.0 mol/l
C,,,,= 12 carbons C,,,, = 10 carbons C,,,, = 10 carbons
(2) [Paraffins] [Benzenes] [Naphthalenes]
10.0 mol/l 0.1 mol/l 10.0 mol/l
C,,,, = 12 carbons C,,,,= 6 carbons Caavg = 16 carbons
(3) [Olefins] [Benzenes]
5.0 mol/l 10.0 mol/l
C,,,,= C,.,,=
7 carbons 6 carbons
and 4 is probably much larger than would occur in a reacting mixture because ring closure reactions are not included in the model. Figure 4, also at 7OO”C, shows the effect of adding a small amount of hydrogen to the initial hydrocarbon mixture. Again, the benzene class is virtually unaffected. However, a smatl amount of paraffin is produced by hydrogenation of olefins. In Fig. 5, substantial hydrogen is added at 6OO’C and the results are markedly different from those shown in the previous two figures. Both the olefin and benzene concentrations become very small within the first 2 s. The paraffin concentration increases rapidly due to hydrogenation. The cycloparaffin concentration increases rapidly at first due to hydrogenation, goes through a maximum, and then decreases more slowly
, Olef ins
16 14 12 IO 8-
Diolefins
0’
’ 0
I
’ 2
’ 3
1 4 Time
I
,
5
6
I
7
I
8
I
9
--
1
IO
i
(seconds)
0
ooa
1 0.005 0004 0003
_y
. 0
0
I
2
1
3
D(olefins-
4 Time
5
6
7
8
9
IO
0.002 ooo,
0
(seconds)
and the compound class average carbon number Fig. 3. Evolution of the compound class concentrations initial composition 3 (olefins and benzenes, see Table 3) with no added hydrogen at 700°C.
for
Compound
class modeling
2851
of hydropyrolysis
91 Olefins
Diolefins Paraffins
Benzenes 01 0
0.8
1 I
1 2
1 3
I 4 Time
1 I 5 6 (seconds)
I 7
I 6
I 9
IO
, 0.008
r
_1 0.003
Diolef ins _
- 0.001 r-l
-0
Fig. 4. Compound
I
2
3
4 Time
class concentrations
5 6 (seconds)
7
and average
benzenes, see Table 3) with hydrogen
as scission reactions open the ring. The sizes of paraffins in the reaction mixture change as time progresses. The average number of carbons in the olefins and paraffins classes increases initially, then decreases as cracking reactions in the paraffins dominate after 2 s. Figures 6 and 7 show aromatic chemistry using initial composition no. 1, made up predominantly of benzenes and naphthalenes. The initial average number of carbon atoms in the benzene molecules is 10, indicating that the benzenes are substituted. Figure 6, at 700°C with no hydrogen, shows the addition of naphthalene and benzene radicals as well as the breaking of substituents from the benzene rings. The increase in paraffin concentration and the decrease in the average number of carbon atoms indicates that the molecules making up the paraffin class are increasingly scission products from the benzene class. Moreover, the average number of carbon atoms in the benzene class decreases over time, indicating that the substituents are being removed. The concentration of the naphthalene class remain nearly constant but the average number of carbons increases. The source of the additional carbons in the naphthalene class is the benzene class as can be seen by observing that the
8
IO
9
carbon numbers for initial composition concentration = 0.1 mol/l at 700°C.
3 (olefins and
benzene class concentration decreases over time. Thus, benzene class radicals are undergoing addition to the naphthalenes (reactions 23 and 30 in Table 2). Figure 7 shows the result of adding hydrogen at 700°C to the same initial mixture as was used to generate Fig. 6. The benzenes rapidly hydrogenate while the naphthalenes do so more slowly. The average carbon number of the naphthalene class stays nearly constant, indicating that the combination of benzenes cant
and naphthalenes
extent.
naphthalene
The
average
molecules
does number increases
not occur
to a signifi-
of carbons very
slowly.
in the The
average number of carbons in the benzene class approaches the same value as that for the naphthalenes after a lag of about 2 s. After the initial supply of benzenes hydrogenate. the naphthalene class is a small but steady supplier of carbon to the benzene class. The average length of paraffins goes to about 10, the average number of carbons in the aromatic classes. Then, the paraffin concentration gradually increases as carbon is transferred through the cycloparaffin class from the aromatics. The rate-limiting steps of hydrogenation are the conversion of naphthalenes to benzenes. Figures 8 and 9 show the interaction between light
RICHARDS S. PARNAS and DAVID T. ALLEN
2852
Benzenes. Cycloporaffins Poraff ins Olefins
I:;/ 0
,
,
,
I
2
3
,
,
,
4 5 6 Time (seconds)
L
,
,
,
7
8
9
IO
1.0 0.9 0.8 -
Cycloporaffins
-0
I
2
3
4 5 6 7 Time (seconds)
8
9
IO
Fig. 5. Compound class concentrations and average carbon numbers for initial composition benzenes, see Table 3) with hydrogen concentration= 10 mol/l at 600°C.
and aromatics in hydropyrolysis using initial composition no. 2, mainly paraffins and naphthalenes. In both Figs 8 and 9 the paraffin concentration and average number of carbons do not change significantly. In the presence of light hydrocarbons only, as in Figs 3-5, cracking reactions were important for paraffins. In Fig. 8, at 700°C with no hydrogen, the naphthalenes condense with themselves slightly and with the small amount of benzenes present. Some paraffin cracking does occur as is evidenced by the small amount of olefins formed. Figure 9 shows the result of adding hydrogen at 700°C to the same initial hydrocarbon mixture as was shown in Fig. 8. The benzene concentration decreases to a low but constant level maintained by naphthalene hydrogenation. That the benzene concentration is maintained by naphthalene hydrogenation is readily seen by observing that the average number of carbons in the benzene class increases rapidly from its initial value of 6 to the same value as the average number of carbons in the naphthalene class, about 16. The cycloparaffin concentration rises steadily but is still quite low after 10 s. At longer times as the cycloparaffin concentration rose further, ring-opening reactions would lead to a transfer of carbon to the paraffin class. hydrocarbons
3 (olefins and
In all of these simulations a single value for the activation energy of initiation reactions was utilized in In order to test the sensitivity of the parameter K,,. the mode1 to the value of K,,, the simulation shown in Fig. 7 was rerun using two larger values for the activation energy of the initiation reactions. Figure 10 shows that the value of this parameter does not affect the shape of the concentration profiles. Rather, it merely alters the time scale of the simulation.
DISCUSSION
The results obtained from the numerical simulations generally agree with experimental results in the literature. However, previous experimental investigations have examined the pyrolysis or hydropyrolysis of pure compounds at low conversions, and most often focused on paraffins, olefins, and single-ring compounds. The compqund class model is explicitly intended to simulate the reactions of complex mixtures and therefore sacrifices detail concerning the specific composition of any single compound class. Nevertheless, several trends that have been observed in past investigations are demonstrated by the above results.
Compound
class modeling
2853
of hydropyrolysis Naphtholenes
Benzenes
2 ;
Paraffins
0.2 -
b r=OL
” I
0
” 3
2
4 Time
I
I
I
I
1
6 5 (seconds)
7
8
9
IO
0.8 0.7
t
Time
(seconds)
Fig. 6. Compound class concentrations and average carbon numbers for initial composition and naphthalenes, see Table 3) with hydrogen concentration = 0 mol/l at 700°C.
kE
1 (benzenes
1.2
2 .= 1.0 B $ 0.8
Paraffins
ZL o 0.6 $
t
gg
,
z”
,
I
0
,
,
2 Time
,
,
3 (seconds)
,
,
4
,
,
5
0.8 0.7
.I
Benzenes
Cyc’oparoffins
i&J+-
Time
[seconds)
Fig. 7. Compound class concentrations and average carbon numbers for initial composition 1 (benzenes and naphthalenes, see Table 3) with hydrogen concentration = 100 mol/l at 700°C.
2854
RICHARDS S. PARNAS and DAVID T. ALLEN
E
ij 0.5 z 0
I
I
1
2
I
3
I
4 Time
I
I
I
I
t
L
5
6
7
0
9
IO
(seconds)
0.008
0.8 0.7
-
-: 0.6 z 50.5 E
CParaff ins KNaphthalenes
i
Benzenes-
s 0.4 m $
0.3 Olef ins 4
-0
I
2
3
4
5
6
7
8
9
IO
-
0.007
-
0.006
- 0.005 -
0.004
-
0.003
-
0.002
-
0.001 ”
Time (seconds)
and average carbon numbers for initial composition 2 (parafins Fig. 8. Compound class concentrations naphthalenes, see Table 3) with hydrogen concentration =0 mol/l at 700°C.
Figures 3-5 show that increasing hydrogen concentration suppresses olefin formation and enhances paraffin cracking as the results of Brooks (1967) indicate. That result is to be expected since hydrogen rapidly converts olefins to paraffins. Figures 6-9 show that increasing hydrogen concentration accelerates the conversion of cyclic and aromatic compounds as Yamada and Amano (1983) have shown. Moreover, the initial hydrogenation of aromatic structures is the rate-determining step in their conversion. That cannot be seen from the figures because the concentrations of hydronaphthalenes and partially hydrogenated benzenes are not shown for the sake of clarity. In all cases, as benzenes are converted to cyclohexanes, the concentrations of intermediate molecular species, cyclodiolefins and cycloolefins, are very small relative to the benzene concentration. Similarly, as naphthalenes are converted to benzenes, the concentrations of dihydronaphthalenes and tetrahydronaphthalenes are very small. The compound class model also shows that naphthalenes are much more refractory than benzene compounds as was shown by Miki et al. (1983) and Hohnholt and Faust0 (1984). Most studies conducted previously focused on elucidating the rate parameters for individual reactions. Reactions were carried out at very low conversions to minimize interference from secondary reactions. That the results discussed above agree with trends found
and
previously reflects the fact that rate parameters and major reaction pathways were selected from the literature. Results not shown clearly in the literature revolve around the effects of mixtures on the individual compound classes. Shah et al. (1973) showed that in olefin-parafIin mixtures undergoing pyrolysis, the paraffins accelerate olefin cracking and the olefins inhibit parafIin cracking. Figures 4 and 5 show that the model accounts for these effects. In Fig. 4 very few paraffins are present and cracking does not occur to a significant extent in either the paraffins or olefins as can be seen from the curves of average carbon number. However, in Fig. 5 a larger concentration of paraffins is created and cracking reactions dominate the reaction sequence after 1.6 s in both the olefins and paraffins. Prior to I.4 s in Fig. 5, cracking reactions play a minor role since the paraffins concentration is low. The transition from addition reaction dominance to cracking reaction dominance is marked in Fig. 5 by the maxima in the curves of average carbon number for the olefins and paraffins. Rebick (1983) predicted that the presence of aromatics would inhibit the cracking of paraffins while, conversely, paraffins would accelerate the conversion of aromatics. A comparison of Figs 5 and 9 bears out that prediction. Paraffin cracking is clearly shown in Fig. 5 but is absent in Fig. 9. Aromatics inhibit paraffin
Compound
class
modeling
of hydropyrolysis
2855
28 2.6
Cycloparoffins
Naphthalenes
0.8
0
I
2
3
4 Time
5 6 (seconds)
7
8
9
IO
0.0
I5
0.014 0.013 0.012 0.01 I 0.010 0.009 0.008 0.007 0.006 Paraffins
0.005
Naphtholenes
0.004 0.003 0.002
Benzenes
-
* 0 Fig.
I
2
class concentrations 9. Compound naphthalenes, see Table
3
4 Time
5 6 (seconds)
8
9
IO
0
and average carbon numbers for initial composition 2 (paraffins 3) with hydrogen concentration = 100 mol/l at 700°C.
because they depress the number of paraffin radicals in the mixture due to the superior resonance stabilization of aromatic radicals. In Fig. 5, at t = 5 s, the concentration of paraffins is approximately 10 mol/l and the concentration of paraffin radicals is 6.9 x 10m5 mol/l. In Fig. 9, the paraffin concentration is about 10 mol/l but the paraffin radical concentration is only 5.4 x 10-s, three orders of magnitude less than in Fig. 5. The converse effect, paraffins accelerating aromatics conversion is not shown because reactions between paraffin radicals and naphthalenes were not included in the model. Preliminary thermal hydropyrolysis experiments were conducted in order to further test the model. The
cracking
7
0.001
and
experiments were performed in a stainless steel bomb reactor using an initial mixture of n-hexane, I-octene, benzene and naphthalene. The initial concentration of each reactant was 0.01 mol/l and the reactor was pressurized to 100 psi with hydrogen. The reaction was carried out at 450°C for periods of time up to 2 h. The liquid product remaining after the experiment was analyzed by gas chromatography using a non-polar (DB- 1) 30-m capillary column. The conversion of benzene and naphthalene after 10 min was correctly predicted by the model as 22 and O%, respectively. The model was able to predict conversions because benzene and naphthalene were the only components in the benzene and naphthalene
2856
RICHARDS S.
0
I
2
PARNAS
4
3
and DAVID
T. ALLEN
5
Time (seconds)
c)
z g 5
Time
4-
0
(seconds)
KEQ = 70K
I
2
Time
3 becondo)
4
Fig. 10. Effect of varying the assumed activation energy of initiation reactions from 60 to 70 kcal/mol. Initial composition 1 was used and the concentrations of the naphthalene (a), benzene(b), and cycloolefin (c) classes are plotted.
classes. The conversion of n-hexane and loctene could not be closely followed by the model because the model follows compound classes rather than individual compounds. Several other paraffins and olefins were present in the liquid product after 10 min. However, reasonable agreement was obtained between the model predictions of paraffin and olefin class concentrations and the experimentally determined n-hexane and I-octene concentrations. In order to follow the concentrations of individual compounds with a compound class model, both the average and the variance of the carbon number distribution function for each compound class must be calculated. These initial results highlight the importance of computing statistical quantities in lumped models in order to validate such models against experiment.
NOTATION
compound
CONCLl-JSrONS
A new type of compound class model has been formulated which computes the structural characteristics of each compound class in addition to the class concentrations. The structural characteristics are given by the average carbon number and the variance of the carbon number. This model was used to simulate thermal hydropyrolysis and adequately summarized the available literature data.
number of carbon atoms in compound class j average number of carbon atoms in the molecules of compound class j C Tij number of carbon atoms per molecule transferred from compound class j by reaction i D average deviation from the norm average deviation of data sample A DA K EQ equilibrium constant for the initiation and termination reactions equilibrium constant between radicals and molKj ecules of compound class j rate constant for initiation reactions ki rate constant for termination reactions k number of molecules transferred from class j by Mij reaction i in a small increment of time, the integrated rate of reaction i N rxn total number of chemical reactions in the simulated reaction scheme R a molecule a molecule in compound class i Ri R’ a radical R; a radical in compound class i norm of data sample A R” REFERENCES
D. T. and Gavalas, G. R., 1983, Kinetics of dialen thermolysis. Inr. J. &em. Kinetics 15, 219.
Allen,
Compound
class modeling
S. W., 1976, Thermochemical Kinetics, 2nd edition. Wiley. New York. Benson, S. W. and Shaw, R., 1967a, Kinetics and mechanism of the pyrolysis of 1,4-cyclohexadiene. Trans. Faraday Sac. 63, 985. Benson, S. W. and Shaw, R., 1967b, Kinetics and mechanism of the pyrolysis of l,3-cyclohexadiene. J. Am. them. Sot. 89, 5351. Bredael, P. and Rietvelde, D., 1979, Pyrolysis of hydronaphthalenes. 2. Pyrolysis of cis-decalin. D. Fuel 58, 215. Brooks, C. T., 1967, High pressure thermal hydrogenolysis of hydrocarbons. Ind. Engng Chem. Prod. Res. Dev. 6, 236. Davis, H. G., 1983, Rate of formation of toluene from ethylbenzene. Int. J. them. Kinetics 15. 469. Dente, M. E. and Ranzi, E. M., 1983, Mathematical modeling of hydrocarbon pyrolysis reactions. In Pyrolysis: Theory and Industrial Practice (Edited by G. R. Gavalas), p. 33. Academic Press, New York. Fabuss. B. M., Duncan, D. A., Smith, J. 0. and Satterfield, C. N., 1965, Elfect of organosulfur compounds on the rate of thermal decomposition of selected hydrocarbons. Ind. Engny Chem. Process Des. Dev. 4, I 17. Hohnholt, J. F. and Fausto, C., 1984, Residual oil upgrading utilizing fixed-bed hydroprocessing technology. Symp. on Petroleum Residual Upgrading, AlChE Annual Meeting. Illes, V., Welther. K. and Szepesy, L., 1974, Pyrolysis of liquid hydrocarbons IV. Acta chim. hung. 80, 1. Johnson, L. W. and Weiss, R. D., 1982, Numerical Analysis, p. 378. Addison-Wesley, Reading, MA. Kossiakoff, A. and Rice, F. O., 1943, Thermal decomposition of hydrocarbons, resonance stabilization and isomerization of free radicals. J. Am. them. Sac. 65, 590. Kuo, J. C. W. and Wei, J., 1969, A lumping analysis in Benson,
of hydropyroIysis
2857
monomolecular reaction systems. Ind. Engng Chem. Fundam. 8, 124. Liu, Y. A. and Lapidus, L., 1973, Observer theory for lumping analysis of monomolecular reaction systems. A.1.Ch.E. J. 19, 467. Miki,Y., Yamadaya,S., Oba, M. and Sigmoto, Y., 1983, Role of catalyst in cracking heavy oil. J. Catalysis 83, 371. Penninger, J. M. L. and Slotboom, H. W., 1973, Kinetics and mechanism of primary cracking reactions in thermal high pressure hydrogenolysis of tetralin and indan. Part I. Recueil 92, 5 13. Rebick, C., 1983. Pyrolysis of heavy hydrocarbons. In Pyrolysis: Theory and Industrial Practice (Edited by G. R. Gavalas), p. 69. Academic Press, New York. Rice, F. O., 1933, The thermal decomposition of organic compounds from the standpoint of free radicals. III. J. Am. them. Sac. 55, 3035. Shah, Y. T., Stuart, E. B. and Kunzru, D., 1973, Thermal cracking of hydrocarbon mixtures. Ind. Enyng C’hem. Process Des. Deo. 12, 344 Shultz, E. B. and Linden, H. R., 1962, Pressure hydrogenolysis of paraffins. Ind. Euyng Chem. Process Rrs. Drv. 1, 1 i 1. Stein, S. E., 1981, Thermochemical kinetics of anthraccnc pyrolysis. Carbon 19, 421. Wei, J. and Kuo, J. C. W., 1969, A lumping analysis in monomolecular reaction systems. Ind. Engng chrm. Fundam. 8. I 14. Yamada, M. and Amano, A., 1983, Pyrolysis: hydrogenolysis of toluene. In Pyrolysis: Theory and Industrial Practice (Edited by G. R. Gavalas), p. 117. Academic Press, New York. Zimmerman, C. C. and York, R., 1964, Thermal demethylation of toluene. ind. Engng Chem. Process Des. Der. 3, 254.