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Feb 11, 2017 - College of Automotive Engineering, Chongqing University, ... proposed. The present model is derived from an original model of Yasunaga ...
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Improved Kinetic Mechanism for Diethyl Ether Oxidation with a Reduced Model Zhigang Tang,*,† Li Zhang,† Xi Chen,† and Gangzhi Tang‡ †

College of Automotive Engineering, Chongqing University, Chongqing 400044, People’s Republic of China College of Mechatronics & Vehicle Engineering, Chongqing Jiaotong University, Chongqing 400074, People’s Republic of China

‡

S Supporting Information *

ABSTRACT: An improved diethyl ether (DEE) reaction mechanism consisting of 174 species and 973 reactions has been proposed. The present model is derived from an original model of Yasunaga et al. [Yasunaga, K.; Gillespie, F.; Simmie, J. M.; Curran, H. J.; Kuraguchi, Y.; Hoshikawa, H.; Yamane, M.; Hidaka, Y. A multiple shock tube and chemical kinetic modeling study of diethyl ether pyrolysis and oxidation. J. Phys. Chem. A 2010, 114 (34), 9098−9109, DOI: 10.1021/jp104070a]. On the basis of shock tube results in the temperature range of 900−1900 K, pressure range of 1−40 bar, and equivalence ratios of 0.5−2 as well as rapid compression machine (RCM) measurements of a stoichiometric DEE/O2/inert gas mixture at temperatures of 500−900 K and pressures of 3−4 bar, the ignition delay times (IDTs) were validated. Two-stage ignition at temperatures below 650 K and negative temperature coefficient (NTC) behavior at temperatures between 621 and 746 K are observed. In addition, the freely propagating flame velocities of a stoichiometric DEE/air mixture were validated at various temperatures as well. Using directed relation graph (DRG)-based methods for the improved mechanism reduction, a reduced mechanism composed of 80 species and 329 reactions has been achieved. Calculations for IDTs, laminar flame velocities, and temperature and species profiles using the reduced mechanism show very close agreement with those obtained using the improved mechanism. Meanwhile, sensitivity analyses of the burning velocity and IDT for the improved and reduced mechanisms were performed. Competing reactions related to DEE + OH and consumption of C2H5OC2H4s and HO2 were identified as being important for IDTs at various temperatures. operation with lower emissions.8 Paul et al. investigated the effect of DEE and ethanol on performance, combustion, and emission of a single-cylinder compression-ignition (CI) engine. Their findings show that diesel fuel blended with 10% DEE and 10% ethanol can produce optimum performance emission characteristics.9 Other explorations were also conducted, such as expecting to improve their respective combustion and emission performance by adding DEE in biodiesel, tire pyrolysis oil, waste plastic pyrolysis oil, and emulsified fuel.10−15 Besides, DEE is used as fuel alone in miniature HCCI and diesel engines as well.16−18 Constructing a wide range of applicable reaction mechanisms of DEE to understand its combustion behavior is therefore of high practical interest. Waddington studied the gaseous oxidation of DEE in the low-temperature region in detail and discussed the principal products generated during the induction period.19 Griffiths and Inomata investigated the oscillatory cool flames of DEE/air in a jet-stirred flow reactor and developed a mechanism with 92 reactions.20 Yasunaga et al.21 assembled a detailed DEE chemical kinetic model with 148 species and 751 reactions (the following is called the original mechanism), which kept generally good agreement with the experiments at pressures from 1 to 3.5 bar and temperatures from 900 to 1900 K. However, the original mechanism is unable to describe the IDTs at pressures above 10 bar.22 To accurately predict the

1. INTRODUCTION As a kind of oxygenated biofuel, diethyl ether (DEE) has drawn much concern as a result of an excessive consumption in oil and fossil fuel and serious atmospheric pollution. It is a clean and renewable alternative fuel and is easily produced by dehydration of ethanol. It has a cetane number of above 125 and a larger lower heating value than that of ethanol.1 Thus, it is considered as an excellent compression ignition fuel.2 Clothier et al. studied the effect of DEE on the ignition delay of a diesel engine under cold-starting conditions.3 They confirmed that diesel fuel doped with DEE lowers the cetane number and lengthens the ignition delay times (IDTs), which has a significant difference in contrast with using DEE alone. This interesting combustion feature is revealed in the study of Rakopoulos et al. as well.4 However, a different finding is presented in the research of Mohanan and Kapilan, whose test results show that a 5% DEE blend gives better performance and low emissions compared to other blends of DEE and diesel fuel.5 DEE can be used as an ignition improver for acetylene in homogeneous charge compression ignition (HCCI) mode. It remarkably reduces nitric oxide and smoke emissions.6 Ethanol mixed with DEE is a prospective alternative fuel. Tomoko et al. discussed the feasibility that solved cold-starting problems of an ethanol-fueled vehicle through on-board catalytic conversion of a portion of the ethanol fuel into DEE. They indicated that a 40−80% ethanol conversion rate was required.7 Nagarajan et al. studied the emission and performance characteristics of neat Ethanol-DEE fueled direct-injection diesel engine. Their results show that ethanol can perform in a similar way to diesel © 2017 American Chemical Society

Received: August 10, 2016 Revised: February 11, 2017 Published: February 28, 2017 2803

DOI: 10.1021/acs.energyfuels.6b02010 Energy Fuels 2017, 31, 2803−2813

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Energy & Fuels Table 1. Relevant Reactions Adjusted and Added for High-Pressure and Low-Temperature Improvementa number R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16 R17 R18 R19 R20 R21 R22 R23 R24 R25 R26 R27 R28 R29 R30 R31 R32 R33 R34 R35 R36 R37 R38 R39 R40 R41 R42 R43 R44 R45 R46

A (cm3 mol s)

reaction

Adjusted Reactions DEE + HO2 = C2H5OC2H4p + H2O2 5.52 × 104 2.208 × 105 DEE + HO2 = C2H5OC2H4s + H2O2 2.948 × 104 1.179 × 105 DEE + OH = C2H5OC2H4p + H2O 9.06 × 10−1 1.766 × 107 DEE + OH = C2H5OC2H4s + H2O 2.26 × 103 3.6 × 105 C2H5OC2H4s = CH3CHO + C2H5 2.86 × 1015 4.923 × 1015 CH3CHO2OC2H5 = C2H5OC2H4s + O2 8.724 × 1020 4.9 × 1018 O2C2H4OC2H5 = HO2C2H4OCHCH3 4.13 × 1010 1.24 × 106 CH3CHO2HOCHCH3 = OH + 2CH3CHO 2.418 × 1014 6.3 × 108 CH3CHO2OC2H5 = CH3CHO2HOCHCH3 4.96 × 1011 4.83 × 106 HO2C2H4OCHO2CH3 = CH3CHO2HOCH2CHO + OH 3.09 × 1010 2.48 × 1010 CH3CHO2HOCHO2CH3 = CH3COOCHO2HCH3 + OH 1.86 × 1011 4.83 × 106 DEE + O2 = C2H5OC2H4s + HO2 5.2 × 1013 2.0 × 1013 HO2C2H4OCHO2CH3 = HO2C2H4OCHCH3 + O2 1.075 × 1021 4.9 × 1018 CH3COOCHO2HCH3 = CH3CHO + CH3CO2 + OH 1.0 × 1015 CH3COOCHO2HCH3 = OH + CH3COOCHOCH3 5.0 × 1016 CH3COOCHO2HCH3 = OH + CH3COOCHOCH3 2.0 × 1016 CH3COOCHOCH3 = CH3CHO + CH3CO2 1.0 × 1011 Supplementary Reactions C2H5OCHO + H = C2H5OCO + H2 2.3 × 106 C2H5OCHO + OH = C2H5OCO + H2O 3.6 × 106 C2H5OCHO + HO2 = C2H5OCO + H2O2 2.24 × 1013 C2H5OCHO + CH3O2 = C2H5OCO + CH3O2H 2.24 × 1013 C2H5OCHO = C2H5O + HCO 5.688 × 1022 C2H5OCO = C2H5O + CO 8.158 × 1018 CH3CHOOC2H5 = C2H5OCHO + CH3 1.0 × 1011 HO2CH2CHOC2H5 = C2H5OC2H3 + HO2 2.13 × 1010 O2C2H4OC2H5 = C2H5OC2H3 + HO2 1.15 × 109 CH3CHO2OC2H5 = C2H5OC2H3 + HO2 1.46 × 1011 CH2CHO2HOC2H5 = CH3CHO2HOCHCH3 2.97 × 104 HO2C2H4OCHCH3 = CYQO16HS + OH 3.97 × 109 CH3CHO2HOCH2CH2 = CYQO16HS + OH 3.68 × 1010 CYQO16HS + OH = H2O + CH3CHO + CH2CHO 3.6 × 105 CYQO16HS + HO2 = H2O2 + CH3CHO + CH2CHO 7.24 × 10−1 CYQO16HS + OH = H2O + C2H4 + CH3CO2 4.25 × 106 CYQO16HS + HO2 = H2O2 + C2H4 + CH3CO2 4.25 × 106 C2H5O + CH3CHO = C2H5OH + CH3CO 1.0 × 1012 CH3CHO2HOCHO2CH3 = CH3CO2HOCHO2HCH3 7.5 × 1011 CH3CO2HOCHO2HCH3 → CH3CHO + CH3CO2 + 2OH 1.0 × 105 CH3CHO + C2H5O2 = CH3CO + C2H5O2H 3.548 × 109 CH3O2H + CH3O = CH3O2 + CH3OH 7.079 × 1011 CH3O2H + CH3O = CH2O2H + CH3OH 7.079 × 1011 C2H6 + C2H4 = C2H5 + C2H5 5.012 × 1011 C2H2 + O2 = HCO + HCO 3.981 × 1012 CH2CO + O = HCO + HCO 1.0 × 1013 HCCO + OH = HCO + HCO 1.0 × 1013 HCCO + O = HCO + CO 3.388 × 1013 CH2 + O = CH + OH 1.905 × 1011 2804

n

Ea (cal mol−1)

reference

2.55 2.55 2.6 2.6 3.65 1.8 2.93 2.3 −0.235 −0.504 −2.0 −0.99 0.0 1.28 0.0 1.3 0.0 1.38 0.0 0.0 0.0 1.38 0.0 0.0 −2.1 −0.99 0.0 0.0 0.0 0.0

1.648 × 104 1.648 × 104 1.391 × 104 1.391 × 104 7.154 × 103 8.55 × 102 4.04 × 103 −1.8 × 103 1.017 × 104 2.335 × 104 3.78 × 104 3.86 × 104 1.676 × 104 1.462 × 104 1.952 × 104 1.409 × 104 1.956 × 104 1.388 × 104 1.746 × 104 1.788 × 104 1.858 × 104 1.388 × 104 4.68 × 104 3.85 × 104 3.818 × 104 3.86 × 104 4.3 × 104 3.9 × 104 3.9 × 104 1.19 × 104

21b 21c 21b 21c 21b 26c 21b 26c 21b 26c 21b 26c 21b 26c 21b 26c 21b 26c 21b 26c 21b 26c 21b 26c 21b 26c 21b 26c 26 26c

2.49 2.0 0.0 0.0 −1.912 −1.775 0.0 0.69 1.060 0.560 2.04 0.730 0.270 2.300 3.980 1.900 1.900 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.7

3.274 × 103 −1.983 × 103 1.684 × 104 1.684 × 104 8.401 × 104 1.525 × 104 1.19 × 104 1.461 × 104 3.128 × 104 2.957 × 104 1.259 × 104 9.378 × 103 1.493 × 104 −1.8 × 103 9.058 × 103 −2.801 × 103 −2.801 × 103 3.577 × 103 1.987 × 104 1.689 × 104 5.05 × 103 4.0 × 103 4.0 × 103 6.0 × 104 2.8 × 104 2.4 × 103 0.0 2.0 × 103 2.5 × 104

26d 26d 26d 26d 26d 26d 26d 25d 25d 25d 25d 25d 25d 25d 25d 25d 25d 20d 20d 20d 27d 27d 27d 27d 27d 27d 27d 27d 27d

DOI: 10.1021/acs.energyfuels.6b02010 Energy Fuels 2017, 31, 2803−2813

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Energy & Fuels Table 1. continued number R47 R48 R49 R50 R51 R52 R53 R54 R55 R56 R57 R58 R59 R60 a

Supplementary Reactions CH2O2H = CH2O + OH 3.981 × 1015 CH3CHO + CH3O = CH3CO + CH3OH 1.148 × 1011 CH3CO3 + CH3O2 → CH3CO2 + CH3O + O2 1.82 × 1012 CH3CO3 + CH3O2 → CH3CO2H + CH2O + O2 3.02 × 1011 CH3CO3 + CH3CO3 → CH3CO2 + CH3CO2 + O2 4.786 × 1012 CH3O2H + OH = CH3O2 + H2O 3.236 × 1013 CH3O2H + OH = CH2O2H + H2O 2.512 × 1013 CH3OH + H = CH3 + H2O 5.248 × 1012 C2H4 + O = CH2O + CH2 2.512 × 1013 CH2CO + OH = CH2O + HCO 2.818 × 1013 CH3O + OH = CH2O + H2O 1.0 × 1012 C2H5 + O = C2H4 + OH 2.5 × 1013 C2H5 + OH = C2H4 + H2O 1.1 × 1013 HO2 + H = H2O + O 3.0 × 1014

Arrhenius equation fitting, k = ATn exp(−Ea/RT). Supplementary reactions.

d

A (cm3 mol s)

reaction

b

n

Ea (cal mol−1)

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

2.3 × 104 1.28 × 103 0.0 0.0 0.0 1.0 × 103 1.0 × 103 5.34 × 103 5.0 × 103 0.0 0.0 6.359 × 103 2.444 × 103 3.974 × 103

reference 27d 27d 27d 27d 27d 27d 27d 27d 27d 27d 28d 28d 28d 28d

Reaction rate constants of the original reaction. cAdjusted reaction rate constants.

adiabatic laminar burning velocities, Gillespie et al. updated the original mechanism with a new C0−C3 sub-mechanism.23 Meanwhile, the low-temperature regime of the original mechanism also needs to be improved.24 Consequently, this study presents a finer DEE chemical kinetic model at low temperature and high pressure on the basis of the mechanism of Yasunaga et al. and provides a dimensionally reduced model.

R38−R60), derived from refs 27 and 28 were supplemented as well. Although the measures mentioned above had been implemented, the performance of the mechanism was not satisfactory in the low-temperature range. The rate of lowtemperature chemistry is largely underestimated in contrast with rapid compression machine (RCM) measurements,22 especially for the first stage of two-stage ignition. Hence, we conducted sensitivity analyses of the two-stage ignition to investigate the corresponding controlling reaction in 530, 630, and 890 K at 3 bar. Reaction R16 was determined as the key reaction toward the first-stage ignition, whose reaction rate constant was estimated on the basis of HO2CH2OCHO = OCH 2 OCHO + OH [reaction R61; k = 2.0 × 10 16 exp(−40500/RT)].26 To better describe the two-stage ignition, we increased the pre-exponential factor of reaction R16 from 2.0 × 1016 to 5.0 × 1016 (reaction R15). The specific methods of IDT sensitivity analysis and two-stage ignition definition were elaborated in the following. The relevant reactions adjusted and added appear in Table 1. Ultimately, an improved DEE reaction mechanism consisting of 174 species and 973 reactions was achieved. To validate the two-stage ignition of the improved mechanism at the low-temperature region, we performed a combination simulation of a closed internal combustion engine (ICE) simulator and a closed homogeneous batch reactor available in CHEMKIN-PRO.29 The combination simulation model was used to simulate the RCM working process. The calculation results of the ICE simulator at the top dead center (TDC) position were considered as the initial conditions of the closed homogeneous batch reactor to simulate the constant volume combustion. Werler et al.22 studied the ignition behavior of DEE at temperatures of 500−1060 K and pressures of 2.5−13 bar in a RCM. To simulate the IDTs under these conditions, we used a similar RCM specification and initial conditions in the ICE simulator (bore, 82 mm; stroke, 78 mm). A speed of 1500 rpm was selected to ensure the same compression time as the RCM. Meanwhile, the Woschni heat loss model30 was used with a wall temperature of 360 K.22 IDT of two-stage ignition was defined from the combustion pressure trace and shown in Figure 1. τ1 and τ2 represented the

2. DEVELOPMENT AND VALIDATION OF THE IMPROVED DEE MECHANISM To strengthen the high-pressure IDT prediction of the original DEE mechanism developed by Yasunaga et al.,21 we drew lessons from the improved method of Werler et al.22 and increased the rate constants of dehydrogenation reactions of DEE at α (R1) and β (R2) C atom positions by HO2 by a factor of 4 while keeping the temperature dependence unchanged, because the two reactions are identified as the highest sensitivity toward IDT at a high pressure. Meanwhile, to accurately predict the laminar flame velocities, we replaced the C0−C3 sub-mechanism of the original mechanism with a new mechanism supported by the Combustion Chemistry Center in the National University of Ireland (NUI) Galway that has an accurate description for pressure-dependent reactions with PLOG format. In addition, to elaborately depict the low-temperature chemistry, we take some adjustments and supplements into account. The rate constants of some low-temperature reactions of DEE and its intermediates were adjusted (reactions R3−R14, where reaction R14 is replaced by reactions R16 and R17). Ethylformate-related reactions (reactions R18−R24) and the unimolecular reactions associated with the ethoxyethylperoxy radical, including C−O bond fission (reaction R25), concerted HO2 elimination (reactions R26 and R27), intramolecular hydrogen rearrangement (reaction R28), and ring-closurerelated reactions (reactions R29−R34), were added, as discussed in ref 25 and 26. The hydrogen abstraction reaction of acetaldehyde (reaction R35) as well as the intramolecular hydrogen shift reaction of the dihydroperoxy radical and its consumption reaction (reactions R36 and R37) was also considered, as described in ref 20. Besides, some lowtemperature reactions about acetaldehyde oxidation (reactions 2805

DOI: 10.1021/acs.energyfuels.6b02010 Energy Fuels 2017, 31, 2803−2813

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conditions. The improved mechanism overestimates the second-stage ignition when the investigated temperature exceeds 800 K at 3 bar. However, it is consistent with the measurements from Sakai et al.26 What makes this difference is that pre-reactions occur for the low-pressure measurements above 800 K in ref 22 as a result of the high initial temperature of the mixture in the mixing vessel, while the tests in ref 26 avoid a higher initial temperature using a higher compression ratio and argon as an inert gas instead. Accordingly, the RCM IDTs of Sakai et al. above 800 K at 3 bar are more reliable. Overall, the improved mechanism can preferably predict the autoignition in the low-temperature region. In contrast, the original mechanism can hardly describe the IDTs at below 900 K. In Figure 3, we investigate the effects of the velocity profile and heat loss on RCM IDT. It indicates that the RCM IDTs

Figure 1. Pressure traces for the stoichiometric 3.38:20.29:76.33 DEE/ O2/N2 mixture at 3 bar and the definition of IDT for two-stage ignition.

first- and second-stage IDTs of two-stage ignition, respectively. The temperature and pressure at the TDC position were used as the effective temperature (Te) and pressure (Pe). At Pe = 3 bar and Te = 579 K, the improved mechanism exhibits an obvious two-stage ignition with τ1 = 17.1 ms and τ2 = 26.8 ms. However, under the same P e , the two-stage ignition phenomenon is not observed and the IDT is longer at Te = 746 K. Therefore, the existence of two-stage ignition and negative temperature coefficient (NTC) behavior was confirmed using the improved mechanism in the simulation model. However, an adequate high temperature could cause the firststage ignition to be too weak to be observed. Given in Figure 2 is a comparison of simulated and measured RCM IDTs. The two-stage ignition phenomenon is reproduced Figure 3. Effects of the velocity profile and heat loss on RCM IDT at 3 bar (3.38:20.29:76.33 DEE/O2/N2 for temperatures above 560 K and 3.38:20.29:38.165:38.165 DEE/O2/N2/CO2 for temperatures below 560 K). Solid line with diamonds, adiabatic RCM IDTs at 1500 revolutions/min; solid line with cycles, constant volume adiabatic IDTs at 1500 revolutions/min; and line without symbols, RCM IDTs including the heat-loss effect at various velocity profiles.

have no significant difference at various velocity profiles, because the different velocity profiles do not cause large differences in heat loss. When the compression is considered as an adiabatic process (solid line with diamonds, 1500 revolutions/min), the RCM IDTs become shorter. In addition, the constant volume adiabatic IDTs were calculated as a reference (solid line with cycles, 1500 revolutions/min). Obviously, the constant volume adiabatic IDTs are much longer than those of the RCM, because the compression process is in favor of the formation of the radical pool and, therefore, shortens the IDTs. Panels a and b of Figure 4 depict the simulated IDTs for various equivalence ratios (ϕ) at 1 and 3.5 bar, respectively. It indicates that the predicted IDTs by the improved mechanism are of slight difference compared to that of the original mechanism. However, it does not deteriorate the consistency with the measurements from ref 21. Shown in Figure 5 is a comparison of IDTs between the simulated results based on the original and improved mechanisms and the measurements by Werler et al.22 for the DEE/O2/Ar mixture at 10, 20, and 40 bar. The original mechanism fails to keep good agreement with the experimental

Figure 2. IDTs for the stoichiometric DEE/O2/inert gas mixtures at 3 and 4 bar (3.38:20.29:76.33 DEE/O2/N2 for temperatures above 560 K and 3.38:20.29:38.165:38.165 DEE/O2/N2/CO2 for temperatures below 560 K). Diamonds and circles, experiment in ref 22; crosses, experiment in ref 26; dotted line, IDTs of the original mechanism; solid lines, IDTs of the improved mechanism for second-stage ignition; and dashed lines, IDTs of the improved mechanism for first-stage ignition.

at temperatures below 650 K using the improved mechanism. The NTC behavior in the temperature range from 621 to 746 K is in agreement with the experimental results as well. However, the simulated results show that both the first- and second-stage ignitions have the NTC behavior, which is observed only in the second stage under the experimental 2806

DOI: 10.1021/acs.energyfuels.6b02010 Energy Fuels 2017, 31, 2803−2813

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Figure 4. Shock-tube IDTs for the DEE/O2/Ar mixture at equivalence ratios of 0.5, 1, and 2: (a) P = 1 bar and (b) P = 3.5 bar. Symbols, experiment in ref 21; solid lines, improved mechanism; and dashed lines, original mechanism.

Figure 6. Adiabatic laminar flame velocities of diethyl ether at various temperatures. Symbols, experiment in ref 23; solid lines, improved mechanism; and dashed lines, original mechanism.

Figure 5. Shock-tube IDTs for the stoichiometric DEE/O2/Ar mixture at 10, 20, and 40 bar. Symbols, experiment in ref 22; solid lines, improved mechanism; and dashed lines, original mechanism.

results, and the higher the pressure, the worse the corresponding prediction of IDTs, especially in the lowtemperature region. In contrast, the improved mechanism fairly well predicts the IDTs at the elevated pressures. Therefore, the improved mechanism has better pressure adaptability. The comparison of laminar flame velocities between the simulated results using the original and improved mechanisms and the measurements from ref 23 at different initial DEE/air mixture temperatures is shown in Figure 6. It indicates that the original mechanism underestimates the measurements and the worst case occurs near the equivalence ratio of 1.1. However, the experimental results are well-predicted by the improved model, and the overall trend in flame velocities is reproduced. The maximum absolute deviation is within 2.5 cm/s. In general, the improved mechanism maintained the hightemperature ignition characteristics of the original mechanism at 900−1900 K, and the autoignition at temperatures below 900 K could also be described, especially the two-stage ignition and NTC behavior. In addition, it well predicted the IDTs from low to high pressure and could reproduce the laminar flame velocities accurately as well. Consequently, the improved mechanism had extensive adaptability.

that are DRG, error-propagation-based DRG (DRGEP), revised DRG (DRGRE), and path flux analysis (PFA).31−34 These reduction methods have different formulas for interaction coefficients (rAB) between species. If the interaction coefficient is smaller than a given threshold value (ε), it means that the effect of species B on species A can be ignored. The reduction efficiencies (η) and errors (δrel) of these methods are not identical, which are respectively defined as η=

Nim − Nrm × 100% Nim

δrel =

|xrm − x im| × 100% x im

(1)

(2)

where Nim and Nrm denote the number of species of the improved and reduced mechanisms, respectively, xim and xrm are the combustion properties calculated by the improved and reduced mechanisms, respectively, which can be the IDTs, laminar flame velocities, adiabatic temperature, etc. In comparison of different reduction methods, it is beneficial to develop a better reduced mechanism. In the reduction process, fuel (DEE), oxidizer (N2 and O2), products (CO2 and H2O), and other interested species (CH3CHO, C2H5OH, CH2O, and CH3OH) were selected as the starting species. The sampling operating conditions were in the equivalence ratio range from 0.4 to 1.6, and the temperature

3. CONSTRUCTION AND VALIDATION OF THE REDUCED MECHANISM For the reduction of the improved mechanism, four kinds of directed relation graph (DRG)-based methods were selected 2807

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for DEE reduction, so that the reduction efficiency is the worst. PFA is developed on the basis of DRG and DRGEP; therefore, it is in favor of the reduction accuracy improved, but it sacrifices the reduction efficiency. Figure 8 exhibits the maximum and average relative errors (δrel) of the IDTs predicted by the resulting mechanisms generated from different reduction methods for DEE/air mixtures at pressures of 1, 10, and 30 bar, ϕ of 0.8, 1, and 1.2, and temperatures from 500 to 1600 K. A comparison between panels a and b of Figure 8 demonstrates that there are three different types of species. The first type of species that is eliminated in the early stage has little effect on the maximum and the average δrel. The second type of species that is removed in the transitional stage has an obvious effect on the maximum δrel but has a relatively weak effect on the average δrel; this characteristic occurs in the number of remaining species of about 60−120. The last type of species that is eliminated in the final stage has a strong effect on both the maximum and average δrel. In the reduction process, the reduction errors increase with the species gradually removed, particularly when the second and third types of species are eliminated. In summary, the reduction errors of the four methods are similar under the same number of remaining species. Further analysis of panels c and d of Figure 8 shows that the maximum δrel exhibits a significant difference against the threshold value because of the different definitions of rAB in the four reduction methods. In some specific threshold values, the maximum δrel presents a steep change, although there is no obvious change in average δrel. For example, the threshold values are 0.1, 0.3, and 0.37 for the DGR method. Consequently, sensitivity analyses were performed to identify the important species that were eliminated in the reduction process for this characteristic. Species C2H5OCHO2HCHO, C2H5OC2H4O2H, and C3H8 were confirmed to have obvious

range between 500 and 1600 K at pressures of 1, 5, 10, 20, and 40 bar. 3.1. Reduced Results and Discussion. Figure 7 describes the number of species contained in the resulting mechanisms

Figure 7. Number of remaining species in the resulting mechanism generated from different reduction methods versus the threshold value.

generated from different reduction methods as a function of the threshold value. It indicates that DRG and DRGEP have advantages in reduction efficiency and η of DRFEP is relatively higher compared to that of DRG under ε below 0.5. However, change occurs when ε exceeds 0.5 with an approximate η; this is due to the different change characteristics of rAB between the two reduction methods.32 In contrast, the reduction efficiencies of DRGRE and PFA are poor. For the DRGRE method, a larger group of isomers tends to result in a smaller value of rAB33 and vice versa. Because the molecular structure of DEE has only four C atoms, its reaction mechanism contains few isomers. Hence, DRGRE cannot give full play to its strengths

Figure 8. Maximum and average relative errors of IDT versus the number of remaining species and threshold value. 2808

DOI: 10.1021/acs.energyfuels.6b02010 Energy Fuels 2017, 31, 2803−2813

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Energy & Fuels Table 2. Reduced Results of Different Reduction Methods method

ε

DRG

0.35

DRGEP

0.1

DRGRE

0.7

PFA

0.67

DRG-CSP

0.5

common remaining species

Nrm

maximum and average δrel of IDTs (%)

different remaining species

C2H3OH, HO2CHO, O2CHO, OCHO, HCCO, HCCOH, HOCH2O, O2C2H4OH, C2H3CHO, C2H3CO, CH3CHCO, C*CC*CCj, C*CC*CC, and C*CC*CCOH 80 24.5/5.9 C2H3OH, HO2CHO, O2CHO, OCHO, HCCO, HCCOH, HOCH2O, O2C2H4OH, CH3CO3, HCOH, C3H8, C3H5s, CH2O2H, CH3CHCO, and HO2CH2CO 87 24.6/7.6 C2H3OH, HO2CHO, O2CHO, OCHO, HCCO, HCCOH, HOCH2O, O2C2H4OH, C2H3CHO, C2H3CO, CH3CHCO, C3H5s, C3H5O, C3H3, C3H2, C3H4a, C3H4p, O2CH2CHO, HO2CH2CO, C*CC*CCj, C*CC*CC, and C*CC*CCOH 79 24.5/7.3 C2H3OH, HCCOH, HOCH2O, O2C2H4OH, CH3CO3, C2H3CHO, C2H3CO, CH3CHCO, C3H3, C3H4a, C*CC*CCj, C*CC*CC, C*CC*CCOH, and C#CC*CCj 80 6.9/3.0 OCHO, HCCO, CH3CO3, CH3CO3H, C3H8, iC3H7, nC3H7, CH3CO2H, C2H4OH, C2H5OCHO, C2H5OCO, C2H5OC2H4O2H, CH3CHO2HOCH2CH2, C2H5OCHO2HCHO, and HO2CH2CHO2OC2H5 H, H2, O, O2, OH, He, H2O, N2, HO2, H2O2, Ar, CO, CO2, CH2O, HCO, HOCHO, CH3OH, CH2OH, CH3O, CH3O2H, CH3O2, CH4, CH3, CH2, CH2(s), C2H6, C2H5, C2H4, C2H3, C2H2, CH3CHO, CH3CO, CH2CHO, CH2CO, CH3CO2, C2H5OH, C2H5O, pC2H4OH, sC2H4OH, C2H5O2, C2H5O2H, C2H3O1−2, C2H4O1−2, C2H5OC2H5, C2H5OC2H4p, C2H5OC2H4s, C2H5OC2H4O, HO2CH2CHOC2H5, CH3CHOOC2H5, CH3CHO2OC2H5, CH3CHO2HOCHCH3, O2C2H4OC2H5, HO2C2H4OCHCH3, HO2C2H4OCHO2CH3, C2H5OC2H3, CH3CHO2HOCHO2CH3, CH3COOCHO2HCH3, CH3COOCHOCH3, CH3CHO2HOCH2CHO, C2H5OCH2, HO2CH2CHO, CHOCH2O, C3H5a, C3H6, and CyQO16hs 79

24.6/7.6

influence on IDTs. Thus, we retained these species as the starting species, and the improved mechanism was re-reduced by the DRG method; a new mechanism was achieved with 80 species and 477 reactions. To further reduce the dimension of this new mechanism, we selected the computational singular perturbation (CSP) method to remove the unimportant reactions.35 Ultimately, a reduced mechanism with only 329 reactions was obtained. Table 2 lists the reduced results derived from different reduction methods. It shows that the maximum δrel of IDTs on the final reduced mechanism is kept at a low level. 3.2. Validation of the Reduced Mechanism. Figure 9 shows the relative error of IDTs predicted by the reduced Figure 10. Comparison of two-stage ignition between the improved and reduced mechanisms.

the reduced mechanism are basically consistent with those of the improved mechanism. Figure 11 shows the laminar flame velocities calculated by the reduced mechanism at different initial mixture temperatures. It indicates that the curves of the reduced mechanism are close to those of the improved mechanism, with a maximum absolute error of less than 2 cm/s. Thus, the reduced mechanism could well predict the laminar flame velocities. Figure 9. Relative error of IDTs predicted by the reduced mechanisms for DEE/air mixtures.

mechanism. It manifests that the reduction error is more sensitive to pressure than the equivalence ratio when the temperature is below 940 K. When the temperature is above 940 K, in addition to pressure, the influence of the equivalent ratio is also quite obvious for the reduction error. However, the reduction error of the reduced mechanism is relatively small within 7%. To further investigate the ignition characteristic of the reduced mechanism, we also validated the two-stage ignition using the RCM simulation model. Figure 10 presents the comparison of the two-stage IDTs between the improved and reduced mechanisms. It indicates that the two-stage IDTs of

Figure 11. Laminar flame velocities simulation at 298, 358, and 398 K. Symbols, reduced mechanism; solid lines, improved mechanism. 2809

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Figure 12. Temperature and (a) major species profiles and (b) minor species profiles for the stoichiometric DEE/air mixture at 358 K and 1 bar. Symbols, reduced mechanism; solid lines, improved mechanism.

Figure 13. Pyrolysis species profile simulation for 2.0% DEE diluted in argon at 2 bar. [DEE]0 and C denote the initial concentration of DEE and the concentration of chemical species, respectively. Effective heating times used at 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, and 1700 K were 1.8, 1.73, 1.65, 1.58, 1.5, 1.43, 1.35, 1.2, and 1.2 ms, respectively. Symbols, experiment from ref 19; dashed line, original mechanism; dotted line, improved mechanism; and solid lines, reduced mechanism.

Figure 14. Sensitivity coefficients showing the 10 most important reactions in burning velocities at 298 and 398 K and ϕ = 1: (a) improved mechanism and (b) reduced mechanism.

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Figure 15. Sensitivity coefficients showing the 10 most important reactions in IDTs at various temperatures: (a) improved mechanism and (b) reduced mechanism.

inactive radicals usually have negative sensitivities. H + O2 = O + OH (reaction R62) and H + OH + M = H2O + M (reaction R63) have the most positive and negative sensitivities, respectively, because of their radical branching and radical annihilation characteristics. Sensitivity coefficients showing the effect of the temperature on IDTs at 3.5 bar and ϕ = 1 are shown in Figure 15. The reduced mechanism retains the important reactions of the improved mechanism, and the sensitivity coefficients of these reactions have significant differences at various temperatures. A positive sensitivity indicates an increase in the value of IDT; conversely, a negative value indicates a decrease in its value. At 550 K, DEE + OH = C2H5OC2H4p + H2O (reaction R3) and CH3CHO2HOCHCH3 = OH + 2CH3CHO (reaction R8) have higher positive sensitivities and DEE + OH = C2H5OC2H4s + H2O (reaction R4) and CH3COOCHO2HCH3 = OH + CH3COOCHOCH3 (reaction R15) have higher negative sensitivities. Reactions R3 and R4 are competing reactions against OH, while reactions R8 and R15 have opposite temperature contributions; thus, different effects on IDTs are presented. At 650 K, C2H5OC2H4s = CH3CHO + C2H5 (reaction R5) and reaction R8 have higher positive sensitivity sensitivities and reaction R4 and CH 3CHO 2OC2 H5 = C2H5OC2H4s + O2 (reaction R6) as well as DEE + CH3O2 = C2H5OC2H4s + CH3O2H (reaction R73) have higher negative values. Reactions R4, R73, and R6 are the most important generation and consumption reactions for C2H5OC2H4s at low temperatures. In these reactions, reactions R5 and R6 are competing reactions against C2H5OC2H4s. At 1200 K, CH3 + HO2 = CH4 + O2 (reaction R67) and HO2 + HO2 = H2O2 + O2 (reaction R75) have higher positive sensitivities because radicals CH3 and HO2 are converted to inactive molecules (CH4, O2, and H2O2), while H + O2 = O + OH (reaction R62) and CH3 + HO2 = CH3O + OH (reaction R76) have higher negative sensitivities as a result of their contribution to OH. Reaction R76 is the competing reaction of reaction R75, which is advantage to decreasing the accumulation of H2O2 at temperatures below 1000 K.36

To see more detailed prediction information on the reduced model, we examined the temperature and species profiles of a premixed flame for the stoichiometric DEE/air mixture at 358 K and 1 bar, and they were plotted in Figure 12. It is seen that the temperature and the mole fractions of both major and minor species predicted by the reduced mechanism across the flame are the same as those of the improved mechanism. The pyrolysis species profiles were simulated on the basis of the homogeneous systems for a mixture of 2% DEE diluted with argon using the improved and reduced mechanisms and were plotted in Figure 13. It shows that the reduced mechanism can accurately predict the concentrations of both major and minor species, although there is a little difference compared to those of the improved mechanism at a temperature over 1400 K for species CO and C2H4. Furthermore, both the improved and reduced mechanisms have slightly better prediction accuracy than that of the original mechanism. Sensitivity analyses of burning velocities and IDTs were performed to investigate the dependence of the important reactions using the sensitivity function available in CHEMKINPRO29 and the brute-force method, respectively. Sensitivity coefficients of IDTs were calculated by eq 321 sensitivity = log(factor+/factor −)/log(2/0.5)

(3)

where “factor+” and “factor−” denote IDTs of increasing and decreasing both the forward and reverse rate constants by a factor of 2, respectively. Figure 14 depicts the 10 most important reactions for the improved and reduced mechanisms in stoichiometric DEE/air mixture burning velocities at 298 and 398 K. The important reactions of the reduced mechanism are the same as those of the improved mechanism. The reactions and their corresponding sensitivity coefficients do not show great differences at different temperatures. A positive sensitivity indicates a promotion in the burning velocities; conversely, a negative value indicates an inhibition in the burning velocities. The reactions of radical contribution or more active radical generation generally have positive sensitivities, while the reactions of the radical generating into molecules or more 2811

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4. CONCLUSION Aiming at the inadequacy of the original mechanism in low temperature and high pressure, an improved mechanism was developed; meanwhile, a reduced mechanism was proposed as well. The following conclusions were drawn: (1) An improved DEE mechanism consisting of 174 species and 973 reactions was obtained, in which the calculated IDTs kept good agreement with the experimental results based on the shock tube at 900−1900 K, 1−40 bar, and ϕ = 0.5−2 and RCM at 500−900 K, 3−4 bar, and ϕ = 1. Meanwhile, the laminar flame velocities could also be reproduced very well at 298−398 K and ϕ = 0.5−1.65. (2) The two-stage ignition at temperatures below 650 K and the NTC behavior in the temperature range from 621 to 746 K were observed. (3) Four kinds of DRGbased methods were selected for the improved mechanism reduction. A comparative analysis for the maximum and average relative reduction errors of IDTs calculated by different reduction methods was employed to develop a better reduced mechanism. In the reduction process, three different types of species were observed. (4) A reduced mechanism including 80 species and 329 reactions was obtained, whose overall introducing error was small in IDTs, two-stage ignition, burning velocities, and temperature and species profiles. In addition, sensitivity analyses were carried out to validate the reduced mechanism. Competing reactions related to DEE + OH and consumption of C2H5OC2H4s and HO2 were identified as being important for IDTs at various temperatures.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.energyfuels.6b02010. Improved mechanism and 80 species reduced mechanism and thermochemical and transport data (ZIP)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Zhigang Tang: 0000-0002-6742-0654 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China under Grant 51175530 and the Foundation and Advanced Research Program General Project of Chongqing City under Grant cstc2016jcyjA0499.

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REFERENCES

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