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Insights into the high-temperature oxidation of methylcyclohexane
Fuel 241 (2019) 273–282
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Insights into the high-temperature oxidation of methylcyclohexane Yalan Liu a b c
a,b
c
, Guangyue Li , Junxia Ding
a,⁎
T
State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, PR China University of Chinese Academy of Sciences, Beijing 100049, PR China College of Chemical Engineering, North China University of Science and Technology, Tangshan 063021, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Methylcyclohexane ReaxFF Oxidation Kinetic behaviors
Reactive molecular dynamics simulations were performed under different conditions in order to investigate indetail the chemical events associated with high-temperature oxidation of methylcyclohexane (MCH). The corresponding kinetic behaviors of the major intermediates and products were systematically analyzed at the atomistic level. Thus the overall reaction scheme of MCH oxidation was established from the initial step to the final products. It was observed that the oxidation of MCH was mainly initiated by two kinds of reactions, including unimolecular decomposition and H abstraction, with the former being more important. In agreement with the available experimental results, C2H4, CH2O, CO, CO2 and H2O were found to be the major products during the oxidation process. The results revealed that %CH3O2, %CH3O and %C3H5O radicals were the precursors for CH2O production, which was the key intermediate to generate CO. Additionally, %C2H3O also had closed relationship with the formation of CO. For a better description of the combustion behavior, small oxides related to intermolecular reactions should be considered in the oxidation of MCH mechanisms. The temperature and density had a positive effect on the oxidation of MCH; it was also found that an increase of the equivalence ratio had a negligible effect on the MCH oxidation.
1. Introduction Cycloalkanes are an important class of constituent compounds in gasoline and jet fuels [1–3]. They have also been found to play a key role in the formation of aromatic pollutants and polycyclic aromatic soot precursors [4,5]. To reduce soot formation, a detailed understanding of the cycloalkanes combustion mechanisms under practical atmospheric conditions is necessary. However, cycloalkanes consist of various kinds of components, and the determination of all relevant kinetics mechanisms is therefore impractical. An alternative approach to this problem is to use a single model fuel to represent these compounds. As the simplest alkylated cyclohexane, methylcyclohexane (MCH) is commonly chosen as a model fuel to study the combustion behaviors of cycloalkanes experimentally and theoretically. In the past decades, a limited number of works focusing on the pyrolysis and combustion of MCH have been reported. Experimentally, Zeppieri et al. [6] performed high-temperature (1050–1200 K) oxidation of MCH in a Princeton turbulent flow reactor. They noted that the pyrolysis and oxidation of MCH produced the same intermediates, with the oxidation proceeding at a faster reaction rate. Yang and Boehman [7] studied the oxidation of cyclohexane and MCH in a motor engine at the temperature of 393.15 K and 473.15 K, respectively. The results ⁎
showed that fuel conversion and carbon monoxide formation were strongly enhanced by the existence of the methyl group. Skeen et al. [8] investigated the chemical compositions of three low-pressure premixed flames of MCH, and indicated that higher temperature resulted in an increase for MCH consumption via isomerization and dissociation. In theoretical studies, several groups have established kinetic models of MCH combustion [9–14]; and tested them against reliable, molecule-specific experimental data; such as the measurements of the species in burner-stabilized flames. Of course, experiments could provide important information regarding the complex combustion system, such as the activation energy. However, reactions such as pyrolysis, combustion and explosion can be extremely fast, especially at high temperatures, and can produce large amounts of intermediates through complex reaction mechanisms and pathways. Therefore, experimental data alone are far from sufficient for establishing an accurate combustion model that describes the MCH oxidation process. Reactive force field (ReaxFF) [15,16] has been developed to be an efficient tool for predicting complex reactions. In this approach, the connectivity of every atom in the system is determined by bond orders calculated from bond distances. Thus, this approach allows an accurate description of bond breaking and bond formation during the reaction process. In addition, the parameters in ReaxFF are derived based on
Corresponding author. E-mail address: [email protected] (J. Ding).
https://doi.org/10.1016/j.fuel.2018.12.022 Received 22 May 2018; Received in revised form 13 November 2018; Accepted 7 December 2018 0016-2361/ © 2018 Published by Elsevier Ltd.
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quantum mechanical (QM) data and can simulate reaction pathways without any preconditions. Therefore, ReaxFF has a relatively high accuracy and good transferability. Recently, ReaxFF has been used to investigate hydrocarbon oxidation processes over a wide range of systems, including toluene oxidation [17], n-octanol [18] and n-dodecane [19] combustion, and n-decane and toluene [20] mixture oxidation. These successful applications prove that ReaxFF can provide important theoretical guidance for hydrocarbon combustion systems. In the present work, reactive molecular dynamics (RMD) simulations were used to investigate the mechanism of MCH oxidation under different conditions, including the initial reaction and intermediate reaction mechanisms. The effects of the temperature, equivalence ratios and density on the combustion mechanism were also investigated. We focused mainly on the analysis of the major intermediates and products; and on the initial mechanisms and the intermediate reaction process of MCH combustion. It is hoped that the analysis presented here will furnish a more complete atomic understanding of the combustion process and will afford a more reliable combustion model for MCH. 2. Computational methods Fig. 1. Initial reaction steps of MCH oxidation. Percentages on arrows present for the MCH consumption contributed by that reaction.
To study the detailed reaction mechanisms of MCH oxidation under different conditions, a wide range of temperatures and pressures of MCH/O2 mixtures were investigated. For the RMD simulations, all systems were equilibrated for 10 ps in the NVT ensemble (maintaining the number of atoms, volume, and temperature constant) at 300 K with a time step of 0.1 fs. This time step has been widely employed in several systems [21–24] and was shown to be efficient for the description of hydrocarbon oxidation. Once the equilibrium configurations were achieved, the systems were used in the NVT-MD simulations, where the cut-off for trajectory analysis was set to 0.3, which is used only for molecule recognition and does not affect the simulation results [22]. For all simulations, the temperature was controlled by the Nosé-Hoover thermostat method [25] with a 0.1 ps damping constant. To further validate the accuracy of the reactive force field, the main initiation reaction channels were calculated by the QM method at the B3LYP/6311G (d,p) level of theory [26,27] using Gaussian 09 [28], and then, the relative electronic energies at 0 K calculated by QM and ReaxFF were compared and discussed.
total. Compared to the C–C bond dissociation, the bond breaking of the C–H bond was less important, with only 8.51% of MCH initiated in this channel. This was mainly caused by the different dissociation energies of the C–C and C–H bonds [29]. In addition to unimolecular decomposition, H abstraction reactions by small active radicals including O2, •H, %OH, %HO2 and %O% were also effective pathways for consuming MCH, constituting up 23.29% of the total. However, it could be deduced that in the oxidation process, the unimolecular pyrolysis was the main pathway for the consumption of MCH molecules, which agreed well with a previous study [7].
3.2. Force field validation The force field used in the ReaxFF MD simulation has been reported by van Duin and Cheoweth [20] were used without modification. Here, we focused on the goodness of the force filed to the MCH system. Table 1 compares the relative reaction energies at 0 K of ReaxFF and QM data for the major initiation reaction channels. The geometrical structure of the reactants and products were performed using the B3LYP functional; together with the 6-311G (d,p) basis set. The maximum deviation reached 13.58 kcal/mol in initial a. As seen in Fig. 2, this reaction pathway involved two steps; firstly, the MCH molecule was isomerized into %CH2CH(CH3)CH2CH2CH2CH2% with the reactive energy of 73.6 kcal/mol by QM and 72.0 kcal/mol by ReaxFF method. Subsequently, the highly reactive %C7H14% radical dissociated into %CH2CH(CH3)CH2CH2% and C2H4 through a transition sate. The reactive energy calculated for the reaction barrier by the QM and ReaxFF was 25.75 kcal/mol and 28.28 kcal/mol respectively. According to the transition state theory, the reaction rate was described by Arrhenius expressionk = A exp(−Ea/ RT ) . Thus, the reaction rate was determined by energy of the transition state. The small deviation of ReaxFF and QM for TS calculation has proved the reliability of the force field to an
3. Results and discussion 3.1. Initial reaction mechanisms of oxidation of MCH To investigate the initial reaction mechanisms of MCH oxidation, 10 independent multimolecular simulations were performed at the density of 0.09 g/cm−3 and the temperature of 2500 K. The flux network for describing the detail reaction pathways with branching ratios are presented in Fig. 1. Percentages on arrows represent for the MCH consumption contributed by that reaction. According to the simulation results, the initial reactions could be divided into two categories: the H abstraction reaction and MCH pyrolysis reaction. It was found that, 76.61% of the fuel molecules were consumed by the dissociation reaction, in which the ring-opening channel accounts for 50.0%. Most of MCH molecules were first isomerized into %C7H14%, which were then either dissociated into %C5H10% and C2H4, or dissociated into %C4H8% and C3H6 with several femto-seconds. The unimolecular decomposition of MCH leaded to %C7H14% was also proposed by previous kinetic models. However, in the simulation process, these reactive biradicals had not survived H transferred reaction to form heptane, instead, continued to dissociate into ethylene and propylene through β-scission reactions. This was due to the high temperature and high pressure promoted the further dissociation of these diradicals. In addition to the ring-opening reactions, the demethylation reaction was also the main reaction pathway for the consumption of the fuel molecule, with the proportion of this pathway reaching 20.48% of the
Table 1 Reaction energies (kcal/mol) at 0 K for major initiation reactions obtained using both ReaxFF and QM method. name initial initial initial initial
274
a b c d
reactions
ΔEReaxFF
ΔEQM
C7H14 → %CH2CH(CH3)CH2CH2% + C2H4 C7H14 → CH3%CHCH2CH2CH2% + C2H4 C7H14 → %CH2CH2CH2CH2% + C3H6 C7H14 → CH2CHCH2CH2CH2CH2% + %CH3
77.54 76.73 78.39 90.52
91.12 87.57 86.12 90.49
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Fig. 2. The detailed reaction process for initial a using QM and ReaxFF method.
extent.
3.3. Intermediate reaction mechanisms of oxidation of MCH 3.3.1. Time-dependent intermediate distributions To obtain an overview of high-temperature MCH oxidation, a series of 10 NVT-MD multimolecular simulations were performed at the temperature of 2500 K under approximately stoichiometric conditions (Φ = 1.0) for 1.0 ns. We put 10 MCH and 110 O2 molecules in a 43.00 Å×43.00 Å×43.00 Å period unit cell with the density of 0.09 g/ cm−3. To facilitate the analysis, the time at which the system reached the target temperature was set to zero in the following discussion. Throughout all RMD simulations, a total of 205 different species, including reactive intermediates and stable products, were identified. In this work, these species were divided into 8 categories denoted as C0, C1, C2, C3, C4, C5, C6 and C7 according to the number of carbon atoms. The intermediate distributions and total energy profile as a function of time are summarized in Fig. 3. It could be seen that; the MCH molecule began to decompose at 15 ps and that most MCH molecules were consumed within 600 ps. In light of the consumption rate of the MCH molecules, the combustion process could be divided into three stages. The first stage was from the initiation time (15 ps) to 200 ps. In this period, the consumption rate of MCH was relatively fast, approximately 65.0% of MCH molecules were decomposed, and the main products were C2 and C3 species. Among these, C2H4 and C3H6 were the most important; their amounts increased significantly with the consumption of MCH molecules. Furthermore, during this stage, few O2 molecules were consumed, and the relative energy of the system increased as the simulation progressed. We can be certain that the whole system began with an endothermic reaction. The second stage lasted from 200 to 400 ps. Compared to the first stage, the MCH dissociation rate was much lower, and only 25.0% of the MCH molecules decomposed in this period, during which a slow increase of C2 and C3 species was observed. Different from the first stage, a considerable amount of C0 and C1 was produced in this period. Meanwhile, the total energy of the system went through a short equilibrium and started to decrease. This indicated that the oxidation reaction was dominant during this period. The last stage was from 400 to 600 ps, during this stage, the rest of the 10.0% MCH molecules were consumed, which was a bit slower than the second stage. After 600 ps, all MCH molecules were dissociated, and the consumption rate of oxygen gas was significantly accelerated. This led to a significant increase in the generation rate of CH2O, which acted as an active intermediate in combustion. During the oxidation process, the major observed species were C2H4, C3H6, CH2O, CO, CO2 and H2O. It could be seen that; the number of C2H4 molecules reached the maximum when the MCH molecules were
Fig. 3. Time evolution of (a) number of Cn species and (b) number of typical species in multimolecular simulations of 2500 K, initial pressure 52.0 MPa system. The bule line denotes the relative energy profile during simulations. These panels were drawn using averaged values from the ten runs.
totally consumed. Zeppieri et al. [6] conducted pyrolysis and oxidation studies of MCH in the high temperature range of 1050–1200 K; and found that when the fuel molecules were totally consumed, the normalized mole fraction of C2H4 was[C2 H4]/[MCH ]0 = 1.07 . The experimental data agreed well with our simulation result (1.2). In our simulations, some key related radicals, such as %H, %HO2, %OH, %CH3, %C2H3 and %C3H5, were also observed. The distributions of these reactive radicals as a function of time were presented in Fig. S1 of the Supporting Information. The amounts of all these reactive radicals changed dramatically during the simulations. This indicated that these reactive species were highly involved in the oxidation of MCH. 3.3.2. Formation mechanisms of key intermediates In our simulations, several kinds of intermediates that were very important for the combustion of MCH were observed. A detailed analysis of the reaction mechanism of these intermediates was critical to understand the entire oxidation mechanism of MCH. Here, we focused on two key intermediates–formaldehyde and hydrogen peroxide. 3.3.2.1. CH2O reaction mechanisms. Formaldehyde is one of the main intermediates appearing in hydrocarbon combustion, and the cool flame is directly related to formaldehyde. The main production and consumption channels of CH2O are shown in Fig. 4. It can be seen that; the methoxy radical (%CH3O) and methyl peroxy radical (%CH3O2) were important intermediates in formaldehyde production. According to our observations, these C1 oxides were mainly derived from the oxidation of methyl, as was also verified by a previous study [29]. Thus, the amount 275
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Fig. 4. The distributions of CH2O related reactions. Red and black denote the production and consumption reactions, respectively.
Fig. 6. The distributions of H2O2 related reaction mechanisms. Red and black denote the production and consumption reactions, respectively.
of methyl radical had a direct influence on the number of formaldehyde molecules. Furthermore, the dissociation of %C3H5O was also a significant channel for CH2O production, accounting for 14.80% of all the production channels. To show the detailed reaction mechanism, Fig. 5 presents the reaction scheme from the initial reaction products to CH2O. According to Fig. 5-a, an O2 molecule reacted with the %CH3 radical to form %CH3O2, producing CH2O through H transfer and the OH release reaction. As seen from Fig. 5-b, the %O% radical was first attached to %CH3, yielding the %CH3O radical, and then decomposed to CH2O through H elimination. Additionally, C3H6 was also an important intermediate for CH2O formation, as presented in Fig. 5-c. First, %C3H5 was obtained by the H abstraction reaction, and then, the %HO2 radical was added to form C3H6O2, which decomposed to the key %C3H5O radical and %OH radical intermediates. Lastly, the final product CH2O was generated by the decomposition of %C3H5O. This reaction process has been proved to be important by a previous experimental study [11]. Orme et al. investigated the oxidation of MCH in high-temperature shock tube experiments; and found that the reaction %C3H5 + %HO2 → %C2H3 + %OH + CH2O was sensitive to shock tube ignition delay times. Generally, %CH3 and C3H6 intermediates contribute the most to the formation of CH2O. This was consistent with a previous theoretical study [29]. For CH2O consumption, the CH2O + %OH → %CH3O2 and %CH3O2 → CH2O + %OH reactions were reversible and were not highly effective pathways for CH2O consumption. Actually, the main consumption channels were the H abstraction reaction (CH2O + O2 → %CHO + %HO2) and H addition reaction (CH2O + % HO2 → %CH3O + O2). The build-up of O2 and %HO2 can accelerate the transformation of formaldehyde.
Fig. 7. The proportion of (a) CO related reaction channels. (b) CO2 related reaction channels.
Fig. 5. Main reaction channels of CH2O production from initiation products. 276
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Fig. 8. Reaction schemes of CO and CO2. (a) The main reaction pathways to produce CO and CO2 from %CH3 radical. (b) The main reaction pathways to produce CO from C2H4.
3.3.2.2. H2O2 reaction mechanisms. The H2O2 intermediate plays a critical role in the combustion atmosphere, and a detailed analysis of H2O2 related reactions is necessary to reveal the combustion mechanisms of MCH. Fig. 6 displays the main consumption and production pathways of H2O2. It can be seen that %HO2 played a very important role in the formation of H2O2. More than 74% of H2O2 produced through the five reaction channels involved %HO2, in which the intermolecular hydrogen attraction between two HO2 radicals (2HO2 → H2O2 + O2) was the primary channel. Such a reaction mechanism has been reported and was considered to be the main pathway for %HO2 consumption by Bahrini et al. [30]. Tian et al. [31–33] performed a comparative study on autoignition and oxidation of cycloparaffin, and found the 2HO2 → H2O2 + O2 was one of the most sensitive reactions for MCH oxidation, especially at relatively higher temperature. This was consistent with our simulation result. According to our observations, most of the H2O2 molecules were consumed by dissociation into %OH radicals, with the proportion of approximately 48.28%. The reactions of HO2 radicals were generally the main source of H2O2 at this temperature, and the consumption of H2O2 resulted in the accumulation of OH radicals. These simulation results were in good agreements with the results of a previous study
Fig. 9. The distributions of H2O related reactions. Red and black denote the production and consumption reactions, respectively.
Fig. 10. Reaction scheme of MCH oxidation. 277
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3.3.3.1. Proposed CO and CO2 formation mechanisms. For the hydrocarbon fuel, CO and CO2 are the main carbonaceous products, the formation mechanism of which is a significant part of the entire combustion mechanism. The main formation pathways associated with the CO and CO2 during MCH oxidation are shown in Fig. 7. It can be seen in Fig. 7a, the production of CO was closely related to the C1 and C2 oxides. For example, 18.9% of the CO was produced by the dehydrogenation of %CHO. This reaction pathway has been verified by previous experimental and theoretical studies [29,34]. Compared to %CHO, the CO production channels involving C2 oxides have received little attention despite their large proportion. According to the simulation results, up to 51.4% of the CO was derived from the dissociation of C2 oxides, including the decomposition of %C2H3O and %C2H3O2, which had the same contribution that was slightly lower than that of the dehydrogenation pathway. Unlike the complex reaction channels of CO, the formation of CO2 was relatively simple, as displayed in Fig. 7b. It can be found that the primary channels for CO2 production were the H elimination reaction (%CHO2 → CO2 + H) and H abstraction reaction (%CHO2 + O2 → CO2 + HO2). Obviously, the amount of CO2 was related to the amount of the %CHO2 key intermediate derived from the two main reaction channels, as shown in Fig. 8a. In the first mechanism, O2 was first added to %CH3 to form intermediate radical %CH3O2, which was then finally converted to CHO2 via the dehydrogenation reaction (%CH3O2 → %CHO2 + H2). In the second mechanism, the dehydration reaction of %CH3O2 to produce %CHO was followed by the addition of the %O% radical to form %CHO2 directly. Furthermore, %CHO2 was also important for the formation of CO, for example, through the %OH elimination reaction. In addition to %CHO and %CHO2, the reactions related to %C2H3O and %C2H3O2 were of crucial importance to the production of CO, as presented in Fig. 8b. As observed, the generation of %C2H3O was mainly through the oxidation of %C2H3 and C2H2. The oxidation of %C2H3 followed two pathways: In the first, the %OH addition reaction was followed by the H elimination reaction. In the second pathway, the %HO2 addition reaction led to the formation of %C2H3O through OH elimination. In addition to the %C2H3 radical, C2H2 could also be converted to %C2H3O by OH radical addition. For %C2H3O, this was the key connection to the formation of CO. On the one hand, %C2H3O could decompose to form CO and %CH3 directly. On the other hand, it could also convert into other C2 oxides (such as %C2H2O2, %C2H3O2 and %C2HO2), which also contributed to the CO formation. Therefore, CO production was closely related to the %C2H3O intermediate; produced by the oxidation of %C2H3 and C2H2. It has been verified the %C2H3 and C2H2 were mainly derived from the dehydrogenation reaction from C2H4 [35]. Hence, the population of C2H4 determined the number of CO molecules in our simulations.
3.3.3.2. H2O formation mechanisms. H2O is another type of stable product of hydrocarbon oxidation. We also analyzed H2O formation and dissociation mechanisms for the MCH oxidation. According to Fig. 9, the OH radical played a vital role in the formation of H2O. The direct combination of the OH radical with the H radical was the most likely channel, with the proportion of 13.33%. Additionally, 52.00% of H2O was derived from the H abstraction by reactive OH from other small molecules, including H2, H2O2 and %HO2. Among these, H abstraction from H2 molecules accounted for 12.00%, slightly lower than the direct combination channel. Moreover, the OH radical also participated in some indirect channels. For example, the reactive OH could react with ethylene to generate %C2H5O, which then decomposed to generate %C2H3 and H2O, and its fraction reached 12.00%. Generally, the production of H2O was determined by the build-up of the OH radical in the system. Compared to H2O generation, the consumption of H2O was relatively simple. The dominant pathway was H abstracted by O atoms to generate the OH radical.
Fig. 11. Time evolution of MCH molecules, O2 consumption, potential energy and major product distributions during MCH oxidation at 2500 K under various equivalence ratio conditions.
[18].
3.3.3. Formation mechanisms of dominant products Here, we focused on the use of the mapping strategy to identify the reaction mechanisms from the initial reaction species to the most common products CO, CO2 and H2O. Starting from the products, we first determined the major pathways; and then identified the main intermediates in the trajectory. Finally, we searched for the reaction in the reverse manner and found the reactions that connected these intermediates. As described below, we were thus able to build up a simple reaction network to describe how these main products were formed. 278
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Fig. 12. Time evolution of the average number of (a) MCH dissociation, (b) C2H4 production, (c) CH2O production, (d) O2 consumption at the temperatures from 2200 to 3000 K in the interval of 200 K (NVT-MD simulation, Φ = 2.0, ρ = 0.09 g/cm−3). These panels were drawn using averaged values from the ten runs.
lean (Φ = 0.5) and fuel-rich (Φ = 2.0) conditions respectively. Fig. 11 presents the distribution of major products under different equivalence ratios at 2500 K. As observed, under fuel-rich conditions, the number of C2H4 molecules increased significantly for 0–400 ps, and then changed slightly as the simulation progresses. Additionally, the number of C2H4 molecules was larger than that under O2 sufficient conditions. Similarly, the number of C3H6 molecules decayed more slowly when the equivalence ratio was increased to 2. This was mainly because a high concentration of O2 can accelerate the dissociation of alkenes by the H abstraction reaction. Unlike for alkenes, the insufficient O2 molecules could reduce the population of the released CH2O. This occurred because insufficient O2 for MCH oxidation lowered the oxidation rate of C3H6 and %CH3, which were the key intermediates for CH2O production. As an important product of MCH oxidation, the number of H2O molecules were closely related to the equivalence ratio. It could be seen that; the population of H2O molecules increased as the simulation progressed under the stoichiometric and fuel-rich conditions, whereas the number of H2O molecules was smaller for insufficient O2 in the system. This was due to that, with an increasing concentration of O2 present, the number of produced OH radicals became higher, thus accelerating the formation of H2O. However, in fuel-lean conditions, the evolution of H2O was quite different. At 0–600 ps, the amount of H2O increased; and then stabilized for 600–800 ps. After 800 ps, the number of H2O molecules increased for the entire remaining simulation time.
3.4. Detailed reaction scheme for MCH oxidation The reaction network proposed based on our simulation results is shown in Fig. 10. It provided a detailed description of the oxidation mechanism of MCH, from the initial step to the final products. MCH oxidation was initiated by C–C bond dissociation leading to the formation of C2H4, C3H6 and %CH3, which were subsequently oxidized to form the final products. As observed, the oxidation of C2H4 generated the %C2H3O, either by direct dissociation, or by a complex conversion to other C2 oxides followed by decomposition to CO. Similarly, the oxidation of C3H6 first produced the %C3H5O, and then dissociated into CH2O, which was also an important intermediate for CO production. The oxidation of %CH3 proceeded mainly through the formation of the %CH3O2, which then decomposed to CO2. Compared to CO and CO2, the formation of H2O was relatively simple, mainly through the combination of H and OH radicals.
3.5. Effects of the equivalence ratio on MCH oxidation The equivalence ratio is one of the most important parameters in the combustion process, significantly influencing the flame propagation, anti-pollution, etc. To predict the complex kinetics mechanisms of MCH oxidation, two periodic cubic boxes with lengths of 51.00 and 36.00 Å were generated with 210 and 53 O2 molecules, referred to as the fuel279
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Fig. 13. Time evolution of (a) the average number of MCH molecules, (b) Relative energies and (c–d) the average number of C2H4 and CH2O molecules at the densities range from 0.09 to 0.35 g/cm−3(NVT-MD simulation, T = 2500 K, Φ = 2.0). These panels were drawn using averaged values from the ten runs.
intermediate, was relatively low at first; and then increases as the simulation progressed. This trend was consistent with the consumption of oxygen molecules. Few CH2O molecules were produced at the first stage because a small amount of O2 participates in the oxidation of CH3 and C3H6. As the rate of O2 consumption increased, the CH2O generation accelerated. Additionally, the time distributions of final products (CO, CO2 and H2O) were presented in Fig. S2 of the Supporting Information. It can be seen that as the temperature increased, the yield rate of the final products was significantly enhanced.
This was mainly due to the fact that on one hand, an increase in O2 concentration can promote the production of the OH radical, leading to greater generation of H2O molecules, while on the other hand, in the presence of a high O2 concentration, the formation of H2O can be reduced by the O2 + H2O → %OH + %HO2 reaction. In addition, the number of CO molecules increased with increasing O2 concentration because a number of CH3 and C2H4 were oxidized to CO.
3.6. Effect of temperature on the oxidation of MCH To analyze the effect of temperature on the oxidation of MCH, 10 parallel NVT-MD simulations were performed at temperatures ranging from 2200 to 3000 K with an interval of 200 K for a total of 1 ns simulations in fuel-rich condition (Φ = 2.0). The time evolutions of MCH molecules, O2 consumption, and CH2O and C2H4 production are shown in Fig. 12. It can be found that; the number of fuel molecules decreased more rapidly with the increase of temperature, and this effect became more obvious at low temperatures. When the temperature reached 2800 K, the increase of temperature had little influence on the dissociation rate of MCH. The yield and the rate of the generation of C2H4 molecules increased with the increasing temperature. However, the final production of C2H4 was highest at the temperature of 2600 K. This was because the higher temperatures accelerated the dissociation of C2H4. The production rate of CH2O, which was another important
3.7. Effect of density on the combustion of MCH The effect of density on the combustion of MCH was investigated at the initial densities of 0.09, 0.22 and 0.35 g/cm−3 (Φ = 2.0, T = 2500 K). The time evolutions of the number of MCH molecules, potential energy and main species distributions are presented in Fig. 13. Examination of the change in the amount of MCH molecules showed that the system at the density of 0.35 g/cm−3 exhibited fast fuel consumption, and the potential energy at this density was the most exothermic. This trend indicated that an increase of the density leaded to rapid consumption of fuel molecules. Moreover, the density effect can also be observed in major species distributions. For C2H4, while increasing density of the system had little influence on the production rate, it could significantly improve the consumption rate. Hence, the 280
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Table 2 Fitted Arrhenius parameters of MCH oxidation.
ReaxFF
Equivalence ratio
Ea (kcal/mol)
R2
0.5 1.0 2.0
59.92 65.79 65.76
97.6 98.7 99.2
Exp
a b
64.00a 60.04b
Experimental result is taken from Ref. [6]. Experimental result is taken from Ref. [37].
similar trends at various densities. As the system density increased, the production of these species was accelerated. 4. Kinetic analysis of MCH oxidation To investigate the kinetics properties of the combustion of MCH in different conditions, the ReaxFF simulations of MCH oxidation were run under fuel lean (Φ = 0.5), stoichiometric (Φ = 1.0) and fuel rich (Φ = 2.0) combustion atmosphere for temperature ranging from 2000 to 2500 K at 100 K intervals with the densities of 0.09 g/cm−3. Ten random simulations were carried out at each temperature and a total of 1 ns data was collected. The second kinetics was employed to describe the reaction of MCH and O2, which was also applied for hydrocarbon combustion in recent literatures [17,36]. The concentration of MCH and O2 were simply replaced by the number of molecules. In the oxidation process, few O2 molecules were involved in the dissociation of fuel molecules, thus the concentration of O2 can be regarded as no change. Therefore the dissociation of MCH can be seen as quasi-firstorder kinetics reaction. Combined the rate constant ln N0 − ln Nt = k [O2 ]0 t with Arrhenius expressionk = A exp(−Ea/ RT ) , the activated energy (Ea) and pre-exponential (A) could be extracted by liner fitting as is presented in Fig. 14. We obtained the overall activity energy values ranging from 59.92 to 65.79 kcal/mol, which are shown in Table 2. The apparent activation energies extracted here were in accord with the MCH pyrolysis experimental results. This was further proved that most of MCH molecules were consumed by pyrolysis reactions under combustion atmosphere. 5. Conclusion High-temperature and high-pressure oxidation of MCH was simulated using NVT-MD in conjunction with the ReaxFF reactive force field. Multimolecular simulations were conducted on the system at the temperature of 2500 K under approximate equivalence ratio conditions. The main species observed in the present simulations were C2H4, C3H6, CH2O, CO, CO2 and H2O. To elucidate the detailed mechanisms of the MCH oxidation, the initiation and intermediate reactions were investigated during the simulation process. At the initial stage, five types of initiation reactions were detected, and most MCH molecules were first isomerized to %C7H14%, and then dissociated into ethylene and propylene through β-scission reactions. This reaction to consume fuel molecules was overlooked in previous theoretical studies and not taken into consideration in the current kinetic models. This finding would help to establish more accurate kinetic models for the combustion of MCH. The intermediate mechanisms related to the major intermediates and common products were also demonstrated in our work. According to our observations, CH2O and H2O2 were the most important intermediates. The amount of CH2O was determined by the oxidation of %CH3 and C3H6 intermediates, and CH2O was also the precursor for CO production. The number of H2O2 molecules was closely related to the accumulation of the HO2 radical, and it also contributed to the formation of OH radicals, which controlled the H2O formation in the
Fig. 14. Fitted rate constant versus temperature from ReaxFF-MD simulations with the density of 0.09 g/cm−3 at various equivalence ratios.
final production of C2H4 decreased with the increase of the system density. For CH2O, raising the density from 0.09 to 0.22 g/cm−3 could improve the amount of CH2O to a large extent, but the influence of the density increase became small when the density continued to increase to 0.35 g/cm−3. This was because a higher density promoted the dissociation of formaldehyde. The product distributions of CO, CO2 and H2O are displayed in Fig. S3 of the Supporting Information, showing 281
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system. The CO and CO2 final products appeared relatively late in the oxidation process. For CO, the formation mechanisms were related to the C1 and C2 oxides and mainly derived from the oxidation of CH2O and C2H4. The population of CO2 was determined by the number of %CHO2 free radical molecules, as has been verified by previous studies. The effects of temperature, density, and the equivalence ratio on high-temperature oxidation of MCH were further investigated. It can be found that increasing the temperature and density could significantly accelerate the oxidation rate of MCH. Unlike the temperature and density effects, changes the equivalence ratio showed only a limited effect on the rate of MCH oxidation. This was due to the domination of the unimolecular dissociation in the initial reaction stage, so the concentration of O2 in the system had little influence on the initiation mechanism.
[13]
[14]
[15]
[16] [17]
[18]
Acknowledgement
[19]
This work was supported by the National Natural Science Foundation of china (No.21403221 and 91441106).
[20]
Appendix A. Supplementary data
[21]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.fuel.2018.12.022.
[22]
[23]
References
[24]
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Fuel journal homepage: www.elsevier.com/locate/fuel
Insights into the high-temperature oxidation of methylcyclohexane Yalan Liu a b c
a,b
c
, Guangyue Li , Junxia Ding
a,⁎
T
State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, PR China University of Chinese Academy of Sciences, Beijing 100049, PR China College of Chemical Engineering, North China University of Science and Technology, Tangshan 063021, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Methylcyclohexane ReaxFF Oxidation Kinetic behaviors
Reactive molecular dynamics simulations were performed under different conditions in order to investigate indetail the chemical events associated with high-temperature oxidation of methylcyclohexane (MCH). The corresponding kinetic behaviors of the major intermediates and products were systematically analyzed at the atomistic level. Thus the overall reaction scheme of MCH oxidation was established from the initial step to the final products. It was observed that the oxidation of MCH was mainly initiated by two kinds of reactions, including unimolecular decomposition and H abstraction, with the former being more important. In agreement with the available experimental results, C2H4, CH2O, CO, CO2 and H2O were found to be the major products during the oxidation process. The results revealed that %CH3O2, %CH3O and %C3H5O radicals were the precursors for CH2O production, which was the key intermediate to generate CO. Additionally, %C2H3O also had closed relationship with the formation of CO. For a better description of the combustion behavior, small oxides related to intermolecular reactions should be considered in the oxidation of MCH mechanisms. The temperature and density had a positive effect on the oxidation of MCH; it was also found that an increase of the equivalence ratio had a negligible effect on the MCH oxidation.
1. Introduction Cycloalkanes are an important class of constituent compounds in gasoline and jet fuels [1–3]. They have also been found to play a key role in the formation of aromatic pollutants and polycyclic aromatic soot precursors [4,5]. To reduce soot formation, a detailed understanding of the cycloalkanes combustion mechanisms under practical atmospheric conditions is necessary. However, cycloalkanes consist of various kinds of components, and the determination of all relevant kinetics mechanisms is therefore impractical. An alternative approach to this problem is to use a single model fuel to represent these compounds. As the simplest alkylated cyclohexane, methylcyclohexane (MCH) is commonly chosen as a model fuel to study the combustion behaviors of cycloalkanes experimentally and theoretically. In the past decades, a limited number of works focusing on the pyrolysis and combustion of MCH have been reported. Experimentally, Zeppieri et al. [6] performed high-temperature (1050–1200 K) oxidation of MCH in a Princeton turbulent flow reactor. They noted that the pyrolysis and oxidation of MCH produced the same intermediates, with the oxidation proceeding at a faster reaction rate. Yang and Boehman [7] studied the oxidation of cyclohexane and MCH in a motor engine at the temperature of 393.15 K and 473.15 K, respectively. The results ⁎
showed that fuel conversion and carbon monoxide formation were strongly enhanced by the existence of the methyl group. Skeen et al. [8] investigated the chemical compositions of three low-pressure premixed flames of MCH, and indicated that higher temperature resulted in an increase for MCH consumption via isomerization and dissociation. In theoretical studies, several groups have established kinetic models of MCH combustion [9–14]; and tested them against reliable, molecule-specific experimental data; such as the measurements of the species in burner-stabilized flames. Of course, experiments could provide important information regarding the complex combustion system, such as the activation energy. However, reactions such as pyrolysis, combustion and explosion can be extremely fast, especially at high temperatures, and can produce large amounts of intermediates through complex reaction mechanisms and pathways. Therefore, experimental data alone are far from sufficient for establishing an accurate combustion model that describes the MCH oxidation process. Reactive force field (ReaxFF) [15,16] has been developed to be an efficient tool for predicting complex reactions. In this approach, the connectivity of every atom in the system is determined by bond orders calculated from bond distances. Thus, this approach allows an accurate description of bond breaking and bond formation during the reaction process. In addition, the parameters in ReaxFF are derived based on
Corresponding author. E-mail address: [email protected] (J. Ding).
https://doi.org/10.1016/j.fuel.2018.12.022 Received 22 May 2018; Received in revised form 13 November 2018; Accepted 7 December 2018 0016-2361/ © 2018 Published by Elsevier Ltd.
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quantum mechanical (QM) data and can simulate reaction pathways without any preconditions. Therefore, ReaxFF has a relatively high accuracy and good transferability. Recently, ReaxFF has been used to investigate hydrocarbon oxidation processes over a wide range of systems, including toluene oxidation [17], n-octanol [18] and n-dodecane [19] combustion, and n-decane and toluene [20] mixture oxidation. These successful applications prove that ReaxFF can provide important theoretical guidance for hydrocarbon combustion systems. In the present work, reactive molecular dynamics (RMD) simulations were used to investigate the mechanism of MCH oxidation under different conditions, including the initial reaction and intermediate reaction mechanisms. The effects of the temperature, equivalence ratios and density on the combustion mechanism were also investigated. We focused mainly on the analysis of the major intermediates and products; and on the initial mechanisms and the intermediate reaction process of MCH combustion. It is hoped that the analysis presented here will furnish a more complete atomic understanding of the combustion process and will afford a more reliable combustion model for MCH. 2. Computational methods Fig. 1. Initial reaction steps of MCH oxidation. Percentages on arrows present for the MCH consumption contributed by that reaction.
To study the detailed reaction mechanisms of MCH oxidation under different conditions, a wide range of temperatures and pressures of MCH/O2 mixtures were investigated. For the RMD simulations, all systems were equilibrated for 10 ps in the NVT ensemble (maintaining the number of atoms, volume, and temperature constant) at 300 K with a time step of 0.1 fs. This time step has been widely employed in several systems [21–24] and was shown to be efficient for the description of hydrocarbon oxidation. Once the equilibrium configurations were achieved, the systems were used in the NVT-MD simulations, where the cut-off for trajectory analysis was set to 0.3, which is used only for molecule recognition and does not affect the simulation results [22]. For all simulations, the temperature was controlled by the Nosé-Hoover thermostat method [25] with a 0.1 ps damping constant. To further validate the accuracy of the reactive force field, the main initiation reaction channels were calculated by the QM method at the B3LYP/6311G (d,p) level of theory [26,27] using Gaussian 09 [28], and then, the relative electronic energies at 0 K calculated by QM and ReaxFF were compared and discussed.
total. Compared to the C–C bond dissociation, the bond breaking of the C–H bond was less important, with only 8.51% of MCH initiated in this channel. This was mainly caused by the different dissociation energies of the C–C and C–H bonds [29]. In addition to unimolecular decomposition, H abstraction reactions by small active radicals including O2, •H, %OH, %HO2 and %O% were also effective pathways for consuming MCH, constituting up 23.29% of the total. However, it could be deduced that in the oxidation process, the unimolecular pyrolysis was the main pathway for the consumption of MCH molecules, which agreed well with a previous study [7].
3.2. Force field validation The force field used in the ReaxFF MD simulation has been reported by van Duin and Cheoweth [20] were used without modification. Here, we focused on the goodness of the force filed to the MCH system. Table 1 compares the relative reaction energies at 0 K of ReaxFF and QM data for the major initiation reaction channels. The geometrical structure of the reactants and products were performed using the B3LYP functional; together with the 6-311G (d,p) basis set. The maximum deviation reached 13.58 kcal/mol in initial a. As seen in Fig. 2, this reaction pathway involved two steps; firstly, the MCH molecule was isomerized into %CH2CH(CH3)CH2CH2CH2CH2% with the reactive energy of 73.6 kcal/mol by QM and 72.0 kcal/mol by ReaxFF method. Subsequently, the highly reactive %C7H14% radical dissociated into %CH2CH(CH3)CH2CH2% and C2H4 through a transition sate. The reactive energy calculated for the reaction barrier by the QM and ReaxFF was 25.75 kcal/mol and 28.28 kcal/mol respectively. According to the transition state theory, the reaction rate was described by Arrhenius expressionk = A exp(−Ea/ RT ) . Thus, the reaction rate was determined by energy of the transition state. The small deviation of ReaxFF and QM for TS calculation has proved the reliability of the force field to an
3. Results and discussion 3.1. Initial reaction mechanisms of oxidation of MCH To investigate the initial reaction mechanisms of MCH oxidation, 10 independent multimolecular simulations were performed at the density of 0.09 g/cm−3 and the temperature of 2500 K. The flux network for describing the detail reaction pathways with branching ratios are presented in Fig. 1. Percentages on arrows represent for the MCH consumption contributed by that reaction. According to the simulation results, the initial reactions could be divided into two categories: the H abstraction reaction and MCH pyrolysis reaction. It was found that, 76.61% of the fuel molecules were consumed by the dissociation reaction, in which the ring-opening channel accounts for 50.0%. Most of MCH molecules were first isomerized into %C7H14%, which were then either dissociated into %C5H10% and C2H4, or dissociated into %C4H8% and C3H6 with several femto-seconds. The unimolecular decomposition of MCH leaded to %C7H14% was also proposed by previous kinetic models. However, in the simulation process, these reactive biradicals had not survived H transferred reaction to form heptane, instead, continued to dissociate into ethylene and propylene through β-scission reactions. This was due to the high temperature and high pressure promoted the further dissociation of these diradicals. In addition to the ring-opening reactions, the demethylation reaction was also the main reaction pathway for the consumption of the fuel molecule, with the proportion of this pathway reaching 20.48% of the
Table 1 Reaction energies (kcal/mol) at 0 K for major initiation reactions obtained using both ReaxFF and QM method. name initial initial initial initial
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a b c d
reactions
ΔEReaxFF
ΔEQM
C7H14 → %CH2CH(CH3)CH2CH2% + C2H4 C7H14 → CH3%CHCH2CH2CH2% + C2H4 C7H14 → %CH2CH2CH2CH2% + C3H6 C7H14 → CH2CHCH2CH2CH2CH2% + %CH3
77.54 76.73 78.39 90.52
91.12 87.57 86.12 90.49
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Fig. 2. The detailed reaction process for initial a using QM and ReaxFF method.
extent.
3.3. Intermediate reaction mechanisms of oxidation of MCH 3.3.1. Time-dependent intermediate distributions To obtain an overview of high-temperature MCH oxidation, a series of 10 NVT-MD multimolecular simulations were performed at the temperature of 2500 K under approximately stoichiometric conditions (Φ = 1.0) for 1.0 ns. We put 10 MCH and 110 O2 molecules in a 43.00 Å×43.00 Å×43.00 Å period unit cell with the density of 0.09 g/ cm−3. To facilitate the analysis, the time at which the system reached the target temperature was set to zero in the following discussion. Throughout all RMD simulations, a total of 205 different species, including reactive intermediates and stable products, were identified. In this work, these species were divided into 8 categories denoted as C0, C1, C2, C3, C4, C5, C6 and C7 according to the number of carbon atoms. The intermediate distributions and total energy profile as a function of time are summarized in Fig. 3. It could be seen that; the MCH molecule began to decompose at 15 ps and that most MCH molecules were consumed within 600 ps. In light of the consumption rate of the MCH molecules, the combustion process could be divided into three stages. The first stage was from the initiation time (15 ps) to 200 ps. In this period, the consumption rate of MCH was relatively fast, approximately 65.0% of MCH molecules were decomposed, and the main products were C2 and C3 species. Among these, C2H4 and C3H6 were the most important; their amounts increased significantly with the consumption of MCH molecules. Furthermore, during this stage, few O2 molecules were consumed, and the relative energy of the system increased as the simulation progressed. We can be certain that the whole system began with an endothermic reaction. The second stage lasted from 200 to 400 ps. Compared to the first stage, the MCH dissociation rate was much lower, and only 25.0% of the MCH molecules decomposed in this period, during which a slow increase of C2 and C3 species was observed. Different from the first stage, a considerable amount of C0 and C1 was produced in this period. Meanwhile, the total energy of the system went through a short equilibrium and started to decrease. This indicated that the oxidation reaction was dominant during this period. The last stage was from 400 to 600 ps, during this stage, the rest of the 10.0% MCH molecules were consumed, which was a bit slower than the second stage. After 600 ps, all MCH molecules were dissociated, and the consumption rate of oxygen gas was significantly accelerated. This led to a significant increase in the generation rate of CH2O, which acted as an active intermediate in combustion. During the oxidation process, the major observed species were C2H4, C3H6, CH2O, CO, CO2 and H2O. It could be seen that; the number of C2H4 molecules reached the maximum when the MCH molecules were
Fig. 3. Time evolution of (a) number of Cn species and (b) number of typical species in multimolecular simulations of 2500 K, initial pressure 52.0 MPa system. The bule line denotes the relative energy profile during simulations. These panels were drawn using averaged values from the ten runs.
totally consumed. Zeppieri et al. [6] conducted pyrolysis and oxidation studies of MCH in the high temperature range of 1050–1200 K; and found that when the fuel molecules were totally consumed, the normalized mole fraction of C2H4 was[C2 H4]/[MCH ]0 = 1.07 . The experimental data agreed well with our simulation result (1.2). In our simulations, some key related radicals, such as %H, %HO2, %OH, %CH3, %C2H3 and %C3H5, were also observed. The distributions of these reactive radicals as a function of time were presented in Fig. S1 of the Supporting Information. The amounts of all these reactive radicals changed dramatically during the simulations. This indicated that these reactive species were highly involved in the oxidation of MCH. 3.3.2. Formation mechanisms of key intermediates In our simulations, several kinds of intermediates that were very important for the combustion of MCH were observed. A detailed analysis of the reaction mechanism of these intermediates was critical to understand the entire oxidation mechanism of MCH. Here, we focused on two key intermediates–formaldehyde and hydrogen peroxide. 3.3.2.1. CH2O reaction mechanisms. Formaldehyde is one of the main intermediates appearing in hydrocarbon combustion, and the cool flame is directly related to formaldehyde. The main production and consumption channels of CH2O are shown in Fig. 4. It can be seen that; the methoxy radical (%CH3O) and methyl peroxy radical (%CH3O2) were important intermediates in formaldehyde production. According to our observations, these C1 oxides were mainly derived from the oxidation of methyl, as was also verified by a previous study [29]. Thus, the amount 275
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Fig. 4. The distributions of CH2O related reactions. Red and black denote the production and consumption reactions, respectively.
Fig. 6. The distributions of H2O2 related reaction mechanisms. Red and black denote the production and consumption reactions, respectively.
of methyl radical had a direct influence on the number of formaldehyde molecules. Furthermore, the dissociation of %C3H5O was also a significant channel for CH2O production, accounting for 14.80% of all the production channels. To show the detailed reaction mechanism, Fig. 5 presents the reaction scheme from the initial reaction products to CH2O. According to Fig. 5-a, an O2 molecule reacted with the %CH3 radical to form %CH3O2, producing CH2O through H transfer and the OH release reaction. As seen from Fig. 5-b, the %O% radical was first attached to %CH3, yielding the %CH3O radical, and then decomposed to CH2O through H elimination. Additionally, C3H6 was also an important intermediate for CH2O formation, as presented in Fig. 5-c. First, %C3H5 was obtained by the H abstraction reaction, and then, the %HO2 radical was added to form C3H6O2, which decomposed to the key %C3H5O radical and %OH radical intermediates. Lastly, the final product CH2O was generated by the decomposition of %C3H5O. This reaction process has been proved to be important by a previous experimental study [11]. Orme et al. investigated the oxidation of MCH in high-temperature shock tube experiments; and found that the reaction %C3H5 + %HO2 → %C2H3 + %OH + CH2O was sensitive to shock tube ignition delay times. Generally, %CH3 and C3H6 intermediates contribute the most to the formation of CH2O. This was consistent with a previous theoretical study [29]. For CH2O consumption, the CH2O + %OH → %CH3O2 and %CH3O2 → CH2O + %OH reactions were reversible and were not highly effective pathways for CH2O consumption. Actually, the main consumption channels were the H abstraction reaction (CH2O + O2 → %CHO + %HO2) and H addition reaction (CH2O + % HO2 → %CH3O + O2). The build-up of O2 and %HO2 can accelerate the transformation of formaldehyde.
Fig. 7. The proportion of (a) CO related reaction channels. (b) CO2 related reaction channels.
Fig. 5. Main reaction channels of CH2O production from initiation products. 276
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Fig. 8. Reaction schemes of CO and CO2. (a) The main reaction pathways to produce CO and CO2 from %CH3 radical. (b) The main reaction pathways to produce CO from C2H4.
3.3.2.2. H2O2 reaction mechanisms. The H2O2 intermediate plays a critical role in the combustion atmosphere, and a detailed analysis of H2O2 related reactions is necessary to reveal the combustion mechanisms of MCH. Fig. 6 displays the main consumption and production pathways of H2O2. It can be seen that %HO2 played a very important role in the formation of H2O2. More than 74% of H2O2 produced through the five reaction channels involved %HO2, in which the intermolecular hydrogen attraction between two HO2 radicals (2HO2 → H2O2 + O2) was the primary channel. Such a reaction mechanism has been reported and was considered to be the main pathway for %HO2 consumption by Bahrini et al. [30]. Tian et al. [31–33] performed a comparative study on autoignition and oxidation of cycloparaffin, and found the 2HO2 → H2O2 + O2 was one of the most sensitive reactions for MCH oxidation, especially at relatively higher temperature. This was consistent with our simulation result. According to our observations, most of the H2O2 molecules were consumed by dissociation into %OH radicals, with the proportion of approximately 48.28%. The reactions of HO2 radicals were generally the main source of H2O2 at this temperature, and the consumption of H2O2 resulted in the accumulation of OH radicals. These simulation results were in good agreements with the results of a previous study
Fig. 9. The distributions of H2O related reactions. Red and black denote the production and consumption reactions, respectively.
Fig. 10. Reaction scheme of MCH oxidation. 277
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3.3.3.1. Proposed CO and CO2 formation mechanisms. For the hydrocarbon fuel, CO and CO2 are the main carbonaceous products, the formation mechanism of which is a significant part of the entire combustion mechanism. The main formation pathways associated with the CO and CO2 during MCH oxidation are shown in Fig. 7. It can be seen in Fig. 7a, the production of CO was closely related to the C1 and C2 oxides. For example, 18.9% of the CO was produced by the dehydrogenation of %CHO. This reaction pathway has been verified by previous experimental and theoretical studies [29,34]. Compared to %CHO, the CO production channels involving C2 oxides have received little attention despite their large proportion. According to the simulation results, up to 51.4% of the CO was derived from the dissociation of C2 oxides, including the decomposition of %C2H3O and %C2H3O2, which had the same contribution that was slightly lower than that of the dehydrogenation pathway. Unlike the complex reaction channels of CO, the formation of CO2 was relatively simple, as displayed in Fig. 7b. It can be found that the primary channels for CO2 production were the H elimination reaction (%CHO2 → CO2 + H) and H abstraction reaction (%CHO2 + O2 → CO2 + HO2). Obviously, the amount of CO2 was related to the amount of the %CHO2 key intermediate derived from the two main reaction channels, as shown in Fig. 8a. In the first mechanism, O2 was first added to %CH3 to form intermediate radical %CH3O2, which was then finally converted to CHO2 via the dehydrogenation reaction (%CH3O2 → %CHO2 + H2). In the second mechanism, the dehydration reaction of %CH3O2 to produce %CHO was followed by the addition of the %O% radical to form %CHO2 directly. Furthermore, %CHO2 was also important for the formation of CO, for example, through the %OH elimination reaction. In addition to %CHO and %CHO2, the reactions related to %C2H3O and %C2H3O2 were of crucial importance to the production of CO, as presented in Fig. 8b. As observed, the generation of %C2H3O was mainly through the oxidation of %C2H3 and C2H2. The oxidation of %C2H3 followed two pathways: In the first, the %OH addition reaction was followed by the H elimination reaction. In the second pathway, the %HO2 addition reaction led to the formation of %C2H3O through OH elimination. In addition to the %C2H3 radical, C2H2 could also be converted to %C2H3O by OH radical addition. For %C2H3O, this was the key connection to the formation of CO. On the one hand, %C2H3O could decompose to form CO and %CH3 directly. On the other hand, it could also convert into other C2 oxides (such as %C2H2O2, %C2H3O2 and %C2HO2), which also contributed to the CO formation. Therefore, CO production was closely related to the %C2H3O intermediate; produced by the oxidation of %C2H3 and C2H2. It has been verified the %C2H3 and C2H2 were mainly derived from the dehydrogenation reaction from C2H4 [35]. Hence, the population of C2H4 determined the number of CO molecules in our simulations.
3.3.3.2. H2O formation mechanisms. H2O is another type of stable product of hydrocarbon oxidation. We also analyzed H2O formation and dissociation mechanisms for the MCH oxidation. According to Fig. 9, the OH radical played a vital role in the formation of H2O. The direct combination of the OH radical with the H radical was the most likely channel, with the proportion of 13.33%. Additionally, 52.00% of H2O was derived from the H abstraction by reactive OH from other small molecules, including H2, H2O2 and %HO2. Among these, H abstraction from H2 molecules accounted for 12.00%, slightly lower than the direct combination channel. Moreover, the OH radical also participated in some indirect channels. For example, the reactive OH could react with ethylene to generate %C2H5O, which then decomposed to generate %C2H3 and H2O, and its fraction reached 12.00%. Generally, the production of H2O was determined by the build-up of the OH radical in the system. Compared to H2O generation, the consumption of H2O was relatively simple. The dominant pathway was H abstracted by O atoms to generate the OH radical.
Fig. 11. Time evolution of MCH molecules, O2 consumption, potential energy and major product distributions during MCH oxidation at 2500 K under various equivalence ratio conditions.
[18].
3.3.3. Formation mechanisms of dominant products Here, we focused on the use of the mapping strategy to identify the reaction mechanisms from the initial reaction species to the most common products CO, CO2 and H2O. Starting from the products, we first determined the major pathways; and then identified the main intermediates in the trajectory. Finally, we searched for the reaction in the reverse manner and found the reactions that connected these intermediates. As described below, we were thus able to build up a simple reaction network to describe how these main products were formed. 278
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Fig. 12. Time evolution of the average number of (a) MCH dissociation, (b) C2H4 production, (c) CH2O production, (d) O2 consumption at the temperatures from 2200 to 3000 K in the interval of 200 K (NVT-MD simulation, Φ = 2.0, ρ = 0.09 g/cm−3). These panels were drawn using averaged values from the ten runs.
lean (Φ = 0.5) and fuel-rich (Φ = 2.0) conditions respectively. Fig. 11 presents the distribution of major products under different equivalence ratios at 2500 K. As observed, under fuel-rich conditions, the number of C2H4 molecules increased significantly for 0–400 ps, and then changed slightly as the simulation progresses. Additionally, the number of C2H4 molecules was larger than that under O2 sufficient conditions. Similarly, the number of C3H6 molecules decayed more slowly when the equivalence ratio was increased to 2. This was mainly because a high concentration of O2 can accelerate the dissociation of alkenes by the H abstraction reaction. Unlike for alkenes, the insufficient O2 molecules could reduce the population of the released CH2O. This occurred because insufficient O2 for MCH oxidation lowered the oxidation rate of C3H6 and %CH3, which were the key intermediates for CH2O production. As an important product of MCH oxidation, the number of H2O molecules were closely related to the equivalence ratio. It could be seen that; the population of H2O molecules increased as the simulation progressed under the stoichiometric and fuel-rich conditions, whereas the number of H2O molecules was smaller for insufficient O2 in the system. This was due to that, with an increasing concentration of O2 present, the number of produced OH radicals became higher, thus accelerating the formation of H2O. However, in fuel-lean conditions, the evolution of H2O was quite different. At 0–600 ps, the amount of H2O increased; and then stabilized for 600–800 ps. After 800 ps, the number of H2O molecules increased for the entire remaining simulation time.
3.4. Detailed reaction scheme for MCH oxidation The reaction network proposed based on our simulation results is shown in Fig. 10. It provided a detailed description of the oxidation mechanism of MCH, from the initial step to the final products. MCH oxidation was initiated by C–C bond dissociation leading to the formation of C2H4, C3H6 and %CH3, which were subsequently oxidized to form the final products. As observed, the oxidation of C2H4 generated the %C2H3O, either by direct dissociation, or by a complex conversion to other C2 oxides followed by decomposition to CO. Similarly, the oxidation of C3H6 first produced the %C3H5O, and then dissociated into CH2O, which was also an important intermediate for CO production. The oxidation of %CH3 proceeded mainly through the formation of the %CH3O2, which then decomposed to CO2. Compared to CO and CO2, the formation of H2O was relatively simple, mainly through the combination of H and OH radicals.
3.5. Effects of the equivalence ratio on MCH oxidation The equivalence ratio is one of the most important parameters in the combustion process, significantly influencing the flame propagation, anti-pollution, etc. To predict the complex kinetics mechanisms of MCH oxidation, two periodic cubic boxes with lengths of 51.00 and 36.00 Å were generated with 210 and 53 O2 molecules, referred to as the fuel279
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Fig. 13. Time evolution of (a) the average number of MCH molecules, (b) Relative energies and (c–d) the average number of C2H4 and CH2O molecules at the densities range from 0.09 to 0.35 g/cm−3(NVT-MD simulation, T = 2500 K, Φ = 2.0). These panels were drawn using averaged values from the ten runs.
intermediate, was relatively low at first; and then increases as the simulation progressed. This trend was consistent with the consumption of oxygen molecules. Few CH2O molecules were produced at the first stage because a small amount of O2 participates in the oxidation of CH3 and C3H6. As the rate of O2 consumption increased, the CH2O generation accelerated. Additionally, the time distributions of final products (CO, CO2 and H2O) were presented in Fig. S2 of the Supporting Information. It can be seen that as the temperature increased, the yield rate of the final products was significantly enhanced.
This was mainly due to the fact that on one hand, an increase in O2 concentration can promote the production of the OH radical, leading to greater generation of H2O molecules, while on the other hand, in the presence of a high O2 concentration, the formation of H2O can be reduced by the O2 + H2O → %OH + %HO2 reaction. In addition, the number of CO molecules increased with increasing O2 concentration because a number of CH3 and C2H4 were oxidized to CO.
3.6. Effect of temperature on the oxidation of MCH To analyze the effect of temperature on the oxidation of MCH, 10 parallel NVT-MD simulations were performed at temperatures ranging from 2200 to 3000 K with an interval of 200 K for a total of 1 ns simulations in fuel-rich condition (Φ = 2.0). The time evolutions of MCH molecules, O2 consumption, and CH2O and C2H4 production are shown in Fig. 12. It can be found that; the number of fuel molecules decreased more rapidly with the increase of temperature, and this effect became more obvious at low temperatures. When the temperature reached 2800 K, the increase of temperature had little influence on the dissociation rate of MCH. The yield and the rate of the generation of C2H4 molecules increased with the increasing temperature. However, the final production of C2H4 was highest at the temperature of 2600 K. This was because the higher temperatures accelerated the dissociation of C2H4. The production rate of CH2O, which was another important
3.7. Effect of density on the combustion of MCH The effect of density on the combustion of MCH was investigated at the initial densities of 0.09, 0.22 and 0.35 g/cm−3 (Φ = 2.0, T = 2500 K). The time evolutions of the number of MCH molecules, potential energy and main species distributions are presented in Fig. 13. Examination of the change in the amount of MCH molecules showed that the system at the density of 0.35 g/cm−3 exhibited fast fuel consumption, and the potential energy at this density was the most exothermic. This trend indicated that an increase of the density leaded to rapid consumption of fuel molecules. Moreover, the density effect can also be observed in major species distributions. For C2H4, while increasing density of the system had little influence on the production rate, it could significantly improve the consumption rate. Hence, the 280
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Table 2 Fitted Arrhenius parameters of MCH oxidation.
ReaxFF
Equivalence ratio
Ea (kcal/mol)
R2
0.5 1.0 2.0
59.92 65.79 65.76
97.6 98.7 99.2
Exp
a b
64.00a 60.04b
Experimental result is taken from Ref. [6]. Experimental result is taken from Ref. [37].
similar trends at various densities. As the system density increased, the production of these species was accelerated. 4. Kinetic analysis of MCH oxidation To investigate the kinetics properties of the combustion of MCH in different conditions, the ReaxFF simulations of MCH oxidation were run under fuel lean (Φ = 0.5), stoichiometric (Φ = 1.0) and fuel rich (Φ = 2.0) combustion atmosphere for temperature ranging from 2000 to 2500 K at 100 K intervals with the densities of 0.09 g/cm−3. Ten random simulations were carried out at each temperature and a total of 1 ns data was collected. The second kinetics was employed to describe the reaction of MCH and O2, which was also applied for hydrocarbon combustion in recent literatures [17,36]. The concentration of MCH and O2 were simply replaced by the number of molecules. In the oxidation process, few O2 molecules were involved in the dissociation of fuel molecules, thus the concentration of O2 can be regarded as no change. Therefore the dissociation of MCH can be seen as quasi-firstorder kinetics reaction. Combined the rate constant ln N0 − ln Nt = k [O2 ]0 t with Arrhenius expressionk = A exp(−Ea/ RT ) , the activated energy (Ea) and pre-exponential (A) could be extracted by liner fitting as is presented in Fig. 14. We obtained the overall activity energy values ranging from 59.92 to 65.79 kcal/mol, which are shown in Table 2. The apparent activation energies extracted here were in accord with the MCH pyrolysis experimental results. This was further proved that most of MCH molecules were consumed by pyrolysis reactions under combustion atmosphere. 5. Conclusion High-temperature and high-pressure oxidation of MCH was simulated using NVT-MD in conjunction with the ReaxFF reactive force field. Multimolecular simulations were conducted on the system at the temperature of 2500 K under approximate equivalence ratio conditions. The main species observed in the present simulations were C2H4, C3H6, CH2O, CO, CO2 and H2O. To elucidate the detailed mechanisms of the MCH oxidation, the initiation and intermediate reactions were investigated during the simulation process. At the initial stage, five types of initiation reactions were detected, and most MCH molecules were first isomerized to %C7H14%, and then dissociated into ethylene and propylene through β-scission reactions. This reaction to consume fuel molecules was overlooked in previous theoretical studies and not taken into consideration in the current kinetic models. This finding would help to establish more accurate kinetic models for the combustion of MCH. The intermediate mechanisms related to the major intermediates and common products were also demonstrated in our work. According to our observations, CH2O and H2O2 were the most important intermediates. The amount of CH2O was determined by the oxidation of %CH3 and C3H6 intermediates, and CH2O was also the precursor for CO production. The number of H2O2 molecules was closely related to the accumulation of the HO2 radical, and it also contributed to the formation of OH radicals, which controlled the H2O formation in the
Fig. 14. Fitted rate constant versus temperature from ReaxFF-MD simulations with the density of 0.09 g/cm−3 at various equivalence ratios.
final production of C2H4 decreased with the increase of the system density. For CH2O, raising the density from 0.09 to 0.22 g/cm−3 could improve the amount of CH2O to a large extent, but the influence of the density increase became small when the density continued to increase to 0.35 g/cm−3. This was because a higher density promoted the dissociation of formaldehyde. The product distributions of CO, CO2 and H2O are displayed in Fig. S3 of the Supporting Information, showing 281
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system. The CO and CO2 final products appeared relatively late in the oxidation process. For CO, the formation mechanisms were related to the C1 and C2 oxides and mainly derived from the oxidation of CH2O and C2H4. The population of CO2 was determined by the number of %CHO2 free radical molecules, as has been verified by previous studies. The effects of temperature, density, and the equivalence ratio on high-temperature oxidation of MCH were further investigated. It can be found that increasing the temperature and density could significantly accelerate the oxidation rate of MCH. Unlike the temperature and density effects, changes the equivalence ratio showed only a limited effect on the rate of MCH oxidation. This was due to the domination of the unimolecular dissociation in the initial reaction stage, so the concentration of O2 in the system had little influence on the initiation mechanism.
[13]
[14]
[15]
[16] [17]
[18]
Acknowledgement
[19]
This work was supported by the National Natural Science Foundation of china (No.21403221 and 91441106).
[20]
Appendix A. Supplementary data
[21]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.fuel.2018.12.022.
[22]
[23]
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