A skeletal n-butane mechanism with integrated simplification method

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Journal of the Energy Institute journal homepage: www.journals.elsevier.com/journal-of-the-energy-institute

A skeletal n-butane mechanism with integrated simplification method Q5 Q1

Fan Li a, b, Haolin Yang b, c, d, *, Liqiao Jiang b, c, d, Jiepeng Huo b, c, d, e, Xiaohan Wang b, c, d, Daiqing Zhao b, c, d, ** a

College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou, 510640, China c Key Laboratory of Renewable Energy, Chinese Academy of Sciences, Guangzhou, 510640, China d Guangdong Provincial Key Laboratory of New and Renewable Energy Research and Development, Guangzhou, 510640, China e University of Chinese Academy of Sciences, Beijing, 100049, China b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 25 August 2019 Received in revised form 19 January 2020 Accepted 20 January 2020 Available online xxx

A new skeletal mechanism of n-butane is developed for describing its ignition and combustion characteristics applicable over a wide range of conditions: initial temperature 690e1430 K, pressure 1 e30 atm, and equivalence ratio 0.5e2.0. Starting with a detailed chemical reaction kinetic model of 230 species and 1328 reactions (Healy et al., Combust. Flame, 2010), the directed relation graph method is applied as the first step to derive a semi-detailed mechanism with 134 species. Then, the reaction path analysis in conjunction with temperature sensitivity analysis is used to remove the redundant species and reaction paths simultaneously under the condition of low-temperature and moderate-to-high temperatures, respectively. Finally, a skeletal n-butane mechanism consisting of 86 species and 373 reactions can be obtained. Mechanism validation indicates that the new developed skeletal mechanism is in good agreement with the detailed mechanism in predicting the global ignition and combustion characteristics. The new skeletal mechanism is further validated using extensive available literature data including rapid pressure machine ignition delay time, shock-tube ignition delay time, laminar flame speed, and jet-stirred reaction oxidation, covering a large range of temperatures, pressures, and equivalence ratios. The comparison results demonstrate that a satisfactory agreement between predictions and experimental measurements is achieved. © 2020 Energy Institute. Published by Elsevier Ltd. All rights reserved.

Keywords: n-Butane fuel Skeletal mechanism Directed relation graph method Reaction path analysis Sensitivity analysis

1. Introduction n-Butane fuel, one of the major components of liquefied petroleum gas [1,2], is a gaseous alkane with the longest carbon chain under normal pressure and temperature conditions. Besides, the combustion chemistry of n-butane is important to understand higher-order hydrocarbon oxidation. However, the autoignition, flashback, blow off, and combustion instability of n-butane hinder its application in many practical engines [3e5]. Thus, deep insights into the ignition and combustion characteristics of n-butane must be obtained to optimize the system design and facilitate the

Q2

* Corresponding author. Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, 2 Nengyuan Road, Guangzhou, 510640, China. ** Corresponding author. Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, 2 Nengyuan Road, Guangzhou, 510640, China. E-mail addresses: [email protected] (H. Yang), [email protected] (D. Zhao).

combustion efficiency. Many autoignition studies on n-butane have been conducted using a variety of devices such as closed vessels [6e8], rapid compression machines (RCMs) [9e11], and shock tubes (STs) [12e14]. Meanwhile, the corresponding oxidation and combustion characteristics of n-butane have been studied in flow reactors [15e17], plane furnaces [18], constant volume combustion bombs (CVCBs) [19e24], jet-stirred reactors (JSRs) [25,26], and homogeneous charge compression ignition (HCCI) engines [27e29]. These experimental cases have covered a wide range of operating conditions for gas turbines and internal-combustion engines. On the basis of these data, many chemical kinetic mechanisms of n-butane oxidation in the atmosphere of air or other oxygen/inert mixtures have been proposed. In general, high-temperature chemistry is the most important for describing flame propagation when the flame temperature approaches the adiabatic combustion temperature. Marinov et al. [30] published a chemical kinetic model involving 156 species and 680

https://doi.org/10.1016/j.joei.2020.01.018 1743-9671/© 2020 Energy Institute. Published by Elsevier Ltd. All rights reserved.

Please cite this article as: F. Li et al., A skeletal n-butane mechanism with integrated simplification method, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2020.01.018

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reactions to provide an insight into the formation mechanism of aromatic and polycyclic aromatic hydrocarbons in premixed laminar n-butane flames. Ranzi et al. [31] hierarchically assessed the previous laminar flame speeds of C1eC4 alkanes/air mixtures with a comprehensive high-temperature pyrolysis and combustion model and subsequently identified certain aspects in the mechanism that need further revisions. In order to investigate the effects of pressure and fuel structure on the moderate-to-high temperature pyrolysis and combustion chemistry of n-butane and i-butane, Li et al. [32] recently constructed a pyrolysis and combustion kinetic model for the two isomers of butane consisting of 148 species and 1174 reactions. Compared to high-temperature chemical reactions, lowtemperature chemical reactions involve more complicated chemical-kinetic mechanisms, including two-stage ignition, negative-temperature coefficient (NTC) region, cool flame and etc. Kojima [33] at an earlier period developed a detailed reaction mechanism of n-butane involving 141 species and 461 reactions, which was validated against a set of RCM experiments in a lowtemperature range of 720e830 K. Warth et al. [34] generated an n-butane oxidation mechanism including 168 species and 797 reactions through computer-aided formulation in the lowtemperature NTC region. Strelkova et al. [35] reported a skeletal mechanism with 54 species and 94 reactions for low-temperature ignition at 500e800 K of n-butane/air mixtures, which could cover practically important ranges of pressure, temperature and equivalence ratio, especially in the low-temperature condition. However, the applicable ranges for the above-mentioned different mechanisms are relatively limited, never including both low- and high-temperature conditions. Based on the previous work of Curran et al. [36], Healy et al. [37] constructed a comprehensive reaction mechanism of 230 species and 1328 reactions and validated it through extensive experiments in RCMs and STs over a wide applicable range of conditions. Recently, this mechanism was further developed by extending the combustion model of 1,3butadiene (Aramco Mech 3.0) [38]. Actually, the detailed mechanisms need a substantial amount of computation resources in the employment of large-scale numerical simulations, even though the available computational power is growing rapidly. Consequently, small and simplified mechanisms with less stiffness are urgently needed. Motivated by this intention, the present work is to develop a skeletal mechanism for n-butane ignition and combustion based on the recognized kinetic model of n-butane reported by Healy et al. [37] using an integrated reduction method consisting of directed relation graph (DRG), reaction path analysis (RPA), and sensitivity analysis (SA). Extensive validations against the available literature data in the RCM, ST, CVCB, and JSR are also performed for the new skeletal mechanism. 2. Combined simplification method As reviewed by Lu et al. [39], mechanism simplification has been widely studied and a large number of new reduction methodologies have been proposed. In this study, an integrated reduction method consisting of DRG, RPA, and SA is employed to produce a skeletal n-butane mechanism. DRG (directed relation graph): The DRG method developed by Lu and Law [40] is commonly applied as the first step to automatically reduce large kinetic mechanisms. In this method, the coupling patterns between various species are represented by a directed graph, in which each vertex denotes a species in the detailed mechanism. A correlation coefficient is established to determine and retain the crucial components and directly remove the reactions corresponding to those unimportant components. In the DRG method, the mathematical algorithm of the normalized

contribution of species B to the production rate of species A (rAB ) can be expressed using the following equation:

P i¼1;N

rAB ¼ P

  nA;i ui dN  B   nA;i ui 

(1)

i¼1;N

where is nA;i and ui are the coefficient of species A and the reaction rate of the ith reaction, respectively; and N is the total reaction quantity. Besides, dN B ¼ 1 if species B participates in certain reN actions, and otherwise dB ¼ 0. $ RPA (reaction path analysis): The RPA method [41e43] is employed for further reduction. In this method, all the elementary reactions in which n-butane participates and these net reaction rates are extracted. Herein, the means of time-integrated production rate indicators are employed to derive the global information. For these extracted reactions, those with relatively higher contribution rates to the production or consumption of n-butane are retained, whereas those with lower contribution rates are removed. The normalized production and consumption contributions for gasphase reactions are determined using the following equations: p r ij

  max nij ; 0 qj ¼ M   P max nij ; 0 qj

(2)

  min nij ; 0 qj M   P min nij ; 0 qj

(3)

j¼1

r dij ¼

j¼1

where r pij and r dij are the value of the production and consumption contributions, respectively; nij is the stoichiometric coefficient of the ith species in the jth reaction; qj is the rate of the jth reaction; and M is the total reaction number. Certain reaction with the greater absolute value means that it has a higher contribution for the product generation/consumption. As a result, the crucial reaction paths and intermediate species are retained and then served as new nodes for subsequent analysis, which progresses downstream of the whole reaction until CO2 (carbon dioxide) formation. Lastly, the entire skeletal oxidation path of n-butane is outlined. $ SA (sensitivity analysis): Temperature sensitivity analysis is usually performed to remove or persist the seemingly unimportant species with a low contribution rate and to reduce the deviation in comparison, so as to prefect the skeletal mechanism. Employing the Jacobi matrix method, this analysis mainly accounts for the effects of temperature interference on the reaction rate of n-butane oxidation. With temperature sensitivity analysis, a series of dominant reactions controlling the oxidation process under different working conditions are explored in detail. The normalized matrix of the local sensitivity coefficient (s) is defined as:

kj vci s¼ ci vkj

!

vlnci ¼ vlnkj

! (4)

where kj is the jth reaction rate constant; ci is the concentration of  the ith species; and vci vk is the sensitivity coefficient of the ith j

species concentration to the jth reaction rate constant. It is well known that positive sensitivity coefficients denote a promoting effect, by which the whole system temperature can significantly increase when the consumption rate of relevant reactants is developed by accelerating the corresponding reaction, thereby, and vice versa.

Please cite this article as: F. Li et al., A skeletal n-butane mechanism with integrated simplification method, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2020.01.018

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3. Mechanism simplification 3.1. DRG method reduction The detailed chemical kinetic mechanism of n-butane developed by Healy et al. [37] is employed as the starting mechanism for simplification. The Zero-dimension Closed Homogeneous Reactor module in CHEMKIN-PRO [44] is employed in the DRG method to simulate the ignition delay time, which is defined as the time at which the OH mole fraction reaches its peak value. The important components of O2, N2, H2O, CO2, and C4H10 are set as target species. Simplification is performed under various conditions of initial temperatures (T ¼ 700e1400 K), pressures (P ¼ 1, 10, 20, and 30 atm) and equivalence ratios (4 ¼ 0.5, 1.0, and 2.0). Each data point (96 points in total) represents different physical status, and the calculated results serve as the basis of subsequent analyses. By setting different threshold values of 0.25, 0.30, 0.35, and 0.40, four different semi-detailed mechanisms are derived and compared, as shown in Table 1. The results show that the 134-species mechanism can satisfactorily predict the ignition delay times with an acceptable average error (ε ¼ jtdetailed  tskeletal j=tdetailed ) less than 10%, wherein tdetailed and tskeletal denote the ignition delay times calculated by the detailed and skeletal mechanisms, respectively. Therefore, the obtained 134-species mechanism is used for further reduction. 3.2. RPA method reduction Prior to the skeletal mechanism construction, the distinctive ignition behavior of n-butane under a wide range of temperatures should be understood. Fig. 1 shows the temperature-dependence of ignition delay time of n-butane/air mixture oxidation at P ¼ 30 atm and 4 ¼ 0.5e2.0. All ignition delay time-temperature curves can be divided into four stages, i.e., low-temperature, NTC (negativetemperature coefficient), moderate-temperature, and hightemperature stages. In contrast to the other three stages, the ignition delay time in the NTC stage is prolonged with increasing temperature. Additionally, it is noted that the equivalence ratio has a significant effect on the ignition delay time in the NTC and moderate-temperature stages. Therefore, important species and reactions under different conditions are identified independently owing to different reaction pathways. In this study, path analysis diagrams of stoichiometric n-butane/air mixture oxidation are investigated during ignition stages under low- and moderate-tohigh temperature ranges respectively at P ¼ 10 atm through the rate of production (ROP) analysis. The timing at which 20% nbutane consumed is selected to finish the integration of ROP, which refers to the work of Black et al. [45]. At low-temperature temperatures of 600e900 K, the oxidation process is composed of the chain-propagation, chain-branching and chain-termination reactions. The interactions among such three paths play a decisive role in low-temperature combustion dynamic. The oxidation behaviors are briefly discussed as follows, as shown in Fig. 2. (1) First, H-atom abstraction reactions involving the active radicals of H, O, OH, CH3, and HO2 are the dominant paths

Fig. 1. Relationship between ignition delay time and initial temperature for n-butane oxidation at P ¼ 30 atm and 4 ¼ 0.5e2.0.

for consuming n-C4H10 to form n-butyl (PC4H9) and sec-butyl (SC4H9), denoted as R, which leads to the initiation of chainbranching reactions. Among them, the reactions involving H atom are the most crucial, followed by those involving OH radical and O2. (2) Then, a small fraction of butyl radicals decomposes to small molecules by b-scission, whereas most of the butyl reacts with O2 to generate butyl peroxy radicals (PC4H9O2 and SC4H9O2, denoted as RO2). (3) Followed by isomerization reaction, RO2 further forms six butyl hydroperoxide radicals (QOOH) mainly through six- or seven-membered ring transition states [35]. Simultaneously, a few amounts of PC4H9O2H and SC4H9O2H (ROOH), and butylene (C4H81 and C4H8-2) are generated through the bimolecular and elimination reactions of RO2, respectively. As the important intermediates, the butylene and other olefins continuously react with OH radicals, greatly increasing the reactive radical concentrations in the reaction pool. These essential chain propagation paths are retained to accurately reproduce the low-temperature oxidation of n-butane. (4) Part of QOOH is either consumed to form cyclic ether, butylene, HO2, and OH radical through chain branching and termination reactions or decomposed into ethylene and ethanol. The remaining substantial number of QOOH form six hydroperoxylbutyl peroxy isomers (QOOHO2) by the second O2 addition reaction. (5) Subsequently, the second internal isomerization of QOOHO2 undergoes quickly and generates keto hydroperoxide (NC4KET). (6) Finally, the decomposition of NC4KET results in the production of second OH radical and numerous C1eC2 molecules. The formed OH radical, as the most important chemically reactive species during oxidation, can promote ignition by capturing H atoms from n-C4H10 with the production of H2O and H2O2 through an established lowtemperature exothermic cycle (see the red dash lines in Fig. 2). The initial temperature has significant effects on the consumption of R (butyl) and RO2 (butyl peroxy) radicals through different reactions during the low-temperature oxidation, as shown in Fig. 3. The consumption is calculated by integrating the consumed species from the beginning of calculation to the time corresponding to 20%

Table 1 The correlation results of four different schemes in DRG method reduction. Threshold value

Species

Reactions

Percentage reduction of species

Percentage reduction of reactions

Average error

0.25 0.30 0.35 0.40

144 134 122 108

807 750 655 560

37.4% 41.7% 46.9% 53.0%

39.2% 43.5% 50.7% 57.8%

7.9% 8.8% 12.3% 31.6%

Please cite this article as: F. Li et al., A skeletal n-butane mechanism with integrated simplification method, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2020.01.018

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Fig. 2. Schematic of reaction paths during the low-temperature oxidation of n-butane at P ¼ 10 atm and T ¼ 600, 700, 800, and 900 K.

Fig. 3. Influence of initial temperature on percentage contributions of (a) R and (b) RO2 consumption by major reaction paths at 600e900 K based on the accumulated consumption from t ¼ 0 s to the time of 20% n-butane conversion (R1: PC4H9 þ O2 ¼ PC4H9O2, SC4H9 þ O2 ¼ SC4H9O2; R2: PC4H9 ¼ C2H5 þ C2H4; R3: SC4H9 ¼ C3H6 þ CH3; R4: PC4H9O2/SC4H9O2 / QOOH; R5: PC4H9O2 ¼ C4H8-1 þ HO2, SC4H9O2 ¼ C4H8-2 þ HO2; and R6: PC4H9O2/SC4H9O2 / ROOH).

n-butane conversion. When the temperature increases from 600 K to 900 K, the R1 path (PC4H9 þ O2 ¼ PC4H9O2 and SC4H9 þ O2 ¼ SC4H9O2) is significantly suppressed in the R consumption, from 100% at 600 K to less than 55% at 900 K, whereas the percentages of R2 (PC4H9 ¼ C2H5 þ C2H4) and R3 (SC4H9 ¼ C3H6 þ CH3) paths increase greatly. Notably, both the R2 and R3 paths participate in the competition with the R1 path. For RO2 consumption, the paths of R4 (PC4H9O2 / QOOH and SC4H9O2 / QOOH) and R6 (PC4H9O2 / ROOH and SC4H9O2 / ROOH) decrease rapidly with increasing

temperature from 600 K to 800 K as the competition from R5 path (PC4H9O2 ¼ C4H8-1 þ HO2 and SC4H9O2 ¼ C4H8-2 þ HO2) increases. However, it should be pointed out that higher temperatures can cause the R þ O2 # RO2 equilibrium to shift toward the reactant side. As a result, the production of RO2 and QOOH effectively ceases, whereas the energetically excited RO2 radical at low to moderate temperatures, either decomposes to alkene þ HO2 or returns back to R þ O2, causing the ignition delay time to increase. Such discussed competitive mechanism can qualitatively explain the

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phenomenon that the ignition delay appears to prolong reversely as the temperature increases in the NTC regime [46]. The same methodology is adopted to select important intermediate species for the moderate-to-high temperature reactions of n-butane. Further increasing the temperature, as shown in Fig. 4, the low-temperature chain reactions involving oxygenation, isomerization, and cracking of some large molecules are almost stopped. Conversely, the decomposition of n-C4H10 as well as its downstream products become important. The butyl formed by dehydrogenation undergoes cracking reaction to form olefins and alkyl groups. C4H8-1 and C4H8-2 are rapidly decomposed into small radicals. Simultaneously, the remaining n-C4H10 is directly cracked into some small alkyl groups consisting of NC3H7, C2H5, and CH3 under the action of a third body at elevated temperatures. Then, the formed NC3H7 is gradually cracked into C2H4 and C3H6, especially at 1200 K. The rapid pyrolysis of macromolecules accelerates the ignition and combustion of fuel. At 1000 K, path analysis reveals that a small portion of NC3H7 successively experiences a series of chain propagation reactions, consisting of oxidation, internal isomerization, and decomposition, which is still important in the prediction of ignition delay in the moderate temperature range. Consequently, all the important paths displayed in Fig. 4 need to be preserved in the simplification process. In essence, the CeH bond energies are lower than those of CeC, CeO and b-bonds, so CeH bonds are easier to break at low temperatures, which promotes the reaction pathways of dehydrogenation and isomerization. When the temperature reaches a higher value, all the bonds are broken, but CeC, CeO, and b-bonds react faster than CeH bonds, resulting in that the proportion of dehydrogenation paths becomes much lower than that of cracking paths.

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3.3. SA method reduction Fig. 5 presents the temperature sensitivity analyses of the 134species mechanism under a series of working conditions. Each panel in Fig. 5 gives the 16 reactions with the highest sensitivity coefficients, including the temperatures of 600, 700, 800, 1000, and 1400 K; the equivalence ratios of 0.5, 1.0, and 2.0; and the pressures of 10, 20, and 30 atm. As observed in Fig. 5(a), in the low-temperature reactions, the elementary reactions with positive temperature sensitivity coefficient are dehydrogenation of n-C4H10, first internal isomerization of PC4H8O2 and SC4H8O2, second isomerization of QOOHO2, as well as NC4KET decomposition. Meanwhile, the elimination reaction of QOOH competes with its internal isomerization to largely produce non-reactive components HO2, thereby reducing the reaction rate and exhibiting negative sensitivity coefficient. In addition, of the six isomers formed by isomerization of QOOH, three of the most sensitive components, C4H8OOH1-3, C4H8OOH2-3, and C4H8OOH2-4, are preserved along with the corresponding downstream species and reactions in the new skeletal mechanism. Lastly, with regard to the important dehydrogenation reaction at relatively lower temperatures, it can be seen that the reaction C4H10 þ OH ¼ PC4H9 þ H2O2 shows the highest positive temperature sensitivity coefficient, whereas the reaction C4H10 þ OH ¼ SC4H9 þ H2O has the lowest negative one. At high temperatures above 1000 K, the chain-branching reaction of large molecules described above can easily reach the required activation energy, rendering that low-temperature branching channels become increasingly insensitive to temperature. As shown in Fig. 5(b) and (c), the cracking reaction C4H10 (þM) ¼ NC3H7 þ CH3 (þM) starts to demonstrate certain positive

Fig. 4. Schematic of reaction paths during the moderate-to-high temperature oxidation of n-butane at P ¼ 10 atm and T ¼ 1000 and 1200 K.

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considered as the ignition moment [47]. These relevant reactions are all preserved in the skeletal mechanism completely. Eventually, the new skeletal n-butane mechanism consisting of 86 species and 373 reactions (see Supporting Information for details) is obtained. 4. Validation of the skeletal mechanism The new developed 86-species skeletal mechanism of n-butane is validated against the available literature data, including ignition delay times obtained in ST and RCM, laminar burning speeds, and species distribution data measured in JSR, as well as the detailed reaction mechanism of Healy et al. [37]. Table 2 summarizes the numerous fundamental data yielded from the combustion experiments of n-butane in different literatures. 4.1. Validation against ignition delay time

Fig. 5. Temperature sensitivity analyses for n-butane oxidation (top 16 reactions).

temperature sensitivity coefficient, indicating a change in the oxidation path. In addition, this reaction becomes more important with a larger normalized sensitive coefficient when further increasing the temperature to 1400 K. Aside from some dehydrogenation reactions of C4H10, the cracking reactions involving C3eC4 species are consistently important in the moderate-to-high temperature region. The other reactions with significant temperature sensitive coefficients are all related to C1eC2 species. The most sensitive reactions are H2O2 (þM) ¼ OH þ OH (þM) and H þ O2 ¼ O þ OH at 1000 and 1400 K, respectively, i.e., the decomposition of H2O2 and the oxidation of H to produce reactive OH radicals. This rapid growth stage of the OH radical concentration is always

Fig. 6 presents the comparisons of the predicted and measured ignition delay times of n-butane/air mixtures for stoichiometric, rich, and lean conditions at various pressures during low-tomoderate temperature oxidations in RCMs. The Closed Homogeneous Reactor module is used to calculate the ignition delay times. The skeletal mechanism reproduces the ignition delay time of the detailed mechanism in the entire parameter ranges fairly well, although slight overestimation occurs at temperatures greater than 850 K due to the removal of many isomers of certain retained components related to the low-temperature ignition process. These removed species have limited contribution to n-butane oxidation in such case, but they collectively account for a nontrivial portion in the detailed mechanism. Overall, the agreement between simulations and experiments [9,11,37] is quite good, and the characteristics in NTC region exhibited in experiments are satisfactorily captured by the present mechanisms. With the increase in pressure, the gradually weakened NTC effect shows the flattening trend of the ignition delay variations, and the boundary of whole NTC region moves toward higher temperature and becomes narrower. On the other hand, the predicted ignition delay times with the skeletal mechanism are approximately twice as slow as those of the experiments from Gerson et al. [48] at 30 atm and in the temperature range of 700e1000 K, but faster than those of Griffiths et al. [11] at 10 atm below 800 K. Comparisons between abundant RCM data must be performed with caution because the whole RCM measurement encompasses a low-temperature region with a long ignition time, causing a large amount of heat loss. As discussed by Würmel et al. [49] in detail, there is significant difference in heat losses caused by different facilities or inert diluted gases during experiments, which is difficult to avoid even in the same facility. The simulation methods in this study have not considered the effects of heat loss, thereby leading to large deviations for some circumstances. Furthermore, for the high-temperature oxidation, the predicted ignition delay time of both skeletal and detailed mechanisms agrees well with the experimental data [37], as shown in Fig. 7. The extensive experimental data [37] were obtained from ST tests at the equivalence ratios of 0.5, 1.0, and 2.0, and a series of pressures in the temperature range of 1000e1430 K. 4.2. Validation against laminar flame speed Fig. 8 shows the experimental and simulated laminar flame speeds of the n-butane/air mixture at T ¼ 300 K and P ¼ 1 atm. Numerical simulations are performed using the Premixed Laminar Flame Speed Calculation module, taking into account the Soret effect and averaged-mixture transport. The new skeletal mechanism satisfactorily predicts the laminar flame speed as a function of

Please cite this article as: F. Li et al., A skeletal n-butane mechanism with integrated simplification method, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2020.01.018

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Table 2 A list of experiment data of n-butane used to validate the skeletal mechanism. Experiment type

Ignition delay time

Laminar flame speed

Component distribution

Measurement method

RCM RCM RCM RCM ST Counterflow Counterflow Spherical flame Flat burner Spherical flame Spherical flame Spherical flame Spherical flame JSR oxidation JSR oxidation

Experimental condition Temperature

Pressure

Equivalence ratio

700e900 K 600e950 K 690e1000 K 660e1010 K 1000e1430 K 298 K 298 K 298 K 298 K 298 K 298 K 300 K 400 K 550e950 K 1050e1250 K

9e11 bar 10 atm 10e30 atm 14e36 bar 1e30 atm 1 atm 1 atm 1 atm 1 atm 1 atm 1e10 atm 1e7 atm 1e10 bar 1 atm 1 atm

0.8, 1.2 1 0.5e2 0.5, 1.0 0.5e2 0.6e1.8 0.7e1.7 0.7e1.9 0.6e1.5 0.6e1.9 0.7e1.7 1 1 1 1

Authors

Ref.

Minetti et al. (1994) Griffith et al. (1993) Healy et al. (2010) Gersen et al. (2010) Healy et al. (2010) Davis et al. (1998) Hirasawa et al. (2002) Kelly et al. (2009) Bosschaart et al. (2004) Tang et al. (2011) Li et al. (2018) Wu et al. (2014) Marshall et al. (2010) Bahrini et al. (2013) Dagaut et al. (2000)

[9] [11] [37] [48] [37] [50] [51] [19] [52] [20] [32] [22] [24] [53] [26]

Fig. 6. Comparison of ignition delay times between simulation and experiment at T ¼ 690e1000 K and P ¼ 10e30 atm for (a) 4 ¼ 0.5; (b) 4 ¼ 1.0; (c) 4 ¼ 2.0. Dash lines are the new skeletal mechanism predications, solid lines are the detailed mechanism of Healy et al. [37] predications, and symbols are experimental data measured in RCMs available in the literatures [9,11,37,48].

equivalence ratio with a maximum deviation of 6% compared with the detailed mechanism. This is because the C0eC2 core mechanism, as the rate determining step of n-butane combustion at high temperature conditions, is retained completely in the new skeletal mechanism. The skeletal mechanism successfully reproduces the experimental data of Davis et al. [50] and Hirasawa et al. [51] at the all tested equivalence ratios. Nevertheless, when the equivalence ratio is 0.8e1.2, the simulation results show slightly higher than those experimental data from Kelly et al. [19], Bosscharrt et al. [52], and Tang et al. [20]. The visible deviation between different

experimental results may be caused by the various systematic errors existing in the combustion apparatuses as well as measurement method in the tests. In addition, the laminar flame speeds of the n-butane/air mixture at some high-pressure situations simulated with the skeletal and detailed mechanisms are also compared with the experimental data from literatures [22,24,32], as shown in Fig. 9. The experimental results of Li et al. [32] were measured at T ¼ 298 K and P ¼ 2, 5 and 10 atm at various equivalence ratios in spherical combustion vessels. Also, Wu et al. [22] reported the experiment

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Fig. 7. Comparison of ignition delay times between simulation and experiment at T ¼ 1000e1430 K and P ¼ 2e30 atm for (a) 4 ¼ 0.5; (b) 4 ¼ 1.0; (c) 4 ¼ 2.0. Dash lines are the new skeletal mechanism predications, solid lines are the detailed mechanism of Healy et al. [37] predications, and symbols are experimental data measured in ST by Healy et al. [37].

the experimental data from Li et al.’s work [32], the mechanism can predict the laminar flame speed very well at P ¼ 5 and 10 atm. However, at the low pressure of 2 atm and equivalence ratios of 0.6e1.2, the mechanisms will over-predict the laminar flame speed up to 13% than those of Li et al. [32], which is still satisfactory within the range of experimental uncertainties. Similarly, the deviations between the measured and simulated results in Fig. 9(b) are acceptable taking into account the actual measurement uncertainty. 4.3. Validation against JSR oxidation

Fig. 8. Laminar flame speed comparison at various equivalence ratios at T ¼ 298 K and P ¼ 1 atm. Dash lines are the new skeletal mechanism predications, solid lines are the detailed mechanism of Healy et al. [37] predications, and symbols are experimental data from literatures [19,20,50e52].

data for pressure up to 7 atm at T ¼ 300 K and 4 ¼ 1.0, and Marshall et al. [24] for pressure up to 10 atm at T ¼ 400 K and 4 ¼ 1.0. Overall, although showing slight overestimation in most conditions, the new skeletal mechanism well reproduces the laminar flame speeds and their dependence on equivalence ratio in high-pressure range predicated by the detailed mechanism [37]. When compared with

Fig. 10 illustrates the predicted mole fraction profiles of n-C4H10, O2, CO, and CH3CHO as a function of temperature with the skeletal and detailed mechanisms, together with the experimental data of Bahrini et al. [53] in a JSR at atmospheric pressure, 550e950 K, residence time of 6 s, and equivalence ratio of 1.0 where n-butane is highly diluted with helium gas (n-C4H10/O2/He of 0.023/0.15/ 0.827). The numerical work is conducted with the Perfectly Stirred Reactor module. In consideration that the applicable temperature range of the detailed mechanism does not cover 550e690 K, the data measured in such conditions are not compared and provided here. Over the entire temperature range, the maximum deviation between the mole fractions obtained by the skeletal and detailed mechanisms is around 15%, because in the low-temperature region, the reactant consumption and product generation are sensitive to the selected chemical models. Clearly, the mechanisms satisfactorily capture the characteristics of NTC occurring between 700 K and 800 K, i.e., the decreases of the consumption rates of n-C4H10 and O2 and the generation rates of CO and CH3CHO, which is in good

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Fig. 9. Laminar flame speed comparison at various equivalence ratios (a) at T ¼ 298 K and P ¼ 2, 5 and 10 atm; and (b) at various pressures at 4 ¼ 1.0 and T ¼ 300, 400 K. Dash lines are the new skeletal mechanism predications, solid lines are the detailed mechanism of Healy et al. [37] predications, and symbols are experimental data from literatures [22,24,32].

Fig. 10. Experimental (symbols) [53] and simulated (solid lines, detailed mechanism [37]; dash lines, skeletal mechanism) results of component mole fraction profiles of n-butane oxidation (n-C4H10/O2/He of 0.023/0.15/0.827) in JSR at residence time of 6 s, P ¼ 1 atm, and 4 ¼ 1.0 under the temperature range of 550e950 K.

agreement with the experimental results of Bahrini et al. [53]. In addition, the mechanisms greatly overestimate the consumption rates of n-C4H10 and O2 and the generation rate of CO when the temperature is higher than 800 K. In order to further improve the accuracy of mechanism prediction, Prince et al. [54] particularly adjusted the set of product species from the ketohydroperoxide decomposition in C4 mechanism, especially NC3H7 resulting in a new reaction OC4H7OOH ¼ OH þ NC3H7 þCO2, because the introduction of NC3H7 in low-temperature oxidation paths can reduce the n-butane reactivity under atmospheric pressure conditions, but without significant changes in predicting ignition delay at higher pressures. However, it should be noted that all the original parameters in the detailed mechanism [37] are kept intact in this study. Furthermore, the concentration profiles of ten major components at the high temperature range of 1050e1250 K from Dagaut et al. [26] are compared with the simulated results by the detailed mechanism [37] and the proposed skeletal mechanism, as shown in Fig. 11. The experimental conditions include 0.22% n-C4H10/O2/N2 at

1 atm, residual time of 0.16 s, and equivalence ratio of 1.0. The skeletal mechanism reaches an acceptable agreement with the detailed one as capturing the characteristics of species mole fraction profiles. It is apparent that the mechanisms agree very well with the experimental data of CO2 and CH4 mole fractions, while the simulated concentrations of other species are basically in the allowable range of experimental uncertainty. 4.4. Extended validation The new skeletal mechanism is extendedly validated with the detailed mechanism of Healy et al. [37] in terms of species distributions under high pressure conditions, because the essential data on the high-pressure combustion characteristics of n-butane remains limited to date. Fig. 12 shows the computed mole fraction profiles of six important species (C4H10, CH2O, CO, H2O, O2, and OH) and the corresponding temperature variations as a function of time at T ¼ 800, 1100, and 1400 K; P ¼ 10, 20, and 30 atm; and 4 ¼ 0.5, 1.0, and 2.0. All simulations are calculated by using the simple module of

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Fig. 11. Experimental (symbols) [26] and simulated (solid lines, detailed mechanism [37]; dash lines, skeletal mechanism) results of components mole fraction profiles of n-butane oxidation (0.22%n-C4H10/O2/N2) in JSR at residual time of 0.16 s, P ¼ 1 atm, and 4 ¼ 1.0 under the temperature range of 1050e1250 K.

Fig. 12. Concentration distribution of species (C4H10, CH2O, CO, H2O, O2, and OH) and temperature distribution comparisons under high pressures. Dash lines are the new skeletal mechanism predictions, solid lines are the detailed mechanism of Healy et al. [37] predications.

Closed Homogeneous Reactor. The results demonstrate that the present skeletal mechanism can feature good extensibility for the combustion characteristics of n-butane in high-pressure cases.

5. Conclusions A new skeletal reaction mechanism consisting of 86 species and 373 reactions for the ignition and combustion of n-butane is proposed based on the detailed mechanism of Healy et al. [37] and validated with the data available in different literatures. The new skeletal mechanism is able to reproduce the detailed mechanism with a maximum deviation of less than 10% under the wide range of conditions in which T ¼ 690e1430 K, P ¼ 1e30 atm, and 4 ¼ 0.5e2.0. More importantly, the comparison results confirm that

the current mechanism is practically applicable despite certain slightly large discrepancies observed between the simulation results and partial experiment data under some special conditions, and some noteworthy points are list as below. (1) The skeletal mechanism can satisfactorily follow the same variation trends of ignition delay time throughout the operation rang in different RCM measurements at the temperature below 1000 K, except for some experimental data by Griffiths et al. [11] and Gerson et al. [48] due to the significant discrepancies of heat loss in different RCMs. Moreover, the predicted high-temperature ignition delay data can be in good agreement with the experimental results obtained from STs.

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(2) The skeletal mechanism can successfully reproduce the laminar flame speed measured by Davis et al. [50] and Hirasawa et al. [51] in normal pressure situations. Although it shows a slight overestimation in most conditions when comparing with other reported experimental data, the deviations are acceptable taking into account the actual measurement uncertainty. (3) Comparison with the component distributions in JSRs demonstrates that the skeletal mechanism can satisfactorily capture the NTC characteristics of Bahrini et al. [53] in lowtemperature region and basically agree with the measured data by Dagaut et al. [26] at high temperate conditions. Considering that the Healy's model is mainly developed for ignition delay predication, the deviation of component distribution prediction is acceptable, which could be further improved by optimizing reaction paths and rate constants. Acknowledgements Q4

This research is supported by the National Natural Science Foundation of China (No. 51006109, No.51336010) and National Basic Research Program of China (973 program, No. 2014CB239601).

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