Thermodynamic Data for the Modeling of the Thermal Decomposition

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Thermodynamic Data for the Modeling of the Thermal Decomposition of Biodiesel. 1. Saturated and Monounsaturated FAMEs† Antoine Osmont,‡ Laurent Catoire,*,§,⊥ and Philippe Dagaut⊥ DGA/CEG, 46500 Gramat, France, Faculte´ des Sciences, UniVersite´ d’Orleáns, 1 Rue de Chartres BP 6759, 45067 Orleáns cedex 2, France, and CNRS, INSTII, ICARE, 1c AVenue de la Recherche Scientifique, 45071 Orleáns cedex 2, France ReceiVed: May 26, 2009; ReVised Manuscript ReceiVed: July 15, 2009

Thermochemical data were computed for numerous species needed for performing detailed chemical kinetic modeling of biodiesel thermal decomposition and combustion. Most of these data concerning large species had not been experimentally determined. A B3LYP/6-31G(d,p) method using the atomization approach derived earlier was used to provide these data. The presently computed thermochemical data are provided in the CHEMKIN-NASA format as Supporting Information. Species considered are fatty acid methyl esters (FAMEs), various oxygenated radicals formed from FAMEs by C-H, C-C, and C-O bond breakings and subsequent chemistries, 1-, 2-, 3-, and 5-saturated alkyl radicals, monounsaturated 1-alkyl radicals, among others. 1. Introduction In the U.S. and in Europe, research on biodiesel has mainly focused on, respectively, soybean oil and rapeseed oil since they represent the most commonly produced vegetable oils in these regions.1 Since the use of pure vegetable oil in recent diesel engines is not appropriate,2 vegetable oil triglycerides are generally transesterified with methanol to get quite complex mixtures of fatty acid methyl esters (FAMEs). Although it can be obtained from wood, nowadays, methanol is mostly obtained from natural gas. At present, mixtures of methyl esters are generally considered as the most reliable biofuels to be added to fossil fuel for diesel engines.3 The composition of biodiesel obtained from rapeseed oil is (weight %)1 palmitic acid methyl ester (or methyl palmitate) 4.8; stearic acid methyl ester (or methyl stearate) 1.5; oleic acid methyl ester (or methyl oleate) 60.3; linoleic acid methyl ester (or methyl linoleate) 21.5; linolenic acid methyl ester (or methyl linolenate) 7.6; eicosenoic acid methyl ester 2; and others 2.3. Similar molecules are present in soybean oil methyl esters but with different amounts (weight %), palmitic acid methyl ester 10.5; stearic acid methyl ester 3.9; oleic acid methyl ester 22; linoleic acid methyl ester 53.3; linolenic acid methyl ester 9; and others 1.3. Therefore, the combustion of these two biodiesels could be simulated by a unique chemical kinetic model, which includes the combustion chemistry of six fatty acid methyl esters, namely, palmitic acid methyl ester, stearic acid methyl ester, oleic acid methyl ester, linoleic acid methyl ester, and linolenic acid methyl ester. In fact, this model may also be able to simulate the combustion chemistry of sunflower oil methyl esters, palm oil methyl esters, and so forth. Writing a chemical kinetic model based on elementary reactions for the combustion of biodiesel is a challenging task because this model requires a large amount of generally unknown † Part of the special issue “Green Chemistry in Energy Production Symposium”. * To whom correspondence should be addressed. ‡ DGA/CEG. § Universite´ d’Orleáns. ⊥ ICARE.

thermodynamic and kinetic data for transient species potentially formed during thermal decomposition and oxidation processes. Therefore, no chemical kinetic model for the combustion of these compounds is available nowadays. Several strategies have been reported in the literature for studying the kinetics of combustion of biodiesel. One consists of studying both experimentally and numerically the combustion of surrogates of increasing complexity (methyl butanoate,4-7 methyl crotonate,7,8 methyl hexanoate9). Another strategy consists of studying experimentally the combustion of RME and then comparing the experimental results with the numerical predictions obtained with n-hexadecane10,11 or methyl decanoate.12 All of these strategies are valuable and scientifically meaningful but indirect, and their ability to predict all of the combustion features of biodiesel remains to be demonstrated. However, the scarcity of experimental data hampers this demon-

10.1021/jp904896r  2010 American Chemical Society Published on Web 08/20/2009

Modeling of the Thermal Decomposition of Biodiesel

J. Phys. Chem. A, Vol. 114, No. 11, 2010 3789 TABLE 1: Thermochemistry for Methyl Acrylate (C4H6O2) Formation from CnH2n-1O2 Radicals (reaction 01) (units: kcal/mol) ∆fH°298 K n

CnH2n-1O2

C4 H6 O2

Cn-4H2(n-4)+1

∆rH°298 K

17 18 19 21

-127.9 -132.6 -137.3 -146.7

-75.2 -75.2 -75.2 -75.2

-24.8 -29.5 -34.3 -43.7

27.9 27.9 27.8 27.8

polyfunctional compounds. The atomic corrections c*i are determined by least-squares fitting of the 311 selected experimental gasphase standard enthalpies of formation at 298.15 K. The gas-phase standard enthalpy of formation of a molecule j at 298.15 K can be determined from the following equation

∆fH°298.15 K (g) ) 627.51 × (Ej + ZPEj + thermal corrections +

∑ Ric*i ) i

stration. For such molecules, the high-temperature combustion chemistry will proceed through thermal decomposition followed by oxidation of the decomposition products formed. The aim of this paper is to propose mechanistic information based on thermokinetic considerations and the related thermochemistry needed for writing kinetic reaction schemes for the combustion of RME and SME (soybean methyl ester). In this paper, we focus on the hightemperature decomposition chemistry, that is, on a submechanism needed to simulate shock-tube ignition delays, for instance. The reaction pathways presented here are necessary but not sufficient for building a detailed chemical kinetic model devoted to the combustion of biodiesel.

where Ri is the number of atom i in molecule j and c*i is the atomic correction for atom i. Ej and ZPEj denote, respectively, the electronic energy and zero-point energy, calculated using the Gaussian 98W and Gaussian 03 softwares.18,19 The units are hartree molecule-1 for Ej, ZPEj, and thermal corrections and -1 hartree atom-1 for c*, i whereas ∆fH°298.15 K (g) is in kcal mol . Thermodynamic data are reported in the CHEMKIN format as Supporting Information.

2. Computational Method

Previous studies mostly concerned the thermochemistry of FAMEs (fatty acid methyl esters).15-17 The thermochemistry of these FAMEs is given as Supporting Information. H-atom abstraction from FAMEs, C-C scission in FAMEs, and C-O, (CdO)-C, and (CdO)-O scissions in FAMEs have been examined and discussed. On these bases, mechanistic information on reaction pathways has been derived. These features are illustrated here for C-H, C-C, and C-O bond scissions in methyl palmitate

Ab initio methods have been shown to be reliable tools to estimate the thermochemistry of many compounds.13 However, the most accurate of these methods, namely, the G3 or G2 methods, are computationally too expensive for large molecules.14 Density functional methods (B3LYP/6-311G(d,p) for instance) using the conventional atomization approach have been shown to provide a reasonable way to treat naphthalene (C10H8), a quite large molecule, but the molecules under consideration in this study are generally larger, up to 21 C atoms. For this reason, a protocol with a smaller basis set is required. Consequently, a B3LYP/6-31G(d,p) method using the atomization approach was derived previously.15-17 A comparative study of several existing approaches indicated that the B3LYP/6-31G(d,p) protocol appears to be a good compromise between numerical accuracy and expense. Four atomic corrections are derived for the molecules here, one for H atoms, one for C atoms, one for O atoms, and one for C• (C radical). In this method, we do not distinguish between O atoms; the correction applied to an O atom in a carbonyl group is also applied to an O atom in a hydroxyl or ether group. The same holds for C atoms; the correction applied to a C involved in single bonds is applied to a C involved in double bonds. The method employed in the present study is based on 311 compounds having well-calibrated enthalpies of formation with uncertainties of less than 1 kcal mol-1 for most of them and validated on a large data set. These 311 compounds are organic compounds pertaining to all chemical classes including

3. Model Development

and in methyl palmitoleate

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Osmont et al. C-C bond scissions are bonds 7 and 17 with a bond enthalpy of about 70 kcal/mol. C-C bond scissions are energetically favored for saturated FAMEs and monounsaturated FAMEs, whereas C-H bond scissions and C-C bond scissions must be both considered for polyunsaturated FAMEs. Of all of the other possible bond scissions in FAMEs (bond scission numbers 1, -1, and -2), only the C-O bond scission in the methoxy group needs to be considered.15 This issue is not further discussed in this paper but the thermochemistry of radicals formed by C-O bond scission in the methoxy group of FAMEs is reported as Supporting Information. 3.1. Initiation through C-H Bond Scission and Subsequent Decomposition Reactions. 3.1.1. Saturated Chains. For the saturated chains examined here, namely, methyl palmitate, methyl stearate, and methyl arachidate, among all of the possible H-atom abstractions, the less endothermic reaction pathway is abstraction of one of the H atoms β to the carbonyl group, that is, on the R-carbon to the carbonyl group (or carbon number 2) according to

There is no methyl palmitoleate in RME and SME, but this molecule is considered here as a representative of monounsaturated FAMEs. Energetically favored C-H bond breaking for methyl palmitate is on carbon 2 with a bond enthalpy of 92 kcal/mol. The same value is obtained for methyl stearate and methyl arachidate. Energetically favored C-H bond breaking for methyl palmitoleate is on carbons 8 and 11 with a bond enthalpy of 82 kcal/mol. The same holds for methyl oleate. For methyl linoleate (a diunsaturated FAME) and methyl linolenate (a triunsaturated FAME), favored C-H bond breaking is on carbon 11 with a bond enthalpy of 70 kcal/mol. These two last species are beyond the scope of the present study. Energetically favored C-C bond breaking for methyl palmitate is at bond 2 with a bond enthalpy of about 83 kcal/mol. This also holds for methyl stearate and methyl arachidate. For methyl palmitoleate, the energetically favored C-C bond scissions are bonds 7 and 11 with a bond enthalpy of 70 kcal/ mol. This also holds for methyl oleate. For methyl linoleate, favored C-C bond breakings are bonds 7 and 14 with a bond enthalpy of 70 kcal/mol, and for methyl linolenate, the favored

with R being C13H27 for methyl palmitate, C15H31 for methyl stearate, and C17H35 for methyl arachidate. All of the other C-H bond scissions are more endothermic than this one by 6-10 kcal/mol and are not further considered. 3.1.1.1. Methyl Acrylate Formation. Then, the radical formed decomposes to give methyl acrylate C4H6O2 and a long-chain n-alkyl radical

This reaction can be generalized as

CnH2n-1O2 f C4H6O2 + Cn-4H2(n-4)+1 Thermodynamic data for these reactions from large ester radicals are reported in Table 1.

TABLE 2: Thermochemistry of Ethylene Elimination from n-Alkyl Radicals (reaction 02)a ∆fH°298 K n

CnH2n+1

3

24.0 ( 0.5; 22.1 (22.7 ( 0.4; 23.4 ( 1.0;23 24.1 ( 0.524) 17.5 (18.6 ( 0.5;25 18.4;23 18.1 ( 0.620,21 19.3 ( 0.5;24 18;22 1628) 12.8 (13.0;22 13.4;28 10.1 ( 0.3;20 13;25 14.6 ( 124) 8.1 (8.025,288.46;308.2231) 3.4 (4.0;22 2;25 1.028) -1.3(-3.828) -6.0(-8.828) -10.7 (-13.928) -15.4 -20.1 -24.8 -29.5 -34.3 -39.0 -43.7

4 5 6 7 8 9 10 11 12 13 14 15 16 17 a

20,21

C2 H4 22

Cn-2H2(n-2)+1

∆rH°298 K

12.3 (12.5 ( 0.2 )

34.5 (35.06 ( 0.1; 35.05 ( 0.07; 35.1; 34.8 ( 0.3;22 35.1 ( 0.1527)

24.7

12.3

21.4

12.3

26.6 (28.0;22 28.4 ( 0.5;23 27.8 ( 0.620,21 28.9 ( 0.429) 22.1

12.3 12.3 12.3 12.3 12.3 12.3 12.3 12.3 12.3 12.3 12.3 12.3

17.5 12.8 8.1 3.4 -1.3 -6.0 -10.7 -15.4 -20.1 -24.8 -29.5 -34.3

21.7 21.7 21.7 21.7 21.7 21.7 21.7 21.7 21.7 21.8 21.8 21.7

22

Literature data (when available) are given within parentheses.

25

26

23

21.6


J. Phys. Chem. A, Vol. 114, No. 11, 2010 3791

TABLE 3: Thermochemistry of 2-Alkyl Radicalsa ∆fH°298 K n

2 - CnH2n+1

3

17.9 (20.0 ( 0.5;23 21.0 ( 0.7;25 22.3 ( 0.6;22 18.2 ( 1;32 19.1 ( 0.620,21) 13.3 (16.2 ( 0.5;25 17.0 ( 0.4;22 13 ( 2;32 15 ( 1.1;23 15.3 ( 0.221) 8.5 (12;25 11.0;28,31 7.4 ( 3.020,21) 3.8 (5.5;28 6.06;30 7.0;22,25 3 ( 320,21) -0.9 (2.022) -5.6 -10.3 -15.0 -19.7 -24.4 -29.1 -33.8 -38.5 -43.3 -48.0

4 5 6 7 8 9 10 11 12 13 14 15 16 17 a

Data within parentheses are literature data.

Methyl acrylate and n-alkyl radicals then undergo further thermal decomposition and oxidation. It is focused hereafter on the thermal decomposition of 1-alkyl radicals. 3.1.1.2. Ethylene Elimination from 1-Alkyl Radicals. The heavy n-alkyl radicals R• formed in section 3.1.1.1 can then decompose through β-scission to form ethylene and a lighter n-alkyl radical.

3.1.1.5. Propylene Elimination from 2-Alkyl Radicals. The 2-alkyl radicals obtained can then decompose further through β-decomposition to form propylene and n-alkyl radical according to

which can be generalized as

CnH2n+1 f Cn-3H2n-5 + C3H6 Table 5 reports the thermodynamics of these reactions for n between 4 and 17. The evolution of the enthalpy of reaction is not monotonous because for n ) 4, the methyl radical is formed and this formation is energetically unfavorable compared to the radicals formed (ethyl radical, propyl radical, etc.) for n > 4. 3.1.2. Monounsaturated Chains. For the monounsaturated chain examined herein, namely, oleic acid methyl ester, the abstraction of one of the H atoms β to the ethylenic bond is preferred. Therefore, two nonequivalent radicals can be formed, one by abstraction on carbon 8 and one by abstraction on carbon 11. 3.1.2.1. Fate of Radical Formed on Carbon 8. The radical formed on carbon 8 can undergo C-C bond breaking according to

This reaction can be generalized as

CnH2n+1 f Cn-2H2(n-2)+1 + C2H4 Table 2 gives the thermodynamics for these reactions for n ) 3 up to 17. Thermodynamic data and rate constants are generally known for n-alkyl radicals up to n ) 10. The data for n < 10 are reported here to assess the accuracy of the method used in this study. n-Alkyl radicals can then react with O2 to form HO2 and the conjugate alkene. O2 addition reactions with R• are also likely to form peroxy radicals ROO•. These reactions are relevant to the low-temperature combustion chemistry and are therefore beyond the scope of the present study, except for the low molecular weight alkyl radicals. 3.1.1.3. Thermochemistry of 2-Alkyl Radicals. Although there is no evidence of the occurrence of 1,2 H-atom shifts in n-alkyl radicals, 2-alkyl radicals are considered to test the predictability of the method used in this study. Furthermore, the chemistry in such systems is very complex, and the formation of 2-alkyl radicals by other reaction pathways than 1,2 H-atom shifts cannot be excluded. Table 3 compares experimental data and calculated data for 2-alkyl radicals for which experimental data are available and provides data for large 2-alkyl radicals for which experimental data are not available. 3.1.1.4. Thermochemistry of 5-Alkyl Radicals. Internal H-atom abstraction occurs generally in n-alkyl radicals through 1,5 H-atom shifts

1 - CnH2n+1 f 5 - CnH2n+1

CnH2n-3O2 f C7H13O2 + Cn-7H2(n-7)-2 The thermodynamics of these reactions are reported in Table 6 for n ) 17, 18, and 19. TABLE 4: Thermochemistry of 1,5 shift in 1-alkyl radicals ∆fH°298 K n

1 - CnH2n+1

5 - CnH2n+1

∆rH298 K

6 7 8 9 10 11 12 13 14 15 16 17 18

8.1 (see Table 2) 3.4 (see Table 2) -1.3 -6.0 -10.7 -15.4 -20.1 -24.8 -29.5 -34.3 -39.0 -43.7 -48.4

3.8 -0.7 -5.5 -10.2 -14.9 -19.6 -24.4 -29.1 -33.8 -38.5 -43.3 -47.9 -52.6

-4.3 -4.1 -4.2 -4.2 -4.2 -4.2 -4.3 -4.3 -4.3 -4.2 -4.3 -4.2 -4.2

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TABLE 5: Thermochemistry of Propylene Elimination from 2-Alkyl Radicals (reaction 03)a ∆fH°298 K n

CnH2n+1

4 5 6 7 8 9 10 11 12 13 14 15 16 17

13.3 (see Table 3) 8.5 (see Table 3) 3.8 (see Table 3) -0.9 -5.6 -10.3 -15.0 -19.7 -24.4 -29.1 -33.8 -38.5 -43.3 -48.0 a

C 3H 6

Cn-3H2n-5

∆rH°298 K

3.6 (4.8 ( 0.2 ) 34.5 (see Table 2) 3.6 26.6 (see Table 3) 3.6 22.1 3.6 17.5 3.6 12.8 3.6 8.1 3.6 3.4 3.6 -1.3 3.6 -6.0 3.6 -10.7 3.6 -15.4 3.6 -20.1 3.6 -24.8 3.6 -29.5 22

24.8 21.7 21.9 22.0 22.0 22.0 22.0 22.0 22.0 22.0 22.0 22.0 22.1 22.1

CnH2n-1O2 f C2H4 + Cn-2H2(n-2)-1O2 or can rearrange (see section 3.1.2.4). Table 8 reports the thermodynamics of ethylene elimination from ester radicals. The evolution of the enthalpy of reaction is not monotonous because for n ) 4, the radical formed is on the carbonyl carbon, and this is energetically unfavorable, whereas for n ) 5, the radical is conjugated with the double bond of the carbonyl group, and this stabilizes the radical formed. For n > 5, this stabilization no longer exists. 3.1.2.4. Ester Radicals’ Rearrangement. Secondary radicals may also form according to

Data within parentheses are literature data.

TABLE 6: Thermochemistry of Reaction 04 ∆fH°298 K n

CnH2n-3O2

C7H13O2

Cn-7H2(n-7)-2

∆rH°298 K

17 18 19

-107.5 -112.2 -116.8

-70.2 -70.2 -70.2

-4.1 -8.8 -13.5

33.2 33.2 33.1

1 - CnH2n-1O2 f 2 - CnH2n-1O2 and to

1 - CnH2n-1O2 f 5 - CnH2n-1O2

TABLE 7: Thermochemistry of Reaction 05 ∆fH°298 K n

CnH2n-3O2

C13H22O2

Cn-13H2(n-13)+1

∆rH°298 K

17 18 19

-107.5 -112.2 -116.9

-91.9 -91.9 -91.9

17.5 12.8 8.1

33.1 33.1 33.1

3.1.2.2. Fate of the Radical Formed on Carbon 11. The radical formed on carbon 11 can undergo C-C bond breaking according to:

the 1,5 shift being preferred. Tables 9 and 10 report the thermochemistry of these radicals. In Table 9, contrary to the primary radicals, the evolution of the enthalpies of formation of secondary radicals is not monotonous. For n ) 4, the secondary radical is conjugated with the double bond of the carbonyl group, and therefore, the radical is stabilized. For n > 5, this conjugation does not exist anymore. 3.1.2.5. Propylene Elimination from Secondary Ester Radicals. Once secondary ester radicals are formed (see section 3.1.2.4), propylene can be eliminated TABLE 8: Thermochemistry of Reaction 06 ∆fH°298 K n

CnH2n-1O2

C2 H4

Cn-2H2(n-2)-1O2

∆rH°298 K

4 5 6 7 8

-56.2 -61.2 -65.3 -70.2 -74.9

12.3 12.3 12.3 12.3 12.3

-41.5 -55.4 -56.2 -61.2 -65.3

27.0 18.1 21.4 21.3 21.9

TABLE 9: Thermochemistry of 2 - CnH2n-1O2 Radicals ∆fH°298 K

CnH2n-3O2 f C13H22O2 + Cn-13H2(n-13)+1

n

2 - CnH2n-1O2

4 5 6 7 8

-66.9 -65.1 -69.8 -74.5 -79.2

TABLE 10: Thermochemistry of 5 - CnH2n-1O2 Radicals ∆fH°298 K

The thermochemistry of these reactions is reported in Table 7. 3.1.2.3. Ethylene Elimination from Ester Radicals. Reactions presented in sec 3.1.2.1 formed ester radicals. These radicals can undergo further reactions according to

n

5 - CnH2n-1O2

7 8 9

-80.7 -79.1 -83.9


J. Phys. Chem. A, Vol. 114, No. 11, 2010 3793 TABLE 13: Thermochemistry of Reaction 09a

TABLE 11: Thermochemistry of Reaction 07 ∆fH°298 K

∆fH°298 K

n

CnH2n-1O2

C3 H6

Cn-3H2(n-3)-1O2

∆rH°298 K

n

CnH2n-2

C5 H7

Cn-5H2(n-5)+1

∆rH°298 K

5 6 7 8

-65.1 -69.8 -74.5 -79.2

3.6 3.6 3.6 3.6

-41.5 -55.4 -56.2 -61.2

27.2 18.0 21.9 21.6

10 11 12 13

-4.1 -8.8 -13.5 -91.9

49.0 49.0 49.0 49.0

12.8 8.1 3.4 -74.9

65.9 65.9 65.9 65.9

a The reactant for 10 e n e 12 is CnH2n-2, and it is C13H22O2 for n ) 13.

TABLE 12: Thermochemistry of Reaction 08a ∆fH°298 K n

CnH2n-2

H

CnH2n-3

∆rH°298 K

10 11 12 13

-4.1 -8.8 -13.5 -91.9

52.7 52.7 52.7 52.7

21.5 16.7 12.0 -66.4

78.3 78.2 78.2 78.2



CnH2n-3

CnH2n-4

H

∆rH°298 K

10 11 12 13

21.5 16.7 12.0 -66.4

11.4 6.7 2.0 -76.4

52.7 52.7 52.7 52.7

42.6 42.7 42.7 42.7


CnH2n+1O2 f Cn-3H2(n-3)-1O2 + C3H6 The thermochemistry of these reactions is reported in Table 11. The evolution of the enthalpy of reaction is not monotonous because for n ) 5, the radical formed is on the carbonyl carbon, and this is energetically unfavorable, whereas for n ) 6, the radical is conjugated with the double bond of the carbonyl group, and this stabilizes the radical formed. For n > 6, this stabilization no longer exists. 3.1.2.6. ReactiVity of Conjugated Species. Reactions presented in sections 3.1.2.1 and 3.1.2.2 yield two conjugated species, one oxygenated and the other nonoxygenated, both abbreviated in this subsection and following subsections as Z-CH2-CH)CHCHdCH2. Their reactivity needs to be further studied. These species can react by C-H or C-C bond breaking. 3.1.2.6.1. H Abstraction.

The thermochemistry of these reactions is reported Table 13. 3.1.2.6.3. Cyclization to Form Cyclopentadiene DeriVatiVes. Species formed in section 3.1.2.6.1 can further react according to reaction 10 (see Table 14)

C13H21O2 f C13H20O2 + H and

CnH2n-3 f CnH2n-4 + H 3.1.2.6.4. ReactiVity of Substituted Cyclopentadiene through H-Atom Abstraction (see Table 15).

and

CnH2n-2 f CnH2n-3 + H C13H22O2 f C13H21O2 + H

C13H20O2 f C13H19O2 + H and

CnH2n-4 f CnH2n-5 + H

The thermochemistry of these reactions is reported in Table 12. 3.1.2.6.2. C-C Bond Breaking.

3.1.2.6.5. ReactiVity of Substituted Cyclopentadiene through C-C Bond Breaking (see Table 16).

CnH2n-2 f Cn-5H2(n-5)+1 + C5H7 and

C13H22O2 f C8H15O2 + C5H7

C13H20O2 f C8H15O2 + C5H5 and

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Osmont et al.

CnH2n-4 f Cn-5H2(n-5)+1 + C5H5

TABLE 18: Thermochemistry of Reaction 15a ∆fH°298 K

3.1.2.6.6. Methylene-Cyclopentadiene (fulVene) Elimination (see Table 17).

n

CnH2n-1

9

7.4

10 11 12

2.8 -2.0 -80.3

C 4H 6 26.4 (26.8 (0.2; 26.0 ( 0.235) 26.4 26.4 26.4

Cn-4H2(n-4)+1 34

∆rH°298 K

12.8

31.8

8.1 3.4 -74.9

31.7 31.8 31.8

a

The reactant for 9 e n e 11 is CnH2n-1, and it is C12H21O2 for n ) 12. Data within parentheses are literature data.

C13H19O2 f C7H13O2 + C6H6

The R-CH2• radicals undergo β-decomposition to form ethylene and a new n-alkyl radical

CnH2n-5 f Cn-6H2(n-6)+1 + C6H6 3.2. Initiation through C-C Bond Scission and Subsequent Decomposition Reactions. 3.2.1. Saturated Chains. For saturated chains, the less endothermic C-C bond breaking always occurs β to the carbon atom of the carbonyl group according to

with R is C13H27 for methyl palmitate and C15H31 for methyl stearate. The thermochemistry of the small oxygenated radical formed in reaction 14 can be considered as known.

and so forth. The related thermochemistry is presented in section 3.1.1.2. 3.2.2. Monounsaturated Chains. For monounsaturated compounds, the C-C bond breaking β to the ethylenic bond are seen to be energetically favored. Two reaction paths are therefore possible

and


CnH2n-4

CnH2n-5

H

∆rH°298 K

10 11 12 13

11.4 6.7 2.0 -76.4

35.5 30.8 26.1 -52.2

52.7 52.7 52.7 52.7

76.8 76.8 76.8 76.9


All of the unsaturated radicals just formed can react according to reaction 15, where Z-CH2-CHdCH-CH2• represents both the oxygenated and nonoxygenated radicals.

The corresponding thermochemistry is reported in Table 18.

TABLE 16: Thermochemistry of Reaction 12a

C12H21O2 f C8H15O2 + C4H6

∆fH°298 K n

CnH2n-4

Cn-5H2(n-5)+1

C5 H5

∆rH°298 K

10 11 12 13

11.4 6.7 2.0 -76.4

12.8 8.1 3.4 -74.9

62.5 (62.5 ( 1.033) 62.5 62.5 62.5

63.9 63.9 63.9 64.0

a

The reactant for 10 e n e 12 is CnH2n-4, and it is C13H20O2 for n ) 13.

CnH2n-1 f C4H6 + Cn-4H2(n-4)+1 The saturated oxygenated radical can further react through ethylene elimination according to

TABLE 17: Thermochemistry of Reaction 13a ∆fH°298 K n 10 11 12 13 a

CnH2n-5 35.5 30.8 26.1 -52.2

Cn-6H2(n-6)+1 17.5 12.8 8.1 -70.2

C6H6(fulvene) 22

54.3 (53.5 ) 54.3 54.3 54.3

∆rH°298 K 36.3 36.3 36.3 36.3

The reactant for 10 e n e 12 is CnH2n-5, and it is C13H19O2 for n ) 13.

The required thermochemistry for these small oxygenated radicals is generally known and was not computed in this study.

Modeling of the Thermal Decomposition of Biodiesel 4. Conclusions Nowadays, commercial liquid fuels for diesel engines include increasing amounts of vegetable oil methyl esters. The modeling of engine combustion requires a good knowledge of the thermochemical properties of these renewable fuel components. Thermochemical data were computed for numerous species needed for the writing of detailed chemical kinetic models for biodiesel thermal decomposition. This information is also needed for writing models dealing with the combustion of biodiesel because it can be expected that such large molecules will first decompose once heated, even if their rate of consumption will be enhanced by oxygen. Most of these data were not available because they concern large species for which experimental data are scarce or missing. The presently computed thermochemical data are provided in the CHEMKIN-NASA format as Supporting Information. This will help modelers’ work and also thermodynamic calculations at equilibrium. Complementary thermochemical data are also needed for species such as hydroperoxides formed via the low-temperature oxidation of biodiesel components. The computational tools used in this work should be useful for providing such data. Supporting Information Available: Thermochemistry of species computed in this study. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Guibet, J. C. Fuels and Engines. Technology - Energy - EnVironment; Technip: Paris, 1999. (2) Bloch, M.; Bournay, L.; Casanave, D.; Chodorge, J. A.; Coupard, V.; Hillion, G.; Lorne, D. Oil Gas Sc. Technol. 2008, 63, 405. (3) Montagne, X. SAE Tech. Pap. 1996, 962065. (4) Fisher, E. M.; Pitz, W. J.; Curran, H. J.; Westbrook, C. K. Proc. Combust. Inst. 2000, 28, 1579. (5) Gail, S.; Thomson, M. J.; Sarathy, S. M.; Syed, S. A.; Dagaut, P.; Dievart, P.; Marchese, A. J.; Dryer, F. L. Proc. Combust. Inst. 2007, 31, 305. (6) Huynh, L. K.; Lin, K. C.; Violi, A. J. Phys. Chem. A 2008, 112, 13470. (7) Gail, S.; Sarathy, S. M.; Thomson, M. J.; Dievart, P.; Dagaut, P. Combust. Flame 2008, 155, 635. (8) Sarathy, S. M.; Gail, S.; Syed, S. A.; Thomson, M. J.; Dagaut, P. Proc. Combust. Inst. 2007, 31, 1015. (9) Dayma, G.; Gail, S.; Dagaut, P. Energy Fuels 2008, 22, 1469. (10) Dagaut, P.; Gail, S. J. Phys. Chem. A 2007, 111, 3992. (11) Dagaut, P.; Gail, S.; Sahasrabudhe, M. Proc. Combust. Inst. 2007, 31, 2955. (12) Herbinet, O.; Pitz, W. J.; Westbrook, C. K. Combust. Flame 2008, 154, 507. (13) Petersson, G. A.; Malick, D. K.; Wilson, W. G.; Ochterski, J. W.; Montgomery, J. J. A.; Frisch, M. J. J. Chem. Phys. 1998, 109, 10570. (14) Curtiss, L. A.; Redfern, P. C.; Frurip, D. J. Theoretical Methods for Computing Enthalpies of Formation of Gaseous Compounds; WileyVCH: New York, 2000; Vol. 15. (15) Osmont, A.; Yahyaoui, M.; Catoire, L.; Gokalp, I.; Swihart, M. T. Combust. Flame 2008, 155, 334.

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JP904896R

Thermodynamic Data for the Modeling of the Thermal Decomposition

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