3498
Ind. Eng. Chem. Res. 1997, 36, 3498-3504
Radiation Effect on the Thermal Cracking of n-Hexadecane. 2. A Kinetic Approach to Chain Reaction Guozhong Wu, Yosuke Katsumura,* Chihiro Matsuura, and Kenichi Ishigure Department of Quantum Engineering and Systems Science, Graduate School of Engineering, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan
Junichi Kubo Central Technical Laboratory, Nippon Oil Company, 8-Chidori-cho, Naka-ku, Yokohama 231, Japan
Rate equations of n-hexadecane decomposition under different conditions were derived on the basis of a simplified radical reaction scheme. Assuming the initiation rate for radiation is temperature-independent, Arrhenius parameters of some important reactions involving nhexadecane cracking have been estimated by a series of kinetic treatments. Our estimated values are shown to be in good agreement with those reported in the literature. for activation energies is used for the sake of consistence with the literature data.
1. Introduction In our previous work (Wu et al., 1997) the cracking process of n-hexadecane was found to be significantly accelerated by γ-radiation even at low dose rates. Moreover, the patterns of cracking products with or without radiation were shown to be the same, only dependent on the phase. Unlike a radical mechanism for thermal cracking (TC) of hydrocarbons which has been proposed for a long time (Kossiakoff and Rice, 1943) and has been accepted by many workers, both radical (Lucchesi et al., 1958; Matsuoka et al., 1974) and ionic (Matsuoka et al., 1975) mechanisms have been suggested for radiation-thermal cracking (RTC) of hydrocarbons since ionizing radiation generates radicals, ions, and excited species as primary products through its interaction with matter. Despite the ions formation in the primary process, it is conceivable that only radicals participate in the chain reaction because of their longer lifetimes (Warman, 1983). In fact, the actual nature of the initiation step is of less importance than the subsequent propagation step. In this paper we discuss the decomposition kinetics from the viewpoint of a radical mechanism. Activation energies for the overall decomposition of long-chain paraffins under various conditions have been reported by many workers (Ford, 1986; Zhou and Crynes, 1986; Khorasheh and Gray, 1993; Song et al., 1994) in recent years, but the kinetic information on radical reactions is still insufficient. However, the determination or estimation of kinetic parameters is of fundamental importance for the quantitative treatment of heavy hydrocarbon cracking. Most of the presently available Arrhenius parameters are evaluated by analogues to the values determined for light hydrocarbons or by computer simulation. Making an assumption that the radiation initiation is temperature-independent, here we made an attempt to estimate the Arrhenius parameters of some reactions involving the cracking process of n-hexadecane on the basis of our experimental results and kinetic treatments. Such reactions include C-C dissociation, H abstraction, β-scission, and addition reaction of radicals to alkenes. Here a unit of kcal/mol * To whom correspondence should be addressed. Tel.: +813-3812-2111 ext. 6979. Fax: +81-3-5800-6858. E-mail: katsu@ quest.gen.u-tokyo.ac.jp. S0888-5885(97)00025-0 CCC: $14.00
2. Experimental Section The experimental details and results of product analysis for RTC and TC of n-hexadecane have been described elsewhere (Wu et al., 1996, 1997), so only a brief introduction will be given here. The cracking of n-hexadecane was carried out in sealed glass ampules at 330-375 °C for pure TC and at 300-400 °C for RTC where γ-rays from a cobalt-60 source were introduced. By controlling the amount of the added n-hexadecane and the volume of the ampule, the runs could be done in the liquid and gas phases. The cracking products were separated and determined by chromatography techniques. The conversions of n-hexadecane were 0.114.5 wt % in TC and 0.6-48.8 wt % in RTC, depending on the residence time and temperature. Only n-alkanes (C1-C15) and 1-alkenes (C2-C15) were found as scission products in most of the runs except that traces of some other products, quite likely resulting from secondary decomposition of 1-alkenes, were detected after a longer duration at higher temperatures. The molar selectivity of different scission products (Ci), given as 1 mol/100 mol of cracked n-hexadecane, was calculated in each run. The concentration of alkene products over the range of C2-C15 was, therefore, calculated by the following expression.
[alkene] )
CiRw
∑Mw × vol × 10
(1)
The concentration of alkanes ranging from C1 to C15 was also calculated by a similar method. The concentration of alkenes in gas-phase cracking can be calculated with complete confidence, because all the components exist in a homogeneous gaseous phase under applied conditions, but in liquid-phase cracking, it is impossible to differentiate what part of the alkenes are present in the gas phase or liquid phase. Lower alkenes must exist in the gas phase, whereas higher ones might exist in both the liquid and gas phases. This fact does not allow an accurate calculation of the alkene concentration, and an assumption that all the alkenes distribute in the whole ampule was made to simplify the calculation. This approximation will make some © 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3499 Scheme 1 liquid phase
gas phase initiation M M
ki
Ri• + Rj• M*
I*
(2)
thermal initiation
Ri• + Rj• and H + M•
radiation initiation
(3)
propagation R• + M M•
kβ
k ′H
RH + M•
R• + M M•
R• + 1-alkene
M• R′•
kβ kβ kβ
kH
RH + M•
(4)
R• + 1-alkene
(5a)
R′• + 1-alkene
(5b)
R• + 1-alkene
(5c)
radical addition M• + 1-alkene
k ′ad
•C
R• + 1-alkene
18+
kad
R′′•
(6)
termination M• + M• R• + M• R • + R• ...
kt kt kt
product ρ1 (7a′)
R′• + M•
product ρ2 (7b′)
R′• + R′•
product ρ3 (7c′)
R• + M• R• + R′• R• + R• ...
R• = •C1–•C15
kt kt kt kt kt
R• = •C1–•C4
product δ1
(7a)
product δ2
(7b)
product δ3
(7c)
product δ4
(7d)
product δ5
(7e)
R′• = •C5–•C15
errors in the calculation but not distort the confidence of the conclusion.
theory is applied, the derived rate equations of nhexadecane decomposition are given below:
3. Description of Reaction Mechanism
in the liquid phase
The reaction mechanisms for liquid-phase and gasphase cracking of long-chain paraffins have been proposed by many workers (Voge and Good, 1949; Ford, 1986; Zhou and Crynes, 1986; Khorasheh and Gray, 1993; Song et al., 1994; Wu et al., 1996) to account for the product distributions. It is generally believed that liquid-phase cracking is subjected to a one-step mechanism, while gas-phase cracking is subjected to a twostep or multistep decomposition model. When radiation is introduced, the radicals resulting from hydrocarbon radiolysis, together with radicals produced by thermal C-C cleavage, initiate a chain reaction leading to n-hexadecane decomposition. As a result, despite the increased initiation rate in RTC, the reaction mechanism and rate constants of various reactions should be the same as those for pure TC. A simplified reaction mechanism for RTC of nhexadecane is given in Scheme 1. If the radiation initiation step is eliminated, the scheme becomes a description of TC. Here isomerization of primary to secondary radicals is not included, because it is already assumed (Kossiakoff and Rice, 1943; Rebick, 1981) that, prior to H abstraction and β-scission, larger radicals isomerize instantaneously through internal hydrogen abstractions with ring formation. Special attention is devoted to termination reactions for a better understanding of the kinetic behavior. In Scheme 1 M indicates the n-hexadecane molecule and M• the parent radical; F1-F3 and δ1-δ5 denote the probabilities of different terminations in the liquid phase and gas phase, respectively. When it is assumed that reaction (4) is the limiting-step and the steady-state
Rp )
x
x
kPk′Hkβ[M] 2kt
1
k′H[M] kβ F1 + F2 + F3 kβ k′H[M]
(8)
F1 + F2 + F3 ) 1 in the gas phase Rp )
x
kPkHkβ[M] × kt
x
1
kH[M] kH[M] 2kβ δ1 + δ2 + δ3 + δ4 + δ5 2kβ 2kβ kH[M]
(9)
δ1 + δ2 + δ3 + δ4 + δ5 ) 1
where kP is the initiation rate, equal to ki[M] in TC or I* + ki[M] in RTC. Equations 8 and 9 imply that Rp is strongly dependent on the termination pathway. Although many termination reactions are possible, only one or two reactions are predominant in specific conditions, determined by the cracking temperature and reactant concentration. The rate equations of the overall decomposition derived for the individual terminations and the estimated activation energies are further shown in Table 1. It is evident that the activation energy for decomposition varies significantly with termination. It is also worth noting that the activation energies for decomposition in the two
3500 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 Table 1. Rate Equations and the Expected Activation Energies for n-Hexadecane Decomposition with Respect to Individual Termination Reactions termination liquid phase
(7a′)
(7b′)
(7c′)
gas phase
(7a)
(7b)
(7c)
(7d)
(7e)
Ed for TCa
Rp
x x x x
kP 2kt
E (kcal mol-1)b
1 Eβ + Ei 2
60-70
1 (E + E′H + Eβ) 2 i
50-60
1 E′H + Ei 2
40-50
1 Eβ + Ei 2
60-70
1 Eβ + Ei 2
60-70
kPkHkβ[M] kt
1 (E + Eβ + Ei) 2 H
50-60
kPkHkβ[M] kt
1 (E + Eβ + Ei) 2 H
50-60
kβ
kPk′Hkβ[M] 2kt kP 2kt
k′H
2kP kt
kβ
x
2K kt
kβ
x x
kH[M]
x
kP 2kt
(E
H
1 + Ei 2
)
40-50
a E for RTC is smaller by a factor of 1/ E where I* is much larger than k [M]. b Roughly estimated by assuming E , E , and E are 10, d 2 i i H β i 30, and 60-80 kcal/mol, respectively (see Table 2).
phases could be the same when different terminations are considered. This is consistent with the work of Ford (1986) and Blouri et al. (1985), who both observed a similarity in decomposition kinetics between liquidphase and gas-phase TC. The activation energies shown in Table 1 cover a range of 40-70 kcal/mol, which is in agreement with the reported values. Although the value for heavy hydrocarbon TC in the gas phase is wellknown to be 60 kcal/mol, the deviation from this value can be explained in terms of the predominance of different terminations controlled by the cracking conditions, not only the experimental errors. Also shown in Table 1 is the difference in activation energies for the overall decomposition with and without radiation. This difference is Ei/2, where the thermal initiation rate is negligible when compared with the radiation initiation rate. Because the activation energy for thermal initiation of n-hexadecane is reported to be 59-80 kcal/mol (Lucchesi et al., 1958; Gavalas, 1966; Doue and Guiochon, 1968; Depeyre and Flicoteaux, 1991), the activation energy for RTC is expected to be 30-40 kcal/mol lower than that for TC, as confirmed in our earlier work (Wu et al., 1997). In this study, we suggest that the recombination or disproportionation of parent radicals, reaction (7a′), is the main termination in the liquid phase because of the much higher concentration of parent radicals relative to smaller radicals. Reactions (7a) and (7b), i.e., the terminations of R′• with R′• and M•, are proposed to be the main terminations in the gas phase, due to the fact that unimolecular decomposition of large radicals is favored over bimolecular H abstraction. 4. Estimation of Activation Energies 4.1. C-C Dissociation. Because radiation initiation is assumed to be temperature-independent, a comparison of the cracking rate constants for RTC and
Figure 1. Plots of ln{[(kRTC/kTC)2 - 1]-1I*} against 103T-1 for n-hexadecane decomposition in the liquid phase and gas phase.
TC enables one to estimate the dissociation energy, Ei, for n-hexadecane. As noted earlier, the initiation rate can be expressed by I* + Ith for RTC, where I* and Ith denote the initiation rates for radiation and thermal dissociation, respectively. Based on our reaction scheme, if RTC and TC are carried out under the same conditions, the ratio of kRTC/kTC would be equal to (1 + I*/ Ith)0.5. Making a rearrangement, we get the formula
Ith ) ki[M] ) [(kRTC/kTC)2 - 1]-1I*
(10)
From the values of kRTC/kTC and corresponding I* reported previously (Wu et al., 1997), the values of Ith at different temperatures can be calculated by eq 10. The Eis, calculated from the Arrhenius plots shown in Figure 1, are 68 ( 4 and 72 ( 2 kcal/mol for liquidphase and gas-phase TC, respectively. The corresponding frequency factors are 4.3 ((0.4) × 1013 and 1.2 ((0.2) × 1015 s-1, estimated from the intercepts and in addition by taking into account the applied reactant concentrations.
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3501
Figure 2. Correlation between Y and residence time for liquidphase RTC of n-hexadecane at different temperatures.
Figure 3. Correlation between Y and residence time for gas-phase RTC of n-hexadecane at different temperatures.
4.2. Chain Length and β-Scission. According to the rate equations of Rp as shown in Table 1, the kinetic chain length can be expressed by eq 11 for the runs in
L)
x
Rp ) kβ Ri
1 kPkt
(11)
both the liquid and gas phases. The coefficient in the expression is ignored for the sake of simplicity. The value of L for hydrocarbon TC can be estimated from the kinetic parameters but cannot be experimentally determined. However, the value of L for RTC can be evaluated from the experimental data by an approximation described as follows. In radiation chemistry, radical yield G(R•), given as the number of radicals made per 100 eV of energy absorbed, is found to be 5.5 for n-hexadecane at room temperature (LaVerne and Wojnarovits, 1994) and appears to be independent of the dose rate and temperature (Weber et al., 1955) in an air-free system. Here apparent G(-M) is defined as the number of converted n-hexadecane molecules per 100 eV of energy absorbed, corrected for thermal contribution in the calculation. The radiation yields Y are, therefore, reported as G(-M)/5.5. Where there is nearly no thermal contribution to RTC, for example, at 330 °C in this study, the Y values would be a direct measure of L. The correlation between Y and residence time is shown in Figure 2 for liquid-phase RTC and in Figure 3 for gas-phase RTC. The dependence of residence time for Y is similar in both cases. It is clear that Y increases with temperature but decreases with residence time. The decrease of Y with residence time is more dramatic
Figure 4. Temperature dependence of ln Y0 for liquid-phase (O, 460 Gy/h) and gas-phase (9, 560 Gy/h) RTC.
at higher temperatures due to the buildup of alkenes during the cracking process, because alkenes are known to be potent inhibitors for radical reactions. The values of Y0, obtained by extrapolating Y to zero time to avoid the influence of alkenes, are assumed to be identical with L. The use of Y0 is very helpful in the followed kinetic treatment. Figure 4 shows the temperature dependence of Y0. The activation energies of 25.0 ( 0.8 and 27.0 ( 1.2 kcal/ mol are calculated from the slopes of the curves for liquid-phase and gas-phase TC. An average value of 26.0 kcal/mol is taken here as the activation energy for the β-scission process, Eβ, by assuming the activation energy for termination is zero. This is in excellent agreement with the value of 25 kcal/mol reported by Lucchesi et al. (1958) with a different treatment. It is necessary to point out that there is a difference between radiation yields Y0 and the true chain length L where there is a thermal background in addition to the radiation-induced process. When the treatment of Lucchesi et al. (1958) is applied, a relationship between Y0 and L is given by
{[
Y0 ) L 1 +
( )[
Ith Ith I* I*
1/2
1+
]}
Ith I*
1/2
(12)
The term in brackets on the right side is composed entirely of Ith/I*; therefore, if Y0 and Ith/I* are known, L can be estimated. In this work, the use of Y0 instead of L makes little difference in consequence because the value of Ith/I* is very small; for example, it is about 1/16 even at 400 °C when estimated from the kRTC/kTC value (Wu et al., 1997). It should be noted that there are apparent printing errors in the formula describing the correlation between Y and L in the work of Lucchesi et al. (1958). 4.3. H Abstraction and Radical Addition. Our experiments (Wu et al., 1996, 1997) revealed that the alkene concentrations always increase with residence time and higher alkene concentrations can be reached after a relatively short duration at higher temperature. In addition, the alkene concentration in liquid-phase TC is found to be about 1 order higher than that in gasphase TC under similar conditions. When the alkenes are present, addition of radicals to alkenes occurs by competition with H abstraction. As inferred in Scheme 1, the radical addition occurring in the liquid phase differs from that in the gas phase due to the difference in reactant density, which requires different kinetic treatments.
3502 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
Figure 5. Plots of Y0/Y against [alkene]/[M]0(1 - R) for gas-phase RTC of n-hexadecane at different temperatures. Dose rate: 560 or 240 Gy/h.
Figure 7. Plots of m against [alkene] for liquid-phase RTC and TC of n-hexadecane at different temperatures. Dose rate: 460 or 150 Gy/h. The solid lines are fittings of data by eq 20.
To the contrary, based on the one-step model for liquid-phase cracking, an equimolar distribution of alkane/alkene products is expected at very low conversions. However, at higher conversions, the addition of parent radicals to alkenes leads to the formation of addition products and the elimination of some part of the alkenes. As a result, the alkene/alkane ratio decreases with residence time or the alkene concentration. The following kinetic treatment is applied to explain the decrease of alkene/alkane with the alkene concentration.
k′H[R•][M] d[alkane]/dt ) d[alkene]/dt kβ[M•] - k′ad[M•][alkene] Figure 6. Plots of ln(kad/kH) against 103T-1 for gas-phase RTC of n-hexadecane. The data are obtained from Figure 5.
k′H[M] )
Since H abstraction and radical-alkene addition are considered to be competing reactions in the gas phase, an equation illustrating the inhibition effect of alkenes on the decomposition process can be derived as follows:
kH[R ][M] G(-M) ) • G(-M)0 kH[R ][M] + kad[R•][alkene]
[R•]
kβ - k′ad[alkene] [M•] kβ + k′ad[alkene]
)
kβ - k′ad[alkene]
•
G(-M)0 G(-M)
)1+
kad [alkene] kH [M]
(13)
(17)
k′ad[alkene]
