report on ongoing progress of c -c model development ... · numerical studies of oxidation...
TRANSCRIPT
SAFEKINEX
SAFe and Efficient hydrocarbon oxidation processes by KINetics and Explosion
eXpertise and development of computational process engineering tools
Project No. EVG1-CT-2002-00072
Work Package 4
Kinetics model Development
Sub Package 4.2
Development of C
4
-C
10
detailed kinetic oxidation models
Deliverable 27
Report on ongoing progress of C
4
-C
10
model
development :
Alkanes and Alkenes
January 2004
Responsible Partner : CNRS DCPR � Nancy University of Leeds
Authors : Frédérique Battin-Leclerc
Roda Bounaceur
Frédéric Buda
Valérie Conraud
René Fournet
Pierre-Alexandre Glaude
Sylvain Touchard
John Griffiths
Table of contents
PRELIMINARY DEFINITIONS ........................................................................................................ 4
INTRODUCTION ................................................................................................................... .............. 5
I. STATE OF THE ART FOR THE EXPERIMENTAL INVESTIGATION OF
AUTOIGNITION OF ALKANES AND ALKENES (C
4
TO C
10
)..................................................... 6
1) GENERALITIES ABOUT AUTOIGNITION ......................................................................................... 6
2) LITERATURE REVIEW ..................................................................................................................... 7
A) DESCRIPTION OF THE EXPERIMENTAL FACILITIES USED ............................................................. 7
B) MAIN RESULTS OBTAINED........................................................................................................... 8
II. AUTOMATIC GENERATION OF KINETIC MECHANISMS FOR THE
AUTOIGNITION OF HYDROCARBONS BY THE SOFTWARE EXGAS ................................ 15
1) GENERAL FEATURES OF EXGAS ................................................................................................ 15
A) COMPREHENSIVE PRIMARY MECHANISM.................................................................................. 15
B) C
0
-C
2
REACTION BASE............................................................................................................... 18
C) SECONDARY MECHANISM......................................................................................................... 19
D) THERMOCHEMICAL AND KINETIC DATA FOR THE OXIDATION OF ALKANES AND ALKENES ..... 20
2) CHANGES MADE IN EXGAS IN ORDER TO IMPROVE THE MODELLING OF AUTOIGNITION
DELAY TIMES ............................................................................................................................... ......... 27
A) GENERAL CHANGES IN THE MECHANISM GENERATION............................................................ 27
B) SPECIFIC IMPROVEMENTS TO MODEL THE AUTOIGNITION OF LARGE ALKENES (CONTAINING
MORE THAN 4 ATOMS OF CARBON)........................................................................................................ 30
III. COMPARISON BETWEEN SIMULATIONS AND EXPERIMENTS FOR ALKANES . 33
1) N-BUTANE AUTOIGNITION ........................................................................................................... 33
A) RAPID COMPRESSION MACHINE................................................................................................ 33
B) SHOCK TUBE .............................................................................................................................. 34
2) N-PENTANE AUTOIGNITION ......................................................................................................... 34
A) RAPID COMPRESSION MACHINE................................................................................................ 34
3) ISO-PENTANE AUTOIGNITION ...................................................................................................... 35
A) RAPID COMPRESSION MACHINE................................................................................................ 35
4) NEO-PENTANE AUTOIGNITION..................................................................................................... 36
A) RAPID COMPRESSION MACHINE ................................................................................................ 36
5) 2-METHYLPENTANE AUTO IGNITION............................................................................................ 38
A) RAPID COMPRESSION MACHINE................................................................................................ 38
B) SHOCK TUBE .............................................................................................................................. 39
6) N-HEPTANE OXIDATION ............................................................................................................... 40
A) SHOCK TUBE ............................................................................................................................. 40
B) RAPID COMPRESSION MACHINE................................................................................................. 43
7) ISO-OCTANE AUTOIGNITION ........................................................................................................ 45
A) SHOCK TUBE ............................................................................................................................. 45
2
B) RAPID COMPRESSION MACHINE................................................................................................. 47
8) N-DECANE AUTOIGNITION ........................................................................................................... 48
A) SHOCK TUBE ............................................................................................................................. 48
IV. COMPARISON BETWEEN SIMULATIONS AND EXPERIMENTS FOR ALKENES.. 49
1) MODELLING OF THE OXIDATION OF PROPENE IN A STATIC REACTOR ..................................... 49
2) MODELLING OF THE AUTOIGNITION OF 1-PENTENE IN A RAPID COMPRESSION MACHINE ..... 49
3) MODELLING OF THE AUTOIGNITION OF 1-HEXENE IN A RAPID COMPRESSION MACHINE ....... 52
CONCLUSION..................................................................................................................... ............... 53
REFERENCES..................................................................................................................... ............... 54
3
Preliminary definitions
Throughout this report, carbon atoms are defined as followed :
Name of the
atom
Primary, noted
C
I
Primary, noted
C
II
Primary, noted
C
III
Primary, noted
C
IV
Number of
hydrogen atoms
linked to the
carbon atom
3 2 1 0
Representation R
1
� CH
3
R
1
� CH
2
� R
2
R
1
H
C R
3
R
2
R
1
C R
3
R
2
R
4
Example CH
3
�CH
3
CH
3
�CH
2
�CH
3
CH (� CH
3
)
3
C (� CH
3
)
4
A hydrogen atom is primary when it is linked to a primary carbon, it is secondary
when linked to a secondary carbon atom, and tertiary when linked to a tertiary carbon atom.
A radical is said to be primary when the radical point is on a a primary carbon, it is
secondary when the radical point is on a secondary carbon atom, and tertiary when the radical
point is on a tertiary carbon atom.
Alkylic hydrogen atom
We call alkylic every hydrogen atom part of an alkane, an ether or an alkene which is
linked to a carbon atom at least in position from a double bond.
Allylic hydrogen atom
We call allylic every hydrogen atom which is linked to a carbon atom in position
from a double bond.
Vinylic hydrogen atom
We call vinylic every hydrogen atom which is linked to a carbon atom taking part in a
double bond.
CH
3
2 2
Alkylic primary
hydrogen atom
Allylic secondary
hydrogen atom
Vinylic tertiary
hydrogen atom
Vinylic secondary
hydrogen atom
4
Introduction
The development of detailed and well-validated kinetic models to reproduce
combustion behaviour of hydrocarbons and to predict auto�ignition delay times would help
understanding the main reaction paths that lead to explosions. The implementation of these
kinetic mechanisms in models for explosion indices prediction would allow the creation of a
database that industry could use when designing efficient, cleaner and safer processes.
Detailed kinetic mechanisms are based on elementary steps, the rate constants of
which depend only of temperature and, pressure and can, therefore, be used in a predictive
way. Detailed reaction mechanisms of the oxidation of hydrocarbons in the gas phase have
been developed world-wide over several decades. Most studies have been confined to
oxidation chemistry at temperatures above about 1000 K with more limited attention of
detailed kinetic models to the important lower temperature regime. A major problem in
constructing a detailed chemical kinetic model, especially at lower temperatures, is the very
large number of possible reactions, products, and reaction intermediates involved. Because
manual assembly of a comprehensive kinetic model is extremely difficult and prone to error,
the only practical way to construct and use large models lies in the use of formal computer-
based methods. Examples of automated procedure for the construction of comprehensive
kinetic mechanisms are found in the work of Chinnick, 1987 ; Chevalier et al., 1990 ;
Blurock, 1995 ; Broadbelt et al., 1996 ; Ranzi et al., 1997. The work presented here is based
on the improvement and the use of EXGAS, a fully automatic software able to generate
detailed reaction mechanisms for gas-phase oxidation reactions, which has been developed by
CNRS in Nancy over two decades (Haux, 1982; Muller, 1987; Bloch-Michel, 1995 ; Warth,
1999).
This report, which is deliverable 27, presents first a review of the literature concerning
the autoignition of alkanes and alkenes. A second part describes the method of automatic
generation which has been used to obtain detailed kinetic oxidation models for C
4
-C
10
alkanes
and alkenes. A third part presents the validations which have been already performed using
the experimental results existing in the literature.
An additional report will be provided together with deliverable 35 �Validated detailed
kinetic model for C
4
-C
10
hydrocarbons�. This next report will detail the method of automatic
generation which will be used to obtain detailed kinetic oxidation models for C
4
-C
10
cyclanes
and the additional validations which will be performed for C
4
-C
10
hydrocarbons using the
experimental results obtained during the SAFEKINEX project.
5
I. State of the art for the experimental investigation of autoignition
of alkanes and alkenes (C
4
to C
10
)
1) Generalities about autoignition
Spontaneous ignition (or autoignition) is the sudden inflammation of a gaseous charge
at a critical condition of pressure, temperature and mixture composition. The way in which
events unfold is determined by the physical environment within which reaction takes place,
through the interplay of complex chain reactions with mass and thermal feedback (called
�thermokinetic� interactions).
Thus, a mixture of hydrocarbons and air can react either in a slow combustion process
or through an uncontrolled exponential increase in rate which leads to ignition. In other
conditions, the ignition might lead to a cool flame, or multiple cool flames in which the rate,
the temperature and the pressure increase strongly over a limited temperature range, and
decays with before combustion is complete. But cool flames can also be followed by a
complete consumption of the reacting mixture in a spontaneous ignition (or autoignition).
This is due to an accumulation of intermediate products that are, themselves, reactive.
In most hydrocarbons, the most reactive conditions for the onset of autoignition exist
in fuel rich mixtures, governed by strong kinetic dependences on the fuel concentration,
whereas generally the fastest propagating flames and highest heat release in combustion is
associated with compositions of gaseous fuels of fuel vapours that are close to the
stoichiometric proportion in oxygen or air.
Specific reference is made below to experiments in rapid compression machines
(RCMs) and shock tubes, as the experimental basis of high pressure and temperature studies
from which the Nancy comprehensive kinetic models are validated. However, many
laboratory studies of autoignition phenomena are also made in closed and flow systems. In
fact, the earliest studies to characterize the modes of behaviour of hydrocarbons, throughout
the 1920s and 30s, were made in such systems. Much of this historical work is documented in
the book by Lewis and Von Elbe (1965), and in other similar text books.
In closed and flow systems, ignition studies of hydrocarbons in oxygen can be
performed at pressures below 1 bar, which permits glass apparatus to be used. Most studies
involving air require reactant pressures of above 1 bar for hydrocarbon ignition to be attained,
for which metal systems are then required. Normally the first step is to characterize the
limiting conditions for cool flames and ignitions as a function temperature, pressure and
composition. In closed vessels these are normally characterized in the pressure � vessel
(ambient) temperature (p � T
a
) ignition diagram for a given fuel + oxygen (or air) mixture.
The complexity of these diagrams and their sensitivity to conditions gives additional, and
important quantitative criteria for testing the validity of thermokinetic models to represent the
combustion of hydrocarbons over very wide temperature ranges.
A fundamental distinction between closed vessel and flow tube studies and those in
RCMs or shock tubes is that, normally, in closed and flow vessels the reaction begins at the
same temperature as that of the vessel surface � perhaps with some brief �warm up� time on
introduction. That is, the initial temperature and the control temperature are essentially the
same. For RCMs and shock tubes, the apparatus itself is set at some ambient temperature
(probably at or close to laboratory temperature) and the reactants are raised rapidly by
compression or shock heating to some initially temperature that is considerably greater than
the ambient condition. Thus the temporal evolution in these systems is governed by the initial
temperature. The main consequence is that there is a finite ignition delay at which ignition
6
ceases to be observed in RCMs and shock tubes � typically of the order of ~ 100 ms in RCMs,
controlled by heat transport to the (relatively cold) apparatus walls, and ~ 10 ms in shock
tubes, subject to the arrival of the expansion fan. By contrast, autoignition in flow systems can
evolve over a number of seconds (governed by flow rate and reactor dimensions) and over
many minutes in closed vessels. Moreover, in closed vessels and flow tubes, if the increasing
ignition delay is tracked as a function of decreasing temperature or pressure one finds that
there is an exponentially increasing duration, such that the �limit of ignition� approximates
well to a criterion at which the ignition delay tends to . In closed vessels and flow tubes,
surface activity may play a part in the evolution of reaction, which is unlikely to be the case in
RCMs and shock tubes.
A comprehensive appendix listing references to low temperature combustion studies,
with outline of the experimental conditions and measurements made, are given for the period
1965 � 94 in �Reduced kinetic models and their application to practical combustion systems�
by Griffiths (1995). There is also a similar appendix, listing low temperature kinetic and
combustion studies, chronologically in 5 year periods from 1976 - 95, in �Experimental and
numerical studies of oxidation chemistry� by Griffiths and Mohamed (1997b).
2) Literature review
Experimental results concerning the autoignition of alkanes and alkenes containing at
least 4 atoms of carbon which have been published in the last ten years are gathered in table 1.
These results have been obtained in two types of experimental systems, namely the shock tube
and the rapid compression machine (RCM).
a) Description of the experimental facilities used
Shock tube
In a shock tube, ignition delay time is usually measured behind a reflected shock
wave, while the corresponding temperature is calculated from the incident shock wave
velocity with an error estimated to 20 K. The apparatus used by Adomeit et al. (Ciezki and
Adomeit, 1993, Fieweger et al., 1997) allowed them to work with air-hydrocarbon mixtures
for pressures behind reflected shock wave up to 50 bar and then to observe autoignition at
temperatures from 660 K. Other authors used much diluted mixtures and then can only
measure autoignition delay times from 1100 K.
Rapid compression machine
Autoignition delay times from three RCM facilities are reported here. One is at Leeds
University with a compression time of 22 ms (Griffiths et al., 1993, Griffiths et al., 1997,
Westbrook et al., 2002). A second one is used by the Université of Lille with a compression
time of 60 ms (Minetti et al., 1995, 1996a, 1996b), and the last one is at National University
of Ireland with a compression time of approximately 16.6 ms (Silke et al., 2003, Curran et al.,
1992). In these RCMs, ignition delay time is measured from the end of the compression. The
temperature, T
c
, of the compressed gas is calculated for an adiabatic core gas from the initial
pressure, P
0
, and temperature, T
0
, the compressed pressure, P
1
, and the ratio of specific heats
(g = Cp/Cv) by the equation,
7
0
1
Tc
T
P
P
ln
1
0
T
dT
, (Minetti et al., 1996a ; Pilling, 1997).
Several experimental studies have demonstrated that the details of the heat transfer in a
rapid compression machine are quite complex, both with respect to the geometry and over the
time history of the experiments (Westbrook et al., 2002). This is of particular importance for
compounds with the longest ignition delay times and it has been shown that simulation with a
simple physical model encounter problems to reproduce the experimental results obtained in
Leeds for very branched alkanes (i.e. iso-octane, 2,2-dimethyl pentane, 2,4-dimethyl pentane,
3,3-dimethyl pentane), for which a region of temperature in which no autoignition was
observed was found for temperature around 750 K (Westbrook et al., 2002). This problem
seems to be of lower importance in the case of the rapid compression machine of Lille, which
has a slower stroke and a somewhat different geometry (Westbrook et al., 2002). In addition,
temperatures gradients have been observed in the combustion chamber of such an apparatus
(Griffiths et al., 2001), which can greatly influence the measurement of the observed
products.
b) Main results obtained
Alkanes
The alkanes which have been studied during the last 10 years are n-butane, n-pentane,
iso-pentane, neo-pentane, 2-methyl-pentane, n-hexane, 2,4-dimethyl-pentane,
3,3-dimethyl-pentane, 2,2-dimethyl-pentane, 2,3-dimethyl-pentane, 3-ethyl-pentane,
2-methyl-hexane, 3-methyl-hexane, 2,2,3-trimethyl-butane, n-heptane, iso-octane and
n-decane. Results for propane ignition in an RCM have not yet been published, probably
because exceptionally high pressures are required to give sufficiantly short ignition delay
times of this relatively unreactive alkane.
n-butane
Results from the RCM (Carlier et al., 1994) show ignition delay times globally
ranging from 20 to 45 ms over the compressed gas temperature range 600�900 K at
compressed gas pressures of 10 bar. A negative temperature coefficient (NTC) of the ignition
delay is exhibited between 750 and 840 K.
In a shock tube, Davidson et al. (2001) have measured OH concentration time
histories, which show an initial rapid rise to an intermediate concentration, followed by a later
rise to a post-ignition concentration.
Horning et al. (2001, 2002) used a CH emission diagnostic at the endwall of a shock
tube to measure ignition delay times. They studied n-heptane, propane, n-butane and n-
decane, from which they obtained a correlation of the ignition delay time ( ) for these four n-
alkanes in stoichiometric mixtures (with a correlation coefficient of 0.992) as :
= 9.4 x 10
-12
P
-0.55
X (O
2
)
-0.63
n
�0.5
exp (+23 245/T)
is in seconds, pressure P is in atmospheres, X (O
2
) is the mole fraction of O
2
in the
mixture, and n is the number of carbon atoms in the n-alkane. The temperature range of
applicability is 1400 - 1500 K.
8
n-pentane
N-pentane ignition has been studied extensively in RCMs. Griffiths et al. (1993 ,1997)
ignition delay times ranging from 5 to 40 ms over the range 600 � 900 K show the presence of
an NTC region between 750 and 825 K. Westbrook et al. (1998) studied the influences of
pressure, temperature and equivalence ratio on the autoignition of n-pentane in a rapid
compression machine. Results show a two-stage ignition, and in some cases the first stage
happens during the compression stroke of the rapid compression machine, making the
interpretation of the meaning of the ignition delay, as normally defined in an RCM, difficult.
Studies by Minetti et al. (1996a) show ignition delays between 6 and 150 ms but with a range
of constant ignition delay, rather than a negative temperature coefficient zone at intermediate
temperatures. This is most likely to be because extensive reaction occurs during the slow
compression of the Lille machine.
Autoignition of n-pentane in a rapid compression machine was also studied by
Ribaucour et al. (1998, 2000), showing a two stage ingition and an NTC region between 770
and 850 K. Autoignition delay times for n-pentane range from 5 to 100 ms.
Iso-pentane
Results in an RCM (Minetti et al., 1999) show ignition delay times ranging from 20 to
100 ms, with a negative temperature coefficient zone between 730 and 825 K.
Neo-pentane
Results in an RCM (Minetti et al., 1999) are very similar to those for n-pentane, with
ignition delay times ranging from 5 to 200 ms and a negative temperature coefficient zone
between 750 and 850 K, where ignition delay times remain almost constant.
Griffiths et al. (1997) also studied the behaviour of neo-pentane, demonstrating the
existence of a NTC region between 800 and 900 K with autoignition delay times ranging from
10 to 30 ms.
Finally, autoignition of neo-pentane in an RCM was investigated by Ribaucour et al.
(2000), showing no NTC region. Autoignition delay times range from 5 to 150 ms.
2-methyl-pentane
In an RCM (Griffiths et al., 1997), results show a negative temperature coefficient
zone between 775 and 840 K. Ignition delay times range from 10 to 50 ms.
Different concentrations and equivalent ratios were investigated by Burcat et al.
(1999) in a shock tube, but no general trend can be concluded. Ignition delay times range
from 10 to 500 s.
n-hexane
Griffiths et al. (1993) showed the presence of a negative temperature coefficient zone
in an RCM.
Burcat et al. (1996) measured ignition delay times and product distribution for
methane, ethene and propene in mixtures of n-hexane-oxygen-argon in a shock tube.
9
Isomers of heptane
Griffiths et al. (1997) and Silke et al. (2003) have studied the isomers of heptane in an
RCM : 2,4-dimethyl-pentane, 3,3-dimethyl-pentane, 2,2-dimethyl-pentane,
2,3-dimethyl-pentane, 3-ethyl-pentane, 2-methyl-hexane, 3-methyl-hexane,
2,2,3-trimethyl-butane and n-heptane. Minetti et al. (1995) have also measured n-heptane
autoignition delay times in an RCM. Characteristic negative temperature coefficient was
observed for all types of isomers, the more branched structures being less reactive. In general,
the NTC zone ranges from 700 to 925 K, and ignition delay times range from 5 to 70 ms.
Considering n-heptane in a shock tube (Ciezki and Adomeit, 1993), there also is a
negative temperature coefficient zone between 720 and 900 K, and autoignition delay times
range from 0.1 to 100 ms.
Davidson et al. (1999, 2000) have obtained OH concentration histories during the
ignition of n-heptane in a shock tube, while Horning et al. (2001, 2002) from the same group
determined the correlation we already discribed :
= 9.4 x 10
-12
P
-0.55
X (O
2
)
-0.63
n
�0.5
exp (+23 245/T)
Iso-octane
Results in an RCM (Minetti et al., 1996) show a very marked negative temperature
coefficient zone between 700 and 800 K. Delays range from 20 to 120 ms. Measurements
done by Griffiths et al. (1997) in a rapid compression machine also demonstrate the presence
of a NTC region between 725 and 800 K. Autoignition delay times range from 3 to 45 ms.
Fieweger et al. (1997), Vermeer et al. (1972), and Davidson et al. (2002) have
measured autoignition delay times for iso-octane in a shock tube. Only in the Fieweger team
experiments can we see a change of slope around 750-900 K in the curve representing the
logarithm of the autoignition delay time versus 1/T. Other experiments were performed at
higher temperatures. In general, ignition delay times range from 0.1 to 1000 ms.
N-decane
In a shock tube (Pfahl et al., 1996), experiments show an NTC zone between 800 and
900 K. Autoignition delay times range from 0.1 to 5 ms.
Skjoth-Rasmussen et al. (2003) also studied the autoignition of n-decane in a shock
tube between 1345 and 1537 K, and their measured ignition delays range from 100 to 10000
s.
Davidson et al. (1999, 2000) have obtained OH concentration histories during the
ignition of n-heptane in a shock tube, while Horning et al. (2001, 2002) from the same group
measured delays varying from 800 to 5000 µs between 1400 and 1515 K, from which the
correlation = 9.4 x 10
-12
P
-0.55
X (O
2
)
-0.63
n
�0.5
exp (+23 245/T) was determined.
Alkenes
Autoignition delay times measurements were performed for 1-butene, iso-butene,
1-pentene, and 1-hexene.
10
1-butene
In a shock tube (Heyberger et al., 2002), ignition delay times range from 10 to 2000 s
for temperatures between 1200 and 1670 K.
Iso-butene
Curran et al. (1992) have measured ignition delay times of iso-butene in a shock tube
between 1100 and 1900 K. Values range between 10 and 1000 s. Baugé et al. (1998) also
measured ignition delays ranging from 3 to 800 s.
1-pentene
Ribaucour et al. (1998) have measured ignition delay times for 1-pentene in a rapid
compression machine from 600 to 900 K. Ignition times range from 20 to 70 ms, and a
negative temperature coefficient zone is shown between 750 and 800 K.
1-hexene
Experiments done by Vanhove et al. (2003) in a rapid compression machine between
615 and 850 K show the presence of a negative temperature coefficient zone where ignition
delay times remain constant between 750 and 800 K. In general, ignition times range from 5
to 350 ms.
11
Table 1 : Summary of experimental results recently published (1992-2003), concerning
the auto-ignition of alkanes and alkenes from C
4
.
ST : Shock tube, RCM : Rapid compression machine. The results given in bold have been
used for the validations presented in this report.
Compounds
Type of
reactor
Temperature
Range
(K)
Pressure
Range
(bar)
Equivalence
ratio range
Reference
RCM
700-900 8.9-11.5 1 Carlier et
al., 1994
1300-1700 1-6 1 Horning et
al., 2001,
2002
n-butane
ST
1530-1760 2.1 1 Davidson et
al., 2001
600-900 6-11 1 Minetti et
al., 1996a
650-900 6-9 1 Griffiths et
al., 1993,
1997
600-900 7.5 1 Ribaucour et
al., 1998
675-980 8-20 0.5-2 Westbrook
et al., 1998
n-pentane RCM
640-900 4-5.3 1 Ribaucour et
al., 2000
iso-pentane
RCM 680-900 8-11 1 Minetti et
al., 1996a
680-950 4-11 1 Minetti et
al., 1996a
750-900 7.5-9 1 Griffiths et
al., 1997
neo-pentane RCM
640-900 4-5.3 1 Ribaucour et
al., 2000
RCM 700-950 7.5-9 1 Griffiths et
al., 1997
2-methyl-pentane
ST 1175-1722 2-4.6 0.5-1 Burcat et
al., 1999
RCM
680-930
6-9 1
Griffiths et
al., 1993
n-hexane
ST 1020-1725 1-7 1
Burcat et al.,
1996
700-950 7.5-9 1 Griffiths et
al., 1997
2,4-dimethyl-pentane RCM
640-1040 15 1 Silke et al.,
2003
12
700-950 7.5-9 1 Griffiths et
al., 1997
3,3-dimethyl-pentane RCM
640-1040 15 1 Silke et al.,
2003
685-868 7.5-9 1 Griffiths et
al., 1997,
Westbrook
et al., 2002 2,2-dimethyl-pentane
RCM
640-1040 15 1 Silke et al.,
2003
2,3-dimethylpentane
RCM 640-1040 15 1 Silke et al.,
2003
3-ethyl-pentane
RCM 640-1040 15 1 Silke et al.,
2003
685-868 7.5-9 1 Griffiths et
al., 1997,
Westbrook
et al., 2002 2-methyl-hexane
RCM
640-1040 15 1 Silke et al.,
2003
3-methyl-hexane RCM
640-1040 15 1 Silke et al.,
2003
2,2,3-trimethylbutane RCM
640-1040 15 1 Silke et al.,
2003
600-900 6-11 1 Minetti et
al., 1995
700-960 6-9 1 Griffiths et
al., 1993,
1997
RCM
640-1040 15 1 Silke et al.,
2003
660-1350 3.2-42 0.5-3 Ciezki et al.,
1993
1400-1550 1.2-2.2 1 Davidson et
al., 1999
1540-1790 2-3.8 1 Davidson et
al., 2000
n-heptane
ST
1300-1700 1-6 0.5-2 Horning et
al., 2001,
2002
13
600-900 6-11 1 Minetti et
al., 1996b
RCM
750-900 7.5-9 1 Griffiths et
al., 1997
660-1350 13-45 1 Fieweger et
al., 1997
Iso-octane
ST
1200-1800 1.3 1 Davidson et
al., 2002
660-1350 12-50 1 Pfahl et al.,
1996
1300-1700 1-6 1 Horning et
al., 2001,
2002
1350-1700 2.2 1 Davidson et
al., 2000
n-decane
ST
1345-1537 5-10 0.5-1.5 Skjoth-
Rasmussen
et al., 2003
1-butene ST
1200-1670 6.7-9 0.5-2 Heyberger et
al., 2002
1100-1900 2-4.5 0.1-4 Curran et al.,
1992
Iso-butene ST
1230-1930 0.95-1.05 1-3 Baugé et al.,
1998
1-pentene RCM
600-900 6-9 1 Ribaucour
et al., 1998
1-hexene RCM
615-850 8.5-10 6.8-10.9 Vanhove et
al., 2003
14
II. Automatic generation of kinetic mechanisms for the
autoignition of hydrocarbons by the software EXGAS
The detailed kinetic mechanisms, which will be provided in the SAFEKINEX project,
will be automatically generated by the computer package EXGAS. Kinetic models generated
by this software have already been validated by simulating experimental results for a wide
range of alkanes (Glaude et al., 1997, Warth et al., 1998, Glaude et al., 1998, Battin-Leclerc
et al., 2000) and alkenes (Heyberger et al., 2001, 2002). But these validations are mainly
based on data obtained in continuous reactors and the models generated by EXGAS have not
been previously much tested to reproduce autoignitions delays. We will recall first the main
features of EXGAS alkanes, which have already been much described, and we will present
the addition of new generic rate constants and the improvements of existing rate constants,
which have been performed during this work to obtain correct simulations of autoignition
delay times.
1) General features of EXGAS
The system provides reaction mechanisms made of three parts, as shown in figure 1.
Lumped
Primary Molecules
Free Radicals
C2- Molecules
and
Free Radicals
Figure 1 : Simplified scheme of the software EXGAS
a) Comprehensive primary mechanism
In the primary mechanism, the only molecular reactants considered are the initial
organic compounds and oxygen.
Figure 2 shows a simplified scheme of the main reactions, which are involved to
model the oxidation of alkanes. Chain carriers are mainly �OH radicals. Branching reactions
are responsible for the multiplication of chain carriers and for an exponential acceleration of
reaction rates, leading in some conditions to spontaneous autoignition or to cool flames. At
low temperature (around 500-600 K), �OH radicals are mainly formed by degenerate
15
branching steps due to the secondary decompositions of hydroperoxides. The reversibility of
the oxygen addition (1) when the temperature increases to the benefit of the oxidation path (2)
leads to an overall reduction of the reaction rate and induces the appearance of a negative
temperature coefficient (NTC) regime. At higher temperature, other branching reactions are
involved (such as H
2
O
2
2OH� and H� + O
2
�OH + �O�) and are responsible for
autoignition in hydrocarbon-air mixtures.
initiation steps
R�
.
�QOOH
�OOH + alkene
+ O
2
ROOH
RH
+ H
2
O
2
RO� + �OH
degenerate
branching
steps
�OH + cyclic ethers,
aldehydes or ketones
RH
+ H
2
O
keto-hydroperoxides + �OH
R•R•
R��
R��
�OOQOOH
�U(OOH)
2
ROO�
degenerate
branching
steps
XO� + �OH
O
2
O
2
O
2
+ alkene
R��
(2)
(1)
RH, O
2
HO
2
�
Figure 2 : Simplified scheme for the primary mechanism of oxidation of alkanes
(Broken lines represent metathesis with the initial alkane RH).
According to the choices of the user, the reactant and the primary radicals can be
systematically submitted in EXGAS to the different types of following elementary steps :
- Unimolecular initiations involving the breaking of a C-C bond.
(e.g. C
3
H
8
�CH
3
+ �C
2
H
5
)
- Bimolecular initiations with oxygen to produce alkyl and �HO
2
radicals.
(e.g. C
3
H
8
+ O
2
�C
3
H
7
+ �OOH)
- Additions of alkyl (R�) and hydroperoxyalkyl (�QOOH) radicals to an oxygen
molecule.
(e.g. �C
3
H
7
+ O
2
C
3
H
7
OO�, �C
3
H
6
OOH + O
2
�OOC
3
H
6
OOH)
- Isomerizations of alkyl and peroxy (ROO� and �OOQOOH) radicals involving a
cyclic transition state.
(e.g. CH
3
CH
2
CH
2
OO� �CH
2
CH
2
CH
2
OOH)
- Decompositions of radicals by -scission involving the breaking of C-C or C-O
bonds for all types of radicals (for low temperature modeling, the breaking of C-H bonds is
not written).
(e.g. �C
3
H
7
�CH
3
+ C
2
H
4
)
16
- Decompositions of hydroperoxyalkyl and dihydroperoxyalkyl (�U(OOH)
2
) radicals
to form cyclic ethers, alkenes, aldehydes or ketones (oxohydroperoxyalkanes),
(e.g. �CH
2
CH
2
CH
2
OOH cyclic-C
3
H
6
O + �OH),
(e.g. CH
2
OOHC�OOHCH
3
CH
2
OOHC(=O)CH
3
+ �OH)
- Oxidations of alkyl radicals with O
2
to form alkenes and HO
2
� radicals.
(e.g. �C
3
H
7
+ O
2
C
3
H
6
+ �OOH)
- Metathesis between radicals and the initial reactants (H-abstractions).
(e.g. �OH + C
3
H
8
H
2
O + �C
3
H
7
)
- Recombinations of radicals.
(e.g. CH
3
� + CH
3
� C
2
H
6
)
- Disproportionations of peroxyalkyl radicals with HO
2
� to produce hydroperoxides
and O
2
(disproportionations between two peroxyalkyl radicals or between peroxyalkyl and
alkyl radicals are not taken into account).
(e.g. C
3
H
7
OO� + �OOH C
3
H
7
OOH + O
2
)
To generate kinetic mechanisms for alkenes, some additions had to be done to this
primary mechanism originally generated only for alkanes. This changes have been detailed in
previous papers (Heyberger et al., 2001, 2002). The additional elementary steps considered
for alkenes are the following :
- Bimolecular initiation steps between two alkenes molecule.
(e.g. CH
3
CH=CH
2
+ CH
3
CH=CH
2
�CH
2
CH
2
CH
3
+ �CH
2
CH=CH
2
)
- Molecular reactions via ene-mechanism
As shown in figure 3, two molecular reactions of propene via an ene-
mechanism are possible and lead to the formation of 1-hexene and 4-methyl 1-pentene, for
which reactions are included in the secondary mechanism. It is worth noting that, for alkenes
larger than butene, the decomposition via molecular retro-ene reactions will be also possible.
2 C
3
H
6
4-methyl 1-pentene
CH
3
CH
2
CHCH
2
CHCH
3
1-hexene
CH
2
CHCH
2
CH
2
CH
2
CH
3
CH
3
CH
2
CH
CH
2
CH
2
CH
H
CH
2
CH
CH
2
CH
CH
2
H
CH
3
Figure 3 : Molecular reaction via ene-mechanism
- Additions of �H, �CH
3
, �O�, �OH and peroxy radicals to the double bond are
considered.
(e.g. �H + CH
3
CH=CH
2
�CH(CH
3
)
2
�OH + CH
3
CH=CH
2
�CH(CH
3
)CH
2
OH )
17
- Isomerizations of peroxy radicals with an alcohol function.
In this case the atom of hydrogen to be transferred is on the OH group, the
cyclic transition state decomposes and gives two aldehydes and �OH. In the case of propene,
the addition of �C
3
H
6
OH to oxygen and the decomposition of �OOC
3
H
6
OH to give
formalhehyde, acetaldehyde and OH� is known as the Waddington mechanism (Stark et al.,
1997). The isomerization/decomposition of an isomer of �OOC
3
H
6
OH is detailed in figure 4.
�OH + CH
3
CHO + HCHO
CH
3
CH CH
2
O O�
H
O
CH
3
CH CH
2
O
H
O
O =
/
Figure 4 : Waddington mechanism
- Internal additions / decompositions.
The peroxy radicals deriving from the allylic radicals react through a cyclic
transition state to give aldehydes. In the case of propene, formaldehyde and acetaldehydes
radicals are produced via the mechanism displayed in figure 5. The direct isomerization-
decomposition of hydroperoxyalkylperoxy radicals (�OOQOOH) to give ketohydroperoxides
and �OH was considered.
CH
2
O + �CH
2
CHOCH
2
CH CH
2
O O�
�CH
2
CH CH
2
O O
=
/
Figure 5 : Mechanism of the reaction of the peroxy radical deriving from allyl
radical
- Oxidations of vinylic radicals are taken into account in the primary mechanism.
(e.g. �CH
2
=CHCH
3
+ O
2
CH
3
CH=O + �CH=O)
- Disproportionations of allyl and peroxy radicals
(e.g. �CH
2
CH=CH
2
+ �OOH CH
3
CH=CH
2
+ O
2
)
b) C
0
-C
2
reaction base
The fact that no generic rule can be derived for the generation of the reactions of small
or very unsaturated compounds makes the use of these reaction bases necessary. The C
0
-C
2
reaction base includes all the reactions involving radicals or molecules containing less than
three carbon atoms (Barbé et al., 1995). The base contains 378 reactions written in both sides,
and 48 direct processes, which means 426 reactions corresponding to 804 elementary
processes. This base is coupled with a reaction base for C
3
-C
4
unsaturated hydrocarbons
(Fournet et al., 1999), such as propyne, allene or butadiene, featuring reactions leading to the
formation of benzene.
The C
0
-C
2
reaction base has been validated with comparison with experimental data in
various setups, such as methane and ethane oxidation in a perfectly stirred reactor (Barbé et
al., 1995), in a shock tube (Baugé, 1997), or methane and acetylene combustion in a premixed
flame (Fournet et al., 1998).
18
c) Secondary Mechanism
The lumped secondary mechanism contains reactions consuming the molecular
products of the primary mechanism, which do not react in the reaction bases. For reducing the
number of reactants in the secondary mechanism, the molecules formed in the primary
mechanism with the same molecular formula and the same functional groups are lumped into
one unique species, without distinguishing between the different isomers. The reactions of
these lumped molecules are not elementary steps but global reactions which produce, in the
smallest number of steps, molecules or radicals whose reactions are included in the reaction
bases. The secondary mechanism includes :
- Degenerate branching reactions occurring first by breaking the peroxydic bond and
followed by subsequent decompositions.
(e.g. C
3
H
7
OOH �OH + HCHO + �C
2
H
5
),
- Reactions of alkanes, aldehydes, alcohols and epoxides, occurring first by a
metathesis step followed by subsequent decompositions.
(e.g. �OH + C
3
H
8
�CH
3
+ C
2
H
4
+ H
2
O),
- Metathesis steps for alkenes leading to resonance-stabilized radicals which are so
unreactive that they react mainly by termination steps.
(e.g. �OH + C
3
H
6
allyl-�C
3
H
5
+ H
2
O),
- Additions of �H, �OH, �CH
3
or �OOH to alkenes followed by decompositions.
(e.g. C
4
H
8
+ �OH HCHO + �CH
3
+ C
2
H
4
),
- Reactions of cyclic ethers.
The secondary reactions of cyclic ethers have been considered in great detail. These
cyclic ethers react first by metathesis to give lumped radicals which can either decompose or
react with oxygen. The reactions with oxygen involve the classical sequence of oxygen
addition, isomerization, second oxygen addition, second isomerization and beta-scission to
lead to the formation of hydroperoxides, which are degenerate branching agents and
decompose to give �OH radical and several molecules or radicals whose reactions are
included in C
0
-C
2
reaction base. These reactions can be an important source of CO
2
at low
temperature. To sum up, we can write a simplified mechanism of reaction of cyclic ethers in
the secondary mechanism :
R(O@) + �R� R�H + �R(O@) metathesis (a)
�R(O@) �R�� + x C
2
H
4
decomposition (b)
�R(O@) + O
2
R(O@)OO� addition to oxygen (c)
R(O@)OO� �RO@ + O
2
(-c)
R(O@)OO� �R(O@)OOH isomerization (d)
�R(O@)OOH R(O@)OO� (-d)
�R(O@)OOH+O
2
R(O@)(OOH)OO�
addition to oxygen (e)
R(O@)(OOH)OO� �R(O@)OOH + O
2
(-e)
R(O@)(OOH)OO� �OH + R(O@)(CO)(OOH) beta-scission (f)
R(O@)(CO)(OOH) �OH + �R��� + CO
2
+ y C
2
H
4
decomposition (g)
Where : R(O@) is a cyclic ether C
n
H
2n
(O@m) with 4 m 6,
�R(O@) is �C
n
H
2n-1
(O@m) with 4 m 6,
�R� is �H, �O�, �OH, �CH
3
, �C
2
H
5
or HO
2
�,
�R�� is �CH
2
CHO if n is even, �CHO if n is odd,
R(O@)(CO)(OOH) is C
n
H
2n-2
O
4
,
�R��� is �CH
2
CHO if n is odd, �CHO if n is even.
19
In this lumped secondary mechanism, steps important from a kinetic point of view,
such as the reactions of resonance-stabilized radicals or the degradation of cyclic ethers, are
carefully taken into account. We can then consider that the globalisation of reactions does not
alter the precision of simulations concerning the overall rate of reaction (e.g. the prediction of
the conversion of reactants). But, of course the prediction of the formation of secondary
products is less accurate : the distribution of products between the different families of
compounds is still respected, but not inside a given family. For instance the global production
of alkenes is mostly correctly predicted, but the amount of ethylene is systematically
overpredicted, when the amounts of propene or butene are underpredicted.
The generation of secondary mechanisms for the oxidation of alkenes (Heyberger et
al., 2001) is based on the same rules as for the oxidation of alkanes or ethers. Cyclic ethers
with a double bond or with an alcoholic function were treated according to the same rules as
unsubstituted and saturated cyclic ethers; unsaturated aldehydes were treated according to the
same rules as saturated aldehydes.
d) Thermochemical and kinetic data for the oxidation of alkanes and alkenes
Thermochemical data for molecules or radicals were automatically calculated and
stored as 14 polynomial coefficients, according to the CHEMKIN II formalism (Kee et al.,
1993). These data were calculated using the software THERGAS (Muller et al., 1995), based
on the group and bond additivity methods proposed by Benson (1976).
Considering the reaction base, kinetic data mostly come from databases by Tsang et
al. (1986) and Baulch et al. (1994), with complements from the database developed by NIST
(1993). Efficiency coefficients for different gases have been added in order to better represent
the effect of pressure on those reactions.
Table 2 presents the set of generic rate constants, which are used by EXGAS for the
primary mechanism of the oxidation of hydrocarbons. The kinetic data of isomerizations,
recombinations and the unimolecular decompositions are calculated using the software
KINGAS (Bloch-Michel, 1995) based on the thermochemical kinetics methods (Benson,
1976). The main features of these calculations have been summarized in a previous
description of EXGAS (Warth et al., 1998).
For instance, intramolecular isomerizations are applied to every radical of the primary
mechanism where the radical point can move from a carbon or oxygen atom to another of
these atoms. A transition cyclic state is observed within the process, for example as
represented here :
Kinetic data for this type of reaction are calculated by the software KINGAS (Bloch-
Michel, 1995) according to the Benson methods (1976). The preexponential factor is
determined from a simplified relation (Brocard et al., 1983) proposed by O�Neal :
A = e
1
(k
B
T / h) x rpd x exp ( n
i,rot
x 3.5 / R ) s
-1
20
With :
k
B
: Boltzmann constant = 1,38 x 10
-23
J.K
-1
,
h : Planck constant = 6,63 x 10
-34
J.s,
T : temperature (K),
rpd : �reaction path degeneracy�, number of transferable hydrogen atoms,
n
i,rot
: variation of the number of internal rotations between the reactant and the
transition state,
R = 1,987 cal.mol
-1
.K
-1
.
We assume that the loss of one internal rotation between the reactant and the transition
state leads to a variation of entropy S
rotor
= 3.5 cal / mol. K.
EXGAS estimates activation energies for isomerization processes by summing the
energy needed to break the hydrogen atom bond and the ring strain of the transition state :
E = E
H
+ E
ring
The energy needed to tear the hydrogen atom comes from the work of Benson et al.
(1979) and Cox (1989). The effect of the presence of an oxygen atom in ethers is neglected.
Values of energy are gathered in table 3.
H atom transferred Primary Secondary Tertiary
Energy for ROO�
tearing the H atom
20000 17000 14000
Energy for R� tearing
the H atom
13500 11000 9000
Table 3 : Activation energy needed to break an hydrogen atom bond within the
internal isomerization process (cal/mol)
Energy values for the cycle tension of the transition state come from isomerization rate
measurement published by the teams of R.W. Walker and M.J. Pilling (Baldwin et al., 1986,
Walker et al., 1997), and are presented in table 4.
Ring Size 4 5 6 7 8
Ring strain
energy for a
cycle with 2
oxygen atoms
(kcal/mol)
23.0 15.5 8 5.0 4.0
Ring strain
energy for a
cycle with 0 or
1 oxygen atoms
(kcal/mol)
26.0 6.3 0 6.4 9.9
Table 4 : Ring strain of the transition state
In the case of recombinations, the activation energy is equal to 0, and the
preexponential factor is calculated by KINGAS.
The data for which the calculation is not possible by KINGAS are estimated from
correlations, which are based on quantitative structure-reactivity relationships and obtained
21
from a literature review. The estimation of the rate constants used in the secondary
mechanism is based on correlations derived from that proposed for the primary mechanism
and has also been previously described (Warth et al., 1998).
22
Table 2 : Kinetic parameters for the primary mechanism of the oxidation of alkanes
and alkenes.
Rate constants are expressed in the form k = A T
b
exp(-E/RT), with the units cm
3
, mol, s, kcal, by H
atoms which can be abstracted. �R
p
, �R
s
, �R
t
are primary, secondary and tertiary alkyl free radicals. The
terms used here are defined in the preliminary definitions.
H-abstraction Primary H Secondary H Tertiary H
lg A b E lg A b E lg A b E
Initiation with O
2
, type of the radical formed :
alkyl 12.62 0 49000 13.00 0 48000 12.30 0 46000
allyl 11.88 0 39200 12.25 0 38200 11.55 0 36200
vinyl - - - 13.00 0 57600 12.30 0 55600
Initiation between two alkenes (abstraction of allylic H atom), type of alkyl radical
formed :
secondary 13..20 0 52300 13.57 0 51300 12.87 0 49300
tertiary 13.92 0 55200 14.28 0 54200 13.58 0 52200
quaternary 11.52 0 50000 11.89 0 49000 11.18 0 47000
Addition on the double bond with :
Secondary C Tertiary C Quaternary C
H 15.12 0 1560 13.12 0 3260 11.08 0.69 3000
CH
3
11.22 0 7400 10.98 0 8000 11.20 0 4970
C
2
H
5
(primary)
11 0 7250 - - - - - -
iC
3
H
7
(secondary)
10.11 0 8700 - - - - - -
tC
4
H
7
(tertiary)
9.49 0 5890 - - - - - -
OH 12.14 0 -1040 12.12 0 -1040 12.14 0 -1040
O 4.78 2.56 -1130 4.78 2.56 -1130 4.78 2.56 -1130
C
IV
=C
IV
C
IV
=C
III
C
IV
=C
II
OOH 11.48 0 7000 11.60 0 14200 11.90 0 12860
OOCH
3
11.15 0 8700 11.18 0 10140 11.60 0 12600
OOR 10.95 0 9770 11 0 11520 11.30 0 13120
C
III
=C
III
C
III
=C
II
OOH 11.70 0 12000 12 0 14200
OOCH
3
11.30 0 9520 11.60 0 11720
OOR 11.60 0 14000 11.90 0 16200
23
Oxidation
Primary H Secondary H Tertiary H
Init. Rad.
Alkyl
Alkylic H
abstraction
11.36 0 5000 11.90 0 5000 11.65 0 5000
Alkenyl
Alkylic H
abstraction
11.36 0 5000 11.90 0 5000 11.65 0 5000
Allylic H
abstraction
- - - 11.90 0 2500 11.65 0 2500
Allyl
Alkylic H
abstraction
11.36 0 9920 11.90 0 9920 11.65 0 9920
Vinylic H
abstraction
- - - - - - 12.00 0 22730
Metathesis of an alkyl and alkenyle H with :
�
O� 13.23 0 7850 13.11 0 5200 13.00 0 3280
�H 6.98 2 7700 6.65 2 5000 6.62 2 2400
�OH 5.95 2 450 6.11 2 -770 6.06 2 -1870
�CH
3
-1 4 8200 11.0 0 9600 11.00 0 7900
HO
2
� 11.30 0 17000 11.30 0 15500 12.00 0 14000
�CHO 4.53 2.5 18500 6.73 1.9 17000 4.53 2.5 13500
�CH
2
OH 1.52 2.95 14000 1.48 2.95 12000 2.08 2.76 10800
�OCH
3
10.73 0 7300 10.86 0 45000 10.36 0 2900
�OOR 12.30 0 20000 12.18 0 17500 12.18 0 15000
�C
2
H
5
11.00 0 13500 11.00 0 11000 11.00 0 9200
i-C
3
H
7
� -2.85 4.2 8700 -2.85 4.2 8000 -2.85 4.2 6000
�R
p
11.00 0 13500 11.00 0 11200 11.00 0 9000
�R
s
11.00 0 14500 11.00 0 12200 11.00 0 10000
�R
t
11.00 0 15000 11.00 0 12700 11.00 0 10500
Metathesis of an allylic H with :
�
O� 10.76 0.7 5900 10.64 0.7 3250 10.53 0.7 1330
�H 4.76 2.5 2510 4.43 2.5 -1900 4.40 2.5 -2790
�OH 6 2.0 -298 6.18 2.0 -1520 6.11 2.0 -2620
�CH
3
-0.13 3.5 5670 10.70 0 7300 10.70 0 5600
HO
2
� 3.51 2.6 13900 3.51 2.6 12400 4.20 2.6 10900
�CHO 6.56 1.9 17000 8.76 1.3 15500 6.56 1.9 12000
�CH
2
OH 1.30 2.95 12000 1.26 2.95 10000 0.38 2.95 8800
�OCH
3
11.81 0 4000 11.94 0 1200 11.45 0 -400
�OOR 11.81 0 17050 11.70 0 14550 11.70 0 12050
�C
2
H
5
-0.13 3.5 6640 0.34 3.5 4140 0.34 3.5 2340
i-C
3
H
7
� -1.66 4 8060 -1.66 4 7360 -1.65 4 5360
Metathesis of a vinylic H with :
�
O� - - - 10.78 0.7 8960 10.78 0.7 7630
�H - - - 5.61 2.5 12280 5.61 2.5 9790
�OH - - - 6.04 2.0 2780 6.04 2.0 1450
�CH
3
- - - -0.17 3.5 12900 -0.01 3.5 11700
24
Others reactions lg A b E
Addition of an alkyl radical to O
2
See text
Addition of an allyl radical to O
2
10.08 0 -2300
Addition of a vinyl radical to O
2
21.73 -2.5 32500
Beta-scission by broken bond and products
�CH
3
+ molecule 13.30 0 31000
�R
p
+ molecule 13.30 0 28700
Csp
3
�Csp
3
�R
s
+ molecule 13.30 0 27700
�R
t
+ molecule 13.30 0 26700
�Vs + alkene 13.30 0 35500
�Vt + alkene 13.30 0 34500
�R + diene 13.30 0 50000
Csp
3
�Csp
2
�CH
3
+ alkyne 13.30 0 31500
�Rp + alkyne 13.30 0 33000
�Rs + alkyne 13.30 0 31000
�Rt + alkyne 13.30 0 30000
�Hp + alkene or diene 13 0 39000
�Hs + alkene or diene 13.18 0 38000
C�alkyl H �Ht + alkene or diene 13.18 0 37500
�Hp + diene 13 0 51500
�Hs + diene 13.18 0 50500
�Ht + diene 13.18 0 46000
�Hs + diene (alkenyl
rad.)
13.20 0 34800
�Ht + diene (alkenyl
rad.)
13.20 0 34300
C�ally l H �Hp + diene (vinyl
rad.)
13.00 0 40000
�Hs + diene (vinyl
rad.)
13.18 0 38000
�Ht + diene (vinyl
rad.)
13.18 0 35000
�Ht + diene (allyl
rad.)
13.15 0 60000
C�vinyl H �Hs + alkyne (vinyl
rad.)
12.60 0 38000
�Ht + alkyne (vinyl
rad.)
12.60 0 36500
25
Aldehyde/ketone + alkyl
rad.
13.30 0 24000
Alkene + alcoxy rad. 13.30 0 26000
C�O
Hydro-
peroxy-
alkyl o
alkenyl
rad.
Alkene or diene + HO
2
� 12.90 0 26000
Hydro-
peroxy-
allyl rad.
Diene + HO
2
� 12.90 0 33200
Hydro-
peroxy-
vinyl rad
Diene or alkyne+ HO
2
� 12.90 0 28000
O�H Hydroxy-
alkyl rad.
Aldehyde or ketone + �H 13.40 0 29000
Hydro-
peroxy-
alkyl rad.
Aldehyde/ketone + �OH 9.00 0 7500
O�O Hydro-
peroxy-
allyl rad
Insaturated
Aldehyde/ketone + �OH
9.00 0 14700
Hydro-
peroxy-
vinyl rad
Insaturated ketone + �OH 9.00 0 9500
Formation cycle with 3 atoms 11.18 0 16500
of saturated cycle with 4 atoms 10.40 0 15250
cyclic cycle with 5 atoms 9.32 0 6500
ethers cycle with 6 atoms 8.18 0 1800
Form. of cycle with 4 atoms 12.28 0 19100
unsaturated cycle with 5 atoms 11.53 0 8600
cyclic ethers cycle with 6 atoms 10.77 0 7400
Form. of sat. cycle with 4 atoms 11.30 0 19100
cyc. ethers w/ cycle with 5 atoms 10.77 0 8600
unsat. branch cycle with 6 atoms 10 0 7400
�OOR and HO
2
�
disproportionation
11.30 0 -1300
Allyl-radical and HO
2
�
disproportionation
10.40 1 -3460
cyclic R� + HO
2
� RH + O
2
11.30 0 -1300
2 cyc. R� ROH + R�O + O
2
10.15 0 -725
2 cyc. R� 2RO� + O
2
10.80 0 -725
Radical isomerisation KINGAS (Bloch-Michel, 1995)
Molecular Reactions of alkenes
C
2
H
4
+ alkene 3.51 2.2 34100
CH
2
=C(R1)(R2) + alkene 2.11 2.5 36700
C(R1)(R2)=C(R3)(R4) + alkene 3.23 2.1 36000
Unimolecular inititiation and combination KINGAS (Bloch-Michel, 1995)
26
2) Changes made in EXGAS in order to improve the modelling of autoignition delay times
Simulations using the previously presented set of kinetic parameters (Warth et al.,
1998, Glaude et al., 1997, 1998) were performed and showed an overprediction of
autoignition delay times in shock tube and rapid compression machine for alkanes and large
alkenes. Sensitivity analyses, flow rate analyses and other tests have allowed us to propose
improvements of the estimation of kinetic and thermochemical parameters for some reactions
and species. In the case of alkenes autoignition, other modifications had to be implemented to
the software in order to better reproduce experimental results.
a) General changes in the mechanism generation
New activation energy for the isomerization of hydroperoxy radicals
We already described how kinetic data were calculated for the internal isomerizations.
EXGAS estimates activation energies for isomerization processes by summing the energy
needed to break the hydrogen atom bond and the ring strain of the transition state :
E = E
H
+ E
ring
In the case of hydroperoxy radicals where the ring contains 2 oxygen atoms, energy
values come from isomerization rate measurement published by the teams of R.W. Walker
and M.J. Pilling (Baldwin et al., 1986, Walker et al., 1997). We have already summed up
these data in Table 4. Different tests made us change the ring strain energy of 6-atoms rings
containing two oxygen atoms from 8.5 kcal/mol to 8 kcal/mol.
New rate parameters for the formation of cycloethers
The formation of cycloethers competes directly with the second addition of oxygen
which leads ultimately to the formation of hydroperoxides, and has then an inhibiting effect
on the global reactivity. The rate constants of these reactions are thus also very sensitive
parameters, but no direct measurements are available and the parameters used relies only on
estimations.
Hydroperoxyalkyl radicals ( QOOH) and dihydroperoxyalkyl radicals ( U(OOH)
2
)
can decompose to o-rings (cyclic ethers) and OH radicals. The rate constants proposed by
Curran et al. (1998) and based on the experimental data from Baldwin et al. (1986) and Cox
et al. (1985) have been chosen, as they allow us to obtain better results than our previous
estimations.
New data (A-E) Previous data (A-E)
(Heyberger, 2002)
Cycle with 3 atoms 1.5 10
11
�16500 1.0 10
12
�16500
Cycle with 4 atoms 2.5 10
10
�15250 2.0 10
11
�15500
Cycle with 5 atoms 2.1 10
9
� 6500 6.0 10
10
� 9000
Cycle with 6 atoms 1.5 10
8
�1800 1.0 10
10
� 6000
Table 5 : Rate constants for the decomposition to cyclic ethers (units : mol, s, cal, K)
27
New rate parameters for the addition of branched alkyl radical to an oxygen molecule
Alkyl radicals addition to oxygen are for example :
R + O
2
= RO
2
This type of reaction is of great importance at low temperature where peroxy radicals
production noticeably increases the reactivity, because it directly competes with the oxidation
involving the formation of alkenes and the very unreactive �OOH radicals.
The rate constant of the reverse reaction is computed using the thermodynamic
properties of the reaction.
For compounds with less than 6 atoms of carbon, the rate constant previously used for
the direct reaction was an average value of those found in the literature :
k = 2.2 10
19
T
-2.5
cm
3
mol
-1
s
-1
This value leads to good results in case of a linear chain and for small branched ones,
such as neopentyl, alkyl radicals, but not in case of larger branched alkyl radicals. For both
linear and branched alkyl radicals, we now use an additivity method (similar to Benson, 1976)
to take into account the structure of each considered radical more closely:
k = n
p
k
p
+ n
s
k
s
+ n
t
k
t
+ n
q
k
q
where :
n
p
= number of primary groups (CH
3
) linked to the carbon with the radical
point
n
s
= number of secondary groups (CH
2
) linked to the carbon with the radical
point
n
t
= number of tertiary groups (CH) linked to the carbon with the radical point
n
q
= number of quaternary groups (C) linked to the carbon with the radical
point
and :
k
p
= 9.0 10
18
T
-2.5
cm
3
mol
-1
s
-1
k
s
= 1.1 10
19
T
-2.5
cm
3
mol
-1
s
-1
k
t
= 0.9 10
18
T
-2.5
cm
3
mol
-1
s
-1
k
q
= 0.1 10
18
T
-2.5
cm
3
mol
-1
s
-1
It is worth noting that the obtained values for linear alkyl radicals are close to those
previously used, while most of them are much lower for branched radicals, such as iso-octyl
radicals, as shown in table 6, which presents an example of use of the proposed additivity
method.
28
Considered radical k
add
k = k
t
= 0.9.10
18
.T
-2.5
cm
3
.mol
-1
.s
-1
k = k
s
+ 2k
p
= 2.9.10
19
.T
-2.5
cm
3
.mol
-1
.s
-1
k = k
t
+ k
q
= 1.0.10
18
.T
-2.5
cm
3
.mol
-1
.s
-1
k = k
q
= 0.1.10
18
.T
-2.5
cm
3
.mol
-1
.s
-1
Table 6 : Kinetic parameters for the addition of iso-octyl radicals to an
oxygen molecule.
New rate parameters for the decomposition of hydroperoxides molecules (secondary
mechanism)
EXGAS takes into account the consumption in the secondary mechanism of the
peroxydes, which can easily decompose by breaking an O-OH bond and induce an increase of
the amounts of �OH radicals, which ensure the propagation of the reaction. At first, EXGAS
used for all these reactions the rate constant of bond breaking calculated by the Benson
methods (Benson, 1976), that is to say a pre-exponential factor of 7 x 10
14
and an activation
energy of 42000 cal/mol. We now use the experimental value measured by Sahetchian et al.
(1992) for radicals deriving from heptane :
k = 1.5 x 10
16
exp (-42000 / RT) s
-1
New method of evaluation of thermochemical properties of branched compounds in the
software THERGAS
Thermochemical properties play an important role in the overall reactivity of the
system, as in the case of the addition of a radical to an oxygen molecule of which the great
influence has already been highlighted, the rate of the reverse reaction is computed through
those values.
In previous versions of THERGAS, thermochemical properties of branched
compounds were calculated using gauche corrections suggested by Benson (1976). These
corrections are necessary to describe steric effects. Sensitivity analyses, flow rate analyses
and other tests made us finally choose the method of methyl-groups corrections used by
Domalski and Hearing (1993). These authors have updated Benson databases with new
molecules, and replaced the gauche corrections used by Benson by methyl-groups correction
that systematically add a correction for each methyl groups depending on whether they are
linked to tertiary or quaternary carbons.
For instance, the estimation of thermodynamic properties of 2-methyl-butane need to
take into account 2 methyl-groups linked to a tertiary carbon correction :
CH
3
CH C
H
2
CH
3
CH
3
29
b) Specific improvements to model the autoignition of large alkenes (containing more than 4
atoms of carbon)
We present here only the generic reactions or kinetic parameters, which have been
modified compared to what was previously described to model the oxidation of propene
(Heyberger et al., 2001) and butene (Heyberger et al., 2002).
Retro-ene reactions
Alkenes larger than propene and butene can decompose via a retro-ene mechanism
with a pre-exponential factor of 4.10
12
s
-1
and an activation energy of 236 kJ/mol based on the
results of Richard et al. (1978). A retro-ene reaction is a 1,5-hydrogen shift reaction concerted
with dissociation. In the case of 1-hexene, it leads to two propene molecules :
H
�
+
Propene and ethylene are obtained from 1-pentene.
Reactions of resonance stabilized radicals
Generic reactions have been considered for the two possible forms of every resonance
stabilized radical. For instance, the addition to oxygen of the ethylallyl radicals can lead to
two different peroxy radicals :
+ O
2
OO
OO
�
�
�
Isomerizations
The activation energy is set equal to the sum of the activation energy for H-abstraction
from the substrate by analogous radicals and the strain energy of the saturated or unsaturated
cyclic transition state. The activation energy of the abstraction of a hydrogen atom is
considered 8.4 kJ/mol lower for an atom of carbon linked to an atom of oxygen than for an
atom of carbon linked to an H or C atom. The activation energy for the abstraction of a
hydrogen atom by allylic radicals is considered 41 kJ/mol higher than by alkyl radicals. Strain
energies of the cyclic transition states containing two oxygen atoms and a double bond were
taken equal to 63 kJ/mol (for a five membered ring), 41 kJ/mol (for a six membered ring),
4 kJ/mol (for a seven membered ring) and 0 kJ/mol (for a eight membered ring). These strain
energies were deduced from the values proposed for saturated cyclic transition states
containing two oxygen atoms (Glaude et al., 2002) and from the differences of ring correction
between saturated and unsaturated cycles proposed by Benson (1976).
30
Decompositions to give cyclic ethers
The application to the case of alkenes of the generic reaction of formation of cyclic
ethers, which is usually considered in alkanes oxidation mechanisms, leads to the formation of
cyclic ethers bearing an alcohol function or an unsaturated chain or including a double bond
in the ring, as shown in the example below :
OOH
O
+
�
OH
�
We consider the formations of these ethers with rate parameters adapted to take into
account the differences with the cyclic ethers formed during the oxidation of alkanes. The rate
constants for the formation of saturated cycles are those presented previously (Warth et al.,
1998, Battin-Leclerc et al., 2000, Glaude et al., 2002). A-factors for the formation of
unsaturated cycles were estimated from those of saturated cycles by considering that an
unsaturated free radical contains one internal rotation less than the corresponding saturated
radical and can then lose one rotation less to give the transition state. Activation energies were
estimated from the differences of enthalpies of formation between cycloalkanes and
cycloalkenes (Benson, 1976). While in the case of propene, only one unsaturated four
membered ring can be formed (with an activation energy of 80 kJ/mol), unsaturated five
membered ring (with an activation energy of 25 kJ/mol) and six membered ring (with an
activation energy of 13 kJ/mol) can be obtained for longer alkenes.
Oxidations involving the abstraction of an allylic hydrogen atom
An example of this reaction is :
�
H
+ O
2
+ HO
2�
In our previous study (Heyberger et al., 2002), the rate parameters for this type of
reaction, which was not possible in the case of propene, were deduced from those of alkylic
H-atoms (A equal to 2.3 x10
11
cm
3
.mol
-1
.s
-1
for the abstraction of a primary H-atom, A equal
to 7.9 x10
11
cm
3
.mol
-1
.s
-1
for the abstraction of a secondary H-atom, E
a
equal to 20 kJ/mol
(Warth et al., 1998)) with an activation energy 10 kJ/mol lower. But, this estimation omitted
the fact that the formation of the conjugated diene from a non resonance stabilized radical
involved a loss of an additional free rotation compared to the formation of an alkene from an
alkyl radical. To take into account this effect, an A-factor divided by 6, compared to that of
alkyl radicals (Warth et al., 1998) is now proposed for this generic reaction. This change has
only a limited influence on our previous results of the oxidation of 1-butene at high
temperature.
Oxidations involving the abstraction of a hydrogen atom next to an allylic radical center
An example of this reaction is :
2
2
This type of reaction was also not possible in the case of propene and of low
importance in the case of the oxidation of 1-butene at high temperature. In our previous study
(Heyberger et al., 2001), the rate parameters used for this generic reaction were deduced from
31
those used for alkyl radicals (i.e. A equal to 2.3 x10
11
cm
3
.mol
-1
.s
-1
for the abstraction of a
primary H-atom, A equal to 7.9 x10
11
cm
3
.mol
-1
.s
-1
for the abstraction of a secondary H-atom,
E equal to 41 kJ/mol) to agree with a rate constant proposed by Baldwin and Walker (1980)
for the formation of 1,3-pentadiene from ethylallyl radicals. Experimental data measured by
Baldwin and Walker (1980) at 753 K were reconsidered using the more recent work of Perrin
et al. (1988), so that a new value of the activation energy of this type of reaction has been
obtained (i.e. 65 kJ/mol).
Oxidations involving the abstraction of a hydroxylic hydrogen atom
An example of this reaction is :
2
2
The formation of carbon atoms bearing a hydroxylic function and a radical center are
more frequent in the case of long chain alkenes than for propene and butene. We have then
added this new generic reaction. Moyoshi et al. (1990) have measured the rate constant of this
reaction at room temperature for several hydroxyalkyl radicals. These results show that the
rate constant is around 10 time higher than that of the oxidation of a non-substituted alkyl
radical for the formation of an aldehyde, while the rate constant is similar to that of the
oxidation of a non-substituted alkyl radical for the formation of a ketone. According to the
rate parameters used for the oxidation of non-substituted alkyl radical (Warth et al., 1998), an
activation energy of 20 kJ/mol and pre-exponential factor of 7.9 x10
12
cm
3
.mol
-1
.s
-1
for the
formation of aldehydes and of 7.9 x10
11
cm
3
.mol
-1
.s
-1
for the formation of ketones have been
used.
Cyclizations of alkenyl radicals
In the case of long chain alkenes, the possible cyclisation of alkenyl radicals, as shown
in the following example, needs to be taken into account.
An A-factor of 1.4x10
11
s
-1
and an activation energy of E
a
= 68 kJ.mol
-1
have been
taken from Gierczak et al. (1986).
32
III. Comparison between simulations and experiments for
alkanes
In this part are gathered the comparisons between our simulations, including the last
changes done in EXGAS, and the experimental results, for a wide set of alkanes and
conditions of temperature and pressure.
Throughout all our report, full lines represent the simulated ignition delay times and
broken lines the simulated cold flame delay. Black points are experimental ignition delay
times and white points are experimental cool flame delay times.
1) N-butane autoignition
a) Rapid compression machine
Carlier et al. (1994) have measured ignition delay times for stoichiometric mixtures
(n-butane/oxygen/nitrogen/argon = 0.0313/0.2034/0.7653) in a rapid compression machine.
Figure 6 shows the comparison between their experimental measurements and our
simulations.
300
250
200
150
100
50
0
900850800750700
Tc (K)
New mechanism
Previous mechanism
Figure 6 : Ignition delay times versus temperature for n-butane / air mixtures in a rapid
compression machine (Carlier et al., 1994). Stoichiometric mixtures with 3.13 % of
n-butane. Pressure ranges from 8.91 bar to 11.44 bar for a load of 179.5 mol/m
3
. Initial
pressure is 400 Torr.
Whereas the simulations do not fully match experimental measurements, the general
shape of our results is good. Besides, the last changes implemented in EXGAS, especially the
one concerning the isomerization through a 6-atoms ring (which is the main isomerization in
the case of n-butane), allowed us to noticeably improve the quality of our calculations
compared to what was obtained before these changes. This can be seen in figure 6 : the
simulations performed with a mechanism generated before the changes strongly overestimates
ignition delay times, while the agreement in strongly improved with a new mechanism .
33
b) Shock tube
Measurements have been done here at the D.C.P.R. to determine ignition delay times
for stoichiometric mixtures n-butane/oxygen/argon (0.02/0.13/0.85) in a shock tube. These
results have not been published yet. Figure 7 shows the comparison between our simulations
and experimental ignition delay times.
1
2
3
4
5
6
7
10
2
3
4
5
6
7
100
2
3
4
5
6
7
1000
0.820.800.780.760.740.72
1000/T (K)
Figure 7 : Ignition delay times versus temperature for stoichiometric
n-butane/oxygen/argon.
These results show that the simulation overpredicts the ignition delay times. That can
be due to the fact that EXGAS do not consider the fall-off effect for unimolecular
decompositions, which can be of importance at high temperature.
2) N-pentane autoignition
a) Rapid compression machine
Minetti et al. (1996a) have measured ignition delay times for
n-pentane/oxygen/nitrogen/argon stoichiometric mixtures with an initial pressure of 300 Torr
or 400 Torr. Figure 8 and 9 show the simulations obtained with a generated mechanism,
compared to the experimental values.
34
140
120
100
80
60
40
20
0
900850800750700650600
Tc (K)
Figure 8 : Ignition delay times versus temperature for n-pentane / air mixtures in a
rapid compression machine (Minetti et al., 1996a). Stoichiometric mixtures with
pressure ranging from 6.00 bar to 10.00 bar for a load of 138.5 mol/m
3
. Initial pressure
is 300 Torr.
80
60
40
20
0
900850800750700650
Tc (K)
Figure 9 : Ignition delay times versus temperature for n-pentane / air mixtures in a
rapid compression machine (Minetti et al., 1996a). Stoichiometric mixtures with
pressure ranging from 8.00 bar to 11.00 bar for a load of 179.5 mol/m
3
. Initial pressure
is 400 Torr.
For this linear alkane, the agreement between our computed autoignition delay times
and the experimental values is good.
3) Iso-pentane autoignition
a) Rapid compression machine
Minetti et al. (1996a) have measured ignition delay times for
iso-pentane/oxygen/nitrogen/argon stoichiometric mixtures with an initial pressure of 400
Torr. Figure 10 compares experimental data and simulation results.
35
100
50
0
950700
Tc (K)
Figure 11 : Ignition delay times versus temperature for
neo-pentane/oxygen/nitrogen/argon mixtures in a rapid compression machine (Minetti et
al., 1996a). Pressure ranges from 4 bar to 6 bar for an initial pressure of 200 Torr.
60
40
20
0
900850750700650
Tc (K)
Figure 13: Ignition delay times versus temperature for
neo-pentane/oxygen/nitrogen/argon mixtures in a rapid compression machine (Minetti et
al., 1996a). Pressure ranges from 8 bar to 11 bar for an initial pressure of 400 Torr.
Except for an initial pressure of 200 Torr for which the agreement deteriorates at low
temperatures, the simulations reproduce globally well the experimental results. We saw a
great improvement of our results with the last modifications implemented in EXGAS, as for
isopentane.
5) 2-methylpentane autoignition
a) Rapid compression machine
Griffiths et al. (1997) have measured ignition delay times for
2-methylpentane/oxygen/nitrogen/argon stoichiometric mixtures in a rapid compression
machine with an initial pressure of 300 Torr. Figure 14 compares experimental data to our
simulation results.
38
200
150
100
50
0
900850800750700650
Tc (K)
Figure 14 : Ignition delay times versus temperature for
2-methylpentane/oxygen/nitrogen/argon mixtures in a rapid compression machine
(Griffiths et al., 1997). Pressure ranges from 6 bar to 10 bar for an initial pressure of
300 Torr and a load of 131 mol/m
3
.
Globally there is a good agreement between our calculations and the measurements
performed by Griffiths et al. This also shows the effect of the changes on thermochemical
properties calculations and of the new values of rate constants for the addition to oxygen.
b) Shock tube
Burcat et al. (1999) have measured ignition delay times for
2-methylpentane/oxygen/argon mixtures in a shock tube, for temperatures between 1300 and
1600 K, pressures between 2 and 4 atm and different equivalent ratios. The results of our
simulations are gathered in table 7 and compared to experimental values.
39
Experimental conditions tig ( s)
2MP % O
2
% Equivalent
ratio
P (atm) T (K) Exp. Simulation
2.820 1309 391 728
3.760 1430 163 127
1.00 9.50 1.00
3.220 1582 47 28
3.850 1231 462 649
4.069 1313 263 200
1.00 19.30 0.49
3.472 1510 29 19
3.360 1478 263 279
3.320 1613 78 76
1.00 4.75 2.00
3.540 1729 42 29
3.720 1386 127 147
4.000 1508 53 32
0.50 9.50 0.50
3.770 1651 17 9
3.720 1355 405 538
3.378 1438 154 226
2.00 9.50 2.00
3.810 1482 158 132
3.762 1361 297 3651.00 8.50 1.12
3.842 1591 45 28
Table 7 : Ignition delay times for 2-methylpentane/oxygen/argon mixtures in a
shock tube (Burcat et al., 1999)
Considering the fact that only 3 points per series are not sufficient to draw any
conclusion we see that our simulations reproduce in a reasonably satisfactory manner the few
experimental data available.
6) N-heptane oxidation
a) Shock tube
Ciezki and Adomeit (1993) have measured ignition delay times for
n-heptane/oxygen/nitrogen mixtures in a shock tube for temperatures between 660 and
1350 K, pressures between 3 and 42 atm. Figure 15, 16 and 17 are for equivalent ratios of 0.5,
1.0, and 2.0 and presents the results of our simulations compared to the experimental data.
40
0.1
1
10
100
1.61.41.21.00.8
1000/T (K)
Figure 15 : Ignition delay times versus temperature for n-heptane/air mixtures in a
shock tube (Ciezki and Adomeit, 1993) at 13.5 bar, for an equivalent ratio of 0.5.
0.1
2
3
4
5
6
7
1
2
3
4
5
6
7
10
2
3
4
5
6
7
100
1.61.41.21.00.8
1000/T (K)
Figure 16 : Ignition delay times versus temperature for n-heptane/air mixtures in a
shock tube (Ciezki and Adomeit, 1993) at 13.5 bar, for an equivalent ratio of 1.0.
41
6
7
1
2
3
4
5
6
7
10
4
5
6
7
100
1.61.41.21.00.8
1000/T (K)
Vermeer et al. (1972) have measured ignition delay times for n-heptane/oxygen/argon
mixtures in a shock tube for temperatures between 1200 and 1600 K and a pressure of 2 bar.
Results are presented in figure 19.
0.001
0.01
0.1
1
10
0.780.760.740.720.700.680.660.64
1000/T (K)
Figure 19 : Ignition delay times versus temperature for stoichiometric
n-heptane/oxygen/argon mixtures in a shock tube (Vermeer et al., 1972) at 2 bar, and an
equivalent ratio of 1.0 .
In this simulation in a shock tube at higher temperature, we also reproduce correctly
experimental results.
b) Rapid compression machine
Minetti et al. (1995) have measured ignition delay times for
n-heptane/oxygen/nitrogen/argon mixtures in a rapid compression machine for temperatures
between 600 and 900 K and for initial pressures of 130, 162 and 313 Torr. Results of our
simulations are presented in Figure 20, 21 and 22, and compared to experimental data.
160
140
120
7) Iso-octane autoignition
a) Shock tube
Fieweger et al. (1997) have measured ignition delay times for
iso-octane/oxygen/nitrogen mixtures in a shock tube for temperatures between 660 and 1350
K, and a pressure of 40 atm. The comparison between experimental results and simulations is
presented in Figure 23.
8
0.1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
10
2
3
4
5
1.51.41.31.21.11.00.90.8
1000/T (K)
Figure 23 : Ignition delay times versus temperature for iso-octane/air mixtures in a
shock tube (Fieweger et al., 1997) at 40 bar, and an equivalent ratio of 1.0.
In this case, we need to improve our simulations to better reproduce the experiments,
especially at high temperature. Changes on the thermochemical properties of branched
compounds and on the addition of branched radicals to the oxygen molecule do apply here,
but as the addition to oxygen is mostly influential at low temperature, these changes did not
improve the results in the highest temperature zone.
Vermeer et al. (1972) have measured ignition delay times for iso-
octane/oxygen/nitrogen mixtures in a shock tube for temperatures between 1200 and 1800 K,
and a pressure of 2.1 bar. The comparison between experimental results and simulations is
presented in Figure 24.
45
1
2
3
4
5
6
7
8
10
2
3
4
5
6
7
8
100
2
3
4
5
6
7
0.800.750.700.650.600.55
1000/T (K)
Figure 24 : Ignition delay times versus temperature for iso-octane/oxygen/argon (2.2 /
27.8 / 70) mixtures in a shock tube (Vermeer et al., 1972) at 2.1 bar, and an equivalent
ratio of 1.0 .
Our simulation are quite satisfactory in this case, except again at very high
temperature (above 1800 K).
Davidson et al. (2002) have measured ignition delay times for
iso-octane/oxygen/nitrogen mixtures in a shock tube for temperatures between 1200 and
1800 K, and a pressure of 1.3 bar. The comparison between experimental results and
simulations is presented in Figure 25.
4
5
6
7
8
9
100
2
3
4
5
6
7
8
9
1000
2
3
4
0.750.700.650.60
1000/T (K)
Figure 25 : Ignition delay times versus temperature for iso-octane/oxygen/nitrogen (0.5 /
6.25) mixtures in a shock tube (Davidson et al., 2002) at 1.3 bar, and an equivalent ratio
of 1.0 .
These results show a correct agreement between experiments and simulation, although
the computed ignition delay times are slightly too low on the whole temperature range.
46
b) Rapid compression machine
Minetti et al. (1996b) have measured ignition delay times for
iso-octane/oxygen/nitrogen/argon mixtures in a rapid compression machine for temperatures
between 600 and 900 K, and for initial pressures of 500 and 600 Torr. Figure 26 and 27 show
the results of the simulations compared to the experiments.
160
140
120
100
80
60
40
20
0
900850800750700650
Tc (K)
Figure 26 : Ignition delay times versus temperature for
iso-octane/oxygen/nitrogen/argon stoichiometric mixtures in a rapid compression
machine (Minetti et al., 1996). Pressure ranges from 11 bar to 14.5 bar for an initial
pressure of 500 Torr and a load of 221 mol/m
3
.
80
60
40
20
0
850800750700
Tc (K)
Figure 27 : Ignition delay times versus temperature for
iso-octane/oxygen/nitrogen/argon stoichiometric mixtures in a rapid compression
machine (Minetti et al., 1996). Pressure ranges from 13 bar to 16.1 bar for an initial
pressure of 600 Torr and a load of 265 mol/m
3
.
47
The simulations permit to reproduce rather correctly the experiments, although
computed autoignition delay times still do not fully match the experimental values. In the
tested temperature range where addition to oxygen is important, we saw a great improvement
of our results with the mechanisms generated by the new version of EXGAS.
8) N-decane autoignition
a) Shock tube
Pfahl et al. (1996) have measured ignition delay times for n-decane/oxygen/nitrogen
mixtures in a shock tube for temperatures between 660 and 1350 K and pressures of 12 and 50
bar. Experiments and simulations are presented in Figure 28.
0.01
0.1
1
10
100
1.41.21.00.8
1000/T (K)
P = 50 bar
P = 12 bar
Figure 28 : Ignition delay times versus temperature for n-decane/air mixtures in a shock
tube (Bikas and Peter, 2001) at 12 and 50 bar, and an equivalent ratio of 1.0 .
These results show that even at very different pressures (12 and 50 bars), our
automatically generated mechanism is able to simulate the autoignition of n-decane in shock
tube in a satisfactory way.
48
IV. Comparison between simulations and experiments for
alkenes
1) Modelling of the oxidation of propene in a static reactor at low temperature
Wilk et al. (1987, 1989) studied the oxidation of propene in a static reactor at 580 to
740 K, equivalence ratios ( ) equal to 0.8 and to 2.0 and a pressure of 79 kPa. Figure 29
displays the consumption of propene at 626, 678 and 715 K, for an equivalence ratio of 0.8.
4
Experiments Simulation
Primary products
1,3-Pentadiene
3.9 7.0
2-Propyloxirane
2.7 1.5
2,4-Dimethyl-oxetane
0.4 0.1
2-Methyl-tetrahydrofurane
0.2 0.4
Cyclic ethers with an
alcohol function
- 4.2
Unsaturated cyclic ethers - 20.2
Cyclopentene
0.4
a
0.4
Secondary products
1,3-Butadiene
3.9 3.0
2-butenal
0.8
a
3.3
Acroleïne
13.0 8.5
Butanal
7.4 2.1
Propanal
0.8 0.3
Ethanal
29.6 22.2
Formaldehyde
- 36.1
Ethylene
25.2
a
17.7
Carbon monoxide
64.1
a
23.5
a
: unpublished results
Table 8 : Experimental and computed selectivity of products for the oxidation of
1-pentene in a rapid compression machine (% molar), at T = 733 K, P = 6.9 bar for
20 % conversion of 1-pentene in the conditions of fig. 3.
Figure 30 shows that a correct agreement is obtained both for cool flame and
autoignition delay times.
The model reproduces also the major trends of the distribution of products, even if
discrepancies up to a factor 4 can be observed, certainly due to the important gradients of
temperature, which are observed inside the combustion chamber of a rapid compression
machine. Nevertheless, it is worth noting that the presence of unsaturated ethers or of ethers
bearing an alcohol function is predicted by the model, but not shown in the present
experimental analyses. While the selectivity of carbon monoxide is underpredicted by the
model, simulations shows that formaldehyde is an important product, which has not been
analyzed here.
51
3) Modelling of the autoignition of 1-hexene in a rapid compression machine
Vanhove et al. (2003) have measured autoignition delay times in a rapid compression
for mixtures 1-hexene/oxygen/argon/nitrogen/carbon dioxide at temperatures after
compression from 615 to 850 K, pressures from 6.8 to 10.9 bar and a fuel equivalence ratio
of 1.
Figure 31 shows that a correct agreement between modelling and experiments is
obtained for autoignition delay times. Simulations reproduce well the fact that 1-hexene is
more reactive than 1-pentene, as indicated by the difference in octane numbers.
400
300
200
100
0
900850800750700650600
Figure 31 : Ignition delay times versus temperature of the 1-hexene
/oxygen/nitrogen/argon stoichiometric mixtures in a rapid compression machine
(Vanhove et al., 2003). Pressure ranges from 6.8 bar to 10.9 bar.
It is worth noting that preliminary products analyses have indicated the formation of
ethers bearing an unsaturated chain, such 2-vinyl-tetrahydrofurane or including a double bond
in the ring, such as 2-ethyl-2,5-dihydrofurane, which are predicted by our mechanism.
52
Conclusion
After a brief literature review of the experiments published on autoignition of alkanes
and alkenes, this report describes our system of computer aided design of a kinetic model of
oxidation and combustion of hydrocarbons and the changes that were needed in order to
reproduce measured autoignition delay times. Our system is then validated for a wide range of
compounds on experimental results taken from the literature, as shown in table 9.
Compound Experimenal
setup
Temperature
range (K)
Pressure range
(bar)
Equivalence
ratio
n-butane RCM, ST 700-1350 8-11,5 1
n-pentane RCM 600-900 6-11 1
iso-pentane RCM 680-900 8-11 1
neo-pentane RCM 680-950 4-11 1
2-methyl-pentane RCM, ST 700-1722 2-9 0.49-2
n-heptane RCM, ST 600-1350 3,2-42 0.5-2
iso-octane RCM, ST 600-1800 1,3-45 1
n-decane ST 660-1350 12-50 1
1-pentene RCM 600-900 6-9 1
1-hexene RCM 615-850 8,5-10 1
Table 9 : Validations of our system EXGAS
It is worth noting that, for both families of compounds, the changes in the generation
of mechanism which were performed during this project have allowed us to noticeably
improve our modelling of autoignition delay times, especially at low temperature.
53
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