Hydrocarbon ignition: Automatic generation of reaction mechanisms and applications to modeling of engine knock

Twenty-Fourth Symposium (International) on Combustion/The Combustion Institute, 1992/pp. 93-101

HYDROCARBON IGNITION: AUTOMATIC GENERATION OF REACTION MECHANISMS APPLICATIONS TO MODELING OF ENGINE KNOCK

AND

C. CHEVALIER*, W. J. PITZ #, J. WARNATZ*, C. K. WESTBROOK ~' AND H. MELENK ~ *Universitat Stuttgart lnstitut fur Technische Verbrennung Pfaffenwaldring 12 D-7000 Stuttgart 80, Germany *Lawrence Livermore National Laboratory P.O. Box 808 Livermore, California 94550 USA § fur lnformationstechnik Berlin Heilbronner Strasse 10 D-IO00 Berlin 31, Germany

A computational technique is described which automatically develops detailed chemical kinetic reaction mechanisms for large aliphatic hydrocarbon fuel molecules. This formulation uses the LISP language to apply general rules which identify the chemical species produced, the reactions between these species, and the elementary reaction rates for each reaction step. Reaction mechanisms for cetane (n-hexadecane) and most alkane filels C7 and smaller are developed using this automatic technique, and detailed sensitivity analyses for n-heptane and cetane are described. These reaction mechanisms are then applied to calculation of knock tendencies in internal combustion engines. The model is used to study the influence of fuel molecule size and structure on knock tendency, to examine knocki,lg properties of fuel mixtures, and to determine the mechanisms by which pro-knock and anti-knock additives change knock properties.

action rate or "'negative temperature coefficient" (NTC). The essential reaction steps in this sequence can be written schematically as

Introduction

Hydrocarbon ignition is controlled primarily by chain branching processes. At high temperatures (above 1100 K at atmospheric pressure) chain branching is provided primarily by the reaction I'2

R + O2 = RO2 (first O2 addition) The RO2 radical can undergo external or internal H atom abstraction:

H + 02 = O + OH a feature essentially independent of the structure or other features of the fuel molecule. At intermediate temperature (900 K -< T <- 1100 K) additional chain branching is introduced by the sequence 3

RO2 + RH = ROOH + R (external abstraction) ROOH = RO + OH or

RO2 = QOOH

(chain branching)

(internal abstraction)

HO~ + RH = H202 + R

QOOH = QO + OH

H202 + M = OH + O t t + M

QOOH = Q + HO2

(chain propagation) (chain propagation)

where R is an alkyl radical, Q is an olefin structure, and the other terms are defined followin~g the common terminology of Benson5 and Pollard. Note that external H atom abstraction leads to pronounced chain branching, while internal abstraction leads only to chain propagation. Under practical conditions of interest, internal H

Finally, at lower temperatures (T -< 900 K), there is degenerate chain branching, 4'5 characterized by prodnction of chain branching precursors, ROe radicals in this context, which decompose as temperature increases above about 800 K. Disappearance of the chain branching agent ROz leads to an inverse temperature dependence of the overall re93

94

NUMERICAL METHODS

atom abstraction dominates these paths and no distinct acceleration of the ignition process can be expected as a result of the first O2 addition step. 7`s This conclusion has been observed in experimental studies. 9-11 In contrast, a second addition of O2 can be shown5'6 to lead to extensive chain branching. The addition is made to the QOOH radical:

4

3 2

~ 1 ~, s

QOOH + O2 = O2QOOH

(second O2 addition)

Again, the radical can undergo external or internal H atom abstraction: O2QOOH + RH = HOzQOOH + R , (external abstraction) HO2QOOH = HO2QO + OH HOzQO = OQO + OH

(chain branching)

(chain propagation)

or O2QOOH = HO2Q'OOH

(internal abstraction)

HOzQ'OOH = HO2Q'O + OH HO2Q'O = OQ'O + OH

(chain branching)

(chain branching)

The OQO and OQ'O indicated here, depending on the details of their structure, can represent relatively stable dicarbonyl species or decompose into two other oxygenated species, often aldehydes. In contrast to the first O, addition, both external and internal H atom abstraction lead to chain branching. Thus the second 02 addition path produces extensive chain branching and accelerated ignition. Low temperature processes outlined above are strongly dependent upon the size and structure of the fuel molecule. Rates of internal H atom abstraction vary, with the type of C--H bond being broken (i.e. primary, secondary, or tertiary) and the number of atoms in the ring-like transition state structure formed to transfer the H atom. 3'6'8 Detailed kinetic reaction mechanisms have been assembled, based on the above sequences of reactions, for a considerable number of fuels from C2 to C7 hydrocarbons 3'7's'12'13 and used to compute ignition delay times and the NTC region. An example of this type of result is shown in Fig. 1 for constant volume ignition of n-heptane at 3, 13.6 and 40 bar plressure, and temperatures between 650 and 1250 K. 0 The reaction mechanism required to carry out these simulations for n-heptane included 1000 elementary reactions among 170 different chemical species.

~ o~176

-1

--2

-31

0.6

...... 40 bar

01.8

1.0

1.2 11.4 1000/1" (K)

11.6

1.8

FIG. 1. Ignition delay times for stoichiometric nheptane/air mixtures. Points are experiments from Adomeit, ~ curves are computed results. perature submechanisms are particularly complex and grow in size and detail very rapidly, involving many isomeric structures. The time and effort required to enumerate individual chemical species and elementary reactions which describe the fuel ignition becomes extremely large, and there is ample opportunity for error in developing the enormous reaction mechanisms. Although these mechanisms are very large, there are a limited number of reaction types. Therefore it is possible to develop and apply families of general rules governing the reactions and their rate expressions. For example, a rule R1 might be R1 If (x is an alkyl radical) Then (/3-decomposition ofx is a possible reaction) We developed an extensive list of the rules for aliphatic hydrocarbon oxidation and a computer program designed to implement those rules and produce automatically a detailed kinetic reaction mechanism for a wide variety of fuel molecules. We also compared mechanisms developed in this way with mechanisms written entirely by hand, a process we have found to be laborious, time-consuming, and filled with misprints and inconsistencies. The LISP language was chosen for its flexibility. It is possible to add, withdraw, activate or deactivate rules independently of each other. The rules act on two levels:

Automatic Generation of Reaction Mechanisms:

1. Reactions are deduced from new or generated species. 2. Each new species is investigated for necessary redefinition (e.g. two neighboring radical sites are connected into a double bond).

As the size of the fuel molecule increases, the reaction mechanism size also increases. Low tem-

Molecules are described as graphs (Sorted Trees), where the heaviest atom is the root, to which

AUTOMATIC GENERATION OF REACTION MECHANISMS branches are linked. Branches have priority orders, which are also determined using atom weights. Radicals are explicitly expressed as artificial elements, in order to control their position. Each molecule can easily be analyzed (e.g. molecules having an O-O-H group, or containing only H and C atoms can be identified), and all possible new species required by the general rules are identified. The mechanism is generated, starting with the considered fuel molecule, down to C4 species. Two different C1-C4 submechanisms were used in these calculations. A new version of the C1-C4 chemistry submechanism (based on the CEC kinetic data evaluation14) was used in some of the calculations, while in other computed results an earlier C1-C4 submechanism was used, based on our previous modeling studies. 3 For the present cases, the computed results were not very sensitive to which C4 submechanism was used, but the more recent version14 is recommended for future work. The entire list of rules cannot be included, due to limits in the extent of the paper. However, most of the details are included in our recent publications3'8 and can be obtained from the authors.

Reaction Types: Ignition is initiated by molecular decomposition, near the center of its main chain, and the rate expression depends only on the type of the C---C bond. The fuel is also consumed by H atom abstraction by radical species, with the rate coefficient dependent on the type of radical and on the type of C - - H bond (i.e. primary, secondary, or tertiary). At elevated temperatures, the resulting alkyl radicals decompose via/3-scission and isomerize by internal H atom abstraction. At lower temperatures (T < 900 K), reactions of alkyl radicals involve primarily addition of molecular oxygen. Following Benson, 5 a bimolecular addition rate coefficient of 2 • 1012 cm3/mol-s was taken, and the reverse reaction rate coefficient recommended by Morgan et al. 15 (2 • I01~ exp(-28000/RT) s -z) was used. The ROe radical can isomerize via internal H atom abstraction, with the rate dependent on the type of C - - H bond being broken and on the size of the ring-like transition state which is formed, producing a QOOH radical. The QOOH radical can decompose into epoxides and OH radicals, or into olefins and HOz radicals, depending on the detailed structure of the QOOH radical, or a second O2 can add to the QOOH species, followed by another internal H atom abstraction. It is assumed that the first decomposition of the HO2Q'OOH species, producing OH and a carbonyl group, has a rate of 1.1 • 10~ exp(-7500/RT), while the second decomposition has a higher activation energy (k = 8.4 • 1024 exp(-43000/RT) s 2). Finally, the OQ'O radicals

95

then decompose via/3-scission. The rates of these steps have all been taken from previous studies. 3'6'8

lgnition Results: Using the techniques described above, we generated a mechanism for the calculation of ignition delay times of n-heptane/air mixtures, containing 2400 reactions and 620 different species. Using an IBM 3090, one ignition delay simulation required 20 minutes. Computed results under constant volume conditions are compared with experimental measurements in Fig. 1, for stoichiometric mixtures at 13.6 and 40 bar pressures. Computed and measured results agree well, and both demonstrate a negative temperature coefficient between 750 and 900 K. A detailed sensitivity analysis based on the OH concentration was carried out, revealing the principal rate limiting reactions. The results, summarized graphically in Fig. 2, report the relative change in peak OH concentration with an increase in the forward rate constant of the reaction indicated and show that in addition to H atom abstractions and alkyl /3-scission, successive Oz addition steps and isomerization reactions are very important. A mechanism for the oxidation of cetane (n-hexadecane) was also generated, consisting of 7000 reactions and 1200 species. One ignition calculation lasted 50 minutes on an IBM 3090. Calculated ignition delay times of stoichiometric cetane-air mixtures at 13.6 bar and constant volume are plotted in Fig. 3. Because no experimental results were available for cetane, experimental results for n-heptane are shown for illustration purposes. Again the computed results display a marked NTC region at essentially the same temperatures as observed for n-heptane. A sensitivity analysis like that in Fig. 2 was carried out with respect to one of the possible hexadecyl radicals, and results are shown in Fig, 4. Although this is not an exhaustive analysis, and many other sensitivity parameters would be needed for a complete study, it is clear from Fig. 4 that the same key reaction types are important in cetane ignition as for n-heptane ignition. The results for cetane ignition serve as a feasibility demonstration that the present LISP approach for automatic mechanism generation can successfully yield a description of ignition of this large class of hydrocarbon fuels and could be applied to any related fuel of interest. A reaction mechanism for oxidation of an isomer of heptane required about 5-10 hours to write. Testing for mistakes and typing errors required additional days of personal effort. The comparable task for cetane would probably consume weeks of personal effort and was not attempted. The execution of the LISP program for such fuels required only minutes of computer time, and although we still must examine

96

NUMERICAL METHODS

C7H16+O2-*3-C7H15+HO2 C7H16+O2-->2-C7H15+HO2 C7H16+OH-*3-C7H15+H20 C7H16+0H-*2-C7H15+H20 C7H16+OH-*1-C7H15+H20 C7H16+HO2-*3-C7H15+H202 C7H16+HO2--~2-C7H15+H202 2-C7H15-*C3H6+p-C4H9 3-C7H15-,1-C4H8+n-C3H7 2-C7H15+O2-*2-C7H1502 2-C7H1502-*2-C7H15+02 3-C7H15+O2-*3-C7H1502 3-C7H1502-*3-CTH15+02 3-C7H1502-*3CT(5OOH) 3C7(5OOH)-*3-C7H1502 3CT(5OOH)+O2-*C7(3OO)(5OOH) C7(3OO)(5OOH)-*3C7(5OOH)+O2 C7(3OO)(5OOH)-*4C73504H2 4C73504H2-*C7(3OO)(5OOH) 4C73504H2-*4C73503H+OH

m

m

m

m /

m

m

m

n

mz

m m I

m

0

-1

m

1

Sensitivity

FIG. 2. Sensitivity analysis for OH concentration in n-heptane/air mixture. Pressure is 13.6 bar, temperature is 833 K.

their mixtures. These fuels (primary reference fuels, or PRF's) were chosen because they define the octane number scale, with n-heptane as octane number 0 and iso-octane as octane number 100. Mixtures of iso-octane/n-heptane then define the octane number scale, with octane number equal to the percent of iso-octane in the mixture. Octane numP ber for another automotive fuel is then conveO) _o niently defined as the octane number of a PRF mixture which knocks at the same condition as the automotive fuel. In the present work we examine the roles that fuel molecule size and structure play in determining knocking tendency, and we have analyzed the kinetic factors by which additives, both 1 I~ 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2~0 pro-knock and anti-knock compounds, alter knock chemistry. 1000/T (K) Reaction mechanisms were established for ethane, Fic. 3. Calculated ignition delay time for a stoi- propane, two isomers of butane, three forms of chiometric cetane-air mixture at 13.6 bar. Points are pentane, five forms of hexane, and seven of nine experimental results for n-heptane/air from Adomeit1~ isomers of heptane. The mechanisms were used to simulate end gas reactions during compression and and shown in Fig. 1. flame propagation periods in an engine. The end gas is the last portion of combustible gas the results very closely, the process is much less mixture to be consumed by the premixed flame in subject to errors and inconsistencies. an engine. 16 This end gas is heated and compressed by piston motion and by the moving flame and would eventually ignite spontaneously and produce Applications: knock, given sufficient time. Under normal engine In a previous paper, 3 we focused on ignition of operation, however, the flame consumes the e n d n-heptane, iso-octane (2,2,4-trimethyl pentane), and gas before this ignition occurs and knock is avoided. 7

'

I

'

I

'

I

I

i

I

i

I

AUTOMATIC GENERATION OF REACTION MECHANISMS

C16H34+O2-->8-C16H33+HO2 C16H34+OH-->8-C16H33+H20 C16H34+HO2-->8-C16H33+HO2 8-C16H33-->1C7H15+1C9H18 8-C16H33+O2-->8-C16H3302 8-C16H3302-->8-C16H33+O2 8-C16H3302-->6-Cet-8OOH 6-Cet-8OOH-->8-C16H3302 6-Cet-8OOH+O2-~Cet-6OO-8OOH Cet-6OO-8OOH-->6-Cet-8OOH+O2 Cet-6OO-8OOH-->7Cet-6,804H2

_

7Cet-6,804H2~Cet-6OO-8OOH 7Cet-6,804H2-->Cet6803H +OH Cet6803H->Cet6802+OH g

nu

97

m

m

g

m

[]

n []

i

m

m

m

m I

[]

m

m

m

0 Sensitivity

1

FIC. 4. Sensitivity analysis for OH concentration in cetane/air mixture. Pressure is 13.6 bar, temperature is 833 K.

We previously 3's showed that computed ignition delay times can be correlated with octane number, with fuels having higher octane numbers igniting later than fuels with lower octane numbers. The model assumes that the end gas follows the pressure-time history taken from a CFR engine operating at 600 rpm with the critical compression ratio for 90 Research Octane Number (RON).17 When fuel with RON less than 90 is used in this engine, knock is observed at about 58 ms after bottom dead center (TDC is at 50 ms). During this time the end gas, compressed against the wall of the engine chamber furthest from the spark plug, loses heat to the chamber wall. This heat transfer is treated in the model by a Newtonian heat loss term in the energy equation and calibrated by requiring that a mixture of 90% iso-octane/10% n-heptane (i.e. 90 octane PRF) ignite at 58 ms, consistent with experimental observations. With the same pressure-time history and heat transfer coefficient, the model then integrates the kinetic rate equations for each fuel being examined. The mixture autoignites at a time which varies from one fuel to another, although several of the very high octane number fuels did not ever ignite with this prescribed pressure history. Computed times for autoignition are interpreted in the following way. Mixtures that ignite earlier than 58 ms are predicted to have octane numbers less than 90, while mixtures that ignite later than

58 ms or do not ignite are interpreted as having octane numbers greater than 90. Furthermore, if one fuel ignites earlier than a second fuel, the model is predicting that the first fuel has the smaller octane number. Results of application of this approach to the present fuels are summarized in Table I. It is evident that all fuels with RON < 90 are calculated to ignite earlier than 58 ms, and all fuels with RON < 90 ignite later than or at 58 ms, with the single exception of n-butane which ignites at 57.6 ms and has RON = 94. In addition, the general trends in relative ordering among the fuels are fairly consistent, except for 3-methyl pentane and 3-ethyl pentane, which are predicted to ignite more slowly than their RON = 74 and 65 would suggest, and 3,3dimethyl pentane, which ignites more rapidly than its RON = 81 would suggest. Note that these three fuels have similar structural features, so these discrepancies may indicate that one or more of the rules used in the model for certain types of internal H atom transfer processes need improvement. Sensitivity analyses of these computations show that, consistent with results in Figs. 2 and 4, the most important reactions include internal H atom abstraction reactions. Rates of those reactions depend strongly on the types of C - - H bonds in the fuel, and on the strain energy barriers involved which in turn depend on the size of the fuel molecule. For fuels which are long and have many

98

NUMERICAL METHODS TABLE I Computed times of ignition for selected alkane fuels using RON 90 pressure history Time of ignition Fuel

n-heptane n-hexane 75% n-heptane/25% iso-octane 2-methyl hexane 50% n-heptane/50% iso-octane n-pentane 3-ethyl pentane 2-methyl pentane 3-methyl pentane 25% n-heptane/75% iso-octane 3,3-dimethyl pentane 2,4-dimethyl pentane 2,2-dimethyl propane 10% n-heptane/90% iso-octane 2-methyl butane 2,2-dimethyl butane 2,2-dimethyl pentane n-butane 2,3-dimethyl butane 2,2,4-trimethyl pentane 2-methyl propane propane 2,2,3-trimethyl butane ethane

CTHl~ C~HI4

C7H16 CsH 1~ C7H16 C6H14 C6HI4 CTH~ CTHI6 C5H~2 C~HI2 C~H~4 CTHj6 C4H~o C6H~4 C~H~8 C4Hlo C3H8 C7H~6 CzH6

RON

(ms)

0 25 25 42 50 62 65 73 74 75 81 83 86 90 92 92 93 94 100 100 102 112 112 115

55.0 55.0 55.3 54.5 55.8 55.9 57.4 55.5 57.2 56.7 55.7 56.2 56.4 58.0 59.1 59.9 57.6 58.0 58.5

*no ignition

rather weakly bound secondary H atoms, isomerization rates are large and lead to rapid ignition. For fuels which are compact, highly branched, and have a large fraction of strongly bound H atoms at primary sites, ignition is inhibited. These trends are responsible for long-known but poorly understood correlations18 that straight-chain hydrocarbon fuels have low octane numbers and knock readily, while highly branched fuels are relatively knock-resistant. The overall correlation between RON and computed ignition time is plotted in Fig. 5. The solid curve is drawn to indicate results for PRF fuel mixtures of n-heptane and iso-octane, and the dashed curves indicate limits of -+0.5 ms about the solid curve. Most computed results lie within this band, with the exceptions already noted above. An interesting feature of the overall trend shown in Fig. 5 is the slow variation in ignition time at small octane numbers and the significant acceleration in this variation as RON increases beyond a value of about 80. This type of sensitization is quite familiar in ignition chemistry, where a very ignition-resistant fuel is rapidly degraded by the addition of a more readily

ignited component. The most common example of this behavior is observed for mixtures of methane with higher hydrocarbons. 19 Fuel Mixtures: Since real automotive fuels consist of complex mixtures of hydrocarbons, it is important to be able to predict the autoignition properties of such mixtures. Often ignition properties of mixtures can be much different from average properties of the separate components. An example of this property is provided by the solid curve in Fig. 5 for mixtures of n-heptane and iso-octane, showing that the ignition time of these mixtures varies nonlinearly with RON. Following the experimental study of Croudace and Jessup, z~ we examined binary mixtures of hexane isomers. For most of these mixtures, linear blending was predicted, meaning that the weighted average of the RON values of the components accurately predicted the computed ignition time of the mixture. Because of the nonlinear relationship between RON and ignition time in Fig. 5, it was

AUTOMATIC GENERATION OF REACTION MECHANISMS 60

99

fect results from decomposition of the hydroperoxide at the O - ~ bond, producing large amounts of ~ OH and alkoxy (RO) radicals as the temperature exceeds 900 K. The key to this process is the 43.0 E 58' kcal/mol activation energy of the O---O bond/ 9 , ~ //'x breaking reaction. In addition, the alkoxy radical r E decomposes rapidly and produces an alkyl radical and another reactive carbonyl species, both of which O 56. further accelerate ignition. H202 was found to be r less effective than the alkyl hydroperoxides as a proknock additive. Although its decomposition produces twice as many OH radicals, its higher dissociation activation energy of 45.5 kcal/mol makes 54 25 50 75 1 0 it decompose somewhat later in time, when the end gas ignition has already begun. Also, the OH radResearch Octane Number ical has a less accelerating impact on the ignition FIG. 5. Computed times of autoignition for C2-'---C7 than the alkoxy radical from ROOH decomposition. fuels, showing the correlation with research octane From previous modeling work, 2~ it is clear that knocking ignition takes place when end gas temnumber (RON). peratures are high enough to produce HzO2 decomposition, so H2Oz addition would not be exalso observed that the weighted average ignition pected to change significantly the time of onset of delay time was generally not the same as the com- ignition. puted ignition time of each mixture. Azo-t-butane and t-butyl peroxide had the greatest pro-knock effects of the additives studied. Although neither species produces OH radicals, both Pro-knock and Anti-knock Additives: decompose quite early in the engine cycle and proMany chemical species have a disproportionately duce large amounts of alkyl radicals which lead to large influence on autoignition and knock. Some chain branching through the low temperature seadditives promote knocking, while others inhibit ig- quences discussed above. Although the concentranition. Previously, we examined the influence of tions considered here are very small, rapid decomtetra-ethyl lead (TEL) as an antiknock additive, 21 position of these additives produces radical levels heterogeneously removing radicals, primarily HO2, much greater than those which can be produced by the fuel at such early times. The timing of these from end-gas reactions. Here we use the numerical model to investigate the kinetic factors involved with decomposition reactions depends on their activation gas-phase additives. Additive species considered were energies, which are sufficiently low (43 and 47 kcal/ acetaldehyde, methanol, acetone, olefins such as mol respectively) that radicals are added to the rehexenes, pentenes, and isobutene, hydroperoxides acting end gases much earlier than ordinarily availincluding methyl-, t-butyl-, p-butyl, and hexyl-hy- able, promoting their ignition. As environmental concerns have virtually elimidroperoxides, ethers including dimethyl ether, methyl tert-butyl ether (MTBE) and ethyl tert-bu- nated lead alkyls in gasolines, other anti-knock spetyl ether (ETBE), and peroxides including hydro- cies have become increasingly useful. In particular, gen peroxide and t-butyl peroxide, and azo-t-bu- partially oxygenated species such as MTBE and tane. These additive species can be fuels themselves ETBE are currently in wide use. However, surand blended with other fuels in mixtures. How- prisingly little is known about the kinetic reasons ever, in the present analyses, these species were for their effectiveness. We used a previously de. 2223 " a added to hexane or heptane fuels in small amounts, veloped reachon meehamsm for MTBE ' oxld usually less than 1% of the total fuel, to identify tion and followed the same procedure described additives which would produce a particularly large above to study MTBE as an additive. Model results reproduced the observed strong anti-knock activity change in the ignition time. The same pressure-time compression history as above was followed until ig- of MTBE. For example, addition of MTBE to nnition was observed or until the engine cycle was hexane where MTBE was only 5% of the total fuel increased the ignition time from 55.0 ms to 55.7 complete. Some of the additives produced little or no change ms. From the correlation of Fig. 5, this is an inin the computed time of ignition, including ace- crease in RON from 25 to 48. Further addition of tone, methanol, acetaldehyde, and the olefin spe- MTBE led to proportionately large increases in cies. All alkyl hydroperoxides produced strong pro- RON, to the point that a mixture of 85% n-hexane/ knock effects, reducing ignition times for all fuels 15% MTBE was predicted to have a RON of 93. The activity of MTBE was found to be the result examined9 The kinetic model showed that this ef/

.

100

NUMERICAL METHODS

of several factors. H atom abstraction from MTBE removes radicals from the reaction, and decomposition of the resulting radicals produces stable intermediate species. The same radicals do not produce degenerate chain branching and OH production at low temperatures. In addition, MTBE produces isobutene which also scavenges radicals and produces very unreactive resonantly stabilized radical species including 2-methyl allyl and allyl radicals. This process effectively produces a significant amount of radical chain termination and greatly retards end gas ignition under end gas conditions. The same processes were demonstrated for ignition inhibition in propane/MTBE mixtures in shock tubes ~ at much higher temperatures. Conclusions For processes as complex as engine knock, kinetic modeling provides a powerful tool for analysis and yields information and kinetic insights that are unavailable by any other means. The above examples demonstrate how a model can interpret experimental observations of the importance of fuel molecular size and structure on knock tendency, and observations of the influence of various additives on knocking, but many other types of applications are also possible. One serious dit~culty and potential obstacle to the development of such kinetic models is their immense size as the size of the fuel species increases. The automatic techniques described above, using computational skills adopted from the artificial intelligence field, greatly accelerate the process of mechanism development and significantly reduce the errors that traditional methods inevitably produce. REFERENCES 1. WARNATZ,J.: Eighteenth Symposium (International) on Combustion, p. 369, The Combustion Institute, 1981. 2. WESTBROOK, C. K. AND DRYER, F. L.: Eighteenth Symposium (International) on Combustion, p. 749, The Combustion Institute, 1981. 3. WESTBROOK, C. K., WARNATZ, J. AND PITZ, W. J.: Twenty-Second Symposium (International) on Combustion, p. 893, The Combustion Institute, 1989. 4. WARNATZ,J., EBERT, K. H., DEUFLHARD,P. AND JAGER, W. (Eds.): Modeling of Chemical Reaction Systems, p. 162, Springer, Heidelberg, 1981.

5. BENSON, S. W.: Prog. Energy Comb. Sei. 7, 125 (1981). 6. POLLARD, R. T.: Comprehensive Chemical Kinetics, Vol. 17, Gas-Phase Combustion (C. H. Bamford and C. F. H. Tipper, Eds.), Elsevier, New York, 1977. 7. CHEVALIER,C., LOUESSARD,P., MULLER, U.-C. AND WARNATZ, J.: Second Int. Syrup. on Diagnostics and Modelling of Combustion in Internal Combustion Engines, p. 93, Kyoto, 1990. 8. WESTBROOK, C. K., PI~Z, W. J. AND LEPPARD, W. R.: Society of Automotive Engineers 8AE912314 (1991). 9. VolNOV, A. S., SKOROLEDOV, D. I., BORISOV,A. A. AND LYUBIMOV,A. V.: Russ. J. Phys. Chem. 41, 605 (1967). 10. KIRSCH, L. J. AND QUINN, C. P.: Sixteenth Symposium (International) on Combustion, p. 223, The Combustion Institute, 1977. 11. ADOMEIT, G.: Personal Communication (1989). 12. WILK, R. D., PITZ, W. J., WESTBROOK, C. K. AND CERNANSKY, N. P.: Twenty-Third Symposium (International) on Combustion, p. 203, The Combustion Institute, 1991. 13. WILK, R. D., CERNANSKY, N. P., PlVZ, W. J. AND WESTBROOK, C. K.: Combust. Flame 77, 145 (1989). 14. BAULCH, D. L., JUST, T., KERR, J. A., PILLING, M., TROE, J., WALKER, R. W. AND WARNATZ,J.: J. Phys. Chem. Ref. Data, in press (1992). 15. MORGAN, C. A.: J. Chem. Soc. Faraday Trans. 2, 1313 (1982). 16. COWART, J. S., KECK, J. C., HEYWOOD, J. B., WESTBROOK, C. K. AND PITZ, W. J.: TwentyThird Symposium (International) on Combustion, p. 1055, The Combustion Institute, 1991. 17. LEPPARD,W. R. : personal communication (1987). 18. LOVELL, W. G.: Indust. Engr. Chem. 40, 2388 (1948). 19. WESTBROOK, C. K.: Combust. Sci. T e c h 20, 5 (1979). 20. CROUDACE, M. C. AND JESSUP, P. J.: Society of Automotive Engineers SAE-881604 (1988). 21. PITZ, W. J. AND WESTBROOK, C. K.: Combust. Flame 63, 113 (1986). 22. BROCARD, J. C., BARONNET, F. AND O'NEAL H. C.: Combust. Flame 52, 25 (1983). 23. CURRAN, H. J., DUNPHY, M. P., SIMMIE, J. M., WESTBROOK, C. K. AND PITZ, W. J.: TwentyFourth Symposium (International) on Combustion, p. xxx, The Combustion Institute, Pittsburgh (1992). 24. GRAY, J. A. AND WESTBROOK, C. K.: submitted for publication (1992).

AUTOMATIC GENERATION O F REACTION MECHANISMS

101

COMMENTS K. Kailasanath, U.S. Naval Research Laboratory, USA. It is fascinating that you are able to generate a reaction mechanism for such complex fuels. Once you have a mechanism, how do you obtain the relevant rate parameters (activation energy, temp. coefficient etc.) for all the reactions? Is that experimental data or do you have a theoretical approach?

Author's Reply. Rate parameters for most reactions of these large species have never been determined, either experimentally or theoretically. This is especially true if one is concerned with site-spe-

cific reaction rates. Therefore, we usually assume that site-specific H atom abstraction rate are equal (per C - - H bond) with rates of the same reactions in smaller molecules which have been studied experimentally. Similarly, rates of other reactions can be modeled after analogous reactions in species which have been studied. Sensitivity analysis then shows that this type of procedure provides rate expressions which, although certainly not exactly precise, are still sufficiently accurate to suit our present modeling needs. The complete explanation of this procedure and the rate expressions used for the present calculations can be found in Reference 8 of the present paper.