The development of detailed chemical kinetic reaction mechanisms for oxidation of n-octane and iso-octane .... tion mechanisms and the concepts used in their.
Twenty-firstSymposium(International)on Combustion/TheCombustionInstitute, 1986/pp. 783-793
CHEMICAL KINETIC MODELING OF THE OXIDATION OF LARGE ALKANE FUELS: N-OCTANE A N D ISO-OCTANE E. I. AXELSSON1 K. BREZINSKY2 F. L. DRYER2 W.J. PITZ3 C. K. WESTBROOK 3
The development of detailed chemical kinetic reaction mechanisms for oxidation of n-octane and iso-octane is described, with emphasis on the factors which are specific to many large hydrocarbon fuel molecules. Elements which are of particular importance are found to include site-specific abstraction of H atoms, radical isomerization of alkyl radicals by internal H atom abstraction, and rapid/3-scission of the alkyl radicals. These features, combined with distinctions in the types of intermediate olefin species produced, are used to explain the significant differences in the rate of oxidation between n-octane and iso-octane. Experimental results from the turbulent flow reactor and low pressure laminar flames, using both n-octane and iso-octane as fuels, are used to test the reaction mechanisms and indicate those parts of the total mechanisms which are in greatest need of further development and refinement. It is found that the submechanisms for consumption of the C2-C4 olefins need further attention, particularly the identification of the major product species distributions and their temperature dependence for reactions of these olefins and radicals including O and OH.
Introduction Analysis of combustion in laminar flames, shock tubes, flow systems, and more recently in internal combustion engines using detailed kinetic modeling has frequently provided more knowledge about the system than was available from the experimental results alone. However, much of this research has been limited to rather small fuel molecules which are uncharacteristic of those found in conventional liquid hydrocarbon fuels. Reaction mechanisms are most often constructed in a sequential m a n n e r , beginning with the simplest fuels such as hydrogen and methane, then proceeding systematically to C2 and C3 hydrocarbon fuels. This development takes a considerable a m o u n t of time, since each additional step must be tested extensively before moving on to the next fuel. The current state of this evolution is primarily at the C3-C4 level. I n addition to the difficulties in constructing reaction mechanisms for large fuel mole-
1Applied Physics Department, A. B. Volvo, GOteborg, Sweden 2 Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 3Lawrence Livermore National Laboratory, Livermore, California
cules through hierarchical approaches 1, few of the detailed experiments which are needed to validate such models have existed. The need for large molecule reaction mechanisms for analysis of combustion problems is exemplified by a particular topic of current interest, the effect of fuel molecular structure on engine knock characteristics 2. Although recent numerical modeling studies have addressed the knock characteristics of C2-C 4 fuels in internal combustion engines2-5, some kinetic processes such as internal H atom abstraction reactions, which may have important roles in controlling knock and the autoignition of typical fuels, do not occur to any extent with fuels smaller than pentanes. In addition, the intermediate chemical species, including branched olefins, produced during combustion of branched-chain fuel molecules such as iso-octane can be distinctly different from those resulting from combustion of n-alkanes, and this distinction must be considered in order to describe properly such processes as autoignition and engine knock. Recent developments in several areas suggest that extensions of modeling capabilities to considerably larger fuels are appropriate at this time. Successes in applications of numerical modeling to oxidation of n-butane, iso-butane, and n-pentane6'7 have extended current mech-
783
784
REACTION KINETICS
anisms to C5 h y d r o c a r b o n fuels and have addressed the issues o f isomeric differences in fuel structure. Continual growth in available computer size and speed has also been a factor. Most important, recent experimental studies of the oxidation o f both n-octane and iso-octane in a turbulent flow reactor s'9 and in laminar flames l~ have a p p e a r e d which possess the degree of detail necessary for development of kinetic reaction mechanisms. In the present paper, these results are used to investigate the improvements a n d remaining deficiencies of detailed models for n-octane and iso-octane which include 1) existing detailed mechanisms for C1-C4 compounds 2) effects of site-specific H atom abstraction reaction rate constants 3) effects of [~-scission on the specific alkyl radicals f o r m e d 4) internal isomerization of alkyl radicals 5) oxidation o f substituted olefins
Experimental Studies Both experimental studies used for the kinetic model d e v e l o p m e n t have been described in detail previously a n d will be summarized here only briefly. T h e turbulent flow reactor measurements s'9 were carried out at atmospheric pressure u n d e r nearly adiabatic conditions. T r a n s p o r t p e r p e n d i c u l a r to the mean flow direction and diffusive flow along the reactor axis are insignificant relative to convective motion, so numerical modeling can be realistically carried out using plug flow assumptions. T h e e x p e r i m e n t s were p e r f o r m e d with the temperature, equivalence ratio ~b, and flow rate for both n-octane and iso-octane as similar as possible. For both fuels, the initial flow rates were: N2 = 0.66 moles/sec, O2 = 0.012 moles/ sec, fuel = 0.00095 moles/sec, and + = 0.99. T h e initial t e m p e r a t u r e in the n-octane case was 1076 K and in the iso-octane case was 1080 K. The t e m p e r a t u r e a n d concentrations of the stable intermediate and product species were measured as functions of distance from the reactor inlet or, equivalently, the reaction time coordinate. T h e laminar flame experiments l~ were carried out using a porous brass b u r n e r at a pressure of 9.3 kPa. Mixtures contained 74% N2, 24% O2, and 2% octane. Coated thermocouples were used to measure the temperatures, and molecular b e a m mass spectrometry was used to detect various species t h r o u g h o u t the flames. T h e observed spatial profiles o f the
mass numbers detected were very complex and could not be completely deconvoluted into unique profiles for each chemical species. However, there is sufficient detail to provide considerable information on the identity and general ranking of relative concentration levels of the major intermediate hydrocarbon species.
Reaction Mechanism Few detailed reaction mechanisms have been developed for fuels as large as octane. Doolan and Mackie 12 p r e s e n t e d a mechanism for n-octane pyrolysis, including features related to site-specific rates o f H atom abstraction as described below. Coats and Williams la proposed a mechanism for oxidation of n-heptane in shock tubes, but distinctions between different heptyl radicals were not considered. Radical isomerization was not included, and all heptyl radicals were assumed to decompose thermally to produce smaller alkyl radicals and ethylene. Warnatz 14 developed a mechanism for the oxidation of n-alkanes u p to n-octane in laminar flames. Rates o f H atom abstraction reactions were estimated in a m a n n e r similar to that used in the present study, but distinctions between different H atom sites in the fuel, the influence of 13-scission on alkyl radical decompositions, and radical isomerizations were neglected. Instead, all large alkyl radicals were assumed to decompose to p r o d u c e mixtures of p r o p e n e and methyl radicals. While each of these previous studies included a level of detail a p p r o p r i ate for its application, none possesses the ability to predict features o f the above experiments 8-al such as formation of large olefins and variations in overall reaction rate with changes in fuel molecular structure. T h e present reaction mechanisms for oxidation of n-octane and iso-octane are based on previous mechanisms for smaller fuels, particularly n-butane 6 for which a comprehensive model was developed to simulate experimental results from laminar flames, shock tubes, and the turbulent flow reactor. E x p a n d i n g this mechanism to larger fuels required primarily the definition and testing of reactions and rate expressions for the additional chemical species l, while the portions of the mechanisms specific to the C4 and smaller species were retained without change. When combined, the mechanisms for the two octanes included over 70 chemical species and 500 elementary reactions; however, many reactions and some species were significant only for one of the two fuels. As a result, the mechanism for each octane consisted of 6 0 - 6 2 species and
KINETIC MODELING OF ALKANE OXIDATION about 350 reactions. Due to limitations of space, the entire reaction mechanism and literature citations for the rate expressions used cannot be given here and are given in a separate report ~5. However, the important features of the reaction mechanisms and the concepts used in their development will be presented. Schematic representations for the two fuel molecules of interest were used to reduce the types a n d total n u m b e r of H atom abstraction reactions appearing in the model. For n-octane, the structure used is 1 IC
2 C
[
-
2
3
4
4
C
C
C
3
4
4
-
3
2
1
C
C
CI
3
2
I
where the n u m b e r i refers to primary H atoms and the numbers 2, 3, and 4 denote mechanistically distinguishable secondary H atoms. For iso-octane, the molecule can be represented a
a aCa aC C a aCa
d
b C b
-
dCd C c
d Cd d
a
T h e letter 'a' denotes the nine mechanistically equivalent primary H atoms, the letter 'd' indicates another six equivalent primary H atoms, and the letters b and c indicate the secondary and tertiary H atoms. T h e octyl radical produced by the abstraction of one of these H atoms will be referred to by a prefix of the n u m b e r or letter of the corresponding H atom. Thus, 2-C8H17 is the radical formed when one of the H atoms labeled '2' above is removed from n-octane. Each mechanistically distinct alkyl radical decomposes into different groups of products, each having a different impact on the overall chain branching properties of the reaction mechanism. For this reason, the present reaction mechanism keeps separate account of each of these structurally distinct alkyl radicals.
Abstraction reactions Few of the elementary reactions and reaction rates for the high temperature (T>-900 K) oxidation of octane have been studied in detail experimentally. However, several factors have provided guidance in defining reasonable reaction mechanisms. Recent studies 16-18 have shown that the rates of abstraction of H atoms by hydroxyl radicals from primary sites are very similar in a variety of relatively large hydrocar-
785
bon alkane fuel molecules. T h e same is true of secondary and tertiary sites. These H atom abstraction rates d e p e n d very weakly on the size of the alkane fuel molecule. This observation has been generalized in the present modeling study to apply to rates of H atom abstraction by other small radicals such as H, O, CH3, and HO2, since site-specific reaction rates are not available from experimental studies. This approach is similar to that summarized in principle by Warnatz 19, using ideas from previous ' 202V experimental studies ' , Each single primary and secondary H atom of the octane is assumed to have the same rate constant of abstraction as a single primary or -secondary H atom 9in p r o p a n e and n-b n ta n e 6 2' 2 , and the rate constant of abstraction of the tertiary H atom in iso-octane is assumed to be equal to that in iso-butane. These rate constants are then multiplied by the n u m b e r of such H atoms in each fuel molecule to arrive at a total rate constant of abstraction of each type of H atom. The resulting rate expressions are shown in Table I.
Alkyl radical decomposition and isomerization As pointed out by Warnatz 23, at atmospheric pressure and below, and for temperatures above about 1000 K, atkyl radicals with three or more carbon atoms will be consumed primarily by thermal decomposition rather than by reactions with radicals or molecular oxygen. Because the present reaction mechanisms are intended eventually to be used in analysis of higher pressure octane oxidation relevant to automotive engine combustion and engine knock similar to past studies of n-butane oxidation 2, the reactions of the octyl radicals with O2 have been retained, but these steps were u n i m p o r t a n t in the present environments. T h e primary decomposition path for the octyl radicals was assumed to be described bv ~-scission24. Following Dryer and Brezinsky ~, the decomposition of the n-octyl radicals can be assumed to be dominated by 1) 1 - C 8 H 1 7 = 1 - C 6 H 1 3 + C 2 H 4 1013 exp ( - 28800/RT) followed 1 -- C 6 H 1 3 = pC4H9 + C 2 H 4 k = exp ( - 25000/RT) 2) 2 - C8H17 = 1 - C5Hll + C3H6 i013 exp ( - 28300/RT) 1 - C5Hll = C2H4 + nC3H7 k = exp ( - 28400/RT) 3) 3 - C8H17 = IC4Hs + pC4H9 k = exp ( - 29100/RT)
k = 2.5 x by 2.0 x 10 a3 k = 1.6 x 3.2 x 1013 5.0 x 1012
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REACTION KINETICS TABLE I Site-specific reaction rates for abstraction of a single H atom Rates are in units of cm3/mole-sec Reaction type H + primary C-H H + secondary C-H H + tertiary C-H OH OH OH O O O HO2 HO2 H02 CH3 CH3 CH3
+ + + + + + + + + + + +
primary C-H secondary C-H tertiary C-H primary C-H secondary C-H tertiary C-H primary C-H secondary C-H tertiary C-H primary C-H secondary C-H tertiary C-H
4) 4 - CsHI7 = 1C5H10 + nC3H7 k = 3.8 x 1012 exp ( - 29100/RT) 4 - CsHI7 = 1C6H12 + C2H5 k = 1.3 x 1013 exp ( - 31000/RT) For iso-octane, t h e p r i n c i p a l alkyl d e c o m p o sition p a t h s a r e a) a - C 8 H 1 7 = iC4H8 + iC4H9 k = 1.3 x 1013 e 88 ( - 2 9 5 0 0 / R T ) with a lesser c o n t r i b u t i o n from a - CsHI7 = CH3 + aCyH14 k = 1.2 x 1013 exp ( - 32800/RT) d) d - C8H17 = neoC5Ha1 + C3H6 k = 1.3 x 1013 e x p ( - 2 9 5 0 0 / R T ) with a lesser c o n t r i bution from d - C 8 H 1 7 = CH3 a - b C 7 H I 4 k = 1.2 x 1013 exp ( - 32800/RT) b) b - C 8 H I 7 = C H 3 + c C 7 H 1 4 k = 1.0 x 10 x3 exp ( - 26000/RT) c) c - CsHI7 = iC4Hs + tC4H9 k = 5.0 x 1012 exp ( - 29000/RT) Activation e n e r g i e s a r e in cal/mole. Rate e x p r e s sions h a v e b e e n t a k e n p r i m a r i l y f r o m t h e c o m p i lation o f A l l a r a a n d S h a w 25, a l t h o u g h t h e p r o d uct d i s t r i b u t i o n s u s e d h e r e a r e n o t always t h e same as in R e f e r e n c e 25. I n g e n e r a l , we h a v e a s s u m e d t h a t in t h o s e cases w h e r e [3-scission c a n lead to m o r e t h a n o n e set o f p r o d u c t s , t h e o n e in w h i c h t h e l a r g e r f r a g m e n t alkyl radical is p r o d u c e d will b e f a v o r e d . T h u s Allara a n d S h a w cite C H 3 + IC7H14 as i m p o r t a n t p r o d u c t s of d e c o m position o f 3-CSH17, while we h a v e i n s t e a d f a v o r e d t h e p r o d u c t s s h o w n above. A l t e r n a t i v e p a t h s for t h e alkyl r a d i c a l d e c o m p o s i t i o n s h a v e b e e n i n c l u d e d in t h e p r e s e n t studies, b u t t h e i r g e n e r a l l y h i g h e r a c t i v a t i o n e n e r g i e s effectively
Rate expression 9.4 • 10 6 T 2 exp ( - 7700/RT) 4.5 • 10 6 T 2 exp ( - 5000/RT) 1.3 x 1013 exp ( - 7300/RT) T 1~ exp ( - 1810/RT) 1.4 • 109 6.5 x l0 s T 1"25 exp ( - 700/RT) 2.0 • 1012 exp ( - 443/RT) 1.7 • 1013 exp - 7850/RT) 1.4 • 1013 exp - 5200/RT) 1.0 • 1013 exp - 3280/RT) 1.9 • 1012 exp - 19400/RT) 1.7 • 1012 exp - 17000/RT) 3.0 • 1012 exp - 14400/RT) 1.3 • 1012 exp - ll600/RT) 1.2 • 1012 exp - 9500/RT) 2.0 • 1012 exp - 7900/RT)
m i n i m i z e t h e i r i m p o r t a n c e relative to t h o s e s h o w n h e r e . S o m e o f t h e s e steps p r o d u c e a n olefin a n d H a t o m , while o t h e r s b r e a k C-C b o n d s at locations w h i c h are e n e r g e t i c a l l y less f a v o r a b l e t h a n t h o s e above. The motivation for retaining the distinctions b e t w e e n m e c h a n i s t i c a l l y distinct octyl radicals c a n be s e e n f r o m t h e a b o v e d e c o m p o s i t i o n p a t t e r n s . F o r e x a m p l e , t h e 3-C8H17 r a d i c a l p r o d u c e s pC4H9 radicals, w h i c h t h e n d e c o m pose f u r t h e r 6 pC4H9 = C2H4 + C2H5 C2H5 = C2H4 + H
T h i s s e q u e n c e p r o v i d e s overall c h a i n b r a n c h ing, since H a t o m s t h e n r e a c t H + 02 = O + OH a n d a c c e l e r a t e t h e o x i d a t i o n process. I n contrast, a n o t h e r s e c o n d a r y octyl radical, t h e 2-CsHI7 r a d i c a l p r o d u c e s only relatively stable olefins a n d nC3Hv, g i v i n g nC3H7 = C 2 H 4 + CH3 a n d effective c h a i n t e r m i n a t i o n 13 as a r e s u l t o f m e t h y l r a d i c a l r e c o m b i n a t i o n . I n t h e case o f iso-octane, o n l y c-CsH17 leads to t h e p r o d u c t i o n o f H a t o m s a n d c h a i n m u l t i p l i c a t i o n , while all 17 o t h e r octyl r a d i c a l s lead to m e t h y l radicals a n d olefins. F o r alkyl r a d i c a l s with six o r m o r e C a t o m s , internal H atom abstraction becomes important as a c o m p e t i t i o n w i t h t h e r m a l d e c o m p o s i t i o n .
KINETIC MODELING OF ALKANE OXIDATION Based on arguments presented by Benson 26, these reaction steps have been included in the following manner. First, formation of sixm e m b e r e d ring structures are assumed to be strain-free, therefore having no additional contribution to the activation energy barrier; fiveand seven-membered rings will have approximately 7 kcal of strain energy which must be a d d e d to the value of the activation energy for a strain-free system. Internal abstraction of H atoms from tertiary sites will have intrinsic strain-free activation energies of 9.1 kcal/mole, with secondary H atoms having an additional 2 kcal/mole because they are m o r e tightly bound and primary H atoms an additional 3 kcal/mole above the 11 kcal/mole for the secondary site. T h e A-factors are all assumed to be 1011 sec -1 p e r H atom 26. T h e r e f o r e , using the diagrams and definitions indicated above and incorporating into the A-factors the different degeneracies involved, rates of unimolecular isomerization via internal H atom abstraction involving six-membered rings are, for n-octane, 1-C8H17 "--'4-C8H17 k = 2 ( - 11100/RT) 4-C8H17---~1-C8H17 k = 3 ( - 14100/RT) 2-C8H17--~3-C8H17 k = 2 ( - 11100/RT) 3-CaH17---~2-C8HIv k = 2 ( - 11100/RT)
x 1011 exp x 1011 exp x 1011 exp x 1011 exp
and for iso-octane, a-CsHl7 ---*d-CsHI7 k = 6 x 101l exp ( - 14100/RT) d-CsH17 ---->a-CsH17 k = 9 x 101l exp ( - 14100/RT) T h e corresponding reactions involving fiveand seven-membered rings are 1-C8H17--->4-C8Hlv k = 2 ( - 18100/RT) 4-C8H17---)1-C8H17 k = 3 ( - 21100/RT) 1-C8H17--9"3-C8H17 k = 2 ( - 18100/RT) 3-CsHI7--*l-CsH17 k = 3 ( - 21100/RT) 2-C8H17---~4-C8H17 k = 2 ( - 18100/RT) 4-C8H17---~2-C8H17 k = 2 ( - 18100/RT) a-CsHI7--'~c-CsH17 k = 1 ( - 16100/RT) c-CsH17---~a-CsH17 k = 9 ( - 21100/RT)
x 1011 exp
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T h e secondary iso-octyl radical b-Call 17 is effectively isolated and, because o f the large strain energies required, does not participate in internal H atom abstraction reactions. The tertiary iso-octyl radical is accessible only through a transition state consisting of a five-membered ring. This is particularly important because, as noted above, the tertiary radical is the only one of the eighteen possible octyl radicals which decomposes thermally to yield H atoms and chain branching.
Reactions of large olefins Experimental observations in both the turbulent flow reactor and laminar flames indicate only minor production of C5--C7 olefins, but the reaction mechanism requires a realistic description of the elementary reactions which consume these species. Because they are formed primarily by 13-scission of larger radical species, these are mainly 1-01efins, with the double bond between the first and second C atoms. T h e r e f o r e it is assumed that H atom abstraction reactions will p r e d o m i n a t e at the end of the olefin which is farthest removed from the location of the double bond, while addition of H and O will be dominant at the location o f the double bond, followed by rupture of a C-C bond and production of smaller oxygenated species such as formyl radicals, formaldehyde and acetaldehyde. Computed results show virtually no sensitivity to the details of the reaction paths and rates consuming these large olefin species, but the present model treatment of their reactions is quite uncertain.
Termination reactions Finally, termination reactions were found to be of particular importance in explaining the experimental results. These consist of reactions between radicals, particularly H atoms, and stable hydrocarbon species, primarily olefins, such as
x l0 ll exp x 1011 exp • 1011 exp x 1011 exp x 1011 exp x 10 II exp x 1011 exp
H + iC4H8 = iC4H9 H + C3H6 = nC3H7
which are important because the adduct subsequently decomposes via a different path, producing methyl or o t h e r radicals which are much less reactive than the H atoms. In these two examples, the iC4H9 decomposes to CH3 t- C3Ho while the nC~H7 produces CH3 + C2H4. F o r b o t h of these addition reactions, alternative products H + iC4H8 = tC4H9 H + C3H6 = iC3H7
788
REACTION KINETICS
exist, but in both cases the adduct falls apart into the original reactants, resulting in no net change in the chain properties of the reaction mechanism. Recombination reactions of two radical species to produce stable molecules, such as H + C4H7 = 1C4H8 CH3 + C3H5 = iC4H8
were also found to be important in restricting the growth of the radical pool in these computations. Rate expressions for each type of reaction were either taken directly from the literature or estimated by analogy with similar reactions for which rate data were available.
Comparisons with Experimental Results
Computed results are compared with experimental observations of some selected species
for n-octane oxidation in the turbulent flow reactor in Fig. 1 and for iso-octane oxidation in Fig. 2. All of the qualitative features of the experiments are correctly reproduced by the model. Two such features are most important. First, fuel consumption is complete quite rapidly for both fuels; the fuel concentrations in Figs. 1 and 2 have disappeared by about 75 msec residence time, with the computed results agreeing well with the observations. Second, consumption of the intermediate hydrocarbon species, followed by oxidation of CO to COz and the majority of the heat release and temperature increase, is essentially complete within the flow reactor observation window in the case of n-octane but not for iso-octane oxidation. This i m p o r t a n t distinction between the two octanes is also well represented by the modeling results. For both fuels, the relative concentrations of the various intermediate species are correctly lO
,.,. ,."'!."".84
i, >(
•
o [--"/7
"~'--I-I
"2..,
[
g
0
lO
I
]
I
C3H6
",C6H12 " ~
0~ 0
'
~
"
C3H6
50
~
-
100
/ ~
150
Time (msec)
FI6. 1. Concentrations of fuel and major intermediate species during turbulent flow reactor oxidation of n-octane. Curves indicate computed results using the detailed reaction mechanism, symbols represent experimental results of Dryer and Brezinsky [8]. Triangles and dotted lines refer to C2H4 and IC6HI2, crosses and solid curves refer to CO and IC4Hs, and circles and dot-dash curves refer to nCsHLsand Call6. Values for n-C8HI8 and IC6H12have been multiplied by a factor of 10 and C2H4 by a factor of 2.
ol o
c2~
1
I
50
1O0
150
Time, ms
FIG. 2. Concentrations of fuel and major intermediate species during turbulent flow reactor oxidation of iso-octane. Curves indicate computed results using the detailed reaction mechanism, symbols represent experimental results of Dryer and Brezinsky [8]. Triangles and dotted lines refer to CO and CH4, crosses and solid curves refer to iC4Hs and C2H4, and circles and dot-dash curves refer to iC8HL8and C3H6. Values for iso-CsHl8 have been multiplied by a factor of 10.
KINETIC MODELING OF ALKANE OXIDATION r e p r o d u c e d by the reaction mechanism, as well as the o r d e r i n g in time of their peak values. For n-octane, the major intermediate is ethylene, followed by propene. O f the larger olefins, lC6H12 is nearly equal to ~C5H10 (not shown) at all times, with both p r o d u c e d from [3-scission of 4-CsHa7 radicals. Very small levels of C7 olefins are predicted, consistent with observations. T h e peak concentrations o f the C5 and C6 olefins occur very early, within the mixing duct of the flow reactor, followed in o r d e r by the C4, C~ and C2 olefins, all in a g r e e m e n t with observations. All of the c o m p u t e d olefin concentrations are within 50% of the experimental values, although the calculations indicate a more rapid conversion of C2-C4 olefins to CO than measured experimentally. Similar conclusions may be drawn from the results for iso-octane oxidation (Fig. 2). The fuel consumption is correcly predicted, and the production of the major intermediate iC4H8 is shown. T h e model results show that the significantly slower rate of oxidation of iso-octane is related to the large amounts of isobutene produced, in a g r e e m e n t with experimental observations [9], which showed that addition of isobutene delays the oxidation of n-octane in the flow reactor. T h e model results indicate that isobutene acts in two i m p o r t a n t ways, both of which contribute to r e d u c e d radical levels. As pointed out by Brezinsky and Dryer 9, H atom abstraction from isobutene produces methyl-allyl radicals which decompose to produce methyl radicals and allene, resulting in chain termination due to methyl radical recombination and a r e d u c e d overall rate of oxidation. However, a second essential sequence of reactions is the addition of H atoms to isobutene to produce isobutyl radicals which then decompose to p r o d u c e methyl radicals and propene iC4H8 + H--+iC4Hg-+C3H6 + CH3 which also provides chain termination. Consistent with this interpretation, the model calculations show that the levels o f H, O, and OH radical concentrations are higher in the noctane models by factors of 5-10 than in the iso-octane modeling results. T h e weakest portions of the reaction mechanisms for both n-octane and iso-octane a p p e a r to be the submechanisms dealing with consumption of the smaller intermediate olefin and other unsaturated hydrocarbon species. For example, product species distributions for olefin reactions with radical species, particularly O H and O, are not firmly established at combustion temperatures 6'19'22, even for ethy-
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lene and propene. O t h e r species such as C3H4 and C4H 6 are present in significant amounts, and products of their reactions with radical species are very poorly understood. Finally, relatively large concentrations of long lived radical species such as C3H5 and C4H7 a r e predicted by the model, and the reactions of these species, particularly the product species distributions, are also poorly understood. Identification of these p r o d u c t species distributions are particularly important, since different products have markedly different influences on the chain reaction properties of the reaction mechanism, as already noted. T h e kinetic model was also applied to examine the two laminar fiat flame experiments r e p o r t e d by Axelsson and Rosengren 1~ In these burner-stabilized flames, the experimentally measured t e m p e r a t u r e profiles were used directly by the model, so the energy equation was not included in the calculations. For both the n-octane and iso-octane, the observed quantities were the spatial variations in the mass spectra. As is well known, most of the large hydrocarbon species in these flames undergo significant degrees of decomposition as a result of the electron impact process in the mass spectrometer system, with a spectrum that d e p e n d s on the electron energy. These spectra overlap a great deal for the species studied in these flames. Although some care was taken to study both flames and a n u m b e r of the pure species, including the octanes and 1C6H12, at a n u m b e r of different ionizing energies, it was not possible to d e t e r m i n e accurate absolute concentration levels of most species due to this extensive overlapping of the spectra. However, some deconvolution of the spectra, combined with the spatial variation in the parent mass n u m b e r measurements, was possible, enabling us to identify which intermediates were present in significant amounts and their approximate spatial variations t h r o u g h each flame. These results are indicated for some of the species in the n-octane flame as the symbols in Fig. 3. Fuel consumption between 0 and 0.2 cm is accompanied by production o f intermediates, primarily olefins, as also observed in the flow reactor results. Ethylene a n d p r o p e n e are produced directly from the octyl radical decomposition and from consumption of the larger olefins as well. As a result, there is a spatial ordering of the olefin curves, with peaks for the smaller olefins occurring later in the flame. Peaks for ~C6H12 and iCsHm (not shown) occur at a position of 0.1 cm. T h e computed species profiles for this flame are shown as the curves in Fig. 3. T h e absolute concentrations indicated in Fig. 3 are those
REACTION KINETICS
790 400
insensitive to variations in rates of reactions involving the large hydrocarbons, consistent with observations of Warnatz in propane and n-butane flames 23, so it is primarily the spatial variations in intermediate olefin species levels which depend on the details of the octyl radical decomposition and isomerization paths.
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Conclusions
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FIG. 3. Concentrations of fuel and major intermediate species in laminar flame oxidation of n-octane. Curves represent computed results using the detailed reaction mechanism, symbols indicate experimental results of Axelsson and Rosengren [11], with crosses indicating nCsH18 and C3H6, circles show C2H2, and triangles show 1C4H8. Experimental data are scaled to match the calculated peak values as explained in the text. from the model calculations; the experimental data points for nCiH18, 1C4H8, C3H6, and C2H2 have been scaled so that the peak values match the computed peaks, so only the shapes of the experimental and computed results and the spatial location of each peak can be compared. Agreement between computed and measured results for this limited set of data is quite acceptable. T h e analogous results for the isooctane flame (not shown) are very similar, except that iC4H8 rather than C2H4 is the dominant intermediate olefin. The model results for both flames show the same general kinetic features as those for the flow reactor simulations. Abstraction of H atoms from the octane is followed by rapid thermal decomposition of the octyl radicals, producing a variety of olefin species including significant amounts of C4-C 6 olefins. Internal H atom abstraction is important, establishing equilibria between those octyl radicals which are related through six- and five-membered ring structures. The flame models themselves are very
The present kinetic model generally predicts the rate of octane fuel disappearance and the levels of the larger intermediate species in both the turbulent flow reactor and in low pressure laminar flames. Site-specific H atom abstraction reactions, internal H atom abstraction and thermal decomposition of the octyl radicals all were found to be important in the oxidation behavior of these large alkane fuels, and the estimation techniques described here provided realistic rate expressions for these processes. Improvements in the agreement between computed and experimental species concentrations could be obtained by systematic variation in the most important reaction rates. However, a major goal of the current work has been to evaluate the predictive abilities of a reaction mechanism constructed primarily by estimation techniques available at the present time. The methods discussed here were illustrated for the cases of n-octane and iso-octane but should be equally appropriate for any other alkane fuel molecules. The modeling results indicate that the area in which the current octane oxidation mechanisms are in greatest need of improvement and refinement is their treatment of the C2-C 4 olefins and other unsaturated hydrocarbon species.
Acknowledgments The authors are grateful for the contributions of L.-G. Rosengren and AB Volvo/The Swedish Technical Board of Development for their financial support of part of this work. Portions of this work were carried out at Princeton University under support from a general grant from the Mobil Research and Development Corporation. Part of this work was carried out under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract No. W-7405-ENG-48.
REFERENCES 1. WESTBROOK,C.K., AND DRYEr, F.L., Eighteenth Symposium (International) on Combustion, p. 749, The Combustion Institute, Pittsburgh, 1981.
KINETIC MODELING OF ALKANE OXIDATION 2. CERNANSKY, N.P., GREEN, R.M., PITZ, W.J., AND WESTBROOK, C.K., Combust. Sci. Technol., in press (1986). 3. SMITH,J.R., GREEN, R.M., WESTBROOK, C.K., AND PITZ, W.J., Twentieth Symposium (International) on Combustion, p. 91, T h e Combustion Institute, Pittsburgh, 1985. 4. PITZ, w.J,, AND WESTBROOK, C.K., Combust. Flame 63, 113 (1986). 5. LEPPARD, W.R., Combust. Sci. Technol. 43, 1 (1985). 6. PITZ, W.J., WESTBROOK, C.K., PROSCIA, W.M., AND DRYER, F.L., Twentieth Symposium (International) on Combustion, p. 831, T h e Combustion Institute, Pittsburgh, 1985. 7. WESTBROOK, C.K., AND PITZ, W.J., Shock Waves and Shock Tubes. D. Bershader and R. Hanson, ed., p. 287, Stanford University Press, 1986. 8. DRYER, F.L., AND BREZINSKY, K., Combust. Sci. Technol. 45, 199 (1985). 9. BREZINSKY, K., AND DRYER, F.L., Combust. Sci. Technol. 45, 225 (1985). 10. AXELSSON, E., AND ROSENGREN, L.-G., Combust. Flame 62, 91 (1985). 11. AXELSSON, E., AND ROSENGREN, L.-G., Combust. Flame, in press (1986). 12. DOOLAN, K.R., AND MACKIE, J.C., Combust. Flame 50, 29 (1983). 13. COATS, C.M., AND WILLIAMS, A., Seventeenth Symposium (International) on Combustion, p. 611, The Combustion Institute, Pittsburgh, 1979. 14. WARNATZ, J., Twentieth Symposium (International) on Combustion, p. 845, T h e Combustion Institute, Pittsburgh, 1985. 15. AXELSSON, E., BREZINSKY, K., DRYER, F.L., PITZ,
16. 17. 18.
19.
20.
21. 22. 23. 24.
25. 26.
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WJ., AND WESTBROOK, C.K., "A Detailed Chemical Kinetic Reaction Mechanism for Oxidation of N-Octane and Iso-Octane", Lawrence Livermore National Laboratory report UCRL-94449 (1986). Presented at the Joint Canadian and Western States Sections Meeting of The Combustion Institute, Banff, Alberta, April 1986. GREINER, N.R., J. Chem. Phys. 53, 1070 (1970). ATKINSON, R., submitted to Int. J. Chem. Kinet., 1986. TULLY, F.P., DROEGE, A.T., KOSZYKOWSKI, M.L., ANn MELIUS, C.F.,J. Phys. Chem., 90, 691 (1986). Droege, A.T., and Tully, F.P.,J. Phys. Chem., 90, 1949 (1986). Tully, F.P., Goldsmith, J.E.M., and Droege, A.T., submitted to J. Phys. Chem., 1986. WARNATZ, J., "Rate Coefficients in the C/H/O System", in Combustion Chemistry, W.C. Gardiner, Jr., ed., Springer-Verlag, New York, 1984. BALDWIN, R.R., BENNETT, J.P., AND WALKER, R.W., Sixteenth Symposium (International) on Combustion, p. 1041, T h e Combustion Institute, Pittsburgh, 1977. HERRON,J.T., AND HUIE, R.E.,J. Phys. Chem. 73, 3327 (1969). WESTBROOK, C.K., AND PITZ, W.J., Comb. Sci. Technol. 37, 117 (1984). WARNATZ,J., Comb. Sci. Tech. 34, 177 (1983). DRYER, F.L., AND GLASSMAN, I., in Alternative Hydrocarbon Fuels, Combustion and Kinetics, C.T. Bowman and J. Birkeland, eds., AIAA, New York, 1979. ALLARA,D.L., AND SHAW, R., J. Phys. Chem. Ref. Data 9, 523 (1980). BENSON, S.W., Thermochemical Kinetics, pp. 16469, J o h n Wiley and Sons, New York, 1968.
COMMENTS
M. Frenklach, Pennsylvania State University, U.S.A. As to the statement that there is no computational limitation for modeling of oxidation of aromatics, our experience ~ shows that the situation for unsaturated and aromatic fuels is significantly different from that for paraffins." While the kinetics of the latter at combustion conditions is dominated by primarly irreversible reactions, the dynamics of the former is controlled by reversible, almost equilibrated, reactions and, hence, the accuracy of thermochemical data becomes crucial. Unfortunately the present state of knowledge of these data presents a barrier to predictive modeling of unsaturated and aromatics systems.
REFERENCE 1. FRENKLACH, M., CLARY, D.W., GARDINER, W.C., AND STrIN, S.E.: this symposium
Author's Reply. We want to distinguish purely computational difficulties from those which are thermochemical or kinetic. The present paper demonstrates that large reaction networks, including at least eight (8) carbon atoms, are not difficult to solve on present-day computers with current numerical techniques. Therefore, systems such as those for benzene, toluene and other n-alkyl benzenes as well as other simple aromatic species should also be computation-
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ally tractable. We agree that the difficulties of modeling aromatic fuel combustion are thermochemical and kinetic. The heats of formation, specific heats, and equilibrium constants of many important species are poorly known, and the major kinetic steps, including ring breaking paths, are also poorly established for aromatic fuels. These are areas where progress is essential for detailed modeling of aromatic fuel oxidation to proceed, but our point was that the mere size o f the required reaction mechanism is not a deterrent to detailed modeling.
j. Keck, Massachusetts Institute of Technology, USA. What are the specific reactions responsible for the formation of the C-O bond in your model? Are your results sensitive to the rates of these reactions?
Author's Reply. For all mixtures, C2H3 + 02 CH20 + HCO is a very important path for producing C - O bonds. Others of importance are: C2H4 + OH --* CH20 + CH~ C2H4 + O--~ HCO + CH.s and reactions of acetylene with O and OH. Note that, even with the large fuel molecules, effectively all C - O bonds are produced by reactions of C2 (and to a lesser extent, C3) species. This supports the overall view of large hydrocarbon oxidation as consisting of fuel pyrolysis to much smaller hydrocarbons prior to their direct oxidation. Computed sensitivities to reactions forming C - O bonds is moderate, but always less than sensitivity to reactions such as H + 02 ~ O + OH, CO + OH + COs + H, and the other reactions familiar from H2-O2-CO oxidation.
alkenes liberated from alkane combustion. Our results show that, at a temperature of 315 K a total of 28% of n-pentane is converted to pentenes (25% pent-2-ene and 3% pent-l-ene), while the values at 380 K are 27% total, with 24% of pent-2-ene and 3% of pent-l-ene. ~'2 This percentage conversion is substantial, although it is already much lower than for alkanes of carbon number 2 - 4 (where it is 70% and higher1'3). For decane, the total conversion to alkenes is only 8%, distributed among the various isomers, at 503K, with somewhat higher results at higher temperatures. 3 Work on 2,2,4 trimethylpentane carried out elsewhere has yielded 7% conjugate alkenes at 608K. 4 This suggests that the percentage conversion to oct-l-ene from n-octane should not be very large, particularly since the proportion of octenes other than oct-l-ene should be signifcam. I understand, however, that there may be a very important effect due to the increase in temperature, so that the results in the temperature range above 1000 K may be quite different from those at lower temperatures.
REFERENCE 1. CULLIS C.F., and HmSCHt.ER M.M.: Proc. Roy. Soc. Lond. A 364, 75 (1978). 2. CULLIS C.F., ANn HmSCHLER M.M.: Proc. Roy. Soc. Lond. A 364, 309 (1978). 3. CCLHS C.F., HmSCHLER M.M., and ROGERSR.L.: Proc. Roy. Soc. Lond. A 382, 429 (1982). 4. BARNA~D J.A., and HARWOOD B.A.: Combust. Flame 21, 55 (1973).
Author's Reply. The steps to which you refer are, indeed, included in the reaction mechanism; and, if they were important, would provide an accelerating influence on the overall rate of reaction. However, the alkyl radical produced by H + olefin addition will generally decay by [3-scission. For alkyl radicals with four (4) or more C atoms, alkyl decomposition nearly always proceeds by breaking a C - C bond, so generation of H atom via the path you suggest is usually negligibly slow relative to alternative decomposition reactions.
Author's Reply. We are aware of a great deal of research carried out on alkane oxidation and pyrolysis at temperatures below about 700 K, including some of the above citations. As pointed out very explicitly in the present paper, our current kinetic model and its results apply only to temperatures above about 900 K. The central kinetic fact at these more elevated temperatures is that [3-scission will result in the breaking of C - C bonds and very low conjugate alkene product concentrations. At temperatures below the "ceiling temperature" (i.e. below about 650-700 K), different kinetic mechanisms will be dominant. In particular, at these lower temperatures, [~-scission will be nearly impossible due to the relatively high activation energies for the process, so the bias against the production of conjugate alkenes no longer applies. Our current work is directed towards extending the kinetic mechanisms to these lower temperatures so that we can examine the types of experimental data which Dr. Hirschler cites.
M.M. Hirschler, BF Goodrich U.S.A. We have, at the City University (London), measured the amount of
G. Smith, SRI International U.S.A. In terms of radical reactions with your numerous amounts of
A. M. Dean, Exxon Research & Engr., USA. You included H + olefins ~ adduct ~ CH3 + olefin as an implicit "termination" step by converting H to CH3. Does this imply the reverse reaction (CH~ + olefin --~ olefin' + H) is also included? Does this play any role?
KINETIC MODELING OF ALKANE OXIDATION 1-olefins, we have observed very rapid abstraction by OH of the weakly bound alylic hydrogens in a series of butenes. At temperatures above 1000K, OH addition to the double bond should no longer be important, but abstraction of the numerous secondary allkyl hydrogens should also occur. You might wish to consider these points in any future refinements of your model.
Author's Reply. The type of mechanistic information you have obtained is precisely what our modeling efforts require for significant improvements. In particular, the site-specific nature o f your results and the temperature variation in the product distributions will be especially useful.
R. W. Walker, Hull University, England. At the lower temperatures of your study, formation of HO2 radicals through alkyl + 02 must be important. How important then is the HOz chemistry of reactions such as HO2 + RH ~ H202 + R and \ / \ / HO2 +/C = C\ ---,/Ck-o- . C \ + O H For the non-selective OH radical at about 1000 K, is it not possible that abstraction from the allylic position in alkenes is insignificant because of the likely unfavorable A-factor due to electron delocalization in the transition state? OH + CH3CH2CH~CH = CHz --~ CH3CHCH2CH = CH2 + H20 CH3CH2CHCH = CH2 + HzO
(a) (b)
If true, then ka/kb may be much greater than unity.
Author's Reply. As you point out, at the lower temperatures of our study, reactions involving HO2 are very important. Abstraction of H atoms by HO~ is quite fast and provides a significant amount of chain branching when the H202 decomposes. Under knock-
793
ing conditions (low temperature range, elevated pressure), this path is the dominant chain branching path. The transfer of O atoms from HO~ to the fuel molecule which you suggest will clearly be important at lower temperatures, but at our conditions (T ~> 900 K), this does not contribute significantly. We had not distinguished the H atom abstraction from the allylic position in the present work, and as stated in the manuscript, computed sensitivity to olefin reactions was small. However, we will introduce this type of site-specific analysis for the olefin reactions in our future model development.
R. ZeUner, Universitat Gottingen, West Germany. Initial fragmentation pattern of hydrocarbons show up most sensitively in ignition delay studies. Indeed, recent shock tube results obtained in our laboratory (K.J. Niemitz and R. Zellner, to be published) for the ignition of stoichiometric i/n-octiane-O2/Ar mixtures between 1200-1550 K show that the i-octane mixture has an ignition delay time larger by approximately a factor of two (2) than the corresponding n-octane mixture, with the difference slightly increasing with decreasing temperature. Have you tested your model for ignition behavior? Author's Reply. We have predicted ignition delay times for n-octane, i-octane, and n-heptane mixtures in oxygen + argon for densities and concentrations similar to those studied by Burcat, et al) We found that n-heptane and n-octane ignite considerably more rapidly than i-octane and slightly more rapidly than n-butane and n-pentane. However, due to lack of experimental data on the octanes in the literature published previously, we have not been able to compare our predictions with actual data. Your results will provide us with a valuable source of information for improving our mechanism.
REFERENCE 1. Burcat, A., Scheller, K., and Lifshitz, A.: Cornbust. Flame I6, 29 (1971)
