&EPA
United States Industrial Environmental Research EPA-600/7-79-096
Environmental Protection Laboratory April 1979
Agency Research Triangle Park NC 27711
Chemical Aspects
of Afterburner Systems
Interagency
Energy/Environment
R&D Program Report
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EPA-600/7-79-096
April 1979
Chemical Aspects
of Afterburner Systems
by
R.H. Barnes, M.J. Saxton,
R.E. Barrett, and A. Levy
Battelle Columbus Laboratories
505 King Avenue
Columbus, Ohio 43201
Contract No. 68-02-2629
Program Element No. INE829
EPA Project Officer: John H. Wasser
Industrial Environmental Research Laboratory
Office of Energy, Minerals, and Industry
Research Triangle Park, NC 27711
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, DC 20460
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ABSTRACT
This report reviews the chemistry and reaction kinetics of oxidation and pyrolysis reac-
tion that occur in afterburners or fume incinerators that are used to destroy organic
pollutants in air or gas streams. Chemical kinetic rate data are compiled for both complex
and global reaction mechanisms of interest for the design and analysis of afterburner sys-
tems. Direct-flame, thermal and catalytic afterburner systems are covered. Details are also
given on techniques for estimating chemical rate data when experimental data are
unavailable.
Appropriate equations are given for calculating the chemical performance character-
istics of afterburner systems, and recommendations are made for using chemical rate data for
the analysis of afterburner systems.
The contents of this report are intended to be included in an afterburner standard prac-
tices manual which is to be prepared for EPA as part of this program. Other chapters in this
manual will be concerned with mass-transfer effects and the use of the chemical data pre-
sented here for the detailed design and evaluation of practical afterburners.
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TABLE OF CONTENTS
Page
ABSTRACT ii
TABLE OF CONTENTS iii
LIST OF FIGURES iv
LIST OF TABLES v
ACKNOWLEDGMENTS viii
INTRODUCTION 1
CHEMICAL ASPECTS OF AFTERBURNER SYSTEMS 4
Oxidation Chemistry of Afterburner Systems 5
Chemical Kinetics 9
Rate Data Compilations 17
Homogeneous Oxidation Reactions 19
Homogeneous Oxidation Rate Data 19
Afterburner Calculations 35
Catalytic Oxidation Reaction 38
Catalytic Oxidation Rate Data 43
Afterburner Calculation 55
ESTIMATION PROCEDURES FOR CHEMICAL KINETIC RATE DATA 59
Reaction Rate Theory 59
Unimolecular Reactions 60
Bimolecular Reactions 61
Estimation Procedures 63
Theoretical Procedures 63
Procedures for Rapid Estimation of Kinetic Data 69
SUMMARY AND CONCLUSIONS 69
REFERENCES 71
APPENDIX A A-1
APPENDIX B B-1
APPENDIX C C-1
in
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LIST OF FIGURES
Page
Figure 1. Schematic of Typical Afterburner 4
Figure 2. Summary of Principal Chemical Reactions Involved in
Hydrocarbon Oxidation 6
Figure 3. Major Reactions Involved in the Oxidation of Methane 7
Figure 4. Reaction Steps in Benzene Oxidation Through Hydroquinone
as an I ntermediate 8
Figure 5. Dependence of Activation Energy Upon Bond Strength
of Weakest C-H Bond 25
Figures. Activation Energy for C2H4 Oxidation from 1000 to 1315°K 27
Figure 7. Arrhenius Plots Showing Temperature Dependence in
Catalytic Oxidation of Methane 46
Figure 8. Plots of the Logarithm of Frequency Factor, A, as a Function
of Activation Energy for Metal Oxides and Metals Supported on Alumina 46
Figure 9. Comparison of Catalytic Combustion of Ci to Ca Hydrocarbons 50
Figure 10. Arrhenius Plots of kr from Naphthalene, Toluene, Benzene, and o-Xylene 52
Figure 11. Arrhenius Plots of ka from Naphthalene, Toluene, Benzene, and o-Xylene 52
Figure 12. Arrhenius Plots for Oxidation Over NiO 57
Figure A-1. Effect of Added Oxygen on the Pyrolysis of Ethylene. Reaction Time:
Homogeneous, 0.19 sec; Stainless Steel Surface, 0.18 sec.
Surface-to-Volume Ratio, 0.7 cm"1. 0.4% Oa Is Roughly 1:1
O2-to-Hydrocarbon Ratio A-4
Figure A-2. Percent Propane Converted to Products. Homogeneous Reaction
Time =* 0.22 sec. Variation in Temperature in °C Is Used to
Attain Varying Product Conversions A-4
Figure A-3. Percent Propane Converted to Products. Conversions Varied with
Temperature in °C; Oxidized Stainless Steel Surface; Surface-to-
Volume Ratio, 0.7 cm"1; Reaction Time — 0.22 sec •• A-5
Figure A-4. Product Distribution Along Reactor Length A-5
Figure A-5. Product Distribution Along Reactor Length A-6
IV
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LIST OF FIGURES
(Continued)
Page
Figure A-6. Arrhenius Plot for Assumed First- and Second-Order Reaction A-7
Figure A-7. Comparison of Decomposition Rates for Propane and Butane
at Atmospheric Pressure A-7
Figure A-8. Percent Isobutane Converted to Products. Conversions Varied with
Temperature in °C. Homogeneous; Reaction Time =* 0.22 sec A-8
Figure A-9. Percent Isobutane Converted to Products. Conversions Varied with
Temperature in °C; Oxidized Stainless Steel Surface Present;
Surface-to-Volume Ratio, 0.7 cm"1; Reaction Time — 0.22 sec A-8
Figure A-10. Kinetic Rate Data for Disappearance of Light Hydrocarbons
by Thermal Pyrolysis A-10
Figure A-11. Reaction Velocity Constants for Heavy Hydrocarbons
Relative to n-CsHi2 A'11
LIST OF TABLES
Page
Table 1. Comparison of Temperatures Required to Oxidize Various
Compounds to CO2 and HzO 5
Table 2. Methane Oxidation Reaction Kinetics 8
Table 3. Activation Energies of Some Elementary Processes 10
Table 4. Conversion Factors for Reaction Rate Constants 11
Table 5. Typical Activation Energies and Frequency Factors 12
Table 6. Reaction Frequency Factors 13
Table 7. Effective Collision Diameters 14
Table 8. Differential and Integrated Forms for Simple-Order Reactions 15
Table 9. Properties of Afterburner Catalysts and Correlations for
Mass Transport Coefficients 17
Table 10. Sources of Reaction Rate Data for Afterburners 18
Table 11. Literature Sources of Chemical Kinetic Rate Data 19
Table 12. Global Rate Constants for CH4 Oxidation to CO 20
Table 13. General Overall Mechanism for Complete Oxidation of Hydrocarbons 21
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LIST OF TABLES
(Continued)
Page
Table 14. Hydrocarbon Oxidation Kinetics for JP-5 Fuel (CeHie) 23
Table 15. Rate Constants for Oxidation of Miscellaneous Organic Compounds 23
Table 16. Rate Constants Measured in Thermal Afterburner System 24
Table 17. Activation Energies (kcal/mole) for Combustion in Air 24
Table 18. Activation Energies for Hydrocarbon-Oxygen Flames 25
Table 19. Ethylene Oxidation Mechanism 26
Table 20. Acetylene Oxidation Mechanism 27
Table 21. Global Rate Data for the Oxidation of Aromatics 28
Table 22. Global Rate Constants for CO Oxidation 29
Table 23. Hydrogen-Oxygen Reaction Mechanism 30
Table 24. Reaction Scheme for Combustion of Hydrogen and Oxygen 30
Table 25. Reaction Rate Constants for Combustion of Hydrogen and Oxygen 31
Table 26. High-Temperature Mechanism for Formaldehyde Oxidation 32
Table 27. Rate Constants for Simple Mechanism for Acetaldehyde Oxidation 32
Table 28. Reaction Mechanism and Kinetic Data 33
Table 29. Reaction Mechanism and Rate Constants for the Oxidation of
Acetaldehyde 34
Table 30. Methanol Oxidation Mechanism 35
Table 31. Integrated Rate Expressions for Surface Catalyzed Oxidation 44
Table 32. Rate Constants for Catalysts for the Oxidation of Methane 47
Table 33. Temperatures for Complete Oxidation of Hydrocarbons 48
Table 34. Rate Parameters for Catalytic Oxidation of Methane 49
Table 35. Empirical Reaction Rate Parameters 50
Table 36. Summary of Reaction Rate Models Tested 51
Table 37. Rate Constants for Model 1 53
Table 38. Reaction Rate Parameters for the Catalytic Oxidation
of Benzo(or} Pyrene 54
Table 39. Reaction Rate Parameters for Catalytic Oxidation of
CO and Propylene 55
Table 40. Kinetic Parameters Over Co3O4 56
Table 41. Specific Rates Over Co3O4 56
VI
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LIST OF TABLES
(Continued)
Page
Table 42. Kinetic Parameters of Oxidations Over Supported CoiO* Catalysts .. 57
Table 43. Specific Rates Over Support Co3O4 Catalysts 58
Table 44. Kinetic Parameters for Hydrocarbon Oxidation Over NiO(l) 59
Table 45. Intrinsic Activation Energies for Bimolecular Reactions 62
Table 46. Additive Volume Increments for Estimating Molar Volumes
at the Normal Boiling Point 65
Table 47. Conventional Basic Values and Decrements for the Calculation
of Bond Strengths 68
Table 48. Upper Limits for <5 in Tolman's Three-Body-Collision Equation 68
Table A-1. Kinetic Rate Data for Disappearance of Light Hydrocarbons
by Thermal Pyrolysis A-9
Table A-2. Kinetic Parameters for the Pyrolysis of Simple Alcohols and Mercaptans . A-9
Table B-1. Reaction Mechanism and Rate Parameters for NO Formation B-2
Table B-2. Kinetic Mechanism for Nitric Oxide Formation B-4
Table B-3. Rate Constants for N2-O2 Reactions B-4
Table C-1. Physical and Combustion Properties of Selected Organic Vapors in Air... C-1
Table C-2. Electron Affinities C-4
Table C-3. The Contributions of Different End Groups to •
Activation Energies C-4
Table C-4. Procedure for Calculating Hard-Sphere Collision Parameters C-5
Table C-5. Parameters for Lennard-Jones Potential * C-5
Table C-6. Lennard-Jones Potential Transport Integral fl(2'2)* C-6
Table C-7. Values of a for Calculating Activation Energies from Bond Strengths C-7
Table C-8. Dissociation Energies, D, of Some Molecules and Radicals C-9
Table C-9. Dissociation Energies of Bonds C-10
Table C-10. Dissociation Energies of Bonds in Kcal C-12
VII
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ACKNOWLEDGMENTS
The authors would like to thank Robert W. Coutant of Battelle and Gerald L. Brewer and
Steven D. Olsen of the Air Correction Division of UOP, Inc. for reviewing the manuscript and
their helpful suggestions. Also acknowledged is the helpful guidance of John H. Wasser who
served as EPA Contract Officer.
vim
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CHEMICAL KINETICS OF FUME
AFTERBURNER SYSTEMS
R. H. Barnes, M. I. Saxton, R. E. Barrett,
and A. Levy
INTRODUCTION
The purpose of this study was to review the chemical kinetics of afterburners or fume in-
cinerators which are used for the destruction of organic vapors in effluent waste streams from
industrial processes. This study is part of a program sponsored by EPA to develop standard
practices for designing afterburners for different applications, and to perform an environmen-
tal assessment of afterburners. The information assembled here on the chemical kinetics is in-
tended to provide data required for the predictive modeling and design of practical after-
burner systems.
Afterburners are usually fairly simple combustors employed to destroy (by oxidation)
waste fumes. The waste fumes to be destroyed come from a wide variety of sources such as
paint drying, baking ovens, coffee roasters, solvent degreasers, asphalt processes, etc.
The elevated temperature required to promote the oxidation reactions may come from
combustion of organic components of the waste stream, or, more generally, from the firing of
an auxiliary fuel. The source of oxygen may be the waste stream or air, generally supplied via
the auxiliary fuel burner. In principle, if combustion of the auxiliary fuel and oxidation of
organics in the waste stream are complete, a noxious or environmentally unacceptable organic
vapor is converted completely to CO2 and
Unfortunately, it is not quite this simple in practice. Frequently combustion is incomplete
and undesirable partially oxidized species can be generated. Products of incomplete combus-
tion may include such species as CO, the odoriferous aldehydes, ketones, and organic acids,
soot, and other organics, possibly including the polynuclear organic materials. It is always
possible to overdesign an afterburner system to insure more complete oxidation of organics;
however, excessive overdesign is not desirable in an age of increasing fuel costs.
Mainly because of the fuel situation, there is strong interest in eliminating the use of after-
burners wherever possible by modifying processes or by recovering the organics for further
use; however, it does appear certain that afterburners will still be required for many
applications. When an afterburner is required it is imperative that it be energy efficient while
reducing effluent concentrations to the required limits. Once developed, good design
procedures should provide a rationale for designing more effective systems in addition to
serving as a basis for comparing contemplated afterburner systems with other alternatives.
Generally afterburners are classified into three categories.
• Direct flame
• Thermal
• Catalytic
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Direct flame and thermal afterburners are similar. The basic difference is that the direct-flame
afterburners provide for destruction of the organic vapors by passing a high percentage of the
vapors directly through a flame. The thermal afterburner provides for exposure of the organic
vapors to a high-temperature oxidizing atmosphere for a sufficient time so that the necessary
oxidation reactions can occur. Temperatures in the range from 1200 to 1500°F (650 to 815°C)
are generally required for successful operation of direct flame and thermal devices. Hydrocar-
bon levels can usually be satisfactorily reduced at temperatures below about 1400°F (760°C),
but higher temperatures may be required to simultaneously oxidize the CO. The catalytic
devices, which incorporate a catalytic surface to accelerate the oxidation reactions, generally
operate at lower temperatures, in the range from about 700 to 900°F (370 to 480°C), and re-
quire less auxiliary fuel. However, catalytic units generally are more expensive and require
more maintenance than the other two types of afterburners.
From a chemical viewpoint, two main types of reactions occur in afterburner systems: ox-
idation and pyrolysis reactions. In the case of the direct-flame and thermal afterburners, these
reactions occur mainly in the gas phase with some influence from surface effects. With the
catalytic devices, however, the reactions take place on the surface of the catalyst. In general,
the detailed mechanisms for the oxidation and pyrolysis of even the simplest organic com-
pounds are not completely understood, but it is well established that the reactions occur in
many complicated sequential and concurrent steps involving a multitude of intermediate
species.
It is the intention of this study not to delve into the detailed mechanisms of any reactions,
but to review available information and put it in a form that can be used conveniently for the
analysis and design of afterburner systems. For this purpose, reaction rates are best expressed
in terms of overall or global reaction rates with corresponding distributions of reaction
products. Data are correlated for different classes of organic compounds so that when infor-
mation is unavailable for specific compounds, it may be possible to use correlations to es-
timate required rate constants and their accuracy. A part of this report also presents
procedures for estimating rate constants using considerations based on kinetic theory and the
statistical mechanics of chemical reaction rate theory. Using either the assembled data and/or
the estimation procedures, it should be possible to obtain fairly reliable estimates of rate data
for the practical design and evaluation of afterburner systems.
A comprehensive design model of an afterburner must take into account both the
chemical and the mass-transport rates of the processes. In most afterburner systems, mixing
controls the overall process with the chemistry playing a minor role. Knowledge of an ap-
proximate chemical rate constant can often be useful in establishing those cases where the
chemical kinetics are not important and can be ignored in design consideration. On the other
hand, when chemical rates are important, practical rate data are necessary to determine
temperatures and residence times required to effectively oxidize specific compounds.
The operation of an afterburner can be described by three characteristic times which are
defined below.
(1) Chemical time. For a first-order reaction the chemical time is defined by rc = 1/k,
where k is the rate constant. For reactions of other orders, the rate constant must
be multiplied by the appropriate average concentrations.
(2) Mixing time. The mixing time can be estimated as rd = L2/D, where L is the length
of the reaction zone in the afterburner, and D is the effective diffusion
coefficient.
(3) Residence time. The residence time is rr = L/V where V is the average gas velocity.
-------
The ratio of the chemical time to the residence time is the reciprocal of the first Damkohler
group:
T, NDKD kL
and the ratio of the diffusion time to the residence time is the Peclet number (NPe) for mass
transfer
S-S-*
These ratios characterize the performance of the afterburner. If they are too small, the
chemistry is rate controlling; if they are too large, mixing is controlling. The reciprocal
Damkohler number can be obtained from the global reaction rates given in this report. The
Peclet number can be found from the Reynolds and Schmidt numbers using the graphical
relationships in Levenspiel and Bischoff.(154)
Much of the oxidation and oxidative-pyrolysis data in the literature have been obtained in
flames or laboratory combustion systems in such a way that many intermediates such as CO,
Hz, and aldehydes are formed, and complete conversion to CCh and HzO does not occur. In
applying global rate data to afterburner design problems, it may be convenient to conceptual-
ly divide the combustion process into more than one stage. In the first stage, for example, the
primary combustion reactions would be taken into account with subsequent stages being
employed to extend the combustion of the partially oxidized species to the desired level of ox-
idation. As an illustration of this approach, the global oxidation data for a specific hydrocar-
bon might be based on a specific yield of CO. To reduce the level of CO further, an additional
stage of combustion would then be incorporated into the design considerations to further ox-
idize the CO to CO:. Calculations for this latter stage would be based on global kinetics for the
oxidation of CO.
The next section of this report discusses the chemical aspects of afterburner systems. This
is followed by a review of chemical kinetic data which is organized under the following
headings:
• Homogeneous oxidation of hydrocarbons
• Catalytic oxidation of hydrocarbons
This section is then followed by a section on procedures for estimating chemical kinetic rate
data where experimental data are lacking. A final summary and conclusions section describes
how the results presented in this report can be used to provide practical rate data for use in
designing afterburner systems. Appendices are also included on the kinetics of the pyrolysis of
hydrocarbons and the kinetics of pollutant formation reactions.
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CHEMICAL ASPECTS OF AFTERBURNER SYSTEMS
Conceptually, afterburners can be considered as being divided into 3 sections: an aux-
iliary fuel combustion section, a fume and combustion product mixing section, and an oxida-
tion (or reaction) section. This afterburner concept is illustrated in Figure 1. Physically, the
afterburners sections shown in Figure 1 may be merged and all the processes may occur in one
chamber.
Auxiliary
Fuel '
X Fume
Combustion
Section
Combustion
Products
(1-X) Fume
Mixing
Section
Oxidation
Section
FIGURE 1. SCHEMATIC OF TYPICAL AFTERBURNER
In the combustion section, an auxiliary fuel is fired to supply the heat to warm the fume to
a temperature that will promote oxidation of the organic vapors. Usually, a portion of the
fume stream supplies the oxygen. (Part of the fume stream must be bypassed or the fuel/air
mixture will be too lean to sustain combustion.) Both gaseous and liquid fuels are used to fire
afterburners. Gaseous fuels have the advantage of permitting firing in multiple-jet (or dis-
tributed) burners. Oil combustion has the disadvantage of producing sulfur oxides (from sul-
fur in the oil) and normally produces higher nitrogen oxides emissions.
The mixing section is designed to provide intimate mixing between the combustion
products (from combustion of the auxiliary fuel) and the remaining fume gases. To insure
good mixing it is necessary to provide high velocity gas flow to produce turbulence. Gas
velocities in afterburners range from 25 to 50 feet per second. Ideally, the temperature profile
at the outlet of the mixing section would be flat. In thermal-type afterburners, the following
temperatures are often used as guidelines:
Odor control: 900-1350°F
To oxidized hydrocarbons: 900-1200°F
To oxidized carbon monoxide: 1200-1450°F.
The oxidation section provides time for the organic vapors in the bypassed fume to be ox-
idized. Oxidation sections typically have length-to-diameter ratios of 2 to 3. Depending on the
type of pollutant, residence times ranging from 0.2 to 1.0 seconds are required for thermal
units. The residence time in most practical afterburner systems is dictated primarily by
chemical kinetic considerations.
-------
Catalytic afterburners provide a catalytic surface to promote oxidation for organic vapors.
Consequently, catalytic afterburners operate at lower temperatures than the thermal types
and require less fuel. The preheat temperature for catalytic devices varies with gas composi-
tion and type of contaminant to be oxidized, but is generally in the range from 650 to 1100°F,
lower than the 1200 to 1500°F of most thermal afterburners.
A comparison of temperatures required in thermal and catalytic afterburners to convert
various compounds to CO: and H2O vapor is given in Table 1.
Catalysts in afterburners typically consist of either a metal mesh, ceramic honeycomb, or a
ceramic matrix with a surface deposit of finely divided platinum or platinum family metals. In
industrial processes, 10 to 100 ft3 of catalyst bed are used per 1000 scfm of gas flow. In after-
burners, however, the requirement is in the range of 1 to 2 ft3 per 1000 scfm. Catalytic after-
burners have the disadvantage that performance efficiency deteriorates as the unit is used, and
require periodic replacement of the catalytic material.
TABLE 1. COMPARISON OF TEMPERATURES
REQUIRED TO OXIDIZE VARIOUS
COMPOUNDS TO CO2 AND H2O("
Ignition Temperature, °F
Compound Thermal Catalytic
Benzene
Toluene
Xylene
Ethanol
MIBK
MED
Methane
Carbon Monoxide
Hydrogen
Propane
1076
1026
925
738
858
960
1170
1128
1065
898
575
575
575
575
660
660
932
500
250
500
OXIDATION CHEMISTRY OF AFTERBURNER SYSTEMS
Hydrocarbons in the gas phase react very slowly with oxygen at temperatures below
200°C, however, as the temperature is increased a variety of oxygen-containing compounds
begin to form. As the temperature is increased further, CO and H2O are formed as major
products and compounds such as CO2, H2O2, and CH2O begin to appear. In the range from
300 to 400°C a faint light often appears. This may be followed by one or more blue flames that
successively traverse the reaction vessel. At yet higher temperatures, 500°C or above, ex-
plosive reactions can occur. Detailed information on the homogeneous combustion of
hydrocarbons can be found in References (2) through (5).
Hydrocarbon combustion at lower temperatures is usually initiated by the reaction
RH + O2 - R + HO2 .
-------
With hydrocarbons, this reaction is endothermic by about 45 to 50 kcal/mole. In the case of
aldehydes, the reaction is 35 to 40 kcal/mole endothermic, and the activation energy is slightly
greater. The hydrocarbon radical, R-, can react with oxygen and go through a wide variety of
reactions and intermediates such as depicted by Bradley' ' as shown in Figure 2. As can be seen
in this figure incomplete combustion can lead to the formation of many oxygenated
compounds. In contrast, thermal-cracking or pyrolytic reactions are known to contribute
significantly to hydrocarbon combustion reactions at high temperatures.
Methane, the simplest of the hydrocarbons, when oxidized at low temperatures (<550°C)
is affected by the surface of the reaction vessel, the surface-to-volume ratio, and the presence
of inert gases. A phenomenological reaction scheme for methane oxidation at low
temperatures is shown in Figure 3. Methane combustion at high temperatures involves mainly
taking into account the oxidation of CO to CO: by the reaction
OH + CO - H + CO2 .
At high temperatures the oxidation of the CO by this reaction competes for the OH resulting
in retardation of the ChU reaction. At high temperatures pyrolytic reactions also become im-
portant. With methane and all other hydrocarbons, the primary initiation step at high
temperatures is the pyrolysis of the hydrocarbon to give alkyl radicals. A detailed mechanism
for the oxidation of methane is given in Table 2.
\
R*-
f s
1
ROi to ROiH
, (via OH) ,
^ or\
1
»^ Df~»U
/ \ \ Alcohols
Aldehydes
I
(decomposition)
RCO3
I
(via OH)
«
RC03H
Per-Acids
1
RCO,
(decomposition)
I
RCOOH
Acids
FIGURE 2. SUMMARY OF PRINCIPAL CHEMICAL REACTIONS INVOLVED IN
HYDROCARBON OXIDATION*31
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chain propagation
chain propagation
chain termination
Cm + 02 — CH3 + HO: chain initiation
CH3 + O2 - CH2 + OH
OH + CH4 - H2O + CH3
OH + ChhO - H2O + CHO
CH2-I-O2 — HO2+HCO chain branching
HCO-i-O2 - CO + HO2
HO2 + CH4 - H2O2 + CH3
HO2 + CH2O - H2O2 + HCO
OH - wall
CH2O - wall )
FIGURE 3. MAJOR REACTIONS INVOLVED IN THE OXIDATION OF METHANE13'
For the oxidation of saturated hydrocarbons above methane, the mechanism of oxidation
is further complicated by the greater instability of the higher alkyl radicals and the wide range
of intermediates that are produced. Below about 400°C, the intermediates are comprised
largely of aldehydes and methanol, while at higher temperatures the olefins become
important. A review of cool flame information for the oxidation of C2 to Cu hydrocarbons
has been reported by Cechaux and Delfosse."60'16"
When unsaturated hydrocarbons are oxidized, addition of oxygen to the double bond is
more likely to occur. The initial adduct is generally unstable and can decompose rapidly to
different intermediates of which the aldehydes are probably the most important
R CH = CHR' + O2 - R CH-CHR' - RCHO + R'CHO
I I
o— o
The aldehydes can then be further oxidized.
The oxidation of aromatic hydrocarbons in general has not really been investigated exten-
sively. The major steps in the mechanism for benzene oxidation are thought to be
C6H6 + O2 - C6H5 + HO2
C6H5 + 02 - C6H5O2
GH6 - C6H5O + C6H5 + OH
C6H5OH + C6H5
C6H5O
The phenol, C6HsOH, which forms in high yields because of its great stability is further oxi-
dized to QH4(OH)2, which is in turn oxidized according to the scheme shown in Figure 4. The
products on the right in the figure can then be oxidized further. Oxidation of the acetylene
generally occurs through a series of chain reactions with formaldehyde and formic acid as in-
termediates. The high-temperature oxidation of acetylene is also complicated by the tendency
of acetylene to polymerize. A short review of the oxidation of aromatic compounds can be
found in an article by Santoro and Classman."62'
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TABLE 2. METHANE OXIDATION REACTION KINETICS"
Reaction
CH4 + M - CH3 + H + M
CH4 + OH - CH3 + H20
CH4 + H - CH3 + H2
CH4 + O - CH3 + OH
CH3 + O - CH2O + H
CH3 + 02 - CH2O + OH
CH2O + O-CHO + OH
CH2O + OH - CHO + H2O
CH20 + H - CHO + H2
CH2O + M - CHO + H + M
CHO + 0-CO + OH
CHO + OH - CO + H2O
CHO + H - CO + H2
CHO + M-CO + H + M
CO + OH - CO2 + H
H2 + OH - H + H2O
H2 + O - H + OH
H + O2 - O + OH
H + OH + Ar - H2O + Ar
H + OH + H2O - H2O + H2O
H + HO2 - OH + OH
H + O2 + M - HO2 + M
OH+OH- H2O + O
Forward Rate Constant*
3.32 X 10~7 exp (-44500/T)
9.96 X 10"'° exp (-6290/T)
3.72 X 10"20 T3 exp (-4400/T)
3.49 X 10"" exp (-4560/T)
1.66X10"10
3.32 X 10"14
8.30 X10~" exp (-2300/T)
8.97 X 10"'° exp (-3170/T)
2.24 X 10"" exp (-1890/T)
6.64 X 10"'2 exp (-18500/T)
1.66X10"10
1.66X10"10
3.32 X 10"'°
8.30 X 10"12 exp (-9570/T)
6.64 X 10"12 exp (-4030/T)
4.82 X 10"10 exp (-5530/T)
5.31 X 10"'° exp (-7540/T)
3.65 X 10"10 exp (-8450/T)
2.31 x io"26 r*
3.86 X 10"25 r2
4.15 X10"10 exp (-950/T)
4.13X10"33 exp (500/T)
9.13X10"" exp (-3520/T)
Forward Rate
Constant
at2000°K
7.2 + 10"'7
4.3X10""
3.3X10""
3.6 X 10"12
1.66X10"'°
3.32 X 10"14
2.63X10""
1.84 X10~'°
8.7 X IO"12
6.38 X 10"16
1.66 X10"10
1.66X10"10
3.32 X 10"10
7.0 X 10"14
8.9 x 10"13
3.0X10""
1.2X10""
5.34 X 10"12
5.8 X 10~33
9.65 X 10"32
2.58 X 10"'°
5.32 X 10"33
1.57X10""
Reverse Rate
Constant
at2000°K
3.05 X 10"31
1.74X10"13
1.34X10"12
1.1X10"13
8.8 X 10"17
7.2 X IO"20
1.5X10"14
1.42 X IO"14
7.0 X10"15
5.4 X IO"32
1.9X10""
2.1 X 10~20
4.6X10""
1.0X10"35
3.8 X10"13
3.0 X10"12
1.1 X 10""
2.3X10""
5.14 X IO"2'
8.56 X IO"20
1.0 X 10""
3.6X10"14
2.0 X10"12
'Units: No. Particles, cm3, sec, °K.
Hydroquinone
O
H^ ^O
OH
v s*^ acetylene
x— ^_
FIGURE 4. REACTION STEPS IN BENZENE OXIDATION THROUGH HYDROQUINONE
AS AN INTERMEDIATE
-------
Solid surfaces can affect combustion in two ways. One is in terms of quenching which can
lead to the formution of oxygenated organic compounds such as the aldehydes which are un-
desirable in afterburner applications. The other involves catalytic effects. Catalytic oxidation is
the basis of the catalytic-type afterburner.
Catalytic oxidation falls into two categories: selective oxidation and complete oxidation.
Only complete oxidation is of interest for afterburners since the main objective is complete
conversion of organics to CO2 and H2O vapor. In general detailed mechanisms for catalytic ox-
idation reactions are not known.
Chemical Kinetics
Hydrocarbon oxidation reactions can be represented by the chemical equation
C.Hb + [a + 7) 02 = aCO2 + ^H2O
\ V 2
where CaHb is any hydrocarbon.* This equation is often called an overall or global reaction. A
global expression shows only the net result of a reaction and neglects the many complicated
reaction steps that lead from initial reactants to the final products. Global reactions are readily
adaptable and useful for the kinetic analysis and engineering design of afterburner systems.
There are many gas-phase and surface catalyzed oxidation reactions for which single
global expressions can be used successfully as a basis for calculating reaction rates. However,
in the case of the homogeneous gas-phase oxidation of paraffinic hydrocarbons, the use of a
quasi-global approach has been required for treating reaction kinetics. The quasi-global ap-
proach is based on the reaction
GHb + |o2 - aCO + | H2
with subsequent oxidation of CO and H2 leading to the final combustion products CO2 and
H2O. The H2 oxidation is quite rapid compared to CO oxidation for which global rate ex-
pressions are available. Thus, in this case, the overall gas-phase oxidation kinetics would be
represented by a series combination of two fairly simple reactions. In considering
heterogeneous reactions on catalytic surfaces, in addition to the chemical kinetics, mass-
transport processes must also be taken into account.
In general, both the homogeneous gas-phase and catalytic reactions involving the
destruction of organics or hydrocarbons in afterburner systems can be represented by the
chemical equation
a F + )8 O2 — Products
where F denotes the hydrocarbon fuel and a and )8 are stoichiometric factors. The chemical
reaction rate for the disappearance of the hydrocarbon can be written as
1 dnt . a B
- -j— = -knF n£
a dt
*Substituted hydrocarbons containing atoms such as O, N, S, Cl, etc., can be taken into account by appropriate
modifications to the above equation.
-------
10
where k is the reaction-rate constant and n the species concentrations. This is basically a
bimolecular reaction of order a + p. Care must be taken to observe how the rate constant is
defined. Sometimes ak is defined as the rate constant. For most afterburner applications, the
reaction expression, to a good approximation, can be reduced either to second order where
both a and ft are taken as unity, or to first order in np. The first-order approximation applies
when the O2 is in large excess, which is usually the case with afterburner systems. In this case,
no2 raised to the appropriate power ft is treated as a constant.
The reaction-rate constant k generally is written in one of two forms. The Arrhenius form
is
k = A €^m
where EA is the Arrhenius activation energy, A is the frequency factor, T is temperature, and R
is the gas constant. Arrhenius activation energies for typical hydrocarbons are given in Table 3.
A more elaborate expression, sometimes used, assumes the form
k = B Tm e-EB/RT
where the value of m ranges usually from -1 to 4. This latter expression is often referred to as
the modified Arrhenius equation. In most cases the influence of the exponential is so much
greater than the Tm term that the relationship essentially reduces to an Arrhenius-type expres-
sion. The relationships between the different reaction rate parameters can be expressed by the
two equations'8'
A = B Tm em
and
EA - EB + mRT .
TABLE 3. ACTIVATION ENERGIES OF SOME
ELEMENTARY PROCESSES'
Reaction EA, kcal/mole
CH4
C2H6
C3H8
n-QHio
CH3 + CH4
CH3 + C2H6
CH3 + C3H8
CH3 + QHu
C2H5
C3H7
C4H,
H + CH4
H + C2H6
H + C3H8
H + QHio
- CH3 + H
-2CH3
- CH3 + C2H5
- 2C5H5
~* CH4 + CH3
- CH4 + C2H5
— CH4 + C3H7
i- CH4 + C4H9
- C2H4 + H
- C2H4 + CH3
— C2H4 + C2Hs
- CH3 4- H2
- C2H5 + H2
- C3H7 + H2
- C4H9 + H2
102
84
84
84
14.7
10.4
5.5
5.5
39
18
22
11-13
9
9
9
-------
11
Rate constants have the dimensions of inverse time in seconds multiplied by concentra-
tion raised to the power (\-v) where v is the overall reaction order. The most common con-
centration units are moles/liter, moles/cm3, and molecules/cm3. In terms of these last units, a
first-order rate constant would have dimensions of reciprocal seconds while a second-order
rate constant has dimensions of cmVmolecule-sec. Reactions with nonintegral overall order
have rate concentrations with concentration units raised to nonintegral powers. Common
conversion factors for second- and third-order reactions are given in Table 4.
Homogeneous Reaction Rates. Bimolecular reactions have frequency factors, A, which lie
in the range from 108 to 1012 liter/mole-sec and Arrhenius activation energies, EA, that range
from 0 to 70 kcal. Some specific values of EA and A are listed in Table 5, while Table 6 presents
values of A for various types of typical reactions.
It is sometimes helpful in understanding reaction rate constants to consider the collision-
theory approximation for a bimolecular rate constant where the rate constant can be ex-
pressed as
k = p Z e'Eo/kBT
where Z is the hard sphere collision frequency, p the steric factor and Eothe energy threshold
for the reaction. The collision frequency can be found from simple kinetic theory to be
2 3
<7AB, cm /molecule-sec
TABLE 4. CONVERSION FACTORS FOR REACTION RATE CONSTANTS
B
cmVmole-sec
liter/mole-sec
cmVmolecule-sec
B
cmVmole2-sec
Iiter/mole2-sec
cmVmolecu Ie2-sec
Second-Order Reactions
A
cmVmole-sec
1
io-3
1.66X10"24
Third-Order
cmVmole2-sec
1
10'6
2.76 X 10~48
liter/mole-sec
10J
1
1.66X10T21
Reactions
A
Iiter/mole2-sec
IO6
1
2.76 X 10~42
cmVmolecule-sec
6.023 X IO23
6.023 X IO20
1
cmVmolecule2-sec
3.628 X 1047
3.628 X 1041
1
To convert a rate constant from units A to units B, multiple A by the conversion
factor found vertically below A in the horizontal row B.
-------
12
TABLE 5. TYPICAL ACTIVATION ENERGIES AND FREQUENCY FACTORS
(9)
Reaction
First-order gaseous decompositions:
Nitrogen tetroxide
Ethyl chlorocarbonate
Ethyl peroxide
Ethylidene dibutyrate
Acetic anhydride
Ethyl nitrite
tert-Butyl chloride
Methyl iodide
Paracetaldehyde
Ethylidene dichloride
Nitromethane
Azomethane
Propylene oxide
Dimethylethylacetic acid
1-Butene
Trimethylacetic acid
p-Xylene
Toluene
Second-order gaseous reactions between
stable molecules:
NO + O3 - NOz + O2
Cyclopentadiene
Cyclopentadiene + crotonaldehyde
Isoprene + acrolein
Butadiene + acrolein
Butadiene + crotonaldehyde
Isobutylene + HBr
2NOCI - 2NO + CI2
1,3-Butadiene
1,3-Pentadiene
Isobutylene + HCI
Ethylene
Propylene
H2 + 12 - 2HI
Isobutylene
Ethylene 4- H2
2HI - H2 + I2
Second-order reactions involving atoms
or radicals:
H + HBr - H2 + Br
H + Br2 - HBr + Br
CH3 + i-GHio
CH3 + n-OH10
CH3 + C2H«
Third-order gaseous reactions:
2NO + O2 - 2NO2
2NO + Br2 - 2NOBr
2NO + CI2 - 2NOCI
I + I+He-L + He
1 + 1 + Ar - I2 + Ar
I + 1 + H2 - L + H2
' I + 1 + CO2 - L + CO2 i
Activation Energy,
kcal/g-mole
13.9
29.1
31.5
33.0
34.5
37.7
41.4
43.0
44.2
49.5
50.6
52.5
58.0
60.0
63.0
65.5
76.2
77.5
2.5
14.9
15.2
18.7
19.7
22.0
22.5
24.0
25.3
26.0
28.8
37.7
38.0
40.0
43.0
43.2
44.0
1.2
1.2
7.6
8.3
10.4
0 or negative
~4
~4
0
0
0
0
Frequency
Factor
sec"1
8.0 X 10"
9.2 X 10'
5.1 X1014
1.8X1010
1.0 X1012
1.4X10"
2.5 X 1012
3.9 X 1012
1.3X10"
1.2 X1012
4.1 X 10IJ
3.5 X 10"
1.2 X1014
3.3 X1013
5.0 X 1012
4.8 X 10M
5.0 X 1013
2.0 X 10"
ml/ mole-sec
8X10"
8.5 X 10'
1 X10'
1.0X109
1.5 X 10'
9.0 X 10'
1.6X1010
9X1012
4.7 X 10'°
3.5 X 10'°
1.0X10"
7.1 X 10'°
1.6 X1010
1 X1014
2.0 X 1012
4.0 X1013
6X10"
m!2/mole2-sec
8X10'
-10"
-10'
0.34 X 10"
0.72 X 10"
0.95 X 10"
2.7 X 10"
-------
13
TABLE 6. REACTION FREQUENCY FACTORS
Reaction
2-atoms
Atom + linear molecule, linear complex
Atom + linear molecule, nonlinear complex
Atom + nonlinear molecule, linear complex
2 linear molecules, linear complex
1 linear + 1 nonlinear molecule, nonlinear complex
2 nonlinear molecules, nonlinear complex
3 atoms, linear complex
A, liter/mole-sec
10'°-1012
10" - 10'°
109-10"
10* - 1010
106 - 10"
107 - 10'
105 - 107
108
Sterk Factor
1
1(T2
10-'
io-2
10~4
io-3
io-4
io-5
where ka is the Boltzmann constant (1.38 X 10~16 erg/°K), /u the reduced mass in grams and a
the hard-sphere collision diameter in cm. For a reaction involving the collision of species A
with species B, the reaction collision diameter is
OAB = '/2(oA + OB)
and
1=^L + JL
M MA MB
where
-------
14
TABLE 7. EFFECTIVE COLLISION DIAMETERS
Molecule Effective Diameter, A* Reference
H2
02
CO
NO
N2
C02
H2O
S02
CH4
C2H6
C3H8
n-QHio
n-C5H12
n-C6Hi4
cyclo-C6Hi2
QH6
C5H5N
CHaCl
C2H4
(C2H5)20
GHsCHa
2.730
3.620
3.766
3.690
3.756
4.630
4.320
2.747
4.19
5.37
6.32
7.06
7.82
8.42
7.620
7.160
7.160
5.662
4.956
7.060
7.800
(13)
(13)
(13)
(13)
(13)
(13)
(13)
(13)
(14)
(14)
(14)
(14)
(14)
(14)
(13)
(13)
(13)
(13)
(13)
(13)
(13)
*1 A = 10'" cm.
Integrated rate equations for first- and second-order reactions are presented in Table 8.
The integrated reactions are expressed in terms of residence time (T) and the fraction of vapor
consumed in a simple isothermal afterburner system under steady-state conditions assuming
plug flow. The residence time can be calculated from
= V = aJ
r Q Q
where V is the volume of the afterburner, a and L its cross-sectional area and length, respec-
tively, and Q the volumetric flow rate. Nonisothermal conditions, kinetics involving reactions
other than those of first and second orders, and other complicating conditions lead to a need
for more detailed modeling and mathematical procedures. A compilation of integrated rate
expressions for both simple and complex homogeneous reaction kinetics can be found in the
Chemical Engineer's Handbook.'9'
Heterogeneous (Surface) Reaction Rates. The overall rate of heterogeneous reactions is
complicated because of the interaction between physical and chemical processes. Rates for
heterogeneous reactions have upper limits which depend on the rate at which reactant
molecules reach the interface where reaction occurs. The rate for a gas reaction catalyzed at a
solid surface of area S can be written in terms of molecules of F reacting per second as
r = ks S CF
-------
15
TABLE 8. DIFFERENTIAL AND INTEGRATED FORMS FOR SIMPLE-ORDER REACTIONS
Reaction Integrated Expression for Fraction of Vapor Removed
Order Differential Rate Expression (Assumes Constant Volume Reactions)
dC
~dT
F _
f. 1
dC
F _
-~
°2
c
'
i.
C°
r°r
for C° = Cf
1/2
dc
f=
^yf, r, o-')
c»Fj I L i(c»Fl"-
C?. = initial concentration of O.,.
°2 2
=
= initial concentration of fuel.
-------
16
The maximum value of the rate constant can be written as
_ , .
I 27rMF / (maximum value)
To account for the fact that all surface collisions do not result in a reaction, the above equation
can be modified to be
where p takes into account a collision efficiency and E the energy barrier for the reaction.
The reaction rate for oxidation in a catalytic bed can be written as
0-—= -k -
where z is the position in the direction of flow through the catalytic bed, S/V is the surface-to-
volume ratio of the catalytic bed, and Q is the volumetric flow rate as defined before. The in-
tegrated form of this equation expressed in terms of the fraction of the hydrocarbon removed
is
where L is the length of the catalytic bed.
In the case where mass transport effects are important in the catalyst bed it is necessary to
replace the catalytic rate constant with the effective or overall rate ke given by
where km is the rate constant for mass transfer. The overall rate constant ke approaches km in
the high-temperature limit and approaches ks, the chemical rate, at low temperatures. km is
controlled by the geometry of the catalyst bed and the aerodynamics of the flow through the
bed.
Relationships involving the Sherwood, Schmidt, and Reynolds numbers are effective for
correlating data on km. The Sherwood number (Nsh) is generally found to be a function of the
Reynolds (NRe) and Schmidt (NSc) numbers
Nsh = -jj- = f(NRe,NSc)
with
The above variables are defined below:
DI = diffusion coefficient for component i
G = superficial mass velocity, mass/area-sec
M = gas viscosity
-------
17
e = void fraction for catalyst matrix
pg = gas density
i = matrix length dimension usually taken as hole diameter.for matrices,
or effective diameter of catalytic wire or pellet.
Appropriate correlations of NSH, Nsc, and NR« for typical afterburner catalysts are presented in
Table 9. Further details on afterburner catalysts are summarized in the article by Hawthorn."0'
The variable X used in Table 9 is basically the length between boundary layer interruptions in
honeycomb matrices or the thickness of individual layers of catalyst in the bed.
TABLE 9. PROPERTIES OF AFTERBURNER CATALYSTS AND CORRELATIONS FOR
MASS TRANSPORT COEFFICIENTS'10'
Catalyst Type
S/V, ft
2, ft
X, ft
Sherwood Number Correlation
Torvex 2B ('/Hn. hexcell
honeycomb)
Thermo Comb (8-c/in.
honeycomb)
Oxycats
Metal Ribbon (D series)
Spherical Catalyst Pellets*
268 0.61 0.0091 0.0833 NSH = 3.66(1 + 0.095 NiuNsc i/X)
695
0.45
0.6
0.00345
36.5 0.515 0.0133
336 0.93 0.004
j- 0.35 - 0.4 dp
0.167-
0.333
= 2.35(1 + 0.095 NR.Nsc .2/X)0'
0.51N°R«56N§c3"
0.129 N£'Ns2-4+ 1.4 NK
*For this case the Reynolds number is defined as NRe = dpG/M where dp is the diameter of spherical catalyst pellet.
Rate Data Compilations
A survey of the literature prior to and through May 1978 was made for chemical-rate data
relevant to afterburner systems. Most of the available kinetic data were found to involve in-
dividual steps in complex reaction mechanisms; detail kinetic calculations can be made using
the more complex kinetic mechanisms, however, these calculations generally require com-
plicated computer modeling and are usually not necessary for afterburner applications. The
data reported in this compilation emphasize mainly the global or overall reaction rates which
are amenable to engineering calculations. In general, the amount of global rate data in the
literature is very limited, however, there is increasing interest in expressing combustion
kinetics in terms of global rate constants; hence, more data of this kind should become
available in the future. When global data are not available, it is often useful to extrapolate rate
constants from other data, or to use estimation procedures as described in another section of
this report.
Most all the detailed data on single-step reaction rates for complex mechanisms can be
found through the sources listed in Table 10. Common sources of new data as they become
available can be found in the references listed in Table 11. New or updated compilations are
also frequently being published by the National Bureau of Standards.5'16'
-------
18
TABLE 10. SOURCES OF REACTION RATE DATA FOR AFTERBURNERS
Author
Type of Information
Reference
NBS
Trotman-Pickenson
and Milne
Kondratiev
Baulch et al.
Baulch et al.
Baulch et al.
Engleman
Westley
Westley
Hampson and Garvin
Franklin
Westley
Walker
Wall
Shtern
McKay
Knox, Fish
Schofield
Hampson et al.
Herron and Huie
Schofield
Wilson
NBS
Aerospace
Corporation
Benson and O'Neal
Jensen and Jones
General homogeneous reaction rate data (17-21)
Bimolecular reactions (22)
Covers bimolecular and termolecular rate constants (23)
reported in literature through 1969
H2-O2 system (24)
H2-N2-O2 system (25)
Ch-Cb and CO-O2H2 systems and sulfur containing (26)
species
Methane-air combustion rate data (27)
Bibliography through June 1971 on kinetics of C-O-S (28)
and H-N-O-S systems
Bibliography on N-O-NO* systems (29)
Rate data for atmospheric species (30)
Kinetic data on hydrocarbon oxidation (31)
Bibliography on rates and mechanisms of hydro- (32)
carbon oxidation
Review of rate constants for hydrocarbon oxidation (33)
Mechanisms for pyrolysis, oxidation, and burning of (34)
organics
Mechanisms for hydrocarbon oxidation (35)
Mechanisms and rate constants for low-temperature (36)
oxidation of hydrocarbons
Oxidation of organic compounds (37)
Reaction rates for H2, O2, N2, H2O, H, O, N, OH, HO2, (38)
Oa, oxides of nitrogen, and hydrocarbons
Atmospheric species (39)
Oxygen atom reactions with organics (40)
Reaction rates for small molecules and atoms involv- (41)
ingH, O, N, C,andS
Reaction kinetics of hydroxyl radicals (42)
Pyrolysis, oxidation, and burning of organics (43)
Compilation of experimental and estimated rate data (44)
which includes many combustion reactions
Rate data on unimolecular reactions (45)
Compilation of rate coefficients for flame (156)
reactions to 1977
-------
19
TABLE 11. LITERATURE SOURCES OF CHEMICAL
KINETIC RATE DATA
Journal of Chemical Physics
Journal of Physical Chemistry
Journal of Physical and Chemical Reference Data
Combustion and Flame
International Journal of Chemical Kinetics
Combustion Science and Technology
Chemical Abstracts
Journal of the American Chemical Society
Journal of Catalysis
Chemical Engineering Science
For completeness, information on pyrolysis and pollutant-formation reactions is also sum-
marized in Appendices A and B.
HOMOGENEOUS OXIDATION REACTIONS
Homogeneous Oxidation Rate Data
The reactions discussed in this section are summarized in terms of global reaction rates.
CH4. A number of investigators have reported global rate constants for CH4.(45"50' Ex-
pressions developed by the different investigators are presented in Table 12. The equation of
Dryer and Classman is considered to be the best rate expression and is the one recommended
here for afterburner applications.
C2H6. For ethane oxidation in the presence of excess oxygen the rate expression,
—L .-I— *in7'^ ^."32,900/RT i\f-* i_j i r/-• i_j i\0.8
(•|t ~ IU G (l<~2H6jo — IC2H6J)
was obtained by Classman, Dryer, and Cohen.'51' The temperature range over which this
relationship applies is about 900 to 1050° K. A detailed 32-step mechanism for the partial oxida-
tion of ethane is described by Geisbrecht and Daubert.'52'
Higher CnH2n+2 Hydrocarbons. Flame speed and kinetic measurements indicate that oxida-
tion rates for paraffinic hydrocarbons in the series from propane (Cshh) beyond decane
(CioH22) are well within an order of magnitude of those of propane.'53'54'
The burning rate of propane has been measured in terms of CCh formation to be
dfCiHul / P V-75
—-i———;'— — "> Q V 1f>10 ^-15,000/RT rO.35 t tOA I ' \ i / 3
, - 2.9 x 10 e fo2 fco fH2o (^ 1 moles/cm -sec
-------
20
TABLE 12. GLOBAL RATE CONSTANTS FOR CH4 OXIDATION TO CO
Investigators
Rate Expression
Temperature
Range Reference
Nemeth and
Sawyer
Kozlov
Williams et al.
-6 x 1010 [CH*]'0"4 [O2] M e'57'000'117
3
mole/cm -sec
>1200°K
4 = -7 X 10" [CH4]-°'5 [02]'5 F' e-60'000/RT 1200-1400°K
mole/cm3-sec
d[CH4]
-57,000/RT
rO.5 fO.S I J__
T0 tH0-
:n — "->•-> ^ iu e rcH4 To2
mole/liter-sec ^1N1 '
f = mole fraction, and P/RT is in moles/liter
1450-1750°K
Dryer and d\£H*\ = _1Qi3j e
Classman
13.2 -48,400/RT
mole/cm3-sec
r/"ui i°-7 r/~» i°-8
[CH4] [O2]
1100-1400°K
(47)
(48)
(49)
(50)
where f represents the mole fraction.'551 The temperature range over which the data were ob-
tained was from about 1400 to 1800°K. Karim and Khan'56' have determined a global rate for
propane from heat release data. They analyzed their data using the expression
m,"' = k mf m§p"+b) e^"1 Ibm/ft3-sec
where m'", the rate of reaction per unit volume per unit time, is given in terms of the mf, the
fuel concentration, m0, the oxygen concentration, and p, the density, all in units of lbm/ft3! For
propane a and b were taken as unity and k and E were found to be 9 x 1013 and 60 kcal/mole,
respectively, below 900°K, and 3.5 X 101 and 8 kcal/mole, respectively, above 900°K. Using the'
detailed chemical kinetic mechanism of Chinitz and Bauer158' which involved 31 chemical
species participating in 69 elementary reaction steps, Edelman and Fortune'54' give the overall
rate expression for propane oxidation as
,
2]
where
k = 1.8 X 109
'•5 D°-2 ^-13,700/RT
[1111
pO-2 e
with P in atmospheres. The applicable temperature range is estimated to be from 800 to
3000°K. The above equation is based on the stoichiometric equation
C3H8 + k>2 - 4H2 + 3CO
-------
21
Complete combustion to CO2 and H2O must take into account the kinetics of the H2 and CO
reactions. A more representative expression for k,
k = 5.52 X 10" p-°'815 T e-'2-20077
has been suggested by Edelman.(5I>59) The above reaction rate expression has also been
suggested as being applicable to the overall oxidation of hydrocarbons represented by the
generalized chemical equation
with the rate given as
JC-^M - - 5.52 X 10" P~°'815 T e'12'200^ [C.Hb]a5 [O2] moles/cm3-sec
A general overall mechanism based on the above rate expression is given in Table 13.
Avery and Hart153'57' developed the equation
d[Cd4tH'°] = - [C4H,0]3/2 [02] 5.4 X 1013 e-21'000'*1 moles/cm3-sec
for butane at a temperature in the range of 800°K.
TABLE 13. GENERAL OVERALL MECHANISM FOR COMPLETE OXIDATION
OF HYDROCARBONS6
k = AT" exp(-E/RT)*
Forward
C.h
CO
OH
OH
0 +
H +
Reaction
a _ b
Hb + 202-2H2+nCO
+ OH = H -1- CO2
+ H2 = H2O + H
+ OH = O+H2O
H2=H + OH
O2 = O + OH
M+O+H=OH+M
M ~T
M "f
M "f
0 + 0 = 02 + M
• H + H = H2 + M
.H + OH=H,0+M
A
5.52 X108 ,.1/2 ^
p0.825 CcftHb L«J2
5.6X10"
2.19 X1013
5.75 X 10"
1.74X10"
2.24 X 1014
1 X 1016
9.38 X 10"
5 X 1015
1 X 1017
b
1
0
0
0
0
0
0
0
0
0
E/R
12.2 X 103
0.543 X 103
2.59 X 103
0.393 X 103
4.75 X 103
8.45 X 103
0
0
0
0
•Units: cm /mole-sec for bimolecular reactions; cm'/mole-sec for termolecular reactions.
-------
22
Roberts et al.'6" have devised a quasi-global mechanism for the vapor-phase combustion
of JP-5 fuel which they treat as C8Hi6. Their mechanism and rate constants, which take into ac-
count the formation of a hypothetical intermediate aldehyde (C^sO), are given in Table 14
Kinetic calculations at combustion temperatures showed the aldehyde to have a negligible
effect on the overall kinetics.
Nettleton'62' developed a global rate expression for hexadecane. His relationship is based
on the expression
where
k = 1014 e-'3'2(m cmVmole-sec.
The above equation is probably applicable over the temperature range from 1000 to 2000° K.
Global rate constants for a number of organic oxidation reactions complied by Seshadri
and Williams'63' are listed in Table 15. In general there is a strong similarity in the rate constants
for the different species.
Hemsath and Susey(64) have made oxidation rate-constant measurements in actual
thermal-type afterburner systems. Their rate constants which are presented in Table 16 are
based on the equation
= -k
A number of values for activation energies have been reported for various hydrocarbon
oxidation reactions. Typical activation energies for the combustion of various species in air are
given in Table 17. Falconer and Van Tiggelen'67' have observed a correlation between activa-
tion energies for hydrocarbon oxidation and the weakest C-H bond in the hydrocarbon. These
results are summarized in Table 18 and Figure 5. For unsaturated compounds, a reaction at the
multiple bond would normally control the activation energy for subsequent branching. In the
case of an unsaturated hydrocarbon containing an easily abstracted hydrogen atom, as, for ex-
ample, propylene, the reaction path with the lower activation energy would be expected to
predominate in the chain branching. By extrapolating Figure 5, an activation energy of about
20 kcal/mole might be expected for propylene, based on a carbon-hydrogen bond strength of
77 kcal/mole in the paraffinic portion of the molecule.
Longwell and Weiss'68' in combustion experiments in a spherical reactor observed the ox-
idation of iso-octane to follow a temperature dependency of \/Te"E/RT with E = 42 kcal/mole.
Overall reaction order was about 1.8 and about 0.8 order in the iso-octane. Temperatures over
which the data was obtained range from about 800 to 2500°K.
Global activation energies for reaction rates can also be obtained directly from ignition
delay data. Henein'69' has determined the global activation energies of diesel No. 2, CITE
(Compression-Ignition Turbine Engine), and gasoline fuels in the vapor phase to be 2920, 5790
and 8210 cal/mole, respectively. The cetane numbers for the above fuels are 57.5, 37.5, and 18,
respectively, with the global activation energy increasing with a decrease in the cetane
number of the fuel.
-------
23
TABLE 14. HYDROCARBON OXIDATION KINETICS
FOR JP-5 FUEL (C«H,«)(62)
C8Hi6 + O2 = 2C4H8O
2C4H8O +3O2 =8CO + 8H2
O + H2O = 2OH
2H + M = H2 + M
2O -I- M = O2 + M
OH + H + M = H2O + M
H + O2 = OH + O
O + H2 = OH + H
CO -I- OH CO2 + H
H -I- H2O = OH + H2
ki = 5 x 107 T15 e"7900/r
k2 =1 X10"T45
k3 = 5.75 X 1013 e-90
-------
24
TABLE 16. RATE CONSTANTS MEASURED IN THERMAL
. AFTERBURNER SYSTEM'64'
Preexponential Constant, Activation Energy,
Compound k, sec ' EA, kcal/mole
Hexane
Cyclohexane
Natural gas
4.5 X1012
5.13 X1012
1.65 X 1012
52.5
47.6
49.3
TABLE 17. ACTIVATION ENERGIES (KCAL/MOLE) FOR COMBUSTION IN AIR1
(65,66)
Vapor
Eictlvl
Vapor
Vapor
Acetal
Acetaldehyde
Acetone
Acetonitrile
Acetonyl acetone
Acetylene (0.9 atm)
Acrolein
Allyl alcohol
Allyl ether
Amyl acetate
n-Amyl alcohol
isoAmyl alcohol
ferl-Amyl alcohol
Amyl nitrate
Amyl nitrite
isoAmyl nitrite
Aniline
o-Anisidine
Anisole
Benzaldehyde
Benzene
Benzyl acetate
Benzyl alcohol
Bromobenzene
Buta gas
n -Butyl acetate
n -Butyl alcohol
/soButyl alcohol
sec-Butyl alcohol
tert-Butylbenzene
n-Butyl nitrite
Butyl phthalate
Calor gas
Carbon disulphide
Carbon monoxide
Cetene
o-Chloroaniline
m-Chloroaniline
m-Cresol
Crotonaldehyde
Cumene
pseudo-Cumene
cyc/oHexane
cyc/oHexanol
cyc/oHexanone
'•"/oHexene
"mene
42.0
45.4
55.0
45.8
48.9
31
35.5
39.6
32.8
37.2
48.0
48.5
48.5
19.7
17.1
23.6
48.0
35.5
30.8
40.0
47.2
36.2
44.0
49.5
50
36.5
48.4
40.0
56.4
39.4
16.5
43.4
52
27.2
78
30.8
35.9
33.9
30.9
33.6
46.7
26.9
46.4
41.7
40.0
43.2
38.1
(rans-Decalin
n-Decyl alcohol
Diacetone alcohol
Diacetyl
Dichloroethylene
2,2-Dichloroethyl ether
Diethanolamine
Diethylamine
Diethylaniline
Diethyl ether
Di-/sobutylenes
Di-isopropyl ether
Dimethylaniline
Dioxan
isoDodecane
Ethane
Ethyl acetate
Ethyl alcohol (methylated spirits)
Ethylbenzene
Ethyl bromide
Ethyl carbonate
Ethyleneglycolmonobutylether
Ethyleneglycolmonoethylether
Ethyleneglycolmonoethylether-
monoacetate
Ethyleneglycolmonomethylether
Ethyl formate
Ethyl nitrate
Ethyl nitrite
Ethyl oxalate
Formamide
Furan
Furfuraldehyde
Furfuryl alcohol
n Heptane
n-Hexane
n-Hexyl alcohol
isoHexyl alcohol
Hydrogen (0.9 atm)
Kerosine
Ligroin
Mesityl oxide
Methane
47.4
51.7
35.6
42.0
25.9
42.5
40.4
37.0
41.1
52.5
36.8
43.0
45.0
50.5
51.0
49
35.8
42.2
45.7
42.0
38.4
48.8
49.7
44.6
52.6
44.0
25.5
23.8
41.0
40.7
43.4
37.0
47.9
60.5
50.7
50.8
50.5
57
46
36.2
42.7
29
Methyl acetate
Methyl alcohol
Methylcyclopentane
Methylene chloride
Methylethyl ketone
Methyl formate
Methylpropyl ketone
Monoethanolamine
Monoisopropylxylenes
Nitrobenzene
Nitroethane
Nitromethane
o-Nitrotoluene
m-Nitrotoluene
iso Octane
Paraldehyde
40-60° Petroleum ether
80-100° Petroleum ether
(aromatic free)
100-120° Petroleum ether
(aromatic free)
p-Phenetidine
a-Picoline
Pinene
n-Propyl acetate
n-Propyl alcohol
isoPropyl alcohol
Propylene dichloride
Propylene oxide
Pyridine
Salicylic aldehyde
Styrene
Tetrahydrofurfuryl alcohol
Tetrahydrosylvan
Tetralin
Tetramethylbenzene
Toluene
o-Toluidine
m-Toluidine
Trichloroethylene
Tri-isobutylenes
Turpentine
Xylene
34.8
41.3
43.3
41.9
49.3
30.7
48.2
32.3
36.6
40.7
42.6
39.2
39.3
36.4
32.4
45.0
45.2
44.8
42.3
49.1
39.3
38.0
32.3
45.3
37.8
31.8
46.4
31.7
36.0
31.8
45.4
38.9
42.5
37.7
41.0
30.4
33.9
35.2
34.8
40.6
34.3
-------
25
TABLE 18. ACTIVATION ENERGIES FOR HYDROCARBON
OXYGEN FLAMES'67'
Hydrocarbon
Weakest C-H Bond,
kcal/mole"1
Activation Energy,
kcal/mole'1
Methane
Ethane
Neopentane
n-Butane
Isobutane
Diethyl ether
Benzene
Ethylene
Acetylene
Hydrogen sulfide
103.9
98.3
99.3
94.6
91.4
95-100
101.8
102.5, 105
121
90
38, 40, 41
39
38.3
33
30.5
38.5
40
36
32
26
45
40
3
o
35
o
I 30
o
25
Benzene.
Ethane
NeopentaneJ
n-Butane
Isobutane
85 90 95 IOO
Bond Strength, kcal mole"
I05
FIGURE 5. DEPENDENCE OF ACTIVATION ENERGY UPON BOND STRENGTH
OF WEAKEST C—H BOND(67)
-------
26
Unsaturated Hydrocarbons. Very few global rate data exist for the oxidation of un-
saturated hydrocarbons. Details on the mechanisms of olefin oxidation mechanisms can be
found in articles by Bolland'70', Bateman'71', and McKeon et al.'72). Detailed mechanisms along
with the associated rate constants have been presented by Jackimowski'73' for the oxidation of
C2H4 and C2H2. These mechanisms are summarized in Tables 19 and 20. An activation energy of
EA= 18,030 cal/mole was observed for €2^2 while a value of 34,250 cal/mole was observed for
C2H4. A more abbreviated mechanism than given for C2H2 in Table 20 has been suggested by
Shaub and Bauer."57' Peeters and Mahnen'74' have observed an oxidation rate of 10~4
mole/cm3-sec for C2H4 in a lean flame at a temperature of 1520°K. Levy and Weinberg(75f76)
have determined the activation energy for C2H4 oxidation to be about 36 kcal/mole at 1250°K
increasing to about 40 kcal/mole at higher temperatures. Induction time measurements by
White'77' showed activation energies of about 39.8 kcal/mole for CzH4, C2H2, and H:. Suzuki et
at.(78) have observed that in the temperature range from about 1000 to 1315°K the activation
energy is a function of the [OaJ/JCaH*] ratio. Their results are summarized in Figure 6. Recent
information on the modeling of the combustion of C2H2 and Cz^4 has been reported by
White and Gardiner."63'
The only data found for the higher alkenes and alkynes were for low-temperature oxida-
tion and are not applicable to the higher temperature afterburner conditions.
Aromatics. Global rate data for the oxidation of toluene based on the first-order equation
dnHC _ , -Ea/RT
—j— — ~K e nHc
dt
are presented in Table 21. The values for benzene given in the table are based on second-
order kinetics.
(73)
TABLE 19. ETHYLENE OXIDATION MECHANISM
Reaction Rate Coefficient*
H + M 1.00X10l4exp(-109000/RT)
2. C2H4 + C2H4 - C2H5+ C2H3 5.00 X 1014 exp (-64700/RT)
3. C2H5 - C2H4 + H 3.16 X 1013 exp (-40700/RT)
4. C2H3 + M - C2H2 + H + M 7.94 X 1014 exp (-31500/RT)
5. H + C2H4 - C2H3 + H2 1.10X10'4exp(-85000/RT)
6. OH + C2H4 - C2H3 + H2O 1.00 X 1014 exp (-3500/RT)
7. O + C2H4 - CH2O + CH2 2.50 X 1013 exp (-5000/RT)
8. O + C2H4 - CH3 + HCO 2.26 X 1013 exp (-2700/RT)
9. CH2O + OH - HCO + H2O 2.30 X 1013
10. CH2O + H - HCO + H2 2.00 X 1013
11. CH2O + O - HCO + OH 2.00 X1013
•Units: cm, °K, cal, mole, sec.
-------
27
TABLE 20. ACETYLENE OXIDATION MECHANISM1
Reaction
Rate Coefficient*
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
C2H2 + M
C2H2 + O2
H + C2H2 -
OH + C2H2
O + C2H2 -
O + C2H2 -
C2H + O2 -
C2H + O -
CH2 + 02
CHi + O-
C2H + H + M
HCO + HCO
C2H + H2
- C2H + H2O
C2H + OH
CH2 + CO
HCO + CO
CO + OH
HCO + OH
CH
CH2 + OH - CH + H2O
CH + O2 - HCO + O
HCO + OH - CO + H2O
HCO + H - CO + H2
HCO + O-CO + OH
HCO + M-H + CO + M
CO + OH - CO2 + H
CO + O + M - CO2 + M
H + O2 - OH + O
O + H2 - OH + H
OH + OH - H2O + O
O2 + M - 2O + M
H + H + M - H2 + M
H + OH + M - H2O + M
1.00 X 10'4 exp (-114000/RT)
1.00 X 1014 exp (-38000/RT)
2.00 X 1014 exp (-19000/RT)
6.00 X 1012 exp (-7000/RT)
3.20 X 1015 T°-6 exp (-17000/RT)
5.20 X 10" exp (-3700/RT)
1.00X10"exp(-7000/RT)
5.00 X 10"
1.00X1014exp(-3700/RT)
1.90 X 10" T0-*8 exp (-25000/RT)
2.70 X 10" I0'67 exp (-25700/RT)
Obtained from ki2 = kn
Obtained from ku = 0.5 kn
1.00X10"
1.00X1014
1.00X1014
1.26X1014
7.00 X1013 exp (-15000/RT)
4.00 X 1012 exp (-8000/RT)
6.00 X1013
5.20 X 1013 exp (-6500/RT)
1.22 X 1017 T^907 exp (-16630/RT)
2.07 X 1014 exp (-13750/RT)
5.5 X 1013 exp (-7000/RT)
2.55 X 1018 T"1 ° exp (-18700/RT)
1.00X1015
8.40 X 1021 T"20
"Units: cm, °K, cal, mole, sec.
50
-s40
30
0 2 4 6 8 10 12 14
[02]/C2H4]
FIGURE 6. ACTIVATION ENERGY FOR C2H4 OXIDATION FROM 1000 TO 1315°K(78)
-------
28
TABLE 21. GLOBAL RATE DATA FOR THE OXIDATION OF AROMATICS
Preexponential Term, Activation Energy,
Compound A EA, kcal/mole Reference
Benzene 6.0 X10H cmVmole-sec 36 (63)
Toluene 6.56 X1013 sec"1 58.5 (64)
CO. A number of investigators have determined global rate constants for CO oxidation.
The important CO oxidation reaction is
CO + OH - CO2 + H
with the direct oxidation reaction
CO + O2 - CO2 + O
being very slow: hence, CO is quite difficult to oxidize in the absence of water.
Rolke et al.(I) and Williams et al.(79) have reviewed the early global rate data for CO oxida-
tion. Selected results and more recent data are summarized in Table 22. A marked variation is
observed in the different rate constants. The only actual afterburner rate data for CO are those
by Hemsath and Susey.(64) These latter results are recommended for afterburner design
applications.
hh. A global rate for H2 oxidation in air has been given as<66)
M = - 1i6 = 10» e-5'000^ [H2] [02]"7 mole/W-sec
A more detailed mechanism has been suggested by Bowman.'81' This mechanism is sum-
marized in Table 23.
Another detailed mechanism has been suggested by Jenkins, Yumlu, and Spalding'821 for
the temperature range from 1330 to 1560°K. The reaction mechanism is given in Table 24 and
the reaction rate data are given in Table 25. Several conclusions were drawn regarding this
reaction scheme by comparing theoretical modeling calculations with the performance
characteristics of a steady-flow adiabatic stirred reaction. In the reaction scheme presented in
Table 24, reactions 1,4, and 7 are probably unimportant under all conditions. Reactions 2 and 5
are important only for near-stoichiometric mixtures. Reaction 9 is important for nearly all con-
ditions and reaction 3 is important for all but the very low equivalence ratio values.* Reaction 6
is important only for large values of the equivalence ratio. Reaction 8 is unimportant for near-
stoichiometric mixtures but even less important for very rich or very lean mixtures.
"Equivalence ratio is defined as = , .. . '"""'— . 0 > 1 is fuel rich, = 1 is stoichiometric and <£ < 1 is fuel
(lUel/air)itoichiometric
lean. Fuel and air concentrations in moles.
-------
TABLE 22. GLOBAL RATE CONSTANTS FOR CO OXIDATION
Investigators
Rate Expression, mole/cm3-sec
Temperature Range
References
Williams, Hottel, and
Morgan
= -1.8 x lO' e-2S,000/RT f f0.5 f0.5 (p/RT)2
\*\J L/9 "9
1450-1750°K
(49)
Howard, Williams,
and Fine
°-1.3x 1014 [CO] [02]1/2 [H20]1/2 e-3°.
840-2360°K
(80)
Dryer and Classman
= -3.9 X 1014 e-40,000/RT [CO]1I> [H20]0.5 ^
0.25
1030-1230°K
(50)
Hottel, Williams, Nerheim d [CO] _ n _16,
j /- i • j —n —l.^xlu e *
and Schneider dt
fo3 fm f H5o (p/RT)
°2 C0 H2U
i.8
1250-1550°K
(55)
Hemsath and Susey
df,
CO
dt
= _1023 e-IOO.OOO/RT f f 0.5
CO Oo
<1400°F (1033°K)
(64)
dfr
= _2.5 x
f0-5 sec''
>1400°F (1033°K)
(64)
All concentrations [ ] in mole/cm^, f is the mole fraction.
-------
30
TABLE 23. HYDROGEN-OXYGEN REACTION MECHANISM
(81)
Reaction
Rate constant, kt*
+ O2-2OH
+ O2~OH + O
+ H2-OH + H
H2O-H2 + OH
H2O-2OH
2.5 X 1012 exp (-19650/T)
2.2 X 10" exp (-8450/T)
1.7X10'3exp(-4760/T)
8.4 X 1013 exp (-10100/T)
5JB X 1013 exp (-9070/T)
H + H +
O + O +
Ar
N2
Ar
_N2
~Ar~
H + OH + N2
H2O
H + 0+ V
2 ' [N2
-H2 +
-02 +
Ar
N2
Ar
_N2
1 Q"
1
1-5_
3.0
4.0
X 10 y~''"
x io17 r'-°
[•Ar-l p.2-1
~ H20+ N2 0.4 x 1020r'°
IH2OJ L4.0J
TArl fi el
«HO2+ LI LO X 1015 exp (504/T)
l_ J L * J
*Units: cm, mole, sec, °K, cal.
TABLE 24. REACTION SCHEME FOR
COMBUSTION OF
HYDROGEN AND
OXYGEN'82'
Reaction
Number
Reaction
1
2
3
4
5
6
7
8
9
H2 + O2 = 2OH
H2 + OH = H2O + H
O2 + H = O + OH
H2O + O = 2OH
H+O+M=OH+M
H + OH + M = H2O + M
-------
31
TABLE 25. REACTION RATE CONSTANTS FOR COMBUSTION OF
HYDROGEN AND OXYGEN182'
(ki = Aj
Reaction j
1
2
3
4
5
6
7
8
9
Aj
8.0 X1014
2.2 X1014
1.9 X1014
2.25 X 1012
8.3 X1013
5.0X10l8r"5
4.7 X 1015 r°'23
5.3 X1015
1.2 X1017
Ej,
kcal/mole
45.0
10.3
17.9
7.75
18.1
0
0
-2.78
0.5
A-j
2.0 X1013
1.1 X1015
1.34 X1013
9.8X10"
7.6 X1012
3.7 X1014
5.1 X 1015
3.6 X1016
9.2 X1017
FH,
kcal/mole
25.0
25.49
1.838
5.88
1.0
97.36
115.0
96.37
117.73
Units of Aj are cm3, mole, sec.
Oxygenated Organics Except for some simple aldehydes no global rate data are available
for oxygenated compounds such as alcohols, aldehydes, and ketones. Information on detailed
reaction mechanisms for these classes of compounds and associated rate constants have been
summarized by Dixon, Skirrow, and Barnard.'4'
(4)
Aldehydes are often observed as intermediates in combustion processes. All aldehydes
except formaldehyde are generally found to promote combustion, however, it is doubtful that
the aldehydes are kinetically important intermediates in terms of contributing to chain
branching in hydrocarbon combustion.'831 The combustion characteristics of the saturated
aldehydes differ from those of the hydrocarbons in that their ease of oxidation does not
generally increase with increasing molecular size. For example, of the first five straight-chain
homologues, formaldehyde is the least reactive while acetaldehyde is the most reactive, and n-
butyraldehyde is less reactive than propionaldehyde while n-valderaldehyde is more reactive.
In general, most aldehydes are far more reactive than the corresponding hydrocarbon. The
fact that formaldehyde is exceptionally resistant to oxidation despite a weak C-H bond is at-
tributed to the stability of the formyl (HCO) radical. The bond dissociation energy for the HCO
radical is much higher than that in the CH3CO radical. The large amounts of CO formed dur-
ing the early stages of acetaldehyde oxidation are attributed to the low bond dissociation
energy of the acetyl radical. The fact that smaller amounts of CO are produced from
propionaldehyde and higher aldehydes indicate that the higher carbonyl radicals are thermal-
ly more stable than the acetyl radicals. Unsaturated aldehydes usually cause a marked inhibi-
tion in the early stages of reaction and an equally marked promotion in later stages. The
promoting effect increases with temperature and eventually is much greater than that of the
saturated analogs.
Most formaldehyde rate studies have been conducted under conditions where wall
effects are important. A reaction scheme suggested for the high-temperature (~850°K) oxida-
tion in vessels coated with boric acid, K2B4O7, KCI, and KBr is presented in Table 26.
-------
32
TABLE 26. HIGH-TEMPERATURE MECHANISM FOR
FORMALDEHYDE OXIDATION'84'
Reaction
Rate Constant,
cm3/molecule-sec
CH2O + O2 = HCO + HO2
HCO + O2 = HO2 + CO
HO2 + CH2O = H2O2 + HCO
H2O2 + M = 2OH + M
OH + CH2O = H2O + HCO
OH + H2O2 = HO2 + H2O
HO2 + HO2 = H2O2 + 02
7.5 X 10"" exp (-41,000/RT)
10"13
1.9X10""exp(-11,000/RT)
2.83 X 10"7 exp (-46,300/RT)
1.6 X 10"'°
1.6X10""
3X10"12
. . ~
H2O2
. ,~
HO2
wall
chain termination 10.5 sec"
chain termination 10.5 sec"
Baldwin, Matchon and Walker'851 have derived a simple rate equation for the oxidation of
acetaldehyde:
d[CH3CHOL
dt ~
1/2
[CH3CHO]3/2 [02]
ll/2
The above rate constants are associated with the following reactions:
CH3CHO + O2 = CH3CO + HO2
CH + CH3CHO = CH4 + CH3CO
(1)
(9)
(10)
Rate constant values are given in Table 27. The above reaction orders are in fairly good agree-
ment with the average experimental values of 1.5 and 0.7 for CH3CHO and O2, respectively,
however, the mechanism is not detailed enough to account for the distribution of oxidation
TABLE 27. RATE CONSTANTS FOR SIMPLE
MECHANISM FOR ACETAL-
DEHYDE OXIDATION'85'
Rate Constant, liter/mole-sec
Reaction
440°C
540° C
(1)
(9)
(10)
0.076
6.0 X 106
1.09X10
io
4.0
9.7 X 106
8.4 X IO9
-------
33
products. Around 540°C, CH4 is a major product and significant yields of C2H«, H2, and CHaOH
occur while at 440°C only minor yields of CH4 and C2Ha are produced. A detailed mechanism
for CHaCHO combustion has been suggested by Beeley, Griffiths, Hunt, and Williams.'861 The
reaction mechanism and kinetic data for the temperature, which range from about 1500 to
1850°K, are presented in Table 28. A global expression for the overall disappearance of
acetaldehyde has been given by Colket, Naegeli, and Classman1*7' as
TABLE 28. REACTION MECHANISM AND KINETIC DATA
(86)
Reaction
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
CH3CHO
CHaCHO
CHaCHO + O2
CHaCHO + CHa
CH3CHO + O
CHaCHO + OH
CHaCHO + H
CHaCO
CHa + O2
CHa + O
CHa + H
CH4 + O
CH4 + OH
CHa + CHa + M
C2H6 + M
C2H6 + OH
C2H4 + O
CH2O
CH2O + O
CH2O + OH
CH2O + H
CH2O + CHa
CHO + O2
CHO
CHO + O
CHO + OH
H + O2
O + H2
OH + H2
H + O2 + M
OH + OH
H + H + M
H + HO2
OH + CO
HO2 + CO
- CHa + CHO
- CHaCO + H
- CHaCO + H2
- CHaCO + CH4
- CHaCO + OH
- CHaCO + H2O
- CHaCO + H2
- CHa + CO
- CH2O + OH
- CH20 + H
-CH4
- CHa + OH
- CHa + H2O
- C2H6 + M
- 2CHa + M
- C2H4 + H + H2O
- CHa + CHO
-CHO + H
-CHO + OH
- CHO + H2O
- CHO + H2
- CHO + CH4
- CO + HO2
-CO + H
- CO + OH
- CO + H2O
-OH + O
-OH + H
- H + H2O
- HO2 + M
- O + H2O
-H2 + M
-OH + OH
- H + CO2
- OH + C02
Rate Constant, cm3 mole ' s"1, unless stated
Activation Energies, k) mole'1
4 X 1014 exp (-333.5/RT) s"1
5 X 1014 exp (-367.8/RT) s"1
1012 exp (-175.56/RT)
1.7X1012exp(-35.28/RT)
1013 exp (-16.72/RT)
5.25 X 1013 exp (-9.99/RT)
8.7 X 1013 exp (-28.97/RT)
2 X 1010 exp (-62.7/RT) s"1
1.2X10"exp(-41.38/RT)
2 X 1013
1.17X10l2exp(-0.2/RT)
2.0 X 10' 3 exp (-9.0/RT)
3.2 X 1013 exp (-5.0/RT)
1.54 X 1012 T1/2 X RRKM factor cm6 mole"2 s
3.2 X 1016 exp (-367.8/RT) X RRKM factor
6.5 X 1013 exp (-5.6/RT)
2.3 X 1013 exp (-2.7/RT)
10l2exp(-171.6/RT)s~I
5 X 1013 exp (-12.54/RT)
3.1 X 1014 exp (-17.72/RT)
6 X 1013 exp (-19.35/RT)
2.2X10l3exp(-21.53/RT)
4.2 X 1013 exp (-30.09/RT)
7 X 1013 exp (-79.5/RT) s"1
1X1013
3X1013
2.2 X 1014 exp (-70.22/RT)
1.8 X 1010 T exp (-35.97/RT)
2.2X10l3exp(-21.53/RT)
1.5X10l5exp(+4.16/RT)
2 X 1014 exp (-9.20/RT)
6.4 X 1017 T"1 cm6 mole"2 s"1
2 X 1014 exp (-9.20/RT)
5.6 X 10" exp (-4.51/RT)
2 X 1014 exp (-96.14/RT)
-------
34
[CH.CHO]
"'
where y = ki + 2k23 [O2]. When [02] is zero, the above expression reduces to the rate expres-
sion for pyrolysis. The rate constants for the above reactions along with those for a more com-
prehensive mechanism are tabulated in Table 29.
Methanol is more resistant to oxidation than formaldehyde. Outside of the global rate
data listed for methanol in Table 15, no information was located for other alcohols. A detailed
mechanism for methanol oxidation proposed by Bowman'88' is tabulated in Table 30.
TABLE 29. REACTION MECHANISM AND RATE CONSTANTS*" FOR THE OXIDATION
OF ACETALDEHYDE187'
No.
Elementary Reaction
Logio A n
E, kcal/mole
1
2
2a
3
4
4a
5
6
7
8
9
10
23
28
29
30
32
33
34
36
38
39
39a
40
41
42
CH3CHO-CH3 + CHO
HCO + M- H + CO + M
HCO + 02 - HO2 + CO
H + CH3CHO - H2 + CH3CO
CH3 + CH3CHO - CH4 + CH3CO
CH3 + CH3CHO - CH4 + ChhCHO
CH3CO-CH3+CO
CH3 + CH3 - C2H6
CH3 + C2H6 - CH4 + C2H5
H + C2H6 - H2 + C2H5
C2H5 - H + C2H4
CH2CHO-H + CH2CO
O2 + CH3CHO - HO2 + CH3CO
CH3O- H + H2CO
H + O2 - OH + O
H + O2 + M - HO2 + M
H2O2 + M - 2OH + M
HO2 + CH3CHO - H2O2 + CH3CO
OH + CH3CHO - H2O -I- CH3CO
CO + OH - CO2 + H
HO2 + HO2 - H2O2 + O2
HO2 + CH3-CH3O + OH
HO2 + CH3 - CH4 + O2
CH3 + H2CO - CH4 + HCO
O + CH3HCO - OH + CH3CO
CO + HO2 - CO2 + OH
15.85
12.3
13.7
-4.23
-7.22
-0.26
13.5
13.34
-0.26
2.73
13.58
13.2
13.3
13.95
14.35
15.5
17.07
12.23
14.51
3.37
13.0
13.3
12.3
-7.22
13.03
14
0
0.5
0
5.6
6.1
4.0
0
0
4.0
3.5
0
0
0.5
0
0
0
0
0
0
2.45
0
0
0
6.1
0
0
81.755
28.8
1.6
-1.36
1.72
8.28
17.24
0
8.28
5.2
38.0
35.0
42.2
30.0
16.8
-1.0
45.5
10.7
4.24
-2.18
1.0
0.0
0.0
1.72
2.3
23
(a) Expressed as k = AT" e"E/RT where A is in units of cm3, moles, sec; E in cal/mole and T in degrees K.
-------
35
TABLE 30. METHANOL OXIDATION MECHANISM*88
Reaction
Rate Coefficient, k
CHjOH + (M) - CH3 + OH + (M)
CH3 + CHjOH - CH2OH + CH4
O + CH3OH - CH2OH + OH
H + CH3OH - CH3 + H2O
OH + CH3OH - CH2OH + H2O
CH2OH + O2 - CH2O + HO2
CH2OH - CH20 + H
CH4 + OH - CH3 + H2O
CH4 + H - CH3 + H2
CH4 + O - CH3 + OH
CH3 + O2 - CH2O + OH
CH20 + OH - CHO + H2O
CH2O + H- CHO + H2
CH2O + O - CHO + OH
CH2O + M - CHO + H + M
CHO + OH - CO + H2O
CHO + H - CO + H2
CHO + O - CO + OH
CHO +M-CO + H + M
H2 + OH - H2O + H
O + H2 - OH + H
H + O2 - OH + O
OH + OH - H2O + O
CO + OH - CO2 + H
H + HO2 - OH + OH
H + OH + Ar - H2O + Ar
H + O2 + M - HO2 + M
4 X 10" exp (-34,200/T)
1.8X1o"exp(-4940/T)
1.7X10l2exp(-1150/T)
1.3X10l3exp(-2670/T)
3.0 X 1013 exp (-3000/T)
5 X 1010
3 X 109 exp (-14600/T)
6 X 1014 exp (-6290/T)
2.24 X104T3 exp (-4400/T)
2.1 X 1013 exp (-4560/T)
1 X 1014
1.2X1o"exp(-5000/T)
5.4 X 1014 exp (-3170/T)
1.35 X1013 exp (-1890/T)
5 X 1013 exp (-2300/T)
1 X 1014 exp (-18500/T)
1 X 1014
2X1014
1 X 1014
5 X 1014 exp (-9570/T)
2.9 X 1014 exp (-5530/T)
3.2 X 1014 exp (-7540/T)
4.4 X 1014 exp (-8450/T)
5.5 X 1013 exp (-3520/T)
4.0 X 1012 exp (-4030/T)
2.5 X 1014 exp (-950/T)
8.4 X 1021 T*
1.5X1015exp(500/T)
Units: cm3, mole, sec, °K.
Afterburner Calculations
Presented below are some examples showing how chemical rate data may be used to
design afterburner systems. The following examples are based on a removal efficiency of 90
percent for 1000 ppm of organic in air, and assume that complete mixing exists. Incomplete
mixing would increase the estimated residence time based on the chemistry alone.
Example 1. Methanol destruction in thermal afterburner
The appropriate rate data can be found in Table 15 to determine the rate constant for
methanol oxidation
-------
36
k = A e"EA/RT = 4.6 X 1015 e40'000'1™ T cmVmole-sec .
At 1300°F (977°K), k is equal to 5.18 X 106 cmVmole-sec. Treating the reaction as pseudo first
order, the rate expression can be obtained from Table 8
f = 1-ek,r
where f is the fraction of organic destroyed, ki is the first-order rate constant, and r the
residence time in the afterburner. The above expression can be rearranged to give T as
r = l|n/1
k.V-«/ '
The pseudo first-order rate constant is obtained by multiplying k by the oxygen concentration
(2.61 X 10~6 moles/cm3) to give ki = 1.35 X 101 sec"1. For 90 percent destruction of the methanol
(f = 0.9), the residence time is
Assuming a linear velocity of 30 ft/sec, the required length of the heat section in the after-
burner would be
L = rv = 0.17X30 = 5.1 ft.
If f were increased to 0.95, the required residence time would be 0.22 sec corresponding to L =
6.6 ft.
Example 2. Cyclohexane destruction in thermal afterburner
Rate parameters from Table 16 give the rate constant expression for cyclohexane oxida-
tion as
k = A e"EA/RT = 5.13 X 1012 e"47'600/1-987T sec'1
At 1300°F (977°K), k = 1.15 X 102 sec"1, and for 90 percent destruction the residence time is
which corresponds to a heat length of 0.6 ft for a gas velocity of 30 ft/sec.
Example 3. Toluene destruction in thermal afterburner
Based on rate data from Table 21, the rate expression for toluene is
k, = A e"E^RT = 6.56 X 103 e-58'SO(VI-9l7Tsec-1
The rate constant at 1300°F would be 5.4 sec"1 which gives a residence time for 90 percent
destruction of the toluene as
which is equivalent to a length of 12.9 ft for a linear velocity of 30 ft/sec.
-------
37
Example 4. Methane destruction in thermal afterburner
The available global rate data for methane oxidation to CO2 and H2O are expressed in two
steps
CH4 + o2 = CO + 2H2O
The first step can be represented by the equation of Dryer and Classman in Table 12
O[v-rUJ _-ml3.2 -4MOO/RT rr~,| l0.7 r-~ ,0.8 , , 3
dt e [CH«] [O2] mole/cm -sec
Step 2 can be obtained from the equation of Hemsath and Susey in Table 22
dtc°] = _10" e-ioo,ooo/RTrrni rn ,I/2 TRT] 1/2
dt IU e lc°J [°2J \~p~\ mole/cm -sec .
At 1400°F (1033°K), assuming the O2 concentration is a constant (2.469 X 10"6) the methane ox-
idation step is
d[CH4]
— -^ = -2.974 X 1(T2 [CH4]07 mole/cm3-sec
which can be integrated to give
[CH4] = (4.185 X 1(T3 - 8.921 X If/3 1)1/03
for an initial methane concentration of 1000 ppm (1.181 X W* moles/cm3). This can be com
bined with the expression for CO oxidation to give
+ 31.76 [CO] = 8.393 X 10'8 (1 - 2.132 t)07/03
d[C01
dt
for 0 ^ t ^ 0.469 sec.
Replacing the right side of the above expression with a quadratic approximation gives
d[CO]
-jp + 31.76 [CO] = 8.393 X W (1 - 4.683t + 5.438t2)
which can be integrated to give
[CO] = 3.001 X 10-' (1 - e-31 76t) - 1.328 X IQ^t + 1.437 X 10'
The formation of CO2 can be determined by integrating the expression
'
=31 .76 [CO]
to give
[C02] = 9.722 X 10-" [t - 1/31.76 (1 - e'31 76t)] - 2.109 X lO'Y + 1.521 X 10-7t3 .
Defining f as [CO2]/[CH4]Q and t as r the residence time, then
- 1.786 X10V + 1.288 X 10' r3 .
-------
38
For a removal of 90 percent of the organic (f = 0.9), a trial-and-error solution of the above
equation gives a residence time r - 0.26 sec, which is equivalent to a length of 7.8 ft for a flow
velocity of 30 ft/sec. Assuming that Step 1 leads directly to CO2 and H2O gives a residence time
of 0.234 sec which indicates that initial oxidation of the methane is the rate controlling step.
CATALYTIC OXIDATION REACTIONS
Heterogeneous catalytic oxidation of hydrocarbon vapors can be considered as falling
into two categories. These are: (1) selective or partial oxidation, and (2) complete oxidation
Selective catalytic oxidation is commonly used in the commercial production of oxygenated
organic compounds, while the intention of complete oxidation is to convert an organic com-
pletely to CO2 and H2O. A typical selective oxidation process would be the conversion of
benzene to maleic anhydride. Most of the information reported here is concerned with com-
plete oxidation or combustion in oxygen or air.
The kinetics and mechanisms of gas-surface oxidations are usually explained in terms of
the redox mechanism or the Langmuir-Hinshelwood mechanism or a combination of the two
mechanisms.'89' In the redox mechanism, the substance to be oxidized is assumed to reduce
the catalyst which in turn is reoxidized by oxygen from the gas phase. The Langmuir-
Hinshelwood mechanism assumes that the molecule to be oxidized and the oxygen are first
absorbed on the surface of the catalyst where the oxidation reaction then occurs.
The mathematical relations generally used to express heterogeneous catalytic reaction
rates fall into two classifications.'9' In one case, a power function equation of the form
r = k PA PB
is used. The reaction rate is represented by r, k is the rate constant, and the P's represent
pressure. This form utilizes the concept of reaction order. The second classification often
possesses the general functional form
kKAPA
r
KAPA + KBPB
where the K's can be interpreted either as absorption equilibrium for active sites on the
catalyst surface, or as empirical constants. Specific forms of this type of expression have been
developed by Hougen and Watson'9" for different rate controlling steps. Details on the redox
approach have been developed by Mars and van Krevelen.(92)
Empirical rate equations representing the catalytic oxidation of hydrocarbons are fre-
quently used to correlate experimental rate data.'93' Assuming ideal plug flow, an isothermal
reactor can be represented by the expression
'df=_V_
Jo r C£q
where
r = k CF Co,
and V is the volume of the catalyst bed, Q the volumetric flow rate, and f is the fraction of the
hydrocarbon or organic oxidized defined as
CF = cS(1-f) .
The zero superscript denotes the initial concentration.
-------
39
When 02 is in excess, the above equation can be written as
ff df V
o k'O
where k' = kCo2. This equation can now be rewritten in terms of f to give
1 Pf df V
J -'
k'(C°F)a 0
For a first-order reaction, a = 1, and the above equation integrates to give
The volumetric flow rate, Q, must be at the temperature of the reactor. The ratio V/Q is essen-
tially the residence time in the reactor or afterburner.
For reactions other than first order, a ^ 1
[
1
Catalysis by surfaces generally involves specific chemical interactions between a surface
and reacting gas molecules which must first become absorbed on the surface before a reaction
occurs. Of the two main types of adsorption that occur on surfaces: van der Waals and
chemisorption; only the chemisorption is sufficiently strong to influence the reactivity of ad-
sorbed molecules. Generally the heat of reaction for chemisorption is in the range from 10 to
100 kcal/mole, the same range as that observed for chemical reactions, while van der Waal ad-
sorption values are less than 5 kcal/mole. Activation energies of about 20 kcal/mole are
associated with chemisorption processes, and consequently adsorption is slow at low
temperatures. Surfaces are usually not uniform and some surface sites tend to be more reac-
tive than others for promoting reactions. Also interactions of a repulsive nature occur between
atoms or molecules adsorbed on a surface causing the heat of chemisorption to decrease with
increasing surface coverage.
Adsorption on surfaces is often represented by the Langmuir adsorption isotherm. If 0 is
the fraction of the surface covered and (1 - 6) the fraction that is bare, then the rate of ad-
sorption can be expressed as K.P(1 - 0) where P is the gas pressure and k. a rate constant. The
desorption rate can be expressed as kd0 where kd is the desorption rate constant. At
equilibrium, the adsorption and desorption rates are equal giving
1 n~ L r ~~ rvr
I — a Kd
where K is an equilibrium constant equal to k./kd. The above equation can be written as
KP
0 =
1 + KP
In a situation where the process of adsorption is accompanied by dissociation, the simple
Langmuir equation requires modification. In this case, the adsorption process can be con-
sidered to be a reaction between a gas molecule and two surface sites with the rate of adsorp-
tion being written as k.P(1 - 0)2; the rate of desorption, which is assumed to involve the reac-
tion between two adsorbed atoms, is written as kd02. At equilibrium where the rates are equal
-------
40
kfpV72-
1-0 \k/;
or
Kl/2p./2
U —
1/21/2
K1/2P
When two gases react on a surface, such as in the case of a catalytic afterburner, the above
equation must be modified to take into account the adsorption of two gases. If the fraction of
the surface covered by molecules A is 6, and the fraction covered by molecules B is 0' then the
fraction of uncovered surface is 1 - 6 - 6'. Molecules A and B are assumed to be adsorbed
without dissociation. Appropriate modifications can be made for dissociation. The rate of ad
sorption of A can be written as k,P(1 -6-6') with the rate of desorption equal to kd0 At
equilibrium the two rates can be set equal to give
0
The equilibrium absorption of B can also be represented by
_0_ = Kr
The two above equations can be solved simultaneously to give
a= KP
1 + KP + K'P'
6' =
1 + KP + K'P7 '
These equations represent what is sometimes called competitive chemisorption, which is
where both gases compete for the same surface sites. In some cases, the adsorption of the two
gases takes place on two different types of sites, in which case competition does not occur.
Surface reactions can be considered to occur in five consecutive steps:
1. Diffusion to surface
2. Surface adsorption
3. Reaction on the surface
4. Desorption of products
5. Diffusion of products away from surface.
In the case of a porous catalyst, the diffusion in the first step involves both mass transport
from the bulk gas to the external surface of the catalyst and mass transport within the internal
pore structure of the catalyst. Details on the effects of pore structure, pore diffusion, effective-
ness factors and catalyst poisoning can be found in a comprehensive article by Wheeler.'1581
The adsorption or desorption steps are most likely to be the slow or rate controlling steps
wh.ch is consistent with the high activation energies usually observed with heterogeneous
reactions. Because it is usually difficult to separate out the desorption step, Steps 3 and 4 are
usually treated as one step. This is the basis of the Langmuir-Hinshelwood mechanism. This ap-
proach is based on obtaining an expression for the concentrations of reactant molecules on
the surface, and then expressing the rate of formation of gaseous products in terms of the sur-
face concentrations. The rate is then expressed in terms of the concentrations of the gaseous
reactants.
-------
41
A less common mechanism, called the Langmuir-Rideal mechanism, assumes that the
reaction occurs between a gas molecule and an adsorbed molecule. In this case only one reac-
tant is adsorbed.
A simple unimolecular reaction can be treated in terms of the Langmuir adsorption
isotherm with the reaction rate, r, expressed as
r=k,»=k'KP
1 + KP
where k2 is a rate constant. This formulation assumes that adsorption equilibrium is not
affected by the reaction which is usually the case.
Frequently a substance other than the reactant is adsorbed on a surface reducing the
effective surface area and the reaction rate. This is called inhibition, and the nonreacting sub-
stance is called an inhibitor or poison. If the fraction of surface covered by the reactant is 0 and
the fraction covered by the inhibitor ft, then
KP
1 + KP +
and the rate of reaction is
k2KP
r
1 + KP + KiPi
where Pi is the partial pressure of the inhibitor and Ki its equilibrium absorption constant.
The rate constant k2 follows the Arrhenius expression
d_ln_k_2= E
dT RT1
and the temperature dependence of the equilibrium constant follows the van't Hoff equation
d_ln_K=_ A
dT RT5
where A is the heat evolved per mole of reactant gas in the adsorption process. If the pressure
is low, then
r = k2KP
and
dlnr = d In k2K = d In k2 din K^ E-A
dT dT dT dT ~W '
The apparent activation E.pp is then given by E - A, which is the true activation energy minus
the heat of adsorption of the reactant. If the pressure is high,
r = k2
and the apparent activation energy is equal to the true activation energy.
When a reaction is inhibited, the activation energy is changed by the heat of adsorption of
the inhibitor, which can be expressed as
d In r _d In k2 d In K _ d In Kj _ E-X + Xi
dT dT dT dT ~ RT2
-------
42
where the apparent activation energy is
E.pp = E - A + \i .
The activation energy is increased by \i because it is necessary for an inhibitor molecule to be
desorbed for a reactant molecule to be adsorbed and undergo reaction.
In the case of bimolecular surface reactions where the reaction occurs between two ad-
sorbed molecules following the Langmuir-Hinshelwood mechanism, the reaction rate
between molecules A and B is given by
(1 + KP + K'P')
nd the reactio
phase reacting with a surface molecule, then the rate expression can be written as
If the Langmuir-Rideal mechanism applies and the reaction involves a molecule from the gas
r =
KP+K'P' '
This mechanism does take into account absorption of the species at P1, however this species
when adsorbed does not react; only the gaseous molecule undergoing a surface collision
roar-tc
reacts.
When adsorption of two gases takes place without mutual displacement and the reaction
is between molecules adsorbed on two different types of surface sites, another mechanism can
be developed. The isotherm for molecules A on sites of type 1 can be represented by
1-0
and for the adsorption of molecules B on sites of type 2
The reaction rate is proportional to 66', so that
r =
(1 + KP)(1 + K'P) '
When a bimolecular surface reaction is inhibited by a substance at partial pressure, PI, the
fraction covered by A and B are
6= KP
6' =
1 + KP + K'P7 + KiPi
K'P*
' 1 + KP + K'P + Ki
which can be combined to give the reaction rate
k2KK'PP'
r = k200' =
KP + Kr + KiPi)2 '
If the inhibitor is a diatomic molecule which is adsorbed as dissociated atoms, then the cor-
responding equation is
kaKK'PP7
(1 + KP + K'P7 + KTPr)2 '
-------
43
When appropriate the partial pressures in the above relationships can be converted to
concentrations.
A summary of kinetic mechanisms for surface catalyzed oxidation reactions assembled by
Young and Greene are presented in Table 31. The integrated expressions listed in the table
are based on the expression
fdf
o r <_F^
which was defined earlier in this section.
Catalytic Oxidation Rate Data
The data presented here should be considered as only typical of the types of catalysts used
for afterburner applications. Information on catalysts actually used in afterburners is
generally of a proprietary nature available only from the catalyst manufacturers.
For complete methane oxidation, it has been found that the activity of catalytic com-
ponents'96' supported on alumina decreases in the following order: rhodium, palladium,
iridium, ruthenium, platinum, and silver. Rate data based on the Arrhenius rate equation
k = A e-E/RT
and the rate equation
r = -k CF
which can be integrated to give
k = -9|n (1-f)
v
are presented in Figures 7 and 8, and Table 32. On alumina, the activity of the metals or metal
oxides per gram of active metal decreases in the order of Pt, Pd, Cr, Mn, Cu, Ce, Co, Fe, Ni,
and Ag. Although Co3O4 is the most active catalyst for oxidizing hydrocarbons, its activity is
decreased by impregnation on alumina. In general methane is the most difficult hydrocarbon
to oxidize. Table 33 compares the temperatures needed for complete oxidation of methane, 2-
pentene, and benzene on four of the most active catalysts. 2-pentene is an easily oxidized
higher hydrocarbon while benzene is one of the most difficult to oxidize.
Mezaki and Watson"7' have investigated the catalytic oxidation of methane on a catalyst
consisting of palladium on alumina over the temperature range from 320 to380°C at a pressure
of 1 atm. The data were analyzed using a Langmuir-Hinshelwood mechanism based on the rate
expression
LS (S — 1) ksR Ko2 acH4 ao2
(1 + ao2 v Ko2 + aco2 Kco2 + 3H2o KHZO
where
= a(1 - f)P
ao2 = (b - 2af)P
aco2 = (c + af)P
3H2o = (d + 2af)P
3N2 = £ P
a = volume fraction of methane in feed
b = volume fraction of oxygen in feed
c = volume fraction of carbon dioxide in feed
d = volume fraction of water vapor in feed
-------
TABLE 31. INTEGRATED RATE EXPRESSIONS FOR SURFACE CATALYZED OXIDATION
(95)
Rate Expression
'A = «V
rA = kCF
r. = kC a
A F
'A'KpV
r = Icf* f* k
A F 02
k1CFk2C02
A IUL £ + k C
Integrated Equation
X = r ° f/up b
O F T/kLo-
^ f.
V _ 1
Q - --£ n (1 -f)
v _ cF0(1~a)r (i_a} ->
Q k(1 - a) (/ ~ ' I
r~ 0(1-»)
v UF r /* i "i
- I n fl'1~a' 1 L
Qu 1 ' ' 1
k(1 - a)Cn b >• J
°2
v - 1 in n fl
Qm ^i - T^
kC0 b
°2
V CF°f 1
V r ' !„ tl f\
6 " (k IMC k t] " '
\^ V^O' ' V^TI " 1
Comments
Empirical model
Zero order wrt hydrocarbon
Empirical order wrt oxygen
Empirical model
First order wrt hydrocarbon
Zero order wrt oxygen
Empirical model
Empirical order wrt hydrocarbon
Zero order wrt oxygen
Empirical model
Empirical order wrt hydrocarbon
Empirical order wrt oxygen
Empirical model
First order wrt hydrocarbon
Empirical order wrt oxygen
Redox model
r* =
k1cFk2Co
A [kjCo +(k1k2/k3)CF(^2 +
Oxygen adsorbs irreversibly onto catalyst surface
Gas phase hydrocarbon reacts with adsorbed
oxygen
Oxygen adsorption is the rate-controlling step
[S-] + oxygen -»• [S-Oja
[S-O] + hydrocarbon -*• [hyd.-S-O]
[hyd.-S-O] -»• [S-] + products
-------
TABLE 31. (Continued)
Rate Expression Integrated Equation
^F V n 1
r — v r* Of ' i._ /-I r\
'A 1+ kCF Q CF f - kl '" <1 - 0
_k1CFk2CO2 y 1 f n 1 1
A /i j. L. /- j /s . ^ CF f • In (1 •• f) >
li T Kjipj W k C I i J
r — ^ 1 ^ 1 In fl fl
kiCFk2c021/2 v cF°f .
r — — I /1 f\
A '/2 Q ft ~"JT ^ " ^
k1k2k3CFCO2 v 2Cp°
A (1 + k2C + k C )2 Q klk3co
1 V 3 O o ^T 2 F / "j^ K*j\^p T
> ^ O f\ ) "\
In M fl I
2k2CF° J
k1k2CpC02 , ,
r~ M+ilnMfl
A 1+k2Co2 0 h ^ k2C02y|mu r)
Comments
Langmuir adsorption model
Assuming hydrocarbon reversibly adsorbs on
catalyst surface
Rate is proportional to surface fraction covered
Independent of oxygen concentration
Langmuir adsorption model as above but
assuming empirical gas phase oxygen
dependence
Redox model assuming reversible oxygen
adsorption
Redox model assuming rate of oxygen adsorp-
tion is Yi order wrt oxygen
Langmuir-Hinshelwood dual-site model assuming
both reactants adsorbed on catalyst surface
with reaction occurring between adsorbed
species
Langmuir-Rideal model assuming equilibrium
oxygen adsorption and reaction with gas
phase hydrocarbon molecule
aS, site; O, oxygen; hyd., hydrocarbon.
-------
46
0.02 -
- 0.046
1.0 1.2 1.4 1.6 1.8
1,000/T°K
2.0
2.2
FIGURE 7. ARRHENIUS PLOTS SHOWING TEMPERATURE DEPENDENCE IN
CATALYTIC OXIDATION OF METHANE
(Activation energies are in kilocalories per mole)'96'
9.5
8.5
BO 7.5
O
6.5
5.5
Rate constants at 450°C <>>
(10~2 cc/g of metal-sec)
Pt
Cr
Ni
Pd
15 20 25 30
Activation Energy, kcal/mole
35
FIGURE 8. PLOTS OF THE LOGARITHM OF FREQUENCY FACTOR, A, AS A FUNCTION
OF ACTIVATION ENERGY FOR METAL OXIDES AND METALS
SUPPORTED ON ALUMINA(96)
(Oblique lines represent constant values of the rate constant at 450°C.
Rate constants and frequency factors are expressed per gram of
active metal.)
-------
TABLE 32. RATE CONSTANTS FOR CATALYSTS FOR THE OXIDATION OF METHANE0
Bulk Activation
Catalyst
No.
Catalyst Components and
Wt % Active Metal
Rate Constants x 10'2
Density, Energy, cc/cc-sec
grams/cc kcal/mole 300°C
450°C
cc/gram-sec
300°C 450°C
Log10 A,
cc/cc-sec
Precipitated and Sintered
6
18
9
25
33
24
19
31
20
29
14
8
1
5
22
10
7
15
28
17
23
13
32
11
21
16
27
26
Co304
ZnCrO4 (48 Zn, 27.5 Cr)
Co-ThO2-MgO-kieselguhr (24.7 Co)
CuCrO4 {33.4 Cu, 17.9Cr)
PbCr04
9.4CO-61 Fe
50 Co-26 Cu
34 Cu-30 Al
30 Cu-45 Fe
38 Fe-39 Cd
Pd on alumina (0.5 Pd)
Pt on alumina (0.5)
Co3O4 on Kaosorb clay (6.5 Co)
Co3O4 on alumina-622 (7.2 Co)
PdOonalumina-151 (3.5 Pd)
Cr2O3 on alumina-151 (3.1 Cr)
Mn203 on alumina-151 (13.6 Mn)
CuO on alumina-151 (7.0 Cu)
Pt on alumina-151 (0.51 Pt)
Co3O4 + K2CO3 on alumina-151
(2.4 Co)
CeC>2 on alumina-151 (1.2 Ce)
Co304 on alumina-151 (2.0 Co)
Fe2O3 on alumina-151 (2.9 Fe)
V2O5 on alumina (8.8 V)
NiO on alumina-151 (3.8 Ni)
Ag on alumina-151 (4.7 Ag)
MoO3 on alumina-151 (3.2 Mo)
TiO2 on alumina-151 (7.9 Ti)
0.80 16.5
0.310 15.4
0.213 19.2
0.541 23.1
1.745 25.0
Decomposition— All
1.30 21.1
1.41 18.4
0.712 22.9
1.30 13.0
1.073 30.7
Impregnated
0.765 21.8
0.861 23.5
0.636 22.2
1.186 20.9
0.851 20.9
0.817 22.6
0.912 24.4
0.836 22.1
0.775 24.6
0.845 1 8.4
0.827 28.9
0.899 21.9
0.753 30.9
0.877 23.9
0.852 31.3
0.784 50.6
0.770 35.9
0.792 32.4
7.2
-
—
-
—
Mixed Oxides
—
—
—
—
-
Catalysts
76
2.8
1.6
1.1
0.88
0.43
0.25
—
—
-
-
-
-
—
-
-
-
—
144
5.3
3.3
0.84
0.056
0.64
0.51
0.48
0.37
0.16
3960
199
90
49
39
26
21
6.4
5.5
4.0
0.79
0.75
0.61
0.43
0.13
0.073
0.069
0.069
9.0 180
17.1
15.5
1.55
0.032
0.50
0.36
0.67
0.28
0.15
99.3 5180
3.3 235
2.5 140
0.93 41
1.03 46
0.53 32
0.25 23
7.7
7.1
4.7
0.96
0.83
0.81
0.49
0.15
0.093
0.090
0.087
5.12
3.35
4.29
4.87
4.26
4.15
3.24
4.57
1.48
6.44
8.14
7.35
6.62
5.97
5.88
6.20
6.66
5.45
6.13
4.13
6.59
4.46
7.07
4.82
6.41
12.07
7.63
6.58
-------
48
TABLE 33. TEMPERATURES FOR COMPLETE OXIDATION OF HYDROCARBONS196'
Temperature for Complete
Catalyst
Number*
6
10
8
14
Catalyst
CosCX (unsupported)
Cf2O3 on alumina
Pt on alumina
Pd on alumina
2-Pentene
200
-
200
250
of Hydrocarbon, °
Benzene
200
350
200
300
Oxidation
C
Methane
400
500
400
300
•Catalyst numbers correspond to those listed in Table 32.
£ = volume fraction of nitrogen in feed
ksR = surface reaction rate constant
KCH4 = adsorption equilibrium constant of methane on catalytically active sites
Kco2 = adsorption equilibrium constant of carbon dioxide
KH2o = adsorption equilibrium constant of water vapor
K\2 = adsorption equilibrium constant of nitrogen
Ko2 = adsorption equilibrium constant of oxygen
L = total concentration of active sites
S = number of equidistant active centers adjacent to each other
f = fraction of methane oxidizer
P = total pressure
6 = LS(S-1)kSR.
Assuming nitrogen is not adsorbed and the nitrogen term in the above equation can be
neglected, the following Arrhenius parameters were determined:
\nO =
36.35 8228
R RT
= 6.71 8631
R RT
._ 9^5079
RT
Ink -
In Kn2o —
K
K
8006
RT
In the above correlations, T and R represent the absolute temperature and the gas constant,
respectively. Typical values of the above rate parameters are listed in Table 34.
Accomazzo and Nobe(93) measured heterogeneous rate constants for the oxidation of
methane, ethane, and propane over a cupric oxide-aluminum oxide (1:1) catalyst with a BET
surface area of 120 sq m/g and a mean pore radius of 65 A. The measurements were conducted
for initial hydrocarbon concentrations in the range from 650 to 5,000 ppm over the
temperature range from 313 to 591°C and gas space velocities from 6,000 to 16,000 hr~'. The
-------
49
TABLE 34. RATE PARAMETERS FOR CATALYTIC
OXIDATION OF METHANE197'
Temperature,
°C
320
350
380
e
79,700
120,000
151,000
Ko2
45,300
30,000
23,200
Kco2
54.2
50.0
36.3
KHZO
86.7
60.4
46.5
results showed that for gas space velocities up to 10,000 hr'1, 90 percent combustion was at-
tained at temperatures above 580, 500, and 480°C for methane, ethane, and propane, respec-
tively. The results indicate that the degree of oxidation increases with increased chain length.
The rate data were correlated using the following relations
rcH4 = 9.0X10loe-23'600/RTcCH4
Concentrations are in moles/cm3 and the activation energies in cal/g-mole.
In more recent work by Accomazzo and Nobe<98) with CuO:AI2O3, complete catalytic ox-
idation measurements were made on a number of hydrocarbons at initial concentrations
between 182 and 1450 ppm at temperatures from 140 to 510°C and at gas flow rates of 160, 275,
and 525 liters per hr (NTP). Empirical rate expressions of the form
r = A e"E/RT PF
were used to correlate the data. PF represents the pressure of the fuel or hydrocarbon in at-
mospheres. The appropriate reaction rate parameters are listed in Table 35. A relative com-
parison of oxidation rates are also shown in Figure 9.
Juusola et al.(99) have measured the catalytic oxidation of o-xylene over a vanadium
oxide/potassium sulfate-promoted/silica catalyst at temperatures from 290 to 310°C and con-
centrations of (0.5 to 3.0) X 10~4 g-mole/liter o-xylene and (5 to 100) X 10~4 g-mole/liter oxygen.
The data were correlated using the models presented in Table 36. Of the 5 models, Model 1
was found to offer the best correlation for the data. The rate constants for o-xylene based on
Model 1 are
, , „ _ 26,000
In k. = 11.8 -- £JT-
, , „ _ 28,000
In kr = 16.8 -- £=—
K I
which apply to the temperature range from 290 to 310°C. Rate data for the o-xylene along with
naphthalene, toluene, and benzene, based on Model 1, are plotted in Figures 10 and 11, and
listed in Table 37.
-------
50
TABLE 35. EMPIRICAL REACTION RATE
PARAMETERS'981
Hydrocarbon
A,
mole/g-sec-atm" E, cal
n
Methane
Ethane
Ethylene
Acetylene
Propane
Propylene
Propadiene
Propyne
Cyclopropane
5.53 X 102
9.20 X 103
5.82 X 10'
6.67 X 102
1.26X101
6.58 X 10'
4.44 X 10°
4.15X10°
2.12 X101
23,000
26,000
18,000
19,000
17,300
17,500
15,000
17,000
16,000
0.9
0.7
0.5
0.2
0.6
0.5
0.3
0.0
0.8
'x
O
+•>
cu
u
t-
0)
Q.
80
60
40
20
0
I40 ISO 220 260 300 340 360 420 460 500 540
Reaction Temperature, °C
Flow rate = 525 liters/hr Initial concentration = 500 ppm
1. Methane 6. Propylene
2. Ethane 7. Propadiene
3. Ethylene 8. Propyne
4. Acetylene 9. Cyclopropane
5. Propane
FIGURE 9. COMPARISON OF CATALYTIC COMBUSTION OF C, TO C3
HYDROCARBONS'98'
-------
51
TABLE 36. SUMMARY OF REACTION RATE MODELS TESTED'
Model
Assumptions
Rate Equation for
Initial Rate Conditions
A steady-state adsorption model (SSAM)—a steady state
is assumed between the rate of adsorption of oxygen
on the surface and the rate of removal of oxygen by
reaction with R from the gas phase
SSAM—additional assumption to Model 1 is made that
oxygen dissociates
SSAM—additional assumption to Model 1 is made that
the oxygen desorption rate is not negligible
Rideal mechanism—equilibrium concentration of oxygen
is assumed established on the surface, with reaction
occurring between adsorbed oxygen and gas phase
hydrocarbon
Langmuir-Hinshelwood model—equilibrium concentra-
tions of oxygen and hydrocarbon are assumed estab-
lished on the surface, with reaction occurring between
adsorbed reactants
k.C0 + n
= k.k,CR(Co)
\'/2
1/2
k.(Co))/2 + n krCR
TR =
k,i -f k.C0 + n k,CR
k,KAC0CR
KAC,
rR=-
KAC0 + KRCR)2
Nomenclature:
Co = concentration of oxygen, moles/liter
CR = concentration of hydrocarbon, moles/liter
k. = specific rate of oxygen adsorption, liter/g catalyst see (in Model 1)
K, = oxygen equilibrium adsorption constant
kd = specific rate of oxygen desorption, liter/g catalyst sec
k, = reaction rate constant, liter/g catalyst sec
KR = hydrocarbon equilibrium adsorption constant
n = stoichiometric number, moles oxygen required/mole hydrocarbon reacted
rR = rate of hydrocarbon reaction, moles/g catalyst sec.
-------
52
10
'2
10"
10'
,-4
10
-6
1.50 1.60 1.70
I/T, °K'' X 103
1.80
FIGURE 10. ARRHENIUS PLOTS OF kr FROM NAPHTHALENE, TOLUENE, BENZENE,
AND o-XYLENE
naphthalene; o, toluene; |, benzene, A, o-xylene)'
k.
io-5
I
I
1.50 1.60 I.70
I/T, °K"' X 103
L80
FIGURE 11. ARRHENIUS PLOTS OF k, FROM NAPTHALENE, TOLUENE, BENZENE,
AND o-XYLENE
O naphthalene; o, toluene; |, benzene; A, o-xylene)(99)
-------
53
TABLE 37. RATE CONSTANTS FOR MODEL 1(99)
Temperature, k., liter/ kr, liter/
Hydrocarbon °C g-catalyst sec g-catalyst sec
Naphthalene
Toluene
Benzene
Oxylene
312
335
300
325
350
350
375
400
290
300
310
1.81 X 10~5
6.17 X 10~5
1.11 X10~5
5.59 X 10~5
1.58X10"4
5.48 X 10~5
1.10X10"4
2.49 X 10~4
8.66 X 10~6
1.26X10"5
1.91X10"5
5.40 X 10~3
7.85 X 10~3
5.24 X 10~5
1.18X10"4
2.38 X 10~4
1.42X10"5
3.07 X 10~5
5.50 X 10~5
2.88 X 10~4
4.39 X 10~4
6.74 X 10~4
Benzo(a)pyrene oxidation on a mixed vanadium pentoxide-molybdenum oxide catalyst
was observed to follow a redox mechanism'951 for temperatures from 275 to 345°C;
benzo(«3)pyrene concentrations 0.002 to 0.05 g-mole/m3; and oxygen concentrations 4 to 26 g-
mole/m . The redox model assumes that the gas-phase hydrocarbon reacts rapidly with an
oxidized catalyst site to form the reaction products and the gas-phase oxygen slowly adsorbs
onto reduced sites (S):
Hydrocarbon + [S-O] ' > Products + [S-]
13Sl
[S-] + Oxygen --+- [S-O]
If it is assumed that N moles of oxygen are required for the oxidation of a mole of hydrocar-
bon, then the redox mechanism can be expressed as
ki CF k2 Co2
~
For a process where the catalyst reoxidation involves atomic oxygen, a = V2; for the molecular
process, a = 1. It appears that the experimental data favors the mechanistic model with a = 1.
An empirical correlation based on
has the reaction rate parameters listed in Table 38. In the above equation the units for rF are g-
mole/hr-kg catalyst for the values given in Table 38. The integrated form of the above equation
can be written as
w
— =
Q
where W represents the weight of catalyst, Q the flow rate, and f the fraction of hydrocarbon
oxidized.
-------
54
TABLE 38. REACTION RATE PARAMETERS
FOR THE CATALYTIC
OXIDATION OF
BENZO(a)PYRENE(95)
Parameter Value
0 (8.3±1.4)X109
E 31.9±4.3kcal/mole
a 0.20 ± 0.03
b 0.60 ± 0.05
Voltz et al. have studied the oxidation of CO and propylene on a platinum-alumina
catalyst between 200 and 370°C.(1001 The oxidation rate was found to increase with increasing
oxygen and was inhibited by CO, propylene, and nitric oxide. The rate data can be
represented by
rco = -k,, (CO)(O2)/R(0)
rc3H6 = -kr2 (C3H6)(O2)/R(0)
where
R(0) = [1 + k., (CO) + kS2 (C3H6)]2 X {1 + k.3[(CO)(C3H6)]2}x [1 + k.4 (NO)0'7] .
The concentration units are expressed as: (CO) = mole percent CO, (02) = mole percent 02;
(CjH6) = ppm propylene, (NO) = ppm of NO; k,, = intrinsic rate constant based on catalyst
volume, sec"'(O2) ; kr2 = intrinsic rate constant based on catalyst volume, sec~'(O2)~'; k,, = ad-
sorption constant for CO, (CO)"1; k>2 = adsorption constant for C3HU, (CsHU)"1; k,3 = adsorption
constant for combined effect of CO and C3H6, [(CO)(C3H6)]~2; and k,4 = adsorption constant
for NO, (NO)"1. The temperature dependency of the rate constants are given by
R(Ts + 460)
0 -L2, 3, 4)
k =
kr
Erj and Eai are activation energies in Btu/lb-mole; R is the gas constant, 1.987 Btu/lb-mole °R,
and Ts the catalyst temperature, °F. Values of the frequency factors and activation energies are
given in Table 39.
The rate for complete catalytic oxidation to CO2 of CO, C2H4, and C2H6 over Co3O4 and
Co3O4 supported on alumina was found"011 to be described by an expression
— I m n „"! «
rs — K pO2 PCO (or HC) PH2O 6
rs is the specific rate in ml (NTP) of COz formed per minute per m2 of catalyst surface, k is the
rate constant, po2, pco, PHC, and pH2o are the partial pressures in mole percent for O2, CO,
hydrocarbon and water, respectively. Kinetic parameters for the unsupported Co3O4 catalyst
-------
55
TABLE 39. REACTION RATE PARAMETERS FOR
CATALYTIC OXIDATION OF CO
AND PROPYLENE'100'
k?, = 1.83X1012 Erl/R = 22,600
k?2 = 3.80 X 1013 Er2/R = 26,200
kill = 6.55 X 10'1 E../R = -1,730
k22 = 2.08 X 1Q-3 E.2/R = -650
k°3 = 3.98 X 10'16 E.3/R = -20,900
k24 = 3.02 X 101 E.4/R = 6,720
are presented in Tables 40 and 41, while data on the alumina-supported catalyst are given in
Tables 42 and 43. For the unsupported Co3O4 it was observed that CO oxidation at 200to250°C
was severely retarded by the presence of C2H4 even though the oxidation of the latter was
negligible at low temperatures. Competition between CO and C2H4 for the surface sites is
more likely responsible for the retardation. Kinetic parameters for the oxidation of CO and
several hydrocarbons are summarized in Table 44 and Figure 12.(I02)
Afterburner Calculation
An example of a design calculation for a catalytic afterburner system is given below.
Example 5. Toluene destruction in catalytic afterburner
Toluene oxidation over a V2O5-type catalyst can be represented by the relationship
1 dcr _ k, kr Co2 CT
Wc dt ka Co2 + n kr CT
from Table 36. Wc is the weight of catalyst per liter and n is defined by
C6H5CH3 + nO2 = 7CO2 + 4H2O
where n = 9. The above expression can be integrated to give
_ n CT ,. 1 . ,- „
Extrapolating the rate data in Figures 9 and 10 to 1000°F (811°K) gives
kr = 1.330 X 10~2 liter/g-catalyst sec
k. = 1.820 X 10"' liter/g-catalyst sec
Wc = 880 g-catalyst/liter.
At 1000° F and 1000 ppm of toluene
co2 = 3.144 X 10~3 mole/liter
CT = 1. 504 X10"5 mole/liter
for which a residence time of 0.20 sec can be determined from the above equation. In the case
of the thermal afterburner (Example 3) a residence time of 0.43 sec was required at 1300°F.
-------
56
TABLE 40. KINETIC PARAMETERS OVER Co3O4(101)(a)
Reactant
CO
CO
C2H4
GH6
Temperature
Range, °C
150-200
300-350
275-450
300-450
0.3
0.1
0.35
0.3
I
±0.1
±0.1
±0.1
±0.1
0
0
0
0
m
.46 +
.10 ±
.29 +
.33 +
0.12
0.04
0.07
0.07
n
0.45 ±
0.93 ±
0.51 ±
0.62 ±
0.10
0.10
0.10
0.08
f
0
0.3 + 0.1
0
0
E,
kcal/mole
20 +
5 +
23 +
21 ±
2
2
?
2
(a) Rate = k(Po2)ra(pCo 0, Hc)"(pH2o)'(flow rate^e'*"7.
TABLE 41. SPECIFIC RATES OVER Co3O4
1101 Hal
Catalyst
Co3O4l
C0304II— 600° C
(diluted with
Linde A)
Co3O4ll— 850° C
Co3O4lll— 600°C
Co3O4lll— 850°C
CoAl2O4
Surface
Area,
m2/g
0.44
10
0.93
5.0
1.2
11.3
CO
T,
°C
150
200
300
150
200
300
150
200
300
150
200
300
150
200
300
300
+ 02
R,
ml CO2/
min-m2
2.2
28
70
1.0
17
120
1.1
20
60
2.3
28
95
1.2
21
35
0.003
C2H4
T,
°C
300
350
400
300
350
400
300
350
400
300
350
400
300
350
400
400
+ O2 C2H6 + O2
R, R,
ml CO2/ T, ml CO2/
min-m °C min-m2
0.3 400 0.6
1.8
10.5
0.3 400 1.3
1.3
4.3
0.4 400 0.8
1.5
5.0
0.45
2.2
9.5
0.3
1.1
3.5
0.0005
(a) CO + Oi, 1% 02,1% CO, 0% H20; C2H4 + O2,1% O2, 0.1% C2H«, 0.1% H2O; C2H6 + O2,1% O2, 0 1% C2H«,
0.1% H2O.
-------
57
TABLE 42. KINETIC PARAMETERS OF OXIDATIONS OVER SUPPORTED
Co3O4 CATALYSTS' 101)(')
Temperature
Reactant Range, °C 1 m n
f
E,
kcal/mole
600° C Pretreatment (25-60 m2/g)
CO
CO
C2H4
C2H6
125-200
250-350
300-450
300-450
0.44 ± 0.11
0.25 ± 0.1
0.4 ± 0.1 0.26 ± 0.08
0.35 ± 0.1 0.24 ± 0.04
0.47 ± 0.14
0.90 ±0.1 3
0.39 ± 0.04
0.53 ± 0.05
0
~0.5
0
0
15 ±1
3-7
20±2
18.5 ± 1
850°C Pretreatment
CO
CO
C2H4
C2H6
150
300
350-450
350-450
0.31 ± 0.07
0.16 ± 0.1
0.3 ± 0.1 0.31 ± 0.07
0.4
0.38 ± 0.11
0.80 ± 0.07
0.47 ± 0.08
0.48
—
—
0
—
10 ±2
—
16 ±2
21
(a) Rate = k(po2)'°(pco or Hc)°(pH2o)'e
l.-E/RT
I.6 I.7
I.8 I.9 2.0
1/T X103
2.I 2.2
FIGURE 12. ARRHENIUS PLOTS FOR OXIDATION OVER NiO(102): O C2H4, 2.5%;
02, 6.2%; H20, 0.4%; (+) C3H6, 0.8%; O2,3.5%; H20,0.4%; (8) C3H6,3.2%; O2,7%;
H20, 0.5%; (•) C4H8-1,1.8%; O2, 5.3%; H2O, 0.5%; (D) C3H8,0.4%; O2, 3.6%;
H20, 0.3%; (A), C3H6,1.6%; O2,2.5%; H20,0.25%; (A) CO, 2.1%;
O2, 2.7%; H20,0%
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58
TABLE 43. SPECIFIC RATES OVER SUPPORT Co3O4 CATALYSTS
wt%
Catalyst Co3O4
Co3O4-DAL(1) 25.2
Co3O4-DAL(3) 45
Co3O4-DAL(4) 10
Co3O4-DAL(6) 13.1
Co3O4-DAL(10) 9.8
Co3O4-DAL(11) 8.4
Co3O4-DAL(13)(c)— 10.1
600 C
Co3O4-DAL(13)(c)— 10.1
850 C (1 day)
Co304-DAL(13)(c)— 10.1
850 C (3.5 days)
Co3O4-Linde A 9.2
Co3O4-Linde B 15.4
Co3O4-Mullite 9.1
Co3O4-Cab-O-Sil 13.3
Co3O4-AI2O3(k)(lmN) 10.4
Co3O4-AI2O3(lmNl) 17.2
Co3O4-Al2O3(lmNN) 3.3
Co3O4-AI2O3(lmA) 5.5
Co3O4-Al2O3(F) 6.05
(ImNN)
Co3O4-DAL(1) 25.2
Co3O4-DAL(3) 45
Co3O4-DAL(6) 10
Co3O4-DAL(10) 9.8
Co3O4-DAL(11) 8.4
Co3O4-Linde A 9.2
Co3O4-Linde B 15.4
Co3O4-Al2O3(lmNN) 17.2
Co3O4-Al2O3(lmA) 5.5
(a) Rate in ml CO2/min-g Co3O4.
(b) 1% O2, 1% CO, 0% H2O.
(c) Co3O4 III— 850 C used as starting
(d) 1% O2, 0.1% C2H4, 0.1% H2O.
(e) 1%O2, 0.1% C2H6, 0.1% H2O.
CO + 02(b)
Riso°c RMO°C
600°C Pretreatment
90 900
46 530
45 1000
75 940
105 700
120 600
6.7 20.5
23.5 105
21 80
140 1000
61
- ~-|
4
- 2
0.3
70 180
12 44
60 450
850°C Pretreatment
33 100
20
27 90
17 74
27 91
20
~6
13 40
11 43
material.
C2H4H
R3so°c
41
28
42
38
29.5
19
0.1
0.5
—
20
6.9
—
—
—
—
1.6
0.6
20.5
3.2
1.6
1.8
1.3
1.7
—
—
—
0.4
H 02(d) C2H6 + 02«>
R«0°C R«M°C
102 12
65
102 14
122 15.5
90
48
0.4
3.6
3.0
—
18
1.6
—
0.6
0.3
8.1
1.35
55
0.8
0.9
3.4
4.2
—
—
—
0.05
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59
TABLE 44. KINETIC PARAMETERS FOR HYDROCARBON OXIDATION OVER NiO(l)(102)U)
Reactant
m
n
(a) Temp, 250-400°C; rate of CO2 produced = k(po2)rapHc"pH2o1.
E, kcal/mole, °C
C2H4
C3H6
C4H8-1
trans-C4H»-2
i-C4H8
C2H6
C3H8
CO
0.33
0.27
0.35
0.33
0.35
0.27
—
0.26
—
0.47
0.53
0.55
0.48
0.58
0.44
0.07
0.29
0.47
0.33
0.23
0.14
0.20
0.10
0.50 (350°C)
0.95 (240°C)
0.53
0.55
25.4
25.0
24.7
~25
~25
17.0
6.8
21.0
~7
25.1
15
(250-400)
(250-400)
(300-350)
(300-350)
(300-350)
(>270)
(<270)
(>230)
(<230)
(>220)
(<220)
ESTIMATION PROCEDURES FOR CHEMICAL
KINETIC RATE DATA
The development of the theory of chemical-reaction rates has received considerable
attention in the past and promises to be an area of intense activity in the future. Theoretical
methods for accurately predicting chemical rate constants are extremely complex to apply and
are only successful for a limited number of very simple reactions. No attempt is made here to
delve into the detailed quantum-mechanical aspects of chemical kinetics. Major emphasis is
on the presentation of simple estimation procedures that can be easily adapted to the design
and analysis of afterburner systems. The estimation procedures presented here are for gas-
phase homogeneous reactions. A recent collection of papers summarizes the current status of
the theory of elementary gas reactions.11991
There are several sources that cover procedures for estimating kinetic rate constants for
combustion reactions."21"127' These references can be consulted for details beyond those
covered here. The approach outlined in this report for estimating oxidation rate constants for
organics is based essentially on modified collision theory.
REACTION RATE THEORY
The simple collision treatment of chemical reactions is based on hard sphere collisions
and suffers from the fact that the internal states of reactants are neglected. A more realistic
theory which has improved the quality of calculated rate constants is commonly called the
transition-state theory. In this approach an attempt is made to follow a reaction in terms of the
changes in potential energy of the reactants and products as they approach each other and
then separate. Unimolecular reactions which typify hydrocarbon pyrolysis can with some
degree of success be treated as a special case of transition rate theory.
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60
From transition rate theory"28', the parameters in the standard rate expression
k=Ae-Ea/RT
can be written as
'ekBTm\ -AS*/R
and E, = AH * + RTm
where Tm is a mean temperature, ks is Boltzmann's constant, and h is Planck's constant. AH*
and AS* are the enthalpy of activation and the entropy of activation, respectively, for the
transition-state complex. In order to determine the thermodynamic parameters of the
transition-state complex it is necessary to know its structure, which is the main limitation in try-
ing to use transition-state theory to obtain practical rate constants. It is often possible to make
good estimates of AS*; however, determination of AH* requires a very detailed knowledge of
the potential energy surface as a function of reaction coordinates. Detailed procedures for es-
timating AS* and AH* for combustion reactions can be found through correlations in
References (125) or (126).
Unimolecular Reactions
In the case of unimolecular reactions the frequency factors, A(AS*), can be estimated with
reasonable success. For the simple removal of an atom from a molecule, the entropy increase
in going to the transition state is usually in the range of 0 to 9 cal/mole. This is equivalent to an
A-value in the range from 10135 to 10 sec1. A more accurate value may be determined by
taking into account whether a light or heavy atom is being removed, or whether multiple
bond formation occurs in the transition state. For detachment of a hydrogen atom from
ethane, 3.6 < AS* < 7 cal/mole-0K and 1014 < A < 6 X 1014 sec"1. If the atom being separated is
relatively heavy such as in the case of the removal of I from CH3I then A ~ 1015 sec" . In cases
where internal changes occur with bond breaking such as in the case of
C2H5 - [H2C — CH2 -- H]* - C2H4 + H
then A ~ 2 X 1013 sec"1. Activation energies of these types of reactions can often be estimated
from the reverse reactions which are about zero for atom-radical reactions and about 2
kcal/mole for atom-molecule reactions of this type. When fission produces two polyatomic
fragments as in the case of
C2H6 - CH3 + CH3
there is a large entropy increase in going from the reactants to the transition state. Most of
these reactions have AS* values of around 11.5 cal/mole°K, which corresponds to an A of
about 1016 sec"1. If the products are stiffened by double bond formation, then the value of A
will be reduced. Activation energies for simple fission reactions can be estimated from
EA (unimolecular)= AE? = AE2°98 +<&Cv> (T - 298°K) .
This is based on the fact that the activation energy of the back reaction, the recombination of
two free radicals, is zero. Strength of the bonds being broken is given by
AHm = AH? (products) - AH? (reactants)
and
= AH° - RT .
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61
where Cv is the constant volume heat capacity and
ACS = r C$ (R) + q C$ (Q) - a C$ (A) - b C$ (B)
based on the chemical reaction
a A + b B- r R + qQ .
Thermodynamic data can be obtained from the JANAF Thermochemical Tables or other com-
pilations of thermodynamic data. General information on a number of organic substances is
given in Table C-1 in Appendix C.
Fissions where two or more bonds are broken and two or more bonds are formed are
generally divided into three classes: four-center, five-center, and six-center reactions. Four-
center reactions which have 4 cyclic transition states such as in the case of the reaction C2H5I -
C2H4 + HI have frequency factors of 10I3±1 sec"1, while five-center reactions, such as C2H5NO2 -
C2H< + HONO have frequency factors of about 1012 sec"1. Six-center reactions fall into 3
groups. In ethers, such as ethyl vinyl ether, where there is nearly free rotation about the vinyl
C-O bond, A is equal to around 3 X 10" sec"1. With esters, where the acyl C-O bond has a
large torsion barrier, the frequency factors run around 3 X 1012 sec"1. On the other hand, for
the pyrolysis of symmetrical trioxanes the A values are about 3 X 1014 sec"1.
A large number of complex fissions occur through rather complex mechanisms involving
biradicals Th.s type of reaction includes the pyrolysis of ring compounds. The simplest reac-
tions involving a biradical transition state are cis-trans isomerizations. For this type of reaction
frequency factors lie in the range from 1011 to 3 X 1013. Further details on the use of transition-
state theory may be found by consulting the paper by Golden"21* and the accompanying
references. A detailed method for estimating Arrhenius A factors for four- and six-center
unimolecular reactions is given by O'Neal and Benson."64'
Bimolecular Reactions
Gas-phase bimolecular reactions can be classified as three main types: atom transfer ad-
dition to double bonds, and association reactions. These types of reactions are often exother-
mic producing products in vibrationally excited states which must be deactivated through
collisions or the products will react further or revert to the original reactants.
From transition-state theory, the frequency factor, A, for a bimolecular reaction is given
by
h
where AS* is the entropy change for forming the transition state from the reactants There is
always a loss of entropy in going to the transition state A + B -AB*, so AS* is always negative
An upper limit for A is about 10ILS liter/mole-sec at 600°K, which corresponds to the gas
kinetic collision frequency. °
For a wide variety of metathesis reactions involving atoms the A's fall in the range from
10 to 10 M sec with minimum values all above 1010 M"1 sec"'. Reactions between
radicals and molecules have A's in the range of 108 M"1 sec"1. A-values for an abstraction or an
addition to a double bond are in the range from 10105 to 1011 ° M"1 sec"1. Reactions involving
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62
the association of two free radicals have A's falling from 10V to 1010 M"1 sec"1. Frequency factors
for association reactions also can be estimated from the A's for the reverse unimolecular
process and the equilibrium constant for the reaction.
There is little difference between the activation energies for bimolecular reactions of
atoms or polyatomic radicals. In the case of both abstraction and addition of atoms and
polyatomic radicals to double bonds, the activation energy, to a good approximation is 8 ± 3
kcal/mole plus an endothermicity. Exceptions are the reactions involving very reactive
halogen atoms, which have activation energies in the range from 0 to 5 kcal/mole, and radical-
radical combination and disproportionation reactions which have values of the order of zero.
Several procedures have been reported recently for estimating activation
energies.1'27'129"131'
The intrinsic activation energy of a reaction, defined as the activation energy in the ex-
othermic direction, is a measure of the amount by which the electron clouds around the reac-
tants must be deformed so that the reaction can proceed. Intrinsic activation energies for the
three different bimolecular reactions are given in Table 45. It has been found by Alfassi and
Benson"291 that for the reaction
A + BC ~ (A-B-C)* - AB + C + energy
the intrinsic activation energy can be correlated using the empirical relationship
EA (intrinsic) = 13.0-3.301
where I is the sum of the electron affinities in eV of A and C with EA (intrinsic) in kcal/mole.
Negative values of EA (intrinsic) are taken as zero. Taking into account the exothermicity of the
reaction, AHr, the expression can be improved in the form
.... . . . 14.8-3.641
EA (mtrmsic)= - .
A simpler and improved form is given by the bond additivity relation
EA (intrinsic) = XA + Xc
where XA and Xc are additive group contributions. Best results are found with the expression
EA (intrinsic) = (FA) (FB) .
Values of electron affinities, X's and F's are presented in Tables C-2 and C-3 in Appendix C.
TABLE 45. INTRINSIC ACTIVATION ENERGIES FOR BIMOLECULAR REACTIONS'
Range of Intrinsic
Reaction Class Electronic Structures Activation Energy, kcal/mole
Molecule + molecule Two closed shells 20-50
Radical-I-molecule One closed shell/one open shell 0-15
Radical + radical Two open shells 0
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63
ESTIMATION PROCEDURES
There are also a number of procedures that can be used for estimating rate constants
when experimental data are unavailable. If data are available at temperatures other than those
in the range of interest, it is sometimes possible to apply extrapolation procedures. One com-
mon method for extrapolating data is to use a plot of the logarithm of the rate constant versus
the reciprocal of the absolute temperature. When the rate data have been correlated in terms
of an Arrhenius equation such as k = A e"1/R1, the procedure is equivalent to using the equa-
tion over a greater temperature range than that covered experimentally.
If reaction rate data are available for the reverse direction of a reaction, it is possible to ob-
tain rate data for the reaction proceeding in the forward direction through use of the
equilibrium constant for the reaction."33' As an example, consider the reaction
aA + bB r cC + dD .
k,
The equilibrium expression is
K = (C)c(P)d
(A)a (B)b '
where K is the equilibrium constant. The rate of the forward reaction can be expressed as kr
(A)a (B)b, while the reverse reaction is given as kr (C)c (D)d. At equilibrium the forward and
reverse reaction rates are equal
k,(A)a(B)b = kr(C)c(D)d ,
which when rearranged give the ratio
kr = (C)c(P)d
kr (A)'(B)b '
where
Thus, if either the reverse or forward reaction is known it is possible to determine the op-
posing reaction rate assuming the principle of microscopic reversibility to be valid.
Theoretical Procedures
Reaction rates may also be estimated on the basis of theoretical considerations. In con-
sidering the derivation of a reaction rate constant, it is often convenient to express it in the
following form
where A is a constant and EA is the Arrhenius activation energy.
For the purpose of afterburner design applications it is recommended that when rate con-
stants cannot be inferred from experimental data, the rate constants be calculated using sim-
ple collision theory augmented by appropriate transition-state corrections. The more com-
plicated theoretical procedures that are available require very expensive computer
calculations and usually do not warrant the effort.
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64
For the simple bimolecular reaction
A+B-C+D
the differential rate equation is
-dCA = -dCB _ dCc _ dCD
dt dt dt dt
_ ,
keA<~
where C represents the species concentration and t is the reaction time. The collision rate of
molecules A and B in a gaseous mixture can be expressed using kinetic theory as
z = (JAB (87rkBT)1/2 I * . . B I nAnB collisions/(sec)(cm3) ,
\ MA MB /
a = molecular diameter, cm
M = molecular weight, g per molecule
kB = Boltzmann constant, 1.38 X 10~16 erg per °K.
The n's represent particle number density.
The equation for z can also be expressed in terms of the gas constant as
/M + M \ l/2
z = OAB (87rRT)1/2 ( * ., runB collisions/(sec)(cm3) ,
\ MA MB /
where
R = gas constant, 8.314 X 107 erg/(°K)(g mole)
M = molecular weight, AMU
Collision diameters for a number of the species of interest in this study are listed in Table 7.
When data are not available, the collision diameter may be approximated using the equation
a = 1.18VB/3 ,
where VB is the LeBas volume or the molal volume at the normal boiling point."34' For organic
compounds, VB can be calculated by adding together the appropriate values for each of the
constituent elements given in Table 46.(135) As an example, the atomic volume of C2H6 can be
calculated to be 2 X 14.8 + 6 X 3.7 = 51.8 cm3 per g-mole.
Correlation techniques for determining molecular volumes of hydrocarbons have also
been developed by Kurtz and Sankin."37'
Hard-sphere collision diameters can also be determined from the Lennard-Jones
parameters. A procedure for these calculations taken from Gardiner's book<8) is outlined in
Table C-4 in Appendix C. Lennard-Jones parameters for a wide variety of compounds are
given in Table C-5.
Not every collision results in the transformation of reactants into products, since only the
more energetic collisions with certain orientations between reacting species lead to a reaction.
From Maxwell's distribution law the fraction of all bimolecular collisions that involve energies
above a certain minimum energy is given approximately by
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65
TABLE 46. ADDITIVE VOLUME INCREMENTS FOR
ESTIMATING MOLAR VOLUMES AT
THE NORMAL BOILING POINT035'136'
Atomic Volume,
Element"" cm3 per g mole
Bromine 27.0
Carbon 14.8
Chlorine
Terminal, as in R-CI 21.6
Medial, as in R-CHCI-R 24.6
Fluorine 8.7
Hydrogen
In compounds 3.7
In hydrogen molecule 7.15
Nitrogen
Double-bonded 15.6
In primary amines 10.5
In secondary amines 12.0
In nitrogen molecule 15.6
Oxygen
Double-bonded 7.4
In aldehydes and ketones 7.4
In methyl esters 9.1
In ethyl esters 9.9
In higher esters and ethers 11.0
In acids 12.0
In union with sulfur, 8.3
phosphorus, nitrogen
Iodine 37.0
Sulfur 25.6
(a) For benzene ring deduct 15; for naphthalene ring deduct 30.
where R is the gas constant, T the absolute temperature, and Eo is an energy term. The orienta-
tion factor, or steric factor, will be discussed in more detail below. If Eo is expressed in calories,
then R is equal to 1.987 cal/(g mole)(°K). For the bimolecular reaction, the disappearance of A
may be expressed as
dnA / it-• * v ../fraction of collisions involvingX ^ ,../.,
- —r- - (collision rate) X . . e ] x (steric factor
dt \ energies in excess of Eo j
= o-2AB (87rRT)1/2 [(MA + MB)/MAMB]1/2 nAnB p
= k nAnB .
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66
Therefore,
k = a2AB (87rRT)1/2 p(MA + MB/MAMB)1/2 e"E<)/RT
= Z'pT1/2 e"E°/RT cmV(molecule)(sec) ,
where
'/2 cm3/(molecule)(sec)(K''2) .
MAMB
If the rate equation is expressed as
Ar.
= kCACB ,
dCA
dt
where CA and CB are in units of g moles per liter, then
T = A, (WIT £ C*^)"1 li.er/(mole,(sec)) ,
where
N = Avogadro's number, 6.023 X 1023 molecules/g mole and
aAB is still expressed in cm. Making the appropriate substitutions:
" M* + ™B 1/2
Z' = 2.76 X 10" OAB * B liter/(mole)(sec)(K1/2) .
Approximate values for the steric factors based on transition-state theory for various types
of reactions are summarized in Table 6.
Several techniques have been proposed for estimating activation energies for bi molecular
reactions. These techniques have been reviewed by Laidler and Polanyi"42' and Szabo(143|.The
most popular method of estimating activation energies is that suggested by Evans and
Polanyi."441 They found that for a series of closely related compounds the activation energy is
proportional to the heat of reaction. Semenov"4 ' has shown that for a number of exothermic
abstraction reactions the activation energy, EA, is approximately related to the heat of reaction,
AH, by
EA = 0.25 AH + 11.5 .
A less reliable method has been proposed by Hirschfelder."46' For an exothermic reaction of
the type
A + BC = AB + C ,
the activation energy follows roughly the relationship
EA = 0.055 DB ,
where DB is the dissociation energy of bond BC. If the reaction is endothermic, it is best to
calculate E for the reverse reaction from which EA can be calculated for the forward reaction.
Szabo(143'l47) has developed an empirical formulation for a homogeneous gas reaction based on
the energies of the bonds broken and the bonds formed where
EA = Z Di (broken) - a 2 Dj (formed) ,
j
and a is a constant for a given type of reaction. Values of a have been determined for several
homologous series of reactions."47' Values of a for several classes of reactions are tabulated in
Table C-7 in Appendix C.
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67
Bond energies or strengths for a number of simple bonds in small molecules are tabulated
in Table C-8. A technique developed by Szabo(7) can be used to calculate strengths for bonds
in large molecules. This approach is based on the bond strengths and decrements given in
Table 47 and takes into account the fact that bond strength between two atoms is influenced
by the adjacent atoms and groups. For example, the strength of the n-CjHv-ChhCeHs bond is
calculated from the values in the table as
161-4X13-16-34 = 59kcal .
The^ general theory of three-body reactions is not well established and very difficult to
apply.048 50) It is sometimes of interest in estimating three-body reaction rates to know the
number of three-body collisions occurring in a reacting system. The number of triple collisions
per unit time and volume has been derived by Tolman' ' as
= nAnBnc(4B,,W.c)S. + collisions/lessee,
where the n's are concentrations in terms of molecules per cm3. This equation assumes that
the colliding species are rigid elastic spheres and that a collision exists when these spheres are
within a small distance, 5, of each other. It is also assumed that 6 is much smaller than the
diameter of a molecule and is in the neighborhood of about 1 X. Upper limits have been
calculated for 6 for several different reactions which are listed in Table 48.(152> For the third-
order reactions
A + B + C — products ,
the differential rate equation is
dnA
dt
= - k nAnBnc
Assuming a collision efficiency factor of pe"E°/RT, the rate constant may be determined from
the collision frequency as
k = (4™AB)
The ternary collision rate per unit volume has also been expressed by Moelwyn-Hughes"31
as the collisions of the molecular pair AB with all the C molecules. On this basis the collision
equation is
where r represents the corresponding molecular radius.
In considering atomic recombination, two mechanisms have been postulated to account
for experimental observations. At low temperatures, it appears that the principal mechanism
involves first the combination of an atom with a molecule, forming a loose complex. Then a
second atom collides with the complex, forming a diatomic molecule and the original
molecule. At high temperatures, though, the principal mechanism appears to involve the
direct single three-body collision as described by the Tolman or Moelwyn-Hughes collision
equations covered in the preceding paragraphs.
The techniques just described are not intended to always produce accurate information.
Often they do prove to be of value, though, when a kinetic analysis is attempted for situations
where only a portion of the data is available. It is also sometimes valuable to be able to assess
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68
TABLE 47. CONVENTIONAL BASIC VALUES AND
DECREMENTS FOR THE CALCULATION
OF BOND STRENGTHS
Conventional Basic Values in kcal
=c-c=
=C-H
=C-F
=C-CI
=C-Br
=c-i
=c-o-
=c=o
161
142
147
120
106
93
147
200
=c-s-
=C-N=
-s-s-
-S-H
-o-o-
-0-H
=N-N=
127
145
103
104
66
123
112
Decrements in kcal
-H
-F
-Cl
-Br
-o
=O
=N
-CH3
=CH2
=CH
-CH2CI
-CHCI2
-CCI3
-C2H5
13
14
19
18
22
33
18
15
25
11
22
32
42
16
-CH=CH2
-COCHj
-CH2C(CH3)=CH2
-OC(CH3)3
-C6H5(a)
-C6H5
o-C6H4CH3
m-C6H4CH3
p-C6H4CH3
(o,m,p)-CH2GH4F
-a-naphthyl(a)
-j3-naphthyl(a)
9-phenanthryl(a)
9-anthracyl(a)
36
18
37
15
32
34
41
39
40
38
35
36
38
40
(a) A carbon atom in the aromatic ring forms part of the affected bond.
TABLE 48. UPPER LIMITS FOR d IN
TOLMAN'S THREE-BODY-
COLLISION EQUATION052'
Reaction 8, cm
H + H + H - H2 + H 5 X 10~9
H + H + H2 - H2 + H2 5 X 10"'°
O + O + O2-O2 + O2 5X10""
N + N + N2-N2 + N2 5X10""
O + O2 + O2-O3 + O2 5X10""
H + O2 + H2 - HO2 + H2 6 X 10
~14
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69
the importance of a particular reaction in an overall reaction scheme by either estimating the
value of the rate constant or establishing an upper limit for it. This information may be used to
determine the conditions for which a particular reaction is unimportant to the overall reaction
scheme, or it may aid in choosing which particular reactions must be studied in the laboratory
to develop a kinetic model of the overall reaction scheme for a complex chemical system.
PROCEDURES FOR RAPID ESTIMATION OF KINETIC DATA
Rate constants may be estimated on the basis of the modified Arrhenius expression
k = A Tn e"EB/RI
using the relations given below for various types of reactions."53' Units for the rate constants
are in terms of cc, g-mole, seconds, °K, and kcal.
• Exothermic termolecular reaction
B + C + M-BC + M
k = 3X1016T °'5
• Exothermic bimolecular reactions with triatomic transition states
B + CD-BC + D
k = 5X1u"T05e~EB/RT
where EB = 5.5 percent of the CD bond energy.
• Exothermic bimolecular reactions with transition states of more than 3 atoms
BC + DE - BCD + E
k = lXlO"T°VEB/RT
where EB = 5.5 percent of the DE bond energy.
• Exothermic bimolecular binary exchange reactions
BC + DE - BD 4- CE
k = 1X10'0T05e-EB/RT
where EB = 28 percent of the sum of the BC and DE bond energies.
Appropriate bond energies for these calculations can be found in the appendix or es-
timated using the procedures outlined in the previous section on Estimation Procedures.
More refined approximations for rate constants may be obtained using the procedures
already described.
SUMMARY AND CONCLUSIONS
Details of mechanisms have been reviewed for oxidation and pyrolysis reactions involving
organic vapors. Rate data have been compiled for both global and complex mechanisms of in-
terest for the design and analysis of fume afterburner systems. The available rate data are quite
limited; so attention has been given to procedures for estimating reaction rates.
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70
For estimating the rates of homogeneous gas phase reactions modified collision theory is
recommended. This estimation procedure requires the determination of three factors: (1) the
collision frequency, (2) the steric factor or collision efficiency, and (3) the activation energy.
Recipes for the calculation of each of these factors and the required data are presented in the
previous section and Appendix C. It is intended that these techniques will provide acceptable
rate data for any afterburner application. Rapid, but probably less reliable, estimates can also
be made by either comparing the unknown reaction with similar reactions for which known
rate data are tabulated or by using the rapid estimation procedures that are outlined.
When kinetic rate data are not defined explicitly for either complete combustion to
and HbO or for a specific yield of CO2 and CO, it is probably reasonable to assume that the
hydrocarbon oxidation results in only CO production which is then converted to CO2 accord-
ing to the kinetics of CO oxidation. The initial attack of an organic by oxygen is generally rapid
and it is often the CO kinetics that largely control the overall kinetics of complete combustion.
Rates for catalytic surface reactions cannot be predicted with any degree of certainty.
Reliable catalytic rate data can only be obtained through well-defined empirical measure-
ments involving the catalyst of interest. However, in some cases, rate data can be estimated us-
ing the information compiled in this report for typical afterburner-type catalysts.
Various integrated rate expressions which can be used to estimate residence times for
afterburner systems are presented in this report. These expressions are based on simple plug-
flow models and do not take mixing and recirculation effects into account. Most afterburners
can be divided conceptually into two sections: a mixing section and a combustion section.
Generally good mixing can be achieved through proper design considerations; however,
recirculation and backmixing in the combustion section and their effect on residence time can
be more difficult to take into account. In many cases, however, the plug-flow model can
provide adequate approximations for design applications.
For reliable modeling of afterburner systems detailed computer analyses are generally re-
quired to couple both the chemical and physical processes. A simplified analysis developed by
Levenspiel and Bischoff"54', though, can often be used with good results to correct residence
times calculated on the basis of plug flow for recirculation and backmixing effects.
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71
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(138) J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids,
Wiley (1954).
(139) D. K. Edwards, V. E. Denny, and A. F. Mills, Transfer Processes, Holt, Rinehart and
Winston (1973).
(140) R. B. Bird, J. O. Hirschfelder, and C. F. Curtiss, "Theoretical Calculation of the Equation
of State and Transport Properties of Gases and Liquids", Trans. Am. Soc. Mech. Eng, 76
1011 (1954).
(141) R. A. Svehla, "Estimated Viscosities and Thermal Conductivities of Gases at High
Temperatures", National Aeronautics and Space Administration Technical Report No
NASA TRR-132 (1962).
-------
80
(142) K. J. Laidler and J. C Polanyi, "Theories of the Kinetics of Bimolecular Reactions",
Progress in Reaction Kinetics, 3, G. Porter (Ed.), Pergamon Press Inc., New York (1965).
(143) Z. G. Szabo, /Advances in the Kinetics of Homogeneous Gas Reactions, Methuen and
Co., Ltd., London (1964).
(144) M. G. Evans and M. Polanyi, "Further Considerations on the Thermodynamics of
Chemical Equilibria and Reaction Rates", Trans. Faraday Soc., 32,1333 (1936).
(145) N. N. Semenov, Some Problems of Chemical Kinetics and Reactivity, Vol. I, Pergamon
Press, Inc., New York (1958).
(146) J. O. Hirschfelder, "Semi-Empirical Calculations of Activation Energies",/. Chem Phys
9,645(1941).
(147) Z. G. Szabo, Chemical Society Special Publication 16 (1962), p 113.
(148) D. W. Jepson and J. O. Hirschfelder, "Idealized Theory of the Recombination of Atoms
by Three-Body Collision",/. Chem. Phys., 30,1032 (1959).
(149) J. C. Keck, "Variational Theory of Chemical Reaction Rates Applied to Three-Body
Recombinations",/. Chem. Phys., 32,1035 (1965).
(150) S. K. Kim, "The Rate of Termolecular Atomic Recombinations", Project Squid Technical
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(151) R. C. Tolman, Statistical Mechanics with Applications to Physics and Chemistry,
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(152) G. von Elbe and B. Lewis, Combustion Flames and Explosions of Gases, Academic Press
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Methane/Air Combustion with Pollutant Formation", U.S. Environmental Protection
Agency Report EPA-650/2-74-045 (1974).
(154) O. Levenspiel and K. B. Bischoff, "Backmixing in the Design of Chemical Reactors" Ind
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(155) M. Szwarc, "The Transition State in Radical Reactions" in The Transition State, A Sym-
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(156) D. E. Jensen and G. A. Jones, "Reaction Rate Coefficients for Flame Calculations", Com-
bustion and Flame, 32,1 (1978).
(157) W. M. Shaub and S. H. Bauer, "The Reduction of Nitric Oxide During the Combustion of
Hydrocarbons: Methodology for a Rational Mechanism", Combustion and Flame, 32,
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81
(158) A. Wheeler, "Reaction Rates and Selectivity in Catalyst Pores" in Advances in Catalysis,
Volume III, pp. 249-327, Edited by W. G. Frankenburg, V. I. Komarewsky and E. K. Rideal,
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(159) Symposium on Current Status of Kinetics of Elementary Gas Reactions: Predictive Power
of Theory and Accuracy of Measurement,). Phys. Chem., 83, No. 1 (January 11,1979).
(160) J. C. Dechaux and L. Delfosse, "The Negative Temperature Coefficient in the C2 to Ci3
Hydrocarbon Oxidation. I. Morphological Results", Combust/on and Flame, 34, 161
(1979).
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Hydrocarbon Oxidation. II. Analytical Results", Combust/on and Flame, 34,169 (1979).
(162) R. J. Santoro and I. Classman, "A Review of Oxidation of Aromatic Compounds",
Combustion Science and Technology, 19,161 (1979).
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(164) H. E. O'Neal and S. W. Benson, "A Method for Estimating the Arrhenius A Factors for
Four- and Six-Center Unimolecular Reactions",/. Phys. Chem., 71, 2903 (1967).
-------
A-1
APPENDIX A
PYROLYSIS
Pyrolysis is included here for two main reasons. One reason is that pyrolysis by itself can
be used to either destroy organics or convert them to less complex compounds. The other
reason is that pyrolysis reactions, even in the presence of excess oxygen, play a role in deter-
mining the overall rate and efficiency of oxidation processes and influence the distribution of
final products.003'
The general kinetics and mechanisms of hydrocarbon pyrolysis have been reviewed by
Gordon"*4' and Purnell and Quinn"05'.
Pyrolysis Rate Data
A detailed discussion of the mechanism for methane has been presented by Chen et al.(106)
A survey of the pyrolysis data available up to about 1970 has been published by Kahn and
Crynes.' °7' At atmospheric pressure methane pyrolysis appears to follow two parallel
reactions'108)
2CH4 - C2H2 + 3H2
CH4 - C + 2H2
The maximum acetylene concentration in the reaction product increases with temperature. A
simple mechanism for methane pyrolysis is based on the three reactions
CH4 - C + 2H2
CH4 —* /2 C2H2 + /2 H2
C2H2 - 2C + H2
for the temperature range 1500 to 2000°C where the reaction rates are given by
_ 1 dncH4 _
_ 1 dncH4 _
1 dnc2H2 _
VR dt 31+kPH2
where VR is the reactor volume in liters, P is partial pressure in atm, and the n's represent the
gram moles of each species. Letting
_ g-mole of CH4 converted by n
g-mole feed
_ g-mole of CH4 converted by r2
g-mole feed
_ g-mole of C2H2 converted by r3
g-mole feed
-------
A-2
The conversion relations can be expressed in terms of position within the reactor using the
differential relationships
ridVR=-Qdxi
r2 dVR = Q dx2
r3 dVR - Q dx3
where Q is the flow rate in gram moles/sec. The parameters for the rate constants are given in
terms of
ki = Ai e-Ei/RT
as
Ei = 16,200 cal/g-mole
E2 = 86,450 cal/g-mole
E3 = 17,700 cal/g-mole
Ai = 25.00 g-mole/sec • liter • atm
A2 = 3.219 x 10'° g-mole/sec • liter • atm
A3 = 2190 g-mole/sec • liter • (atm)2
k -1.535 atm"1
The reaction associated with r\ can also be expressed in terms of the solid carbon by
rc = 17.7ccH4e-l6'200/RTg/cm2-sec
where cCH4 is the methane concentration, g/cm3.
Palmer et al.(l09' have reported a first order rate constant for methane decomposition over
the temperature range from 1000 to 1700°K:
logic k(sec~') = 13.0 - 18.6 X 103/T(°K)
corresponding to an activation energy of 85 kcal. This rate constant is based on the equation
~ ~a? = kcc"4
where the methane concentration is expressed in mole fraction.
Recent work"10' on high-temperature (1500 to 2000°C) pyrolysis of methane assuming the
concentration of C2H6 is low at high temperatures has resulted in the mechanism described by
the following differential equations
nCH4
j
dnc2H2
_ , .
— /2 ki
-------
A-3
The reaction volume is given by
v_n,RT_ o . RT
v - ~JT ~ (2ncH4 - nCH4 - nc2H4) —
m is the total number of moles, ncH4 is the initial number of moles of methane, and P is the
total pressure. The rate constants are
k, = 4.5X10l3e-9I'000/RT,sec-1
k2 = 2.58 X 10" e-40'0007*7, sec'1
k4 = 10' ' e-44'370/RT, liter/mole-sec.
For pure ethane pyrolysis0"1, a first order homogeneous rate constant has been reported
as
k = 10'4-8e-7l'800/RTsec-1 .
Pyrolysis can be quite sensitive to the presence of small amounts of oxygen. At very low con-
versions the homogeneous rate of pyrolysis is less with oxygen present than when oxygen is
absent. A reversal occurs above 0.13 percent conversion after which oxygen increases the rate
of pyrolysis. The main pyrolysis products are ethylene and methane. With pure ethane no sur-
face effects are observed. In the presence of oxygen, a surface promoting effect is observed at
very low conversions. At higher conversions, a surface inhibition occurs.
The homogeneous rate constant for ethylene pyrolysis is
= H.O -65,400/RT
High yields of acetylene are produced both in the presence or absence of oxygen. The
presence of oxygen does, however, increase the reaction rate. Methane is the only other ma-
jor product amounting to about 10 percent of the acetylene. Within an oxidized stainless steel
tube the reaction rate is modified by the surface to
I, — in11-3 ^-67,500/RT -1
K — iu e sec
for a surface-to-volume ratio (S/V) of 1.4 cm'1. Oxygen has a significant surface as shown
Figure A-1.
in
Propane pyrolyzes to propylene, ethylene, and methane with propylene
predominating in the absence of surfaces as shown in Figure A-2. The homogeneous rate
For a stainless steel reactor with S/V = 0.7 cm"1, the rate is
k = io12-3 e-60-200/RT sec"1
and the corresponding product distribution is shown in Figure A-3.
Results by Crynes and Albright"121 indicate that the pyrolysis of propane is not a simple
order reaction. Pyrolysis measurements performed in a tubular stainless-steel reactor at 700
and 750°C are presented in Figures A-4 and A-5, respectively. Data were correlated using both
first-order and second-order kinetics based on the equations below for isothermal plug flow.
For first-order kinetics:
O RT
---
-------
A-4
A C2H2 Homogeneous
B C2H2 Surface
C CH4 Homogeneous
D CH4 Surface
02 03
,O2inN2
Q4
Q5
FIGURE A-1. EFFECT OF ADDED OXYGEN ON THE PYROLYSIS OF ETHYLENE.
REACTION TIME: HOMOGENEOUS, 0.19 SEC; STAINLESS STEEL
SURFACE, 0.18 sec. SURFACE-TO-VOLUME RATIO, 0.7 cm '
0.4% O2 IS ROUGHLY 1:1 O2 TO HYDROCARBON RATIO1' "
o
•*-*
"8
t
I
o
u
710
750 770
Temperature, °C
FIGURE A-2. PERCENT PROPANE CONVERTED TO PRODUCTS. HOMOGENEOUS.
REACTION TIME - 0.22 sec. VARIATION IN TEMPERATURE IN °C
IS USED TO ATTAIN VARYING PRODUCT CONVERSIONS01"
-------
A-5
700 720 740 760
Temperature, °C
FIGURE A-3. PERCENT PROPANE CONVERTED TO PRODUCTS. CONVERSIONS
VARIED WITH TEMPERATURE IN °C; OXIDIZED STAINLESS STEEL
SURFACE; SURFACE-TO-VOLUME RATIO, 0.7 cm '; REACTION
TIME ^0.22 sec"1"
700°C, 1 atm
304 S.S. Reactor
0.2 0.4 0.6 0.8
Fractional Reactor Length
FIGURE A-4 PRODUCT DISTRIBUTION ALONG REACTOR LENGTH
(112)
-------
A-6
750°C, 1 atm
304 S.S. Reactor
0.2 0.4 0.6 0.8
Fractional Reactor Length
FIGURE A 5 PRODUCT DISTRIBUTION ALONG REACTOR LENGTH
(112)
and for second-order kinetics
The above equations assume that 2 moles of product are produced per mole of propane
pyrolyzed which was observed experimentally. In these equations, P is total pressure; Q, flow
in moles/sec; VR, the reactor volume; and x is the fractional conversion of propane in terms of
moles reacted per moles of feed. Rate constants for both the first- and second-order kinetics
are plotted in Figure A-6.
Rate data for the pyrolysis of propane and n-butane at atmospheric pressure are plotted in
Figure A-7.
The homogeneous rate constant for the pyrolysis of isobutane'1"' is
k = 10"-V56'300/RTsec-' .
For a stainless steel tube with S/V = 0.7 cm"1 the rate is given by
k = lOIO-V50'700/RTseC-1 .
The product distributions for both the homogeneous and heterogeneous cases are shown in
Figures A-8 and A-9.
Zdonik et al.1"4'"5' have compiled pyrolysis data on a number of organics. Data based on
unimolecular disappearance kinetics for several light hydrocarbons are given jn Table A-1 and
Figure A-10. In general it has been found that the rate of disappearance of a reactant is in-
dependent of both pressure and the surface-to-volume ratio. Data for various classes of heavy
hydrocarbons are given as a function of the number of carbon atoms in Figure A-11.
A listing of kinetic data for the pyrolysis of alcohols and mercaptans is given in Table A-2.
-------
A-7
2000
1000 -
_*
c
X
a
c
5
i/>
c
o
U
a
ro
500 -
9.6 100 10.4 10.8 11.2 11.5
Reciprocal Temp. X 104,1/°K
FIGURE A-6. ARRHENIUS PLOT FOR ASSUMED FIRST- AND SECOND-ORDER REACTION"12'
10
8
7 6
o
u
c
o
'5
n
o>
Qi
de
8
f>
b 6
r~
X 4
E x 6
975 1025 1075 1125 1175
Temperature, °F
FIGURE A-7. COMPARISON OF DECOMPOSITION RATES FOR PROPANE AND
BUTANE AT ATMOSPHERIC PRESSURE0131
-------
A-8
01
c
o
u
D
720 740 760 780
Temperature, °C
FIGURE A-8. PERCENT ISOBUTANE CONVERTED TO PRODUCTS. CONVERSIONS
VARIED WITH TEMPERATURE IN °C. HOMOGENEOUS;
REACTION TIME = 0.22 see"11'
14
730 750 770 790
Temperature, °C
FIGURE A-9. PERCENT ISOBUTANE CONVERTED TO PRODUCTS. CONVERSIONS
VARIED WITH TEMPERATURE IN C; OXIDIZED STAINLESS
STEEL SURFACE PRESENT; SURFACE-TO-VOLUME RATIO, 0.7 cm ';
REACTION TIME =* 0.22 sec(111)
-------
A-9
TABLE A-1. KINETIC RATE DATA FOR
DISAPPEARANCE OF LIGHT
HYDROCARBONS BY THERMAL
PYROLYSIS1114)
Compound
Ethane
Propylene
Propane
1 so butane
n-Butane
n-Pentane
log A
14.6737
13.8334
12.6160
12.3173
12.2545
12.2479
E.,
Btu/lb mole
130,133
120,976
107,593
103,138
101,354
99,758
= Ae-E»/RT,secf1
TABLE A-2. KINETIC PARAMETERS FOR THE PYROLYSIS OF SIMPLE ALCOHOLS
AND MERCAPTANS11161
Compound
MeOH
EtOH
n-PrOH
/-PrOH
n-BuOH
t-BuOH
t-BuOH
t-BuOH
t-BuOH
t-AmylOH
t-BuSH
t-BuOEt
t-BuOMe
EtSH1"
MeSH("
PhCH2SH("
Major Products
H2, H2C=0, CO
CH3CHO, CO, CH4
CH4, CH3CHO
Me2CO
H2CO, CO, ChU
Me2C=CH2, H2O
Me2C=CH2, H20
Me2C=CH2, H2O
Me2C=CH2, H20
Me2C=CHMe, CH2=CMeCH2CH3
Me2C=CH2, H2S
Me2C=CH2, EtOH
Me2C=CH2, MeOH
C2H4, H2S
C2H4, H2S
CH4+ H2S
(PhCH2)2, H2S
Temperature,
°C
669
525
576-624
570-622
524-615
573-629
487-620
~500
~750
153
~500
~700
450
450
393
-500
~750
600
E.
68.00
57.40
49.95
34.00
56.70
54.50
65.50
61.60
60.00
55.00
59.74
61.53
40.00
55.00
67.00
53.00
Log A
10
17.6
8.4
12.2
11.51
14.68
13.4
13.52
13.3
14.13
14.38
(a) Mercaptans also undergo a radical decomposition to R and HS-.
-------
A-10
0002
IOOO I.IOO 1,200 1,300 1,400 1,500 1,600
Temperature, °F
FIGURE A-10. KINETIC RATE DATA FOR DISAPPEARANCE OF LIGHT HYDROCARBONS
BY THERMAL PYROLYSIS(114)
-------
A-11
10
9
8
7
6
5
«, 2.0
J
* 1.5
1.0
Q9
08
07
0.6
0.5
0.4
03
Curve
No. Hydrocarbon Type
JLJ
Normal paraffins
Branched paraffins with
single methyl group attached
to 2nd carbon atom
Branched paraffins with two
methyl groups attached
to separate carbon atoms
Alkyl cyclohexanes
Alkyl cyclopentanes
Normal alpha olefins
I I LJ
7 8 9 10
15
20 25 30 40
n = Carbon Number
FIGURE A-11. REACTION VELOCITY CONSTANTS FOR HEAVY HYDROCARBONS
RELATIVE TO n-C5H,2
-------
B-1
APPENDIX B
POLLUTANT FORMATION REACTIONS
Primary pollutants are generally considered to be those which are emitted directly to the
atmosphere while secondary pollutants are formed by subsequent chemical or photochemical
reactions involving primary pollutants after they have been emitted and interact with the at-
mosphere. Unburned hydrocarbons, aldehydes, oxides of nitrogen, oxides of sulfur, and par-
ticulates are examples of primary pollutants. Examples of secondary pollutants are compounds
like ozone and peroxyacetyl nitrate (PAN). Only primary pollutants are of concern in this study
on afterburner chemistry.
Nitrogen Oxides (NOX). In combustion systems NO appears to be the predominant oxide
of nitrogen. Small amounts of NOj are often present and, occasionally, larger amounts of NOz
are observed than expected. Some investigators attribute the high NCh to sampling effects.
NO in combustion systems can come from two sources: (1) thermal reactions involving at-
mospheric nitrogen and (2) reactions involving chemically-bound nitrogen. The latter source
is often referred to as fuel-bound nitrogen.
The thermal source is only active at relatively high temperatures (>2400°F) and would
probably not be an important source of NO in afterburner systems where the hydrocarbon ox-
idation section usually operates at temperatures below 2000°F. NO can be generated, though,
within the auxiliary fuel flame zone, where the temperatures exceed 2500°F. In the fuel rich
part of a flame, CN radicals can form which can be oxidized and contribute to NO formation.
In a premixed system the NO present can be estimated on the basis of the equilibrium
reaction
N2+ O2 ~ 2 NO .
Usually the kinetics of NO formation are analyzed in terms of the Zeldovich mechanism'5':
0 + N2-NO + N k = 1.4 X 1014 e"78'500/RT
N + O2 - NO + O k - 6.4 X 109 e~6'280/RT
which is often modified to include the reaction
N + OH - NO + H k = 2.8 X 1013
The O + N2 reaction is the rate controlling step because of its high activation energy. For flame
calculations, the O-atom concentration is often taken as its equilibrium value at the flame
temperature. In hydrocarbon flames, especially fuel-rich flames, NOM (called prompt NO) also
may be formed within the flame zone by the reactions
CH + N2 - HCN + N
C2 + N2 - 2 CN .
The N atoms then form NO through the modified Zeldovich mechanism, and the CN yields
NO through reactions with O-atoms and O:. An overshoot in the O-atom concentration
within the flame zone could also account for the so-called "prompt" NO. Stable HCN which is
found in highly fuel-rich flames, is thought to be controlled by the equilibrium reactions
-------
B-2
CN + H2 - HCN + H
CN + H2O~ HCN + OH .
A mechanism proposed by Harris, Nasralla, and Williams'117' for NO formation in a high-
temperature methane-air flame is presented in Table B-1. For fuel-lean CH4-O2-N2 flames at
temperatures above 2500°K the rate of NO formation can be expressed as
d [NO] 2.44 X 10~5
dt - T(oK) ki [O] [N2] ppm m/sec .
Since radical overshoot is small in these flames, [O] can be approximated by the equilibrium
expression
[O] - exp (m4> + 0.00553 T - 17.73)
where
8.291 X 104 10.363 X 107
ni = ^ :p 18.71
and 0 is the stoichiometric ratio and ki = 9.1 x 107 e~38'000/T, mVmole.
TABLE B-1. REACTION MECHANISM AND RATE PARAMETERS
FOR NO FORMATION"17'
Rate Constant, m'/mol ' sec
Reaction kr kr
0+N2 = NO + N 7 X 107 exp (-37,997/T) 1.55 X107
N + O2 = NO + O 1.33 X 103 T exp (-3563/T) 3.2 X 103T exp (19,678/T)
N + OH - NO + H 4.1 X 107 4.1 X 107/0.429 exp (23,815/T)
N2 + OH = N2O + H 1.18X106exp(-38,148/T) 3 X 107 exp (-5,420/T)
N2 + O2 = N2O + O (kr)/1.05exp(42,008/T) 1.18 X 108 exp (-14,092/T)
O + N2O = 2NO 1.42 X 108 exp (-14,092/T) 2.6 X 106 exp (-32,109/T)
NO from compounds containing chemically-bound nitrogen, such as amines, can be
formed at quite low temperatures compared to those required to generate thermal NO.
Therefore, significant levels of NO* could be produced when nitrogen containing organics are
destroyed in afterburners. During combustion, compounds containing chemically-bound
nitrogen decompose to form free radicals or intermediates (e.g., NH, NH2, CN, HCN, NH3,
etc.) which serve as precursors for the formation of NO. The formation of NO from bound-
nitrogen compounds is rapid and appears to be only slightly dependent on temperature. Un-
der fuel-lean conditions where it is often desirable to operate to reduce hydrocarbon and CO
emissions, bound-nitrogen compounds generally result in high NO production. The reason is
that the reactions such as
NO + O - N + O2
NO + NO - N2O + O
NO + RH - product ,
-------
B-3
which lead to the destruction of NO are quite slow. Under certain fuel-rich conditions CH and
NH radicals can contribute to the reduction of NO. Several reactions involving pyrolysis
fragments NH and CN which could lead to NO are listed below.15' A general mechanism can be
expressed as
NH| ( 02 } NO + OH
CN )
A more detailed mechanism involving NH has been suggested to be
NH + O- NO + H
NH + O- N + OH
N + O2 - NO + O
N + OH - NO + H
which are highly exothermic. A suggested CN mechanism is through the reactions
CN + O2 - OCN + O
OCN + O - CO + NO
which are also highly exothermic. N-atoms, which lead to enhanced NO production in flame
zones, can also be contributed by reactions such as
CH + N2 - HCN + N
C2 + N2 - 2 CH
C + N2 - CN + N .
A detailed analysis of NO generation from atmospheric and fuel nitrogen in hydrocarbon
flames has been performed by Leonard, Plee, and Mellor."181 A listing of the reactions used in
their analysis is given in Table B-2.
NO2 in flames is thought to be controlled through the formation reaction
NO + HO2 - NO2 + OH
and the destruction reaction
NO2 + O - NO + O2 .
A detailed mechanism suggested by Laurendeau<119) presented in Table B-3 can also account
for both NO and NO2 formation. The two-step mechanism:
NO + O + M - NO2 + M
O + NO2 - NO + O2
rapidly converts NO to NO2 in the presence of atomic oxygen. The mechanism is favored at
high pressure and low temperatures from 600 to 1200°K. This mechanism may also explain the
anomalously high levels of NO2 sometimes observed.
Sulfur Oxides. In most combustion situations the final form of sulfur is SO2 with only a few
percent of SO3. Under fuel-rich conditions, H2S, COS, and elemental sulfur are also observed.
Much of the kinetics of SO2 formation are controlled by the SO radical with the three-body
reaction
-------
B-4
TABLE B 2 KINETIC MECHANISM FOR
NITRIC OXIDE
FORMATION" I8)
Reaction No.
Reaction
O2-OH
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
O_l_ II ., /"Ml i i i
~t~ ri2 LJH T n
H2 + OH ~ H2O+H
OH + OH-H2O + O
O + O + M — O2 + M
H + H + M~H2 + M
H + O + M-OH + N
H + OH + M«H2O +
N2 + O- NO + N
N + O2~ NO + O
N+OH-NO+H
NH + O-H + NO
NH + OH - N + H2O
NH + H — N + H2
NH + O-N + OH
NH + NO — N2O + H
i
i
4
M
CN + NO - CO + N2(a)
CN + O2 - CO + NO1
CN + O-CO + N
HCN + H -CN + H2
a)
(a) Nonelementary.
TABLE B-3. RATE CONSTANTS FOR N2-O2 REACTIONS
Reaction
(1) O+N2-NO+N
(2) NO + O - N + O2
(3) NO2 + M-NO + O + M
(4) NO + O2 - O + NO2
(5) NO + NO - N2O + O
(6) N2O + M-N2-I-O + M
(7) NO2 + NO2 - NO + NO + O2
(8) O2 + M - O + O + M
Forward Rate Constant
10""58 exp (-75.58/RT)
10" •'" T1 ° exp (-38.34/RT)
10'6
-------
B-5
O + SO2 + M - SO3 + M
being responsible for the SOs formation. For combustion at low excess air (<1 percent ox-
ygen), SO3 is generally less than 1 percent of the SO2 level; at higher excess air, SO3 may reach
2 or 3 percent of the SO2 level.
Polycyclic Aromatic Hydrocarbons. During combustion processes, even with substantial
amounts of oxygen, hydrocarbons can break down to produce unsaturated compounds such
as olefins or polyacetylenes that can then polymerize to form large polycyclic aromatic
hydrocarbons which are highly stable at flame temperatures.
Hydrogen Halides. Hydrogen chloride produced from incineration of chlorinated
hydrocarbons is the most common hydrogen halide associated with afterburner systems.
Generally when hydrogen halides are processed in afterburners the stack gases require special
treatment. Either scrubbers or adsorbers are usually used to provide this special treatment.
Recommended temperatures for the incineration of chlorinated hydrocarbons lie in the range
from 1800 to 2700°F which is considerably higher than required for many afterburner
applications."20'
No overall or global rate data were located for halogenated organic compounds, but ther-
modynamics indicate that chlorine products are readily converted to HCI in combustion.
-------
TABLE C-1. PH\S\CAl AND COMBUSTION PROPERTIES OF SELECTED ORGANIC VAPORS IN AIR
Fuel
Acetaldehyde
Acetone
Acetylene
Acrokin
Acrylonitrile
Allcne (propadierK)
Ammonia
Aniline
Benzene
.n-bulyk
.ler-butyl-
.fen-bulyr-
,1.2-diethyl-
,1,3-diethyl-
.1.4-diethyl-
,1,2-dirnethyl- (o-xytene>
,1.3-diraeUiyl- (m-xykne)
,1,4-dimelhyl- (p-xylenc)
•ethyt-
jaobtityl-
.taoptopyr- (cumene)
,l-methyi-2-ethyl-
,1 -methyl- 3-elhyl-
.I-melhyM-elhyr-
,l-methyl-3.S-dkthyl-
^titro-
.pronyl-
,1,2.3-trimethyl- (hemimellilene)
,1,2.4-trintcthyl- (pseudocumene)
,1,3,5-trimethyl- (meiilylene)
.vinyl- (Jtyrene)
Benzyl alcohol
Brphenyl
,2-buiyl-
,2-eihyl-
.2-methyt-
,2-propyl-
1,2-Butadiene (melliybllene)
1,3-Butadkne (dmnyl. vinyklhyletie)
,2,3-dinietliyl-
.l-methyl- (isoprene)
n-Butanc
,2-eydopropyl-
,2,2-dimelhyt-
.2,J-dimetrlyl-
,1,1-diphcnyl-
,2-roethyl- (iaopcntanc)
•2.2.3-trinKthyt-
Bulanone (melhykthyl ketonel
1-Blltene
,2-cyck>propyl-
iJ-dimelhyr-
,2-c(hyl-
>methyl-
,3-methyl- fe~iioimy1cne}
,2,3.3-trimethyr-
ffwif-2-Butene
2.3-dimethyl-2-biilene
2-fneUiyr-2-butene
3-Buwn-J-yne (rrnybcefylene)
n-Butyl chloride
l-Butyne
,3,J-dimelhyl-
2-Thityne
d-Camphor
Carbon dnulflde
Carbon monoxide
Cyanogen
Cydobutane
.ethyl-
jaopropyl-
.rnethyl-
.methylene-
MoL
44.1
58.1
26.0
56.1
53.1
40.1
17.0
93.1
78.1
134.2
134.2
134.2
134.2
134.2
134.2
106.2
106.2
106.2
106.2
134.2
120.2
120.2
120.2
120.2
148.2
123.1
120.2
120.2
120.2
120-2
104.1
108.1
154.2
210.3
182.3
168.2
196.3
54.1
54.1
82.1
68.1
58.1
98.2
86.2
86.2
210.3
72.1
100.2
72.1
56.1
96.2
84.2
84.2
70.1
70.1
98.2
56.1
84.2
70.1
52.1
92.6
54.1
82.1
54.1
J52.2
76.1
28.0
52.0
56.1
84.2
9«.2
70.1
68.1
»«.
Gra«.
0.783
.792
.62)
.841
.797
C.8I7
1.022
.885
.865
.866
.871
.884
.868
.866
.885
.869
.866
.872
.858
.866
.885
.869
.866
.867
1.199
.867
.899
.880
.870
.911
1.050
1.180
-
-
1.010
-
S.6S!
B.627
.731
.686
S.584
_
.654
.666
-
.62$
.695
.805
(.601
-
.68)
.694
.656
.63)
.710
C.6IO
.71)
.661
.687
.884
'.650
_
.697
.990
1.263
_
.866
.703
_
_
.691
TBoi
-70
134
b-H9
127
173
-30
-28
364
176
362
344
336
362
358
363
292
282
281
277
343
306
329
322
324
393
412
319
349
337
328
293
401
490
-
-
500
-
52
24
156
93
31
-
122
136
-
82
178
175
21
-
132
148
88
68
172
34
164
101
41
172
47
_
81
b399
115
-310
-S
55
97
Hot
of Vap.
3820
4430
4430
-
-
4150
4185
_
4175
-
4205
-
-
-
-
-
-
-
-
-
-
-
4180
-
-
-
-
-
4355
4275
4170
4220
4060
-
4055
4055
-
4055
4035
4175
4215
3970
4110
4135
4150
-
4115
4520
4345
4210
4320
4155
4125
3900
If*. Fniaaj Qainrhhaj Dart.
(10-Sjode) (in.)
Stoich. alb Saoieh. ab»
37.6 - 0.09
115 - .15
C3 - .03
CI7.5 - .06
L36 d!6 .09 0.06
-
-
55 J22.5 .11 .07
- ' -
-
- ' -
-
-
-
-
_
- - - -
-
-
-
- - - -
-
-
- - - -
- - - -
-
- - - -
-
-
_
-
-
- - - -
-
- - - -
- - - -
'23.5 12.5 .07 .05
- - - -
- - - -
76 26 12 .07
- - - -
164 d2S 18 07
- - - -
-
=96 d21 14 .07
100 - 14
53 28 10 .08
- - - -
-
- - - -
-
-
-
-
-
-
8.22 - .04 -
CI24 .15
-
-
-
- - -
1.5 - .02
-
-
-
n
-------
TABLE C-1. (Continued)
Fuel
CyclohexaiM
.ethyV-
jnethyl-
,l-methyl-2-i«rr-butyl-
Cyclohexene
Cydopentadiene
Cydopentane
.methyl-
.it-propyl-
Cydopeiiten:
Cyclopropane
fit-l ,2-dimethyl-
,n»r»-l,2-dimethyi-
tCthyl-
.methyl-
,1,1,2-uimeUlyl-
mu-Decaliii (decahydronaphthalenc)
n-Oecane
1-Decene
Oietliyl ethet
Dihydropynn
Dowpropyl ether
Dimethoxynethane
Dimethyl ether
Dimethyl mlfide
Di-cen-butyl peroxide
DMnyletha
Ethane
,1,1-dipnenyl-
Ethene-
Ethyl acetate
Ethyl alcohol
Ethytamine
Ethykne oxide
Ethylenimrne
Furaa
.tetrahydro-
.thio- (thiophene)
--Heptane
,3,3-dimethyl-
1-Heptene
1-Heptyne
Hexadecane
l-Hexadecent
l,5-Hexadje»e
•-Hexane
,2,3-dtoKthyl-
1-Hexene
l-Hexyne
3-Heiyne
Hydroeen
Hydrogen nafide
bopropyl alcohol
boptopybirane
bopropyl chloride
bopropyl mercaptan
dHomonene
Methane
.drphenyl-
Methyl alcohol
Methyl formite
Naphthalene. 1-ethyl-
,1-methyl-
n-Nonane
,2-methyl-
n-Octane
,2,3-dimelhyl-
,4-ethyl-
,2-melhyl-
,3-methyl-
,4-methyl-
1-Octene
Mot
Wt
84.2
112.2
98.2
154.3
82.1
66.1
70.1
84.2
112.2
68.1
42.1
70.1
70.1
70.1
56.1
84.2
138.2
142.3
140.3
74.1
84.1
102.2
76.1
46.1
62.1
146.2
70.1
30.1
182.3
28.1
88.1
46.1
45.1
44.1
43.1
68.1
72.1
84.1
100.2
128.3
98.2
96.2
226.4
224.4
82.1
86.2
114.2
84.2
82.1
82.1
2.0
34.1
60.1
59.1
78.5
76.2
136.2
16.0
168.2
32.0
60.1
156.2
142.2
128.3
142.3
114.2
142.3
142.3
128.3
128.3
128.3
112.2
Sbec.
Cm.
.783
.792
.774
.810
.805
.751
.754
.781
.772
'.720
X
-
-
'.691
.874
.734
.745
.714
-
.726
.856
-
.846
_
.774
-
1.006
-
.901
.789
.706
1.965
.832
0.936
-
1.064
.688
.730
.702
.738
.777
.785
.697
.664
.717
.678
.721
.726
-
_
.785
.690
.859
.836
.842
-
1.001
.793
.975
1.012
1.025
.722
.732
.707
.742
.744
.718
.725
.724
.719
V
177
269
214
181
109
121
161
268
112
-30
-
-
-
41
369
345
339
94
-
154
111
-11
100
_
102
-128
522
-153
171
173
62
51
132
90
149
183
209
279
201
212
548
544
139
156
240
146
161
_
-423
-79
180
93
96
154
351
-259
503
148
89
498
472
303
332
258
327
334
290
292
288
250
Heal
or v.p.
IWu/lb)
154
133
139
_
_
167
148
_
_
-
-
-
-
-
-
119
-
151
_
-
-
_
_
_
_
210
-
208
_
368
263
250
-
172
-
-
136
118
_
-
98
_
-
144
126
-
_
_
194
237
286
_
-
125
219
_
473
203
_
_
124
_
129
_
_
123
123
123
-
Heat
or Comb.
(Bru/lb)
18.846
18.816
1 8,797
_
_
19.001
18.930
18.907
-
_
-
-
-
_
19.175
19.094
-
_
_
_
_
_
_
20.416
-
20.276
_
_
_
-
-
_
_
_
19,314
_
19.202
19,262
19,052
19,000
_
19,391
19.236
19.262
19.334
_
51,571
_
_
_
_
-
_
21,502
_
_
_
_
_
19.211
_
19.256
_
_
_
_
_
19.157
Sloichlometry
* VoL f
.0227
.0171
.0195
.0125
.0240
.0312
.0271
.0227
.0171
.0290
.0444
.0271
.0271
.0271
.0337
.0227
.0142
.0133
.0138
.0337
.0312
.0227
.0497
.0652
.0444
.0179
.0402
.0564
.0118
.0652
.0402
.0652
.0528
.0772
.0605
0.0444
.0366
.0337
.0187
.0147
.0195
.0205
.0085
.0086
.0240
.0216
.0165
.0227
.0240
.0240
.2950
.1224
.0444
.0383
.0422
.0337
.0147
.0947
.0129
.1224
.0947
.0138
.0153
.0147
.0133
.0165
.0133
.0133
.0147
.0147
.0147
.0171
.0678
.0678
.0678
.0678
.0701
.0738
.0678
.0678
.0678
.0706
.0678
.0678
.0678
.0678
.0678
.0678
.0692
.0666
.0678
.0896
.0939
.0824
.1381
.1115
.1001
.0923
.1017
.0624
.0756
.0678
.1279
.1115
.0873
.1280
.0962
0.1098
.0951
.1017
.0661
.0665
.0678
.0698
.0671
.0679
.0701
.0659
.0663
.0679
.0701
.0701
.0290
.1650
.0969
.0817
.1199
.0922
.0706
.0581
.0763
.1548
.2181
.0755
.0764
.0665
.0666
.0663
.0666
.0666
.0665
.0665
.0665
.0678
FlammabiUry
Limit!
(* Sloichio.)
Lean
48
"54
45
43
"58
-
45
36
'55
_
_
_
'50
_
50
_
41
"61
_
_
-
_
53
„
_
_
_
SI
_
52
_
_
_
_
_
_
_
_
46
_
148
47
51
46
Rich
401
"420
359
368
"276
356
392
'2640
_
_
'330
272
-
>6IO
"236
_
450
_
_
_
_
400
_
393
_
_
_
_
_
_
_
164
'408
434
425
384
Spont
Ian.
Temp.
518
507
509
597
725
614
545
928
521
449
471
366
_
_
662
_
680,
882
909
914
907
738
804
477-
626
505
446
464
501-
820
521
1060
554
852
_
505
1170
962
878
898
1017
453
418
464-
447
458
440
442
450
493
Fuel for
Max. Flame
Speed (»
Sloichio.)
] 17
125
100
117
122
12 1
113
1 16
118
125
116
109
105
112
115
_
119
1 12
115
^100
125
100
122
108
118
117
118
124
*I70
100
114
,
_
106
107
Relative
Max. Flame
Speed
99
96
103
101
96
92
104
122
1 19
119
122
126
1 1 2
f79
'94
'96
102
_
117
103
175
83
234
101
99
f95
113
99
108
124
1 16
679
89
68
_
87
r?7
122
Flame
Temp, at
Max. Ft
Speed (° R)
4050
3935
4075
4010
4190
4170
4160
4125
4170
41SS
4000
4115
4135
4055
_
_
4010
_
4040
4275
4340
3985
4115
4030
4115
4200
4150
4030
4025
4280
(10-5 jouto)
Stoich. Mb
138 d22.3
d2,
t-
67
C83
"•'24 C23
-
49 d28
C56
114
42
C45
C65
C42 d24
9.6
142 48
240
10.5 6.2
48
22.5
54
C60
CM5 d24
g,j !
95 23
2.0 1.8
L'7.7
65
200
155
33 29
21.5 d!4
C62
Q~.cr.ia, DM.
(in.)
Stoich.
.16
.13
1 1
.13
.07
.10
.11
15
.09
.09
.12
.11
.09
.05
.17
.21
.05
.10
0.07
.1 1
.1 1
.15
.13
.14
.025
.04
.1 1
.19
.17
.13
.10
.07
.1 1
Mb
.07
_
.07
_
.07
-
_
.08
_
_
_
.07
.10
.04
0.07
.07
.024
.08
.06
n
i
K)
-------
T \BltC-1. IContmued)
Fuel
1.2-Penudiene (ethyblkne)
ca-l,3-Pentadiene
rrtf/ll-l,3-Pentadienc (piperykne)
,2-methyHd> or rrans)
l,4-Pentad>ene
2,3-Pentadiene
if-Pentane
,2,2-dimethyl-
,2.3-dimeUiyl-
,2.4-dimelhyl-
rt-Pcnlane, 2,4-dimcthyl-3-etnyl-
,3.3-dimethyl-
.2-methyl-
,3-methyl-
,2,2.3, 3-tetramethyl-
,2,3,3,4-tetramethyl-
.2,2.3-bimethyl-
,2,2,4-trimethyl- (isooctane)
,2,3,3-trimethyl-
1-Pentene
,2-melhyl-
.4-methyl-
.2,3.4-trimethyl-
,2,4,4-trimethyl- (diisobulylene)
c«-2-Pentene
,2.4,4-tnrnethyl-
,3,4,4-trimetliyMe'* or trent)
rratnf-2-Pentene
1-Pentyne
,4-melhyl-
2-Pentyne
,4-methyl-
«-Pinene
Propadiene (see Allene)
Propane
,2-eydopropyl-
,1-deutero-
,l-ttajtero-2-methyl-
,2-deutero-2-methyl-
,2,2-dimethyl- (neopenune)
,1.1-diphenyl-
,2-methyl- (iiobutane)
Propene
,2-cydopropyl-
,2-methyl-
Propwruldehyde
n-Propyl alcohol
n-Propyl chloride
Propylene oxide (1,2-epoxypropanc)
1-Propyne
Spirocenunc
1-Tetradecene
Tetrahydropyran
Tetralin (tetrahydronaphthakne)
Toluene (methylbenzene)
Triethybmine
Turpentine (mainly^-pinene)
Vinyl acetate
Gasoline, 73-octane
Gasoline. 100-octane
Jet fuel, trade JP-I k
Jet fuel, padc JP-3k
Jet fuel, pade JP-4k
Jet fuel, padc JP-5k
a Tube open at lower end.
b Sublimes.
^ I'langcd electrodes.
c Unflanped electrodes.
11 0.0225-UKh tlauilevs-Meel electrodes.
MoL Spec.
Wt Grav.
68.1 .698
68.1 .696
68.1 .681
82.1 .724
68.1 .666
68.1 .700
72.1 .631
100.2 .678
100.2 .699
100.2 .677
128.3 .742
100.2 .698
86.2 .658
86.2 .669
128.3 .761
128.3 .759
114.2 .720
114.2 .696
114.2 .730
70.1 .646
84.2 .687
84.2 .669
112.2 .733
112.2 .719
70.1 .661
112.2 .726
112.2 .743
70.1 .653
68.1 .695
82.1
68.1 .716
82.1
1 36.2 .858
44.1 '.508
84.2
45.1
59.1
59.1
72.1 .597
196.3
58.1 8.563
42.1 8.522
82.1
56.1 8.600
58.1 .807
60.1 .804
78.5 .890
58.1 .831
40.1
68.1
196.4 .775
86.1 .854
132.2 .971
92.1 .872
101.2 .723
-
86.1 .932
150 .81
112 .76
126 .78
170 .83
TBoi
Heal Heat
of Vap. of Comb.
( °F) (Btu/lb) (Bni/lb)
113
108
169
79
119
97
175
194
177
278
187
140
146
284
287
230
211
239
86
141
129
226
215
99
221
234
97
104
_
133
-
309
-44
-
-
-
_
49
-
11
-54
_
20
120
207
117
95
-10
-
484
179
405
231
193
162
-
_
154
125
130
127
119
127
139
140
118
117
121
117
123
_
-
_
_
-
-
-
_
_
_
_
-
-
183
-
-
_
_
136
_
158
188
-
169
-
295
_
_
_
-
_
_
156
_
19.444
19.018
19.016
19.190
19.399
19.499
19.235
19,265
19.253
_
19.255
19.356
19.369
-
-
19.212
19,197
19.226
19.346
19.185
19,225
_
_
19.308
-
-
19.280
19.436
_
19.338
_
-
19.929
-
-
_
_
_
_
19.593
19,683
_
19,346
_
_
_
_
19.849
_
19.022
_
_
17.601
'18.500
'18.700
'18.700
1 18.500
Flammability
Limita
Stoic hiometry- (% Stoichio. >
% VoL
.0290
.0290
.0290
.0240
.0290
.0290
.0255
.0187
.0187
.0187
.0147
.0187
.0216
.0216
.0147
.0147
.0165
.0165
.0165
.0271
.0227
.0227
.0171
.0171
.0271
.0171
.0171
.0271
.0290
.0240
.0290
.0240
.0147
.0402
.0227
.0402
.0312
.0312
.0255
.0109
.0312
.0444
.0240
.0337
.0497
.0444
.0422
.0497
.0497
.0290
.0099
.0290
.0158
.0227
.0210
.0444
.013
.017
.015
.Oil
/ Lean Rich
.0706
.0706
.0706
.0701
.0706
.0706
.0654 54 359
.0661
.0661 69 437
.0661
.0665
.0661
.0659 60 372
.0659
0665 "54 "344
.0665
.0663
.0663 48 360
.0663
.0678 '47 '370
.0678
.0678
.0678
.0678
.0678 '49 )345
.0678
.0678
.0678
.0706
.0701
.0706
.0701
.0706
.0640 51 283
.0678
.0655
.0660
.0660
.0654 54 283
.0750
.0649 60 321
.0678 48 272
.0701
.0678
.1054
.0969
.1199
.1054 47
.0728
.0706
.0678
.0893
.0738
.0743 43 322
.0753
-
.1388
_
_
.068
.068
.068
.069
" Measured at -IIO'l .
spark duration. 1 milliv
1 Measured a
£ Saturation
1 elevated tempe
pressure.
latures hy
rapo all.
Bunsen-burner schlieien
in room temperature
c. h Diy air: 0.97 percent hydrogen in carbon munuxide.
Spout
Temp.
( F)
~
_
544
_
640
_
734
,
585
580
845
818
816
837-
806
569-
582
580
495
788
. 587
626
_
_
_
_
-
506
940-
_
_
_
_
853
870
890-
1036-
_
_
^
812
_
-
_
-
463
794
1054-
_
486
-
570
800-950
'480
_
'502
468
i Measured at -4 =
Fuel for
Max. Flame Relative
Speed (% Mix. Flame
Slokhio.) Speed
119
120
119
115
115
119
115
119
119
in
„
_
115
116
_
^
_
117
_
114
124
117
_
_
124
_
_
_
122
120
115
125
_
1 14
118
no
no
no
_
no
114
119
114
131
_
_
128
119
120
_
^90
101
105
106
107
107
1.
133
119
117
100
119
130
99
89
94
92
_
94
94
_
_
89
_
109
102
104
111
_
_
_
136
115
132
117
_
100
109
86
86
86
85
_
90
112
115
96
126
_
_
179
179
154
_
105
f84
f90
-
-
-
'88
'86
'89
Flame
Temp, at
Max. PL
Speed <°R)
4285
4205
4230
4220
4270
4280
4050
4040
3995
4025
4050
4040
_
_
_
4020
_
4165
4025
4130
_
4035
_
_
_
4265
4220
4280
416*0
4050
_
_
_
_
4060
_
4065
4210
_
_
3855
_
_
4170
4450
_
_
_
4175
4220
-
-
-
Ipu Eneigv Qw*c.i^ Din.
(1 0-5 joule I (in.)
Stolen. Min SUicK. Mil
: ; ; ;
_
C82 d22 .13 .07
_
_
_
_
_
_
_
_
_
_
C29 28 .08 .07
_
_ _
_
_ _ _
_
C175 - .18
C82 dI8 .13 .06
_
_
_
_
^ _ _
_ _ _
_
_
30.5 - .08 .07
_
_
_
_
C157 - .17
_
_
28.2 - .08
_-
_
49 - .10
_ _ _
108 - .15
19 d|4 .07 .06
.06 05
_
_ _ _
121 d22 .15 .07
_
_
115 - .15
-
C120 - .15
_
_
_
_
1 Unpublished NAt'A dala.
' Ixiwer healing v
alue: i.e..
liquid lo uas.
n
u>
-------
C-4
TABLE C-2. ELECTRON AFFINITIES02"
Species Electron Affinity, eV
F
Cl
Br
I
H
Na
O
OH
SH
NO
CH3
C2H5
CH3O
H02
CF3
CCI3
3.40
3.61
3.36
3.06
0.75
0.54
1.47
1.83
2.30
0.9
-0.2
~0.4
~1.40
~1.07
~1.0
-0.5
TABLE C-3. THE CONTRIBUTIONS OF THE DIFFERENT
END GROUPS TO THE ACTIVATION
ENERGIES029'
Atom or Group X (kcal/mol ') F (kcal/mol')
Kl/2
H
F
Cl
Br
r
0
Na
OH
SH
NH2
HO2
CHO
CH3
CF3
C2H5
4.7
-3.8
-2.3
-4.8
-5.7
2.0
2.6
-0.2
-1.7
-1.6
1.1
0.3
6.2
4.1
4.2
3.00
0.35
0.57
0.32
0.15
2.15
2.30
1.30
0.84
1.30
1.70
1.55
3.50
2.95
2.85
-------
C-5
TABLE C-4. PROCEDURE FOR CALCULATING HARD-SPHERE COLLISION
PARAMETERS'81
Step
Operation
1 Calculate the average inverse temperature T = TiT2/(Ti + T2) for the temperature
range under consideration
2 Find e/k for each molecule from Table C-5
3 Form T* = f k/t
4 Find n(2>2)* for each molecule by interpolation in Table C-6
5 Calculate aA from value of a in Table C-5 using aA = a2n(2>2>*
6 The collision cross section for a pair of A and B molecules is given by
= /2(aA + OB)
TABLE C-5. PARAMETERS FOR LENNARD-JONES POTENTIAL"3!M41)
Gas
Al
AIO
AI2
Air
Ar
Br2
C
C(CHj)4
CCI2
CCI2F2
ecu
CH
CHBrCIF
CHCh
CH2CI2
CH2CNCH)
CHjCCH
CH,CI
CHjCOCH3
CHjCOOCHj
CHjCOOC2Hs
CH3OCHj
CHjOH
CH.
CN
CO
C02
COS
CS2
C2
a, A
2.655
3.204
2.940
3.711
3.542
4.27
3.385
6.464
4.692
5.25
5.947
3.370
5.13
5.389
4.759
4.68
4.761
3.375
4.600
4.936
5.205
4.31
3.626
3.758
3.856
3.690
3.941
4.13
4.483
3.913
«/k, °K
2750
542
2750
79
93
520
31
193.4
213
253
323
69
345
340
406
299
252
855
560.2
469.8
521.3
395
482
149
75
92
195
355
467
79
G«
C2H2
C2H2CHCHj
C2H«
C2H5CI
C2H,OC2H,
C2H,OH
C2H6
C2N2
n-CsHiOH
C3H,
n-C.Hio
/so-QHio
n-CjH,,
C.H,
C»Hij
n-C«Hu
n-CrHu
n-CiH,,
c-hexane
Cl
CI2
H
HCN
HCI
H2
H2O
H2O2
H2S
He
o,A
4.033
4.678
4.163
4.90
5.678
4.530
4.443
4.361
4.549
5.118
4.687
5.278
5.784
5.27
6.182
5.949
8.88
7.45
8.45
6.09
3.613
4.217
2.708
3.630
3.339
2.827
3.737
4.196
3.623
2.551
t/k, °K
232
299
225
300
313.8
363
216
349
576.7
237
531
330
341
440
297
399
282
320
240
324
131
316
37
569
345
60
32
289
301
10
Gas
Hg
Kr
Li
LiO
Li;
Li2O
Mg
N
NHj
NO
N2
N2O
Na
NaCI
NaOH
Na2
Ne
O
OH
02
s
so
SO2
Si
SiO
Si02
UF6
Xe
Zn
o,A
2.969
5.160
3.655
2.850
3.334
3.200
3.561
2.926
3.298
2.900
3.492
3.798
3.828
3.567
4.186
3.804
4.156
2,820
3.050
3.147
3.467
3.839
3.993
4.112
2.910
3.374
3.706
5.967
4.047
2.284
e/k, °K
750
474
179
1899
450
1899
1827
1614
71
558
117
71
232
1375
1989
• 1962
1375
33
107
80
107
847
301
335
3036
569
2954
237
231
1393
-------
C-6
TABLE C-6. LENNARD-JONES POTENTIAL TRANSPORT
INTEGRAL n(2>2|*(138)
T*
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
1.55
1.60
1.65
1.70
1.75
1.80
' 1.85
1.90
1.95
2.00
2.10
2.20
2.30
2.40
2.50
2.60
n(2>2)*
2.785
2.628
2.492
2.368
2.257
2.156
2.065
1.982
1.908
1.841
1.780
1.725
1.675
1.629
1.587
1.549
1.514
1.482
1.452
1.424
1.399
1.375
1.353
1.333
1.314
1.296
1.279
1.264
1.248
1.234
1.221
1.209
1.197
1.186
1.175
1.156
1.138
1.122
1.107
1.093
1.081
T*
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.0
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5
6
7
8
9
10
20
30
40
50
60
70
80
90
100
200
300
400
n(2>2)*
1.069
1.058
1.048
1.039
1.030
1.022
1.014
1.007
0.9999
0.9932
0.9870
0.9811
0.9755
0.9700
0.9649
0.9600
0.9553
0.9507
0.9464
0.9422
0.9382
0.9343
0.9305
0.9269
0.8963
0.8727
0.8538
0.8379
0.8242
0.7432
0.7005
0.6718
0.6504
0.6335
0.6194
0.6076
0.5973
0.5882
0.5320
0.5016
0.4811
-------
C-7
TABLE C-7. VALUES OF a FOR CALCULATING ACTIVATION ENERGIES FROM
BOND STRENGTHS'155'
cxp. CA ciic.
Unimolecular Decomposition, Two-Center Activated Complex; a = 0.95
CH3-CH2-CH2- - C3H6 + H- 38.0 37.7
(CHj)rG - (CH3)2C:CH2 + H- 40.0 40.6
CH3-CH2-CH2- - CH3- + C2H4 20.0 20.8
CH2OCH3 - CH3- + CH20 19.0 14.2
Unimolecular Decomposition, Four-Center Activated Complex (Closed); a = 01]75
CH2 — CH2
I I ^2C2H4 61.0 62.9
CH2 — CH2
CH2 — CH2
| | -C2H4 + -CH2O 600 54.5
CH2-0
CH2 — CH2
| | -C2H4 + -CH2CO 52.0 57.6
CH2 — C = O
Unimolecular Decomposition, Four-Center Activated Complex (Open); a = 0.73
CH3-CH2 CH2CI - HCI + C3H6 550 469
(CH3)3-CCI - HCI + (CH3)2C:CH2 41.4 45.9
CH3-CH2 CH2Br - HBr + C3H6 47.7 45.4
Cyclohexyl bromide — Cyclohexene + HBr 46.1 44 3
Bu'OH - H20 + C4H8 54.5 58.9
Unimolecular Decomposition, Six -Center Activated Complex (Closed); a = 0.72
1
^
CH2 HC \
., CH2 | | CH2 + CH2:CH-CHO 33.6 34.0
HC CH-CHO HC /
X ^7
Unimolecular Decomposition, Six-Center Activated Complex (Open); a = 0.76
H-CO-0-CH2-CH3 - H-CO-OH + C2H4 44.1 45.3
-------
C-8
TABLE C 7 (Continued)
LA «p.
HI+HI
Transfer Reactions, Four-Center Activated Complex; a = 0.71
H2 +12 44.0
LA calc.
Transfer Reactions, Three-Center Activated Complex; a = 0.96
H- + D2 - HD + H- 6.5 5.1
H- + C6H6 - H2 + CeHj- 7.0 7.9
Cl- + H2 - HCI + H- 5.5 4.2
Br- + H2 - H- + HBr 17.6 19.3
Br- + C2H6 - HBr + C2HS- 13.9 14.1
CHr + H2 - H' + CH4 9.9 7.2
CH3 + CH2:CH2-CH2:CH +CH4 10.0 5.0
CF3- + H2 - H- + CF3H 9.5 10.0
CF3- + C2H6 - C2H5 + CF3H 7.5 4.9
C2H5-+ H2 - H-+ C2H6 11.5 9.1
C3Fr + CH4 - CH3 + C3F7H 9.5 9.8
44.8
Transfer reactions, Three-Center Activated Complex (Exothermic Reactions);
a = 0.0109, AH = + 0.943
H2 + CH3-
CHj-CHrCHrCH3 - H2
H- + cyclo-C4H8 - H2 + cyclo-C4H7-
D- + D2 - D2 + D
D- + CH3-CH2-CH2-CH3 - DH + QH9-
D- + (CH3)2CO - DH + CH3-CO CH2-
D' 4- cyclo-C4Hs - DH + cyclo-OH7-
CI-+CH4-HCI
C6H5-CH2-
C2H5-
Br- + C6H5-CH3 - HBr
O + N2O- 2-NO
NO + O3 - NO2 + O2
Na + C2H5CI - NaCI +
0.908
0.854
0.856
0.831
0.943
0.845
0.845
0.824
0.909
0.844
0.873
0.764
0.801
0.736
11-13
8.9
9.2
8.2
6.0
7.1
8.0
7.7
6.2
3.4
7.2
15.5
2.5
10.2
9.3
6.9
7.6
8.2
6.0
7.1
7.1
7.6
6.3
7.0
4.7
19.0
1.3
6.9
-------
C-9
TABLE C-7. (Continued)
Otctlc. EA tup. EA calc.
Transfer Reactions, Three-Center Activated Complex (Exothermic Reactions);
a - 0.0109, AH = + 0.943
CHrH
CHrH
CHrH
CHrH
CHrH
CHrH
CHrH
CHrH
CHrH
CD3 +
CFr +
CFr +
C2H5-
- CHrCH2-CHrCH3 - CH4 + QH9-
- CH3-CH(CH3)-CH(CH3)-CH3 - CH4 + CeHn-
h cyclo-C5Hio - CH4 + cyclo-C5H9-
- CH3OC(CH3):CH2 - CH4 + QH7
- C6H5-CH3 - CH4 + C6H5-CH2-
h CH2-CH(OH)-CH3 - C3H6-OH + CH4
h CHrCHO - CH3CO + CH4
H (C2H5)rCO - C2H5 CO C2H4 + CH4
h CH3CI - -CH2CI + CH4
CH3-CH2-CH2-CH3 - QH9- + CD3H
CH3-CH2-CH2-CH3 - C4H9- + CF3H
C6H5-CH3 - C6H5-CH2- + CF3H
+ CHrCH2-CO-CH2-CH3 - C2H5-CO-C2H4- + C2H6
0.888
0.867
0.878
0.681
0.714
0.801
0.823
0.867
0.878
0.845
0.921
0.867
0.888
8-6
7.4
8.3
7.3
8.3
7.3
7.5
7.0
9.4
9.3
5.1
6.0
7.4
6.2
6.3
6.2
7.9
7.6
6.9
6.7
6.3
6.2
7.4
5.7
5.9
6.0
TABLE C-8. DISSOCIATION ENERGIES, D, OF SOME MOLECULES AND RADICALS
Molecule D, eV D, kcal/mole Molecule D, eV D, kcal/mole
C2
CN
CO
CI2
F2
H2
H;
HCI
HBr
HF
H2O
H2S
HCN
HCN
N2O
N2O
C02
OC5
NH
4.9 ± 0.3
8.1 ± 0.3
11.11
2.476
1.6 ±0.35
4.4776
0.649
4.431
3.75 ± 0.02
5.8 ± 0.2
5.1136
3.26
9.69 (C-N)
5.6s (C-N)
4.9303 (N-N)
1.6771, (N-O)
5.453
3.71
3.73
173
187
256
57
37
103
15
102
86
134
118
75
223
130
114
39
126
86
85.9
N02
NO2
HI
Hg2
N2
NO
Na2
NaCI
02
OH
S2
SH
03
SO2
NH3
CH4
C2H4
N204
H02
3.114« (N-O)
4.5056 (NO2)
3.06 ± 0.01
0.060 ± 0.003
9.762
6.49 ± 0.05
0.75 ± 0.03
4.24 ± 0.05
5.084
4.45 ± 0.2
4.4 ± 0.1
3.85 ± 0.2
1.04
5.613
4.38
4.406
7.26 ±0.3 (C-C)
0..5937 (N-N)
(H-02)
72
104
71
1.4
225
150
17.3
98
117
103
101
89
23
129
101
101
167
13.7
47
-------
C-10
TABLE C-9. DISSOCIATION ENERGIES OF BONDS'
,(145)
Compound
CCIjBr
CBr4
CHBr3
CHChBr
CH2Br2
CH3Br
CF3Br
(C4H5)3C-C(C6H5)3
C6H5CH2-CH2CH3
C6HjCH2-CH3
C6H5CH2-CH2CH2CH3
C6H5CH2-H
CH3CO-COCH3
C6H5CH2-CH2C6H5
C«H5CH2-Br
CH2=CH-CH2Br
C6H5CH2NH2
H2N-NH2
(CH3)3CO-OC(CH3)3
OHsCOBr
/3-doH7Br
a-CioHvBr
C6H5Br
9-Bromophenanthrene
9-Bromoanthracene
n-C3H7SH
H2S
CH4
CH3
CH2
CH
CF4
CF4
CF3H
CF3CI
CF3I
CF3CH3
CF3CF3
Bond
C-Br
C-Br
C-Br
C-Br
C-Br
C-Br
C-Br
c-c
c-c
c-c
c-c
C-H
c-c
c-c
C-Br
C-Br
C-N
N-N
o-o
C-Br
C-Br
C-Br
C-Br
C-Br
C-Br
c-s
S-H
C-H
C-H
C-H
C-H
C-F
C-F
C-H
c-ci
C-I
c-c
c-c
Q, kcal
49.0
49.0
55.5
53.5
62.5
67.5
64.0
11.0
57.5
63.2
65.0
77.5
60
47
50.0
47.5
59.0
60.0
36.0
57.0
70.0
70.9
70.9
67.7
65.6
71.4
92.2
101.4
85.3
89.9
80
123 ±2
116
103 ±4
83 ±3
57 ±4
90
97
Compound Bond
CHCI3 C-H
CCI3F C-F
ecu c-ci
CH3SH C-S
C2H2SH C-S
fert-C4H9SH C-S
CH3SCH3 C-S
C2H5SC2H5 C-S
CH3ONO O-N
C2H5ONO O-N
C3H7ONO O-N
/so-C3H7ONO O-N
n-CiHsONO O-N
iso-C3H7Cl C-CI
iso-C3H7Br C-Br
iso-C3H7I C-I
CH=C-CH2Br C-Br
CH=C-CH2I C-I
p-Fluorobromobenzene C-Br
p-Chlorobromobenzene C— Br
m-Chlorobromobenzene C-Br
o-Chlorobromobenzene C— Br
p-Dibromobenzene C-Br
o-Dibromobenzene C— Br
p-Bromotoluene C— Br
m-Bromotoluene C-Br
o-Bromotoluene C— Br
p-Bromodiphenyl C— Br
m-Bromodiphenyl C-Br
o-Bromodiphenyl C-Br
p-Bromophenyl cyanide C— Br
m-Bromophenyl cyanide C-Br
o-Bromophenyl cyanide C— Br
p-Bromophenol C-Br
o-Bromophenol C-Br
3-Bromopyridine C-Br
2-Bromopyridine C-Br
2-Bromothiophene C-Br
Q, kcal
88.9 ± 3
102 ±7
67.9
70
69
65
73
69
36.4
37.7
37.7
37.0
37.0
73.3
58.8
42.4
57.9
45.7
70.4
70.3
69.9
69.7
70.6
69.1
70.7
70.7
70.1
70.7
70.1
68.2
70.6
70.1
70.3
67.0
67.1
75.9
71.5
68.5
-------
C-11
TABLE C-9. (Continued)
Compound
CH3Br
CH2Bn
CHBr3
CHjCI
CH2CI2
CHCIj
ecu
CeHj-CaHj
C«HS-CH3
C6He
C6Hs-CH2CH2CH}
Bond
C-H
C-H
C-H
C-H; C-CI
C-H; C-CI
C-H; C-CI
C-CI
C-C
c-c
C-H
c-c
QC-H kcal
95.2
87.7
80.2
97.4
93.2
89
-
94.5
87.5
99
84.6
Qc-ci, kcal
—
-
-
83.5
78.5
73.5
68.4
-
-
-
-
-------
TABLE C-10. DISSOCIATION ENERGIES OF BONDS IN KCAL
(145)
X f>"
K\^
CH3
C2H5
CH2=CH
CH=C
n-C3H7
iso-C3H7
CH2=CH-CH2
n-C4H9
KJ
*Determined indirectly and may be questionable.
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/7-79-096
2.
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
Chemical Aspects of Afterburner Systems
5. REPORT DATE
April 1979
6. PERFORMING ORGANIZATION CODE
7. AUT
R.H.Barnes, M.J.Saxton, R.E.Barrett, and
A. Levy
8. PERFORMING ORGANIZATION REPORT NO.
DON NAME AND ADDRESS
Battelle Columbus Laboratories
505 King Avenue
Columbus, Ohio 43201
10. PROGRAM ELEMENT NO.
1NE829
11. CONTRACT/GRANT NO.
68-02-2629
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
PERIOD COVERED
14. SPONSORING AGENCY CODE
EPA/600/13
15. SUPPLEMENTARY NOTES IERL_RTp project Qfficer fc John
2476.
H. Wasser, MD-65, 919/541-
The report reviews the chemistry and reaction kinetics of oxidation and pyrolysis
reaction that occur in afterburners (or fume incinerators) that are used to destroy
organic pollutants in air or gas streams. Chemical kinetic rate data are compiled
for both complex and global reaction mechanisms of interest for the design and
analysis of afterburner systems. Direct-flame, thermal and catalytic afterburner
systems are covered. Details are also given on techniques for estimating chemical
rate data when experimental data are unavailable. Appropriate equations are given
for calculating the chemical performance characteristics of afterburner systems,
and recommendations are made for using chemical rate data for the analysis of
afterburner systems.
7.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
COSATI Field/Group
Pollution
Afterburners
Fumes
Incinerators
Chemical Properties
Kinetics
Oxidation
Pyrolysis
Organic Compounds
Catalysis
Pollution Control
Stationary Sources
Chemical Rate Data
13B
21J
07D
2 OK
07B,07C
8. DISTRIBUTIOI
Unlimited
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
117
20. SECURITY CLASS (Thispage)
Unclassified
22. PRICI
EPA Form 2220-1 (9-73)
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