Report on ongoing progress of C 4 -C 10 model development :

Transcription

1 SAFEKINEX SAFe and Efficient hydrocarbon oxidation processes by KINetics and Explosion expertise and development of computational process engineering tools Project No. EVG1-CT 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

2 Table of contents PRELIMINARY DEFINITIONS... 4 INTRODUCTION I. STATE OF THE ART FOR THE EXPERIMENTAL INVESTIGATION OF AUTOIGNITION OF ALKANES AND ALKENES (C 4 TO C 10 ) ) GENERALITIES ABOUT AUTOIGNITION ) 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 ) GENERAL FEATURES OF EXGAS A) COMPREHENSIVE PRIMARY MECHANISM B) C 0 -C 2 REACTION BASE C) SECONDARYMECHANISM D) THERMOCHEMICAL AND KINETIC DATA FOR THE OXIDATION OF ALKANES AND ALKENES ) CHANGES MADE IN EXGAS IN ORDER TO IMPROVE THE MODELLING OF AUTOIGNITION DELAY TIMES A) GENERAL CHANGES IN THE MECHANISM GENERATION B) SPECIFIC IMPROVEMENTS TO MODEL THE AUTOIGNITION OF LARGE ALKENES (CONTAINING MORE THAN 4 ATOMS OF CARBON) III. COMPARISON BETWEEN SIMULATIONS AND EXPERIMENTS FOR ALKANES.33 1) N-BUTANE AUTOIGNITION A) RAPID COMPRESSION MACHINE B) SHOCK TUBE ) N-PENTANE AUTOIGNITION A) RAPID COMPRESSION MACHINE ) ISO-PENTANE AUTOIGNITION A) RAPID COMPRESSION MACHINE ) NEO-PENTANE AUTOIGNITION A)RAPID COMPRESSION MACHINE ) 2-METHYLPENTANE AUTOIGNITION A) RAPID COMPRESSION MACHINE B) SHOCK TUBE ) N-HEPTANE OXIDATION A) SHOCK TUBE B) RAPID COMPRESSION MACHINE ) ISO-OCTANE AUTOIGNITION A) SHOCK TUBE

3 B) RAPID COMPRESSION MACHINE ) N-DECANE AUTOIGNITION A) SHOCK TUBE IV. COMPARISON BETWEEN SIMULATIONS AND EXPERIMENTS FOR ALKENES..49 1) MODELLING OF THE OXIDATION OF PROPENE IN A STATIC REACTOR ) MODELLING OF THE AUTOIGNITION OF 1-PENTENE IN A RAPID COMPRESSION MACHINE ) MODELLING OF THE AUTOIGNITION OF 1-HEXENE IN A RAPID COMPRESSION MACHINE CONCLUSION REFERENCES

4 Preliminary definitions Throughout this report, carbon atoms are defined as followed : Name of the atom Number of hydrogen atoms linked to the carbon atom Primary, noted C I Primary, noted C II Primary, noted C III Primary, noted C IV Representation R 1 CH 3 R 1 CH 2 R 2 R 1 H C R3 R 4 R 2 R 1 C R 3 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 R 2 We call allylic every hydrogen atom which is linked to a carbon atom in from a double bond. position Vinylic hydrogen atom We call vinylic every hydrogen atom which is linked to a carbon atom taking part in a double bond. Alkylic primary hydrogen atom Vinylic tertiary hydrogen atom CH Vinylic secondary hydrogen atom Allylic secondary hydrogen atom 4

5 Introduction The development of detailed and well-validated kinetic models to reproduce combustion behaviour of hydrocarbons and to predict autoignition 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 computerbased 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., 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

6 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

7 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 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 , 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

8 Tc T0 dt 1T ln P1 P 0, (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 K at compressed gas pressures of 10 bar. A negative temperature coefficient (NTC) of the ignition delay is exhibitedbetween 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 P X (O 2 ) n 0.5 exp ( /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 K. 8

9 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 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

10 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 P X (O 2 ) n 0.5 exp ( /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 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 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 P X (O 2 ) n 0.5 exp ( /T) was determined. Alkenes Autoignition delay times measurements were performed for 1-butene, iso-butene, 1-pentene, and 1-hexene. 10

11 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

12 Table 1 : Summary of experimental results recently published ( ), 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 n-butane n-pentane iso-pentane neo-pentane 2-methyl-pentane n-hexane Type of reactor RCM ST RCM Temperature Range (K) Pressure Range (bar) Equivalence ratio range Reference Carlieret al., Horninget al., 2001, Davidson et al., Minetti et al.,1996a Griffiths et al., 1993, Ribaucouret al., Westbrook et al., Ribaucour et al., 2000 RCM Minetti et al.,1996a Minetti et al.,1996a RCM Griffiths et al., Ribaucour et al., 2000 RCM Griffiths et al., 1997 ST Burcat et al.,1999 RCM ST Griffithset al., 1993 Burcatet al., Griffiths et al., ,4-dimethyl-pentane RCM Silke et al.,

13 Griffiths et al., ,3-dimethyl-pentane RCM Silke et al., 2,2-dimethyl-pentane 2,3-dimethylpentane 3-ethyl-pentane 2-methyl-hexane 3-methyl-hexane 2,2,3-trimethylbutane n-heptane RCM Griffiths et al., 1997, Westbrook et al., Silke et al., 2003 RCM Silke et al., 2003 RCM Silke et al., 2003 RCM RCM RCM RCM ST Griffiths et al., 1997, Westbrook et al., Silke et al., Silke et al., Silke et al., Minetti et al., Griffiths et al., 1993, Silke et al., Ciezki et al., Davidson et al., Davidson et al., Horninget al., 2001,

14 Iso-octane n-decane 1-butene Iso-butene 1-pentene 1-hexene RCM ST ST ST ST RCM RCM Minetti et al., 1996b Griffiths et al., Fiewegeret al., Davidsonet al., Pfahlet al., Horninget al., 2001, Davidson et al., Skjoth- Rasmussen et al., Heybergeret al., Curran et al., Baugéet al., Ribaucour et al., Vanhove et al.,

15 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. Free Radicals Lumped Primary Molecules 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 K), OH radicals are mainly formed by degenerate 15

16 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. RH, O2 initiation steps R + H2O2 RH R R (2) O2 OOH + alkene (1) R O2 ROO. + alkene HO2 ROOH+ O2 R+ H2O RH QOOH OH + cyclic ethers, aldehydes or ketones O2 OOQOOH RO + OH degenerate branching steps U(OOH)2 XO + OH degenerate branching steps keto-hydroperoxides + OH 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

17 - 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 OOHCOOHCH 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 enemechanism 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. CH 2 CH H CH 2 CHCH 2 CHCH 3 CH 2 CH 2 CH 3 CH 4-methyl 1-pentene 2 C 3 H 6 CH 3 CH 2 CH H CH 2 CHCH 2 CH 2 CH 2 CH 3 CH 2 CH CH 3 1-hexene CH2 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

18 - 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. H O CH 3 CH CH 2 O O H O O O CH 3 CH CH 2 OH + CH 3 CHO + HCHO 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 isomerizationdecomposition of hydroperoxyalkylperoxy radicals (OOQOOH) to give ketohydroperoxides and OH was considered. CH 2 CH CH 2 O O O O CH 2 CH CH 2 CH 2 O + CH 2 CHO 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

19 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 RH + 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) addition to oxygen (e) R(O@)OOH+O 2 R(O@)(OOH)OO 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

20 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 ONeal : A = e 1 (k B T / h) x rpd x exp ( n i,rot x 3.5 / R ) s -1 20

21 With : k B : Boltzmann constant = 1,38 x J.K -1, h : Planck constant = 6,63 x 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 Energy for R tearing the H atom 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 Ring strain energy for a cycle with 2 oxygen atoms (kcal/mol) Ring strain energy for a cycle with 0 or 1 oxygen atoms (kcal/mol) 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

22 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

23 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. Rp, Rs, Rt 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 allyl vinyl Initiation between two alkenes (abstraction of allylic H atom), type of alkyl radical formed : secondary tertiary quaternary Addition on the double bond with : Secondary C Tertiary C Quaternary C H CH C 2 H 5 (primary) ic 3 H 7 (secondary) tc 4 H 7 (tertiary) OH O C IV =C IV C IV =C III C IV =C II OOH OOCH OOR C III =C III C III =C II OOH OOCH OOR

24 Oxidation Primary H Secondary H Tertiary H Init. Rad. Alkyl Alkylic abstraction H Alkenyl Alkylic abstraction H Allylic abstraction H Allyl Alkylic abstraction H Vinylic abstraction H Metathesis of an alkyl and alkenyle H with : O H OH CH HO CHO CH 2 OH OCH OOR C 2 H i-c 3 H R p R s R t Metathesis of an allylic H with : O H OH CH HO CHO CH 2 OH OCH OOR C 2 H i-c 3 H Metathesis of a vinylic H with : O H OH CH

25 Others reactions lga b E Addition of an alkyl radical to O 2 See text Addition of an allyl radical to O Addition of a vinyl radical to O Beta-scission by broken bond and products CH 3 + molecule R p + molecule Csp 3 Csp 3 R s + molecule R t + molecule Vs + alkene Vt + alkene R + diene Csp 3 Csp 2 CH 3 + alkyne Rp + alkyne Rs + alkyne Rt + alkyne Hp + alkene or diene Hs + alkene or diene Calkyl H Ht + alkene or diene Callyl H Cvinyl H Hp + diene Hs + diene Ht + diene Hs + diene (alkenyl rad.) Ht + diene (alkenyl rad.) Hp + diene (vinyl rad.) Hs + diene (vinyl rad.) Ht + diene (vinyl rad.) Ht + diene (allyl rad.) Hs + alkyne (vinyl rad.) Ht + alkyne (vinyl rad.)

26 CO OH OO Hydro- Aldehyde/ketone + alkyl peroxy- alkyl o rad. alkenyl Alkene + alcoxy rad rad. Alkene or diene + HO Hydroperoxyallyl rad. Hydroperoxyvinyl rad Diene + HO Diene or alkyne+ HO Hydroxyalkyl Aldehyde or ketone + H rad. Hydro- Aldehyde/ketone + OH peroxy- alkyl rad. Hydroperoxyallyl rad Insaturated Aldehyde/ketone + OH Hydro- Insaturated ketone + OH peroxy- vinyl rad Formation cycle with 3 atoms of saturated cycle with 4 atoms cyclic cycle with 5 atoms ethers cycle with 6 atoms Form. of cycle with 4 atoms unsaturated cycle with 5 atoms cyclic ethers cycle with 6 atoms Form. of sat. cycle with 4 atoms cyc. ethers w/ cycle with 5 atoms unsat. branch cycle with 6 atoms OOR and disproportionation HO Allyl-radical and disproportionation HO cyclic R + HO 2 RH + O cyc. R ROH + RO + O cyc. R 2RO + O Radical isomerisation KINGAS (Bloch-Michel, 1995) Molecular Reactions of alkenes C 2 H 4 + alkene CH 2 =C(R1)(R2) + alkene C(R1)(R2)=C(R3)(R4) + alkene Unimolecular inititiation and combination KINGAS (Bloch-Michel, 1995) 26

27 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 Cycle with 4 atoms Cycle with 5 atoms Cycle with 6 atoms Table 5 : Rate constants for the decomposition to cyclic ethers (units : mol, s, cal, K) 27

28 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 = 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 point point and : n s = number of secondary groups (CH 2 ) linked to the carbon with the radical 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 k p = T -2.5 cm 3 mol -1 s -1 k s = T -2.5 cm 3 mol -1 s -1 k t = T -2.5 cm 3 mol -1 s -1 k q = 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