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1985

Soot Formation During Pyrolysis of AromaticHydrocarbons (Modeling, Shock-Tube, Acetylene,Butadiene).David Warren ClaryLouisiana State University and Agricultural & Mechanical College

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Recommended CitationClary, David Warren, "Soot Formation During Pyrolysis of Aromatic Hydrocarbons (Modeling, Shock-Tube, Acetylene, Butadiene)."(1985). LSU Historical Dissertations and Theses. 4121.https://digitalcommons.lsu.edu/gradschool_disstheses/4121

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8610631

C lary , David W a rre n

SOOT FORMATION DURING PYROLYSIS OF AROMATIC HYDROCARBONS

The Louisiana State University and Agricultural and Mechanical Col. Ph.D. 1985

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SOOT FORMATION DURING PYROLYSIS OF AROMATIC HYDROCARBONS

A Dissertation

Submitted to the Graduate Faculty of the Louisiana State University and

Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of •

Doctor of Philosophyin

The Department of Chemical Engineering

byDavid W. Clary

B.S., Louisiana State University, 1981 December, 1985

ACKNOWLEDGMENTS

I wish to thank Dr. Michael Y. Frenklach for his time, advice and support as my dissertation advisor. These wishes must also be extended to Dr. Arthur Sterling for serving as acting chairman of my advisory committee. I would like to express my appreciation to Dr. David Miller for his valuable comments and suggestions and especially to my wife Pamela for her love and support.

This work was sponsored in part by the Office of Fossil Energy, U. S. Department of Energy, under the auspices of Grant No. DE-FG22-80PC30247, and NASA-Lewis Research Center, Contract No. NAS 3-23542 and Grant No. 3-477. I wish to acknowledge support from the National Science Foundation's Graduate Fellowship Program.

TABLE OF CONTENTS

ACKNOWLEDGMENTS ............................................. iiTABLE OF C O N T E N T S ............................................iiiLIST OF T A B L E S ............................................... viLIST OF F I G U R E S .............................................viiiA B S T R A C T .....................................................xiv

Chapter pageI. INTRODUCTION...................................... . 1II. LITERATURE SURVEY .................................. 6

Experimental Observations ....................... 6General Comments ............................. 6Structure of S o o t .............................. 7Shock-tube and High-Temperature Flow

Studies ................................ 8Aromatic Hydrocarbons .................... 10Aliphatic Compounds ....................... 15

Laminar Flames ................................ 17Laminar Premixed Flames .................. 17Laminar Diffusion Flames ................ 21

Pathways for Soot Formation...................... 24Initial Reactions ........................... 24

Nonaromatic Fuels ......................... 24Aromatic Fuels ........................... 25

Particle Inception ........................... 31Chemical Nucleation ....................... 31Physical Nucleation ....................... 35

Ions in Soot Formation........................ 38Surface Growth, Coagulation and

A g g r e g a t i o n .............................42Surface Growth ........................... 42Coagulation and Aggregation .............. 45

S u m m a r y .............................................46III. EXPERIMENTAL FACILITIES AND PROCEDURES ........... 48

IV. EXPERIMENTAL R E S U L T S .................... ........... 57V. EMPIRICAL MODELING OF SOOT FORMATION FROM

A R O M A T I C S ...................................... 77Introduction .................................... 77D i s c u s s i o n ........................................ 79

Statement of the P r o b l e m ...................... 79Derivation...................................... 81Model F i t ...................................... 86

Summary . . . . . . . . ......................... 98VI. DETAILED KINETIC MODELING OF SOOT FORMATION

IN SHOCK-TUBE PYROLYSIS OF ACETYLENE . . . . 99Introduction ....................................99Computational Model ........................... 100

Reaction Species Nomenclature.............. 101Reaction Mechanism ......................... 149

Results and Discussion ....................... 166Formation of the First Aromatic Ring . . . 166Formation of Two-Ring Aromatics.. ......... 169Further Growth of Fused Polycyclic

A r o m a t i c s ........................... 172Species Concentration Profiles . . . . . 174Formation of S o o t .................. 185

Conclusions ........................... 194VII. SENSITIVITY ANALYSIS OF THE SOOT-FORMATION

M E C H A N I S M .................................. 195Introduction .................................. 195Computer Experiments ......................... 196Results and Discussion ....................... 200Conclusions....................................... 208

VIII. MODELING OF FUEL-STRUCTURE EFFECTS ON SOOTF O R M A T I O N ..................................... 209

Introduction . 209Butadiene and Ethylene ....................... 210

Computer Model .............................. 210Results and Discussion .................... 250

B u t a d i e n e ...................................250E t h y l e n e ...................................256

B e n z e n e ............................................263Computer Model ....................... 263R e s u l t s ....................................... 268

Conclusions....................................... 279

- iv -

IX. CONCLUSIONS AND RECOMMENDATIONS . . . . . . . . 280X. LITERATURE CITED ................................... 283

Appendix pageA. DETAILS OF EXPERIMENTAL D A T A ........................297B. V I T A ................................................... 302

- v -

LIST OF TABLES

Table IV. 1 V. 1

VI. 1

VI.2 VI.3

VI.4 VI.5 VI .6

VII. 1 VII.2

VII.3

VIII. 1

VIII.2

VIII.3

VIII.4

TitleRanges of experimental conditions.Ranges of experimental conditions.Reaction species structures and assigned names.Core reactions of acetylene mechanism.Reaction classes and rate coefficient expressions.Reaction list.Formation of the first aromatic ring.Sensitivities of soot yield with respect to rate coefficients and equilibrium constants.Sets of thermodynamic data.Sensitivities of soot yield with respect to rate coefficients and equilibrium constants for reaction classes.Sensitivities of soot yield with respect to rate coefficients and equilibrium constants for initiation reactions with thermochemical set S4.Core reactions for butadiene and ethylene mechanisms.Reaction list for butadiene and ethylene mechanisms.Additional reaction species and assigned names.Additional reaction classes and rate coefficient expressions.

Page5887

102150

152155168

193199

204

205

2 1 1

215

224

249

- vi -

VIII .5

VIII .6

VIII.7 VIII.8

VIII.9

Sensitivities of soot yield with respect to rate coefficients and equilibrium constants for butadiene pyrolysis.Sensitivities of soot yield with respect to rate coefficients and equilibrium constants for ethylene pyrolysis (Case B).Core reactions for benzene pyrolysis.Additional reactions using for modeling soot formation during benzene pyrolysis.Sensitivities of soot yield with respect to rate coefficients and equilibrium constants for benzene pyrolysis.

257

262264

267

278

- v i i -

LIST OF FIGURES

Figure III. 1III.2

IV. 1

IV.2

IV.3

IV.4

IV.5

IV.6

IV.7

IV.8

IV.9

IV. 10

TitleThe conventional shock tube facility.Typical pressure and laser-extinction traces behind a reflected shock wave. C0742: T s = 1816 K, P 5 = 2.29 bar.Soot yields vs. temperature at reaction times for the mixture benzene-argon (Series A).Soot yields vs. temperature at reaction■times for the mixture toluene-argon (Series B).

different0.31%

different0.31%

Soot yields vs. temperature at different reaction times for the mixture 1.00% toluene-argon (Series C).Soot yields vs. temperature at different reaction times for the mixture 0.10% toluene-argon (Series D) .Soot yields vs. temperature at different reaction times for the mixture 0,56% toluene-argon (Series E).Comparison of soot yield at 1.0 ms for the mixtures 0.31% benzene-argon and 0.31% toluene-argon.Comparison of soot yield at 1.0 ms for the mixtures 0.10% toluene-argon, 0.31% toluene-argon and 1.00% toluene-argon.Comparison of soot yield at 1.0 ms for the mixtures 0.56% toluene-argon and 0.10% toluene-argon.Definitions of induction time for soot appearance, 7g00t , and rate of sootformation, RsootComparison of induction times for soot appearance for the mixtures 0.31% benzene- argon and 0.31% toluene-argon.

Page4953

60

61

62

63

64

65

67

68

70

71

- viii -

IV. 1 1

IV. 12

IV. 13

IV. 14

V. 1

V. 2

V . 3

V . 4

Comparison of induction times for soot 72appearance for the mixtures C.10% toluene- argon, 0.31% toluene-argon and 1.00% toluene-argon.Comparison of induction times for soot 73appearance for the mixtures 0.10% toluene- argon and 0.56% toluene-argon.Soot formation rates for the mixtures 740.31% benzene-argon and 0.31% toluene- argon .Soot formation rates for the mixtures 750.31% toluene-argon, 1.0% toluene-argon,0.10% toluene-argon, and 0.56% toluene- argon .Comparison of the model prediction with 92experimental observations for Series B.(First parameter set). Time development.The symbols represent actual experimental points; the solid lines are the predicted values.Comparison of the model prediction with 93experimental observations for Series B and F. (First parameter set). The effect of pressure. The symbols represent actual experimental points; the solid lines are the predicted values.Comparison of the model prediction with 94experimental observations for Series B,C and D. (First parameter set).Concentration dependence. The symbols represent actual experimental points; the solid lines are the predicted values.Comparison of the model prediction with 95experimental observations for Series A.(Second parameter set). Time development.The symbols represent actual experimental points; the solid lines are the predicted values.Comparison of the model prediction with 96experimental observations for Series Band F. (Second parameter set). The effectof pressure. The symbols represent actualexperimental points; the solid lines arethe predicted values.

- ix -

V. 6

VI. 1

VI .2

VI . 3

VI .4

VI .5

VI .6

VI .7

VI .8

Comparison of the model prediction with experimental observations for Series B and D. (Second parameter set). Concentration dependence. The symbols represent actual experimental points; the solid lines are the predicted values.Principal reaction pathways for formation of two-ring aromatics. For a given reaction step, the difference in the lengths of the arrows represents the difference in forward and reverse reaction rates as computed for the test case (see text) at T = 1700 K and time = 0.5 ms.Principal reaction pathways for formation of fused polycyclic aromatics. For a given reaction step, the difference in the lengths of the arrows represents the difference in forward and reverse reaction rates as computed for the test case (see text) at T = 1700 K and time = 0.5 ms.Computed species concentrations as functions of reaction time for an initial temperature of 1700 K. H (equil) is the hypothetical concentration of hydrogen atoms which would be in equilibrium with the computed concentration of molecular hydrogen.Computed species concentrations as functions of reaction time for an initial temperature of 1700 K.Computed species concentrations as functions of reaction time for an initial temperature of 1700 K.Computed species concentrations as functions of reaction time for an initial temperature of 1700 K.Computed species concentrations as functions of reaction time for an initial temperature of 1700 K.Computed species concentrations as functions of initial reaction temperature temperature at a reaction time of 0.5 ms. H(equil) is the hypothetical concentration of hydrogen atoms which would be in equilibrium with the computed concentration of molecular hydrogen.

- x -

97

171

173

175

176

177

178

179

180

VI .9

VI . 10

VI . 1 1

VI . 12

VI . 13

VI . 14

VI. 15

V I . 16

VII. 1

VII.2

VIII. 1

Computed species concentrations as 181functions of initial reaction temperature at a reaction time of 0.5 ms.Computed species concentrations as 182functions of initial reaction temperature at a reaction time of 0.5 ms.Computed species concentrations as 183functions of initial reaction temperature at a reaction time of 0.5 ms.Computed species concentrations as 184functions of initial reaction temperature at a reaction time of 0.5 ms.Principal reaction pathway for further 187growth of polycyclic aromatic hydrocarbons.Computed soot yields at different 189temperatures and reaction times in a 1.09% acetylene-argon mixture at ps = 3.8 x 10-5 mol/cm 3.Experimental soot yields in a 1.09% 190acetylene-argon mixture at ps = (3.82 - 3.90) x 10-5 mol/cm 3 using laser extinction at 3390 nm (Series B of Ref. 31). The soot yields are calculated assuming Rayleigh scattering (166) and using the value of Lee and Tien (200) for the complex refractive index at 3390 nm.Computed soot yield versus reaction time 191for an initial temperature of 1700 K.Soot yields versus temperature computed 201with thermodynamic datasets in TableVII.1 for a reaction time of 0.5 ms.Soot yields versus temperature computed 206at a reaction time of 0.5 ms: middle curve - with set S2, upper - K 30 x 5, lower - k 30 / 5.Principal reaction paths for the formation 252of two-ring aromatics during pyrolysis of butadiene. The most important route is shown at the top; a secondary route is shown at the bottom.

- xi -

VIII .2

VIII .3

VIII. 4

VIII.5

VIII.6

VIII.7

VIII.8

Computed soot yields at different 254temperatures for a 0.54% butadiene-argon mixture at p5 = 1.5 x 10"5 mol/cm3 and a 1.09% acetylene-argon mixture at p5 =3.8 x 10"5 mol/cm3. Both curves represent reaction times of 0.5 ms and thermodynamic properties matching those of set S8 of Chapter VII.Experimental soot yields for a 0.54% 255butadiene-argon mixture at p5 = (1.49-1.53) x 10"5 mol/cm3 using laser extinction at 633 nm (Series J of Ref. 31). The soot yields are calculated assuming Rayleigh scattering (166) and using the value of Lee and Tien (200) for the complex refractive index. The symbols designate experimental points, the lines cubic spline fits.Computed soot yields at different 259temperatures for a 1.09% ethylene-argon mixture at p5 = 1.5 x 10-5 mol/cm3 and a 1.09% acetylene-argon mixture at p5 = 3.8 x 10"5 mol/cm3. Both curves represent reaction times of 0.5 ms and thermodynamic properties matching those of set S8 of Chapter VII.Experimental soot yields for a 4.65% 261acetylene-argon mixture at p 5 = (0.87-0.92) x 10"5 mol/cm3 and an ethylene-argon mixture at p5 = (0.87-0.90) x 10_s mol/cm3 using laser extinction at 633 nm (Series J of Ref.31). The soot yields are calculated assuming Rayleigh scattering (166) and using the value of Lee and Tien (200) for the complex refractive index. The symbols designate experimental points, the lines cubic spline fits.Principal reaction pathway for the 270formation of small polycyclic aromatics from benzene.Reaction pathway for further growth of 272polycyclic aromatic hydrocarbons via reaction with small aromatic and nonaromatic species.Computed soot yields at different 273temperatures for a 0.31% benzene-argon mixture at p5 = 1.5 x 10"5 mol/cm3.

- xii -

VIII .

VIII. 10

VIII. 1 1

Computed soot yields at different 274temperatures for a 0.31% benzene-argon mixture at ps = 1.5 x 10"5 mol/cm3 and a 1.09% acetylene-argbn mixture at ps - 3.8 x 10“5 mol/cm3 at a reaction time of 0.5 ir.s.Experimental soot yields for a 0.31% 275benzene-argon mixture at p5 = (1.49-1.56) x 10“5 mol/cm3 using laser extinction at 633 nm (Series J of Ref. 31). The soot yields are calculated assuming Rayleigh scattering (166) and using the value of Lee and Tien (200) for the complex refractive index.Experimental soot yields for a 0.31% 276benzene-argon mixture at ps - (1.49-1.56) x 10"5 mol/cm3 and a 1.09% acetylene-argon mixture at pB = (3.82 - 3.90) x 10"s mol/cm3 using laser extinction at 633 and 3390 n m , respectively. The soot yields are calculated assuming Rayleigh scattering (166) and using the values of Lee and Tien (200) for the complex refractive indexes. The symbols designate experimental results, the lines cubic spline fits.

- xiii

ABSTRACT

A study combining experimental, empirical modeling, and detailed modeling techniques has been conducted to develop a better understanding of the chemical reactions involved in soot formation during the high-temperature pyrolysis of aromatic and other unsaturated hydrocarbons. Theexperiments were performed behind reflected shock waves in a conventional shock-tube with soot formation monitored via attenuation of a laser beam at 633 nm. Soot-formation measurements were conducted with toluene-argon and benzene-argon mixtures.

Detailed kinetic models of soot formation were developed for pyrolyzing acetylene, butadiene, ethylene and benzene. The computational results indicate the importance ofcompact, fused polycyclic aromatic hydrocarbons as soot intermediates and the importance of the reactivation ofthese intermediates by hydrogen atoms to form aromatic radicals. The overshoot by hydrogen atoms of their equilibrium concentration provides a driving kinetic force for soot formation. The results with ethylene and butadiene indicate that acetylene is an important growth species for soot formation for these fuels. The benzene model suggeststhat reactions between aromatic species may be important forsoot formation from aromatic fuels.

- xiv -

Chapter I INTRODUCTION

Soot is the carbonaceous particulate matter which is formed during the gas-phase combustion or thermal degradation of hydroca: cons (1-6). Soot is normally blackbut Is different from graphite in that it is not purecarbon; soot particles contain from one to ten mole percent hydrogen and even more when first formed (5,7) as well as traces of other elements, such as oxygen (2,3). Much of the hydrogen is contained in condensed aromatic ring compounds which can be extracted from the soot using organic solvents (2,8). As soot particles age, they come to resemble graphite more closely and may contain only one percent or so of hydrogen (3,6). Inspection of soot flocculates shows that the basic unit of soot is the spherule, a sperical or near-spherical elementary soot particle with a mean diameter of 10-50 nm, corresponding to 105 — 107 carbon atoms (1-4). These particles adhere to each other to form straight or branched chains.

Soot and polycyclic aromatic hydrocarbons (PAH) areassociated with incomplete combustion and are generally recognized as potential pollutants (7,9). Some of the PAH produced in flames and adsorbed onto soot particles are

known to be carcinogenic (9), while the size of smaller soot particles (0.01 to 0.1 microns) allows them to easily be ingested deep into the lungs (10). Aside from the environmental aspects, soot formation in turbine combustors limits operating conditions by causing overheating of the combustion chamber from enhanced flame radiation (7). However, for flames in furnaces and boilers, soot is desirable as a radiation source for efficient heat transfer. For these combustors, the best course is to generate as much soot as is possible to burn up before exhausting the combustion gases.

These problems of soot formation will become increasingly important when conventional petroleum-based fuels have to be supplemented by coal-derived liquid fuels (11). Liquid fuels derived from coal are very prone to sooting because of their higher aromaticity. Strong economic incentives exist to learn how to burn fuels of high aromatic content without particulate formation; for example, elimination of the restrictions on the aromatic content of coal-derived synfuels could reduce their cost by 250/gal (5).

The sequential and overlapping steps that govern sootformation are broadly depicted by the six categories below:

0Pyrolysis or Oxidative PyrolysisParticle InceptionCoagulationSurface GrowthAggregation (to form chains)

3Oxidation

Soot particles are formed from the hydrocarbon fuel during the pyrolysis and particle inception stages. The small spherules grow to sizes of 10-50 nm via surface growth and coagulation. Coagulation is the process whereby two particles collide and coalesce to form a single larger particle. Finally, the spherules aggregate into chains (2,4).

The early stages of particle generation and growth are followed by a phase of oxidation in which the soot is burnt in the presence of oxidizing species such as 0, 0 2 and OH to form gaseous products such as CO and C02. The eventual emission of soot from any combustion device will depend on the balance between these processes of formation and burnout. The oxidation of soot will not be discussed here.

The focus of this work is the study of the chemical reaction pathways leading from fuel molecules to soot. Indeed, the central question of soot-formation research is how simple fuel molecules containing only a few carbon atoms are converted so rapidly into huge aggregates. As Calcote questioned in his recent review (12), "The basic problem . .

is how does the process proceed from molecular size to particles with diameters three orders of magnitude greater, or equivalent molecular weights ten orders of magnitude greater, than the starting materials in times on the order of milliseconds?"

Soot formation in most combustion systems is quite complex, involving chemical kinetics, fluid dynamics and transport phenomena. Investigation of the individual chemical steps of the soot-formation process in such complex environments is both extremely difficult and scientifically unwise since direct interpretation of experimental results in terms of chemical kinetics generally is not possible. Therefore, simplified combustion environments have been used in attempts to isolate the effects of chemical kinetics on observed soot formation. Most recent research work on the kinetics of soot formation has been conducted in one of three principal combustion environments:

1. high-temperature pyrolysis using shock-tubes and flow reactors;

2. laminar premixed flames;3. laminar diffusion flames.

Soot formation in other types of flames, such as turbulent diffusion flames or fuel-spray flames, . has been investigated; however, the complexity of such flames makes it difficult to obtain fundamental knowledge about the kinetics of the soot formation process. Even data from laminar diffusion flames are difficult to interpret in terms of chemical kinetics.

Although the process of soot formation has been studied for over a century by many investigators, the mechanism and kinetics of soot formation are still not well understood.

The extent of soot formation exhibits a complicated dependence upon the type of combustion system, type of fuel, pressure, temperature and other factors (1,4,7). Many researchers agree on the importance of polycyclic aromatic hydrocarbons (PAH) as intermediates in a reaction scheme dominated by free radical reactions.

Chapter II LITERATURE SURVEY

2.1 EXPERIMENTAL OBSERVATIONS2.1.1 General Comments

Soot usually forms at temperatures from 1300 to 3000 K,depending on the fuel and the conditions, with a time scaleof formation on the order of milliseconds. Soot generationis generally accompanied or preceded by the formation ofunsaturated hydrocarbons, especially acetylene and polyacetylenes (2,4,12) and polycyclic aromatic hydrocarbons (PAH) (2-4,12). These acetylenic or aromatic hydrocarbons are thermodynamically relatively stable at combustion temperatures (13,14). A certain amount of some of these hydrocarbons will remain in the gas phase after soot is formed and later condense onto the soot particles when the burned gases are cooled (2).

Aromatic and unsaturated ring compounds have a much greater sooting tendency in most combustion environments than do aliphatic compounds (1,6,15,16). The relative predilection to soot formation of alkynes depends on the type on combustion involved. In premixed flames alkanes and alkenes are more prone to sooting than are alkynes: indiffusion flames the trend is reversed (2,7,17).

- 6 -

2.1.2 Structure of SootWork with X-ray diffraction (1,4,5) and high-resolution

phase-contrast electron microscopy (4 and references therein, 18) has indicated that within a soot particle there are randomly dispersed domains of considerable order consisting of approximately hexagonal-plane (graphitic) lattice structures. The layer planes have a slightly greater interlayer spacing (ca. 3.44 A) than does graphite (ca. 3.35 A). Between the graphitic regions, orcrystallites, the structure is less ordered and many dislocations and lattice defects exist. Some researchers believe that the number of domains of high organizational order per spherical unit is comparable to the number of young or primary particles agglomerated in each spherule (7) .

The density of the soot particles is slightly less than 2 g/cm3 (4,5). Heat treatment improves the internal order of the particles and causes the interplanar spacing to approach that of graphite (4); it also reduces the hydrogen content (2) .

The sperules exhibit a Gaussian size distribution which has often been assumed to be narrow; a common practice has been to consider only an average size, although this assumption may lead to erroneous analysis of experimental results (19). When chaining begins, the size distribution of the particles becomes log-normal (4,20). As recognized

by Palmer and Cullis (1), the size and structure of soot particles formed in flames under a wide variety of conditions do not vary much, though the extent of soot formation depends strongly on factors such as the type of flame, the nature of the fuel, etc. (1,7,21)

Electron diffraction indicates the presence of single C-C bonds in soot (22), though double and triple bonds predominate (1,4,22). Soot particles collected during their growth show much stronger electron spin resonance signals than do older particles, indicating the radical character of the young soot particles (4,23,24). Mayo and Weinberg (25) concluded from ion mobility measurements with electrical potentials across counterflow diffusion flames that each soot particle carries unit positive charge. Ball and Howard (26) drew a similar conclusion from work with flat premixed propane-oxygen flames in the absence of imposed electric fields.

2.1.3 Shock-tube and High-Temperature Flow StudiesA common method of studying the complex process of soot

formation is to simplify the soot-formation environment. One simplification is to investigate the thermal degradation, or pyrolysis, of hydrocarbons in the absence of oxygen. These studies can be combined with oxidationresults to reveal the individual effects on soot formation of temperature and oxygen, allowing one to evaluate the

separate roles of hydrocarbon-oxidation chemistry and pyrolysis reactions; Another important application of pyrolysis studies is to the understanding of the diffusion and mixing-limited flames of practical interest; pyrolysis chemistry is important in these flames (17,27) but experimental results in such complex environments are difficult to interpret.

A versatile tool for the study of hydrocarbon pyrolysis and soot formation is the shock-tube, which allows a given gaseous mixture to be brought almost instantaneously to a known and controlled high temperature and pressure for one or two milliseconds and then suddenly cooled. The time scale of the system implies that heterogeneous reactions will not be important. The gas behind the shock wave is homogeneous, so experimental results are dependent primarily on the chemistry which is occurring. Interpretation of these results is simplified by the unimportance of concentration or temperature gradients.

Flow reactors have also been used for moderate- to high-temperature pyrolysis and oxidation studies (28,29). These reactors provide steady-state rather than transient operating conditions. Experiments performed understeady-state conditions are more easily studied than are experiments conducted under transient conditions; however, flow reactors have disadvantages such as the presence of concentration gradients (and hence diffusion), possible

10non-ideal flow patterns, and inflexibility in operating conditions which makes experimentation at typical combustion conditions nearly impossible.

When a hydrocarbon-argon mixture is shock heated, soot formation is observed only after a certain induction time (30,31). Emission, light absorption and light scattering have been used to detect the first soot particles. The induction or delay period before soot is detected has been used as a descriptive measure of the overall soot-formation process and has been correlated in terms of exponential temperature and power concentration dependences (31,32,33).

There are problems in interpreting the induction period. First, its experimental definition may vary somewhat from researcher to researcher. Secondly, the correlations produced do not provide any direct indication of the nature of the rate determining step. However, the correlations may serve as possible constraints for modeling.

2.1.3.1 Aromatic HydrocarbonsSome insights into the mechanisms controlling soot

formation from aromatic compounds come from investigations of fractional soot yields (defined as the fraction of carbon atoms converted into soot) as functions of various experimental factors, such as hydrocarbon type and pyrolysis temperature. Graham et al. (30) studied soot formationduring incident shock pyrolyses of benzene, toluene,

\>

■ . ... . 11

ethylbenzene and other compounds, highly diluted in argon, at temperatures in the range 1600 - 2300 K. In thispioneering work, soot was monitored by laser— light extinction measurements at two wavelengths (488 nm and 632.8 nm) and by light scattering (488 nm). Graham et al. demonstrated the existence of a pronounced maximum in the conversion of benzene and other aromatics to soot at a temperature of approximately 1800 K. They interpreted this behavior as arising from the competition between two pathways for aromatic hydrocarbon pyrolysis: at lowertemperatures the molecules undergo condensation reactions without ever losing their aromatic structure, with the resulting products rapidly and efficiently leading to soot; at high temperatures soot formation occurs via a second, "indirect” route in which the fuel molecules initially decompose into small nonaromatic species which then form soot rather slowly. This model provided an explanation for higher sooting propensity of aromatic compounds relative to nonaromat ics.

Wang et al. (34,35) conducted pyrolysis and oxidationexperiments with toluene-argon mixtures and oxidation experiments with benzene-argon mixtures behind reflected shock waves. The authors confirmed the existence of a maximum in soot yield for aromatic fuels as a function of temperature near 1800 K. The maximum soot yield for toluene pyrolysis was estimated to be greater than 90%. They

12observed that addition of oxygen or hydrogen decreased soot yields, while pressure had only a slight effect on soot yield.

Frenklach et al. (36) observed that in shock-tube pyrolysis of toluene, decreases in pressure caused the soot yield maximum to shift to higher temperatures. The influence of pressure was most pronounced at low pressures. Frenklach et al. concluded that Graham’s model did not correctly predict the pressure dependence of the soot yield, while Frenklach’s conceptual model for soot formation from aromatic fuels, which is summarized below, could do so:

A ==> X A + X ==> S

where A = species with intact aromatic rings

X = nonaromatic intermediates S = large aromatic species absorbing

light at a given wavelength.Frenklach and coworkers (37) extended the shock-tube

studies to include soot formation during oxidation and pyrolysis of benzene, chlorobenzene and toluene. Toluene and benzene exhibited similar sooting behaviors during both oxidation and pyrolysis; however, chlorobenzene produced soot at lower temperatures than toluene or benzene. The addition of oxygen generally reduced soot formation from the aromatic fuels, although it increased soot formation at some conditions.

13Vaughn and other workers at Kansas State University

4*.

conducted studies (38-40) on the high-temperature pyrolysis of benzene-argon mixtures in a single-pulse shock-tube. Soot yields were determined by weighing the amount of soot deposited on an aluminum liner which was placed in the shock-tube (40). Stable products were analyzed by gas chromatography and mass spectrometry (38,39). Vaughn et al. found mhat the major products were acetylene and styrene. Smaller concentrations of diacetylene, methane,vinylacetylene, ethylene, toluene, phenanthrene and pyrene were also observed. In contrast to earlier works (41-46) no biphenyl was detected. Vaughn et al. (38) concluded thatbenzene added on to high molecular weight products as a unit and that acetylene addition was not an important growth mechansim for these large molecules.

Nelson et al. (47) extended these studies to includelaser extinction experiments. Soot samples collected from the shock-tube were analyzed using transmission electron microscopy. Soot yields determined by the optical method exhibited maxima similar to those of other workers (30,34,36,37). Nelson et al. reported that soot yields formed in pyrolyses of toluene were larger (ca. 70%) than those obtained in pyrolyses of benzene (ca. 50%). Induction times for soot appearance were determined by the laser extinction technique. The authors suggested that "the primary impact of ring fragmentation is not on the nucleation of soot, but rather on the surface growth" (47).

14Evans and Williams (48) conducted oxidation and pyrolysis

experiments behind reflected shock waves with benzene and toluene. They found that the extent of agglomeration of the primary spherules into chains was dependent on the experimental conditions. They agreed with Graham (30) about the existence of two routes to soot, one direct and one indirect, but found that the direct route was the more important one under all conditions. The peak in the soot yield when plotted versus temperature was attributed to reverse reactions becoming important at high temperatures.

Kern et al. (49,50) investigated product distributionsduring reflected-shock thermal decompositions of benzene and toluene at pressures near 0.4 bars. They detected the reaction products with a time-of-f1ight mass spectrometer. Kern et al. estimated that the products detected with the mass spectrometer accounted for 75-93% of the carbon atoms initially cresent when benzene was the fuel (50) and for 70-100% when toluene was the fuel (49). They accepted the estimated gaps in the carbon mass balance as upper bounds for fractional soot yields. These assumed upper bounds are much lower than yields determined by researchers using optical techniques (30,34,36,47). Although the mass-spectrometric technique does not measure soot yields directly, it can provide information about theconcentrations of small stable intermediates under conditions where soot forms. This information will be discussed later in the chapter.

15Smith and coworkers (28,51,52,53) studied hydrocarbon

pyrolysis in a Knudsen cell using raass-spectrometric analysis. They attempted to estimate fractional soot vields using carbon-atom balances. For their conditions (pressures less than one torr) benzene was thought to produce more soot than toluene or acetylene. An upper limit of 80% was placed on fractional soot yields from benzene at 1600° C; estimates of soot yields at other temperatures were restricted to lower values because of smaller mass-balance deficits.

2.1.3.2 Aliphatic CompounasMar'yasin and Nabutovskii (15) investigated soot

formation from acetylene in shock waves. They reported that acetylene produced less soot than did benzene. Soot formation measured by an optical emission technique began at longer reaction times from acetylene than from benzene.

Frenklach et al. studied soot formation during shock-tube pyrolysis (31) and oxidation (37) of acetylene, allene and 1,3-butadiene. Soot formation was measured by monitoring attenuation of laser beams in both the visible (632.8 nm) and the infrared (3390 nm) regions of the spectrum. Frenklach et al. found a bell-shaped dependence of soot yield on temperature for these nonaromatic compounds similar to that observed previously for aromatics (30,34,36). The nonaromatics in general produced less soot than did the aromatic species and had soot maxima at higher temperatures;

16the fractional conversion of acetylene into soot after one millisecond had a maximum near 2150 K 031). Allene was found to produce much more soot than 1,3-butadiene. The authors found that oxygen in small amounts promoted soot formation from nonaromatics at low temperatures and pressures, especially for acetylene (37).

Evans and Williams (48) . studied pyrolysis and oxidation of n-heptane in shock waves. In this work the soot samples were studied using transmission electron microscopy. They found that n-heptane gave lower soot yields than benzene or toluene and required higher temperatures to produce soot than did the aromatic compounds. Graham et al. (30) andWang et al. (34), in separate experiments, reported that fractional soot yields measured by optical methods were lower for nonaromatic fuels than for aromatic fuels.

Fussey et al. (33) pyrolyzed ethane, ethylene and acetylene behind incident shock waves. They monitored the induction periods for the formation of soot particles using both emission and laser-extinction techniques and found that ethylene exhibited a concentration dependence different from that of acetylene or ethane. This was explained by "the inhibiting effect of the hydrogen evolved in the initial decomposition reaction." Acetylene had the shortest induction times of the three compounds studied, leading Fussey et al. to conclude that acetylene followed a more direct route to soot than did the other fuels and possibly served as an intermediate for nonaromatic fuels.

2.1.4 Laminar Flames2.1.4.1 Laminar Premixed Flames

Laminar premixed flames are the simplest type of flame to study because the chemistry of the flame is not as coupled with transport phenomena as in diffusion flames. The laminar premixed flame ideally is a plug-flow reacting system but the preferential diffusion of atomic hydrogen and molecular hydrogen can alter the local H/C and 0/C ratios. Low-pressure premixed flames are often used to study the chemical kinetics of the soot-formation process (4,8,54) because their lengthened reaction zones decrease concentration and temperature gradients in the flames and so increase sampling accuracy because flow disturbances caused by probes are less important.

The C/0 ratio at which a fuel/oxidizer mixture is just rich enough to form soot in a premixed flame is called the "critical C/0 ratio” . This experimentally determinedquantity is often taken as an inverse measure of sooting tendency. The C/0 ratio at which the characteristic yellow luminosity of the soot particles is just visible usually occurs near C/0 = 0.5 (2,55-57). A second common measure of the "richness" of a mixture is the "equivalence ratio". The eauivalence ratio is defined as the (fuel/oxidizer) ratio of the actual mixture divided by the (fuel/oxidizer) ratio at stoichiometric conditions, with the reaction products usually assumed to be C0Z and H 20.

1 8An extensive sooting-limit, study was performed by Street

and Thomas (56), who observed the following ranking of hydrocarbons (in order of increasing tendency to soot): acetylene < alkenes < isoalkanes < alkanes < benzene and alkylbenzenes < alkyl naphthalenes. Calcote and Manos (58) recently confirmed the sooting order described by Street and Thomas.

The importance of temperat ire in determining the critical equivalence ratio for soot formation in premixed flames has recently been emphasized by Glassman and coworkers (17,59). Dyer and Flower (60), Street and Thomas (56) and Milliken (61) also observed that increases in temperature decreased the quantity of soot formed in premixed systems.

The problem of defining and measuring the C/0 limit is nontrivial. As Homann (6 ) has pointed out, "there is no property of the flame which shows a sudden change when the carbon limit is exceeded." This observation implies that the definition of the critical C/0 ratio is rather arbitrary, leaving its mechanistic significance unclear.

Beyond the soot limit, the yield of soot in premixed flames initially increases rapidly with increasing C/0 ratio (4,62-64). At long reaction times, this increase in soot production is reflected more by increased particle size than by increased particle number densities (62,64). As the rich limit of flammability is approached, the soot yield drops again.

The soot yield is not always well correlated with the critical C/0 ratio. In an example taken from Haynes and Wagner (4) in flat benzene- and ethylene-air flames, benzene, with a critical C/0 ratio of 0.65, appears to resist the onset of sooting more effectively than does ethylene, which has a critical C/0 ratio of 0.60 . However, the actual soot volume fractions are the same at C/0 = 0.68, while at C/0 = 0.72, benzene forms three times as much soot as ethylene (62).

In contrast to the weak influence of pressure on the critical C/0 ratio (5,65,66), the soot yield is usually strongly enhanced by increasing pressure (66,67). Haynes and Wagner have suggested that the influence of pressure may result from a shifting of any gas-solid absorption balances to favor more condensation at higher pressures (4 ); they believe this to be consistent with the weak pressure effect on the critical C/0 ratio, i.e. in the absence of a surface on which such growth can occur.

The effect of temperature on the soot yield seems to be complex. Near the critical C/0 value, an increase in temperature reduces the amount of soot (61,62); this has been interpreted as arising from differences in activation energy of the steps forming soot and those opposing it, such as oxidation (61). In very fuel rich flames, an increase in temperature has been observed to promote soot formation (67). This effect was presumably due to enhanced pyrolysis at higher temperatures (67).

20Additions of small quantities of most substances to

premixed flames have little effect on soot formation. Notable exceptions are some metals which reduce sooting behavior even when present at ppm levels.

Inert diluents tend to reduce the amount of soot at constant temperature (16). However, dilution often produces a fall in temperature which may promote sooting, so the net result depends on the balance between these effects. Generally, rather high concentrations of inert diluents (>5%) are required + produce significant changes in the soot concentration.

Other additives, such as NH3, NO and N02 (65,69) or H 2S and S02 (56,69) are more effective than inert gases in reducing soot yields and raising the limiting C/0 ratio. A 1% addition of either H 2S or S02 to a moderately sooting ethylene/air flame reduces the yield by about 85% (4).Addition of S03 or H 2S04 has been found to either reduce (69) or increase (4,56) sooting, while addition of H z tends to weakly promote sooting (56,65).

Additives of the types discussed here affect the average particle size rather than the number density of soot particles present in the flame. These additives seem to affect surface growth rather than growth by particle coalescence (4,69).

The most striking effects of additives are those exhibited by various metals. Studies in gaseous flames have

2 tgenerally found that alkaline and alkaline earth metals are particularly effective in reducing soot formation. These effects have been attributed to the supposed importance of ions to soot nucleation or to particle coagulation (70-72). Cotton et al. (73) offered an alternative explanation involving metal catalysis of the radical equilibrium H 20 = OH + H. Haynes et al. (70,72) found evidence for both ionicand chemical effects.

2.1.4.2 Laminar Diffusion FlamesPractical combustion devices seldom use premixed-flame

type burning. Fuel and oxidizer enter through separate inlets and the combustion process is diffusion controlled, or, in more general terms, mixing controlled. It is obvious that under such circumstances the C/0 ratio cannot everywhere stay below its critical value. Unlike premixed flames, where at a given equivalence ratio the adiabatic flame temperature can be used to describe the temperature at the reaction front where most of the soot formation processes take place, for a diffusion flame the reactions occur over a broad temperature range (74). The fact that the flame reactions occur over wide ranges of temperature and composition make it difficult to discover the details of soot-formation chemistry from experimental diffusion-flame results.

22From the works of several laboratories (7,74-76), in

which over 75 hydrocarbons were studied, the propensity of various fuels to form soot in laminar diffusion flames increases in the following order: n-alkanes < isoalkanes <alkenes and cycloalkanes < alkynes < benzene and alkyl benzenes < naphthalenes. Generally, the smaller the molecule, the greater the resistance to soot emission. Another trend is that compact isomers are more prone to soot ing.

The effects of flame structure and heat and mass transfer on the soot formation process are illustrated dramatically by the switch on going from premixed to diffusion flames in the order of tendency to soot of acetylene relative to alkanes and alkenes. In laminar diffusion flames, molecular diffusion controls the rate of mixing of fuel and oxidizer. Since the principal oxidation reactions are very fast relative to diffusion rates, sharp concentration and temperature gradients exist and pyrolysis and soot formation occur in a very fuel-rich environment. In premixed flames, pyrolysis and soot formation reactions occur simultaneously with oxidation reactions throughout the flame. Rapid oxidation of the fuel and pyrolysis products can either prevent the occurrence of or remove precursors of soot

Glassrnan and coworkers have recently discussed the importance of fuel structure and temperature (17,27,74) in determining sooting tendency. Glassrnan attributes the high

23sooting tendency of acetylene in diffusion flames to its

I'SSiat ic f lame temperature!The effect of pressure on soot formation in diffusion

flames has been investigated over a wide range of conditions. Generally speaking, low pressures reduce soot formation (1,4,77) while high pressures promote it (1 ,77,78).

The effects of addition of various gaseous substances to the fuel flow has been investigated. Simple dilution by inert gases such as He, Ar and N 2 generally decreases the tendency to soot (4,74,79). Additives such as Hz, C02, H 20 and S02 also decrease soot-formation tendencies (80-82). A recent study of the effects of additives on soot formation in laminar diffusion flames has shown that most reductions in sooting tendency are caused by thermal effects of the additives (74); Glassrnan (59,74) has sugaested that in diffusion flames the precursor growth processes take place in the absence of any oxidizing radicals and a decrease in temperature decreases the rate of pyrolysis and thus the tendency to soot.

The effect of oxygen addition to the fuel is complex. Both enhancement and reduction of soot yield have been reported for various hydrocarbons (59,74,82,83). The effect of increased yield is not purely thermal as it is far greater than that observed at the same maximum flame temperature produced by oxygen enrichment of the air (82).

24It has been suggested that the presence of small amounts of 0 2 accelerates the pyrolysis (59,74,82) or polymerization reactions (79) occurring in the hot fuel.

The effect of adding certain metals to diffusion flames can be dramatic. However, these results are qualitatively similar to those in premixed flames and will not be discussed.

2.2 PATHWAYS FOR SOOT FORMATION2.2.1 Initial Reactions2.2.1.1 Nonaromatic Fuels

Many investigators have studied the reaction products of the pyrolysis or oxidation of nonaromatic hydrocarbons. Pyrolysis of paraffin hydrocarbons under neai— sooting conditions leads to the formation of molecular hydrogen, alkenes and acetylenes (84,85). Acetylene will react to form polyacetylenes (86-89).

Cundall et al. (87) studied the shock-tube pyrolysis of acetylene and ethylene and concluded from a rather rough analysis that the formation of polyacetylenes from acetylene was first order in acetylene concentration. Kistiakowski and coworkers (90,91) measured polyacetylenesmass-spectrometrically as products of acetylene pyrolysis. They concluded that the reaction proceded as:

C 2H 2 =■> C 4H 3 => C*H2 => Cs'.lz => C 8H 2 => . . . Experiments and kinetic modeling of C 2H 2 pyrolysis by

25Tanzawa and Gardiner (86,92) and by Koike and Morinaga (93)support, this interpretation-, although Back (94) and Bopp and

*Kern (95) have proposed instead a self-reaction of acetylene to form C 2H and C 2H 3. Mar'yasin and Nabutovskii found that acetylene formed vinylacetylene before diacetylene, in contrast to Kistiakowski’s mechanism (90).

Kern et al. (49) conducted shock-tube pyrolyses of butadiene and acetylene. The reaction products were detected with a time-of-flight mass spectrometer. The dominant reaction products for butadiene pyrolysis were C 2H 2

and C 4H2 , with minor amounts of C 6H 6, C 2H 4> C 3H 3 and C 4H 4 at higher temperatures. Acetylene formed C 4H 2 , C 6H 2 and traces of C8 H2 .

The reactions of nonaromatic hydrocarbon-oxygen mixtures have been extensively investigated. A few of the more recent works are Refs. 96 - 101. Most of the studiesinvolved fuel-lean combustion where production of soot did not occur.

2.2.1.2 Aromatic FuelsThe chemistry of aromatic compounds at high temperatures

is not well understood. It is unclear whether ring fragmentation is extensive.

The immediate reactions of the aromatic ring will depend on the local residence time, temperature and chemical environment. Stehling et al. (102) studied benzene

26* pyrolysis in a flow reactor at rather low temperatures (973 - 1173 K). The major products observed were hydrogen,biphe nyi, tar and carbon. Stehling et al. found that the rate of disappearance of benzene and the rate of production of molecular hydrogen were accelerated by the presence of acetylene. The rate of acetylene disappearance was not affected by the presence of the benzene.

Slysh and Kinney (43) studied benzene pyrolysis at 1473 K in a flow system. Under these conditions, benzenedecomposed according to first order kinetics, and acetylene, diacetylene and hydrogen were the primary decomposition products; smaller amounts of biphenyl were also observed.

Bauer and Aten (44) monitored the decomposition of benzene- and hexafluorobenzene-argon mixtures behind shock waves using absorption spectra over the temperature range 690 - 1900 K. The disappearance of benzene was first-order in benzene concentration. On the basis of their results and the earlier work of Slysh and Kinney, they proposed a chain mechanism for the pyrolysis of benzene:

C 6K 6 = C 6Hs + Hc 6h 6 + h = c 6h 5 + h 2

c 6k 5 = c 4h 3 + C 2H 2C 4H 3 = C 4H 2 + H

c 4h 3 + c 6h 6 = c 6h 5 + cAm

plus terminating radical recombinations. This mechanism has two parallel chain propagation series, the first producing

as stable products C<,H2, C 2H 2 and H while the second produces C 4H 4 .

Hou and Palmer (42) studied the pyrolysis of benzene in a flow tube between 1173 and 1523 K. They found some first-order contribution from processes involving the wall in their apparatus. but believed that the second-order reaction that they observed was the homogeneous, bimolecular formation of biphenyl and molecular hydrogen from two molecules of benzene. Hou and Palmer found an activation energy of about 40 kcal/mol for this reaction. Brooks et al. (46) reported a fractional order of 3/2 for this reaction over the temperature range of 873 - 1036 K.

Mar'yasin and Nabutovskii (32,45) pyrolyzed benzene-argon mixtures behind reflected shock waves at temperatures of 1400 - 2500 K. The concentrations of the stable speciesbenzene, diacetylene, vinylacetylene, acetylene, ethylene, methane and •hydrogen were measured using a gas chromatograph. They found that the pyrolysis of benzene was second-order in benzene concentration (45). They concluded "The value of the activation energy for the pyrolysis of benzene is close to the heat of formation of biphenyl from benzene, which indicates that at temperatures not exceeding 1700 - 1800 K the decomposition of benzene occurs withoutdestruction of the ring. At higher temperatures the pyrolysis occurs with the destruction of this ring, as is shown by the abrupt increase in the concentration of acetylene in the reaction products."

28. ' / i? . f

Asaba and Fujii (41) studied the pyrolysis of 10% - 20%benzene-argor. mixtures in a single-pulse shock-tube. Theconcentrations of the reactant, intermediates and final

*products were monitored using light absorption supplemented by gas chromatographic analysis. Asaba and Fujii found that the addition of methane promoted the pyrolysis reaction while hydrogen slowed it. The authors proposed that even at high temperatures the primary pathway for benzene disappearance was through biphenyl rather than ring rupture to acetylene and diacetylene. Fujii and Asaba later extended their investigation to include rich mixtures of benzene and oxygen diluted in argon (103). They found that the presence of oxygen did not change the main reaction route for the disappearance of benzene.

Graham et al. in turn offered two competing pathways for the disappearance of aromatic fuels (30). They believed ring rupture to be dominant at temperatures above 1800 K and ring fusion to be dominant below 1800 K. This theory is discussed in more detail in the 'Experimental Observations' section of this chatter.

Wang et al. (34), in a shock-tube pyrolysis study,proposed that fragmentation of the aromatic ring was not an important route for soot formation from aromatic fuels, while condensation of aromatic rings and dehydrogenation were believed crucial to soot formation. Evans and Williams (48) reached a similar conclusion on the relative importance

29of fragmentation and condensation reactions to soot formation from aromatic fuels.

Smith and Johnson (51,53) recently reported the absence of phenyl radical during the high-temperature pyrolysis of benzene at very low pressures (less than 5 torr) using a Knudsen cell - mass spectrometer system. They believed that this absence was not due to detection difficulties because phenyl radical was readily observed during experiments with chlorobenzene; they therefore concluded that loss of a hydrogen atom was not the first reaction step. They proposed instead a bimolecular self-reaction of the benzene leading to the formation of biphenyl, augmented at higher temperatures by a "more direct route" (53) producing acetylene, diacetylene and molecular hydrogen. Rao and Skinner (104), who studied the pyrolysis of benzene behind shock waves by measuring hydrogen and deuterium atom concentrations, did see evidence for the production of phenyl radicals.

Smith (28,52) also studied the pyrolysis of toluene. He concluded that at his conditions (pressures less than one torr) the first reaction to occur is the loss of a hydrogen atom to form benzyl radical. He observed the formation of PAH and polyacetylenes up to C 8H 2. The maximum concentration of higher molecular weight species occurred near 1300 - 1400° C. Above 1500° C and at "higher"pressures (near one torr) the products became dominated by

30species containing even numbers of carbon atoms. Astholz et al. (105) and Rao and Skinner (106) also reported that toluene initially forms benzyl radical during thermal decomposition.

Kern et al. (49,50) studied the pyrolysis of benzene andtoluene in shock waves using a time-of-flight mass spectrometer. The major products observed were acetylene and polyacetylenes up to C 8H2. The only products detected with m/e greater than 92 (for toluene) or 78 (for benzene) were C 8H 2 and C 8H G (phenylacetylene), with an estimated detection limit of 5000 ppm. No evidence of biphenyl or styrene was obtained, in contrast to other shock-tube works (39,40,45,103); phenyl radicals were not detected during the pyrolysis of benzene. Benzene was found to disappear according to a second—order reaction, which was proposed to be a direct ring fragmentation (50,107).

Vaughn et al., in a single-pulse shock-tube study of benzene pyrolysis (39,40), also failed to detect biphenyl. Styrene was reported as a product, with a maximum mass yield of 5% near 1500 K. Acetylene and diacetylene were the major products. Fragmentation of the ring was found to be the dominant reaction pathway at temperatures above 1500 K.

312.2.2 Particie Inception

Nucleation, or particle inception. involves a transition from the radical and molecular intermediates generated by the oxidative-pyrolytic reactioris of the hydrocarbon fuel to a two-phase, particulate system. The initial reaction products typically include various unsaturated hydrocarbons, particularly acetylene and its higher analogues, polycyclic aromatic hydrocarbons, and their radicals. Thesehydrocarbons are thermodynamically stable at typical combustion temperatures and are considered the most likely precursors of soot (1-6 ,12).

The term "nucleation" should be used with caution because of its connotation of physical condensation phenomena. Combining comments of Calcote and Thomas, nucleation involves the formation of reactive species which grow faster than they decompose, and whose products are as active as the parent species (12,56).

2.2.2.1 Chemical NucleationA. Nonaromatic Fuels

The mechanism by which ring closure of the reactive soot precursors is brought about has not been established. Many of the proposed mechanisms involve free-radical reactions (e.g. Refs. 8 and 108). The possible contribution of ionic mechanisms will be discussed in a later section.

32The importance of C-C double and triple bonds in the

step-wise growth of small radicals to larger species was pointed out by Porter (109) who noted that' hydrocarbon radicals can add to such unsaturated molecules without losing their radical character. Several researchers(1,23,33,54,110) ha.ve suggested that for nonaromatic fuels the important soot intermediate is acetylene. Homann and Wagner (23,54) proposed that acetylene reacts to form polyacetylenes, branched chain species and finally substituted aromatic compounds via a free radical mechanism (8,54). The role of polyacetylenes in the growth of long chain compounds was later discounted by Homann et al. (111) who speculated that polyacetylenes were side products of the growth process. Other workers (112,113) have alsointerpreted their results as ruling out polyacetyle es as important soot precursors.

Homann and Wagner (8 ) observed that in premixed acetylene flames two classes of PAH were formed in the oxidation zone. Grouped into one class were PAH without sidechains such as naphthalene, anthracene, phenanthrene and pyrene, whose concentrations were observed to continuously increase. Concentrations of polycyclic aromatic species with sidechains reached maxima in the oxidation zone and decreased near the point where soot production oegan. Homann and Wagner concluded from these observations that the substituted PAH are important intermediates in soot

33formation while the PAH-without-sidechains were not. These substituted PAH may be formed by the addition of hydrocarbon radicals to linear hydrocarbons. D'Allesio et al. (64), ina study of atmospheric-pressure premixed methane-oxygen flames, confirmed the dissimilar behavior of substituted and unsubstituted PAH noted by Homann and Wagner.

Glassman and coworkers (27,74) studied soot formation from several fuels in premixed flames where the temperature was held constant. They found that butadiene produced more soot than did acetylene and speculated that butadiene might be a soot intermediate for other nonaromatic fuels. Ray and Long (114) have suggested that the acetylene and butadiene theories are not mutually exclusive in that at lower temperatures butadiene may be formed from acetylene. However, Frenklach et al. recently demonstrated that butadiene and acetylene produce less soot than another nonaromatic fuel, allene (31).

Long and coworkers (115,116) reported that, contrary to Homann's findings, the concentrations of PAH did have an early maximum, followed by a later increase. They concluded that the PAH could not be excluded from consideration as possible soot precursors. Later workers (31,108,113,117) also have concluded that PAH are critical intermediates for soot formation.

Frenklach et al. (31,37) have proposed a conceptual modelfor soot formation from nonaromatic fuels. In the model.

34both aromatic and nonaromatic products of fuel pyrolysis are required to produce soot,

Abrahamsor. (118) presented arguments for the existence of "saturated platelets" formed from acetylene. Theseplatelets, with an initial. C/H ratio of 1, would gradually lose hydrogen and so graphitize. This idea has not been widely accepted.

B. Aromatic FuelsAny general mechanism that is presented to explain soot

formation must account for the propensity of aromatics to form more soot than do nonaromatics (1-4,30,31). In studies of low-pressure flat premixed acetylene-oxygen and benzene-oxygen flames at the same C/0 ratio, Homann and Wagner (8 ) found that the larger amount of soot in the benzene flames was due more to the higher soot-particle number density than to the slightly larger mean particle diameters. This would indicate that nucleating species are more plentiful in benzene flames.

Several authors have proposed a progressive polymerization of aromatic rings beginning with biphenyl through large polycyclics and on to the polybenzoid soot structure (30,38,103,119). Such a process would go through stages of PAH that do not necessarily have aliphatic, olefinic or acetylenic side chains.

Some ring rupture does occur from the oxidative and pyrolytic reactions in flame systems. Graham et al. (30)

attributed the decrease in soot yield at high temperatures to ring fragmentation, since he assumed that the nonaromatic fragments would form soot less efficiently than intact rings. Bittner and Howard (120) and Frenklach et al. (31,36) have suggested that the interaction of unsaturated nonaromatic hydrocarbons and their radicals with an intact aromatic ring initiates the rapid production of higher molecular weight aromatics.

Scully and Davies (16,119) concluded that ring fragmentation did not promote soot formation. They measured soot yields from 25 aromatics and substituted aromatics injected into the combustion products of a rich town-gas/air flame. Components with hetero-atoms contained in and attached to aromatic rings (believed to promote ring rupture) gave lower soot yields than did benzene, and cyclohexane produced much less soot than did aromatics. Wang et al. came to similar conclusions about the effect of ring fragmentation on soot formation (34). However, some researchers have proposed that aromatic compounds fragment to form acetylene or other nonaromatic intermediates which then form soot (75,102,110,121).

2.2.2.2 Physical NucleationElectron micrographs indicate that the basic soot

particles, the spherules, are spherical or nearly spherical. This has led some researchers to ask whether soot particles

36are liquid for part of their lifetime (122-124). One of the main attractions of this suggestion is that the transition from coalescent to chain-forming collisions during the growth of the particles would be explained by the solidification of the liquid droplets.

Such explanations generally assume that macromolecules are formed in a slow step by polymerization of the hydrocarbon pyrolysis products. These macromolecules can then undergo a classical condensation to produce liquid droplets which subsequently pyrolyze to form soot.

Lahaye and Prado (123,125) examined soot formation during benzene pyrolysis in terms of condensation to liquid particles, following classical condensation theory. From this simple model, they predicted that:

1. at constant benzene concentration the number of nuclei formed is independent of the reaction time at constant temperature;

2 . at a given temperature, the number of nuclei is independent of the benzene concentration;

3 . the number of nuclei formed increases with temperature.

To test their model they measured the particle number density at the exit of a flow reactor and found the number density to behave as predicted by their model.

However, as pointed out by Haynes and Wagner (4), in equating the number of particles collected (after reaction

37times greater than 100 milliseconds) with the number of particles generated, Lahaye and Prado appear to neglect the intervening effects of coagulation, which also could explain many of their observations.

Graham (30,126;127 as reported in Ref. 4) found that no droplets are present before soot appears, as signaled by the simultaneous onset of light scattering and infrared absorption. Thus, in place of a homogeneous nucleation, he suggested that as soon as some solid phase material is present, the supersaturated gas-phase species condense rapidly to give a two-phase, predominantly liquid particle.

Homann (128) has argued that, based on estimated vapor pressures for large PAH, the minimum size of polymers which could condense to liquid at high temperatures is quite large. Haynes and Wagner (4) also discussed this point, noting that if one neglects the effects of electric charge (see e.g. Ref. 124) and droplet curvature (see e.g. Ref. 129) on vapor pressure, the molecular weight of the first condensable species at the conditions of Graham (30) (1800K) is 2700 amu. The formation of such large molecules would require many polymerization steps and it is not clear why these molecules should not continue to condense in a chemical sense. This would not necessarily require rigid chemical structures since such large macromolecules are likely to have a high degree of internal mobility.

382.2,3 Ions in Soot Formation

In much of the proceeding discussion radical mechanisms have been exploited to describe the nucleation process, implying that these mechanisms lead to a series of radical-molecule reactions which develop either long, chain molecules or polycyclic aromatic hydrocarbons. However, the presence of ions in hydrocarbon flames is well documented (130-133) and it long has been conjectured that such ions might influence the processes of soot particle formation. Some important questions are: How are the ions produced?How do they interact with other precursor species?

Mass spectra of the ions arising in the sooting region of premixed flames have been obtained by various electrical discrimination techniques (131,134,135). The mechanism of formation of ions in the sooting region has been a point of some discussion. The very high levels of ionization found by Wersborg et al. (134) seem inconsistent with the thermalionization of hydrocarbon molecules or soot particles (136). However, other investigations (131,135) show much lower ion concentrations and thermal (equilibrium) ionization may in fact be responsible.

When the first soot particles occur, the apparent ionization energy drops from 8-9 eV to approximately 5 eV. However, it is not clear that equilibrium ionization is responsible in this region because the charged particles are smaller than the uncharged ones (12) and one would expect

39the opposite trend. Therefore, Homann (135) proposed a kind of chemi-ionization due to the exothermicity of the surface growth reactions which dominate particle growth in this region.

Calcote (12) has argued that while thermal ionization could account for the ionization of particles with masses greater than 10,000 amu, it ''uld not account for the smaller charged particles. He proposed a mechanism for soot formation based on ion-molecule reactions. The primary chemi-ion was proposed to be either CH0+ or C 3H 3+, which may be formed by reaction of CK with an oxygen atom or an acetylene molecule, respectively. Wersborg et al. concluded that concentrations of large hydrocarbon ions (probably PAH) are high enough to support the view that ionic nucleation could play a role in soot formation in flames (134). However, other researchers have reported that chemi-ions formed in the primary reaction zone may be less numerous than the small soot particles arising later on (131.135). Haynes et al. (70) found that ionizing additives had noeffect on early soot growth in atmospheric-pressure premixed ethylene-air flames, while Mayo and Weinberg (25) found that even in the presence of electric fields some fraction of the soot nuclei must have been formed without growing on ions as nuclei.

A fact that has troubled researchers looking for a single unifying mechanism to explain soot nucleation has been that

40oxygen is required in the only mechanism of chemi-ionization that has beer, shown to operate in flames to date (136-138). Therefore, production of ions in pyrolysis svstems has been assumed to be unlikely. However, two experimenters have detected ion currents during the pyrolysis of hydrocarbons in electric fields (139;140 as cited by Ref. 7). Bowser and Weinberg (139) interpreted their measurements as indicating ion concentrations of between 1011 and 1015 ions/cm3 in ethylene pyrolyzed in shock waves.

A second troublesome observation has been that total ionization in nonsooting hydrocarbon flames maximizes at a fuel equivalence ratio near one (7). Therefore, as the fuel equivalence ratio increases, total ionization would be expected to decrease although soot formation increases. Wittig and Lester (141) discussed the possibility of a dual nucleation route involving ionic species under fuel-lean conditions and free-radical species under fuel-rich conditions,

Recently, Homann and Wolf (142) studied charged and neutral soot particles in low-pressure flat flames of acetylene and benzene. They found that soot particles acquire charge (positive or negative) only after the decrease in particle number due to coagulation has begun. Moreover, the number density of the charged particles is much smaller than that of the neutrals in the early stages of soot growth. Ball and Howard (26) also concluded that

41the soot particles form and begin agglomeration before acquiring charge. These observations argue against an important role for hydrocarbon ions in soot nucleation.

Once particles are charged, whatever the mechanism, they are subject to electrical effects. For example,electrostatic charges between charged particles have long been suspected of influencing their coagulation (131,143). Measurements of the coagulation rate constant in the presence of ionizing (alkali metal) additives have shown that coagulation is inhibited by these additives (70,72). When most particles are charged they will resist subsequent coagulation and hence on the average remain smaller and more susceptible to oxidation.

Weinberg and coworkers (143-145) demonstrated that the application of electric fields to sooting diffusion flames can decrease the amount of soot formed. Soot particles in flames subjected to electric fields move to the negative electrode, indicating that the particles are positively charged under such conditions. Stronger electric fields can cause soot particles to acquire positive or negative charges and can influence the residence time of soot particles in certain parts of the flame.

In conclusion, it is apparent that, regardless of their mechanism of formation, soot particles can and often do carry an electric charge. Weinberg's work shows how such charged particles can be manipulated by electric fields, and

42this may offer hope for emissions control (144.146). However, it appears that the high levels of ionization associated with soot in premixed flames are a product of soot particle generation rather than a necessary precursor.

2.2.4 Surface Growth. Coagulation and AggregationSurface growth is the means by which the bulk of the

solid phase material is generated. This growth involves the attachment of gas phase species to the surface of the particles and their incorporation into the particulate phase.

Surface-growth reactions lead to an increase in soot mass but the number of particles remains unchanged by this process. The opposite is true for growth by coagulation, where particles collide and coalesce, thereby decreasing the particle number density while the soot mass remains constant. Particle growth is the result of simultaneous surface growth reactions and coagulation. Agglomerationinvolves the aggregation of older, more rigid, particles into chains.

2.2.4.1 Surface GrowthIn a comparison of flat premixed benzene-oxygen and

acetylene-oxygen flames that form the same amount of carbon (i.e., different C/0 ratios were used), Homann and Wagner (23) found that of the carbon in the unburned gas in excess

of that- at the limit of soot formation, 30% aoes to soot in the benzene flame while only 5% goes to soot in the acetylene flame. The particle number density in the benzene flame was greater by about a factor of two. The post-flame gases of aromatic fuels have PAH concentrations about 100 times those of the post flame gases of aliphatic fuels (8). Nevertheless, acetylene is still the principal hydrocarbon in these burned gases (120).

Several groups have made measurements of soot formation and growth in premixed flat flames. Bonne et al. (54) andHomann and Wagner (8) made mass spectral measurements of the post flame gases of low-pressure acetylene and benzene flames. They argued that only the larger observed polyacetylenes such as C i0H 2 and Ci2H2 were important as surface growth species. Wersborg et al. (20) found thatthe surface growth rate dropped steeply with height above the burner (that is, with the age of the particles) and also believed that polyacetylenes might be the principal surface growth species. Wersborg et al. (147) later concluded that very large hydrocarbons (massing more than 250 amu) might make significant contributions to surface growth, while Prado and Lahaye (148) have suggested that polyacetylenes or polyaromatics could be important. D'Alessio et al. (62)speculated that unsubstituted PAH would be rather inert inthe post flame environment, while the more reactivePAH-with-sidechains are present in such low concentrations

that they could not contribute significantly to surfacegrowth.

Karris and Weiner (149,150) studied premixed ethylene-air flames and concluded that the increase of soot growth rate with increasing equivalence ratio is accounted for primarily by the increased surface area available for growth rather than by increased concentrations of surface growth species. Thus, the processes controlling the ultimate soot loadingmust occur prior to the growth stage: that is, duringnucleation. Although nearly all the final mass of the soot is contributed by surface growth, it appears that richer flames produce more soot because they have a higher nucleation rate and thereby more surface area from the beginning of the growth stage. The surface growth in Harris and Weiner’s flames could be accounted for if acetylene were the primary surface growth species. Harris and Weiner speculate that surface growth processes are essentially similar in all aliohatic flames (150) and that therefore acetylene is the common growth species for all such flames.

Harris and Weiner (151) later extended their soot formation studies to include several toluene/ ethylene premixed flames. Although the presence of toluene enhanced soot formation, Harris and Weiner found that the surface growth in the toluene/ ethylene flames involved only acetylene, as had been observed in pure ethylene flames.

452.2.4.2 Coagulation and Aggregatioi

Graham and coworkers (30,122,126) studied coagulation of soot particles in shock-tube pyrolyses of aromatic hydrocarbons by monitoring laser— light extinction at 488, 633 and 3390 nm and laser— light scattering at 488 nm. They interpreted their measurements of the coagulation rate in terms of "a model aerosol, of spherical sticky particles which have the self-preserving size distribution characteristic of free molecule coagulation'' (30). Graham (126) suggested that collisions in the first one or two milliseconds are ccalescent rather than chain-forming. He believed that the young particles act as liquid droplets in the sense that all collisions are perfectly coalescent and sticky (122).

The line between coagulation and agglomeration can be a fine one, since surface growth continues during the early stages of agglomera.tion (26) and may fill in between the agglomerated particles. Wersborg et al. (20,152), in workwith premixed acetylene flames, noted that the marked appearance of chainlike clusters occurred just after surface growth became very slow and speculated that the earliest collisions are hidden by the rapid simultaneous surface growth which tends to fill in the boundaries between particles. This interpretation has been supported by ultrahigh-resolution electron micrographs (153).

The use of alkali and alkaline earth metal additives presumably creates positive charges on the young soot particles (70). Such additives cause the final soot particles to be much smaller and more numerous. This effect is consistent with positive charges on the young soqt particles inhibiting coagulation.

Wersborg et al. (20,134) found that coagulation of soot particles occurs at all positions in the flame; this process combines with surface growth to form particle clusters that gradually change from roughly spherical, at low positions in the flame, to chainlike in the flame tail. They believed that electrostatic interactions between particles are responsible for the formation of particle clusters in chains rather than more compact shapes.

2.3 SUMMARYThere are several questions about the method of formation

of soot particles to which current experimental techniques have not provided conclusive answers. Three examples are the following:

1. Are unsubstituted polyaromatics important as intermediates in the soot-formation process or are they merely stable byproducts?

2. Is either butadiene or acetylene important as a soot precursor for most nonaromatic fuels?

473. Can free-radical chemistry explain the rapid growth

of large polyaromatics?The purpose of the detailed kinetic model described in

Chapters V - VII is to attempt to answer questions such as those posed above. The results of computational simulations can complement those of physical experiments and lead to greater understanding of the complex chemical processes leading to particulate formation.

Chapter III EXPERIMENTAL FACILITIES AND PROCEDURES

Experiments measuring soot yield of benzene-argon and toluene-argon mixtures were performed behind reflected shock waves in a 7.62-crn inside diameter stainless-steel conventional shock-tube (see Fig. III.1). A shock-tube uses the irreversible adiabatic compression of a shock wave to produce high temperatures in gaseous mixtures (154-157). The shock wave is created by the expansion of a high-pressure gas into a low-pressure gas. The section of the shock-tube initially containing the high-pressure gas is termed the "driver" section; the low-pressure half is called the "driven" section. These two sections are initially separated by one or two diaphragms which are ruptured to initiate the shock wave.

The length of the driver section of the shock-tube was 3 m and that of the driven section was 7.3 m. The double-diaphragm burst technique was used to initiate the shock wave for most of the experiments. A single diaphragm was used for several low-pressure experiments. The diaphragms used were made of Mylar and ranged in thickness from 0.5 to 2.0 mil. Aluminum foil was used as diaphragm material for some experiments in Series E (Table IV.1),

- 48 -

Figure III.1 The conventional shock tube facility.

Televac Thermocouple Gauge

9

Back-fill gas (Argon)

Edwards ED 500 Roughing Pump

Driver Section

r ~

Argon

Aromatic Hydrocarbons

Digital DatametriC6 Gauge

S] a< er

Heise Precision Gauge

Helium

Edwards E-0i* Diffusion Pump —j |Edwards ES 150 Backing Pump

'Televac Ion Gauge

-Storage TanksRCAPhotomultipli

Power Supply

t W - i

7,62cm i.d.___ Driven SectionPressure Trpnsduccfs Amplifier

He-Ne Laser pofcr Sup'p

I . Timer INicolet Digital

OscilloPower Supply

50Before an experiment, the driven section of the

shock-tube was evacuated by an Edwards model ED-500 mechanical vacuum pump. After a sufficiently low pressure (ca. 0.01 torr) was achieved, the driven section of the shock-tube was evacuated to 1.0 • 10~5 torr or less using anEdwards Speedivac E-04 oil diffusion pump. The diffusion pump was backed by a.n Edwards model ES-150 mechanical vacuum pump.

Pressures during the evacuation of the driven section were monitored by a Datametrics model 1174 capacitance manometer having a pressure range of 0 to 100 psia, by a Televac model 2A thermocouple gauge having a range of 0.001 to 1.0 torr and by a Televac model 3B ion gauge having a range of 1.0 • 10“8 to 1.0 • 10"3 torr. The capacitancedigital manometer and the thermocouple gauge were located in the gas-handling manifold and the ion gauge was located in the intake section of the diffusion pump. The pressure of the test gas introduced into the driven section of the shock tube was monitored using either a 0 to 800 torr Wallace and Tiernan model FA-145 precision dial manometer or the capacitance manometer. The high pressures of the driver section were measured using a Heise model C (0 ~ 500 psia)precision gauge.

Incident shock velocities were measured using fourAtlantic Research LD-25 pressure transducers locatedsequentially along the top of the shock-tube. The

transducers triggered the start and stop channels of an interval timer built at the Chemistry Department of the University of Texas so that the times at which the shock wave reached three succeeding locations (the first transducer defined zero time and distance) could be measured. All time measurements were accurate within one microsecond (out of an observation time of 1500 - 2500microseconds). These times and calculated velocities were used to find the parameters in a linear extrapolation of the velocity of the incident shock wave to the end wall of the shock-tube (158). The incident shock wave decelerates because of boundary layer growth due to viscous drag between the shock wave and the tube wall. The observed shock wave attenuation was approximately 2%/m. All pressuretransducers and optical windows were mounted flush with the surface of the shock-tube to minimize flow distortion.

The temperature, pressure and concentrations behind the reflected shock wave at the end wall were determined from the incident shock velocity at the end wall, the pre-shock gas temperature and composition, the thermochemical properties of the' appropriate gaseous species (159) and the steady-state, one-dimensional equations of momentum, energy and mass conservation rearranged into a suitable form (160). The calculations assumed no chemical reaction behind the incident shock wave and full vibrational relaxation.

The soot, conversion was determined by measuringattenuation of a beam from a 15-mw cw Spectra-Physics He~Ne laser which was operated in the visible (632.8 nm) region of the spectrum. The laser beam crossed the shock-tube at a point 10 mm from the end plate. High quality sapphire windows were used. The attenuated laser light was monitored by an RCA 1P28 photomultiplier. The design of the optical system was optimized so that emission was only a negligible component of the extinction signal (161). This was achieved by using the laser beam at maximum power, a narrow-band interference filter centered at 632.8 nm and a number of optical stops. Careful alignment and adjustment of theoptical system resulted in an excellent signal-to-noiseratio of the absorption signal (see Fig. III.2).

The soot yields were calculated according to Graham’s model (30). Graham assumed that young soot particles are spherical and that the particle diameters are small compared to the wavelength of the incident light. In such a case, the smal1-particle ("Rayleigh”) limit of Mie theory applies (162). Below the Rayleigh limit the ratio of scattering efficiency to extinction efficiency has been calculated to be very small, so soot particles are considered to be only emitters and absorbers. The emission signal from soot has been shown to be quite small in comparison with the absorption signal and can be neglected (18). Therefore, the soot yield Y, defined as the fraction of carbon atoms

Laser

Inte

nsit

y,

(arbitrary

scal

e)

5 3

Figure III.2 Typical pressure and laser-extinction traces behind a reflected shock wave. C0742: T 5 = 1816 K,Ps = 2.29 bar.

Maximumtesttime

Expansion wave arrivalReflected

shockarrival

Time / ms

(arbitrary

scal

e)

54initially present which has become soot, can be calculated as :

Y = N P X In [1(0)/I (t) ] / (72tt 1 E(m) [C]0>

where:Y is the fractional soot yield,N is Avagadro’s number,p is the density of a soot particle,X is the wavelength of the incident light,1 is the optical pathlength,[C ]o is the initial concentration of carbon atoms, [l(0)/I(t)] is the absorbance,m is the complex refractive index of a soot particle,

and E (m ) = -Im [(m2 - 1)/(m2 + 2)].

The complex refractive index, m, is the quantity least well known in this expression for soot yield. To emphasize the uncertainty in its value, the soot yields determined in this work are presented in the form Y * E(m).

There are questions concerning the lasei— extinction model itself. First, Graham et al. (30) believed that in theearly stages of soot formation the laser extinction was due not only to the solid particles but also to large gas-phase species. Light at 632.8 nm may be absorbed by compounds with as few as six aromatic rings (163); however, Rawlins and coworkers (164) and Menna and D ’Alessio (165) concluded that light extinction at this wavelength is caused primarily by soot particles.

55Frenklach et al. (166) have noted that soot particles may

exceed the Rayleigh size-limit causing ovei— estimates ofsoot yield if the Rayleigh limit is assumed. Dyer and Flower (60) argued that optical techniques may overstate soot yields by as much as a factor of two or three. These concerns about the absolute magnitude of soot yield as determined by optical techniques provide an additional basis for the presentation of relative values of soot yields.

The pressure behind the reflected shock waves was monitored by a PCB model 113A24 piezoelectric pressure transducer with built-in amplifier, which had a rise time of less than one microsecond. This pressure transducer was located on the upper surface of the shock-tube above the optical station, 10 mm away from the end wall. A PCB model 482B power supply was used with the pressure transducer.

Output signals from the pressure transducer and the photomultiplier were digitized, displayed and recorded on Nicolet model 2090-3 digital oscilloscopes capable of sampling dynamic information with two channels of sequentially accessed memory. Each channel could store 2048 data points. The oscilloscope had 12-bit resolution and a maximum digitizing rate of 2 MHz. The displayed oscillograms could be stored permanently on a magnetic diskette for later analysis. An example experimental traceis displayed in Fig. III.2.

56The data were transferred from one of the Nicolet

oscilloscopes to an Apple 11+ microcomputer via a GPIB/IEEE-488 interface (167). The data were reduced in the Apple 11+ using Pascal language programs before being transferred to an IBM 370-3081 mainframe computer (168).

Two cylindrical stainless steel tanks having volumes of 37 1 each were used to prepare and store test mixt.ures. Before a test mixture was prepared, the tank to be used was heated for at least twelve hours at temperatures near 180° C while being continuously evacuated by the rotary mechanical pump. The tank then was cooled to room temperature while being evacuated by the mechanical pump before being pumped down to a pressure of 5.0 • 10"6 torr or lower with thediffusion pump. The tanks were heated using electical resistance cable (AnaConda Industries, 19 AWG) which had been spot welded to the exterior of each tank ( 160). The heating cable was covered with aluminum foil and one inch of insulation to reduce heat losses.

The test gas mixtures were prepared manometrically. The argon had a stated purity of 99.998% (prepurified, Matheson) and was used without further preparation. The toluene (Reagent grade, Baker) and benzene (Spectranalyzed, Fisher) were purified by repeated freezing and evacuation. The driver gas was helium (99.99%, Big Three Industries), which was also used without further purification. The shock-tube was cleaned after every experiment.

Chanter IV EXPERIMENTAL RESULTS

Five experimental series involving a total of 117experiments were performed in this study. The range of experimental conditions for each of the test mixtures is summarized in Table IV.1; Appendix A contains a complete list of the conditions and results of these experiments. The experiments were conducted at temperatures from 1460 to 2930 K, pressures from 0.32 to 3.73 bar and initial molar percentages in argon of 0.10% to 1.0%. Series A of Table IV.1 was used to study the sooting behavior of benzene under pyrolytic conditions; Series B, C, D and E were used tostudy soot formation during pyrolysis of toluene. Theconditions for Series B through E were chosen to isolate the effects on soot formation from toluene of temperature, initial carbon-atom concentration and pressure. Series B, C and D were conducted over similar pressure ranges but at different carbon-atom concentrations. The range ofcarbon-atom concentration studied was from 0.64 • 1017atoms/cm3 to 6.4 • 1017 atoms/cm3. Series D and E were performed at identical carbon-atom concentrations but at different pressures (see Table IV.1). The mixtures were each studied over temperature ranges of several hundred degrees Kelvin.

- 57 -

Table IV.1 Ranges of experimental conditions.

Series Percent(vol.) T 5 P 5 [Carbon]x10"17in argon (K) (bar) (atoms/cm3)

A 0.31% C 6H6 1561-2272 1.93-2.87 1.67-1.75B 0.31% C 7H8 1600-2374 2.08-3.02 1.96-2.05C 1.00% C 7H 8 1529-2931 1.98-3.73 6.25-6.78D 0.10% C 7H8 1647-2050 2.15-2.64 0.64-0.66E 0.56% C 7H8 1462-2479 0.32-0.58 0.60-0.69

59Soot yields obtained from these five mixtures at

different reaction times are plotted versus temperature in Figs.’ IV. 1 through IV.5. The symbols represent actual

^ ' f

experimental data and the lines are cubic spline approximations to the data. The mixture of 1.0% toluene-argon (Series C) produced so much soot at reaction temperatures between 1900 K and 2600 K that observation times were limited to 0.5 ms.

Figure IV.6 compares soot yields obtained during pyrolysis of benzene and toluene (Series A and B). As seen in the Figure, the results obtained from the benzene and toluene mixtures are not significantly different.

Figure IV.7 presents results from pyrolysis of toluene at three different carbon-atom concentrations; Fig. IV.8 demonstrates the effect of pressure (see Table IV.1). The points to note are the shift of the soot-bell to higher temperatures for lower pressures and the increase in fractional yield and the shift to high temperatures for higher carbon-atom concentrations. These results are explained qualitatively by the conceptual model of Frenklach et al. (36,169). According to this model, soot formation from aromatic fuels requires both intact aromatic rings and nonaromatic fragments. The conceptual model can besummarized using the skeleton mechanism

k iA --------------X

k zA + X ------- ► S

SOOT

YIELD

m xE

(m)

60

oo 0. 311 7. C6H6co­co □ 0. 50 ms

o 1 . 0 0 ms

oA 1 .5 0 ms

aLfj-CM

+ 2. 00 ms

f t/

r v ^ 'U 2

^MOO. 1600. lbOO. 2000.T E M P E R R T U R E / K 2200. 2U00.

Figure IV.1 Soot yields vs. temperature at differentreaction times for the mixture 0.31% benzene—argon(Series A ).

SOOT

YIELD

{'/.) x

E (m)

61

ooO'cn

ooID'C\J

0.3 11 V. C7Ha + fir

□ 0. 50 msO 1. 00 ms A 1 . 5 0 ms

+ 2. 00 ms

^ 500. 1700. 1900. 2100.T E M P E R R T U R E / K 2300. 2500.

Figure IV.2 Soot yields vs. temperature at differentreaction times for the mixture 0.31% toluene-argon(Series B).

SOOT

YIELD

(7.) xE

(m)

62

oo(Vi

0. 25 ms

0. 50 ms

1 .0 0 ms

ooo~(VI

oco~

oo( \ l “

oCD

oo=r

oo3000.2700.2100.T E M P E R R T U R E / K

Figure IV.3 Soot yields vs. temperature at differentreaction times for the mixture 1.00% toluene-argon(Series C).

SOOT

YIELD

r/J xE

(m)

63

o1 .0 0 ms

1 .5 0 ms

2. 00 ms

C\J-

oo

CO

ooco

o

ooCM

2100.1900. 2000.1600.T E M P E R R T U R E / K1700.

Figure IV.4 Soot yields vs. temperature at differentreaction times for the mixture 0.10% toluene-argon(Series D ).

SOOT

YIELD

(X)x

E(m)

64

o0 . 5 0 ms1 . 0 0 ms

1 .5 0 ms2 . 0 0 ms□

oaCO

o

oo

aoCM

2500.2300.2100 .1900.1700. T E M P E R R T U R E / K

Figure IV.5 Soot yields vs. temperature at differentreaction times for the mixture 0.56% toluene-argon(Series E).

SOOT

YIELD

iX) x

E Cm)

oID'

T IM E = I . 0 ms□ --------- 0 .311 XC6H8 + flr

o

oCD

oCO

oCD

OD2000. 2200.1600. 1800.TEMPERflTURE/K

Figure IV.6 Comparison of soot yield at 1.0 ms for the mixtures 0.31% benzene-argon and 0.31% toluene-argon.

66where A, X and S denote initial product, intermediate species and final product, respectively.

A simplified summary of the results of this model is that the yield of final product, S, is a function of r, defined as r = ki/(k2 [A]0>. A maximum of yield versus r occurs only when r is varied by changing its numerator (36,169).

The fragmentation rate constant ki is assumed to be pressure dependent (Ref. 36 and references therein); thus a decrease in pressure will reduce its value. However, ki is also more temperature sensitive than thepolymerization-reaction rate constant k 2 , so a simultaneous decrease in pressure and increase in temperature will maintain the same value of r. Thus, the shift of low-pressure soot bells to higher temperatures can be rationalized within the conceptual model. The decreased sensitivity of the bell to pressure while at high pressures is also explained, since pressure-dependent rate constants become independent of pressure at high pressures.

The explanation of the concentration dependence is more complex. As presented here, the skeleton mechanism of the conceptual model predicts a monotonic increase in yield as fuel concentration increases (169). The shift of the soot-yield maximum to higher temperatures as fuel concentration decreases makes sense in the context of the explanation given for pressure decreases, i.e. the maximum soot yield occurs at a characteristic value of r.

SOOT

YIELD

m xE

Cmj

67

oooc*>

T IM E = ! .0 ms

o

oo

o

o

oom

oo2700. 3000.2 1 0 0.1800. T E M P E R R T U R E / K

Figure IV.7 Comparison of soot yield at 1.0 ms for themixtures 0.10% toluene-argon, 0.31% toluene-argon and1.00% toluene-argon.

SOOT

YIELD

m xE

(m)

68

om

TIME=1. 0 ms

— 0.563*: C7Hb + flpoCD

aIf)

OaCD

□IS)

J D

2350. 2600.1850. 2100.T E M P E R R T U R E / K

Figure IV.8 Comparison of soot yield at 1.0 ms for the mixtures 0.56% toluene-argon and 0.10% toluene-argon.

69If, however, one postulates that side products of the

chain process can interfere with the production of S by removal of A or chain carriers, then a bell-shaped dependence of yield on fuel concentration will result. Thedependence of yield on concentration will then varyaccording to the initial concentration of fuel. In fact, opposite dependences of soot yield on toluene concentration have been previously observed (170,171).

Figure IV.9 presents the definitions of the induction time for soot appearance, r(soot), and the rate of sootformation, R(soot). The results of r(soot) are reported in Figs. IV.10 - IV.12 while the results for R(soot) are shown in Figs. IV.13 - IV.14. There were some instances when the induction time and/or rate of soot formation could not be measured. They were: 1) when the shape of the laser tracewas such that the inflection point on the trace was notclearly defined, as was occasionally true for the low-pressure toluene mixture (Series E of Table IV.1); 2) at very low temperatures when the induction time was longer than the observation time; and 3) at very high temperatureswhen the induction time was close to zero. It was sometimespossible to measure the rate of soot formation undercondition 3).

A comparison of the induction times for soot appearancefor the 0.311% benzene-argon and the 0.311% toluene-argonmixtures is presented in Fig. IV.10. The toluene mixture

Laser

Inte

nsit

y,

(arb

itra

ry

scal

e)

Maximum test t i me

Reflectedshockarrival

Expansion wave arrival

4.03.02.01 .0

T i m e / ms

Figure IV.9 Definitions of induction time for sootappearance, Tsoot , and rate of soot formation, Rsoot

(arb

itra

ry

seal'')

71om

0 oc\j.1

oLf)

o 7-d)in

•V oo°.O m.in i

t-o-* o cn m

cn - — I I

oa■

=1*.i

oLD=ri

o

■0.311 7. CgHg + Rr CCD'vl. 71 xlO17 carbon atoms/cm3 •0.311 C7Hb + Rr CCD~2. 00 x 1017 carbon atoms/cm3

//m /

/ m / t D

//O

[2

/ -0

f /

/o

4. 50 s'.oo 5.50 6.00103 K / T 6.50 7.00

Figure IV.10 Comparison of induction times for sootappearance for the mixtures 0.31% benzene-argon and0.31% toluene-argon.

ooa

CM.I

OinCM.I

aoO© to,in i

oo °S 1".

- CO. I

CDO O _J o

=f.I

oLO

■

I

oaLOi

□ ----- 0. 10 X C7H8 + flrCCI3~0. 64 «1017 carbon atoms/cm3

O ---------0 . 3 11 V. C7H8 + flrCC3~2.00 *1017 carbon atoms/cm3

A ----- 1.00 V. C7H8 + flrCC3~6. 40 *1017 carbon atoms/cm3 .

& y

q ^ / o

/

4.00 41. 50 5.00 5.50103 K / T 6.00 6.50

Figure IV.11 Comparison of induction times for sootappearance for the mixtures 0.10% toluene-argon, 0.31toluene-argon and 1.00% toluene-argon.

0 oc\j.1

oinc\j_

00in O

0-MO rn_

1Oin

t-w 00 in

■O) cn_1O 1

_l

ooa

=r.i

aLO

■

=ri

□o

- -0. 10 X C 7Hb + flr • — 0. 5632 C7H8 + flr

4.00

' o

O V C J E ]

4T 50 5r.OO 5^ 50103 K / T 6.00 6.50

Figure IV.12 Comparison of induction times for soot appearance for the mixtures 0.10% toluene-argon and 0.56% toluene-argon.

Log10

(Rat

e/se

c-1)

2.00

2.

20

2.140

2.

60

2.80

3.

00

3.2

0I .

__ I

I I

I I

I

74

0

A

.00

0.311 X C6Hs + flrC C 3 ~ 1 .71 *1017 carbon atoms/cm30.311 Z C 7H8 + flrCCI]~2. 00 *1017 carbon atoms/cm3

Ao

A00

A

0A0

A

5. 0014.50 5.00 5.50103 K / T

6.50

Figure IV.13 Soot, formation rates for the mixtures0.31% benzene-argon and 0.31% toluene-argon.

Log10 (

Rate

/sec

-1)

a.

20 1.

80

2.110

3.00

3.

60

>1.20

4

.80

I

1 I

I I

I I

75

A 0.311 Z C 7Hb + HrCCIK2. 00 xlO17 carbori* atoms/cm3

+ 1. 00 V. C7Hb + flrCC3~6.U3«1017 carbon atoms/cm3

X 0. 10 X C7H8 + flrCCU'v.O. 6*4 *1017 carbon atoms/cm3

O 0.563'/. C7H8 + flrC C 3 ~ 0 .64 *1017 carbon atoms/cm3

+++

++

oX

.00 3.00 4.00 5.00 6.00 7.00103 K / T

Figure IV.14 Soot formation rates for the mixtures0.31% toluene-argon, 1.0% toluene-argon, 0.10%toluene-argon, and 0.56% toluene-argon.

76exhibited slightly shorter induction periods than did the benzene mixture. Figure IV.11 shows the effect of toluene concentration on induction time: higher carbon-atomconcentrations lead to shorter soot induction times. Finally, Fig. IV.12 demonstrates that pressure does not have a strong effect on induction times for soot appearance from toluene.

The rates of soot formation from Series A and B of TableIV.1 are compared in Figure IV.13. The conclusion to be drawn from the Figure is that soot-formation rates for these conditions are not significantly different for toluene and benzene. The slightly larger soot-formation rates for toluene are probably a result of the higher carbon-atom concentration of that mixture; as noted in Fig. IV.14, soot-formation rates are larger for mixtures with higher fuel concentrations

Chapter VEMPIRICAL MODELING OF SOOT FORMATION FROM

AROMATICS

5.1 INTRODUCTIONThe ability to oredict the amount o£ soot formed under

various experimental conditions is one of the challenging problems for combustion science. Although detailed modeling (172) will play an increasingly important role in the development of this predictive ability, empirical models are still necessary. Empirical models allow one to summarize the abundant experimental data on soot formation in a systematic manner. These models have two prominentapplications: to predict soot yield within the range ofexperimental conditions for which the model was developed and, within this limitation, to be used for design and optimization of practical combustion devices; and to serve as quantitative restrictions for the development of detailed models (173). In this regard, it is pertinent to recall the practice of using Arrhenius-like exponential models to summarize ignition delays in individual sets of measurements. These correlations have been usedsuccessfully for prediction of the explosive properties of gaseous mixtures (174-176). At the same time, without

- 77 -

7 8

directly revealing the physical nature of the phenomenon, these empirical ignition-delay models have been important quantitative guides in the derivation of detailed kinetic models, which in turn did lead to understanding of the underlying reaction pathways to ignition (98,177-179).

Several empirical approaches for correlating the tendency to soot in flames with the fuel characteristics have been suggested recently (58,180,181). It is also of interest to consider the correlation of soot yields for transient rather than steady-state conditions. To account for soot formation under transient conditions, measures such as induction time for soot appearance and rate of soot formation have been considered (34). However, not only are these oversimplified measures poorly defined experimentally (31), they can not adequately predict soot yields, which have non-trivial experimental dependencies. A purely analytical approach to modeling of soot formation in thermal decomposition of hydrocarbons was recently proposed by Gordiets et al. (182). Although their model was found to be in qualitative agreement with experimental data, the authors pointed out the presence of a "marked divergence between theory and experiment."

In this chapter, a quantitative approach to empirical modeling of soot formation is presented (183). The objective of the modeling is to predict soot yield for a given reaction time at various temperatures, pressures, and

79initial reactant concentrations. This approach could be extended to include various fuels; however, the technique will be introduced by considering a simple case of soot formation, that of shock-tube pyrolysis of toluene.

5.2 DISCUSSION5.2.1 Statement of the Problem

The empirical model is postulated as ki

A

A + X 0

A + X i

gin X i

X 2

fragmentation

polymerization { 1 }

A + Xi X i+1 /

which is the mathematically simplest (i.e. allowing closed form analytical solution) kinetic scheme that has all the features of the conceptual model for soot formation in pyrolysis of aromatic hydrocarbons suggested recently by Frenklach et a l . (36). Reactant A in the mechanism denotesa species with an intact aromatic ring and Xi denotes the i-th intermediate. The reactions are assumed to be irreversible; nevertheless this does not necessarily eliminate thermodynamic resistance - since the model is empirical by definition, this resistance will be reflected

80». -irin the parameter values. I£, however, the reversibility were included explicitly, i.e. by considering reactions {1} to be reversible, no analytical solution of the resulting differential equations would be possible.

Species Xj , X J+i, ... of the system constitute what we will call soot, i.e.

Soot { X j , Xj + ... }•The soot yield is defined as

00

Y = 2 (i+1> C[Xi]/[A]o) {2}.1 = J

where: Y is the soot yield}[ X i ] is the concentration of species X i j

[A] o is ‘the initial concentration of A.Defined in this manner, the soot yield is the fraction of fuel initially present which is converted to soot. This definition is in agreement with its experimental counterpart. The (i+1) in Eq. {2} accounts for the number of molecules of A "contained” in X,.

The objective is to derive an expression for Y as a function of experimental parameters. The derivation of this expression is given below.

815.2.2 Derivation

The differential equations for reaction system {1} take the form

COd/dt [A] = - k,[A] - 2 k2 [A][Xj]

i=0d/dt [X0] = ki[A] - k 2 [A][X0] d/dt [Xx] = k 2[A][X0] “ k 2[A][Xi] \ {3}

d/dt [Xi + 1] = k2 [A][Xi] - k 2[A][Xi + J

with the initial conditions [A]|(t=0) = [A]o[Xi] |(t=0) = 0 , i = 0,1,2,...

Introducinq the "dimensionless concentrations" a = [ A ] / [ A ]0 and Xi = [ X i ] / [ A ] 0 ,

dividing both sides of each differential equation {3} bykia, and substituting, as discussed by Holland and Anthony( 1 84-) ,

k i adt = dr {4-}we obtain

COda/dr = - 1 - 2 Xi/r (5a}

i=0dx0/dr = 1 - x 0/rdxi/dr = x 0/r - x t/r ( (5b}« • • • • • • • • •

d X i / d r = X j - t / r - X j/r

82

with the initial conditionsa |(r=0)= 1 {5c)Xi|(r=0)= 0, i= 0,1,2,...,

where:r = k 1/(k2[A]0). {6}

The resultant system of linear differential equations {5b}can be readily solved by, for example, the Laplace transformtechnique (185). The Laplace transforms of equations {5b} are

f0 Cs) = 1/s • 1/(s + 1/r)fi(s) = f 0 (s ) / {r ■ (s + 1/r)}

fi(s) = fi-!(s)/{r-(s + 1/r)}• • • » • • • • • • • • • •

where fi(s) is the transform of the i-th dimensionless concentration, x,. The set of transformed eauations can be solved by substitution to show that

i i + 1f i(s) = 1/r ■ 1/s • {1/(s + 1/r)} i= 0,1,2,...

Application of the convolution theorem (185) to find the inverse Laplace transform yields the solution

Xi = [X j]/[A ]o = r P(i+1, r/r), i= 0,1,2,..., {7}where:

r/rP(i+1, r/r) = 1/i! J" exp(-u)u du

0

83is the incomplete Gamma function (186). It can be noted that 1

4

CO2 Xi = r {8}i=0

as is demonstrated below:r/r

1CO OO CO2 Xi = 2 r P(i+1, r/r) = r 2 1/i! / exp(-u)u dui=0 i=0 i=0

0/

r/r t / tCO i

= r 2 exp(-u)u / i ! = r / ( 2 exp(-u)u /i!)dui=0

0 0/ OO

( 2 < i=0

r/r= r j du = t

0since by definition of the Poisson distribution (187)

CO i2 exp(-u)u / i ! = 1. i = n

Substituting {8} into {5a}, we obtain da/dr = - 1 - r/r,

the solution of which, taking into account the initial conditions {5c}, is

a = 1 - T - rV2r. {9}Substituting {9} into {4}, we obtain

t T

d t / ( 1 - t - r 2 / 2 r )

0 0

Lr 7/k dt = /or

k tt = 1/q In {(r/X2-r)/(r/X!~r)}

84

where:

X ! = -1 + q

X 2 — — 1 ~ q q = >/l + 2/r;

orr = r { l-exp(qkit)}/{1/X2 - 1/Ai • expCqk^)} . {10}

The last expression relates the "transformed time" tau, the physical meaning of which is disclosed through Eq. {8}, withthe real time t. Hence, substitution of {6} and {10} into {7} and {9} determines the kinetic behavior of reaction system {1}.

The expression for soot yield {2} can be developed in the following manner. Let us rewrite expression {2} as

CO CO j — 1

Y = 2 (i+Dx, = 2 (i+1 ) x i - 2 (i+1 ) x i {11}i=j i=0 i=0

where the first sum on the right-hand side of thisexpression is easily determined:

CO OO CO

2 (i+1)Xi = 2 iXi + 2 Xi {12}i=0 i=0 i=0

As seen in {8}, the last term in {12} equals tau. For the other term on the right-hand side of Eq. {12}, we obtain

t / t

CO CO CO r i2 iXi = 2 i-r P(i+1,r/r) = r 2 i • 1/ i ! I exp(-u)u du i = 0 i= 1 i= 1 J

0

85r/r

08 f= r 2 I exp(-u)u /{(i-1)!} dui = 1 J

0T/r

= r J { 2 exp(-u)u /(i-1)!} du 0

T/r r/r/ °° k fu { 2: exp(-u)u /k! } du = r / udu = r2/2rk=0 J

0 0where:

=0 k 'k = i - 1 and 2 exp(-u)u /k! = 1k=Q

That is,OO2 (i+1)x i = r + rz/2r. {13}i=0

In order to determine the second sum on the right-hand side of expression {11}, let us recall one of the properties of the incomplete Gamma function (186), i.e.

P(i+1, T/r) = P (i ,r/r) - exp(-r/r) ■ (r/r) / i!or

i kP(i+1, r/r) = 1 - 2 exp(-r/r) • (r/r) / k! .k=0

Therefore, using expression {7},i k

Xi = r { 1 - 2 exp(-r/r) • (T/r) / k!}k=0

and then

86

j-1 J-1 i2 (i+1)Xi = 2 (i+1)r { 1 - 2 expC-r/r) • (r/r) / k ! }i=0 i=0 k=0

j~1 j“ 1 i= r { 2 (i+1) - 2 (i+1) 2 exp(-r/r) • (r/r) /k! }i=0 i=0 k=0

= r { j(j+1)/2 -• T-1 i2 (i+1+j)(j-i)(r/r) exp(-r/r)/(2)(i !) }. {14}i=0

Thus, substituting {13} and {14} into {11}, we obtainY = r {r/r + t z/2rz - j(j+1)/2

j - 1 i 0 5 }+ 2 (i+1+j) (j-i )exp(-7-/r) (r/r) /(2)(i!)}.i=0

5.2.3 Model FitThe results from five series of experiments on soot

formation during pyrolysis of toluene were used for the development of the empirical model. The experimental conditions are listed in Table V.1. These conditions were chosen in order to isolate the effects of temperature, pressure and carbon-atom concentration on soot yield. Theresults of four of the Series (B, C, D and F) are presentedin Figs. V . 1 - V.3. Series F is taken from the work ofFrenklach et al. (36); the other data are from this work andare discussed in more detail in Chapters III and IV.

Expression {15} together with relationships {6} and {10} constitute an empirical model for soot formation which

Table V.1 Ranges of experimental conditions.

Series Percent(vol.) T 5 P 5 [Carbon]X10"17in argon (K) (bar) (atoms/cm3)

B 0.31% C 7H 8 1600-2374 2.08-3.02 1.96-2.05C 1.00% c 7h 8 1529-2931 1.98-3.73 6.25-6.78D 0.10% C 7H8 1647-2050 2.15-2.64 0.64-0.66E 0.56% C 7H 8 1462-2479 0.32-0.58 0.60-0.69F 1.75% C 7H 8 1654-2347 0.31-0.53 1.65-2.00

88contains three unknowns: j, ki and k 2. A general approachfor fitting the model would be to minimize

2 {Y(calc,i,t) - Y (expt,i ,t )}2 , {16}i , t

where Y(expt,i,t) and Y(calc,i,t) are the experimentally observed and the calculated soot yields for the i-th experiment at observation time t. The summation would be taken over the entire set of experiments and the chosen number of reaction times (20 to 25 in this work). A difficulty with this approach is that the experimental determination of soot yields depends strongly on the knowledge of the complex refractive index (36), the value of which is not well-established. Therefore, it was desirable that the modeling results not depend on the refractive index. This was achieved as follows. Instead of minimizing objective function {16}, we minimized

2 {YCcalc,i,t)/Y#(calc) - Y(expt,i ,t)/Y#(expt)}2, {17}i , t

where Y*(expt) is the experimental soot yield at specified reference conditions and Y*(calc) is the soot yield calculated by Eg. {15} at these conditions. The reference conditions in our modeling were chosen as the 0.311% C 7H 8-Ar mixture at T = 1977 K, density = 1.54x10-5 mol/cm3 and time = 1.0 ms. These conditions correspond to an experimental point at the approximate center of the ranges of the experimental variables of interest.

89Since the present modeling is empirical in nature,

meaning the goal is simply to fit experimental data, the objective function for minimization {17} can be rewritten as

2 {(Y/Y*)(calc,i ,t ) - (Y/Y*)(expt,i ,t )}2. {18}i . t

The form of expression {18} implies that (Y/Y*)(calc) should be considered as a single entity and no physical meaning should be attached to Y(calc) or Y*(calc) alone. That is, the empirical model predicts relative values and in order to obtain the absolute value-of soot yield at given conditions one must multiply the corresponding (Y/Y*)calc by the actual soot yield at reference conditions, Y*(expt). One way to estimate the value of Y*(expt) is to use the relationship Y*(expt) • E(m) = 10.11; this method requires one to choose a value for the complex refractive index, m. The quantity E(m) is defined as E(m) = -Im{(m2 - 1)/(m2 + 2)} (30) andthe number 10.11 is an experimental result determined in this work.

After several trials, the following forms for the rate constants were assumed

kj = A exp (-0i/T) par yk 2 = B exp (-02/T) p [a] o

w h e r e :

T is the initial reaction temperature in K;P is the total density in mol/cm3;

[A]0 is the initial concentration of toluenein mol/cm3;

the units of k t and k2 are mol, cm3 and s.

90Thus there are eight parameters to determine, namely A.B. .0Zl a,0,7 and j. Minimizing expression {18} for all five toluene-argon series, the following results were obtained:

A = 6.67 • 101 1

•i = 2.38 • 10“a = 0.858B = 2.68 • 101 0

= 6.47 • 10“B = 0. 1397 = -0.413

j = 6 (assumed!Although the quality of the fit was slightly better for j=3,for physical reasons (163) j=6 was assumed. Figures V.1-V.3 compare the experimental and computed values of Y/Y*. Figure V.1 shows the time development, Fig. V.2 - pressure dependence, and Fig V.3 - concentration dependence of soot yields. Although the quality of fit is generally good., itcan be improved if Series B of Table IV.1 is not taken intoaccount. Thus, by minimizing expression {18} for only four series, A,C,D and E, the following results were obtained:

A = 1.94 • 10“= 2.68 • 10“

a = 1.27B = 6.05 • 108®2 = -4.38 • 1036 = -0.361

91y = 0.0114j = 6 (assumed).

Figures V.4 - V.6 compare the experimental and new computed values of Y/Y*. As can be seen in these Figures, the quality of fit is significantly improved. It is not clear, however, whether this improvement is due to some experimental problems with Series B or simply the result of the empirical nature of the modeling.

It must be stressed that from the statement of the problem the model developed here is an empirical one. Therefore, although the numerical values of the obtained parameters can be rationalized conceptually (e.g., the difference of the temperature coefficients, - 9z, is alwaysa large positive number regardless of the specific form assigned to the rate coefficients ki and k 2; this result is in accord with a recent conceptual model (36)), one should refrain from assigning physical meaning to the parameter values of an empirical model (173,188). The parameters would contain physical meaning only if reaction sequence {1} has a strong physical basis.

92

oCO

oLDCM 2.0 ID 5

ooCM

Oin A A>-\>-

oo

oun

2000. 2200.icnr,1 uuu . 1600.T E M P E R R T U R E / K

Figure V . 1 Comparison of the model prediction with experimental observations for Series B. (First parameter set). Time development. The symbols represent actual experimental points; the solid lines are the predicted values.

93

oin

1.75 XC7Hb + flr

oorvj

x>—\>- oo

oino

oo1800. 2400.2100. 2700. 3000.T E M P E R R T U R E / K

Figure V.2 Comparison o£ the model prediction with experimental observations for Series B and F.(First parameter set). The effect of pressure. The symbols represent actual experimental points; the solid lines are the predicted values.

94

ooCO

0. 10 XC7Ha + nr

in(V

oCM

oin

oino

A A

3C00.2700.2100.1800. T E M P E R R T U R E / K

Figure V.3 Comparison of the model prediction with experimental observations for Series B, C and D. (First parameter set). Concentration dependence.The symbols represent actual experimental points; the solid lines are the predicted values.

95

o

msmsmsLn

CVI ms

ooCM

X oin>-\>-

oo

220 0 .1800. 2000.1600. T E M P E R R T U R E / K

Figure V.4 Comparison of the model prediction with experimental observations for Series A. (Second parameter set). Time development. The symbols represent actual experimental points; the solid lines are the predicted values.

96

in<M

oCM

>->- oo

omo

oo3000.2700.2100.TEMPERflTURE/K

Figure V.5 Comparison of the model prediction with experimental observations for Series B and F. (Second parameter set). The effect of pressure. The symbols represent actual experimental points; the solid lines are the predicted values.

oCM

RnoCO

oCM

>-\>- o

COo

o=r

O q

2500.2300.1900. 2100.1700. TEMPERFITURE/K

Figure V.6 Comparison of the model prediction with experimental observations for Series B and D. (Second parameter set). Concentration dependence. The symbols represent actual experimental points; the solid lines are the predicted values.

985.3 SUMMARY

A method for empirical modeling of soot formation during shock-tube pyrolysis of aromatic hydrocarbons has been developed. The method was demonstrated using data from shock-tube pyrolysis of toluene. As seen in Figures V.1 -V.6, the resultant model is in good agreement with experiment, reflecting the effects on the soot yield of thevarious experimental variables. The model can be used tosummarize the complex experimental dependencies observed in experiments on soot formation; thus it can be used fordesign and optimization of practical combustion devices and for quantitative tests of detailed kinetic models. It should be stressed that this model is empirical in nature. Therefore, one should neither expect soot yields to bepredicted adequately outside the operating ranges tested nor attribute physical meaning to the model parameters.

Chapter VI

DETAILED KINETIC MODELING OF SOOT FORMATION IN SHOCK-TUBE PYROLYSIS OF ACETYLENE

6.1 INTRODUCTIONSoot formation is an important and persistently

investigated aspect of combustion (4,5,12,189,190). Nevertheless, the elementary chemical reactions leading to soot formation are still unknown. There is growing evidence that the reactions leading to soot formation involve only carbon- and hydrogen-containing species, as oxygen is bound in rich flames as CO and H 20. For this reason a large number of studies of soot formation in hydrocarbon pyrolysis have been undertaken using flow reactors and shock tubes. While these experiments have not provided detailed composition profiles, they cover wide ranges of conditions and are more easily subjected to interpretive modeling studies at this time.

The object of the present investigation was to discover the main chemical reaction pathways to soot by experimenting with detailed kinetic models of soot formation under the conditions used in shock-tube pyrolysis of acetylene (31). The approach taken was to develop a mechanism composed of

- 99 -

100conventional elementary reactions and to compare the predicted time scale of soot formation and absolute values of soot yields with their experimental counterparts. Nearly all of the equilibrium constants and rate coefficients had to be estimated. A method to account for the infinite growth of soot mass also had to be developed.

After the reaction paths implied by our assumed thermochemistry and rate constants had been identified by study of the simulations, we became aware of a paper by Bockhorn et al. (108) in which astonishingly similarconclusions had been drawn from consideration of experimental composition profiles in sooting flames.

6.2 COMPUTATIONAL MODELThe reaction mechanism has three logical components: a

set of reactions describing acetylene pyrolysis, a set of reactions describing the formation of larger molecules and radicals and eventually small aromatic molecules and radicals, and a description of the further growth of aromatic rings. A total of approximately 600 elementary reversible reactions of 180 species were considered during the course of this modeling study.

The model consists of the simultaneous solution of the ordinary differential equations obtained from microscopic balances on the concentration of each species, the temperature and the fractional soot yield. The equations

101for species concentrations include both reaction terms and volume-change effects.

6«2.1 Reaction Species NomenclatureThe chemical species used in the mechanism are listed in

Table VI.1 with both their structures and assigned computer names. Small species, such as H and H 2 , whose computer names are identical with those used conventionally, are not listed in Table VI.1. The names were chosen for two principal reasons: first, complete IUPAC names were toolong and unwieldy; and second, each name was required to provide a reasonable description of the species' structure. This nomenclature system is not an attempt to design a universal method; it was developed to address the needs of our specific modeling work on soot formation. The task of developing a completely general nomenclature system is nontrivial (188).

The chemical species are described usina 12 or fewer characters. The following terms are used to specify the basic structure of a compound:

An: species of type A containing n fused aromaticrings. Species with these names include highly condensed polyaromatics such as pyrene, A4, and coronene, A7, (see Table VI.1) and the intermediates (of Route 1 of Fig. VI.2) leading to their formation, such as phenanthrene, A3, and

102

Table VI.1

c2h

c2h2

C2H3

C2H4

c4h

c4h2

c4h3s

c4h3u

Reaction species structures and assigned names.

•CsC-H

H-CsC-H

C = C H"' ^ HH /H.C=CH H

•C=C-C=C-H

H-C3 C-Cs C-H

H-C = C~ C ^ C - HiH

HiH - C = C - C. C-iH

103

c4h4HIH - C s C - C * C - H

iH

c4h5s H - C = C - H . HH ✓ N c -c : H

c4h5u H . ^ HC : = C ^,C = CH

c4h6 H^ C = C C H „H H H

c6h • C=C-C=C-C=C-H

c6h2 H-CsC-CsC-C sC-H

.O-Os0-O=O-HH-0i

H% 0 H0 H X*H9D

H

H-0 sHI

0 - 0 , 0-0S0-HIH* H 90

H 3 5> - ^ 0 , H

H

HI• o * 0 - O h O - O s O - H

iH

n€H9o

H -H

o - o = o SsH90

1701

105

O

o\ •oIIX o

\ / \O X IIo / \

x x

x\o%O X

\ / oII

X o \ / • oIIo / \

X X

XI

• owo-xIo-x

- oIoIII01X

XIx-o*o-xIo-x

If1 - 0Io

III01X

cninXC0o

3inx(0o

<£>X<0o

X X\ / oIIo / \ • x oIIx o

\ / \ O X IIo / \

X X

X X \ / oIIO X / \ / x o

IIX o\ /\ o xIIo • \

X

X -O

0 = 0 - / \

O.^ / 0 - 0 ./ l x

X X

toN-X(0o

3X(0o

S5CD(T

106

CcH6 n 8 H' c = c C H H» c ' H H h ^ C = C ' h ' H

c 8h • C = C - C = C ~ C = C ~ C = C “H

CoH8 n 2 H-CsC-C = C-Cs C — C = C-H

H- C= C - C. C_ C s C” HiChiCIH

H-C=C-C=C-C C~C=C-HiH

HIH-C=C-C=C-C C-C=C-H

H - C = C - C = C - C = C - C ^ C-HiH

o

XI

on01

0 -0 5 0 -X

xiohi01o - x//

//x - o

IoMl01X

x - oIoIII01

oIII01X

XI

o - x//

■oI

oIII01

oIII01

oIII01

X

XI

o - xII

• oI

O -O S O -X//

x - oI

oIII01

X

\o

X/

o#

o o \ / oIIo

. /\O X IIo / \

X X

XI

x - o*0 •1

o - x//

x - oI

oII01

oII01

Xo0)

X00

o

COm

X00o

c8h5sx

109

XIoIII01x-owo-xIo-x

ftx-oIoIII01X

X\

X/o o

o o \ /01X o

\ / \ O X IIo / \X X

o0)

\oo x \ / o

IIo / \ • X o IIX o \ / \ O X

IIo / \X X

tt>XGOo

(/)h-XCOo

X X \ /01O X / \/ o o

fft IIox o/X \ / o

flo / \ X X

XIo-x

//x-oIx-o*o-xIo-x

//• oIoIII01

X

XCOf"-I00o

1 10

CoH8 n 8c = c ^ c = c :

H HH K

H: c = c " H % - c ' c H " H i c = c C H

,H

H

CI0H2 H-C=C-C=C-C=C-C=C-C=C-H

10 3 H C_C C-C *C-C= C- C=C- HIH

H-C^C-C. C — CaC - C = C - C = C — H IH

H - C= C“ C^C-Cs C— C= C-H ICincIH

etc.

I

C|0 H4

CI0H5S

111HlChicIcIIIcI

H - C s C - C * C-CsC-HiH

HiCinc

H- C = C-C. C-CsC-HicIIIcIH

HiCincI

H - C 2 C - C * C-C = C-C =C-H IH

etc

H• IH- CsC- Cs. _^C-C= C-H

C VH CinCi

1 12

C I0H 6

HH-Cs C-C

* c - c=c-c^i iH H

HC-Cs C-H

H

.C'. c = c C ^ C

u ^ c _ c > *r H C * ^

H

Hetc.

C,0H7 SH

H - C = C - C * C _ C *I •cIIIcIH

H Hi ic - c . C-HiH

H . HH - C = C - C ^ C - C ^

i iCincIH

HC-HiH

Hi HiH - C = C - C * c _ c * C - C

i • cH miCiH

HIC-H

etc.

1 13

/O

XIo-x

//x-oIx-owo - 0 = 0 - 1Io-x//• oIoIII01

X

*I o \ / oIIo / \

X oO X \ / oII

X o \ / \ o x91o

• \X

XCON

Xoo

3h-Xoo

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ftfo o \/ oIIo X / \/ X oIIx o

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• \X

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X o \ o \/oo o \ / \ O X

IIX o \ / \O X IIo

• \Xoa)

1 14

XIO - X//

X - OI

x - o*O - O S O - X I

o - x//

x - oIoin01

X

XI

o - x

x - oI

x - owo - xI

o - x//

I — o = 0 — 0 I

oIII01

X

00Xo

o

XI

O - X//

x - oI

x - o \\o - xIO - O S O - X//

x - oI

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oa>

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i/i0>

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o

1 15

1 ' ' y

C|2H2 H - C ^ C - C ” C-C = C-C = C-C-C-C = C-H

HIC|2 H3S H - C= C - C = C - C - C - C ^ C_C = C„C=C_H

H " C = C C-C-C-C-C-C=C-H 1C111cIH

H1c12h4 h - C s C -C s C -CsC-c *c-c-c-c*c-h

IH

HH"C = C " C ^ c _ c = c _ c = c _ c = c _ h

IcIIICy\

etc

1 1 6

C j g H s S H - C= C 1C C - C S C-C2 C-Hc - c1 1cIIIcIH

H

Vh - c = c - c = c - c * c _ c * c _ c - C - h

IcIIIcIH

H

etc.

c I2h6H

H- C- C-C^ C-C 1 1c cIII IIIc c b b

HC-C=C-H

HH-C=C-C * c - c1 1

HC-CsC-H

C111Cb

H

etc.

1 17

X/

OX\

X/

ooto o

\ /01O X / \ / o o

to I O x o/X \ / ■ o

IIo / \X x

/o*/o. 'oII too o/ \ / x o

IIX o\ / \ O XIIo / \X X

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\ / \/O 1 o^ IIo o

V / \o xIIo / \X X

if)f-XCVJo

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>•if)h-X

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o

X/o cin too o

• t / o oii too o / \/X o

IIX o\ / \ o X IIo

/ \X x

X/ XIo-x

//x-oIx-o*O-OEO-XIo-x

//X- 0=0-0

IoIII01X

Nif)h-XCVJ

o

00X

CVJo

CI2 H 9 S

1 19

CioHI2n 10H * L H-Ci

■? Yc - c

H - C » C - C , C _ C

cIIIcHi

C-HiH

C-HiH

HH C»C

etc.

H * " C = C " c * cH

C - C ^ Hh " > = c;

H c ^ cH

C1aH14 4H

H-CS C-C5C - C S C-C s C"CsC~ CSC ~ HcIIIcIH

HiCinc

H_ C = C- C^C"C = C~C-C”C-C“ HicIIIcIH

C,4H5S

I I I IoIII O I o

a *

T XI ->l0 0 C O

n a

in x

I X X

W o Oo o oII II I'l

O O o o

I I I I X

o o o/ / \ 1CCH o

0/ ^ //o o CiH

/ \ iHC o0/ ino o/ 1i I

IIIII

I o o o\ / \ \ / \ \ / \ I IO I O O O I o • oII II * II // IIIO I O I ° o I x-o o/ \ / / \ / K / \ / I I

O O O o 1 o O I - O E O - O o •/// ii # ii t// si ^ ft- ^ r ~ \ —T 1-0I/ /\ / / \ . ,

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O O O o o O O X-o o-l' / \ / \ / \ I I— — ° -r o 0 - 0 5 0 - 1

//1 - 0II

121

122

C|4H8X

c,4h9s

Hi Hi

HiC«icI

H - C s C - C s C - C * c _ c * C - C ^ r _

iH iCmCIH

CiHH

Hh - c = c - L

Hi

HiCincI

c - c 1I Ic - c

H CincIH

C” C= C“ HiH

HIH Hi i

H-C=C-C* *C _ C * C - CI IC H-C in ^CiHC*iCincIH

C-HA

H-Cs C-CHi

HiChi

cIc - cI IH H

HiCinc

H H

etc.

123

C..H14 10

HH - C = C - C « C _ ^

i iC H-C*incIH

H Hi iC - C

C-HicIIIcIH

C-HiH

HH-CsC-C

etc.

Hi

HiCinCI

c - 9 1 H H

C-C

HiCh ic

c - 6 - c - hIH iH

HiChiCI

CieHHi

HICinCII6n8 H-C e C-C s C-C*

c - c *C-C

IH iChicIH

C-HA

HIc c

H" c s c - ^ c - c -H CIII

cIH

HI

HiCincI

c - c * C-CsC-HIH

124

A|

A,C2H-

a ,c 2 h

A|C2H2U

A i C 2H 3

®

„ c ' H

a,c2 h* © ^. C ' H

®c ' Hc * c

H

© ' C = C ' H

0H ' c = c ' H^ 'H

\ / oIIX o \ / \O X II/

X

\/ oIIX o \ / • o

IIo / \I X

01 OI

0JkXCM1

oAXro(J)

125

X I \ / oII

X o \ / \ O XIIo

inXM-o

X/

oIIIo/o

o/oIIo/ \

X <2>

X/

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O/

OX O

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cnCM

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129

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131

t c - c c ® “ C %1a ,C|2h 6 s c . . h©

V - r ' H c ' > c = c C

HH ©'

Hc=c:

,H

H

a ,c ,2 h 8 s

H _ , C - CH

H..C - C

H

c= cC

H

H

; c = c:S • - C/ C a C. c +

H

H

A| C,4 H 6 S © H ' c = c : H : c - c ;

H

H.C= c C

c * c

H

/

A|C2H)2-

A,C2H )2

A, C2H)2X

A,C2HC2H2U

aic2hc2h3

c * c

132

©©

c ' HSN»

c * 1;" H

, c * c

c.,

H

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/H

©:©•. c = c .H H

_ c , o -

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cA,C2HC2 H3X | O JIcIIIcIH

1 3 3

a ,c 2 h c 4 h

a ,c 2 h c 4 h x

© e ' H. c * c

' C * c' C * C . H

c * c ' H

c * c '

IcIIIcIH

A 1C 2 H C 4 H 2 S

C ' H , C * C ^ H

«•

H "

C - HA,C2H C 4 H 3 { ° ) ^ r - r ' CH ^ C - C v h

H : c = c c Ha , c 2 h c 4h 3 x ( o ) ' C 4 > c - h

IcincIH

orox

oroxrvT'O&XCM

oroX

ro''oX

_>o

roXCM

1- 0= 0-

X-0=0-0o o o

: - o = 0 - 0 = 0 -(D

o oill0 o1 V X 3

I - O E O - I

1 3 5

a2- x

a2c2h*

a2c2h *x

a2c 2h-

a2c2h

o o

0 T 0

0 T 0

HIcIIIc

o o

.H

Cs®' .*c-

HH

oTo

HICincI

a2c 2h)2 x

A2R5

A2R5

O O

HIH- C*

a2c2hc2h2u qo o

o o

A2R5C2H* [ ° I ° #I

A2R5C2H

A2 R 5C2H)2

AoR5CoHCoHoU

138

C g H

H

A3C2H

H

A 3 C 2 H 2 U

H C=C

A3C 2HC2H2U

H C~ H1H

139

A3R5-

A3 R5

A3R5C2H

H

A3 R5C2H2U

O CH

O j O j ^Tofo

A 4 C 2 H #

A 4 C 2 H

A 4 C 2 H ) g

A 4 C 2 H C 2 H 2 U

H

H1H

HC - H

1H

B 4 -

b 4

B 4 C 2 H

H- C = C

142

B 4 C 2 H ) 2

B4C2HC2H2U

143

144

a 6

H

a 7 -

A7 C 2 H *

H'

145

A 7 C 2 H

H

A y C 2 H ) 2

A7C2HC2H^H-C

A 8 “

A 8

146

a 8c 2h

AgCg H

HiC

147benzo[a]pyrene, A5. Species of type A with four or more rings are both ortho- and peri-fused: that is, the aromatic rings share i common faces but less than 2i common carbon atoms;

Bn: species of type B containing n fused aromaticrings. These species are involved in the external cyclization route (Route 2 of Fig. VI.2). Examples of species with these names are benzo[c ]phenanthrene, B5, and dibenzo[c,d]phenanthrene, B6 (see Table VI.1). Species of type B with fewer than seven rings are ortho-fused; i.e., the aromatic rings share i common sides and 2i common carbon atoms;

R n : nonaromatic ring containing n carbon atoms;CnHm: non-ring structure containing n carbon atoms and m

hydrogen atoms; neither n nor m is printed if it equals one.

If a structure contains both aromatic and nonaromatic rings, the aromatic rings are specified first. For example, acenaphthalene is named as A2R5 (see Table VI.1).

Ring substituents are listed as suffixes. They are listed in order of increasing number of carbon atoms; free-radical substituents come last. If two groups have an equal number of carbon atoms, they are listed in order of increasing number of hydrogen atoms. Multiple identical substituents are denoted by placing a right parenthesis and the number of such groups after the substituent name.

148The names of all free radicals,, other than ethynyl

radicals, contain a. special symbol indicating the type of radical. The symbol is placed after the structure description. These symbols are:

U: a vinyl radical with the unpaired electron locatedon a terminal carbon atom. Example: C4H3U (seeTable VI.1). The only exception to this naming rule is for C2H3, which was named in accordance with convention;

S: a vinyl radical with the unpaired electron locatedon an internal carbon atom. Example: C4H3S (seeTable VI.1);

*: a radical with the unpaired electron located on anaromatic ring and adjacent to a C2H substituent. Example: A1C2H* (see Table VI.1);

-: a radical which has the unpaired electron locatedon an aromatic ring and which is not described by

. Example: A1- (see Table VI.1);%: a radical with the unpaired electron located on a

nonaromatic ring. Example: R6% (see Table VI.1).If more than one structure would be assigned the same

name using these rules, the structures are distinguished by letters placed at the ends of the names; e.g. the second species name would end with X, the third would end with Y and so on. When computer experimentation established that distinctions between particular isomers were not important, the isomers were lumped under one name (see Table VI.1).

1496.2.2 Reaction Mechanism

The core.of the acetylene pyrolysis model is based on the mechanism of Tanzawa and Gardiner (86) whose development entailed comparison with all of the available data. It thus was calibrated overall against the measured chain and non-chain rates. Their mechanism was subsequently extended to higher temperatures and also found to be suitable for describing ethylene pyrolysis (89). In our work wedistinguish between the isomers of the C 4H 3 radical, namely H-C=C-C=CH2 and H-C=C-CH=CH; thus, the product of reaction C2H2 + C 2H2 = C 4H 3 + H was assumed to be the latter, in line with the theoretical study of Dewar and coworkers (191). The reactions and their rate coefficients are listed in Table VI.2 .

The rest of the mechanism was generated according to physical organic chemistry principles to comprise the likely radical and atom reactions (no migrations of hydrogen atoms or complex isomerizations were included) that could lead eventually to cyclization and growth of aromatics. For the purpose of assigning rate coefficient expressions the reactions were grouped into classes as shown in Table VI.3. The rate coefficient expression chosen for a prototype reaction was assigned to the rest of the class without change. We assume thereby that a decrease in reaction rate due to increasing mass is offset by growing reaction-path degeneracy. To assign rate coefficients for classes where

Table VI.2 Core reactions of acetylene mechanism.

ReactionNumber Reaction

Rate Coefficient for Forward Direction Remarks

R1 C2H2 + H = c 2h ♦ h + M A.2 xR2 V . + C2H2 = «-cAH3 + 11 2.0 X

R3 H + C2"2 = C2H3 5.5 X

RA C2H3 + C2H2 = ca"a + ii 1.6 X

R5 '-Vs + H + H = V a + M 1.0 X

R6 C2H + H2 = H 2.5 X

R7 c2r + C2H2 = CAH2 + H A.O XR8 c2h + V a C2H2 + i-V 3 A.O X

R9 ' - V s + n = CAH2 + 11 + M 1.0 X

RIO V 2 + H = c4h + H + M 3.5 XRll V + v 2 = C6H2 + H A.O X

R12 C4H + C2»2 = V 2 + H A.O X

R13 c6k + C2H2 = C8H2 + II 1.0 XRlA V + C6H2 = C8"2 + H 1.0 X

R15 v 2 + C.H A = C8H2 + H 1.0 XR16 C6H2 + M = c6h ♦ H + M 5.0 XR17 C8H2 + M = c8h ♦ II + M 5.0 X

R18 H2 + H - H + II + M 2.2 XR19 n- v 3 + H «• M = V a + H 1.0 XR20 n-C/,H3 + H = H + M 1.0 XR21 c2h + ICAl,A = c2h2 + n"CAH3 A.O X

I16)12)12)13315312313 313 916 017 a13D13o12o12012016„16

exp (-AA8/RT) exp (-192/RT) exp (- 10/RT) exp (-105/RT)

exp (-250/RT) exp (-335/RT)

exp (-335/RT)exp (-335/RT)

12 T0'5 exp (-387/RT) 15

I16.13 exp (-250/RT)

Ref. 86 Ref. 86 Ref. 86 Ref. 86 Ref. 86see Refs. 31 ,93Ref. 86Ref. 86Ref. 86Ref. 86Ref. 66Ref. 86Ref. 86Ref. 86Ref. 86Ref. 86Ref. 86Ref. 86

R19 = *5 *^20 = kR9 ^21 = 8

a ' ' 'The units are cm3, K, kJ, mol, s. The reverse rate constants are computed via equilibrium constants.

151no experimental data were available, the viewpoint was adopted that reasonable upper limits based on collision theory would be preferable to transition state theory estimates based on assumed transition structure properties. The values of the rate coefficients were limited to 2x10 l3 cm3/mol/s for bimolecular reactions of organic species and to IxlO1 cm3/mol/s if hydrogen atom is a reactant. The principle of detailed balancing was always obeyed except for reactions of class 31 (see Table VI.3 and the discussion below), which were assumed to be irreversible, as discussed in the following paragraph. The reactions considered in this work are listed in Table VI.4.

Since our modeling indicated that it is not important to describe some reaction sequences in complete detail, these sequences were simplified to keep the reaction mechanism of manageable size. The first simplification involved reaction class 31, the irreversible fragmentation of aromatic radicals, which is not a true reaction class. It was used to include ring fragmentation effects for large aromatic radicals after detailed models of ring fragmentation (including e.g. A2— = A1C4H3-) indicated that although ring rupture was an important reaction route for aromatic radicals with one ring, it was not important for aromatic radicals with more than one ring. Even with this overestimate of fragmentation rates for the polycyclic radicals, fragmentation was not a significant reaction route

Table VI. 3 Reaction classes and rat-e coefficient expressions.

Number Reaction Class Prototype ReactionRate Coefficient

for Forward Direction Remarks

1 Ethynyl radicals plus H2 * c2n + h 2 = C2»2 + H 3..5 x 10

2 H abstractions of olefinic H. H + C211a = C2»3 + H2 1..5 x 10

3 Ethynyl abstractions of ethynyl H. c 2h + c a h 2 = C2«2 + C.H4 2 X 1013

4 Ethynyl abstractions of olefinic H. c2h + c2h4 = c2r2 c2h 3 2 X 1013

5 H additions to triple bonds. H + C2I12 = C2H3 5 .5 x 10

6 H additions to double bonds. H + C2Ha = C2»5 1 X io13

7 Recombinations of organic radicals. C2H + C2H = C4H2 1 X 1013

8 Ethynyl additions to triple bonds. C,,H + C.H„ 2 4 2 = C6H3 1 X 1013

9 Polyacetylene formations. C2H + C2H2 = C4H2 + H 2 X io13

10 Ethynyl attacks on triple bonds followed by C-C bond rupture.

c2r + c6h2 = C4H2 + C.H4 1 X io13

11 Vinyl attacks on triple bonds,H loss.

12 Vinyl attacks on triple bondsfollowed by C-C bond rupture.

13 Vinyl additions to triple bonds.

14 Vinyl attacks on double bondsfollowed by C-C bond rupture.

15 Vinyl abstractions of olefinic H.

C2h3 + C2H2 = CaH4 + H

C2H3 + C4H2 " C4H4 + C2H

C2H3 + C4H2 = C6H5

C2H3 + C4H4 = C2H + C4»6

C2H3 + C4H4 = C2H4 + C4»3

3.5 x 10^ exp(-8.8/RT) Warnatz'*^

^ exp(-42.7/RT) Warnatz*^

For exothermic direction

12 192

1921 x 10 exp(-6.3/RT) Warnatz , k

,13

For exothermic direction

891.6 x 10 exp(-105/RT) Kiefer et al.

,131 x 10

1 x 1013

1 x 1013

kl2 = k10

k13 = k8

kl4 = k10

,121 x 10 exp(-68/RT) Ebert et al.193

Number Reaction Class Prototype ReactionRate Coefficient

for Forward Direction Remarks9316

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Vinyl attacks on oletinic bonds,H loss.

Ethynyl attacks on olefinic bonds, H loss.

C2H3 + C2H4 = C4H6 + H

C„H + C„H, = C.H. + H 2 2 4 4 4

Irreversible non-radical cyclizations.

H2C=CH-CH=C-CH=CH2 -» phenyl+H+H

H+benzene = benzene-HH additions to aromatics.

Radical cyclizations.

H recombinations with aryl radicals. H+phenyl = benzene

C10H? = Ar(C2H)2+H

1 x 1010 exp(-34/RT)

6 x 1011 exp(-l6/RT)

1 x 105

1 x 1013 exp(-6.3/RT) AO1 x 10

Aromatic fragmentations.

H abstractions of aryl H.

Ethynyl abstractions of H from aromatics.

H attacks on aryl acetylenes.

Aryl attacks on triple bondsfollowed by C-C bond rupture.

Aryl additions to triple bonds.

H recombinations with ethynyl.

h recombinations with vinyl

Radical cyclization via triple bond.

benzene = products

H+benzene = phenyl + H2

C2H+benzene = phenyl+C2H2

H+phenylacetylene = C2H2+phenyl

phenyl+C^H2 = phenylacetylene+C2H

phenyl+C^H2 = phenylC^H2

H + C2H = C2H2

H + C2H3 = C2HA

HChC-CH=CH-CH=CH = phenyl

1 x 1013

1 x 1016 exp(-AH°/RT)

1 x 1014

2 x 1013

1 x 1014

2 x 1013

1 x 1013

2 x 1013

2 x 1013

1 x 1010

Ebert et al.

k9kl6^

k19 = k6

k24 " k3

k26 " k9

k27 = k8

Gardiner and Troe

k30 = k20

194

153

Number Reaction Class Prototype ReactionRate Coefficient

for Forward Direction Remarks

31. Irreversible fragmentation of aromatic radicals.

a 2c 2h* = A jC2H* (net rate of A2- = A1C4H3-) (concentration of A2-) reverse rate

constant = 0; forward rate

32. Radical disproportionation. H * C2H3 = H2 + C2H2 1 x 1013 k32 = k733. Phenyl abstraction of olefinic H. A - + C.H. = A. + C.H 1 6 4 1 6

133S 2 x 10 k33 = k4The units are,cm3, K, kJ, mol, s. The rate coefficients for the reverse direction are computed via equilibrium constants. When the reverse rate coefficients were limited (see text), the forward rate coefficients were computed via equilibrium constants.

155 ■#• V' v ‘ - v-t* ' v

Table VI.4 Reaction list.

REACTIONS REACTION CLASS A n ^ Q O , fcj

1) C2H2 + M - H + C2H + H 0 505.92) C2H2 + C2H2 - H + C4H3U 0 289.73) C2H2 + H «= C2H3 0 -174.64) C2H2 + C2H3 - H + C4H4 0 4.05) H ♦ C4H3S + M - C4H4 + H 0 -426.86) H2 + C2H « C2H2 + H 0 -57.27) C2H2 + C2H - H ♦ C4H2 0 -63.5B) C2H + C4H4 » C2H2 + C4H3S 0 -79. 19) C4H3S + n *= H + C4H2 + n 0 186.310) C4H2 ♦ M ■ H + C4H + n 0 508.01 1 ) C2H + C4H2 ■ H + C6H2 0 -61.412) C2H2 + C4H ■ H + C6H2 0 -63.513) C2H2 + C6H - H + C8H2 0 -63.514) C2H + C6H2 « H + C8H2 0 -61.415) C4H + C4H2 * H + C8H2 0 -61.416) C6H2 ♦ M ■ H + C6H H 0 508.017) C8K2 + M “ H + C8H + n 0 508.018) H 2 + M - H * H + H 0 448.719) H + C4H3U + M « C4H4 + M 0 -460.320) C4H3U + M = H + C4H2 + M 0 152.821 ) C2H + C4H4 « C2H2 + C4H3U 0 -45.622) C2H2 + C2H = C4H3U 8 -216.223) H2 + C4H3U « H + C4H4 -2 -1 1 .624) C2H2 + C4H30 *= C6H5U 13 -221.125) C6H5U = Al- 30 -202.326) C6H5U = H + C6H4 -5 205.327) H + C6H5U « C6H6 .29 -460.328) H2 + C6H5U « H + C6H6 -2 -1 1.629) C2H + C6H5U • « C8H6 7 -521.730) C2H2 + C6H5U * C2H ♦ C6H6 -4 45.631) C4H2 + C4H3U « C4H + C4H4 -4 47.732) C4H2 + C4H3U = C8H5SX 13 -252.533) C8H5SX « A1C2H- 30 -149.134) C8H5SX - H + C8H4 -5 238.835) H + C8H5SX ■ C8H6 29 -426.836) H2 + C8H5SX •= H + C8H6 -2 21.637) C2H2 + C8H5SX “ C2H ♦ C8H6 -4 79. 138) H + C4H2 *> H2 + C4H -1 59.339) H + C6H2 « H2 + C6H -1 59.340) H + C6H2 •> C6H3S 5 -186.341 ) H + C8H2 « H2 + C8H -1 59.342) H + C8H2 » C8H3S 5 -186.343) C2H ♦ C4H2 ■ C2H2 + C4H 3 2. 144) C2H + C6H2 « C2H2 + C6H 3 2. 145) C2H ♦ C4H2 - C6H3S 8 -247.646) C2H + C6H2 - C8H3S 8 -247.647) C4H + C4H2 « C2H + C6H2 -10 0.048) C4H + C6H2 « H + C10H2 9 -61 .449) C4H + C4H2 « C8H3S 8 -247.650) C4H + C6H2 - C10H3S 8 -247.651) C4H2 + C6H ■ C2H + C8H2 -10 0.052) C4H2 + C6H « H ♦ C10H2 9 -61.453) C4H2 ♦ C6H • C10H3S 8 -247.654) C6H + C6H2 - C4H ♦ C8H2 -10 0.055) C6H + C6H2 ■ H ♦ C12H2 9 -61.456) H + C6H3S • C6H4 29 -426.857) H2 + C6H3S - H + C6H4 -2 21.858) C2H2 ♦ C6H3S » C2H ♦ C6H4 -4 79. 159) C2H2 * C6H3S • N + C8H4 1 1 17.760) C4H2 + C6H3S - C4H + C6H4 -4 81.261 ) H ♦ C8H3S - C8H4 29 -426.862) H2 + C8H3S ■ H + CBH4 -2 21.863) C2H2 + C8H3S • C2H + C8H4 -4 79. 164) H ♦ C10H2 - C10H3S 5 -186.3

156

65) H2 ♦ C2H3 - H 4 C2H4 -2 -11.666) C2H2 + C2H3 - C2H 4 C2H4 -4 45.667) H + C2H3 - C2HA 29 -460.368) CaH5U « C2H2 4 C2H3 -13 221 . 169) C2H3 + CAH2 « C6H5S 13 -232.770) C2H3 + CAH2 ■ C2H 4 C4H4 12 67.57) ) C2H3 ♦ C4H2 » C2HA 4 C4H -4 47.772) H2 + CAH3S ■ H 4 C4H4 -2 21.873) C2H2 + CAH3S ■ H 4 C6H4X 1 1 17.77fl) caH2 + CAH3S - C4H 4 C4H4 -4 81.275) H + C4HA « C4H5U S -225. 176) C2H cana » C6H5S 8 -300.277) C6H6 ■= C2H3 4 C4H3U -7 506.878) C6H5S - H 4 C6HAX -5 238.879) H + C6H5S - C6H6 29 -426.880) C2H + C6H5S • C8H6 7 -488.281 ) H2 + C6H5S * H 4 C6H6 -2 21 .882) C2H2 4 C6H5S « C2H 4 C6H6 -4 79. 183) C2H2 4 C6H5S * H 4 C8H6 1 1 17.78a) C8H5S ■> H 4 C8HA -5 238.885) H 4 C8H5S « C8H6 29 —A26.886) HZ 4 C8H5S • H 4 C6H6 -2 21.887) C2H2 4 C8H5S « C2H 4 C8H6 -4 79. 188) H 4 A1 - « A 1 21 -470.889) A 1 ■= H 4 C6H5U 22 673.090) C2H 4 A1- • A1C2H 7 -512.491 ) A1C2H = H 4 C8H5SX 22 619.892) H 4 AIC2H- ■= A1C2H 21 -A70.893) H2 4 A1C2H- « H 4 A1C2H -23 -22. 19a) C2H2 4 A1C2H- *= C2H 4 A1C2H -24 35.295) C2H2 4 A1C2H- *= H 4 A1C2H)2X -25 -6.596) H2 4 Al- * H 4 A1 -23 -22. 197) C2H2 4 A 1 - « C2H 4 A1 —2A 35.298) C2H2 4 A 1- « H 4 A1C2H -25 -6.599) can 2 4 A 1 “ « CAH 4 A 1 -24 37.2100) CaH2 4 A1 - * C2H 4 A1C2H 26 57.0101 ) CaH2 4 A1 - ■ A 1CAH2S 27 -181.6102) H 4 A1CaH2S « A1CAH3 29 -A26.8103) A1C4H3 *= CAH3U 4 Al- -7 455.7i oa > H2 4 A 1CAH2S ■= H 4 A1CAH3 -2 21.8105) C2H2 4 A 1C4H2S ■= C2H 4 AICAH3 -4 79. 1106) C2H2 4 A1CAH2S = H 4 A1C6H3 1 1 17.7107) CaH2 4 A1CAH2S *= A1C8HAS 13 -219.0108) A1C8H4S * H 4 A2C2HJ2X 20 44.2109) H 4 A1C8H4S «= AIC8H5 29 -426.81 10) H2 4 A1CBHAS « H 4 A1C8H5 -2 21 .8111) C2H2 4 A 1C8HAS « C2H 4 A1C8H5 -4 79. 11 12) C2H2 4 A 1C8HAS « H 4 A1C10H5 1 1 17.71 13) C2H2 4 A 1 - = A1C2H2U 27 -170.01 ia> A1C2H2U « H 4 A1C2H -5 163.51 15) H 4 A1C2H2U « A1C2H3 29 -460.31 16) H2 4 A 1C2H2U = H 4 A1C2H3 -2 -11.61 17) C2H 4 A1C2H2U « A1CAH3 7 -501.91 18) C2H2 4 A 1C2H2U « AtCAHAU 13 -221.1119) CaH2 4 A1C2H2U « A1C6HAS 13 -232.7120) AtCaHAU « H 4 A2 20 -8.9121 ) A1CAHAU « H 4 A1CAH3 -5 225. 1122) u 4 AlCAHAU ■ A1CAH5 29 -460.3123) H2 4 A 1CAHAU » H 4 A1C4H5 -2 -11.612a) C2H2 4 A1CAHAU » C2H 4 A1CAH5 -4 45.6125) C2H2 4 A 1CAHAU - H 4 A1C6H5 1 1 A. 0126) AIC6HAS « H 4 A2C2H 20 24.5127) A1C6H4S - H 4 AIC6H3 -5 238.8128) H 4 A1C6HAS « A1C6H5 29 -426.8129) H2 4 A 1C6HAS ■ H 4 A1C6HS -2 2 1.8

157

(130 C2H2 + A1C6H4S m C2H(131 C2H2 + AIC6H4S m H(132 C2H2 + A1C4H2S m A1C6H4U(133 A 1C6H4U - H * A2C2H(13a A1C6H4U » H + A1C6H3(135 H + A1C6H4U K AIC6H5( 136 H2 + A1C6H4U m H(137 C2H2 + AIC6H4U m C2H(138 C2H2 + A1C6H4U M H(139 H + A2- a: A2( 140 H2 + A2- B H(141 C2H + A2- B A2C2H( 142 C2H2 + A2- « C2H( 143 A1C2H « H + A 1C2H*( 144 H + A1C2H B H2( 145 C2H + A1C2H B 02H2( 146 A1C2H> = C8H5U( 147 H + C8H5U B C8H6( 148 H2 + C8H5U B H( 149 C2H2 + C8H5U B C2H(150 C2H2 + C8H5U B H( 151 C8H5U = H + C8H4( 152 C8H5U * C2H2 + C6H3U( 153 H + C6H3U S C6H4( 154 H 2 + C6H3U S H( 155 C2H2 + C6H3U S C2H(156 C2H2 + C6H3U B H(157 C6H3U ■ C2H + C4H2(158 C2H2 + A 1C2H« B A 1C2HC2H2U( 159 C2H2 + A1C2H* B H( 160 A 1C2HC2H2U = H + A 1C2H)2( 161 A 1C2HC2H2U = A2-X( 162 H + A1C2HC2H2U S A1C2HC2H3(163 H2 + AIC2HC2H2U « H(164 C2H2 + A1C2HC2H2U B C2H( 165 H + A2-X « A2(166 H2 + A2-X B H( 167 C2H2 + A2-X B C2H( 168 C2H + A2-X e A2C2H(169 C4H2 + A1C2H» B A 1C2HC4H2S(170 A I C2HC4H2S = H + A 1C2HC4H( 171 A 1C2HC4H2S « A2C2H-( 172 H + A1C2HC4H2S e A 1C2HC4H3( 173 H2 + A1C2HC4H2S B H(174 C2H2 + A 1C2HC4H2S B C2H( 175 H + A2C2H-X * A2C2H( 176 H2 + A2C2H-X U H( 177 C2H2 + A2C2H-X B C2H(178 C2H2 + A2C2H«X B H(179 H + A1 B R6X(180 R6X « C6H7U(181 C2H2 + A2-X B H(182 C2H2 ♦ A 2- B H(183 C2H2 + A2C2H* B C2H(184 H + A2C2H* « A2C2H(185 H2 + A2C2H" B H( 186 C2H2 + A2C2H- « H(187 C2H2 + A2C2H* B A2C2HC2H2U( 188 A2C2HC2H2U ■ H ♦ A2C2H12( 189 A2C2HC2H2U » A3-( 190 H + A3- B A3( 191 H2 ♦ A3- B H(192 C2H2 + A3- B C2H( 193 C2H2 + A3- B H( 194 C2H2 ♦ A3- “ A3C2H2U

+ A1C6H5 -4 79. 1+ A1C8H5 1 1 17.7

13 -135.120 -61 .5-5 152.629 -512.8

A1C6H5 -2 -64.2♦ A 1C6H5 -4 -6.9♦ AIC8H5 1 1 -68.3

21 -470.8+ A2 -23 -22. 1

7 -512.4+ A2 -24 35.2

-21 470.8♦ A1C2H« 23 22. 1+ A1C2H* 24 -35.2

-30 162.529 -460.3

♦ C8H6 -2 -11.6+ C8H6 -4 45.6+ C10H6 1 1 -15.8

-5 205.3-13 221. 129 -460.3

* C6H4 -2 -11.6♦ C6H4 -4 45.6+ C8H4 1 1 -15.8

-8 214.227 -170.0

+ A 1C2H)2 -25 -6.5-5 163.530 -223.529 -460.3

+ A1C2HC2H3 -2 -1 1.6♦ A1C2HC2H3 -4 45.6

21 -470.8+ A 2 -23 -22. 1+ A2 -24 35.2

7 -512.427 -181.6-5 177.230 -190.129 -426.8

+ A1C2HC4H3 -2 21.8* A1C2HC4H3 -4 79. 1

21 -470.8+ A2C2H -23 -22. 1+ A2C2H -24 35.2* A2R5C2H 27 -134.2

19 -90.7-20 78.4

+ A2C2H -25 -6.5+ A2C2H -25 -6.5+ A2C2H -24 35.2

21 -470.8+ A2C2H -23 -22. 1+ A2C2HJ2 -25 -6.5

27 -170.0-5 163.530 -232.721 -470.8

+ A3 -23 -22. 1+ A3 -24 35.2* A3C2H -25 -6.5

27 -170.0

158

(195) A3C2H2U » H + A4(196) A2- » A1C4H3-( 197) H + A1C4H3- K A1CAH3( 198) H 2 + A1C4H3- ■ H(199) C2H2 + A1C4H3- m C2H(200) C2H2 + AIC4H3- K H(201 ) A1C4H3- - C10H7U(202) C10H7U ■ H + C10H6(203) C10H7U « C2H2 + C8H5U(20a> H + A4- m A4(205) H2 + Aa- m H(206) C2H2 + Aa- m C2H(207) C2H2 + A4- m H(208) H + A4C2H" m A4C2H(209) H2 + A4C2H* B H(210) C2H2 + A4C2H* K C2H(21 1) C2H2 + A4C2H» B H(212) C2H2 + AaC2H* e A4C2HC2H2U(213) A4C2HC2H2U ■ H + A4C2H12(21 a) AaC2HC2H2U = A5-(215) H + A5- m A5(216) H2 + A5- m H(217) C2H2 + A5- m C2H(218) C2H2 + A5- K H(219) C2H2 + A5- K H(220) H + A6- B A6(221 ) H2 ♦ A6- B H(222) C2H2 + A6- B H(223) C2H2 + A6- B C2H(22a) C2H2 + A6- B H(225) H2 + A3C2H* s H(226) H + A3C2H* B A3C2H(227) C2H2 + A3C2H* B C2H(228) C2H2 + A3C2H* B H(229) C2H2 + A3C2H* B A3C2HC2H2U(230) A3C2HC2H2U * H + A3C2H)2(231 ) A3C2HC2H2U ■ B4-(232) H2 + Ba- s H(233) H + Ba- B B4(23a) C2H2 + Ba- B C2H(235) C2H2 + B4- B H(236) H2 + BaC2H" B H(237) H + BAC2H* B B4C2H(238) C2H2 + BAC2H" B C2H(239) C2H2 * BAC2H- B H(2ao) C2H2 + BAC2H* E BAC2HC2H2U(2a 1 ) B4C2HC2H2U - H + B4C2H)2(2a 2) BAC2HC2H2U « B5-(2a3) B5- « H + A6(2aa> H + B5- B B5(2a5) H2 + B5- B H(2a6 ) C2H2 * B5- B C2H(2a7) A2C2H* « A 1C2H*(2a8) A4C2H* - A3-(2a9> H » A7- B A7(250) H2 + A7- B H(251 ) C2H2 + A7- B C2H(252) C2H2 + A7- B H(253) H * A7C2H* B A7C2H(25a) H2 + A7C2H- B H(255) C2H2 + A7C2H" B C2H(256) C2H2 + A7C2H" B H(257) C2H2 + A7C2H® B A7C2HC2H2U(258) A7C2MC2H2U « H ♦ A7C2H)2(259) A7C2HC2H2U » AB-

20 -50.6-30 229. 121 -465.8

+ A1C4H3 -23 -17.2+ AIC4H3 -24 40. 1* A1C2HC4H3 -25 -1.6

-30 125.9-5 205.3

-13 221. 121 -470.8

A4 -23 -22. 1+ A4 -24 35.2+ A4C2H -25 -6.5

21 -470.8+ A4C2H -23 -22. 1* A4C2H -24 35.2+ A4C2HJ2 -25 -6.5

27 -170.0-5 163.530 -24 1.921 -470.8

+ A5 -23 -22. 1+ A5 -24 35.2+ A5C2H -25 -6.5+ A6 27 -220.6

21 -470.8+ A6 -23 -22.1+ A6C2H -25 -6.5♦ A6 -24 35.2+ A7 27 -220.6+ A3C2H -23 -22. 1

21 -470.8+ A3C2H -2a 35.2+ A3C2H)2 -25 -6.5

27 -170.0-5 163.530 -203.4

+ B4 -23 -22. 121 -470.8

+ B4 -24 35.2+ B4C2H -25 -6.5+ B4C2H -23 -22. 1

21 -470.8+ B4C2H -24 35.2♦ B4C2H)2 -25 47.9

27 -115.6-5 163.530 -274.527 -83.021 -428.9

+ B5 -23 19.7+ B5 -24

3131

77.0

21 -470.8♦ A7 -23 -22. 1+ A 7 -24 35.2t- A7C2H -25 -6.5

21 -470.8♦ A7C2H -23 -22. 1* A7C2H -24 35.2♦ A7C2H12 -25 -6.5

27 -170.0-5 163.530 -241.9

159

(2 6 0 H + A8- m A8(261 H2 ■f A 8 - ■ H(2 6 2 C2H2 AB- « C2H(2 6 3 C2H2 + A 8 - m H(2 6 4 C2H2 •f A 8 - m H(2 6 5 H + A 9 - m A9(2 6 6 H2 ■f A 9 - * H(2 6 7 C2H2 A 9 - * H(2 6 8 C2H2 + A 9 - ■ C2H(2 6 9 C2H2 ■f A 9 - tt H(2 7 0 C2H2 + A 2-X m H(271 H ♦ A 2R 5- m A2R5(2 7 2 C2H2 + A 2R 5- s C2H(2 7 3 H2 + A 2R 5- ■ H(2 7 4 C2H2 ♦ A 2R 5- m H(2 7 5 H + A2R5C2H m H2(2 7 6 H + A2R5C2H* B A2R5C2H(2 7 7 C2H2 •f A2R5C2H* » C2H(2 7 8 C2H2 + A2R5C2H* m H(2 7 9 C2H2 + A2R5C2H* s A2R5C2HC2H2U(2 8 0 A2R5C2HC2H2U * H + A2R5C2HJ2(281 A2R5C2HC2H2U » A 3R 5-(2 8 2 H + A 3R 5- A3R5(2 8 3 H2 A 3R 5- at H(2 8 4 C2H2 + A 3R 5- te C2H(2 8 5 C2H2 ♦ A 3R 5- X A3R5C2H2U(2 8 6 A3R5C2H2U s H A3R5C2H(2 8 7 A3R5C2H2U B H •f A4R5(2 8 8 C2H2 •f C6H5U m H(2 8 9 C2H ■f C8H5SX = C10H6(2 9 0 C2H2 + C8H5SX B H(291 C4H C6H e C10H2(2 9 2 C6H + C6H s C12H2(2 9 3 C6H •f C6H2 SB C12H3S(2 9 4 C4H * C6H3S K C10H4(2 9 5 C2H3 + C6H3S « C8H6(2 9 6 C4H3S + C6H3S K C10H6(2 9 7 C6H3S ■f C6H3S = C12H6(2 9 8 C6H2 + C6H3S m C2H(2 9 9 C6H2 + C6H3S e C 12H5S(3 0 0 C2H + C8H3S X C 1 0H4(301 C2H3 C8H3S c C10H6(3 0 2 C4H3S + C8H3S B C12H6(3 0 3 C6H3S + C8H3S C14H6(3 04 C2H2 + C8H3S H(3 0 5 C4H2 C8H3S C2H(3 0 6 C4H2 •f C8H3S C12H5S(3 0 7 C6H2 ■f CBH3S C4H(3 0 8 C6H2 + C8H3S C2H(3 0 9 C6H2 + C8H3S C14H5S(3 1 0 H + C10H3S C10H4(31 1 H2 ♦ C10H3S H(312 C2H + C10H3S C12H4(3 1 3 C2H2 + C10K3S C2H(3 14 C2H2 + C10H3S H(3 1 5 H ■+ C12H2 C12H3S(3 1 6 C2H + C12H35 C14H4(3 1 7 H + C12H3S C12H4(3 1 8 H2 + C12H3S H(3 1 9 C2H2 ■f CI2H3S C2H(3 20 C2H2 C12H3S H(321 C 10H5S ■ H C10H4(3 2 2 H * C10H5S C10H6(3 2 3 C2H •f C10H5S C12H6(3 2 4 H2 ♦ C10H5S H

21 -470.8if A8 -23 -22. 1+ A8 -24 35.2♦ A8C2H -25 -6.5■f A9 27 -220.6* 21 -470.8* A9 -23 -22. 1+ A9C2H -25 -6.5+ A9 -24 35.2+ A7 27 -220.6+ A2R5 27 -134.2

21 -470.8+ A2R5 -24 35.2+ A2R5 -23 -22. 1f A2R5C2H -25 -6.5+ A2R5C2H- 23 22. 1

21 -470.8■f A2R5C2H -24 35.2f A2R5C2H12 -25 -6.5

27 -170.0-5 163.530 -232.72! -470.8

+ A3R5 -23 -22.1+ A3R5 -24 35.2

27 -170.0-5 163.520 -50.6

+ CBH6 11 -15.87 -488.2

+ C10H6 1 1 17.77 -569.47 -569.48 -247.67 -488.27 -473.37 -459.67 -459.6

+ C10H4 12 81.28 -219.07 -488.27 -473.37 -459.67 -459.6

+ C10H4 1 1 17.7+ C10H4 12 81.2

13 -219.0+ C10H4 12 81.2+ C12H4 12 81.2

13 -219.029 -426.8

+ C10H4 -2 21.87 -488.2

■f C10H4 -4 79. 1■f C12H4 1 1 17.7

5 -186.37 -488.229 -426.8

+ C12H4 -2 21 .8+ C12H4 -4 79. 1■f C14H4 1 1 17.7

-5 236.829 -426.87 -488.2

♦ CI0H6 -2 21.8

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20 127. 1

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165for these species. A second detail which requires clarification is species A4R5, formed in reaction 287. The reactions of this species, not shown in Table VI.4. are similar to those of pyrene, A 4 , and they were lumped together.

Reliable thermodynamic properties were available from the literature for only a few of the species of interest. Group additivity estimation methods C195) therefore were used by Dr. S. E. Stein of the National Bureau of Standards to obtain a large fraction of the necessary thermodynamic data. A detailed discussion of all group values used in this work along with illustrations of their applications to carbon polymerization reactions will be reported separately (196).

The main test mixture used in the computer experiments was 1.09% C2H 2-Ar at a total density of 3.8 x 10-5 mol/cm3 with T 5 values from 1500 to 2100 K, to simulate Series B of Ref. 31. The pressure range of this series, 5-7 bar, is consistent with the choice of high-pressure limits for unimolecular rate coefficients. The computations were carried out to a reaction time of 2 ms using a constant-pressure model which is described earlier in this chapter. The computed temperature changes were at most a few degrees. The computations were done with an IBM 370-3081 computer using the LSODES integrator (197).

1666.3 RESULTS AND DISCUSSION

The primary objective of our investiaation was todiscover the principal routeCs) for formation of soot. Other important aspects, e.g. product distributions for various experimental conditions, are also discussed in this chapter.

6.3.1 Formation of the First Aromatic RingThe initial working hypothesis was that a multiplicity of

cyclization pathways would account for the overallcyclization rate. Following this hypothesis, a reactionnetwork was composed that included 26 different cyclizationreactions of species up to C 14Hi. These reactions are oftwo classes, non-radical and radical cyclizations (TableVI.3). An example of the former is (see Ref. 31)

H H\ \ c = c c = c/ \ / \

H - C C - K ----- H - C C - H + H + H\ S % //CH HC C - C // \ / \

H H H HThe second cyclization class can be further subdivided intoa) cyclization of more stable radicals, e.g.

1 6 7

H H H H' ■ / \ /.C = c c = cH \ / \

H-C = C - C* C-H — ► H-C = C - C C-H + H^ // ^ ^c - c c - c/ \ / \H C v H C

\<> vVc c\ \H H

b) cyclization o£ less stable radicals, e.g.H H H H

\ / \ /c = c c = c

H ^ \ / \H-C* C-H — ---- *► H-C C-H + H

c - c c - cy \ / \ .

H H H Hand c) radical cyclization via interaction of an unpaired electron with a triple bond, e.g.

H H/ . /H-C = C - C V C - C❖ / / %C-H --------- ► H-C C-Hy \ /c = c c = c

/ \ / \H H H H

The computational results indicated that for the conditionsstudied cyclization by the above reaction has three, fiveand eight orders of magnitude more forward flux than theradical, (a) and (b), and non-radical cyclizaxions,respectively. The dominant reaction pathway for theformation of the first aromatic ring is given in Table VI.5.

A second important reaction of subclass (c)

Table VI.5 Formation of the first aromatic ring.

H - C = C - H+H

► :c = c+C2H2

/ XH C = CH X H

(-H) H. .H— ^ =

+ C2«2 (-c 2h )

+H (-H2)

H x H> = Cx H - C\ .C-x c - c^

X H

HX = CxH - Cp.

H/+C2«2

C*r'X,

For a given reaction step, the difference in the lengths of the arrows represents the difference in

forward and reverse reaction rates as computed for the test case (see text) at T = 1700 K and a reaction

time of 0.S ms. The vertical arrows between and represent the net reaction rates: the right arrow

for reaction C.H. + H *■ C.H0 + H„ and the left arrow for reaction C.H, + C„H *■ C.H,, + C„H_.4 4 4 3 2 4 4 2 4 3 2 2

169

H H H H H H HI \ / \ / \ /c c = c c = c c = cII! • \ / \ _*. / \c C * H-C C H-C C*I ^ ^ ^ ^ //C + c c c c - cIII \ / • \ / \C H C H C Hi c * / /

H7 , /appeared to proceed rapidly but in the reverse direction, being the major fragmentation reaction of the single-ring aromatic hydrocarbons.

6.3.2 Formation of Two-Ring AromaticsAbout ten different pathways for the formation of

two-ring aromatic species were considered. As in the first-ring cyclization, a single route (Fig. VI.1) dominated the formation of the second ring for the conditions tested by at least three orders of magnitude. Also shown in Fig. VI.1 is the next fastest route - a two-step acetyleneaddition as suggested by Bittner and Howard (120), which appeared to be most important among similar two-stepadditons such as acetylene addition followed by diacetylene addition, diacetylene addition followed by acetyleneadditon, two-step diacetylene addition, or similar reactions involving vinyl acetylene (198). The computational results indicated that the two-step mechanism is slow because the

170first intermediate adduct, such as phenyl-CH=CH in Fig. VI.1, is so unstable that stabilization via loss of a hydrogen atom is much faster than the next addition reaction.

An important question is why the dominant route is sot

much faster than the rest. The reason is that formation of the more stable molecular intermediate phenylacetylene occurs in the dominant route (Fig. VI.1) whereas in the minor routes the molecular species produced are relatively unreactive side products and all the reactive intermediates are radicals. At first glance one would expect the formation of a stable molecule followed by its reactivation via hydrogen-atom abstraction to be slower than radical-reactant interactions, which is true for irreversible kinetics. In the case of consecutivereversible reactions the formation of stable intermediates appears to be the more decisive factor.

Recently, Bockhorn et al. (108) suggested a cyclizationmechanism very similar to the one proposed in this work. Their reaction mechanism was developed to explain the product distributions obtained in sooting laminar flat flames with a variety of hydrocarbons. The agreement in the cyclization steps suggested independently and from such different viewpoints as product distribution in flames in their work and a computer experiment in this one is remarkable.

DOMINANT ROUTE fragmentation fragmentationr * rCs» +CaH2(-H) +H1-H2)i “= = O —= O .

.V*c*

m = c cH H

MINOR ROUTE

iH

Figure VI.1 Principal reaction pathways for formation of two-ring aromatics. For a given reaction step, the difference in the lengths of the arrows represents the difference in forward and reverse reaction rates as computed for the test case (see text) at T = 1700 K and time = 0.5 ms.

1726.3.3 Further Growth of Fused Polvcvclic Aromatics

Based on the computational results for two-ring formation, only the dominant mechanism of cyclization discussed above was considered for the further growth of fused polycyclic aromatics. Two main pathways considered in this study are presented in Fig. VI.2. Although in the figure they stop at pyrene (and cyclopenta[cd]pyrene), both routes were continued in the computer experiments to benzo[ghi]perylene which was followed by formation of coronene. Route 1 in Fig. VI.2 generally dominated the carbon mass flux, although both routes proceeded with approximately equal rates at the lowest temperatures tested (1500 K). At these temperatures, however, the computed soot yields were extremely low, as discussed in the next section. Thus for the growth of fused polycyclic aromatics, from coronene to ovalene and further, only Route 1 of Fig. VI.2 was considered.

Routes 1 and 2 in Fig. VI.2 are similar in that both proceed through radical as well as molecular intermediates. The molecular intermediates of Route 2 are substituted ortho-fused polycyclic aromatics, the compact, unsubstituted fused molecules such as acenaphthylene, pyrene and coronene having the role of relatively unreactive side products. On the other hand, these unsubstituted compact polyaromatics (the cyclopenta group is relatively unstable and must be partially lost, in one way or another, along the reaction

173

ROUTE I

+ C2 H2(-H )r----i

+C2H2 (-H )

tl+ H (-H 2)

+ h ( - h 2)

ROUTE 2

4C2H2(-H)f<^4-C2H2(-H),

Figure VI.2 Principal reaction pathways for formation of fused polycyclic aromatics. For a given reaction step, the difference in the lengths of the arrows represents the difference in fo-rward and reverse reaction rates as computed for the test case (see text) at T = 1700 K and time = 0.5 ms.

174pathway; to indicate this on the diagram of Fig. VI.2, the group is drawn with dashed lines) are include in Route 1 as reactive intermediates. What distinguishes theseintermediates is their high thermodynamic stability, increasing from acenaphthalene to pyrene, to coronene and ovalene. These irreversible reactions have an effect of "pulling” the chain of reversible steps, which is crucial for soot formation.

6.3.4 Species Concentration ProfilesThe time development of the concentrations of selected

species at a temperature of 1700 K is presented in Figs. VI.3 - VI.7. Figure VI.3 presents the concentrations of H, H 2 and Heq. Heq is the hypothetical hydrogen atom concentration which would be in equilibrium with the calculated concentrations of H2 ; that is, [Heq] = Vk t 8[H 2], where KiS is the equilbrium constant of reaction 18 (see Table VI.4). The temperature dependences of theconcentrations of the same species at a reaction time of 500 microseconds are shown in Figs. VI.8 - VI.12.

175ooCO

oo

cnEO

ooH 2oE CD*"

Oi— i ooI—CECO

UJCJ oEDCJ

o

aoo ( E Q U I L )CDED

oru

5 0 0 .3 0 0 .100. 200.T I M E / i u s

Figure VI.3 Computed species concentrations as functions of reaction time for an initial temperature of 1700 K.H (equil) is the hypothetical concentration of hydrogen atoms which would be in equilibrium with the computed concentration of molecular hydrogen.

LOGin

(CON

CENT

RflT

ION/

mol

cm-3

)

176oo

H2

oaer>-

o

C2H3a

C2H

ooCM

OCO

200 T I ME/jusFigure VI.4 Computed species concentrations as functions

of reaction time for an initial temperature of 1700 K.

L0G1O

(CON

CENT

RATI

0N/m

ol

cm"3)

oaa.oo

-ai.oo

-ia.0

0 -17

.00

-is.0

0 -1

3.00

C4H5U

C6H5U

C6H7U

100. 200. 30Q. UOO. 500.T I M E / m s

Figure VI.5 Computed species concentrations as functions of reaction time for an initial temperature of 1700 K.

LOG.n

(CON

CENT

RAT

I ON/

mol

cm"3

)

(D

C2H2oo

oCD“

ooc n ~

C6H2ooo

CDCD

OO<M

500300.200 T I M E / juls

100

Figure VI.6 Computed species concentrations as functionsof reaction time for an initial temperature of 1700 K.

LOGm

(CONCE

NTRAT

I ON/mo

l on-

3)

17.9.

□oo

ao

aCM

CO

m

ao

R7oLO

Oaco

100 200 T I M E / m s300 500

Figure VI.7 Computed species concentrations as functions of reaction time for an initial temperature of 1700 K.

LOGm

(CON

CENT

RRTI

ON/m

ol

cm'3)

180OOCD'

O

OO H2

o

Oo

(EQUIL)o

ooC\l

1650. 1750. 1850.1550.1M50. 1950.TEMPERflTURE/K

Figure VI.8 Computed species concentrations as functions of initial reaction temperature at a reaction time of 0.5 ms. H (equil) is the hypothetical concentration of hydrogen atoms which would be in equilibrium with the computed concentration of molecular hydrogen.

LOG.n

(CQNC

ENTRf

lTION/

mol

cm'3)

181O=c•(O-I

oLI)l>“-I

oCOCD-I

Ocn-i

ocoo•H “I

ocn

H2

C2H3

C2H

ooCO

H150. 1550. 1650. 1750.TEMPERflTURE/K 1850. 1950.

Figure VI.9 Computed species concentrations as functionsof initial reaction temperature at a reaction time of0.5 ms.

LOG

,n

(CGN

CENT

RRTI

GN/m

ol

cm’3)

Oa

C 4H5Uoain

C 6 H 5Uoo

o

o

C 6 H 7 Uo<ncud— 1450 1550 1650 1750 19501850T E M P E R R T U R E / K

Figure VI.10 Computed species concentrations as functionsof initial reaction temperature at a reaction time of0.5 ms.

LOGm

(CGN

CENT

RRTI

ON/m

ol

cm'3)

183ooCD-I

oo•r*--i

ooOD-I

ooOJ-I

oom0•H"1

oo

C 2H 2

C 6H 2

OoCVJ

1850.1U50. 1550. 1650. 1750.TEMPERflTURE/K 1950.

Figure VI.11 Computed species concentrations as functions of initial reaction temperature at a reaction time of 0 . 5 ms.

R2R 5

C D o I —<i

o ocoi____________,____________,____________,____________r”1450. 1550. 1650. 1750. 1850. 1950.TEMPERflTURE/K

Figure VI.12 Computed species concentrations as functionsof initial reaction temperature at a reaction time of0.5 ms.

1856.3.5 Formation of Soot

For modeling purposes we defined soot, as in the experimental work (31), as a collection of species absorbing light of a specific wavelength, or, similarly (163), as a collection of species above a certain size. In the present modeling the list of these species was chosen to begin at coronene. The choice of a larger species would not greatly affect the soot yields at longer reaction times. The computed soot yield was defined, again as in the experimental work (31), as the number of carbon atomsaccumulated in soot divided by the initial number of carbon atoms of acetylene.

To compute soot yields we assumed an infinitely long reaction sequence of Route 1 (Fig. VI.2), all species of this route beginning with coronene constituting soot. This is, of course, a simplification: somewhere in the growthprocess mechanisms such as physical condensation, particlecoagulation and surface reactions become more efficient and take over the soot formation process. In view of this, the model of an infinitely long reaction sequence provides only a lower— limit estimate of soot yield.

As discussed in the previous section, the fusedpolycyclic aromatic molecules are formed by practically irreversible reactions. Therefore, Route ! can be viewed as a sequence of similar strings of reversible reactions, from acenaphthalene to pyrene, from pyrene to coronene, from

186coronene to ovalene, etc., the strings being connected by irreversible reactions (Fig. VI.13). Given such a model, the total number o£ carbon atoms accumulated in soot species can be computed exactly. In this computation we assumed the equilibrium constants of corresponding reversible reactions in the strings t’c be unchanged after -coronene. The summation technique requires this assumption to be made at some point in the growth of the polycyclic aromatics, although not necessarily at coronene. Derivation of the summation procedure has been discussed separately (199).

Soot yields computed in the above manner are given in Fig. VI.14. Figure VI.15 presents the corresponding experimental results (31). Except for the shift in the temperature range (see below), the computed soot yields compare well with the experimental ones (cf. Figs. VI.14 and VI.15). The model predicts both the soot bell and its shift to lower temperatures with reaction time. The width of the bell is in good agreement with experiment. The absolute values of the soot yields also agree well if one takes into account that the lasei— extinction methodoverestimates actual soot yields by a factor of two to three (60,166). The model also correctly predicts the existence of an induction time of soot appearance as observed experimentally (Fig- VI.16). Additional computerexperiments showed that computed soot yields aredramatically reduced by decreases in the initial

(+ C 2H)

iOiOX'broip.( + C . H )

Figure VI.13 Principal reaction pathway for further growth of polycyclic aromatic hydrocarbons. 00

188concentration of acetylene or by addition of hydrogen, in accord with experimental observations.

The computational results support the conjecture (31) that competition between kinetic and thermodynamic factors is responsible for the bell-shaped profile of soot yield versus temperature. At the lower temperature bound of the bell, pyrolysis reactions are rate controlling. As temperature increases, the thermodynamic stability of the intermediates (13), particularly of small aromatic radicals, decreases and eventually limits the soot yield. At high temperatures fragmentation is dominant even at the first-ring level.

Table VI.6 presents the results of a sensitivity analysis for selected reaction classes. Somewhat surprisingly, only a small number of reaction classes, and sometimes only a simgle reaction within a class, have large sensitivities (Table VI.6). The strongest kinetic effect, i.e. the

Ylargest value of Sk, is caused by the practically irreversible formation of the fused polycyclic aromatics (Class 27) and their reactivation by hydrogen atoms (Class 23). It, is interesting to note that the ratio [H]2/[H2] is much larger than the corresponding equilibrium value. Only at high temperatures, when most initial pyrolysis reactions reach a state of partial equilibrium, does the concentration of hydrogen atoms relax to its equilibrium value on the time scale of interest here. Later work (154) has further

SOOT

YIEL

D

189

ino

2 . 0 ms

tooo

t\j

□o

2000.1800.1600.moo.T E M P E R A T U R E / KFigure VI.14 Computed soot yields at different

temperatures and reaction times in a 1.09% acetylene -argon mixture at ps = 3.8 x 10"5 mol/cm3. The symbols designate computational results, the lines cubic spline fits.

190

t\j

ocuo

m□ _I obJ

>-I—DOCO o

ino

2500.2300.2100.1900.1700. 1900. 2100.T E M P E R R T U R E / K

Figure VI.15 Experimental soot yields in a 1.09% acetylene - argon mixture at ps = (3.82 - 3.90) x 10"5 mol/cm3 using laser extinction at 3390 nm (Series B of Ref. 31). The soot yields are calculated assuming Rayleigh scattering (166) and using the value of Lee and Tien (200) for the complex refractive index at 3390 nm. The symbols designate designate experimental points, the lines cubic spline fits.

SOOT

YIEL

D

191

«oo

C\J

o

oo

R E A C T I O N T I M E / m s

Figure VI.16 Computed soot yield versus reaction time foran initial temperature of 1700 K.

192indicated the importance to soot formation of this overshoot by hydrogen atoms of their equilibrium concentration.

Analysis of the sensitivities with respect to equilibriumYconstants, SK , indicates that the thermodynamic bottleneck

for the growth in soot yield is at the formation of the first aromatic ring. The largest values of SK, obtained for Classes 13 and 8 (Table VI.6 ), are basically the sensitivities for the reactions

C 2H 2 + HC=C-CH=CH == HC=C-CH=CH-CH=CH and C 2H 2 + C2H == HC=C-CH=CH,respectively.

The results of the sensitivity analysis (Table VI.6 ) indicate a strong interaction between rate coefficients and eauilibrium constants. This is believed to be the cause for the mismatch in the temperature ranges of the experimental and numerically simulated soot-yield bells. More recent work (Ref. 202 and Chapter VII) has confirmed that the location of the soot bell is strongly influenced by the selection of different experimentally-determined values for certain bond dissociation energies.

193

Table VI.6 Sensitivities of soot yield with respect to rate coefficients and equilibrium constants.

Reaction Class SYbk SYK

1 -0.10 0.10

3 -0.04 -0.20

5 -0.01 0.03

8 -0.02 0.78

13 0.16 0.79

23 2.02 0.12

24 -0.06 0.06

25 0.27 -0.28

27 1.30 0.24

29 -0.03 0.00

30 0.70 0.56

173The sensitivities are defined as

SY = £n(Yk/Y0 )/JHn(l/5) and SY = £n(YK /YQ )/jen5,

where Yq is the soot yield computed for 1.09% C 2 H 2 ~Ar mixture at p,. =

3.80 x 10 5 mol/cm3 , Tj. = 1700K, and reaction time of 0.5 ms; Y^ and Y^

are the soot yields computed for the same conditions but with the rate

coefficient reduced by a factor of 5 and with the equilibrium constant

increased by a factor of 5, respectively, for a given reaction class.

The reaction classes omitted have absolute sensitivity values less

than 0.005.

1946.4 CONCLUSIONS

It was demonstrated that soot formation in shock-tube pyrolysis of acetylene can be explained by a detailed kinetic mechanism composed of conventional hydrocarbon reactions. The main mass growth was found to proceed through a single dominant route in which fused polycyclic aromatics play a particularly important role: theirpractically irreversible formation reactions have the effect of "pulling" chains of reversible reactions in which H atoms reactivate aromatic molecules. The overshoot by atomic hydrogen of its equilibrium concentration also provides a driving force for growth of large polycyclic species. The main reaction bottleneck apoears at the formation of the first aromatic ring. The model is in accord with product distributions observed in flames.

Chapter VIISENSITIVITY ANALYSIS OF THE SOOT-FORMATION

MECHANISM

7.1 INTRODUCTIONA detailed chemical kinetic mechanism of soot formation

under the conditions of shock-tube pyrolysis of acetylene was presented in Chapter VI. The model correctly accounts for the time and temperature dependences observed experimentally (31) except for a mismatch in the temperature of the soot-yield maximum. On the basis of computational results demonstrating the sensitivity of species concentrations to both rate coefficients and thermodynamic parameters, it was suggested in Chapter VI that the mismatch is probably due to uncertainties in thermochemical data. This suggestion is supported by the results of a recent modeling study (203). This study determined that at short reaction times inclusion of coagulation and surface growth does not significantly affect the temperature at which the maximum calculated soot yield occurs.

In this chapter, the effect of thermodynamic parameters on the model prediction for soot yield is investigated, the influence of changes in thermodynamic data on the dominant reaction pathway to soot is analyzed, and the sensitivity analyses presented in Chapter VI and Ref. 20 1 are expanded.

- 195 -

1967.2 COMPUTER EXPERIMENTS

All computer experiments discussed in this chapter were performed using the model developed for the study described in Chapter VI. Briefly, the reaction mechanism has three logical components: initiation - a set of reactionsdescribing the initial stages of acetylene pyrolysis; cyclization - reactions describing the formation of larger molecules and radicals and eventually small aromatic molecules and radicals; and polymerization - a description of the further growth of aromatic rings.

The initiation set is composed of 21 reactions and is based on the mechanism of Tanzawa and Gardiner (8 6 ). One reaction of their mechanism, namely

C 2H 2 + C 2H 2 = C 4H 3 + H , (R 2 ')

has been of particular concern. Originally, Tanzawa andGardiner (92) introduced this reaction in an attemot to account for the rapid appearance of C 4H 3 in acetylene pyrolysis reported by Gay et al. (91). We now recognize that the vinylacetylene radical, the structure assigned to the product of reaction (R2’) in Chapter VI and related work (Refs. 172 and 201), is so unfavored thermodynamically that no reactions could raise its concentration to a level that would have been observed in time-of-f1ight (TOF) mass-spectrometric experiments; for example, no C 4H 3 or C 4H 4

was reported in a more recent TOF study (4-9). Furthermore,

computations performed at the University of Texas (202) at the experimental conditions of Tanzawa and Gardiner (92) indicated that replacing reaction (R2’) by reaction

C 2H 2 + C 2H 2 = C 2H + C 2H 3 (R2)

does not affect the computed lasei— schlieren signals. Since reaction (R2') has never been identified by a direct experiment, it has been replaced here by the conceptually simpler, disproportionation reaction (R2), with a rate coefficient value for the reverse direction of 1 0 13

cm3/mol/s.The cyclization and polymerization reactions of the

mechanism were grouped into classes as discussed in ChapterVI. The rate coefficient expression chosen for a prototype reaction within a class was assigned to the rest of the class. Thermodynamic properties of the chemical species were estimated by Dr. S. E. Stein of the National Bureau of Standards using group additivity methods (195,196). The computer experiments were performed at the same initial conditions as in the previous study: a 1.09% C 2H 2-Ar mixture at a total density of 3.8x10" 5 mol/cm3. The details of the calculations are discussed in Chapter VI.

To test the effects of thermodynamic data, three basic and yet not well-established properties, namely C 2H-H and C 2H 3 —H bond energies and the Ct-(Ct) group additivity value for aH298. were varied. Since in this work thermodynamic

properties are estimated by group additivity methods, variations in these basic values result in systematic, simultaneous variations in the properties of all the species. Six sets of thermodynamic data, S3 throuqh S8, were constructed; they are shown in Table VII.1. , Also shown in Table VII.1 is set S 2 , which was used in a previous modeling of soot formation in acetylene systems (201). Set S2 is the same as set S4 except for reaction (R2) being replaced by reaction (R2').

Table VII.1 Sets of thermodynamic data.

SetNo.

Bond Energy, C2H - h c

kJ/mol 2H 3 - H

Ct - (Ct) Group Value

a H°298, kJ/mol

C 2H 2 + C 2H 2 Reaction

Used

S2 502 452 107 R2'S3 552 452 107 R2S4 502 452 107 R2S5 502 452 125 R2S6 552 452 125 R2S7 502 427 107 R2S8 552 427 107 R2

66 t

2007.3 RESULTS AND DISCUSSION

Soot yields computed with the sets in Table VII'. 1 are shown in Fig. VII.1. As seen in this Figure, replacement of reaction (R2') by reaction (R2) shifts the position of the soot-yield maximum by about 75 K to higher temperatures with a reduction in the maximum value of soot yield. Further examination of Fig. VII.1 reveals that: (a) arelatively small change in the C 2H-H bond energy stronglyaffects the temperature of the soot-yield maximum and theabsolute values of soot yield; (b) a change in the Ct-(Ct)group additivity value has a pronounced effect on themaximum value of the soot yield but not on its temperature dependence; and (c) variation in C 2H 3-H bond strength has no significant influence on the computed soot yields. Computer simulations performed at the conditions of the Tanzawa and Gardiner lasei— schlieren experiments resulted in longer induction times and smaller maximum deflection values for sets S4, S5 and S7 compared to those for sets S3, S6 and S8 (202). As mentioned earlier, no difference was obtained between cases S2 and S 4 .

It should be pointed out, however, that no decision can be made on which thermodynamic set is best based on the above analysis alone. The presented results identify computational trends. To determine the best-fit values, the entire acetylene pyrolysis mechanism must be reoptimized with respect to both thermodynamic and rate-coefficient data with all available experimental facts taken as constraints.

LOGin

(S00T

YIEL

D)

20101

i

moo. 1600. 1800. 2000. TEMPERflTURE/K

2200. 2U00.

Figure VII.1 Soot yields versus temperature computed with thermodynamic datasets in Table VII.1 for a reaction time of 0.5 ms.

, 202 It. is nevertheless of interest to analyze the effects of

the changes in thermochemical data on the reaction mechanism for soot formation. Inspection of the computational results revealed that for sets S2, S4, S5, S6, S7 and S8 the mainreaction pathways to soot remain exactly as identified in previous work (Chapter VI and Ref. 172). In the case of set S3, the dominant reactions leading to the formation of the first aromatic ring are

C2H 3 + C 2H 2 = C 4H 5 C 4H5 + C 2H 2 = C 6H 7 C6H7 = c-C6H 7 c-C&H7 = c-C6H 6 + H

(where the prefix ”c~” indicates a cyclic species), which are different from those in all other cases, namely

C 4H 5 = C 4H 4 + H C 4H 4 + H = C 4H 3 + H z C4H 3 + C 2H 2 = C 6H 5 CfeHs = C — CfeHsa

It should also be mentioned that the difference in the net rates of the dominant and minor routes of the second-ring formation (see Fig. V I .1) is smaller for sets S3, S7 and S8 compared with that for the other sets. This is particularly true at shorter times when the difference is less than an order of magnitude.

Tables VII.2 and VII.3 present computed sensitivities. The sensitivities are defined as in Chapter VI:

Sk = ln(Yk/Y0)/ln(1/5) and s[ = In(YK/Y0)/ln(5)

203where Y 0 is the soot yield computed for the 1.09% C 2H 2-Ar mixture at p5 = 3.80x10-5 mol/cm3 , a reaction time of 0.5 ms, and at the temperature of the corresponding soot-yield maximum: 1675 K for set S 2 , 1975 K for set S3 and 1750 K for set S4. Y k and Y« are the soot yields computed at the same conditions but with the rate coefficient reduced by a factor of five and with the equilibrium constant increased by a factor of five, respectively, for a given reaction (Table VII.3) or reaction class (Table VII.2). The reactions and reaction classes omitted have absolute sensitivity values less than 0.005. The pR values in Table VII.3 are defined in the usual manner (173). Their values are given at two reaction times, 0.3 and 0.5 ms.

Table VII.2 presents the sensitivities computed with sets S2, S3 and S4. The results indicate that a change in thermodynamic data affects the sensitivity values. For some reaction classes the influence is significant; however, the relative ranking of the sensitivity values is not changed much. It should be pointed out that an analysis at fixed conditions can be incomplete; this is illustrated by Fig.VII.2, which depicts a sensitivity analysis performed for a single reaction class, class 30, over the entire temperature range for the S2 thermochemistry set. As seen in the Figure, a change in the equilibrium constant, Kao. both increases the soot yield and causes a small shift in the temperature of the maximum.

204

Table VII.2 Sensitivities of Soot Yield With Respect to Rate Coefficients and Equilibrium Constants for Reaction Classes.

Reactionriass S2 S3 S4 S2 S3 S4

1 -0.09 -0.01 -0.07 0.09 0.01 0.072 0. 00 0.04 0.00 0. 00 0.00 0.003 0.05 0.30 0.04 -0.18 -0.32 -0.215 -0.01 0.07 -0.01 0. 02 ( o • o 00 0.028 -0.15 -0.37 -0.02 0.89 1 .28 0.9713 0.00 -0.27 -0.02 0.97 1 .65 1 .0320 0.00 0.02 0.01 0.00 0.01 0.0021 0.00 -0.01 -0.01 0.00 0.00 0.0023 2.45 1 . 05 2.38 0. 19 0.10 0.3224 0.11 -0.01 -0.13 0.11 0.01 0.1325 0.76 0.34 0.85 -1.16 I o o -1 .3527 1 .34 1 . 18 1 .66 0.29 1 . 03 0.3429 -0.03 -0. 05 -0.01 0.00 0.00 0. 0030 0.45 0.53 0.62 1 .03 2. 10 1.01

Table VII.3 Sensitivities of soot yield with respect to rate coefficients and equilibrium constants for initiation reactions with set S4.

No. Reaction Sk S pRa o o pRso 0

R 1 C2H2 + M = c 2h + h + m 0.29 0.00 16.00 -15.23R2 c 2h 2 + c 2h 2 = C 2H 3 + C ZH 0.03 0.00 -15.27 14.43R3 C 2H z + H = c 2h 3 0.00 -0.01 18. 10 17.68R6 CZH + H2 = C2H 2 + H 3.49 -3.49 -19.87 -19.86R7 c 2h 2 + c 2h = C 4H 2 + H -0.41 0.00 19.87 19.81RIO c 4h 2 + n = C„H + H + M 2.83 0.57 18.35 -17.03R 1 1 c 4h 2 + c 2h = C 6H 2 + H -0.04 -0.05 18.02 18.81R 1 2 c 4h + c 2h 2 = C 6H 2 + H 0. 17 0. 13 18.36 18.62R16 C 6H 2 + M = C6H + H + m 0.00 0.01 16.06 -16.89

205

SOOT

YIEL

D206

a

co­co

o

=hOo

X =p-C\i

oCO“

oCO

a20001600. 1700 1800 1900T E M P E R R T U R E / K

Figure VII.2 Soot yields versus temperature computed at a reaction time of 0.5 ms: middle curve - with set S2, upper - K 30 x 5, lower - k 30 / 5.

207Sensitivity information for the initiation reactions is

given in Table VII.3. There are only a few reactions with large sensitivity values, the largest being that of reaction (R6). The reason for this sensitivity is that (R6) and (R7) constitute the fastest reaction chain, which controls the concentration of hydrogen atoms and C2H radical. The rate of this chain is determined by the reverse reaction of (R6), because its rate coefficient is much smaller than that of the forward reaction of (R7) (173). Decreasing the ratecoefficient of the latter does not affect the reaction rate but increases the concentration of C 2H, which explains the negative value of the sensitivity for reaction (R7). The surprisingly high sensitivity for reaction (RIO) is due to the additional supply of hydrogen atoms, this being a dominant factor in the polymerization kinetics of soot formation (Chapter VI and Ref. 201). However, production of hydrogen atoms by reaction (R10) occurs only during the initial (induction) period of the pyrolysis, with the most significant contribution taking place during soot inception; after this point the reaction proceeds in reverse, as seen from the pR values in Table VII.3.

208t

7.4 CONCLUSIONSIt. is demonstrated that both the magnitude and the

temperature location of the soot-bell maximum are affected by variations in thermochemical data. It is important to note that the chemical reaction pathway to soot remains basically unchanged with these variations. This observation supports the reaction mechanism for soot formation suggested in Chapter VI. A more general conclusion is that the accuracy of thermodynamic data is as important as that of rate coefficients in modeling of high-temperature chemical kinetics.

Chapter VIIIMODELING OF FUEL-STRUCTURE EFFECTS ON SOOT

FORMATION

8.1 INTRODUCTIONIn Chapters VI and VII a detailed model of soot formation

in shock-tube pyrolysis of acetylene was presented. Extensions of this model have been shown to correctly predict the effects of oxygen (201) and chlorine (204) on soot formation from acetylene. It is of interest to consider soot formation from fuels other than acetylene since fuel structure strongly influences sooting tendency (161,205).

Acetylene has been suggested as an important precursor for the production of soot from nonaromatic hydrocarbons, although some researchers believe that butadiene is the principal intermediate (27,74). If two-carbon species such as acetylene are indeed important intermediates for nonaromatic fuels, then the detailed reaction mechanism for soot formation from acetylene presented in earlier chapters should be the correct starting point for detailed soot-formation models for other fuels. As a test of this hypothesis, detailed models of soot formation during pyrolysis of two model fuels, ethylene and butadiene, were

- 209 -

210developed; these models will be discussed in the first section of this chapter.

The most dramatic effect of fuel structure on sooting tendency is the difference in sooting propensity between aromatic and nonaromatic fuels. As noted in Chapter II, aromatic fuels produce more soot than nonaromatic fuels under almost all combustion conditions. There is disagreement concerning the question of 'whether intact aromatic rings react with each other to form soot nuclei or whether ring fragmentation occurs first. A detailed model of soot formation from benzene was developed to address this question. The model and the conclusions drawn from it are discussed in the second section of this chapter.

8.2 BUTADIENE M ETHYLENE8.2.1 Computer Model

As in the model for acetylene pyrolysis described in Chapter VI, these reaction mechanisms have three components: reactions describing the initial stages of fuel pyrolysis, reactions describing the formation of larger molecules and radicals and eventually small aromatic molecules and radicals, and reactions summarizing the further growth of polycyclic aromatic species. The set of initiation reactions used for acetylene pyrolysis was augmented with some reactions from the butadiene pyrolysis mechanism of Kiefer et al. (206). The reactions and their ratecoefficients are presented in Table VIII.1.

Table VIII.1 Core reactions for butadiene and ethylene mechanisms.

Reaction Reaction Rate Coefficient Reference/Number for Forward Direction Remarks

A n E

R 1 C 4H 6 = C 2H 3 + C 2H3 2.58+15 361 Ref. 206 (value forR2 C2H4 + M = C2H2 + H2 + M 2.51 + 17 332 Ref. 206

6 atm)

R3 C 2H z + M = C 2H + H + M 4.2 + 16 448 Ref. 206R4 C 2H + C 2H 3 = C 2H 2 + C 2H2 1 .0 + 13 - - Ref. 202R5a C 2H3 + M = C 2H2 + H + M 2.0 +38 -7.17 212 Ref. 206 (high temp.R5b H + C2H2 = C 2H3 5.5 + 12 10 Ref. 86

value)

R6 c 2h 2 + C 2H 3 = H + C 4H 4 1 .6 + 13 105 Ref. 86R7 H + i-C4H 3 + M = C 4H4 + M 1 .0 + 15 - - Ref. 86R8 H2 + C 2H = C 2H 2 + H 2.5 + 12 - - Refs . 31 , 93R9 C 2H2 + C 2H = h + c 4h 2 4.0 + 13 - - Ref. 86RIO C 2H + C 4H4 = C 2H 2 + i-C4H3 4.0 + 13 — — Ref. 86

R 1 1 i-C4H 3 + M = H + C 4H 2 + M 1 .0 + 16 — 250 Ref. 86R 12 C4H 2 + M = H + C 4H + M 3.5 + 17 - 335 Ref. 86R 1 3 C ZH + C 4H 2 = H + C 6H 2 4.0 + 13 - - Ref. 86R 14 C 2H 2 + C 4H = H + C 6H 2 4.0 + 13 - - Ref. 86R 15 c 2h 2 + C 6H = H + C 8H 2 1 .0 + 12 - - Ref. 86R 1 6 c 2h + C 6H 2 = H + C 8H 2 1 .0 + 12 - - Ref. 86R 17 C4H + C 4H 2 = H + C 8H2 1 .0 + 12 - - Ref. 86R 18 C6H2 + M = H + C 6H + M 5.0 + 16 - 335 Ref. 86R 1 9 C8H2 + M = H + C 8H + M 5.0 + 16 - 335 Ref. 86R20 H2 + M = H + H + M 2.24+12 0.5 387 Ref. 86R21 H + n-C4H 3 + M = C 4H 4 + M 1 .0 + 15 - - = k(R7)R22 n-C4H3 + M = H + C 4H 2 + H 1 .0 + 16 - 250 = k(R11)R23 C 2H + C 4H4 = C 2H2 + n-C4H3 4.0 + 13 - - = kCRIO)R24 C 2 H a + M = C zH 3 + H + M 4.0 + 17 — 41 1 Ref. 206

The units are mol, s. cm3, kJ, K . The form of the rate coefficientsk = A * T n * exp(-E/RT); rate coefficients for the reverse direction are calculated from equilibrium. 212

213Kiefer et al. concluded from their experimental results

that the dominant initiation reaction in butadiene pyrolysis is the pressure-dependent fragmentation of butadiene to form two vinyl radicals. The pyrolyses of butadiene and ethylene thus seem closely related, since the first products ethylene forms under pyrolytic conditions are vinyl radical and acetylene (via separate reactions) (89). Therefore, the computer models for butadiene pyrolysis and ethylene pyrolysis used the same set of initiation reactions. The only difference in the reaction sets was for reaction R5, the decomposition of vinyl radical to form acetylene. Kiefer et al. proposed a pressure-dependent rate coefficient (reaction R5a) for their butadiene mechanism: reaction R5bhas the pressure-independent rate coefficient of Tanzawa and Gardiner (86). Butadiene pyrolysis was modeled using reaction R5a to be entirely consistent with the mechanism of Kiefer et al., while ethylene was modeled using two cases: Case A, with reaction R5a; and Case B, with reaction R5b.

The cyclization and polymerization reactions of the mechanism presented in Chapter VI served as the core of the soot-growth models developed for butadiene and ethvlene. Additional reactions were added in accord with physical organic principles (no migrations of hydrogen atoms or complex isomerizations were included) to broaden the mechanism to include possible contributions from species produced in greater concentrations during pyrolysis of

214ethylene or butadiene than during acetylene pyrolysis. The reactions considered in these models are presented in TableVIII. 2. Species used for the acetylene pyrolysis model are listed with their chemical structure in Table VI.1; the additional species added for modeling pyrolysis of ethylene and butadiene are listed in Table VIII.3.

As in previous work (172,201,202) the cyclization and polymerization reactions were grouped in classes. The rate coefficient expression chosen for a prototype reaction was assigned to the other reactions of that class. Reaction classes 1 through 31 are identical with those of Chapter VI. The additional reaction classes used in this work are presented in Table VIII.4. Thermodynamic properties were estimated by Dr. S. E. Stein of the National Bureau of Standards using group additivity methods (196,202). The group values of thermodynamic set S8 of Chapter VII were chosen for these models in order to match the values used by Kiefer et al. (206). The computer experiments wereperformed at a total concentration of 1.5 * 10-5 mol/cm3 and molar fuel percentages of 1.09% and 0.54% for ethylene and butadiene, respectively. The conditions were chosen to match those of experimental Series J of Ref. 31. The computations were done with a constant-pressure model using IBM 370-3081 and 4341 computers and the LSODE and LSODES integrators (197). Computed temperature decreases for these cases were between 25 and 100 degrees.

215

T a b l e V I I I . 2 R e a c t i o n l i s t f o r b u t a d i e n e a n d e t h y l e n em e c h a n i s m s .

AHfgpsREACTIONS REACTION CLASS

25) C4H6 + C2H3 «= C2H4 + C4H5U 15 0 . 0

26) C4H6 + C2H3 = C2H4 + C4H5S 15 -33.521) C2H3 + C4H4 e C4H3S + C2H4 15 -33.528) C2H3 + C4H4 s C4H3U + C2H4 15 0.029) C4H6 + H = H2 + C4H5U 2 -16.930) C4H6 + H &s H2 + C4H5S 2 -50.431) C4H6 + H s C2H3 + C2H4 -16 -41.332) C2H2 + C2H = C4H3U 8 -289.033) H2 + C4H3U = H + C4H4 -2 t6.934) C2H2 + C4H3U - C6H5U 13 -161.235) C6H5U — A ’r 30 -233.336) C6H5U = H C6H4 -5 174.737) H + C6H5U = C6H6 29 -435.538) H2 + C6H5U = H + C6H6 -2 16.939) C2H + C6H5U 2~ C8H6 7 -541.940) C2H2 + C6H5U = C2H + C6H6 -4 1 19.941 ) C4H2 + C4H3U - C4H + C4H4 -4 122.742) C4H2 + C4H3U = C8H5SX 13 -191.843) C8H5SX = A1C2H- 30 -180.044) C8H5SX m H + C8H4 -5 208.245) H + C8H5SX = C8H6 29 -402.146) H2 + C8H5SX - H + C8H6 -2 50.447) C2H2 + C8H5SX = C2H + C8H6 -4 153.348) H + C4!i2 - H2 + C4H -1 105.849) H + C6H2 = H2 + C6H -1 105.850) H + C6H2 S C6H3S 5 -213.35! ) H + C9H2 = H 2 + C8H -1 105.852) H + C8H2 = C8H3S 5 -213.353) C2H + C4H2 = C2H2 + C4H 3 2.854) C2H + C6H2 - C2H2 + C6H 3 2.855) C2H + C4H2 = C6H3S 8 -319.756) C2H + C6H2 = C8H3S 8 -319.757) C4H + C4H2 = C2H + C6K2 -10 0.058) C4H + C6H2 = H + C10H2 9 -106.359) C4H + C4H2 = C8H3S 8 -319.760) C4H + C6H2 = C10H3S 8 -319.761 ) C6H + C4H2 = C2H + C8H2 -10 0.062) C6H + C4H2 = H + C10H2 9 -106.363) C6H + C4H2 = C10H3S 8 -319.764) C6H + C6H2 = C4H + CSH2 -10 0.065) C6H + C6H2 = H + C12H2 9 -106.366) H + C6H3S = C6H4 29 -402.167) H2 + C6H3S = H + C6H4 -2 50.468) C2H2 + C6H3S = C2H + C6H4 -4 153.369) C2H2 + C6H3S = H + C8H4 1 1 47.070) C4H2 + C6H3S = C4H + C6H4 -4 156.271 ) H + C8H3S - CSH4 29 -402.172) H2 + C8H3S = H + C8H4 -2 50.473) C2H2 + C8H3S = C2H + C8H4 -4 153.374) H + C10H2 = C10H3S 5 -213.375) H2 + C2H3 = H + C2H4 -2 16.976) C2H2 + C2H3 C2H + C2H4 - 4 1 19.977) C4H5U = C2H2 + C2H3 -13 161 .278) C4H2 + C2H3 = C6H5S 13 -172.079) C4H2 + C2H3 = C2H + C4H4 -10 142.580) C4H2 + C2H3 = C4H C2H4 -4 122.781 ) H2 + C4H3S cr H + C4H4 -2 50.482) C2H2 + C4H3S = H + C6H4X 1 1 47.083) C4H2 + C4H3S = C4H + C4H4 -4 156.284) H + C4H4 ■c C4H5U 5 - 194.685) C2H + C4H4 KS C6H5S 8 -314.68 6 ) C6H6 m C2H3 + C4H3U -7 394.287) C6H5S ■ H + C6H4X -5 208.28 8 ) H + C6H5S e C6H6 29 -402.1

216

89) C2H + C6H5S £ C8H6 7 -508.490) H2 + C6H5S £ H + C6H6 -2 50.491 ) C2H2 + C6H5S £ C2H + C6H6 -4 153.392) C2H2 + C6H5S £ H + C8H6 1 1 47.093) C8H5S s H + C8H4 -5 208.294) H + C8H5S = C8H6 29 -402.195) H2 C8H5S £ H + C8H6 -2 50.496) C2H2 + C8H5S £ C2H + C8H6 -4 153.397) H + A 1 - £ Al 21 -471.190) Al = H + C6H5U 22 704.499) C2H + A1- £ A1C2H 7 -557.6100) A1C2H £ H + C8H5SX 22 651 . 1101 ) H + A1C2H- £ A1C2H 21 -471.1102) H2 + A1C2H- £ H + A1C2H -23 -18.7103) C2H2 + A 1C2H- £ C2H + A1C2H -24 84.3104) C2H2 + A1C2H- £ H + A1C2H)2X -25 -2.2105) H2 + A 1 — £ H + Al -23 -18.7106) C2H2 + Al- £ C2H + Al -24 84.3107) C4H2 + Al- £ C4H + Al -24 87. 1108) C2H2 + A 1- £ H + A1C2H -25 -2.2109) C4H2 + A1- £ C2H + A1C2H 26 107.01 10) C4H2 + A1- £ A1C4H2S 27 -203.4111) H + A 1C4H2S £ A1C4H3 29 -402.1112) A1C4H3 £ C4H3U + A 1 - -7 425.61 13) H2 + A1C4H2S £ H + A1C4H3 -2 50.4114) C2H2 + A1C4H2S £ C2H + A1C4H3 -4 153.31 15) C2H2 + A1C4H2S £ H + AIC6H3 1 1 47.01 16) C4H2 + A1C4H2S £ A1C8H4S 13 -158.4117) A1C8H4S £ H + A2C2H)2X 20 15. 11 18) H + A1C8H4S £ AIC8H5 29 -402.11 19) H2 + A1C8H4S £ H + A1C8H5 -2 50.4120) C2H2 + A 1C8H4S £ C2H + A1C8H5 -4 153.3121 ) C2H2 + A1C8H4S £ H + A1C10H5 1 1 47.0122) C2H2 + A 1 - £ A1C2H2U 27 -192.6123) A1C2H2U £ H + A1C2H -5 190.4124) H + A 1C2H2U £ A1C2H3 29 -435.5125) H2 + A1C2H2U £ H + A1C2H3 -2 16.9126) C2H + A 1C2H2U £ A1C4H3 7 -522.0127) C2H2 + A1C2H2U £ A1C4H4U 13 -161.2128) C4H2 + A 1C2H2U £ A 1C6H4S 13 -172.0129) A 1C4H4U - H + A2 20 -38.2130) A1C4H4U ~ H + A1C4H3 -5 194.6131 ) H + A 1C4H4U £ A1C4H5 29 -435.5132) H2 + A1C4H4U £ H + A1C4H5 -2 16.9133) C2H2 + A1C4H4U £ C2H + A1C4H5 -4 1 19.9134) C2H2 + A1C4H4U £ H + A1C6H5 1 1 33.4135) A1C6H4S £ H + A2C2H 20 -4.7136) A1C6H4S £ H + A1C6H3 -5 208.2137) H + A1C6H4S £ A 1C6H5 29 -402.1138) H2 + A 1C6H4S £ H + AIC6H5 -2 50.4139) C2H2 + A1C6H4S £ C2H + A1C6H5 -4 153.3140) C2H2 + A1C6H4S £ H + A1C8H5 1 1 47.0141 ) C2H2 + A1C4H2S £ A1C6H4U 13 -132.9142) A1C6H4U £ H + A2C2H 20 -33.0143) A1C6H4U £ H + A1C6H3 -5 179.9144) H + A1C6H4U £ A1C6H5 29 -430.4145) H 2 + A1C6H4U £ H + A1C6H5 -2 22.0146) C2H2 + A1C6H4U £ C2H + A1C6H5 -4 125.0147) C2H2 + A1C6H4U £ H + A1C8H5 1 1 18.6148) H + H2- £ A2 21 -471.1149) H2 + A2- £ H + A2 -23 -18.7150) C2H + A2- £ A2C2H 7 —557.6151 ) C2H2 + A2- £ C2H + A2 -24 84.3152) A1C2H £ H + A 1C2H* -21 471. 1153) H + A1C2H £ H2 + A1C2H« 23 18.7

217

< 154) C2H + A1C2H S C2H2 + A1C2H* 24 -84.3(155) A1C2H* b C8H5U -30 213.5(156) H + C8H5U s C8H6 29 —435.5(157) H2 + C8H5U ts H + C8H6 -2 16.9( 158) C2H2 + C8H5U B C2H + C8H6 -4 119.9(159) C2H2 + C8H5U B H + C10H6 1 1 13.5(160) C8H5U b H + C8H4 -5 174.7( 161 ) CBH5U B C2H2 + C6H3U -13 161 .2(162) H + C6H3U B C6H4X 29 -435.5(163) H2 + C6H3U S H + C6H4X -2 16.9( 164) C2H2 + C6H3U s C2H + C6H4X -4 119.9(165) C2H2 + C6H3U s H + C8H4 1 1 13.5(166) C6H3U IS C2H + C4H2 -8 286.2( 167) C2H2 + A1C2H" 55 A1C2HC2H2U 27 -192.6(168) C2H2 + A1C2H- S H + A1C2H)2 -25 -2.2(169) A1C2HC2H2U s H + A1C2H)2 -5 190.4(170) A1C2HC2H2U B A2-X 30 -197.2( 171 ) H + A1C2HC2H2U B A1C2HC2H3 29 -435.5( 172) H2 + A1C2HC2H2U S H + A 1C2HC2H3 -2 16.9( 173) C2H2 + A1C2HC2H2U S C2H + A1C2HC2H3 -4 119.9(174) H + A2-X 55 A2 21 -471.1(175) H2 + A2-X S H + A2 -23 -18.7(176) C2H2 + A2-X 55 C2H + A2 -24 84.3(177) C2H + A2-X 55 A2C2H 7 —557.6( 178) C4H2 + A1C2H" S A 1C2HC4H2S 27 -203.4(179) A 1C2HC4H2S B H + A 1C2HC4H -5 204.0(180) A 1C2HC4H2S B A2C2H- 30 -163.7( 181 ) H + A1C2HC4H2S = A1C2HC4H3 29 -402.1(182) H 2 + A 1C2HC4H2S s H + A1C2HC4H3 -2 50.4(183) C2H2 + A1C2HC4H2S s C2H + A1C2HC4H3 -4 153.3( 184) H + A2C2H&X as A2C2H 21 -471.1(185) H2 + A2C2H-X = H + A2C2H -23 -18.7(186) C2H2 + A2C2H-X s C2H + A2C2H -24 84.3(187) C2H2 + A2C2H«X = H + A2R5C2H 27 -129.8(188) C2H2 + A2-X s H + A2C2H -25 -2.2(189) C2H2 + A2C2H" s C2H + A2C2H -24 84.3(190) H + A2C2H* s A2C2H 21 -471.1( 191 ) H2 + A2C2H* s H + A2C2H -23 -18.7( 192) C2H2 + A2C2H* s H + A2C2H)2 -25 -2.2(193) C2H2 + A2C2H* 55 A2C2HC2H2U 27 -192.6( 194) A2C2HC2H2U B H + A2C2H)2 -5 190.4( 195) A2C2HC2H2U B A3- 30 -206.4(196) H + A3- s A3 21 -47 1 .1(197) H2 + A3- = H + A3 -23 -18.7(198) C2H2 + A3- = C2H + A3 -24 84.3(199) C2H2 + A3- s H + A3C2H -25 -2.2(200) C2H2 + A3- = A3C2H2U 27 -192.6(201 ) A3C2H2U B H + A4 20 -23.5(202) A 2— S A1C4H3* -30 228.5(203) H + A1C4H3" 55 A1C4H3 21 -466.9(204) H2 + A1C4H3« S H + A 1C4H3 -23 -14.5(205) C2H2 + A1C4H3* S C2H + A1C4H3 -24 ... . ..88.. 5(206) C2H2 + A1C4H3« 55 H + A 1C2HC4H3 -25 2.0(207) A1C4H3- B C10H7U -30 213.5(208) C10H7U B H + C10H6 -5 174.7(209) C10H7U B C2H2 + C8H5U -13 161 .2(210) H + A4- B A4 21 -471.1(211) H2 + A4- B H + A4 -23 -18.7(212) C2H2 A4- B C2H + A4 -24 84.3(213) C2H2 + A4- S H + A4C2H -25 -2.2(214) H + A4C2H- B A4C2H 21 -471.1(215) H2 + A4C2H" B H + A4C2H -23 -18.7(216) C2H2 + A4C2H* S C2H + A4C2H -24 84.3(217) C2H2 + A4C2H« s H + A4C2H) 2 -25 -2.2(218) C2H2 A4C2H* B A4C2HC2H2U 27 -192.6

218

(219) A4C2HC2H2U = H + A4C2H)2 -5 190.4(220) A4C2HC2H2U = A5- 30 -215.6(221 ) H + A5- = AS 21 -471.1(222) H2 + A5- s H + A5 -23 -18.7(223) C2H2 + A5- s C2H + A5 -24 84.3(224) C2H2 + A5- «; H + A5C2H -25 -2.2(225) C2H2 + A5- = H + A6 27 -216.1(226) H 2 ■f A6- B H + A6 -23 -18.7(227) C2H2 + A6- B C2H + A6 -24 84.3(228) H2 A3C2H" S H + A3C2H -23 -18.7(229) H + A3C2H" = A3C2H 21 -471.1(230) C2H2 + A3C2H» S C2H + A3C2H -24 84.3(231) C2H2 + A3C2H* = H + A3C2H)2 -25 -2.2(232) C2H2 + A3C2H- s A3C2HC2H2U 27 -192.6(233) A3C2HC2H2U s H + A3C2H)2 -5 190.4(234) A3C2HC2H2U s B4- 30 -177.1(235) H2 + B4- = H + B4 -23 -18.7(236) H + B4- B B4 21 -471.1(237) C2H2 + B4- = C2H + B4 -24 84.3(238) C2H2 + B4- B H + B4C2H -25 -2.2(239) H 2 + B4C2H” = H + B4C2H -23 -18.7(240) H + B4C2H« = B4C2H 21 -471.1(241) C2H2 + B4C2H® = C2H + B4C2H -24 84.3(242) C2H2 + B4C2H" = H + B4C2H)2 -25 52.2(243) C2H2 + B4C2H* = B4C2HC2H2U 27 -138.2(244) B4C2HC2H2U B H + B4C2H)2 -5 190.4(245) B4C2HC2H2U = B5- 30 -248.2(246) H + B5- = B5 21 -429.2(247) H2 + B5- = H + B5 -23 23.2(248) C2H2 + B5- = C2H + B5 -24 126.2(249) A2C2H* B A1C2H* 31 -239.4(250) A4C2H* B A3- 31 -384.7(251 ) H + A7- = A7 21 -471.1(252) H2 + A7- = H + A7 -23 -18.7(253) C2H2 + A7- = C2H + A7 -24 84.3(254) C2H2 + A7- = H -*• A7C2H -25 -2.2(255) H + A7£2H» = A7C2H 21 -471.1(256) H2 + A7C2H* = H + A7C2H -23 -18.7(257) C2H2 + A7C2H« = C2H + A7C2H -24 84.3(258) C2H2 + A7C2H« = H + A7C2H)2 -25 -2.2(259) C2H2 + A7C2H* = A7C2HC2H2U 27 -192.6(260) A7C2HC2H2U = H + A7C2H)2 -5 190.4(261 ) A7C2HC2H2U = A8- 30 -215.6(262) H + A8- = A8 21 -471.1(263) H2 + A6- = H + A8 -23 -18.7(264) C2H2 + A8- = C2H + A8 -24 84.3(265) C2H2 + A8- = H + A8C2H -25 -2.2(266) C2H2 + A8- = H + A9 27 -216.1(267) H A9- = A9 21 -471.1(268) H2 + A9- S H + A9 -23 -18.7(269) C2H2 + A9- = H + A9C2H -25 -2.2(270) C2H2 + A9- = C2H + A9 -24 84.3(271) C2H2 + A9- = H + A7 27(272) C2H2 + A2-X = H + A2R5 27 -129.8(273) H + A2R5- = A2R5 21 -471.1(274) C2H2 + A2R5- = C2H + A2R5 -24 84.3(275) H2 + A2R5- s H + A2R5 -23 -18.7(276) C2H2 + A2R5- = H + A2R5C2H -25 -2.2(277) H + A2R5C2H B H 2 + A2R5C2H" 23 18.7(278) H + A2R5C2H* B A2R5C2H 21 -471.1(279) C2H2 + A2R5C2H* S C2H + A2R5C2H -24 84.3(280) C2H2 + A2R5C2H* B H + A2R5C2H)2 -25 -2.2(281 ) C2H2 + A2R5C2H* B A2R5C2HC2H2U 27 -192.6(282) A2R5C2HC2H2U B H + A2R5C2H)2 -5 190.4(283) A2R5C2HC2H2U B A3R5- 30 -206.4

219

(284) H + A3R5- s A3R5 21 -471.1(285) H2 + A3R5- s H + A3R5 -23 -18.7(286) C2H2 + A3R5- s C2H + A3R5 -24 84.3(287) C2H2 + A3R5- a; A3R5C2H2U 27 -192.6(288) A3R5C2H2U b H + A3R5C2H -5 190.4(289) A3R5C2H2U m H + A4 20(290) H + C2H3 B C2H2 + H2 32 -249.9(291) C2H2 + C4H5U B C6H7U 13 -161.2(292) C6H7U s R6X 20 -161.3(293) H + Al = R6X 19 -87.0(294) C2H + C6H7U B C2H2 + C6H6 32 -360.8(295) H + C6H7U B H2 + C6H6 32 -257.8(296) H + C6H6 S C6H7U 5 -194.6(297) H + C4H3U S H2 + C4H2 32 -272.6(298) H + C4H3S B H2 + C4H2 32 -239.1(299) H + C6H3U = H2 + C6H2 32 -272.6(300) H + C6H5U B H2 + C6H4 32 -277.7(301) H + C4H5U B H2 + C4H4 32 -257.8(302) H + C6H7U B C6H8 29 -435.5(303) H 2 + C6H7U B H + C6H8 -2 16.9(304) C2H2 + C6H7U B C2H + C6H8 -4 1 19.9(305) C2H + C4H5U B C6H6 7 -522.0(306) H + C8H5U B H2 + C8H4 32 -277.7(307) C4H3U + C6H3U B C4H2 + C6H4X 32 -255.7(308) C2H2 + A6- B H + A7 27 -216.1(309) B5- = H + A6 27 -82.0(310) H + A6- B A6 21 -471.1(311) C2H2 + A6- B H + A6C2H -25 -2.2(312) C4H6 ■f C2H B C2H2 + C4H5S 4 -153.3(313) C2H4 + C6H5U B C2H3 + C6H6 -15 0.0(314) C2H4 + C8H5SX B C2H3 + C8H6 -15 33.5(315) C6H + C2H4 B C6H2 + C2H3 4 -122.7(316) C6H3S + C2H4 B C2H3 + C6H4 -15 33.5(317) C8H3S + C2H4 B C2H3 + C8H4 -15 33.5(318) C2H4 + C6H5S B C2H3 + C6H6 -15 33.5(319) C2H4 + A2- B C2H3 A2 33 -35.6(320) C2H4 + A1C2H» B C2H3 + A1C2H 33 -35.6(321 ) C2H4 + C8H5U B C2H3 + C8H6 -15 0.0(322) C2H4 + A 1C2HC4H2S B C2H3 + A 1C2HC4H3 -15 33.5(323) C2H4 + A2C2H»X B C2H3 + A2C2H 33 -35.6(324) C2H4 + A3- B C2H3 + A3 33 -35.6(325) C2H4 + A4- B C2H3 + A4 33 -35.6(326) C2H4 + A5- B C2H3 + A5 33 -35.6(327) C2H4 + A3C2H* B C2H3 + A3C2H 33 -35.6(328) C2H4 + B4C2H* B C2H3 + B4C2H 33 -35.6(329) C2H4 + A7- B C2H3 + A7 33 -35.6(330) C2H4 + A8- B C2H3 + A8 33 -35.6(331 ) C2H4 + A2R5- B C2H3 + A2R5 33 -35.6(332) C2H4 + A3R5- B C2H3 + A3R5 33 -35.6(333) C2H4 + C8H5S B C2H3 + C8H6 -15 33.5(334) C2H4 + A1C2H- B C2H3 + A1C21* 33 -35.6(335) C2H4 + A 1 — B C2H3 + Al 33 -35.6(336) C2H4 + A1C4H2S B C2H3 + A1C4H3 -15 33.5(337) C2H4 + A1C8H4S B C2H3 + A 1C8H5 -15 33.5(338) C2H4 + AIC4H4U B C2H3 + A1C4H5 -15 0.0(339) C2H4 + A1C6H4S S C2H3 + A1C6H5 -15 33.5(340) C2H4 + A1C6H4U B C2H3 + A1C6H5 -15 5. 1(34 1 ) C6H3U + C2H4 B C2H3 + C6H4X -15 0.0(342) C2H4 + A 1C2HC2H2U B C2H3 + A 1C2HC2H3 -15 0.0(343) C2H4 + A2-X B C2H3 + A2 33 -35.6(344) C2H4 + A2C2H* B C2H3 + A2C2H 33 -35.6(345) C2H4 + A 1C4H3“ B C2H3 + A 1C4H3 33 -31.3(346) C2H4 + A4C2H" B C2H3 + A4C2H 33 -35.6(347) C2H4 ♦ A6- B C2H3 + A6 33 -35.6(348) C2H4 + B4- = C2H3 + B4 33 -35.6

220

(349) C2H4 + B5- t= C2H3 + B5 33 6.3(350) C2H4 + A7C2H* B C2H3 + A7C2H 33 -35.6(351) C2H4 + A9- B C2H3 + A9 33 -35.6(352) C2H4 + A2R5C2H" e C2H3 + A2R5C2H 33 -35.6(353) C2H4 + C6H7U s C2H3 + C6H8 -15 0.0(354) C4H6 + C2H = C2H2 + C4H5U 4 -119.9(355) C4H5S e H + C4H4 -5 228.0(356) C4H4 + C4H5U C8H9S 13 -186.7(357) C8H9S = H + A1C2H3 20 -36.6(358) C4H2 + C4H5U b C8H7SX 13 -172.0(359) CSH7SX ffi H + A1C2H 20 -40.8(360) C4H4 + A 1 - B A1C4H4S 27 -218.1(361 ) H2 + A1C4H4S = H + A1C4H5 -2 50.4(362) C2H2 + A1C4H4S B C2H + A1C4H5 -4 153.3(363) C2H4 + A1C4H4S B C2H3 + A 1C4H5 15 33.5(364) H2 + A 1C4H5* B H + A1C4H5 -23 -18.7(365) C2H2 A 1C4H5* B C2H + A1C4H5 -24 84.3(366) C2H4 + A 1C4H5* B C2H3 + A1C4H5 33 -35.6(367) H + A1C4H5* B AIC4H5 21 -471.1(368 > C2H2 + A 1C4H5* B A1C4H5C2H2U 27 -192.6(369) A1C4H5C2H2U = H + A 1C2HC4H5 -5 190.4(370) A1C4H5C2H2U E H . + A2C2H3 20 -21.0(371 ) A 1C4H5* = H + A2 20 -73.7(372) C4H3U + C4H4 B C8H7SY 13 -186.7(373) C8H7SY = A1C2H3- 30 -195.6(374) H + A1C2H3- B A1C2H3 21 -471.1(375) H2 + A1C2H3- B H + A1C2H3 -23 -18.7(376) C2H2 + A1C2H3- B C2H + AIC2H3 -24 84.3(377) C2H4 + A1C2H3- B C2H3 + A1C2H3 33 -35.6(378) C4H6 + C4H3S B C4H4 + C4H5U 15 33.5(379) C4H6 + C4H3S B C4H4 + C4H5S 15 0.0(380) C4H3S + A 1 B C4H4 + A1- -33 69.0(381 ) C4H3S + A2 B C4H4 + A2- -33 69.0(382) C4H3S + A3 B C4H4 + A3- -33 69.0(383) C4H3S + A4 B C4H4 + A4- -33 69.0(384) C4H3S + A5 B C4H4 + A5- -33 69.0(385) C4H3S + A6 B C4H4 + A6- -33 69.0(386) C4H3S + A7 B C4H4 + A7- -33 69.0(387) C4H3S + A8 B C4H4 + A8- -33 69.0(388) C4H3S + A9 B C4H4 + A9- -33 69.0(389) C4H3S + A1C2H B C4H4 + A1C2H« -33 69.0(390) C4H3S + A2C2H B C4H4 + A2C2H* -33 69.0(391 ) C4H3S + A2C2H B C4H4 + A2C2H»X -33 69.0(392) C4H3S + A3C2H B C4H4 + A3C2H* -33 69.0(393) C4H3S + A2 B C4H4 + A2-X -33 69.0(394) C4H3S + A2R5 B C4H4 + A2R5- -33 69.0(395) C4H3S + A3R5 B C4H4 + A3R5- -33 69.0(396) C2H3 + A1- B A1C2H3 7 -425.6(397) H + A1C2H3 B H2 + A1C2H3" 23 18.7(398) C2H + A1C2H3 B C2H2 + A1C2H3* 24 -84.3(399) C2H3 + A1C2H3 B C2H4 + A1C2H3* -33 35.6(400) C2H4 + A 1 - B H + A1C2H3 -46 10.0(401 ) C2H2 + A1C2H3* B A 1C2H3C2H2U 27 -192.6(402) A 1C2H3C2H2U B H + A2 20 -42.4(403) C4H6 + C2H3 B H + C6H8 16 41.3(404) C2H3 + C4H4 B H + C6H6 16 41 .3(405) A 1C2H3C2H2U IS H + A 1C2HC2H3 -6 190.4(406) A2C2H3C2H2U E H + A2C2HC2H3 -6 190.4(407) C4H4 + A 1 - B H + A 1C4H3 -46 10.0(408) C4H6 + A 1 — S H + A1C4H5 -46 10.0(409) C2H3 Al B H + A1C2H3 -47 45.5(410) C2H3 + A1C2H* E A 1C2HC2H3 7 -425.6(411) C2H4 + A2C2H-X E H + A2C2HC2H3 -46 10.0

(412) C2H4 + A4C2H" S H + A4C2HC2H3 -46 10.0(413) C2H4 + A7C2H" E H + A7C2HC2H3 -46 10.0

221

(414) C2H3 + A2C2H = H + A2C2HC2H3 -47 45.5(415) C2H3 + A4C2H E H + A4C2HC2H3 -47 45.5(416) C2H3 + A7C2H b H + A7C2HC2H3 -47 45.5(417) H + A2C4H3 a A2C4H4U 6 -259.6(4 1 B) A2C4H4U B H + A3 20 17.7(419) A2C4H3* S A3-X 30 -241.9(420) C4H2 + A2-X m H + A2C4H -25 0.6(421) C4H4 + A2-X = H + A2C4H3 -46 10.0(422) H + A2C4H3 B H2 + A2C4H3" 23 18.7(423) C2H + A2C4H3 = C2H2 + A2C4H3* 24 -84.3(424) C2H3 + A2C4H3 S C2H4 + A2C4H3* -33 35.6(425) A2C4H3 e H + A2C4H3" -21 471 . 1(426) H2 + A3-X B H + A3 -23 -18.7(427) C2H2 + A3-X B C2H + A3 -24 84.3(428) C2H4 + A3-X B C2H3 + A3 33 -35.6(429) H + A3-X B A3 21 -471.1(430) H + A2C4H5 = H2 + A2C4H4U 2 -81.9(431 ) C2H A2C4H5 B C2H2 + A2C4H4U 4 -184.9(432) C2H3 + A2C4H5 B C2H4 + A2C4H4U 15 -65. 1(433) C4H4 + A 1 - = H + A1C4H3X -25 0.G(434) H + A1C4H3X = H2 + A1C4H3-X 23 23.8(435) C2H + AIC4H3X = C2H2 + A1C4H3-X 24 -79.2(436) C2H3 + A1C4H3X B C2H4 + A1C4H3-X -33 40.7(437) A1C4H3X = H + A 1C4H3*X -21 476.2(438) C2H2 + A 1C4H3*X 55 A 1C4H3C2H2UX 27 - 197.7(439) C2H2 + A 1C4H3* = A1C4H3C2H2U 27 -188.3(440) H + A1C2H3- B A1C2H3 21 -471 . 1(441 ) H + A2C2H3« - A2C2H3 21 -471. 1(442) H + A4C2H3- B A4C2H3 21 -471. 1(443) H + A7C2H3* ~ A7C2H3 21 -471. 1(444) A1C4H3C2H2UX s H + A1C2HC4H3Y -5 199.7(445) A 1C4H3C2H2U = H + A1C2HC4H3 -5 190.4(446) A 1C4H3C2H2UX = A2C2H3* 30 -187.8(447) A 1C4H3C2H2U = H + A2C2H 20 -42.4(448) C4H2 + A 1 — = H + A1C4H -25 0.6(449) H + A1C4H = H2 + A 1C4H« 23 18.7(450) C2H + A1C4H = C2H2 + A1C4H* 24 -84.3(451 ) C2H3 + A1C4H 3 C2H4 + A1C4H" -33 35.6(452) A1C4H = H- + A1C4H" -21 471 . 1(453) C2H2 + AIC4H" B A1C4HC2H2U 27 -192.6(454) A 1C4HC2H2U = H + A1C2HC4H -5 190.4(455) A 1C4HC2H2U = A2C2H-X 30 - 177 . 3(456) C4H2 + A2- = H + A2C4H -25 0.6(457) H + A2C4H B H2 + A2C4H* 23 18.7(458) C2H + A2C4H = C2H2 + A2C4H* 24 -84.3(459) C2H3 + A2C4H - C2H4 + A2C4H" -33 35.6(460) A2C4H e H + A2C4H" -21 471 . 1(461 ) C4H4 + A2- B H + A2C4H3 -46 10.0(462) C4H6 + A2- B H + A2C4H5 -46 10.0(463) C2H3 + A2C2H- = A2C2HC2H3 7 -425.6(464) C2H3 + A2C2H-X S A2C2HC2H3 7 -425.6(465) C2H3 + A1C2H3* B A1C2H3>2 7 -425.6(466) C2H3 + A1C2H3 B H + A 1C2H352 -47 45.5(467) C2H4 + A 1C2H3* = H + A 1C2H3) 2 -46 10.0(468) H + A1C2H3)2 B H2 + A1C2H3C2H2U 2 -16.9(469) C2H4 + A1C2H« E H + A1C2HC2H3 -46 10.0(470) C4H4 + A1C2H* E A 1C2HC4H4S 27 -218.1(471 ) A1C2HC4H4S m A2C2H3- 30 -159.5(472) C2H2 + A2C2H3- B C2H + A2C2H3 -24 84.3(473) C2H4 + A2C2H3- B C2H3 + A2C2H3 33 -35.6(474) H2 + A2C2H3- B H + A2C2H3 -23 -18.7(475) C2H + A2C2H3 B C2H2 + A2C2H3" 24 -84.3(476) C2H3 + A2C2H3 B C2H4 + A2C2H3* -33 35.6(477) H + A2C2H3 B H2 + A2C2H3* 23 18.7(478) C2H2 + A2C2H3- « A2C2H3C2H2U 27 -192.6

222

(479) A2C2H3C2H2U e H A3 20 -51 .6(480) C2H2 + A3-X IB H + A3C2HX -25 -2.2(461 ) C2H2 + A2C4H» e A2C4HC2H2U 27 -192.6(482) A2C4HC2H2U = A3C2H-X 30 -206.4(483) A2C4HC2H2U E H + A2C2HC4H -5 190.4(484) C2H2 + A2C4H3- s A2C4H3C2H2U 27 -192.6(485) A2C4H3C2H2U E A3C2H3* 30 -206.4(486) C2H2 + A3C2H3* * A3C2H3C2H2U 27 -192.6(487) A3C2H3C2H2U = H + A3C2HC2H3 -5 190.4(488) A3C2H3C2H2U E H + A4 20(489) H + A3C2H3« e A3C2H3 21 -471.1(490) H2 + A3C2H3" s: H + A3C2H3 -23 -18.7(491 ) C2H2 + A3C2H3® &: C2H + A3C2H3 -24 84.3(492) C2H4 + A3C2H3* e C2H3 + A3C2H3 33 -35.6(493) C2H3 + A3-X s A3C2H3 7 -425.6(494) C2H4 + A3-X BE H + A3C2H3 -46 10.0(495) C2H3 + A3 BE H + A3C2H3 -47 45.5(496) A2C4H5 s H + A2C4H5" -21 471.1(497) H + A2C4H5 0= H2 + A2C4H5* 23 18.7(498) C2H + A2C4H5 s C2H2 A2C4H5* 24 -84.3(499) C2H3 + A2C4H5 BE C2H4 + A2C4H5» -33 35.6(500) A2C4H5* s H + A3 20 -82.9(501 ) C2H3 + A2- S A2C2H3 7 -425.6(502) C2H4 A2- El K + A2C2H3 -46 10.0(503) C2H3 + A2 ss H + A2C2H3 -47 45.5(504) A4C4H5 s H + A4C4H5" -21 471 . 1( 5 0 5 ) H + A4C4H5 = H2 + A4C4H5" 23 18.7( 5 0 6 ) C2H + A4C4H5 = C2H2 + A4C4H5* 24 -84.3(507) C2H3 + A4C4H5 = C2H4 + A4C4H5" -33 35.6(508) A4C4H5" = H + A5 20 -21.0(509) C2H3 + A4- S A4C2H3 7 -425.6(510) C2H4 + A4- EE H + A4C2H3 -46 10.0(511) C2H3 + A4 S H + A4C2H3 -47 45.5(512) H + A4C2H3 = H2 + A4C2H3» 23 18.7(513) C2H + A4C2H3 EE C2H2 + A4C2H3" 24 -84.3(514) C2H3 + A4C2H3 BE C2H4 + A4C2H3« -33 35.6(515) C2H2 + A4C2H3" BE A4C2H3C2H2U 27 -192.6(516) A4C2H3C2H2U = H + A5 20 -60.8(517) C2H3 + A7- B! A7C2H3 7 -425.6(518) C2H4 + A7- = H + A7C2H3 -46 10.0(519) C2H3 + A7 = H + A7C2H3 -47 45.5(520) H + A7C2H3 = H2 + A7C2H3" 23 18.7(521 ) C2H + A7C2H3 = C2H2 + A7C2H3* 24 -84.3(522) C2H3 + A7C2H3 C C2H4 + A7C2H3* -33 35.6(523) C2H2 + A7C2H3* S A7C2H3C2H2U 27 -192.6(524) A7C2H3C2H2U = H + A8 20 -60.8(525) A4C2H3C2H2U sr H + A4C2HC2H3 -6 190.4(526) A7C2H3C2H2U s H + A7C2HC2H3 -6 190.4(527) C2H3 + A4C2H" E A4C2HC2H3 7 -425.6(528) C2H3 + A7C2H* E A7C2HC2H3 7 -425.6(529) C2H4 + A2C2H* E H + A2C2HC2H3 -46 10.0(530) C4H6 + A4- E H -f A4C4H5 -46 10.0(531 ) H2 + A3C2H«X E H + A3C2HX -23 -18.7(532) C2H2 + A3C2H-X E C2H + A3C2HX -24 84.3(533) C2H4 + A3C2H*X E C2H3 + A3C2HX 33 -35.6(534) H + A3C2H»X E A3C2HX 21 -471.1(535) C2H2 + A3C2H-X E H + A4 27(536) H 2 + A2C2H- E H + A2C2H -23 -18.7(537) C2H2 + A2C2H- E C2H + A2C2H -24 84.3(538) C2H4 + A2C2H- E C2H3 + A2C2H 33 -35.6(539) C4H2 + A4- E H + A4C4H -25 0.6(540) H + A4C4H S H2 + A4C4H* 23 18.7(54! ) C2H + A4C4H S C2H2 4- A4C4H« 24 -84.3(542) C2H3 + A4C4H E C2H4 + A4C4H® -33 35.6(543) A4C4H s H + A4C4H« -21 471 . 1

223

CM O — ©r«! ui O«t <t «3CM CM *-

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2 2 4

T a b l e V I I I . 3 A d d i t i o n a l r e a c t i o n s p e c i e s a n d a s s i g n e d n a m e s .

C * CC6H5UX H '

H ^

C8H7U ^ 'c = C ' r**'' ^ *"*h ' c “ cH v H

s _ ✓C8H7SY

H H mC = C ^ ^ C = C

' H " * CH ' C = C _H

2 2 5

H ' C = C C " _ „ HC 8 H 9 S W' H " CmC'c=C*v H

h ' H . c - c : H

H HA 1 C 2 H 3 * _ N C S C /

o

A 1 C 2 H 3 - _ SC B C® "H

c *«'A 1 C 4 H * -

C ' Hc * c

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A 1C4H3*X

A 1C4H5*H@

2 2 7

H ' c = c ' H

A 1C2H3C2H2Uh ,' c ’ Cv h

H - c = c ' H✓ ^ uA 1C2H3)2 i ^ i n^ r = r H

H ' C H

A 1C2HC4H3YL J w

c© t c ' H

c = c ' HH H

A 1C2HC4H4S r —© c c ' H

HH ' C = C ; C = C C

H H

H vA 1C2HC4H5 _ _

C

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H®r.

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w '

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© '

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A2C2H3*

A2C2H3

A2C4H* C§X°3.cinCiCMcIH

O 1.0A2C4H

cin CiCMCIH

A2C4H3*

A 2 C 4 H 3

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A2C4H5*

A 2 C 4 H 5

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A2C2HC4H I O I OI C >5.? C ' HIII MCIcIIcIH

A 2 C 2 H 3 C 2 H 2 U

2 3 3

A2C4HC2H2Uc ' h

H i _ CS C - H

H - C * U *C - W

' C

A2C4H3C2H2UO l O j

A 2 R 5 C 2 H 3

ANC2H3C2H2U

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H-C H*C*H

<2r®

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2 3 6

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2 3 7

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P 3 - X

IH

C-HH-C

iH

2 3 8

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P3C2H2U

c= c

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• H Hc = c: H

2 3 9

A4C2H3

HC“ C /H ^ H

A4C4H*

A4C4H

A4C4H3*

2 4 0

A 4 C 4 H 3

H

C *.H

A4C4H5*

' H Hv c= c ^ H

A4C4H5c= c ' H „H

i C - C x H

A 4 C 2 H C 2 H 3

H 6 - H

c "H - CH

2 4 1

A4C2H3C2H2U

HH-C V

*C-H ii ' C.

H

H

A4C2HC4H

A4C4HC2H2U

A 3 P 1 - X

2 4 2

D 4 C 2 H

H

D4C2H2U

H C-C

2 4 4

A7C2H3*

c=c

A 7 C 2 H 3

c - c ✓ ’ ■ " H

2 4 5

A7C4H*

A7C4H

A7C2HC2H3 c-H - C

A 7 C 2 H C 2 H 2 Uc=c

2 4 6

A7C2HC4H

A7C4HC2H2U

2 4 7

A 6 P 1

A8C2H*

H

A9P1-

A 9 P 1

A11-

A 1 1

Table VIII.4 Additional reaction classes and rate coefficent expressions.

Number Reaction Class

Prototype ReactionRate Coefficient

for Forward Reference/ Direction RemarksA E

46 H attacks on aryl ethylenes to yield ethylene

47 H attacks on aryl ethylenes to yield vinyl

48 Aryl addition to aromatic rings

H + styrene = C 2HU + phenyl 1.0+14

H + styrene = C 2H 3 + benzene 1.0+14

phenyl + benzene = biphenyl + H 1.0+13

as class 25, Ref. 172

as class 25, Ref. 172

estimated

The units of the rate coefficients are mol, s, cm3, kJ, K.

249

2 5 0

8.2.2 Results and Discussion 8.2.2.1 Butadiene

A major objective of this study was to determine how fuel structure affects the chemical reaction routes to soot. In particular, does a fuel molecule with four carbon atoms such as butadiene have a more direct route to soot than a two-carbon fuel such as acetylene?

The computational results at the temperature of maximum soot yield (1825 K) indicate that a single reaction path dominates the formation of the first aromatic ring. The reaction sequence is very similar to that noted for acetylene pyrolysis in Chapter VI, the only difference being the path leading to formation of vinylacetylene (C4H 4). The reaction sequence for butadiene pyrolysis is

C4H6 + H = i-C4H 5 + H2 i-C4H5 = C 4H4 + H C4H 4 + H = n-C4H3 + Hz n-C4H 3 + C 2H 2 = n-C6H 5 n-C6H 5 = phenyl radical.

Of the several pathways considered for formation of two-ring aromatic species, the most important is shown at the top of Fig. VIII.1. The only other cyclization route with forward mass flux within an order of magnitude of this fastest route is shown at the bottom of the Figure. None of the other routes involving foui— carbon species proved to be as important. The fast route in Fig. VIII.1 was not

251important- in acetylene pyrolysis (172); its prominence here is due in large part to high concentrations of vinyl radicals, which were more than ten times those of hydrogen atoms for an initial temperature of 1825 K and reaction times less than 400 microseconds. The cyclization mechanism observed in acetylene pyrolysis (see Fig. VI.1) proceeds in reverse, being the major fragmentation reaction for two-ring aromatics. *

The growth mechanism shown at the top of Fig. VIII.1 also proved important for the further growth of polycyclic aromatics, especially at short reaction times. However, at longer times, when the concentration of acetylene is high, the cyclization mechanism seen in acetylene pyrolysis is the fastest route. These two mechanisms dominate the growth of higher polycyclic aromatics during pyrolysis of butadiene.

An interesting question is why the role of the two-step acetylene-addition route to cyclization (Fig. VI.1) is different for formation of two-ring aromatics. The net fragmentation observed for this route is the result of very fast forward and reverse rates approximately canceling. This is not true for larger polyaromatics, where the cyclization reactions are not equilibrated. Thisobservation is in concord with the previous comment (172) that thermodynamic resistance to polymerization is seen primarily during the formation of small aromatic species.

2 5 2

M A J O R R O U T E

r, if H "C = C''H + K H^_ _^H© • ^ © f ' H ^ © ; H

1 K+ c, Ha n z

O O~ H © C •= C

V H

% c » c*H '

M I N O R R O U T EH

C'" H - C ^ - CSC-H0 , h v _ C * V _ ^ H+ vC B Cv H H 0+ H

] \ C-H2)H ' r = C " C

0 :Figure VIII.1 Principal reaction paths for the formation of

two-ring aromatics during pyrolysis of butadiene. The most important route is shown at the top; a secondary route is shown at the botx-om.

253The reaction sequence at the top of Fig. VIII.1 faces a

smaller thermodynamic harrier than that of Fig. VI.1 because the attachment of a vinyl radical to a phenyl radical has a more favorable equilibrium constant than does the attack of a phenyl radical on acetylene. This combines with the high concentration of vinyl radicals (formed by reaction R1 of Table VIII.1 and by

n-CaH5 = C 2H z + C 2H 3) to provide the impetus for formation of two-ring aromatic species via this route.

As in earlier work (172), soot is defined as the collection of species as large as or larger than coronene. The computed soot yield is calculated as in the experiments (31) as the fraction of carbon atoms accumulated in soot. Computed soot yields for butadiene at a reaction time of 500 microseconds are presented in Fig. VIII.2. Also presented in this Figure are computed soot yields for acetylene for the same set of thermochemical group values (set S8 of Chapter VII). The corresponding experimental results for butadiene (31) are shown in Fig. VIII.3. The model correctly predicts that the maximum soot yield occurs at lower temperatures than for acetylene and that the soot bell is narrower for butadiene than for acetylene (see Figs. VIII.3 and VI.15). As seen in Fig. VIII.2, the maximum computed soot yields for butadiene and acetylene are comparable in magnitude, in qualitative agreement with experiment.

SOOT

YIEL

D

254

U3cn

□cn

But ad i ene

CM

fleet y 1eneCD

CO

a

2150.2000.1850.1700. 2300.T E M P E R A T U R E / K

Figure VIII.2 Computed soot yields at different temper— atures for a 0.54% butadiene-argon mixture at p5 = 1.5 x 10"5 mol/cm3 and a 1.09% acetylene-argon mixture at p5 = 3.8 x 10"5 mol/cm3. Both curves represent reaction times of 0.5 ms and thermodynamic properties matching those of set S8 of Chapter VII.

SOOT

YIEL

D

2 5 5

co

CCIk.2 . 00 xlO17 carbon atoms/cmm

(VI

cnoo

COoo

o o 1a

o2500.2300.1900. 2100.T E M P E R R T U R E / K1700.

Figure VIII.3 Experimental soot yields for a 0.54%butadiene - argon mixture at ps = (1.49-1.53) x 10-5 mol/cm3 using laser extinction at 633 nm (Series J of Ref. 31). The soot yields are calculated assuming Rayleigh scattering (166) and using the value of Lee and Tien (200) for the complex refractive index. The symbols designate experimental points, the lines cubic spline fits.

256Table VIII.5 presents the results of a sensitivity

analysis for reaction classes; the classes omitted have absolute sensitivity values less than 0.005. Thesensitivities are defined as in Chapter VI. Comparison of these sensitivity values with those for acetylene pyrolysis (172,202) shows that while there are differences, generally the same reaction classes show high sensitivities for both fuels. Two exceptions are classes 2 and 20, which have higher sensitivities for butadiene pyrolysis. The kinetic sensitivity for class 2 is basically that for reactions

C«H6 + H = H2 + n-C*Hs and C 4H 6 + H = H 2 + i-C4H5.

The sensitivity for class 20 is due to the importance of the cyclization route shown in Fig. VIII.1.

8.2.2.2 EthyleneTwo reaction sets were used to model soot formation from

ethylene. Case A used the rate coefficient of Kiefer et al. (206) (reaction R5a of Table VIII.1) while Case B used the rate coefficient of Tanzawa and Gardiner (86) (reaction R5b). The reaction sets were otherwise identical.

An analysis of mass-flux pathways was done for each case at the respective temperature of maximum soot yield (see Fig. VIII.4). The only qualitative differences in the reaction course to soot between the two cases are the reactions leading to formation of the first aromatic ring.

2 5 7

T a b l e V I I I . 5Sensitivities o£ Soot Yield with Respect to Rate

Coefficients and Equilibrium Constants for Butadiene Pyrolysis

Y YReaction S SClass k K

2 -0.54 -0.273 -0.02 0.4 0.05 0.015 0. -0.017 0.05 -0.038 -0.65 0.671 1 0.01 0.13 0. 0.8115 -0.02 0.16 0. 0.0120 0.37 0.23 0.79 2.2725 0.41 -0.7127 2.77 0.9229 0.01 -0.0130 0.06 1 .6332 -0.60 0.33 0.04 -0.2946 0.19 -0.3747 0. -0.16

2 5 8

In Case A, the first ring is formed via the reaction sequence

C 2H3 + C 2H2 = n-CaH5 n-C4H5 + C 2H 2 ~ n-C6H7 n-C6H 7 = c-C6H 7 c -C6H 7 = benzene + H.

However, in Case B, the cyclization proceeds via C 2H3 + C 2H 2 = n-C4H 5 n-C^Hs = C 4H 4 + H C4H4 + H = n-C4H 3 + H 2 n-C4H 3 + C 2H 2 = n—CfeHs n-C6H 5 = phenyl radical.

One might ask if the observed difference in the reaction route to the first aromatic ring is a consequence of the difference in temperature (as seen in Fig. VIII.4, the two soot-yield maxima are separated by 150 K ) . The simulation results show that this is partially true. When the computational results for an initial temperature of 2000 K are examined, one sees that the two cyclization mechanisms are of roughly equal importance for Case A. However, the second cyclization path is still dominant for Case B. Therefore, although temperature has an effect on the system dynamics, it can not completely explain the observed difference between the two reaction sets.

The further growth of polycyclic aromatics follows a course similar to that of butadiene for both ethylene cases.

LQGin

(SOOT

YIELD

)

2 5 9

oT O '

OAcetylenein-

o

Ethylene (Case B)o0 5 “

O

O

Ethylene (Casein

T T1600. 1750. 1900. 2050. 2200. 2350.T E M P E R A T U R E / K

Figure VIII.4 Computed soot yields at differenttemperatures for a 1.09% ethylene-argon mixture at p5 =1.5 x 10“s mol/cm3 and a 1.09% acetylene-argon mixture at ps = 3.8 x 10~5 mol/cm3. Both curves represent reaction times of 0.5 ms and thermodynamic properties matching those of set S8 of Chapter VII.

Tibfetween the ethylene and butadiene cases are basically those of degree: the growth route seen inacetylene pyrolysis is slightly more important for ethylene than for butadiene, and routes involving foui— carbon species are less important.

No experiments have been done with ethylene at the conditions modeled. However, experimental results for a 4.65% acetylene-argon mixture (31) and a 4.65%ethylene-argon mixture (204) are shown in Fig. VIII.5. Since these experiments were performed at differentcarbon-atom concentrations and pressures than the conditions of interest* here, only qualitative observations can be made. A comparison of Fig. VIII.5 with the computational results presented in Fig. VIII.4 shows that the model correctly predicts that ethylene will produce much less soot than acetylene. The model (especially the reaction set of Case A) also correctly predicts that the maximum soot yield for ethylene will occur at higher temperatures than foracetylene.

A sensitivity analysis for Case B is presented in Table VIII.6. The trends in sensitivity are similar to those seen in butadiene pyrolysis (Table VIII.5) and acetylene pyrolysis (Tables VI.5 and VII.2).

SOOT

YIEL

D

261

ino

TIME=1. 5 msflr

flr

o

o

COo

ino

(Vi

o

2850.2600.1850. 2100. 2350.T E M P E R R T U R E / KFigure VIII.5 Experimental soot yields for a 4.65%

acetylene - argon mixture at pB = (0.87-0.92) x 10's mol/cm3 and an ethylene-argon mixture at ps - (0.87-0.90) x 10-5 mol/cm3 using laser extinction at 633 nm (Series J of Ref. 31). The soot yields are calculated assuming Rayleigh scattering (166) and using the value of Lee and Tien (200) for the complex refractive index. The symbols designate experimental points, the lines cubic spline fits.

262

T a b l e V I I I . 6Sensitivities of Soot Yield with Respect to Rate

Coefficients and Equilibrium Constants for Ethylene Pyrolysis (Case B)

Y YReaction S SClass k K

2 - 0.01 0.013 0.01 -0.014 -0.05 0.5 0.05 -0.067 -0.02 0.028 -0.30 0.8711 0.03 0.0113 -0.03 1.3220 0.35 0.0123 1.13 3.0925 0.58 -1.5327 3.38 1.2430 0.09 2.1632 -0.30 . -0.0633 -0.11 0.46 0.54 -0.6347 -0.18 0.

2638.3 BENZrNE8.3.1 Computer Model

The soot-formation model for benzene has the same basic structure as the acetylene, ethylene and butadiene models. The initial reactions for benzene are taken principally from the benzene pyrolysis mechanism of Kiefer et al. (207) andare presented with their rate coefficients in Table VIII.7. The reaction set describing cyclization and polymerization for butadiene pyrolysis served as the core of the benzene mechanism; these reactions were augmented by inclusion of

* i.reactions of aromatic species with other aromatics. Thus, the final soot-formation mechanism for benzene was built upon those developed for both two-carbon (acetylene and ethylene) and foui— carbon (butadiene) fuels. The reactions added specifically for modeling benzene pyrolysis are listed in Table VIII.8. Structures of the chemical species used in the mechanism are shown in Tables VI.1 and VIII.3. Thermodynamic properties of all chemical species were calculated using the thermochemical group values of set S8 of Chapter VII (Table VII.1) to match the values of Kiefer et al. (207). The computer experiments were conducted at a total concentration of 1.5 * 10~5 mol/cm3 and an initialmolar concentration of benzene of 0.311%, to match the corresponding experimental conditions (Chapter VI). Computed temperature decreases for these initial conditions after a reaction time of 500 microseconds were between 10 and 100 degrees.

Table VIII.7 Core reactions for benzene pyrolysis.

ReactionNumber

Reaction Rate Coefficient for Forward Direction

Reference/Remarks

n

R 1 benzene = H + phenyl 2.0 + 17 - 497 Ref. 207 (high-pressurelimit)

R2 benzene + H = phenyl + H2 2.5 + 14 — 70 Ref. 207R3 n-C6,H5 = phenyl 1 .0 + 10 - - Ref. 172R4 n-C4H 3 + M = H + C 4H 2 + M 3.3 +51 -10 264 Ref. 207R5 C 6H 2 = C 6H + H 7.8 + 14 - 502 Ref. 207R6 h 2 + m = h + h + m 2.2 + 12 ino 387 Ref. 86R7 C 2H z + M = H + C 2H + M 4.2 + 16 - 448 Ref. 86R8 H2 + C 2H = C 2H 2 + H 7.4 + 12 - - Ref. 207R9 C 2H 2 + C 2H = C4H 2 + H 4.0 + 13 - - Ref. 207R 1 0 C4H2 = C 4H + H 7.8 + 14 - 502 Ref. 207R 1 1 C2H + C 4H2 = C 6H 2 + H 4.0 + 13 - - Ref. 86R 12 C 4H + C 2H 2 = C 6H 2 + H 4.0 + 13 — — Ref. 86

264

R 1 3 CfeH + C 2H 2 = C 8H 2 + H 4.0 + 13R 1 4 C ZH + C 6H 2 = C 8H 2 + H 4.0 + 13R 15 C 4H + C 4H2 = C 8H2 + H 4.0 + 13R 16 C4H + H 2 = H + C 4H2 2.0 + 13R 1 7 C6H + H 2 = H + C 6H2 2.0 + 13R 1 8 C 8H + H 2 = H + C 8H2 2,0 + 13R 1 9 benzene + C 2H = phenyl + c 2h 2 2.0 + 13R20 benzene + C 4H = phenyl + c 4h 2 2.0 + 13R21 benzene + C6H = phenyl + c 6h 2 2.0 + 13R22 benzene + C aH = phenyl + c 8h 2 2.0 + 13R23 c 4h 6 = C 2H 3 + C 2H 3 2.58+15R24 C2H 4 + M = C 2H 2 + H z f M 2.51+17R25 C 2H + C 2H 3 = C 2H2 + C ZH2 1.0 + 13R26 C 2H3 + M = c 2H 2 + H + M 2.0 +38R27 c 2h 2 + C 2H 3 = H + C 4H 4 1 .6 + 13R28 H * i-C4H3 + M = C 4H4 + M 1.0 + 15

361332

17 212105

Ref. 207 Ref. 207 Ref. 207 Ref. 207 Ref. 207 Ref. 207 Ref. 207 Ref. 207 Ref. 207 Ref. 207 Ref. 206 Ref. 206 Ref. 202 Ref. 206 Ref. 86 Ref. 86

(value at 6 atm)

(high temp, value)

265

R29 C 2H + C 4H4 = C 2H2 + i-C4H 3 4.0 +13 - - Ref. 86R30 i-C4H3 + M = H + C 4H 2 + M 1.0 +16 - 250 Ref. 86R31 C 8H2 + M = CSH + H + M 5.0 +16 - 335 Ref. 86R32 n~C4H3 + H + M = C 4H 4 + M 1.0 +15 - - Ref. 86R33 C ZH + C 4H4 = C 2H2 + n-C4H 3 4.0 +13 - - Ref. 86R34 C 2H4 + M = H + C 2H3 + M 4.0 +17 - 411 Ref. 206R35 C2H 2 + n-C4H 3 = n-C6H 5 1.0 +13 - - Ref. 172

The units are mol, s, cm3 , kJ, K. The form of the rate coefficients is k = A * T n * exp(-E/RT); rate coefficients for the reverse direction are calculated from equilibrium.

266

267

Table VIII.8 Additional reactions using for modeling soot formation during benzene pyrolysis.

REACTIONS REACTION CLASS AHf70o,icj

( 5 7 9 ) A l + A l — ■i H + P2 4 8 1 1 . 3( 5 8 0 ) H + P2 = H2 + P 2 - 2 3 1 9 . 7(5 81 ) C2H + P2 is C2H2 + P 2 - 24 - 8 4 . 6( 5 8 2 ) C2H3 + P2 s C2H4 + P 2 - - 3 3 3 5 . 6( 5 8 3 ) P2 c H + P 2 - -2 1 4 7 1 . 1( 5 8 4 ) C2H2 + P 2 - P2C2H2U 2 7 - 1 9 3 . 3( 5 8 5 ) P2C2H2U = H + A3 2 0 - 1 4 . 9( 5 8 6 ) C2H2 + P 2 - = H + P2C2H - 2 5 - 3 . 4( 5 8 7 ) H + P2C2H «= P2C2H2U 5 - 1 8 9 . 9( 5 8 3 ) A l + A 3 - = H + A3P1 4 8 1 1 . 3( 5 8 9 ) A 1 — + A3 Si H 4 A3P1 4 8 1 1.3( 5 9 0 ) H + A3P1 Si H2 + A 3 P 1- X 2 3 1 9 . 7(591 ) C2H + A3P1 s C2H2 + A 3 P 1 -X 2 4 - 8 4 . 6( 5 9 2 ) C2H3 + A3P1 = C2H4 + A 3 P 1 -X -33 3 5 . 6( 5 9 3 ) A3P1 = H + A 3 P 1 -X -2 1 471 . 1( 5 9 4 ) A 3 P 1 -X = H + A5 2 0 - 4 0 . 5( 5 9 5 ) A l + A 6 - = H + A6P1 4 8 1 1 . 3( 5 9 3 ) A 1 - A6 = N + A6P1 4 8 1 1 . 3( 5 9 7 ) H + A6P1 = H2 + A 6 P 1 - 2 3 1 9 . 7( 5 9 3 ) C2H + A6P1 is C2H2 + A 6 P 1 - 2 4 - 8 4 . 6( 5 9 9 ) C2H3 + A6P1 = C2H4 + A 6 P 1 - - 3 3 3 5 . 6( 6 0 0 ) A6P1 = H + A 6 P 1 - - 2 1 471 . 1(6 0 1 ) A 6 P 1 - = H + A8 2 0 - 4 0 . 5( 6 0 2 ) A 1 + P 2 - =s H + P3 4 8 1 1 . 3( 6 0 3 ) A 1 - + P2 = H + P3 4 8 1 1 .3( 6 0 4 ) H + P3 s H2 + P 3 - 2 3 1 9 . 7( 6 0 5 ) C2H + P3 = C2H2 + P 3 - 2 4 - 8 4 . 6( 6 0 6 ) C2H3 + P3 = C2H4 + P 3 - - 3 3 3 5 . 6( 6 0 7 ) P3 = H + P 3 - - 2 1 471 . 1( 6 0 3 ) P 3 - = H + D4 2 0 - 3 1 . 4( 6 0 9 ) H + D4 SI H2 + D 4 - 2 3 1 9 . 7( 6 1 0 ) C2H + D4 = C2H2 + D 4 - 2 4 - 8 4 . 6(61 1 ) C2H3 + D4 Si C2H4 + D 4 - - 3 3 3 5 . 6( 6 1 2 ) D4 = H + D 4 - -2 1 471 . 1( 6 1 3 ) C2H2 + D 4 - is D4C2H2U 2 7 - 1 9 3 . 3( 6 1 4 ) C2H2 + D 4 - Si H + D4C2H - 2 5 - 3 . 4( 6 1 5 ) D4C2H2U = H + D4C2H - 5 1 8 9 . 9(616) D4C2H2U = H + A5 20 - 2 4 . 0(617) H + P3 = H2 + P 3 -X 2 3 1 9 .7(618) C2H + P3 = C2H2 + P 3 -X 24 - 8 4 . 6( 6 1 9 ) C2H3 + P3 = C2H4 + P 3 -X -33 3 5 . 6( 6 2 0 ) P3 = H + P 3 -X - 2 1 471 . 1(621 ) C2H2 + P 3 -X = P3C2H2U 2 7 - 1 9 3 . 3( 6 2 2 ) C2H2 + P 3 -X Si H 4 P3C2H - 2 5 - 3 . 4( 6 2 3 ) P3C2H2U = H + P3C2H - 5 1 8 9 . 9( 6 2 4 ) P3C2H2U = H + A3P1 20 - 1 4 . 9( 6 2 5 ) A 1 + A 9 - = H 4 A9P1 4 8 1 1 . 3( 6 2 6 ) A 1 — + A9 IS H 4 A9P1 4 8 1 1 .3( 6 2 7 ) H + A9P1 Si H2 4 A 9 P 1 - 2 3 1 9 .7( 6 2 8 ) C2H + A9P1 is C2H2 4 A 9 P 1 - 24 - 8 4 . 6(6 2 9 ) C2H3 + A9P1 IS C2H4 4 A 9 P 1 - -33 3 5 . 6( 6 3 0 ) A9P1 - H + A 9 P 1 - -2 1 471 . 1(631 ) A 9 P 1 - = H + A 1 1 2 0 - 4 0 . 5( 6 3 2 ) H + A l 1 ss H2 4 A1 1 - 23 1 9 .7( 6 3 3 ) C2H + A l 1 s: C2H2 4 A 1 1 - 24 - 8 4 . 6( 6 3 4 ) C2H3 + A l 1 s C2H4 4 A1 1 - - 3 3 3 5 . 6( 6 3 5 ) A 1 1 = H + A l 1 - - 2 1 4 7 1 . 1( 6 3 6 ) C2H2 + A l 1 - Si H 4 A9 27

2688.3.2 Results

The principal uncertainty in soot formation during pyrolysis or oxidation of aromatic fuels is the role of the aromatic ring. One of the main points of this work was to investigate the importance of reactions between two aromatic species. Reactions of the nonaromatic products of benzene pyrolysis with each other and with aromatic species were already included since the core of the reaction set used was developed in models of nonaromatic fuels.

Fragmentation of the benzene ring proved to be a very important process, with a mass flux more than one order of magnitude greater than for growth processes. The fastest reaction path for fragmentation is

benzene + H = phenyl + H 2 phenyl = n-C6K s n-CfeH5 = C 2H 2 + n-C4H 3

andn-C4H 3 + M = C 4H 2 + H + M

orn-C4H3 = C 2H + C 2H 2 ,

where M is any third body. Of course, at very short times the reaction

benzene = phenyl + H starts the fragmentation sequence. The reaction sequence shown above and other, slower ones cause a rapid rise in the concentrations of acetylene and other small species.

269Phenyl radical can grow by attacking acetylene (Fig.

VI.1) or benzene (Fig. VIII.6). Reaction with benzene toform biphenyl and eventually pyrene proved to be the mostimportant route, strongly dominating the formation of smallpolycyclic aromatic compounds. Two factors promote thebiphenyl route to higher products (Fig. VIII.6): 1) the highconcentration of benzene and 2) the short reaction sequence

** •>producing stable polycyclic intermediates such as pyrene from the original benzene fuel.

Reactions of biphenyl and its radicals with aromatic species are not as important as reactions with acetylene. Addition of acetylene causes the direct formation of phenanthrene, which is much more stable than biphenyl. It should be noted that both aromatic and nonaromatic species participate in this growth pattern, with the nonaromatic species (acetylene) serving as the "mortar" which holds the aromatic-ring "bricks" together.

Additional reactions of polycyclic aromatic species with benzene or phenyl radical, followed by reaction with acetylene, were included in the mechanism (see Table VIII.8). An infinitely long sequence of similar reactions was assumed (Fig. VIII.7) in order to assess the relative contributions of acetylene and aromatic species to the growth of large polycyclics. On the basis of carbon atoms converted to soot, the acetylene-addition route (Fig. VI.13) was two to three times as important as the growth mechanism

2 7 0

Figure VIII.6 Principal reaction pathway for the formation of small polycyclic aromatics from benzene.

<oXo> + h

(O ^ O ) + H-C = OH

< o * o > + h 2

h '9= c; h

<§*§>

V c ' H+ H

-I- H-

H<

271of Fig. VIII.7 at, a reaction time of 500 microseconds. The difference was much smaller at shorter reaction times.

Predicted soot yields for benzene are presented in Fig. VIII.8 and are compared with computed soot yields for acetylene for the same set of thermochemical values (set S8 of Chapter VI.I) in Fig. VIII. 9. The experimental results for benzene are shown in Fig. VIII.10; Fig. VIII.11 contrasts experimental soot yields for benzene and acetylene. The model successfully predicts that benzene will produce much more soot than will acetylene and that the peak soot yield for benzene will occur at lower temperatures than for acetylene, though the difference in yield is overstated by the model. The shape of the calculated soot bell is in good agreement with that seen experimentally. As with all the fuels studied, however, the calculated soot production is smaller in magnitude and occurs at lower temperatures than seen in experiment. As noted in Chapter VI, the former mismatch is probably due to inaccuracies in the (experimental) optical determination of soot yields and to the fact that the model neglects the effects of coagulation and surface growth of soot particles. The second mismatch is proposed (183) to be the effect of uncertainties in thermochemical parameters; the location of the soot bell is sensitive to the values used for certain bond-dissociation energies.

Figure VIII.7 Reaction pathway for further growth of polycyclic aromatic hydrocarbons via reaction with small aromatic and nonaromatic species.

/

+

( - H )

H

272

SOOT

YIEL

D

273

o

inoo

CM

OO

cnooo

COooo

cnooo

ooo22001800 1800 2000T E M P E R R T U R E / K

Figure VIII.8 Computed soot yields at differenttemperatures for a 0.31% benzene-argon mixture at p5 = 1 .5 x 10"5 mol/cm3 at a reaction time of 0.5 ms.

o

o■

•«4"i Benzene

LU

D

cn*i

ED trrcn 10fH^ a ED ■1 r-*— 1 i

05*I

2200.moo. 1600. 1800. 2000. T E M P E R R T U R E / K 2400

Figure VIII.9 Computed soot yields at differenttemperatures for a 0.31% benzene-argon mixture at =1.5 x 10“5 mol/cm3 and a 1.09% acetylene-argon mixture at p5 = 3.8 x 10-5 mol/cm3 at a reaction time of 0.5 ms

SOOT

YIEL

D

275

oID

+ flr

IDCVI

OO

ID

O

oIDO

IDru

o1500. 1700. 1900. 2100. 0 0.T E M P E R R T U R E / K

Figure VIII.10 Experimental soot yields for a 0.31% benzene - argon mixture at p5 = (1.49-1.56) x 10-5 mol/cm3 using laser extinction at 633 nm (Series J of Ref. 31). The soot yields are calculated assuming Rayleigh scattering (166) and using the value of Lee and Tien (200) for the complex refractive index. The symbols designate experimental points, the lines cubic spline fits.

SOOT

YIEL

D

276

oS\J

TIME=1. 5 ms

D 0 .3 1 1 7 . CgHg + Rr

D 1 . 0 9 X C2H2 + flroo

o0DO

Otoa

a

aC\J

o

a2300.2100.1900.1700.1500. T E M P E R R T U R E / K

Figure VIII.11 Experimental soot yields for a 0.31% benzene - argon mixture at /=s = (1.49-1.56) x 10*5 mol/cm3 and a 1.09% acetylene-argon mixture at p5 = (3.82 - 3.90) x 10-s mol/cm3 using laser extinction at 633 and 3390 nm, respectively. The soot yields are calculated assuming Rayleigh scattering (166) and using the values of Lee and Tien (200) for the complex refractive indexes. The symbols designate experimental results, the lines cubic spline fits.

Table VIII.9 summarizes the results of a sensitivity analysis for reaction classes; the omitted classes have absolute sensitivity values less than 0.005. Thesensitivities are defined as in Chapter VI. An interesting point is the small number of significantly sensitive reaction classes. With the exception of class 48, which is applicable only to the benzene mechanism, all reaction classes with large sensitivities also were important for other fuels.

2 7 8

Table VIII.9Sensitivities of Soot Yield with Respect to Rate

Coefficients and Equilibrium Constants for Benzene Pyrolysis

Y YReaction S SClass k K

2 -0.02 0.3 -0.01 0.8 0.07 -0.0813 -0.02 0.0219 0. -0.0820 0. 0.0221 -0.03 0.23 1 .80 0.6625 -0.02 -0.1027 0.62 0.2430 -0.02 0.2432 -0.06 0.33 0.03 -0.0448 -1 .03 0.86

2798.4 CONCLUSIONS

The results reported in this chapter support the physical validity of the proposed detailed model of soot formation since the model correctly predicts the trends seen in experiments with different fuels. The model predicts that the two-carbon species C 2Hi, i = 1,2,..., are the mostimportant soot-precursors for nonaromatic fuels, especially for reaction times longer than a few hundred microseconds. It also indicates that reactions of aromatic species with other aromatics to form small polycyclic compounds are partially responsible for the high soot yields observed during combustion of aromatic compounds; however, large polycyclic aromatic hydrocarbons grow mainly by addition of acetylene even when aromatic fuels are used.

Chapter IX CONCLUSIONS AND RECOMMENDATIONS

It is important to understand the process of soot formation because of the effects of soot on both human health and combustion efficiency. The data gathered and the analysis performed during this study provide both practical and theoretical information concerning soot formation during hydrocarbon pyrolysis.

The experiments on soot formation during pyrolysis of benzene and toluene were conducted behind reflected shock waves in a conventional shock-tube. Soot yields were measured by the attenuation of a laser beam at 633 nm. The experiments covered broad ranges of pressure (0.32 - 3.73atm), temperature (1462 - 2931 K) and carbon-atomconcentration (0.60 * 1017 - 6.78 * 1017 atoras/cm3).

An empirical model for soot formation during pyrolysis of aromatic hydrocarbons was developed. The model allows oneto summarize experimental data for use in design and optimization of practical combustion systems; it also provides quantitative restrictions for the development of detailed models.

A detailed kinetic model of soot formation during hydrocarbon pyrolysis was developed. It has no adjustable

- 280 -

281parameters but rather provides 'a priori’ lower-boundpredictions of soot formation. The model successfullypredicts many of the trends observed in experiments with different fuels and additives. There is a shift in temperature of as much as 400 degrees K between experimental and computational results. This difference depends upon a few basic thermochemical properties which do not have well-established values. The correct prediction of trends observed experimentally provides validation for the model and furnishes incentive for studying the reaction pathways to soot formation predicted by the mechanism.

The modeling results indicate the importance of the highly stable, compact polycyclic aromatic molecules and their reactivation by hydrogen atoms to form organic radicals. The overshoot by hydrogen atoms of their equilibrium concentration during the first few hundredmicroseconds is a driving kinetic force for soot formation.The chief equilibrium barrier to growth of polycyclic aromatic hvdrocarbons (PAH) from nonaromatic fuels (and so to growth of soot) occurs during the formation of small aromatic species. Two-carbon species such as C 2H, C 2H 2 and C 2H 3 are key intermediates to soot formation for nonaromatic fuels and play a significant role for aromatic fuels as well. Reactions between aromatic species maxe acontribution to PAH growth for aromatic fuels.

282It is recommended that work be done on the following

topics:1. The computational simulation of soot formation from

allene (C3H 4). Allene produces considerablequantities of soot during pyrolysis and oxidation but is unlikely to go through butadiene or acetylene as intermediates.

2. The careful study of basic kinetic and thermochemicalparameters. The rate coefficients of the initial fraqmentation reactions of a fuel can affect predicted soot yields. Predicted soot formation is also affected by thermochemistry; some important bond dissociation energies have uncertainties of ± 6-8kilocalories.

3. Flame modeling. Several authors have done extensive studies of product distributions in near— sooting flat acetylene flames. These studies would provide a strict test of the product distributions predicted by the computational model for these flames.

Chapter X LITERATURE CITED

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3. Levy, A . : Nineteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, 1983, p. 1223.

4. Haynes, B. S. and Wagner, H. Gg.: Prog. Energy Combust. Sci. 7:229 (1981).

5. Wagner, H. Gg.: Seventeenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh,1979, p . 3.

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62:335 (1978).8. Homann, K. H. and Wagner, H. Gg.: Eleventh Symposium

(International) on Combustion. The Combustion Institute, Pittsburgh, 1967, p. 371.

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- 283 -

28410. Seinfeld, J. H . : Air Pollution - Physical and Chemical

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(1962).15. Mar’yasin, I. L. and Nabutovskii, Z. A.: Kin. Cat,

11:706 (1970).16. Davies, R. A. and S,cully, D. B.: Combust. Flame 10:165

(1966).17. Glassman, I. and Yaccarino, P.: Eighteenth Symposium

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19. Dobbins, R. A. and Mulholland, G. W.: Comb. Sci. Tech. 40:175 (1984).

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21. Prado, G. P., Lee, M. L., Hites, R. A., Hoult, D. P. and Howard, J. B . : Sixteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, 1977, p. 649.

22. Bauer, S. H . : comment in Tenth Symposium(International) on Combustion. The Combustion Institute, Pittsburgh, 1965, p. 511.

23. Homann, K. H. and Wagner, H. Gg.: Proc. Roy. Soc.A307:141 (1968).

24. Ingram, D. J. E., Tapley, J. G., Jackson, R., Bond, R. L. and Murnaghan, A. R.: Nature 174:797 (1954).

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26. Ball, R. T. and Howard, J. B . : Thirteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, 1971, p. 353.

27.

28.29.

30.

31 .

32.

33.

34.

35.

36.

37.

38.

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201. Frenklach, M., Clary, D. W., Yuan, T., Gardiner, W. C., Jr. and Stein, S. E.: submitted for publication.

202. Frenklach, M., Clary, D. W., Gardiner, W. C . , Jr. and Stein, S. E . : Fifteenth International Symposium onShock Waves and Shock Tubes. to appear.

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207. Kiefer, J. H., Mizerka, L. J., Patel, M. R. and Wei, H. C . : to be published.

SERIES A.INITIAL HOLE FRACTIONS: C.H, = 0.311 %

Ar = 99.689 *RUN DISK T a SOOT YIELDCX)xE(m), AT TIHE (DS) TIHE RATE Pa T, T, c. ( C ) m X l O ' 17NO. NO. (K ) 0 . 2 5 0 . 5 0 0 . 7 5 1 .0 0 1 . 2 5 1 . 5 0 1 . 7 5 2 . 0 0 (ma) < m a "1 ) ( b a r ) ( K ) (C ) ( a t o n / c a * )

1 C0721 15 61 . 0 . 2 0 0 . 18 0 . 16 0 . 15 0 . 0 8 0 . 0 7 0 . 0 7 0 . 0 2 0 . 0 0 0 0 . 0 0 0 1 .9 3 8 5 0 . 2 3 . 2 1 4 .9 0 1 .6 72 C 0 7 I 1 1602. 0 .2 1 0 . 2 2 0 . 17 0 . 17 0 . 15 0 . 17 0 . 18 0 . 2 2 0 . 0 0 0 0 . 0 0 0 2 . 0 7 eC 7 . 2 2 . 2 1 5 .5 5 1 .7 53 C 0 7 I 2 1638 . 0 . 2 2 0 . 2 3 0 . 2 6 0 .2 1 0 .2 1 0 . 2 4 0 . 3 6 0 . 5 9 2 . 2 9 6 0 . 2 9 0 2 . 12 8 6 3 . 2 3 . 0 1 5 .5 5 1 .7 54 C 0722 1711. 0 . 2 3 0 . 2 5 0 . 2 8 0 .4 1 0 .8 1 1 .7 8 3 . 5 3 6 . 2 9 1 .4 3 0 0 . 4 3 7 2 . 2 2 9 1 4 . 2 3 . 3 1 5 .5 9 1 .7 55 C 073 I 1735 . 0 .4 1 0 . 4 2 0 .5 1 0 . 8 8 1 . 7 6 3 .4 1 5 . 9 7 9 . 7 2 1 .261 0 . 4 7 8 2 . 2 3 9 2 4 . 2 3 . 4 1 5 .4 7 1 .7 46 C 0732 1766. 0 . 4 9 0 . 6 6 1 .01 2 . 2 3 4 . 5 9 8 . 15 1 2 .3 0 1 6 . 5 9 0 . 8 8 6 0 . 4 7 6 2 . 2 5 9 3 7 . 2 3 . 4 1 5 .3 5 1 .7 27 C 0742 1816 . 0 . 3 2 0 . 6 3 1 . 8 5 4 . 9 0 9 . 1 1 1 3 .6 1 1 7 .6 6 2 1 .1 1 0 . 6 4 8 0 . 5 3 5 2 . 2 9 9 5 9 . 2 3 . 6 15. 18 1.718 C0741 1851. 0 . 5 4 1 .0 5 2 . 5 3 5 . 4 1 9 . 5 3 14 . 10 18 . 10 2 1 . 4 3 0 . 5 8 8 0 . 5 1 0 2 . 3 9 9 7 4 . 2 3 . 6 1 5 .4 9 1 .7 49 C 075 I 1862 . 0 . 5 9 1 . 7 2 4 . 6 2 8 . 8 4 13 . 19 1 6 .9 6 1 9 .9 8 2 2 . 2 8 0 . 4 0 0 0 . 5 4 5 2 . 3 8 9 7 6 . 2 2 . 7 1 5 .3 6 1 .7 3

10 C0821 1869 . 0 .6 1 2 . 10 5 . 2 5 9 . 3 7 1 3 .3 5 1 6 .5 9 1 8 .9 3 2 0 .9 1 0 . 3 2 2 0 . 5 1 5 2 . 3 8 9 8 1 . 2 3 . 0 1 5 .31 1 .7 21 1 C0822 1908 . 0 .7 1 2 . 4 2 5 . 7 9 9 . 9 5 1 3 .4 8 16. 18 1 8 .0 7 1 9 .6 3 0 . 2 9 4 0 . 4 0 0 2 . 4 4 9 9 7 . 2 3 . 1 1 5 .4 0 1 .7 312 C 0752 1920 . 0 . 6 9 2 . 6 3 6 . 0 3 10. 14 1 3 .6 9 1 6 .4 8 1 8 .9 0 2 0 . 7 6 0 .3 1 1 0 . 5 3 2 2 . 4 6 1 0 03 . 2 3 . 2 1 5 .3 9 1 .7 313 C0761 1973 . 1 .31 4 . 3 3 7 .6 1 1 0 .2 3 1 1 .9 9 1 3 .2 8 1 4 .2 9 1 5 .3 2 0 . 125 0 . 4 6 3 2 .5 1 1025. 2 3 . 6 15 .31 1 .7 214 C0762 1977. 0 . 9 3 3 . 6 8 6 . 7 9 9 . 3 0 1 1 .0 7 1 2 .3 9 13 .31 1 4 .5 3 0 . 163 0 . 4 2 3 2 . 4 8 1027. 2 3 . 8 1 5 .0 9 1 .7 015 C 0772 2 0 4 3 . 1 .21 3 .5 1 5 . 4 7 6 . 8 5 7 . 7 6 8 . 4 2 9 . 0 8 9 . 8 7 0 . 0 8 7 0 . 3 4 9 2 . 5 9 1055 . 2 4 . 0 1 5 .2 6 1 .7 216 C0831 2 0 9 0 . 1 .51 3 . 14 4 . 4 3 5 . 4 3 6 . 18 6 . 7 9 7 . 3 4 7 . 7 7 0.000 0 . 2 6 6 2 . 6 8 1075 . 2 3 . 2 15 .41 1 .7 317 C0771 21 19. 1 . 3 5 2 . 4 8 3 . 2 2 3 . 8 9 4 . 5 4 5 . 17 5 . 6 4 6 . 4 1 0.000 0 . 2 6 5 2 .7 1 1086 . 2 3 . 9 1 5 .3 9 1 .7 318 C0781 2 1 3 5 . 1 . 0 3 1 . 6 8 2 . 16 2 . 4 6 2 . 7 5 3 . 1 1 3 . 4 7 3 . 8 8 0.000 0.000 2 .7 1 1094. 2 4 . 0 1 5 .2 9 1 .7 219 C 0782 2 1 6 2 . 0 . 7 4 1 .0 4 I . 3 4 1 . 4 9 1 .6 4 1 . 8 2 1 . 9 3 2 . 10 0.000 0.000 2 . 7 3 1 106. 2 4 . 0 15. 18 1.7120 C081 1 2 2 0 5 . 0 . 8 3 1 . 12 1 .2 7 1 . 3 7 1 . 5 3 1 . 6 5 1 .61 1 . 6 8 0.000 0.000 2 . 7 9 1 123. 2 2 . 7 15 .21 1.7121 COS 12 2 2 7 3 . 0 . 5 9 0 . 7 4 0 . 7 9 0 . 8 6 0 . 9 4 0 . 9 7 1 .01 1 . 10 0.000 0.000 2 . 8 7 1 152. 2 3 . 0 1 5 .2 0 1.71

DETAILS OF

EXPERIMENTAL DATA

SERIES B.INITIAL MOLE FRACTIONS: C7H, = 0.311 *

Ar = 99.689 XRUN DISK To SOOT Y I E L D ( X ) x E ( n ) , AT T IM E ( a s ) T IME RATE Pa T , T , CB ( C ) a X l O ' 17NO. NO. (K> 0 . 2 5 0 . 5 0 0 . 7 5 1 .0 0 1 .2 5 1 .5 0 1 .7 5 2 . 0 0 (DS) ( m s ' 1 ) ( b a r ) ( K ) (C ) ( m o l / m 1 ) ( a t o m / c m * )

1 C 0832 1600 . 0 . 13 0 . 16 0 . 17 0 . 2 4 0 . 3 4 0 . 4 8 0 .7 1 1 . 0 9 1 . 8 2 0 0 . 165 2 . 0 8 8 6 8 . 2 3 . 7 1 5 .6 6 2 . 0 52 C0841 1646 . 0 . 2 8 0 . 3 6 0 . 4 3 0 . 5 4 0 . 7 9 1 . 2 3 1.91 3 . 0 0 1 .6 6 5 0 . 3 3 4 2 . 14 8 8 8 . 2 3 . 8 1 5 .6 4 2 . 0 53 C 0842 1672 . 0 . 3 2 0 . 4 8 0 . 7 4 1 .1 3 1 .8 7 3 . 0 2 4 . 6 0 6 . 9 5 1 . 178 0 . 3 6 5 2 . 16 8 9 9 . 2 3 . 9 1 5 .5 3 2 . 0 44 C 085 I 16 73 . 0 . 2 0 0 . 3 7 0 . 7 7 1 .5 8 2 .9 1 4 . 9 6 7 . 8 0 1 1 .4 1 1 .0 3 0 0 . 4 4 4 2 . 15 8 9 9 . 2 2 . 3 1 5 .4 4 2 . 0 25 C 0852 1703. 0 . 5 3 0 .9 1 1 . 7 0 2 . 9 7 4 .9 1 7 .4 1 1 0 .6 2 1 4 .5 3 0 . 7 3 5 0 . 4 1 3 2 . 19 9 1 1 . 2 2 . 6 1 5 .4 6 2 . 0 36 C 0982 1 7 6 1 . 0 . 4 9 1 .2 9 2 . 6 4 4 . 6 4 7 . 3 0 1 0 .7 2 1 4 .3 8 1 8 .0 0 0 . 4 8 8 0 . 4 1 9 2 . 2 7 9 3 7 . 2 3 . 7 1 5 .5 3 2 . 0 47 C 086 I 1767. 0 . 4 3 0 . 9 6 1 . 9 6 3 . 7 4 6 . 18 9 . 3 4 1 3 .0 5 1 6 .8 9 0 . 6 1 8 0 . 4 2 3 2 . 2 8 9 3 9 . 2 2 . 9 1 5 .51 2 . 0 38 C 0862 1814. 0 . 5 5 1.71 3 . 6 6 6 . 4 0 10 . 10 1 4 .0 9 1 7 .8 7 21 . 3 2 0 . 4 2 9 0 . 4 8 8 2 . 3 4 9 5 9 . 2 3 . 2 1 5 .4 9 2 . 0 39 C 087 I 1847. 0 . 3 8 1 .6 5 3 . 9 6 7 .4 1 1 1 . 3 9 1 5 .4 4 1 8 .91 21 .91 0 . 3 9 8 0 . 5 1 7 2 . 3 8 9 7 3 . 2 2 . 1 1 5 .4 9 2 . 0 3

10 C 0962 1863 . 0 . 6 9 2 . 0 4 4 . 2 3 7 . 2 7 1 0 .9 8 1 4 .6 5 1 7 .7 8 2 0 . 4 3 0 . 3 7 8 0 . 4 6 7 2 . 3 3 9 8 0 . 2 3 . 8 1 5 .0 7 1 .9 81 1 C0981 1880 . 0 . 7 9 2 . 5 6 5 . 3 5 8 . 8 4 1 2 .3 4 1 5 .4 6 1 7 .8 8 1 9 .7 0 0 .2 5 1 0 . 4 6 7 2 . 3 6 9 8 8 . 2 3 . 8 1 5 .0 9 1 .9 812 C 0872 1887 . 0 . 6 6 2 .5 1 5 . 4 9 9 . 3 9 1 3 .0 7 1 6 .2 8 1 8 .7 6 2 0 . 8 9 0 . 2 8 8 0 .5 4 1 2 . 4 3 9 9 0 . 2 2 . 5 1 5 .4 5 2 . 0 313 C 088 I 1903 . 0 . 7 8 3 .0 1 6 . 0 5 9 . 8 4 1 3 .5 3 1 6 .6 6 1 8 .9 8 2 0 . 9 0 0 . 2 1 6 0 . 5 0 4 2 . 4 2 9 9 7 . 2 2 . 7 15 .31 2 .0 114 C 0972 1908 . 0 . 7 2 2 .7 1 5 . 6 4 9 . 3 6 12 .81 1 5 .9 6 1 8 .5 3 2 0 . 6 2 0 . 2 6 4 0 . 4 9 9 2 .4 1 9 9 9 . 2 3 . 8 15 .21 1 .9 915 C 0882 1977 . 1 . 0 7 3 . 6 9 6 . 9 6 10 . 1 1 1 2 .4 7 14 .21 1 5 .5 6 1 7 .0 0 0 . 151 0 . 4 9 2 2 . 5 3 1 0 2 8 . 2 3 . 1 1 5 .4 0 2 . 0 216 C091 1 1989 . 1.01 3 . 7 8 6 . 7 9 9 . 13 1 0 .8 8 1 2 .2 2 13. 35 1 4 .5 6 0 . 137 0 . 4 8 0 2 . 5 3 1 0 33 . 2 2 . 9 1 5 .2 8 2 . 0 017 C0971 1992 . 1 . 18 3 . 5 8 6 . 3 6 8 . 8 7 1 0 .8 4 1 2 .4 0 1 3 .6 8 14 .71 0 . 103 0 . 4 3 5 2 . 5 6 1 0 35 . 2 3 . 8 1 5 .4 5 2 . 0 318 C 0922 2 0 1 0 . 1 .0 4 3 . 5 8 6 . 4 ! 8 . 9 0 1 0 .7 6 1 2 .2 0 1 3 .4 4 1 4 .6 3 0 . 124 0 . 4 4 2 2 . 5 0 1042 . 2 2 . 3 1 4 .9 5 1 .9 619 C 0912 2 0 5 1 . 1 . 3 2 3 . 6 8 5 . 7 3 7 . 3 6 8 . 6 6 9 . 7 7 1 0 .9 5 1 2 .0 5 0 . 0 9 6 0 . 4 0 7 2 . 6 2 1060. 2 3 . 0 1 5 .3 3 2 .0 120 C 096 I 2 0 6 4 . 1 . 2 8 3 . 4 5 5 . 2 4 6 . 5 9 7 . 5 4 8 . 2 9 8 . 9 9 9 . 7 6 0 . 0 8 6 0 . 3 8 0 2 . 6 2 1066. 2 3 . 8 1 5 .2 8 2 . 0 021 C09ZI 2 1 2 2 . 1. 3 0 2 . 8 5 3 . 9 8 4 . 7 3 5 . 18 5 . 3 7 5 . 5 8 5 . 9 9 0 .0 4 1 0 . 3 0 3 2 .7 1 1 0 9 0 . 2 3 . 0 1 5 ,3 9 2 . 0 22 2 CC931 2 1 5 2 . 1 . 2 9 2 . 3 6 3 . 14 3 . 7 4 4 . 2 3 4 . 7 6 5 . 13 5 . 3 0 0.000 0 . 2 2 5 2 . 7 2 1 103. 2 2 . 5 15 . 18 1 . 9 923 C 0932 2 2 1 6 . 0 . 7 0 1 .0 9 1 . 2 7 1 . 3 8 1 . 5 ! 1 . 7 5 1 . 8 5 1 .9 7 0.000 0.000 2 . 7 8 1 130. 2 3 . 4 1 5 .0 9 1 .9 824 C0952 2 2 3 5 . 0 .5 1 0 . 6 3 0 . 6 9 0 . 7 7 0 . 9 3 1 . 0 3 1 . 0 9 1 . 2 3 0.000 0.000 2 . 8 4 1 138 . 2 3 . 8 1 5 .2 8 2 . 0 025 C 095 I 2 2 6 7 . 0 . 3 9 0 . 5 0 0 . 5 5 0 . 6 2 0 . 6 8 0 . 7 4 0 . 8 3 0 . 9 2 0.000 0.000 2 . 8 8 1 152 . 2 3 . 9 1 5 .2 7 2 . 0 026 C 0942 2 3 5 8 . 0 . 2 8 0 .3 1 0 . 3 7 0 . 3 6 0 . 3 8 0 . 4 5 0 . 5 3 0 . 5 7 0.000 0.000 3 .0 1 1 191 . 2 3 . 8 1 5 .3 8 2 . 0 227 C0941 2 3 7 5 . 0 . 2 2 0 . 2 7 0 . 3 3 0 . 3 5 0 . 4 0 0 . 4 9 0 . 5 0 0 . 5 3 0.000 0.000 3 . 0 2 1 198. 2 3 . 6 1 5 .31 2 .0 1

298

SERIES C.INITIAL MOLE FRACTIONS: C7H, = 1.000 %

Ar = 99.000 SRUN DISK t 8 SOOT Y I E L D ( * ) X E ( n ) , AT TIM E ( 0 3 ) TIME RATE Pa T» T , C8 ( C ) . X 1 0 - ,TNO. NO. (K ) 0 . 2 5 0 . 5 0 0 . 7 5 1 .0 0 1 . 2 5 1 .5 0 1 .7 5 2 . 0 0 (DS) ( a s * 1) ( b a r ) ( K ) (C ) ( B o l / a * ) ( a t o m / c n * )

1 C0541 1 5 29 . 0 . 18 0 . 2 6 0 . 3 3 0 . 3 4 0 . 3 3 0 .4 1 0 . 4 5 0 . 5 8 0 . 0 0 0 0 . 0 0 0 1 . 9 8 8 5 1 . 2 2 . 3 1 5 . 5 9 6 . 5 72 C 0 4 I 2 1572 . 0 . 0 0 0 . 0 0 0 . 0 4 0 . 1 3 0 . 2 7 0 . 5 3 0 . 8 7 1 . 3 7 1 .3 5 8 0 .5 1 1 2 . 0 3 8 7 0 . 2 2 . 1 1 5 .5 2 6 . 5 43 C 043 2 1638. 0 . 17 0 . 3 4 0 . 5 8 0 . 9 9 1 .7 2 2 . 9 3 4 . 8 4 7 . 4 4 0 . 9 2 6 0 . 6 5 2 2 . 0 2 8 9 9 . 2 2 . 5 1 4 . 8 3 6 . 2 54 C 042 I 1639 . 0 . 0 0 0 . 0 8 0 . 3 7 0 . 6 8 1 .3 3 2 . 2 2 3 . 6 0 5 . 4 6 0 . 9 7 8 0 . 5 9 3 2 . 13 9 0 0 . 2 2 . 2 1 5 .6 0 6 . 5 75 C 0422 1670. 0 . 2 6 0 . 5 3 1 . 0 0 1 . 8 7 2 . 8 9 4 . 2 5 6 . 2 1 8 . 6 0 0 . 4 9 7 0 .5 1 1 2 . 14 9 1 4 . 2 2 . 3 1 5 . 3 9 6 . 4 96 C 0 4 3 I 1678. 0 . 2 0 0 .6 1 1 .2 7 2 . 5 3 4 . 5 2 7 . 3 5 1 1 .1 7 - 1 . 0 0 0 .5 2 1 0 . 7 1 9 2 . 14 9 1 7 . 2 2 . 4 1 5 .3 1 6 . 4 57 C 0532 1759 . 0 . 4 3 1 .5 3 3 . 5 5 6 . 5 6 1 0 .6 7 -1 .0 0 - 1 . 0 0 - 1 . 0 0 0 . 2 3 3 0 . 8 8 3 2 . 2 5 9 5 2 . 2 2 . 2 1 5 .4 2 6 . 5 08 C0441 1787. 0 . 4 6 1 .7 4 4 . 17 7 .9 1 1 2 .6 5 -1 .0 0 - 1 .0 0 -1 . 0 0 0 . 2 5 7 1 .0 0 9 2 . 2 8 9 6 5 . 2 2 . 5 1 5 .3 4 6 . 4 69 C 0442 1871. 0 . 9 4 3 . 4 7 7 . 3 5 1 2 .3 6 - 1 . 0 0 - 1 . 0 0 - 1 . 0 0 - 1 . 0 0 0 . 1 13 1 .2 1 5 2 . 4 0 1 0 0 2 . 2 2 . 4 1 5 .4 4 6 .5 1

10 C 045 I 1885 . 1 . 2 3 4 . 7 4 9 . 7 5 - 1 . 0 0 - 1 .0 0 -1 . 0 0 -1 . 0 0 -1 .0 0 0 . 120 1 .4 9 5 2 . 3 9 10 08 . 2 2 . 6 1 5 .2 5 6 . 4 31 1 C 0452 1921 . 1 .5 7 5 . 5 5 1 0 .9 5 - 1 . 0 0 -1 .0 0 - 1 . 0 0 -1 . 0 0 - 1 . 0 0 0 . 106 1 .6 1 1 2 . 4 2 1024 . 2 2 . 6 15. 17 6 . 4 012 C0461 1973. 1 .9 6 6 .9 1 1 2 .6 6 -1 . 0 0 - 1 . 0 0 -1 . 0 0 -1 . 0 0 - 1 . 0 0 0 . 0 8 9 1 .81 1 2 . 4 9 10 46 . 2 1 . 9 15 . 19 6 . 4 013 C0462 2 0 3 5 . 2 . 6 6 8 . 2 5 1 4 .3 9 -1 . 0 0 - 1 .0 0 -1 . 0 0 -1 . 0 0 - 1 . 0 0 0 . 0 6 5 1 .9 3 0 2 . 5 7 10 74 . 2 2 . 1 1 5 .2 1 6 .4 114 C0471 2 1 0 5 . 3 . 2 8 8 . 9 8 1 5 .0 5 - 1 . 0 0 - 1 . 0 0 - 1 . 0 0 -1 . 0 0 - 1 . 0 0 0 . 0 5 ! 1 .9 9 7 2 . 6 6 1 105. 2 2 . 2 1 5 . 2 2 6 . 4 215 C0472 2131 . 3 . 4 3 9 . 3 6 - 1 . 0 0 - 1 .0 0 -1 . 0 0 - 1 . 0 0 -1 . 0 0 -1 .0 0 0 .0 4 1 2 . 159 2 . 6 7 1 1 16. 2 2 . 4 1 5 . 0 9 6 . 3 616 C0481 2 1 9 6 . 3 . 9 6 1 0 .0 7 -1 . 0 0 -1 . 0 0 -1 . 0 0 -1 . 0 0 -1 . 0 0 - 1 . 0 0 0 .0 3 1 2 . 4 7 0 2 . 7 6 1 145 . 2 2 . 8 15. 1 1 6 . 3 717 C 0 5 I 1 2 2 5 9 . 4 . 2 2 10. 15 - 1 . 0 0 - 1 . 0 0 - 1 . 0 0 - 1 . 0 0 -1 . 0 0 -1 . 0 0 0 .0 2 1 2 . 3 8 9 2 . 8 3 1 173 . 2 3 . 0 1 5 .0 8 6 . 3 618 C0521 2 3 4 5 . 4 . 4 5 9 . 9 2 - 1 . 0 0 -1 .0 0 -1 .0 0 - 1 .0 0 -1 .0 0 - 1 . 0 0 0.000 0.000 2 . 9 2 1 2 1 0 . 2 2 . 9 1 4 . 9 8 6 . 3 219 C0512 2 3 6 5 . 4 . 3 5 1 0 .0 5 -1 . 0 0 - 1 .0 0 - 1 .0 0 -1 . 0 0 -1 . 0 0 - 1 .0 0 0.000 0.000 2 . 9 9 1219 . 2 3 . 0 1 5 .2 2 6 . 4 220 C 0522 2 4 3 2 . 4 . 2 7 9 . 2 7 - 1 . 0 0 - I . 0 0 -1 . 0 0 - 1 . 0 0 - 1 . 0 0 -1 . 0 0 0.000 2 . 5 8 0 3 . 0 4 1 2 48 . 2 2 . 8 1 5 .0 5 6 . 3 521 C0482 2 6 0 6 . 2 . 5 6 4 . 9 0 6 . 9 3 8 . 8 4 1 0 .5 6 - 1 . 0 0 -1 .0 0 -1 . 0 0 0.000 1 . 5 0 4 3 . 4 9 1 3 2 5 . 2 2 . 8 16 . 10 6 . 7 822 C 0 5 3 I 2641 . 1 .8 8 3 . 5 2 4 . 8 2 6 . 19 7 . 8 2 9 . 3 6 1 0 .7 9 - 1 . 0 0 0.000 1 . 135 3 . 3 3 1340 . 2 2 . 9 15. 15 6 . 3 923 C 0542 2 6 9 4 . 1 .0 5 1 .9 7 2 . 6 9 3 .3 1 4 . 0 0 5 . 0 4 6 . 3 4 - 1 . 0 0 0.000 0 . 7 3 9 3 . 4 0 1 3 63 . 2 2 . 4 15. 16 6 . 3 924 C 055 I 2 7 4 2 . 1 .51 2 . 5 3 3 . 5 6 4 . 3 6 5 . 16 6 . 0 6 6 . 9 3 - 1 .0 0 0.000 0 . 9 3 7 3 . 4 6 1384 . 2 2 . 6 15 . 18 6 . 4 025 C0562 2 7 7 3 . 0 . 9 9 1 . 4 2 1 .6 4 1 . 9 7 2 . 3 4 - 1 . 0 0 - 1 . 0 0 - 1 . 0 0 0.000 0 . 6 5 0 3 . 4 6 1397 . 2 2 . 3 1 5 .0 2 6 . 3 326 C 0552 2 8 0 9 . 0 . 9 3 1 .5 6 1 .81 1 .91 2 . 0 5 - 1 .0 0 -1 .0 0 - 1 . 0 0 0.000 0 . 5 2 3 3 . 5 4 1 4 13 . 2 2 . 6 15. 15 6 . 3 927 C 0 5 7 I 2 9 3 2 . 0 . 6 6 1 .1 3 1 . 5 0 1 . 8 8 - 1 . 0 0 - 1 . 0 0 - 1 . 0 0 -1 . 0 0 0.000 0 . 3 7 7 3 . 7 3 1467 . 2 2 . 4 1 5 .2 9 6 . 4 4

N)>0>0

SERIES D.INITIAL MOLE FRACTIONS: C7Ha = O.IOO %

Ar = 99.900 XRUN DISK Ts SOOT Y I E L D ( % ) x E ( m ) , AT T IH E ( b b ) T IM E RATE P B T , T , c. ( C ) . X 1 0 ' * TNO. NO. ( K ) 0 . 2 5 0 . 5 0 0 . 7 5 1 .0 0 1 . 2 5 1 .5 0 1 . 7 5 2 . 0 0 (m s) ( m s * 1) ( b a r ) ( K ) (C ) ( m o l / m * ) ( a t o m / c m * )

1 C0362 1647 . 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 4 8 0 . 0 0 1 . 0 5 2 . 2 1 1 0 . 1 10 2 . 15 8 8 3 . 2 3 . 5 1 5 .7 3 0 . 6 62 C 0 6 5 I 1672. 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 .3 1 1 .4 6 2 . 6 6 1 .7 8 6 0 . 129 2 . 17 8 9 2 . 2 0 . 6 1 5 .6 3 0 . 6 63 C 0 3 6 I 1686 . 1 .6 2 2 .3 1 1 . 4 4 1 . 8 2 1 . 4 7 2 . 4 3 3 . 5 7 4 . 0 5 1. 148 0 . 0 9 0 2 . 19 9 0 0 . 2 3 . 5 1 5 .6 4 0 . 6 64 C 0672 1 7 18 . 0 . 0 0 0 . 0 0 0 . 6 2 0 . 5 0 1 . 7 5 2 . 2 9 4 . 4 2 5 . 5 9 1 .4 4 0 0 . 139 2 . 2 2 9 1 2 . 2 2 . 9 1 5 .5 6 0 . 6 65 C 06 I 1 17 36 . 0 . 7 7 0 . 9 3 1 . 4 6 1 . 6 4 2 . 3 2 2 . 9 0 4 . 4 6 6 . 4 7 1 .2 5 8 0 . 134 2 . 2 5 9 1 9 . 2 1 . 7 1 5 .5 9 0 . 6 66 C 068 I 1768 . 1 . 0 8 1 .5 0 1 . 7 0 2 . 6 0 3 . 6 4 5 . 5 1 6 . 3 7 8 . 9 0 0 .8 9 1 0 . 1 16 2 . 2 9 9 3 4 . 2 3 . 1 1 5 .5 7 0 . 6 67 C0631 1788. 0 . 4 0 0 . 5 6 0 . 8 9 1 . 6 9 3 . 12 4 . 6 0 6 . 4 8 8 . 5 7 0 . 8 3 3 0 . 1 10 2 . 3 2 94 1 . 2 0 . 6 1 5 .6 2 0 . 6 68 C 0622 1804. 0 . 3 7 0 . 6 5 0 . 9 3 1 . 7 8 3 . 10 4 . 5 4 5 . 9 5 7 .5 1 0 . 7 1 6 0 . 0 8 4 2 . 3 5 9 4 7 . 2 0 . 6 1 5 .7 0 0 . 6 69 C0641 1622 . 0 . 2 8 0 .5 1 1 . 9 5 2 . 5 5 3 . 5 0 5 . 1 1 6 . 8 2 8 . 8 4 0 . 7 3 7 0 . 102 2 . 3 6 9 5 5 . 2 0 . 8 1 5 .5 6 0 . 6 6

10 C0632 1857 . 0 . 0 0 0 . 17 1 . 18 2 . 2 4 3 . 5 9 4 .7 1 6 . 2 0 7 . 2 9 0 . 4 6 3 0 . 0 7 0 2 .4 1 9 6 9 . 2 0 . 7 1 5 .6 3 0 . 6 61 1 C0642 1875 . 0 . 2 6 0 . 7 7 1 . 5 5 2 . 6 8 4 . 0 0 5 . 4 5 6 . 6 0 7 . 8 5 0 . 3 8 7 0 . 0 7 4 2 . 4 2 9 7 7 . 2 0 . 7 1 5 .5 4 0 . 6 512 C 066 I 1898. 0 . 6 0 1. 13 1 . 9 7 2 . 9 9 4 . 15 5 . 0 0 6 . 13 6 . 9 3 0 . 2 0 6 0 . 0 5 6 2 . 4 5 9 8 7 . 2 0 . 3 1 5 .5 2 0 . 6 513 C 0 6 2 I 1924 . 0 . 0 0 0 . 5 0 1 .5 0 2 . 3 0 3 . 16 4 . 0 8 4 . 4 8 5 . 0 9 0 . 3 1 2 0 . 0 5 3 2 . 4 7 0 9 9 8 . 21 . 4 1 5 .4 5 0 . 6 514 C0612 1932 . 0 . 5 4 1. 12 2 . 2 2 3 . 3 3 4 . 4 2 5 . 4 6 6 . 3 4 7 . 2 0 0 . 2 1 3 0 . 0 6 2 2 . 4 8 1 0 02 . 2 2 . 8 1 5 .4 5 0 . 6 515 C0652 1945 . 0 . 2 9 0 . 6 6 1 . 5 2 2 . 4 2 3 . 0 8 3 . 5 4 4 . 13 4 . 3 9 0 . 2 6 4 0 . 0 3 8 2 .5 1 1 0 07 . 2 0 . 6 1 5 .5 0 0 . 6 516 C0662 1992 . 0 . 4 7 0 . 7 9 1 . 19 1 . 3 9 1 . 6 6 1 . 7 9 1 . 9 9 2 . 2 5 0 . 0 0 0 0 . 0 0 0 2 . 5 7 1026 . 2 0 . 3 1 5 .5 0 0 . 6 517 C0671 2 0 4 0 . 0 . 7 8 1 .7 3 1 . 7 0 1 .8 3 1 . 8 0 1 .8 3 1 .7 8 1 . 9 5 0 . 0 0 0 0 . 0 0 0 2 . 6 4 1 0 46 . 2 0 . 2 1 5 .5 7 0 . 6 618 C 0682 2 0 5 1 . 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 0 0 . 0 3 0 . 0 0 0 . 0 0 0 0 , 0 0 0 2 . 6 0 10 53 . 2 3 . 4 1 5 .2 3 0 . 6 4

300

SERIES E.INITIAL MOLE FRACTIONS: C7H, = 0.563 X

Ar = 99.437 *RUN DISK T , SOOT Y I E L D ( X ) x E ( m ) . AT T IM E (m s ) TIME RATE Pa T , T , Ca ( C ) « xNO. NO. (K ) 0 . 2 5 0 . 5 0 0 . 7 5 1 .0 0 1 .2 5

oin 1 .7 5 2 . 0 0 ( o s ) (m s ” 1 ) ( b a r ) ( K ) (C ) (b o I/'b *) (a tom .

1 C0231 1 4 63 . 0 . 0 3 0 . 0 6 0 . 0 6 0 . 16 0 . 16 0 . 16 0 . 13 0 . 13 0 . 0 0 0 0 . 0 0 0 0 . 4 9 8 1 4 . 2 3 . 4 2 . 6 4 0 . 6 32 C 0342 1 4 99 . 0 . 16 0 . 2 0 0 . 2 4 0 . 2 8 0 . 2 8 0 . 3 6 0 . 3 6 0 . 4 0 0 . 0 0 0 0 . 0 0 0 0 . 3 2 8 3 1 . 2 5 . 1 2 . 5 5 0 . 6 03 C 033 I 1615 . 0 . 18 0 . 3 6 0 . 4 0 0 . 6 2 0 . 8 0 1 .0 2 1 .2 5 1 .7 7 0 . 0 0 0 0 . 0 0 0 0 . 3 6 8 8 1 . 2 4 . 7 2 . 6 9 0 . 6 44 C 0332 1708. 0 . 0 4 0 . 2 9 0 . 4 3 0 .6 1 0 . 7 6 i . O 2 1. 16 1 .3 5 0 . 0 0 0 0 . 0 0 0 0 . 3 9 9 2 2 . 2 4 . 9 2 . 7 6 0 . 6 65 C0371 1710. 0 . 2 3 0 . 3 5 0 . 6 7 0 . 7 5 1 . 0 2 1 . 2 2 1 .5 8 1 .7 8 0 . 0 0 0 0 . 0 0 0 0 . 4 0 9 2 2 . 2 5 . 5 2 . 7 8 0 . 6 66 C 0322 1783 . 0 .2 1 0 . 5 4 0 . 8 4 1 .2 9 1 .7 4 2 . 17 2 . 6 3 3 .4 1 0 . 3 9 8 o.ooo 0 . 4 2 9 5 3 . 2 3 . 7 2 . 8 5 0 . 6 87 C 0262 1 8 56 . 0 . 2 0 0 . 5 3 1 . 0 3 1 .6 5 2 . 5 3 3 . 3 9 4 . 4 1 5 . 7 7 0 . 4 8 7 0 . 0 0 0 0 . 4 4 9 8 5 . 2 4 . 0 2 . 8 5 0 . 6 88 C0341 1887. 0 . 17 0 . 6 7 1 . 34 2 . 2 4 3 . 15 4 . 15 5 . 3 6 6 . 9 8 0 . 8 7 4 0 . 0 9 4 0 . 4 4 9 9 9 . 2 5 . 0 2 . 8 3 0 . 6 79 C 0352 1907. 0 . 18 0 . 7 4 1 .5 3 2 . 4 8 3 . 4 5 4 . 5 9 5 . 8 3 7 . 3 9 0 . 3 6 7 0 .0 7 1 0 . 4 6 1 0 0 8 . 2 5 . 4 2 . 8 9 0 . 6 9

10 C 035 I 1910 . 0 . 2 2 0 . 6 9 1 .3 9 2 . 7 0 3 . 6 9 4 .8 1 6 . 0 8 7 . 5 4 0 . 3 5 0 0 . 0 7 5 0 . 4 6 10 09 . 2 5 . 3 2 . 8 8 0 . 6 81 1 C0232 1912. 0 . 2 4 0 .8 1 1 . 7 0 2 . 7 2 3 . 5 7 4 . 3 7 5 . 3 7 6 . 5 2 0 . 2 4 7 0 . 0 5 3 0 . 4 4 1009 . 2 3 . 5 2 . 7 6 0 . 6 612 C 0242 1938 . 0 . 2 8 1 . 0 0 1 .9 6 3 . 0 5 4 . 10 5 . 19 6 . 4 3 7 . 8 9 0 . 2 4 7 0 . 0 6 2 0 . 4 6 1020. 2 2 . 9 2 . 8 4 0 . 6 713 C 0 3 2 I 2001 . 0 .3 1 1 . 2 0 2 . 5 9 3 . 8 3 5 . 3 9 7 . 2 1 8 . 6 6 9 . 8 3 0 . 2 0 9 0 . 174 0 . 4 3 1047 . 2 3 . 7 2 . 5 9 0 .6 114 C024 1 2 0 2 5 . 0 . 3 8 1 . 5 0 2 . 9 3 4 . 2 8 5 . 3 9 6 . 4 0 7 . 5 8 8 . 7 2 0 . 141 0 . 0 8 3 0 . 4 7 1 0 5 7 . 2 2 . 5 2 . 7 8 0 . 6 615 C0221 2 0 5 8 . 0 . 4 0 1 . 6 0 3 . 0 3 4 . 2 0 5 . 3 6 6 . 7 3 8 . 3 6 9 . 5 4 0 . 161 0 . 0 7 7 0 . 4 9 1 0 7 1. 2 2 . 4 2 . 8 5 0 . 6 816 C 0272 2 0 7 5 . 0 . 5 0 1 . 9 8 3 . 2 0 4 . 0 6 4 .8 1 5 . 5 6 6 . 2 7 6 . 9 8 0 . 1 10 0 . 0 8 4 0 . 4 6 1078. 2 2 . 1 2 . 6 8 0 . 6 417 C0271 2 0 9 1 . 0 . 4 9 1 . 8 2 2 . 8 3 3 . 5 6 4 . 0 4 4 . 5 3 5 . 0 6 5 . 5 5 0 . 127 0 . 0 7 0 0 . 4 7 1086 . 2 3 . 8 2 . 7 3 0 . 6 518 C0282 21 15. 0 .6 1 2 . 4 2 3 .9 1 5 . 1 1 5 . 9 2 6 . 8 8 7 . 5 6 7 . 9 6 0 . 0 9 6 0 . 0 9 8 0 . 4 7 1 0 96 . 2 3 . 2 2 . 6 5 0 . 6 319 C0381 2 1 2 8 . 0 . 3 6 1 . 5 4 2 .4 1 2 . 9 7 3 . 4 2 3 . 8 5 4 . 2 8 4 . 6 9 0 . 147 0 . 0 6 8 0 . 4 7 1 103. 2 5 . 9 2 . 6 4 0 . 6 320 C0382 2141 . 0 . 3 2 1 .3 9 1 . 9 5 2 . 3 4 2 . 6 2 2 . 9 0 3 . 18 3 .4 1 0 . 127 0 . 0 5 0 0 . 4 6 1 109. 2 6 . 0 2 . 6 0 0 . 6 221 C0372 2 1 8 7 . 0 . 0 0 0 . 0 0 0 . 0 8 0 . 4 6 0 . 5 0 0 . 8 8 1. 13 1 . 8 6 0 . 0 6 5 0 . 0 0 8 0 . 4 9 1 128 . 2 5 . 7 2 . 6 8 0 . 6 422 C 03 I 1 2 2 0 7 . 0 . 6 7 1.81 2 . 2 7 2 . 5 6 2 . 8 3 3 . 13 3 . 2 3 3 . 4 0 0 . 0 7 9 0 . 0 7 2 0 . 4 9 1 136. 2 3 . 4 2 . 6 8 0 . 6 423 C0312 2 2 8 5 . 0 .3 1 0 . 5 4 0 . 6 0 0 . 8 8 0 . 7 6 0 . 9 8 0 . 8 5 0 . 8 8 0.000 0.000 0 . 5 2 1 169. 2 3 . 5 2 . 7 5 0 . 6 524 C 028 I 2 4 8 0 . 0 . 15 0 . 2 6 0 . 2 6 0 . 2 9 0 . 2 9 0 .4 1 0 . 4 7 0 . 6 7 0.000 0.000 0 . 5 8 1253 . 2 3 . 2 2 .8 1 0 . 6 7

Appendix B VITA

David Warren Clary graduated from Louisiana State University in December 1981 with a B. S. degree in Chemical Engineering. He entered the Ph. D. program in Chemical Engineering at Louisiana State University in 1982 and hopes to complete requirements for the degree during the fall of 1985.

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E X A M IN A T IO N AND THESIS REPORT

Candidate:

Major Field:

T itle of Thesis:

David W. Clary

Chemical Engineering

Soot Formation During Pyrolysis Of Aromatic Hydrocarbons

Approved:

M ajor Professor and Chairman

:e SchoolDean of the Graduate

E X A M IN IN G CO M M ITTEE:

A

Date of Examination:

September 19, 1985