A Comprehensive Modeling Study of iso-Octane Oxidation · 2-methyl pentane, because the two former...

A Comprehensive Modeling Study of iso-Octane Oxidation

H. J. CURRAN,*,† P. GAFFURI, W. J. PITZ and C. K. WESTBROOKLawrence Livermore National Laboratory, Livermore, CA 94551, USA

A detailed chemical kinetic mechanism has been developed and used to study the oxidation of iso-octane in ajet-stirred reactor, flow reactors, shock tubes and in a motored engine. Over the series of experimentsinvestigated, the initial pressure ranged from 1 to 45 atm, the temperature from 550 K to 1700 K, theequivalence ratio from 0.3 to 1.5, with nitrogen-argon dilution from 70% to 99%. This range of physicalconditions, together with the measurements of ignition delay time and concentrations, provide a broad-rangingtest of the chemical kinetic mechanism. This mechanism was based on our previous modeling of alkanecombustion and, in particular, on our study of the oxidation of n-heptane. Experimental results of ignitionbehind reflected shock waves were used to develop and validate the predictive capability of the reactionmechanism at both low and high temperatures. Moreover, species’ concentrations from flow reactors and ajet-stirred reactor were used to help complement and refine the low and intermediate temperature portions ofthe reaction mechanism, leading to good predictions of intermediate products in most cases. In addition, asensitivity analysis was performed for each of the combustion environments in an attempt to identify the mostimportant reactions under the relevant conditions of study. © 2002 by The Combustion Institute

INTRODUCTION

There is continued interest in developing abetter understanding of the oxidation of largehydrocarbon fuels over a wide range of operat-ing conditions. Currently, there is a lot of inter-est in using iso-octane as a fuel in investigationsof homogeneous charge compression ignitionengines (HCCI), in which iso-octane is usedboth as a neat fuel and as a component in aprimary reference fuel blend [1–4]. This interestis motivated by the need to improve the effi-ciency and performance of currently operatingcombustors and reduce the production of pol-lutant species emissions generated in the com-bustion process. Iso-octane is a primary refer-ence fuel (PRF) for octane rating in spark-ignition engines, and when used in compressionignition engines, has a cetane number of ap-proximately 15.

Previous experimental studies of iso-octaneoxidation have focused on shock tubes [5–7],jet-stirred reactors [8–11], rapid compressionmachines [12–16], engines [17–19], flow reactors[20–22] and [23], in which a dynamic behaviouris observed. All of these systems exhibit phe-nomena including self ignition, cool flame, andnegative temperature coefficient (NTC) behav-

ior. Furthermore, variation in pressure from 1to 45 bar changes the temperature range overwhich the NTC region occurs.

Come et al. [24, 25] have used an automaticgeneration mechanism package to createchemical kinetic mechanisms for n-heptaneand iso-octane. Ranzi et al. [15] used a semi-detailed model to simulate the oxidation ofPRF mixtures. This mechanism was furtherused to perform a wide range simulation ofiso-octane oxidation [26]. Roberts et al. [27]developed a semi-detailed kinetic mechanismto simulate autoignition experiments in a co-operative fuels research engine. More re-cently, Curran et al. [28] used a detailedchemical kinetic mechanism to simulate theoxidation of PRF mixtures. This mechanismwas also used to simulate flow reactor exper-iments on the lean oxidation of iso-octane inthe intermediate temperature regime at ele-vated pressures [23]. Davis and Law [29] useda semi-detailed chemical kinetic mechanismto predict laminar flame speeds for iso-oc-tane/air and n-heptane air flames.

In this study we include all of the reactionsknown to be pertinent to both low and hightemperature kinetics. We show how the detailedkinetic model reproduces the measured resultsin each type of experiment, including the fea-tures of the NTC region. We discuss the specificclasses of elementary reactions and reactionpathways relevant to the oxidation process, how

* Corresponding author. E-mail: [email protected]†Currently at Galway-Mayo Institute of Technology, DublinRd., Galway, Ireland.

COMBUSTION AND FLAME 129:253–280 (2002)© 2002 by The Combustion Institute 0010-2180/02/$–see front matterPublished by Elsevier Science Inc. PII S0010-2180(01)00373-X

we arrived at the rate constants for each class ofreaction, and indicate which reactions are themost important in consuming the fuel at bothlow and high temperature. In addition, a sensi-tivity analysis was carried out on each set ofexperimental results by changing the rate con-stants for different classes of reaction in thekinetic mechanism. The results of this analysisindicate the relative important of each class ofreaction and also the variation in contributionof these classes of reactions over the range ofconditions of the experiments.

MODEL FORMULATION

Computer modeling of iso-octane oxidation wasperformed using the HCT (Hydrodynamics,Chemistry and Transport) program [30], whichsolves the coupled chemical kinetic and energyequations, and permits the use of a variety ofboundary and initial conditions for reactivesystems depending on the needs of the particu-lar system being examined. The present detailedreaction mechanism was constructed based onthe hierarchical nature of hydrocarbon-oxygensystems. The mechanism was built in a stepwisefashion, starting with small hydrocarbons andprogressing to larger ones. Much of this workhas been documented previously [31–34], andhas been enhanced by our experience in simu-lating propane [35], neopentane [36, 37], thepentane isomers [38], the hexane isomers [39,40], n-heptane [41], and primary reference fuelblends [28, 40].

The current detailed mechanism incorporatesboth low- and high-temperature kinetic schemes.At higher temperatures, unimolecular fuel andalkyl radical species decomposition and isomeriza-tion reactions are especially important, while atlow temperatures H atom abstraction from thefuel molecule and successive additions of alkylradicals to molecular oxygen, leading to chainbranching, dominate the oxidation process.

The low temperature submechanism is basedon our detailed n-heptane chemical kineticmechanism published previously [41]. In theinterim, due to increased accuracy in both ex-perimental and computational methods, thethermodynamic parameters associated with thelow-temperature hydroperoxide species havebeen modified. The thermodynamic properties

for the relevant radicals and stable parents werebased on the group additivity method of Benson[42] using THERM [43, 44] with updatedH/C/O groups and bond dissociation groups[44]. We have updated the H/C/O and bonddissociation group values based on the recentstudies of Lay and Bozzelli [45] and have mod-ified these slightly so that the thermodynamicfunctions of R � O2 º RO2 reactions agreewith the experimental and calculated values ofKnyazev and Slagle [46] for ethyl radical. Thesecomparisons can been found in a paper byCurran et al. [47].

Classes of Reactions

The oxidation mechanism developed for iso-octane is formulated in the same way as thatpublished previously for n-heptane [41]. Themechanism is developed in a systematic way,with each type of reaction in the oxidationprocess treated as a class of reaction with theappropriately assigned rate constant expres-sion. Because of recent changes in thermody-namic data, and in an attempt to improve ourtreatment of some of our estimated rate ex-pressions, some of those expressions pub-lished in our n-heptane paper have beenchanged. We outline these changes in thediscussion below. The complete reactionmechanism for iso-octane oxidation includes3,600 elementary reactions amoung 860 chem-ical species. The mechanism is not presentedhere due to its length, but a complete copycan be obtained from the authors at theLivermore combustion website [48].

The major classes of elementary reactionsconsidered in the present mechanism includethe following:

1. Unimolecular fuel decomposition2. H atom abstraction from the fuel3. Alkyl radical decomposition4. Alkyl radical � O2 to produce olefin � HO2

directly5. Alkyl radical isomerization6. Abstraction reactions from Olefin by oH, H,

O, and CH37. Addition of radical species to olefin8. Alkenyl radical decomposition9. Olefin decomposition

254 H. J. CURRAN ET AL.

10. Addition of alkyl radicals to O211. R � R�O2 � R�O � RO12. Alkyl peroxy radical isomerization (RO2 º

QOOH)13. RO2 � HO2 � RO2H � O214. RO2 � H2O2 � RO2H � HO215. RO2 � CH3O2 � RO � CH3O � O216. RO2 � R�O2 � RO � R�O � O217. RO2H � RO � OH18. RO decomposition19. QOOH � cyclic ether � OH (cyclic ether

formation via cyclisation of diradical)20. QOOH � olefin � HO2 (radical site � to

OOH group)21. QOOH � olefin � carbonyl radical (radical

site � to OOH group)22. Addition of QOOH to O223. Isomerization of O2QOOH and formation

of carbonylhydroperoxide and OH24. Decomposition of carbonylhydroperoxide

to form oxygenated radical species and OH25. Cyclic ether reactions with OH and HO2

The naming conventions used above are R andR� denoting alkyl radicals or structures and Qdenoting CnH2n species or structures. For each ofthese classes of reactions we use the same reactionrate constant for analogous occurrences in differ-ent molecules. Thus, we assume that the abstrac-tion of a tertiary H atom by reaction with OHradicals has exactly the same rate in 2-methylbutane, 2-methyl pentane, 3-methyl pentane, andin iso-octane. Correspondingly, the total rate oftertiary H atom abstraction by OH in 2,3-dimethylbutane and in 2,4-dimethyl pentane is twice that in2-methyl pentane, because the two former fuelshave two such H atoms at tertiary sites. Then-heptane mechanism contains C4, C5, and C6submechanisms. We treat all of the differentreaction classes provided above in exactly thesame way regardless of whether the fuel is n-butane, n-pentane, n-hexane, or n-heptane. Ourtreatment of these reaction classes in described inthe following sections.

HIGH TEMPERATURE MECHANISM

Reactions in classes 1 through 9 are sufficient tosimulate many high temperature applications ofiso-octane oxidation. We have made a number ofad hoc assumptions and approximations that may

not be suitable for some problems involving alk-ene and alkyne fuels and further analysis is neededto refine details for these fuels. However, under theconditions of this study, iso-octane oxidation is rela-tively insensitive to these assumptions.

Reaction Type 1: Unimolecular FuelDecomposition

These reactions produce two alkyl radicals orone alkyl radical and one hydrogen atom. Sim-ilar to our work on n-heptane, we calculate therate constant expressions in the reverse direc-tion, the recombination of two radical species toform the stable parent fuel with the decompo-sition reaction being calculated by microscopicreversibility. For recombinations of an alkylradical and a hydrogen atom we assume a rateconstant expression of 5 � 1013 cm3 mol�1 s�1,based on half that recommended by Allara andShaw [49] for H � R recombination reactions.

There is very little information available on therate of recombination reactions for C2 alkyl radi-cals and larger. For the recombination of CH3 �C7H15 radicals our high-pressure rate expressionsare based on the recommendations of Tsang [50]for CH3 � tC4H9 (methyl addition to a tertiarysite), namely 1.63 � 1013 exp(�596 cal/RT) cm3

mol�1 s�1 and half Tsang’s [51] recommendationfor CH3 � iC3H7 (methyl addition to an iso-propyl site) resulting in a rate constant of 6.80 �1014 T�0.68 cm3 mol�1 s�1. For the recombinationof tC4H9 � iC4H9 we used Tsang’s [50] recom-mendation of 3.59 � 1014 T�0.75 cm3 mol�1 s�1.Finally for the recombination of neoC5H11 �iC3H7 we used a rate expression of 4.79 � 1014

T�0.75 cm3 mol�1 s�1, similar to the value used fortC4H9 � iC4H9 above.

All of these rate constant expressions wereused as input in HCT and the high-pressuredecomposition rate expressions calculated.These were then treated using a chemical acti-vation formulation based on Quantum Rice-Ramsperger-Kassel (QRRK) theory, as de-scribed by Dean [52, 53] and rate constantexpressions were produced at various pressures.

Reaction Type 2: H Atom Abstraction

At both low and high temperatures H atom ab-straction takes place at primary, secondary and

255OXIDATION OF ISO-OCTANE

tertiary sites of iso-octane, which leads to theformation of four distinct iso-octyl radicals, Fig. 1.

The rate constant for abstraction is depen-dent on the type of hydrogen atom beingabstracted, be it either a 1°, 2°, or 3° hydrogenatom. It is also dependent on the local envi-ronment of the hydrogen atom that is ethane,propane, isobutane, and neopentane all have1° hydrogen atoms but their local environ-ment is different and, on a per-hydrogen atombasis, 1° hydrogen atom abstraction by a par-ticular radical species is slightly different.Therefore, we consider abstraction of a hy-drogen atom from site (a) to be analogous tothree quarter times the rate of abstractionfrom neopentane; hydrogen atom abstractionfrom site (b) analogous to 2° hydrogen atomabstraction from propane; hydrogen atom ab-straction from site (c) analogous to 3° hydro-gen atom abstraction from isobutane, andhydrogen atom abstraction from site (d) anal-ogous to 1° hydrogen atom abstraction frompropane. We summarize these rate constantexpressions in Table 1, and calculate thereverse rate constants from thermochemistry.Note that our estimates for hydrogen atomabstraction by CH3O2 and RO2 radicals areequal to and 0.72 times those for abstractionby HO2 radicals, respectively.

Reaction Type 3: Alkyl Radical Decomposition

We estimate the decomposition of alkyl radicalsin the way described in our n-heptane paper[41]. Because alkyl radical �-scission is endo-thermic we calculate the rate constant in thereverse, exothermic direction that is the addi-tion of an alkyl radical (or H atom) across thedouble bond of an alkene. In this way we avoidthe additional complexity of the enthalpy of reac-tion, allowing the forward, �-scission rate constantto be calculated from thermochemistry.

Rate constants for the addition of radicals

across a double bond depend on (1) the site ofaddition (terminal or internal C atom) and (2)the type of radical undergoing addition. Ourrate constants for these addition reactions arebased on the recommendations of Allara andShaw [49]. Typically, the rate of addition of aH atom across a double bond has a pre-exponential A-factor of 1 � 1013 cm3 mol�1

s�1 with an activation energy of 1,200 cal/molif the H atom adds to the terminal C atom ofthe alkene, and 2,900 cal/mol if the H atomadds to an internal C atom. The rate constantfor the addition of an alkyl radical has a lowerA-factor and higher activation energy than forthe addition of a H atom. For the addition ofan alkyl radical, the A-factor is approximately8.5 � 1010 cm3 mol�1 s�1 with an activationenergy of approximately 7,800 cal/mol if ad-dition occurs at the terminal C atom and10,600 cal/mol if addition occurs at an internalC atom. We assume these reactions are intheir high pressure limit for the conditionsconsidered in this study.

Reaction Type 4: Alkyl Radical � O2 �Olefin � HO2

This reaction type was discussed in some detail inour n-heptane paper. For reasons, described inthat paper, we do not included reaction type 4 inour mechanisms for alkyl radical containing morethan four carbon atoms. We have obtained goodagreement between experimental and computa-tional results for both C5, C6, and C7 species usingthis assumption [39–41]. Further discussion isgiven below for reaction type 20.

Reaction Type 5: Alkyl Radical Isomerization

Our treatment of this reaction type has beendescribed in our n-heptane paper. In sum-mary, the rate constant depends on the type ofC-H bond (1°, 2°, or 3°) being broken, and thering strain energy barrier involved. The acti-vation energy (Ea) is estimated, Ea using theexpression,

Ea � �Hrxn � ring strain � Eabst

where �Hrxn is taken to be the enthalpy ofreaction and is only included if the reaction is

Fig. 1. Iso-octane with its four distinct sites for H-atomabstraction.


endothermic. The activation energy for abstrac-tion is determined, following the analysis ofBozzelli and Pitz [54], from an Evans-Polanyiplot, Eabst versus �Hrxn (taken in the exothermicdirection) of similar H atom abstraction reac-tions, RH � R� � R � R�H, leading to thefollowing expression:

Eabst � 12.7 � (�Hrxn � 0.37)

The A-factors were estimated to be similar tothose determined for alkyl-peroxy radicalisomerization (reaction type 12) described below.The rate constants employed for iso-octyl radicalisomerizations are summarized in Table 2.

TABLE 1

Rate constant expressions for H atom abstraction from the fuel (cm3–mol–sec–calunits)

Radical Site Rate expression per site Citation

A n �a

H Primary (a) 7.34 � 105 2.77 8147. †a

H Secondary (b) 5.74 � 105 2.49 4124. †b

H Tertiary (c) 6.02 � 105 2.40 2583. †c

H Primary (d) 1.88 � 105 2.75 6280. †d

OH Primary (a) 2.63 � 107 1.80 278. [84]OH Secondary (b) 9.00 � 105 2.00 �1133. [84]OH Tertiary (c) 1.70 � 106 1.90 �1451. [84]OH Primary (d) 1.78 � 107 1.80 1431. [84]O Primary (a) 8.55�103 3.05 3123. †a

O Secondary (b) 4.77 � 104 2.71 2106. †b

O Tertiary (c) 3.83 � 105 2.41 893. †c

O Primary (d) 2.85 � 105 2.50 3645. †d

CH3 Primary (a) 4.26 � 10�14 8.06 4154. †a

CH3 Secondary (b) 2.71 � 104 2.26 7287. †b

CH3 Tertiary (c) 8.96 � 103 2.33 6147. †c

CH3 Primary (d) 1.47 � 10�1 3.87 6808. †d

HO2 Primary (a) 2.52 � 1013 0.0 20435. [85]HO2 Secondary (b) 5.60 � 1012 0.0 17686. [85]HO2 Tertiary (c) 2.80 � 1012 0.0 16013. [85]HO2 Primary (d) 1.68 � 1013 0.0 20435. [85]CH3O Primary (a) 4.74 � 1011 0.0 7000. [86]CH3O Secondary (b) 1.10 � 1011 0.0 5000. [86]CH3O Tertiary (c) 1.90 � 1010 0.0 2800. [86]CH3O Primary (d) 3.20 � 1011 0.0 7000. [86]O2 Primary (a) 6.30 � 1013 0.0 50760. [86]O2 Secondary (b) 1.40 � 1013 0.0 48210. [86]O2 Tertiary (c) 7.00 � 1012 0.0 46060. [86]O2 Primary (d) 4.20 � 1013 0.0 50760. [86]C2H5 Primary (a) 1.50 � 1011 0.0 13400. [49]C2H5 Secondary (b) 5.00 � 1010 0.0 10400. [49]C2H5 Tertiary (c) 1.00 � 1011 0.0 7900. [49]C2H5 Primary (d) 1.00 � 1011 0.0 13400. [49]C2H3 Primary (a) 1.50 � 1012 0.0 18000. [87]C2H3 Secondary (b) 4.00 � 1011 0.0 16800. [87]C2H3 Tertiary (c) 2.00 � 1011 0.0 14300. [87]C2H3 Primary (d) 1.00 � 1012 0.0 18000. [87]

† This study, see text.a 3/4 � analogous rate expression for neopentane [37].b NIST database [83] fit to C3H8 � R � iC3H7 � RH.c By analogy with Tsang’s [50] recommendation for iC4H10 � R � tC4H9 � RH.d NIST database [83] fit to C3H6 � R � nC3H7 � RH.


Reaction Type 6: H Atom Abstraction fromOlefinOur treatment of this reaction type is as de-scribed in our n-heptane paper. We assume thatfor olefins larger than C4, each alkene canundergo hydrogen atom abstraction by H, O,OH, and CH3 radicals. An approximate ratevalue is assumed for each abstracting radical,intended to provide a rate constant averagedover primary, secondary, allylic, and vinylic C-Hsites. As olefins get larger in carbon number, thedouble bond affects only a small portion of themolecule, the rest of which remains paraffinic incharacter. Thus, for large olefins, we expect therate constants for H atom abstraction to lookmore like those for alkanes than smaller olefins.Furthermore, only one radical is assumed to beproduced from each large olefin, which wedesignate as an ‘alkenyl’ radical, an ‘average’of the possible vinylic, allylic, primary, andsecondary radical species formed from n-hep-tane fuel.

We are aware that the most important Hatom abstraction reactions from olefins arethose from allylic sites. We are currently gener-ating the appropriate thermodynamics for theradical species formed with the associated reac-tions and rate constant expressions. We hope toinclude this analysis in a later work.

Reaction Type 7: Addition of Radical Speciesto Olefin

This reaction type is discussed in our earliern-heptane paper. The addition reactions of Hand CH3 radicals to olefins are treated as type 3(�-scission) reactions above. HO2 addition to

olefins is considered later as the reverse ofreaction type 20. RO2 addition to olefins is notconsidered.

The addition of an OH or a O radical to alarge olefin results in the formation of an adductbut the adduct is not specifically included in thereaction mechanism. Instead, we have examinedthe likely �-scission products of the adduct andused those as products in this case.

Reaction Type 8: Alkenyl RadicalDecomposition

Because hydrogen atom abstraction from anolefin is greatly simplified, so too is the thesubsequent consumption of the average ‘alk-enyl’ radical formed to consist only of unimo-lecular decomposition to products we selectedas being ‘reasonable’ for the fuel. The rateconstants of these decompositions are all as-sumed to be 2.5 � 1013 exp(�45,000 cal/RT)s�1.

Reaction Type 9: Olefin Decomposition

We have found that in model computations, thelarge olefin species decompose at appreciablerates. We have used, for all of these reactions, arate constant expression of 2.5 � 1016

exp(�71,000 cal/RT) s�1 as recommended byEdelson and Allara [55] for 1-hexene decompo-sition, and we have tried to select productdistributions which would be expected on struc-tural and thermochemical grounds. This is an-other area in which further work would improvethe mechanism.

TABLE 2

Rate constant expressions for C8 alkyl radical isomerization reactions(cm3–mol–sec–cal units)

Isomerization Ring size Rate expression

A n �a

aC8H17 º dC8H17 6 1.39 � 1011 0.00 15400.reverse 4.16 � 1011 0.00 16200.aC8H17 º cC8H17 5 3.71 � 1011 0.00 20400.reverse 1.86 � 1010 0.58 26190.


LOW TEMPERATURE MECHANISM

At temperatures below approximately 900 K,the predominant reactions of alkyl radicals, R, istheir addition to molecular oxygen,

R � O2 � RO2

followed by internal hydrogen atom isomeriza-tion, a second addition to O2, hydrogen atomisomerization and subsequent decomposition toyield two reactive hydroxyl radicals and a car-bonyl radical. This sequence, as it producesthree radicals from one iso-octyl radical, isresponsible for the low-temperature chain-branching process. In many ways, the first addi-tion of an alkyl radical to O2 is the mostimportant reaction for low temperature oxida-tion, even though it does not immediately de-termine the overall rate of chain branching.

Pollard [56] carried out an extensive kineticanalysis of hydrocarbon oxidation under lowtemperature conditions and identified the mostimportant features of the low temperature sub-mechanism. Many recent modeling studies haveincorporated these features in their mecha-nisms. Most of these models assume that thechemical details of fuel autoignition are socomplex that many simplifications are essentialto be able to simulate the oxidation process.Some of the most prominent of these simplifiedmodel treatments of hydrocarbon ignition arethe “Shell Model” [57] and related develop-ments by Hu and Keck [58] and Cox and Cole[59]. A recent survey and critical analysis ofthese simplified approaches by Griffiths [60] hassummarised the strengths and limitations ofthese models. However, our recent studies indetailed kinetic modeling of hydrocarbon oxida-tion [33, 37, 39, 41] have made it possible toaddress a wide variety of issues related toignition, and have led to improved descriptionsof ignition in internal combustion engines andengine knock.

In the following section we describe our lowtemperature submechanism, which includes de-tailed chemistry associated with the most impor-tant reactions associated with low temperatureoxidation of hydrocarbon fuels as identified byearlier workers above.

Reaction Type 10: R � O2 Addition

Additions of radical species to O2 were assumedto be dependent on the type (1°, 2°, or 3°) ofalkyl radical undergoing addition. For 1° and 3°alkyl radical addition we use the Lenhardt et al.[61] measured rates of addition for n-butyl andtert-butyl radicals to O2 which are 4.52 � 1012

and 1.41 � 1013 cm3 mol�1 s�1, respectively.Dilger et al. [62] measured the rate of tert-butylradical addition to be 4.09 � 1012 exp(�572cal/RT) cm3 mol�1 s�1, which is is a little lessthan half Lenhardt’s value at 700 K.

In addition, in their review, Atkinson et al.[63] recommend a rate expression of 6.62 � 1012

cm3 mol�1 s�1 for iC3H7 addition to O2 whileLenhardt et al. measured a rate expression of1.00 � 1013 cm3 mol�1 s�1 at 298 K. We use an“intermediate” rate expression of 7.54 � 1012

cm3 mol�1 s�1.The reverse decomposition rate constants are

calculated from microscopic reversibility. Weassume that any C8 H17 O2 radical, with 75(3N-6) vibrational modes, is rapidly stabilized toits ground state, so the energy released duringC—O bond formation is easily dissipatedthroughout the molecule. In addition, colli-sional stabilization is fast under the high pres-sure (13.5–40 bar) conditions of this study. Theactivation energy for the addition reaction iszero but is quite large (�30 kcal/mol) in thereverse, dissociation direction. Therefore, theequilibrium constant for this reaction is verystrongly temperature dependent. At very lowtemperatures this reaction proceeds rapidly toproduce the alkylperoxy species very efficiently;at high temperatures RO2 dissociates rapidlyand the concentration of RO2 is very small.

In a previous neopentane oxidation study [37]a rate expression of 1.99 � 1017 T�2.10 cm3

mol�1 s�1 measured by Xi et al. [64] wasemployed for neopentyl radical addition to mo-lecular oxygen. Furthermore, Tsang [50], in hisisobutane review recommended a rate expres-sion of 1.63 � 1019 T�2.70 cm3 mol�1 s�1 for theaddition of isobutyl radicals to molecular oxy-gen. From these studies and the measurementsof Dilger et al. for the addition of tert-butylradicals to O2 there appears to be a negativetemperature dependence for the addition ofalkyl radicals to molecular oxygen. However, we


do not include this dependence in our currentiso-octane mechanism, but intend to add thisfeature to later mechanisms.

Reaction Type 11: R � R�O2 � RO � R�O

Reactions of alkyl radicals with alkylperoxyradicals are estimated to occur at 7.0 � 1012

exp(�1,000 cal/RT) cm3 mol�1 s�1. This rateexpression is based on the recommendation ofKeiffer et al. [65] for the reaction CH3 �CH3O2 � CH3O � CH3O. They recommend arate expression of 5.06 � 1012 exp(�1,411 cal/RT) cm3 mol�1 s�1.

Reaction Type 12: RO2 Isomerization

Our treatment of these reactions has beenadopted from Benson [66], Pollard [56], Bald-win et al. [67] Bozzelli and Pitz [54], and hasbeen described in detail in our n-heptane paper[41]. Because of changes in thermodynamicparameters it has been necessary to alter ourrates of isomerization. In particular, the pre-exponential A-factors have been reduced by anorder of magnitude in comparison to thosepublished in the n-heptane paper. In addition,because isomerization involves a transition-state ring, which may incorporate five, six,seven, or eight atoms, we decrease the A-factorby a factor of eight as the ring size increasesbecause of the increased change in entropy aswe progressively tie up an additional rotor. This

is consistent with the recommendations of Bald-win et al. [67] and Hughes and Pilling [68, 69] intheir analysis of peroxy radical isomerizations.We summarize our recommended rates of RO2

isomerization in Table 3. Using these expres-sions we were able to reproduce the computa-tions for n-heptane. However, in simulatingiso-octane oxidation, these expressions led to anover-prediction of the reactivity of the fuel inthe temperature range 600 to 800 K. To reducereactivity, all of the A-factors were reduced by afactor of 0.3 from the values in Table 3. Fur-thermore, only the A-factors involving iso-oc-tylperoxy radicals were reduced and not those ofthe smaller alkyl-peroxy radicals which formpart of the submechanism.

The rate expressions recommended by Bald-win et al. [67] and Hughes and Pilling [68, 69]are qualitatively similar to those used in thispaper. However, our recommendations haveA-factors that are approximately an order ofmagnitude lower and activation energies thatare also lower than those recommended in theBaldwin and Pilling studies. Our modeling stud-ies suggest that, in order to reproduce experi-mentally observed low to intermediate temper-ature alkane fuel reactivity profiles, it isnecessary to use these lower activation energyvalues. Otherwise fuel consumption is predictedto be too slow at the start of the NTC region andtoo fast as the temperature increases throughthe NTC region.

TABLE 3

Rate constant expressions for RO2 isomerization reactions (cm3–mol–sec–cal units)

Ring size Site Rate expression (per H atom)

A n �a

5 Primary 1.00 � 1011 0.0 29400.Secondary 1.00 � 1011 0.0 26850.tertiary 1.00 � 1011 0.0 24100.





Reaction Type 13: RO2 � HO2 � RO2H � O2

This reaction, when followed by the decompo-sition of RO2H, converts a HO2 radical to anOH radical, which can accelerate the overallrate of reaction. However, the RO2H species isquite stable, and at sufficiently low temperature,this reaction terminates chain branching andreduces the overall rate of reaction. There is notmuch information available on this reactiontype except for methyl and ethyl radicals. Light-foot et al. [70] carried out a literature review ofthe reaction CH3O2 � HO2 � CH3O2H � O2

and recommended a rate expression of 2.47 �1011 exp(�1,570 cal/RT) cm3 mol�1 s�1. Later,Atkinson et al. [63] also performed a literaturereview and recommended 2.29 � 1011

exp(�1,550 cal/RT) cm3 mol�1 s�1, similar tothe value of Lightfoot et al.. In addition, Fenteret al. [71] measured the rate of the reaction:C2H5O2 � HO2 � C2H5O2H � O2 to be 9.71 �1010 exp(�2,504 cal/RT) cm3 mol�1 s�1 whileMaricq and Szente [72] measured the rate to be4.16 � 1011 exp(�1,395 cal/RT) cm3 mol�1 s�1.

We employ a rate expression of 1.75 � 1010

exp(�3,275 cal/RT) cm3 mol�1 s�1. Our ratechoice is about a factor of two slower and has astronger temperature dependence than the rec-ommendations mentioned above. However, weexpect the rate constant to decrease with in-creasing size of the R radical and thus ourrecommended rate constant.

Reaction Type 14: RO2 � H2O2 � RO2H �HO2

We treat this reaction type in exactly the sameway as described in our n-heptane paper. Wehave used rate constant expressions that are thesame in both forward and reverse directions,

2.4 � 1012 exp(�10,000 cal/RT) cm3 mol�1 s�1

There is little information available for thisreaction rate constant except for the case whereR is CH3. Our choice of rate constant is basedon Tsang’s recommendation [73] for CH3O2 �H2O2 � CH3O2H � HO2 of 2.41 � 1012

exp(�9,940 cal/RT) cm3 mol�1 s�1 from 300 to2500 K with an uncertainty of a factor of 5. For

this isoergic reaction, the reverse rate is thesame as the forward rate by analogy.

Reaction Type 15: RO2 � CH3O2 � RO �CH3O � O2

The rate constants of these reactions are notparticularly well known, but have been esti-mated as follows. Lightfoot et al. [74] used flashphotolysis to study the reaction CH3O2 �CH3O2 � products. They reported a total rateexpression of 6.02 � 1010 exp(�826 cal/RT) cm3

mol�1 s�1 for the two sets of products (a) CH3O� CH3O � O2 and (b) CH3OH � CH2O � O2.In addition, they reported a ratio of ka/kb � 45exp(�2911 cal/RT). We calculated the rate ofreaction (b) from 300 to 1000 K and results fitthe expression 3.11 � 1014 T�1.61 exp(�1051cal/RT) cm3 mol�1 s�1. The rate expression ofreaction (a) was then calculated to be 1.40 �1016 T�1.61 exp(�1,860 cal/RT) cm3 mol�1 s�1.The rate expression for type (a) above is the onewe currently use for all type 15 reactions.

Reaction Type 16: RO2 � R�O2 � RO � R�O� O2

This is another reaction which interconverts ROand RO2 radical species. We use the rate ex-pression 1.40 � 1016 T�1.61 exp(�1860 cal/RT)cm3 mol�1 s�1 as used in the similar type 15reaction above.

Reaction Type 17: RO2H � RO � OH

It had been thought in the past that this reactionstep was important as it produces two veryreactive radical species. However, as alreadyexplained for type 13 reactions above, RO2

radical preferentially undergoes unimolecularisomerization to QOOH. Therefore, very smallconcentrations of stable RO2H species areformed at low temperatures. RO2H species canbe used as sensitizers or cetane improvers andso its decomposition in those circumstances willbe very important. We use a rate expression of1.26 � 1016 exp(�42,500 cal/RT) s�1 for thistype of reaction which is approximately a factorof two faster than that recommended by Baulchet al. [75], and similar to the recommendations


of Sahetchian et al. [76] for 1-heptyl and 2-hep-tyl hydroperoxide decomposition.

Reaction Type 18: RO Decomposition

Large alkoxy radicals undergo �-scission to gen-erate smaller stable oxygenated species, primar-ily aldehydes or ketones, and a hydrogen atomor an alkyl radical species. Because alkoxy rad-ical �-scission is endothermic we calculate therate constant in the reverse, exothermic direc-tion, that is, the addition of an alkyl radical (orH atom) across the double bond of an aldehydeor ketone. In this way we avoid the additionalcomplexity of the enthalpy of reaction, allowingthe forward, �-scission rate constant to be cal-culated from thermochemistry. The rate con-stant used for the reverse, addition reaction was1.0 � 1011 exp(�11,900 cal/RT) cm3 mol�1 s�1.

Reaction Type 19: QOOH � Cyclic Ether �OH

This reaction type is treated in a similar way tothat published in our n-heptane paper, but hasbeen slightly altered to be consistent with ourapproach of estimating A-factors for RO2 radi-cal isomerization. Taking into account loss inentropy as described earlier, we reduce thepre-exponential factor by a multiple of 8 ratherthan 12 as one extra rotor is tied up in goingfrom a three to four and progressively largerring heterocycles. The rate parameters we usefor these reactions are reported in Table 4.

Reaction Type 20: QOOH � Olefin � HO2

QOOH species that have a radical site beta tothe hydroperoxy group can decompose to yield

TABLE 4

Rate constant expressions for cyclic ether formation from QOOH radicals(cm3–mol–sec–cal units)

Cyclic etherRing size Rate expression

A n �a

3 6.00 � 1011 0.0 22000.4 7.50 � 1010 0.0 15250.5 9.38 � 109 0.0 7000.6 1.17 � 109 0.0 1800.

TABLE 5

Rate constant expressions for H atom abstraction from cyclic ether by OH and HO2

(cm3–mol–sec–cal units)

Type ofH atom Radical Site Rate expression (per H atom)

A n �a

Primary 3.83 � 107 1.53 775.OH Secondary 2.34 � 107 1.61 �35.

H-C-C Tertiary 5.73 � 1010 0.51 64.Primary 3.33 � 103 2.55 15500.

HO2 Secondary 7.40 � 103 2.60 13910.Tertiary 3.61 � 103 2.55 10532.Primary 9.50 � 107 1.61 �35.

OH Secondary 8.84 � 109 1.00 �149.H-C-O Primary 3.00 � 104 2.60 13910.

HO2 Secondary 1.08 � 104 2.55 10532.


a conjugate olefin and HO2 radical. The rateconstant for this reaction was considered in thereverse direction that is, the addition of an HO2radical at an olefinic site, in the same way asalkyl radical decomposition (type 3 above). Theenergy barrier for the addition reaction is takenfrom the study of Chen and Bozzelli [77] on thekinetic analysis for HO2 addition to ethylene,propene, and isobutene. They recommend anactivation energy for the addition of HO2 to theterminal carbon atom in the double bond ofapproximately 12.5 kcal/mol. For HO2 additionto the “internal” carbon atom on propene theyrecommend an activation energy of 11 kcal/moland for HO2 addition to the “internal” carbonatom on isobutene an activation energy of 7.6kcal/mol is recommended. All values are in thehigh-pressure limit. Thus, following Chen andBozzelli we use the activation energies recom-mended above by them depending on the typeof carbon atom the HO2 radical bonds to. Apre-exponential A-factor of 1.0 � 1011 is typi-cally used. It is worth nothing that the activationenergy for this class of reaction decreases withthe type (1°, 2°, or 3°) of olefinic carbon atom towhich the HO2 radical is bonding. However, fortype 3 reactions above the activation energyincreases with the type of olefinic carbon atom.

Recent studies have shown that, for the caseof ethyl radical adding to O2, the reaction doesnot proceed through the QOOH path to olefinplus HO2 radical, but reacts through a HO2radical elimination channel [78]. It is reasonableto expect that other larger alkyl radicals reactwith O2 and proceed through a HO2 radicalelimination channel as well. We have not, as yet,included this new information in our reactionmechanism. If this molecular elimination chan-nel is the important channel for all alkyl radicalsthen the QOOH � olefin � HO2 reaction willbe replaced in our mechanism by an alkyl �O2 � olefin � HO2 reaction whose rate isdetermined by the rate of HO2 radical elimina-tion from the excited state alkylperoxy radicaladduct.

Reaction Type 21: QOOH � Olefin �Carbonyl Radical

QOOH species, produced by an RO2 isomeriza-tion with an intermediate ring structure of six

atoms can undergo �-scission. We treat thisclass of reaction in exactly the same way as analkyl radical (type 3), alkoxy radical (type 18) orQOOH � olefin � HO2 (type 20) �-scission.The reverse addition of the carbonyl radical tothe olefin is estimated to be 1.00 � 1011

exp(�11,900 cal/RT) cm3 mol�1 s�1 with theforward rate expression calculated from ther-mochemistry.

Reaction Type 22: Addition of QOOH to O2

The rate expressions for this class of reactionare identical to those for alkyl addition to O2type 10. The reverse dissociation rate was thencalculated from microscopic reversibility.

Reaction Type 23: O2 QOOH Isomerization toCarbonylhydroperoxide � OH

The rate constant for this and other isomeriza-tions via an internal hydrogen atom transfer areanalogous to those for RO2 º QOOH isomer-ization. Similar to our n-heptane work, theactivation energy has been reduced by 3 kcalmol�1 as the hydrogen atom being abstracted isbound to a carbon atom which is bound to ahydroperoxy group and should be more easilyremoved. In addition, the A-factors have beenreduced by a factor of three consistent with ourtreatment of alkyl-peroxy radical isomerization,reaction type 12.

Reaction Type 24: CarbonylhydroperoxideDecomposition

The decomposition of carbonylhydroperoxidemolecules leads to the formation of two radi-cals, a carbonyl radical and a second OH radi-cal, which results in chain branching as tworadical species are produced from one stablereactant.

A rate expression of 1.5 � 1016 exp(�42,000cal/RT) s�1 was chosen for the decompositionof each carbonylhydroperoxide molecule eventhough each species has slightly different ther-modynamic properties. Our rate constant ex-pression is similar to that used for alkylhy-droperoxide decomposition based largely on therecommendations of Sahetchian et al. [76] for1-heptyl and 2-heptyl hydroperoxide decompo-


sition. Carbonylhydroperoxide decomposition isespecially important at low temperatures as thehigh activation energy ensures an inductionperiod during which carbonylhydroperoxideconcentration builds up. The subsequent de-composition products help accelerate the over-all rate of fuel oxidation, raising the tempera-ture and allowing the remainingcarbonylhydroperoxide species to decomposemore easily.

Reaction Type 25: Cyclic Ether Reactions withOH and HO2

Cyclic ethers are produced under low tempera-ture conditions during hydrocarbon oxidationand, in the present study are large C8 specieswith an oxygen atom embedded in the molecule.Therefore, it is reasonable to assume that thereaction proceeds by means of hydrogen atomabstraction. As the two most prevalent radicalsare OH and HO2 at low and intermediatetemperatures, where the cyclic ethers are pro-duced, these are the only two radical attackreactions included. The rate expressions usedare provided in Table 5 [41]. In addition, hydro-gen atom abstractions can be easily extended toinclude abstractions by H, CH3, and O radicals,for example. However, we have not includedthese reactions in the current study.

REACTION MECHANISM

The overall reaction scheme included in thisstudy for iso-octane oxidation is depicted in Fig.2. The naming conventions used are R and R�,denoting alkyl radicals; in xC8H16 OOH � y, xdenotes the site of the hydroperoxyl group andy the radical site for two of the four distinct siteson the iso-octane molecule shown in Fig. 1, andiC8 ket refers to iso-octyl carbonylhydroperox-ide species.

At high temperatures, the overall reactionpathway proceeds via �-scission of the alkylradicals R proceeding rapidly to a smaller olefinand other species, with chain branching dueprimarily to the reaction H � O2 � O � OH. Atlow temperatures, chain branching is mainlybecause of the reaction pathway leadingthrough the carbonylhydroperoxide species. As

the temperature increases, the chain propaga-tion reactions of QOOH species increase, be-cause the energy barrier to their formation ismore easily overcome, leading to the formationof cyclic ether species, conjugate olefins, and�-decomposition products, at the expense of thereaction pathways through the carbonylhy-droperoxide species. The increasing importanceof these propagation channels leads to a lowerreactivity of the system which is observed as theNTC region. The difference in the chainbranching mechanisms at low and high temper-atures leads to varying reactivity depending onthe fuel to air equivalence ratio. Because thechain branching mechanism at high tempera-tures is because of the H � O2 � O � OHreaction, fuel lean mixtures are more reactive inthis regime. However, at low temperatures, be-cause chain branching is dependent on radicalspecies formed directly from the parent fuel,fuel rich mixtures are oxidized more quickly.

MECHANISM VALIDATION

An explaination of the chemical kinetic mecha-nism formulation has been given in in thepreceeding section. Below, we describe how this

Fig. 2. Simplified kinetic scheme for iso-octane oxidation.


mechanism was used to simulate experimentalresults obtained in an atmospheric pressure flowreactor [20], a variable pressure flow reactor[15, 22] at 12.5 atm, and a complementarilydifferent flow reactor [23]. Moreover, resultsobtained in a jet-stirred reactor [10], shocktubes [5–7], and in a motored engine [17] arealso simulated. Overall, good agreement is ob-tained between model and experiment. We in-dicate the major pathways responsible for fueloxidation under the specific conditions of eachstudy and also point out where we believeimprovements may be made.

Atmospheric Pressure Flow Reactor

Experiments, carried out in an adiabatic flowreactor, provide a well-characterized environ-ment that is designed to minimize mixing anddiffusion effects. Dryer and Brezinsky [20] stud-ied the oxidation of iso-octane in an atmospher-ic-pressure flow reactor at 1080 K, and at anequivalence ratio of one. It was found that theoxidation of iso-octane produced primarily iso-butene (iC4H8) and propene (C3H6) as interme-diate products. In addition, methane (CH4),ethane (C2H6), ethylene (C2H4), 2-methyl-1-butene (aC5H10), allene (C3H4�a), carbonmonoxide (CO), and carbon dioxide (CO2)were also quantified. Simulations were per-formed under the assumption of plug flow: thevelocity and temperature profile in the reactor isradially uniform and axial diffusion of speciesand energy is negligible. Constant pressure andadiabatic walls were also assumed. The experi-mental results together with the model predic-tions are depicted in Fig. 3.

Analysis of HCT output reveals that, at 50%fuel consumption, unimolecular decomposition

and hydrogen atom abstraction from the fuel byhydrogen atoms predominates the consumptionof the fuel. The reactions are, in order ofcontribution:

iC8H18 ™™™327.8

tC4H9 � iC4H9

iC8H18 � H ™™™311.4

aC8H17 � H2

iC8H18 ™™™310.5

yC7H15 � CH3

iC8H18 � H ™™™39.7

cC8H17 � H2

iC8H18 � H ™™™38.5

bC8H17 � H2

iC8H18 � H ™™™36.2

dC8H17 � H2

iC8H18 � OH ™™™35.0

aC8H17 � H2O

iC8H18 ™™™34.9

neoC5H11 � iC3H7

The values over the arrows give the impor-tance, on a scale of 0 to 100, of each reaction tothe consumption of iso-octane at 50% consump-tion. Isobutene and propene are the majorintermediates produced under these conditionsand it is apparent, from the equation arraysabove and below, why this is so.

tC4H9 ¡ iC4H8 � H

aC8H17 ¡ iC4H8 � iC4H9

cC8H17 ¡ iC4H8 � tC4H9

neoC5H11 ¡ iC4H8 � CH3

yC7H15 ¡ iC4H8 � iC3H7

iC4H9 ¡ C3H6 � CH3

iC3H7 ¡ C3H6 � H

Fig. 3. 0.14% iso-octane oxidation at 1.0 atm, � � 0.99, T � 1080 K in a flow reactor. Experimental results (points) [20] versusmodel predictions for major intermediate products. Dashed line corresponds to open symbols.


dC8H17 ¡ C3H6 � neoC5H11

pC7H15 ¡ C3H6 � tC4H9

(yC7H15 � 2,4-dimethyl-propan-2-yl radical andpC7H15 � 2,2-dimethyl-propan-2-yl radical).

Methane is produced via hydrogen atom ab-straction from the fuel by methyl radicals, andethane by the recombination of methyl radicals.2-methyl-1-butene is produced by the reactionof methyl radicals with 2-methyl-allyl radicals.The decomposition of 2-methyl-allyl radicalsproduces allene and a methyl radical.

iC8H18 � CH3 ¡ a, b, c, d � C8H17 � CH4

CH3 � CH3 ¡ C2H6

iC4H7 � CH3 ¡ aC5H10

iC4H7 ¡ C3H4 � a � CH3

The experimental carbon monoxide profile isnot well reproduced by the model, Fig. 3a. Itappears from the experimental result that thereis a direct path forming CO while the modelpredicts that CO is mainly formed from form-aldehyde oxidation via formyl radical consump-tion, that is, secondary processes.

The concentration of ethylene and methaneare also underpredicted by the model. We be-lieve that there may be a mechanism that we arenot fully reproducing correctly in the model.Namely, we believe that there is a sequence ofreactions of isobutene and propene as follows:

iC4H8 � H ¡ iC4H9

iC4H9 ¡ C3H6 � CH3

C3H6 � H ¡ nC3H7

nC3H7 ¡ C2H4 � CH3

Of course, addition of a hydrogen atom toisobutene and propene can also lead to theproduction of a tert-butyl and an isopropylradical, respectively. However, the above se-quence converts isobutene and a hydrogen atominto propene and an methyl radical and simi-larly, propene and a hydrogen atom into ethyl-ene and a methyl radical. Our chemical kineticmodel does contain all of these reactions butmay not be accurately represented. Certainly,increasing the importance of this sequence of

reactions would make our predictions of meth-ane and ethylene more consistent with thosemeasured experimentally.

Princeton Variable Pressure Flow Reactor

Iso-octane was studied under very high dilution(99% N2), the initial concentration of fuel being0.14%, at � � 1.0 in the temperature range600–850 K and at a constant pressure of 12.5atm [15, 22]. Data were obtained for the molefractions of CO, CO2, H2O, O2, and the tem-perature at the fixed sampling locations. Thesedata together with the model simulations aredepicted in Fig 4.

It is clear that, in the temperature range 600to 675 K, the model simulation predicts morereactivity than observed experimentally, withmore O2 reacted and more CO, CO2, and H2Oproduced. We have not been able to gain betteragreement as to do so would result in pooreragreement with the shock tube ignition-delaydata of Fieweger et al. [6, 7], discussed below.

Lean Oxidation in a Variable Pressure FlowReactor

Complementary to the experiments performedabove under stoichiometric conditions, Chen etal. [23] investigated iso-octane in a high pres-sure flow reactor at a temperature of approxi-mately 925 K, at 3, 6, and 9 atm pressure andwith a fuel/air equivalence ratio of approxi-mately 0.05, in which the mole fractions ofiso-octane, oxygen, and nitrogen were 0.08%,20.99%, and 78.92%, respectively. Many hydro-carbon and oxygenated hydrocarbon intermedi-ates were identified and quantified as a function

Fig. 4. 0.14% iso-octane oxidation at 12.5 atm, � � 1.0, � �1.8 s in a PFR F O2, E CO, � H2O, { Temperature rise.Experimental results (points) [22] versus model predictions.Dashed line corresponds to open symbols.


of time. These experimental results provide astringent test of the low temperature chemistryportion of the kinetic model as they emphasisethe importance of alkyl radical addition to mo-lecular oxygen and internal H-atom isomeriza-tion reactions relative to alkyl radical decompo-sition reactions. Comparisons of modelpredictions with many experimentally measuredspecies at 6 atm and 945 K are depicted in Figs.5 and 6.

Overall, there is good agreement betweenmodel and experiment, and so it is reasonable toassume that the mechanism is predicting themajor production routes correctly. Olefins arethe main products formed in the oxidationprocess, of which isobutene (iC4H8) is formed inhighest concentrations followed by propene(C3H6), Fig. 5b. Below, we list the reactionsresponsible for isobutene and propene forma-tion in order of decreasing importance.

aC8H17 ¡ iC4H8 � iC4H9

cC8H17 ¡ iC4H8 � tC4H9

i,tC4H9 � O2 ¡ iC4H8 � HO2

iC4H9 ¡ C3H6 � CH3

dC8H17 ¡ C3H6 � neoC5H11

iC4H8OOH � i ¡ C3H6 � CH2O � OH

In iC4H8OOH-i the hydroperoxyl group is at-tached to one of the substituted methyl groupswhile there is a radical site on one of the othertwo methyl groups.

Methane (CH4) is generated by the reactionof methyl radicals with hydroperoxyl radical andwith the fuel, Figs 5b.

CH3 � HO2 ¡ CH4 � O2

iC8H18 � CH3 ¡ xC8H17 � CH4

Significant quantities of the C7 olefins areformed including 4,4-dimethyl-pent-2-ene

Fig. 5. 0.09% iso-octane oxidation in a flow reactor, � � 0.05, P � 6 atm, T � 945 K. Experimental results (points) [23] versusmodel predictions. Dashed line corresponds to open symbols.

Fig. 6. 0.09% iso-octane oxidation in a flow reactor, � � 0.05, P � 6 atm, T � 945 K. Experimental results (points) [23] versusmodel predictions for selected oxygenates. Dashed line corresponds to open symbols.


(oC7H14), 2,4-dimethyl-pent-2-ene, (yC7H14),2,4-dimethyl-pent-1-ene (xC7H14) and 4,4-di-methyl-pent-1-ene (pC7H14), Fig. 5c.

bC8H17 ¡ oC7H14 � CH3

bC8H17 ¡ yC7H14 � CH3

aC8H17 ¡ xC7H14 � CH3

dC8H17 ¡ pC7H14 � CH3

The model indicates that the C7 olefins areformed almost exclusively by �-scission of iso-octyl radicals under the conditions of this study.Note that the decomposition of 2,4,4-trimethyl-pent-3-yl radical, (bC8H17), leads to the forma-tion of almost equal quantities of 2,4- and4,4-dimethyl-pent-2-ene. C7 olefins can also beformed through low temperature reactionpaths. The model indicates that very smallamounts (� 5%) are generated from octyl-hydroperoxide radical �-scission.

dC8H16OOH � b ¡ oC7H14 � CH2O � OH

aC8H16OOH � b ¡ yC7H14 � CH2O � OH

aC8H16OOH � a ¡ xC7H14 � CH2O � OH

dC8H16OOH � d ¡ pC7H14 � CH2O � OH

In dC8H16OOH � b, ‘d’ refers to the site atwhich the hydroperoxyl group is attached and‘b’ to the radical site on iso-octane.

There are various other hydrocarbon speciesproduced, including allene (C3H4-a), ethylene(C2H4), ethane (C2H6), 2,4,4-trimethyl-pent-1-ene (jC8H16), and 2-methyl-1-butene, (aC5H10),Fig. 5d. Allene is formed in appreciable concen-trations and is predicted to be generated fromthe reaction of 2-methyl-allyl radical with mo-lecular oxygen via the overall reaction:

iC4H7 � O2 ¡ C3H4 � a � CH2O � OH

Small concentrations of 2,4,4-trimethyl-pent-1-ene (jC8H16) were measured and this olefin ispredicted to be formed from the �-scission of ahydroperoxy-octyl radical:

dC8H16OOH � c ¡ jC8H16 � HO2

bC8H16OOH � c ¡ jC8H16 � HO2

2-methyl-1-butene (aC5H10) is predicted tobe formed by the reaction of 2-methyl-allyl withmethyl radicals, although it is very much under-predicted by the model indicating that theremay be an alternative route to its formation.(Note that in the atmospheric-pressure experi-ments of Dryer and Brezinsky [20] 2-methyl-1-butene is slightly over-predicted.)


In Fig. 5c the lowest solid line corresponds tothe model predicted 2-methyl-but-1-ene con-centrations.

Of the oxygenates, acetone (CH3COCH3),methacrolein (iC3H5CHO) and isobuteralde-hyde (iC3H7CHO) are formed in relatively highconcentrations, Fig. 6a. Acetone, although un-derpredicted by just less than a factor of two, ispredicted to be formed through the Wadding-ton mechanism [79, 80] mainly from isobutene,Fig. 7 with a small quantity formed from the C7olefins at high fuel conversion.

2-methyl-allyl radicals can react with hy-droperoxyl radicals creating methallyl-oxyl rad-icals which decompose to yield methacroleinand a hydrogen atom. As these experimentswere performed under very lean conditionssome methallyl-oxyl radicals also react withmolecular oxygen to produce methacrolein andhydroperoxyl radicals.

iC4H7O ¡ iC3H5CHO � H

iC4H7O � O2 ¡ iC3H5CHO � HO2

bC8H16OOH � a ¡ iC3H7CHO

� iC4H8 � OH

iC4H8O ¡ iC3H7CHO

zC7H14O � yO2H ¡ iC3H7CHO

Fig. 7. Formation of acetone via the Waddingtonmechanism.


� CH3COCH3 � OH

yC7H14O � zO2H ¡ iC3H7CHO

� CH3COCH3 � OH

Isobuteraldehyde is mainly produced from the�-scission of 2,4,4-trimethyl-3-hydroperoxy-pent-1-yl radical (bC8H16OOH-a) and also fromthe isomerization of isobutene oxide [81]. Athigher fuel conversion some isobuteraldehyde(and acetone) is also produced from 2,4-di-methyl-pent-2-ene via the Waddington mecha-nism.

Relatively low concentrations of cyclic etherswere measured including 2,2,4,4-tetramethyl-tetrahydrofuran (TMTHF, iC8eterac),isobutene oxide (iC4H8O), 2-isopropyl-3,3-di-methyl oxetane (iC8eterab) and 2-tert-butyl-3-methyl oxetane (iC8eterbd), Fig. 6b. In thisfigure the lower dotted line corresponds toiC8eterbd.

The C8 cyclic ether species are predicted tobe formed from the corresponding hydroper-oxy-octyl radical, see for example Fig. 8.

It is evident from Fig. 6b that all of the C8cyclic ethers are grossly underpredicted by thekinetic model. It appears that the above mech-anism cannot account for their formation. Incontrast, isobutene oxide is well predicted bythe model. It is formed by the direct reaction ofisobutene with a HO2 radical as recommendedby Baldwin et al. [82].

iC4H8 � HO2 ¡ iC4H8O � OH

We use the rate expression of Baldwin et al. of1.29 � 1012 exp(�13,340 cal/RT) cm3 mol�1 s�1

for this reaction. Obviously, we need to improveour treatment of olefin plus hydroperoxyl radi-cal addition reactions. In particular, it seemsappropriate to include some chemically acti-vated pathways, consistent with that postulatedby Baldwin and co-workers for isobutene plushydroperoxyl radical above.

Jet Stirred Reactor

Dagaut et al. [10] investigated iso-octane oxida-tion in a jet-stirred reactor at 10 atm, in thetemperature range 550 to 1150 K, with equiva-lence ratios of 0.3, 0.5, 1.0, and 1.5, and 99%dilution by nitrogen with a residence time of 1 s.Simulations were performed under isothermal,constant pressure conditions, and assumed per-fect mixing of the reactants. Time dependentcalculations were run for long times until asteady state solution was obtained. Reactantconcentrations and intermediate and final prod-uct concentrations were quantified and the re-sults, together with the mechanism simulations,are depicted in Figs. 9–11.

Fig. 9 shows comparisons between computedand experimental results for stoichiometric mix-tures of 0.1% iso-octane. Overall, species con-centrations are reproduced quite well by themodel. Figure 9a shows the profiles for the fuel,carbon monoxide and carbon dioxide. All pro-files are well simulated by the model. Figure 9bdepicts profiles for methane, isobutene, ethyl-ene, and propene. Methane and ethylene peakat 975 K, while isobutene and propene peak at850 K. In addition, all of the C7 olefins peak at850 K, Fig. 9c and d. The products formed atlower temperature appear as ‘primary’ productsof the oxidation process while those that peak athigher temperature are produced as ‘secondary’products. At 820 K, under stoichiometric con-ditions where 60% of the fuel has been oxidized,iso-octane undergoes hydrogen atom abstrac-tion, primarily by hydroxyl radicals but also byhydrogen atoms and hydroperoxyl radicals, pro-ducing the four iso-octyl radicals. These radicalsdecompose to produce isobutene, propene andthe C7 olefins as illustrated in the equationarrays earlier during the discussion of iso-oc-tane oxidation in a flow reactor.

The production of methane and ethane at 950K is a consequence of the formation of methyl

Fig. 8. Formation of 2-isopropyl-3,3-dimethyl oxetane.


radicals which can recombine or abstract ahydrogen atom from another species. In Fig. 9dthe higher concentration solid line correspondswith the over-prediction of 2,4-dimethyl-1-pen-tene (xC7H14) while the lower solid line is thesimulated underprediction of 2-methyl-1-butene (aC5H10). Moreover, our model over-predicts the formation of 2-methyl-1-butene inthe atmospheric flow reactor experiments butalso underpredicts its formation in lean oxida-tion flow reactor experiments at 6 atm. Webelieve that 2-methyl-1-butene is generatedfrom the recombination of methyl and 2-methy-allyl radicals.


A pressure dependent treatment of this reactionis needed in order to improve the mechanism’scapability of accurately simulating 2-methyl-1-butene formation.

Variations in equivalence ratio at constantpressure were found to change the overall reac-tivity of this system. Under fuel-lean conditions,Fig. 10, the fuel is oxidised at lower temperaturerelative to stoichiometric conditions, while, un-der fuel-rich conditions, oxidation occurs athigher temperatures relative to the stoichiomet-ric experiments, Fig. 11. This behaviour is well

Fig. 9. 0.1% iso-octane oxidation at 10 atm, � � 1.0, � � 1 s in a JSR. Experimental (points) [10] and model predictions(lines). Dashed line corresponds to open symbols.

Fig. 10. 0.1% iso-octane oxidation at 10 atm, � � 0.5, � � 1 s in a JSR. Experimental (points) [10] and model predictions(lines). Dashed line corresponds to open symbols. (d) The solid line with the highest peak value corresponds to �C7H14.


reproduced by the simulation. In addition, un-der fuel-lean conditions, lower concentrationsof hydrocarbon intermediates are produced,while under fuel-rich conditions higher concen-trations are produced relative to the stoichio-metric condition.

Shock Tube

Our detailed chemical kinetic model has beenused, assuming constant-volume, homogeneous,adiabatic conditions behind the reflected shockwave, to simulate the autoignition of iso-octane,at high temperatures studied by Vermeer et al.[5] and at low temperatures as studied byFieweger et al. [6, 7]. Vermeer et al. studied theautoignition of iso-octane/oxygen/argon mix-tures behind reflected shock waves in the pres-sure range of 1 to 4 atm and the temperaturerange of 1200 to 1700 K. Stoichiometric fuel-oxygen mixtures were diluted with 70% argon toreduce the influence of the boundary layer. Wehave obtained good agreement between exper-iment and simulation as observed in Fig. 12. Itshould be noted that in our n-heptane study [41]we also simulated data for n-heptane underalmost identical conditions. However, the sim-ulation was substantially faster than the experi-mentally measured delay times. We speculatedthat this may have been because of our estima-tion of the unimolecular decomposition of thefuel being in the high pressure limit and that we

should include a pressure-dependent treatmentof this type of reaction to improve our predic-tions. In our description of unimolecular de-composition (reaction type 1) we have includeda pressure-dependent treatment and we haveobtained good agreement with the experimentalresults.

Fieweger et al. studied the ignition of iso-octane/air mixtures behind both incident andreflected shock waves at equivalence ratios of0.5, 1.0, and 2.0 in the temperature range 700 to1300 K at reflected-shock pressures from 13 to45 bar, conditions similar to those in an operat-ing engine. Overall, good agreement is observedbetween the model and the experimental re-sults, Figs. 13 through 15. However, at temper-atures below about 800 K the model is consis-tently slower than the experimental

Fig. 11. 0.1% iso-octane oxidation at 10 atm, � � 1.5, � � 1 s in a JSR. Experimental (points) [10] and model predictions(lines). Dashed line corresponds to open symbols. (d) The solid line with the highest peak value corresponds to xC7H14.

Fig. 12. 2.2% iC8H18, 27.8% O2, 70% Ar, P5 � 2.1 atm, � �0.989. Experimental (points) [5], and model predicted igni-tion delay times. Dashed line corresponds to open symbols.


measurement. Figure 13 depicts ignition delaytimes versus inverse temperature for the stoichi-ometric oxidation of iso-octane in air at 13 barin the temperature range 950 to 1300 K. Thecomputed results very clearly depict a veryfundamental feature of fuel oxidation kinetics.Namely, that under these conditions at temper-atures below approximately 1150 K, fuel-richmixture ignite faster than fuel lean mixtures. At1150 K all mixtures ignite at approximately thesame time and at temperatures above 1150 Kfuel lean mixtures ignite faster than fuel richmixtures. This is due to the nature of thechain-branching process. At high temperature itis because of the reaction of hydrogen atomwith molecular oxygen to produce a hydroxylradical and an oxygen atom. At low tempera-tures, the production of carbonyl-hydroperoxidespecies, which lead to chain branching, is di-rectly proportional to the fuel concentration.

Figure 14 shows comparisons of model pre-dicted and experimentally measured ignition

delay times versus inverse temperature at areflected shock pressure of 40 bar for lean,stoichiometric and rich mixtures. In the temper-ature range 770 to 910 K, both model andexperiment depict an obvious negative temper-ature coefficient (NTC) behavior, in which theignition delay time becomes longer as the tem-perature increases.

Finally, Fig. 15 shows the influence of pres-sure on ignition delay for stoichiometric fuel inair mixtures. As the pressure is increased theignition delay times become shorter. In addi-tion, at reflected shock pressures of 34 bar andhigher it is possible to measure ignition delaysto a temperature of 700 K and thus observe anNTC behavior. There is good agreement be-tween model and experiment in all instances,even though the mechanism consistently over-predicts the ignition delay time at low temper-atures.

Co-Operative Fuels Research Engine

Leppard [17] performed autoignition experi-ments in a CFR engine motored at 500 RPMusing n-heptane, iso-octane and PRF mixtures,and speciated the exhaust gases. At an intakemanifold pressure of 120 kPa and temperatureof 448 K, Leppard started sampling the exhaustgas at a compression ratio (CR) of 6.0. Thecompression ratio was increased in steps of 0.5,with continuous sampling, until iso-octane au-toignited. Figure 16 depicts the experimentallymeasured profiles for carbon monoxide andmolecular oxygen (points) are plotted togetherwith the model predictions (lines). Iso-octane is

Fig. 13. Influence of equivalence ratio for iso-octane oxida-tion in a shock tube at 13 bar, � � 1.0 in air. Experimental(points) [6, 7] and model predictions (lines). Dashed linecorresponds to open symbols.

Fig. 14. Influence of equivalence ratio for iso-octane oxida-tion in a shock tube at 40 bar, � � 1.0 in air. Experimental(points) [6, 7] and model predictions (lines). Dashed linecorresponds to open symbols.

Fig. 15. Influence of pressure on iso-octane oxidation in ashock tube at � � 1.0 in air. Experimental (points) [6, 7] andmodel predictions (lines). Dashed line corresponds to opensymbols.


observed to autoignite at a critical compressionratio (CCR) of 10.7, while at a CR of 10.5autoignition is not observed although 36% ofthe fuel had reacted. Thus, autoignition occursat any CR higher than 10.7, that is, to the rightof the straight dashed line in Fig. 16. The modelpredicts a CCR of between 10.5 and 10.75 with61.6% of the fuel oxidized at a compressionratio of 10.5. Moreover, even though the CCRfor iso-octane is well reproduced by the model,it is apparent that, because the concentration ofcarbon monoxide formed is a direct measure ofreactivity, at all compression ratios the modelpredicts more reactivity than is observed exper-imentally.

The prediction of intermediate speciationdata measured in engine experiments is ex-tremely difficult, as the system passes through awide range of temperature and pressure withinthe engine, and the exhaust flow which is ana-lyzed here is also unsteady. We believe thatoverall, good agreement is observed betweenmodel prediction and experimental observation,although some refinements may be possible inthe chemistry. Table 6 shows experimentallyquantified species concentrations together withthose predicted by the detailed mechanism,both at 36% fuel conversion. Isobutene was thelargest measured alkene component by a factorof five, with propene, di- and tri-methylpentenes composing the remainder. The modelpredicts isobutene formation in greatest abun-dance, but is overpredicted by a factor of two,while propene is overpredicted by less than afactor of two. Of the olefins, the predictedconcentrations of 2,4-dimethyl-2-pentene, 2,4,4-trimethyl-1-pentene and 2,4,4-trimethyl-2-pen-tene are quite good even though the relativeconcentrations of the tri-methyl pentenes arereversed. In addition, 4,4-dimethyl-2-pentene isunderpredicted by about an order of magnitude.

The only alkanes identified were methane (intrace amounts) and iso-octane. Of the measured

Fig. 16. F CO and E O2 formed in a CFR engine (@ 500RPM) for iso-octane fuel, � � 1.0. Experimental results(points) [17] vs model predictions. Dashed line correspondsto open symbols.

TABLE 6

Comparison of major intermediates formed in a CFR engine (@ 500 RPM) at 36%fuel conversion for iso-octane fuel, � � 1.0

Iso-octane intermediates Species mole fraction

Experiment Model prediction

carbon monoxide 2.31e-3 3.64e-3isobutene 1.69e-3 3.52e-3formaldehyde 1.17e-3 3.05e-32,2,4,4-tetramethyl-tetrahydrofuran 1.01e-3 4.34e-4acetone 8.18e-4 2.06e-32-t-butyl-3-methyloxetane 5.51e-4 1.95e-42-isopropyl-3,3-dimethyloxetane 4.74e-4 3.72e-4propene 3.23e-4 4.89e-44,4-dimethyl-2-pentene 2.52e-4 8.09e-52,4,4-trimethyl-1-pentene 2.32e-4 1.48e-4isobuteraldehyde 2.07e-4 3.53e-4methacrolein 1.86e-4 1.64e-42,4-dimethyl-2-pentene 1.68e-4 1.25e-42,4,4-trimethyl-2-pentene 1.52e-4 2.08e-42,3-epoxy-2,4,4-trimethylpentane 1.43e-4 5.00e-5isobutene oxide 1.39e-4 1.02e-42,2-dimethyl propanal 1.30e-4 6.02e-5


oxygenates, formaldehyde, 2,2,4,4-tetrameth-yl-tetrahydrofuran (TMTHF) and acetonewere present in the greatest amounts, fol-lowed by 2-tert-butyl-3-methyl oxetane, 2-iso-propyl-3,3-dimethyl oxetane, isobuteralde-hyde and methacrolein. Both formaldehydeand acetone are overpredicted by more than afactor of two. TMTHF is underpredicted byless than a factor of three and the oxetanesare also underpredicted by almost an order ofmagnitude. Isobuteraldehyde and methacro-lein are reasonably well predicted by themodel.

Li et al. [19] studied iso-octane autoigni-tion in a motored, single-cylinder engineand obtained in-cylinder samples at differ-ent points prior to autoignition. They foundthat isobutene and TMTHF were the majorintermediates formed during iso-octane oxi-dation in agreement with Leppard’s experi-ments. In addition, the di- and tri-methylpentenes were also observed, as were the C1to C4 aldehydes and C8 oxetane species. 2,2-dimethyl propanal was also detected in traceamounts.

SENSITIVITY ANALYSIS

A detailed analysis was carried out to investi-gate the sensitivity of each class of reactiondenoted earlier, to the oxidation of iso-octane ineach experiment. Sensitivity analyses were per-formed by multiplying the rate constants of aparticular class of reaction by a factor of two(both forward and reverse rates) and then cal-culating the percent change in reactivity. In thecase of the shock tube experiments of Fiewegeret al. [6, 7] for example, we calculated thepercent change in ignition delay time comparedwith the baseline simulation. A positive percentchange indicates a longer ignition delay and adecreased overall reaction rate, and a negativechange indicates an increased overall reactivityof the system. Three different temperatureswere chosen to help indicate sensitivity of eachclass to the onset, middle and end of the NTCregion at an average pressure of 40 bar. Thereaction rate constants that exhibited the high-est sensitivity are shown in Fig. 17. Reactions inwhich we multiplied both forward and reverserate constants by a factor of two are denoted

Fig. 17. Sensitivity coefficients in a shock tube [7]. Stoichiometric fuel in air, P5 � 40 bar.


with an equal to “�” sign between reactants andproducts and reactions in which we multipliedonly the forward rate constant (i.e., effected achange in the equilibrium constant) are denotedwith an arrow “f” between reactants and prod-ucts. In addition, for the low temperature shocktube experiments of Fieweger et al. our analysishas mainly focused on the classes of reactionwhich are represented in Fig. 2. We did includesensitivity to reactions such as OH � OH �M � H2O2 � M. We have used the chemistryedits from the HCT code to identify the impor-tant reactions occuring under these conditions.However, because we performed a brute-forceanalysis we cannot be certain that we haveidentified all of the sensitive reactions.

To understand the sensitivity analysis pertain-ing to the shock tube results of Fieweger et al. itis appropriate to refer to Fig. 2. In particular, atthe relatively low temperatures of this study thefate of the QOOH species is all important.Reactions which promote the route leading toQOOH formation and its subsequent route tochain branching via its addition to molecularoxygen result in a negative sensitivity coefficient(increased reactivity), while reactions whichlead to the decomposition of the QOOH radicalshow a positive sensitivity coefficient (decreasedreactivity).

The reaction with the highest negative sensi-tivity, and thus increases the rate of oxidation isthe reaction of the fuel with alkyl-peroxyl radi-cals:

iC8H18 � RO2 ¡ xC8H17 � RO2H

This sensitivity was not observed in our studiesof n-heptane oxidation. However, we have re-duced our rate expressions for RO2 º QOOHisomerization reactions and this has led to anincreased importance of the bimolecular reac-tion above. The negative sensitivity to this reac-tion is understandable because this reactionleads to the formation of alkyl radicals in addi-tion to stable alkylhydroperoxide species whichcan decompose to form an alkyoxyl- and ahydroxyl radical.

RO2 º QOOH isomerization reactions alsoshow a strong negative sensitivity coefficient.Indeed, either increasing the rate expression bya factor of two, with or without a change in

equilibrium constant, leads to almost identicalnegative sensitivity coefficients at all tempera-tures.

Another reaction type that increases the over-all reactivity of the system is the addition ofalkyl radicals to molecular oxygen, reaction type10. Interestingly, increasing the rate expressionsby a factor of two without affecting the equilib-rium constants has very little effect. However, achange of a factor of two in the equilibriumconstants shows a high negative sensitivity coef-ficient. This result indicates that our simulationsare predicting the R � O2 º RO2 to be inequilibrium at all reflected shock temperaturesand that the thermodynamic parameters usedfor the alkyl and alkylperoxy radicals are veryimportant. This behavior is also observed forthe addition of hydroperoxyl alkyl radicals tomolecular oxygen, reaction type 22. A change inequilibrium constant leads to an increase inreactivity, while a change in overall rate has verylittle effect on the reactivity of the system.

The isomerization of the peroxy-alkylhy-droperoxide radical to form a carbonyl-hy-droperoxide molecule and OH radical, reactiontype 23, also shows a high negative sensitivity.

xC8H16OOH � yO2º23

iC8ketxy � OH

In xC8H16OOH � yO2 x refers to the carbonatom to which the OOH group is attached andy refers to the site where the O2 group isattached. In iC8ketxy, x refers to the carbon withthe carbonyl group attached and y refers to thesite where the hydroperoxy group is attached.We have also observed identical sensitivity tochanging the equilibrium constant of this reac-tion by a factor of two, that is, multiplying theforward rate by two but maintaining the reverserate at its usual value. This result is expected, asthe reverse rate of addition of OH radical to thecarbonylhydroperoxide is very slow and is notobserved computationally.

In addition, we observe high negative sensi-tivity coefficients to hydrogen atom abstractionreactions from the fuel by HO2, CH3O2, andOH radicals. In particular, the importance ofthe abstractions by HO2 and CH3O2 radicalsbecomes more pronounced at higher tepmera-tures. This is a reflection of the importance of


intermediate temperature kinetics in the range825 to 1000 K.

Hydroperoxyl radical chemistry and H �O2 � O � OH chain branching reactions arealso important.

H � O2 ¡ O � OH

H � O2 � (M) ¡ HO2 � (M)

In the above sequence the reaction producingoxygen atoms and hydroxyl radicals is chainbranching and thus promotes reactivity whilethe second, competing reaction, reduces thereactivity because it produces just one reactiveradical.

Moreover, the self reaction of hydroperoxylradicals shows a positive sensitivity coefficientas it consumes hydroperoxyl radicals whichcould otherwise abstract a hydrogen atom froma stable species to ultimately produce two hy-droxyl radicals from one hydroperoxyl radical,as depicted in the equation array above.

HO2 � HO2 ¡ H2O2 � O2

The reaction which shows the highest positivesensitivity and therefore reduces the reactivityof the system is the �-scission of the alkylradical, reaction type 3. This reaction shows aparticularly high sensitivity at 825 K, in themiddle of the NTC region.

Other reactions which show a high positivesensitivity coefficient (reducing reactivity) arethe decompo-sition reactions of the QOOHradical, namely:

QOOH ™™™319

cyclic ether � OH

QOOH ™™™320

olefin � HO2

QOOH ™™™321

olefin � carbonyl radical

We also performed a sensitivity analysis onthe flow reactor experiments of Chen et al. [23]at a temperature of 945 K, at 6 atm pressure andat an equivalence ratio of 0.05. We define thesensitivity coefficient as the percentage changein time taken for 20% and 60% of the fuel to beconsumed. The results of this analysis are de-

Fig. 18. Sensitivity coefficients in a flow reactor [23] at 20% and 60% fuel conversion. 0.09% iso-octane oxidation at 6 atm,� � 0.05, T � 945 K.


picted in Fig. 18. A general observation is that,under these conditions, the low temperaturemechanism is of minor importance. In addition,at 945 K and 6 atm, the system is in theintermediate to high temperature regime and sohydroperoxyl- and methylperoxyl radical chem-istry, as described above, is important.

The reaction with the highest negative sensi-tivity coefficients and thus most effective inpromoting the overall rate of reaction are thoseinvolving the hydroperoxyl and hydroxyl radi-cals. In addition, hydrogen atom abstraction bymethyl-peroxy radicals is also important.

H2O2 � (M) ¡ OH � OH � (M)

iC8H18 � HO2 ¡ xC8H17 � H2O2

iC8H18 � OH ¡ xC8H17 � H2O

iC8H18 � CH3O2 ¡ xC8H17 � CH3O2H

Increasing the rate of unimolecular fuel de-composition also promotes the reactivity of thesystem and we observe a high negative sensitiv-ity coefficient for this type of reaction.

In addition, the CH3 � HO2 reaction shows a

high sensitivity. The reaction producing a me-thoxy and a hydroxyl radical promotes reactivitywhile that producing methane and molecularoxygen understandably reduces the overall re-activity.

CH3 � HO2 ¡ CH3O � OH

CH3 � HO2 ¡ CH4 � O2

Finally, we performed a sensitivity analysis at812 K and 900 K for the jet-stirred reactorexperiments of Dagaut et al. [10] with 0.1%iso-octane at an equivalence ratio of 1.0, at apressure of 10 atm, with a residence time of 1 s,at 812 K. The sensitivity coefficient is defined asthe percentage change in fuel consumed relativeto the baseline case (52.1%). For consistency,an increase in fuel consumption is assigned anegative sensitivity coefficient as it correspondswith an increased overall reactivity. The resultsof this analysis are depicted in Fig. 19.

The experimental conditions again fall in theintermediate to high temperature oxidation re-gime and therefore hydroperoxyl- and methyl-peroxyl radical chemistry is sensitive. We see

Fig. 19. Sensitivity coefficients in a JSR [10]. 0.1% iso-octane oxidation at 10 atm, � � 1.0, � � 1 s.


little or no sensitivity to the low temperaturemechanism and a low sensitivity to unimolecularfuel decomposition.

CONCLUSIONS

A detailed chemical kinetic mechanism hasbeen developed to simulate iso-octane oxida-tion over wide ranges of temperature, pressureand equivalence ratio. This mechanism is basedon our previous modeling of hydrocarbon oxi-dation and, in particular, of n-heptane. Theoverall reactivity of iso-octane oxidation is wellreproduced by the model, as indicated by thegood agreement between modeling and experi-ment in the shock tube experiments. In addi-tion, experimentally quantified intermediatespecies profiles in flow reactors and jet-stirredreactors are well reporduced by the model,indicating that the chemical pathways leading totheir formation are well understood. However,we are unhappy that, in order to reproduce thevery low reactivity observed experimentally atlow temperatures (600–770 K), we had to de-crease the rates of alkyl-peroxyl radical isomer-ization (reaction type 12) and peroxy-alkylhy-droperoxyl radical isomerization (reaction type23) by a factor of three relative to our n-heptanework. There must be some reason why the ratesof these isomerization reactions are slower foriso-octane than for n-heptane or there may besome other pathway(s) occurring at lower tem-peratures.

This study was performed under the auspices ofthe U.S. Department of Energy by the LawrenceLivermore National Laboratory under contractNo. W-7405-ENG-48. This work was supportedby the US Department of Energy, Office of Trans-portation Technologies, Gurpreet Sing and JohnGarbatz program managers, and by the Office ofBasic Energy Sciences, Division of Chemical Sci-ences, Frank Tully, program manager.

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Received 12 October 2001; revised 18 December 2001; ac-cepted 18 December 2001


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