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A Multiple-step Overall Kinetic Mechanismfor the Oxidation of HydrocarbonsD. J. HAUTMAN, F. L. DRYER, K. P. SCHUG & I. GLASSMANa Department of Mechanical and Aerospace Engineering, PrincetonUniversity, Princeton, New Jersey 08544

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Combustion Science and Technology, 1981, Vol. 25, pp. 219-235 © 1981 Gordon and Breach Science Publishers, Inc.O010-2202/81/2505-O219S06.50/0 Printed in Great Britain

A Multiple-step Overall Kinetic Mechanism for the Oxidationof Hydrocarbons

D. J. HAUTMAN. F. L DRYER. K. P. SCHUG and I. GLASSMAN Department of Mechanical andAerospace Engineering. Princeton University. Princeton. New Jersey 08544

(Received May 5, 1980; in final form January 22,1981)

Abstract—Extensive experimental results were obtained on the oxidation of many aliphatic hydrocarbons ina high temperature, turbulent flow reactor developed for kinetic studies. These results indicated the viability

• of presenting this complex kinetic situation in the format of a simplified, overall kinetic scheme which couldaccurately predict the major species formed and the temperature-time history (rate of heat release) of thesystem. The proposed overall mechanism follows the general form:

(10)

(ID(9)

(12)

where C2H4 represents a class of olefinic intermediates which are known to be primarily ethene and propene.The corresponding rate expressions, developed primarily from propane oxidation results, are

= - 1 0 * exp( -E/RT)[CnU2n+2]a [O2p [C2H4]< mole/cc-s (III)

dt

= -10* exp(-£/«r)[C2H4]°[O2]6[CnH2 n + 2]

c mole/cc-s (VII)dt

d[CO]

dt= {-10* exp(-E/RT)[CO]a[O2p[H2O]

C} X5mole/cc-s (XI)

— - — = -10*exp(-£/Kr)[H2]a[O2p[C2H4]cmoIe/cc-s. (IX)

dt

where the parameters for III are x = 17.32±0.88, E = 49,6OO±240O, a = 0.50±0.02, b = 1.07±0.05, andc = O.4O±O.O3; for VII, x = 14.70±2.00, E = 50,0O0±500O, a = 0.90±0.08, b = 1.18±0.10, andc = -0.37±0.04; for IX, x = 13.52±2.2, E= 41,000±6400, a = 0.85±0.16, 6=1.42±0.11, andc = -0.56±0.20; and for XI, x = 14.6±0.25, E= 40,000±1200, a = 1.0, 6 = 0.25, and c = 0.50.S — 7.93 exp(—2.48^), where is the initial equivalence ratio and S cannot take values greater than 1.

The rate expressions were found to predict within reasonable accuracy flow reactor and shock tube resultson propane oxidation which encompass an equivalence ratio range 0.12 to 2.0, a temperature range 960 to1540 K and a pressure range 1 to 9 atm. With minor modification, experimental flow reactor results on theoxidation of butane, 2- and 3-methylpentane, and n-octane are also predicted.

I. INTRODUCTION carbon chemistry has frequently been described byvery simple expressions. However, it is becoming

Successful combustion system modelling depends increasingly apparent that success in understandingon a correct description and coupling of the perti- a significant portion of present combustion prob-nent fluid mechanic, turbulent, heat transfer, and Jems depends on a detailed and correct under-chemical processes entailed. Until recently, hydro- standing of the hydrocarbon chemistry.

219

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220 D. J. HAUTMAN el al.

Kinetic information is generally provided eitherby a detailed or overall mechanism which attemptsto describe the chemistry in a reacting environmenton a microscopic or molecular level and whichconsists of a number of elementary kinetic stepswhich occur concurrently. Using the Law of MassAction ordinary differential equations for eachspecie can be obtained from the set of elementaryreactions and these can be integrated to obtainspecie concentrations as a function of time.

Unfortunately, for hydrocarbon oxidation aninordinately large number of species, and thus alarge number of differential equations, are requiredfor an explicitly correct kinetic representation.These differential equations are usually stiff andrequire special integration techniques. In addition,the specific rate constants of the elementary reac-tions and the elementary reactions themselves, ascurrently reported in the literature, are not necess-arily well known and can be a source of large error.Further problems appear when these detailed kin-etic mechanisms are coupled with other physicalprocesses, such as atomization, vaporization, tur-bulence, etc., which are involved in combustionphenomena. Particularly, for two- and three-dimensional problems, the use of large detailedkinetic mechanisms leads to very expensive andtime consuming computer requirements (Dryer andWestbrook, 1979). Overall kinetic schemes attemptto simplify the chemistry in order to predict im-portant physical quantities, such as the rate ofenergy release and the concentration of importantprincipal species, fuel, CO, CO2, H2, and H2O.

The assumption invoked when using overallkinetics is that a macroscopic chemical event, whichis represented by a number of elementary reactions,can be simplified to one overall reaction which isassumed to have the same form as an elementarystep. The rate at which this overall reaction pro-gresses is defined in terms of a semi-empiricalexpression which has a functionality similar to thatwhich results from the Law of Mass Action. Theform of the expression contains an overall rateconstant and reactant or product concentrations.Although these overall expressions are developedconceptually from knowledge of the details of thehydrocarbon oxidation or pyrolysis process, theyshould never be interpreted to represent any ofthe detailed processes. As mentioned earlier, theyare only useful for predicting certain macroscopicevents.

Extensive specie profiles have been obtainedon hydrocarbon oxidation processes, particularly

C3H8, in high-temperature flow reactor exper-iments. These data provided the insights whichwere necessary in the development of a new overallkinetic mechanism for hydrocarbon oxidation. Adescription of the flow reactor, experimentalresults, the overall kinetic mechanism, and themechanism's capability to predict experimentaldata over a wide range of equivalence ratios, tem-peratures, pressures and initial reactant concen-trations are presented in the remaining sections.

II. EXPERIMENTAL APPARATUS ANDPROCEDURES

The experimental hydrocarbon oxidation results,upon which this study was based, were obtainedusing a .turbulent, adiabatic flow reactor (Dryer,1972). This reactor is basically a cylindrical quartztube with an inner diameter of 10 cm throughwhich a hot inert carrier gas, nitrogen, flows atvelocities sufficient to result in turbulent con-ditions. As a result, the fluid mechanics can becharacterized as one-dimensional plug flow, andthe transformation from distance to time is verystraightforward. Wall effects are minimized bythe small surface to volume ratio and the largeconvective flow. The design of the reactor systemis such that it is essentially adiabatic (Dryer, 1972).In order to maintain adiabaticity and to ensuresmall longitudinal gradients of reactive species, theamount of fuel injected is less than 1 percent on amolar basis. These conditions, coupled with thelarge convective flow, make the effects of longi-tudinal diffusion of mass and energy negligible.Rapid mixing of small amounts of a gaseous reac-tant with the carrier stream is provided by highvelocity radial injection at the reactor inlet (fordetails see Dryer, 1972; Dryer and Glassman, 1973).Liquid hydrocarbon fuels are pre-vaporized beforeinjection into the carrier stream. By the properadjustment of the initial carrier temperature, flowvelocity, and reactant concentrations, various por-tions of the reaction zone can be spread on theorder of 100 cm. Product samples are withdrawnwith a water-cooled stainless steel sampling probeat 20 longitudinal positions along the center lineof the reactor duct. Simultaneous temperaturemeasurements are obtained with a Pt 30 percentRh/Pt 6 percent thermocouple coated with silica tominimize heterogeneous reactions. Samples arestored in glass bottles and analyzed using gaschromatography (Hautman, 1980).

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THE OXIDATION OF HYDROCARBONS 221

Principal hydrocarbons which were investigated III.here were C3H8, w-GjHio, M-C6H14, 2-methyl-pentane, 3-methylpentane, and M-CSHIS. Someinitial stages of this research were reported in thePh.D. thesis of Cohen (1977). All hydrocarbonsused had a purity of at least 99 percent. Oxygen(99.5 percent purity) injected into the carrier streamprior to the fuel ranged from 1 to 21 percent on amolar basis. The complete range of experimentalconditions used in this investigation is given inTable I.

QUALITATIVE CONSIDERATIONS OFHYDROCARBON OXIDATION

TABLE IExperimental conditions

TemperaturePressureCarrier(CnH2n+2)((O2)iEquivalence ratio

960-1145 K1 atmosphereN21 x 10-8-l x 10-' mole/cc1 x 10-'-5 x 10"6 mole/cc0.03-2.0

Examples of the species and temperature profilesobtained in the C3H8 and «-CsHi8 studies are pre-sented in Figures 1, 2, 3, and 4. The symbols arethe actual experimental data and the lines representthe smoothed functional description of the data.The initial experimental conditions for these figuresare given in Table II.

Unfortunately, reaction characteristics dictatethat the initial temperature, velocity, and equiv-alence ratio are not the same in all of the exper-iments; thus a direct quantitative comparison isnot possible among the various figures. However,several interesting qualitative observations can bemade with respect to the oxidation process. Inall cases, the oxidation can be described in terms of3 sequential and overlapping macroscopic events.First, the hydrocarbon is transformed into smallerintermediate hydrocarbon species, primarily olefins.

1320

u.

d3E

.008

.004

97 49 61 73 85 97DISTANCE FROM INJECTION (cm)

109 121

FIGURE 1 Specie concentrations (mole fraction percent) and temperature (K) versus distance from injection(cm) for a lean C3H8 oxidation experiment.

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222 D. J. HAUTMANf/fl/.

.3

.2

<li.

O2

.04

.02

1300

• - ^ 1

PHI =0.98

Q -D-

-C,H,

• • — • • 8-/S

-6*

THE OXIDATION OF HYDROCARBONS 1 223

Figure

I234

//;, mole/sec(total molarflow rate)

0.970.730.760.73

TABLE IIExperimental initial conditions

T,,K

102111311148978

(CnH2n+2)i,mole/cc

4.25x10-83.11X10-8

5.32xl0-8

2.67xl0-8

(O2)(,mole/cc

1.7 xlO-6

1.58x10-'1.67 xlO-7

1.7 xlO-6

(Phi),

0.120.981.590.18

This process is iso-ergic, slightly exothermic, orslightly endothermic, and depends on the stoichi-ometry which in turn determines how much H2Ois formed in comparison to H2. The intermediatehydrocarbons are then oxidized to CO, which issubsequently oxidized to CO2. These last twosteps are the exothermic stages which are respons-ible for the release of energy during hydrocarbonoxidation.

The description of the oxidation process in termsof overlapping, sequential stages has been reportedpreviously in the literature. For example, Orr(1963) and Levinson (1959) observed the formationof olefins during a shock tube investigation of theoxidation of C7H14 and iso-CsHis. These exper-iments were conducted in the temperature range of1000 K to 1200 K. Unfortunately, no quantitativeinformation could be obtained from these investi-gations, but the results did reveal a staged oxidationprocess. Other shock tube investigations (Burcatet al., 1971, 1972; Cooke and Williams, 1975),which were primarily concerned with the ignitiondelay characteristics of various alkanes, did pro-vide quantitative information as to the formation ofintermediate hydrocarbons and CO before theactual formation of CO2.

Small amounts of intermediate hydrocarbons(mainly olefins), and somewhat larger amounts ofCO, were observed to form prior to significantproduction of CO2 in CaHs/air (Fristrom andWestenberg, 1957) and C2 hydrocarbon/oxygen(Fristrom et al., 1958). Fristrom and Westenberg(1965) suggested a general pattern for the oxidationof hydrocarbons in flames. Essentially the flamewas divided into two zones: the primary zone inwhich the initial hydrocarbons are oxidized to CO,H2, H2O, and the various radicals {i.e. H, O, OH,etc.) and the secondary zone in which CO and H2are oxidized to CO2 arid H2O. In contrast to pre-vious investigations, only a small quantitity of

intermediate hydrocarbons were observed to bepresent. This difference is the direct result of thesteep diffusion gradients and the high temperaturesobtained in laminar flames. In other words, theconcentration profiles are not simply the result ofthe chemistry, but are distorted by the effect ofdiffusion. Consequently, the acquisition of kineticrate data from flame concentration profiles is verycomplicated and susceptible to serious error ifproper diffusion data are not used.

On the other hand, the flow reactor specie profiles,presented in Figures 1, 2, 3, and 4 are the result ofgas phase chemistry only. Further, a much moredetailed picture of the oxidation process is pro-vided by these profiles than can be obtained fromthe shock tube results. The quantitative indentifi-cation of the intermediate hydrocarbon species,which are being formed as a function of time, isobtained readily from the present results. Moreimportantly, the figures show that the intermediatesare primarily olefinic, the largest fraction beingcomposed of C2H4 and C3H6. Even when hydro-carbon chain length has been increased by a factorof 3, the first observed macroscopic event in theoxidation process is the breakdown to the simpleolefins. This experimental trend provided the basisof hope for an overall kinetic mechanism which isindependent of the number of carbon atoms (Dryerand Glassman, 1978).

The temperature profile, which is a direct resultof the energy release due to chemical reaction,

. exhibits an interesting shape. During the earlystages of reaction, when the intermediate olefinsare being formed, the temperature remains rela-tively constant. In fact, over 50 percent of the fueldisappears before any significant temperature riseappears. The oxidation of the intermediate olefinsto CO marks the beginning of the overall energyrelease. As the CO is oxidized to CO2, the tem-perature continues to rise. The oxidative pyrolysis

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224 D. J. HAUTMAN el al.

of the original paraffin to the olefins is endothermic.This endothermicity is balanced by the energyrelease due to the oxidation of H2 formed duringthe pyrolysis. Thus as is observed, the early partof the overall hydrocarbon oxidation process isthermochemically neutral.

Figures 1, 2, and 3 present results from C3H8oxidation at various equivalence ratios. The gen-eral trends observed are not affected by varyingequivalence ratio. The degree of oxidation, whichis dependent on the amount of oxygen present, isthe major distinguishing characteristic. As theequivalence ratio is increased, the capability forcomplete conversion of C3H8 to CO2 and H2Odiminishes; succinctly, more CO and H2 are presentas the stoichiometry becomes richer.

The above observations enable a significant con-clusion to be reached with respect to the formu-lation of an overall kinetic mechanism. In order toproperly characterize the oxidation process a mini-mum of 3 overall reactions is required. These over-all reactions would describe the breakdown of thehydrocarbon to the intermediate olefins, the oxi-dation of the intermediate olefins to CO, and theoxidation of CO to CO2. Any mechanism notaccounting for these processes will not predict cor-rectly the major specie profiles or the correctenergy release rate. It was with this perspectivethat previous attempts to develop overall mech-anisms were reviewed.

IV. OVERALL KINETIC MECHANISMCONCEPTS

The simplest mechanism and the one which is themost convenient for numerical modelling is the one-step overall kinetic mechanism. This approachconsiders the oxidation process to occur directlytoCO 2 and H2O:

CnH2n+2 + J(3« + l)O2->«CO2+(«+l)H2O (1)

The advantages are immediately obvious in thatonly 4 chemical species are involved in the formu-lation. Since it is a linear function of the amountof fuel which is reacted, the heat release calculationis also quite simple. Unfortunately, this mechanismdoes not account for the previously describedcharacteristics of hydrocarbon oxidation. The for-mation of intermediate hydrocarbons and CO is nottaken into account. As a result, the rate of oxi-dation to CO2 proceeds much too fast in comparisonwith the experimental results.

The next stage of complexity introduced hasbeen the two-step overall kinetic mechanism whichseparates the highly exothermic oxidation of COto CO2 from the less exothermic oxidation of thehydrocarbon to CO:

(2)

(3)->O2->CO2

Since no prediction is made as to the formation ofintermediate olefins, this mechanism still does notaccount for the time delay in the initial release of asignificant amount of energy.

Earlier in this laboratory Cohen (1977) postu-lated an overall mechanism which consisted of thefollowing three steps:

(4)

(5)

(6)CO + JO2->CO2

and reported rate expressions for the overall Reac-tions (4) and (5). Unfortunately, no verifications ofthe mechanism or rate expressions with respect topredicting specie and temperature profiles werereported at that time.

The final approach to be discussed is the quasi-global kinetic mechanism originally reported byEdelman and Fortune (1969). This kinetic mech-anism attempts to combine overall and elementarykinetics. The oxidation of the hydrocarbon to COand H2 is represented by an overall expression.Subsequent oxidation of CO and H2 to CO2 andH2O is modelled primarily by use of elementarysteps. The major advantages of such an approachare the potential of including the prediction ofradical concentration information and high tem-perature dissociation effects. An obvious dis-advantage involves the large number of speciesinvolved in the mechanism, which compromisesthe objective of the overall kinetic approach. How-ever, the Edelman reaction scheme, similar to theothers discussed, neglects any intermediate olefinformation and therefore cannot predict the timedelay to significant energy release. Further nocoupling between hydrocarbon, CO, and H2 oxi-dation processes exists. In actual oxidative environ-ments competition for radical species exists betweenthe hydrocarbons, CO and H2, present. This com-petition reduces the CO and H2 oxidation rates and

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THE OXIDATION OF HYDROCARBONS 225

does not evolve from the Edelman-Fortune reac-tion mechanism. Thus, the calculated energyrelease will occur too early, the predicted rates ofreaction will be too large, and radical species con-centration cannot be properly modelled. Therefore,even discounting the disadvantage of a large num-ber of species, several aspects of this mechanismrequire modification before it can provide adequateinformation on hydrocarbon oxidation chemistry.

It was in this context, and insight from thedetailed experimental measurements in the flowreactor, that we began to analyze other possibleoverall mechanisms for hydrocarbon oxidation.

V. PROPOSED MULTI-STEP OVERALLKINETIC MECHANISM

The flow reactor experimental results stronglysuggested that the hydrocarbon oxidation mech-anism could be represented by three overall reac-tions:

CnH2n+2 + -o)H 2 O (7)

(4-2a)C2H4+ O2->2CO+2aH2+(2-2a)H2O (8)

(9)

where a is a function of equivalence ratio and theconcentration of C2H4 represents the mass of allhydrocarbon intermediates which are formed dur-ing the oxidation process. These species are mainlythe l-olefins and are given the properties of thesimple olefin, C2H4, as a result of the experimentalobservation that the dominant intermediate isethene. Reaction (7) may be considered to be theresult of the oxidative pyrolysis of the aliphatic fuelto the olefin and hereafter will be referred to as thefuel pyrolysis step. Obviously, the quantity a is afunction of the equivalence ratio. At very leanstoichiometries, a approaches zero, and as thestoichiometry becomes richer, o increases.

A similar, but more kinetically correct approachwould be to set a equal to one and add anotheroverall reaction to represent the oxidation of H2;that is,

C 2 H 4 +O 2 ^2CO+2H 2 (11)

CO + iO2->CO2 (9)

H2 + !O 2 ^H 2 O (12)

In order to use this kinetic mechanism quanti-tatively, semi-empirical overall rate expressionsmust be derived from the experimental data.

o2

TIME (s)

FIGURE 5 Pictorial representation of an experimentalfuel disappearance profile, an experimental temperatureprofile, and the fuel disappearance profile resulting fromthe integration of Eq. (1).

The initial clue to determining a rate expressionfor Reaction 10 evolves from examining the sig-moidal shape of the fuel disappearance profileduring oxidation (Figure 5). The rate of disappear-ance increases early in the reaction until a maximumis achieved and then decreases. Thus, a function-ality which is to reproduce this shape must containterms which exhibit these characteristics. In thepast, the proposed overall rate expressions havehad the following simple functional form:

dt

(10)

= -Atxp(-E/RD[CnH2n+2]a

X[O2pmole/cc-sec (I)

Since the fuel and oxidizer concentrations decreaseas the reaction progresses, the reaction constant isthe only term which can have an accelerating effecton the rate of fuel disappearance. Therefore, thetemperature must be increasing at the beginning ofthe reaction in order for the overall specific rateconstant to increase. However, the experimentalresults indicate that the temperature remains rela-tively constant throughout most of the fuel dis-appearance process. Thus, integration of Eq. (I)

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226 D. J. HAUTMAN et al.

only results in a profile with a continuouslydecreasing slope (see Figure 5).

Semenov (1935) suggested that the shape of thefuel disappearance profile is the result of thebranching characteristics of hydrocarbon oxidationkinetics. Early in the reaction a radical buildupoccurs as a result of the branching which thenaccelerates the fuel disappearance. As the reactionprogresses, the fuel concentration decreases andthus enables the secondary radical reactions tobecome more important. This competition forradical species eventually results in a decreasingfuel disappearance rate. Semenov (1935) proposesan empirical expression which describes the abovekinetic behavior. However, this expression pro-vides only the hydrocarbon concentration as afunction of time. A differential rate equation ismuch more suitable for the development of anoverall kinetic mechanism for hydrocarbon oxi-dation. With a few appropriate assumptions theempirical expression of Semenov can be differen-tiated (Hautman, 1980) and Eq. (II) is the result:

d[CnU2n+2]

It= -Ae\p{-E/RT)

X-[CnH2 n + 2]«[O2]6([CnH2 n + 2]( - [CnH2 n + 2])c

[CnH2 n+2]j

X mole/cc-s. (II)

The term ([CnH2n+2]f-[CnH2n+2]), which is theamount of fuel reacted, is a measure of the accel-erating effect of the radical buildup on the rate offuel disappearance. The subscript / denotes initialconcentration. The term [CnH2n+2], the unreactedfuel concentration, has a decelerating effect on therate and eventually leads to a decrease in the rateof fuel disappearance. The increasing importanceof secondary reactions is taken into account by thislatter term.

The quantities

THE OXIDATION OF HYDROCARBONS 227

from the multiple regression analysis of lean andrich C3H8 oxidation data only was:

! = _1017.32±0.88eXp(-(49.600dt

±2400)/«r)[CnH2n+2]0-50±0-02[O2]

1-07±0-05

X [C2H4]°-40±0-03 mole/cc-s (III)

A plot of the log of the experimental and predictedoverall rate constant versus 1000/r is presented inFigure 6. In order to further verify the validity ofthis expression, similar ones must be developed orchosen for the remaining overall steps.

.94 .931OOC/T (I/K)

1.06

FIGURE 6 Logarithm™ of the experimental and least-squares overall rate constant versus 1000/r for Reaction(10) (symbols: experimental; lines: least-squares fit).

For the overall step which depicts the oxi-dation of the intermediate (Reaction 11), the formrecommended was

(IV)

dt

Again, the experimental determinable quantitiesare d[C2Wi]ldt, T, [CzH*], [CnH2n+2], and [O2].The rate of intermediate disappearance, however,is not derived directly from the experiment. Basic-ally it is determined from the following equality:

J[C2H4]\

dt /total production

dt /formation

228 D. J. HAUTMAN et al.

before its maximum was reached was found to beslower than that observed after the maximum. Thetemperature was somewhat higher in the later por-tions of the reaction, and an overall rate constantwith a higher activation energy could account forthese higher experimental rates when consideringan individual experiment. However, applicationof this higher activation energy rate constant todifferent experimental data at different initial tem-peratures resulted in very poor comparisons. Conse-quently, it was concluded that the temperature didnot appear to be the cause of the higher rates ofintermediate disappearance. Only one other factorremained to be considered and that was the extentof reaction, or how far the reaction had progressed.This approach would lead once again to the idea ofcompetition for the radical species. During thelater stages of reaction, fuel was present in verysmall amounts and cannot compete as effectivelywith the primary products for the radical speciesin the reaction environment. By assuming the rateof intermediate disappearance to be a function ofthe fuel concentration, the term [CnH2n+2]

c withthe realization that c would be a negative exponent,was thus included to account for this effect. Com-petition for radical species was now a factor in thedetermination of the rate for intermediate disap-pearance. The parameters which resulted from theregression analysis of the experimental intermediatedata from the C3H8 oxidation experiments forthese expressions were as shown in Eq. (VII):

= _ 1 QU -7O±2.ooe x p ( _ (5O,OOO±5O65)/RT)

x [C2H.,)0-90-t°-08

x[CnH2«+2]-°-37±0-04 mole/cc-s (VII)

Both lean and rich experimental data were used inthe generation of these parameters. Once againFigure 7 shows a plot of the logarithm of theexperimental and overall rate constant versusiooo/r.

The hydrogen oxidation step in this overallscheme (Reaction 12) has been represented as:

d[H2] -d[U2O]

dt dt= -A exp(-EjRT) [H2]0

x[O2]b[C2H4]

c mole/cc-s (VIII)

Once again the experimentally determined quan-tities were the temperature T, [H2], [O2], and

10.88 .92 .96

1000/T (I /K)

FIGURE 7 Logarithm™ of the experimental and least-squares overall rate constant versus 1000/r for Reaction(11) (symbols: experimental; lines: least-squares fit).

[C2H4]. d[UoO]/dt was calculated from the ex-perimental data as well. The H2O concentrationwas determined from H atom balance consider-ations and the rate of H2O production is obtainedfrom the H2O concentration versus distance profiledetermined from this calculation. Similar to thecase of the intermediate rate of disappearance arate expression in terms only of the temperature,the H2 concentration, and the O2 concentration wasfound to be an inadequate representation of the H2oxidation kinetics. Late in the reaction C2H4 isoxidized to CO at a very fast rate and leads to arapid increase in the production of H2. The rateof H2 destruction, when only a function of the H2concentration, O2 concentration, and the tem-perature, cannot adjust to this sudden increase inthe rate of H2 production. The result is a largeovershoot in the H2 concentration. Since the tem-perature is increasing during this stage of the reac-tion, an adjustment of the activation energy couldreduce this overshoot. However, as in the case ofthe intermediate rate expression, a particular adjust-ment in the activation energy is not universal fromexperiment to experiment. Therefore, the inter-mediate specie concentration was included in the

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THE OXIDATION OF HYDROCARBONS 229

rate expression in an attempt to enable the rate ofH2 destruction to increase as the rate of inter-mediate oxidation increases.

Analysis of the rich and lean data which resultedfrom the C3H8 oxidation experiments generatedthe following parameters given in Eq. (IX):

d[H2] d[H2O]= -1013-52±2-2exp(-(41,000

dt dt

±6400)/RT) [H2]°-85±o.

X [C2H4J-0-56±0-20 mole/cc-s (IX)

A plot of the logarithm^ of the experimental andpredicted overall rate constant versus 1000/r canbe found in Figure 8. It is immediately apparentthat this functionality does not describe the exper-imental data in this case as well as in the othersteps. As a result, the disagreement between pre-dicted and experimental H2 and H2O concen-trations is expected to be larger than in the case ofthe other species.

10

10'

104.80 .68 .92

1000/T (I/K).96 1.00 1.04

FIGURE 8 Logarithm^ of the experimental and least-squares overall rate constant versus 1000/rfor Reaction(12) (symbols: experimental; lines: least-squares fit).

The initial rate expression for the oxidation ofCO was taken from an investigation on the oxi-dation of CO by Dryer and Glassman (1973).These experiments were for moist and lean exper-imental conditions. If one reviews the specie pro-files reported earlier for the lean oxidation ofhydrocarbons, the formation of C0 2 can be ob-served to occur with only very small amounts ofhydrocarbons being present. This observationsuggests the likelihood that the rate expression forCO oxidation reported by Dryer and Glassman(1973) would be a valid description of the CO oxi-dation rate during lean hydrocarbon oxidation.The expression reported was:

d[CO]

dtexp(-(40,000±1200)/7?r)

x [H2O]°-5 mole/cc-s (X)

Unfortunately, the use of Eq. (X) in rich stoi-chiometric environments resulted in a CO oxidationrate which was too large. In order to apply theDryer-Glassman (1973) results to rich conditions,it was found that a suppression factor, which was afunction of the initial equivalence ratio, wasnecessary in Eq. (X). Thus, Eq. (X) was rewrittenas:

d[CO]

dt= {-1014-5±°-25exp(-(40,000

±1200)/7?r)[CO][H2O]0-5

x[O2]°-25}x S mole/cc-s (XI)

The experimental data of Figures 2 and 3 wereused to evaluate S in the form

= 7.93 exp( -2 .4$ , (XII)

where $ is the initial equivalence ratio. The maxi-mum oxidation rate of CO is given by Eq. (X),which implies the suppression factor, S, has amaximum value of 1. If the suppression factor iscalculated to be greater than 1 by Eq. (XII), thenit is set equal to 1; this condition, of course, occursat j> = 0.84.

In summary, then, the total reaction schemeproposed to model lean and rich hydrocarbon oxi-dation consists of 4 overall Reactions, (10), (11),(9), and (12). Equations (III), (VII), (XI), and (IX)are the corresponding rate expressions and Eq.(XII) describes the suppression factor for the COoxidation rate.

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230 D. J. HAUTMAN et at.

VI. COMPARISONS OF PROPOSEDMECHANISM WITH EXPERIMENTALDATA

The worth of an overall reaction mechanism isdetermined by its ability to predict experimentaldata from various sources with a wide range ofinitial conditions. It is important to reiterate thatone major purpose in developing such a mechanismis to facilitate the calculation of the concentrationof the major stable intermediate and productspecies and the temperature (or heat release) his-tory. This section evaluates our proposed mech-anism in this context. The temperature profile wasdetermined by calculating the heat of reaction ofeach of the overall reactions. The symbols in thefigures to be presented are experimental results andthe lines are the calculated results from the pro-posed mechanism. The integration of the differen-tial equations was performed using a fourth orderRunge-Kutta numerical scheme. The time step foran individual calculation was always chosen toensure that there was no effect of the time step onthe calculated specie concentration profiles. Thevalues of the time steps were always around 3orders of magnitude smaller than the total reactiontimes.

In the integration of the proposed kinetic mech-anism it was still necessary to assume that a smallamount of fuel had reacted to form the intermediatespecie. However, in contrast to the extent of reac-tion rate expression (Eq. (II)) the resulting specieprofiles were somewhat insensitive to the initialconcentration of the intermediate specie. In otherwords, for the initial temperatures and specie con-centrations of this investigation the calculatedspecie profiles were not appreciably differentwhether it was assumed that 0.1 or 0.001 percent ofthe initial fuel had reacted to form the intermediatespecie. Consequently, in using this kinetic mech-anism it is recommended that the time step beapproximately 3 orders of magnitude smaller thanthe total calculation time and that the initial amountof fuel which is assumed to have reacted be on theorder of 0.01 percent of the initial fuel concen-tration. Of course, as with any numerical calcu-lation the sensitivity of the computed results to achange in these quantities should be investigatedthroughly.

Figures 9, 10, and 11 show comparisons betweenpredicted specie and temperature profiles and theexperimental data presented in Figures 1, 2, and 3.It is important to emphasize that these experiments

•51rr

3

- 0 4 i

20 40 60 80 100 120

DISTANCE FROV INJECTION (err.)

\

.A//C O * CVS ' ' yf •

./ -'A'

20 40 60 80 100 120

DISTANCE FRCM IN.'ECTICN (cm]

0.4 i

0.2-

0 .,-t

TEVPERATL'SE

nz? »o.3-;

/

20 40 60 80 100 120 140DISTANCE FROM INJECTION (cm)

FIGURE 9 Experimental and calculated specie concen-trations (mole fraction percent) and temperature (K) versusdistance from injection (cm) for a lean C3H8 oxidationexperiment (symbols: experimental; lines: calculated).

cover a wide range of equivalence ratios (0.12-1.59).These figures also reveal that the predictive abilityof the proposed mechanism is quite good. Further,they illustrate that the mechanism can predict boththe time delay in the release of the energy, which isobserved experimentally, and the time at which themacroscopic chemical events are occurring. Themajor deviations are with the H2 and H2O specieprofiles. As the intermediate reaches a maximumand begins to disappear at a very fast rate, the H2disappearance rate is not fast enough to prevent anovershoot in the H2 concentration. Since too muchH2 is produced, the H2O concentration is under-evaluated. Unfortunately this H2 overshoot hasnot been resolved and therefore extension of thismechanism to the richer equivalence ratios stillpresents some problems.

The calculations presented in Figures 9, 10, and11 were all started at the first measurement pos-ition. This procedure was necessary since the exactposition of time equal to zero in the flow reactor isunknown due to the initial mixing of the reactants.

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THE OXIDATION OF HYDROCARBONS 231

40 60 60 100

DISTANCE FROM INJECTION (cm)

120

CjH.xO.S6

20 40 60 80 100 120 140

DISTANCE FROM INJECTION (cm)

40 60 80 100

DISTANCE FROM INJECTION (cm)

120

1-1290 2

40 60 80 100DISTANCE FROM INJECTION (cm)

FIGURE 10 Experimental and calculated specie con-centrations (mole fraction percent) and temperature (K)versus distance from injection (cm) for a stoichiometricC3H8 oxidation experiment (symbols: experimental; lines:calculated).

20 40 60 80 (00 120

DISTANCE FROM INJECTION (cm)

',260 §

20 40 60 80 100 120 140DISTANCE FROM INJECTION (cm)

FIGURE 11 Experimental and calculated specie con-centrations (mole fraction percent) and temperature (K)versus distance from injection (cm) for a rich CaHs oxi-dation experiment (symbols: experimental; lines: calcu-lated).

The effect of this mixing zone is one of a dis-placement in the reaction time. Very fast^elemen-tary reactions enable the rapid adjustment of thechemistry to the local conditions as the flowapproaches radial uniformity. Consequently thereis no effect on the downstream kinetic results.However, as a result of the mixing zone the flowreactor data cannot provide any information on theinitiation kinetics of the oxidation process. Further,the validity of the proposed overall kinetic mech-anism in describing the initiation kinetics cannotbe ascertained from comparisons with the flowreactor experimental data. This determination canonly be made by extension of the proposed mech-anism to other experimental data where the initialmixing of the reactants is not a problem.

In an attempt to determine the validity of theproposed overall kinetic mechanism in the descrip-tion of the total oxidation process further com-parisons were made with data from a shock tubeinvestigation. The use of the shock tube techniquealleviates any problems associated with the initial

mixing of the reactants. Further, the temperatureand pressure ranges which are covered by theseinvestigations are very different from the con-ditions of the flow reactor technique. In par-ticular the shock data of Burcat et al. (1971a) wereutilized. Burcat et al. (1971a) used a reflected shockto raise the temperature and pressure to the initialreaction conditions. The initial reaction tempera-tures ranged from 1250 to 1600 K, the initial reac-tion pressures from 2 to 10 atmospheres, and theequivalence ratios of the various mixtures from0.125 to 2.0. Some specie profiles were reported inthis investigation, but sufficient information con-cerning the initial conditions was not provided toallow its use in the verification of the overallkinetic mechanism. Only ignition delay times wereavailable for this purpose. These times were definedas those corresponding to the advent of significantincreases in temperature and pressure. Some cri-terion was therefore necessary to obtain a calcu-lated ignition delay time from the proposed mech-anism. On careful examination of the flow reactor

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232 D. J. HAUTMAN et al.

TABLE IIIShock tube experimental initial conditions

Exp.no.

2A-751B-281D-441C-292B-794B-1564A-1302A-764A-1423A-112

T,K

1292137412741302153913401425130512621492

P,atmosphere

6.637.559.058.298.328.308.086.757.877.67

(C3H8),,mole/cc

5.00x10-" i3.2 xlO-7

3.42 xlO"6

I.24xlO-6 <5.53 x 10"7

6.04 xlO-7

2.83 xlO~7

5.04 xlO-7

3.12 xlO-7

2.57 xlO~7

(O2);,mole/cc

i.OOx 10-5

.61x10-6

.71 xlO-5

5.21 x 10-«l.38xlO-6

.21 xlO"5

.13xlO-5

5.04x10-6.25xlO-5

2.57x10-°

Phii

0.5001.0001.0001.0002.0000.2500.1250.5000.1250.500

results it was decided that significant energy releasebegan to occur as the intermediate concentrationreached a maximum. Therefore, with respect tofuture comparisons the calculated ignition delaytime was defined as the time to the occurrence of amaximum in the intermediate specie profile.

The initial conditions of the shock tube exper-iments used for comparison can be found in TableIII. The temperatures, pressures and initial fueland oxygen concentrations are larger than the flow

reactor conditions. Figure 12 presents for the firstset of shock tube initial conditions a plot of molefractions and temperature predicted by the new,overall mechanism versus time. The experimentalignition delay was 425 jusecs, whereas the calcu-lated ignition delay was 300 /xsecs. The experimen-tal time was a factor of 1.5 longer than the calcu-lated time. Comparisons with the experimentalignition delay times of the other shock tube experi-ments are presented in Table IV. Generally thereis a deviation of about a factor of two.

•I60O 5

O 0.008 0.016 0.024 0.032 0.040TIME (SI x 10"*

COj/3

0.006 0.016 0.024 0.032 0.040TIME(S)*IO"*

,H2O/4

0.008 O.C!6 0.024 0.032 0.040TIWE (Slx'0"1

FIGURE 12 Calculated specie concentrations (molefraction percent) and temperature (K) for a lean C3H8oxidation in a shock tube.

TABLE IVIgnition delay time comparisons (3rd generation)

Exp.no.

2a-751B-281D-441C-292N-794B-1564A-1302A-764A-1423A-112

fien(exp), s

4.25 xlO-1

4.15x10-"3.65x10-"3.90x10-"2.30x10-"1.40x10-"4.00x10-55.25x10""3.40x10-"7.70X10-5

/ign(calc), s

3.00x10-"3.18x10-"4.68x10-"2.94x10-"6.40x10-55.70x10-51.80x10-52.50x10-"1.50x10-"4.50x10-5

/ign(exp)/ign(calc)

1.421.300.781.333.592.462.222.102.271.71

When evaluating the degree of agreement inTable IV, it is necessary to consider a few miti-gating factors. The ignition delay times for theseshock tube experiments are at least 200 timesshorter than those under flow reactor conditions.Consequently, as the reaction time decreased by afactor of 200 the error increased only by a factor

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THE OXIDATION OF HYDROCARBONS 233

of 2. Further, the reaction temperature reported byBurcat et al. (1971a), is a calculated quantity basedon the measured shock velocity. An error of 5 per-cent in the reported reaction temperature resultsin deviations between the calculated and exper-imental ignition delay time being decreased from afactor of 2 to a factor of 1.2. A 5 percent error intemperature corresponds to a smaller percent errorin the velocity measurement (approximately 2.5percent). With these factors taken into account,the agreement between the calculated and exper-imental times can be considered excellent andindicates that the proposed mechanism is valid forthe total oxidation process as well as for a widerange of temperatures (960-1540 K) and pressures(1-9 atmospheres).

Under very lean conditions there can be furthersimplification of the scheme proposed, becauseunder such conditions the oxidation of H2 to H2Ooccurs very rapidly and a in Reactions (7) and (8)becomes very small. In fact, for equivalence ratiosless than 0.84 only Reactions (7), (8), and (9), witha = 0, are required to model the oxidation process.In addition, as predicted by Eq. (XII), no sup-pression of the CO oxidation rate is required. Therate expression for these overall reactions remainsas those given by Eqs. (VIII), (VII), and (X). If thespecific combustion phenomenon to be modelledalways operates in an equivalence ratio less than0.84, then there is no need to include the specie H2(i.e. another differential equation) in the calcu-lations.

Essentially the developments and comparisonsmade to this point were exclusively for propaneoxidation. Since a generalized overall kinetic mech-anism applicable to any paraffin fuel is also desir-able and the initial functionality (Eq. (I)) for therate expression of the first overall reaction wasobserved to be valid for a number of hydrocarbons,the ability of the proposed overall kinetic mech-anism to be extended to other hydrocarbons,C4H10, 3-methylpentane, and CsHis, was alsoinvestigated. The initial comparative results werenot as good as those which were presented for theC3H8. The predicted rates of reaction were fasterthan those of the C4H10 oxidation experiment andwere slower than the oxidation rates of 3-methyl-pentane and CsHis. Agreement can be improvedby a ±20 percent change in the pre-exponential ofthe fuel disappearance overall rate constant. Thecomparisons between the experimental and calcu-lated specie and temperature profiles are shown inFigures 13, 14, and 15. This correction is within

the scatter of the experimental data used in gen-erating Eq. (III). Therefore, the proposed overallkinetic mechanism and overall rate expressions area valid quantitative description of the oxidation ofhydrocarbons.

40 60 BO 100

DISTANCE FROM INJECTION (cm)

_ 04

40 60 80 100 120

DISTANCE FROM INJECTION (cm)

40 60 60 100 120DISTANCE FROM INJECTION (cm)

140

FIGURE 13 Experimental and calculated specie con-centrations (mole fraction percent) and temperature (K)for a lean C4H10 oxidation (symbols: experimental; lines:calculated).

The idea that the rates of oxidation of complexhydrocarbons are very similar has previously beenreported in the literature by Burcat et al. (1971b)and Siminski and Wright (1972). These investi-gators reported that the ignition delay times forvarious complex hydrocarbons were very similar.Once again the ignition delay time was defined asthe time to significant pressure and temperatureincrease. From the flow reactor data this eventcorresponds to substantial fuel disappearance.Therefore, their results indicate that the time tocomplete fuel disappearance for each of the complexhydrocarbons is nearly the same. In other words,an overall rate expression which descrjbes the rateof fuel disappearance should be very similar for allof these hydrocarbons.

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234 D. J. HAUTMAN el al.

C,H4X 0.34

20 40 60 60 100 120 110

DISTANCE FROM INJECTION (cm)

40 60 60 100 120

DISTANCE FROM INJECTION (cm!

980 £LJ

20 40 60 60 10.) 120 140DISTANCE FROM INJECTION

THE OXIDATION OF HYDROCARBONS 235

Cohen, R. S. (1977). Ph.D. Thesis, The high temperatureoxidation and pyrolysis of ethane. Department ofMechanical and Aerospace Engineering, PrincetonUniversity.

Cooke, D. F., and Williams, A. (1975). Shock tube studiesof methane and ethane oxidation. Combustion andFlame, 24, 245.

Dryer, F. L. (1972). Ph.D. Thesis, High temperature oxi-dation of carbon monoxide and methane in a turbu-lent flow reactor. Department of Mechanical andAerospace Engineering, Princeton University.

Dryer, F. L., and Glassman, I. (1973). High-temperatureoxidation of CO and Clij. 14th Symposium (Inter-national) on Combustion, The Combustion Institute,p. 987.

Dryer, F. L., and Glassman, I. (1978). Combustionchemistry of chain hydrocarbons, in alternate hydro-carbon fuels: Combustion and chemical kinetics,Vol. 62, Progress in Aeronautics and Astronautics,Amer. Inst. of Aero, and Astro., New York, p. 255.

Dryer, F. L., and Westbrook, C. K. (1979). Chemicalkinetic modelling for combustion applications, 54thMeeting of the Propulsion and Energetics Panel ofAGARD.

Edelman, R. B., and Fortune, O. F. (1969). A quasi-globalchemical kinetic model for the finite rate combustionof hydrocarbon fuels with application to turbulentburning and mixing in hypersonic engines and nozzles.AIAA Paper No. 69-86, presented at the AIAA 7thAerospace Sciences Meeting.

Fristrom, R. M., and Westenberg, A. A. (1957). Flamezone studies. IV: Microstructure and material trans-port in a laminar propane-air flame front. Com-bustion and Flame, 1,217.

Fristrom, R. M., Avery, W. H., and Grunfelder, C. (1958).Reactions of simple hydrocarbons in flame fronts—Microstructure of C2 hydrocarbon-oxygen flames.Seventh Symposium (International) on Combustion,p. 304.

Fristrom, R. M., and Westenberg, A. A. (1965). FlameStructure, McGraw-Hill, pp. 324 and 350.

Hautman, D. J. (1980). Ph.D. Thesis, Pyrolysis andoxidation kinetic mechanisms for propane. Depart-ment of Mechanical and Aerospace Engineering,Princeton University.

Levinson, G. S. (1959). High temperature preflame reac-tions of H-hepatne, Combustion and Flame, 9, 63.

Orr, C. R. (1963). Combustion of hydrocarbons behind ashock wave. Ninth Symposium (International) onCombustion, p. 1034.

Semenov, N. (1935). Chemical Kinetics and Chain Reac-tions, Clarendon Press.

Shtcrn, V. (1964). The Gas Phase Oxidation of Hydro-carbons, Pergamon Press, pp. 59-79.

Siminski, V. J., and Wright, F. J. (1972). Effect of homo-geneous additives on the auto ignition of hydrocarbonfuels. AFAPL-72-74, Air Force Propulsion Lab.,Air Force Systems Command.

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