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A Combined ab Initio, Kinetic Modeling and Shock Tube Study of the Thermal Decomposition of Ethyl Formate Hongbo Ning, Junjun Wu, Liuhao Ma, Wei Ren, David F. Davidson, and Ronald K. Hanson J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b05382 • Publication Date (Web): 09 Aug 2017 Downloaded from http://pubs.acs.org on August 10, 2017

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The Journal of Physical Chemistry

A Combined ab Initio, Kinetic Modeling and Shock Tube Study of the Thermal Decomposition of Ethyl Formate Hongbo Ninga,b, Junjun Wua, Liuhao Maa, Wei Rena, b, *, David F. Davidsonc, and Ronald K. Hansonc a

Department of Mechanical and Automation Engineering, The Chinese University of Hong

Kong, New Territories, Hong Kong b

Shenzhen Research Institute, The Chinese University of Hong Kong, New Territories, Hong

Kong c

Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA

*

Corresponding author. Email: [email protected] (W.R.)

ABSTRACT: The potential energy surfaces (PESs) and reaction rate constants of the unimolecular decomposition of ethyl formate (EF) were investigated using high-precision theoretical methods at the CCSD(T)/CBS(T-Q)//M06-2x/6-311++G(d,p) level of theory. The calculated PESs of EF dissociation and molecular decomposition reactions indicate that the intramolecular H-shift to produce formic acid and ethylene is the dominant decomposition pathway. A detailed chemical kinetic mechanism for EF pyrolysis was constructed by incorporating the important reactions of EF and its radicals into an existing mechanism previously developed for small methyl esters. The updated mechanism was first used to reproduce CO, CO2 and H2O concentration time-histories during EF pyrolysis in the shock tube reported by Ren et al. [Ren, W.; Mitchell Spearrin, R.; Davidson, D. F.; Hanson, R. K. J. Phys. Chem. A 2014, 118, 1785−1798]. The rate of production and sensitivity analyses show that the competing dehydration and decarboxylation channels of the intermediate formic acid control the final product yields of EF pyrolysis. The EF mechanism was further validated against the shock tube data of OH, CO, CO2 and H2O time-histories measured during EF oxidation (equivalence ratio Φ = 1.0) at 1331−1615 K and 1.52−1.74 atm. This revised EF mechanism captured all the species time-histories over the entire temperature range. Such modeling capability was due to the more accurate rate constants of EF reactions determined by high-precision theoretical calculations and a high-fidelity C0−C2 basis mechanism.

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1. INTRODUCTION Worldwide energy demand including the demand for petroleum-based transport fuels is estimated to continue to grow by 48% from 2012 to 2040 according to the International Energy Outlook 2016 (IEO2016). The ubiquitous use of fossil fuels has led to critical societal issues such as energy security and climate change. One promising solution is to reduce the energy dependence on fossil fuels by using other alternative fuels such as biodiesel. Biodiesel is typically produced through the transesterification of vegetable oils or animal fats with methanol yielding fatty acid methyl esters (FAMFs).1,2 Considering that the use of methanol in the transesterification process achieves only 90% wt renewable,3 biodiesel can be a fully renewable fuel if the alcohol used in the conversion process also comes from a renewable source such as bioethanol. Moreover, bioethanol is less toxic, corrosive and volatile than methanol, providing a safer work environment during the transesterification process.4 Hence, biodiesel in the form of fatty acid ethyl esters (FAEEs) produced through the conversion of biolipids with bioethanol could further enhance the sustainability of biofuels.5,6 Regarding the combustion research of biodiesels, most previous chemical kinetics studies were mainly focused on methyl esters with C1−C4 in the aliphatic chain7−10 and larger methyl esters.11,12 Ethyl esters have received relatively less attention on combustion research in the past decade. They were mainly selected as the molecular counterparts for comparison studies with the corresponding methyl esters to investigate the effects of different molecular structures on combustion chemistry. Osswald et al.13 examined the influence of fuel-specific destruction pathways of isomers, methyl acetate (MA, CH3COOCH3) and ethyl formate (EF, HCOOC2H5), in rich flames and measured the stable and radical species using molecular-beam sampling and isomer-selective VUV-photoionization mass spectroscopy. However, no kinetic modeling was studied in that work. Westbrook et al.14 developed a detailed oxidation mechanism to describe the laminar premixed flames of four small alkyl esters including methyl formate (MF, HCOOCH3), MA, EF and ethyl acetate (EA, CH3COOC2H5). The model development employed a principle of similarity of functional groups containing the H-atom abstraction and unimolecular decomposition reactions for each of these fuels. We recently studied the thermal decomposition of C3−C5 ethyl esters by measuring the concentration time-histories of CO, CO2 and H2O in the shock tube,15 and developed a pyrolysis mechanism for EF, EA and EP (ethyl propanoate) based on the Westbrook et al.14 and Metcalfe et al.16 mechanisms. However, the rate constants of several key fuel-specific reactions must be modified without any theoretical verifications to reproduce the experimental results. Akih-Kumgeh and


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Bergthorson17 investigated different ignition behaviors of three pairs of methyl and ethyl esters including MF/EF, MA/EA and MP/EP in the shock tube. A new chemical kinetic model based on the USC-II mechanism18 was proposed to understand the combustion chemistry of MA, EF and EA. Wang et al.19 systematically studied the oxidation characteristics of several small alkyl esters with = 200(/300) ." cm1

. The Lennard-Jones collision diameter σ = 3.54 Å and well-depth ɛ = 64.8 cm-1 were

applied for Ar; the LJ parameters σ =5.12 Å and ɛ = 427.0 cm-1 were used for EF.30 The LJ parameters for EF radicals, CH3CH2OC(=O), HC(=O)OCHCH3 and HC(=O)OCH2CH2, were treated the same as EF. A quantum tunneling correction was included for all TSs using the asymmetric Eckart approximation.31 2.2 Kinetic Modeling The detailed EF mechanism was constructed by updating the recent methyl ester (MF, MA and MP) combustion model developed by Felsmann et al.9 The added EF sub-mechanism


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includes the EF unimolecular decomposition and subsequent reactions of EF radicals with their rate constants determined in this work, as well as the H-abstraction reactions of EF by H, OH and CH3 with their rate constants adopted from our unpublished results. The Habstraction reaction rate constants were calculated using transition state theory at CCSD(T)/CBS(D-T) and CCSD(T)/CBS(T-Q)//M06/6-31G(d,p) level of theory with 1-D hindered rotor and Eckart tunneling corrections over the temperature range of 500−2500 K. Considering the importance of the key intermediate during EF pyrolysis, the HCOOH reactions were also updated in the Felsmann et al.9 mechanism by adopting the recent experimental and theoretical results.32,33 All the thermodynamics parameters are taken from Felsmann et al.9 and Ren et al.15 Apart from the EF and HCOOH sub-mechanisms, the updated mechanism also contains the chemical reactions of small species C0−C2 that are available in the Felsmann et al.9 mechanism without any modification. Finally, we obtain the updated EF mechanism with 133 species and 977 reactions, which is provided in the Supporting Information. This mechanism can be used to simulate both pyrolysis and oxidation of EF at high temperatures. 2.3 Shock Tube Experiment All the experiments were performed in a stainless-steel high-purity shock tube at Stanford University. Laser absorption diagnostics were employed in shock tube experiments to monitor the time-resolved species concentration time-histories. We have recently reported the CO, CO2 and H2O time-histories measured during the pyrolysis of 2000 ppm EF in argon,15 which were cited in this study for kinetic modeling analysis. Further details of the pyrolysis experiments can be found in reference [15]. It is known that fuel molecules break first at the early times of high-temperature combustion. The fuel decomposition chemistry significantly affects the oxidation chemical kinetics. Hence, we performed additional shock tube measurements of EF oxidation to further validate the current EF mechanism. All the oxidation experiments were also conducted in the Stanford shock tube by monitoring OH, CO, CO2 and H2O concentration time-histories. The EF mixtures (equivalence ratio Φ = 1) of 0.11% EF/0.4% O2/Ar were used for all the oxidation experiments; the relatively low fuel concentration was employed to reduce the temperature variation during oxidation. Technical details of laser absorption diagnostics for shock tube multi-species measurements can be found in our recent study.8 3. RESULTS AND DISCUSSION 3.1 Potential Energy Surface



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EF has conformational isomerism due to its two internal rotations. The rotations around O=C−O and O−C2H5 bonds generate trans and gauche conformers, respectively. The energy of trans-geometry was predicted to be 0.35 kcal mol-1 lower than that of gauche-geometry at the CCSD(T)/CBS(T-Q) level. Hence, only the most stable conformer with the lowest energy was used in this study with its molecular properties incorporated into RRKM/ME calculations. The Cartesian coordinates, frequencies and internal rotors are provided in the Supporting Information. EF can decompose via the direct bond fissions of C−C, C−O and C−H, and the intramolecular H-shift. Figure 1 depicts 13 reaction pathways of EF unimolecular decomposition considered in this study. Among all these reactions, the following four reaction channels dominate EF decomposition: EF = HC(=O)OCH2 + CH3

(R1)

EF = HC(=O)O + C2H5

(R2)

EF = HC(=O)OH + C2H4

(R3)

EF = CO + C2H5OH

(R4)

In particular, reaction R3 proceeds via two different reaction pathways to form HCOOH + C2H4 shown in Figure 1. One pathway involves a four-member ring transition state (TS-6) with a barrier of 65.0 kcal mol-1, and the other one takes a six-member ring transition state (TS-7) with a barrier of 50.2 kcal mol-1. The rate constants of R3 are thus obtained by the summation of these two pathways. These two decomposition channels have lower energy barriers compared with the other pathways. Moreover, the decomposition product of reaction R3, formic acid (HCOOH), could further decompose through the dehydration (HCOOH = CO + H2O) and decarboxylation (HCOOH = CO2 + H2) reactions to form the final pyrolysis products. Hence, the key intermediate (HCOOH) significantly affects the final product yields of EF pyrolysis. For barrierless reactions of EF, minimum energy potentials (MEPs) were obtained using the multi-reference method CASPT2/6-311++G(d,p)//CASSCF/6-311++G(d,p).34,35 In order to obtain more accurate MEPs, the complex energy at each point on the MEP was multiplied by a scaling factor that accounts for the ratio of the CCSD(T)/CBS(T-Q) reaction enthalpy to the CASPT2 reaction energy.36 The active space (2e, 2o) including the bonding and antibonding (σ and σ*) was chosen to describe the dissociation bonds C−C and C−H. The active space (8e, 6o) consisting of the π and π* orbitals of C=O, two O-atom 2s lone pairs and the σ and σ* orbitals was selected to describe the dissociation bond C−O. A level shift of 0.3


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Hartree was considered in the CASPT2 calculation of the barrierless reactions. All the MEPs are provided in Figure S1 of the Supporting Information.

Figure 1. Potential energy diagram for EF unimolecular decomposition at the CCSD(T)/CBS(T-Q)//M06-2x/6-311++G(d,p) level of theory (including the zero-point vibrational energies). EF can also be consumed by the H-abstraction reactions by small radicals such as H, CH3 and OH leading to three EF radicals, i.e. CH3CH2OC(=O), HC(=O)OCH2CH2, and HC(=O)OCHCH3. Figure 2 depicts the calculated potential energy diagram for the decomposition and isomerization reactions of these radicals (denoted as W1, W2 and W3) at the CCSD(T)/CBS(T-Q) level of theory. The W1 radical with its trans-conformer 0.2 kcal mol-1 lower than the cis-conformer involves four $-scission and isomerization pathways. For the $-scission reactions, the cis-geometry transition state (cis-TS-R-1) for the CO2 + C2H5 channel is 18.0 kcal mol-1 lower than the trans-geometry; in contrast, the trans-geometry (trans-TS-R-2) for the CO + C2H5O channel is 3.6 kcal mol-1 lower than the cis-geometry. The isomerization of W1 occurs by 1,3-H and 1,4-H shift via TS-R-4 and TS-R-3 transition states to form W3 and W2 with a barrier of 37.0 and 23.7 kcal mol-1, respectively. Similarly, W2 and W3 radicals also take the $-scission and isomerization reactions with their reaction pathways shown in Figure 2. However, for W2 radical reactions, no local minimum was found for the geometry optimization of the transition state (TS-R-5, to form HCOO + C2H4) at the uM06-2x/6-311++G(d,p) level. Hence, the TS-R-5 transition state was optimized at the uHF/6-311G(d,p) level. To evaluate the energy deviation using this



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optimized method, we further selected another reaction EF = HCOOH + C2H4 (via TS-6 or TS-7 shown in Figure 1) to recalculate the energies at the CCSD(T)/CBS(T-Q)//uHF/6311G(d,p) level of theory. The calculated results indicate that the average deviation for TS and product is only 1.4 and 0.3 kcal mol-1, respectively.

Figure 2. Potential energy diagram for EF radical decomposition and isomerization reactions at the CCSD(T)/CBS(T-Q) level of theory (including the zero-point vibrational energies). 3.2 Rate Constant Calculation The detailed information of the obtained high-pressure limit (HPL) and pressuredependent rate constants of the major reactions are given in Table S2 and S3 of the Supporting Information. To our knowledge, very few direct measurements of the rate constants for EF and its radicals have been reported. Thus the theoretical calculation and estimation are the primary sources of knowledge of these rate constants. Figure 3(a) and (b) compare our calculated HPL rate constants for the major dissociation and intramolecular H-shift reactions of EF with the estimated values from the analogous reactions used in the previous combustion mechanisms for small methyl esters.14,17 There exist certain discrepancies between the estimated HPL rate constants and our theoretical calculations especially for reactions EF = HCOO + C2H5, EF = HCOOH + C2H4 and EF = CO + C2H5OH at lower temperatures (500−1000 K). However, both mechanisms14,17 directly used the HPL rate constants for EF unimolecular reactions without considering their pressure dependence. Hence, the pressure-dependent rate constants obtained by theoretical calculations are indispensable for the combustion model development. In this study, the pressure-dependent rate constants were determined by solving the timedependent multi-well master equation in the MESS code.28,29 The master equation in the


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MESS code is written as %&(%' = )&, where matrix G describes the chemical exchanges between different wells and products, and the collisional energy transfer in each well; w(t) is a vector containing the populations of energy states in all the wells at time t. At sufficiently low temperatures, the eigenvectors of G could be divided into two types: slow eigenmodes (chemically significant eigenmodes, CSEs) and fast eigenmodes (internal energy relaxation eigenmodes, IEREs). The CSEs correspond to the N−1 least negative eigenvalues of G, where N is the number of species or chemical configurations. The IEREs describe the collisional energy relaxation within each well. In general, the number of IEREs is very large in a meaningful calculation and their eigenvalue spectrum is almost continuous. The N−1 CSEs are distinctly discretized outside the IERE continuum. When the temperature is sufficiently high, the fastest CSEs would merge into the IERE continuum, implying that the chemical reaction and the collisional energy relaxation occur on the same time scale. Physically, such a merging occurs when species equilibrate with each other as rapidly as their internal energy relaxes, leading to two chemically indistinguishable species. Further discussion can be found in the recent study by Zhang et al.37 Hence, the rate constants for the isomerization reactions of W1, W2 and W3 radicals are given in a low-temperature range as these wells become chemically unstable at higher temperatures. For example, radical W1 equilibrates with W2 very fast on the time scale that is comparable to the collisional relaxation at temperatures > 900 K and pressure near 1 atm. It means that W1 and W2 are indistinguishable and the corresponding CSEs lay in the quasicontinuum of IERE. Hence, these EF radical isomerization reactions are not included in the updated EF mechanism as the shock tube experiments are usually conducted at relatively high temperatures >1000 K. Huang et al.38 have also reported the similar well merge phenomena. In addition, Kaiser recently measured the rate constants of W1 radical decomposition CH3CH2OC(=O) = CO2 + C2H5 at 1 atm and 297−400 K using gas chromatography-flame ionization detection analysis.39 Figure 3(c) compares the calculated rate constants of this radical decomposition reaction with the reported experimental data over the same temperature range of 297−400 K. Our calculations are found 4−5 times lower than the experimental results. Considering the uncertainty of the relative energy using the CCSD(T)/CBS(T-Q) method is about ±1.0 kcal mol-1, we expect an uncertainty factor of 5.4 at 297 K and 3.5 at 400 K, respectively. Kaiser has also estimated that the experimentally determined rate constant has an uncertainty factor of ~2 at 297−400 K and the uncertainty of



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the activation energy is around ±0.85 kcal mol-1.39 Hence, our calculations are within the range of measurement uncertainties and considered acceptable. In addition, the ab initio calculations of an analogous reaction CH3OCO = CO2 + CH3 performed by Huynh et al.40 and Tan et al.7 are also plotted in Figure 3(c) for comparison. It is seen that our calculations are in good agreement (difference less than a factor of 2) with the results reported by Tan et al.7 The pressure dependence of rate constant was also investigated and compared with the values available in the literature; see Figure S2 of Supporting Information. Figure 3(d) plots the rate constants of the representative reaction EF = HCOOH + C2H4 at 0.01 atm, 1 atm, and HPL; the HPL rate constants estimated by Westbrook et al.14 and Akih-Kumgeh et al.17 are also plotted for comparison. The pressure dependence becomes more significant at higher temperatures, i.e., the rate constant at the HPL is ~50 times larger than that at 0.01 atm at T >1000 K.

Figure 3. HPL rate constants (solid line, this work; dashed line, Akih-Kumgeh et al.17; dotted line, Westbrook et al.14) for (a) EF dissociations and (b) EF molecular channels between 500 and 2000 K. (c) Rate constants for the radical decomposition reaction CH3CH2OC(=O) =


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CO2 + C2H5 at 297−400 K and 1 atm; line 1, experimental results;39 line 2, this work; rate constants of an analogous reaction CH3OC(=O) = CO2 + CH3 calculated by Huynh et al.40 (line 3) and Tan et al.7 (line 4) are plotted for comparison. (d) Pressure-dependent rate constants for reaction EF = HCOOH + C2H4 at 0.01 atm, 1 atm, and HPL obtained in this work; the HPL rate constants estimated by Akih-Kumgeh et al.17 and Westbrook et al.14 are plotted for comparison. 3.3 Chemical Kinetic Mechanism The EF pyrolysis sub-mechanism mainly contains three types of reactions: (a) the unimolecular decomposition of EF, both the dissociation and intramolecular H-shift reactions; (b) H-abstraction reactions of EF; and (c) EF radical decomposition reactions. The EF submechanism was then incorporated into the combustion mechanism previously developed for small methyl esters by Felsmann et al.9 The key intermediate species (HCOOH) also exists in the Felsmann et al.9 mechanism with its reaction rate constants calculated by Chang et al.41 at high- and low-pressure limits. Farooq et al.32 recently performed shock tube measurements of the rate constants for the two competing decomposition channels HCOOH = CO + H2O and HCOOH = CO2 + H2 at 1 and 6.5 atm, respectively. Considering our shock tube experiments were conducted at the pressure of ~1.5 atm, it is more accurate to use the rate constants obtained by interpolating the experimental data at pressures of 1 and 6.5 atm reported by Farooq et al.32 Rate constants of the other HCOOH reactions including H-abstractions and the subsequent HOCO and OCHO radical decompositions were recently calculated by Marshall et al.33 and updated in the Felsmann et al.9 mechanism. All the chemical reactions added or with their rate constants updated in the Felsmann et al.9 mechanism are summarized in Table 1; the full mechanism is provided in the Supporting Information. Table 1. EF Pyrolysis Mechanism (Only the Added or Updated Reactions). Rate Constants Are Given as * = +,- ./0 (− No. R1

R2

Reactions EF = HCOOCH2 + CH3

EF = HCOO + C2H5

2 3,

), Units in s-1, cm-3 and cal mol-1.

Pressure (atm)

LogA

n

E

Ref.

0.01

49.78

-11.49

95292.5

This work a

0.1

44.84

-9.37

95515.7

1

34.25

-5.83

92967.3

10

24.96

-2.87

90158.6

100

19.50

-1.16

88377.3

HPL

16.87

-0.35

87484.1

0.01

50.52

-11.59

92872.5


This work a


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

R3

R4

R5

R6

R7

R8

EF = HCOOH + C2H4

EF = CO + C2H5OH

W1 = CO2 + C2H5

W1 = CO + CH3CH2O

W2 = HCOO + C2H4

W3 = HCO + CH3CHO

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0.1

43.29

-8.86

92142.0

1

31.63

-5.03

89095.2

10

22.61

-2.16

86340.9

100

17.76

-0.64

84753.8

HPL

15.52

0.05

83995.1

0.01

21.13

-2.97

49934.0

0.1

14.56

-0.86

48029.0

1

7.85

1.25

45879.3

10

3.56

2.58

44452.5

100

1.63

3.18

43794.6

HPL

-1.70

4.16

42082.7

0.01

17.30

-1.92

62810.7

0.1

8.83

0.90

60825.6

1

-1.15

4.08

57802.5

10

-7.85

6.18

55631.6

100

-11.21

7.22

54503.5

HPL

-15.20

8.40

52586.7

0.01

20.13

-3.47

12975.5

0.1

24.87

-4.65

14864.4

1

24.81

-4.28

15639.9

10

24.61

-3.90

16493.6

100

21.21

-2.58

16311.0

HPL

12.47

0.43

14577.8

0.01

-13.22

7.41

20034.9

0.1

-13.90

7.91

19846.4

1

-29.18

12.60

11260.1

10

-2.33

4.18

16771.0

100

14.56

-0.75

22251.4

HPL

12.42

0.52

23563.7

0.01

15.68

-1.85

22978.9

0.1

27.58

-5.19

27304.4

1

27.77

-4.90

28435.0

10

23.75

-3.43

27971.8

100

19.88

-2.10

27225.5

HPL

12.52

0.26

25079.7

0.01

39.21

-8.74

35030.4

0.1

36.22

-7.53

35083.2

1

31.11

-5.72

34268.5


This work a

This work a

This work a

This work a

This work a

This work a

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10

26.22

-4.05

33287.7

100

21.72

-2.56

32182.6

HPL

13.94

-0.10

29754.5

R9

EF + OH = W1 + H2O

HPL

3.48

3.10

-891.5

This work a

R10

EF + CH3 = W1 + CH4

HPL

1.16

3.85

9010.5

This work a

R11

EF + H = W1 + H2

HPL

6.88

2.23

7299.2

This work a

R12

EF + OH = W2 + H2O

HPL

3.08

2.78

-855.6

This work a

R13

EF + CH3 = W2 + CH4

HPL

0.50

3.88

11639.6

This work a

R14

EF + H = W2 + H2

HPL

7.18

2.21

9866.2

This work a

R15

EF + OH = W3 + H2O

HPL

1.02

3.13

-4263.9

This work a

R16

EF + CH3 = W3 + CH4

HPL

-0.12

3.84

8814.5

This work a

R17

EF + H = W3 + H2

HPL

6.59

2.22

6360.0

This work a

R18

HCOOH = CO + H2O

1.0

11.01

0.00

50970.9

[32] b

6.5

12.96

0.00

60159.2

1.0

8.25

0.00

41993.3

6.5

8.44

0.00

39888.9

R19

HCOOH = CO2 + H2

[32] b

R20

HCOOH + H = HOCO + H2

HPL

2.36

3.27

4858.0

[33] b

R21

HCOOH + H = OCHO + H2

HPL

5.62

2.26

14091.0

[33] a

R22

HCOOH + CH3 = HOCO +CH4

HPL

-6.41

5.80

2200.0

[33] b

R23

HCOOH + O = HOCO + OH

HPL

1.71

3.42

4216.0

[33] b

R24

HCOOH + O = OCHO + OH

HPL

5.23

2.10

9880.0

[33] a

R25

HCOOH + OH = HOCO + H2O

HPL

-5.11

5.57

-2365.0

[33] b

R26

HCOOH + OH = OCHO + H2O

HPL

-4.31

4.91

-5067.0

[33] a

R27

HCOOH + HO2=HOCO + H2O2

HPL

-0.33

3.98

16787.0

[33] b

R28

HCOOH + HO2=OCHO + H2O2

HPL

1.59

3.08

25206.0

[33] a

R29

HOCO + HO2=HCOOH + O2

HPL

11.60

0.00

0.0

[33] a

R30

HCOOH + O2 = OCHO + HO2

HPL

13.48

0.00

63000.0

[33] a

R31

CO + OH = HOCO

0.013158

15.23

-2.68

859.0

[33] a

0.13158

18.77

-3.35

887.0

1.0

20.30

-3.50

1309.0

1.3158

20.41

-3.50

1309.0

13.158

20.85

-3.32

1763.0

131.58

20.04

-2.78

2056.0

HPL

11.91

0.41

35335.0

LOW

26.78

-3.15

37116.0

TROE

/ 0.39 1.0E-30

R32

HOCO(+M) = CO2 + H(+M)

[33] a

1.0E30 /

R33

HOCO + H = CO2 + H2

HPL

17.49

-1.35

555.0

[33] a

R34

HOCO + H = CO + H2O

HPL

15.78

-0.53

2125.0

[33] a



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R35

HOCO + O = CO2 + OH

HPL

12.95

0.00

0.00

[33] a

R36

HOCO + OH = CO2 + H2O

HPL

12.66

0.00

-89.0

[33] a

HPL

6.98

2.00

-89.0

DUPLICATE HOCO + OH = CO2 + H2O DUPLICATE R37

CO + H2O2 = HOCO + OH

HPL

4.56

2.50

28660.0

[33] a

R38

HOCO + HO2 = CO2 + H2O2

HPL

13.60

0.00

0.0

[33] a

R39

HOCO + O2 = CO2 + HO2

HPL

9.60

1.00

0.0

[33] a

R40

OCHO = CO2 + H

HPL

10.00

0.00

0.0

[33] a

R41

OCHO + O2 = CO2 + HO2

HPL

13.70

0.00

0.0

[33] a

Note:

a

Added reactions.

b

Updated reactions. EF, HCOOCH2CH3; W1, CH3CH2OCO; W2,

HCOOCH2CH2; W3, HCOOCHCH3.

3.4 Shock Tube Species Time-Histories 3.4.1 EF Pyrolysis The species concentration time-histories measured behind reflective shock waves were simulated using the Chemkin-pro software42 to gain further insight into the pyrolysis mechanism of EF. Figure 4 presents the simulation results using the current EF mechanism compared with the shock tube pyrolysis data of 2000 ppm EF/Ar and the previous simulation results reported by Ren et al.15 Note that several reaction rate constants were modified by Ren et al.15 to match the experimental data without providing theoretical validations. The current EF mechanism also shows very good agreement with the measured time-histories of CO, H2O and CO2 over the entire temperature range of 1314−1636 K. For the major pyrolysis products of CO and H2O, our model accurately captured the early-time formation and the final plateau level (within 5%). Additionally, CO2 was also predicted to be a minor product (less than 100 ppm yield at 1636 K) during EF pyrolysis, in relatively good agreement with the experimental results.


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Figure 4. Comparisons of the shock tube measured concentration time-histories of (a) CO, (b) H2O and (c) CO2 with the model predictions during the pyrolysis of 2000 ppm EF/Ar. Solid line, experiment;15 dotted line, simulation using the Ren et al. mechanism;15 dashed line, simulation in this work. Additionally, it is of interest to compare the simulation performance of the current EF mechanism with other mechanisms available in the literature.14,17 Here, we only demonstrate the comparison at a representative temperature for each of the measured species. Figure 5 presents the measured CO and H2O time-histories at 1402 K and CO2 time-history at 1449 K along with the different model simulations. It is evident that the Westbrook et al.14 mechanism underpredicted the overall thermal decomposition of EF. The Akih-Kumgeh et al.17 mechanism overpredicted CO and CO2 production, but underpredicted H2O formation. Such discrepancies are due to the different branching ratios of EF unimolecular decomposition used in the mechanism. There is no surprise that the Ren et al.15 mechanism predicted all three time-histories relatively well as that mechanism was modified to fit the experimental data. In comparison, the current EF mechanism with the rate constants of EF reactions calculated by high-level theoretical methods shows very good agreement with the experimental data.



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Figure 5. Comparisons of the measured (a) CO at 1402 K, (b) H2O at 1402 K, and (c) CO2 at 1449 K during EF pyrolysis15 with the simulation results obtained using the mechanisms developed by Westbrook et al.14, Ren et al.15, Akih-Kumgeh et al.17, and in this work.


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Figure 6. ROP (a−c) and sensitivity (d−f) analyses for CO, H2O and CO2 for 2000 ppm EF/Ar at 1467 K using the current mechanism. Figure 6 plots the rate of production (ROP) and sensitivity analyses of CO, H2O and CO2 for 2000 ppm EF/Ar at 1467 K. The ROP analyses of all three species indicate that CO and H2O are mainly produced by the dehydration reaction of HCOOH. The CO formation is also sensitive to the EF molecular channel EF = C2H5OH + CO at the very early times, but is negligible in the H2O sensitivity shown in Figure 6(e). In comparison, the ROP analysis of CO2 shown in Figure 6(c) indicates the decarboxylation reaction of HCOOH controls the CO2 formation, and the EF dissociation reaction EF = C2H5 + OCHO appears significant to the CO2 formation at the early times. However, the branching ratios of the two competing pathways of HCOOH decomposition are > 0.95 for the CO + H2O channel and < 0.05 for the CO2 + H2 channel at 1300−1600 K and 1 atm. Hence, CO2 is predicted as a minor product during EF pyrolysis, which is consistent with the experimental observation. 3.4.2 EF Oxidation As discussed in Section 2, the updated EF mechanism can also be used to simulate EF oxidation at high temperatures. Hence, a further model validation was performed by simulating the EF oxidation in the shock tube. The oxidation experiments covered a temperature range of 1331−1615 K, pressure of 1.52−1.74 atm, and equivalence ratio of 1.0 for 0.11% EF/0.4% O2/Ar. Figure 7 compares the simulated CO, CO2, H2O and OH timehistories using the updated EF mechanism with the shock tube data. The current mechanism predicted all the measured species time-histories in an excellent way over the entire temperature range. The difference of the ignition delay time, defined as the time when the



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OH concentration reaches half of the final plateau level, between the simulation and experiment is within 8% over 1331−1615 K. Moreover, OH shows the evident two-stage formation in Figure 7(d), which is well captured by the current EF mechanism. At the temperature of 1352 K, the first plateau level of OH concentration measured at the early times is ~65 ppm, in excellent agreement with the model prediction of 69 ppm. The second plateau measured at the later times is ~130 ppm, also in excellent agreement with the model prediction of 138 ppm. In addition, the differences of the plateau levels for all the species are within 10%, mostly less than 5% for OH, CO and H2O.

Figure 7. Comparisons of the measured concentration time-histories of (a) CO, (b) CO2, (c) H2O and (d) OH with the model simulations for 0.11% EF/0.4% O2/Ar (Φ = 1.0). Solid line, experiment; dashed line, model simulation. Figure 8 depicts the sensitivity analysis of CO2 at 1476 K performed and t = 5 µs and 1000 µs, respectively. Note that only the top ten reactions are illustrated in the sensitivity plot. At t = 5 µs corresponding to 50% of EF consumption, the dissociation reaction EF = C2H5 + OCHO shows the largest positive sensitivity, whereas the molecular channel EF = HCOOH + C2H4 demonstrates the largest negative sensitivity for CO2 formation. The H-abstractions of EF by H-atom to form W1 and W2 radicals promote the CO2 formation. However, at t = 1000


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µs corresponding to 100% EF consumption, the CO2 formation is mainly controlled by the secondary reactions, particularly the reactions of C0−C2 species.

Figure 8. CO2 sensitivity analysis for 0.11% EF/0.4% O2/Ar (Φ = 1) at 1476 K and (a) t = 5 µs, (b) t = 1000 µs. We also performed the sensitivity analysis of the key intermediate OH radical at 1352 K. At the early time (30 µs) shown in Figure 9(a), the EF dissociation EF = C2H5 + OCHO again shows the strong positive sensitivity, in addition to the chain-branching reaction H + O2 = OH + O that controls the ignition process. At the later time (t = 1000 µs) in Figure 9(b), the OH formation is mainly controlled by the chain-branching reaction H + O2 = OH + O. Different from the early-time chemical kinetics, the OH formation has modest sensitivity to several secondary reactions such as CH3 + H(+M) = CH4(+M) and HCO(+M) = H + CO(+M).

Figure 9. OH sensitivity analysis for 0.11% EF/0.4% O2/Ar (Φ = 1) at 1352 K and (a) t = 30 µs, (b) t = 1000 µs. Based on these sensitivity analyses, it can be concluded that the EF unimolecular decomposition plays a significant role during EF pyrolysis and at the early times of EF oxidation. The C0−C2 core mechanism appears with modest sensitivity to affect the overall reactivity in the pyrolysis/oxidation system. Hence, the current kinetic mechanism with the



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EF reactions calculated using the high-precision theoretical methods and the C0−C2 core mechanism validated in the previous study9 can well predict the shock tube experimental data. To further verify the updated mechanism obtained in this work, we compared the model simulations with the ignition delay times measured by Akih-Kumgeh et al.43 over a wide range of shock tube conditions: (1) Φ = 1.0, Ar/O2 = 18.8, P = 12 atm; (2) Φ = 0.5, Ar/O2 = 8.88, P = 13 atm; (3) Φ = 0.5, Ar/O2 = 8.88, P = 1 atm; and (4) Φ = 2.0, Ar/O2 = 18.8, P = 12 atm. Figure 10 presents the detailed comparisons of ignition delay times at 1200−1550 K, 1−13 atm, and equivalence ratios of 0.5−2.0. In general, the current mechanism well predicted the ignition delay times of EF over all the experimental conditions. Particularly the pressure dependence of the ignition delay times was accurately captured according to the two measurements at 1 and 13 atm for the same equivalence ratio of Φ = 0.5.

Figure 10. Comparisons of the measured and simulated ignition delay times (τ) for EF/Ar/O2 mixtures at 1200−1550 K, 1−13 atm, and equivalence ratios of 0.5−2.0. Symbol:43 (●), Φ = 1.0, Ar/O2 = 18.8, P = 12 atm; (▼), Φ = 0.5, Ar/O2 = 8.88, P = 13 atm; (▲), Φ = 0.5, Ar/O2 = 8.88, P = 1 atm; (■), Φ = 2.0, Ar/O2 = 18.8, P = 12 atm. Solid line, simulation in this work. 4. CONCLUSIONS The PESs and rate constants of EF and its radical decomposition were investigated using high-precision quantum chemical methods. The PES calculations confirmed the EF molecular channel to produce HCOOH + C2H4 the dominated decomposition pathway. A detailed kinetic mechanism of EF (133 species and 977 reactions) was developed based on the previous kinetic model for methyl esters proposed by Felsmann et al.9 by adding the major EF reactions. In addition, the reaction rate constants of the key intermediate HCOOH were updated in the mechanism by using the recent experimental results32 and the ab initio calculations.33 The simulation results agree well with the measured CO, H2O and CO2 timehistories during EF pyrolysis at 1314−1636 K in the shock tube reported previously by Ren et


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al.15 ROP and sensitivity analyses indicate that the two competing decomposition channels of HCOOH determine the final product yields of EF pyrolysis. Our kinetic model was further used to simulate the OH, CO, CO2 and H2O time-histories measured during the oxidation of EF in the shock tube. Again the current mechanism can reproduce well all the species concentration profiles. In particular, our mechanism predicted the ignition delay times of EF within 8% and the plateau concentration levels within 10% compared with the experimental results at 1331−1615 K. Such a good modeling capability is mainly due to the more accurate EF reaction rate constants determined by high-precision theoretical calculations and the C0−C2 core mechanism with a relatively high fidelity. We expect that this updated mechanism could be used as a base mechanism to study the pyrolysis chemistry of other large ethyl esters.

ASSOCIATION CONTENT Supporting Information The optimized geometries of reactants, products and transition states, internal rotors, harmonic vibrational frequencies, rotational constants, Table S1−S3, Figure S1−S2 are provided in the Supporting Information. This Supporting Information is available free of charge on the ACS Publications website.

ACKNOWLEDGMENTS The authors are very grateful to Dr. Stephen J. Klippenstein at Argonne National Laboratory and Dr. Jingbo Wang at Sichuan University for their kind help with the MESS calculations, and Dr. Peng Zhang at Hong Kong Polytechnic University for useful discussions on well merge phenomenon. We are also thankful for Shenzhen Supercomputing Center and Combustion Kinetics Center of Sichuan University for providing computational facilities. This work is supported by National Natural Science Foundation of China (11502222) and Research Grants Council of the Hong Kong SAR, China (14234116). Ronald Hanson and David Davidson acknowledge support by the Combustion Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001198.



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