A comparative single-pulse shock tube experiment and kinetic modeling study on pyrolysis of cyclohexane, methylcyclohexane and ethylcyclohexane

Jin-hu Ling , Shu-tong Co , Fei Li , Xio-ling Li , Rui-ning He , Xin Bi ,Qun-De Wng , Yng Li ,*

a School of Environmental and Safety Engineering, North University of China, Taiyuan, 030051, People's Republic of China

b Science and Technology on Combustion, Internal Flow and Thermostructure Laboratory, School of Astronautics, Northwestern Polytechnical University,Xi'an 710072, People's Republic of China

c Low Carbon Energy Institute and School of Chemical Engineering,China University of Mining and Technology, Xuzhou 221008,People's Republic of China

Keywords:Cyclohexane Alkylated cyclohexane Single-pulse shock tube Pyrolysis Kinetic modeling

ABSTRACT The pyrolysis of cyclohexane, methylcyclohexane, and ethylcyclohexane have been studied behind reflected shock waves at pressures of 5 and10 bar and at temperatures of 930-1550 K for 0.05%fuel diluted by Argon.A single-pulse shock tube(SPST)is used to perform the pyrolysis experiments at reaction times varying from 1.65 to 1.74 ms.Major products are obtained and quantified using gas chromatography analysis.A flame ionization detector and a thermal conductivity detector are used for species identification and quantification.Kinetic modeling has been performed using several detailed and lumped chemical kinetic mechanisms.Differences in modeling results among the kinetic models are described.Reaction path analysis and sensitivity analysis are performed to determine the important reactions controlling fuel pyrolysis and their influence on the predicted concentrations of reactant and product species profiles.The present work provides new fundamental knowledge in understating pyrolysis characteristics of cyclohexane compounds and additional data set for detailed kinetic mechanism development.

1.Introduction

Real fuels, i.e., conventional petroleum-derived gasoline, jet fuels, and diesel fuels are complex mixtures of thousands of hydrocarbon species [1,2].Major classes of these hydrocarbon compounds in these fuels include normal alkanes, iso-alkanes,cycloalkanes, alkenes and aromatics.Due to the large number of hydrocarbon species in real fuels, it is impossible to explicitly analyze the molecular structure and corresponding concentration of every fuel constitute.Consequently, to mimic real fuel combustion behaviors,the surrogate-fuel approach which uses a surrogate fuel composed of several neat compounds to represent the hydrocarbon classes in real fuels is widely used in combustion community [3-11].Thus, a basic understanding of the combustion properties of representative hydrocarbon compounds is of critical importance toward the development of detailed combustion kinetic mechanisms of real fuels.

Cycloalkanes are an important class of compounds in real fuels,i.e., approximately 20% in conventional jet fuels, 10% in gasoline,and up to 90% in alternative direct coal liquefaction jet fuels[10,12].Gasoline fuels usually contain large number of C5-C7 cycloalkanes, e.g., cyclopentane, cyclohexane, and methylcyclohexane, while jet fuels typically contain larger alkylated cyclohexane, i.e., ethylcyclohexane,n-propylcyclohexane, andnbutylcyclohexane.Among these, methylcyclohexane, and ethylcyclohexane are frequently used as a candidate surrogate compound in the development of surrogate model of real fuels[1,13-15].Due to the hierarchical nature of the development of detailed combustion mechanism, cyclohexane represents the foundation toward the development of detailed mechanisms for large cyclohexanes.Therefore, fundamental experimental and kinetic modeling studies on cyclohexanes are critical for combustion behaviors of real fuels.

Due to the significant importance of cyclohexanes in combustion, various fundamental studies have been conducted for cyclohexane compounds.These studies include experimental measurements of low-to-intermediate temperature and high temperature ignition delay time [16-23], laminar flame speeds[24,25], species profiles in flow reactor, jet-stirred reactor, or premixed laminar burner-stabilized flame facility [13-15,26-28].Correspondingly, detailed combustion kinetic models are also developed to predict the measured experimental results[26,27,29,30].Theoretical studies are also performed on importance reactions and species to obtain accurate reaction rate coefficients and thermodynamic data for the optimization of detailed mechanisms [31,32].However, most experimental and kinetic modeling studies were focused on low-temperature oxidation and global combustion properties studies.Only a few investigations have performed pyrolysis characteristics of cyclohexane.The decomposition of cyclohexane was studied in a shock tube using the laserschlieren technique over the temperature range 1300-2000 K and pressure range 25-200 torr by Kiefer et al.[33].The main purpose in their study is to elucidate the mechanism and rate constant of the process of cyclohexane isomerizes to 1-hexene.Peukert et al.[34]also investigated the pyrolysis characteristics of cyclohexane using a shock tube by measuring the formation of Hatoms over a temperature range of 1320-1550 K, at pressures ranging from 1.8 to 2.2 bar.The overall rate coefficients were deduced for the global reaction cC6H12→Product+H from H-atom time profiles.Wang et al.[28]performed the pyrolysis of cyclohexane from 950 to 1520 K using a plug flow reactor coupled with a synchrotron VUV photoionization mass spectrometry.Although a kinetic model including 148 species and 557 reactions was proposed by them,the pyrolysis experiments pressure is only 40 Mbar due to the pressure limitation of the facility.Recently, the initial unimolecular decomposition mechanism of cyclohexane was studied by flash pyrolysis coupled with molecular beam sampling and VUV-PI-MS at the pressure about 16 torr by Shao et al.[35].However,there are little experimental and kinetic modeling studies focusing on high-pressure pyrolysis properties studies for the three reactants and comparing the experimental and modeling results of them.

High temperature pyrolysis process of cyclohexane represents an important part of combustion mechanism development and validation.The oxidation kinetics of hydrocarbons highly depends on both temperature and pressure,while,at high temperature,fuel molecule typically undergoes high pyrolysis process to produce various smaller molecules, which depends on the structure of fuel molecule, thereafter, the kinetics of C0-C4species oxidation becomes dominant [12,33,34].Following this idea, the HyChem model and various lumped models were proposed to develop detailed combustion mechanisms [12,35-39].Hence, a basic understanding of high pyrolysis characteristics of large hydrocarbon compounds is of crucial importance in the optimization of these models.Besides this, pyrolysis process of hydrocarbon is also important to improve petroleum process [40,41], product light olefins [42], and develop advanced hypersonic aircrafts via regenerative cooling technique which employs fuel pyrolysis as the foundation[43,44].Although pyrolysis of some cyclohexanes were also studied using various facilities,the studied temperature ranges or pressure were usually limited to low pressure or low temperature conditions.

Based on the above considerations,this work intends to perform a comparative study on the high temperature pyrolysis of cyclohexane, methylcyclohexane, and ethylcyclohexane using single-pulse shock tube(SPST)in order to provide complementary data for the development and validation of detailed chemical mechanisms and illustrate the molecular structure effect on the pyrolysis characteristics.The paper is organized as follows.Section 2 briefly describes the experimental methods together with uncertainty analysis, while Section 3 shows the kinetic modeling details.Section 4 provides the experimental and modeling results together with detailed analysis on the results.Major conclusions are summarized in Section 5.

2.Experimental methods

2.1.SPST experimental method

The pyrolysis experiments of cyclohexane, methylcyclohexane,and ethylcyclohexane are performed in a SPST facility at the North University of China.Detailed description of the shock tube has been described in detail previously [11,45]and will only be briefly described.The shock tube is designed with a 1.5 m driver section and a 3.05 m driven section with an inner diameter of 44 mm.The driver and driven sections are separated via a polycarbonate diaphragm.A pressure vessel named dump tank is used to consume the reflected shock waves and to ensure the reaction mixture solely single heated condition.Incident shock velocity is measured using 4 PCB 113B21 piezoelectric pressure transducers mounted on the sidewall of the driven section.The pressure-time profiles are measured by a Kistler 603CBA piezoelectric pressure transducers at the end of the driven section.All pressure traces are recorded via two digital TiePie Handyscope HS4 oscilloscopes.The reflected shock wave pressure (P5) and temperature (T5) are determined using the one-dimensional normal shock relations implemented in the Gaseq program [46].The reaction/residence time is defined as the time interval between the arrival of the reflected shock wave and the 80% of the pressure signal recorded by Kistler pressure sensor.The shock-heated products were sampled using a solenoid valve from the endwall through a 3 mm inner diameter stainless steel tube that protruded 10 mm into the SPST, and the products were analyzed by using a gas chromatography(Agilent 7820A).The sampling time is controlled by a fast-acting solenoid valve and the sampling event is initiated approximately 3 ms after the passing of the reflected shock wave from the endwall,and ends 100 ms later.Due to the small diameter of the sampling tube and the minimal dead volume(71 mm3),it was assumed that the unreacted mixture could be negligible.The sample section is also heated to the same temperature as the shock tube driven section.A flame ionization detector and a thermal conductivity detector are used for reaction products.

The reaction mixture is prepared in stainless steel mixture tanks according to the Dalton’s law of partial pressure and is maintained for 12 h before experiments to ensure complete vaporization and homogeneity.A heating system with seven thermocouples placed along the mixing tank,shock tube and the sampling tube is used to maintain the experimental system with a temperature of 333 K to avoid adsorption of the fuels.The fuels, i.e., cyclohexane, methylcyclohexane, and ethylcyclohexane are provided by Shanghai Aladdin Biochemical Technology Co., LtdChina with the purity larger than 99.9%.Helium (He) is used as driver gas, Argon (Ar) is used as diluent gas,and Krypton(Kr)is used as an internal standard gas.Thepurity of the three gases is 99.99%.The system is calibrated using a 16 gas GC standard obtained from Beijing Haipubeifen gas Ltd China.The 16 reference chemicals with the concentration of 150 ppm are hydrogen, methane, ethane, propane, butane,ethylene, propene,1-butene, 2-butene, allene,1, 3-butadiene, isobtylene, acetylene, propyne, benzene, toluene.The calibrated standard is used to calculate the concentration of the pyrolytic products, while the effective carbon number method is used to estimate concentrations of species with no calibration standard.Table 1 lists the detailed experimental conditions.The high-diluted experimental condition is adopted to equalize the temperature because the fuel pyrolysis process is endothermic.

2.2.Experimental uncertainty

The overall uncertainty of the studied properties using the experimental procedure is generally consisting with the other similar facilities and related researches [11,47-49].Specifically,uncertainty of the reflected temperature is approximately ±2%based on the analysis by Petersen et al.[50]using a standard error analysis procedure.The uncertainty of reaction time has been validated that it can be controlled within±5%based on several test experiments under different temperature conditions during the SPST debugging period [11,47].For the measured species concentrations,the uncertainty for the calibrated species using repetitive sampling of the standard gas is approximately ±10%, while the uncertainty of the estimated species via the effective carbon number method is approximately±20%[51,52].The carbon balance in SPST mainly relies on the absorption in the mixture tank,shock tube, sampling tube and the GC analysis method.Although the accurate carbon balance at some conditions cannot be determined accurately due to the unidentified species and the formation of soot precursor species, the carbon balance at low temperature conditions and previous studies using the same facility reveal that the present experimental method can ensure the current experimental uncertainty of the carbon balance within 15%.Therefore, the measured pyrolysis characteristics exhibits high accuracy, and can provide valuable complementary data for detailed kinetic mechanism validation and development.

3.Kinetic modeling

Kinetic modeling is performed by assuming a closed homogeneous batch reactor at constant volume to mimic the SPST facility.The reaction time approach is employed due to simplicity and efficiency of this method.Previous detailed analysis and kinetic modeling results has confirmed that the modeling results from the reaction time approach exhibit no significant differences compared with that based on the recorded pressure profiles [52-54].All kinetic modeling and analysis are performed using the Cantera software [55].

Previous experimental studies led to the development of a series of chemical kinetic mechanisms to model experimental measured combustion properties.One of the widely used detailed mechanisms is the JetSurF 2.0,focusing on high-temperature combustion chemistry of n-alkanes up ton-dodecane, and mono-alkylated cyclohexanes, includingn-propylcyclohexane, ethylcyclohexane,methylcyclohexane,and cyclohexane[30].To reduce the model size of the detailed mechanisms, Zhang et al.[37]recently used the decoupling methodology to develop a lumped kinetic model for 50 hydrocarbons including n-alkanes, iso-alkanes, cyclo-alkanes and alkylbenzenes by using the same base model adopted in JetSurF 2.0.Based on previous analysis on high temperature pyrolysis of large hydrocarbons, the C0-C4base model generally controls the mutual transformation of the measured small pyrolysis products.Thus, to facilitate computational efficiency, the recently updated based model (NUIGMech1.1) at the National University of Ireland,Galway [47,53,56]is also coupled with the lumped kinetic model[37]to investigate the effect of base model in prediction of the pyrolysis process,and is denoted as Zhang-NUIG mech in this work.Besides these, experimental and kinetic modeling studies on methylcyclohexane and ethylcyclohexane were also performed by the Fei Qi group [13,15,57].The above four representative kinetic mechanisms are then employed to predict the experimental measured results in this work.

4.Results and discussion

4.1.Experimental and modeling results

Fig.1 and Fig.2 show the major pyrolysis product distributions as a function of temperature for 0.05% cyclohexane pyrolysis experimental results at around 5 and 10 bar together with the kinetic modeling results, respectively.The pyrolysis experimental results at around 5 bar with kinetic modeling results for 0.05%fuel diluted in Ar for methylcyclohexane and ethylcyclohexane are displayed as Fig.3 and Fig.4, respectively, while the experimental and modeling results at 10 bar are provided as supplementary materials.From the experimental and kinetic modeling results shown in Fig.1-Fig.4, the employed detailed mechanisms can mostly capture the tendencies of the product distributions as a function of temperature.However, the prediction accuracy from different mechanisms exhibits large differences for different species.As shown in Fig.1 and Fig.2,the pressure change hardly affects the product distributions as a function of temperature, and the product yields of the major species are still not greatly influenced.One of the major reasons can be attributed to the pressureindependent β-scission reactions that control the formation of these small products.

For the pyrolysis of cyclohexane,ethylene is the most abundant product, and reaches a maximum product yield at approximately 1400 K.As temperature further increases, the concentration of ethylene tends to decrease, while the yield of acetylene continues to increase due to the transformation from ethylene.Methane and 1,3-butadiene are the other two major products.For the studied temperature ranges, it can be seen that the concentration of methane tends to increase as temperature rises.Compared with pyrolysis of linear alkanes[58],1,3-butadiene is largely formed due to the β-scission reaction of the radical via the ring-opening reaction.It is also noted that the species profiles for propene, 1,3-butadiene, and 1-butene are very similar, and the concentrations increase first to the maximum value at around 1400 K when cyclohexane is consumed thoroughly.Then, they are quickly consumed since these species are unstable at high temperaturecondition.The product distributions of allene and propyne as a function of temperature are nearly the same since the two species can be mutual transformation.The adopted four kinetic mechanisms can well predict the tendencies of the measured species profiles; however, the prediction accuracy still varies for different species.For the two lumped mechanisms, it can be seen that they exhibit very similar performance, indicating that the two base models do not affect the prediction accuracy because the pyrolysis mainly involve high temperature chemistry that has been well studied [10,56,59].Overall, the detailed JetSurF 2.0 and Fei Qi mechanisms show better performance for most of the products except for ethane and propyne.Since the formation of propene and 1-butene is not included in the global lumped reactions for cyclohexane, the two lumped mechanisms tend to significantly underestimate their concentrations.

Table 1Pyrolysis experimental conditions in this work.

Fig.1. Species profiles as a function of temperature for 0.05% cyclohexane pyrolysis experiment at 5 bar together with kinetic modeling results.The labelled Zhang mech was developed in Ref.[37],while the Zhang-NUIG mech represents the mechanism via the combination of the global fuel pyrolysis reactions[37]with the skeletal NUIG base model[56].The employed Fei Qi mechanisms were developed from a series of experimental and modeling work on cycloalkanes [13,15,57].

Fig.2. Species profiles as a function of temperature for 0.05% cyclohexane pyrolysis experiment at 10 bar together with kinetic modeling results.

Fig.3. Species profiles as a function of temperature for 0.05% methylcyclohexane pyrolysis at 5 bar together with kinetic modeling results.

Compared with cyclohexane, although the major product distributions from pyrolysis of methylcyclohexane and ethylcyclohexane are similar from Fig.3 and Fig.4, the relative product yields and distributions still show a degree of difference.Specifically, ethylene is still the most abundant product compared with cyclohexane pyrolysis.However, the concentrations of 1,3-butadiene from methylcyclohexane and ethylcyclohexane pyrolysis are lower than of cyclohexane pyrolysis.The production yields of propene and ethane are larger compared with cyclohexane pyrolysis, indicating the pyrolysis of alkylated cyclohexane is different with cyclohexane.The concentrations of some species from pyrolysis of methylcyclohexane and ethylcyclohexane are also different.Concretely speaking, the species profiles for ethylene,methane, ethane, acetylene, 1,3-butadiene, and propyne from methylcyclohexane and ethylcyclohexane pyrolysis are very similar, but the relative concentrations of propene and 1-butene remain different.The concentration of 1-butene from ethylcyclohexane pyrolysis is relatively larger than that from pyrolysis of methylcyclohexane.

From Fig.3 and Fig.4, an obvious phenomenon is that the prediction accuracy of the employed four kinetic mechanisms tends to show large deviations for ethylene, methane, and acetylene compared with experimental measured results under high temperature conditions.Overall,the two lumped mechanisms together with the Fei Qi mechanism shows better performance than the JetSurF 2.0 mechanism at temperature below 1300 K,while all the four mechanisms tend to significantly overestimate the major species including ethylene, methane, and acetylene.The major reason should be induced by the formation of soot at high temperature conditions as observed during experimental procedures for methylcyclohexane and ethylcyclohexane.The formation of undetected soot and related precursor such as polycyclic aromatic hydrocarbons significantly affect the carbon balance at high temperature.Yet, this is not the same for cyclohexane pyrolysis.Fig.5 shows the carbon balance for the three fuels at 5 bar under different temperature conditions during the experiments.It can be seen that during experimental procedure at around 1400 K for cyclohexane, soot is not observed, and carbon balance for cyclohexane at 1400 K remains with a value of 83% within the uncertainty as discussed in section 2.2.However, due to the formation of soot, carbon balance is broken from the detected products and the initial fuel concentrations.In addition, the carbon balance for ethylcyclohexane is lower than that of methylcyclohexane, indicating the soot formation is larger of ethylcyclohexane than that of methylcyclohexane.The experimental observations and carbon balance analysis indicates that the soot formation tendency shows the following tendency as ethylcyclohexane>methylcyclohexane>cyclohexane,which is in good accordance with previous studies on soot formation studies[60].Consequently, due to the lack of soot formation mechanism,the current detailed mechanisms tend to aggravate the production yield of acetylene, ethylene and methane since the formation of acetylene, ethylene and methane is the most important reaction path.However, investigations on a detailed soot model for three fuel molecules are beyond the scope of this paper.In addition, the lumped mechanisms and the Fei Qi mechanism still capture the variation tendencies of most of the species.

Fig.4. Species profiles as a function of temperature for 0.05% ethylcyclohexane pyrolysis at 5 bar together with kinetic modeling results.

Fig.5. Carbon balance for the three fuels as a function of temperature at 5 bar under different conditions.

Fig.6. Comparative product distributions of major products and fuel molecules of the fuel pyrolysis at 5 bar.

Fig.6 shows a comparative analysis of the major products and fuel molecules from experimental measurements at 5 bar.From Fig.6, the initial pyrolysis of ethylcyclohexane and cyclohexane tends to be earlier than that of methylcyclohexane, revealing that ethylcyclohexane and cyclohexane can occur pyrolysis process at lower temperature around 1000 K.The pyrolysis of methylcyclohexane begins to occur at around 1150 K, indicating the reactivity of methylcyclohexane is the lowest among the three fuels.Similar reactivity trends were also observed for cyclohexane,methylcyclohexane andn-butyl cyclohexane during the oxidation studies[22].As shown by Hong et al.[22],the ignition delay times exhibited the following tendency at high temperature conditions:methylcyclohexane >n-butyl cyclohexane ≈cyclohexane, indicating that methylcyclohexane demonstrates the slowest reactivity,which is similar in the present work.Thus,it may be concluded that increasing the length of alkylated groups above than ethyl may be not significantly affect the high-temperature reactivity of the fuels.However, the product distributions are affected by the alkylated groups compared with cyclohexane as shown in Fig.6.For ethylcyclohexane, the formed ethylene is larger than of methylcyclohexane and cyclohexane, which may probably induce by the decomposition reaction to the formation of cyclohexyl and ethyl radicals and further to the formation of ethylene, increasing the formed ethylene.Obviously, methane formation from pyrolysis of methylcyclohexane is larger than the other fuels,especially at hightemperature conditions during the methyl group in methylcyclohexane.The large amount formation of methyl radical tends to affect the oxidation reactivity of fuels due to the low reactivity of methyl radical as discussed in detail by Ranzi et al.[61].The concentration of acetylene tends to the same for the three fuels because its formation mainly at high temperature conditions due to the pyrolysis small radicals.For the formation of propene, it is shown that the pyrolysis of methylcyclohexane forms the most,following is ethylcyclohexane,while the pyrolysis of cyclohexane is the slowest.The pyrolysis of ethylcyclohexane can form 1,3-butedien earlier, however, the amount does not exhibit large difference among the three fuels.Details to the formation of these products are analyzed through ROP and sensitivity analysis as shown in the following section.

4.2.Reaction path analysis (RPA) and sensitivity analysis (SA)

To demonstrate the kinetic differences among these employed mechanisms,reaction path analysis is performed for the three fuels at 1400 K with pressure of 5 bar when fuel is consumed by 20%.Since the two lumped mechanisms exhibit similar model performance, and the base model used in lumped mechanism by Zhang et al.[37]is the same as that used in JetSurF 2.0, thus, detailed discussions are mainly focused on the JetSurF 2.0, NUIG lumped,and Fei Qi mechanisms.For cyclohexane (cC6H12), the initial reactions are dominated by the ring-opening reaction to the formation of 1-hexene (C6H12-1) and abstraction reaction by H radical from JetSurF 2.0 and Fei Qi mechanisms,i.e.,cC6H12=C6H12-1,andcC6H12+H=cC6H11(cyclohexyl)+H2.The corresponding percent conversions from JetSurF 2.0 are 23.8%and 76.2%,while the percent conversions from Fei Qi mechanism are 38.6%and 54.1%due to the different reaction rate coefficients employed in the two mechanisms.However, the subsequently controlling reactions of 1-hexene and cyclohexyl from the two mechanisms are almost the same.The thermal decomposition reaction of 1-hexene to the formation of allyl (aC3H5) and propyl (nC3H7) is dominant with percent conversions of 91% and 86% for JetSurF 2.0 and Fei Qi mechanisms, respectively.The cyclohexyl radical undergoes two reactions, i.e.,cC6H11= PXC6H11(1-hexen-6-yl) andcC6H11=cC6H10(cyclohexene)+H with percent conversions of 69%and 31%for both the two mechanisms.The 1-hexen-6-yl radical can either undergo β-scission reaction to form ethylene and 1-butene-4-yl (C4H7) radical or undergo isomerization reaction to the formation of SAXC6H11 (1-hexen-3-yl), which quickly decomposes into 1,3-butadiene and ethyl radical.About 93%cC6H10will directly decompose into 1,3-butadiene and ethylene.It is also noted that the allyl radical plays an important role in the transformations among propyne (aC3H4), 1-butene (C4H8-1), and propene (C3H6) through the three competitive reactions, i.e., aC3H5= aC3H4+ H,aC3H5+ CH3= C4H8-1, and C3H6= aC3H5+ H.For the lumped mechanism, the global reaction of cC6H12with H radical, i.e.,cC6H12+H => H2+ 0.802C4H6+1.198C2H4+ 0.198C2H2+ H controls the fuel consumption with 95%, while the decomposition reaction cC6H12=> aC3H4+ C2H4+ CH3+ H only contributes 5% to the fuel consumption,indicating the direct decomposition reaction is difficult.Due to the lack of 1-butene and propene in the global fuel consumption reactions, the lumped model will significantly underestimate the production of the two products because it is hard to form them at high temperature conditions from small radical combination reactions.

Due to the alkyl group in ethylcyclohexane and methylcyclohexane, the dominant initial reactions of methylcyclohexane and ethylcyclohexane are different with that of cyclohexane,which can be much easily understood through a simple comparison of the bond dissociation energies (BDEs) [62].Generally, the BDE of the C-H bond in cyclohexane is 99.5 kcal/mol, while the BDEs of the C-H bond in methylcyclohexane and ethylcyclohexane at the alkyl position are 94.3 kcal/mol and 94.5 kcal/mol, respectively, indicating the alkyl group weakens the C-H bond.However, the C-H bond energies are larger than that of the C-C bond energies.Specifically, the BDE of the C2H5-cC6H11bond in ethylcyclohexane is 87.4 kcal/mol, which is the lowest compared with the CH3-cC6H11and CH3-CH2cC6H11bonds with a value of 90 kcal/mol.The different BDEs in the fuel molecules thus affects the major reaction path and the corresponding products.Fig.7 shows the major initial reaction path analysis at 1400 K and 5 bar when the fuel is consumed about 20%using the JetSurF 2.0 and Fei Qi mechanisms.Obviously,the dominant initial reactions from the two mechanisms exhibit large differences.Specifically, for methylcyclohexane, the direct transformation to 1-heptene and 2-heptene via ring-opening reaction is dominant in the JetSurF 2.0 mechanism, while the thermal decomposition reaction of methylcyclohexane to cyclohexyl and CH3radicals together with the abstraction reactions by H and CH3radical are dominant in the Fei Qi mechanism.In JetSurF 2.0 mechanism, the thermal decomposition of 1-heptene and 2-heptene and the following β-scission reactions to the formation of small products control the formation of the experimentally measured products.Although the major subsequent reactions of the cyclohexyl radical and the fuel radicals formed via abstraction reactions are also β-scission reactions,the additional reaction paths and the relative slow reaction rate constants of these reactions defer the formation of small products and also decrease the formation of the measured major products as shown from Fig.3.The predicted species profiles of methylcyclohexane as shown in Fig.3 also reveals the same tendency during the pyrolysis studies of methylcyclohexane using flow reactor [57].The major initial reaction path of ethylcyclohexane is similar to that of methylcyclohexane, however, the relative contributions from each reaction path from the two mechanisms are not as larger as that from methylcyclohexane as shown in Fig.7.The direct ring-opening reactions of ethylcyclohexane to 3-octene and 3-methyleneheptanestill contribute 14.6% to the fuel consumption form JetSurF 2.0 mechanism, which are the most important reactions.However, this is significantly lower that of methylcyclohexane.The contributions from abstraction reactions from the two mechanisms tend to close with each other.Thus,the deviations of the predicted results from the two mechanisms are not larger than that of methylcyclohexane as shown in Fig.3 and Fig.4.Similar to the reaction path analysis of cyclohexane from the lumped mechanism, the lumped global fuel decomposition reaction and abstraction reactions by H radical are dominant reactions during pyrolysis of methylcyclohexane and ethylcyclohexane with the latter abstraction reactions are important with contributions about 60% for both the two fuels.The decomposition reactions also contribute about 30%to fuel consumption of methylcyclohexane and ethylcyclohexane, indicating the decomposition of alkylated cyclohexane is easier compared with cyclohexane as revealed from the BDE analysis at the beginning.Besides these initial reactions with some subsequent β-scission reactions leading to the formation of some small alkenes, i.e., ethylene and propene, the controlling reactions of the formation of measured small products are related with mutual transformation of the C1-C4species, revealing the importance of base model in accurately predicting the pyrolysis process [11,56,63].

Fig.7. Reaction path analysis of(a)methylcyclohexane and(b)ethylcyclohexane when fuel is consumed 20%at temperature of 1400 K with pressure at 5 bar.The number above the arrow denotes the percent conversions from the JetSurF 2.0 mechanism, while the number below the arrow denotes the percent conversions from Fei Qi mechanism.

Fig.8. The important sensitive reactions for the fuel molecule and major products including ethylene, methane, and 1,3-butadiene.Sensitivity analysis is performed for 20% fuel consumption at 1400 K and 5 bar using the Fei Qi mechanism: (a) Cyclohexane; (b) Methylcyclohexane; (c) Ethylcyclohexane.

To further identify the controlling reactions of important products, sensitivity analysis is performed for fuel molecules,ethylene, methane, and 1,3-butadiene at 1400 K and 5 bar when fuel is consumed 20%using the Fei Qi mechanism due to its overall prediction accuracy for the three fuels.Sensitivity analysis using the other two mechanisms are provided in supplementary materials.The results with sensitivity coefficients larger than 0.10 for the targeted species are explicitly shown as Fig.8.It can be seen that the direct ring-opening reaction of cyclohexane to form 1-hexene shows large effect during cyclohexane pyrolysis, while the thermal decomposition of alkylated cyclohexane to the formation of cyclohexyl and alkyl radical tends to be more important for methylcyclohexane and ethylcyclohexane pyrolysis,which can also be easily understood via the BDEs.Such results are also in correlation with ROP analysis.For the three fuels,it is demonstrated that important sensitive reactions to ethylene formation are closely related to the initial reactions of fuel because these reactions are generally rate-determining steps since the following β-scission reactions responsible for ethylene production are fast.For methane,besides the two competitive reactions to the formation of methane and ethane, i.e., CH3+ H(+M) = CH4(+M) and 2CH3(+M)=C2H6(+M),the abstraction reactions of fuel molecules by CH3radical that receives less attention is important in accurately predicting the methane yields.Specifically, the abstraction reactions by CH3radical with the fuel molecules contributes 72.4%,58.3%, and 55.9% of methane formation in correspondence with cyclohexane, methylcyclohexane and ethylcyclohexane using the Fei Qi mechanism, respectively, indicating the importance of this reaction class during pyrolysis prediction.Ethylene is mainly formed via β-scission reactions during high-temperature pyrolysis process.However, the β-scission reactions are usually very fast,thus,the rate-determining steps towards the formation of ethylene are mostly relevant to the previous radical formation steps as revealed from sensitivity analysis in Fig.8.It is shown that the formation of cyclohexane radical via fuel decomposition reaction is critical for the formation of ethylene for methylcyclohexane and ethylcyclohexane because further ring decomposition reaction of this radical and following β-scission reaction quickly form ethylene and other small products.However, this is a little different for cyclohexane because of the direct ring-opening reactions to the formation of 1-hexene.However, the major phenomena observed are similar for the three fuels.Since the formation of 1,3-butadiene is also mainly via β-scission reactions, thus, important reactions affecting the formation of 1,3-butadiene are very similar to the results of ethylene,which means that the reactions to the formation of radicals than can quickly undergo β-scission reactions to form 1,3-butadiene show large sensitivity coefficients for 1,3-butadiene.In addition, the sensitivity analysis results using the Fei Qi mechanism are very similar to the results from JetSurF 2.0 mechanism,even though some of the relative sensitivity coefficients are different.Sensitivity analysis using the lumped mechanism obviously demonstrates that the most important reactions of these products are directly related with the global fuel decomposition reaction,and the global lumped abstraction reactions by H and CH3radical except that the two reactions,namely,CH3+ H(+M) = CH4(+M) and 2CH3(+M) = C2H6(+M) are also important for methane prediction.

5.Conclusions

Alkylated cycloalkanes are important components in gasoline,aviation, and diesel fuels; however, the pyrolysis of this class of compound that is important for combustion chemistry has received less attention compared to other hydrocarbon classes.For this purpose, this work reports an experimental and kinetic modeling study on the pyrolysis of cyclohexane, methylcyclohexane, and ethylcyclohexane.Single-pulse shock tube facility is employed to perform the pyrolysis experiments for 0.05% fuel concentration diluted in Ar at averaged pressure of 5.0 and 10.0 bar in the temperature range around 930-1550 K with the reaction time around 1.70 ms.Major products including ethylene, methane, acetylene,propene, allene, propyne, and 1,3-butadiene are detected and quantified.Several detailed and lumped kinetic mechanisms are used to model experimental results.Major conclusions are summarized as follows:

(1) The initial pyrolysis of ethylcyclohexane and cyclohexane can occur at lower temperature around 1000 K, while the pyrolysis of methylcyclohexane begins to occur at around 1150 K,indicating the reactivity of methylcyclohexane is the lowest among the three fuels.

(2) Ethylene is the most abundant product for all the three fuel pyrolysis processes, and the other important species including methane, 1,3-butadiene, and acetylene are also detected and analyzed.The pyrolysis of methylcyclohexane and ethylcyclohexane at high temperature conditions tend to form soot,which can affect the carbon balance.

(3) Several contemporary detailed or lumped kinetic mechanisms are used to predict the experimental results, and it is shown that they can generally predict the product distributions as a function of temperature.However, accurate quantitate predictions of all the measured species remain a challenge for current kinetic mechanisms.

(4) The competitions between the initial direct ring-opening reactions of the cycloalkane fuels to the formation of corresponding alkenes and the traditional initial fuel decomposition and abstraction reactions due to the usage of different reaction rate constants in the JetSurF 2.0 and Fei Qi mechanisms significantly affect the reaction paths.

(5) Rate-of-production analysis and sensitivity analysis are conducted to identify the important reactions related to the fuel pyrolysis and major products.It is shown that the fuel abstraction reactions by CH3radical are important for accurately predicting the concentration profiles of methane,while the fuel decomposition reactions and ring-opening reactions are rate-determining steps towards the formation of ethylene and 1,3-butadiene.

(6) Finally, to summarize, further experimental or theoretical studies to obtain accurate reaction rate constants for the fuel decomposition, abstraction reactions and direct ringopening reactions in combination with the addition of soot formation model are required to optimize detailed kinetic models for the accurate prediction of cycloalkane pyrolysis.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A.Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.dt.2022.05.013.