Chemistry of high temperature combustion of alkanes up to octane

Twentieth Sym|~)sium (Intt'rnational) on Combustion/The Combustion Institute. 1984/pp. 845-856

CHEMISTRY OF HIGH TEMPERATURE COMBUSTION OF A L K A N E S UP TO O C T A N E JL'RGEN WARNATZ Angewandte Physikalische Chemic der Universit?it 11eidelberg 6900 Heidelberg, West-Germany Alkanes are initially attacked by H, O, and OH radicals generated in the oxyhydrogen reaction. The alkyl radical forlned in this way decomposes to smaller alkyl radicals by fast thermal elimination of alkenes. Only the relatively slow thermal decomposition of the smallest alkyl radicals, CH3 and C2H~, competes with recombination and with oxidation reactions by O atoms and ()~. This part of the mechanism is rate-controlling in the combustion of alkanes (and alkenes) anti must be described hy a detailed mechanism consisting of elementary reactions. Alkyl radical decomposition and the reactions leading to C~- and C~,-fragments are too fast to be rate-limiting and can therefore he descrihed by simplified reaction schemes disregarding alkyl ismneric structures. Simulations of flames of higher alkanes (up to octane) using these simplifying assumptions show agreement with the experimental material available. The mechanism derived by these considerations can then he used to explain of phenolnena (like non-Zeldovich NO formation or formation of soot precursors), which can be interpreted fi'om a detailed knowledge of the Ci,/C_,-chemistry. 1. Introduction

A previously given mechanism of high temperature oxidation of alkanes, alkenes, and acetvlenc [1] enabled the description of the oxidation of aliphatic hydrocarbons tip to butane for lean and moderatelv fuel-rich conditions. Combination with recent work on the formation of higher hydrocarbons in acetylene combustion [21 made it possible to include the description of the oxidation of aliphatic hydrocarbons (up to C4-species) under very fuel-rich conditions [3-5]. From this work, a general mechanism for the oxidation of higher alkanes (number of C-atoms >2) seelus to he derivable, which can be verified at least for propane and butane high temperature combustion [1,3]. According to this scheme, the first attack on the alkanc is provided by tt, O, and O1t radicals generated in the chain-branching steps of the oxyhydrogen reaction system, whereas ~ittack by 1tO2 or alkyl radicals is too slow to be important. As with to CH:~ and Cell5 oxidation (see Fig. 2), there are four possible types of reaction (Fig. la): (1) The first reaction is the thermal decomposition which is known from experiments to involve elimination of an alkene to form a smaller alkyl radical [4,6,7]. (2) The second is the reaction with Oz to form the corresponding alkene [4,8]. (3) The third possibility is the reaction with 0 845

atoms to form an aldehyde and a smaller alkyl radical [4,9]. (4) Finally, there is the possibility of recombination or disproportionation with another alkyl radical (or H atom) [4,8]. Simulations of CH4, C2H6, Calls, and C4ttto flames including these four reaction types and the subsequent mechanisms show a very simple re'suit which probably can be extended to the higher alkanes. Thermal decomposition turns out to be the onlv relevant reaction of the higher alkyl radicals in lligh temperature combustion. The alkyl radicals formed in the initial attack on the hydrocarbon decompose to smaller alkyl radicals by fast thermal elimination of alkenes (Fig. lb). Only the relatively slow thermal decomposition of the smallest alkyl radicals CIt 3 and CzHs [4] competes with recombination and with oxidation reactions by 0 atoms and 02. This last part of the mechanism is ratecontrolling in the combustion of alkanes (and alkenes), and is therefore the reason for the similarity of all alkane (and alkene) flames. Up to the present, this oxidation scheme is hypothetical for higher alkanes (pentane and larger compounds) due to the lack of detailed reaction mechanisms for alkyl radical decomposition. This lack of knowledge is understandable if the large number of alkyl isomeric structures and the necessarily resulting number of potential reaction paths is considered (number of C8H17 radicals, 89; number of

846

REACTION KINETICS

ntdehyde

+0 l -H,alkyl *02 _ olkene -HO2

disp.,rec. , +H,alkyl

+M

the (rather sparse) experimental material available. The purpose of this procedure is to use the mechanism derived from these considerations to explain phenomena like non-Zeldovich NO formation [11] or formation of soot precursors [2,5,11], which can only be explained from a detailed knowledge of the Ct/C~ chemistry.

-alkene

ctlky['

2. Calculation Method 2.1 Numerical Procedure For a quantitative simulation and interpretation of measurements, the corresponding conservation equations for a premixed laminar fiat flame must be solved. Conservation of enthalpy and of mass of species i leads to the time-dependent equations [1,12,13]

*H,O,OH1 -Hz'OH'H/O

aT _~ = -r at

aT aT - - - jrI - az az

1 a (k0T~

alky[

~r,h,

"JF ----

c~ az \

+M [-alkene

az /

cp

aWi aWi aji q ~ = -qv . . . . + ri Ot az az

smaller olky[

(1) (e)

where the diffusion fluxes ji and the mean diffusion flux JH are given by "z%,di

eft.

+M I-alkene

CH3,C2Hs FIG. 1. Upper drawing: Reaction paths of an alkyl radical, lower drawing: General scheme for the decomposition of an alkane.

jH = - %

awi

; jl = --Di.Mq - az

a In T

az

(3)

where cp = specific heat capacity, h = specific enthalpy, r = mass scale chemical rate of formation, t = time, T = temperature, v = flow velocity, w = mass fraction, z = cartesian space coordinate, h = mixture heat conductivity, <2 = density. A simplified transport model given by Eq. (4) 1 -- Wi

,,,. = j~i E 1,7s C7H15 radicals, 39 e.g. [10]). There will be no possibility in the next decades to develop detailed mechanisms to describe the complex chemistry of this system of dozens of alkyl compounds. Therefore, the idea of this paper is to make use of the fact that alkyl radical decomposition and the reactions leading to C1- and C2-fragments are too fast to be rate-limiting. For this purpose, simplified decomposition paths (ignoring isomeric structures) will be derived and tested, showing the independence of simulations of flames of higher alkanes (pentane to octane) of these simplifying assumptions, and showing agreement with

DT i '

XM = ~

1)

xi x~ + ~ x,lX,

(4)

i

where x = mole fraction is used, because comparison with multicomponent transport models results in relatively small errors [12,14,15]. Here the binary diffusion coefficients ~ q and the pure species heat conductivities h i are calculated from angle-independent Stockmaier potential parameters, including an extended Eucken correction for thermal

CHEMISTRY OF ALKANES COMBUSTION

CHa,

847

C2H6 +H,0,OH +0

CH 3 "

-

CzHs . . . . . . .

+H,O,OH ~" CH3CHO . . . . . . .

+M

"

CH3CO . . . . . .

~ CH3

+HII+H'02

--~ CH20

I

+H,O,OH

- - " CliO

C2H~

+O,OH

> CH 3 ,CH20, CHO

--,,

+H,OH

C2H3

l

+0 -

CHACO

+H,O,0H

,.CH 3,CH20,CHO

+M,02,H

CO

+O

§ C2H2

,

CHCO

-

CO

1.0/ C2H

CH2

§

,

CH

C2H21[+ 0,02

1+

CO

CO2

( q, H2)

(C3H~)

CO

FIG. 2. Reaction schemefor the oxidationof Ci- and C2-hydrocarbons. conductivity [12,14,16]. The thermal diffusion coefficient DT,i (important only for the light species H and H2) is calculated by use of a simplified binary model [12,14,16]. Due to the stiffness of the system of differential equations (1) and (2), an implicit finite difference method is chosen for solution [1,12]. This method starts with arbitrary S-shaped profiles of temperature T and mass fractions w~ at time zero. With, the aid of a grid point system (35 points with nonuniform distribution) the derivatives are replaced

by finite difference expressions assuming a parabolic approach between three neighbouring grid points in each case. This procedure reducesthe given problem to the solution of a tridiagonal linear equation system, if at the edges of the grid point system the values of temperature T and mass fractions wi are specified by means of proper boundary conditions. For freely propagating flames (burner-stabilized flames are not considered here), the coordinate system is extended well into the cold gas region, where gra-

848

REACTION KINETICS

dients of temperature and mass fractions vanish; at the hot boundary constant gradients are assumed [12,14,17] (c,h = cold, hot boundary; u = unburnt gas): Tc = T~ -~z h = eonst

(5)

wi,c = wi,, \ dz ] h = const

(6)

2.2 Input Data The input data for the determination of transport properties are ~aken from [3,16] and from [18] for the higher alkanes. Thermochemical data are taken from the JANAF Tables [19] and addenda, or (if not referenced in these tables) from [20] or [21]. The mechanism and rate data are discussed in Chapter 3.

2.3 Choice of the Reaction Mechanism The reaction mechanism used is an extension of a mechanism developed for the simulation of flame

propagation [1,3] and ignition [22] for hydrocarbons up to C4-species. It is based on a critical review of about 200 elementary reactions occurring in the combustion of small hydrocarbons [4]. The essential reactions of the mechanism of higher alkane oxidation can be derived from this collection of elementary steps by elimination of the unimportant reactions by the methods given in [1,23], using subsets of this mechanism, i.e. the H2/O2 system [23,24], the H z / O f f C O system [13], the C1/C2-hydrocarbon oxidation system [1,2], the C3/C4-hydrocarbon oxidation system [1-3], and the oxidation of higher alkanes (this paper).

3. Reaction Mechanism The mechanism used in this work is an extension of a mechanism developed for the simulation of propagation of flames in alkane/alkene-air mixtures [1,3] under lean and moderately rich conditions. It is modified here to describe combustion of higher alkanes, using the fact that alkyl radicals formed in the initial attack on the hydrocarbon have relatively simple reaction paths. Extremely fuel-rich mixtures or sooting flames are not considered here.

TABLE 1 Mechanism of the oxidation of H2 and CO E No.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Reaction

A[cm, mol, s]

b

Hw-O2 Chain Propagation and Branching Reactions H + 02 ~ OH + O 1.2.10 iv -0.91 OH + O ~ H + 02 7.1.10 is -0.91 O + H2 ~ OH + H 1.5.10 7 2.00 OH + H ---> O + H2 6.7" 106 2.00 OH + H2 ~ H20 + H 1.0'10 s 1.60 H20 + H ~ OH + H2 4.6" 108 1.60 OH + OH ~ H20 + O 1.5"10 Q 1.14 H20 + O -'-> OH 1.5" 101~ 1.14

kJ/mole

69.1 0 31.6 23.3 13.8 77.7 0 72.2

: Recombination Reactions H + H + M' --~ H2 + M' 1.8-10 is H + OH + M' ~ H20 + M' 2.2-102z

-1.00 -2.00

0 0

Formation and Consumption of HO~ H + O2 + M' ---* HO2 + M' 2.0.10 Is H + HO2 ~ OH + OH 1.5.1014

-0.80 0

0 4.2 2.9 0 0

H + HO2 ~ O + HO2 ~

H2 + 02 OH + O~

OH + HO2 ~ H20 + Oz CO + OH ---* CO2 + H CO2 + H ~ CO + OH

2.5.1013 2.0.1013

0 0

2.0'101~

0

Oxidation of CO 4.4-106 1.6.1014

1.50 0

[M'] = 1.0[H21 + 0.4[02] + 0.4[Nz] + 1.0[C H] + 0.75[CO1 + 1.5[CO2] + 6.5[H20]

-3.1

110.0

CttEMISTRY OF ALKANES COMBUSTION 3.1 t t 2 / O z / C O

Subsystem

Reactions in the H 2 / O 2 / C O system are part of the main chain-branching process that maintains high-temperature combustion of hydrocarbons. Due to their importance, these reactions have been investigated in detail bv many workers using a variety of techniques. Because of the relative simplicity of this system, it is possible to give a complete picture of the reactions involved (Table 1). The mechanism used is based on a compilation by Baulch et al. [25] including new results published later [4]. Flames in the llz/O2 and the 112/O2/CO systems are discussed elsewhere [13,23,24,26]. 3.2 Cx/C2

Subsystem

A reaction scheme describing the high-temperature oxidation of CI- and C2-hydrocarbons is given in Fig. 2. It is similar to that presented earlier [1],

849

except for a revised description of acetylene oxidation [2]. Details of the mechanism of oxidation of C1- and Ca-species are given in Table 2 (rate coefficients from [4]). 3.3 C3/C 4

Subsystem

As in the combustion of CH3 and C2Hs, the reactions of H and OH and to a lesser extent of O with the hydrocarbon consume fuel consumption in flame propagation, whereas reactions of HO2 and alkvl radicals are unimportant due to the low HO,2 and alkyl radical concentrations and the small rate coefficients. In contrast to CH3 and CzHs, for higher hydrocarbons not only the global rate coefficients are of interest for the attack of H, O, and OH, but also specific rate coefficients for the attack on single C - - H bonds, because the formation rates of different alkyl isomers, e.g. n-C3H7 and i-C3H7 for

TABLE 2 Mechanism of the oxidation of C1/C2 hydrocarbons E Reaction

No.

A[cm,mol,s]

b

kJ/mole

-1.00 3.00 3.00 2.10 2.10 2.10 2.10

0 36.6 32.4 31.9 19.6 10.3 70.3

18 19 20 21 22 23 24

Formation and Consumption of CH4 a) 6.0' 1016 CH3 + H ~ CtI4 CH4+ H ~ CHa + H.~ 2.2' 104 CH3 + Hz--~ CIt4 + H 6.6" 10~ CH4 + O ~ CI13 + OH 1.2-107 CH3 + OH ----, CH4 + O 1.3-105 CH4 + OH ~ CH3 + HzO 1.6" 106 CH3 + 1"120 ~ CH4 + OH 2.9- 105

25

CHa + O ~ CH20 + H

7.0" 1013

0

26 27 28

CHzO Consnmption CH20 + H ---, CHO + Hz CH20 + O ~ CHO + OH CHzO + OH --* CHO + IibO

2.5" 1013 3.5' 1013 3.0' 1013

0 0 0

16.7 14.7 5.0

29 30 31 32 33 34

CHO CHO CHO CHO ClIO CHO

CHO Consumption H ~ CO + H2 O--* CO + OH O--* COb + H OH ~ CO + HbO O b ~ CO + HO: M' ~ CO + H + M'

2.0-10 l~ 3.0' 10 ~a 3.0' 1013 5.0' 1013 3.0-1012 7.1" 1014

0 0 0 0 0 0

0 0 0 0 0 70.3

35 36 37 38

CHb CH2 CHb CHb

CHb Consumption H ~ CH + H2 O ~ CO + H + H O b ~ CO2 + H + H CH3 ~ C2H4 + H

4.0-1013 5.0'10 ~a 1.3' 1013 4.0' 1013

0 0 0 0

0 0 6.3 0

39 40

CH + O ~ CO + H CH + 02 ~ CO + OH

4.0.10 ~a 2.0" 1013

0 0

0 0

CH3 Consumption

+ + + + + + + + + +

CH Consumption

850

REACTION KINETICS T A B L E 2 (continued) M e c h a n i s m of t h e oxidation of C1/Ca h y d r o c a r b o n s E No.

Reaction

A[cm,mol,s]

b

kJ / m o l e

41 42 43

F o r m a t i o n of C2-Hydrocarbons by CH3 R e c o m b i n a t i o n CH3 + CH3 --* CzH~ a) 2.4" 1014 -0.40 CH3 + CH3 ~ Call5 + H 8.0.1013 0 CH3 + CH3---> C2H4 + Ha 1 . 0 - 1 0 TM 0

44 45 46 47 48 40 50

Call8 C2H6 C2H6 CaH~ Call5 C2H5 C2H5

+ + + + + + ~

Call6 C o n s u m p t i o n H ~ C2H5 + H2 O---> C2H5 + O H O H ---* Calls + H 2 0 H ~ CH3 + CH3 O ~ CH3CHO + H Oz "* C2H4 + HO2 Call4 + H a)

5.4" 10 ~ 3.0"107 6.3" 106 3.0" 10 ~3 5.0" 1013 2.0" 1013 2.0" 1013

3.50 2.00 2.00 0 0 0 0

21.8 21.4 2.7 0 0 20.9 166.0

51 52 53 54

C2H4 C2H4 Call4 Call4

+ + + +

C2H4 C o n s u m p t i o n H ---) C~H5 a) O ---) C H O + CH3 O H ---* C2H3 + H 2 0 H ---) C2H3 + H2

1.0.1013 1.6-109 7.0.1013 1.5.1014

0 1.20 0 0

6.3 3.1 12.6 42.7

55 56 57

C2H3 C o n s u m p t i o n Call3 + H --* CzHa + H2 C2H3 + Oa -'-> C2H2 + HO2 C2H3 ~ C~Ha + H

2 . 0 ' 1013 1.O" 1012 1 . 0 . 1 0 '~

0 0 0

58 59 60

C2H2 C o n s u m p t i o n (abstraction reactions excluded) C2H2 + H ~ C2H3 a) 5.5" 10 la C2H2 + O ~ CH~ + C O 4.1" 108 C~Ha + O H ~ C H 2 C O + H a) 3 . 0 . 1 0 la

O 1.5 0

10.1 7.1 4.6

61 62 63

CH3CHO Consumption C H 3 C H O + H---* CH3 + C O + H b) 4.0.1013 C H a C H O + O ~ CH3 + C O + O H b) 5 . 0 . 1 0 la C H 3 C H O + O H ---) CH3 + C O + HaO b) 1.0.1013

0 0 0

17.6 7.5 0

64 65 66 67

CH2CO CHACO CH2CO CH2CO

7 . 0 . 1 0 la 2 . 0 ' 1013 1.0" 1013 1.0-1016

0 0 0 0

12.6 9.6 0 248.0

68 60 70

C H C O F o r m a t i o n and C o n s u m p t i o n C2H2 + O ---) C H C O + H 4.3" 1014 C H C O + H ~ CH2 + C O 3 . 0 ' 1013 C H C O + O---* C O + C O + H 1.2.1012

0 0 0

50.7 0 0

71 72 73 74 75

C2Hz + C2H2 + Call + Call + C2H +

C2H F o r m a t i o n and C o n s u m p t i o n H ~ C2H + He 1.5.1014 O H ---) C2H + H 2 0 1.0.1013 O ----> C O + C H 1.0.1013 H2 ~ Calla + H 3.5" 1012 02 ~ C O + C H O 5.0" 1013

0 0 0 0 0

79.6 29.3 0 8.8 6.3

+ + + +

CHzCO Consumption H ~ CH3 + C O O ---* C H O + C H O O H ---) CH2 + C H O M ---) CH2 + C O + M

0 111.0 134.0

0 0 178.0

[M'] = 1.0[H2] + 0.4[O2] + 0.4 + 1.0[C2H2] + 0.75[CO] + 1.5[CO2] + 6.5[H~O] + 0.35[Ar] a) = High p r e s s u r e value; in addition a R R K factor m u s t be included; see section 3.4. b) = Fast t h e r m a l decomposition of t h e i n t e r m e d i a t e C H 3 C O is a s s u m e d .

CHEMISTRY OF ALKANES COMBUSTION

851

TABLE 3 Mechanism of the oxidation of Ca-hydrocarbons (C3H4 chemistry excluded) E

No.

Reaction

Calls Formation and Consumption 7.0.10 TM CH3 ~ Calls H ~ n-CaH7 + H2 1.3" 10~4 1.0" 1014 H ~ i-C3H 7 + H2 O ~ n-Call7 + OH 3.0' 10~3 O ~ i-CsHr + OH 2.6' 1013 OH ~ n-CaH7 + H20 3.7' 1012 OH ~ i-C3H7 + H20 2.8" 10~2

76 77 78 79 80 81 82

C2H5 Calls Calls Calls Calls Calls Calls

83 84 85 86 87 88 89

n-CaH7 + i-C3H7 + n-CaH7 + i-CaH7 + n-CaH~ ~ n-CaHr ~ i-C3H7 ~

90 91 92 93

Call6 CaH6 C3H~ CaH~

+ + + + + + +

+ + + +

A[cm, mol, s]

C3H7 Consmption 2.0 1013 H ~ Calls H ~ Calls 2.0 10~3 1.0 1012 O2 ~ C3H6 + HO2 1.0 1012 O2 ~ C3H6 + HO2 3.0 1014 C2H4 + CH3 1.0 1014 C3H6 + H 2.0 10~4 C3H6 + H

C3H6 Consumption H ~ n-CaHr H ~ i-C3H7 O ~ CH3 + CHa + CO* OH ~ CHaCHO + CH3

4.0.1012 4.0.10 ~2 5.0.1012 1.0.1013

b

kJ/mole

0 0 0 0

0 40.6 34.9 24.1 18.7 6.9 3.6

0 0

0 0 20.9 12.5 138.0 156.1 161.9 11.0 4.0 1.9 0

*Fast thermal decomposition of the intermediate CHACO is assumed. propane, n-C4H9 and s-C4H9 for butane, are different. Data for these specific rate coefficients of attack on C - - H bonds can be derived from experiments with hydrocarbons with different distributions of primary, secondary, and tertiary C atoms (see [4]). There is no evidence that reactions of propene may play a rate-controlling part in high-temperature combustion. Since the data available are scarce [4] and may be complicated by potential pressure dependence, more knowledge on the rate coefficients and products of these reactions is desirable. This is supported by the fact that propene (but not butene [3]) is an important intermediate in the decomposition of propyl and butyl radicals, respectively, and must somehow be consumed in the reaction zone. Details on the oxidation of Ca-species are given in Table 3 (Call4 is excluded since no extremely fuel-rich flames are considered). 3.4

Chemistry of Higher Alkane Combustion

From work on the high-temperature combustion of propane and butane it is known that the alkyl radical formed in the initial reaction is decomposed to smaller alkyl radicals by elimination of alkenes [1,3,4]. The detailed mechanism of this alkyl de-

composition is given by the "one bond removed rule" (see [7]) which is verified up to C4 radicals. This rule says that when a radical decomposes, a bond once removed from the radical site is broken. In addition, when there is a choice between a C - - H bond and a C - - C bond, the C - - C bond usually is broken due to the lower bond strength. However, because of the variety of alkyl and alkene isomeric structures, it seems to be hopeless to develop a detailed mechanism for alkyl radical decomposition within the next decades. The only realistic possibility is to find "representative reactions" and "representative species" to describe these complex processes, avoiding fitting procedures or global reaction mechanisms which cannot lead to a further development. Rate coefficients for the reactions of H, O, and OH with alkanes can be derived from experiments with hydrocarbons with different distributions of primary, secondary, and tertiary C - - H bonds [27,28]. Assuming additivity of these rates, one can derive rate coefficients of reactions of higher hydrocarbons with H, O, and OH [4]. Results for pentane to octane are given in Table 4. As for propane and butane (see Section 3.3), reactions of HO2 and alkyl radicals with the alkane fuel can be excluded.

852

REACTION KINETICS

TABLE 4 Rate coefficients for the attack of alkanes by H, O, and OH, k = A exp(E/RT) A

E

cm3/mol 9s

kJ/mol

n-CsHl8 + H +O + OH n-CTHl6 + H +O + OH

7.1.10 l' 1.8.10 ~4 2.0" 10x3 6.1.101' 1.6.1014 1.7.1013

35.3 19.0 3.9 35.4 19.1 4.0

n-C6HI, + H +O + OH

5.1.1014 1.3.1014 1.5.10 ~3

35.4 19.2 4.1

n-CsHI~ + H +O + OH

4.1.1014 1.0.10 ~4 1.2.1013

35.6 19.3 4.2

Reaction

perimental results. A detailed mechanism [3] was used in this ease. The short mechanism of Tables 1-3 (omitting reactions in very fuel-rich flames) was used to calculate corresponding results for propane which are also shown in Fig. 3 (broken line), leading to high values in rich mixtures. Both for propane and butane, the "representative mechanism" described in Section 3.4 would be very similar to the real detailed mechanism. 4.2 Results Using the Representative Mechanism for Pentane to Octane Results for the high-temperature combustion of alkanes from n-pentane up to n-octane are given in Vu/cm.s

"1

50 ~0

From sensitivity tests in methane-, ethane-[1], and butane-air flames [3] it is known that alkyl radical decomposition by alkene elimination and subsequent alkene oxidation are not rate-limiting processes. This leads to the idea of replacing the complex alkyl radical decomposition reactions by a simple reaction path leading to only one small alkyl radical and only one small alkene, both contained in the detailed C1/C2/C3-hydrocarbon oxidation mechanism discussed above. Because of the marked chain-branching character of CzH5 [22], CH3 was chosen as the alkyl radical. Furthermore, the largest alkene for which a reasonable detailed chemistry can be presented is chosen as the representative alkene, namely, propene. Thus, the alkyl decomposition reactions are

30

\

20 10

2 Vu/cm-s

i

i

i

t

3

t~

5

6

"1

50

..... . t 9

CsH17--+ CH3 + 2.333 C3H6

(7)

C7H15--+ CH3 + 2.000 C3H6

(8)

C6HI3 --+ CH3 + 1.667 C3Hs

(9)

CsHI1 ~ CH3 + 1.333 C3H6

(10)

Since rate coefficients for these reactions are not known, the rate coefficient of n-butyl radical decomposition was chosen. 4. Results and Discussion

4.1 Results for Propane and Butane Using a Detailed Mechanism Results for the combustion of propane and butane are shown in Fig. 3 in comparison with ex-

/

2O

% C~.H10

I Pr~ %*"

t

10 l

i

J

~

I

i

3

~

5

6

7

%

C3H9

FIG. 3. Flame velocities v~ for freely propagating

flames in propane-air (upper drawing) and butaneair mixtures (lower drawing) at atmospheric pressure, T, = 298 K. Points: measurements (for reference see [3]). Full lines: calculations with the detailed mechanism given in [3]. Broken line: calculations with the mechanism given in this paper.

CHEMISTRY OF ALKANES COMBUSTION

Vu/cm.s -~

853

Influence of the Rate Coefficient of Alkyl Radical Decomposition 4.3

The rate coefficient of thermal decomposition of pentyl to octyl radicals has to be estimated due to the lack of experimental data. For this reason, the rate coefficient for C4Hg thermal decomposition has been used in the calculations.

~0 9

j ~

"~176

d~

v u /cm.s -1 50

I Hexane ]

20

~0

30 I

I

I

1.5

2.0

2.5

@

% C6H14

Ioctanel

20

v u/cm.s -1 10

I 1.5

40

1.0

I 2.0

% C8H+8

v u / c m . s -1

50 IPenfane I

20

z,O

9

-

0

30 i 2.0

i 2.5

I 3.0

% CsH12

Fic. 4. Flame velocities v, for freely propagating flames in n-pentane-air and n-hexane-air mixtures at atmospheric pressure, T. = 298 K. Points: experimental results 9 Ref. [29], O Ref. [30]. Lines: calculations. Figs. 4 and 5 in comparison with corresponding experimental results. The representative mechanism leads to flame velocities which agree with the (sparse) measurements available, if the error limits of the experiments are taken into consideration.

I Heptane I

20

10

I

I

I

1.5

2.0

2.5

% C7H16

FIG. 5. Flame velocities v, in n-heptane-air and n-octane-air mixtures (conditions given in Fig. 4).

854

REACTION KINETICS gating n-octane flame. There is no real sensitivity of this flame velocity with respect to the variation within a large range of rate coefficients in the neighbourhood of the original values used for the calculations in Figs. 4 and 5. This result is eminently important for two reasons:

Vu/u

1.5

1.0

~0

( ~ 0 ~ 0

-0/0/

O.S

I 0.001

I 0.01

I 0.1

I 1

I 10

I 100

k k,

FIG. 6. Influence of the rate coefficient of thermal decomposition of the alkyl radical on the flame velocity v, of a stoichiometric n-octane-air flame at atmospheric pressure, T= = 298 K. The index "o" refers to the original values of k and v,. A central point of the considerations leading to the results presented above was the assumption that alkyl radical thermal decomposition is too fast to be rate-limiting. This must be proven by varying this rate coeflqcient. Fig. 6 shows the influence of this variation on the flame velocity of a freely propaV u / C m . s -1

lt~O

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120 100

80

olkenes

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5. Conclusions It has been shown that the decomposition of alkyl radicals formed in the initial attack on n-pentane to n-octane can be represented by a simple mechanism leading to methyl radicals and propene, and that this process is not rate-limiting. The ratecontrolling process in the combustion of alkanes up to octane is the oxidation of C1- and C2-species. These results lead to certain conclusions: (1) It is now possible to describe the combustion of alkanes up to n-octane in agreement with corresponding experiments, as well as simple alkene and alkynes (Fig. 7). (2) It should be possible now to explain phenomena like non-Zeldovich NO formation or formation of soot precursors, which can only be explained by a detailed C1/C2 oxidation mechanism. (3) For more complex flames, it should be possible to simplify C1/C2-chemistry by concepts similar to that developed in this paper.

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60

fuel-air]

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(1) It demonstrates the assumptions using the representative mechanism (7) to (10) to be reasonable. (2) It shows that the representative mechanism (7) to (10) can be expected to hold for a large range of conditions around the conditions considered here (fuel-air mixtures, atmospheric pressure). This behaviour is due to the large influence of the chain-branching caused by the hydrogen-oxygen system which is ratelimiting in any case. This important influence of the oxyhydrogen system also is the reason for the similarity of the flame velocities of all the flames considered here [1].

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Acknowledgment 20

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I

2

I

I

I

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6

I

I

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atom

number

8

FIG. 7. Flame velocities v, of stoichiometric flames in mixtures of alkanes, alkenes, and alkynes with air at atmospheric pressure, T= = 298 K. Lines: calculations. Points: measurements (Ref. [3,29-32] for alkanes, Ref. [1] for alkenes, Re{'. [29,32] for alines).

The financial support of the "Deutsche Forschungsgemeinschaft," the "Fonds der Chemischen Industrie," and the "Volkswagen-Stiftung" is cordially acknowledged. REFERENCES 1. J. WAI~NATZ,18th Symposium (International) on Combustion, p. 369, The Combustion Institute, Pittsburgh (1981).

CHEMISTRY OF ALKANES COMBUSTION 2. J. WARNATZ, H. BOCKHORN,A. MOESER, H. W. WENZ, 19th Symposium (International) on Combustion, p. 197, The Combustion Institute, Pittsburgh (1983) 3. J. WARNATZ,Comb. Sci. Technol. 34, 177 (1983). 4. J. WARNATZ, in: W. C. Gardiner jr (Ed.), Chemistry of Combustion Reactions, Springer, New York (1984); J. Warnatz, Survey of Rate Coefficients in the C / H / O System, Sandia Report SAND83-8606, Sandia National Laboratories, Livermore (1983). 5. J. WARNaXZ,in: J. Lahaye, G. Prado (Eds.), Soot in Combustion Processes and Its Toxic Properties, Plenum, London (1983). 6. R. M. FRISTROM,R. PRESCOTr, C. GRUNFELDER, Combust. Flame 1, 102 (1957). 7. F. L. DRYER, I. GLASSMAN,in: C. T. Bowman, J. Birkeland (Eds.), Alternative Hydrocarbon Fuels, Combustion and Kinetics, AIAA, New York (1979). 8. R. W. WALKER, in: P. G. Ashmore, R. J. Donovan (Eds.), SPR Gas Kinetics and Energy Transfer, Vol. 2, p. 296, The Chemical Soceity, London (1977). 9. B. BLUMENBERG, K. HOYERMANN, R. SIEVERT, 16th Symposium (International) on Combustion, p. 841, The Cmnbustiou Institute, Pittsburgh (1977). 10. H. EDERER, private communication. 11. K. H. HOMaNN, J. WARNaTZ, VDI-Berichte Nr. 423, 29 (1981) 12. J. WaRNATZ, Ber. Bunsenges. Phys. Chem. 82, 193 (1978). 13. J. WARNATZ,Ber. Bunsenges. Phys. Chem. 83, 950 (1979). 14. J. WARNaTZ, in N. Peters, J. Warnatz (Eds), Numerical Methods in Laminar Flame Propagation, Vieweg, Wiesbaden (1982). 15. J. M. HEIMERL, T. P. COFFEE, in: N. Peters, J. Warnatz (Eds.), Numerical Methods in Laminar Flame Propagation, Vieweg, Wiesbaden (1982). 16. R. J. KEE, J. A. MILLER, J. WARNATZ,A FORTRAN Computer Code Package for the Evaluation of Gas-Phase Viscosities, Conductivities, and Diffusion Coefficients, Proc. Eastern States

17. 18. 19.

20. 21.

22.

23. 24. 25.

26.

27.

28. 29. 30. 31.

32.

855

Section Combustion Meeting, Providence, Rhode Islands (1983). J. WARNaTZ, Ber. Bunsenges. Phys. Chem. 82, 834 (1978). E. A. HaLKInDaKIS, R. G. BownEY, Chem. Eng. Sci. 30, 53 (1975). D. R. STULL, H. PROPHET (Project Directors), JANAF Thermochemical Tables, 2nd edition, NBS, Washington, D.C. (1971). S. W. BENSON,Thermochemical Kinetics, Wiley, New York (1976). A. BURCaT, in: W. C. Gardiner jr. (Ed.), Chemistry of Combustion Reactions, Springer, New York (1984). W. C. GaRDINER, K. J. NIEMITZ, J. M. SIMMIE, J. WARNATZ, R. ZELLNER, in: J. R. Bowen, N. Manson, A. K. Oppenheim, R. I. Soloukhin (Eds.), Flames, Lasers, and Reactive Systems, p. 252, AIAA, New York (1983). J. WaRNATZ, Ber. Bunsenges. Phys. Chem. 82, 643 (1978). J. WARNATZ,Comb. Sci. Technol. 26, 203 (1980). D. L. BauLcrl, D. D. DRYSDaLE, D. G. HORNE, A. C. LLOYD, Evaluated Kinetic Data for High Temperature Reactions, Vol. 1: Homogeneous Gas Phase Reactions of the H2-Oe System, Butterworths, London (1972). G. DIXON-LEWIS, D. J. WILLIAMS, in: C. H. Bamford, C. F. H. Tipper (Eds.), Comprehensive Chemical Kinetics, Vol. 17, Elsevier, Amsterdam (1977). R. R. BALDWIN,J. P. BENNE'IT, R. W. WALKER, 16th Symposium (International) on Combustion, p. 1041, The Combustion Institute, Pittsburgh (1977). J. T. HERRON, R. E. HULL, J. Phys. Chem. 73, 3327 (1969). G. J. GIBRS, H. F. CALCOTE, J. Chem. Eng. Data 4, 226 (1959). M. GERSTEIN, O. LEVINE, E. L. WONG, J. Am. Chem. Soc. 73, 418 (1951). G. DIXON-LEwlS, S. M. ISLAM, 19th Symposium (International) on Combustion, p. 488 (1983). R. GUENTHER, G. JaNISCH, Chemie-Ing.-Technik 43, 975 (1971)

COMMENTS K. Brezinsky, Princeton University, USA. The type of scheme you have outlined for alkane oxidation works well for the simulation of flames since their speeds are not particularly sensitive to the details of fuels decomposition. Isn't it time, however, that for other applications, such as the description of the

chemistry of engine knock, that more chemical detail especially of the decomposition of isomers would be necessary?

Authors" Reply. As pointed out in the paper, the large number of species and reactions involved in

856

REACTION KINETICS

the oxidation of higher hydrocarbons excludes the use of detailed mechanisms for these species. However, it seems to be promising, to describe the pyrolysis of alkyl radicals by detailed chemistry (1, 2) and to use global mechanisms for the decomposition of the alkenes eliminated in this pyrolysis because alkene oxidation seems not to be a rate-limiting process. Studies of ignition processes using this simplification are in progress.

REFERENCES 1. J. WARNATZ, Survey of Rate Coefficients in the C / H / O System, in: W. C. Gardiner (ed.), Chemistry of Combustion Reactions, Springer, New York (1984). 2. F, L. DRYER, I. GLASSMAN, Combustion Chem-

istry of Chain Hydrocarbons, in: C. T. Bowman, J. Birkeland (eds), Alternative Hydrocarbon Fuels: Combustion and Chemical Kinetics, AIAA, New York (1979).

W. C. Gardiner, University of Texas, USA. For modeling octane ignition it will be important to get a suitable balance between CHa-producing and C~Hsproducing decay steps. Would it be correct to conclude from the insensitivity of flame speed to the rates of the large-molecule and large-radical decay that the ratio of the decay channels can be adjusted to match ignition results without endangering the match to the flame speed? Authors" Reply. YES.