Ind. Eng. Chem. Res. 1997, 36, 1965-1972
1965
KINETICS, CATALYSIS, AND REACTION ENGINEERING Pyrolysis of Polycyclic Perhydroarenes. 3. 1-n-Decylperhydropyrene and Structure-Reactivity Relations Phillip E. Savage,* Scott Ratz, and Jose´ Dı´az† Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136
1-n-Decylperhydropyrene (DPP) was pyrolyzed neat at temperatures between 400 and 475 °C. DPP disappearance followed first-order kinetics, and the Arrhenius parameters for the firstorder rate constant were A (s-1) ) 109.5(5.0 and E ) 42.9 ( 16.5 kcal/mol, where the uncertainties are the 95% confidence intervals. DPP pyrolysis generated numerous primary products, and the primary products with the highest initial selectivities were, in order of decreasing abundance, perhydropyrene plus 1-decene, methylene perhydropyrene plus n-nonane, tetradecahydropyrene plus n-decane, and methylperhydropyrene plus nonene. This ordering of product pairs is completely analogous to that observed from pyrolysis of an alkylcyclohexane, but it differed from that observed for the pyrolysis of other polycyclic n-alkylnaphthenes. Eight other n-alkylperhydroarenes were pyrolyzed at temperatures between 400 and 450 °C. The resulting kinetics data were used to test three structure-reactivity correlations in the literature for the pyrolysis kinetics of saturated cyclic compounds and to update one of these correlations so that it becomes consistent with the kinetics of long-chain n-alkylperhydroarenes. Introduction Naphthenic (perhydroarene) moieties decorated with n-alkyl substituents exist in heavy hydrocarbon resources such as coal, heavy oils, and asphaltenes. Additionally, these types of chemical structures are present in the endothermic jet fuels being developed for the next generation of high-performance jet aircraft. Given the presence of these structures in these materials, which experience elevated temperatures of around 400 °C during their processing or use, it is clear that information about the thermal decomposition of saturated cyclic compounds with alkyl substituents at temperatures around 400 °C would be useful. Until this year, the relevant literature was limited to kinetics data at a single temperature (700 K) for 28 saturated cyclic compounds (six were polycyclic), most of which bore short chains (Fabuss et al., 1964) and more extensive kinetics data and mechanistic information for a single one-ring compound, tridecylcyclohexane (Savage and Klein, 1988; Mushrush and Hazlett, 1984). Indeed, prior to the publication of the first two papers in the present series (Humburg and Savage, 1996; Mizan et al., 1997), the literature provided no information about the pyrolysis kinetics, pathways, or mechanisms for any polycyclic perhydroarenes bearing a long (>C4) n-alkyl chain. This lack of information about the behavior of polycyclic n-alkylperhydroarenes and previous results showing that the pyrolysis of other polycyclic hydrocarbons led to products that differed from those of their single-ring analogs (Savage et al., 1989; Virk et al., 1979) motivated our work with n-alkyl-substituted polycyclic perhydroarenes. We recently reported extensive results for the pyrolysis of a two-ring compound, 1-undecylperhydronaph* Corresponding author. E-mail:
[email protected]. Fax: (313) 763-0459. Phone: (313) 764-3386. † Present address: Department of Chemical Engineering, University of Puerto Rico, Mayaguez, Puerto Rico 00681. S0888-5885(97)00110-3 CCC: $14.00
thalene (Mizan et al., 1997), and a three-ring compound, 9-dodecylperhydroanthracene (Humburg and Savage, 1996). In this paper we report on the pyrolysis of a fourring compound, 1-decylperhydropyrene (DPP). Additionally, we provide new kinetics data for the pyrolysis of eight other long-chain n-alkyl perhydroarenes (2octylperhydrochrysene, 1-dodecylperhydrophenanthrene, 9-dodecylperhydrophenanthrene, and hexyl-, heptyl-, decyl-, dodecyl-, and n-tridecylcyclohexane). These kinetics data are then used to test structure-reactivity correlations for the pyrolysis of compounds in this class. Experimental Section 1-n-Decylperhydropyrene (DPP), 2-n-octylperhydrochrysene (OPC), 1-n-dodecylperhydrophenanthrene (1DPPh), and 9-n-dodecylperhydrophenanthrene (9-DPPh) were all obtained from the Thermodynamics Research Center at Texas A & M University. n-Hexyl-, n-heptyl-, and n-dodecylcyclohexane were from Pfaltz and Bauer, n-decylcyclohexane was from TCI Organics, and n-tridecylcyclohexane was from Wiley Organics. All chemicals were used as received. All pyrolyses were conducted neat in batch microreactors fashioned from a nominal 1/4 in. stainless steel Swagelok port connector and two caps. The reactor volume was approximately 0.6 mL. Previous experimental work showed that the addition of stainless steel filings had no statistically significant effect on the pyrolysis kinetics (Humburg and Savage, 1996). We loaded between 10 and 40 mg of the reactant and about 10-15 mg of biphenyl (an internal standard) into each reactor, and these quantities were weighed to within (0.1 mg. The loaded reactors were placed in a fluidized sand bath maintained at the desired pyrolysis temperature. DPP was pyrolyzed at 400, 425, 450, and 475 °C and at holding times between 15 and 240 min. The other saturated cyclic compounds were pyrolyzed at 400 °C © 1997 American Chemical Society
1966 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997
in eq 1 that best describes DPP disappearance.
C (-E RT )
m rate ) kCDPP ) A exp
m DPP
(1)
We will consider the reaction order first and begin by noting that the pyrolysis of two other long-chain, polycyclic perhydroarenes followed first-order disappearance kinetics (Humburg and Savage, 1996; Mizan et al., 1997). For the present compound, we used the integral method to determine the global reaction order that was consistent with the experimental results. The integral method, as employed here, consists of integrating the design equation for the constant-volume batch reactor
dCDPP m ) -rate ) -kCDPP dt
Figure 1. First-order plots for DPP disappearance. Discrete points are experimental data. The lines are the fit of the data to eq 4.
for 120, 180, or 240 min, 427 °C for 60 min., and 450 °C for 30 min. The experiments with these compounds were done in triplicate, and they were designed to provide first-order rate constants for the disappearance of each compound at each temperature. When the desired batch holding time had elapsed, the reactors were removed from the sand bath, and the reaction was quenched by immersing the reactors in water at room temperature. The reactors were then opened and their contents retrieved by repeated additions of methylene chloride. The reaction products were identified and quantified via capillary-column gas chromatography (GC) with either a mass spectrometric (MS) or flame-ionization detector. Product identification was accomplished by comparing the retention time and mass spectrum of the GC peak for a reaction product with those of authentic samples (when available) or with mass spectra in the GC-MS computer library. Product molar yields, calculated as the number of moles of product formed divided by the number of moles of reactant initially loaded into the reactor, were obtained from the chromatographic analysis using experimentally determined detector response factors. The response factors for the substituted polycyclic perhydroarene reactants, which existed as multiple isomers and hence give multiple GC peaks, were calculated using the sum of their peak areas. Additional details about the experimental methods appear in the previous papers in this series (Humburg and Savage, 1996; Mizan et al., 1997). Decylperhydropyrene Pyrolysis This section presents the experimental results obtained from a thorough study of 1-n-decylperhydropyrene pyrolysis. These results will be used to determine the reaction rate law for DPP disappearance and to develop the reaction network for DPP pyrolysis. Kinetics. The objectives of this kinetics analysis are to determine the global reaction order (m) and Arrhenius parameters (A, E) for the power-law rate expression
(2)
assuming a value for the reaction order (we considered m ) 1/2, 1, and 3/2 because only integer or half-integer reaction orders possess mechanistic significance) and then casting the resulting algebraic equation in linear form. Doing so leads to
MY1/2 - 1 )
-kt 1/2 2CDPP,o
-ln(MY) ) kt MY
-1/2
1/2 kt CDPP,o -1) 2
for m ) 1/2 for m ) 1
(3) (4)
for m ) 3/2
(5)
where MY is the molar yield of DPP (MY ) CDPP/CDPP,o). One then plots the experimental data in the form suggested by the linearized equation (f(MY) vs t). The assumed reaction order that leads to the best straight line through the origin for the experimental data is then accepted as the reaction order for the global power-law rate equation. Examining the plots and the linear regression statistics for the three rival reaction orders revealed that first-order kinetics provides the best description of the experimental data. As a consistency check, we also performed an integral method analysis of the data at 450 °C without any a priori assumption of the value of the reaction order. In this analysis, we integrated eq 2 with the reaction order, m, as an unspecified parameter, to obtain m-1 MY ) [1 + (m - 1)CDPP,o kt]1/(1-m)
for m * 1 (6)
A nonlinear regression, which minimized the relative difference between the experimental molar yields at 450 °C and the molar yields calculated from eq 6, led to an optimal value of the reaction order of 1.16. As a result of these analyses of the data, we conclude that DPP pyrolysis can be reasonably described by first-order disappearance kinetics, as was the neat pyrolysis kinetics of other polycyclic alkylperhydroarenes. We next used the data for DPP disappearance during neat pyrolysis to determine the global first-order rate constant at each temperature investigated. The rate constant was determined via unweighted linear regression of the data according to eq 4. Figure 1 shows the experimental data and the best-fit lines, and Table 1 lists the rate constants and the associated 95% confidence intervals determined at each temperature.
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 1967 Table 1. Rate Constants for DPP Neat Pyrolysis temp (°C)
k × 104 (s-1)
95% C.I. × 104 (s-1)
temp (°C)
k × 104 (s-1)
95% C.I. × 104 (s-1)
400 425
0.288 1.47
0.103 0.180
450 475
4.03 9.08
0.290 1.58
Table 2. Molar Yields (%) of Products from DPP Neat Pyrolysis 400°C time (min)
425°C time (min)
450°C time (min)
475°C time (min)
products
30
60
90
240
30
90
120
15
75
120
15
45
90
120
octene octane nonene nonane decene decane perhydropyrene (PHP) tetradecahydropyrene methyl-PHP methylene-PHP ethenyl-PHP ethyl-PHP propenyl-PHP propyl-PHP butenyl-PHP butyl-PHP pentenyl-PHP pentyl-PHP hexenyl-PHP hexyl-PHP heptenyl-PHP heptyl-PHP octenyl-PHP octyl-PHP nonenyl-PHP nonyl-PHP pyrene methyl pyrene DPP
0.2 0.4 0.2 0.9 0.8 0.6 1.2 0.2 0.3 0.5 0.1 0.1
0.5 0.7 0.3 1.6 1.4 1.1 2.2 0.3 0.7 1.0 0.2 0.4
0.8 1.5 0.5 3.1 2.2 1.9 4.3 0.5 0.9 1.4 0.4 0.3
0.9 2.3 0.7 5.1 2.3 3.7 8.7 0.6 3.0 1.5 0.4 1.3
0.6 0.9 0.7 2.6 2.8 2.4 5.2
0.6 1.4 0.8 3.6 2.8 4.1 7.6
1.0 2.6 0.5 4.9 1.5 4.4 18.3 1.1 9.8
1.7
0.9
0.8 2.2
0.6 2.2
0.1 0.1 0.1 0.1 0.1
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
0.2
0.9 0.3 0.9 0.1 0.8 0.1 0.7 0.1 0.6
1.1
0.6
1.7 2.8 1.2 5.8 3.7 4.6 13.0 2.0 7.1 4.2 2.3 2.7 0.7 1.5
0.3 1.0
0.5 0.4
1.6 2.2 1.3 5.0 4.0 4.0 12.7 2.3 7.2 4.3 3.0 2.5 1.4 1.6
0.4 1.5
3.5
1.0 1.2 1.0 3.1 4.0 2.5 6.3 1.5 3.8
0.8 2.0
1.3 0.7
1.0 2.2 0.7 5.5 3.2 5.2 12.2 0.4 5.3 0.6
1.1 17.4 0.3 8.6 0.9 0.8 1.9 0.4 0.3
0.6 13.2 0.2 6.0 0.5 0.5 1.2 0.2 0.5
1.1 0.4 0.9 0.2 1.1 0.1 0.8 0.2 0.2 0.1 0.1 0.7 0.1 29.6
1.2 0.2 0.9 0.1 1.0 0.1 0.9 0.2 0.2 0.1 0.1 0.8 0.1 29.9
0.1 0.1
0.2 0.2 0.3 0.3
0.7
1.1 0.7
3.7 0.9 3.6 16.9 9.3
0.4 0.8
0.7
0.6
0.8
0.7
0.6
0.7
1.2
1.3
67.9
35.7
3.1 1.5 12.0
0.1 0.1 98.0
0.1 77.8
0.1 98.8
56.9
68.9
The first-order rate constants in Table 1 were then used to estimate numerical values for the parameters in the Arrhenius equation. This was accomplished by using a nonlinear least-squares parameter estimation protocol wherein the reciprocal of the square of the 95% confidence interval was used as the statistical weight of each data point. The results of this nonlinear regression analysis led to Arrhenius parameters of A (s-1) ) 109.5(5.0 and E ) 42.9 ( 16.5 kcal/mol. Note that the 95% confidence intervals for these parameter estimates are equal to the product of the standard error and the relevant t statistic. The 95% confidence intervals for a, where a ) log A, and E are large because the t statistic is 4.30 for the two degrees of freedom in this regression (four data points minus two parameters). Thus the large uncertainties are a reflection of having data at only four temperatures rather than a reflection of parameter estimates with large standard errors. Smaller uncertainties, if desired, could be obtained by performing experiments at other temperatures, but we do not expect the inclusion of additional experimental data to have much effect on the values of the Arrhenius parameters themselves. The activation energy of 42.9 kcal/mol is comparable to the values of 47.8 and 44.7 kcal/mol recently reported for 1-undecylperhydronaphthalene (Mizan et al., 1997) and 9-dodecylperhydroanthracene (Humburg and Savage, 1996), but it is lower than the value of 59.4 kcal/ mol reported for a single-ring n-alkylnaphthene, n-tridecylcyclohexane (Savage and Klein, 1988). If this trend persists as data accumulates for other compounds, it would appear that substituted polycyclic alkylnaphthenes pyrolyze with a lower global activation energy than do substituted cyclohexanes.
66.0
5.6 2.9 6.6
0.1 0.9
1.1
0.5
0.7
0.4
0.3
16.1 2.8 0.4
20.1 2.4 0.4
The covariance of the parameters a and E (Cova,E) is 4.4882 kcal/mol, which becomes 83.089 kcal/mol at the 95% confidence level where it is multiplied by t2. This covariance is required to estimate the uncertainty in the rate constant (∆k) calculated from the Arrhenius equation at a given temperature (He´berger et al., 1987). The governing relationship is and substituting the 95%
( ) ∆k k
2
) (∆a ln 10)2 +
( ) ( ∆E RT
2
-
)
Cova,E ln 100 RT
(7)
confidence values for ∆a, ∆E, and Cova,E into eq 7 leads to
(∆kk)
2
) 134.089 +
192552 -( (8317 ) T T ) 2
(8)
so that at 700 K, for example, ∆k/k ) 0.44 at the 95% confidence level. Note that one must retain several significant figures for the variances and covariance in eq 7 to get an accurate estimate of the uncertainty in the rate constant. The nonlinear regression also led to a value of the χ-square statistic, χ2v ) 1.68. Values of χ2v ≈ 1.0 indicate a moderately good fit of the data to a proposed model. Thus, we conclude that the Arrhenius equation provided a good fit of the experimental kinetics data for DPP pyrolysis. Pyrolysis Products, Network, and Mechanism. The neat pyrolysis of DPP led to numerous reaction products, and the product spectrum comprised n-alkanes, 1-alkenes, perhydropyrenes substituted with alkyl or alkenyl chains, and partially hydrogenated pyrenes. Perhydropyrene was the most abundant prod-
1968 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997
Figure 2. General reaction network for alkylperhydroarene neat pyrolysis.
uct under all conditions except at very high DPP conversions (>99%) where pyrene became the most abundant product. Table 2, which provides representative results for DPP pyrolysis at different temperatures and reaction times, shows that the only products present in at least 1% yield after pyrolysis for 60 min at 400 °C were nonane, decene, decane, perhydropyrene, and methylene perhydropyrene. These are five of the six major primary products one would expect if DPP pyrolysis followed the same reaction network and mechanism previously advanced for two- and three-ring alkylperhydroarenes (Humburg and Savage, 1996; Mizan et al., 1997). Previous work with these compounds showed that a perhydroarene with an n-carbon-containing alkyl substituent pyrolyzed to form three pairs of major primary products and numerous minor primary products. This network is illustrated in Figure 2 for DPP. The major primary product pairs are the perhydroarene plus a Cn olefin (perhydropyrene plus decene for DPP), the methylene perhydroarene plus a Cn-1 alkane (methylene perhydropyrene plus nonane for DPP), and a cyclic olefin plus a Cn alkane (tetradecahydropyrene plus decane for DPP). Of these six expected products, the only one not present in at least 1% yield from DPP pyrolysis at 400 °C and 60 min is the cyclic olefin, tetradecahydropyrene. The low yield of this cyclic olefin is consistent with the low yields exhibited by all of the unsaturated products of DPP pyrolysis. If DPP neat pyrolysis does follow the reaction network in Figure 2, then the two products formed in each pathway in Figure 2 should possess equal selectivities at DPP conversions sufficiently low that the effect of secondary reactions is negligible. Figure 3 displays the temporal variations of the molar yields of the three major primary product pairs and a fourth product pair (methylperhydropyrene plus nonene) that appeared in slightly lower yields for DPP pyrolysis at 400 °C. Figure 3a shows that perhydropyrene and decene were formed in nearly equal yields at short times. The perhydropyrene yield increased steadily, whereas the decene yield reached a maximum value around 2% and then decreased. Likewise, methylperhydropyrene and nonene were present in nearly equal yields at short times, consistent with their formation in a common reaction
Figure 3. Temporal variations of molar yields of major primary products from DPP neat pyrolysis at 400 °C: (a) perhydropyrene, decene, methylperhydropyrene, nonene; (b) methylene perhydropyrene, nonane, tetradecahydropyrene, decane.
step. The yield of methylperhydropyrene increased steadily whereas the yield of nonene reached a maximum value and then decreased. Figure 3b shows the temporal variations of nonane plus methylene perhydropyrene and decane plus tetradecahydropyrene. Once more it is apparent that the yield of the saturated product always exceeds the yield of its unsaturated counterpart and that the unsaturated products appear to be more reactive as evidenced by their exhibiting maxima in the molar yield curve. We conclude that the data in Figure 3 are consistent with the primary reaction network in Figure 2. The molar yields of the unsaturated compounds always being lower than the yields of their saturated counterparts is a reflection of the unsaturated compounds participating in secondary reactions, even at low DPP conversions. Although the identities of the three major primary product pairs from DPP are analogous to those formed by other n-alkylperhydroarenes, the relative abundances of these products differ for the different compounds. The ring-containing products from the neat pyrolysis of the two- and the three-ring compounds were, in order of decreasing selectivity, the cyclic olefin, the methylene perhydroarene, and the perhydroarene. DPP pyrolysis, on the other hand, led to the perhydroarene being the most abundant product, followed by the methylene perhydroarene and the cyclic olefin. The product spectrum from DPP more closely resembled that of an alkylcyclohexane, wherein the major primary pyrolysis products are cyclohexane, methylene cyclohexane, and lesser amounts of cyclohexene and methylcyclohexane. This comparison of the major primary products from neat pyrolysis of one-, two-, three-, and four-ring n-alkylperhydroarenes shows that an analogous set of three major product pairs forms in all cases. The compound-to-compound differences involve only the
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 1969 Table 3. Rate Constants (in s-1) for Neat Pyrolysis of Long-Chain n-Alkylnaphthenes T ) 400 °C
T ) 427 °C
T ) 450 °C
compound
k × 104
95% C.I.
k × 104
95% C. I.
k × 104
95% C.I.
2-octylperhydrochrysene (OPC) 9-dodecylperhydrophenanthrene (9DPPh) 1-dodecylperhydrophenanthrene (1DPPh) tridecylcyclohexane (TDC) dodecylcyclohexane (DDC) decylcyclohexane (DC) heptylcyclohexane (HPC) hexylcyclohexane (HXC)
0.635 1.22 0.512 0.467 0.692 0.440 0.255 0.212
0.253 0.822 0.393 0.089 0.270 0.270 0.063 0.063
2.97 4.22 3.73 2.90 2.75 2.57 1.63 1.01
1.64 0.38 0.78 0.86 0.70 0.96 0.30 0.49
11.4 11.6 11.1 10.7 8.53 11.0 5.93 3.88
3.78 0.05 5.95 4.27 3.53 1.67 3.10 1.16
Table 4. Arrhenius Parameters and Related Statistics for Neat Pyrolysis Kinetics of Long-Chain n-Alkylperhydroarenes
d
compound
log A ( 95% C.I.a
E ( 95% C.I.a
Cova,E (95% C.I.)
∆k/k at 450 °C
χ2v
2-octylperhydrochrysene (OPC) 9-dodecylperhydrophenanthrene (9DPPh) 1-dodecylperhydrophenanthrene (1DPPh) tridecylcyclohexane (TDC) tridecylcyclohexaneb dodecylcyclohexane (DDC) decylcyclohexane (DC) heptylcyclohexane (HPC) hexylcyclohexane (HXC) 1-undecylperhydronaphthalenec (UPN) 9-dodecylperhydroanthracened (DDPA) 1-decylperhydropyrene (DPP)
13.94 ( 4.67 10.4 ( 0.77 16.0 ( 26.2 15.6 ( 6.0 14.7 ( 11.4 11.6 ( 2.4 16.0 ( 2.6 15.7 ( 9.8 13.58 ( 3.7 10.9 ( 2.6 10.5 ( 1.9 9.55 ( 5.0
55.9 ( 15.0 44.2 ( 2.5 62.4 ( 83.3 61.3 ( 18.9 58.9 ( 36.6 48.5 ( 7.7 62.6 ( 8.6 62.6 ( 31.0 56.2 ( 11.7 46.5 ( 8.4 44.7 ( 6.1 42.9 ( 16.5
69.9927 1.956 2184.145 148.387 419.491 18.510 22.474 302.709 43.315 22.014 11.5 83.089
0.47 0.003 2.84 0.72 1.13 0.234 0.122 1.09 0.41 0.23 0.55 0.44
0.013 0.003 0.53 0.040 0.39 0.003 0.004 0.085 0.013 1.22 not reported 1.68
a Units are kilocalories, moles, seconds. Humburg and Savage, 1996.
b
Analysis of data from Savage and Klein (1988) and Savage (1986). c Mizan et al., 1997.
relative abundance of these different product pairs. This similarity in the reaction network suggests a corresponding similarity in the underlying reaction mechanism. Thus, the free-radical reaction steps advanced previously for one-, two-, and three-ring alkylperhydroarenes (Savage and Klein, 1988; Humburg and Savage, 1996; Mizan et al., 1997) appear to be general. Structure-Reactivity Relations The reaction kinetics for compounds in a single family can often be correlated using a structure-based reactivity index. Such structure-reactivity correlations are useful in computer models of the reactions of complex materials such as fossil fuels and for predicting the reactivity of compounds that have not been investigated experimentally. One needs a large set of reliable kinetics data to develop structure-reactivity correlations. Fabuss et al. (1964) provide data for the pyrolysis kinetics at 800 °F (700 K) of 28 saturated cyclic compounds that were either unsubstituted or bore short (eC4) alkyl substituents. Lai and Song (1996) presented data for the pyrolysis kinetics at 723 K of 38 compounds that included n-alkanes, branched alkanes, and various one- or two-ring saturated cyclic compounds with and without alkyl substituents. In this section, we expand these existing databases by reporting new kinetics data for the pyrolysis of long-chain and polycyclic perhydroarenes at 400, 427, and 450 °C. The last two temperatures were chosen so that the new data could be used to check structure-reactivity relations that employ data at these temperatures, and experiments were also done at 400 °C so that Arrhenius parameters could be determined for each compound. Table 3 provides new kinetics data for the neat pyrolysis of saturated cyclic compounds with long alkyl chains. The rate constants reported are average values calculated from at least three independent experiments at a given temperature. Since the experiments were replicated, we are also able to report the 95% confidence interval for each experimental rate constant. Table 4
provides the Arrhenius parameters obtained from a weighted nonlinear regression of the kinetics data in Table 3. Data in the literature also appear in Table 4 so that the table provides a complete listing of the available kinetics data for long-chain n-alkylperhydroarene pyrolysis. We will now use these new data in Table 3, along with that previously reported for tridecylcyclohexane, TDC (Savage and Klein, 1988; Mushrush and Hazlett, 1984), undecylperhydronaphthalene, UPN (Mizan et al., 1997), dodecylperhydroanthracene, DDPA (Humburg and Savage, 1996), and now decylperhydropyrene, DPP, to assess the predictive ability of existing structurereactivity relations and to expand them so they more accurately correlate the kinetics of both short- and longchain compounds. We begin by first reviewing the previous attempts to develop structure-reactivity relations for saturated cyclic compounds. The pioneering work was done by Fabuss et al. (1964), who correlated the disappearance kinetics at 700 K for 28 different compounds. They used a “characterization number”, n, as the reactivity index, and their correlation is
k (h-1) ) 0.044-0.0114n + 0.0008n2
(9)
The characterization number can be determined by inspection of the structure of the compound, and it is based on group additivity. The characterization number for decylcyclohexane, for example, is 49 (12 for the cyclohexane ring, plus 4 for each of the nine CH2 group in the alkyl chain, plus 2 for the terminal methyl group in the chain, and -1 for the one C-H bond in the ring structure replaced by an alkyl substituent). We note that the equation above shows 0.0114 as the coefficient for the second term, whereas the equation that appears in Fabuss et al. shows 0.114. We believe the equation in Fabuss et al. contains a typographical error because using 0.114 in eq 9 leads to negative values for the rate constants.
1970 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 Table 5. Summary of Nonlinear Regression Results for Structure-Reactivity Correlation k ) r + βn2 at 700 K parameter
estimate
R (h-1) β (h-1) χ2v Cova,b@95% C.I.
-0.0407 3.47 × 10-4 7.37 3.1225 × 10-7
95% C.I. 0.008 4.2 × 10-5
Figure 4. Structure-reactivity relation of Fabuss et al. (solid curve) and experimental data for long-chain n-alkylperhydroarenes (discrete points).
Figure 4 shows the correlation of Fabuss et al. along with experimental data for 11 different long-chain n-alkylperhydroarenes. It is clear that the correlation fails to predict the kinetics for these compounds. Fabuss et al., to their credit, anticipated that the performance of their correlation would deteriorate as the length of the alkyl substituent exceeded four carbon atoms. Indeed, none of the compounds they pyrolyzed had characterization numbers that exceeded 40, and Figure 4 shows that the correlation performs poorly when extrapolated to these higher characterization numbers. We next sought to combine the data provided by Fabuss et al. with our more recent data for long-chain compounds to develop a new structure-reactivity relation that uses the characterization number as the sole correlating parameter. We fit the experimental kinetics data in Table 2 of Fabuss et al., which provides average first-order rate constants at 700 K and the associated standard deviations, along with the data in Tables 3 and 4 of this report to a quadratic equation of the form originally used by Fabuss et al. (eq 9). We used a nonlinear regression routine and employed the square of the reciprocal of the 95% confidence interval for each rate constant as the weighting parameter in the objective function. The resulting correlation is
k (h-1) ) -0.066 + 0.0031n + 0.00026n2 (10) The χ2v statistic is 7.35, which is high largely because many of the rate constants in Fabuss et al. have small uncertainties. The detailed results from the nonlinear regression showed that the uncertainty in the parameter 0.0031 in eq 10 exceeded the value of the parameter itself. In fact, a value of zero is contained within the 95% confidence interval for this parameter. Consequently, we repeated the nonlinear regression of the kinetics data but omitted the second term on the righthand side of eq 10. The resulting correlation is
k (h-1) ) -0.041 + 0.00035n2
(11)
and the χ2v statistic is 7.37, which is only slightly larger than the χ2v statistic for the three-parameter regression. We believe that eq 11 provides a more meaningful correlation of the available kinetics data. Table 5 provides the details of the nonlinear regression results, and the level of agreement between the new correlation and the experimental data is apparent upon inspection of Figure 5. We expect that the correlation of eq 11 will provide reasonable estimates of the rate constants for
Figure 5. Updated structure-reactivity relation for saturated cyclic compounds.
Figure 6. Confirmation that rate constants for neat pyrolysis of long-chain n-alkylcyclohexanes are linear functions of the number of carbon atoms in the alkyl chain. The data at 427 and 400 °C were multiplied by factors of 2 and 5, respectively, to improve the appearance of the figure.
long-chain alkylperhydroarenes. The only compound for which the correlation performs poorly is decylperhydropyrene. The reason for this failure is not clear, and additional experiments with other polycyclic compounds are required to address this issue. A second structure-reactivity relation, which Savage and Klein (1989) advanced for long-chain n-alkylcyclohexanes, is
k ) R + β(chain length)
(12)
This relationship was deduced from the kinetics as derived from the governing free-radical chain reaction mechanism, but it was not tested against any experimental data. The new data for alkylcyclohexanes in Table 3 allow this proposed correlation to be tested. Figure 6 shows that the rate constants at each of the three temperatures do indeed scale linearly with the chain length. Additionally, Lai and Song (1996) recently presented experimental data for the pyrolysis of nalkylcyclohexanes at 450 °C that also verify the linear relation between chain length and the first-order rate constant that Savage and Klein (1989) had predicted to exist. Since the pyrolysis reaction networks and mechanisms for polycyclic alkylperhydroarenes are similar to
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 1971
Figure 7. Structure-reactivity relation of Lai and Song (solid line) and experimental data for long-chain n-alkylperhydroarenes (discrete points). Diamonds are the present data, the triangle is from Savage and Klein (1988), and the square is from Mushrush and Hazlett (1984).
those for alkylcyclohexanes, one might anticipate that the kinetics of polycyclic alkylperhydroarenes would also be a linear function of the chain length. Unfortunately, there are no data available that allow this hypothesis to be tested. The third and final structure-reactivity relation that we will consider has been developed by Lai and Song (1996). These authors correlated the pyrolysis kinetics of saturated compounds at 450 °C with a reactive structure index (RSI), which is calculated according to a group contribution method. This approach is based on the same chemical logic employed 30 years earlier by Fabuss et al. (1964). The RSI for n-decylcyclohexane, for example, is 124, calculated as 30 for the cyclohexane ring, plus 10 for each of the nine CH2 groups, plus 4 for the terminal methyl group. The Lai and Song correlation is
k (h-1) ) -0.54 + 0.0178RSI
(13)
Figure 7 shows this correlation along with our experimental data at 450 °C for the five alkylcyclohexanes and the single alkyldecalin (UPN) and literature data at 450 °C for tridecylcyclohexane (Mushrush and Hazlett, 1984; Savage and Klein, 1988). Lai and Song do not provide the value of the group contribution for three- or fourring structures, so we could not test the correlation against the data for these larger compounds. Our rate constants are consistently higher than those predicted by the Lai and Song correlation, but the 95% confidence interval for the experimental rate constants for DDC, HPC, and UPN include the value predicted by the correlation. For the other three compounds there is no intersection of the value predicted by eq 13 and the 95% confidence interval for the measured rate constant. The rate constant for TDC from the Mushrush and Hazlett (1984) data is much lower than that predicted by the Lai and Song (1996) correlation and those reported in this study and by Savage and Klein (1988). This assessment of existing structure-reactivity correlations shows that none of them can satisfactorily predict the kinetics for any given long-chain, polycyclic n-alkylperhydroarene. Indeed, neither of the first two structure-reactivity relations was even intended to apply to all long-chain saturated cyclic compounds. Fabuss et al. (1964) only considered compounds with short alkyl chains, and the correlation of Savage and Klein (1989) applies only to cyclohexanes with long n-alkyl chains. Note, however, that we were able to use the data in Tables 3 and 4 to extend the correlation of
Fabuss et al. so that it now correlates the kinetics data available for long-chain polycyclic perhydroarenes. The correlation of Lai and Song (1996), on the other hand, is intended to be general. They developed it by using data for alkanes and saturated cyclic compounds with both short and long n-alkyl chains. Because the group contributions are empirical, however, and because the authors did not provide the values of these groups for three- or four-ring structures, the Lai and Song correlation was of no utility for predicting the kinetics data for the five three- and four-ring compounds in Tables 3 and 4. The structure-reactivity relations of Fabuss et al. and Lai and Song qualitatively incorporate some fundamental aspects of hydrocarbon pyrolysis kinetics in their characterization number and RSI. For example, a CH2 group adds more to the characterization number and the RSI than does a CH3 group, which is consistent with secondary C-H bonds being weaker and hence more reactive than primary C-H bonds. These correlations are empirical, however, because the relative contributions of the different structural groups were determined by fitting data rather than by building squarely upon the foundation of the governing reaction mechanism. The mechanism for the pyrolysis of saturated cyclic hydrocarbons is reasonably well established, and closedform analytical rate expressions are available (Savage, 1990). A mechanism-based structure-reactivity relation has already appeared for n-alkylbenzenes (Savage and Korotney, 1990), and a subsequent paper in this series will report our progress toward a mechanismbased structure-reactivity relation for n-alkylperhydroarenes. Summary and Conclusions This paper provides only the third report on the pyrolysis of a long-chain polycyclic n-alkylperhydroarene and the first report on the pyrolysis of an alkylperhydropyrene. 1-Decylperhydropyrene (DPP) neat pyrolysis follows first-order kinetics. The Arrhenius parameters are A (s-1) ) 109.55(5.0 and E ) 42.9 ( 16.5 kcal/ mol, where the uncertainties are the 95% confidence intervals. The reaction network for DPP pyrolysis is analogous to that determined recently for other longchain n-alkylperhydroarenes. It includes parallel primary reactions to form 1-decene plus perhydropyrene, nonane plus methylene perhydropyrene, and decane plus tetradecahydropyrene. The numerous minor primary products were other n-alkanes, R-olefins, alkylperhydropyrenes, and alkenylperhydropyrenes. Pyrene and methylpyrene appeared as products at the more severe reaction conditions. Kinetics data for the pyrolysis of eight other nalkylperhydroarenes are reported herein. These data revealed that the correlation of Fabuss et al. (1964) cannot be extrapolated to predict the reactivity of longchain and polycyclic perhydroarenes. Equation 11 provides a new correlation, based on the Fabuss et al. characterization number, that is consistent with both their data and that reported herein. This correlation can be used to predict the kinetics of a wide variety of saturated cyclic compounds. Acknowledgment We thank the Department of Energy University Coal Research Internship Program for sponsoring Jose Diaz’s internship at the University of Michigan.
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Nomenclature a ) log10 of the Arrhenius preexponential factor A ) Arrhenius preexponential factor CDPP ) concentration of DPP E ) Arrhenius activation energy k ) reaction rate constant m ) global reaction order MY ) molar yield n ) structure-based characterization number for saturated cyclic compounds R ) gas constant RSI ) reactive structure index t ) time, t statistic T ) absolute temperature Covi,j ) covariance of parameters i and j Greek Letters R ) parameter in eq 12 β ) parameter in eq 12 ∆ ) uncertainty χ2v ) chi-square statistic, per degree of freedom
Literature Cited Fabuss, B. M.; Kafesjian, R.; Smith, J. O.; Satterfield, C. N. Thermal Decomposition Rates of Saturated Cyclic Hydrocarbons. Ind. Eng. Chem. Process Des. Dev. 1964, 3, 248. He´berger, K.; Keme´ny, S.; Vido´czy, T. On the Errors of Arrhenius Parameters and Estimated Rate Constant Values. Int. J. Chem. Kinet. 1987, 19, 171. Humburg, R. E.; Savage, P. E. Pyrolysis of Polycyclic Perhydroarenes. 1. 9-n-Dodecylperhydroanthracene. Ind. Eng. Chem. Res. 1996, 35, 2096. Lai, W.; Song, C. Reactive Structure Index for Correlation of High Temperature Thermal Stability of Saturated Hydrocarbons. ACS Div. Petrol. Chem. Prepr. 1996, 41, 524.
Mizan, T. I.; Savage, P. E.; Perry, B. Pyrolysis of Polycyclic Perhydroarenes. 1. 1-n-Undecylperhydronaphthalene. Energy Fuels 1997, 11, 107. Mushrush, G. W.; Hazlett, R. N. Pyrolysis of Organic Compounds Containing Long Unbranched Alkyl Groups. Ind. Eng. Chem. Fundam. 1984, 23, 288. Savage, P. E. Chemical and Mathematical Modeling of Asphaltene Reaction Pathways. Ph.D. Dissertation, University of Delaware, Newark, DE, 1986. Savage, P. E. Pyrolysis of a Binary Mixture of Complex Hydrocarbons: Reaction Modeling. Chem. Eng. Sci. 1990, 45, 859. Savage, P. E.; Klein, M. T. Asphaltene Reaction Pathways. 4. Pyrolysis of Tridecylcyclohexane and 2-Ethyltetralin. Ind. Eng. Chem. Res. 1988, 27, 1348. Savage, P. E.; Klein, M. T. Asphaltene Reaction Pathways. 5. Chemical and Mathematical Modeling. Chem. Eng. Sci. 1989, 44, 393. Savage, P. E.; Korotney, D. J. Pyrolysis Kinetics for Long-Chain n-Alkylbenzenes: Experimental and Mechanistic Modeling Results. Ind. Eng. Chem. Res. 1990, 29, 499. Savage, P. E.; Jacobs, G. E.; Javanmardian, M. Autocatalysis and Aryl-Alkyl Bond Cleavage in 1-Dodecylpyrene Pyrolysis. Ind. Eng. Chem. Res. 1989, 28, 645. Virk, P. S.; Korosi, A.; Woebcke, H. N. Pyrolysis of Unsubstituted Mono-, Di-, and Tricycloalkanes; Oblad, A. G., Davis, H. G., Eddinger, R. T., Eds.; ACS Advances in Chemistry Series 183; American Chemical Society: Washington, DC, 1979; p. 67.
Received for review February 3, 1997 Revised manuscript received March 31, 1997 Accepted March 31, 1997X IE970110N
X Abstract published in Advance ACS Abstracts, May 15, 1997.
