Minimized Skeletal Mechanism for Methyl Butanoate Oxidation and Its

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Minimized Skeletal Mechanism for Methyl Butanoate Oxidation and Its Application to the Prediction of C3−C4 Products in Nonpremixed Flames: A Base Model of Biodiesel Fuels Kuang C. Lin,*,† Hairong Tao,*,‡ Fan-Hsu Kao,† and Chuang-Te Chiu† †

Department of Mechanical and Electromechanical Engineering, National Sun Yat-Sen University, Kaohsiung 80424, Taiwan College of Chemistry, Beijing Normal University, Beijing 100875, China

‡

S Supporting Information *

ABSTRACT: Kinetic database of methyl butanoate (MB) combustion has been widely used as a base component for formulating kinetic mechanisms describing oxidation of larger methyl esters for biodiesel fuel surrogates. In this study, the detailed mechanism of Dooley et al. (Dooley, S.; Curran, H. J.; Simmie, J. M. Combust. Flame 2008, 153, 2−32) is minimized without empirical adjustment of rate constants in elementary reactions, using a combination of methods including a path flux analysis, removal of individual species, and peak molar concentration analysis. In the first phase, a basic skeletal mechanism with 38 species and 170 reactions for the oxidation of MB is developed, toward understanding the capability and limits of the reduced descriptions on high-temperature ignition delay times and major species profiles in 1-D counterflow flames. A comprehensive analysis of the decomposition pathways associated with preserved and removed reactions provides a scheme for mechanism developers with a clear foundation for creating new skeletal mechanisms of large methyl ester combustion. In the second phase, the MB skeletal mechanism takes into account additional 10 species and 33 reactions in order to predict experimentally measured products in a coflow nonpremixed methane/air flame doped with methyl butanoate. This 48-species skeletal mechanism combined with a 2-D computational fluid dynamic (CFD) flamelet model, for the first time, is able to predict the magnitude and shape of seven C3−C4 intermediate products, which are comparable to the experimental results. Moreover, the present skeletal mechanism, compared with published skeletal mechanisms, not only features a significant reduction in computational cost but also retains more significant products mass-spectrometrically determined.

1. INTRODUCTION Fatty acid methyl esters (FAMEs) are major components of biodiesel and have been widely investigated due to their compatibility with current liquid fuel energy infrastructure and potential effect on mitigation of current environmental issues associated with climate change. Over the last years, the surge of interest in biodiesel typically includes fuel production, fatty acid compositions, properties and specifications of fuels, fuel combustion, emission production, and engine performance. A wide variety of experimental studies have indicated that addition of biodiesel to conventional diesel fuel is able to lower ignition delay times, unburned hydrocarbons, particulate matters (PMs) and carbon monoxide (CO) while increasing ignition temperature, pressure, peak heat release and nitrogen oxides (NOx). Much of this work has been discussed in several review articles.1−5 However, aside from empirical observation of these phenomena, a fundamental understanding of the chemical processes involved is currently lacking in engine simulations. Such knowledge aids in the development of technologies that can mitigate pollutant emission from engines. The main challenge will be to handle the coupling between fluid dynamics and chemical interactions, in which 3-D engine simulations with large kinetic mechanisms including hundreds or thousands of species are infeasible. Due to the complexity of biodiesel and the size of its constituent molecules, direct detailed kinetic modeling studies have been limited. This challenge can be seen in a detailed © XXXX American Chemical Society

chemical kinetic reaction mechanism for soy and rapeseed biodiesel fuels in which more than 4800 species and 20 000 reactions are involved.6 Accordingly, the need for kinetic studies has prompted intensive research in biodiesel surrogates, where a mechanism is generally composed of hundreds of species. A number of papers7−9 have reviewed the chemical kinetic mechanisms for oxidation of biodiesel surrogates including methyl formate (C2H4O2), methyl butanoate (C5H10O2), methyl crotonate (C5H8O2), methyl hexanoate (C7H14O2), methyl octanoate (C9H18O2), methyl decanoate (C11H22O2), and methyl decenoate (C11H20O2). Generally, a detailed mechanism of biodiesel surrogate is still too large for use in CFD (computational fluid dynamics) simulations. Creation of reduced mechanisms by removing unimportant species and reactions in achieving certain computational targets, such as species concentrations or temperature profiles, is therefore of crucial importance to obtain suitable balance between detailed chemistry and manageable computational complexity. A recent review by Lu and Law10 has described a variety of reduction methods, as well as advantages and disadvantages of reduction processes that have been extensively studied over the last few decades. Subsequently, over the past few years, numerous reduced or Received: October 11, 2015 Revised: January 4, 2016

A

DOI: 10.1021/acs.energyfuels.5b02389 Energy Fuels XXXX, XXX, XXX−XXX

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mechanisms for biodiesel surrogates.12−23 Different validation efforts associated with these skeletal mechanisms include ignition delay times,12−23 laminar burning velocity,12,17,19,20 opposed-diffusion flame,12,20,22 heat release rates,13,16,18,21 incylinder pressure, 1 3 , 1 5 , 1 6 , 1 8 , 2 1 , 2 3 in-cylinder chemistry,13,14,16,19−21 jet-stirred reactors,19,20,22,23 flame-lift off length,19,20 extinction temperature,19,20 and premixed flame.22 These studies, mostly published in the past three years, indicate the need of using chemical kinetic mechanisms in CFD biodiesel combustion modeling. The pioneering studies of skeletal mechanisms for biodiesel surrogates were carried out by Akih-Kumgeh and Bergthorson12 and Brakora et al.,13 who utilized MB as a fuel surrogate to derive mechanisms with a species number less than 100. Nevertheless, MB is neither able to capture the behavior of negative temperature coefficients (NTC) in low-temperature combustion of biodiesel fuels nor formation of hydrocarbons from unsaturated methyl ester molecular structures.7 To overcome this problem, several research groups proposed the solutions including the addition of (1) n-heptane to describe the NTC caused by the HO2 formation in isomerization of alkyl peroxy radicals ROO•13−17 and (2) methyl crotonate to represent a CC double bond in the alkyl chain of methyl esters.15,16 Besides the attention given to C5 methyl esters, initiatives are also taken regarding C11 methyl esters, which compared to MB show better representation for the length of alkyl chains in biodiesel fuels. These skeletal or reduced mechanisms for large biodiesel surrogate combustion generally comprise methyl decanoate (CH3(CH2)8C(O)OCH3) and a monounsaturated C11 methyl ester.18−22 Very recently, Chang et al.23 proposed a series of skeletal oxidation mechanisms for the saturated FAMEs from methyl butanoate to methyl palmitate using a decoupling methodology24 with special emphasis on engine relevant conditions from low to high temperatures at high pressures. Generally, the mechanism reduction methodologies that were employed in biodiesel surrogates (Table 1) include directed relation graph (DRG),14 directed relation graph-aided sensitivity analysis (DRGASA),14,19,20 directed relation graph with error propagation (DRGEP),25 direct-relation graph with

skeletal mechanisms for biodiesel surrogates have become available for use in CFD. Such outcomes have led a recent review by Cheng et al.11 to discuss published surrogate chemical kinetic mechanisms, mechanism reduction methods, and thermodynamic data associated with CFD modeling of incylinder biodiesel combustion. Table 1 summarizes the chemistry complexity and autoignition prediction quality of the published skeletal/reduced Table 1. Reduced/Skeletal Mechanisms of Biodiesel Surrogates for CFD Biodiesel Combustion Modeling ref

surrogate components

Akih-Kumgeh MB and Bergthorson12 Brakora et al.13 MB MB/NH Liu et al.14 MB/NH Ng et al.15 MB/MC/NH Ismail et al.16 MB/MC/NH Golovitchev MB/NH/ and Yang17 PME An et al.18 MD/MD9D/ NH MD/MD9D/ Luo et al.19 NH MD/MD9D/ Luo et al.20 NH Brakora and MD/MD9D Reitz21 Chang et al.22 MB/MHX/ MHP/MO/ MD/MP/ ND MD/MD5D/ Chang et al.23 ND

no. of species

no. of reactions

no. of rate constants adjusted

max. ID errorsa

88

843

0

121%

41 53 145 80 113 88

150 156 869 299 399 363

2 2 0 4 3 3

31% 40% 31% 29% 73% 65%

112

498

4

60%

123

394

0

40%

115

460

0

50%

69

192

3

38%

42

135

60

172

10

a

Maximum ignition delay errors with respect to detailed mechanisms. MB: methyl butanoate; PME: phenyl methyl ether; MC: methyl crotonate; MD: methyl decanoate; MD9D: methyl-9-decenoate; MD5D: methyl-5-decenoate; MHX: methyl hexanoate; MHP: methyl heptanoate; MO: methyl octanoate; MP: methyl palmitate; NH: nheptane; ND: n-decanoate.

Figure 1. Overview of the skeletal mechanism generation. B

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Energy & Fuels error-propagation and sensitivity analysis (DRGEPSA),16,18 decoupling methodology,22,23 and sensitivity reduction approach.12 Additionally, a few studies13,15,25 carried out the mechanism reduction by combination of methods, including peak molar concentration analysis, reaction flux analysis and the removal of individual species. As seen in Table 1, a reduced or skeletal mechanism with a number of species less than 50 generally requires tuning values of Arrhenius parameters to minimize differences between calculated and measured ignition delay times. These significant adjustments of the rate parameters in skeletal mechanisms have remained questionable as to whether those newly adjusted rate constants naturally yield consistent prescriptions validated in detailed mechanisms. This fact, in turn, implies the need to take extraordinary actions on identifying and eliminating unimportant species, rather than modifying the retained species, their elementary reactions, or the associated reaction rate parameters. Although methyl butanoate was determined to be not an ideal surrogate for biodiesels,26,27 it is regarded as an essential model molecule for representing the reactions of ester groups in large saturated fatty acid methyl esters.23 Motivated by this consideration, in this study we derive an untuned skeletal mechanism of MB using a path flux analysis method combined with removal of individual species and a peak molar concentration analysis to obtain a trade-off that processes the minimum species number while preserving reasonable accuracy to predict fuel oxidation. The results of the examination for the reaction classes constructed in the skeletal mechanism yield valuable insight into the development of oxidation mechanisms for methyl esters used in CFD. In addition, the newly generated skeletal mechanism is applied to predict measured C3−C4 hydrocarbon and oxygenated hydrocarbon formation in a coflow nonpremixed methane/air flame doped with methyl butanoate. Notably, these experimental observations have not been previously validated against computational modeling.

measure the degree of interaction among species involved in these two chemistry modules, a threshold value (ε) as defined below is set for evaluating the significance of species in the mechanism: ε=

PAB + CAB + max(PA , CA) +

∑ Mi ≠ A , B

∑ Mi ≠ A , B

CAMi

PAMi

PMiB

max(PA , CA) max(PB , CB) C M iB

max(PA , CA) max(PB , CB)

(1)

The first term on the right-hand side of eq 1 represents the first generation flux that considers the interaction for production (P) and consumption (C) of species A via B. The second and third terms on the right-hand side of eq 1 describe the second generation that measures the flux ratios between A and B via a third reactant (Mi). P and C in all the denominators are, respectively, production and consumption fluxes for individual species, subscripted by A or B. The dual subscripts in all the numerators denote the production and consumption fluxes of a species due to the existence of another one. If a calculated threshold value is greater than our specified value, species B is retained in the mechanism. Accordingly, an increase of ε means the raised criteria for evaluating important species. For the detailed description regarding this method, the interested reader is referred to the studies of Sun et al.28 and Gou et al.29 The present PFA calculations are carried out by the program of Chem-RC28,29 with input parameters including threshold values (ε), temperatures (T), pressures (P) and equivalence ratios (ϕ). We choose basic reactant mixtures MB, O2, N2 and Ar as target species to ensure the existence of a minimized skeletal mechanism for MB oxidation. The code that does not require massive user interaction with the reduction process benefits the development of skeletal mechanisms in such complex fuel combustion chemistry. 2.2. Simulations of 0-D Autoignition Chemistry and 1-D Flames. The modules of “Reflected Shock Reactor” and “OpposedFlow Flame” in the Chemkin 4.1 package31,32 are used to simulate experiments of ignition delay times26 and species concentration profiles in the counterflow flame,33 respectively. The ignition delay time analysis is to identify a skeletal mechanism that is sufficiently small to be accommodated into CFD codes while keeping sufficient accuracy to quantitatively describe the detailed chemistry. Using the 1D counterflow flame model of Gail et al.,33 this validation permits refinement of the skeletal mechanism in terms of target species predictions. 2.3. Simulations of 2-D Nonpremixed Flames. This numerical simulation is to reconstruct the experiment of Schwartz et al.30 which investigated atmospheric-pressure coflowing laminar nonpremixed flames of esters. Figure 2 presents the schematic of the model and 2-D axisymmetric block mesh adopted in the study of nonpremixed flames. The tube radius (R) is 0.6 cm. 2-D conservation equations are solved for laminar unsteady flow, heat transfer and chemical reactions by means of ANSYS FLUENT 14.0.34 A second-order upwind scheme is used for discretization and the numerical model uses an implicit finite volume scheme based on the iterative SIMPLE algorithm employed for pressure−velocity coupling. The thermodynamic and transport properties corresponding to each species are modeled as temperature-dependent. The in situ adaptive tabulation (ISAT) method is employed to implement detailed chemical kinetics with an ISAT tolerance of 1 × 10−5. A full multicomponent diffusion model along with thermal diffusion is enabled in order to obtain coefficients of multicomponent diffusion as a function of binary diffusion coefficients. A total cells of 90 × 40 are used after grid independence checks.

2. COMPUTATIONAL DETAILS In the present work, the generation process of a skeletal mechanism starts with an original MB mechanism of Dooley et al.26 comprising 275 species and 1549 reactions. A path flux analysis (PFA) method developed by Sun et al.28 and Gou et al.29 is employed to identify species which are important to the target species. Figure 1 illustrates an overview of the processes to generate a skeletal mechanism for predicting detailed chemistry of a nonpremixed flame. First, different skeletal mechanisms are obtained using PFA subject to different sets of threshold values, initial temperatures, and pressures. The comparison of these generated skeletal mechanisms allows the selection of a particular skeletal mechanism (V1) with a trade-off between the model complexity and the accuracy of autoignition prediction attainable with a detailed mechanism. Then, the species profile prediction in 1-D counterflow flames is used to improve the quality of V1 that becomes V2, followed by a further elimination stage of unimportant reactions that shrinks skeletal mechanism V2 down to 38 species and 170 reactions (V3). In order to predict the formation of hydrocarbon and carbonyl products for MB in a nonpremixed flame,30 we employ sensitivity and rate of production (ROP) analyses to manually choose related species and reactions from the detailed mechanism26 and then add them back to skeletal mechanism V3 that eventually forms skeletal mechanism V4 with 48-species and 203 reactions. 2.1. Mechanism Reduction. The aim of the PFA method, which is based on net production and consumption rates of target species, is to identify important reaction pathways in two reaction systems, one for ignition delay time of homogeneous mixtures with constant pressure and the other for extinction in a perfectly stirred reactor. To

3. RESULTS AND DISCUSSION In section 3.1, we report the effects of target parameters on the complexity of skeletal mechanisms. The validation and analysis for the chosen skeletal mechanisms are discussed in sections 3.2 and 3.3, respectively. Finally, section 3.4 presents the capability of reproducing the experiments of coflow nonpremixed flames C

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Figure 3. Number of species in the reduced mechanism as a function of the threshold values (ε) for a stoichiometric MB/air mixture and different target temperatures and pressures. Figure 2. Computational mesh, boundary conditions, and predicted temperature contour for the nonpremixed flame model. Velocities at the fuel nozzle and air inlet are 0.0973 and 0.505 m/s, respectively. The molar composition of the fuel mixtures introduced at 450 K is 49.5% CH4, 0.5% MB, 25% N2, and 25% Ar.

reduction, except for the mechanisms produced at T = 1500 K for ε = 0.5 and 0.6. It is seen that the variation of P = 1−40 atm is less sensitive than that of T = 900−1800 K to the mechanism complexity. Although the sizes of skeletal mechanisms produced at low pressures are relatively small and ideal for CFD calculation, examination for their prediction accuracy at high reaction pressure is needed and discussed in the next section. 3.2. Mechanism Validation. In this section, the validation for selected skeletal mechanisms (SM) generated in section 3.1 is obtained by starting with predictions of ignition delay time and oxidation in a counterflow flame for MB. On the basis of the nonpremixed flame study of Schwartz et al.,30 we choose the skeletal mechanisms produced at T = 900, 1200, 1500, and 1800 K under stoichiometric and atmospheric conditions with ε = 0.5 and 0.6, respectively. We also validate these skeletal mechanisms at a high pressure condition for the purpose of wide applicability of the reduced kinetic schemes. The simulation based on the experimental study of Dooley et al.26 presents shock tube oxidation of each fuel and air for temperatures of 1333, 1429, and 1667 K and pressures of 1 and 40 atm (values after reflected shock). Figure 4 shows the errors of ignition delay time predictions introduced by removing the species and eliminating the reaction pathways in the original detailed mechanisms.26,35 We also compare the results with those obtained from a single skeletal mechanism (SM-A and B) generated by summing species and reactions identified at multiple temperatures (900, 1200, 1500, and 1800 K) and pressures (1, 20, and 40 atm). Different ε values are used for classification of SM-A and SM-B in terms of sizes which are comparable to those of SM-C to F and SM-G to J, respectively. As seen in Figure 4, considerable errors relative to its original mechanism35 (255% in average) are introduced by the published 41-species mechanism,13 in spite of intentional adjustments of rate constants for reaching desired ignition delay times. Although the 88-species mechanism shows negligible errors relative to the detailed mechanism, SM-A to D that yield

by 2-D numerical simulations with the newly developed skeletal mechanism. 3.1. Effect of Reaction Parameters. The effect of target temperatures, pressures and equivalence ratios on sizes of skeletal mechanisms is analyzed in terms of the conditions that are chosen to match the range of conditions studied by Dooley et al.26 In particular, each single skeletal mechanism is generated at a chosen temperature, pressure and equivalence ratio. The analysis indicates that the variation of ϕ = 0.5−1.5 is less sensitive than those of T = 900−1800 K and P = 1−40 atm to the mechanism complexity. Figure 3 shows the number of species in the skeletal mechanism as a function of threshold values at ϕ = 1 for each interval of target parameters across the initial temperatures 900−1800 K and pressures 1−40 atm. The corresponding variations of number of reactions are documented in Figure S1 in the Supporting Information. Note that an increased threshold value (ε) results in enhanced criteria for filtering out species that do not achieve a degree of interaction with others in terms of reaction path relations. Within the ranges of target parameters used in this study, we discover that threshold values (ε) in the range of 0.4−0.6 allow us to capture a minimum skeletal mechanism that can at least accurately predict the ignition and diffusion flame experiments. It is observed in Figure 3 that the effect of target temperatures on the mechanism complexity at different levels of reduction (ε) does not appear to be straightforwardly classifiable. Upon varying the temperature at P = 1 atm, the mechanism complexity at different values of ε achieves a local maximum at T = 1500 K. In examining the effect of pressure in Figure 3, we note that the number of species is slightly proportional to the increase of P at fixed temperatures for different levels of D

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Figure 4. Errors of ignition delay times predicted using different skeletal mechanisms (SM). SM-C to J are selected from Figure 3. SMA and B are, respectively, produced at ε = 0.75 and 0.8 with specified ranges of parameters: T = 900−1800 K and P = 1−40 atm. SM-C to J are generated at atmospheric and stoichiometric conditions for ε = 0.5 (C−F) and 0.6 (G-J) and T = 900 K (C and G), 1200 K (D and H), 1500 K (E and I), and 1800 K (F and J). Figure 5. Errors of mole fraction profiles in a counterflow flame predicted using the 88-species mechanism,12 SM-D-V1 and SM-D-V2. SM-D-V2 is based on the addition of C2H6 decomposition reactions R1, R2, and R3 to SM-D-V1. The errors are relative to the detailed mechanism.26

an average error of 32% are about one-half of the size of the 88species mechanism. As indicated in Figure 4, there is no significant difference in the accuracy of the skeletal mechanisms A−D in simulating the ignition delay times at varied equivalence ratios and pressures. On the other hand, SM-F, I and J, which are generated at relatively high target temperatures, lead to relatively large errors for ignition delay times at low temperatures. In addition, SM-A and B show no advantage of ignition delay time predictions over skeletal mechanisms generated at a single target temperature, specifically 900 K (SM-C and G) and 1200 K (SM-D and H). Instead of using a full range of parameters to generate skeletal mechanisms, applying the intermediate temperature of 1200 K under a stoichiometric and atmospheric condition to perform mechanism reduction is able to minimize the size of the skeletal mechanisms while preserving the dominant reactions at different equivalence ratios in fuel combustion. This minimized skeletal size will serve as a foundation toward the development of a more robust skeletal model that preserves the dominant reactions at higher temperatures and pressures. Among the mechanisms investigated in Figure 4, SM-D and G are considered as the candidate skeletal mechanisms for being examined in a counterflow flame studied by Gail et al.33 It is found out that SM-G with 31 species is not able to describe chemical reactions in this reactor under the conditions employed. We thus rule out the use of SM- G as a valid kinetic model. Figure 5 presents the mole fraction errors introduced by the mechanism reduction. In view of the considerable errors involved in estimating mole fractions using the first version of SM-D (SM-D-V1), the rate-of-production analysis for the target species is subsequently performed to seek missing reactions which affect the prediction capability. The refinement of SM-D-V1 shown in Figure 5 is eventually achieved by the addition of ethane and its related reactions

(listed below) to SM-D-V1, which makes up SM-D-V2 (43 species and 189 reactions): C2H6( +M) ↔ CH3 + CH3( +M)

(R1)

C2H6 + H ↔ C2H5 + H 2

(R2)

C2H6 + CH3 ↔ C2H5 + CH4

(R3)

As indicated in Figure 6, SM-D-V2 in comparison with SMD-V1 also yields less errors of ignition delay time, particularly at low temperatures. 3.3. Reaction Analysis. In order to understand how the newly refined 43-species skeletal mechanism (SM-D-V2) has led to a kinetic scheme that predicts MB oxidation, one must comprehend what reaction pathways associated with the medium-temperature combustion (1200 K) are retained and in what way the scheme differs from the original mechanism. The preserved and eliminated reaction pathways are, therefore, distinguishably illustrated in Figures 7−10. Initiation reactions of MB oxidation in the original mechanism, as clearly shown in Figure 7, are primarily kept for mechanism reduction except for H atom abstraction from all four distinct sites in MB by the radicals of ethyl (C2H5), methyl peroxy (CH3O2), and methoxy (CH3O), bond breaking between C4 and C3, and unimolecular six-centered dissociation reactions. The removal of these reactions may be ascribed to relatively high activation energy or structural limitations of methyl esters that prevent the unimolecular six-center dissociation reaction from occurring. In particular, the reactions kept for the mechanism reduction produce ten major E

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Figure 6. Comparison of ignition delay time errors predicted using SM-D-V1 (42 species and 186 reactions) and SM-D-V2 (43 species and 189 reactions). The error is relative to the detailed mechanism.26

Figure 8. Reaction pathways for the decomposition of fuel alkyl ester radicals in SM-D-V2. Dashed boxes are reactions removed from the original MB mechanism of Dooley et al.26 R represents alkyl or alkyl ester radicals.

Figure 7. Reaction pathways for the fuel decomposition in SM-D-V2. Dashed boxes are reactions removed from the original MB mechanism of Dooley et al.26

intermediates (MB2J, MB3J, MB4J, MBMJ, BAOJ, nC3H7CO, nC3H7, ME2J, CH3OCO, and C2H5) that subsequently decompose to yield small products. Figure 8 presents the reactions that consume four alkyl-ester radicals (MBXJ) produced in the H atom abstraction from MB and C−H bond breaking of MB. The C−C and C−O bond βscission reactions and isomerizations of MBXJ radicals are retained in the skeletal mechanism, except for the β-scission of the bond C1−O in MB2J. Five major intermediates formed by the MBXJ decomposition include MP2D, C3H6, CH3OCO, ME2J, and nC3H7CO, in which the last three species are also present in the initially formed intermediates produced by MB decomposition (see Figure 7). Besides, three reaction types omitted from the skeletal mechanism are identified: (1) βscission of C−H bonds in MB2J, MB3J, and MB4J, (2) addition of O2 to MBXJ radicals, and (3) recombination between MBXJ and peroxyl radicals (RO2). It is worth noting that the omitted reaction types (2) and (3) are associated with low-temperature kinetics described by bimolecular reactions decomposing MBXJ radicals. Figure 9 shows the reactions destroying the rest of the intermediates (BAOJ, C2H5, ME2J, nC3H7CO, nC3H7, and

Figure 9. Reaction pathways for the decomposition of the initially formed intermediate radicals in SM-D-V2. Dashed boxes are reactions removed from the original MB mechanism of Dooley et al.26 R represents alkyl or alkyl ester radicals.

CH3OCO) produced from the C−C or C−O bond breaking reactions of MB. It is seen that β-scission reactions of these intermediates are preserved in the skeletal mechanism except for β-scission of C−H bonds in nC3H7CO. As shown in Figure 9, the ethyl radical (C2H5) in the skeletal mechanism is consumed primarily via (1) three termination reactions (H abstraction) producing major products (C2H4, H2, and CH4) and (2) a chain branching reaction forming methyl radicals. In the consumption fluxes of radicals BAOJ, nC3H7, ME2J, F

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studied at Yale University (Schwartz et al.30), is reproduced for the first time by computational fluid dynamics coupled with detailed chemistry. Since the mass spectrometry used in their study was not able to directly distinguish between different isomers of each product, authors30 deduced isobaric species using an analytical estimate from basic reaction pathways and product spatial locations. Thus, motivated by the need to classify isomer compounds using chemical kinetics, the present CFD model coupled with the skeletal mechanism offers an efficient solution to interpret the formation of primary products. We pay particular attention to the use of a skeletal mechanism in the prediction of C3−C4 hydrocarbon and oxygenated hydrocarbon compounds analyzed by Schwartz et al.30 The corresponding isobaric species available in the detailed mechanism of Dooley et al.26 are identified: C3H6, C3H4, C3H4O, C4H8, and C4H6O. Since only propene (C3H6) is present in SM-D-V3, there is a need for adding reactions and species to this skeletal mechanism in order to represent the chemistry of the other four compounds. Accordingly, we evaluate the significance of the corresponding products in the mechanism of Dooley et al.26 using a model of CH4/MB oxidation in a jet stirred reactor. In the JSR modeling, the inlet concentrations and residence time together with a constrained temperature and pressure are obtained from the flame operating conditions of Schwartz et al.30 As shown in Table S1 in the Supporting Information, out of 12 species listed, propyne [C3H4-p (CHC−CH3)], propadiene [C3H4-a (CH2CCH2)], methyl ketene [CH3CHCO (CH3− CHCO)], prop-2-enal [C2H3CHO (CH2CH−CH( O)], but-1-ene [C4H8-1 (CH2CH−CH2−CH3)], and ethyl ketene [C2H5CHCO (CH3−CH2−CHCO)] better represent chemical formulas/compounds according to the normalized molar proportions for different isomers. Ten species and 33 reactions that govern the chemistry of these products are determined by the cross-checking of the independent findings on the sensitivity and ROP analyses in the 1-D counterflow flame configured in section 3.2. These represented species and reactions, listed in Table S2 in the Supporting Information, are combined with SM-D-V3 to form SM-D-V4. The kinetic submodel in Table S2 is able to be comprehensively understood in view of the following detailed description. The intermediate radical C3H5-a [CH2CH− CH2(•)], which is formed by R4: C3H6 ↔ C3H5-a + H and R5−7: C3H6 + R ↔ C3H5-a + RH, decomposes to propadiene (C3H4-a) and prop-2-enal (C2H3CHO) via R9: C3H5-a ↔ C3H4-a + H and R28: C3H5-a + O2 ↔ C2H3CHO + OH, respectively. Propadiene (C3H4-a) further isomerizes to propyne (C3H4-p) in R15: C3H4-a ↔ C3H4-p. Besides, the addition of O to propene (C3H6) produces methyl ketene (CH3CHCO) in R31: C3H6 + O ↔ CH3CHCO + H + H. In particular, but-1-ene (C4H8-1) is mainly produced by reversed reactions R22: C4H8-1 ↔ C3H5-a + CH3 and R23: C4H8-1 ↔ C2H3 + C2H5. The allyl radical C4H71−3 [CH2CH− CH(•)−CH3] formed by but-1-ene (C4H8-1) in R24 (C4H81 ↔ C4H71−3 + H) subsequently reacts with O to produce prop-2-enal (C2H3CHO) in R29: C4H71−3 + O ↔ C2H3CHO + CH3. Furthermore, ethyl ketene (C2H5CHCO) is formed by β-scission of the initially formed intermediates MB2J and nC3H7CO. Through the sensitivity analysis, reaction R36 (MB3J ↔ MB2D + H) that describes C−H β-scission of MB3J to form MB2D and H is added back to the skeletal mechanism

CH3OCO, and C2H5, their isomerizations or recombination reactions, as compared with C−C or C−O bond β-scission, are less pronounced and therefore are removed by the PFA method. Furthermore, CH2CO, C2H4, and C3H6 are the three major nonradical products produced by the decomposition of intermediates in Figure 9. As shown in Figure 10, PFA preserves reactions decomposing four nonradical products CH2CO, MP2D, C3H6, and C2H4,

Figure 10. Reaction pathways for the decomposition of the nonradical products produced by the initially formed intermediates in SM-D-V2. Dashed boxes are reactions removed from the original MB mechanism of Dooley et al.26 R represents alkyl or alkyl ester radicals.

which are the main unsaturated molecules produced by the initially formed intermediates shown in either Figure 8 or 9. The primary reaction types are addition of radicals to CC double bonds, H atom abstraction through radicals, and single bond breaking. The reactions that are eliminated in the skeletal mechanism include a part of H atom abstraction by small radicals in MP2D, C3H6, and C2H4, breaking of C−H bonds in C3H6, and three radical addition reactions of CH2CO. In this reaction class (Figure 10), the oxygenated radical C2H3CO is the only product newly formed. Subsequent decomposition of this oxygenated radical leads to no newly produced species, which implies that the reactions in Figure 10 are the closure of the kinetic mechanism complexity. Eventually, the revised mechanism, called SM-D-V3 (38 species and 170 reactions), is defined by manual removal of five species (MP2DMJ, C 2H 3CO2 , CH2CHO, CH3 CO and C2H3O1−2) and related 19 reactions from SM-D-V2. Comprehensive validation for SM-D-V3 by means of the process in section 3.2 reveals that its prediction capability is almost exactly the same as that of SM-D-V2 (see Figure S2 in the Supporting Information). Thus, we conclude that the basic skeletal mechanism, SM-D-V3, offers promising predictive results for MB ignition delay times and formation of major small products. 3.4. CFD Modeling of Nonpremixed Flames. The coflow nonpremixed flames of CH4/air/MB, experimentally G

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height (∼3.86 cm) where the peak flame temperature is located along the axial direction. As indicated in Figure 11a, the agreement between the experimental and computational data profiles is satisfactory, with the exception of the region z/HT higher than 0.75, where predicted temperature and CO2 mole fraction are, respectively, ∼ 200 K and ∼0.01 higher. As also shown in Figure 11a, the presently reduced description with 48 represented species agrees well with the 88-species mechanism except for the slightly higher O2 mole fraction around z/HT = 0.2−0.4. This overprediction by SM-D-V4 is believed to be caused by the removal of low-temperature combustion intermediates that consume O2. One of the evidences is that the fuel alkyl ester radial CH3CH2CH2C(O)OCH2(•) reacting with O2 is diminished in SM-D-V4 but present in the 88-species mechanism of Akih-Kumgeh and Bergthorson.12 In Figure 11b, we see that the profiles of C3H4, C3H6, and C3H4O/C4H8 are predicted very well by SM-D-V4 and the peak values are reasonably captured, both in terms of the absolute values and positions. Since in the detailed mechanism of Dooley et al.,26 reactions related to the compounds of C3H2O2 and C5H10 are not available, it seems more appropriate to compare the profiles of C4H6O/C3H2O2/C5H10 only qualitatively. It is seen that the 88-species mechanism12 (1) does not account for the existence of C3H4 compounds; and (2) slightly under-predicts the formation of C3H4O/C4H8 products that are shifted toward lower axial position, due to the absence of CH3CHCO. Figure 12 presents the corresponding contours of temperature and mole fractions of O2, CO2, MB, CH4, and radical OH as well as C3−C4 products from the descriptions of SM-D-V4 and 88-species12 skeletal mechanisms. Note that the 41-species mechanism13 of Brakora is not presented in Figure 12 due to the fact that it does not have most of the C3−C4 products except for C3H6. Overall, the presently reduced description with 48 represented species agrees well with the available data predicted by the description of the 88-species kinetic scheme, except for C2H3CHO, which is lower by a factor of around 3 in the present mechanism. Finally, Table 3 reveals that, in comparison with the reduced description with 88-species mechanism,12 the compact kinetic model SM-D-V4 with 48 species achieves a speedup factor of 3.6.

since it indirectly influences the formation of ethyl ketene (C2H5CHCO). The closure of this kinetic submodel in Table S2 is achieved by destruction reactions in which C3−C4 hydrocarbons and oxygenated hydrocarbons are consumed by small radicals (OH, O, H, and CH3). Through the CFD analysis, we show the capability and accuracy of the newly derived skeletal mechanism SM-D-V4 and its gain in run-time comparing against results obtained using published skeletal mechanisms.12,13 Table 2 shows the Table 2. Tg1%a Experimental and Computed Values Using Different Skeletal Mechanisms

Tg1% (K)

experiments of Schwartz et al.30

48 species, 203 reactions (SM-D-V4)

88 species, 841 reactions (AkihKumgeh and Bergthorson12)

41 species, 150 reactions (Brakora et al.13)b

1385.23

1380.14

1389.77

1411.95

a

Temperature point is captured at MB concentration of 1% of the initial amount (50 ppm mol). bRate constants were tuned for two key reactions by the authors.

CFD-computed centerline flame temperature point (Tg1%) at MB concentration of 1% of the initial amount (50 ppm mol) using different skeletal mechanisms. It is seen that the temperatures of SM-D-V4 and the 88-species mechanism12 are in better agreement with the experimental value than that of the 41-species mechanism.13 Figure 11 presents the comparison between 2-D simulations and measurements along the centerline of the CH4/air/MB flame. We define the flame

4. CONCLUSIONS Using a path flux analysis together with a systematic validation process, a compact skeletal mechanism that offers desirable prediction capability of methyl butanoate oxidation is able to be derived from a 275-species detailed mechanism without empirically adjusting rate constants of elementary reactions. The validation test cases used for mechanism reduction include ignition delays in 0-D shock tube and major species profiles in 1-D counterflow flames. An assessment of initial parameters used for a path flux analysis leads to the conclusion that skeletal mechanism complexity is sensitive to the temperatures of 900−1500 K rather than the pressures of 1− 40 atm and equivalence ratios of 0.5−1.5. The skeletal mechanism which is produced at an initial temperature of 1200 K under stoichiometric and atmospheric conditions is selected as a trade-off between model complexity and predictive ability. It is suggested that an examination of major species (MB, O2, CO2, CH4, C2H2, C2H4, C3H6, and CH2CO) profiles in 1-D counterflow flames together with a rate of production analysis can provide a useful means of determining the missing

Figure 11. (a) Gas temperature and major species profiles and (b) C3−C4 product profiles along the centerline in the nonpremixed flame of CH4/air/MB: comparison between experimental data of Schwartz et al.30 (symbols) and numerical simulations. The detailed chemistry in CFD is, respectively, described by the skeletal mechanisms, SM-DV4 (48-species; solid lines) and Akih-Kumgeh and Bergthorson12 (88species; dash lines). Note that isomers of C3H4 are unavailable in the 88-species mechanism.12 H

DOI: 10.1021/acs.energyfuels.5b02389 Energy Fuels XXXX, XXX, XXX−XXX

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We comprehensively analyze the reaction pathways in the skeletal mechanism and show that the majority of eliminated reactions are those in which initially formed intermediate radicals decompose into variety of products with the methyl ester moiety. With manual removal of unimportant reactions based on a reaction pathway analysis, the basic skeletal mechanism ends up with 38 species and 170 reactions, which is able to model ignition time and major small product profiles in MB combustion. Average deviations of ignition delay and major species profiles in counterflow flames with respect to detailed mechanisms are around 78.97% and 18.70%, respectively. The minimized skeletal mechanism leads to better accuracy in prediction of autoignition compared with a published 41-species mechanism in which rate constants for important reactions were tuned. It is worth emphasizing that we introduce for the first time, a computational fluid dynamics simulation in predicting experimentally detected compounds C3H6, C3H4, C3H4O, C4H8, and C4H6O in a 2-D coflow nonpremixed flame of CH4/air/MB. We identify that these measured compounds mainly correspond to the unsaturated products in the detailed mechanism of MB oxidation. Based on the sensitivity and rate-ofproduction analyses in a 1-D counterflow flame, additional seven products and three radicals from the detailed mechanism are selected to be added to the 38-species skeletal mechanism in order to describe the experimentally measured compounds. This skeletal mechanism consisting of 48 species and 203 reactions not only results in satisfactory agreement between experimental measurements and numerical prediction, but also interprets experimental data using represented species which are unavailable in previously published 41- and 88-species skeletal mechanisms of MB oxidation. Besides, the newly derived skeletal mechanism achieves a speedup factor of 3.6 over the performance of the 88-species skeletal mechanism on a Windows machine running a 3.4-GHz CPU with 6 cores in parallel. Future work is recommended to extend the current investigation to a model with inclusion of polycyclic aromatic hydrocarbon formation. This model shall aid in examining formation of benzene and naphthalene as well as other related products in the present 2-D flame configuration.

Figure 12. Contours of (a) gas temperature, O2 and CO2 and (b) MB, CH4, OH, and C3−C4 products in CH4/air/MB nonpremixed flames are displayed as functions of radial position (r) and dimensionless axial position (z/HT) in a portion of the computational domain. The detailed chemistry in CFD is, respectively, described by the skeletal mechanisms, SM-D-V4 (48-species) and Akih-Kumgeh and Bergthorson12 (88-species). Note that products C3H4-a, C3H4-p and CH3CHCO are not available in the 88-species skeletal mechanism.12

■

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.energyfuels.5b02389. Supplementary figures and tables (PDF) Skeletal mechanism V3 (38 species) (TXT) Skeletal mechanism V4 (48 species) (TXT)

Table 3. Performance Comparisons of Skeletal Mechanisms in Solving Chemistry in the 2-D Nonpremixed Flame of CH4/Air/MB after 2500 Time-Steps in a Total Grid Cell Number of 3600 in Parallela

CPU time (hours) no. of major C3− C4 products presentedb

48 species, 203 rxns (SM-D-V4)

88 species, 841 rxns (Akih-Kumgeh and Bergthorson12)

41 species, 150 rxns (Brakora et al.13)c

32.07

116.63

27.4

7

4

1

ASSOCIATED CONTENT

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (K.C.L.). *E-mail: [email protected] (H.T.). Notes

a

The authors declare no competing financial interest.

reactions which are important when molecular diffusive transport is considered in fuel oxidation.

ACKNOWLEDGMENTS The authors would like to thank Prof. Lam K. Huynh of Vietnam National University for his comments on the assessment of critical reactions. In addition, we would like to

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The computations are done on a Windows machine running a 3.4GHz CPU with 6 cores. bC3−C4 species are shown in Figure 12b. c Rate constants were tuned for two key reactions by the authors.

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(33) Gaïl, S.; Sarathy, S.; Thomson, M.; Diévart, P.; Dagaut, P. Combust. Flame 2008, 155, 635−650. (34) Fluent 14.0 User’s Guide; ANSYS Inc. 2011. (35) Fisher, E. M.; Pitz, W. J.; Curran, H. J.; Westbrook, C. K. Proc. Combust. Inst. 2000, 28, 1579−1586.

express our gratitude to Dr. Bill Schwartz of Yale University for kindly providing experimental data of esters in the nonpremixed flame study.30 The present study is financially supported by Ministry of Science and Technology in Taiwan under Contract No. MOST 103-2221-E-110-073-MY2.

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DOI: 10.1021/acs.energyfuels.5b02389 Energy Fuels XXXX, XXX, XXX−XXX