63_westbrookdryer_chemical kinetic modeling of hydrocarbon combustion

Proy. Energy Combust. Sci. 1984, Vol. 10, pp. 1-57. 0360-1285/8450.00+ "50 Printed in Great Britain. Pergamon Press Ltd.

CHEMICAL KINETIC MODELING OF HYDROCARBON COMBUSTION

CHARLES K. WESTBROOK* and FREDERICK L. DRYER t *Lawrence Livermore National Laboratory, University of California, Livermore, California 94550, U.S.A.

tDepartment of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, U.S.A.

Abstract--Chemical kinetic modeling of high temperature hydrocarbon oxidation in combustion is reviewed. First, reaction mechanisms for specific fuels are discussed, with emphasis on the hierarchical structure of reaction mechanisms for complex fuels. The concept of a comprehensive mechanism is developed, requiring model validation by comparison with data from a wide range of experimental regimes. Fuels of increasing complexity from hydrogen to n-butane are described in detail, and further extensions of the general approach to other fuels are discussed.

Kinetic modification to fuel oxidation kinetics is considered, including both inhibition and promotion of combustion. Simplified kinetic models are then described by comparing their features with those of detailed kinetic models. Finally, application of kinetic models to study real combustion systems are presented, beginning with purely kinetic-thermodynamic applications, in which transport effects such as diffusion of heat and mass can be neglected, such as shock tubes, detonations, plug flow reactors, and stirred reactors. Laminar flames and the coupling between diffusive transport and chemical kinetics are then described, together with applications of laminar flame models to practlcal combustion problems.

1. INTRODUCTION

In recent years, chemical kinetic modeling has become an important tool in the analysis of combustion systems. Availability of large amounts of elementary kinetic data, improved techniques for estimating specific reaction rates, development of efficient "stiff equation" solution techniques, and continual growth in the size, speed, and availability of large computers have contributed to the increasing application of detailed chemical kinetic modeling. For at least twenty years this approach has been employed in the simu- lation of controlled laboratory experiments. More recently, kinetics models have become useful in the analysis of practical energy conversion systems such as internal combustion engines. The influences of kinetic factors on other combustion fields such as the assessment of safety factors involved with large scale storage, transportation and use of liquid and gaseous fuels are only beginning to receive attention. Other important kinetic problems including particularly the oxidation of practical fuels in turbulent flows also need a great deal of examination.

Although many fuel types are encountered in combustion environments, hydrocarbons comprise the vast majority. In this review we will devote most of our attention to the combustion of hydrocarbon fuels, but it should be pointed out that the same types of analyses can be applied to other fuels such as ammonia, hydrazine, carbon disulfide, and many others based on N-H, C-S, N-C-H, or other com- binations rather than C-H systems. We will only briefly discuss the kinetics of the formation of chemical pollutants, a subject which has been treated in detail elsewhere.i -3 Detailed reviews of hydrocarbon oxidation have appeared quite recently, 4-7 emphasizing those processes which are dominant at temperatures below about 700 K. Here we will deal primarily with

JP~CS IO:I-A

higher temperature conditions encountered in flames and explosions (T >/1000 K). High temperature combustion studies are complicated by the fact that typical time scales are very short, often of the order of micro- seconds. As a result, spatial scales are also very small, making experimental studies very difficult. On the other hand, high temperature reaction mechanisms can be conceptually simpler than those for combustion below 700 K.

We will first discuss in detail the kinetic mechanisms which are used to describe the combustion of hydrocarbon fuels. Applications of these kinetic models to the analysis of selected types of problems will then be examined.

2. PROBLEM FORMULAT ION

The general mathematical formulation of the problem of chemically reactive flow systems s- l l consists of equations for conservation of mass, momentum, energy, and concentration of each chemical species, together with equation of state and other thermodynamic relationships. Chemical kinetics provides the coupling among the various chemical species concentrations, and with the energy equation through the heat of reaction. In many combustion problems the kinetics terms determine the characteristic space and time scales over which the equations must be solved.

When spatial transport effects can be neglected, the conservation equations become a coupled set of ordinary differential equations (ODE's) for the species concentrations and the energy (or temperature) with time as the independent variable. If transport terms must be considered, then the equations are coupled partial differential equations involving derivatives with respect to both time and space. Examples of both types of systems will be presented in the second half of this paper.

2 C.K. WESTBROOK and F. L. DRYER

The computational requirements for solving these differential equations depend very strongly on the details of the reaction mechanism. For problems without transport, one differential equation must be solved for each of N chemical species, together with the energy (or temperature) equation, producing (N + 1) equations. Both the computer storage requirements and the CPU time needed increase roughly as (N+I ) z. When transport effects are included, the same (N+ 1) equations must then be solved for each spatial zone, in addition to equations for conservation of mass and each component of momentum. For many typical applications, 30-40 spatial zones are needed in each dimension, so that two-dimensional problems might contain 1000 zones, with 30,000 zones in three dimensions. Current reaction mechanisms for oxidation of methane or methanol, to be discussed later, contain 25-30 chemical species, so the use of these fuels could require the solution of approximately 30, 1000, 35,000, and 1,000,000 coupled differential equations for zero-dimensional (i.e. no transport), one-dimensional, two-dimensional, and three-dimensional models, respectively. Furthermore, these equations must be solved at each time step in the numerical solution of the combustion problem.

The kinetics equations themselves form a set of coupled rate equations describing the reactions between chemical species. Each equation has its own characteristic time scale. The well known "stiffness" problem 12'~3 results when widely disparate time scales occur within a single problem. During the early development of solution methods for kinetics equations, these stiffness difficulties caused severe problems, but there are now many convenient techniques available ~4 for solving such equations. General computer software packages ~5'16 implementing these methods are in common use.

2.1. Reaction Rates

For modeling chemical kinetics, it is necessary to adopt a uniform way of expressing the variation of reaction rates with temperature. Conventionally these are expressed in modified Arrhenius form

k = AT"exp( -E~/RT) (eq. 1)

where the rate k depends on the temperature T and an activation energy E,, with a pre-exponential collision frequency factor A. In many cases all of the temperature dependence can adequately be incorporated into the single exponential term (i.e. with n = 0), since most binary elementary reactions exhibit classical Arrhenius behavior over modest ranges of temperature. However, over temperature ranges encountered in combustion, significant non-Arrhenius behavior can be exhibited, 17 and additional variation of the rate coefficient with temperature must be included. Most often this additional variation is taken into account by finding an appropriate value of n such that the resulting expression accurately fits the available experimental data. It is also possible but less common

to express the reaction rate in terms of other functions or in tabular form. Few reactions have received enough experimental attention to determine completely their behavior for the temperature range of concern here (1000K ~< T ~< 2500K).

The use of transition-state theory ls'~9 and other theoretical methods can provide valuable estimates of elementary reaction rates, 2-22 and modeling studies can also provide rate estimates, ~4 particularly for reactions which are very difficult to observe directly.

A number of important compilations and discus- sions of elementary rate data for reactions involved in hydrocarbon oxidation have appeared, 23 35 consisting of critical evaluations of experimental, theoretical, and modeling values for specific reaction rates. In the next section of this paper we will discuss many of these elementary reactions. An extensive list of these reactions has been collected into Appendix I, together with rate expressions and references indicating the source of the rate expression. These are not intended to be definitive evaluations of these rates but rather representative values which might serve as estimates with which to begin assembling a reaction mechanism. The critical evaluations cited above contain extensive references for the reactions being surveyed. However, reaction rate evaluation is a difficult and time-consuming process 36 which has not been carried out for many of the reactions which are important in hydrocarbon and other combustion reaction mechanisms.

Direct experimental evaluations of reaction rates are the fundamental sources for the specific coefficients for use in eq. (1). Realistic kinetic models must adhere strictly to those rate expressions which have been measured experimentally, within their stated uncertainty limits. Occasionally, computed model results will be unable to reproduce observed data unless one or more rate expressions are assigned values which disagree dramatically with known experimental values. Invariably this indicates that the assumed reaction mechanism is incomplete or that other parts of the mechanism or physical model are incorrect.

An illustration of this point is given in Fig. 1, using experimental data for CO oxidation in a turbulent flow reactor. 37 Measured values for temperature and concentrations of CO and CO2, indicated by the open circles, are plotted as functions of axial position from the inlet section of the reactor. An initial mechanism was postulated, 38 including reactions involving CO, CO2, O, OH, H, H2, and H20. If all of the reactions are assigned rates consistent with experimentally determined values, the best possible agreement between computed and measured results is shown by the upper set of curves. In order to force the model to agree with the observations, the rate of the key reaction

CO+OH = CO 2 +H

has to be reduced by a factor of ten below its known value. The magnitude of this disagreement indicates

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Modeling of hydrocarbon combustion

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FJ6.1. Comparisons between experimental flow reactor data (open circles) and computed values (continuous curves), showing CO and CO 2 mole fractions and temperature as functions of position. The top curves

show results without HO2 chemistry, the bottom curves show results with HO 2 chemistry.

that the initial mechanism is inadequate. Subsequent inclusion of reactions with HO 2 and H202 dramatically improves the model predictions. The lower set of curves in Fig. 1 agree well with the data, using the more complete mechanism and rate expressions which are completely consistent with experimental deter- minations. Another example of the way in which problems with model predictions necessitate major revisions in reaction mechanisms is provided by the problem of CH 3 radical recombination reactions in methane oxidation, discussed in detail later in this paper.

Non-Arrhenius temperature dependence can generally be treated adequately through the T" term in eq. (1). However, the pressure dependence of some elementary reactions has been somewhat more difficult to prescribe conveniently. Many unimolecular decomposition reactions and their associated recombination reactions exhibit significant pressure dependence in some experimental regimes. Other apparently bimolecular reactions actually proceed through an adduct state and display a dependence on pressure as well. Although a great deal of progress has been made in recent years in both understanding and predicting falloff behavior of important combustion reactions,39 42 further improvements in dealing with pressure dependence for modeling purposes are still needed.

3. REACT ION MECHANISMS

Generally speaking, the reaction mechanism provides a description of the elementary steps which occur during the conversion of the fuel and oxidizer to final products. The term "elementary" is used

advisedly, since any mechanism is really an approxi- mation in which all intermediate states with characteristic lifetimes too small to be resolved or to affect the observable features of the combustion are usually neglected. Often the mechanism to be used can depend on the combustion environment or on the types of results which are needed from the model. For example, ionized species or vibrationally excited states of molecules must be considered in some applications, while they can be completely neglected in other models. Further illustrations of these points will be presented below.

In practical terms, the mechanism consists of all the chemical species which affect a given combustion event, together with the elementary reactions among those species. At first glance this might seem to require an enormous number of reactions. For N species, there would be N: reactant pairs, and for each pair there could be a number of possible products. Fortunately such a situation does not actually prevail. Many reactions which are mathematically possible either do not occur at all chemically or with rates which are vanishingly small. Therefore the construction of a realistic reaction mechanism involves princi- pally the identification of those reactions which actually occur and are rapid enough to have an impact on the overall progress of the combustion event.

The combustion of a hydrocarbon fuel consists primarily of the sequential fragmentation of the initial fuel molecule into smaller intermediate species which are ultimately converted to final products, usually dominated by H20 and CO z. In many cases these intermediate species can be fuels themselves. For example, ethylene (C2H4) is an important inter-


C 3 species I

I CH4 C2H 6 - C2H 4 - C2H 2 C2H5OH

] [ c.2o H c.3o. 1

CO

H2 -0 2

FIG. 2. Hierarchical structure and overall interrelationships between oxidation mechanisms for simple hydrocarbon fuels.

mediate in the combustion of propane (C3H8) and other higher hydrocarbons, but ethylene can also be a primary fuel. Carbon monoxide (CO) and hydrogen (H2) are common species which are observed during the oxidation of all hydrocarbons, and the same radical species H, O, OH, HO 2, HCO, and others are common to all hydrocarbon combustion. These observations can be used to great advantage in establishing kinetic mechanisms for the reaction of complex practical fuels. A mechanism can be developed systematically, beginning with the simplest species and reactions which are common subelements in the combustion of more complex species, and sequentially constructed by incorporating new species and reactions in order of increasing complexity. At each level the newly added portions of the mechanism must be tested and validated by thorough comparison between numerically predicted and experimentally observed results. However, because of the sequential ordering, only those features which have been added need be examined closely. This hierarchical structure is summarized in Fig. 2.

The validation of each level in a reaction mechanism is itself a complicated and involved process. It is not sufficient to test a mechanism by comparison with a single experiment, because different elementary reactions can be dominant in different experimental re-

gimes. For example, with many hydrocarbon systems, reactions between fuel molecules and H atoms are dominant in fuel-rich conditions but much less important in fuel-lean conditions where reactions between fuel and O or OH radicals are most important. Some reactions are negligible except under high temperature shock tube conditions, while others become completely unimportant for temperatures above 1000 K. Unless a mechanism is to be used only for a restricted class of applications under a specific set of system parameters, it should be validated by comparison with experimental data over wide ranges of physical conditions. Some of the experimental con- figurations which generate kinetics information useful in establishing combustion reaction mechanisms are summarized in Fig. 3, together with the parameter ranges most often covered by each type of experiment. We term reaction mechanisms which have been tested and validated for these wide parameter ranges "comprehensive reaction mechanisms". 43-46 This type of mechanism represents a numerical modeling tool of exceptional generality. Unlike a reaction mechanism which has been developed only for a specific regime (e.g. for shock tube conditions), a comprehensive mechanism can be applied in a predictive fashion with some confidence that the important features of the fuel consumption process have not been omitted. For

P T Shock tube high ~1300K Plug flow reactor atmospheric 850-1300K Flames low 800-2500K

Transport Dilution limits effects

yes none no

yes none no no flammability yes

limits

FIG. 3. Summary of some of the types of experimental regimes which provide high temperature kinetic rate data for detailed reaction mechanisms and for which experimental data exist for model validation. Typical parameter ranges are shown, together with an indication of whether or not transport effects are important

in simulations.

Modeling of hydrocarbon combustion 5

example, comprehensive mechanisms developed for oxidation of methanol 43 and ethylene 45 have been used to predict laminar flame 47 and detonation 4s 50 properties with the same fuels, with results in good agreement with experimental observations.

Another essential element in mechanistic studies is the description of the thermochemical properties of all of the chemical species involved. This information, including heats of formation, temperature dependent specific heat data, and specific entropy and enthalpy, is generally as important a part of a kinetic model as the elementary reaction rate data. Many of these data are available in convenient tabulations. 5 ~,52 However, thermochemical data for some minor intermediate and radical species are not well known, resulting in significant uncertainties in computed rates of important reactions. For example, the heat of formation of ketene is given by Benson ~8 as - 14.6 kcal/mol and as 4.0kcal/mol by Bahn. 52 The 1971 revision of the JANAF Thermochemical Tables 5~ revised the heat of formation of the formyl radical from -2.9 to 10.4 kcal/mol, while Benson gives a value of 7.2 kcal/mol. These differences reflect a steady improvement in the precision with which such data are known, but they also can cause dilemmas when one is assembling a reaction mechanism. Other species for which large changes have been made recently or for which significant uncertainties still remain in the heat of formation include C2H, NH, and NH2. Since errors in the heat of formation are translated into errors in the activation energy of equilibrium constants and rates of reverse reactions, poorly known thermochemical data can be a serious problem in the modeling of some combustion systems.

3.1. Specific Mechanisms

In this section we will summarize the important features in the reaction mechanisms for the combustion of hydrocarbon fuels. The hierarchical structure noted above will be emphasized by first discussing the H2-O2 submechanism, followed in order by CO, CH20, and others in order of increasing complexity.

3.1.1. H2-O 2 Historically, the hydrogen-oxygen system was the

first combustion mechanism to be developed for a practical fuel. Analytical solutions were initially obtained for the rate equations. 53-57 This system was also used in the earliest detailed numerical models of fuel oxidation in shock tubes, stirred reactors, and laminar flames. 5 s -63 Because the reaction mechanism required for hydrogen oxidation is much smaller than for hydrocarbon oxidation, H2-O 2 mechanisms have been used in the first models for multidimensional fluid mechanics-chemical kinetics, 64'65 sensitivity analysis,66,67 detonations,6S 73 and ignition. 74-76

The important reactions for H 2 oxidation and their rates have been extensively studied and documented. The radical species pool is evolved among OH, O, and H by the reactions

H+O 2 = O+OH (1)

O+H 2 = H+OH (2)

H 2 +OH = H20 +H (3)

O+H20 = OH+OH. (4)

The principal termination reactions include

H+H+M = H2+M (5)

O+O+M = O2+M (6)

O+H+M = OH+M (7)

H+OH+M = HEO+M. (8)

where M refers to any available third body species, required to conserve both momentum and energy in this type of reaction.

The hydroperoxyl radical HO2, originally proposed to explain the explosion limit behavior of H 2 0 2 mixtures, 5'77 is formed primarily by

H+O2+M = HO2+M (9)

and consumed by reactions with various radicals, including

HO2+H = H2+O 2 (10)

HOz+H = OH+OH (11)

HO2+H = H20+O (12)

HO2 +OH = H20+O 2 (13)

HO2+O = O2+OH. (14)

The reaction of HO 2 with itself produces hydrogen peroxide (H20 2)

HO 2 + HO 2 = H20 2 + 02 (15)

which is consumed by reactions with radicals and by thermal decomposition

H20 2 + OH = H20 + HO2 (16)

H202+H = H20+OH (17)

H202+H = HO2+H 2 (18)

H202+M = OH+OH+M. (19)

An additional reaction which is occasionally encountered involving HO2 is

O + OH + M = HO 2 + M (20)

but there is no indication that it has any role in the H2-O 2 mechanism and there are no reliable data on its rate. 23 Rates of HO 2 reactions at combustion temperatures have been reviewed, 35"78,79 while others have recently been redetermined 8 84 at lower temperatures.

In the high temperature combustion of hydrogen and hydrocarbons, reaction (1) is the single most important chain branching reaction, consuming one H atom and producing two radical species O and OH. Any type of kinetic perturbation which increases the production of H atoms will accelerate the overall rate of combustion by increasing the net amount of chain branching from reaction (1). Conversely, processes which reduce the H atom population and reactions which compete with reaction (1) for H atoms will tend


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to inhibit the combustion. There are several good il lustrations of this behavior. For example, reaction (9) competes directly with reaction (1) for H atoms, but the rate of the third order reaction (9) is much more pressure dependent than that of reaction (1). The variation of laminar flame speed in CH4-air , 47'85 CHaOH-a i r .7 and CzH4-air s6 flames can be linked directly to this competit ion between reactions (1) and (9) and is i l lustrated in Fig. 4. In each case there is a very gradual decrease in laminar flame speed S, as the pressure is increased, for pressures below atmospheric. Then, between 1 and 5atm. pressure, the decrease in Su with increasing pressure becomes more pronounced. The reason for this change in behavior is that reaction (9) begins to compete effectively with reaction (1) for H atoms at pressures above 1 arm. Below atmospheric pressure, reaction (9) does not compete effectively and the effect of pressure on the flame speed is very small. Because the explanation for this phenomenon is independent of the specific fuel being used, any hydrocarbon fuel will exhibit the same non-l inear dependence of burning velocity on pressure. Furthermore, the same argument can be extended to non-hydrocarbon fuels such as ammonia (NH3) , hydrazine (NzH4) and other N-H species for

which reaction (1) still provides the majority of the chain branching.

In addit ion to their different dependence on pressure, the rates of reactions (1) and (9) have distinctly different activation energies. While E 1 is approximately 16.8 kcal/mol, 23 E 9 has a small negative value, so k 9 actually decreases with increasing temperature. Therefore reaction (1) will dominate at high temperature and low pressure, while reaction (9) will be n'iore rapid at lower temperature and elevated pressure. These regimes will overlap in many cases, and there is usually a region in which both reactions have comparable rates. While reaction (1) provides chain branching, reaction (9) produces chain termination under some conditions, while under other conditions it is part of a chain propagat ion path consisting in large part of reactions (9) and (11) or reactions (9), (15), and (19).

Another example of the way in which competit ion for H atoms affects the rate of combustion is provided by the observation that the addition of small amounts of various chemicals to f lammable mixtures can dramatically reduce the overall rate of combustion. As we will discuss later in greater detail, the addition of many halogenated species inhibits the combustion process by removing H atoms from the radical pool, forming H 2 by a catalytic cycle of reactions. The removal of H atoms means that they are then unavailable for reaction with 0 2 through reaction (1), thereby reducing the rate of chain branching and slowing the overall rate of combustion.

Rates of reaction between H atoms and many hydrocarbon species are considerably larger than the rate of reaction (1) at the temperatures which are encountered in flames. These rate expressions are illustrated in Table 1 for a variety of simple hydrocarbons, with all the rates evaluated at 1000K. The rates of reaction between H atoms and the saturated hydrocarbons as well as methanol, formaldehyde, and ethylene are larger than the rate of reaction (1). Therefore, these reactions will compete effectively for H atoms with reaction (1), reducing the chain branching rate. This explains why many hydrocarbon species act as inhibitors for the H2-O 2 system, sT'ss Even

TABLE 1. Rates of reactions between H atoms and 02 or hydrocarbon molecules in cm ~ mol sec kcal units

Reaction Rate expression Rate at 1000 K

H+O 2 -~ O+OH H + CH 4 -* CH 3 + H 2 H+C2H 6 - ' C2Hs +H2 H+C2H 4 -~ C2H3 + H 2 H+CH20 ~ HCO+H 2 H + CH3OH --, CHzOH + H 2 H +CH3OH ~ CH a +H20 H+C3H 8 ~ iC3H~ +H 2 H+C3Hs ~ nC3H 7+H2 H+C2H2 ~ C2H+H2 H + C4 H 10 ~ nCcH9 + H2 H q~C4Hlo --* sC4H 9 + H 2

5.13 1016T o.816 exp ( - 16507/RT) 2.24 104T 3 exp ( - 8750/RT) 5.37 x 10aT 3"5 exp ( - 5200/R T) 1.50 x 107 T 2 exp ( - 6000/R T) 3.30 x 1014 exp ( - 10500/RT) 3.00 1013 exp ( - 7000/RT) 5.25 1012 exp ( - 5340/RT) 1.46 x 107T 2 exp ( - 5000/RT) 9.38 107 T 2 exp ( - 7700/R T) 2.00 101*exp ( - 19000/RT) 1.30 x 1014 exp ( - 9700/RT) 2.00 1014 exp ( - 8300/RT)

4.5 x 101 2.7 101 t 1.2 x 1012 7.3 1011 1.7 1012 8.9 x 101 l 3.6 l0 Is 1.2 1012 2.0 x 1012 1.4 x 101 9.9 1011 3.1 x 1012


though the hydrocarbon provides additional fuel to the system and may in fact increase the final mixture temperature, the interference with reaction (1) results in an overall inhibition.

At elevated pressures (P/> 20 atm.) and at relatively low temperatures (T - 1000K), reaction (9) will dominate over reaction (1). In such environments the sequence of reactions (9), (15), and (19)provides chain propagation (i.e. two H atoms consumed, and two OH radicals produced). In contrast, the sequence of reaction (9) followed by

Fuel + HO 2 = Radical + H20 2

and then reaction (19) results in chain branching (one H atom yields two OH radicals). Under these conditions increased fuel concentration will therefore result in an accelerated overall rate of reaction, while at lower pressures an increased fuel concentration will provide an inhibiting effect by competing with reaction (1).

Reaction (2) provides additional chain branching in H2-O: systems, although its importance is not as great as that of reaction (1). Reaction (3) is responsible for the majority of H 2 consumption under normal circumstances, so when the OH level is low, H 2 oxidation will be slow. The reverse of reaction (10) provides a mechanism for initiation of H2-O 2 mixtures which accuratel)~ reproduces experimental ignition delay measurements in shock tube and detonation conditions. 89 Reaction (10)dominates over reaction (21),

H2+O 2 =OH+OH (21)

suggested in the early modeling literature 5s as a possible alternative initiation mechanism. Recent evaluations 23 conclude that reaction (21) does not occur as written or has a very small rate.

In their review of advances in kinetic rate data through 1979, Gardiner and Olson 33 state that all of the important mechanistic steps and rate expressions for the H2 Oz mechanism are now well known. They point out that important work still needs to be done, particularly in determining chaperon efficiencies for different third bodies in reaction (9). The importance of these effects can sometimes be very great, as we will demonstrate in the next section dealing with CO oxidation. Dixon-Lewis and his collaborators 9'9~ have devoted a great deal of attention to the problem of third body or chaperon efficiencies. As a general rule, the efficiency of each species which is present in quantities larger than about 5 ~ should be considered. Water molecules are particularly good chaperons, with efficiencies which can be 10-50 times larger than those of Ar or He. The chaperon efficiency increases with the number of degrees of freedom available to share collisional energy. Atomic species like argon or helium are comparatively inefficient, followed by dia- tomic species such as N 2 and O2, followed in turn by polyatomic species.

3.1.2. 03 An interesting submechanism of the H2-O 2 system

is the ozone decomposition mechanism. Ozone is

occasionally considered in combustion environments since it is an oxidizer which contributes much more chemical potential energy to a given fuel-oxidizer mixture than does ordinary oxygen 02, and its use provides significantly higher product temperatures and pressures than does 02 . Mixtures of 0 3 and 02 will support a laminar "flame" consisting of a narrow decomposition front which will propagate at a fairly high speed. 92 The reaction mechanism for the ozone decomposition flame is the simplest one which has all of the requisite features of a truly detailed mechanism, consisting of only three species O, O 2, and 0 3, with three reactions, reaction (6) together with

O3q-M = O2q-O+M (22)

0 3 + O = 02 + 02. (23)

Direct coupling between the 0 3 system and H 2 oxidation can be provided by reactions including

H+O 3 = OH+O2 (24)

OH+O 3 = HO2+O 2. (25)

Because of its simplicity, the ozone decomposition flame has been used frequently 93-1o2 as a convenient vehicle for testing laminar flame models. The ozone mechanism is of minor practical importance in combustion environments, but its application to model validation can make it valuable.

3.1.3. CO The oxidation mechanism for carbon monoxide is

very simple, consisting of

CO+O+M = CO2+M (26)

CO+O2 = CO2 +O. (27)

The rates of both these CO oxidation reactions are quite small at combustion temperatures, so that CO oxidation in hydrogen-free environments is very slow. However, if H atoms are present, even in amounts as small as 20ppm H20,13 the CO mechanism becomes strongly coupled to that of H2-O2, primarily through

CO+OH = CO2+H (28)

CO + HO 2 = CO 2 + OH. (29)

Reaction (29) is rarely as important as reaction (28), 14'15 although at very high pressures or in the initial stages of hydrocarbon oxidation, the high HO 2 concentrations can make it competitive. All hydrocarbon oxidation eventually involves H2 and CO oxidation kinetics, and most of the CO2 that is produced results from reaction (28).

The coupling between the CO and the H2 02 sub- mechanisms is further complicated by the unusually large chaperon efficiency of water molecules for some reactions. For example, Dryer and Glassman 37 found that, at temperatures near i000 K and at atmospheric pressure, the rate of CO oxidation in a turbulent flow reactor depended on the concentrations of CO, 02, and H20, even though the water concentration was quite small (i.e. 2.5~). Modeling analysis 16 found that the role of H20 as a third body in the recombina-

C. K, WESTBROOK and F. L. DRYER

TABLE 2. Rates of reactions between OH radicals and selected other species in cm 3 mol sec kcal units

Reaction Rate expression Rate at 1000 K

CO+OH ~ CO2+H H2+OH ~ H20+H CH20 +OH ~ HCO+H20 CHa + OH ~ CH 3 + H20 CH3OH +OH ~ CH2OH +HzO C2H6 +OH --* C2H5 + H20 C2H4 + OH ~ C2H3 + H20 CEHa + OH --, CH 3 + CH20 C2H2 + OH -+ CH2CO + H C2H 2 + OH ~ C2H + H20 C2H 2 + OH --~ CH 3 + CO C3H 8 + OH ~ iC3H 7 + H20 C3H s+OH ~ nCaH 7+H20

1.50 107 T 1"3 exp ( + 765/RT) 1.8 x 101~ 2.20 x 1013 exp ( - 5146/RT) 1.7 1012 7.50 x 1012 exp ( - 170/RT) 6.9 1012 3.50 x 103T 3's exp ( - 2000/RT) 2.2 x 1012 4.00 1012 exp ( - 2000/RT) 1.5 1012 1.12 1013 exp ( - 2450/RT) 3.3 x 1012 4.80 x 1012 exp ( - 1230/RT) 2.6 x 1012 2.00 x 1012 exp ( - 960/RT) 1.2 x 1012 3.20 x 1011 exp ( - 200/RT) 2.9 101 t 6.30 x 1012 exp ( - 7000/RT) 1.9 x 1011 1.20 x 1012 exp ( - 500/RT) 9.3 1011 4.80 I08T l'a exp ( - 850/RT) 5.0 x 1012 5.76 10STl4exp ( - 850/RT) 6.0 1012

tion reaction (9) is especially important. The chaperon efficiency for H20 in this reaction was varied, showing that the sensitivity of the computed results to this one kinetic parameter is large. The best agreement was obtained by setting the third body efficiency of water molecules in reaction (9) equal to that determined from shock tube experiments by Getzinger and Schott. 1 o 7

The importance of reaction (28) in all of hydrocarbon oxidation cannot be overemphasized. Like reaction (1), it plays a dominant role in the combustion of all hydrocarbon fuels. However, reaction (28) is an exceedingly complex "elementary" reaction, actually proceeding through a four-atom activated complex) v'x8 As a result, the reaction rate exhibits some pressure dependence and variation with the relative efficiency of different third bodies.~ 09

Because reaction (28) consumes nearly all of the CO which reacts to produce CO2, the rate of CO oxidation depends very much on the availability of OH radicals. It was observed earlier that the presence of hydrocarbon species inhibited chain branching because the rate of reaction (1) is considerably less than the rate of reaction between H atoms and hydrocarbons. In a very similar way the rate of reaction (28) is considerably less than the rate of reactions between OH radicals and typical hydrocarbon species, as shown in Table 2. As a result, the presence of most hydrocarbon species, even in quite small amounts, will effectively inhibit the oxidation of CO. During

1.0

0.8

o= 0.6

! 0.4

E

o 0.2

O.C

I I I

__ - - - - - CH 4 / / /4 . J ' / -

_ / / / " / /

. . . . - . /%z . .

-1.0 -0.5 0.0 0.5 1.0 Relative flame position (mm)

FIG. 5. Computed temperature and normalized fuel and CO profiles in laminar stoichiometric fuel-air flames at atmos-

pheric pressure.

the oxidation of hydrocarbons, CO is produced in substantial amounts, but the subsequent oxidation of CO to CO 2 is usually retarded until after the original hydrocarbon and the fragment intermediate hydrocarbon species have all been consumed. Only then does the OH concentration rise to higher levels, rapidly converting the CO to CO 2. This can be illustrated in Fig. 5, using computed results from three hydrocarbon air laminar flames. 86 The CO concentration grows steadily as fuel is consumed, but very little CO is consumed until all of the fuel has dis- appeared, whereupon the OH concentration (not shown) rises sharply and reaction (28) rapidly consumes the CO.

3.1.4. CH20 Formaldehyde is an intermediate in the oxidation

of most hydrocarbon fuels. However, oxidation and pyrolysis studies with formaldehyde as the original fuel have been relatively rare, primarily because the preparation of a combustible mixture of formaldehyde and oxidizer or diluent is relatively difficult. Kinetic studies of formaldehyde pyrolysis and oxidation have appeared recently, 11 l la primarily in simulations of shock tube experiments.

There is some debate concerning the thermal dissociation products of CH20. The two possibilities are

CH20 + M = HCO + H + M (30)

CH20 + M = CO + H 2 + M. (30a)

Most studies 11'11L~ 13 support the first channel, but other work ~ ~4,1 is favors the alternate path. The chain branching characteristics of the two paths are vastly different. Reaction (30) produces one H atom directly, and in most environments the formyl radical HCO rapidly decomposes further into CO and H. Thus the net difference between reactions (30) and (30a) is H + H as opposed to H 2. Together with reaction (1), reaction (30) is therefore a very active chain branching sequence in oxidizing environments while reaction (30a) is effectively a termination sequence. With these differences, it would at first appear that the resolution of the dispute should be straightforward. However, all of the mechanisms are strongly dependent on rates of other CH20 reactions and reactions of formyl radicals.


Uncertainties in these rates, particularly the reactions of HCO, have been so large that they have obscured resolution of this issue. It is probable that both paths actually occur at the same time x 16 with different rates and different impacts on the chain properties of the overall combustion rate. It appears from modeling analysis of CH4, CHaOH and other flame and shock tube systems 47,4s that when formaldehyde exists only as an intermediate, the thermal decomposition reaction is not important and may in fact proceed in the reverse direction. The reactions between CH20 and radical species are dominant in most situations.

Formaldehyde is consumed primarily by reactions with OH, H, and O radicals to produce HCO.

CH20 + OH = HCO + H20 (31)

CH20 + H = HCO + H 2 (32)

CH20 + O = HCO + OH. (33)

The most recent evaluations of the rates of these reactions are by Dean and co-workers, lt'11~ who examined both pyrolysis and oxidation experiments in shock tubes, with 02 and N20 as oxidizers over a wide range of fuel-oxidizer proportions and initial temperatures. This represents the closest approach yet to a comprehensive mechanism for formaldehyde combustion.

Some confusion exists from early CH4 combustion modeling efforts, carried out before the importance of methyl radical recombination had been established. Methyl radicals were assumed to react directly to produce CH20, but CH20 was not observed in large amounts. Therefore the reactions consuming CH20 were required by these modeling studies to be very rapid. However, recent direct measurements of these CH20 consumption rates have shown that the earlier values were much too high and that the low concentrations of formaldehyde were due instead to relatively low formation rates of formaldehyde. This is an ex-

ceilent example of the way in which an inadequate reaction mechanism can lead to incorrect estimates of rate data. In almost every case, the problem is caused by the omission of significant portions of the complete mechanism. Current CH, oxidation mechanisms in which CH3 recombination reactions and subsequent consumption of C 2 species are correctly included no longer require artificially high rates of reactions between CH20 and radical species.

The particular reaction environment being examined determines the relative importance of reactions (31-33). In fuel-rich mixtures, reaction (32) dominates, while in lean and stoichiometric conditions reactions (31) and (33) dominate. Another reaction which is less important but which can contribute to CH20 consumption in some cases is

CH20 + HO2 = HCO + H202. (34)

The formyl radicals produced by reactions of C H 20 and other species are in turn consumed in a variety of elementary reactions. The two most important reactions of HCO are

HCO+M = H+CO+M (35)

HCO + O 2 = CO + HO 2. (36)

Benson and O'Neal 117 discuss reaction (35) in their summary of unimolecular gas phase reactions, point- ing out that it is actually second order in most combustion environments. This pair of reactions for a hydrocarbon radical illustrates a pattern that will be repeated for many larger radicals; a reaction with 02 competes with a thermal decomposition reaction, and their relative rates determine much of the behavior of the overall mechanism. Typically the activation energy of the decomposition reaction is substantially higher than that of the reaction with 02. For the formyl rad ica l , Es5 = 19kcal/mol and E36 = 7.0kcal/mol. Therefore the decomposition reaction will dominate at high temperatures such as those encountered in

TABLE 3. Rates of thermal dissociation reactions and reactions with 02 molecules for selected hydrocarbon radical species in cm 3 mol sec cal units

Reaction Rate expression

HCO + 02 -~ CO + HO 2 3.30 x HCO+M ~ CO+H+M 1.45 x

CH2OH +O 2 ~ CH20 + HO 2 1.00 x CH2OH + M ~ CH20 + H + M 2.50 x

C2H 5 + 0 2 --" C2H 4 + HO 2 1.00 x C2H5 + M --~ C2H4 + H + M 2.00x

C2H 3 +O 2 ~ C2H 2 +HO 2 1.00 x C2H3 + M --* C2H2 + H + M 8.00X

CH3+O 2 --* CH30 +O 4.80x CH3+M --* CH2 +H+M 1.95 x

nC3H 7 + 0 2 -~ C3H 6 + HO 2 1.00 x nCaH 7 --~ C3H6 + H 1.25 x nC3n 7 ~ C2H 4 + CH 3 9.60 x

iC3H7 + 02 ~ C3H6 + HO2 1.00 iC3H 7 ~ C3H 6 + H 6.30 x iC3H 7 ~ CzH 4 + CH 3 2.00 x

1012 exp (-- 7000/R T) 1014 exp ( - 19000/R T)

1012 exp ( - 6000/RT) 101 a exp ( - 29000/R T)

1012 exp ( - 5000/R T) 10 Is exp ( - 30000/RT)

1012 exp ( - 10000/RT) 1014 exp ( - 31500/RT)

1013 exp ( - 29000/R T) 1016 exp (-91600/RT)

1012 exp ( - 5000/RT) 1014 exp ( - 37000/R T) 101 a exp ( - 31000/RT)

1012 exp ( - 5000/R T) 1013 exp ( - 36900/RT) 10 l exp ( - 29500/RT)


many shock tube experiments, while the reaction with 0 2 will dominate at lower temperatures. In Table 3 the rate expressions for analogous reaction pairs involving other hydrocarbon radicals are summarized, illustrating that the pattern noted here for HCO radicals applies to many other radical species as well. Most of the radical decomposition reactions have been written as second order reactions, which may not always be adequate. Still, the trends already noted, particularly the relative values of the activation energies, will follow the pattern shown in Table 3. In each case, the thermal decomposition reaction will be most important for rich mixtures and at high temperatures while the R + O 2 reaction will dominate for lean mixtures and at low temperatures. The boundary separating these two regimes will not always be very well defined, and there is usually a regime in which both reactions are important. The rates of the decomposition reactions increase as the radical species become larger, so that eventually the R + Oz reaction will become relatively unimportant. For example, in laminar flame environments Warnatz 118 showed that the decomposition reactions of propyl and butyl radicals were so fast that all their other reactions, including those with 02 molecules, could be neglected. However, for radicals smaller than propyl both reaction paths must be considered.

The effects of these two reaction types on the chain properties of the mechanism are quite different. In nearly every case, the decomposition reaction yields a stable intermediate species and highly reactive H atoms which provide subsequent chain branching through reaction (1). In contrast, the radical-O2 reaction produces the same stable intermediate and HO 2 radicals which are usually much less reactive than H atoms. Therefore the overall chain behavior of the mechanism varies with temperature and equivalence ratio due to the balance between the two principal radical consumption paths.

The formyl radical reacts also with other radical species, with rates that are close to collisional, having negligible activation energies. These include

HCO+OH = CO+H20 (37)

HCO+H = CO+H 2 (38)

HCO+O = CO+OH. (39)

Since radical concentrations are usually so much smaller than concentrations of the stable reactant and intermediate species, the radical radical reactions are rarely as significant as the radical decomposition or radical-O 2 reactions. Reactions (37-39) actually tend to inhibit the overall rate of combustion by competing with reaction (35) and by reducing the size of the available radical pool. In rich CO oxidation, formyl radical formation by reaction ( - 35) and consumption by reactions (36-39) can be important. 119 In such conditions, reaction ( -35) is a termination reaction and its inclusion leads to a slight reduction in computed flame speeds in CO/H2/O z flames diluted by N 2 and Ar.

3.1.5. CH4 More modeling work has been devoted to methane

oxidation than to all other hydrocarbon fuels combined. The early mechanisms 12 124 have gradually been refined until current models 38'48'85'114'x25 144 can involve nearly one hundred elementary reactions. While methane has often been used in mechanistic studies because of its apparent simplicity, it is ironic that the methane oxidation mechanism exhibits subtleties which are not encountered in the oxidation of many larger fuel molecules. Methane is an exceedingly important practical fuel, constituting approximately 90~ of the composition of natural gas. It is also a significant byproduct in many industrial processes and is produced during the combustion of most other hydrocarbons.

The construction of a complete reaction mechanism for methane combustion is complicated by a feature which will be observed below for other fuels. During the pyrolysis and oxidation of methane, radical recombination reactions produce significant amounts of larger hydrocarbons containing two or more carbon atoms.38,136-138 In particular, the C 2 species ethane, ethylene and acetylene are observed. The subsequent consumption reactions of these C a species must therefore be included in a complete CH 4 mechanism. Since the levels of C 2 species during CH~ combustion are considerably smaller than the CH 4 concentration, further growth of C 2 species to C 3 and C 4 hydrocarbons usually need not be considered. However, for very fuel-rich conditions under which soot production can occur, polymerization reactions forming species up to C4 levels have been proposed. 134

The thermal decomposition of CH 4 has been studied in detail, 1 x5,145 147 yielding methyl radicals

CH 4 + M = CH 3 + H + M. (40)

Another possible initiation reaction under oxidation conditions has been suggested ~ 24.~ ~s

CH4+O 2 = CH3+HO 2 (41)

but has been shown 11s to be much less important than reaction (40), at least under shock tube conditions.

Hydrogen abstraction from CH4 occurs by several reactions, including

CH 4+H = CH 3+H 2 (42)

CH 4 + OH = CH 3 + H20 (43)

CH 4 + O = CH 3 + OH (44)

CH4 + HO2 = CH3 + H202. (45)

The rates of the first three of these reactions have been shown149-15a to exhibit substantial non-Arrhenius temperature dependence over the range required for combustion modeling.

A major problem in methane combustion concerns the identification of the primary paths for methyl radical consumption. The earliest mechanisms assumed that methyl radicals reacted directly with O2

CH 3 -}- 0 2 = HCO + H20 (46a)


while later mechanisms replaced this "overall" reaction with

CH 3 + 0 2 = CH20 + OH. (46b)

Bowman 129 pointed out that reaction (46b) was probably not an elementary reaction, but rather a convenient model for simulating CH 3 oxidation. Computed model results were found to be very sensi- tive to variations in the rate of reaction (46b), with a rather large rate and relatively low activation energy required in order to reproduce observed combustion rates.

Two developments substantially changed this pic- ture of CH3 oxidation. First, the importance of methyl radical recombination

CH 3 +CH 3 = c2n 6 (47)

as a major contributor to CH 3 radical consumption was established. 3s'13s In earlier models this path had been neglected, so in order to reproduce observed rates of CH 3 consumption an artificially high rate had been assigned to reaction (46b). The second major development was the direct measurement of the rate of reaction between methyl radicals and 0 2 molecules.~S2 At 1200 K the observed rate of reaction was at least two orders of magnitude smaller than that computed from commonly used rate expressions. The combination of these two factors effectively eliminated reaction (46b) from consideration in methane oxidation mechanisms. It now appears that the principal products of this reaction are

CH 3 + 0 2 = CH30 + O. (46)

This reaction path was initially suggested by Brabbs and Brokaw 125 and has been confirmed more recently.~ 53,154 The activation energy of reaction (46) is quite large (i.e. ~ 29 kcal/mol) and the rate expression in the Appendix agrees well with the observations at 1200 K.

In addition to reaction (47), other methyl recombination reactions include

CH 3 + CH 3 = C2H 5 + H (48)

CH 3 + CH 3 = C2H 4 + H 2. (49)

At normal combustion temperatures reaction (47) dominates over reactions (48) and (49), but at high temperature shock tube conditions these alternative product distributions can contribute to the overall rate of reaction. Of these reactions, reaction (48) provides a great deal of chain branching, due to the H atom product as well as an additional H atom produced from ethyl radical decomposition. In contrast, reactions (47) and (49) produce relatively stable products.

Reactions of methyl radicals include a variety of additional channels,

CH 3 q- O = CH20 q- H (50)

CH3 +OH = CH20+Hz (51)

CH 3 + OH = CH30 -I- H (52)

CH3 + CH20 = CH4 + HCO (53)

CH 3 + HCO = CH,, + CO (54)

CH3 +HO2 = CH30+OH (55)

while at very high temperatures CH 3 may also dis- sociate 1 s 5

CH 3 + M = CH 2 + H + M. (56)

When methyl recombination reactions and the subsequent oxidation of the C 2 species are properly included in CH 4 oxidation mechanisms, it is possible to reproduce experimental data for methane oxidation without requiring an artificially large rate for reactions between CH 3 and 02 or for the reactions between formaldehyde and radical species as discussed earlier. This is another example of the way that inadequacies in the reaction mechanism (i.e. omission of CH 3 recombination) can lead to erroneous values for specific reaction rate expressions such as CH 3 + 0 2. It is also interesting to see how the use of sensitivity analysis, to be discussed in detail later, can assist in the development and validation of reaction mechanisms. Brute force sensitivity analysis of early mechanisms showed that computed results depended strongly on the rate used for reaction (46b), leading to an increased interest in that reaction. This attention led to the direct measurement of its rate and a re- evaluation of the entire mechanism.

Methoxy radicals (CH30) react primarily by means of

CH30+M=CH20+H+M (57)

CH30 + 02 = CH20 + HO2 (58)

CH30+H = CHzO+H 2 (59)

with the decomposition providing the major fraction. Other reactions between CH30 and radicals such as O and OH probably occur at fairly high rates, but such paths have not yet been incorporated into detailed mechanisms. The competition between reactions (57) and (58) follows the pattern discussed earlier for formyl radicals, with the reaction with O z competing only for very lean mixtures and at lower temperatures (see Table 3). Reaction (57) is generally very rapid, and a comparison between reaction (46b) and the combination of reactions (46) and (57) shows how a relatively low rate for reaction (46) can still result in a rapid consumption of (CH3) radicals. Both paths produce CH20, but the two-step methoxy radical route gives O and H separately while the one-step path produces OH. The radical multiplication, along with the very reactive H atom, in the methoxy radical path provides considerably more chain branching than the single step. Bhaskaran et al. 126"153 in fact write reaction (46) as

CH3q-O 2 = CH20+O+H

which is equivalent to the combination of reactions (46) and (57).

At shock tube temperatures, methyl radical recombination can yield C2H6, C2H s + H, and C2H 4 -[-H2, while at lower temperatures characteristic of flames and plug flow reactors only the C2H 6 product channel


is important. The C 2 species thus formed then react as discussed below. Methane oxidation therefore occurs through two roughly parallel paths, the first consisting of direct oxidation of methyl radicals to methoxy radicals and/or formaldehyde and the second of methyl recombination followed by oxidation of the resulting C 2 species. The balance between the two paths depends on the fuel-air equivalence ratio. For example, in atmospheric pressure methane-air flames, Warnatz x36,13v estimates that for lean or stoichiometric conditions, about 30 ~o of the methyl radicals are consumed by recombination, with the percentage increasing to 80% for fuel-rich flames. In other mechanisms methyl radical recombination is less dominant, but the importance of this path for methyl radical consumption is now firmly established.

Methane oxidation is somewhat unique among simple hydrocarbon fuels because the primary radical product CH 3 is so difficult to oxidize. Unlike many radicals such as formyl, ethyl, vinyl, and propyl, methyl radicals do not decompose readily to provide additional H atoms (see Table 3). The rate of reaction between cn 3 and 0 2 is slow and does not simply abstract another H atom to produce HO2. Therefore recombination of CH 3 plays a proportionally greater role in CH4 oxidation than analogous reactions for other fuels. For these reasons, methane oxidation chemistry is not typical of most other hydrocarbon fuels. The laminar flame speed of stoichiometric CH 4 air mixtures is lower than that for other fuels such as propane or ethane, is 6,a 57 the effective activation energy for shock tube ignition of CH4 air mixtures is higher than that of other alkane-air mixtures, ass and many other properties of methane-air mixtures are also somewhat anomalous. Thus the use of methane as a reference or standard hydrocarbon fuel is to be discouraged, although its convenience and availability often make it a desirable fuel for both experimental and modeling studies.

3.1.6. C2H 6 Detailed models of ethane combustion have been

developed for laminar flames, isothermal flow systems and shock tubes. 132'136'137'159-164 In addition, we have already seen that ethane oxidation is an important part of methane oxidation mechanisms.

Ethane decomposition reaction ( -47) is at neither its high nor low pressure limit in most combustion regimes, so some treatment or estimate of its falloff behavior is usually necessary. Another initiation reaction with 0 2 may also contribute, 162A63 but only at low temperature and in oxidizing environments

C2H 6 + 0 2 = C2H 5 + HO 2. (60)

A second, relatively faster reaction follows immedi- ately upon production of methyl radicals,

C2H 6 +CH 3 = C2H 5 +CH 4. (61)

This important step provides a path for the relatively non-reactive CH3 to produce reactive ethyl radicals. The key reactions involving C2H 6 include

C2H 6 + H = C2H 5 + H E (62)

C2H 6 + O = C2H 5 + OH (63)

C2H 6 + OH = C2H 5 + H20. (64)

The rates of these reactions exhibit substantial non- Arrhenius behavior. 149,165

Two principal reactions involving CzH5 occur,

C2Hs(+M) = C2H4+H(+M) (65)

C2H s + O 2 = CzH 4 + HOE. (66)

In shock tube conditions, reaction (65) can be assumed to be second order) 66 while other studies at lower temperature a6" indicate first order behavior. It is clear that this reaction is in the falloff region in most typical combustion environments. 33'44'136 Competition between reactions (65) and (66) (see Table 3) is also a key feature of the ethane oxidation mechanism, since the H atom from reaction (65) is highly reactive.

Other reactions of the ethyl radicals include

C2H 5 +O = CH3CHO+H (67)

C2H 5 +0 = CH20 +CH 3 (68)

CzH5 + H = CH 3 + CH 3 ( - 48)

but again, because radical concentrations are usually quite low, these reactions which depend on two radical species concentrations are usually less important than reactions (65) and (66). However, like many other radical-radical reactions, their importance often lies in their role as chain termination steps rather than their direct effect on the rate of ethyl radical consumption. The ratio k67/k68 is approximately 5 : 1 at room temperature, a6s but high temperature rate data are not available for these reactions. The reaction of CzH 5 with OH is fast 169 but neither the absolute rate nor the primary products have been determined.

When ethane is the primary fuel, another key feature of the oxidation mechanism is the recombination of C2 and Ca radicals to produce C3 and C4 species, including

CzH 5 +Ca l l 5 = C,HI0 (69)

CEHs+CH 3 =C3H 8 ( -70)

CH3 +C2H 3 = C3H 6 ( -71)

C2H 5 +CzH 3 = C4H s (72)

C2H 3 +C2H 3 = C4H 6. (73)

For ethane oxidation, reaction ( -70) is the most important of these, a36 The effect of these radical recombination reactions on the chain reaction properties of these mechanisms is primarily one of termination, with two radicals consumed and a relatively stable molecule being produced. The larger fuel species are eventually consumed, but the immediate effect of their production is one of inhibiting the overall oxidation process.

Recombination reactions (69) and ( -70) were included in a recent C2H 6 oxidation mechanism, a62'163 used to describe ethane pyrolysis and oxidation over a wide temperature range (900 K < T < 1800 K)and


for both shock tube and plug flow conditions. In this comprehensive mechanism, the importance of two reaction paths was demonstrated, one consisting of CH 3 radical oxidation leading to formaldehyde and formyl radicals, and the other involving a dehydro- genation sequence leading through C2H5, C2H4, C2H3, and C2H 2.

3.l.7. C2H 4 Ethylene is a primary fuel itself and is also produced

in large amounts during the combustion of CH~., C2H 6 and other higher hydrocarbons. A recent study of ethylene combustion 45 has provided a detailed comprehensive reaction mechanism which is able to reproduce experimental data over wide ranges of operating conditions, including shock tubes, laminar flames, plug flow reactors, and detonations. The elementary reactions of C2H and its product species demonstrate some properties which are not encountered with alkane fuels. Although many features of ethylene combustion have begun to be resolved, other details remain uncertain.

Three initiation reactions can be important, including

C2H4+M = CzH2+H2+M (74)

C2H4+M = C2H3+H+M (75)

C2H4+C2H4 = CzH 3 +C2H 5. (76)

Reaction (74) is fastest in most cases 17'171 while reaction (76) rarely competes except in conditions in which C2H 4 concentrations are very large. 172'j73 In typical shock tube experiments only dilute mixtures of C2H 4 in argon or other diluents are considered, and reaction (76) is negligible under those conditions.

The two important reactions of the vinyl radical are

C2H 3 + M = C2H 2 + H + M (77)

C2H 3 + 02 = C2H 2 + HO 2. (78)

An interesting series of shock tube experiments by Just et al. 174 involved the pyrolysis of extremely dilute C2H 4 in argon over a temperature range of 1700-2200K. Hydrogen atom concentrations were measured as a function of time. Under these very

E

4

1.5

0.5

t I

~ " P = 1.95 bar

_

- I I / " T2P"~c ~H ' / P = 1.77 bar

0 I [ I 0 200 400 600

Time - #s

FIG. 6. Hydrogen atom profiles from shock tube pyrolysis of C2H 4. Open circles show experimental data of Just el a]., 1 "14 curves are computed resultsff 5


dilute conditions, only the initiation reactions (74) and (75), together with the vinyl decomposition reaction (77) need be considered. Since the vinyl decomposition is rapid compared with the other two reactions, the rate of H atom production is very nearly twice the rate of reaction (75). The results of this analysis are illustrated in Fig. 6, showing the measured data as solid circles. With E75 = 98.16kcal/mol as determined originally by Just et al., the agreement between the model and measurements is fairly good (dashed curves), but when E75 is increased slightly to 108.72kcal/mol, the agreement (solid curves) is excellent. The extreme simplicity of the mechanism for this series of experiments made it possible to evaluate one of the key kinetic parameters. However, even within this context the value determined by the modeling study is dependent on the other parameters which were assumed. In particular, possible falloff behavior of reactions (74) and (75), not included explicitly in the analysis, may have a significant influence on the rate expressions finally derived from the modeling analysis.

Reactions of radicals with ethylene fall into two general classes. One consists of H atom abstraction reactions,

C2H 4 + H = C2H 3 + H 2 (79)

C2H 4 + OH = C2H 3 + H20 (80)

but another family of reactions involves the formation of an activated complex followed by rearrangement and fragmentation. These include

C2H4+0 = CH3+HCO (81)

C2H 4 + O = CH20 + CH 2 (82)

C2H4+OH = CH3+CH20. (83)

The addition reactions (81 83) generally have smaller activation energies than the abstraction reactions. Therefore, at room temperature the abstraction reactions are often negligibly slow, but under high temperature conditions such as in shock tube oxidation, the abstraction reactions can be very important. There also appears to be a temperature dependence for the product distribution from the two CzH, ,+O reactions. The total rate of reaction has been observed 175 to be curved on an Arrhenius diagram, which could be explained if E8z is not equal to E 8 r At present there is still some uncertainty both in the rates and the product distributions of CzH4 +O and C2H 4 + OH reactions and their variations with temperature. 176 178 Further- more, because some of these reactions involve the formation of an activated complex,179 the rate expressions are somewhat pressure dependent.

One problem encountered in C2H 6 oxidation which is less important in C2H4 combustion is the formation of larger species by radical recombination. However, for rich conditions, recombination reactions such as reactions (71-73) can still provide significant chain termination. Acetaldehyde has been detected in C2H4 oxidation, ls'181 but the amounts are quite small and may be a product of reactions between 0 2 and excited

C2H s radicals 167 formed by reaction (-65), reaction (67), or isomerization of the adduct in reactions (81) and (82).

Additional reactions of vinyl radicals include

CzH 3 + H = C2H 2 + FI 2 (84)

C2H3+0 = CH2CO+H (85)

C2H 3 +OH = C2H 2 +H20. (86)

The combined effects of reactions (84) and ( -77) can provide an inhibitory effect on the oxidation rate of both ethylene and acetyleneff 6 catalyzing the recombination of H atoms to form relatively inert H2. Otherwise reactions (84-86) are generally much less important than reactions (77) and (78), since radical concentrations are usually relatively small.

A reaction which has been suggested 17'~s2 as a possible step leading to soot formation is

C2H 3 + C 2 H 4 = C4H 6 + H (87)

producing 1-3 butadiene. The generation of large molecules with C/H ratios close to or greater than unity, beginning with small species such as ethylene and acetylene, is currently a rather poorly understood kinetic problem which deserves further attention.

3.1.8. C2H 2 Acetylene is a practical fuel and is also believed to

be an important contributor to the formation and growth of soot. In addition, CzH 2 and its pyrolysis and oxidation reactions are part of the reaction mechanisms for most other hydrocarbon fuels, particularly in fuel-rich conditions. A number of modeling studies143.18z -189 have examined pyrolysis and oxidation of acetylene, but there was still a great deal of uncertainty involved in identification of major reaction paths, product distributions, and rate expressions. Very recently, studies of acetylene oxidation in laminar flames, 19 191 and a combined modeling study of shock tube and laminar flame oxidation of acetylene by Miller et al. '.6 have begun to provide valuable additional information on the mechanism.

The important initiation reactions include

C2H2 +M = C2H+H+M (88)

CzH 2 + CzH 2 = C4H 3 + H (89)

C2H 2 + 0 2 = HCCO + OH (90)

C2H 2 +O z = HCO+ HCO. (91)

In acetylene pyrolysis, reaction (88) dominates under dilute conditions while reaction (89) is more important at high fuel concentrations. It is interesting to note that, unlike the other hydrocarbons already discussed, the pyrolysis of acetylene is exothermic, so that a decomposition "flame" or detonation are possible 193 even in pure C2H2.

Under oxidation conditions, the reaction of C2H 2 with O2 is extremely important 46 but there is not yet positive identification of the product distribution. Miller et al. assumed that reaction (90) predominated while Jachimowski~S3 employed reaction (91 ).


Reactions between C2H 2 and radical species are complex. As discussed earlier in C2H4, many reactions with C2H2 involve the formation of activated species. Miller et al. suggest that as a result, pressure dependence may be the rule rather than the exception for many elementary reactions of species with multiple carbon-carbon bonds such as acetylene and ethylene. Hydrogen atom abstraction

C2H 2 + H = C2H +H 2 (92)

competes with the recombination reaction ( -77) only at high temperatures. Reactions between C2H 2 and O atoms include

C2H 2 +O = C2H +OH (93)

C2H2 +O = CH 2 +CO (94)

C2H 2 + O = HCCO + H (95)

with reaction (94) being predominant under most conditions. 46 Miller et al. showed that in laminar flame and shock tube simulations, the most important means of C2H2 consumption for lean, stoichiometric and even slightly rich conditions involved reaction with O atoms. Reactions with OH radicals include

C2H 2 + OH = CHzCO + H (96)

C2H2+OH = C2H+H20 (97)

C2FI 2 +OH ~ CH 3 +CO (98)

as well as an addition path proposed by Miller et al. 46

C2H z + OH = C2H2OH (99)

followed by the reactions involving C2H2OH, including

C2HzOH+H = CH2CO+H 2 (100)

C2HzOH+O = CH2CO+OH (101)

C2H2OH + OH -~ CH2CO + H20 (102)

CzH2OH + 02 = CH2CO + HO2 (103)

C2HzOH+M -- CH2CO+H+M. (104)

Reaction (98) was included in many early C 2 species oxidation mechanisms, but recent results 46'136 con- firm that it does not occur directly but was rather a shorthand for reaction (96) followed by reaction (113) (see below). Warnatz 136 and Levy et al. 191A92 assumed that the only path leading to ketene was reaction (96). That is nominally a chain propagation step but in practice it accelerates the rate of fuel oxidation because the H atom produced is then available for reaction (I). The paths involving C2H2OH also lead to ketene, but at the cost of two radicals for reactions (I00) and (102), or the loss of one radical in the case of reaction (101). Therefore the sequence initiated by the addition reaction (99) is somewhat more inhibiting than the direct reaction (96).

An alternative path for acetylene oxidation under rich conditions has been examined recently, 46'19'~91 proceeding by means of

C2H 2 +CzH = C4H z +H (105)

C4Hz+OH = C3H2 +HCO (106)

followed by reactions between C3H 2 and radical species to give a variety of other products. Warnatz et al. 19 attributed as much as 35 ~ of the fuel consumption in rich acetylene flames to this sequence, which avoids ketene formation entirely. Other intermediate species found in these mechanisms include C3H 4 and C3H3. Elementary reactions of these C 3 species and their rates are not yet well established and further work is needed.

3.1.9. CH2CO Ketene oxidation has not been studied extensively

under combustion conditions. It has been examined in a number of studies 46'~ 36,191,192,194-197 in its role as an intermediate, primarily in acetylene oxidation. Identification of specific product channels is not very far advanced. A summary of the reactions which have been used in modeling studies includes

CH2CO+M = CH 2 +CO+M (107)

CHzCOWOH = CHzO+HCO (108)

CH2CO+OH = HCCO+HzO (109)

CHzCO+O = HCCO+OH (l l0)

CHzCO + O = HCO + HCO ( 111 )

CH2CO+H -- HCCO+H2 (112)

CH2CO + H = CH 3 + CO. (113)

Another possible product path for CH2CO+O is CH20 + CO, although no modeling studies have considered it. Rate expressions for reactions (107) 198 and (108) 10 have been obtained from experimental studies, but rate expressions for the other reactions represent either estimates or results of modeling studies rather than direct measurements.

Ketyl radicals produced from ketene, directly from acetylene by reaction (95), or by reaction (132) between C2H and O z discussed below, can be consumed by a number of reactions, all of which are somewhat speculative at present. Miller et al. 46 suggested a set of reactions

HCCOWO 2 = COWCO+OH (114)

HCCO+O = CO+CO+H (115)

HCCO+H = CHz+CO (116)

HCCO+OH = HCO+H +CO (117)

HCCO +CH2 = C2H 3 +CO (118)

based on room temperature flow experiments, 199'~ but there is no information available on these reactions at the higher temperatures of flames or shock tubes. As a result, most detailed mechanisms avoid modeling the reactions involving the ketyl radical by including only reactions (107), (111), and (113). As we noted earlier for the reactions forming and consuming methoxy radicals, the ketyl radical can often be eliminated from viable reaction mechanisms. How- ever, the chain reaction properties of the paths involving HCCO are considerably different from those


which eliminate it. Like the methoxy radical, inclusion of ketyl reactions usually increases the chain branching rate of the mechanism.

Other species produced during the oxidation of ketene and acetylene include C2 H, CH2, and CH. The reactions of methylene near room temperature have been reviewed recently by Laufer 20 ~ and include

CH 2 + 0 2 = CO 2 + H 2 (119)

CH2+O 2 = CO2+H+H (120)

CH2+O 2 = CO+H20 (121)

CH2+O 2 = CO+OH+H (122)

CH2 + 02 = HCO + OH (123)

CH 2 + O = CH + OH (124)

CH2+O = CO+H+H (125)

CH 2 + O = CO + H 2 (126)

CH 2 + OH = CH + H20 (127)

CH 2 +H = CH + H 2 (128)

CH 2 +CH 2 = CzH 3 +H (129)

CH 2 +CH 2 = C2H 2 +H E (130)

CH 2 + C2H 3 = CH 3 + C2H 2. (131)

Although there have been kinetic studies of the reactions of methylene in low pressure flames, 22 very little solid information is available concerning product distributions of given reactions. Most of the rates summarized in Appendix I represent the results of modeling studies in which the branching ratios of these reactions were varied in order to provide the needed chain branching rate. Some of these reactions are redundant under certain conditions. For example, reaction (123) followed by the formyl decomposition reaction (35) results in the same product distribution as reaction (122) alone. Under rich and sometimes stoichiometric conditions, this compression of the mechanistic sequence can be appropriate, but under lean conditions the formyl radical will instead react preferentially with 02 (reaction (36)), so that reaction (122) would be inappropriate. Much more information is needed, particularly on the product distributions of these reactions.

Reactions of C2H and CH include

C2H + 0 2 = HCCO + O (132)

C2H+O 2 = HCO+CO (133)

C2H + O = CO + CH (134)

C2H+C2H 3 = C2H 2 +C2H2 (135)

CH+O2 = HCO+O (136)

CH+O2 = CO+OH. (137)

Reactions of C2H with alkanes 2a and with 02204. have been examined at low temperatures. However, at high temperatures, many of these reactions have not been observed directly or the product distributions are still uncertain. The rate expressions represent reasonable estimates which have then been adjusted

to match experimental observations. Commonly the data consist of shock tube ignition delay times or laminar flame speeds, which are not sufficient to determine rates or product distributions of specific reactions. Usually only the overall chain branching rate and rate of heat release are really needed in modeling such systems. If individual species' histories or spatial profiles have been measured, including radic.al and trace species, then the rates and product distributions for each series or family of reactions can be determined. Unfortunately such data are rarely available, so the modeling process can only select reaction rates which reproduce the correct branching rates. The selection of these rates is of course restricted by the known thermochemistry of each species involved in a given reaction. However, even the thermochemical data for these species are not always well established. For example, the standard heat of formation of C2H was recently found 25 to be 127 kcal/mol rather than the earlier value ~1 of 113 kcal/mol, resulting in substantial modifications to computed equilibrium coefficients and reverse rates for reactions involving C2H.

An additional acetylene pyrolysis submechanism has been proposed lsLls6 as a possible factor in soot formation. This path, proceeding by means of formation of polyacetylene species, consists of

C4H3 +M = C4H2+H+M (138)

C2H2 +CzH = C4H2 + H (139)

C4H 2 + M = C4H + H + M (140)

in addition to reactions (88), (89), (92) and others listed earlier. Mechanisms including these species 4L 1 "/0,18 5,18 6 have been used primarily t o model acetylene pyrolysis in shock tubes. Computed results, including H atom profiles and induction times, are relatively insensitive to variations in their rates. The submechanism itself is plausible on kinetic grounds, but the mechanism through which the resulting poly- acetylenes eventually produce soot has not yet been established.

3.1.10. CH30H Several models for methanol combustion have

appeared, including pyrolysis 26 .and oxidation. 43'4v' 126,207-217 The first mechanisms were developed for specific environments including shock tubes and turbulent flow reactors. Based on these specialized models, a comprehensive reaction mechanism was developed 43 which simultaneously reproduced all of the existing experimental data. Subsequently, that comprehensive mechanism was used to predict properties of methanol oxidation in laminar flames 47'211.217 and detonations. 48

Possible initiation reactions include

CH3OH+M = CH3+OH+M (141)

CH3OH+M = CH30+H+M (141a)

CH3OH+M = CH2OH+H+M (141b)

CH3OH+O 2 = CH2OH+HO 2 (142)


but reactions (141a) and (141b) can be rejected on the basis of relative bond energies. The addition of reactions (141a) and (141b) to a mechanism already containing reaction (141) had no appreciable effect on computed induction times under shock tube oxidation conditions. 4a Reaction (141) provides a much different chain initiation function than do the alternate initiation reactions, since both the methoxy and hydroperoxyl radicals quickly decompose, producing an additional H atom. Reaction (141) yields only a relatively non-reactive methyl radical and the chain propagating radical OH. On this basis it might at first appear that, even with substantially slower rates, reactions (141a) and (141b) might have strong influences on computed combustion histories. However, as we shall describe later, the influence of the initiation reaction persists for only a small fraction of the induction period until a modest radical population has been established, after which only the fuel-radical reactions are significant. Therefore, the lower rates and the short period over which initiation reactions are important make reactions (141a) and (141b) negligible. Reaction (142) is also unimportant at high temperature conditions relative to reaction (141).

Abstraction of H atoms proceeds primarily by breaking C-H bonds rather than the O-H bond, including

CH3OH+H = CH3+HzO (143)

CHaOH+H = CH2OH+H z (144)

CH3OH+OH = CH2OH+H20 (145)

CH3OH+O = CH2OH+OH (146)

CH3OH+CH 3 = CHzOH+CH 4 (147)

CH3OH+HO z = CH/OH+H20 2. (148)

For the reactions between CH3OH and H, reaction (143) is faster below 650 K, z's while the rates reverse at higher (T > 1000K) temperatures. 43 If reaction (143) or any other fast reaction produced CH a radicals in large amounts, then methyl radical recombination (reactions (47-49)) would result in considerable amounts of C2 species. However, very low concentrations of C2 species are observed in CH3OH-air flames. 219 The influences on the mechanism of reactions (143) and (144) are substantially different. Reaction (144) produces Hz and CH2OH which decomposes rapidly to yield H atoms

CHzOH+M = CH20+H+M (149)

while reaction (143) produces the much less reactive CH 3 radical and the inert species HzO. In fuel-lean conditions, reaction (145) with OH is responsible for the majority of the CHaOH consumption, while in rich mixtures, the reactions with H atoms are most important.

The CHzOH radicals which are produced then decompose by means of reaction (149) or react with 02 and H

CH2OH+O2 = CH20+HO2 (150)

CH2OH + H = CH20 + H 2. (151 )

Although they are not considered in current mechanisms, reactions between CH2OH and OH or O must also occur. The decomposition reaction is dominant in rich conditions and reaction (150) is more important in lean mixtures. Both reactions produce CH20, consistent with experimental observations 22,22x of high formaldehyde concentrations during methanol oxidation.

The oxidation path for methanol proceeds in a sequential manner through

CHsOH --* CH2OH -0 CH20 -0 HCO ~ CO ~ CO 2.

Because only small amounts of CH3 are formed, subsequent oxidation of C2 species is of less importance than in CH4 oxidation. The validation of the methanol oxidation mechanism is greatly simplified by the linearity of the overall reaction path. Some of the techniques and principles involved in the validation of a comprehensive reaction mechanism can be illustrated very effectively for the case of methanol.

The starting point for this mechanism was a previously established CH4 reaction mechanism, including a treatment of C z species oxidation. Elementary reactions were added dealing with CH3OH and its immediate product species CH2OH (reactions (141- 150)). These additional reactions were assembled after a search of the literature for data on specific reactions involving CHaOH and CHzOH. In some cases the initial rate expressions were estimated. This composite mechanism was then used to simulate a number of experiments dealing with methanol oxidation. Rate expressions for only these newly incorporated reactions were varied to obtain the best agreement between computed and experimental results.

The experiments to be analysed were selected care- fully so that each emphasized different parts of the new mechanism. Intermediate temperature (T ~ 1000K) turbulent flow reactor data 222 for lean conditions depended most on the rates of reactions (145) and (150), while similar data from a rich mixture depended on the rates of reactions (143), (144), and (149). Models for high temperature (1545 K < T < 2180K) shock tube data 2v in contrast emphasized the initiation reaction (141). In addition, the rich shock tube models depended on the rates of the same CH3OH- radical reactions as the rich flow reactor calculations, and similarly for the lean mixtures. Therefore, an array of experimental data could be used to isolate one or two elementary reactions at a time, greatly simplifying the determination of reasonable rate expressions. The computed results also showed that some of the reactions, including reactions (142) and (147), contributed negligibly to the observed rate of methanol consumption under these conditions. This conclusion does not necessarily mean that such reactions should be omitted from future mechanisms. Reaction (147) is relatively unimportant in part due to the low methyl radical concentrations encountered in methanol oxidation. However, in fuels consisting of CH4-CH3OH mixtures for example, reaction (147) might be important.

JPEC$ IO : I -B


In a study of methane-oxygen combustion in flames, Harvey and MacCol1223 detected significant amounts of CH3OH. The reverse of reaction (141) is too slow to be able to account for the observed formation rate of methanol. However, an alternative mechanism in the cooler parts of these flames (800 K < T


CH 3 radicals and CO. The methyl radicals produce CH4 and recombine with other methyl radicals to produce C2H6 . Subsequent reactions of C2H 6 lead to C2H4, C2H2 and other related species as already discussed. These trends are consistent with experimental data in which relatively high levels of CO, CH 4, C2H6, and C2H 4 are observed. Thus ketene is a minor product, perhaps arising as much from the secondary C2H 4 oxidation as directly from acetaldehyde.

3.1.13. C3H 8 As we have seen already, construction of a detailed

reaction mechanism is a sequential or hierarchical process, beginning with the simplest species and building up to include larger and more complex molecules. At present the frontier in this development pattern is represented by the C 3 and C 4 hydrocarbons. Recently substantial progress has been made, with mechanisms describing the pyrolysis and oxidation 118'136'137'195-197'227-243 of propane and pro-

pylene in flow reactors, shock tubes, and laminar flames. Many of the principal overall features of the combustion of propane have now been identified.

The primary initiation step is

C3H 8 = CH 3 +C2H s (70)

which is much faster than the reactions involving the breaking of a C H bond

C3H s = H + iC3H 7 or

C3Hs = H + nC3H 7

due to the smaller C-C bond energy. For oxidation conditions, other initiation reactions can include

C3H s + 0 2 = iC3H 7 + HO e (171)

C3H s + 02 = nC3H7 + HO 2 (172)

although they will be much slower than reaction (70) at shock tube temperatures. Propane is the first species to be encountered here in which distinctions between isomeric forms of a given species must be considered. For modeling purposes each isomeric form can conveniently be considered as a unique species, together with reactions involving both forms, such as

iC3Hv+C3H 8 = nC3HT+C3H s. (173)

Radical species reactions with C3H 8 include, for pyrolysis

C3H s +H = iC3H 7 +H 2 (174)

C3H8+H = nC3H7 +H 2 (175)

C3H 8 + CH 3 = iC3H 7 + CH 4 (176)

C3Hs+CH 3 = nC3HT+CH 4 (177)

C3Hs+C2H 3 = iC3H7+C2H 4 (178)

C3H8+C2H 3 = rtC3H7 +C2H 4 (179)

C3H8 +C2H 5 = iC3H7+C2H 6 (180)

C3Hs+C2H s = nC3H7+C2H 6 (181)

C3Hs+C3H 5 = iC3HT+C3H 6 (182)

C3Hs+C3H 5 = r/C3H7 +C3H 6 (183)

and for oxidation

C3H s +O = iC3H 7 +OH (184)

C3H s + O = nC3H 7 + OH (185)

C3H 8 + OH = iC3H 7 + H20 (186)

C3Hs +OH = nC3H7 +H20 (187)

C3Hs+HO 2 = iC3HT+H20 2 (188)

C3Hs+HO 2 = nC3HT+H202. (189)

As observed previously for similar reactions with methane and ethane, the rate expressions for H atom abstraction by O, H, and OH all display significant non-Arrhenius temperature dependence. 19L244 Furthermore, reactions with OH are generally most important for propane consumption in lean and stoichiometric conditions, and reaction with H atoms and CH 3 radicals most important for rich conditions.195'235

The thermal decomposition of the propyl radicals gives

nC3H 7 = C2H 4 + CH 3 1190)

nCaH 7 = C3H6+H (191)

iC3H7 = C2H 4 + CH 3 (192)

iC3H 7 = C3H 6 + H (193)

although on structural grounds 245 the rate of reaction (192) will be very small. Reactions (191) and (193) have a somewhat accelerating overall effect on propane oxidation rates since they produce H atoms, while reaction (190) produces two relatively inactive species, CzH 4 and CH 3. For this reason, an important feature of the reaction mechanism for Call 8 consumption concerns the relative amounts of n-propyl and iso-propyl radicals which are produced in reactions (174-189). Some theoretical arguments have been presented 165 for these relative rates, and modeling results 195 can use the sensitivity to these branching rates to estimate them, but direct experimental deter- minations of the independent rates of abstraction of primary and secondary H atoms in C3H 8 at combustion temperatures would be very useful.

Some models have included

nC3H7 + 0 2 = C3H 6 + HO 2 (194)

iC3H 7 + 0 2 = C3H 6 + HO 2 (195)

with estimated rate expressions. Although analogous reactions involving HCO, C2Hs, C2H3, and CH2OH have been shown to be important in stoichiometric and lean mixtures, Warnatz 11s'~36 has shown that, compared with the t

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