A Comprehensive Modeling Study of iso-Octane Oxidation
H.J.CURRAN,*,†P.GAFFURI,W.J.PITZ and C.K.WESTBROOK
Lawrence Livermore National Laboratory,Livermore,CA94551,USA
A detailed chemical kinetic mechanism has been developed and used to study the oxidation of iso-octane in a jet-stirred reactor,flow reactors,shock tubes and in a motored engine.Over the series of experiments investigated,the initial pressure ranged from1to45atm,the temperature from550K to1700K,the equivalence ratio from0.3to1.5,with nitrogen-argon dilution from70%to99%.This range of physical conditions,together with the measurements of ignition delay time and concentrations,provide a broad-ranging test of the chemical kinetic mechanism.This mechanism was based on our previous modeling of alkane combustion and,in particular,on our study of the oxidation of n-heptane.Experimental results of ignition behind reflected shock waves were used to develop and validate the predictive capability of the reaction mechanism at both low and high temperatures.Moreover,species’concentrations fromflow reactors and a jet-stirred reactor were used to help complement and refine the low and intermediate temperature portions of the reaction mechanism,leading to good predictions of intermediate products in most cases.In addition,a sensitivity a
nalysis was performed for each of the combustion environments in an attempt to identify the most important reactions under the relevant conditions of study.©2002by The Combustion Institute
INTRODUCTION
There is continued interest in developing a better understanding of the oxidation of large hydrocarbon 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 investigations of homogeneous charge compression ignition engines(HCCI),in which iso-octane is used both as a neat fuel and as a component in a primary reference fuel blend[1–4].This interest is motivated by the need to improve the effi-ciency and performance of currently operating combustors 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 compression ignition engines,has a cetane number of ap-proximately15.
Previous experimental studies of iso-octane oxidation have focused on shock tubes[5–7], jet-stirred reactors[8–11],rapid compression machines[12–16],engines[17–19],flow reactors [20–22]and[23],in which a dynamic behaviour is observed.All of these systems exhibit phe-nomena including self ignition,coolflame,and negative temperature coefficient(NTC)behav-ior.Furthermore,variation in pressure from1 to45bar changes the temperature range over which the NTC region occurs.
Coˆme et al.[24,25]have used an automatic generation mechanism package to create chemical kinetic mechanisms for n-heptane and iso-octane.Ranzi et al.[15]used a semi-detailed model to simulate the oxidation of PRF mixtures.This mechanism was further used to perform a wide range simulation of iso-octane oxidation[26].Roberts et al.[27] developed a semi-detailed kinetic mechanism to simulate autoignition experiments in a co-operative fuels research engine.More re-cently,Curran et al.[28]used a detailed chemical kinetic mechanism to simulate the oxidation of PRF mixtures.This mechanism was also used to simulateflow reactor exper-iments on the lean oxidation of iso-octane in the intermediate temperature regime at ele-vated pressures[23].Davis and Law[29]used a semi-detailed chemical kinetic mechanism to predict laminarflame speeds for iso-oc-tane/air and n-heptane airflames.
In this study we include all of the reactions known to be pertinent to both low and high temperature kinetics.We show how the detailed kinetic model reproduces the measured results in each type of experiment,including the fea-tures of the NTC region.We discuss the specific classes of elementary reactions and reaction pathways relevant to the oxidation process,how
*Corresponding author.E-mail:henry.curran@gmit.ie
†Currently at Galway-Mayo Institute of Technology,Dublin
Rd.,Galway,Ireland.
COMBUSTION AND FLAME129:253–280(2002)
©2002by The Combustion Institute0010-2180/02/$–see front matter Published by Elsevier Science Inc.PII S0010-2180(01)00373-X
we arrived at the rate constants for each class of reaction,and indicate which reactions are the most important in consuming the fuel at both low and high temperature.In addition,a sensi-tivity analysis was carried out on each set of experimental results by changing the rate con-stants for different classes of reaction in the kinetic mechanism.The results of this analysis indicate the relative important of each class of reaction and also the variation in contribution of these classes of reactions over the range of conditions of the experiments.
MODEL FORMULATION
Computer modeling of iso-octane oxidation was performed using the HCT(Hydrodynamics, Chemistry and Transport)program[30],which solves the coupled chemical kinetic and energy equations,and permits the use of a variety of boundary and initial conditions for reactive systems depending on the ne
eds of the particu-lar system being examined.The present detailed reaction mechanism was constructed based on the hierarchical nature of hydrocarbon-oxygen systems.The mechanism was built in a stepwise fashion,starting with small hydrocarbons and progressing to larger ones.Much of this work has been documented previously[31–34],and has been enhanced by our experience in simu-lating propane[35],neopentane[36,37],the pentane isomers[38],the hexane isomers[39, 40],n-heptane[41],and primary reference fuel blends[28,40].
The current detailed mechanism incorporates both low-and high-temperature kinetic schemes. At higher temperatures,unimolecular fuel and alkyl radical species decomposition and isomeriza-tion reactions are especially important,while at low temperatures H atom abstraction from the fuel molecule and successive additions of alkyl radicals to molecular oxygen,leading to chain branching,dominate the oxidation process.
The low temperature submechanism is based on our detailed n-heptane chemical kinetic mechanism published previously[41].In the interim,due to increased accuracy in both ex-perimental and computational methods,the thermodynamic parameters associated with the low-temperature hydroperoxide species have been modified.The thermodynamic properties for the relevant radicals and stable parents were based on the group additivity method of Benson [42]using THERM[43,44]with
updated H/C/O groups and bond dissociation groups [44].We have updated the H/C/O and bond dissociation group values based on the recent studies of Lay and Bozzelli[45]and have mod-ified these slightly so that the thermodynamic functions of R˙ϩO2ºRO˙2reactions agree with the experimental and calculated values of Knyazev and Slagle[46]for ethyl radical.These comparisons can been found in a paper by Curran et al.[47].
Classes of Reactions
The oxidation mechanism developed for iso-octane is formulated in the same way as that published previously for n-heptane[41].The mechanism is developed in a systematic way, with each type of reaction in the oxidation process treated as a class of reaction with the appropriately assigned rate constant expres-sion.Because of recent changes in thermody-namic data,and in an attempt to improve our treatment of some of our estimated rate ex-pressions,some of those expressions pub-lished in our n-heptane paper have been changed.We outline these changes in the discussion below.The complete reaction mechanism for iso-octane oxidation includes 3,600elementary reactions amoung860chem-ical species.The mechanism is not presented here due to its length,but a complete copy can be obtained from the authors at the Livermore combustion website[48].
The major classes of elementary reactions considered in the present mechanism include the following:
1.Unimolecular fuel decomposition
2.H atom abstraction from the fuel
3.Alkyl radical decomposition
4.Alkyl radicalϩO2to produce olefinϩHO˙2
directly
5.Alkyl radical isomerization
6.Abstraction reactions from Olefin by o˙H,H˙,
O˙,and C˙H3
7.Addition of radical species to olefin
8.Alkenyl radical decomposition
9.Olefin decomposition
254H.J.CURRAN ET AL.
10.Addition of alkyl radicals to O2
11.R˙ϩRЈO˙2ϭRЈO˙ϩRO˙
12.Alkyl peroxy radical isomerization(RO˙2º
Q˙OOH)
13.RO˙2ϩHO˙2ϭRO2HϩO2
14.RO˙2ϩH2O2ϭRO2HϩHO˙2
15.RO˙2ϩCH3O2ϭRO˙ϩCH3O˙ϩO2
16.RO˙2ϩRЈO˙2ϭRO˙ϩRЈO˙ϩO2
17.RO2HϭRO˙ϩO˙H
18.RO˙decomposition
19.Q˙OOHϭcyclic etherϩO˙H(cyclic ether
formation via cyclisation of diradical) 20.Q˙OOHϭolefinϩHO˙2(radical site␤to
OOH group)
21.Q˙OOHϭolefinϩcarbonyl radical(radical
site␥to OOH group)
22.Addition of Q˙OOH to O2
23.Isomerization of O˙2QOOH and formation
of carbonylhydroperoxide and O˙H
24.Decomposition of carbonylhydroperoxide
to form oxygenated radical species and O˙H 25.Cyclic ether reactions with O˙H and HO˙2 The naming conventions used above are R˙and RЈdenoting alkyl radicals or structures and Q denoting C n H2n species or structures.For each of these classes of reactions we use the same reaction rate constant fo
r analogous occurrences in differ-ent molecules.Thus,we assume that the abstrac-tion of a tertiary H atom by reaction with O˙H radicals has exactly the same rate in2-methyl butane,2-methyl pentane,3-methyl pentane,and in iso-octane.Correspondingly,the total rate of tertiary H atom abstraction by O˙H in2,3-dimethyl butane and in2,4-dimethyl pentane is twice that in 2-methyl pentane,because the two former fuels have two such H atoms at tertiary sites.The n-heptane mechanism contains C4,C5,and C6 submechanisms.We treat all of the different reaction classes provided above in exactly the same way regardless of whether the fuel is n-butane,n-pentane,n-hexane,or n-heptane.Our treatment of these reaction classes in described in the following sections.
HIGH TEMPERATURE MECHANISM Reactions in classes1through9are sufficient to simulate many high temperature applications of iso-octane oxidation.We have made a number of ad hoc assumptions and approximations that may not be suitable for some problems involving alk-ene and alkyne fuels and further analysis is needed to refine details for these fuels.However,under the conditions of this study,iso-octane oxidation is rela-tively insensitive to these assumptions.
Reaction Type1:Unimolecular Fuel Decomposition
These reactions produce two alkyl radicals or one alkyl radical and one hydrogen atom.Sim-ilar to our reactive carbonyl species
work on n-heptane,we calculate the rate constant expressions in the reverse direc-tion,the recombination of two radical species to form the stable parent fuel with the decompo-sition reaction being calculated by microscopic reversibility.For recombinations of an alkyl radical and a hydrogen atom we assume a rate constant expression of5ϫ1013cm3molϪ1sϪ1, based on half that recommended by Allara and Shaw[49]for H˙ϩR˙recombination reactions. There is very little information available on the rate of recombination reactions for C2alkyl radi-cals and larger.For the recombination of C˙H3ϩC˙7H15radicals our high-pressure rate expressions are based on the recommendations of Tsang[50] for C˙H3ϩtC˙4H9(methyl addition to a tertiary site),namely1.63ϫ1013exp(ϩ596cal/RT)cm3 molϪ1sϪ1and half Tsang’s[51]recommendation for C˙H3ϩiC˙3H7(methyl addition to an iso-propyl site)resulting in a rate constant of6.80ϫ1014TϪ0.68cm3molϪ1sϪ1.For the recombination of tC˙4H9ϩiC˙4H9we used Tsang’s[50]recom-mendation of3.59ϫ1014TϪ0.75cm3molϪ1sϪ1. Finally for the recombination of neoC˙5H11ϩiC˙3H7we used a rate expression of4.79ϫ1014 TϪ0.75cm3molϪ1sϪ1,similar to the value used for tC˙4H9ϩiC˙4H9above.
All of these rate constant expressions were used as input in HCT and the high-pressure decomposition 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 constant expressions were produced at various pressures.
Reaction Type2:H Atom Abstraction
At both low and high temperatures H atom ab-straction takes place at primary,secondary and
255
OXIDATION OF ISO-OCTANE
tertiary sites of iso-octane,which leads to the formation of four distinct iso-octyl radicals,Fig.1.The rate constant for abstraction is depen-dent on the type of hydrogen atom being abstracted,be it either a 1°,2°,or 3°hydrogen atom.It is also dependent on the local envi-ronment of the hydrogen atom that is ethane,propane,isobutane,and neopentane all have 1°hydrogen atoms but their local environ-ment is different and,on a per-hydrogen atom basis,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 to three quarter times the rate of abstraction from neopentane;hydrogen atom abstraction from site (b)analogous to 2°hydrogen atom abstraction from propane;hydrogen atom ab-straction from site (c)analogous to 3°hydro-gen atom abstraction from isobutane,and hydrogen atom abstraction from site (d)anal-ogous to 1°hydrogen atom abstraction from propane.We summarize these rate constant expressions in Table 1,and calculate the reverse rate constants from thermochemistry.Note that our est
imates for hydrogen atom
abstraction by CH 3O
˙2and RO ˙2radicals are equal to and 0.72times those for abstraction by HO 2radicals,respectively.
Reaction Type 3:Alkyl Radical Decomposition We estimate the decomposition of alkyl radicals in the way described in our n-heptane paper [41].Because alkyl radical ␤-scission is endo-thermic we calculate the rate constant in the reverse,exothermic direction that is the addi-tion of an alkyl radical (or H
˙atom)across the double bond of an alkene.In this way we avoid the additional complexity of the enthalpy of reac-tion,allowing the forward,␤-scission rate constant to be calculated from thermochemistry.
Rate constants for the addition of radicals
across a double bond depend on (1)the site of addition (terminal or internal C atom)and (2)the type of radical undergoing addition.Our rate constants for these addition reactions are based on the recommendations of Allara and Shaw [49].Typically,the rate of addition of a H
˙atom across a double bond has a pre-exponential A -factor of 1ϫ1013cm 3mol Ϫ1s Ϫ1with an activation energy of 1,200cal/mol
if the H
˙atom adds to the terminal C atom of the alkene,and 2,900cal/mol if the H
˙atom adds to an internal C atom.The rate constant for the addition of an alkyl radical has a lower A -factor and higher activation energy than for the addition of a H atom.For the addition of an alkyl radical,the A -factor is approximately 8.5ϫ1010cm 3mol Ϫ1s Ϫ1with an activation energy of approximately 7,800cal/mol if ad-dition occurs at the terminal C atom and 10,600cal/mol if addition occurs at an internal C atom.We assume these reactions are in their high pressure limit for the conditions considered in this study.
Reaction Type 4:Alkyl Radical ؉O 2؍
Olefin ؉HO
˙2This reaction type was discussed in some detail in
our n-heptane paper.For reasons,described in that paper,we do not included reaction type 4in our mechanisms for alkyl radical containing more than four carbon atoms.We have obtained good agreement between experimental and computa-tional results for both C 5,C 6,and C 7species using this assumption [39–41].Further discussion is given below for reaction type 20.
Reaction Type 5:Alkyl Radical Isomerization Our treatment of this reaction type has been described in our n-heptane paper.In sum-mary,the rate constant depends on the type of C-H bond (1°,2°,or 3°)being broken,and the ring strain energy barrier involved.The acti-vation energy (E a )is estimated,E a using the expression,
E a ϭ⌬H rxn ϩring strain ϩE abst
where ⌬H rxn is taken to be the enthalpy of reaction and is only included if the reaction
is
Fig.1.Iso-octane with its four distinct sites for H-atom abstraction.
256H.J.CURRAN ET AL.
endothermic.The activation energy for abstrac-tion is determined,following the analysis of Bozzelli and
Pitz[54],from an Evans-Polanyi plot,E abst versus⌬H rxn(taken in the exothermic direction)of similar H atom abstraction reac-tions,RHϩRЈϭR˙ϩRЈH,leading to the following expression:E abstϭ12.7ϩ(⌬H rxnϫ0.37)
The A-factors were estimated to be similar to those determined for alkyl-peroxy radical isomerization(reaction type12)described below. The rate constants employed for iso-octyl radical isomerizations are summarized in Table2.
TABLE1
Rate constant expressions for H atom abstraction from the fuel(cm3–mol–sec–cal
units)
Radical Site Rate expression per site Citation
A n⑀a
H˙Primary(a)7.34ϫ105  2.778147.†a
H˙Secondary(b)  5.74ϫ105  2.494124.†b
H˙Tertiary(c)  6.02ϫ105  2.402583.†c
H˙Primary(d)  1.88ϫ105  2.756280.†d
O˙H Primary(a)  2.63ϫ107  1.80278.[84] O˙H Secondary(b)9.00ϫ105  2.00Ϫ1133.[84] O˙H Tertiary(c)  1.70ϫ106  1.90Ϫ1451.[84] O˙H Primary(d)  1.78ϫ107  1.801431.[84] O˙Primary(a)8.55ϫ103  3.053123.†a
O˙Secondary(b)  4.77ϫ104  2.712106.†b
O˙Tertiary(c)  3.83ϫ105  2.41893.†c
O˙Primary(d)  2.85ϫ105  2.503645.†d
C˙H3Primary(a)  4.26ϫ10Ϫ148.064154.†a
C˙H3Secondary(b)  2.71ϫ104  2.267287.†b
C˙H3Tertiary(c)8.96ϫ103  2.336147.†c
C˙H3Primary(d)  1.47ϫ10Ϫ1  3.876808.†d HO˙2Primary(a)  2.52ϫ10130.020435.[85] HO˙2Secondary(
b)  5.60ϫ10120.017686.[85] HO˙2Tertiary(c)  2.80ϫ10120.016013.[85] HO˙2Primary(d)  1.68ϫ10130.020435.[85] CH3O˙Primary(a)  4.74ϫ10110.07000.[86] CH3O˙Secondary(b)  1.10ϫ10110.05000.[86] CH3O˙Tertiary(c)  1.90ϫ10100.02800.[86] CH3O˙Primary(d)  3.20ϫ10110.07000.[86] O2Primary(a)  6.30ϫ10130.050760.[86] O2Secondary(b)  1.40ϫ10130.048210.[86] O2Tertiary(c)7.00ϫ10120.046060.[86] O2Primary(d)  4.20ϫ10130.050760.[86] C˙2H5Primary(a)  1.50ϫ10110.013400.[49] C˙2H5Secondary(b)  5.00ϫ10100.010400.[49] C˙2H5Tertiary(c)  1.00ϫ10110.07900.[49] C˙2H5Primary(d)  1.00ϫ10110.013400.[49] C˙2H3Primary(a)  1.50ϫ10120.018000.[87] C˙2H3Secondary(b)  4.00ϫ10110.016800.[87] C˙2H3Tertiary(c)  2.00ϫ10110.014300.[87] C˙2H3Primary(d)  1.00ϫ10120.018000.[87]†This study,see text.
a3/4ϫanalogous rate expression for neopentane[37].
b NIST database[83]fit to C
3H8ϩR˙ϭiC3H7ϩRH.
c By analogy with Tsang’s[50]recommendation for iC
4H10ϩR˙ϭtC4H9ϩRH.
d NIST database[83]fit to C
3H6ϩR˙ϭnC3H7ϩRH.
257
OXIDATION OF ISO-OCTANE

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