A wide range kinetic modeling study of the pyrolysis and combustion of naphthenes

Combustion and Flame 132 (2003) 533–544

A wide range kinetic modeling study of the pyrolysis and combustion of naphthenes Silvia Granata, Tiziano Faravelli, Eliseo Ranzi* CMIC Department, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy Received 24 April 2002; received in revised form 12 July 2002; accepted 15 August 2002

Abstract The aim of this paper is to analyze and discuss the kinetics of the pyrolysis and combustion of naphthenes. The primary propagation reactions of cyclohexane and methylcyclohexane are presented to extend the validity of a semi-detailed kinetic model for the pyrolysis and oxidation of hydrocarbons. Naphthenes are relevant species as reference components in liquid fuels and surrogate blends. A lumped approach is used to reduce the complexity of the overall scheme in terms of species and reactions. Particular attention is devoted to the role of the isomerization or internal abstraction of H atoms in competition with ␤⫺decomposition ones. Primary oxidation and decomposition reactions of the cyclohexyl radical are discussed to explain and justify this lumping procedure. The modeling predictions are compared with different sets of measurements. The validation of the low temperature oxidation mechanism of cyclohexane is based on the ignition delay times obtained both in the rapid compression machine at Lille and in closed vessels. Jet-stirred reactors at different pressures and stoichiometric ratios also confirm the reliability of the overall mechanism of oxidation. The comparisons between the model’s predictions and the measurements relating to the pyrolysis and oxidation of methylcyclohexane in the Princeton turbulent flow reactor further support this extension of the kinetic scheme to naphthenes. Finally, the agreement with the oxidation experiments using mixtures of toluene ⫹ methylcyclohexane is a primary and simple example of the model’s ability to deal with the combustion of real fuels or surrogate blends. © 2003 The Combustion Institute. All rights reserved. Keywords: Kinetic modeling, Naphtenes, Oxidation, Pyrolysis

1. Introduction Naphthenes are always present in real liquid fuels and an in-depth knowledge of their combustion properties is of great interest for several reasons. The attention being paid to homogeneous charge compression ignition (HCCI) as a clean and valid alternative to the SI engine has also resulted in a deeper understanding of the combustion characteristics of

* Corresponding author. Tel.: ⫹39-02-23-99-32-50; fax: ⫹39-02-70-63-81-73. E-mail address: [email protected] (E. Ranzi).

liquid fuels in general and naphthenes in particular [1]. The HCCI engine operates as a homogeneous process in which the typical control aspects are governed by the chemistry of the system and chemical models of typical fuels must be developed to optimize both design and performance. Alkanes are the dominant components in complex fuels, such as diesel or jet kerosene, accounting for as much as 80 to 90% of the fuel. In general, the alkanes contain straight chain and branched molecules, but there is also a significant presence of mono-cyclo alkanes. Linear dodecane and/or tetradecane are typical reference components for straight molecules, while iso-octane is often used as a model component

0010-2180/03/$ – see front matter © 2003 The Combustion Institute. All rights reserved. doi:10.1016/S0010-2180(02)00465-0

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for branched alkanes [2]. Cyclohexane and methylcyclohexane are assumed as the reference molecules in the cycloalkane fraction [3]. The detailed kinetic modeling of normal and branched alkanes, typically n-heptane and iso-octane, has already been widely discussed [4 –9] and clarified in recent years. The definition of primary reaction classes and their reference kinetic parameters allows the automatic generation of detailed kinetic models [10 –13], as well as the development of expert systems with proper kinetic rules [14,15]. This also makes it clear that the extension of detailed kinetic models to the pyrolysis and combustion of larger hydrocarbons, such as ndecane or n-dodecane, is feasible and free of major uncertainties [16 –18]. Naphthenes, on the other hand, have received scant attention, and a kinetic knowledge of their combustion is less defined and accurate. However, some measurements were presented recently by various researchers. Bonner and Tipper [19], as well as Zeelenberg and De Bruijn [20], studied the cool flame behavior of mixtures of cyclohexane⫹oxygen in closed vessels at low pressures (0.1– 0.3 atm) and they also discussed some features on the low temperature oxidation mechanism. Slow reacting H2⫹O2 mixtures with added cyclohexane were studied by Gulati and Walker [21] at ⬃750 K, without any evidence of important ring rupture. Billaud et al. [22] studied the pyrolysis of cyclohexane in a plug flow reactor at ⬃1100 K and observed the prevailing yield of butadiene and ethylene, but only slight formation of cyclohexene. The oxidation of cyclohexane in a jet stirred reactor (JSR) at 10 atm was studied by Voisin et al. [23]. An extension of this study, again at lower pressures, was presented by El Bakali et al. [24] together with a detailed kinetic mechanism where the dehydrogenation of cyclohexyl radicals dominated over ring opening decomposition to 5-hexenyl. Further interesting measurements on the pyrolysis and oxidation of methylcyclohexane (MCH) in a turbulent plug flow reactor were also presented by Zeppieri et al. [25]. The purpose of this paper is also to contribute to a better understanding of the primary propagation reactions of naphthenes to define the kinetic parameters of these reaction classes for the extension of the detailed kinetic models of combustion toward a description of real fuels. The experiments conducted by Zeppieri et al. [25] also analyzed the oxidation of MCH/toluene blends and constitute a valid test for verifying the reliability of the kinetic models. On the basis of a general and semi-detailed kinetic scheme, already validated for the pyrolysis, partial oxidation and combustion of hydrocarbon fuels [8,9, 17], we adopted a lumped approach to extend the scheme to these reference cycloalkane components. As already discussed elsewhere [26], this lumped

approach is a very useful and convenient means of progressively extending a kinetic model toward new reference fuels and heavier species. In simple terms, the first step of this simplification procedure is the classification of the primary propagation reactions together with the definition of a limited set of reference kinetic parameters. The second phase is the automatic generation of all the possible primary reactions aimed at building up a detailed reaction scheme. Finally, the lumping approach consists of reducing the overall complexity of this scheme, both by cutting the number of primary ‘equivalent’ reactions and by grouping different primary intermediate isomers in a limited number of ‘lumped’ components. This reduction is obtained by fitting the initial selectivities of the detailed and lumped schemes into a wide range of temperatures and pressures.

2. Cyclohexane reaction mechanism The study of the pyrolysis and combustion of cyclohexane should be relatively simple, due to the high symmetry of the molecule, and in fact, only one cyclohexyl radical can be formed as a result of the H abstraction reactions. The possible primary elementary reactions of this radical are schematically reported in Fig. 1. The cyclohexyl radical can form cyclohexene, both via a direct dehydrogenation reaction and with an O2 interaction: cy-C 6H11• ⫹ O2 3 cy-C6H10 ⫹ HO2• The O2 addition reaction forms the peroxy radical and justifies the low and intermediate temperature mechanism. The ␤-decomposition reaction of the cyclohexyl radical opens the ring and forms the linear 5-hexenyl radical. The kinetic parameters of these elementary reactions are reported in Table 1 and are directly evaluated on the basis of the reference kinetic parameters of the primary pyrolysis and oxidation reactions of linear and branched alkanes [13,17]. For instance, the rate constant for the dehydrogenation of the cyclohexyl radical to form cyclohexene (reaction 1 of Fig. 1): k1 ⫽ 1014.3 exp (⫺18900/T) s⫺1 is that used for the dehydrogenation of the 3-pentyl radical to form 2-pentene: CH3-CH2-CH•-CH2-CH3 3 CH3-CH⫽CH-CH2-CH3⫹ H• Similarly, the rate constant of the decomposition of the 5-hexenyl radical to form C2H4 and the 3-butenyl radical k2 ⫽ 1014 exp (⫺15100/T) s⫺1 is the same as used for the ␤-decomposition of primary alkyl radicals to form ethylene and smaller primary radicals. It is important to emphasize that this suc-

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Fig. 1. Primary propagation reactions of cyclohexyl radical.

cessive ␤-decomposition of the 5-hexenyl radical is in competition with the isomerization reaction to form resonantly stabilized hexenyl radicals. Moreover, as clearly depicted in Fig. 1, the internal addition reaction to form methylcyclopentyl structures must also be taken into account. Successive isomerization and ␤-decomposition reactions of these radicals may explain the primary formation of propene, butadiene, pentadiene, and cyclopentene. As already mentioned, a semi-detailed or lumped approach was adopted to reduce the overall complexity of the kinetic scheme. The steady state assumption for all the intermediate C6 radicals from Fig. 1 can be assumed. It is thus easy to solve the corresponding linear system and to verify the relative importance of the different reaction paths. Figure 2 reports the cumulative initial selectivity of the different primary products (moles of products/mole of cyclohexyl radical decomposed) at different reaction temperatures. Panel (a) of this figure shows that, in the case of pure pyrolysis conditions, the product distribution is not very sensitive to the reaction temperature. The main products are cyclohexene, propene, butadiene, pentadiene, and ethylene, while cyclopentene is of minor importance. Only at very high temperatures (1500 – 2000 K) does the direct decomposition of the 5-hex-

enyl radical to form C2H4 and the 3-butenyl radical become the main reaction path. It seems worthwhile observing that this linear analysis disregards the interactions of intermediate radicals with the reacting system, therefore it is very important to clarify the correctness of this simplification. The impact of such a hypothesis can be tested by introducing all the primary reactions of the oxidation of cyclohexane directly into the scheme. The self-recombination reactions of the intermediate resonantly stabilized radicals and also their recombination reactions with allyl radicals are included, assuming kinetic parameters of k ⫽ 1010 l/mole/s. On this basis, it is easy to determine that, despite their relative stability, the concentration of these radicals is always very low and consequently the sum of all these recombination products always remains lower than 0.1%, even at very high pressures. The linearity of the system, i.e. the absence of interactions of intermediate radicals with the reacting mixture, can be then accepted, and also justifies the adoption of a lumped approach with the consequent simplification of the kinetic model, both in terms of species and reactions. Panel (b) of Fig. 2 shows the same selectivities when oxygen is present in the reacting system. At temperatures lower than 800 K, the low temperature

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Table 1 Kinetic parameters of the primary propagation reactions of the cyclohexyl radical. Units are kmol, m, K, s. Reactions are numbered as in Fig 1. Radical decomposition reactions n.

Log(A)

E/R

n.

Log(A)

E/R

1 2 3 4 5

14.3 14 14 14 14

18900 15100 15600 16600 16600

6 7 8 9

14 14 14 14

14100 18100 14100 15100

Cyclic-radical decomposition reactions Forward reaction 10 15 16 18 19

14 14 14 14 14

15600 15600 15100 15600 14600

Reverse reaction ⫺10 ⫺15 ⫺16 ⫺18 ⫺19

10.3 11 11 11 11

3800 6550 7550 6550 7050

Radical isomerization reactions Forward reaction 11 12 13 14 17

11.3 11.3 10.2 10.5 11.3

7550 10300 9800 11100 9200

Reverse reaction ⫺11 ⫺12 ⫺13 ⫺14 ⫺17

11.5 11.5 10.2 10.6 11.5

12800 11100 5550 6300 11100

O2 addition and decomposition of ROO• add

9

0

dec

13.5

14600

mechanism is responsible for more than 60% of the primary products. Cyclohexene formed via the oxydehydrogenation reaction is included in the oxidation products and is ⬃8% at 800 K. These simulation results were obtained at PO2 ⫽ 0.1 atm (e.g., at 10 atm and 1% of oxygen). In this case too, the kinetic parameters of oxygen addition to cyclohexyl radical (cy-C6H11•) and successive isomerization reactions of intermediate radicals were all evaluated on the basis of the similar reactions of alkyl and alkylperoxy radicals [13]. In our estimation, with the referred rate constants, more than 95% of the role of the peroxy radicals and of the corresponding low temperature mechanism is due to the successive reactions of the cy-C6H11OO• radical. In other words, the O2 addition reactions with the remaining linear hexenyl radicals to form the corresponding peroxy radicals play a negligible role. The isomerization reactions of peroxy radicals to form alkyl hydroperoxy radicals involve the presence of double rings in the transition state. This fact is accounted for by modifying the corresponding reference rate constants. The activa-

Fig. 2. Cumulative yields of primary products from the pyrolysis and oxidation of cyclohexane vs. reaction temperatures [K]. Panel (a) Pyrolysis. Panel (b) Oxidation at PO2 ⫽ 0.1 atm.

tion energies are increased by 12,500 kJ/kmol, due to the extra strain of the cyclohexane ring. The reference frequency factors are also increased by 100.8, corresponding to the rotor already blocked by the aliphatic ring. On this basis, the semi-detailed and lumped mechanism of the primary oxidation and decomposition reactions of cyclohexane was reduced very simply to the reactions of Table 2. Only one ␤-decomposition reaction of the cy-C6H11• radical is assumed and its global stoichiometry is directly taken from the simulation results of panel a) of Fig. 2 at 1000 K. The kinetic parameters of the H abstraction reactions (R12-R14) are estimated on the basis of analogy and similarity rules [27]. Reactions R21 and R22 are responsible for the formation and decomposition of the lumped ketohydroperoxide component (cyC6H10O3). ‘Oxygenated cyclo-C6’ (cy-C6H10O) and ‘hexenal’ (C5H9CHO) are lumped species (i.e., they group different isomers) and are the only cyclohexane primary products not already contained and considered in the existing kinetic scheme. Both these components are formed [20,28] by the decomposition reactions of the cycloalkylhydroperoxy radicals (R17-R18) and they were also observed by O’Connor and Schmidt in the catalytic assisted oxidation of cyclohexane in a single gauze reactor [29]. For these

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Table 2 Primary reactions and lumped mechanism of the pyrolysis and oxidation of cyclohexane. Units are kmol, m, K, s n.

High Temperature Reactions

A

E/R

R1

cy-C6H113 .41 (C2H5 ⫹ C4H6) ⫹ .25 (cy-C6H10⫹H) ⫹.1 (C5H8 ⫹ CH3) ⫹ .12 (C3H6 ⫹ aC3H5) ⫹.1 (C2H4 ⫹ pC4H7) ⫹ .01 (cy-C5H8 ⫹ CH3) ⫹ .01 (C2H4 ⫹ aC4H7) H⫹cy-C6H103 cy-C6H11 OH⫹cy-C6H10 ⫽ C2H3CHO⫹1-C3H7 cy-C6H93 .6cy-C6H8⫹.6H⫹.4cy-C5H6⫹.4CH3 cy-C6H9⫹HO23 OH⫹cy-C5H8⫹HCO cy-C6H12 ⫽ 1-C6H12 cy-C6H12 ⫽ cy-C6H10⫹H2 cy-C6H10 ⫽ cy-C6H8 ⫹ H2 cy-C6H10 ⫽ C2H4⫹C4H6 cy-C6H8 ⫽ Benzene⫹H2 cy-C6H11⫹O2 ⫽ cy-C6H10⫹HO2 H abstraction Reactions R⫹cy-C6H123 RH⫹cy-C6H11 R⫹cy-C6H103 RH⫹cy-C6H9 R⫹cy-C6H83 RH⫹Benzene⫹H Low Temperature Reactions cy-C6H11⫹O2 ⫽ cy-C6H11OO cy-C6H11OO ⫽ cy-C6H10OOH cy-C6H10OOH ⫽ C5H9CHO⫹OH cy-C6H10OOH ⫽ cy-C6H10O⫹OH cy-C6H10OOH ⫽ cy-C6H10⫹HO2 cy-C6H10OOH⫹O2 ⫽ cy-OOC6H10OOH cy-OOC6H10OOH ⫽ OH⫹cy-C6H10O3a cy-C6H10O3a3 OH⫹CH2CHO⫹CH2CO⫹C2H4

5.0 1013

15100

2.0 5.0 1.0 3.0 1.5 2.0 1.0 1.0 1.0 7.5

1010 109 1014 109 1016 1015 1014 1015 1014 108

1250 0 21100 0 41500 35200 34700 33700 30200 1500

1.0 3.0 1.0 1.0 1.0 1.0 3.0 5.0

109 1012 1012 1012 1014 109 1012 1014

0 12100 8050 9050 12100 0 12100 21100

R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16 R17 R18 R19 R20 R21 R22 a

cycloketohydroperoxide

components it was necessary to study and include their primary propagation reactions in the overall kinetic model. Only H abstraction reactions of these species were considered, always with the kinetic parameters estimated on the basis of the analogy rules. Pentadiene, butadiene, and acrolein are formed from hexenal, while cyclopentene is the main product from cyclohexanone: R• ⫹ C5H9CHO 3 RH ⫹ .4(CO ⫹ C2H4 ⫹ aC3H5•) ⫹ .4共C4H6 ⫹ CH2CHO•) ⫹ .1(C5H8 ⫹ HCO•) ⫹ .1(C2H3CHO ⫹ aC3H5•) R• ⫹ cy-C6H10O 3 RH ⫹ .5(cyC5H8 ⫹ H• ⫹ CO)

previous kinetic scheme to extend its simulation capability to the pyrolysis and oxidation of cyclohexane, pure or mixed with different hydrocarbons, to represent real or surrogate fuels. In fact, all the successive reactions of the primary and intermediate products are already contained within the scheme. To these ends, it seems relevant to underline that the overall kinetic scheme [17], available upon request, is not fully compatible with CHEMKIN format, for two different basic reasons. Firstly, we are considering lumped reactions with several products and non-integer stoichiometric coefficients. Secondly, we build and treat all the H abstraction reactions in a compact way on the basis of the aforementioned analogy rules [27].

⫹ .4(CO ⫹ C2H4 ⫹ aC3H5•) ⫹ .1(•CH2CO ⫹ pC4H7•) The lumped stoichiometry of the H abstraction reaction from C5H9CHO clearly shows the prevailing importance of the acylic H atom abstraction (with the successive formation of CO) and of the allylic one (with the formation of butadiene). Due to the hierarchical modularity of the detailed kinetic schemes, only these reactions need to be inserted into the

3. Comparisons with experimental measurements Different sets of experiments were analyzed to validate the proposed kinetic model. The first set of these measurements relates to the low temperature mechanism and refers both to the low pressure study of cyclohexane cool flames and spontaneous ignition in a closed vessel [19], and to the ignition delay times

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Fig. 4. The oxidation cyclohexane in a rapid compression machine. Ignition delay times [ms] versus temperature [K] [28].

Fig. 3. Panel a) Cool flame limits for cyclohexane oxygen mixtures (from Bonner and Tipper [19]). Panel (b) Calculated temperature profiles for cyclohexane combustion in an uncoated vessel at different reactor temperatures.

630 K. Panel (b) of the same figure shows that the model predictions of the temperature profiles along the time for different reactor temperatures agree with the experimental behavior, moving from slow combustion to 3 cool flames, by varying the initial reactor temperature from 530 up to 600 K. The induction times before the cool flames predicted by the model (⬃ 25 s at 553 K and 160 torr) also agree very well with the experimental ones reported by Bonner and Tipper for the uncoated vessel [19]. 3.2. Ignition delay times of cyclohexane in the rapid compression machine

in the Lille rapid compression machine [28]. A second set of experiments, on the other hand, studies the partial oxidation and combustion of cyclohexane in a jet stirred reactor at 800 –1200 K, 1 to 10 atm and different stoichiometric ratios, as well as going into great detail about the intermediate and final products [23,24]. Finally, measurements on cyclohexane laminar flame speed [30] extend the mechanism validation to temperatures above 2000 K. 3.1. Cool flames and the spontaneous ignition of cyclohexane in a closed vessel Bonner and Tipper [19], and Zeelenberg and De Bruijn [20] studied the induction period and the cool flame behavior of cyclohexane-oxygen mixtures in closed vessels at low pressures (0.1– 0.3 atm). Important features of the low temperature oxidation mechanism are discussed, also on the basis of a careful identification of a large number of oxidation products. Panel (a) of Fig. 3 [19] shows the experimental ignition diagram for an equimolar cyclohexane-oxygen mixture in a cylindrical Pyrex reaction vessel of 1.5 ⫻ 10⫺4 m3. At low pressures (0.1– 0.25 atm), this mixture shows slow reaction, 1, 2, and 3 different cool flames in the temperature range between 530 –

Lemaire et al. [28] studied the oxidation of cyclohexane, cyclohexene, and cyclohexa-1,3-diene in a rapid compression machine in engine-like conditions. These measurements are of particular interest in verifying the low temperature mechanism and the ignition delay time of cyclohexane. The pressure at top dead center (TDC) varied between 0.7 and 0.9 MPa with temperatures between 650 and 900 K. The stoichiometric ratio was 1, with dilution as in air. The experimental ignition delay times vs. core gas temperature are plotted in Figs. 4 and 5, together with the model predictions. Simulation results neglect the compression phase and refer to a constant volume, adiabatic, perfectly stirred reactor. Figure 4 shows the excellent agreement obtained in the whole temperature range from 650 to 900 K, and the simulation results correctly reproduce the experimental evidence of low temperature ignition delays up to temperatures of ⬃750 K and the successive NTC behavior of the reacting system. Figure 5 shows the predicted mole fraction profiles for different species at TTDC ⫽ 722 K and PTDC ⫽ 0.75 MPa. The lack of experimental data on temperature and cyclohexane conversion makes direct comparisons with measurements less important. Nevertheless, it is still possible to observe the agreement

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Fig. 5. The oxidation cyclohexane in a rapid compression machine at TTDC ⫽ 722 K [28]. Mole fractions of relevant species as a function of time [s]. Predicted (lines) and experimental (symbols: circles, Cyclohexene; squares, hexenal; triangles, oxigenated cyclo-C6).

on the prevailing presence of cyclohexene over oxygenated C6 and also the larger amount of hexenal in respect of epoxycyclohexanes and cyclohexanone. In our model, all these different oxygenated isomers of cyclo-C6 are lumped into a single equivalent species. Cyclohexene is overpredicted by a factor of 2, while there is quite a good agreement on oxygenated C6 species. Finally, Fig. 5 also shows the predicted concentration of cycloketohydroperoxide which is the main cause of the cool flame. Before this low temperature ignition, the quantity of ketohydroperoxide is even larger than that of cyclohexene. Unfortunately, the corresponding measurements are not available. 3.3. Oxidation of cyclohexane in the jet stirred reactor Voisin et al. [23] and El Bakali et al. [24] studied the oxidation of cyclohexane in a jet stirred reactor (JSR) at 1–10 atm and different stoichiometric ratios (⌽ ⫽ 0.5, 1. and 1.5). As an example of the good agreement between the measurements and model predictions, Fig. 6 reports the intermediate and final products obtained at 10 atm and ⌽ ⫽ 1 in detail. Only butadiene and C3H4s (propadiene and methylacetylene) show large overpredictions, while C2H4 is underestimated by the model. Similar deviations are also observed with different equivalence ratios. The agreement on the C5-C6 species is particularly significant in confirming the assumed simplifications. H abstractions from cyclohexane are the major disappearance reactions, while the OH• radical is the most effec-

tive one. H•, CH3•, HO2• and O• are active radicals, the importance of which depends on the operating conditions. Four center reactions R6 and R7 of Table 2 do not contribute significantly to the overall reactive process but are responsible for the formation of 1-hexene. The dehydrogenation reaction is indeed responsible for only 3% of the formation of cyclohexene at 1050 K, while the isomerization reaction: cy-C 6H12 ⫽ 1-C6H12 explains the formation of 1-hexene. The estimated kinetic parameters, k ⫽ 1.5 ⫻ 1016 exp (⫺41,500/T) [s⫺1], well tested under pyrolysis conditions [31], are slightly higher than those proposed by Tsang [32]. The measurements for 1-hexene, with a maximum of ⬃2 ⫻ 10⫺6 at 1 atm and ⌽ ⫽ 1, are closely reproduced by the model. In agreement with model predictions, which indicate a mole fraction of 10⫺8, the experiments detect no 1-C6H12 at 10 atm. Cyclohexadiene is the main source of benzene in all the conditions examined. It is formed largely through the dehydrogenation of the cyclohexenyl radical and only marginally by the molecular dehydrogenation of cyclohexene. Pentadiene, formed by the previously discussed decomposition of the cyclohexyl radical, forms butadiene and cyclopentadiene, via H addition and H abstraction reactions respectively. As already observed [23,24], the cyclohexenyl radical (cyC6H9•) plays a very important role in the formation of cyclopentene through the following reaction: cy-C6H9• ⫹ HO2• 3 OH•⫹ cy-C5H8 ⫹ HCO•

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Fig. 6. The oxidation cyclohexane in the JSR [24] at 10 atm and ⌽ ⫽ 1. Mole fractions versus temperature [K].

Cyclopentadiene is mainly formed via the H abstraction reactions from cyclohexene and the successive radical isomerization and demethylation. Figure 7 shows the model’s ability to reproduce the effect of different stoichiometric ratios for different components at 10 atm. Figure 8 compares the experimental and predicted pressure effects. It is interesting to observe that at 1 atm butadiene and C3H4s too are correctly predicted by the model.

3.4. Cyclohexane laminar flame speed To verify the model at high temperatures as well, model predictions were also compared with experimental laminar flame velocities. Laminar flame speeds of cyclohexane-air mixtures were recently presented by Davis and Law [30], at atmospheric pressure and different equivalence ratios. As shown in Fig. 9, model predictions agree with the experi-

Fig. 7. Effect of stoichiometric ratios (⌽ ⫽ 0.5, 1, 1.5) on the oxidation cyclohexane in the JSR [23]. Mole fractions versus temperature [K].

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Fig. 8. Pressure effect on the oxidation cyclohexane in the JSR [24]. Mole fractions versus temperature [K] (P ⫽ 10 atm empty symbols and solid lines; P ⫽ 1 atm filled symbols and dashed lines).

mental burning rates. These results were obtained with a version of the PREMIX code [33] slightly modified to handle lumped reactions. In these conditions, the sensitivity analysis performed, not only in stoichiometric conditions, but also at fuel rich equivalence ratios (⌽ ⫽ 1.44), shows that the important reactions are always the usual high temperature reactions, such as: H• ⫹ O2 ⫽ OH• ⫹ O• CO ⫹ OH• ⫽ CO2 ⫹ H• HCO•⫹[M] ⫽ CO ⫹ H•⫹ [M] In other words, this analysis confirms that the flame speed is mainly influenced by the typical high temperature reactions and is only slightly dependent on the fuel primary reactions.

4. Extension of the kinetic scheme to methylcyclohexane As already mentioned, methylcyclohexane (MCH) is also a commonly used reference component in describing the important amount of naphthene fraction in liquid fuels. Analogously to what was discussed for cyclohexane, Fig. 10 shows the possible primary propagation reactions of MCH and primary decomposition products are singled out in dashed boxes. All radicals can abstract hydrogen atoms from MCH forming 5 different cyclic radicals (RC7H13•). Via ␤-decomposition reactions, these radicals can open the ring structure giving rise to linear or branched C7H13 radicals. At the intermediate temperatures of combustion processes (900 –1200 K), these radicals can either decompose or can easily isomerize, forming resonantly stabilized radicals. It is possible to refer to the following kinetic parameters for these ␤-decomposition and isomerization reactions [13,17]: k DEC ⫽ 1014 exp (⫺15100/T) [s⫺1] k ISOM ⫽ 1010.5 exp (⫺5800/T) [s⫺1]

Fig. 9. Comparison between experimental [30] and predicted laminar flame speeds of cyclohexane-air mixtures at 298 K and 1 atm.

These rate expressions describe the competition between ␤-scission and isomerization reactions and show the larger importance of the isomerization reactions, at least for temperatures lower than 1200 K. The same reference kinetic parameters, already referred to in Table 1 for cyclohexane, were also used to study all these primary decomposition reactions. Apart from the reactions described in Fig. 10, all intermediate radicals can also dehydrogenate to form methylcyclohexenes and methylhexadienes, and we used the same reference kinetic parameters already assumed for reaction 1 from Table 1. Again, the selectivities of all the primary decom-

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(1000 –1100 K). At low temperatures, the oxidation process mainly moves through peroxide and ketohydroperoxide components. At high temperatures, the primary cycloalkyl radicals (and their intermediate products) promptly decompose to small olefins (ethylene, propene, and butadiene) and radicals (H•, CH3•, C2H3•.), and the oxidation process is mainly dictated by the successive and typical high temperature mechanism. As already discussed, the lumped high temperature mechanism for the pyrolysis of MCH is reduced very simply to the primary reactions reported in Table 3, where a single lumped RC7H13• groups all the 19 isomers C7H13• and its decomposition reaction summarizes the different high temperature decomposition paths. All products and intermediate components were already studied and contained in the semidetailed kinetic scheme. To extend the model to account for the low temperature oxidation mechanisms also, it would be necessary to consider oxygen additions to the ‘lumped’ RC7H13• and to study and include the successive reactions of peroxy radicals, analogously to the reactions reported in Table 2 for cyclohexane. The lack of measurements on the low temperature oxidation of MCH (both in RCM and in closed vessels) actually means that this further extension is of lesser importance and priority.

5. Comparisons with experimental measurements

Fig. 10. H abstraction reactions from methylcyclohexane.

position products can be simply obtained by solving the mass balance equations for all the intermediate radicals, by assuming the steady state hypothesis. From this analysis, it is possible to deduce the product distribution in the temperature range of interest

An interesting set of measurements relating to the pyrolysis and oxidation of MCH in the Princeton Turbulent Flow Reactor was presented by Zeppieri et al. [25]. Figure 11 shows the good agreement between the measurements and predicted results, both under pyrolysis and oxidation conditions. The slight overprediction of reactivity under oxidative conditions is responsible for the undepredictions of both the concentration and time peak of the benzene. Zeppieri et al. [25] also studied the oxidation and combustion of several mixtures of methylcyclohexane and toluene. The study of these simple blends

Table 3 Lumped high temperature reactions of methylcyclohexane (CH3cy-C6H11). Units are kmol, m, K, s High Temperature Reactions CH3cy-C6H113 .05 H ⫹ .35 CH3 ⫹ .3C2H5⫹ .05 cy-C6H10 ⫹ .3 C4H6 ⫹ .3C2H4 ⫹ .35 C3H6 ⫹ .2 C4H8 ⫹.15 i-C4H8 ⫹ .2 C5H10 R ⫹ CH3cy-C6H113 RH ⫹RC7H13 RC7H133 .05 H ⫹ .28 CH3 ⫹ .35 C2H5 ⫹ .15 n-C3H7 ⫹.1 i-C3H7 ⫹ .12 pC4H7 ⫹ .20 C2H4 ⫹ .12 C3 H6 ⫹ .39 C4H6 ⫹ .05cy-C5H8 ⫹ .05 cyC5H6 ⫹ .29 C5H8 ⫹ .1 cy-C6H10

A

E/R 18

.50 10

41300.

.50 1014

15100.

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543

Fig. 11. Pyrolysis and oxidation of MCH in a PFR [25]. Experimental (symbols) and predicted (lines) mole fractions of relevant species as a function of time [s]. Pyrolysis: T ⫽ 1155 K, P ⫽ 1 atm, MCH ⫽ 0.166 vol. %, in N2 (filled symbols and dashed lines). Oxidation: T ⫽ 1160 K, P ⫽ 1 atm, MCH ⫽ 0.185 vol. %, O2 ⫽ 1.9 vol. % in N2 (empty symbols and solid lines). Measurements are shifted toward higher residence times by 5 ms.

containing substantial amounts of aromatics constitutes a first step toward a comprehensive kinetic model of real fuels. This mixture is a simple way of investigating the effect of dilution and the different reactivity of the two fuels. The oxidation reactions of toluene [34] were already contained in the whole kinetic scheme and had been discussed elsewhere [35]. It is convenient to simply recall that H abstraction from toluene forms the very stable benzyl radical and that pure toluene reactivity is very low. Selfrecombination of benzyl radicals and its recombination with methyl radicals regulate the important termination process. In the mixture, propagation reactions on MCH generate active radicals which promote the oxidation of toluene. H abstractions from toluene, on the other hand, form the resonantly stabilized benzyl radical, whose recombination reactions are partially responsible for active radical depletion and for the consequent reduction of MCH reactivity. The model correctly predicts the lower conversion of toluene, both in the case of pure toluene and in mixtures. As shown in Fig. 12, MCH conversion correctly decreases due to the addition of toluene; conversely, the mixture’s effect increases the reactivity of toluene. Toluene conversion in the mixture is overestimated in respect of the experimental indication only in the blend: MCH 1229 ppm—Toluene 1475 ppm.

6. Conclusions A semi-detailed kinetic model was extended to include naphthenes as reference components to broaden its capabilities and include heavy practical fuels, such as jet fuels, kerosene, and diesel oils. This knowledge of the combustion characteristics of naphthenes could also improve the understanding and design of HCCI engines. The role and importance of the primary propagation reactions of naphthenes as reference components was outlined and discussed. Particular attention was devoted to the role of isomerization reactions to justify the intermediate and final products from primary propagation reactions. Moreover, several comparisons with experimental results confirm the reliability of the overall kinetic model, as well as the validity of the lumped approach. The model was also tested in comparison with cyclopentene flames [36]. Recently [3], the model was also successfully extended to cover the combustion of JP8 surrogate blends and was validated in comparison with measurements relating to a kerosene laminar premixed flame [37].

Acknowledgments The authors wish to thank Prof. Mario Dente and Prof. Adel Sarofim for their helpful discussions, also

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Fig. 12. Mixture effect on the oxidation of MCH and Toluene in a PFR at 1160 K; ⌽ ⫽ 1.3 [25]. Normalized mole fractions of MCH (panel a) and Toluene (panel b) as a function of time [s]. Pure MCH: 1815 ppm and pure Tolene 2559 ppm (solid lines and filled circles). Blend: MCH 1229 ppm - Toluene 1475 ppm (dotted lines and squares). Blend: MCH 240 ppm - Toluene 2592 ppm (dashed lines and empty circles).

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