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Article
REDUCED CHEMICAL KINETIC MECHANISM
FOR METHYL PENTANOATE COMBUSTION
Ilya E. Gerasimov, Tatyana A. Bolshova, Ivan A. Zaev, Alexander V.
Lebedev, Boris V. Potapkin, Andrey G. Shmakov, and Oleg P. Korobeinichev
Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b01907 • Publication Date (Web): 24 Oct 2017
Downloaded from http://pubs.acs.org on October 26, 2017
Just Accepted
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Energy & Fuels is published by the American Chemical Society. 1155 Sixteenth Street
N.W., Washington, DC 20036
Published by American Chemical Society. Copyright © American Chemical Society.
However, no copyright claim is made to original U.S. Government works, or works
produced by employees of any Commonwealth realm Crown government in the course
of their duties.
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REDUCED CHEMICAL KINETIC MECHANISM FOR METHYL PENTANOATE
COMBUSTION
I.E. Gerasimov1, T.A. Bolshova1, I.A. Zaev2, A.V. Lebedev2, B.V. Potapkin2,
A.G. Shmakov1,3, O.P. Korobeinichev1
1
Voevodsky Institute of Chemical Kinetics and Combustion, Novosibirsk, Russia
2
Kintech Lab Ltd., Moscow, Russia
3
Novosibirsk State University, Novosibirsk, Russia
ABSTRACT
A reduced mechanism for combustion of methyl pentanoate (MPe), consisting of 330 elementary
reactions involving 92 species, has been developed based on the previously proposed combustion
mechanism for MPe using the Mechanism Workbench software. The reduced model has been
validated against experimental data on the structure of burner-stabilized stoichiometric and fuel-rich
MPe/O2/Ar flames at pressures of 20 Torr and 1 atm. The modeling results for the full and reduced
mechanisms are in good agreement for major flame species and for most of the intermediates,
including hydrogen, methane, methyl radical, ethylene, acetylene, propyne, butadiene, methyl
propenoate, and other intermediates. The proposed kinetic model also was validated against
experimental data on MPe/air flame propagation velocities and extinction strain rates at atmospheric
pressure, as well as autoignition delay times of stoichiometric MPe/air mixtures at T = 815 K and
pressures p=10−18 bar.
Key words: methyl pentanoate, chemical kinetic mechanism, flame speed, reduced mechanism.
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INTRODUCTION
Recently, there has been enormous interest in renewable fuels. Their use in transport and power
system reduces the consumption of oil and net emissions of greenhouse gases and other harmful
substances into the atmosphere. The major components of biodiesel fuel derived from vegetable oils
and animal fats are fatty acid methyl esters.1 The most important feature of this fuel is that its
physical properties such as density, viscosity, and cetane number are close to the characteristics of
conventional diesel fuels. This allows it to be used both as an individual fuel and in mixtures with
conventional diesel fuel without substantially modifying the design of existing engines. It has also
been established that even partial replacement of conventional diesel fuel with biodiesel fuel
significantly reduces the formation of CO, NOx, and soot particles in internal combustion engines
and other combustion processes.2,3
The components and intermediate combustion products of biodiesel fuels have a high
molecular weight and a complex structure. The current combustion mechanisms for complex
hydrocarbons and oxygen-containing compounds contain hundreds of components and thousands of
reactions and are, thus, extremely large and require substantial computing power for
implementation.4 This necessitates the optimization of kinetic models used in combustion
calculations for real engines. In most cases, not all of the fuel conversion pathways included in
kinetic models occur in practice. The development of a skeletal mechanism makes it possible to
optimize the kinetic scheme of fuel conversion, identify the main pathways and the main reactions
involved in this conversion, and analyze the rate constants of key reactions.
Methyl pentanoate (C6H12O2, MPe) is a light model biodiesel fuel whose oxidation
mechanism can also be used to explore the oxidation kinetics of biofuels based on valerates (ethers
of pentanoic acid) derived from vegetable oils and cellulose.5 A mechanism for the oxidation of
MPe was first proposed by Dayma et al.,6 and was developed as part of the oxidation mechanisms of
methyl hexanoate,7 methyl heptanoate,8 and ethyl valerate9 based on experimental data on the
oxidation of MPe in a jet-stirred reactor at a pressure of 10 atm. Thus, the development of a reduced
model for MPe will make it possible not only to perform calculations for actual gas-dynamic
systems, but also to revise the mechanisms of heavier component of biofuels.
The combustion of MPe and its difference from other hydrocarbon fuels have been
investigated in a number of experimental and theoretical studies. In particular, the low-temperature
oxidation of MPe was investigated by HadjAli et al.,10 who presented data on its ignition delays in a
rapid compression machine at a temperature of 815 K and pressures from 10 to 17 bar. Lowtemperature processes were also studied by quantum chemical methods.11 In that work the kinetic
parameters of MPe oxidation by various possible pathways were calculated and some features of
peroxide formation in ester flames were identified.
Diévart et al.12 measured extinction strain rates for opposed-flow diffusion flames and
studied the reactivity of various methyl esters from methyl formate to methyl decanoate. They also
developed a reduced model for studied esters, which was validated with obtained data. This work
has revealed that the smaller methyl esters (C2 to C4) exhibit unique behavior while methyl esters
inclusive and larger than methyl butanoate exhibit similar global reactivity to that of the n-alkanes.
Data on the flame structure of two esters ― MPe and methyl hexanoate ― at pressures of 20
Torr and 1 atm are presented in ref 13. The investigations were carried out using molecular beam
mass spectrometry and microthermocouples. A new detailed mechanism was proposed that
satisfactorily described the concentration profiles for most species in the flames, including measured
concentrations of various intermediates.
The effect of MPe on soot formation was also examined,14 using the same methods as in the
previous study. Investigation of the structure of atmospheric flames showed that substitution part of
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Energy & Fuels
the initial fuel mixture in fuel-rich n-heptane/toluene flame (φ = 1.75) by methyl pentanoate
decreased the concentration of naphthalene, which is a typical representative of soot precursors.
Thus, sufficient experimental data are available in the literature that can be used to validate
the reduced mechanism of MPe combustion. Therefore, the objectives of this study were to test a
new approach to the reduction of detailed chemical kinetic mechanisms, develop a reduced kinetic
model of MPe combustion, and validate the reduced mechanism against the experimental data
available in the literature.
MECHANISM DEVELOPMENT
The reduced kinetic mechanism presented in this paper is based on the mechanism proposed by
Dayma, et al.6 This mechanism of chemical reactions has already been used15 to model the structure
of burner-stabilized flat flames at low (20 Torr) and atmospheric pressures and calculate the burning
velocity of atmospheric MPe/air flames. Calculations have shown a good overall agreement with
experimental data and sufficiently less discrepancies with flame speed measurements than other
models of MPe combustion. The original kinetic model consisted of 1630 reactions and 215 species,
which contain oxygen-containing compounds and hydrocarbons up to C5 inclusive, methyl
pentanoate, and its conversion products, but did not include low-temperature chemistry like O2
addition to MPe radicals and subsequent reactions.
To develop a reduced model, we used the Mechanism Workbench integrated software
(Kintech Lab),16 which allows kinetic models to be automatically reduced based on parameters
specified by the user, such as the type of modeled process, process conditions, and target
characteristics. The mechanism reduction algorithm is iterative and implements an optimal sequence
of application of the following mechanisms reduction techniques: Directed Relation Graph (DRG),
Rate of Production (ROP), and Computational Singular Perturbation (CSP). Detailed
implementations of these techniques are described in ref 17. During the iterations, the algorithm
compares the values of the variables defined by the user as reduction targets in calculations using
the full and reduced models. Based on the results of the comparison, selection of the reduction
parameters or switching between the indicated methods occurs. Also, the algorithm allows one to
simultaneously set one or more types of processes for modeling and choose their corresponding
reactor models: 0-dimensional models, burner-stabilized flames, and freely propagating premixed
flames (one-dimensional models).
To reduce the mechanism, we used an adiabatic calorimetric bomb reactor model which
describes autoignition processes. Its use as a model for reduction allows to describe all the main
steps in the chain of reactions, from initiation and branching to the reactions of the pool of
accumulated radicals with fuel molecules. The fuel was a MPe/O2/Ar mixture with different
equivalence ratios. The initial temperature was varied from 1100 K to 1700 K in increments of 50 K.
To obtain the reduced mechanism, several reduction targets were set. The induction period (ignition
delay) was set as the first target. The second target was the criterion of similarity of temperature
profiles with an absolute deviation of no more than 50 K scaled to the induction period. During the
reduction, we also controlled the maximum concentrations of H and OH radicals and some
important intermediate compounds: C2H2, H2, CH4, and methyl propenoate (C4H6O2). The reduced
models obtained for different mixtures and conditions were combined together to provide adequate
operation of the obtained reduced mechanism over the entire range of conditions. The reduced
mechanism was manually checked for any inconsistencies which could remain after automatic
reduction procedure with several reduction targets. For example, several species involved in only
one reaction and, hence, playing no significant role in the conversion of the fuel and its
decomposition products, were removed. Transport properties of MPe species were updated with data
from ref 12, to achieve a better agreement with extinction strain rate measurements (see
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Page 4 of 15
corresponding part). The resulting kinetic scheme describing the combustion of methyl pentanoate
mixtures consists of 330 elementary reactions for 92 species. 129 reactions which describe the
conversions of methyl pentanoate and the primary products of its decomposition summarized in
Table 1 (full reduced mechanism is available in supplemental material). Table 2 shows the
designations of the compounds used in the mechanism, the formulas of these compounds, and
thermodynamic data for them.
Table 1. Reduced methyl pentanoate submechanism (units: cm3, mole, 1/s, cal).
No.
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reaction
mpe+O2=mpe5j+HO2
mpe+O2=mpe4j+HO2
mpe+O2=mpe3j+HO2
mpe+O2=mpe2j+HO2
mpe+O2=mpemj+HO2
mpe+H=mpe5j+H2
mpe+H=mpe4j+H2
mpe+H=mpe3j+H2
mpe+H=mpe2j+H2
mpe+H=mpemj+H2
mpe+O=mpe5j+OH
mpe+O=mpe4j+OH
mpe+O=mpe2j+OH
mpe+O=mpemj+OH
mpe+OH=mpe5j+H2O
mpe+OH=mpe4j+H2O
mpe+OH=mpe3j+H2O
mpe+OH=mpe2j+H2O
mpe+OH=mpemj+H2O
mpe+HO2=mpe5j+H2O2
mpe+HO2=mpe4j+H2O2
mpe+HO2=mpe3j+H2O2
mpe+HO2=mpe2j+H2O2
mpe+HO2=mpemj+H2O2
mpe=mpe4j+H
mpe=mpe3j+H
mpe2j+H=mpe
nC4H9CO+CH3O=mpe
mpe=mb4j+CH3
mpe=mp3j+C2H5
mpe=me2j+nC3H7
mpe=CH3OCO+pC4H9
mpe+CH3=mpe5j+CH4
mpe+CH3=mpe4j+CH4
mpe+CH3=mpe3j+CH4
mpe+CH3=mpe2j+CH4
mpe+CH3=mpemj+CH4
mpe+CH3O=mpe3j+CH3OH
ACS Paragon Plus Environment
A
2.00E+13
4.00E+13
4.00E+13
4.00E+13
2.05E+13
9.40E+04
1.30E+06
1.30E+06
5.40E+04
1.44E+13
9.65E+04
4.77E+04
8.80E+10
9.65E+04
5.25E+09
4.68E+07
4.68E+07
3.00E+06
7.10E+06
8.40E+12
5.60E+12
5.60E+12
6.40E+03
9.64E+10
5.00E+15
5.00E+15
1.00E+14
1.50E+13
7.90E+22
1.58E+17
1.58E+17
1.13E+16
4.52E-01
2.70E+04
2.70E+04
1.00E+11
3.57E+11
1.10E+11
n
0
0
0
0
0
2.8
2.4
2.4
2.5
0
2.7
2.7
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2.7
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1.6
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2.6
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-1.8
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3.6
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2.3
0
0
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E
50870
47690
47690
45200
44910
6280
4471
4471
-1900
6095
3716
2106
3250
3716
1590
-35
-35
-1520
-596
20440
17690
17690
12400
12580
94990
94990
0
0
88630
87040
87040
81700
7154
7287
7287
7300
8663
5000
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mpe+CH3O=mpe2j+CH3OH
mpe+CH3O=mpemj+CH3OH
mpe+CH3O2=mpe5j+CH3O2H
mpe+CH3O2=mpe4j+CH3O2H
mpe+CH3O2=mpe3j+CH3O2H
mpe+CH3O2=mpe2j+CH3O2H
mpe+CH3O2=mpemj+CH3O2H
mpe+C2H5=mpe4j+C2H6
mpe2j=C2H5+mp2d
mpe2j=mpe5j
mpe2j=>mpemj
mpe3j=>1-C4H8+CH3OCO
mpe3j=CH3+mb3d
mpemj=>CH2O+nC4H9CO
mpe3j=H+mpe3d
mpe3j=H+mpe2d
mpe3j=>mpemj
mpe3j+O2=mpe3d+HO2
mpe3j+O2=mpe2d+HO2
mpe4j=H+mpe4d
mpe4j=H+mpe3d
mpe4j=mpemj
mpe4j+O2=mpe4d+HO2
mpe4j+O2=mpe3d+HO2
mpe4j=>C3H6+me2j
mpe5j=C2H4+mp3j
mpe5j+O2=mpe4d+HO2
memj=>CH2O+CH3CO
me2j=memj
HCO+CH3OCO=me2*O
mp3j=>C2H4+CH3OCO
mpmj=>CH2O+C2H5CO
mp2d+H=>mp3j
mp3j+O2=mp2d+HO2
mp3j=>mpmj
mpmj=>mp3j
mp2d=C2H3CO2+CH3
mp2d+H=mp2dmj+H2
mp2d+O=mp2dmj+OH
mp2d+OH=mp2dmj+H2O
mp2d+HO2=mp2dmj+H2O2
mp2d+CH3=mp2dmj+CH4
mp2d+OH=mp2d3j+H2O
mp2d3j=C2H2+CH3OCO
mp2d3j=mp2dmj
mp2d3j+O2=HCO+me2*O
mp2d+O=CH3OCO+CH2CHO
ACS Paragon Plus Environment
1.78E+12
3.01E+11
8.40E+12
5.60E+12
5.60E+12
6.40E+03
8.40E+12
5.00E+10
2.00E+13
1.50E+08
1.50E+08
4.53E+12
2.00E+13
1.23E+13
3.00E+13
3.20E+13
2.50E+07
1.95E+12
2.60E+11
3.00E+13
3.00E+13
4.35E+06
8.07E+11
1.95E+12
5.25E+11
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1.95E+12
1.23E+13
1.50E+08
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3.03E+13
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1.44E+13
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4.52E-01
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2.50E+07
4.60E+16
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2.6
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1.6
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0
2.7
1.8
0
3.6
2
0
1
-1.4
1.8
1200
4070
20440
17690
17690
12400
20440
10400
30700
19800
19800
34269
32000
36714
38000
34800
14500
5000
2500
39000
38000
19900
5000
5000
26591
28700
5000
36714
19800
0
34667
36714
1697
2500
14500
15500
83070
6095
3716
-596
12580
7154
2780
45000
14900
1010
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mb4j=>C2H4+me2j
mb4j=H+mb3d
mb4j+O2=mb3d+HO2
mb3d=CH3OCO+aC3H5
mb3d+OH=mb3d2j+H2O
mb3d+HO2=mb3d2j+H2O2
mb3d+HO2=mb3dmj+H2O2
mb3d2j=mb3dmj
mb3dmj=>CH2O+aC3H5CO
mpemj=>mpe3j
mpemj=>mpe2j
mpe3d+O2=mpe3d2j+HO2
mpe3d+H=mpe4d3j+H2
mpe3d+H=mpe3d2j+H2
mpe3d+OH=mpe4d3j+H2O
mpe3d+OH=mpe3d2j+H2O
mpe2d+OH=mpe3d2j+H2O
mpe3d+CH3O=mpe3d2j+CH3OH
mpe2d+CH3O=mpe3d2j+CH3OH
mpe4d3j=CH3OCO+C4H6
mp2d=mp2dmj+H
mp2d+O=me2j+HCO
mib3j=C3H6+CH3OCO
mp2d+CH3=mib3j
mb3d+H=mb3d2j+H2
mb3d+H=mb3dmj+H2
C2H4+me2j=>mb4j
mpe2d+O2=mpe3d2j+HO2
mpe2d+H=mpe3d2j+H2
mb3d+CH3O=mb3d2j+CH3OH
mb3d+O=mp3j+HCO
mpe3d+O=mpe4d3j+OH
mpe3d+O=mpe3d2j+OH
mpe2d+O=mpe3d2j+OH
mpe3d+CH3O=mpe4d3j+CH3OH
mpe4d3j=mpe4d2d+H
mpe4d2j=mpe4d2d+H
mpe4d+H=mpe4d3j+H2
mpe4d+OH=mpe4d2j+H2O
mpe3d+HO2=mpe4d3j+H2O2
mp2dmj=>C2H3CO+CH2O
mp2j=>mpmj
mp2j<=mpmj
mpe4d+OH=mpe4d3j+H2O
mpe4d2d+OH=H2O+nC4H5+CH2O+CO
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5.25E+11
3.00E+13
1.95E+12
7.94E+15
3.00E+06
6.40E+03
9.64E+10
1.50E+08
1.23E+13
1.70E+07
1.50E+08
4.00E+12
5.40E+04
5.40E+04
3.00E+06
3.00E+06
3.00E+06
1.88E+12
1.88E+12
1.30E+13
7.90E+15
1.58E+07
2.00E+13
1.58E+11
5.40E+04
1.44E+13
2.41E+02
4.00E+12
5.40E+04
1.88E+12
1.00E+11
8.80E+10
8.80E+10
8.80E+10
1.88E+12
3.00E+13
3.16E+13
5.40E+04
3.00E+06
6.40E+03
2.83E+11
1.50E+08
1.50E+08
3.00E+06
2.00E+11
Table 2. Thermodynamic data for MPe and its primary decomposition products.
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0
0
0
2
2.6
0
1
0.4
1
1
0
2.5
2.5
2
2
2
0
0
0
0
1.8
0
0
2.5
0
2.9
0
2.5
0
0
0.7
0.7
0.7
0
0
0
2.5
2
2.6
0.5
1
1
2
0
26591
38000
5000
70740
-1520
12400
12580
27800
36714
14000
20300
37000
-1900
-1900
-1520
-1520
-1520
1200
1200
35900
97970
-1216
24000
4970
-1900
6095
7533
40000
-1900
1200
-1050
3250
3250
3250
1200
51500
34780
-1900
-1520
12400
29999
19800
18300
-1520
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Molecular
№ Designation
weight
1
mpe
116.16
2
mpe5j
115.15
3
mpe4j
115.15
4
mpe3j
115.15
5
mpe2j
115.15
6
mpemj
115.15
7
mpe4d
114.15
8
mpe3d
114.15
9
mpe2d
114.15
10
mpe4d3j
113.14
11
mpe3d2j
113.14
12
mpe4d2j
113.14
13 mpe4d2d
112.13
14
mb4j
101.13
15
mib3j
101.13
16
mb3d
100.12
17
mb3d2j
99.11
18
mb3dmj
99.11
19
me2*o
88.06
20
mp3j
87.10
21
mpmj
87.10
22
mp2j
87.10
23
mp2d
86.09
24
mp2d3j
85.08
25
mp2dmj
85.08
26
memj
73.07
27
me2j
73.07
S0(298),
∆H0f(298),
Formula kcal/mol kcal/(mol×K)
C6H12O2
-113.29
108.20
C6H11O2
-64.48
110.31
C6H11O2
-66.68
110.46
C6H11O2
-66.68
110.46
C6H11O2
-73.09
105.73
C6H11O2
-65.18
110.31
C6H10O2
-83.34
105.88
C6H10O2
-84.87
112.01
C6H10O2
-86.67
105.47
C6H9O2
-51.84
104.67
C6H9O2
-54.31
102.38
C6H9O2
-43.14
103.38
C6H8O2
-60.45
101.06
C5H9O2
-59.54
100.94
C5H9O2
-61.33
99.74
C5H8O2
-77.16
104.04
C5H7O2
-50.74
95.54
C5H7O2
-35.24
107.98
C3H4O3
-106.80
84.45
C4H7O2
-54.59
91.58
C4H7O2
-55.29
91.58
C4H7O2
-63.20
87.38
C4H6O2
-73.94
87.80
C4H5O2
-27.36
81.84
C4H5O2
-25.80
80.64
C3H5O2
-49.86
81.87
C3H5O2
-51.76
78.89
Figure 1. Atoms numbering in MPe molecule.
The numbering of hydrogen atoms in the methyl pentanoate molecule is shown in Figure 1.
According to the reaction mechanism, the main pathway of MPe decomposition is the abstraction of
an H atom from one of the positions to form one of the MPe radicals, which are denoted by adding
'j' with an indication of the abstracted atom position: mpe2j, mpe3j, mpe4j, mpe5j, and mpemj. In
the case of successive abstraction of two hydrogen atoms and formation of a double bond, the
radicals are denoted by adding 'd' and the double bond position number: mpe4d, mpe3d, mpe2d,
mpe4d3j, mpe3d2j, mpe4d2j, and mpe4d2d. As it was earlier shown in calculations for methyl
butanoate,18 because the electron density is pulled to oxygen atoms in the ester group, the lowest CH bond energy is observed for position '2'. Thus, the abstraction from this position is the fastest
decomposition pathway of the initial methyl pentanoate molecules. The highest С-Н bond energy is
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observed for positions '5' and 'm', and, hence, the formation of mpe5j and mpemj radicals is less
probable under all conditions. All MPe radicals formed in this process decompose via unimolecular
reactions with formation of lighter hydrocarbons and oxygen containing compounds or radicals.
Also, the mechanism includes six unimolecular reactions involving the breaking of C-C or C-O
bonds in the MPe molecule with the formation of two radicals (R1 and R2) different for various
reactions.
Comparison of the primary decomposition reactions of methyl pentanoate in the full and
reduced mechanisms showed that the number of elementary reactions of MPe conversion was
reduced by 30 reactions. The unimolecular decomposition reactions of methyl pentanoate with
abstraction of H atoms from positions '5' and 'm' virtually do not occur under the test conditions. The
activation energy of these reactions is too high (97.97 kcal/mol). The reduced mechanism also does
not include the reaction of MPe with HCO and CH2OH radicals producing MPe radicals (mpe2j,
mpe3j, mpe4j, mpe5j, and mpemj) and CH2O or CH3OH correspondingly. Moreover, the rate of
conversion of methyl pentanoate by the reactions: mpe + CH3O = (mpe4j or mpe5j) + CH3OH, was
found to be low and these reactions were not included in the reduced model. The reduced
mechanism included four decomposition reactions of MPe involving the breaking of C-C and C-O
bonds. In the reduced mechanism also were not included the reactions of methyl pentanoate with
large С2 and С3 hydrocarbon radicals (13 reactions), except for the reaction: mpe + C2H5 = C2H6 +
mpe4j, which had a slighter larger yield than other reactions of MPe with C2H5 in fuel-rich
conditions. All main reaction pathways for conversion of MPe radicals and light hydrocarbon
chemistry were kept. Excluded reactions were mostly associated with C4 and C5 oxygen containing
compounds which are not formed directly from MPe and its radicals.
MODELING RESULTS
The numerical modeling of various MPe/O2 flames was performed using the PREMIX, PSR, and
OPPDIF codes of the CHEMKIN-II package.19 Flame speed and structure were calculated by
solving the Navier-Stokes equations for laminar premixed flame using the PREMIX code.
Concentration flammability limits were calculated from the flame extinction strain rate using
the OPPDIF code, which solves the quasi-one-dimensional equations for axisymmetric opposedflow flames. In the calculation, the rates of supply of fuel and oxidizer were gradually increased as
long as the solution obtained with the code corresponded to flame burning (this can be determined
by the maximum temperature since, in the absence of combustion in the resulting solution, the
temperature does not increase compared to the initial value). To reduce the calculation time, as the
initial condition at each point we used the solution obtained for the previous flow rate value. To
simplify the procedure, equal flow rates of the combustible mixture and their increments were
chosen on both sides of the burner. This approach was implemented and described in greater detail
in ref 20.
Ignition delay times were calculated using the constant-volume adiabatic reactor model with
the SENKIN code.
STRUCTURE OF FLAMES STABILIZED ON A FLAT BURNER
To verify the obtained kinetic model, we simulated the structure of the fuel-rich MPe/O2/Ar (φ =
1.5) flames from ref 13 at a pressure of 20 Torr and 1 atm. The molar compositions of the fuel-rich
MPe/O2/Ar flames were 0.047/0.253/0.700 (1 atm) and 0.079/0.421/0.500 (20 Torr). Linear flow
velocities of the cold mixtures were 7.5 cm/s and 72.1 cm/s correspondingly. Temperature of the
burner surface was set to 368 K. The simulations were performed using fixed temperature profiles
measured experimentally.13 Figure 2 shows the mole fraction profiles of the major (a) and
intermediate (b) species in a fuel-rich MPe/O2/Ar flame (φ = 1.5) at a pressure of 20 Torr (the
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modeling results for the mixtures at atmospheric pressure are similar and given in supplemental
materials for space-saving reasons). It can be seen from the graphs that for the major flame
components, the profiles and absolute values of mole fractions simulated using the reduced
mechanism are in good agreement with the experimental data and the calculations using the full
mechanism.
Figure 2a. Temperature and mole fraction profiles of major products and reactant species in the
premixed MPe/O2/Ar (φ=1.5) flame at a pressure of 20 Torr. Symbols - experiment13: ○ - H2O, ◊ CO2, □ - O2, + - CO, ∆ - MPe; solid lines - simulation with the reduced mechanism, dashed lines simulation with the full mechanism,6 dash-and-dot line - temperature.
Comparison of the mole fraction profiles of intermediate species has shown that for methyl
propenoate (C4H6O2) and methane (CH4), the profiles obtained using the full model and the reduced
model coincide, which is due to the fact that the maximum concentration of these components were
controlled during the reduction of the kinetic model. Maximum differences between the models are
observed for methanol (CH3OH) and acetaldehyde (CH3CHO), for which the reduced model
predicts higher maximum concentrations than the full kinetic model. For propyne (C3H4), the
reduced model predicts a lower concentration, which better fits the experimental values. Good
reproduction of acetylene (C2H2) and ethylene (C2H4) profiles by reduced mechanism shows that
reduced mechanism also can be used for estimations of soot precursors’ formation.21
To make sure that there are no significant differences in conversion pathways between the
full and reduced kinetic mechanisms, we analyzed the primary pathways of methyl pentanoate
decomposition. For this, we calculated the integrated rates of all reactions involving MPe and its
primary decomposition products in the same manner as was done in ref 13 and 22:
∞
∞
ω′
ω i = ∫ ω i′dt = ∫ i dx
v
0
0
where ω'i is the instantaneous chemical reaction rate i (mol/(cm3*s)), υ is the local gas velocity
(cm/s), and x is the distance from the burner surface (integration is performed over the whole
computation domain). Next, the obtained values were normalized to the sum of integrated rates of
consumption of the initial fuel (MPe) in all reactions. Because the fuel was consumed almost
completely in all investigated flames, the obtained values are mole fractions of the initial fuel
converted to the corresponding products during the entire combustion process. The schematic
diagram in Figure 3 shows the intermediate products of conversion of methyl pentanoate in flames,
with an indication of the percentage of the fuel converted by corresponding reaction pathways. In
cases where several different reactions corresponded to the same conversion, in particular, the
reactions of the fuel with various radicals, the sum for all such reactions is indicated in the diagram.
Furthermore, the unimolecular decomposition reactions of MPe involving the breaking of C-C and
C-O bonds were combined into one conversion pathway. The calculation was performed for fuelrich MPe/O2/Ar flames at a pressure of 20 Torr and 1 atm. As can be seen from the diagram, the
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main pathways for the consumption of methyl pentanoate in these flames are reactions with atoms
and radicals involving hydrogen abstraction and subsequent decomposition of the radicals formed
via β-scission reactions. In addition, important reactions in this process are the isomerization
reactions of the primary radicals generated from the initial ester. The further decomposition of the
primary radicals usually occurs by breaking of C-C or C-O bonds to form methyl and methoxy
radicals.
Figure 2b. Mole fraction profiles of intermediate species in the premixed MPe/O2/Ar (φ=1.5) flame
at a pressure of 20 Torr. Symbols - experiment13, solid lines - simulation with the reduced
mechanism, dashed lines - simulation with the full mechanism.5
Comparison of the conversion pathways of methyl pentanoate in the full and reduced
mechanisms shows that the reduced scheme is similar to the full kinetic model, the ratios between
the primary pathways of MPe conversion are the same, and the reaction rates for individual
pathways are not changed. The largest difference in reaction rates is observed for the unimolecular
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decomposition reactions mpe → R1 + R2 at atmospheric pressure. This is due to an increase in the
role of unimolecular decomposition with increasing pressure.
Although differences in mole fraction profiles of several intermediates simulated by full and
reduced mechanism can be observed, mole fraction profiles still lies within accuracy of experimental
measurements, and no modification to reduced mechanism seems necessary.
Figure 3. Reaction flux diagram for premixed MPe/O2/Ar (φ=1.5) flames at a pressure of 20 Torr
(grey numbers under arrows) and 1 atm (black numbers above arrows). Numbers in parentheses
correspond to the reduced mechanism.
FLAME SPEED OF MPE/AIR MIXTURES
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Data on the dependence of the burning velocity of premixed methyl pentanoate/air flames on their
composition are taken from ref 15. The measurements were carried out over a wide range of
equivalence ratios (φ) using a Mache–Hebra burner23 and total area method24 from shadow
photographs of the flame. The initial temperature of the combustible mixture was 363 K. The total
flow rate of the combustible mixture was chosen so that the shape of the flame cone was as regular
as possible in order to reduce the measurement error. The error in flame speed measurements using
the Mach–Hebra burner is approximately ±5% for stoichiometric flames. For fuel-lean and fuel-rich
flames, due to flame fluctuations, the measurement error included the standard deviation of the
flame speed determined from several photographs, and therefore, the error for these flames was up
to ±25%.
Figure 4 shows the results of the experiment, with an indication of the measurement error at
each point, and the results of modeling using four kinetic mechanisms of chemical reactions (full
mechanisms6,12,13 and the new reduced mechanism) for the MPe/air flame speed. It can be seen from
Figure 4 that the calculations for all detailed mechanisms gave significantly higher values than the
experimental results. Nevertheless, the modeling results for the mechanism from ref 6 can be
considered to be in satisfactory agreement with the experiment in the region of lean and
stoichiometric flames and at high equivalence ratios (φ > 1.5). The largest error is observed for fuelrich flames in the range 1.2 < φ < 1.5, where the differences between the results of the experiment
and numerical modeling reach 30% for the mechanism from ref 6 and a factor of about 2 for the
mechanisms from ref 12 and 13.
Figure 4. Flame speed of premixed MPe/Air flames (T0=363 K, Р=1 atm). Symbols – experiment,15
lines – modeling: solid - reduced mechanism, dashed - full mechanism ref 6, dotted - ref 12, dashand-dot - ref 13.
The results of modeling using the reduced model are slightly closer to the experimental data
throughout the range of high equivalence ratios and mostly reproduce the results of full mechanism.
Analysis of reaction pathways in the detailed kinetic mechanisms showed that the primary steps of
conversion of MPe and its primary decomposition products are mostly the same for different
detailed mechanisms. A more thorough analysis of reaction rate constants and thermochemistry data
therefore is required to understand this large difference in flame speed calculations.
AUTOIGNITION DELAY TIMES AT HIGH PRESSURE
Kinetic models of MPe combustion was also tested against data on the autoignition delay times of
stoichiometric MPe/air mixtures at pressures from 10 to 18 atm at a temperature T0=815 K.10 Figure
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5 shows the experimental and computation results for the dependence of autoignition delay time (in
logarithmic scale) from initial pressure. As can be seen in this figure, mechanism from ref 6 predicts
values of ignition delay ∼5 times higher than experimental values. We assume that this disagreement
caused by the absence of low-temperature reactions such as O2 addition. This kind of reactions was
included in the mechanism proposed by Diévart et al.12 However calculations with this mechanism
predicted ignition delay times almost 10 times shorter than in experiment. The difference in ignition
delays for reduced and full mechanism from ref 6 was found to be no more than 2.5%.
Figure 5. Autoignition delay times for stoichiometric MPe/air mixtures (T0=815 K). Symbols –
experiment,10 lines – modeling: dashed - full mechanism ref 6, dotted - full mechanism ref 12.
Calculations of the sensitivity coefficients of autoignition delay time to reaction rate
constants have shown that in both mechanism the highest sensitivity coefficients are observed for
the reactions: H2O2 (+M) = OH + OH (+M), and 2HO2 = H2O2 + O2. However these two mechanism
utilize different reactions rate constants and constants used in mechanism from ref 12 gives
significant higher value of reaction rate at 715 K and thus their adjustment should allow to obtain a
better agreement with experimental data.
DIFFUSION FLAME
Figure 6 presents the data of Diévart et al.12 who determined the extinction strain rate for burnerstabilized opposed-flow diffusion MPe/air flames experimentally and numerically. A mixture of fuel
and diluent (nitrogen) was fed through one tube, and air through the other tube. The initial air
temperature was 298 ± 5 K, and the temperature of the fuel–diluent mixture was 500 K. The points
in the graph (Figure 6) correspond to the flame extinction conditions. This calculation results are in
good agreement with the experimental data at low concentrations of MPe (0.06–0.14 mole fraction),
but are underestimated for fuel concentrations above 0.15 mole fraction.
Figure 6 also shows the results of modeling the extinction strain rate for different fuel
concentrations using the new reduced mechanism. Calculations with the full mechanism from ref 6
have produced the same results as the reduced mechanism and thus are not shown. The modeling
results are in satisfactory agreement with the experimental data over the entire range of conditions,
although the model predictions are slightly higher than the measured values. The maximum
difference between the experimental data and the calculation for the reduced mechanism are about
15%.
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Figure 6. Extinction strain rate for burner-stabilized opposed-flow diffusion MPe+N2/Air flames.
Symbols – experiment,12 lines – modeling: dotted line – ref 12, dashed line - initial reduced
mechanism, solid line – final reduced mechanism with modified transport data.
However, it is known that transport properties can have a considerable influence on results of
flame propagation limits calculations. Analysis of transport datafiles provided for these two
mechanisms has shown that diffusion coefficients in ref 12 were evaluated with a higher precision.
By replacing transport properties for most esters and their decomposition products in our reduced
mechanism with properties from ref 12 we managed to achieve a very good agreement with the
experimental data for the whole range of MPe concentrations (solid line on figure 6). All other
calculations presented in this work were not sufficiently affected by this modification. Reduced
mechanism provided in supplemental materials already contains modified diffusion coefficients.
CONCLUSIONS
A reduced kinetic mechanism consisting of 330 reactions and 92 species for combustion of methyl
pentanoate was developed using the Mechanism Workbench software. The resulting kinetic model is
in good agreement with the experimental data on the structure of burner-stabilized premixed
MPe/O2/Ar flames, MPe/air flame speeds at atmospheric pressure and extinction strain rates for
MPe/air diffusion flames with fuel concentrations of 0.07–0.18 mole fraction in mixtures with
nitrogen. However to achieve agreement with experiments on autoignition delay times of
stoichiometric MPe/air mixtures at a pressure of 10–18 atm addition of low-temperature oxidation
pathways or modification of some reaction rate constants is necessary.
The reduced model was developed using published experimental data on the structure of
MPe/O2/Ar flames. This allowed control of the concentrations of the most important intermediates
that were selected as targets in the reduction of the mechanism. The approach implemented using the
Mechanism Workbench software gave good results at moderate computational cost and can be
useful in developing other reduced mechanisms. The resulting kinetic model can be used
independently to describe methyl pentanoate combustion and as part of kinetic models for
combustion of other heavy fatty acid esters in the pressure range 20 Torr–1 atm.
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