Study of the low temperature oxidation of propane

Article abstract of DOI:10.1021/jp309821z

The low-temperature oxidation of propane was investigated using a jet-stirred reactor at atmospheric pressure and two methods of analysis: gas chromatography and synchrotron vacuum ultraviolet photoionization mass spectrometry (SVUV-PIMS) with direct sampling through a molecular jet. The second method allowed the identification of products, such as molecules with hydroperoxy functions, which are not stable enough to be detected by gas chromatography. Mole fractions of the reactants and reaction products were measured as a function of the temperature (530-730 K), with a particular attention to reaction products involved in the low temperature oxidation, such as cyclic ethers, aldehydes, alcohols, ketones, and hydroperoxides. A new model has been obtained from an automatically generated one, which was used as a starting point, with a large number of re-estimated thermochemical and kinetic data. The kinetic data of the most sensitive reactions, i.e., isomerizations of alkylperoxy radicals and the subsequent decompositions, have been calculated at the CBS-QB3 level of theory. The model allows a satisfactory prediction of the experimental data. A flow rate analysis has allowed highlighting the important reaction channels.

Full text of DOI:10.1021/jp309821z

Article
pubs.acs.org/JPCA
Study of the Low Temperature Oxidation of Propane
Maximilien Cord,† Benoit Husson,† Juan Carlos Lizardo Huerta,† Olivier Herbinet,†,*
Pierre-Alexandre Glaude,† Rene Fournet,† Baptiste Sirjean,† Frederique Battin-Leclerc,†
́
́
́
Manuel Ruiz-Lopez,‡ Zhandong Wang,§ Mingfeng Xie,§ Zhanjun Cheng,§ and Fei Qi§
†Laboratoire Rea
France
‡Laboratoire Structure et Rea
BP 70239, 54506 Vandœuvre-les
́
ctions et Gen
́
ie des Proced
́
es
́
, Universite
́
de Lorraine, CNRS, ENSIC, BP 20451, 1 rue Grandville, 54000 Nancy,
́
ctivite
́
des System
-Nancy, France
̀
es Molec
́
ulaires Complexes, Universite de Lorraine, CNRS, Boulevard des Aiguillettes,
́
̀
§National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei, Anhui 230029, P. R. China
S
* Supporting Information
ABSTRACT: The low-temperature oxidation of propane was
investigated using a jet-stirred reactor at atmospheric pressure and
two methods of analysis: gas chromatography and synchrotron
vacuum ultraviolet photoionization mass spectrometry (SVUV-PIMS)
with direct sampling through a molecular jet. The second method
allowed the identification of products, such as molecules with
hydroperoxy functions, which are not stable enough to be detected by
gas chromatography. Mole fractions of the reactants and reaction products were measured as a function of the temperature
(530−730 K), with a particular attention to reaction products involved in the low temperature oxidation, such as cyclic ethers,
aldehydes, alcohols, ketones, and hydroperoxides. A new model has been obtained from an automatically generated one, which
was used as a starting point, with a large number of re-estimated thermochemical and kinetic data. The kinetic data of the most
sensitive reactions, i.e., isomerizations of alkylperoxy radicals and the subsequent decompositions, have been calculated at the
CBS-QB3 level of theory. The model allows a satisfactory prediction of the experimental data. A flow rate analysis has allowed
highlighting the important reaction channels.
coefficient in the range 750−775 K. They detected and
quantified many reaction products by gas chromatography, the
main ones being carbon oxides, ethylene, propene, form-
aldehyde, and acetaldehyde. They also observed the formation
of minor species such as acetone, propanal, propylene oxide
(methyloxirane), acrolein, methanol, and n-butane.
INTRODUCTION
■
In contrast to larger n-alkanes,1,2 the low temperature oxidation
of propane in the gas phase has been the subject of very few
experimental studies, mainly due to its very low reactivity. This
C3 hydrocarbon is not very reactive because of the short size of
the alkyl chain which limits the low temperature branching
paths. Therefore, conditions which are required to observe
some reactivity for propane are close to the domain of
explosion.
In the purpose of reinvestigating the low temperature
oxidation of propane in the light of the recent new kinetic
knowledge gained for light alkanes4,5 and alkenes,6 this study
presents new experimental results for the oxidation of propane
in a jet-stirred reactor, as well as a new model largely based on
quantum calculations. To widen the range of analyzed species,
two different analytical methods have been used: online gas
chromatography (GC) (experiments made in Nancy, France)
and synchrotron vacuum ultraviolet photoionization mass
spectrometry (SVUV-PIMS) with direct sampling through a
molecular jet (experiments made in Hefei, China). The
advantage of the second method is that reactive species, such
as branching agents, are frozen in the molecular jet and can be
detected in the mass spectrometer, whereas this type of species
would have already decomposed before the injection in a gas
chromatograph.7 But a major disadvantage of this technique is
Vogin et al.2 studied the oxidation of propane in a closed
vessel at the temperature of 623 K and at subatmospheric
pressures (initial pressure of 125 Torr) for equimolar mixtures
of propane and oxygen (ϕ = 5). They recorded the evolution of
the partial pressures of reaction products as a function of
reaction time. They observed the formation of numerous
reaction products: hydrocarbons such as methane, ethylene,
propene, and oxygenated species such as carbon oxides,
formaldehyde, methanol, acetaldehyde, methyloxirane, oxetane,
acetone, propanal, and hydrogen peroxide. The authors
proposed some routes for the formation of the main reaction
products.
More recently, Koert et al.3 studied the oxidation of lean and
diluted propane-oxygen mixtures through the negative temper-
ature coefficient region in a plug flow reactor at pressures
ranging from 2 to 15 atm. They showed that propane was
reactive from 675 K with a strong negative temperature
Received: October 4, 2012
Revised: November 23, 2012
Published: November 26, 2012
© 2012 American Chemical Society
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the difficulty to distinguish between the different isomers (as
the signal is the sum of all species having the same mass) when
their ionization energies are close. Another difficulty is the
quantification of species with unknown cross sections. Both
techniques appear to be fully complementary since the
identification of isomers is relatively easy in gas chromatog-
raphy coupled to mass spectrometry.
chromatographs were used for the quantification of the
different species.
The first gas chromatograph, equipped with a Carbosphere-
packed column, a thermal conductivity detector (TCD), and a
flame ionization detector (FID), was used for the quantification
of O2, CO, CO2, methane, ethylene, acetylene and ethane. The
second one was fitted with a PlotQ capillary column and a FID.
It was used for the quantification of molecules from methane to
reaction products with up to 5 carbon atoms and 1 or 2 oxygen
atoms maximum. Maximum relative errors in mole fractions are
estimated to 10%, and the limit of detection for species is
about 1 ppm for species analyzed using flame ionization
detector and 100 ppm for species analyzed using thermal
conductivity detector.
The identification of reactions products, which were not
calibrated before, was performed by thermodesorption (after a
beforehand sorption of the outlet gas reactor on Tenax TA
adsorbent) coupled with a gas chromatograph equipped with a
PlotQ capillary column and a mass spectrometer. The mass
spectra of all detected reaction products were available in the
NIST 08 mass spectral library making the identification work
relatively simple.
Analytic Method (Hefei). Species from the reactor were
analyzed by a reflectron time-of-flight mass spectrometer with
photoionization by synchrotron radiation. The reactor was
coupled to the low pressure photoionization chamber through a
lateral fused silica cone-like nozzle which was inserted in the
spherical part. The tip of the cone was pierced by a 50 μm
orifice. A nickel skimmer with a 1.25 mm diameter aperture was
located 15 mm downstream from the sampling nozzle. The
sampled gases formed a molecular beam, which was passed
horizontally through the 10 mm gap between the repeller and
extractor plates of the RTOF MS. The molecular beam was
intersected perpendicularly with synchrotron vacuum ultra-
violet light beam. The ion signal was then detected with a
RTOF MS, which was installed in the photoionization chamber
vertically. Additional details about this experimental apparatus
are available in previous work.7
The experiments performed in France (gas chromatographic
analyses) have been repeated in China (SVUV-PIMS) under
exactly the same conditions. Some species were detected in
both studies and mole fractions of some of them were
compared to check the consistency between both sets of
experiments. Mole fractions of some reaction products which
were not detected using gas chromatography (water, hydrogen
peroxide and formaldehyde) have been only calculated using
the experimental data obtained using SVUV-PIMS.
EXPERIMENTAL METHOD
■
The oxidation of propane was performed in a jet-stirred reactor
which can be modeled as a perfectly stirred reactor.8 This type
of reactor has often been used for gas phase kinetic studies
(e.g., refs 9−11). Experiments were performed at a constant
pressure of 1.06 bar, at a residence time of 6 s, at temperatures
ranging from 550 to 730 K, under stoichiometric conditions
and the fuel was diluted in an inert gas. Note that due to the
low reactivity of this hydrocarbon under these conditions, a
particularly large mole fraction of propane (0.12) had to be
used. The inert gas was helium in Nancy and argon in Hefei.
The use of argon was required in Hefei because its signal at an
ionization energy of 16.6 eV is used for the normalization of the
signals of other peaks. Gases used in Nancy were provided by
Messer with purities of 99.999, 99.995 and 99.95% for helium,
oxygen and propane, respectively. In China, gases were
provided by Nanjing Special Gas Factory Co., Ltd. Purities
were 99.99, 99.999 and 99+% for argon, oxygen and propane,
respectively.
The reactor, made of fused silica, consists of a quartz sphere
(volume =95 cm3) into which the diluted reactant enters
through an injection cross located at its center. The reactor was
operated at constant temperature and pressure and it was
preceded by an annular preheating zone in which the
temperature of the gases was increased up to the reaction
temperature before entering inside the reactor. Gas mixture
residence time inside the annular preheating was very short
compared to the residence time inside the reactor (a few
percent). In Nancy, both the spherical reactor and the annular
preheating zone were heated by Thermocoax heating
resistances rolled up around their walls. In Hefei, because of
the lateral cone connecting the reactor to the mass
spectrometer, it was difficult to use heating resistances for the
heating of the spherical part.7 A special oven with the shape of
the reactor (sphere and cone) was designed and used for the
heating. The accuracy of the temperature with the two types of
heating device is 5 K. Gas flow rates for the feed of the reactor
were controlled by mass flow controllers provided by
Bronkhorst for the experiments in Nancy and by mass flow
controllers provided by MKS and Bronkhorst in Hefei. The
error in the flow measurements is around 1% for each
controller. This results in a maximum error of about 2% in the
residence time.
Analytic Method (Nancy). The outlet species were
analyzed online by gas chromatography. The online analysis
of products which are liquid under standard conditions was
enabled by a heated transfer line connecting the reactor outlet
and the chromatograph sampling gate which was also heated.
The temperature of the transfer line can be set at our
convenience between ambient temperature and 473 K
maximum. During the propane study, the temperature of the
transfer line was set at 423 K and sufficiently low to avoid
thermal reaction in the line. This temperature is high enough to
keep all the reaction products in the gas phase. Two gas
EXPERIMENTAL RESULTS
Hereafter are presented both sets of experimental data obtained
in Nancy and in Hefei, respectively.
■
Analyses Using Gas Chromatography (Nancy). The
mole fraction profiles of propane and oxygen are displayed in
Figure 1. Under the conditions of this study, propane is not
very reactive: the reaction starts lately around 613 K and the
conversion only reaches 20% in the temperature range 625−
650 K. The reactivity becomes very low in the negative
temperature coefficient zone (650−700 K) and slightly rises
again around 725 K. No investigation was performed at higher
temperature to avoid explosion due to the very high
concentration of fuel. As shown in Table 1, 21 one reaction
products (plus the two reactants) were detected and quantified
in this study. Their mole fraction profiles are displayed in
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energies and to obtained mole fraction profiles. A few species
could not be quantified because of a lack of data of
photoionization cross sections.
Identification of the Species. Figure 3 displays a mass
spectrum obtained at 635 K (corresponding to the temperature
range where the reactivity is highest) and at a photon energy of
11.00 eV. Under these conditions, the main peaks are obtained
for m/z 30, 42, and 44. The identification of the species that
correspond to the detected m/z was obtained using photo-
ionization efficiency spectrum shown in Figure 4 (the scan in
energy was made from 9.43 to 11.70 eV). The larger signals
correspond to the following masses:
• m/z 30: the peak likely corresponds to formaldehyde
(ionization energy (IE) of 10.88 eV12).
• m/z 42: the peak is likely for propene (IE of 9.73 eV12).
• m/z 44: the peak corresponds to acetaldehyde (IE of
10.23 eV12) and oxirane (IE of 10.56 eV12). At photon
energies larger than 11.00 eV, the peak at m/z 44 is also
for propane (the reactant) which has an IE of 10.94 eV
according to the literature.12
Smaller peaks were detected for m/z 28, 32, 58, 60, 74, and
76:
• m/z 28: the peak corresponds to ethylene (IE of 10.51
eV12) and to carbon monoxide which has the same mass,
but an IE of 14.01 eV.12 The large increase in the signal
+
around 11.50 eV likely corresponds to the C2H4
fragment from propane. The large contribution of this
fragment masked the contribution of carbon monoxide
(at photoionization greater than 14.01 eV) making a
precise quantification of this species impossible here.
• m/z 32: this corresponds to methanol (IE of 10.84 eV12).
This m/z also corresponds to oxygen molecule but the IE
is much higher (IE of 12.07 eV12).
• m/z 58: this peak is for several isomers with the formula
C3H6O: acetone, propanal, oxetane, methyloxirane, and
2-propen-1-ol. All these species are present in similar
amounts and have a very close IE (9.70, 9.96, 9.65, 10.22,
and 9.67, respectively12). The scan for m/z 58 (Figure 4)
shows that the signal starts increasing at about 9.70 eV,
which is consistent with the IE of oxetane, acetone, and
2-propen-1-ol.
Figure 1. Mole fraction profiles of propane, oxygen, reaction products
having up to two carbon atoms, and propene (stoichiometric mixture;
residence time = 6 s).
Figures 1 and 2. These reaction products are hydrocarbons, and
oxygenated species having one, two or three carbon atoms.
Species with one or two carbon atoms are carbon monoxide,
methane, ethylene, oxirane, acetaldehyde, methanol, and acetic
acid. Note that a large peak of formic acid is shown by GC-MS
but cannot be quantified by FID. C3 species are: propene,
methyloxirane, oxetane, propanal, acetone, acrolein, n-propanol,
2-propanol, 2-propen-1-ol, and 1-hydroxy-2-propanone. All
these species are observed above 613 K, i.e., from the
temperature at which the reaction starts. Note that 1-
hydroxy-2-propanone has a very different mass spectrum
compared to the other compounds of the same mass which
could have been envisaged according to the kinetic model (see
later in the text), e.g. 3-hydroxypropanal and saturated C3
hydroxyl cyclic ethers.
Some differences are visible in the mole fraction profiles of
these species. For some of them (e.g., methanol or acetone),
the mole fraction increases sharply at 625 K and then decreases
in a monotonous way up to 675 K. For some others, the mole
fraction increases more smoothly before passing through a
maximum and then decreasing (e.g., carbon monoxide or
methane).
• m/z 60: this likely corresponds to acetic acid, n-propanol
and 2-propanol (IE of 10.65, 10.22 and 10.17,
respectively12).
• m/z 74: there are several possible C3H6O2 isomers.
According to the photoionization efficiency spectra for
m/z 74 (Figure 4), the signal starts increasing from 10.00
eV. This value is not in agreement with the ionization
energies of propanoic acid (10.44 eV12), allylhydroper-
oxide (9.52 eV) and 2,3-methyl,hydroxyl-oxirane (8.79
eV). Note that ionization energies of allylhydroperoxide
and 2,3-methyl,hydroxyl-oxirane were not available in the
literature and were calculated theoretically. Table 2
presents zero-point energy corrected adiabatic ionization
energies (AIE) calculated from the composite CBS-QB3
method13 using Gaussian09.14 For each species, geom-
etry optimization, at the B3LYP/cbsb7 level of theory
was performed for the molecule and the corresponding
cation. From these optimized geometries, an energy
calculation, at the CBS-QB3 level, was done at 0 K, both
for molecule and cation. Zero point energy (ZPE) was
added to the previous energies and the AIE was obtained
Analyses Using SVUV-PIMS (Hefei). The experiments
performed in Nancy were repeated in Hefei under the same
conditions. The data obtained using SVUV-PIMS have been
used to identify the reaction products from their ionization
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a
Table 1. List of Species Detected Using Gas Chromatography and SVUV-PIMS
Molecular
formula
ionization energy
(eV)
quantification using gas
quantification using SVUV-
maximum mole
c
name
m/z
chromatography
PIMS
fraction
methane
water
CH4
16
18
28
12.61
12.62
10.51
14.01
10.88
10.84
12.07
10.58
9.73
×
4.14 × 10−5
4.38 × 10−2
1.27 × 10−3
1.36 × 10−2
3.08 × 10−2
4.61 × 10−3
−
H2O
×
×
ethylene
C2H4
×
×
carbon monoxide
formaldehyde
methanol
CO
CH2O
CH4O
O2
30
32
×
×
oxygen (reactant)
hydrogen peroxide
propene
×
×
×
d
H2O2
34
42
44
2.55 × 10−2
C3H6
×
×
×
×
×
×
×
×
×
×
×
×
×
×
7.37 × 10−3
3.47 × 10−3
3.76 × 10−4
−
acetaldehyde
oxirane
C2H4O
C2H4O
C3H8
10.23
10.56
10.94
10.11
9.65
propane (reactant)
acrolein
×
C3H4O
C3H6O
C3H6O
C3H6O
C3H6O
C3H6O
C3H8O
C3H8O
C2H4O2
C3H6O2
C3H8O2
56
58
3.96 × 10−5
1.18 × 10−4
7.83 × 10−5
2.03 × 10−4
3.79 × 10−5
5.61 × 10−4
6.96 × 10−5
4.15 × 10−5
1.35 × 10−4
1.08 × 10−4
e
oxetane
2-propen-1-ol
acetone
9.67
9.70
propanal
9.96
methyloxirane
2-propanol
10.22
10.17
10.22
10.65
10.00
60
n-propanol
acetic acid
×
1-hydroxy-2-propanone
74
76
b
propyl hydroperoxide
isomers
9.42−9.50
×
a
b
c
Ionization energies come from the NIST WebBook.12. Ionization energies calculated in this study (see Table 2). When the species was quantified
d
using both methods, the maximum mole fraction is the one obtained using gas chromatography. The cross section of this species was unknown. A
value of 10 Mb was used for the quantification. Propyl hydroperoxide isomers could not be quantified due to the lack of data concerning their cross
e
sections.
from the difference between these two quantities. The
precision of the ionization energies calculated with this
method is 0.09 eV. Contrary to the ionization threshold
of the isomers cited above, the experimental ionization
energy of m/z 74 seems to be in good agreement with
that of 1-hydroxy-2-propanone (10.0 0.1 eV15), which
was also detected in the gas chromatography analyses.
• m/z 76: this peak likely corresponds to hydroperoxide
species with the formula C3H8O2 (Table 2). There are
no data about their IE in the literature and calculations
were performed using the same method as for the two
C3H6O2 isomers. The calculated IEs are 9.42 and 9.50 eV
for isopropyl-hydroperoxide and propyl-hydroperoxide,
respectively. No conclusion can be given about
isopropyl-hydroperoxide since the calculated IE is
below the energy at which our scan has been started.
However there is a very good agreement between the
calculated and the experimental value (9.49 eV, see
Figure 4) for propyl-hydroperoxide. We will nevertheless
consider the peak at m/z 76 as due to the sum of both
isomers.
total flow rate and the reaction temperature effect on the
sampling). For propane and oxygen (Figure 1), the inlet mole
fractions were known and the calibration was performed
assuming no reaction at 575 K. Then the mole fractions of the
reaction products were calculated using the following equation:
σ (E)
D
ref
Si(T)
ref
xi(T) = xref(T) ×
×
×
Sref (T)
σ(E)
D
i
i
(1)
xi(T) and Si(T) are the mole fraction and the signal of a species
i at the temperature T, respectively. σi(E) is the photoionization
cross-section of the species i at the photon energy E. Di is the
mass discrimination factor of species i.
The mole fraction of propene was calculated from the
propane data at 13.00 eV in order to compare with the mole
fractions obtained using gas chromatography. Cross sections of
propane and propene at 13.00 eV were estimated as 15.11 Mb16
and 25.21 Mb,17 respectively. Figure 1 displays both sets of
propene mole fractions, showing a very good agreement
between both experimental sets.
Mole fractions of water, hydrogen peroxide, and form-
aldehyde (not quantified in Nancy) were calculated using the
same procedure using the signals at 13.00 eV. The cross
sections used for the quantification of water and formaldehyde
are from Katayama et al.,18 and Cooper et al.,19 respectively. As
far as hydrogen peroxide is concerned, there is no cross section
data available. However as in our previous work on n-butane,7
an arbitrary value of 10.00 Mb was used for the calculation. The
mole fraction profiles of these species are displayed in Figure 5.
Acetic acid was quantified using the signal of ethylene as a
reference. Signals obtained at 11 eV were used for the
Note that, contrary to our previous work for larger alkanes
(n-butane,7 n-heptane11), it has not been possible to detect
ketohydroperoxides (m/z 90).
Quantification of the Species. The quantification of
reaction products was performed for the reactants (propane
and oxygen), propene, acetic acid, water, hydrogen peroxide,
and formaldehyde (the last three species were not detected by
GC). For the quantification of all these species, we used the
normalized signal (i.e., the signal which was normalized by the
one of argon at 16.60 eV to take into account the change in
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Figure 4. Photoionization efficiency spectra of mass 30, 42, 44, 58, 60,
74, and 76 for a reaction temperature of 630 K. Signals are in arbitrary
units. For masses 30 to 60, the numbers given in graphs are ionization
energies (in eV) taken from the NIST Webbook12 for the species of
Table 1; for masses 74 and 76, calculated values (see text) are
displayed.
Figure 2. Mole fraction profiles of oxygenated C3 oxidation products
(stoichiometric mixture; residence time = 6 s).
the oxidation of propane. The generic reactions used in EXGAS
are derived from the current understanding of the low-
temperature oxidation of alkanes25−27 and alkenes1,26. How-
ever, in the case of several classes of reaction the
thermochemical and kinetic parameters have been revised
using calculations based on quantum methods (see method
description hereafter). As propene is the most important C3
product of the oxidation of propane, the mechanism has been
generated considering as the initial reactants both propane and
propene. In the next paragraphs, after a reminder on the
specificities of the low temperature oxidation chemistry of
alkanes and alkenes, we will describe, first the mechanism
proposed for propane, then that of propene, and finally the
thermochemical data and reactions of C0−C2 species.
Theoretical Calculations. This part describes the method
used to perform the theoretical calculations the results of which
are presented further in the text. The calculations of
thermochemical data for molecules, radicals, and transition
states were performed at the CBS-QB3 level of theory13
implemented in Gaussian 09 Rev. B.01.14 For each species
considered, the conformer with the lowest energy has been
identified, by performing relaxed scans, in particular for radicals
which involve hydrogen bonding. Intrinsic reaction coordinates
(IRC) calculations have been done at the B3LYP/cbsb7 level of
theory to ensure that the transition states correctly connect the
Figure 3. Mass spectrum obtained at a photoionization energy of 11
eV and at a temperature of 635 K.
quantification. Cross sections of acetic acid and ethylene at
11.00 eV were 7.56 Mb11 and 7.48 Mb,20 respectively. The
mole fraction profile of acetic acid is displayed in Figure 1. Note
that there is a good agreement between measurements made by
GC with FID and by SVUV-PIMS. Figure 5 also displays the
signal obtained for an energy of 11.00 eV at m/z 76, i.e. for C3
propyl hydroperoxides. In this case, due to absence of
photoionization cross sections, the quantification was not
possible.
MODEL DEVELOPMENT FOR THE OXIDATION OF
PROPANE
As in our previous work about the oxidation of n-butane,5 a
model generated using the EXGAS software which has already
been extensively described in the case of alkanes (e.g., refs 21
and 22), and alkenes23,24 has been used as a basis for a model of
■
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Table 2. Ionization Energies of Two C3H6O2 Isomers (m/z 74) and of C3H8O2 Hydroperoxides (m/z 76) Calculated at the
CBS-QB3 Level of Theory (Uncertainty of Calculated Ionization Energies Is 0.09 eV)
were obtained by fitting the rate constant values obtained from
TST at several temperatures between 500 and 1200 K, using
the modified-Arrhenius expression:
⎛
⎞
⎟
E
RT
n
⎜
k∞ = AT exp −
⎝
⎠
Low Temperature Oxidation of Alkanes and Alkenes.
Except from resonance stabilized allylic (e.g., allyl, C3H5)
radicals, which are obtained from alkenes by H-abstraction and
have a low reactivity with a predominance of termination
reactions,1 the most important type of radicals involved in the
oxidation of alkanes and alkenes are alkylic radicals. At low
temperature, i.e. below 900 K, alkylic radicals (R•) are
produced by H-abstraction from alkanes mostly by •OH
radical, or by addition of •OH radical to the double bond of an
alkene. Figure 6 shows a simplified scheme of the reactions with
Figure 5. Mole fraction profiles of propane oxidation products that
were quantified only using SVUV photoionization mass spectrometry
and signal at m/z = 76 obtained at 11 eV (stoichiometric mixture;
residence time = 6 s).
reactants and the products. Enthalpies of formation at 298 K
have been obtained from isodesmic reactions. For vibrational
partition function, Qvib, the harmonic oscillator approximation
has been assumed, except for low frequency vibrations which
correspond to internal rotations. In these latter cases, a
hindered rotor treatment was used. The rotational barriers have
been estimated by relaxed scans at the B3LYP/cbsb7 level of
theory and have been used to correct Qvib from Pitzer and
Gwinn tabulations.28 For transition states, we have used the
same procedure, but by freezing the atoms involved in the
reaction coordinate (i.e., the cyclic part of the transition states
for isomerizations), and by taking into account the remaining
torsions. Reduced moments of inertia for internal rotations as
well as thermochemical properties as a function of temperature
have been calculated using the ChemRate software29 according
to statistical mechanical principles.
Figure 6. Simplified scheme of the reactions with oxygen which are
now usually included in models in the case of alkylic radicals (R•). R•
can be either an alkyl radical or an hydroxyalkyl radical.
High pressure limit rate constants were calculated with the
software ChemRate,29 using canonical transition state theory
(TST):
oxygen which are now usually included in models in the case of
alkylic radicals (R•).26 Alkyl radicals add thereafter to O2 and
yield peroxy radicals ROO•. Some consecutive steps then lead
to the formation of hydroperoxides, which are degenerate
branching agents explaining the high reactivity of alkanes at low
temperatures. Alkylhydroperoxides can be directly obtained by
≠
⎛
exp⎜−
⎝
⎞
⎟
⎠
kbT
h
ΔG (T)
k∞ = rpdκ(T)
RT
where ΔG≠ is the Gibbs energy of activation, rpd the reaction
path degeneracy, and κ(T) the transmission coefficient.
Tunneling effects were taken into account for internal hydrogen
atom transfers. Transmission coefficients were calculated
following the Eckart-1D method.30 The kinetic parameters
•
reaction of ROO• radicals with a HO2 radical. In another
pathway, ROO• radicals first isomerize to give hydroperoxyalkyl
radicals (•QOOH). This first isomerization, which occurs via an
intramolecular H-abstraction through a cyclic transition state,
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has a very large influence on the low-temperature oxidation
chemistry. According to the size of the cyclic ring involved in
the transition state, the formation of the conjugated alkene or
alkenol can compete with the isomerization, mainly, at low
initiations, as well as H-abstractions producing propyl radicals
with kinetic data proposed by Buda et al.22 This mechanism
also includes the reactions of propyl radicals with oxygen, which
are of particular importance at low temperature, as well as the
subsequent reactions of propylperoxy radicals. The current
understanding of these reactions for small alkyl radicals, such as
ethyl or propyl radicals, is in agreement with the fact that the R•
+ O2 reaction proceeds through a barrierless addition pathway
to form the chemically activated ROO* adduct, which can
either be stabilized or react via a concerted elimination of •HO2
to give the conjugated alkene.32 Combining theoretical
calculations with an experimental investigation of the time-
resolved formation of OH, DeSain et al. reported kinetic
parameters for the different possible channels at different
pressures in the case of propyl radicals. We have then used the
values proposed under 1 atm for all the reactions of oxygen
with propyl radicals. In the case of the addition to oxygen of
hydroperoxypropyl radicals, the kinetic parameters have been
derived from the values proposed by DeSain et al.4 for propyl
radicals just considering whether the radical was primary or
secondary.
•
temperature, by a direct elimination of HO2 •from ROO•. For
hydroxyalkyl radicals, the isomerizations of QOOH radicals
can also occur through the Waddington mechanism shown in
Figure 731 and lead to the formation of aldehydes (form-
4
•
Figure 7. Isomerization of 1-hydroxy-2-propylperoxy radicals accord-
ing to the mechanism of Waddington.28
aldehyde and acetaldehyde in the case of radicals deriving from
propene) and •OH radicals. This type of reaction does not lead
to the formation of branching agents and is then one of the
causes of the lower reactivity of alkenes compared to alkanes.
•QOOH radicals can thereafter add on O2 and yield
•OOQOOH radicals that react by a second internal isomer-
ization producing •U(OOH)2 radicals. The rapid unimolecular
decomposition of •U(OOH)2 radicals leads to one radical and
a degenerate branching agent (ketohydroperoxide), which is
the source of the chain branching occurring at low temper-
atures:
The rate constants for the isomerizations of propylperoxy
radicals involving a cyclic transition state including five or six
atoms, as well as the formation of cyclic ethers (methyloxirane
and oxetane) have been estimated as described by Cord et al.5
and deduced from CBS-QB3 quantum chemical calculations for
n-butane oxidation.13
•
•U(OOH)2 ⇄ R(O)(OOH) + OH
Since the number of possible isomerizations of C3 peroxy
radicals is more limited than for larger radicals, we have
considered not only the isomerizations involving a transition
state including five or six atoms, but also those with a four-
membered transition state, with the kinetic data proposed by
Buda et al.22 These isomerizations are usually neglected in the
mechanism proposed for the oxidation of larger alkanes. The
product of this isomerization is a α-hydroperoxyalkyl radical
which has been shown to be unstable or metastable.33 A global
step involving the isomerization and the decomposition of the
•
R(O)(OOH) ⇄ R(O)O• + OH
(secondary reaction)
In this scheme, a •OH radical reacting by H-abstraction with
the initial alkane leads to the formation of three free radicals,
two •OH and a R(O)O• radical. This autoaccelerating
process strongly promotes the oxidation of alkanes below 700
K. If the Waddington mechanism is not the main fate of the
involved hydroxy radicals, a •OH radical adding to the double
bond of an alkene can be the cause of a radical multiplication
and of an accelerating effect.
•
obtained QOOH radical by the β-scission of the O−O bond
•
has then been written yielding OH radical and acetone or
propanal. The correlations performed by Cord et al.5 have also
been used to estimate the rates constant of the globalized
reactions of isomerization/decomposition from hydroperox-
ypropylperoxy radicals yielding ketohydroperoxides.
When the temperature increases, the equilibrium R• + O2 ⇆
ROO• begins to be displaced back to the reactants and the
formation of ROO• radicals is less favored compared to the
•
strongly inhibiting oxidation reaction R• + O2 ⇆ HO2 +
The mechanism generated by EXGAS for propane also
includes all the possible β-scission reactions of all the radicals
obtained by oxygen additions and isomerization with kinetic
data proposed by Buda et al.22 However, the rate constant of
the beta-scission of the 1-hydroperoxy-3-propyl radical,
produced by the isomerizations of a C3-alkylperoxy radical
involving a six-membered ring transition state has been
calculated using the quantum mechanics method. This reaction
leads to the formation of ethylene, formaldehyde and a
hydroxyl radical. The calculated rate constant is k = 6.8 × 1011
T0.551 exp(−28100/RT) (in s−1 with R the gas constant in
cal·mol−1·K−1). At 700 K, this value is 1.9 faster than the
EXGAS rate constant.
All the above-described reactions (primary mechanism)
produce stable molecules (primary products) for which
consumption reactions need also to be written. The generation
of these consumption reactions (secondary mechanism) is also
automatically performed by EXGAS, but in the more globalized
way than what is considered the primary mechanism, involving
lumped species and globalized reactions.34 In order to better
conjugated alkene or alkenol. This reaction is equivalent to a
termination step since •HO2 radicals react mostly by
disproportionation (2•HO2 ⇆ H2O2 + O2). Unimolecular
decompositions of •QOOH radicals compete with O2 addition:
•QOOH radicals can decompose into cyclic ethers or ketones
•
•
and OH radicals, or by β-scission into HO2 radicals and
conjugated unsaturated molecules or smaller species. Because
of the decrease in the production of hydroperoxides, the
reactivity decreases in the 700 to 800 K temperature range.
This temperature region is consequently called the negative
temperature coefficient (NTC) zone. At higher temperatures,
the decomposition of H2O2 (H2O2 (+M) ⇆ 2•OH (+M)) is a
new source of the chain branching leading to an increase of the
reactivity. This reaction becomes very fast above 900 K. NTC
behaviors are usually less pronounced in the cases of alkenes
than for alkanes but can nevertheless still be observed.23,24
Primary and Secondary Mechanism of the Oxidation
of Propane. The mechanism generated by EXGAS for the
oxidation of propane contains unimolecular and bimolecular
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Figure 8. Detailed pathways considered for the decomposition of the propylhydroperoxides obtained from 1-propyl and 2-propyl radicals,
respectively.
Figure 9. Pathways for the decomposition of aldo-hydroperoxide.
represent the way of formation of some products, especially
minor ones, we have revisited the reactions of C3 hydro-
peroxides. These latter compounds are an important family of
primary products of the oxidation of propane. The C3
hydroperoxides produced during the oxidation of propane
can be of two main types: propylhydroperoxides and C3
hydroperoxides including a carbonyl group (ketohydroper-
oxides). Propylhydroperoxides are obtained from propylperoxy
radicals by reaction with •HO2 radical. Ketohydroperoxides
including a carbonyl group are obtained from peroxypropyl
radicals by isomerization followed by a second addition to
oxygen.
The decomposition of hydroperoxides occurs through the
breaking of the O−O bond to form an alkoxy group and a
hydroxyl radical. The rate constant is that proposed by
Sahetchian et al.35 Figures 8 and 9 present the different
pathways which have been considered for the consumption of
propylhydroperoxides and C3 aldo-hydroperoxide, respectively.
The latter species is the most important C3 hydroperoxide
including a carbonyl group since it is the only one formed
through an isomerization involving six-membered ring
transition states in the sequence of reactions producing
degenerate branching agents.
Five types of reaction are considered for the obtained
saturated alkoxy or aldo-alkoxy radicals:
• The H-abstractions from propane to form alcohols with
the same rate constants as that of the reactions of
metathesis of propane by •OH radical, these values being
much higher than the values for the reactions of
metathesis of propane by CH3O• radical.
• The disproportionation with •HO2 to also produce
alcohols using the rate constant for a disproportionation
22
•
between alkylperoxy and HO2 radicals.
• The reactions with oxygen molecules to form a carbonyl
function using the rate constant proposed by Atkinson et
al.36 for the primary alkoxy function and by Atkinson37
for the secondary alkoxy function.
• The reactions of beta-scissions by breaking of a C−C
bond yielding formaldehyde and CH2CHO radicals or of
a C−H bond giving propanedial.
• An isomerization, in the case of the aldo-alkoxy radicals.
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Table 3. Kinetic Parameters Calculated for the Reactions of β-Scissions and Isomerizations Involved in the Decomposition of
Alkoxy and Aldo-Alkoxy Species and Comparison with kRauk, the Values Proposed by Rauk et al.38
⎛
⎞
⎟
E
RT
n
⎜
k∞ = AT exp −
⎝
⎠
reaction for which the calculation has been performed type of reaction log (A × s)
n
E (kcal·mol−1
)
k (s−1) at 700 K kRauk (s−1) at 700 K
•
CH3CH2CH2(O•) ⇆ CH3CH2CHO + H
β-scission
β-scission
β-scission
β-scission
β-scission
β-scission
isomerization
10.8
13.9
11.4
13.7
11.3
12.3
10.7
1.04
0.079
0.77
0.24
0.97
0.43
0.31
19.8
14.1
17.9
14.3
22.1
12.2
9.2
3.8 × 107
5.3 × 109
1.0 × 108
8.3 × 109
1.4 × 107
5.2 × 109
5.1 × 108
6.7 × 106
2.7 × 109
3.0 × 107
3.0 × 109
CH3CH2CH2(O•) ⇆ CH3CH2(•) + HCHO
CH3CH(O•)CH3 ⇆ CH3COCH3 + H
•
CH3CH(O•)CH3 ⇆ CH3CHO + CH3
•
CH2(O•)CH2CHO ⇆ CHOCH2CHO + H
CH2(O•)CH2CHO ⇆ HCHO + CH2(•)CHO
CH2(O•)CH2CHO ⇆ CH2(OH)CH2C(•)O
•
Table 4. Kinetic Parameters Calculated for the Isomerizations of Hydroxyalkylperoxy Radicals, the Waddington Reactions, and
the Formation of Cyclic Ethers Involved in the Mechanism of Propene and Comparison with the Data Used by EXGAS21
⎛
⎞
⎟
E
RT
n
⎜
k∞ = AT exp −
⎝
⎠
log (A ×
E
k (s−1) at
k/kEXGAS at
reaction for which the calculation has been performed
type of reaction
isomerization
s)
n
(kcal·mol−1
)
700 K
700 K
CH2(OH)CH(OO•)CH3 ⇆ CH2(OH)CH(OOH)CH2
−2.81
1.72
2.98
4.38
9.47
9.18
10.6
4.53
2.99
2.52
2.17
0.45
0.54
0.46
26.4
22.2
20.2
20.2
21.5
24.5
11.0
6.8 × 101
2.0 × 103
7.0 × 103
1.8 × 104
1.4 × 104
1.2 × 103
3.0 × 108
2.2
2.9
•
CH2(OH)CH(OO•)CH3 ⇆ CH(•)(OH)CH(OOH)CH3
CH3CH(OH)CH2(OO•) ⇆ CH3C(•)(OH)CH2(OOH)
CH3CH(OH)CH2(OO•) ⇆ CH2(•)CH(OH)CH2(OOH)
isomerization
isomerization
2.3
isomerization
23
•
CH2(OH)CH(OO•)CH3 ⇆ OH + CH3CHO + HCHO
Waddington’s reaction
Waddington’s reaction
15.2
1.8
•
CH3CH(OH)CH2(OO•) ⇆ OH + CH3CHO + HCHO
•
CH2(OH)CH(OOH)CH2 ⇆ 1 hydroxymethyloxirane +
formation of cyclic
ether
201
•OH
CH(•)(OH)CH(OOH)CH3 ⇆ 1 hydroxy-2-methyloxirane + formation of cyclic
12.4
13.2
12.4
0.067
−0.096
−0.19
11.2
10.5
20.7
1.2 × 109
4.5 × 109
2.5 × 105
801
3144
0.37
•OH
ether
CH3C(•)(OH)CH2(OOH) ⇆ 1 hydroxy-1-methyloxirane +
formation of cyclic
ether
•OH
•
CH2(•)CH(OH)CH2(OOH) ⇆ 1 hydroxy-oxetane + OH
formation of cyclic
ether
The rate constants of the two last types of reactions have
been calculated using the theoretical method previously
described. Table 3 presents the kinetic parameters of these
reactions, as well as a comparison with the rate constants
calculated at the CBS-RAD and B3LYP/6-31G(d) level of
theory by Rauk et al.38 for the same reactions. Our rate
constants are larger than those of Rauk et al.38 by factors from
1.9 to 2.8 for C−C bond breaking, and by factors from 3.3 to
5.6 for C−H bond breaking.
have been used. Note also that all the possible β-scission
reactions of all the radicals which are produced are systemati-
cally considered by EXGAS with rate constants proposed by
Heyberger et al.23 The combinations and disproportionations
of allyl radicals, especially the reaction with •HO2 radicals
yielding allylhydroperoxide were also taken into account.23
The kinetic data of the reactions of hydroxypropyl and
hydroxyhydroperoxypropyl radicals with oxygen, as well as
those for the second addition to oxygen, were derived from the
values proposed for propyl radicals at 1 atm by DeSain et al.4 In
The carbonyl radical deriving from the isomerization of the
aldo-alkoxy radicals has been considered to react either by an α-
scission producing CO and C2H4OH radicals, or by an addition
to oxygen. The latter pathway is followed by a six-membered
ring isomerization and a β-scission producing ethenol, carbon
dioxide and a hydroxyl radical. The same type of reaction has
been considered for the aldocarbonyl radicals obtained by H-
abstraction from propanedial, which is produced by dispro-
portionation from aldo-alkoxy radicals. The rate constants of
the reactions of carbonyl radicals have been evaluated based on
the reactivity of CH3CO• radicals obtained from acetaldehyde.
Primary and Secondary Mechanism of the Oxidation
of Propene. The mechanism generated by EXGAS for the
oxidation of propene contains unimolecular and bimolecular
initiations, as well as H-abstractions to produce allyl radicals
with kinetic data proposed by Heyberger et al.23 It also contains
the addition of small radicals on the double bond with kinetic
•
the case of the formation of propenol and HO2 radicals from
oxidation reactions, we have calculated the contributions of the
different types of abstracted H atoms. While the case is found
for instance in 2-hydroxy-1-propyl radicals, DeSain et al.4 do
not study the case of tertiary radicals for the addition of oxygen
•
and of tertiary hydrogen for the eliminations of HO2, so we
used the values for secondary radical and secondary hydrogen,
respectively.
The rate constants for the isomerizations of hydroxypro-
pylperoxy radicals involving a transition state including 5 or 6
atoms, as well as the subsequent formation of hydroxy cyclic
ethers have been calculated using the theoretical method
previously described. Calculations were performed for the 10
reactions presented in Table 4, which are representative of the
main reactions which can occur starting from the two
hydroxypropylperoxy radicals that can be obtained by additions
•
data also from Heyberger et al., except in the case of OH
or et al.25
of OH radicals to propene followed by addition to oxygen.
•
radical for which the values recently proposed by Zad
́
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Among these reactions, there are isomerizations involving the
internal transfer of an alkylic H atom and the formation of
cyclic ethers, but also the reactions following the mechanism of
Waddington.28 Table 4 shows a comparison between the
calculated rate constants for the studied hydroxyl radicals and
those obtained from the structure-reactivity relationships used
by EXGAS.23 This comparison leads to the same trends as
those observed by Cord et al.5 for the reactions of radicals
deriving from alkyl radicals: i.e., there are large deviations
between EXGAS and calculated values for the isomerizations
involving a six-membered transition state cycle and for the
formation of oxiranes. Note also that as in ref 5, the spin
contamination is important for all the transition states involved
in the formation of cyclic ethers. For reactions following the
mechanism of Waddington, EXGAS correlations consider the
same rate constant for the two reactions in Table 4, whereas
calculated rate constants are very different (almost 1 order of
magnitude), one being in good agreement with the EXGAS
data. The reason for this difference is unknown, since the
chemical processes seem to be similar in the two reactions. Sun
et al.39 have also used the CBS-QB3 method to calculate the
rate constants of reactions following the mechanism of
Waddington in the case of iso-butene considering the
stabilization of the obtained hydroperoxyalkoxy radicals. Figure
10 presents a comparison between the rate constants proposed
Figure 11. Comparison between the rate constants calculated for the
different possible channels for the isomerizations of (a) •OOCH-
(CH3)CH2OH and (b) OOCH2CH(OH)CH3 radicals.
•
The rate constant of the β-scission for the 2-hydroxy-1-
hydroperoxy-3-propyl radical produced by the isomerization of
a C3-hydroxyalkylperoxy radical involving a six-membered ring
transition state has also been calculated. This reaction leads to
the formation of acetaldehyde, formaldehyde and a hydroxyl
radical. The calculated rate constant is k = 5.0 × 1010 T0.172
exp(−26300/RT) s−1. At 700 K, this value is 23 slower than the
EXGAS rate constant.
A specific decomposition giving a water molecule and an
alkoxy radical has also been investigated for 2-hydroxy-1-
hydroperoxy-2-propyl radical produced by the isomerizations of
a hydroxypropylperoxy radical involving a five-membered ring
transition state:
Figure 10. Comparison between the high pressure limit rate constants
(k∞) proposed in the present work and those of Sun et al.39 for the 2
reactions involved in the mechanism of Waddington deriving from
propene: reaction 1, CH3C (R)(OH)CH2OO• ⇒ •OH + CH3C(R)O
+ HCHO, with R being H in the present work and CH3 in the work of
Sun et al.39 and reaction 2, CH3C(R)(OO•)CH2OH ⇒ •OH +
CH3C(R)O + HCHO.
CH2(OOH)C•(OH)CH3 ⇄ CH2(O•)C(O)CH3 + H2O
The rate constant of this decomposition involving a six-
membered ring transition state has been calculated as equal to k
= 2.52 × 1013 T−0.54 exp(−14000/RT) s−1 and shown to be 143
times lower at 700 K than the formation of oxirane which can
also occur from 2-hydroxy-1-hydroperoxy-2-propyl radical. This
reaction has then not been considered in the model. However,
note that calculations show that this type of decomposition
could compete with the formation of cyclic ethers, especially
oxetane formation, in the case of larger alkenes.
by Sun et al.39 and those displayed in Table 4. It shows that,
despite similar methods have been used in both cases, the
values of Sun et al.39 are larger than ours by almost an order of
magnitude. However it is interesting to note that a good
agreement is obtained between our calculations and those of
Sun et al.39 for the ratio between the rate constants of the two
channels.
Figure 11 presents a comparison between the rate constants
of the different possible isomerization channels of hydrox-
ypropylperoxy radicals. It shows that, contrary to the work of
Sun et al.39 in which the reactions following the mechanism of
Waddington are always the preponderant ones, in the present
study, it is only the case for the peroxy radicals with the alcohol
function carried by the terminal atom of carbon. In the case of
peroxy radicals with the alcohol function carried by the carbon
atom in the middle, both possible isomerizations are the fastest
channels.
In the secondary mechanism, the reactions of the unsaturated
alkoxy radicals deriving from allylhydroperoxide have been
considered in more details. They can react by H-abstraction
from propane with the same rate constants as that of the
•
reactions of metathesis of propane by OH radicals, or by β-
scission by breaking of a C−C bond to give vinyl radicals and
formaldehyde, or of a C−H bond yielding H atom and acrolein.
The rate constants of these two last reactions were taken from
Rauk et al.38
Thermochemical Data. The major part of the thermo-
chemical data for molecules or radicals considered in the
present model have been calculated by the software
THERGAS,40 based on the group and bond additivity methods
proposed by Benson,41 and stored as 14 polynomial
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Table 5. Enthalpies of Formation (kcal·mol−1), Entropies, and Heat Capacities (cal·mol−1·K−1) for the Allyl Radical and for C3
Hydroxyalkyl, Hydroxyalkylperoxy, Hydroxyhydroperoxyalkyl, and Hydroxyhydroperoxyalkylperoxy Radicals, Calculated at the
a
CBS-QB3 Level of Theory
a
In italics: data calculated using software THERGAS.40
coefficients, according to the CHEMKIN formalism.42
However, at low-temperature, a small energy difference in
thermochemical data can have a significant impact on the global
reactivity as the kinetic parameters of the reverse reaction (for
reversible reaction) are calculated from the ones of the direct
reaction and from the thermodynamic properties of the species
involved in the reaction. It is then important to use accurate
thermochemical data, in particular for the reactions R + O2 =
ROO. Enthalpies of formation, entropies and heat capacities of
the major C3 radicals involved in the oxidation of propane and
propene have been calculated by the quantum chemical methods
described above.
The data related to propyl, propylperoxy, hydroperoxypropyl,
and hydroperoxypropylperoxy radicals were already presented
by Cord et al.5 Table 5 presents the calculated data for the C3
hydroxy radicals of the four types at different temperatures, as
well as a comparison with those obtained by group additivity
methods using the THERGAS software.40 As an example, the
enthalpy of formation obtained for the allyl radical using
THERGAS is deduced from the enthalpy of formation of
propene (which is tabulated43) and from the energy of the C−
H bond which is broken to give the allyl radical (the energy of
which is known44). Table 5 shows that calculated enthalpies of
formation are about 1 kcal·mol−1 lower for hydroxypropylper-
oxy radicals and about 2 kcal·mol−1 higher for hydroxyhy-
droperoxypropyl radicals compared to the values calculated by
THERGAS.40 Calculated entropies are about 3 cal·K−1·mol−1
lower for hydroxyalkylperoxy radicals and about 6
cal·K−1·mol−1 lower for hydroxyhydroperoxyalkyl radicals
compared to the values calculated by THERGAS.40 In
THERGAS,40 calculations do not take into account the effect
of hydrogen bond hindering some rotations in the molecule.
Reactions of C0−C2 species. As in all EXGAS
mechanisms,22 a C0−C2 reaction base as been added to the
final mechanism of the oxidation of propane and propene in
order to well consider the reactions of small species. This C0−
C2 reaction base includes all the reactions involving radicals or
molecules containing less than three carbon atoms. The kinetic
data used in the C0−C2 reaction base were taken from the
literature. The pressure dependent rate constants follow the
formalism proposed by Troe45 and efficiency coefficients have
been included. As in our previous work about the oxidation of
n-butane,5 the kinetic parameters of four reactions in the C0−
C2 reaction base have been up-dated: the rate constant
proposed by Troe has been used for the reaction: H2O2
(+M) ⇆ 2•OH (+M),46 that proposed by You et al.47 for
•
the reaction CO + HO2 ⇆ CO2 + OH•, that proposed by
Vasudevan et al.48 for the reaction OH + HCHO ⇆ H2O +
•
•HCO, and that proposed by DeSain et al.4 for the reaction
•
•HCO + O2 ⇆ CO + HO2. The two following reactions,
C2H5OO• + CH3OO• ⇆ C2H5OH + HCHO + O2 and
C2H5OO• + CH3OO• ⇆ CH3OH + CH3CHO + O2, have
been considered with the same rate constant as that of the
disproportionation for two C2H5OO• radicals.
As acetic acid was not previously found among combustion
intermediates, its reactions were not considered in the C0−C2
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Figure 12. Flow rate analysis of the primary reactions of consumption of propane and propene under the conditions of Figure 1 at 630 K. The sizes
of arrows are proportional to the net global fluxes and dotted arrows are for channels related to less than 3% of the propane consumption.
Compounds in blue have been experimentally observed.
reaction base. In the present work, its formation has been
considered from CH3COOO• radical which is formed by O2
addition to CH3CO• radicals obtained from acetaldehyde by H
atom abstractions. CH3COOO• radical reacts then to give
acetic acid by the following reactions: CH3COOO• + CH3OO•
⇆ CH3C(O)OH + HCHO + O2, and CH3COOO• + •HO2 ⇆
CH3C(O)OH + O2 + •O•. The rate constant of the first
reaction is that proposed by Maricq et al.49 The total rate
of consumption being well simulated. The level of agreement is
overall rather good for most of the reaction products, that is to
say less than a factor 2. The shape and the position of the
maximum of the profile of propylhydroperoxides is also well
reproduced. More significant deviations are obtained in the
cases of hydrogen peroxide, acetic acid, oxetane, acrolein, and
2-propen-1-ol. Note also that the formation of 1-hydroxy-2-
propanone is not considered by the model, since its possible
ways of formations are very uncertain.
constant of the reaction CH3COOO•
+
•HO2 and the
branching ratio between the 2 possible channels giving either
CH3COOOH + O2 (already considered in the C0−C2 reaction
base), or CH3C(O)OH + O2 + •O• were taken from an
The overprediction of the formation of hydrogen peroxide by
a factor of 2.5 is due to the uncertainty on the photoionization
cross-section of this compound, which is not available in
literature and has then been roughly estimated. The over-
prediction of the formation of acetic acid is more difficult to
explain since the same reactions of CH3COOO• radicals have
been used in recent models of the oxidation of n-butane7 and n-
heptane11 leading to a good simulation of this acid under
experimental conditions very close to those of the present
study. The only difference is that the hydrocarbon initial mole
fractions were lower in our previous studies (0.04 for n-butane,
and 0.005 for n-heptane instead of 0.12 here) since larger
alkanes are more reactive fuels. We were not able to identify a
second order reaction which can explain this discrepancy.
Figure 12 presents a flow rate analysis performed under the
conditions of this study at 630 K and shows that propane reacts
experimental determination by Le Cran
̂
e et al.50 The
consumption of acetic acid has been described by pericyclic
reactions, CH3C(O)OH ⇆ CH4 + CO2, CH3C(O)OH ⇆
CH2CO + H2O, and by H-abstraction by •OH radicals,
CH3C(O)OH + •OH ⇆ •CH3 + CO2 + H2O. The rate
constants of the first two reactions are from Duan et al.51 and
the rate constant of the last reaction is from Huang et al.52
DISCUSSION
■
The complete mechanism (1159 reactions) described in this
paper is available as Supporting Information. Simulations have
been performed using the CHEMKIN software package.42
Simulations for a jet-stirred reactor were performed assuming a
homogeneous isothermal reactor and the computed profiles are
shown in Figures 1, 2, and 5. The agreement between modeling
and experimental results is very good for the profiles of the
reactants with the temperature and the extent of the maximum
•
mainly by H-abstractions mostly with OH radicals to give
almost equal amounts of 1-propyl and 2-propyl radicals. Both
radicals mostly react by addition to oxygen to form peroxy
radicals, but about 15% of 2-propyl radical also yield propene
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by reaction with oxygen. The obtained propylperoxy radicals
•
react by elimination of HO2 radical yielding propene (15% of
the consumption of propyl-1-peroxy radical, and about 47% for
propyl-2-peroxy radical), disproportionation with •HO2 radicals
to give alkylhydroperoxides (34% of the consumption of
propyl-1-peroxy radical, and about 20% for propyl-2-peroxy
radical), and isomerizations to give hydroperoxypropyl radicals
(44% of the consumption of propyl-1-peroxy radicals, and
about 2% for propyl-2-peroxy radicals). A minor channel from
propyl-2-peroxy radical also leads to the formation of acetone
and a still smaller one yields propanal from propyl-1-peroxy
radical (not shown in Figure 12).
While only about 2% of propyl-2-peroxy radical yields
hydroperoxypropyl radicals, this channel leads to the major
cyclic ether obtained: methyloxirane, the formation of which is
very well predicted. The hydroperoxypropyl radicals formed
from propyl-1-peroxy radicals react mainly by a second addition
to oxygen and are a source of ketohydroperoxides. Only about
0.1% of these hydroperoxypropyl radicals lead to cyclic ethers,
explaining the small formation of oxetane observed. The very
large underprediction of this species is certainly due to the
uncertainty in the calculated rate constant due to spin
contamination as reported by Cord et al.5
Figure 13. Simulated mole fraction of (a) the major hydroperoxides
considered in the present mechanism and (b) hydroxyl cyclic ethers
and 3-hydroxypropanal.
difficult isomerizations of small size peroxy radicals (the total
isomerization rate constant at 700 K is equal to 5.0 × 104 s−1
for 1-peroxybutyl radical, and to 1.8 × 104 s−1 for 1-
peroxypropyl radical). The fact that the formation of propene
is well predicted supports the correctness of the values used for
the rate constants of the reactions of propyl radicals with O2
which were taken from the work of DeSain et al.4 At 630 K,
under the conditions of Figure 12, the rate of consumption of
propene is about 2/3 that of its production. Three ways of
consumption of propene are important: the addition of H
atoms to the double bond to give propyl radicals, the addition
of •OH radicals yielding hydroxypropyl radicals, and H-
abstractions producing mainly allyl radicals.
Hydroxypropyl radicals react with oxygen similarly to propyl
radicals and are a source of propenol via reactions yielding
•HO2 radicals, and of formaldehyde and acetaldehyde through
the mechanism of Waddington, but also of hydroxyl cyclic
ethers (mainly 2,3-methyl,hydroxyoxirane), which have not
been observed experimentally, while a mole fraction up to
0.0025 (as shown in Figure 13b) is predicted. Note that 2,3-
epoxycyclohexan-1-ol (but not 1,2-epoxycyclohexan-1-ol) has
been observed during the oxidation of cyclohexene and would
Alkoxy radicals obtained by the decomposition of C3
saturated hydroperoxides mostly react by breaking a C−C
bond yielding formaldehyde with ethyl radicals, and acetalde-
hyde with methyl radicals. It is the main way of formation of
acetaldehyde. Methyl and ethyl radicals are the main source of
methane and ethylene, respectively. Oxirane derives from
ethylene via reactions with methylperoxy and ethylperoxy
radicals obtained also from methyl and ethyl radicals,
respectively. Methanol is also obtained from methylperoxy
radicals through the formation of methylhydroperoxide and
CH3O• radicals. The formation of both isomers of propanol
also derives from these alkoxy radicals obtained via H-
abstractions from propane. The prediction of these compounds
has been shown to be very sensitive to the value of the rate
constants used for the H-abstractions from propane. The used
rate constants, which are those of the reactions of metathesis of
•
propane by OH radical, are much higher than the values for
the reactions of metathesis of propane by CH3O• radical and
lead probably to an upper limit for the predicted formation of
alcohols. Nevertheless when using the same values as in the
case of methoxy radicals, almost no prediction of alcohols was
observed.
53
•
derive from the formation of OH addition to cyclohexene..
The possibility of reactions of 2,3-methylhydroxyoxirane during
the gas chromatographic analyses leading to 1-hydroxy-2-
propanol, a compound with a significant experimental mole
fraction (see Figure 2) but no obvious way of formation in the
model, cannot be excluded. Note that while the formation of
•QOOH radicals is often neglected in models of the oxidation
of alkenes in the literature, the formation rate through this
channel in the case of 2-hydroxypropyl-1-peroxy radicals is
much larger than that of its decomposition through the
Waddington mechanism.54
Figure 13a displays the predicted mole fraction of the major
C3 ketohydroperoxide showing that it is lower by a factor 2
than that of propylhydroperoxides. This certainly does not fully
explains why m/z 90 is not present in the measured mass
spectra (see Figure 3), since its maximum fraction of 600 ppm
should have been observed by SVUV-PIMS. The alkoxy radicals
obtained by decomposition of the ketohydroperoxide deriving
from propyl-1-peroxy radicals mostly decompose by breaking a
C−C bond yielding formaldehyde. These aldo-alkoxy radicals
are also a source of 3-hydroxypropanal through H-abstractions
from propane. This last product, for which a mole fraction up
to 20 ppm is computed (see Figure 13b), has not been
observed experimentally. This discrepancy could both be due to
a more difficult detection in GC analysis of compounds
including 2 oxygenated functions and to uncertainties in the
reactions deriving from ketohydroperoxides.
To show the influence of the reactions deriving from
hydroxypropyl radicals, Figure 14 shows the results of a
simulation using a model in which the additions of •OH radical
on propene have been removed. It can be seen in this figure,
that these reactions have only a very small effect on the global
reactivity indicated by the consumption of propane, but a much
more significant one on the formation of propene, acetaldehyde
and acrolein.
Compared to longer alkanes, a larger fraction of fuel (about
40%) is consumed to give the conjugated alkene, due to
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AUTHOR INFORMATION
■
Corresponding Author
*E-mail: Olivier.herbinet@univ-lorraine.fr. Telephone: 33 3
83175360. Fax: 33 3 83378120.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
This work was supported by European Commission (“Clean
ICE” ERC Advanced Research Grant) and by the COST
Action CM0901. This work was granted access to the HPC
resources of CINES under the allocation c2012086686 made by
GENCI (Grand Equipement National de Calcul Intensif).
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ASSOCIATED CONTENT
* Supporting Information
Cartesian coordinates of the optimized structures of molecules,
radicals, and transition states and complete mechanism of the
low-temperature combustion of propane at 1 atm. This material
is available free of charge via the Internet at http://pubs.acs.org.
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