3.1. Multimolecular Annealing Simulation Results.
The multimolecular ReaxFF annealing calculations are performed at temperatures ranging from 1000 to 3400 K. To get a more complete picture of the iso-octane decomposition and eliminate statistical uncertainty, ten independent calculations for the iso-octane RMD simulations are carried out. Figure 2 pictures the averaged time evolution of the iso-octane (C8H18) molecules and major fragment distributions during the annealing simulations as well as the temperature change. It is found that the pre-equilibrated iso-octane molecules start to dissociate at 111 ps at around 2068 K. It takes about 210 ps to complete the whole pyrolysis of iso-octane. According to the thermal decomposition rate of iso-octane, the pyrolysis process can be separated into three gradations. The first stage is from the initiation of the iso-octane decomposition at 111 ps to 150 ps. In this range, due to the lower temperatures, the rate for the iso-octane cracking is relatively low and only 15.6% of the iso-octane molecules decompose. The second stage is from 150 to 190 ps with the corresponding temperature from 2440 to 2824 K. In this period, the decomposition rate of iso-octane is greatly increased, and most of the iso-octane molecules (73.3%) are consumed. The last stage is from 190 to 210 ps, and the rest of the iso-octane molecules are consumed. After 210 ps, the whole decomposition reaction enters a deeper level, and the formed intermediates by the iso-octane dissociation continue to produce various smaller products, including hydrogen, alkanes, alkenes, unstable intermediates, and highly active free radicals. A large number of unstable methyl radicals are produced in the early stage of iso-octane cracking, which can be attributed to the unimolecular C−C bond dissociation reactions, and due to more branched chains in the iso-octane molecular geometry, more •CH3 radicals are produced in the pyrolysis system. The amount of •CH3 reaches the maximum at around 200 ps, and then gradually decrease with the formation of methane molecules, indicating generations of •CH3 might be directly correlated to the consumption of iso-octane. At about 250 ps, most of •CH3 are consumed, which is accompanied by the methane molecules reaching a maximum.
The amount of these alkenes intermediates reaches its maximum in the middle stage of the iso-octane pyrolysis, and then gradually decreases. For the alkenes products in the decomposition of iso-octane, isobutene and propylene are found to be the most abundant olefins in the experimental study of Wang et al. [39], while propylene and ethylene are the most abundant alkenes in this work. This is probably attributed to the lower experimental temperatures (723–1123 K) by Wang et al. [39] compared to the RMD simulations of this work (1000–3500 K), and high temperature will lead to deeper decomposition and more low carbon alkenes such as ethylene will be produced. With the decrease of olefins, the alkynes molecules, as well as other high unsaturated hydrocarbons, are increasing. Hydrogen is the most abundant product whose amount quickly increases with time and reach its stabilization at the end of the simulation.
3.2. Initial decomposition mechanism and force constant validation against QM data
Since the initial decomposition reactions are very important for predicting the distributions of main intermediates and products, a detailed description about them is required to establish the complex pyrolysis mechanisms of iso-octane.
Ten parallel multimolecular simulations at 2800 K with the same starting configuration are performed at the density of 0.183 g cm−3. Figure 3 displays the average distribution of main consuming reactions of iso-octane based on our NVT-RMD simulation results. It can be found that the iso-octane decomposition has two main initial pathways. One is the unimolecular C−C and C−H bond dissociations, and the other is the hydrogen abstraction reaction of iso-octane by small free radicals, i.e., •H and •CH3. The unimolecular C–C dissociation reaction is the most important in the iso-octane decomposition reactions and accounts for about 66.9% of the total iso-octane consumptions, while the C−H bond scission pathway contributes only 3.7% to the overall initial decomposition stage of iso-octane. This is probably attributed to the larger dissociation energies of the C−H bonds compared to those of the C−C bonds. Based on the symmetry, four kinds of C−C bond scission channels of iso-octane could be observed and each one produces two free radicals. Since there are five C−C bond scissions in an iso-octane molecule to produce methyl radicals, the C8H18 → •CH3 + •C7H15 initial pathway provides the major sources for the overall initial decomposition stage of iso-octane. The other important pathway for the consumption of iso-octane is the hydrogen abstraction reactions to form iso-octyl radicals. These reactions together contribute 28.8% at 2800 K. The sensitivity analysis also shows that the hydrogen-abstraction reactions by methyl radicals are more sensitive than the reactions by •H atom attack. This is probably attributed to more methyl radical formation compared to the •H radical in the initial decomposition step of iso-octane. This is consistent with the previous experimental results [39].
To evaluate the reliability of the ReaxFF NVT-MD simulations, the initial C−C bond dissociations of iso-octane are also studied by performing QM calculations at the M062X/MG3S and CCSD(T)/6-311++g(2df,2p)//M062X/MG3S levels. Table 1 shows the estimations for the bond dissociation enthalpies at 298.15 K by both NVT-MD and QM calculations. The experimental data [61] and previously calculated results [40] at 298.15 K are also included in Table 1 for comparison. Here it should be noting that the CCSD(T)/6-31+G(d,p)//M062X/MG3S level is simply as CCSD(T)//M062X in Table 1.
Table 1
Reaction energies of iso-octane pyrolysis (kcal mol−1) at 298.15 K for the unimolecular C−C bond dissociations obtained using both ReaxFF and QM methods.
bond dissociations
|
ReaxFF
|
M062X/MG3S
|
CCSD(T)//M062X
|
Ref. [61]
|
Ref. [40]
|
C1−C2
C2−C3
C3−C4
C4−C5
|
80.0
77.6
81.1
85.1
|
82.8
81.9
83.2
84.5
|
80.8
80.7
81.6
82.1
|
/
81.3 ± 1.3
83.3 ± 1.5
/
|
83.3
83.4
84.5
84.6
|
Compared with the experimental data [61], the QM results are more reliable than the RMD values. The maximum relative error for these RMD reaction energies to the experimental data is found to be lower than 4.5%, indicating that the RMD simulations using ReaxFF is appropriate to characterize the bond dissociation reactions. Furthermore, our RMD simulations are observed to give the same energetic tendency as the QM results. Here it should be noting that our QM calculations predict the BDEs for C1−C2 is 0.1 kcal mol−1 higher than that of C2−C3 bond, which is different from the energetic order of Ning et al. [40]. It may be caused by the different theoretical levels. According to our RMD and QM estimations, it is obvious that the bond dissociation energies of the two C−C bonds to Y•C7H15 + •CH3 and tert-•C4H9 + iso-•C4H9 are slightly lower than those of the two channels to P•C7H15 + •CH3 and iso-•C3H7 + neo-•C5H11. Lower dissociation energies will accelerate the decomposition process, leading to an increase of the sensitivity coefficients of the reactions for the total consumption of iso-octane, which also explains the higher sensitivity of C2−C3 and C1−C2 bond dissociations than C3−C4 and C4−C5 bond scissions for the initial decomposition of iso-octane.
3.3. Intermediate Reactions.
Because the thermal cracking of hydrocarbons is a complex chain reaction of free radicals, the intermediate decomposition mechanism of iso-octane has not been studied in detail up to now. Additionally, for the endothermic hydrocarbon fuel, the unsaturated hydrocarbons in the product will directly affect its endothermic capacity. Therefore, it is very important to understand the production and consumption pathways of these intermediates. Here, we focus on four key intermediates – propylene, ethylene, acetylene, and methane. Results in Figures 4–7 are obtained by averaging ten independent NVT-MD simulations at 2800 K.
Propylene is the most importantly produced alkene in the thermal cracking process of iso-octane. Figure 4 depicts the time-dependent distributions of iso-octane and propylene (C3H6) during the iso-octane pyrolysis process. The number of propylene molecules increases rapidly in the early stage of the iso-octane pyrolysis. After reaching the maximum, it presents a decreasing trend along with the thermal decomposition process. At the end of the whole pyrolysis from 85 to 95ps, it can be found that the amount of propylene molecules has a small increase because production reactions are more than the consumption reactions. The different characteristics in the production and consumption evolutions can be attributed to the different primary reactions related to C3H6. As can be seen from Figure 3, there are two pathways for the iso-octane molecules to produce high carbon alkyl radicals: C–C bond dissociation and hydrogen-abstraction reactions. The formed large alkyl radicals continue to decompose primarily via the C–C β-scissions to generate 1-alkenes molecules and by intramolecular hydrogen-transfer reactions, a small amount of these species isomerizes to other alkyl radicals which then also produce an important contribution to the formation of alkenes. These 1-alkene molecules are the major intermediates during the iso-octane pyrolysis and their numbers can be used to measure the heat sink capacity of endothermic hydrocarbon fuels. According to our observation, the main reaction to form propylene is the β-scission reaction of the •C4H9 free radicals which are produced by the C−C bond fission of iso-octane in the early pyrolysis stage. By comparing the amounts of iso-octane and propylene molecules at the same time, we can find that the iso-octane molecules start to decompose at approximately 3 ps, and at this time, propylene molecules begin to arise. In addition, when the amount of propylene molecules reaches the maximum at 26 ps, 89% of iso-octane is consumed. This indicates that the amount of propylene molecules is directly related to the decomposition of iso-octane, which is in agreement with experimental results [40]. The reactions related to propylene could be found throughout the pyrolysis process. Later, the addition reaction between free radical and propylene, the further dissociation of propylene, and H-abstraction reaction (CH2CHCH3 + •CH3→ •C3H5 + CH4) cause the decrease of propylene molecules in the system. Some of the channels are reversible (such as CH2CHCH3 + •CH3 ↔ •CH2CH(CH3)2 and CH2CHCH3 ↔ •C2H3 + •CH3). Thus, the evolution of the propylene production varies as the amount of free radical changes.
Ethylene is the second abundantly produced alkene product following propylene. The time-dependent distribution of ethylene during the iso-octane pyrolysis process is pictured in Figure 5. The change trend of ethylene is similar to that of propylene. There is a large number of ethylene molecules generated in the initial and middle stages. The production number is much bigger than the consumption one in the two stages and the ethylene molecules reach the maximum at 55 ps. The time for peak amount of ethylene molecules is later than that for propylene. According to the RMD calculations, the main reactions to produce the ethylene are the C−C bond β-scission reactions of •C3H7 (nearly 60 percentage), and the production of •C3H7 is related to propylene, shown as in Figure 4. Thereby the evolution of the ethylene production varies as the amount of the •C3H7 radicals. As the pyrolysis proceeds, the C2H4 number is declined since production of ethylene gradually decreases while the consumption is still increasing. The primary consumption channels of ethylene include the ethylene addition reactions (CH2CH2 + •CH3 → •CH2CH2CH3 and CH2CH2 + •H → •CH2CH3, and they are reversible) and the hydrogen abstraction reactions (CH2CH2 + •CH3 → CH2CH• + CH4 and CH2CH2 + •H → CH2CH• + H2). In the consumption path of ethylene, the addition of methyl radical to ethylene molecule appears to play the most important role. At the end of the iso-octane pyrolysis reaction, there is a small increase of C2H4 because the production reactions are slightly larger than the consumption reactions.
The high unsaturated intermediates, such as acetylene, methylene radical, and vinyl radical, appear relatively later during the pyrolysis process. Figure 6 shows the time-dependent distribution of the production and consumption for acetylene (C2H2). Only small amounts of acetylene (C2H2) molecules are observed to be produced. It is found that, the formation of acetylene is related to the secondary dissociation of propylene (CH2CHCH3 → •CHCHCH3 + •H and •CHCHCH3 →CHCH + •CH3) and ethylene (C2H4 → •C2H3 + •H and •C2H3→ C2H2 + •H), which is consistent with the previous pyrolysis mechanism of methylcyclohexane [42]. The consumption of acetylene is mainly through the addition of free radicals (such as •CH3). At the end of the iso-octane cracking, the number of acetylene gradually rises with the decrease of propylene and ethylene. The dehydrogenation of propylene and ethylene to acetylene would be the rational explanation of this feature [40].
Among the stable products, methane is the most abundant alkane in the pyrolysis process of iso-octane because its free radical (•CH3) are very active. We find that the hydrogen-abstraction reactions can occur easily in the pyrolysis system, and methane is relatively stable. The conditions required for its cleavage reactions are very strict with high activation energies. Figure 7 depicts the time-dependent distributions of methane during the pyrolysis process. It could be seen that, at the simulated temperature, methane begins to appear at 4 ps. The rate of production for methane is relatively high from 4 ps to 50 ps and then it slows down. On the whole, the number of the methane continues to grow with the reaction time because of its stable structure, as depicted in Figure 7. Comparing with the experimental results [39], the yields of methane are relatively over-predicted in the current simulation condition. Since the final product distributions are directly correlated to the reaction conditions, high temperature would be responsible for the difference. According to our observation, the production and consumption of methane are closely related to methyl radical. The production of methane is mainly through the H-abstraction by methyl radical. In addition, the H-addition reactions (•H + •CH3 → CH4) can also produce methane. Meanwhile, the reversible reactions are primary consumption channels (e.g., CH4 + •H→ H2 + •CH3 and CH4 → •H+ •CH3).
As for other stable products, such as H2 and ethane, they have the same character as methane. The present RMD simulations show that the H free radical is the most abundant intermediate. Under high temperature conditions, the •H radicals have a very high reactivity to undergo hydrogen abstraction reactions to form H2. It is also found that most of the production and consumption reactions of H and H2 are closely correlated, similar to •CH3 and CH4.
This chapter describes the detailed reaction mechanisms related to the main products, including propylene, ethylene, acetylene, and methane. Note that both propylene and ethylene appeared in the early stage of isooctane cracking, but the peak value for the amount of propylene molecules appears earlier than that of ethylene. Acetylene appears later, and the quantity is related to the second dissociation of small alkenes. Methane appear as stable products in our simulations and its number continues to increase during the iso-octane pyrolysis.
3.4. Reaction networks for iso-octane pyrolysis
Reaction networks have been proposed for iso-octane pyrolysis based on the RMD simulation results at 2800 K, as shown in Figure 8. As mentioned above, iso-octane decomposes mainly through C–C bond dissociations and H-abstraction reactions by the attack of small radicals such as •H and •CH3 to form alkyl radicals, such as •C8H17, •C4H9, •C7H15, •C5H11. The C–C bond dissociation reactions dominate the consumption of iso-octane (close to 70%). The formed alkyl radicals with high carbon can continue to decompose into smaller C2–C7 1-alkenes and alkyl radical products through C−H or C−C bond scissions quickly. Minor part of the C3 to C8 alkyl radicals isomerizes to other alkyl radicals via intramolecular H-transfer reactions, which are also important for the formation of alkenes. Meanwhile, active radicals such as hydrogen and methyl also react with alkyl radicals to form smaller intermediates.
3.5. Kinetic analysis of iso-octane decomposition
To analyze the effect of temperature on the thermal decomposition of iso-octane, temperature-dependent NVT-MD calculations are performed over the temperature range 2400–3200 K with an interval of 200 K. At each fixed temperature, a total of 100 ps of the RMD calculated results are used. Figure 9 shows the time evolution of the total number of iso-octane molecules at the density of 0.183 g cm−3. We can find that from Figure 9 the decomposition rates of iso-octane molecules increase remarkably with temperature. The rate of thermal decomposition of iso-octane is very slow when the reaction temperature is 2400 K, and in the simulation time of 100 ps, thirty-two iso-octane molecules are consumed. When the temperature rises to 3200 K, all the iso-octane molecules have dissociated within 18 ps. It can be argued that the effect of temperature on the decomposition of iso-octane is very significant.
This work employs first-order kinetic model to characterize the iso-octane pyrolysis. The concentrations of iso-octane are simply represented by its numbers (N). The rate constant for the iso-octane pyrolysis at each temperature is derived by the linear fitting of N versus the calculation time t
lnN – lnN0 = – kt (1)
where N0 represents the initial number of iso-octane. Figure 10 shows the rate constants for the iso-octane decomposition at various temperatures based on the RMD simulations. Results of the previous rate constant measurements are also illustrated in Figure 10 for comparison.
The Arrhenius kinetic parameters are obtained by fitting the equation as follows
lnk = lnA – Ea/RT (2)
employing the rate constants for the iso-octane pyrolysis at various temperatures.
Table 2 summarizes our derived pre-exponential factors (A) and the activation energies (Ea), as well as previous experimental and MD evaluations.
Table 2
Comparison of the Arrhenius Parameters Obtained by Previous Experimental Studies and ReaxFF Dynamic Simulations for Thermal Decomposition of iso-Octane
sources
|
temperature range (K)
|
A (s−1)
|
Ea (kcal mol−1)
|
ref. [38]
ref. [44]
ref. [46]
this work
|
723–1123
2200–3000
2500–3000
2400–3200
|
5.20 × 1015
1.23 × 1015
6.28 × 1013
7.21 × 1014
|
67.80
60.22
42.36
52.12
|
From Figure 10, it can be seen that the RMD rate constants in this work compare well with the previously calculated results in the high temperature range 2200–3000 K. We extend the experimental kinetic model proposed by Davidson et al. [38] to the RMD temperature range 2400–3200 K. Our RMD rate constants are predicted to be consistently larger than those extrapolated from the kinetic model of Davidson et al. [38] at the same temperature (i.e., the ratios of kRMD : kDavidson are calculated to be 3.71 at 2400 K, 2.32 at 2800 K, and 1.63 at 3200 K). Higher temperature in the RMD simulations in this work compared to the experimental conditions would be responsible for the difference. One can see from Table 2 that the activation energy for the thermal decomposition of iso-octane was evaluated to be 42.36–67.80 kcal mol−1 under various conditions. By fitting the standard Arrhenius plot with our RMD simulations, the activation energy is estimated to be 52.12 kcal mol−1, comparing well with the experimental data. Here it can be argued that the RMD simulations in this work are suitable to describe the iso-octane pyrolysis.
Figure 11 presents the comparison of the rate constants for thermal decompositions of iso-octane (in this work), n-heptane, and methylcyclohexane48 based on the RMD calculations with the same settings. It is found that the rate constants are in the iso-octane > n-heptane > methylcyclohexane order, which is consistent with the inverse C−C bond dissociation energies order. This indicates that our RMD simulations give a reasonable description of the thermal decompositions of normal alkanes, branched alkanes, and cycloalkanes.
3.6 Calculation of endothermic capacity
Heat sink is one of the most important properties of endothermic hydrocarbon fuels, which is also evaluated in the RMD simulations. Figure 12 shows the time evolution of the potential energy of iso-octane at 2800 K. It is clear that the potential energy increases basically with time as the thermal decomposition reactions proceed. We can find that the endothermicity of the cracking reaction is very large, about 10000 kcal mol−1 based on the RMD simulations, indicating that iso-octane has satisfactory heat absorption capacity. However, due to the lack of related experimental data for comparison, it is challenging to explain this phenomenon in detail.