Fuel 115 (2014) 132–144

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Fuel

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Hexadecane mechanisms: Comparison of hand-generated andautomatically generated with pathways

0016-2361/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.fuel.2013.06.055

⇑ Corresponding author. Tel.: +46 70 6633463.E-mail address: edward.blurock@gmail.com (E.S. Blurock).

Ismail E. Mersin a,c, Edward S. Blurock a,e,⇑, Hakan S. Soyhan b,d, Alexander A. Konnov a

a Combustion Physics Department, Lund University, Swedenb Mechanical Engineering Department, Sakarya University, Turkeyc Energy Systems Engineering Department, Yalova University, Turkeyd Team-SAN Co., www.teamsan.com.tr, Technology Center of Sakarya University, Sakarya, Turkeye http://www.esblurock.info, Lund, Sweden

h i g h l i g h t s

� A detailed hexadecane mechanism with 2176 species and 7269 (reversible) reactions was developed.� The hexadecane mechanism was created with the automatic generation system: REACTION.� A systematic comparison showed that a automatic generation and by hand generation can be similar.� Ignition delay times and the sensitivity of different reaction classes was calculated.

a r t i c l e i n f o

Article history:Received 28 April 2013Received in revised form 10 June 2013Accepted 27 June 2013Available online 16 July 2013

Keywords:HexadecaneDetailed mechanismLow temperature chemistry

a b s t r a c t

In this paper, the automatically generated mechanism for hexadecane with both high and low tempera-ture chemistry included is compared to a systematically generated mechanism by hand. In contrast toother systems for automatic generation, the REACTION system uses pathways to organize the applicationof reaction classes. A pathway is a sequence of reaction classes where only those species produced by theprevious step of the pathway are used in the current step of the pathway. This ‘‘controlled’’ generationprocess not only mimics what is done by hand, but also helps to limit the size of the generated mecha-nisms. Both systematic reaction by reaction comparisons and numerical simulation (zero-dimensionalconstant volume) comparisons were done and the mechanisms were found to have minor differences.Both mechanisms used the same set of reaction classes to model the high and low temperature combus-tion chemistry of all n-alkanes up to hexadecane. In addition, a sensitivity analysis of all the reaction clas-ses was performed. The generated mechanism has 2176 species and 7269 (reversible) reactions.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction of diesel (and jet fuels) is long chain n-alkanes [3] and hence they

Gasoline, diesel and jet fuels, particularly those derived frompetroleum sources are composed of hundreds to thousands of com-pounds. For example, diesel fuel is a complex mixture of manyclasses and sizes of hydrocarbons and although the compositionof diesel fuel is highly variable, there are some trends. The carbonnumbers of the components range from approximately 10 to 22,with an average carbon number of 14 or 15 [1]. In addition tothe fuels complexity, modern engines, such as HCCI, are dependentnot only on the pyrolysis regimes of combustion, but also on thecomplex chemistry of the so-called ‘‘low temperature’’ (see forexample, [2]) combustion region. Modeling of such fuels requiressimplifications in the components of the fuel through the use ofsurrogate fuel formations. In particular, a significant component

are a significant component of surrogate formulations (see, forexample, [4]). N-hexadecane, a long chain n-alkane, has been in-cluded in several surrogate models in the literature [5–8].

There are a multitude of techniques to model a combustion pro-cess (see, for example, [9–14]). On one side there are global reactionmechanisms [15,16] used in computational fluid dynamic wherethe engine configuration is the focus of study. On the other sidethere are detailed chemical modeling where physical conditionsare simplified (for example, zero-dimensional) and the combustionchemistry, such as intermediate and product emission species, isthe focus of the study [17,18]. This paper focuses on the latter.

1.1. Automatic generation

In detailed combustion modeling, as the hydrocarbon speciesgrows, so does the mechanism size, reflected in the number ofnecessary species and reactions needed to model the hydrocarbon

I.E. Mersin et al. / Fuel 115 (2014) 132–144 133

oxidation, and hence the computational effort. However, with thegrowing computational efficiency of available computers, morecomplex mechanisms involving larger hydrocarbons are becomingfeasible [19].

To aid in the study the chemistry of diesel fuels, mechanisms forn-alkanes up to hexadecane have been developed. One of the firstexperimental and modeling studies of hexadecane was the auto-matically generated pyrolysis model for n-hexadecane that in-cluded a detailed primary mechanism (reactions directly fromthe fuel), a lumped secondary mechanism leading to their basemechanism pyrolysis model with 265 species and 1787 reactions[20]. Biet et al. [21] extended this model to a set of automaticallygenerated mechanisms of n-alkanes up to n-hexadecane with alsoa detailed primary mechanism, a lumped secondary mechanismand a base mechanism. In this set, the mechanism for hexadecanehas over 1600 species and almost 10,000 reactions. Ranzi et al. [22]developed an automatically generated and highly lumped mecha-nism for all large n-alkanes up to n-hexadecane, modeling boththe high and low temperature regimes. Westbrook et al. [23] hasdone remarkable work in generating by hand comprehensivemechanisms for large hydrocarbons, i.e. those including not onlythe ‘‘primary’’ fuels, but all smaller ‘‘fuels’’. For example, the n-hexadecane mechanism with 2115 species and 8157 reactionshas the complete high and low temperature sub-mechanisms forall n-alkanes from propane until n-hexadecane. This mechanismwas based on the systematic application of the reaction classesoutlined by Curran et al. [24].

A significant difference between producing detailed mecha-nisms for small hydrocarbons, such as methane or propane andfor large hydrocarbons such as n-hexadecane is the source of therate constants for the individual reactions. As the size of the spe-cies increases, the likelihood of direct experimental evidence, oreven quantum mechanical computational models, decreases. Reli-ance on general physical principles relating to functional groups ofthe species increases for larger species. The fundamental assump-tion is that the influence of functional groups around the reactivecenter, i.e. those atoms directly involved in bond making, bondmaking and valence changes, decreases with increasing ‘‘distance’’from the reactive center. Distance, in most instances, for examplethose without resonance, is measured as the number of bondsaway from the reactive center. For example, the hydrogen abstrac-tion from a primary carbon on a n-heptane can be assumed to bethe same as from a primary carbon on a n-hexadecane. The addi-tion of more carbons in the chain away from the primary carbondoes not significantly affect the forward rate constant. This philos-ophy naturally leads to the concept of reaction classes, i.e. general‘‘rules’’ of reactivity among chemical species. Whether one is pro-ducing a large mechanism by hand, or doing it automatically usingan automatic mechanism generator, the modeler has to choosewhich reaction classes are significant for the chemical regimebeing studied and apply them systematically.

Another feature of large mechanisms is their combinatorialstructure [25]. A natural consequence of the increase in numberof carbons is the combinatorial increase of the number of possiblereactions. This combinatorial structure and the systematic and er-ror-free application of reaction classes lead naturally to the use ofautomatic mechanism generators. Given a set of valid reactionclasses and a defined procedure on how to apply them, an auto-matic generator can relieve the modeler of the painstaking and er-ror-prone work of mechanism generation.

1.2. Automatic generation: REACTION

Though they have fundamental commonalities, reaction gener-ators can differ in the set of reaction used (and how they are rep-resented) and how the reaction classes are applied to generate the

final mechanism (see for example, EXGAS [26], [27], MAMOX[28,22] and RMG [29–31]). REACTION [32,33], the generator usedin this paper, has several significant features that made the workin this paper possible.

First, a fundamental principle of REACTION is that it is ‘‘data-driven’’, i.e. the chemical information is not hard-coded and comesfrom an external database. The external database for reaction clas-ses stem from those defined by Curran et al. [24] and were trans-lated to the reaction pattern database of REACTION [34,35].

Another feature is that different ‘‘base’’ mechanisms, i.e. thatpart of the total mechanism made up of smaller species (4 carbonsor less) that is not generated, can be used in conjunction with thegeneration mechanism. For example, for the previously generateddecane mechanism by Moreac et al. [33], the mechanism derivedfrom Hoyerman et al. [36] was used and for the work in this paper,the chemistry of (linear) C0–C4 chemistry was extracted from theWestbrook et al. hexadecane mechanism [23].

A third important feature, that is unique to REACTION, is thestrategy by which the reaction classes are applied. Instead of anexhaustive combinatorial strategy, the concept of reaction path-ways is implemented. A reaction pathway is defined as a sequenceof reaction classes, or sets of reaction classes, that are applied oneafter the other. In REACTION, a pathway is defined by the user inthe external database. This also gives added flexibility to the chem-istry which can be modeled. The complete generated mechanism isthe combined total of the submechanisms generated from a set ofseed molecules applied to a set of pathways. The concept of path-ways and how they were applied to generate the n-hexadecanemechanism is discussed later in this paper.

The thermodynamic constants for each of the products comefrom one of two sources. Some of the species thermodynamic datais within the REACTION database. All of the species in the basemechanism fall in this category. If the species are not in the data-base, then REACTION uses simple Benson additivity rules to calcu-late the thermodynamics. The radical species are calculated byusing the radical group additivity rules. The given values at eachtemperature from the Benson rules are then converted to NASApolynomial form.

One of the goals of this work is to demonstrate, through the useof the flexibility of REACTION in defining reaction classes, pathwaysand the use of arbitrary base mechanisms, that the automatic pro-duction and the by-hand construction of mechanisms are notmutually exclusive. With the tools in REACTION the modeler canuse the advantages of automatic generation and produce or repro-duce detailed mechanisms created by hand. One purpose of this pa-per is to substantiate this with a systematic comparison of the handgenerated mechanism of n-alkanes up to hexadecane of Westbrooket al. [23] and the generated mechanism, with 2176 species and7269 reactions, of REACTION. A reaction by reaction comparisonis done along with a validation against a wide range of experimentaldata covering the cool flame region, the negative temperature coef-ficient (NTC) regime and the high temperature oxidation range. Inaddition, a sensitivity analysis is made with the generated mecha-nism with respect to reaction classes which further demonstratesthat with automatic generation the modeler is not thinking at thelevel of individual reactions, but at a higher conceptual level.

1.3. Reaction classes and reaction patterns

In the development of the heptane and the isooctane mecha-nisms Curran et al. [24,37] defined a set of reaction classes describ-ing the oxidation of hydrocarbons. Each class describes thereactivity of a local region within a species. The fundamental phi-losophy behind a reaction class is that only ‘‘local’’ features in themolecule, usually defined as functional groups at or near thereactive center, can affect the reaction rate constant. Within each

Table 1The classes and corresponding reaction patterns with their rate coefficients of the ‘‘high temperature’’ reactions. The preexponential A is given in units of (cm3 mol�1)n�1 s�1 andthe activation energy Ea in kj/mol. The individual patterns and names have been explained in detail by Blurock [34,35].

Classes Reaction patterns Reaction rates

Forward Reverse

A n Ea A n Ea

Class 1: Unimolecular decomposition Decomp-(rhh)(hhh) 5.895e+24 �2.33 382.46 1.000e+13 0.00 0.000Decomp-(rhh)(rhh) 2.616e+22 �1.56 367.77 4.000e+12 0.00 �2.490HlossDecomposition-(rhh) 3.348e+19 �0.89 429.72 1.000e+14 0.00 0.000HLossDecomposition-(rrh) 2.269e+20 �1.34 421.13 3.610e+13 0.00 0.000

Class 2: Hydrogen abstraction H-Abstraction-Hydroxyl-Radical-Primary 1.128e+06 2.75 26.293 8.926e+03 2.70 44.170H-Abstraction-Hydroxyl-Radical-Secondary 1.040e+07 2.40 18.719 3.928e+03 2.74 47.143H-Abstraction-Oxygen-Radical-Primary 1.158e+06 2.68 15.558 4.025e+03 2.63 24.670H-Abstraction-Oxygen-Radical-Secondary 3.816e+05 2.71 8.817 6.330e+01 3.05 28.461H-Abstraction-Oxygen-Primary 3.600e+14 0.00 221.063 5.175e+10 0.28 �1.699H-Abstraction-Oxygen-Secondary 1.600e+14 0.00 209.968 1.098e+09 0.67 �2.265H-Abstraction-PeroxylRadical-Primary 1.008e+14 0.00 85.578 2.050e+13 -0.38 35.164H-Abstraction-PeroxylRadical-Secondary 4.480e+13 0.00 74.064 4.348e+11 0.01 34.185H-Abstraction-Methoxy-Primary 1.896e+12 0.00 29.307 1.200e+10 0.00 38.518H-Abstraction-Methoxy-Secondary 8.760e+11 0.00 20.934 8.900e+09 0.00 30.144H-Abstraction-EthylRadical-Primary 6.000e+11 0.00 56.103 3.200e+11 0.00 51.497H-Abstraction-EthylRadical-Secondary 4.000e+11 0.00 43.542 1.000e+11 0.00 54.009H-Abstraction-EthenylRadical-Primary 6.000e+12 0.00 75.362 2.570e+12 0.00 106.344H-Abstraction-EthenylRadical-Secondary 3.200e+12 0.00 70.338 2.000e+12 0.00 101.320H-Abstraction-MethylPeroxyl-Primary 1.212e+13 0.00 85.44 3.600e+12 0.00 40.980H-Abstraction-MethylPeroxyl-Secondary 8.080e+12 0.00 74.02 2.376e+11 0.00 15.470H-Abstraction-Hydrogen-Radical-Primary 6.300e+10 0.97 6.6570 1.500e+10 1.05 97.678H-Abstraction-Hydrogen-Radical-Secondary 3.760e+08 1.61 -0.146 6.148e+05 1.95 91.732H-Abstraction-Methyl-Primary 5.424e+00 3.65 29.952 1.121e+00 3.60 49.864H-Abstraction-Methyl-Secondary 2.164e+05 2.26 30.509 2.135e+03 2.60 60.917

Class 3: Radical decomposition HLoss-ethyl-radical(rh)(hhh)-to-olefin 1.338e+15 �0.55 162.09 1.000e+13 0.00 5.020HLoss-ethyl-radical(hh)(rhh)-to-olefin 2.071e+16 �0.89 158.71 1.000e+13 0.00 12.130HLoss-ethyl-radical(rh)(rhh)-to-olefin 1.639e+14 �0.36 153.61 1.000e+13 0.00 12.130

Class 4: Alkly radical oxidation to Olefin Ethyl-Radical(rh)(hhh)-Oxidation-to-Olefin 3.000e�09 0.00 12.57 2.747e�09 0.00 81.79Ethyl-Radical(hh)(rhh)-Oxidation-to-Olefin 3.000e�09 0.00 12.57 2.747e�09 0.00 81.79Ethyl-Radical(rh)(rhh)-Oxidation-to-Olefin 3.000e�09 0.00 12.57 2.747e�09 0.00 81.79

Class 5: Alkyl radical ısomerization HShift-12-Alkyl-(rh)(hh) 1.740e+07 2.01 172.63 – – –HShift-12-Alkyl-(hh)(rh) 5.480e+08 1.62 162.09 – – –HShift-12-Alkyl-(rh)(rh) 9.587e+08 1.39 166.03 – – –AlkylIsomerization4Ring-(hh)(rh) 3.312e+11 0.39 141.75 – – –AlkylIsomerization4Ring-(rh)(hh) 1.386e+09 0.98 141.346 – – –AlkylIsomerization4Ring-(rh)(rh) 1.760e+09 0.76 145.282 – – –AlkylIsomerization5Ring-(hh)(rh) 3.433e+12 �0.39 97.42 – – –AlkylIsomerization5Ring-(rh)(hh) 2.541e+09 0.35 82.731 – – –AlkylIsomerization5Ring-(rh)(rh) 3.220e+09 0.13 86.666 – – –AlkylIsomerization6Ring-(hh)(rh) 4.280e+11 �1.05 49.18 – – –AlkylIsomerization6Ring-(rh)(hh) 4.280e+11 �1.05 49.23 – – –

Class 6: Abstraction from Olefin AlphaHAbstractionFromOlefinH-(hh) 3.700e+14 0.00 16.328 2.255e+14 �0.46 100.441AlphaHAbstractionFromOlefinH-(rh) 3.700e+14 0.00 16.328 2.255e+14 �0.46 100.441AlphaHAbstractionFromOlefinO-(hh) 1.000e+13 0.00 16.747 7.000e+11 0.00 125.18AlphaHAbstractionFromOlefinO-(rh) 1.000e+13 0.00 16.747 7.000e+11 0.00 125.18AlphaHAbstractionFromOlefinOH-(hh) 3.000e+14 0.00 5.149 7.917e+14 �0.46 152.734AlphaHAbstractionFromOlefinOH-(rh) 3.000e+14 0.00 5.149 7.917e+14 �0.46 152.734AlphaOlefinRadicalDecompO-(hh) 1.800e+15 0.00 0.00 – – –AlphaOlefinRadicalDecompOH-(hh)(h)(hh) 1.500e+14 0.00 0.00 – – –AlphaOlefinRadicalDecompOH-(rh)(h)(hh) 1.500e+14 0.00 0.00 – – –AlphaOlefinRadicalDecompOH-(hh)(h)(rh) 1.500e+14 0.00 0.00 – – –AlphaOlefinRadicalDecompOH-(rh)(h)(rh) 1.500e+14 0.00 0.00 – – –AlphaOlefinRadicalDecompHO2-(hh)(h)(hh) 5.000e+13 0.00 0.00 – – –AlphaOlefinRadicalDecompHO2-(rh)(h)(hh) 5.000e+13 0.00 0.00 – – –AlphaOlefinRadicalDecompHO2-(hh)(h)(rh) 5.000e+13 0.00 0.00 – – –AlphaOlefinRadicalDecompHO2-(rh)(h)(rh) 5.000e+13 0.00 0.00 – – –

Class7: Addition of radical species to Olefin OlefinToAldehydeDecomp-(rh)(hh) 1.000e+11 0.00 16.747 – – –OlefinToAldehydeDecomp-(hh)(rh) 1.000e+11 0.00 16.747 – – –

Class 8: Alkenyl radical decomposition PropylRadicalToEthene-(rh)(hh)(hhh) 4.988e+11 �0.42 122.49 8.500e+10 0.00 32.620PropylRadicalToEthene-(hh)(hh)(rhh) 3.175e+17 �2.08 130.50 8.500e+10 0.00 32.620PropylRadicalToEthene-(rh)(hh)(rhh) 1.885e+14 �0.89 124.33 8.500e+10 0.00 32.620

Class 9: Olefin decomposition BetaOlefinDecomp(qq)(q)(hh)(hhh) 1.000e+17 0.00 297.262 1.000e+13 0.00 0,000BetaOlefinDecomp(qq)(q)(hh)(rhh) 1.000e+17 0.00 297.262 1.000e+13 0.00 0,000BetaOlefinRadicalDecomp(qq)(q)(hh)(hh) 2.000e+13 0.00 148.46 – – –

134 I.E. Mersin et al. / Fuel 115 (2014) 132–144

class there can be subdivisions which describe reactive distinctionsleading both to different sets of bond making and breaking and todifferent rate constants. For example, Class 1 of Curran et al. [24]describes the uni-molecular (high temperature) decomposition ofalkanes. Within this class two types of reactions are included,

decomposition through the breaking of the carbon–carbon bondin an alkane and the loss of a hydrogen in an alkane. Within thesetwo types there are further distinctions in terms of whether thecarbon involved is primary, secondary or tertiary. Each of these dis-tinctions can lead to a different reaction rate constant. Within

I.E. Mersin et al. / Fuel 115 (2014) 132–144 135

REACTION, a given reaction class is defined as a set of ‘‘reactionpatterns’’ [25,32]. Each reaction pattern describes a specific typeof reactivity within the reaction class. Each reaction pattern hasits own rate constant in Arrhenius form. The reaction patternsthemselves are represented by Lewis structures [38,39], repre-sented in 2D-graphical form [40,41]. These graphical structures de-scribe the reactive center and significant functional groups whichcan affect the rate constant. There is a graphical description ofthe reactive center of the reactants and a graphical structure ofhow the bonding in the reactive center changes with the reaction.For example, the decomposition reaction discussed previouslyconsists of two sets of reaction patterns, one for radical decompo-sition of the carbon–carbon bond and then another for loss ofhydrogen. The carbon–carbon decomposition reactions have intotal nine reaction patterns reflecting the three types of carbons,primary, secondary or tertiary, on either side of the breaking car-bon–carbon bond (3 � 3 = 9). The hydrogen loss reaction has threereaction patterns, one for each type of carbon, primary, secondaryor tertiary.

The rate constants in the reaction classes (reaction patterns) ofREACTION are defined to be those used in Westbrook‘s hexadecanemechanism. The reaction classes, broken up in their respectivereaction patterns with corresponding rate constants, are shownin Tables 1–3. Tables 1 and 2 show the original 25 reaction classesdefined by Curran with their corresponding reaction pat-terns, defined by Blurock [35], and rate constants. The rate con-stants correspond to those of Westbrook et al. hexadecanemechanism. Table 3 shows the reaction classes of Blurock [35]which were derived from the original heptane mechanism of Cur-ran et al. [24] with corresponding reaction patterns and rate con-stants. For basically historical reasons, the rate constants for agiven reaction class in Westbrook’s hexadecane are not all thesame. Only for species with eight or more carbons are the rate con-stants consistent, i.e. the same are used in all instances of the samereaction class. For species with four to seven carbons, some matchthe general rate constants, but some have been optimized or matchcurrently accepted experimental or calculated values. The rate con-stants used for the generated mechanism of this paper matchthose, when possible (see below), of the hexadecane mechanismfor species with eight or more carbons.

In general, the reverse reaction rate is calculated using thermo-dynamics. However, for the generated reactions and for (most of)the reactions of hexadecane by-hand mechanism specific reverserates (for species with more than eight carbons) are given andare the same for all applications of the class. In REACTION, themodeler can choose whether the reverse is calculated with ther-modynamics or whether the reverse is specified exactly.

2. Generation using pathways

A unique feature of REACTION is the use of pathways as a gen-eration strategy in the production of complex combustion mecha-nisms. Instead of applying recursively a pool of reaction classes, thereaction classes are arranged a linear sequence of sets of reactionclasses, i.e. a pathway. Given a starting species, for example, thefuel, the first step, consisting of a set of reaction classes repre-sented as reaction patterns, is applied. The result is a set of productspecies. These product species and only these product species areused as input to the next step of the pathway. This strategy contin-ues in that only the products of the previous step are used as inputto the next step.

When describing or modeling a mechanism, the modeler oftendelineates submechanisms on the basis of pathways. One impor-tant example in the literature is the differentiation between thehigh temperature pathway leading to radical decomposition (pyro-lysis) and the low temperature pathway leading to branching

agents [2]. There are also pathways branching from the main lowtemperature pathway through, for example, alkenes, cyclic ethersand hydroperoxyl alkanes. There are also pathways which resultin the decomposition or oxidation of functional groups within spe-cies, such as aldehydes, ketones, alkenes and alkynes.

The primary difference between the pathway strategy and the‘‘exhaustive’’ application strategy is in which the product specieswill be added to the total ‘‘pool’’ of reacting species and the totalpool of reaction classes used in each recursion. In the exhaustivestrategy, the reactive pool increases with every application of areaction class. In addition, the entire set of reaction classes areavailable at every iteration. However, the concept of pathway is stillimplicit in the exhaustive strategy. Only the applicable reactionclasses, i.e. the functional group of the reaction class present inthe species, can be used. For example, reaction classes involving asingle radical are only applicable after the radical has been formedin the previous reaction class application. However, exactly in theexample with a single radical, with exhaustive generation, ‘‘all’’possible reactions with a single radical can be applied. This can leadto a combinatorial explosion of possibilities. With pathways, themodeler can actively decide which reaction class to use. The ‘‘by-hand’’ modeler avoids the combinatorial explosion of results byselecting out what is a ‘‘reasonable’’ next step in the reactive pro-cess. Unless there is an accurate and computationally affordableway to filter out from the possible those reactions which are ‘‘signif-icant’’, a combinatorial explosion of possibilities is probable. Thisphilosophy is followed, for example, by the RMG system [42]. Thepathway approach uses the knowledge of the modeler to determinewhat is significant based on the literature and experience.

In summary the governing philosophy for the use of reactionpathways is threefold:

� It is a more controlled form of generation which inhibits thecombinatorial explosion of possible reactions.� It mimics the way a modeler thinks and builds a complex

detailed mechanisms.� It provides a means of introducing a generation strategy in the

database without hard-coding the strategy in the generationengine.

2.1. Pathway definition

There are no fundamental restrictions on how a pathway can bedefined. However, within the pathways used for the generation ofhexadecane, several simple rules were followed:

� The rule of thumb is that the ‘‘end products’’ of the pathwayshould be reacted further in other pathways or submechanisms.� The pathways should be designed to produce end products, i.e.

those after the last step of the pathway, with only one func-tional group, such as a single radical, aldehyde or olefin. Ofcourse, in the steps inbetween, multifunctional species canappear.� Some pathways should be designed to react species with spe-

cific functional groups.� The number of carbons of the end products should be less than

the seed given to the pathway.

Using these ‘‘rules of thumb’’ nine pathways were designed togenerate hexadecane:

1. HighTemperatureRadical: This represents the ‘‘high tempera-ture’’ pathway. This pathway involves simple decompositionand single loss of hydrogen in the first step and intramolecularisomerizations and decomposition to an olefin and radical inthe second step.

Table 2The reaction classes and corresponding reaction rates of the ‘‘low temperature’’ reactions The preexponential A is given in units of (cm3 mol�1)n�1 s�1 and the activation energy Ea

in kj/mol The individual patterns and names have been explained in detail by Blurock [34,35].

Classes Reaction patterns Reaction rates

Forward Reverse

A n Ea A n Ea

Class 10: Addition of Alkyl Radicals to O2 Primary-Carbon-Radical-(R + O2 ? RO2) 4.520e+12 0.00 0.00 2.657e+20 �1.67 148.040Secondary-Carbon-Radical-(R + O2 ? RO2.)

7.540e+12 0.00 0.00 1.357e+23 �2.36 157.540

Class 11: RO2 + R ? RO and Class 12: Alkyl peroxyradical isomerization

– – – – – –

RO2-Isomerization-5RingPrimary 3.000e+11 0.00 123.091 8.060e+11 �0.52 60.122RO2-Isomerization-5RingSecondary 2.000e+11 0.00 112.415 2.123e+10 �0.11 59.620RO2-Isomerization-6RingPrimary 3.750e+10 0.00 102.157 1.384e+12 �0.91 38.392RO2-Isomerization-6RingSecondary 2.500e+10 0.00 87.294 2.653e+09 �0.11 34.499RO2-Isomerization-7RingPrimary 9.376e+09 0.00 93.574 2.518e+10 �0.52 30.605RO2-Isomerization-7RingSecondary 3.125e+09 0.00 79.758 3.317e+08 �0.11 26.962RO2-Isomerization-8RingPrimary 5.860e+08 0.00 106.972 2.163e+10 �0.91 43.207RO2-Isomerization-8RingSecondary 3.906e+08 0.00 92.318 4.146e+07 �0.11 39.523

Class 13: RO2 + HO2 = RO2H + O2 ROOHFromPeroxy-RHH 1.750e+10 0.00 �13.711 5.974e+13 �0.85 146.119ROOHFromPeroxy-RRH 1.750e+10 0.00 �13.711 5.974e+13 �0.85 146.119

Class 14: RO2 + H2O2 = RO2H + HO2 PeroxyFromHydrogenPeroxide-RHH 2.400e+12 0.00 41.868 2.400e+12 0.00 41.868PeroxyFromHydrogenPeroxide-RRH 2.400e+12 0.00 41.868 2.400e+12 0.00 41.868

Class 15: RO2 + CH3O2 = RO + CH3O + O2 RO2ToAlkoxy-(hhh)(rhh) 1.400e+16 �1.61 7.787 – – –RO2ToAlkoxy-(hhh)(rrh) 1.400e+16 �1.61 7.787 – – –

Class 16: RO2 + RO2 = RO + RO + O2 RO2ToAlkoxy-(rhh)(rhh) 1.400e+16 �1.61 7.787 – – –RO2ToAlkoxy-(rhh)(rrh) 1.400e+16 �1.61 7.787 – – –RO2ToAlkoxy-(rrh)(rrh) 1.400e+16 �1.61 7.787 – – –

Class 17: RO2H = RO + OH AlkoxyFromPeroxy-RHH 1.500e+16 0.00 177.939 – – –AlkoxyFromPeroxy-RRH 1.250e+16 0.00 174.170 – – –

Class 18: RO decomposition AlkoxyDecomp-(rh)(hhh) – – – 1.000e+11 0.00 49.822AlkoxyDecomp-(hh)(rhh) – – – 1.000e+11 0.00 49.822AlkoxyDecomp-(rh)(rhh) – – – 1.000e+11 0.00 49.822

Class 19: QOOH = QO(cyclic)+OH CyclicEtherFromQOOH-3Ring 6.000e+11 0.00 92.109 – – –CyclicEtherFromQOOH-4Ring 7.500e+10 0.00 63.848 – – –CyclicEtherFromQOOH-5Ring 9.375e+09 0.00 29.307 – – –CyclicEtherFromQOOH-6Ring 1.172e+09 0.00 7.5362 – – –

Class 20: QOOH = olefin + HO2 BetaHPeroxyToOlefin-HHRH 1.610e+20 �2.52 89.388 1.000e+11 0.00 48.273BetaHPeroxyToOlefin-RHHH 1.610e+20 �2.52 89.388 1.000e+11 0.00 48.273BetaHPeroxyToOlefin-RHRH 1.610e+20 �2.52 89.388 1.000e+11 0.00 48.273

Class 21: QOOH = Olefin + carbonyl + OH OlefinCarbonylFromPeroxy-HH 2.470e+18 �1.55 113.127 – – –OlefinCarbonylFromPeroxy-RH 2.470e+18 �1.55 113.127 – – –

Class 22: Addition of QOOH to O2 Activated-Secondary-Carbon-Radical-(R + O2 ? RO2)

7.540e+12 0.00 0.00 1.367e+23 �2.37 157.591

Activated-Primary-Carbon-Radical-(R + O2 ? RO2)

4.520e+12 0.00 0.00 1.668e+20 �1.65 147.710

Class 23: Isomerization of O2QOOH and formation ofketohydroperoxide and OH

OOQOOH-Isomerization-5Ring-Primary 2.000e+11 0.00 110.531 1.384e+05 1.22 195.900

OOQOOH-Isomerization-5Ring-Secondary

1.000e+11 0.00 99.855 1.179e+04 1.40 198.245

OOQOOH-Isomerization-6Ring-Primary 2.500e+10 0.00 89.597 3.303e+03 1.41 188.573OOQOOH-Isomerization-6Ring-Secondary

1.250e+10 0.00 74.734 1.615e+02 1.83 185.056

OOQOOH-Isomerization-7Ring-Primary 3.125e+09 0.00 81.014 4.128e+02 1.41 179.990OOQOOH-Isomerization-7Ring-Secondary

1.563e+09 0.00 67.198 2.019e+01 1.83 177.520

OOQOOH-Isomerization-8Ring-Primary 3.906e+08 0.00 94.412 5.160e+01 1.41 193.388OOQOOH-Isomerization-8Ring-Secondary

1.953e+08 0.00 79.758 3.190e+00 1.75 191.420

Class 24: Decomposition of ketohydroperoxide KetoHydroPeroxideDecompToAldRadical-HRH

1.050e+16 0.00 174.170 – – –

KetoHydroPeroxideDecompToAldRadical-RHH

1.500e+16 0.00 175.845 – – –

KetoHydroPeroxideDecompToAldRadical-RRH

1.050e+16 0.00 174.170 – – –

KetoHydroPeroxideDecompToAldRadical-CHHHH

1.500e+16 0.00 175.845 – – –

KetoHydroPeroxideDecompToAldRadical-CHHRH

1.050e+16 0.00 174.170 – – –

KetoHydroPeroxideDecompositionC4 1.000e+16 0.00 179.83 – – –KetoHydroPeroxideDecompositionC5 1.000e+16 0.00 179.83 –

Class 25: Cyclic ether reactions with OH and HO2 CyclicEther-3Ring-(hh) 2.500e+12 0.00 0.00 1.000e�30 0.00 0.00CyclicEther-3Ring-(rh) 2.500e+12 0.00 0.00 1.000e�30 0.00 0.00CyclicEther-4Ring-(h) 2.500e+12 0.00 0.00 1.000e�30 0.00 0.00CyclicEther-4Ring-(r) 2.500e+12 0.00 0.00 1.000e�30 0.00 0.00CyclicEther-5Ring-(h) 2.500e+12 0.00 0.00 1.000e�30 0.00 0.00

136 I.E. Mersin et al. / Fuel 115 (2014) 132–144

Table 2 (continued)

Classes Reaction patterns Reaction rates

Forward Reverse

A n Ea A n Ea

CyclicEther-5Ring-(r) 2.500e+12 0.00 0.00 1.000e�30 0.00 0.00CyclicEther-6Ring-(h) 2.500e+12 0.00 0.00 1.000e�30 0.00 0.00CyclicEther-6Ring-(r) 2.500e+12 0.00 0.00 1.000e�30 0.00 0.00

I.E. Mersin et al. / Fuel 115 (2014) 132–144 137

2. HabstractionBySimpleRadical: These pathways abstract ahydrogen from the seed molecule using 10 different abstractors.

3. BasicLowTemperature: This is the basic low temperature path-way to branching agents (with no side reactions), meaningaldehydes and ketones. The aldehydes formed are assumed tobe reacted in another pathway (for example, AldehydeDecom-position). Additional step is added to react the ketones.

4. BasicLowTemperatureSideRxnsRO2: This is the side reactionsthat occur after the first addition of oxygen to the radical.

5. BasicLowTemperatureSideRxnsQOOH: This is the side reactionsinvolving QOOH, i.e. after the first intramolecular abstraction ofthe low temperature pathway (but not including cyclic ethers).

6. CyclicEtherFromQOOH: This is the side reactions involving theformation of cyclic ether and subsequent decomposition.

7. AldehydeDecomposition: This is the decompositon of aldehydesto simple radicals

8. AlphaOlefinDecomp: The reactions of the alkenyls with the rad-ical alpha to the alkenes.

9. OlefinDecompToRadical: This reaction class concentrates onalkenyls where the radical is ‘‘distant’’ from the alkene group.These radicals are not influenced by the alkene group.

The approach in designing pathways that the end productsshould have only one functional group was presented as a ’’ruleof thumb’’ to facilitate the design of pathways because treatingthe reactions of one functional group in another pathway is morestraightforward. In the description of the low temperature path-way, such as in Curran et al., the last reaction with the ketohydrop-eroxide (class 25 of Curran) produces a ketone radical, a productwith two functionalities, where the radical can be in several placesrelative to the ketone group. Instead of designing a pathway to re-act this multifunctional group, the low temperature pathway usedwas supplemented with reactions. If the radical is on the ketonegroup, or on the alph or beta position relative to the ketone group,specific reaction patterns have been designed (see [33]). If the rad-ical is further away relative to the ketone group, then the reactionsdeal with the ketone or the radical as isolated functionalities. Thesereactions produce as products ketyl radicals where the radical iscloser to the ketone group.

Another ‘‘rule of thumb’’ in designing reaction pathways is thatthe number of carbons should be reduced. The motivation for thisrule is that significant reactions should take place in the pathwayand the end products of the pathway should react further in otherpathways. Two exceptions to this rule of thumb are the intramo-lecular abstractions (within the HighTemperatureRadical pathway)and abstractions of hydrogens by various small radicals (the Hab-stractionBySimpleRadical pathway). Here, nevertheless, the prod-ucts of these pathways have the same number of carbons, butthe products, simple radicals, are used in the other pathways.

To generate the comprehensive hexadecane mechanism, theseed molecules used for all of the pathways are the n-alkanes frombutane to hexadecane. Firstly, this ensures that the full high andlow temperature mechanism is present for each of the n-alkanes.Secondly, the full set of n-alkanes is used because the pathwaysare designed to produce end products which are ‘‘smaller’’, butnot necessarily in the base mechanism. For example, the decompo-

sition reactions in the high temperature mechanism (HighTemper-atureRadical) produce single radicals that are smaller than the seed(actually, all radicals from n�1 to 1, where n is the number of car-bons in the seed). There is no step to further react these species inthe pathway definition. It is assumed that using a smaller hydro-carbon as a seed in another pathway in which a single radical isgenerated will react these species further.

Each seed applied to all the pathways producing a submecha-nism. These submechanisms are then combined to form the finalfull mechanism. In the generation process, the 2D-graphical struc-ture [40] describing the Lewis structure [38] of all the generatedspecies is known. This information is used to recognize duplicatespecies through graphical isomorphism [41]. The species are alsocompared with REACTION’s species database. When a generatedspecies matches a species in the database, then the species infor-mation, namely the name and the thermodynamic data, is used.Duplicate reactions are recognized when the same products andreactants are present and when the same reaction class is involved.

3. Base mechanism in automatic generation

The generation process produces a submechanism for the largerspecies. The ‘‘products’’ of the generated reactions should react fur-ther. These products can react further via ‘‘known’’ reactions fromthe literature. These reactions make up the non-generated ‘‘base’’mechanism. The generated submechanisms are combined withthis ‘‘base’’ mechanism to form the complete mechanism. REAC-TION has the capability to integrate any base mechanism. Forexample, for the previously generated decane mechanism [33],the mechanism derived from Hoyerman et al. [36] was used. Forthis study, the chemistry of linear alkane C0–C4 chemistry was ex-tracted from the Westbrook et al. hexadecane mechanism [23], i.e.the by-hand generated mechanism being compared in this paper.The by-hand mechanism actually includes mechanisms containingbranched alkanes. This means that the base mechanism includes‘‘small’’ species which are not ‘‘needed’’ for the normal alkane com-bustion being studied in this paper. These small branched specieswere not included in the base mechanism used with the generatedmechanism.

During the generation process, the generated mechanism hasthe structure of each species and thus facilitating the combinationof generated submechanisms. However, the base mechanismcomes from the literature and the species do not necessarily havethe 2D-graphical information of the species. The species are just la-bels, a name to identify how the species is used in reactions and itscorresponding thermodynamic information. The ‘‘extra’’ structuralinformation is not needed for numerical simulations. In a sense thespecies structure is only in the mind of the modeler who producedit. However, if a generated mechanism, using different labels, is tobe combined with the base mechanism, some algorithm is neededto synchronize the labels. The key step in incorporating a basemechanism into a generated mechanism is to establish a speciesname to species structure correspondence list.

In generated mechanisms, there are two types of species labels, alabel that is automatically generated and a label in the externaldatabase of species used in conjunction with REACTION. Every

Table 3Additional set of classes(out of first 25 classes), oxidation of alkenes, aldehydes and ketones, reactions on the right column and the reaction rates belong that reactions are comingfrom Westbrook et al. hexadecane mechanism [23]. The preexponential A is given in units of (cm3 mol�1)n�1 s�1 and the activation energy Ea in kj/mol. The individual patternshave been explained in detail by Blurock [34,35].

Generated reactions (reaction patterns) Forward and reverse reaction rates Example of Westbrook‘s reactions [23]

A n Ea A n Ea

AldehydeHAbstractionOH-(rh) 1.000e+13 0.00 0.00 2.000e+13 0.00 154.732.690e+10 0.76 -1.42 1.740e+10 0.76 130.62 nc14h29cho + oh = nc14h29co + h2o

AldehydeHAbstractionH-(rh) 4.000e+13 0.00 17.56 1.800e+13 0.00 100.37 nc14h29cho + h = nc14h29co + h2AldehydeHAbstractionCH3-(rh) 1.700e+12 0.00 35.30 1.500e+13 0.00 117.10 nc14h29cho + ch3 = nc14h29co + ch4AldehydeHAbstractionO-(rh) 5.000e+12 0.00 7.49 1.000e+12 0.00 79.46 nc14h29cho + o = nc14h29co + ohAldehydeHAbstractionO2-(rh) 2.000e+13 0.50 176.48 1.000e+07 0.00 167.28AldehydeHAbstractionHO2-(rh) 2.800e+12 0.00 56.88 1.000e+12 0.00 41.82 nc14h29cho + ho2 = nc14h29co + h2o2AldehydeHAbstractionCH3O-(rh) 1.150e+11 0.00 5.35 3.000e+11 0.00 75.28 nc14h29cho + ch3o = nc14h29co + ch3ohAldehydeHAbstractionCH3O2-(rh) 1.000e+12 0.00 39.73 2.500e+10 0.00 41.82 nc14h29cho + ch3o2 = nc14h29co + ch3o2 hH-Abstraction-AlphaToKetoneOH-(h)(rh) 4.670e+07 1.61 -0.15 3.317e+09 1.25 128.97 nc5h11cho + oh = c5h10cho-2 + h2oH-Abstraction-AlphaToKetoneO2-(h)(rh) 2.000e+13 0.50 176.48 1.000e+07 0.00 167.28H-Abstraction-AlphaToKetoneO-(h)(rh) 5.000e+12 0.00 7.49 1.000e+12 0.00 79.46H-Abstraction-AlphaToKetoneH-(h)(rh) 5.000e+12 0.00 7.49 1.000e+12 0.00 79.46H-Abstraction-AlphaToKetoneHO2-(h)(rh) 2.950e+04 2.60 58.17 1.244e+07 1.91 55.70

2.760e+04 2.55 68.69 3.330e+04 2.22 18.59 nc5h11cho + ho2 = c5h10cho-1 + h2o2H-Abstraction-AlphaToKetoneCH3-(h)(rh) 1.700e+12 0.00 35.30 1.500e+13 0.00 117.10H-Abstraction-AlphaToKetoneCH3O2-(h)(rh) 1.150e+11 0.00 5.35 3.000e+11 0.00 75.28

6.030e+12 0.00 81.14 2.990e+13 �0.51 27.70 nc5h11cho + ch3o2 = c5h10cho-1 + ch3o2 hH-Abstraction-AlphaToKetoneCH3O-(h)(rh) 3.980e+12 0.00 71.30 6.897e+15 �0.86 65.82AlkenylDecompToAlkyne-(h)(h)(hhh) 1.260e+14 0.00 139.64 6.310e+11 0.00 32.20AlkenylDecompToAlkyne-(h)(h)(rhh) 1.260e+14 0.00 139.64 6.310e+11 0.00 32.20KetoneRadicalDecomp-RHH 1.000e+11 0.00 40.15 1.000e+11 0.00 0.00 nc14h29co = c14h29–1 + coKeteneFormationRadicalDecomp-(hh)(rhh) 1.570e+13 0.00 125.46 2.110e+11 0.00 30.74

2.000e+13 0.00 129.79 2.000e+11 0.00 30.77 c13h27coch2 = c13h27–1 + ch2coKeteneDecompHToCO-(hh) 1.760e+13 0.00 6.10 – – –KeteneDecompHToCO-(rh) 1.760e+13 0.00 6.10 – – –BetaOlefinRadicalDecomp(qq)(q)(hh)(hh) 2.000e+13 0.00 148.46 – – –PentenylDecompToPropenyl-(hh)(hh)(hh) 2.500e+13 0.00 188.19 – – –KeteneDecompHOToCO2-(hhh)(h) 1.730e+12 0.00 �4.22 – – –KeteneDecompHOToCO2-(rhh)(h) 1.730e+12 0.00 �4.22 – –AldehydeDecompToKetylAlkene-Alkyl-(h)(hh)(hhh) 3.174e+14 �0.39 125.04 1.230e+11 0.00 32.62

2.425e+13 �0.27 94.07 1.000e+11 0.00 32.65 ic3h6cho = c2h3cho + ch3AldehydeDecompToKetylAlkene-Alkyl-(h)(hh)(rhh) 1.863e+18 �1.30 128.93 1.000e+11 0.00 32.62

1.564e+19 �1.53 139.46 1.000e+11 0.00 32.65 c5h10cho-5 = c2h3cho + nc3h7KetoneDecompToAlkene-Alkyl-(hh)(hh) 5.398e+17 �1.45 108.90 2.500e+11 0.00 32.62

5.000e+17 �1.5 108.85 2.500e+11 0.00 32.65 c12coc2h4p = nc12h25co + c2h4KetoneDecompToAlkeneAndch2co-Alkyl-(hh)(hh)(hh) 1.426e+18 �1.53 102.17 2.500e+11 0.00 32.62

5.000e+17 �1.5 108.85 2.500e+11 0.00 32.65 c11coc3h6p = c11h23coch2 + c2h4

138 I.E. Mersin et al. / Fuel 115 (2014) 132–144

species in this database has a set of labels, a structure and the asso-ciated thermodynamic data from the literature. One of the specieslabels in the database is (at least close to) standardized IUPAC namefor the species. Another label that is found in the database is a short-er name that can be used for numerical simulations. If a generatedspecies is found in the database, then its corresponding databaseinformation, including the name and thermodynamic data, is used.

To synchronize the labels of the base mechanism and the gener-ated mechanism a correspondence list is made between the labelused in the base mechanism and the standardized name of REAC-TION’s database. When the final full mechanism is assembled, thecommon name between the generated mechanism and the basemechanism is used. This means that in order to incorporate a basemechanism, all the species (or at least all the species which are incommon with the generated mechanism) have to be in REACTION’sexternal species database. If a base mechanism is not found in thedatabase, the database has to be supplemented. Part of the initialwork of this paper was to expand REACTION’s species database withthe necessary species from Westbrook et al. C0–C4 submechanism.

4. Reaction by reaction comparison

In the first analysis, a reaction by reaction comparison betweenthe generated hexadecane mechanism of REACTION and the ‘‘byhand’’ hexadecane of Westbrook was done. In general, for the pur-poses of this analysis, the Westbrook mechanism can be said to bein three submechanisms: the base submechanism of species with

four carbons or less, the ‘‘heptane/isooctane’’ submechanism basedon the previous work of Curran et al. [24,37] and then the newlyproduced n-nonane to hexadecane submechanism.

For this study, the REACTION mechanism used the same basemechanism of the Westbrook et al. mechanism with the exceptionthat branched hydrocarbon species of the Westbrook et al. werenot included. The primary focus of this paper is n-alkanes. Theseneglected branched species would only be significant for branchedfuels, for example isooctane. The numerical comparisons shown la-ter substantiate this assumption.

The submechanism for n-octane to hexadecane of the West-brook mechanism was systematically produced by hand and it isthat portion that is systematically compared with REACTION’s gen-erated reactions. These results are shown in Table 4 for the 25 reac-tion classes of Curran et al. [24,37]. As a result of the comparison,three difference categories were established: ‘‘Exactly the same’’,‘‘Westbrook has more’’ and ‘‘Generated has more’’. ‘‘Exactly thesame’’ means there is one-to-one correspondence for all reactionsin both REACTION’s and Westbrook’s. ‘‘Westbrook has more’’ and‘‘Generated has more’’ takes into account that even though thereis a correspondence between the two mechanisms, there are stillremaining reactions for Westbrook et al. mechanism or the REAC-TION mechanism. In addition, difference classifications weremade: Class A, One-to-One correspondence, Class B: Westbrookcontains lumped species, and class C: the Westbrook was non-sys-tematic. .The ‘‘heptane/isooctane’’ submechanism means the sub-mechanism of n-heptane and isooctane (and other branched

Table 4Comparison of the reactions, for hand-generated Westbrook et all hexadecane mechanism which generated by hand at LLNL and the automatic generated by reaction mechanism.Reaction rates are the same between C8 and C14 atoms.

Name of classes Comparison of reactions Differences

Exactly the same Westbrook has more Generated has more A,B,C (see text)

1-Unimoleculer fuel decomposition X A2-H Atom abstraction X X A3-Alkyl radical decomposition X A4-Alkyl radical + O2 to produce olefin + HO2 directly5-Alkyl Radical Isomeration X A6-H Atom abstraction from Olefin X B7-Addition of radical species to Olefin X X C8-Alkenyl radical decomposition X X B9-Olefin decomposition X C10-Addition of alkyl radicals to O2 X A11-R + R‘O2 = RO + R‘O12-Alkyl peroxy radical isomeration X A13-RO2 + HO2 = RO2H + O2 X A14-RO2 + H2O2 = RO2H + HO2 X A15-RO2 + CH3O2 = RO + CH3O + O2 X A16-RO2 + R‘O2 = RO + R‘O + O2 X A17-RO2H = RO + OH X A18-RO decomposition X C19-Cyclic ether formation X A20-QOOH = Olefin + HO2 X A21-QOOH = Olefin + Carbonyl + OH X A22-Addition of QOOH to O2 X A23-Isomerization of O2QOOH and Formation of ketohydroperoxide and OH X A24-Decomposition of ketohydroperoxide X A25-Reaction of cyclic ether (QO) with OH and HO2 X X C

Table 5An example of changing the reaction rates up to molecule numbers. (Class 1HLossDecomposition, Forward reaction rates for C8–C14 molecule reactions are thesame C4, C5, C6 and C7 molecule reactions are different). The preexponential A is givenin units of (cm3 mol�1)n�1 s�1 and the activation energy Ea in kj/mol.

Molecules HLossDecomposition-(rhh)

Forward reaction rates

A n Ea

C8–C16 1.000e + 14 0.00 0.00C7 1.340e+88 �21.17 1.428e+05C6 2.947e+19 �1.00 1.032e+05C5 1.227e+22 �1.80 1.039e+05C4 4.559e+21 �1.69 1.037e+05

I.E. Mersin et al. / Fuel 115 (2014) 132–144 139

species) with the number of carbon larger than the base mecha-nism. In principle, these reactions, including their rate constantsare based on the original Curran et al. papers [24,37], but for ‘‘his-torical’’ or optimization purposes, the rate constants for these reac-tions have been modified and do not necessarily fit a systematicpattern. However, the reactions themselves are systematic and,in fact, match the generated reactions of REACTION in basicallythe same way as shown below in the systematic comparison. Anexample is shown in Table 5 showing the reaction rates of the uni-molecular loss of hydrocarbon class corresponding to the reactionpatter HlossDecomposition-rhh (loss of primary hydrogen). For thehydrocarbons greater than 8, a generic value is used. The values forn-butane to n-heptane come from optimized values.

4.1. Class A: one-to-one

For those reaction classes with this classification, there is one-to-one correspondence between the C8–C16 species reactionswhich were found in both mechanisms. The forward reaction rateconstants for these classes are all the same and match REACTION’sgenerated reactions. The reverse is either fixed or calculated fromthermodynamics. The comparison of the reaction rates belongingto Class A revealed that the reaction rates are all the same forthe C8–C16 submechanism reactions, but in the heptane/isooctanemechanism the reaction rates between the C4–C7 molecule reac-tions can be different due to optimizations done by the authors.

Though there is one-to-one correspondence to the reactions thehand-generated and the REACTION generated mechanism for thereaction classes which belong to Class A, there can still be sets ofreactions missing from either. For instance, in the hydrogenabstraction classes of class 2, the abstraction with methoxy radicaland methylperoxy radical is missing in the hand-generated mech-anism. In the hand generated reaction, there are abstractions witha peroxy group on large hydrocarbons, i.e. the reactionRH + RO2 = R + ROOH. This set of reactions does not appear in theREACTION generated mechanism. In fact, in the current generationstrategy of REACTION adding this type of class is not possible in ageneral way. The reason being that although specific species can be

included in the species pool at every pathway step, including ageneric species such as RO2 is not. This could only be artificially in-cluded by defining a pathway step in which all the large hydrocar-bon abstractors are specifically listed. The main problem is todesign a pathway to ‘‘generate’’ two functional groups simulta-neously (the RH and the ROO) that in the next step they can react.Even in this strategy, this would only include R of the same typeand size. These and other potential solutions will be consideredfor future work. Class 25, the reaction of a cyclic ether with hydro-xyl radical to an aldehyde and a radical is one-to-one for all reac-tions. However, in this version of the generated mechanism, thereaction with peroxy radical, which was included in the by-handversion, was not included.

4.2. Class B: lumped species

The reactions corresponding to this difference cannot be di-rectly compared. The generation procedure did not producelumped reactions as did the by hand generated mechanism. Theby-hand generated mechanism chose to lump alkenyl isomers toa single species. Class 6 generates these alkenyl species and class8 ‘‘decomposes’’ them. In these classes, reactions with several sig-nificantly different radical alkenes are possible. In the generation

140 I.E. Mersin et al. / Fuel 115 (2014) 132–144

process, REACTION makes the distinction between two types: theabstraction from the alpha position from the double bond andabstraction from carbons further away.

Two pathways describe the interaction between class 6, the cre-ation of a alkenyl radical and class 8, the further reaction of thealkenyl:

AlphaOlefinDecomp: This is a simple two step pathway:⁄Formation of alpha alkenyl: The alkenyl is formed by either

by abstraction of a hydrogen alpha to the alkene group by a methylradical (AlphaHAbstractionFromOlefinCH3), a hydroxyl radical(AlphaHAbstractionFromOlefinOH), a hydrogen radical (AlphaH-AbstractionFromOlefinH) or an oxygen radical (AlphaHAbstrac-tionFromOlefinO) or by loss of the carbon chain, i.e. carbon–carbon bond breaking, at beta to the alkene group(BetaOlefinDecomp).⁄Reaction of alkenyl: The alkenyl further reacts in two ways.

First, in a reaction with an oxygen radical, an alkenyl with onecarbon less is formed with an aldehyde (AlphaOlefinRadicalDe-compO). Second, in a reaction with hydroxyl, an alkene withone carbon less is formed with an aldehyde (AlphaOlefin-RadicalDecompOH).

OlefinDecompToRadical: This is a multiple step pathway lead-ing to alkenyl where the radical is further away in the carbon chainfrom the olefin:⁄Formation of alkenyl: The formation is through simple single

bond carbon–carbon breaking (Decomp). This is the same classused for alkane decomposition. This forms two primary carbonradicals with one having a double bond further down the carbonchain.⁄First Reaction of alkenyl: The primary radicals can react in

several ways. In this step all possible (except alpha, which is takencare of in the other olefin decomposition pathway) combinationsof alkene group and radical group are considered:⁄⁄Beta radical alkenyl: With the loss of an ethene, an alkenyl

where the radical is on the alkene itself is formed(BetaOlefinRadicalDecomp)⁄⁄Gamma radical alkenyl: This produces an ethene and an

alkenyl where the radical is alpha to the alkene group(PentenylDecompToPropenyl).⁄⁄Radical distant alkene group: The smaller primary radical is

formed through loss of ethene (PropylRadicalToEthene). The reac-tion pattern is the same as for single bonded carbons. The class canbe applied to the alkenyl if the radical is more than 3 carbons fromthe alkene to produce a smaller alkenyl.⁄Second stage: In this stage, the radicals on the alkene itself are

reacted:⁄⁄Radical on Alkene group: With the loss of an alkyne a simple

radical is formed.The by-hand generated mechanism lumps the alkenyls into one

generic species. They can be formed from simple alkenes byabstraction with hydroxyl radical, hydrogen radical, oxygen radicaland methyl radical. This corresponds in the generated mechanismto the abstraction from the alpha position. An alkenyl can also beformed by decomposition of an alkenyl to another alkenyl and a al-kene. This corresponds to the PropylRadicalToEthene reaction pat-terns in the generated mechanism, i.e. in the ‘‘Radical distantalkene group’’ step in the ‘‘OlefinDecompToRadical’’ pathway. Analkenyl (with size up to 10 carbons) can also be formed by decom-position, single carbon–carbon breaking, of an alkene to a alkenyland a simple radical. In the generated mechanism, this correspondsto the ‘‘Formation of alkenyl’’ step in the ‘‘OlefinDecompToRadical’’pathway, i.e. the Decomp reaction classes. The OlefinDecompTo-Radical illustrates the usefulness of the pathway concept to selec-tively use desired reaction classes. For akenyl formation anddecomposition where the radical is ‘‘distant’’ from the alkene func-tional group reactions which were designed for single bonded

alkanes were used. Here, these reaction classes are usedselectively.

4.3. Class C: non-systematic

Automatic generation is systematic in its application of reactionclasses. There is no reason that ‘‘by-hand’’ generation cannot be assystematic. However, the modeler can make the decision to not in-clude certain applications for the reason that the resulting mecha-nism would be even larger. Often the modeler can make thedecision that the pathway should exist, but not all variants needbe included. In the by-hand mechanism, classes 7, 9 and 18 fall intothis category.

Class 7 involves the addition of small radical species to an al-kene. One example is the addition of hydroxyl to the n-alkene:R1�CH = CH�R2 + OH. When R1 and R2 are not the same, thereare four possible products:

1. ? CH2R1 + R2CHO2. ? R1CHO + CH2R2

3. ? R1CH2 CHO + R2

4. ? R1 + R2CH2 CHO

Howewer, in the by-hand mechanism, only two of the four wereincluded. The modelers chose only to include those products wherethe aldehyde is smaller than the radical. Although the productionof alkenyls is lumped, their production by class 9 decompositionof an n-alkene, the modelers chose to only include one of the prod-ucts. For example, the decomposition 4-decene (C4H10-4), decom-position produces the lumped alkenyl c6h11 (and 1-butyl radical)and not the c5h9 lumped alkenyl.

Similarly with the class 18, the decomposition of alkoxyl to analdehyde and a simple primary radical. As with class 7, the productpair with the smallest aldehyde was chosen.

5. Zero-dimensional constant volume simulations

Supplementary to the reaction-by-reaction comparison of theautomatically generated mechanism of REACTION and the by-handmechanism produced by Westbrook et al. [23] some numericalsimulations of shock tube experiments were performed usingCHEMKIN Pro. In the previous section, the reaction by reactioncomparison showed that at least for the submechanism of eightcarbons or more, the two-mechanisms are very similar. The sub-mechanism involving carbon species with five to seven carbonswas also found to be very similar, but as implied previously, thissubmechanism has undergone ‘‘optimization’’ since its originalproduction [24,37] and for this reason a systematic comparisonwas not done. The remaining submechanism, the base mechanismof species have zero to four carbons (C0–C4), is a subset of the C0–C4

of the by-hand generated mechanism. This section verifies and val-idates the generated mechanism with the by-hand producedmechanism with zero-dimensional ‘‘ignition’’ calculations simulat-ing shock tube experiments.

Fig. 1 shows the results of the numerical simulations showingthe ignition delay times for a constant pressure zero-dimensionaloxidation calculations at 13 bar with an equivalence ratio = 1.Fig. 1a shows the results for n-decane and n-hexadecane usingboth the by-hand mechanism and Generated mechanism. Theexperimental results are from Pfahl et al. [45]. The two mecha-nisms have a quite close agreement. Fig. 1b shows the ignition de-lay times for all n-alkanes from n-decane to n-hexadecane usingthe generated mechanism. The ignition delay times of these fuelsare quite close at each temperature. However, for the entire rangeof temperatures one can see the trend that as the number of car-

I.E. Mersin et al. / Fuel 115 (2014) 132–144 141

bons increases, the ignition delay time increases. There is a slightdeviation for n-hexadecane at high temperatures.

Some differences in the ignition delays times were observed.One of the major differences between the two mechanisms ishow olefins, specifically alkenyl radicals are treated. The generatedmechanism has a more detailed accounting while Westbrook’set al. is highly lumped. As can be seen from the following sensitiv-ity analysis alkenyl reactions are indeed sensitive. The use of de-tailed as opposed to lumped rate constants can indeed be a causefor differences between the two mechanisms. Sensitivity is in boththe high temperature region as well as the NTC region.

6. Sensitivity analyses of the reaction groups

The systematic use of reaction classes in the automatic genera-tion allows the modeler to think about combustion at a higher le-vel. In other words, instead of thinking about individual reactions,the modeler thinks of classes of reactions. The individual reactionsbecome ‘‘details’’ of the calculation. In classical sensitivity calcula-tions individual reactions are singled out as being significant. How-ever, when dealing a highly branched reaction mechanism ofthousands of reactions, an individual intermediate reaction canlose significance. In fact, those reactions occurring close to the fuelor those occurring close to the combustion products have morenumerical significance due only to the fact that the reaction flowhas to go through these reactions. However, for the intermediatereactions, this flow is ‘‘diluted’’ because of the large number of pos-sible parallel pathways. The reactions from a reaction class for alarge hydrocarbon can be used tens to hundreds of times. However,if the mechanism is viewed as an ensemble of individual reactions,a single reaction is just one out of thousands. The application of asingle reaction class represents a parallel branching of pathways.When compared with individual reactions, the significance of areaction class is diluted by this branching. However, if treated asa whole, the significance is better represented. In a sense, the appli-cation of a reaction class can be viewed as an entire submechanismand looking at the sensitivity of the class is giving insight into thesignificance of the submechanism due to that reaction class.

Fig. 1. Ignition delay times for the oxidation in shock tube, at 13 bar, for equivalence ramechanism and Generated mechanism. The experimental results belong to Pfahl et al., [4to hexadecane.

For the work of this paper, the sensitivity of each reaction classwas analyzed by multiplying and dividing the original Arrheniusconstant by a factor of ten. For a reaction class made up of severalreaction patterns, all the Arrhenius constants of the reaction pat-terns were changed simultaneously. Several reaction classes donot show a sensitivity to this change. Those reaction classes whichshowed a significant sensitivity are shown in Fig. 2.

7. Discussion

Although large mechanisms can be produced by hand, as pro-ven by Westbrook et al. [23,43,44], automatic generation providesa systematic tool that should simplify and systematize mechanismproduction. One of the goals of the REACTION software is to simu-late methods used by modelers to generate large mechanisms. Thispaper illustrates that the techniques of automatic generation usedby REACTION and the techniques used by by-hand generation arenot mutually exclusive. An important concept/technique used byREACTION which is needed to achieve this is that of reaction path-ways. When the iterative strategy used by automatic generation isreplaced by the reaction pathway strategy, then, as shown in thispaper, the results of automated and hand-generated mechanismscan be made to be the same.

Furthermore, with the use of reaction classes and pathways ofreaction classes the modeler can evaluate the structure of a de-tailed mechanism at a higher level. A mechanism is not just a sim-ple list of reactions, but a hierarchy submechanisms generatedwith respect to species size and pathways. In addition, the conceptof reaction classes allows evaluation of reactivity at a higher level.For example, in this paper, the sensitivity of reaction classes wasevaluated. This in turn can be used to evaluate the importance ofthe reactive pathways using these reaction classes.

This study represents only the beginning of the evaluation ofreaction classes, reaction pathways and reaction submechanismsusing automatic generation tools. With automated tools the mod-eler can systematically evaluate the importance of entire submech-anisms, defined in terms of either reaction classes, reactionpathways and/or species size, in the combustion process. In con-clusion, as this paper has shown, automatic generation does not

tio = 1, (a) n-decane and n-hexadecane results are plotted for the Westbrook et al.5]. (b) Ignition delay times using the generated mechanism for fuels from n-decane

(a) AlphaOlefinRadicalDecomp-Group (b) AlphaHAbstractionFromOlefin-Group

(c) CarbonRadical-Group (d) OlefinCarbonylFromPeroxy-Group

(e) HLoss-EthylRadical-To-Olefin-Group (f) BetaOlefinDecomp-Group

Fig. 2. The sensitivity to changing all the Arrhenius constants within a reaction class by a factor of 10 (multiplying and dividing). The sensitivity for all reaction classes weretested and only those with significant sensitivities are shown.

142 I.E. Mersin et al. / Fuel 115 (2014) 132–144

(g) CyclicEtherFromQOOH- Group (h) QOOQOOH-Isomerization-Group

(i) RO2ToAlkoxy-Group

Fig. 2 (continued)

I.E. Mersin et al. / Fuel 115 (2014) 132–144 143

exclude techniques done by the modeler by hand, but automatesand systematizes them providing more efficient tools for combus-tion study.

Acknowledgements

The financial supports of this work by Sakarya University Scien-tific Research Foundation (Project Number 2012-50-02-018) and ofthe Ph.D. Student (first author) by ‘‘the Higher Education Council ofTurkey’’ are gratefully acknowledged.

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