- Email: [email protected]
Non-quasi-stationary state pyrolysis of ethane
Volume
80, number
1
CHEMICAL
NON-QUASISTATIONA , Serge CORBEL,
PHYSICS
LE-I-I.ERS
$5 May 1981
STATE PYROLYSIS OF ETHANE
Paul-Marie MARQUAIRE
and Guy-Marie &ME
Laboratoire de Cinkique Appliquke, Equipe de Recherche Associ6e au C.N.R.S. no. 136. Universit; de Nancy I et Itutitut National Polytechniqrre de Lorraine, 54042 Nancy, France Received
2 February
1981
An Induction period has been observed in the pyrolysis of ethane m a continuous-flow stirred tank reactor The rate constants of the initiation, determining propagation and termination steps, have been determined.
I. Introduction The study of a pyrolysis reaction in nonquasistationary state (NQQS) conditions provides direct information about reaction mechanisms and radical reactivlties. Induction periods have actually been observed in the pyrolysis of neopentane in a continuousflow stirred tank reactor (CFSTR) around 440°C [I] and in a tubular reactor at 550°C [2] _These NQSS experlments have provided kinetic parameters for the initiation, propagation and termination steps occurring in neopentane pyrolysis. In this paper, we report on the observation of an induction period in the pyrolysis of ethane in a CFSTR at 530°C and 40 Torr. From these experiments, independent values of the rate constants of the initiation step, and of the determining propagation and termination steps of ethane pyrolysis have been deduced.
at 530°C.
3. Results . A singular perturbaticn theory of chain radical reaction mechanisms [3] allows one to predict a priori, from an assumed reaction mechanism and corresponding kinetic parameters_ experimental conditions for which NQSS kinetics can be observed_ In the case of ethane pyrolysis, it was concluded that an induction period of the order of 1 s should occur around 530°C. Accordingly, experiments were carried out at 53O”C, under a constant ethane pressure of 40 Torr and for space times between 0.7 and 7 s. Under these conditions, the degree of conversion of ethane was very low (between 10e3 and 10-2%)_ We observed the formation of two main primary reaction products, ethylene and hydrogen, in equal amounts, in agreement with the stoichiometric equation: C,H6 = CzH‘, + H, _
2. Experimental The principle of the apparatus used in this study has been described [I]. The reactor is a Pyrex CFSTR, operated at constant temperature and pressure, and steady-state gas flow. Ethane reactant, obtained from Air Liquide Company, containing less than 1 ppm 02, was carefully degassed before each experiment by bulk-to-bulk distillation. Analyses of the reaction products were carried out by gas chromatography, using flame ionization and catharometer detectors_ 34
The rormation of a minor primary reaction methane, was also observed_ The termination n-butane, was not measured, for sensitivity Since the reactor is a CFSTR, with quite tents of reaction, the rateSRC,H4 and &Ha formation of C2Hq and CHq are given by RC2H4 =
K$-k+l/~ 9 &-I,+ =
W41/~
product, product, reasons. low exof
,
where r is the space time (reactor volume divided by the input volumetric flow rate)_ In fig. 1 plots of versusr are shown. These plots apply to k2H4 andRCH4
0 009-2614/81/0000-0000/$02.50
0 North-Holland
Publishing Company
Volume 80, number 1
CHEMICAL
15 May 1981
PHYSICS LETTERS
it can be concluded that chains are long. Since methane only appears in the elementary process (2) and since ethylene mainly appears in process (3) (Le. chains are long), the rates of formation of these two products are given by %H4
Fig. 1. Rates of formation of ethylene 2nd methane as 2 function of space time T. T = 530”c;pc,~, = 40 Torr. o RC*H~, 0 &-H, (euperimental), theoretical line.
the constant temperature (530°C) and (because the small conversion of ethane) constant reactant ethane pressure (40 Torr) condition. It is apparent that the rate of formation of methane remains constant, whereas the rate of formation of ethylene increases with increasing reaction times, despite the invariance of temperature and ethane concentration.
= k2
IC,H61 I-Q1 2
&HI,
= k, [C$j
1 .
At constant temperature, k, and k, are constant and, since ethane concentration is also constant, the concentrations of methyl and ethyl radicals are proportional to &H, and RC2H4 respectively. From the results shown in fig. 1, it can be concluded that, in the terminology used by Cdme [3], the “non-determining” methyl radicals are in a quasi-stationary state, whereas the “determining” ethyl radicals are not in a quasistationary state. This demonstrates the occurrence of an induction period for the ethane pyrolysis under the stated conditions. The non-determining radicals are the most reactive and, accordingly, the least concentrated. Therefore, they do not participate in the termination processes. The determining radicals are the least reactive and the most concentrated. They are involved in termination processes_ Since hydrogen atoms are more reactive than methyl radicals, the “pseudo-stationary state” approximation can also be applied to them, even though they are chain carriers. Therefore, the following inequalities will be assumed: 1, kq[C2Hg]+
k,[C,H,]TS
1.
(6)
4. Interpretation
The inequalities (6) mean that the pseudo-stationary state approximation can be applied to CHJ and H-
The pyrolysis of ethane at small extents of reaction has been generally interpreted by the following straight chain radical mechanism [4-lo]:
[31-
From the above mechanism and appro,xirnations, the following rate laws can be deduced
C2Hg + 2CHj ,
Cl>
kH4
(2)
@C,H,)-2
(3)
with
CHj
C,Hj
+
C2H6 --f CH, + C2Hj , + CzH4 + H- ,
Ho + C,H,
--f HZ + C2Hj ,
(4)
2C2H; -+ n-CqHIO ,
(0
+C2Hg
(5”)
+ C2H4 _
This mechanism accounts for the observed reaction products, H,, CzHe and CH4 _As the amounts of CHq are much smaller than those ofCzH4 (cf. fig_ I),
= =,
&H6
= @&H,)-2
k5 =k5’ +ksR&H4
(7)
1,
+d1C2H41>
(8)
,
= k3(kllk5)112
p = l/2klk3 [C2H6].
[c2H611’2
>
(9) (10)
RCH~ and Rc*H~ are the rates of formation of CH4 and C2H4 respectively, and R&H4 is the quasi-stationary initial rate of formation of C2H4 (i.e. after the induction period is over)_ 35
CHEMICAL
Volume &O, number 1
PHYSICS
LETTERS
15 May 1981
Remark: From the numerical values of the rate constants, it can easily be checked that the approximations (6) assumed for the establishment of the rate laws are met and, furthermore, that chains are long.
5. Discussion
4
0
[C2H4]-’
I>
1'0 x IO -‘o
(t-ml
-‘,cm3)
versus l/[CaH4]_ T=530”C;J’C,H,= Fig. 2. Plot of l/R6,~~ 40 T0r-r. o Experiment,rI points, theoretical line.
At constant temperature and ethane concentration, in agreement with relationship (7), a constant rate of formation of methane is observed (fig. 1); and, in agreement with relationship (8), a plot of l/R&H4 versus l/ [CzH4] is actually linear (fig. 2). From the plot ofRcH, versus r (fig. I), a value of the initiation rate constant k, can be deduced, through relationship (7) (table 1). Also, from the plot of l/R&H4 versus l/[C2H4] (fig. 2), values Of R&H4 and p can be determined. These values, in turn, through relationships (9) and (lo), give values for rate constants k, and k, (table 1).
Table 1 Rate constants of ethane pyrolysis at 530°C
Around 530°C and at not too small pressures, the QSS initial rateREaH4 of ethylene formation in ethane pyrolysis is known to be roughly first-order with respect to ethane concentration, in contrast to the apparent halforder exhibited in eq_(9)_ Deviations of reaction order ‘from l/2 are explained on the basis of the pressure fall-off of rate constants k, and k, _Therefore, the comparison of the present pressure fall-off values of k, and k, with others from the literature (table 1) is only indicative of a correct order of magnitude, as long as a determination of kF and k; has not been achieved. As regards k, , the agreement is quite good (table 1). In conclusion, nonquasi-stationary state pyrolysis appears to be a powerful method both for elucidating reaction mechanisms and determining independent rate constants of chain radical reactions_
References [l]
Society, London, 1977); React.Kin.Cat
[2] [3] [4] [S] [6] [7]
kl (s-l) k3 (s-l) k5 (mol-r
,
cm3 s-r)
This work (40 Torr)
Ref. [ll] (“high-pressure”)
4.1 x 10-s 2.0 x 102 5.6 x lOr*
3.8 x 102
3.8 x 10-a
[S] [9] [lo]
4.5 x 10’2 [ 1 l]
/
36
PM. IMarquaire, Thkse de 32me cycIe.‘Nancy (1975), P.M. hlarquaire and GM. Gme, Frfth International Symposium on Gas Kmetics. Paper 2 (The Chemical
Letters 9 (1973)
165,171. P-D. Pacey and J.H. Wihnaiasena, Chem. Phys. Letters 53 (1978) 593; J. Phys. Chem. 84 (1980) 2221. GM. CBme, J. Phys_Chem_ 81(1977) 2560. C.P. Quinn, Proc. Roy_ Sot_ A275 (1963) 190. A-B. Trenwith, Trans. Faraday Sot. 62 (1966) 1538. MC. Lin and M.H. Back,Can. J. Chem. 44 (1966) 505, 2357,2369. G. Scacchi, R. Martin and M. Niclause, Bull. Sot. Chim. 3 (197i) 731. P.D. Pacey and J-H. PumeII, J. Chem. Sot. Faraday I 68 (1972) 1462. A-B. Trenwith, J. Chem. Sot. Faraday I75 (1979) 614. G. Pratt and D. Robers, J. Chem. Sot. Faraday I 75 (1979) 1089_ D.L. AUara and R. Shaw, J. Chem. Phys. Ref. Data 9 (1980) 523.
80, number
1
CHEMICAL
NON-QUASISTATIONA , Serge CORBEL,
PHYSICS
LE-I-I.ERS
$5 May 1981
STATE PYROLYSIS OF ETHANE
Paul-Marie MARQUAIRE
and Guy-Marie &ME
Laboratoire de Cinkique Appliquke, Equipe de Recherche Associ6e au C.N.R.S. no. 136. Universit; de Nancy I et Itutitut National Polytechniqrre de Lorraine, 54042 Nancy, France Received
2 February
1981
An Induction period has been observed in the pyrolysis of ethane m a continuous-flow stirred tank reactor The rate constants of the initiation, determining propagation and termination steps, have been determined.
I. Introduction The study of a pyrolysis reaction in nonquasistationary state (NQQS) conditions provides direct information about reaction mechanisms and radical reactivlties. Induction periods have actually been observed in the pyrolysis of neopentane in a continuousflow stirred tank reactor (CFSTR) around 440°C [I] and in a tubular reactor at 550°C [2] _These NQSS experlments have provided kinetic parameters for the initiation, propagation and termination steps occurring in neopentane pyrolysis. In this paper, we report on the observation of an induction period in the pyrolysis of ethane in a CFSTR at 530°C and 40 Torr. From these experiments, independent values of the rate constants of the initiation step, and of the determining propagation and termination steps of ethane pyrolysis have been deduced.
at 530°C.
3. Results . A singular perturbaticn theory of chain radical reaction mechanisms [3] allows one to predict a priori, from an assumed reaction mechanism and corresponding kinetic parameters_ experimental conditions for which NQSS kinetics can be observed_ In the case of ethane pyrolysis, it was concluded that an induction period of the order of 1 s should occur around 530°C. Accordingly, experiments were carried out at 53O”C, under a constant ethane pressure of 40 Torr and for space times between 0.7 and 7 s. Under these conditions, the degree of conversion of ethane was very low (between 10e3 and 10-2%)_ We observed the formation of two main primary reaction products, ethylene and hydrogen, in equal amounts, in agreement with the stoichiometric equation: C,H6 = CzH‘, + H, _
2. Experimental The principle of the apparatus used in this study has been described [I]. The reactor is a Pyrex CFSTR, operated at constant temperature and pressure, and steady-state gas flow. Ethane reactant, obtained from Air Liquide Company, containing less than 1 ppm 02, was carefully degassed before each experiment by bulk-to-bulk distillation. Analyses of the reaction products were carried out by gas chromatography, using flame ionization and catharometer detectors_ 34
The rormation of a minor primary reaction methane, was also observed_ The termination n-butane, was not measured, for sensitivity Since the reactor is a CFSTR, with quite tents of reaction, the rateSRC,H4 and &Ha formation of C2Hq and CHq are given by RC2H4 =
K$-k+l/~ 9 &-I,+ =
W41/~
product, product, reasons. low exof
,
where r is the space time (reactor volume divided by the input volumetric flow rate)_ In fig. 1 plots of versusr are shown. These plots apply to k2H4 andRCH4
0 009-2614/81/0000-0000/$02.50
0 North-Holland
Publishing Company
Volume 80, number 1
CHEMICAL
15 May 1981
PHYSICS LETTERS
it can be concluded that chains are long. Since methane only appears in the elementary process (2) and since ethylene mainly appears in process (3) (Le. chains are long), the rates of formation of these two products are given by %H4
Fig. 1. Rates of formation of ethylene 2nd methane as 2 function of space time T. T = 530”c;pc,~, = 40 Torr. o RC*H~, 0 &-H, (euperimental), theoretical line.
the constant temperature (530°C) and (because the small conversion of ethane) constant reactant ethane pressure (40 Torr) condition. It is apparent that the rate of formation of methane remains constant, whereas the rate of formation of ethylene increases with increasing reaction times, despite the invariance of temperature and ethane concentration.
= k2
IC,H61 I-Q1 2
&HI,
= k, [C$j
1 .
At constant temperature, k, and k, are constant and, since ethane concentration is also constant, the concentrations of methyl and ethyl radicals are proportional to &H, and RC2H4 respectively. From the results shown in fig. 1, it can be concluded that, in the terminology used by Cdme [3], the “non-determining” methyl radicals are in a quasi-stationary state, whereas the “determining” ethyl radicals are not in a quasistationary state. This demonstrates the occurrence of an induction period for the ethane pyrolysis under the stated conditions. The non-determining radicals are the most reactive and, accordingly, the least concentrated. Therefore, they do not participate in the termination processes. The determining radicals are the least reactive and the most concentrated. They are involved in termination processes_ Since hydrogen atoms are more reactive than methyl radicals, the “pseudo-stationary state” approximation can also be applied to them, even though they are chain carriers. Therefore, the following inequalities will be assumed: 1, kq[C2Hg]+
k,[C,H,]TS
1.
(6)
4. Interpretation
The inequalities (6) mean that the pseudo-stationary state approximation can be applied to CHJ and H-
The pyrolysis of ethane at small extents of reaction has been generally interpreted by the following straight chain radical mechanism [4-lo]:
[31-
From the above mechanism and appro,xirnations, the following rate laws can be deduced
C2Hg + 2CHj ,
Cl>
kH4
(2)
@C,H,)-2
(3)
with
CHj
C,Hj
+
C2H6 --f CH, + C2Hj , + CzH4 + H- ,
Ho + C,H,
--f HZ + C2Hj ,
(4)
2C2H; -+ n-CqHIO ,
(0
+C2Hg
(5”)
+ C2H4 _
This mechanism accounts for the observed reaction products, H,, CzHe and CH4 _As the amounts of CHq are much smaller than those ofCzH4 (cf. fig_ I),
= =,
&H6
= @&H,)-2
k5 =k5’ +ksR&H4
(7)
1,
+d1C2H41>
(8)
,
= k3(kllk5)112
p = l/2klk3 [C2H6].
[c2H611’2
>
(9) (10)
RCH~ and Rc*H~ are the rates of formation of CH4 and C2H4 respectively, and R&H4 is the quasi-stationary initial rate of formation of C2H4 (i.e. after the induction period is over)_ 35
CHEMICAL
Volume &O, number 1
PHYSICS
LETTERS
15 May 1981
Remark: From the numerical values of the rate constants, it can easily be checked that the approximations (6) assumed for the establishment of the rate laws are met and, furthermore, that chains are long.
5. Discussion
4
0
[C2H4]-’
I>
1'0 x IO -‘o
(t-ml
-‘,cm3)
versus l/[CaH4]_ T=530”C;J’C,H,= Fig. 2. Plot of l/R6,~~ 40 T0r-r. o Experiment,rI points, theoretical line.
At constant temperature and ethane concentration, in agreement with relationship (7), a constant rate of formation of methane is observed (fig. 1); and, in agreement with relationship (8), a plot of l/R&H4 versus l/ [CzH4] is actually linear (fig. 2). From the plot ofRcH, versus r (fig. I), a value of the initiation rate constant k, can be deduced, through relationship (7) (table 1). Also, from the plot of l/R&H4 versus l/[C2H4] (fig. 2), values Of R&H4 and p can be determined. These values, in turn, through relationships (9) and (lo), give values for rate constants k, and k, (table 1).
Table 1 Rate constants of ethane pyrolysis at 530°C
Around 530°C and at not too small pressures, the QSS initial rateREaH4 of ethylene formation in ethane pyrolysis is known to be roughly first-order with respect to ethane concentration, in contrast to the apparent halforder exhibited in eq_(9)_ Deviations of reaction order ‘from l/2 are explained on the basis of the pressure fall-off of rate constants k, and k, _Therefore, the comparison of the present pressure fall-off values of k, and k, with others from the literature (table 1) is only indicative of a correct order of magnitude, as long as a determination of kF and k; has not been achieved. As regards k, , the agreement is quite good (table 1). In conclusion, nonquasi-stationary state pyrolysis appears to be a powerful method both for elucidating reaction mechanisms and determining independent rate constants of chain radical reactions_
References [l]
Society, London, 1977); React.Kin.Cat
[2] [3] [4] [S] [6] [7]
kl (s-l) k3 (s-l) k5 (mol-r
,
cm3 s-r)
This work (40 Torr)
Ref. [ll] (“high-pressure”)
4.1 x 10-s 2.0 x 102 5.6 x lOr*
3.8 x 102
3.8 x 10-a
[S] [9] [lo]
4.5 x 10’2 [ 1 l]
/
36
PM. IMarquaire, Thkse de 32me cycIe.‘Nancy (1975), P.M. hlarquaire and GM. Gme, Frfth International Symposium on Gas Kmetics. Paper 2 (The Chemical
Letters 9 (1973)
165,171. P-D. Pacey and J.H. Wihnaiasena, Chem. Phys. Letters 53 (1978) 593; J. Phys. Chem. 84 (1980) 2221. GM. CBme, J. Phys_Chem_ 81(1977) 2560. C.P. Quinn, Proc. Roy_ Sot_ A275 (1963) 190. A-B. Trenwith, Trans. Faraday Sot. 62 (1966) 1538. MC. Lin and M.H. Back,Can. J. Chem. 44 (1966) 505, 2357,2369. G. Scacchi, R. Martin and M. Niclause, Bull. Sot. Chim. 3 (197i) 731. P.D. Pacey and J-H. PumeII, J. Chem. Sot. Faraday I 68 (1972) 1462. A-B. Trenwith, J. Chem. Sot. Faraday I75 (1979) 614. G. Pratt and D. Robers, J. Chem. Sot. Faraday I 75 (1979) 1089_ D.L. AUara and R. Shaw, J. Chem. Phys. Ref. Data 9 (1980) 523.