Ind. Eng. Chem. Res. 1997, 36, 585-591
585
Kinetics of Supercritical-Phase Thermal Decomposition of C10-C14 Normal Alkanes and Their Mixtures Jian Yu and Semih Eser* Fuel Science Program, Department of Materials Science and Engineering, 209 Academic Projects Building, The Pennsylvania State University, University Park, Pennsylvania 16802
Kinetics of thermal decomposition of C10-C14 n-alkanes and their mixtures was studied under near-critical and supercritical conditions. Supercritical-phase thermal decomposition of n-alkanes can be represented well by an apparent first-order kinetics, even though the decomposition was not a true first-order process. A generalized expression was developed to predict the apparent first-order rate constants for the decomposition of C8-C16 n-alkanes at 425 °C. Pressure had a significant effect on the apparent first-order rate constant in the near-critical region. This large pressure effect can be attributed to the significant changes in density and possibly to the changes in the rate constants of elementary reactions with pressure in this region. Individual compounds interacted with each other in the thermal reaction of n-alkane mixtures. The overall first-order rate constants for n-alkane mixtures can be predicted satisfactorily from the rate constants for pure compounds. Introduction
Table 1. Composition of n-Alkane Mixtures
Long-chain alkanes are the major components in petroleum-derived jet fuels and the significant ones in coal-derived jet fuels. For example, JP-8P, a petroleumderived jet fuel, and JP-8C, a coal-derived jet fuel, contain about 60 and 10 wt % of C7-C18 normal and branched alkanes, respectively (Lai and Song, 1995). Therefore, studying the thermal decomposition of longchain alkanes is important for understanding the thermal degradation behavior of jet fuels. In a companion paper, the results from the thermal decomposition of n-decane (n-C10), n-dodecane (n-C12), and n-tetradecane (n-C14) in near-critical and supercritical regions were discussed in terms of product distributions and reaction mechanisms (Yu and Eser, 1997). This article will focus on kinetics of supercriticalphase thermal decomposition of C10-C14 n-alkanes and their mixtures. Experimental Section Three n-alkanes, n-C10, n-C12, and n-C14, were used in thermal stressing experiments. They were obtained from Aldrich, all with 99+% purity. Several binary and ternary n-alkane mixtures were also used in this study. Table 1 lists the composition of these mixtures, excluding impurities. Some experiments were conducted on a petroleum-derived jet fuel, JP-8P, which consists of 61% of C7-C18 alkanes, 14% of C6-C14 cycloalkanes, 16% of C6-C14 benzenes, and other minor components. Thermal reaction experiments were carried out in a Pyrex glass tube reactor with a total volume of 45-50 µL. The sample loading, experimental apparatus and procedure, and the methods for product analyses were similar to those described in the preceding paper (Yu and Eser, 1997). Results and Discussion Rate Constants. Kinetic analyses were conducted for the thermal decomposition of n-C10, n-C12, and n-C14 at 400, 425, and 450 °C for different times. Previous studies show that the simple first-order kinetics holds reasonably well for the thermal decomposition of straightchain alkanes (Voge and Good, 1949; Fabuss et al., S0888-5885(96)00393-4 CCC: $14.00
mole fraction of component reactant
n-C10
n-C12
n-C10 + n-C12 n-C10 + n-C14 n-C12 + n-C14 n-C10 + n-C12 + n-C14 Norpar-13
0.5299 0.5588
0.4701
0.3718
0.5546 0.3422 0.1396
n-C13
n-C14
0.5204
0.4412 0.4454 0.2860 0.3400
1964b; Rebick, 1983). Therefore, the rate constants were determined by the following first-order expression
k)
1 1 ln t 1-x
(1)
where x is the fraction of the reactant converted (conversion), k is the apparent first-order rate constant (h-1), and t is the reaction time (h). The conversions were obtained from the thermal decomposition experiments in the glass tube reactor at different temperatures for different times. A fixed loading ratio, defined as the ratio of the initial sample volume at room temperature to the reactor volume, of 0.36 was used in the experiments. For three different temperatures (400, 425, and 450 °C), the rate constants were determined from the method of least squares by plotting ln[1/(1 - x)] as a function of time. Figure 1 shows the relationship between ln[1/(1 - x)] and time for the thermal decomposition of n-C10. Similar linear relationships between ln[1/(1 - x)] and time were obtained for n-C12 and n-C14. From the slopes of the lines in Figure 1, the apparent first-order rate constants at three different temperatures can be obtained. Table 2 shows the calculated rate constants, with their standard deviations, for three n-alkanes. The standard deviation σk indicates the precision of the k calculated by the least-squares fit. The relatively small σk values suggest that the first-order kinetics assumption (for a fixed loading ratio of 0.36) is reasonable. From Table 2 one can see that for the three n-alkanes, the apparent first-order rate constant increases with the increasing carbon number (at the same temperature). According to the first-order rate constants shown in Table 2, the apparent activation energies (Ea, kcal/mol) © 1997 American Chemical Society
586 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 Table 2. Kinetic Parameters for Thermal Decomposition of n-Alkanes rate constant, h-1
a
reactant
400 °C
425 °C
450 °C
Eaa
log Ab
n-C10 n-C12 n-C14
0.0341 ( 0.0006 0.0453 ( 0.0013 0.0640 ( 0.0020
0.174 ( 0.003 0.231 ( 0.010 0.364 ( 0.010
0.758 ( 0.015 1.13 ( 0.06 1.67 ( 0.05
60 ( 1 62 ( 2 63 ( 2
18.0 ( 0.2 18.8 ( 0.5 19.3 ( 0.4
Ea, apparent activation energy in kcal/mol. b A, preexponential factor in h-1.
Figure 1. ln[1/(1 - x)] versus time from thermal decomposition of n-C10.
Figure 3. Relationship between rate constant and carbon number for three temperatures.
(Depeyre et al., 1985); 61 kcal/mol at 517-589 °C and 0.1 MPa (Groenendyk et al., 1970); 59 kcal/mol at 400440 °C and 2 MPa (Blouri et al., 1985); 57 kcal/mol at 330-370 °C and liquid phase (Ford, 1986); 61 kcal/mol at 380-450 °C and 13.9 MPa (Khorasheh and Gray, 1993). The activation energies obtained in this work for the three n-alkanes are in good agreement with the above literature values. Rate Constant Correlations for n-Alkanes. The rate constants shown in Table 2 can be correlated to the carbon number in n-alkane molecule. Figure 3 shows the relationship between the rate constant and carbon number, m, for three different temperatures. From the method of least squares, the following three expressions can be obtained corresponding to three temperatures, 400, 425, and 450 °C, respectively Figure 2. Arrhenius plots from thermal decomposition of nalkanes.
and preexponential factors (A, can be determined using the following Arrhenius law
k400 ) (7.48m - 41.9) × 10-3 h-1
(3)
k425 ) (4.75m - 31.4) × 10-2 h-1
(4)
k450 ) (2.28m - 15.5) × 10-1 h-1
(5)
h-1)
k ) A exp(-Ea/RT)
(2)
Figure 2 shows the Arrhenius plots for the three n-alkanes. The apparent activation energies and preexponential factors obtained from the Arrhenius plots are also shown in Table 2. The slight differences between the apparent activation energies for the three n-alkanes may arise from the experimental uncertainty. The apparent activation energies for the first-order decomposition of long-chain alkanes usually fall in the range of 60 ( 5 kcal/mol (Fabuss et al., 1964b; Rebick, 1983). Kunzru et al. (1972) reported an activation energy of 63 kcal/mol for n-C9 at 650-750 °C and 0.1 MPa. Zhou and Crynes (1986) obtained an Ea of 65 kcal/ mol for n-C12 at 350-400 °C and 9.2 MPa. It seems that the temperature and pressure conditions do not affect the observed activation energies significantly. For example, for the thermal decomposition of n-C16 at different conditions, the following activation energies were reported: 57 kcal/mol at 600-850 °C and 0.1 MPa
When eqs 3-5 were used to estimate the rate constants of the three n-alkanes, it was found that the average percent deviations of the calculated rate constants from the measured values were 3.7%, 7.3%, and 3.6% for 400, 425, and 450 °C, respectively. There are two correlations available in the literature for the relationship between the rate constant and carbon number. Tilicheev (1939) gave the following correlation for C12-C32 n-alkanes at 425 °C and 15 MPa pressure
k ) (2.3m - 15.6) × 10-5 s-1
(6)
Equation 6 can also be extended to n-C10 and n-C11 according to the kinetic data given by the above author. Voge and Good (1949) presented the following expres-
Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 587
Figure 4. Relationship between rate constant and carbon number at 425 °C.
Figure 5. Relationship between k/k12 and carbon number at 425 °C.
sion for n-alkanes from C4 to C16 at 500 °C and 0.1 MPa pressure
k ) (m - 1)(1.57m - 3.9) × 10-5 s-1
(7)
Figure 4 shows the relationship between the rate constant and carbon number at 425 °C, calculated by eqs 4, 6, and 7. The unit of the rate constant from eqs 6 and 7 was converted to h-1. For Voge and Good’s correlation, the rate constants at 425 °C were calculated from those at 500 °C using an activation energy of 60 kcal/mol. From Figure 4 one can see that the first-order rate constants calculated by the present correlation fall in the middle between those predicted by Tilicheev and those by Voge and Good. The differences between the rate constants calculated by three different methods may be due to the differences in pressure. The pressures used in the present work are in the range of 1-10 MPa (initial pressure) which are between the pressures used by Tilicheev and by Voge and Good. It seems that in the pressure range presented here (0.1-15 MPa) the first-order rate constant increases as pressure increases. This is not always the case, as presented in the next section. From the three correlations presented above, a generalized expression can be developed for the thermal decomposition of C8-C16 n-alkanes at 425 °C and a given pressure in the range of 0.1-15 MPa
k/k12 ) (1.89m - 12.3) × 10-1
(8)
where k12 is the first-order rate constant of n-dodecane at 425 °C and a given pressure. In developing the above equation, it was assumed that eq 4 can be extended to the range C8-C16. This assumption is reasonable since eq 4 is good for the range C10-C14 and the extrapolation is not large. The rate constants of C8-C16 n-alkanes at 500 °C obtained from Voge and Good’s correlation were converted to those at 425 °C using an activation energy of 60 kcal/mol. Since Tilicheev’s correlation does not cover C8-C11 n-alkanes, the original experimental data were used for these compounds (Tilicheev, 1939). Figure 5 shows that the generalized correlation can represent the three sets of data. Since it is not usual to encounter very high pressures in the thermal decomposition of long-chain n-alkanes, eq 8 can be used to predict the rate constants of C8-C16 n-alkanes at 425 °C and a given pressure (or a fixed loading ratio in the case of sealed batch reactor) if the rate constant of one of these compounds is known under similar conditions.
Figure 6. Conversion versus Pr from thermal decomposition of n-alkanes.
Effects of Pressure on Conversion. The effects of pressure on conversion were studied in the nearcritical and supercritical regions for the three n-alkanes. Different loading ratios were used to obtain different initial pressures. The experiments were carried out at 425 °C for 15 min. For n-C12, the experiments were also carried out at 400 °C for 60 min. All the experiments with the same compound at the same temperature and same run length were conducted on the same day to minimize the experimental uncertainty. The flow rate of air in the sand bath was always kept constant, and the glass tube reactor was always plunged into the same position in the sand bath. Figure 6 shows the change in conversion with the initial reduced pressure for the thermal decomposition of n-C10, n-C12, and n-C14 under the conditions indicated. The initial reduced pressure (Pr ) P/Pc) was calculated at the given temperature and loading ratio using the Soave-Redlich-Kwong (S-R-K) equation of state (Soave, 1972). It can be seen that pressure has a significant effect on the conversion in the near-critical region. For example, for the thermal decomposition of n-C12 at 400 °C (Tr ) T/Tc ) 1.02) for 60 min, an increase in Pr from 1 to 1.5 results in a decrease in conversion from ≈5% to ≈3.5%. It seems that the significant changes in conversion with pressure fall in the nearcritical region and do not extend to a farther supercritical region. This can be seen from Figure 6 which shows that at Pr > 1.5 the conversion only exhibits slight decrease with the increasing pressure. For n-C10 there is no large decrease in conversion with an increase in
588 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997
pressure from Pr ) 1-1.5 since the reaction temperature is much higher than the critical temperature (Tr ) 1.13) and thus the reaction condition is away from the nearcritical region. The large change in conversion with pressure in the near-critical region of the reactant can be attributed to the unique properties of the fluid in this region. In its near-critical region, the fluid exhibits very high compressibility and many physicochemical properties change significantly with pressure (McHugh and Krukonis, 1986). When the reaction is carried out in the nearcritical region, pressure may influence the rate constant significantly. This can be explained by means of transition state theory (Kohnstam, 1970). For an elementary reaction occurring in a solvent, the pressure dependence of the rate constant kc (expressed in pressure-dependent concentration units, such as mole/liter) is given by the following expression
(
)
∂ ln kC ∂P
T
)-
( )
∆Vq ∂ ln F + ∆nq RT ∂P
T
Figure 7. Density versus Pr from three compounds at temperatures indicated.
(9)
where ∆Vq, the volume of activation, is the difference between the partial molar volumes of the transition state species and the reactants, ∆nq is the difference between the stoichiometric coefficients of the transition state species and the reactants, and F is the density of the solvent. In conventional liquid solutions, which are relatively incompressible, pressure changes in kilobars are required to affect the rate constant significantly because ∆Vq is usually in the range of (25 cm3/mol (Kohnstam, 1970). However, for a reaction occurring in a fluid near its critical point, the magnitude of ∆Vq can be much larger. For example, Simmons and Mason (1972) found activation volumes larger than -3000 cm3/mol for the dimerization of chlorotrifluoroethylene near its critical point. Johnston and Haynes (1987) reported activation volumes as large as -6000 cm3/mol for the unimolecular decomposition of R-chlorobenzyl methyl ether in the near-critical region of 1,1-difluoroethane. Since the thermal decomposition process is the summation of a series of elementary reactions, such as hydrogen abstraction, radical decomposition, and radical addition, which may have very large activation volumes in the near-critical region of the reactant, the large changes in conversion with pressure can be observed in this region. In the farther supercritical region, the activation volumes may be similar to those observed in conventional liquid solutions (relatively low), and thus, the pressure dependence of the conversion would not be large. The change in pressure in the near-critical region of the reactant can also result in the significant change in density. This can be illustrated by Figure 7 which shows the relationship between density and reduced pressure, calculated using the S-R-K equation of state (Soave, 1972), for three pure n-alkanes at temperatures above their critical values. It can be seen that density exhibits strong pressure dependence in the near-critical region. See, for example, n-C14 at 425 °C (Tr ) 1.01) and n-C12 at 400 °C (Tr ) 1.02). The large variation in density or concentration results in substantial changes in the reaction mechanisms, as discussed in the preceding paper (Yu and Eser, 1997). These substantial changes in the reaction mechanisms can also result in the large changes in conversion. It is expected that the conversion will exhibit a smooth change with the concentration or loading ratio, as observed in Figure 8.
Figure 8. Conversion versus loading ratio from thermal decomposition of n-alkanes.
It is interesting to note that the conversion (thus the apparent first-order rate constant) exhibits different pressure (concentration) dependence in different pressure (concentration) ranges for n-C14 at 425 °C, as shown in Figures 6 and 8. The conversion for the decomposition of n-C14 first increases and then decreases as pressure (loading ratio) increases. This observation can be explained by examining the general reaction scheme for the thermal decomposition of organic compounds, as shown below (Rice and Herzfeld, 1934; Steacie, 1946; Savage and Klein, 1989) initiation propagation propagation termination termination termination
M f 2β β + M f βH + µ µ f β + M1 2β f M2 β + µ f M3 2µ f M4
(10) (11) (12) (13a) (13b) (13c)
where β and µ are free radicals which propagate chain via bimolecular hydrogen abstraction and unimolecular decomposition, respectively. Using steady state approximation for β and µ radicals and long-chain assumption (overall decomposition rate . initiation rate), the rate of disappearance of the reactant can be obtained. Equation 14 shows a general rate expression for the disappearance of the reactant
-
d [M] ) kn[M]n dt
(14)
where n is the order of the overall reaction and kn is the rate constant for the reaction with an order of n.
Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 589 Table 3. Rate Expressions and Overall Activation Energies Ea for Three Different Termination Modes termination mode
- d[M]/dt
()
ββ
kH
βµ
(
µµ
kdec
ki kt
1/2
[M]3/2
52.8
)
[M]
61.8
[M]1/2
70.8
kikHkdec 2kt
() ki kt
Ea, kcal/mol
1/2
1/2
The apparent first-order rate constant can thus be expressed as
k1 ) kn[M]n-1
(15)
When the initiation reaction is a first-order process, which is generally the case for the thermal decomposition of long-chain alkanes, the overall reaction order n depends on the mode of termination (Laidler, 1965). If the termination occurs by recombination of two β radicals (eq 13a), the overall reaction would have an order of 1.5. On the other hand, if the termination occurs by recombination of two µ radicals (eq 13c), the overall reaction order would be 0.5. The termination by recombination of β and µ radicals (eq 13b) would give an overall reaction of the first order. Table 3 shows the rate expressions and corresponding overall activation energies for three different modes of termination. In calculating the overall activation energies, the following activation energies were used for the elementary reactions: 81.5 kcal/mol for initiation (homolytic C-C bond dissociation energy (Benson, 1976)), 12.0 kcal/mol for hydrogen abstraction and 30.0 kcal/mol for radical decomposition (Ranzi et al., 1983), and zero for termination reactions. It can be seen from Table 3 that the overall activation energy would increase from 52.8 to 70.8 kcal/mol as the overall reaction process changes from a three-halves-order kinetics to a one-half-order kinetics. For the thermal decomposition of hydrocarbons at low concentrations (low loading ratios), unimolecular decomposition would predominate bimolecular reaction and thus β radicals would be predominant ones. This would result in eq 13a as the main termination step, and the reaction would have an overall order between 1 and 1.5. Under these conditions, k1 (thus conversion) would increase with the increasing loading ratio. As the loading ratio increases, the rate of bimolecular reaction and thus the concentration of µ radicals would increase. When the loading ratio increases to a region where µ radicals are dominant, the main termination step would be eq 13c and the overall reaction order would be between 0.5 and 1. This would result in decreasing k1 (thus conversion) with the increasing loading ratio. Ideally, one should get kinetic data at very low and very high loading ratios and use the true kinetic expressions to calculate the rate constants. However, in this study it was not possible to work at very low or very high loading ratios. The overall reaction orders for the thermal decomposition of the three n-alkanes under the conditions used can be determined by plotting log(k1) versus log(loading ratio), as shown in Figure 9. Table 4 shows the calculated overall reaction orders for the three n-alkanes under different reaction conditions. It can be seen that the thermal decomposition of n-alkanes does not follow
Figure 9. Relationship between first-order rate constant and loading ratio. Table 4. Overall Reaction Orders for Thermal Decomposition of n-Alkanes under Different Conditions reactant
temperature, °C
loading ratio range
overall reaction order
n-C14 n-C14 n-C12 n-C12 n-C10
425 425 425 400 425
0.07-0.13 0.13-0.45 0.06-0.45 0.08-0.46 0.08-0.46
1.06 0.82 0.85 0.76 0.83
a true first-order kinetics. However, if the true overall reaction order is close to the first-order, the observed activation energy would not be far away from 61.8 kcal/ mol, the theoretical value for the first-order decomposition of long-chain alkanes (Table 3). For example, if we assume that the overall activation energy is inversely proportional to the overall reaction order in the range of 0.5-1.5, then the overall activation energies would be in the range of 57.3-66.3 kcal/mol if the overall reaction orders are between 0.75 and 1.25. It is not surprising that the observed activation energies usually fall in the range of 60 ( 5 kcal/mol for the first-order decomposition of long-chain alkanes (Fabuss et al., 1964b; Rebick, 1983) since most decomposition reactions are not far away from the first-order kinetics. There are some literature data about the effects of pressure or concentration on the first-order rate constant (and, thus, conversion). Voge and Good (1949) observed that the first-order rate constant for the thermal decomposition of n-hexadecane at 500 °C increased from ≈10 h-1 at 0.1 MPa to ≈28 h-1 at 2.1 MPa. Appleby et al. (1947) reported that the first-order rate constants for n-heptane pyrolysis at 580 °C were essentially the same at 0.1 and 0.88 MPa. Fabuss et al. (1962) studied the thermal cracking of n-hexadecane at temperature range of 593-704 °C and found no pressure dependence of the rate constant in the pressure range from 1.5 to 7.0 MPa. For the thermal decomposition of tert-butylcyclohexane at 427 °C over the pressure range of 2.9-7.0 MPa, the first-order rate constant doubled for a pressure increase of about 2.3 MPa (Fabuss et al., 1964a). After reviewing the literature, Fabuss et al. (1964b) concluded that for the thermal decomposition of alkanes, the first-order rate constant increases with the increasing pressure between 0.1 and about 10-30 MPa pressure. In the low-pressure range the first-order rate constant may double for a pressure increase of about 3.5-4.1 MPa. It should be mentioned that the above conclusions came from limited literature data and are not necessarily applicable to all alkanes. For example, the rate constant for the thermal decom-
590 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997
Figure 10. Conversion versus loading ratio from Norpar-13 at 425 °C for 15 min.
position of 2,4,8-trimethylnonane at 371 °C decreased from 0.0226 h-1 at 1.75 MPa to 0.0150 h-1 at 2.33 MPa (Fabuss et al., 1964b). From above discussion it can be concluded that the effects of pressure (or loading ratio) on the apparent first-order rate constant (and, thus, conversion) are not only related to the structure of compound itself but also dependent upon the temperature and pressure ranges studied. A different or even inverse pressure dependence of the rate constant may be obtained for a different compound and/or different temperature or pressure range. Figure 6 clearly shows that the conversion (thus first-order rate constant) for the thermal decomposition of n-C14 under supercritical conditions decreases with the increasing pressure, contrary to what is observed under subcritical conditions. Thermal Decomposition of n-Alkane Mixtures. Several binary and ternary n-alkane mixtures were stressed under similar conditions. Figure 10 shows the changes in conversions of individual compounds with loading ratio from the thermal decomposition of Norpar13 at 425 °C for 15 min. Also included is the change in overall conversion with the loading ratio. The overall conversion (the fraction of the feed converted) was calculated using the following expression
x)
∑y°ixi
(16)
where yi° is the initial molar fraction of the component i in the mixture and xi is the apparent conversion of the component i. As the loading ratio increases, the conversion of n-C12 decreases while that of n-C14 first increases and then decreases. The conversion of n-C13 remains almost unchanged before a 0.25 loading ratio and then decreases with the increasing loading ratio. The compound with longer chain has the higher conversion in the mixture. It seems that individual compounds interact with each other during the thermal reactions of the mixture. While the conversions for the thermal decomposition of n-C12 in Norpar-13 are slightly higher than those for the decomposition of pure n-C12, the conversions for the thermal decomposition of n-C14 in Norpar-13 are lower than those for the decomposition of pure n-C14 at similar conditions. These results suggest that the lighter alkane inhibits the decomposition of the heavier one and the heavier alkane accelerates the decomposition of the lighter one. It should be mentioned that the conversions of n-C12 in Norpar-13 are apparent values. The real conversions for the
Figure 11. Conversion of n-C14 versus reaction time from thermal decomposition of pure compound, in Norpar-13, and in JP-8P at 425 °C. Table 5. Overall First-Order Rate Constants for Thermal Decomposition of n-Alkane Mixtures at 425 °C rate constant at 425 °C, h-1 reactant
exptl
calcd
deviation,a %
n-C10 + n-C12 n-C10 + n-C14 n-C12 + n-C14 n-C10 + n-C12 + n-C14 Norpar-13
0.197 0.241 0.299 0.263 0.298
0.201 0.258 0.290 0.248 0.314
2.0 7.1 3.0 5.7 5.4
a
Deviation ) |calculated - experimental|/experimental × 100.
thermal decomposition of n-C12 in Norpar-13 would be higher than those shown in Figure 10 if one excludes the amount of n-C12 produced from the decomposition of n-C13 and n-C14 in calculating the n-C12 conversions. The amount of n-C12 produced from the decomposition of n-C13 and n-C14 may have a significant effect on the n-C12 conversion calculation because of much higher concentrations of n-C13 and n-C14 than that of n-C12 in Norpar-13 (Table 1). Figure 11 shows the conversion of n-C14 as a function of reaction time for the thermal decomposition of the pure compound, in Norpar-13, and in a petroleumderived jet fuel, JP-8P, under similar conditions. It can be seen that the conversions for the thermal decomposition of n-C14 in Norpar-13 are lower than those obtained for the decomposition of pure n-C14. The conversions for the thermal decomposition of n-C14 in JP-8P are much lower than those obtained for the decomposition of pure compounds. This is because JP-8P contains significant amounts of cycloalkanes and aromatics (Lai and Song, 1995) which inhibit the decomposition of n-alkanes. It seems that the apparent overall first-order rate constants for the thermal decomposition of mixtures can be predicted from the rate constants for the decomposition of pure compounds. Table 5 shows a comparison of the observed and predicted overall first-order rate constants for the thermal decomposition of n-alkane mixtures at 425 °C. The observed overall first-order rate constants were determined by using the first-order expression as shown in eq 1. The overall conversions were calculated using eq 16. The predicted overall firstorder rate constants km for the mixtures were determined by the following equation
km )
∑y°ik*i
(17)
Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 591
where ki* is the first-order rate constant for the thermal decomposition of pure compound i. From Table 5 one can see that the overall first-order rate constants for the thermal decomposition of n-alkane mixtures can be predicted satisfactorily by eq 17. Conclusions Thermal decomposition of C10-C14 n-alkanes under supercritical conditions can be represented well by an apparent first-order kinetics, although the decomposition is not a true first-order process. The estimated kinetic parameters for three n-alkanes are in good agreement with literature values. The first-order rate constants for the thermal decomposition of n-alkanes have been correlated to the carbon number in the reactant. A generalized expression was developed to predict the rate constants of C8-C16 n-alkanes at 425 °C and a given pressure. Pressure affects the first-order rate constant. This effect depends on temperature and pressure. In the near-critical region, pressure has a significant effect on the first-order rate constant. This large pressure effect can be attributed to the significant changes in density and possibly to the changes in the rate constants of elementary reactions with pressure in this region. Individual n-alkanes interact with each other in the mixture thermal reactions. The lighter alkane inhibits the decomposition of the heavier one, while the heavier alkane accelerates the decomposition of the lighter one. The overall first-order rate constants for the thermal decomposition of n-alkane mixtures can be predicted satisfactorily from the rate constants for the decomposition of pure compounds. Acknowledgment This work was supported by the U.S. Department of Energy, Pittsburgh Energy Technology Center, and the Air Force Wright Laboratory/Aero Propulsion and Power Directorate, Wright-Patterson AFB. Funding was provided by the U.S. DOE under Contract DE-FG2292PC92104. We express our gratitude to Prof. Harold H. Schobert of Penn State for his support. We also thank Mr. Douglas A. Smith for the fabrication of the glass tubes. We thank Mr. W. E. Harrison III and Dr. T. Edwards of AFWL/APPD and Dr. S. Rogers of PETC for many helpful discussions. Literature Cited Appleby, W. G.; Avery, W. H.; Meerbott, W. K. Kinetics and Mechanism of the Thermal Decomposition of n-Heptane. J. Am. Chem. Soc. 1947, 69, 2279-2285. Benson, S. W. Thermochemical Kinetics; John Wiley & Sons: New York, 1976. Blouri, B.; Hamdan, F.; Herault, D. Mild Cracking of HighMolecular-Weight Hydrocarbons. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 30-37. Depeyre, D.; Flicoteaux, C.; Chardaire, C. Pure n-Hexadecane Thermal Steam Cracking. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 1251-1258. Fabuss, B. M.; Kafesjian, R.; Smith, J. O.; Satterfield, C. N. Thermal Decomposition Rates of Saturated Cyclic Hydrocarbons. Ind. Eng. Chem. Process Des. Dev. 1964a, 3, 248-254.
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Received for review July 8, 1996 Revised manuscript received December 5, 1996 Accepted December 6, 1996X IE9603934
X Abstract published in Advance ACS Abstracts, January 15, 1997.
