EPA-650/2-74-045
June 1974
Environmental Protection Technology Series
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EPA-650/2-74-045
KINETIC MECHANISM
OF METHANE/AIR COMBUSTION
WITH POLLUTANT FORMATION
by
C. H. Waldman, R. P. Wilson, Jr. , and K. L. Maloney
Ultrasystems, Inc.
2400 Michelson Drive
Irvine, California 92664
Contract No. 68-02-0270
ROAP No. 21ADG-10
Program Element No. 1AB014
EPA Project Officer: W. S.Lanier
Control Systems Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
June 1974
-------
This report has been reviewed by the Environmental Protection Agency
and approved for publication. Approval does not signify that the
contents necessarily reflect the views and policies of the Agency,
nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
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ABSTRACT
A large set of chemical reactions describing methane/air combustion
was evaluated to determine the significant reactions at atmospheric pressure,
1500 < T < 2500°K, and equivalence ratio in the range 0.8 < 0 < 1.25. The
reactions were screened to eliminate (a) reactions whose net contribution to
heat evolution or pollutant formation was negligible, (b) species which had
no discemable effect on either major species or temperature, and (c) groups
of reactions constituting only species exchange loops. A set of 26 reactions/
17 species was derived which can duplicate to _+ 5% the predictions of the
134 reaction/25 species master set. Ten additional pyrolysis reactions are
cited for low-temperature and fuel-rich applications. The Zeldovich mechanism
is the principal route to NO for stoichiometric combustion, but under lean con-
ditions, a path to NO involving NO is also active. For fuel-rich conditions,
comparison with stirred reactor data suggest that NO formation cannot be
explained by the Zeldovich mechanism alone, and an alternate path involving
species of the type RN may be of importance. Finally, prompt NO arising
from O-atom overshoot was not predicted for an idealized plug flow ignition
case.
This report was submitted in partial fulfillment of Contract No.
EPA 68-02-0270 by Ultrasystems, Inc. under sponsorship of the Environmental
Protection Agency. Work was completed as of February 1974.
iii
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iv
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TABLE OF CONTENTS
Section Page
ABSTRACT iii
LIST OF FIGURES vii
LIST OF TABLES , viii
ACKNOWLEDGEMENTS ix
CONCLUSIONS x
RECOMMENDATIONS xii
I. INTRODUCTION 1
A. Chemical Kinetics—An Important Factor in Combustion-
Generated Nitrogen Oxides 1
B. Detailed vs. Global Hydrocarbon Kinetics 1
C. Objectives 2
D. Methods for Determining the Kinetic Mechanism 3
II. A SYSTEMATIC METHOD OF ANALYZING COMPLEX
REACTION MECHANISMS 5
III. SELECTION OF SPECIES, REACTIONS, RATES, AND
CONDITIONS 7
A. Problem Statement: Flame Conditions in Gas-Fired
Combustors 7
B. Species, Reactions, and Rates 9
C. Screening Criteria 13
IV. RESULTS FOR PERFECTLY-STIRRED COMBUSTION 16
A. Stoichiometric (<£= 1) Perfectly-Stirred Reactor 16
B. Fuel Rich ( = 1.25) Perfectly-Stirred Reactor 25
C. Fuel Lean (c£ = 0.8) Perfectly-Stirred Reactor 29
D. Simplifications to the Methane Oxidation Mechanism ... 32
V. RESULTS FOR PYROLYSIS, IGNITION, AND POST-FLAME
REACTIONS 34
A. Pyrolysis and Ignition at Stoichiometric (<£ = 1) 34
B. Post-Flame Reactions at Stoichiometric (0=1) 46
-------
TABLE OF CONTENTS (Cont)
Section Page
VI. SYNTHESIS OF THE SCREENED REACTION SET 51
A. Union Reaction Set for Five Test Cases 51
B. Corroboration with Three New Cases 51
VII. EVALUATION OF REACTION SET AGAINST STIRRED
REACTOR DATA 56
A» Purpose 56
B. Representation of Experimental Conditions with KAP . . 57
C. Predictions Based on Screened Reaction Set 60
D. Kinetic Revisions to Reconcile Theory with Data .... 62
REFERENCES 72
Appendix
A Description of the Numerical Program 78
B Approximation Techniques for Arrhenius Rate Coefficients . 85
C Thermochemical Properties of Methoxyl, CH-O 87
O
vi
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LIST OF FIGURES
3.1 8-Case Screening Matrix 7
4.1 Methane Oxidation Paths, WSR (0 = 1) 22
4.2 Nitric Oxide Formation Paths, WSR (0 = 1) 24
4.3 Methane Oxidation Paths for Fuel-Rich Stirred
Reactor [WSR (0 > 1)] 28
4.4 Methane Oxidation Paths for Fuel-Lean Stirred
Reactor [WSR (0 < 1)] 31
5.1 Schematic of Ignition Model 34
5.2 Comparison of Formaldehyde Profiles for IGN (0 = 1) 36
5.3 Effect of Methoxyl (CHgO) on Ignition Delay [IGN (0 = 1)]
(Temperature and Oxygen Mass Fraction) , 39
5.4 Methane Oxidation Paths for Ignition [IGN (0 = 1)] 42
5.5 Mass Fraction Profiles for Ignition [IGN (0 = 1)] 43
5.6 Nitric Oxide Profile for Ignition of Preheated Reactants ( = 1) 44
5.7 Detailed Structure of Ignition Runaway 45
5.8 Profiles for Post-Flame Case (Plug Flow, 0=1) 46
5.9 Methane Oxidation Mechanisms in Simulated Post
Flame Conditions, PFR (0 = 1) 49
5.10 Nitric Oxide Mechanisms in Simulated Post Flame
Cases, PFR (0=1) 50
6.1 Nitric Oxide Decomposition Observed for PFR (0 > 1) 55
7.1 Jet-Stirred Reactor 57
7.2 Comparison of Experimental Data from Jet-Stirred Reactor
with Predictions Based on Various Reaction Sets 61
7.3 Parameter Study on CH2 + N2-* CRN + HN 68
vii
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LIST OF TABLES
3.1 Species Included in Present Study 10
3.2 Master Reaction Set 11
4.1 Selected Test Cases for WSR (= 1) 16
4.2 Comparison of Results for WSR ( = 1)] 18
4.4 Screened Reaction Set (22 Reax) for Stoichiometric
Stirred Reactor [WSR ( = 1)] 20
4.5 Screened Reaction Set (21 Reax) for Fuel-Rich Stirred
Reactor [WSR (0 > 1) 26
4.6 Screened Reaction Set (23 Reax) for Fuel-Lean Stirred
Reactor (WSR (<£ < 1) 30
5.1 Controlling Reaction Sets for Ignition Case [IGN (<£ = 1)] 40
5.2 Screened Reaction Set (23 Reax) for Adiabatic Plug Flow
Reactor (0=1) 47
6.1 Union of Controlling Reaction Sets 52
6.2 Comparison of Controlling Reaction Set with Those
of Previous Investigators 53
7.1 Thermal Conductivity of Firebrick 59
7.2 Determination of Heat Transfer Coefficient for
let-Stirred Reactor 60
7.3 Rate Revisions Intended to Boost O-Atom Levels 65
7.4 Candidate R + N2~^R»N + N Reactions 66
7.5 Empirically Adjusted 33-Reaction Set for CH./Air with
Revisions to Table 6.1 Noted (*) 70
B.I Bond Dissociation Energies 86
C.I Thermodynamic Functions for Methoxyl (CHgO) 89
viii
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ACKNOWLEDGEMENTS
The authors gratefully acknowledge many helpful discussions with
Dr. Victor S. Engleman of ESSO Research and Engineering Co. and Dr.
Robert Shaw of Stanford Research Institute.
The research was financed under Contract 68-02-0270 with the U. S.
Environmental Protection Agency; Messrs. David W. Pershing and Steve Lanier
served as most helpful contract monitors.
IX
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CONCLUSIONS
1. Twenty-six reactions can duplicate to + 5% the predictions of a 134-
reaction master set for methane/air combustion at P = 1 atm, 1500 < T < 2500°K/
and 0.8 < 0 < 1.25 (see Table 6.1). (page 52)
2. Stirred reactor measurements suggest that NO formation can occur via
reactions of the form R + NZ — RN + N which were not included in the 134-
reaction set. The possibility that such reactions may be active is corroborated
by observations of HCN [Bachmaier et al. (1973)]. A list of potential candidate
reactions is given in Table 7.4. (page 66)
3. The controlling mechanism for methane oxidation appears to be similar
to that postulated by Fenimore (1964) and Fristrom and Westenberg (1965) and
later exercised by Bowman (1970, 1971). There are three departures: (a) The
O-radical rather than OH appears to be the major oxidation agent X in reactions
CH3 + X - , and CH2O + X -*. (b) Five parallel paths [reactions (36), (44),
(47), (52), and (143)] are available between CHO and CO. (c) In CO oxidation,
termolecular recombination may be significant.
4. Methane pyrolysis at intermediate temperature (1200 < T < 1500 K)
appears to be controlled by reactions of the form CH + CH-O = CHO + CH
n Z n+1
Ten additional reactions appear to be significant (see Table 6.1). (page 52)
5. The bottleneck in NO formation is the rate of breaking up molecular
nitrogen, and from our study it appears that the Zeldovich mechanism (N. + O-»
£»
NO + N) appears to be controlling. Two alternative mechanisms have surfaced:
N. can collide with an active radical such as CH or OH (see item 2 above) or
6t ft
N_ can combine with O in a three-body reaction to form NO, a fraction of which
£t £•
subsequently goes to NO via N.O + O -» NO + NO.
Ct
6. For ignition idealized as plug flow, the O-atom overshoot is too brief
(~. 1 msec) to generate nitric oxide and therefore cannot explain "prompt NO"
(see, however, item 2 as an alternate explanation of "prompt NO").
x
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7. The following backward rate of the O + N_ -» NO + N reaction gives
t*
best fit for comparison with stirred reactor data:
k, = 6.31 x 1011 T1/2 [Baulch (1969)]
b
This rate is a factor of X2 greater than that widely used.
8. Nitric oxide appears to decompose in the prolonged presence of formal-
dehyde at high temperatures, a curiosity which upon further study may have
obvious practical applications.
9. Eight species appear to be insignificant to methane oxidation: CH,
CN, NO , CH0/ HN, CH..O, CHN, and HNO. Four of the species may
22 >3
have to be restored to account for NO formation, especially under fuel-rich
conditions (CH0, CHN, CN, HN).
xi
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RECOMMENDATIONS
1. The NO-formation mechanisms in fuel-rich flames should be charac-
terized with further numerical studies and experiments. Particular attention
should be paid to detection of species CH and RN which may participate in
j£
alternate (non-Zeldovich) mechanisms.
2. Experiments to reduce the uncertainties in the rates of certain key
reactions (e.g., CO + HO = CO + H, O + N = NO + N, and N. + O + M =
*•* l» £t
N2O + M) should be undertaken.
3. The sensitivity of the screening method to variations of the reaction
rates should be determined.
4. Chemical reaction mechanisms capable of scavenging NO should be
H
identified and tested in appropriate experiments.
5. The 26-reaction set derived herein should be exercised on other stirred
reactor data and shock-tube data on the CH./air system.
6. The screening procedure should be reapplied periodically as rates of
individual reactions become better defined.
7. Nitric oxide measurements in well-stirred reactors fired by CHVair
should be repeated with direct measurements of the heat-transfer rate (which
is currently the greatest source of uncertainty in existing data).
8. The effect of stirred-reactor unmixedness upon NO emissions should
be studied in order to more authoritatively fit rate constants.
9. In order to provide an extremely simple CH. oxidation mechanism for
complex fluid models such as the Gosman or UARL codes, the 26-reaction set
should be screened with relaxed criteria.
xii
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I. INTRODUCTION
A. CHEMICAL KINETICS—AN IMPORTANT FACTOR IN
COMBUSTION-GENERATED NITROGEN OXIDES
It is well known that NO and CO production in flames is rate-limited,
and is strongly coupled to hydrocarbon oxidation through the heat release and
radical-generation mechanisms. Limited knowledge of the mechanism of
hydrocarbon combustion has impeded an understanding of the kinetics of NO
J\
formation in flames. Of course, heterogeneous effects, flowfield mixing pro-
cesses and radiation must be described before the kinetic mechanisms can be
used for any given flame.
Whatever complexities attend the description of the combustion flow-
field, there is no doubt but that the coupled rates of chemical processes
ultimately determine the pollutant formation rates. It is with the kinetic
mechanisms of combustion with pollutant formation that the present study is
concerned. We have selected the methane/air system for study, since it is
crucial to see if combustion of this simplest of hydrocarbons can be adequately
modeled kinetically before attempting more complex gaseous fuels, not to men-
tion those in liquid form with bound nitrogen.
B. DETAILED VS. GLOBAL HYDROCARBON KINETICS
Approximate kinetic schemes have been used to describe the oxidation
of nearly all practical hydrocarbon fuels. The models generally assume a
relatively fast partial oxidation of the hydrocarbon to yield CO, followed by
the presumably well-known detailed kinetics ascribed to the H9/O9/CO/to0
" £» €•»
system [Mellor (1972)]. These "global" methods have previously proved
useful for calculations of system performance and stability [Edleman and
Fortune (1969)].
-------
However, these approximate kinetic models have been shown to be
unreliable to predict pollutant formation [Mellor (1972)]. Global reaction rates
may be adequate for simulation of energy release, but detailed kinetic calcu-
lations are needed for pollutant formation because small changes in the hydro-
carbon chemistry model strongly influence local temperature and composition.
Serious disagreement has been found between detailed and approximate tech-
niques for calculation of NO formation. For example, various partial equili-
J±
brium models for the H./O./CO/N. system give widely differing results as
shown by Bowman and Kesten (1971).
The weakness of approximate kinetic methods are clearly demonstrated
by recent results using a well-stirred reactor. Engleman et al. (1973) first
tested the reliability of a postulated H_/O /CO/N reaction set by calcu-
t* I* £*
lating NO formation in H0/air and moist CO/air mixtures; they obtained good
Zt
agreement with stirred reactor measurements at 1 atm. They then compared
their predictions with experiments using propane, adding a global C_H0 —» CO
o o
partial oxidation step to the kinetic mechanism. On the lean side, they under-
predicted NO formation by a factor of 2; moreover, an order of magnitude dis-
agreement existed under fuel-rich conditions. On the other hand, earlier pre-
dictions obtained from the same reaction set compared favorably with experimental
results for NO formation in a shock tube for CH./air at 3 atm over a wide range
of equivalence ratios [Seery and Bowman (1970)]. Clearly it will be necessary
to establish the detailed mechanism of hydrocarbon combustion in order to
accurately predict NO formation.
C. OBJECTIVES
In order to elucidate the role of chemical kinetics in pollutant formation
in gas-fired combustors, we have attempted to determine the necessary and
sufficient set of species, reactions, and rates to describe the heat release and
pollutant formation from methane/air combustion. In the course of studying the
CH /air system, the following additional questions were analyzed:
-------
1. What reactions control the pyrolysis of CH. ?
2. What reactions control the oxidation of CH. and what
are the intermediate species ?
3. What reactions control the formation of NO? Is the
Zeldovich mechanism (O + N_ — NO + N) the only
significant path? How important is the hydroxyl
radical (N + OH -* NO + H) ?
4. In addition to NO, are other nitrogen-bearing pollu-
tants formed during combustion, and if so, which
reactions are responsible?
5. Is NO formed predominantly in the flame (during
radical overshoot) or mainly in the post-flame region?
The final objective of the present study is to examine whether the
screened reaction set is complete and able to predict the heat release and
pollutant emissions experimentally measured in laboratory flames.
D. METHODS FOR DETERMINING THE KINETIC MECHANISM
The following difficulties present themselves:
(i) The selection of intermediate species requires
knowledge of undetermined critical reaction paths.
(ii) The set of conceivable elementary reactions is
extremely unwieldy and its complexity defies
attempts to use intuition to arrive at the necessary
and sufficient subset.
(iii) The paucity of measured rate data makes it difficult
to select rate coefficients.
(iv) Once the problem is set up, coupled non-linear rate
expressions must be solved subject to widely differ-
ing time constants.
Our approach has been to develop and apply a procedure for reaction
screening to deal with problems (i) and (ii) in a systematic fashion. Engineers
are often confronted with complex chemical systems; without a convenient way
to select the reaction paths of importance for a particular application, the '
reaction sets chosen usually will omit one or more reactions of importance
and/or include unnecessary ones. Such incorrect reaction sets may lead to
-------
incorrect results and/or wasted computation time. In order to alleviate this
problem, a formal procedure is developed for the systematic examination of
reactions in order to reduce their numbers while retaining any desired degree
of accuracy. In this way the necessary and sufficient set of reactions and
species to describe the phenomenon of interest can be obtained with the mini-
mum effort. The rate uncertainties [item (iii)] can be reduced by adjusting
rates in the screened set until it can predict experimental stirred-reactor cases,
As for the computation problem [item (iv)], modem numerical analysis
techniques [Tyson and Kliegel (1968)] and high-speed computers permit com-
putations with very large numbers of reactions and so can remove the guess-
work involved in intuitively selecting reaction subsets of complicated chemical
systems.
The remainder of this report is arranged as follows. The chapter to
follow presents the description of a systematic method for screening large
numbers of reactions (Chapter II). Following this we deal in succession with
the selection of flame conditions and reaction data (Chapter III), with the
detailed screening on perfectly-stirred combustors (Chapter IV), and on
ignition, pyrolysis, and post-flame relaxation (Chapter V). Finally, these
results are synthesized into a master set (Chapter VI), and some comparisons
with stirred-reactor measurements are presented (Chapter VII).
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II. A SYSTEMATIC METHOD OF ANALYZING COMPLEX
REACTION MECHANISMS
The screening analysis is carried out in a systematic manner as des-
cribed in the eight steps outlined below:
(1) Problem Statement; The non-equilibrium combustion problem is defined
in terms of the reactants and ranges of stoichiometry, pressure and temperature.
Sample cases are set up to cover this three-dimensional matrix (
-------
a species are unimportant if the production of that species far exceeds the
destruction (i.e. the reaction is far from equilibrated).
(5) Species Screening: The Jacobian elements dX /dX. (see Appendix A)
are examined to find species j which seem to have a negligible effect on the rate
of change of any species or temperature. Such species can be screened out if
a rerun of the sample case confirms no sensitivity to their presence.
(6) Analysis of Reaction Groups; Frequently a group of reactions has no
significance other than to form a species-exchange loop which makes its mem-
ber reactions appear active [preventing their detection in step (4)]. By syste-
matic inventory of the paths involved with species, it is possible to recognize
and eliminate these non-productive reaction groups.
(7) Synthesis; A "master" set of reactions is synthesized by taking the
union of all reaction sets which describe sample cases. Further refinements
and corroboration can be made by exercising this "master" set on new sample
cases. It is revealing and useful to identify subsets such as the intersection
(reactions important in all cases) and special reaction groups which need only
be included for low-temperature pyrolysis, low pressure, or fuel-rich conditions.
(8) Rate Adjustment; Given the reduced master reaction set, values of the
more uncertain rate coefficients are selected on the basis of best-fit of data
taken from idealized kinotically controlled experiments such as the stirred
reactor and shock tube.
The systematic procedure outlined above formalizes the steps taken
by past investigators, and supplements the intuition with an efficient numeri-
cal screening tool. Portions of the procedure have been used by prior investi-
gators to suggest reactions of importance in calculating rocket engine perfor-
mance [Kliegel et al. (1969)] and to analyze ethane/air combustion [Chinitz
and Bauer (1966)].
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III. SELECTION OF SPECIES. REACTIONS. RATES. AND CONDITIONS
A. PROBLEM STATEMENT: FLAME CONDITIONS IN GAS-FIRED COMBUSTORS
A matrix of test cases was designed to reflect conditions corresponding to
ignition, burning, and post-flame zones, as shown in Figure 3.1.
Figure 3.1
8-CASE SCREENING MATRIX
Schematic of Reaction Progress:
(CH4,02)
(Radicals and Intermediates)
(C02,H20)
0 = 1.25
0= 1.00
0 = 0.80
IGNITION/COMBUSTION
Without Backmixing
(Plug flow)
COMBUSTION POST FLAME
With Backmixing Without Backmixing
(2msec Stirred reactor) (Plug flow)
Those cases denoted * were made at high enthalpy (AT = 300 K) to test the
effect of preheat.
Ignition presumably occurs in combustors after reactants are injected
into the primary zone and mixed with hot products. For this study, ignition
is modeled as a plug flow (zero backmixing), with initial composition taken
to be a mixture of reactants and equilibrium combustion products. The exact
reactant/product fraction was found unimportant in the present application; it
only affected the delay to ignition but not the detailed mechanism of the chem-
ical runaway. It is essential to recognize that methane/air reactants are not
heated to the ignition point (~1200 K) without dilution.
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For gas-fired combustors, the extent of backmlxing of hot products
with unbumed reactants during the heat release process is not well established.
Characteristic heat-release times are known to be on the order of .1 msec, so
backmixing is expected to be negligible on a scale much more than L = vDt «
-2 -1
10 cm, for example in a diffusion flame of 10 -cm thickness. On the other
hand, the very thin deflagration waves characteristic of premixed flames would
permit backmixing and indeed require it in order to propagate.
In the present study we consider two extremes of backmixing: plug
flow and perfect backmixing. The plug flow extreme is analyzed by observing
the ignition case after the chemical runaway. The stirred reactor extreme is
set up as separate cases as noted in Figure 3.1. Starting conditions are critical
in the numerical solution of the WSR, since the first iteration must "ignite".
However the steady state WSR solution has only CH./air as input and retains
no memory of the starting concentrations.
These WSR cases were run with a residence time of 2 msec. Using
screening criteria to be described in the next section, we examined residence
time of two to three times as great as this for the WSR (= 1) case. As shown
below, we found only one extra reaction screened out at 4 msec, compared to the
2 msec case, and four additional reactions eliminated at 6 msec (out of 134
reactions)
X Indicates Screened Out
at Residence Time of
Reaction 4msec 6msec
(31) CN+H = CHN+H X
£t
(82) H, + NO = H + HNO X
£
(83) H2 +0 = H +HO X
(93) H + NO2 = HNO+O X X
It appears that the reaction set obtained for a 2 msec residence time should
be more general than the sets obtained at longer residence times. Reactions
(31), (82), and (93) were later determined to be insignificant at 2 msec as well
because the species CN, CHN, HNO, and NO. were eliminated as unimportant.
* Reaction numbers refer to Table 3.1 (page 11).
8
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Finally, plug-flow cases were set up to represent the hot combustion
gases in the post-flame zone. For some combustors, it is in this "cooking"
period that most of the pollutants are formed; certainly most of the CO -»CO-
£t
conversion occurs here. The post-flame zone of a real combustor is affected
by heat transfer, but for these calculations the zone was taken as adiabatic.
The composition at the entrance to the post-flame zone region is taken to be
the exit condition from a stirred reactor; in this way relaxation of a gas mixture
which is out of equilibrium can be observed.
In addition to the above-described burning modes, variations in the
equivalence ratio and the level of air preheat were studied. The pressure is
taken at atmospheric for all cases. These conditions, along with the burning
mode, should suffice to approximate, if not exactly describe, the conditions
in any particular region of a combustor.
B. SPECIES, REACTIONS, AND RATES
For the present study, the species and reaction inventory was taken
from the work of Engleman et al. (1973a) as was their assignment of "best
guess" suggested rates. Since the species and reaction inventory and rate
assignments were proceeding concurrently with the present program, there was
ample opportunity to experiment with different reaction sets which had been
used by other investigators, including some reactions which were not in the
134-reaction set of Engleman et al. (1973a). These will be discussed later.
The set of species included in the present study is shown in Table 3.1.
Recent experimental evidence has suggested the presence of the species C in
methane/air combustion [Pratt and Malte (1973)]. This species was not
included in the present study.
*Defined here as $ = (F/A)/(F/A)stoichiometric. The equivalence ratio 0 may
be thought of as the fraction of the supplied air which would be utilized if
the complete combustion were required.
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Table 3.1
SPECIES INCLUDED IN THE PRESENT STUDY
CH
CHN
CHO
CH2
CH20
CH3
CH30
CH4
CO
co2
CN
H
HN
Methylidyne
Hydrogen cyanide
Formyl
Methylene
Formaldehyde
Methyl
Methoxyl
Methane
Carbon monoxide
Carbon dioxide
Cyano
Hydrogen, monatomic
Imidogen
HNO
HO
HO
H2°
N
NO
NO.
Nitroxyl
Hydroxyl
Hydroperoxyl
Hydrogen, diatomic
Water
Nitrogen, monatomic
Nitric oxide
Nitrogen dioxide
Nitrogen, diatomic
Dinitrogen monoxide
Oxygen, monatomic
Oxygen, diatomic
All possible reactions that might occur among the species of Table 3.1
were collected by Engleman and Bartok (1973). Those reactions which appeared
to be sterically improbable, spin forbidden, or not fundamental reaction steps
were eliminated. This resulted in a set of 322 reactions in 25 species. Of
these, 134 reactions in 25 species were taken as the master set, these being
selected on the basis that their rates had been either measured or estimated by
previous researchers. The master set of 134 reactions is shown in Table 3.2,
along with the rates recommended by Engleman and Bartok. Of these reactions,
more than half have estimated rates, i.e., the absence of experimental rate
data indicates that they have never been observed, though each has received
some attention in the literature. A complete accounting of the 134-reaction
set is given by Engleman and Bartok. The reverse reaction rate was determined
from the forward rate and thermochemical data.
10
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Table 3.2
REACTION SET USED AS THE BASIS FOR SCREENING
Rate Coefficients* k, = AT~n e~E//RT
Reaction
Number Reaction
I
A
n
E
Reference
Termolecular Reactions**
008
023
026
036
043
061
077
079
OB*
089
092
099
101
109
112
121
12*
132
136
1*0
1*2
1*7
1*9
CH
CH
CN
CHO
Cn2
CM*
CoH
H?
H20
H
H
H
H
HN
HO
H02
N2
NO
N02
N?0
0?
*H
»0
• M
0
*N
• NO
*0
*02
*0
•N
Cn20
= CMO
«CHN
=co
sCMO
SCH3
=CO
= H
= HO
= HN
srlMO
= HO
= H02
sHfgQ
= HNO
= HO
SN
CN
= NO
= N2
= 0
=co
«H
«H
*H
«0
«H
*H
+ 0
«N
«0
*0
*0
*0
*H£
Cn30 =CH20*rl
Bimolecular
001
002
003
00*
OOa
006
009
on
012
013
015
016
017
018
022
02*
027
028
029
030
031
032
033
03*
035
037
038
039
0*0
0*1
0*2
04*
0*5
046
047
0*8
049
050
051
052
CH
CH
CH
CH
CH
CH
Cn2
CH
CH
Cn2
CH
CH
Cn2
CH2
CH
CH
CH?
Cn3
CH*
CHO
CHN
CHKI
CN
CN
CnN
CnO
CnO
CHO
CnO
CHO
C-»2
CHO
CNO
I
2
R
2
1
?
3
3
2
R
1
1
1
4
*
4
1
1
?
1
4
.
»
•
•
t
•
•
•
•
•
*
,
•
•
•
•
•
•
•
,
t
iilil;
50E*20
OOE*33
OCfc»l7
OOf *li.
00t*l4
OOE*1S
"OE*16
00£«l6
OOE*15
50r*15
OOE* 1 6
OOE*15
OOE»1S
P0p.*21
OOE»20
OOE»16
C0p+l4
50E* 19
OOg* 1 2
COF»40
1
4
0
1
1
1
1
-1
7
.5
.5
,5
.5
.5
.0
•
.0
.0
.5
.0
.0
.0
.5
.5
.5
.6
.5
.0
.0
.0
.0
.5
0.
o.
0.
16.8
87.
88.
100.
96.
105.
0.
o.
0.
1.
0.
o.
6*.
225.
150.
65.
50.
118.7
65.
22.6
ESTIMATE
TUNDERU967)
HENSONU973)
bENSONI 1973)
HA«TlG(l97l)
CLARK (1971)
BAULCHU972)
BAULCHU972)
TUNDE.RU9b7)
SCOFIELD<1973)
BAULCHU972)
TUNDFP 1 19t>7)
TUNPEP11967)
BENSONI1973)
BAULCHI1973)
BAU|_CH<1973)
BAULCH11973)
ENGLEMAN(I973)
JOHKSTON(1968)
BENSONI 1973)
BENSONI1973)
Reactions
*CrlN
*CHO
= CH2
= CH«J
•CH20=Ch2
• CHJ
v C r: ^
*C02
»N
*HNO
»HO
»0
»H02
»H02
»H
*MO
»o
+ 02
D*CN
*CN
*CIN
*CN
*H
*HO
*HN
»HNO
»0
«CHO
«CH2
•CH3
«CH3
*CH4
*0
«H
*HNO
C«20«0
CnO «HD
Cn20*H
CH() *N
CnO *NO
CnO «0
= CH2
— C~3
=CHO
= CH
=CH2
sCHO
= CH
= CHO
= CH2
= CH
cCH
sCU
*CHO
= CHN
= CHN
sCHN
= CMN
= CN
= CN
= CHN
=CMN
= CN
= C"2f)
= CHJ
eCH2
sCH4
*CN
*co
+ CHO
*CH<;
*C~3
*cu
*HN
»NO
*H
*HQ
«HO •
*02
»H2
»H«iO
«H
«0
•CrtO
*Crt2
«Ci3
*CO
»H«i
*H20
*N
*NO
*HO
*co
*co
*C>-i2o
»C-'
=CH20*CH3
*CHO
sCO
«CH?n
«CHO
=co
•CO
«co
»H
*H«J
*NO
«h«;o
• HO
3
3
1
1
^
1
6
*S
5
?
f^
1
3
5
=>
5
1
1
3
2
2
2
1
4
3
j
3
1
3
R
5
3
3
?
3
•
»
,
•
•
•
»
t
t
•
.
f
•
•
.
.
•
•
•
•
»
t
•
•
•
,
,
•
•
*
t
•
•
•
t
00E»11
OOF»10
f OF»I i
25E*11
•Z.C:;_»i i
OOE«10
00£*11
OOE»11
OOE*11
OOE*11
OOE*1 1
00£»10
OOE»11
OOE»11
00£*1 1
OOE*1 1
?5F*11
C0£* 1
OOE» 1
OOE* 1
5C'E» 1
OOE* 1
OOF* 1
OOE«11
00t»ll
50F » 1 1
OOE* 1 0
50E*11
OOE*11
OOE*11
OOE»1 1
OOE»11
OOE*11
OOE* 1 "
COf »0<3
OOF*11
POE*11
_
-
.
-
V
m
m
-
-
-
•
-
-
_
_
.
-
m
-
-
•»
-
-
_
-
-
-1
-
-1
-1
-1
-1
•
-1
.6
.7
.7
.7
t f
.5
.7
.5
.5
.7
.5
.5
.7
.5
.5
.5
.7
.7
.7
.5
.7
.6
.5
.5
.7
,5
.7
.7
.5
.6
.5
•
.5
t
•
•
t
.5
.5
•
8.
1.
*.
5.
•
t>\
*0.5
0.
10.
26.
6.
15.
26,
6.
*.
6.
3.
3.
5.
0.
18.
5.
2.
o.
17.
0.
1.
*.
ft.
9.
*.
0.
o.
*.*
o.
3.2
1.
2.
2.
.5
TUNnER«l967)
TUNOERtl967)
TUNPER ( 1967)
TUNDERU967)
v *j^if\t. rt « i M«_ r |
TUN(5ER(i967)
MAYEH(1967>
TUNnER(l967)
TUNDER(1967)
M*YF«(19b7)
TUNOER(1967)
TUNDER(1V67)
MAYEH(l9b7)
TUNDER(1967)
TUNOER(1967)
TUNDE«(19b7)
TUNDE«(1967)
TUNC>ER(1567>
TUNOER( 1967)
TUNDEP. ( 1967)
TUNOERUV67)
TUNnER(1967)
TUNDEH«l9b7)
TUNQER ( 1967)
TUNDE:R(1967)
TUNOERI1967)
TUNOER(1967)
TuNDER ( 1 9b7)
TUNDER(1967)
TUNOE.RI1967)
BENSONK1973)
TUNDERI1967)
DEAN(I97I)
BENSON11973)
WESTENBERG(I972)
bEN5UN(lv73)
TllNnE»(1967)
7UNPt-;R(l967)
BENSL)N(1973)
*Units: molo, cc, sec, °K,
**Tho third body term, M, is
these equations.
kcal
understood to appear on each side of
11
-------
Table 3.2 (Cont)
Reaction
Number Reaction
053
05*
055
056
057
058
059
060
062
063
064
065
066
067
068
069
070
07!
072
073
07*
075
078
080
081
082
083
OB5
086
087
088
, 090
091
093
09*
095
096
097
098
100
lo*
105
106
107
108
110
111
113
114
115
116
117
118
1?0
122
125
127
128
12V
130
131
133
135
136
137
139
141
1*3
1*8
IhO
151
CH2 *CH4 «CH3 *CH3
C^;2 *r;\0 »CW3 »MO
Cn2 «HO «=CH3 »0
Cn3 *H »CH2 «H2 SHNO »NO
HN *N20 sHNO *N2
N *NO *N2 *0
N *N02 sNO *NO
N «N02 &N2 «0»0
N »N02 sN2 «02
N *N02 EN^O *0
N *N20 sNO *N2
N «02 rNO *0
N20 »0 =NO *NO
NO *N02 cN20 *02
NO *N20 CMQ2 »N,OOE«12
5.00E«08
6,00£*09
i.OOL»U
l.tOE*12
2.ftOF»12
1.00E*13
l.OOf*!*
R.OOF «1?
2.50E*OQ
1 ,OOF»12
1.00E»11
. 12
n
- .7
- .5
- .5
- .7
- .7
• .5
• .5
- .0
- .5
•1.
- .5
-1.
- .0
• .0
- .0
- .5
- .0
- .5
• .5
* • 0
- .0
- .0
- .5
- .5
- .0
- 1.
• .0
- .0
- .0
- .0
- .5
- .5
- .5
- .0
- .5
" .5
- .6
- .0
- .0
- .5
• .5
- .5
- .5
- .5
- .5
' - .0
- .0
- .0
- .5
- .0
- .0
- .0
- .0
- .0
- .0
• .0
- .0
- .0
- .0
- .0
- 1.
- .0
- .0
- .0
- .0
- .0
- .0
-1.
- .0
.5
E
20.
o.
6.
3.
?•
7.
- .3
30.
0.
8*
6.
10.
5.
0.
0.
7.
0.
12.
15.
25.
30.
23. "
60.
B.
13.
2.5
7.
1.9
.7
1.
5.2
0.
8.
0.
l.b
0.
30.
3.
15.
o.
2.
2.
5.
3.
B.
7.
0.
1.
26.
0.
39.
1.
1.
3.
1.
0..
0.
o.
o.
o.
10.
6.3
28.
60.
*o.
1.
28.
0.
28.5
0,
4.73
Reference
TUNOEPM1967)
TUNOERU967)
T'J^Bt0 '1967)
TUNOER(1967)
TUNDEPU967)
TUNO-P 11967)
MOHPISI1973)
BEMSUNHV73)
TUNDER (i*)67)
«EST£NBEKG<1969>
TUNnER<19b7)
WALKER (1968)
WILSUNU972)
BOOENI1968)
BASCO(1965)
TUNDERU967)
ENGLEMAN(I973)
BENSON(l973)
TUNOERU967)
BENSON (1973)
JOHNSTON (1957)
L1NU969) '
OEAN(1971)
BENSONC1973)
TUNDERU967)
HAMPSONt 1973)
BAULCH(I972)
BAULCH11972)
BAULCHH972)
LLOYO(1971)
BAULCH(1972)
BENSOM1973)
BENSONC1973)
TUNOERU967)
BA'JLCH'. IV ,'JJ
BENSUN11973)
TUNDERU967)
TUNDLRU967)
BAULCHU973)
BAULCH(1972)
TUNnER(l967)
TUNDERU967)
TUNDE»(1967)
TUNDE&U967)
BENSON(i973)
TUNOERI1967)
KWETSCMMtH(l963)
BENSOMU973)
WILOEI1969)
TUNDER<1967)
RIPLEY(1966)
BAULCHI1972)
LLOYO(1971)
B£NSON<1973)
LLOYDU971)
BAULCH{I973)
PHIIL1PS<1965>
PHILLIES (1965)
PHILLIPSU965)
PHILL1PS(1965)
Untift'tt.'O t 1 Q 4% *1 \
D U t' 1 i L " * 4 " " J J ^
BAULCH(I973)
BAULCHI1973)
BOHTNErt (1963)
KAUFHANI1955)
BAULCHI1970)
UAULCHI1973)
PE£TtRS(l973)
BENSON 1 1973)
BOOEN I l9bb)
ESTIMATE
-------
In the course of the present study, some reactions for which rate data
was not available from Engleman et al. were hypothesized and are included in
the set [reactions (8), (140), and (151), see Table 3.1)]. The rates for these
reactions were determined by the methods shown in Appendix B. It was necessary
to generate such data for the species methoxyl (CH_O) which is not available in
o
the JANAF Tables (1971). The procedure and results are shown in Appendix C.
These calculations are in reasonable agreement with some sparse data which
are recently available.
C. SCREENING CRITERIA
1. General
The screening is accomplished by elimination of those reactions whose
contribution to the production or destruction rate of any particular species parti-
cipating in that reaction is less than some specified percentage at each integra-
tion step. The specified percentage is the screening criterion.
In the present application of methane combustion in air with pollutant
formation, some "key" species were assigned more stringent criteria than the
other species. It is useful to use different criteria for different species because
the same accuracy or relative importance is not attached to all species.
2. Screening for Pollutant Formation (Key species NO, O, CO)
Screening reactions for their importance in pollutant formation can be
accomplished by placing stringent criteria on the pollutants of interest (NO
and CO). Since intermediate radicals such as O-atoms affect NO formation,
a criterion is also placed on one of the intermediate radicals (HO or H or O).
It is not necessary to place criteria on all radicals since they are safely
assumed to be interrelated through the O-H chain mechanism. For example,
our studies show that the ratio (O2)(H)/(O)(OH) takes its equilibrium value for
combustion around T « 2000°K.
13
-------
3. Screening for Heat Release (Key species CH , CO, H.O)
o ^
Screening reactions for their importance in heat release is done by
placing criteria on the three groups of species in the hydrocarbon breakdown
scheme: main reactants, key intermediates, and products. The key species
are thus chosen from the following chart:
Reactants Intermediates Products
CH,CH,,O. CO;OH,H,O CO.,H0O
O fi Z 6
It was presumed that we need only place a criterion on two of the three groups,
since they are necessarily related by conservation of carbon atoms (e.g., if
the main reactants and key intermediates are known then the products are known).
Originally two key oxidation species were selected, these were CH4 and
CO, reflecting a key reactant and intermediate product. The key reactant was
switched from CH to CH, and this switch had little effect on computed species
4 o
concentrations. The temperatures computed with screened reaction sets were
quite sensitive to the choice of CH. vs. CH as key species. In an attempt to
fx O
screen on the heat release per se, we designated HO as a key species, since
£4
H.O production is closely related to the heat release. The addition of H2O as
a key species increased the resulting reaction set by a few reactions, but greatly
improved the heat release authenticity.
4. Stringency of Retention Criterion
The 5%/10% criterion was adopted, where the first digit indicates the
criterion on the "key" species and the second digit gives the criterion for all
other species considered. It was felt that this was conservative but not overly
Several different computer runs for WSR (<£ = 1) case were carried out in
order to examine the effect of the retention criterion. Three criteria were exa-
mined: these are noted as 5%/10%, 5%/25%, and 10%/25%. Recall that the
reaction screening is carried out by elimination of any reaction whose percentage
contribution to the production or destruction rate of the particular species is less
than the criterion.
14
-------
Case I. Key Species: CH , CO, NO, O
o
The following reactions were screened out with a 10%/25% criterion but
retained with a 5%/25% criterion:
(47) CHO + HO = CO + HO
(99) HO + M = H + O+M
Case II. Key Species: CH4/ CO, HO, NO, O
The following reactions were screened out with a 5%/25% criterion but
retained for a 5%/10% criterion:
(12)
(22)
(68)
(83)
(118)
(143)
CHO + H
CO + H
CO + NO
H2 +O
H20 + 02
CO + HO2
= CH + HO
= CH +O
= CN + O2
= H +HO
= HO + HO2
= CHO + O2
Accordingly, the more stringent 5%/10% criterion was adopted. Reactions (83),
(143), and (99) ended up in the final controlling set (see Table 6.1, p. 52).
Reaction (68) was restored in order to match predictions with data on fuel-rich
stirred reactors (see Table 7.4 , p.66 ).
15
-------
IV. RESULTS FOR PERFECTLY-STIRRED COMBUSTION
A. STOICHIOMETRIC (0= 1) PERFECTLY-STIRRED REACTOR
1. The WSR (0 = 1) Case History—An Illustration of the Screening Methods
It is instructive to summarize the specific steps taken to determine the
controlling mechanisms for the WSR (<£= 1) case before documenting the results
of the reaction screening and elimination of species in more detail. A 22 reaction
16 species mechanism was derived from the original reaction set of 134 reactions
and 25 species. Table 4.1 shows how the reduced set evolved.
Table 4.1
SELECTED TEST CASES FOR WSR (0=1)
Orig.
Purpose of Run Run*
To establish reference
solution
To apply 5V10X screen-
Ing criteria and confirm
validity of screened set
Attempt to remove more
reactions
Compute Jacoblan to
identify marginal
species
Explore validity of remov-
ing eight species
Explore validity of remov-
ing 10 species (2 add'l
over Run #5)
Attempt to reproduce
temperature of reference
Final reduced set
1,13
3.14
f
4
6
S
8
12
1$
REACTIONS
No.
134
53
46
46
26
18
33
22
Remarks
Master set
Only those reactions
satisfying 5%/10X
criteria
Remove seven more
reactions which were
(a) marginal (screened
out by S*/25%
criteria
(b) Important to gross
production but not
to net production
Same as above
Remove reactions
associated with Insig-
nificant species: 10
reax Involving CN.HN,
CHN,HNO: S reax
Involving CI!,CH2; 4
reax Involving NO2,
Same as above; also
remove six reax involv-
ing IIO2 and two reax
involving CHjO
Starting with 46 reax
of Run 414 , remove 14
reax Involving CN ,
NOj.N.O, and ClljO.
Also restore O+H*M-
OH *M (screened out
by Runs #3,14)
Starting with 18 reax
of Run 18, retained
O+H+M - OH«M and
retained three HO
reactions
SPECIES
No,
25
25
25
25
*
17
15
21
16
Master set
Master set
Master set
Master set
Based on above, remove
eight species: NOj.CH,
CN,CHN,N20,CH2,HN,
HNO (retain CH3O)
Same is above: alto
remove HOj and CHjO
Remove CN,NO,,N,O,
CHjO
'
Remove nine species:
NO,.CH.CN,CHN.
N20,CH,,HN.HNO.
CHjO (HOj retained)
RESULTS
NO
34
33
34
34
33
32
32
13
°r
2064
2050
20SO
2050
2050
2038
2058
2059
11 reactions eliminated
Temperature somewhat
low (see Table 4.2)
Changes appear to be
permissible
Nine marginal
species Identified:
CH.CN.NO,,CH,.HN.
KjO.CHjO.CHNTHNO
Changes appear to be
permissible
e CHjO Insignificant
e HO2 significant
(Intolerable tempera-
ture error)
Better agreement with
reference temperature
Predictions appear to be
more accurate than Run
•3 (see Table 4. 2)
16
-------
2.
Application of Screening Criteria
The master set of 134 reactions in 25 species were screened with a
retention criterion of 5% on the key species and 10% on all the others. The
key species were taken as CH4, CO, H_O, O, and NO. After the screening
there remained 53 reactions in 25 species. The results are compared in Table
4.2, and show excellent agreement except for CH3O (10 ° vs 10 ).
Table 4. ?.
COMPARISON OF RESULTS
FOR WSR (0 = 1) CASE
Species
CM
CHO
CH?0
CH10
CN
co?
HN
HO
H2
N
N?n
ny
CHN
rw?
CH3
CH4
CO
H
HO?
H20
NO
N2
0
T,°K
Reference Case
134 reax; 25 sp
Mass Fraction
S.44B525E-08
1 .OQ7949E-06
B.556080E-06
1.2BS174E-10
1.724417E-14
J .U99303E-01
1 t 9R93Q6E "09
5.137354F-03
8.50S206E-04
1 t004477E-0*
1.737365E.-07
1 ,99fl9HHE-02
8.6276B7E-12
1 §822494E-07
1 . '9?
-------
Comparing the results of the 53 reaction set to the 134 reaction set in
Table 4.2, it was felt that the observed temperature difference was too large.
The deleted reactions were examined individually for the dual properties of having
been marginally deleted as well as having a large heat of release. The reaction
(99) H04M = H + 0 + M, AH = 102.229 kcal/mole
failed to meet the 5% criteria because it contributed 4% of the destruction of
0-atoms (and less than 3% to the net production of HO and H). Its restoration
in the reaction set increased temperature from 2050°K to 2058°K (compared
with 2064 K for the complete reaction set).
3- Determination of Insignificant Species
After the first screening, the Jacobian elements of the set of ordinary
differential equations, viz.,
3 dci (where CA can represent concen-
d(C ) dt tration or temperature)
were calculated and displayed for i = CH., CO, H_O, O, and NO, and tempera-
ft £t
ture. This Jacobian matrix is examined for candidate species whose influence
on methane oxidation or pollutant formation is small. There were nine candidate
species: CH, CH , CH O, CHN, CN, HNO, HN, NO0, and N0O (as shown in
£,» o fL ft
Table 4.3) which were examined individually for their influence.
Table 4.3
MARGINAL SPECIES
[WSR (0 = 1)]
Relative Influence Variable
of ] Compared to Most
Species Influence of Affected
_] Important Species bv I Remarks
CHgO
CH2
CH
CHN
HNO
CN
HN
ID'6
ID'2
ID'4 .
ID'4
ID'1
i«f4
1U-5
T
T
NO
T.OH
___
[potentially Important for fl» 1 (see Chap VII)]
[potentially Important for 4>1 (see Chap VII)]
[found to be In a "loop"]
NO. 10"3 NO [exists via exchange reactions with NO]
f3
NO 10"7 [potential alternate path to NO (see Tig. 4.2)]
18
-------
In some cases species may be eliminated because they occur in a chain
of reactions which is of minor consequence. In other cases we are led to loops
of reactions which exhibit steady state exchange of atoms with negligible net
effect on hydrocarbon oxidation or pollutant formation. The species and loop
screening are carried out by hand with the help of the computer output (Jacobian
matrix and reaction screening) described above. Some examples are given below.
Example; Elimination of the Species Methlidyne, CH
(18) CH + HO — CH + HO
(24) CH + O2 — CHO + O
Reactions (18) and (24) in sequence constitute a path from CH0 to CHO/
£*
with CH the intermediary competing with CH O. However this path is
£»
very minor: reaction (24) contributes only .13% to the production of CHO
and reaction (18) destroys only 0.4% of the CH,,. These reactions were
it
retained by the reaction screening because of their obviously large effect
on CH, but can be neglected because they do not affect the principal
CH. oxidation scheme.
Example: Elimination of HNO and its Effect on NO-Formation
This loop concerns the conversion of nitric oxide to nitroxyl (HNO) and
then back to nitric oxide. _ . , , inn !«,/„-„
Rate based on 100 moles/sec
Reaction Production rate of NO
(92)
(115)
(82)
(113)
(69)
(90)
NO +H
HNO +
HNO +
HNO +
HNO +
HN + O
+ M — HNO + M
O -» HO + NO
H — H + NO
£
OH -» H2O + NO
CO -* HN + CO-
— H +NO
-43
+23
+11
+ 3
+ 4
- 2 net
The net destruction rate of NO due to these reactions is 4% of the net
production of NO due to all sources (48 units—see Figure 4.2). More-
over, the concentration of HNO is of the order of 25 ppb. On these bases,
these reactions and the HNO species were deleted.
19
-------
Proceeding in the manner indicated above for species and loop screen-
ing, all of the species CH, CH2, CHgO, CHN, CN, HN, HNO, NC>2, and
N O were eliminated for the case WSR (= I), resulting in 22 reactions in 16
ft
species; The results from this reduced set were actually closer to the refer-
ence solution than the 53 reaction set discussed previously, as may be seen
in fable-4.2. The only noticeable deviations are in CH4 (9% lower), HO2 (30%
higher), and CH2
-------
5. Critical Paths for Methane Oxidation
Figure 4.1 shows the principal paths identified for methane pyrolysis
and oxidation. This figure shows the progressive oxidation sequence CH .—*
CH, —'CH O -> CHO -* CO. The number above each path indicates the
O M
relative rate of carbon transfer by that reaction path. The major
initiating reaction is CH4 + OH -* CH + H2O, presumably because OH is
prevalent under backmixed conditions. Surprisingly, the initiating reactions
(61) CH + M = CH + H + M
T O
(64) CH4 + 02 = CH3 + H02
are of no consequence and are omitted. Indeed, this turns out to be true under
lean and rich conditions as well. Three paths from CH, to CHO were found and
O
are discussed below.
a. Formaldehyde Path
The principal path from methyl (CH,) to formyl (CHO) is by a series of
O
simple oxidations through formaldehyde (CH O). This accounts for 35% of CHO
formation.
b. M ethylene Path
A large percentage goes through reactions of the form CH + CHgO—»
CHO+CH .. . These reactions involve methylene (CHj. This path becomes
n+l z
increasingly more important with increasing equivalence ratio (fuel rich condi-
tions) . This loop has only a net 1% effect on the destruction of CU^, however,
it has a very substantial effect on CHO formation. Since the rate of CH2 +
CH_O—»CHO + CH, is quite uncertain, and since parallel path (a) was available and
L o
gave nearly identical WSR concentrations, we arbitrarily eliminated CH and
path (b) from the set, saving three reactions.
c. Methoxyl Path
Another path for the destruction of CH is through the radical methoxyl
O
(CH-O), through the reactions
u
21
-------
Figure 4.1
COMPLETE MECHANISM
(Based on 134 reactions)
INPUT
FROM
CH20+CH2
METHANE OXIDATION PATHS
WSR (0= 1)
TO CH3
to
to
Rate numbers based on
100 mole/sec production
of (CO + CO2)
75
OUTPUT
SIMPLIFIED MECHANISM
(22 reactions)
too
too
-------
(148) CH3 + 02 = CH30 + O
(149) CH O + M = CH2° + ° + M
but these turn out to be too slow to have an appreciable effect on the CH_,
O
so they can be safely omitted from the scheme.
d. Oxidation of Formyl
It is seen in Figure 4.1 that there are five parallel paths for the con-
version of formyl to carbon monoxide; of these,
(143) CHO + O- = CO+HO9
Lt £*
is not important in the methane breakdown scheme but is in HO_ production.
6. Critical Paths for Nitric Oxide Formation
The detailed pollutant formation mechanism is shown in Figure 4.2.
The bottleneck in the rate of NO formation is the process of breaking up mole-
cular nitrogen, and for this there are three alternatives. N can collide with
O atoms, giving NO + N (the Zeldovich mechanism); N can combine with O in
a three-body reaction to form NO; or N can collide with an active hydrocarbon
it Lt
radical such as CH . For the 134-reaction set considered here, we see that of
all possible paths to NO, only the extended Zeldovich mechanism, viz.,
(125) O + N = NO + N
£t
(133) N + O = NO + O
(91) OH + N = NO + H
survives the screening process. Other reactions of the type R + N = RN + N
£
(not in the 134-reaction set) may also be important (see Chapter VII). Without
these reactions, the master set indicates that 99 .4% of the non-N2 nitrogen
ends up as NO, rather than in the form of HN, HNO, NO, NO_, or CHN.
Z £t
The potential importance of N9O can be seen from Figure 4.2 which
tt
shows that N destruction to form NO nearly equals the rate of reaction (125)
shown above. While most of this N2O returns to NZ/ about 1% of the NO is
formed by reaction (135):
23
-------
Figure 4.2
tfe.
NITRIC OXIDE FORMATION PATHS
WSR ($= 1)
+CO
COMPLETE MECHANISM
(Based on 134-reaction set
for CH4/air)
Numbers based on
100 moles/sec pro-
duction rate of NO
(48 of which is
output)
+0+M
SIMPLIFIED MECHANISM
(22-reaction set
for CH4/air)
OUTPUT
48
OUTPUT
-------
(135) N O + O -» NO + NO
£i
Because of the potential importance of NO, the rates of the following reac-
tions should be better established: y
(140)
(98)
(135)
(96)
(114)
N + O + M
b
NO + H
£t
N20 + 0
NO +H
NO + OH
- N20 + M
— N + OH
-» NO + NO
— NH + NO
— NO + HNO
4
In this regard, the rate of reaction (140) seems uncertain to a factor of X 10 .
Compared to the rate used in this study, Barton and Dove (1969) recommend
a rate 103 faster, whereas Olschewski, Troe, and Wagner (1967) list a rate
of X 200 slower.
These nitrogen oxide reactions are coupled to the hydrocarbon oxida-
tion reactions through the O-H chain reactions. Methane breakdown generates
radicals which then react with nitrogen.
B. FUEL RICH (0 = 1.25) PERFECTLY STIRRED REACTOR
1. Application of Screening Criteria
As in the WSR (<£ = 1) case, the residence time is 2 msec here. How-
ever, in order to explore the effect of preheat the WSR ( > 1) case was run at
a specified temperature of 3960°R as opposed to the 3700°Radiabatic tempera-
ture of the 0= 1 case. The reaction screening reduced the original set of 134
reactions to 48 reactions.
2. Elimination of Insignificant Species
Following the procedures previously discussed, we were able to eli-
minate the following eight species: CH, CHQO, CHN, CN, HN, HNO, NO0,
•j 2
and N_O. In addition, methylene (CHj was eliminated due to uncertainties
over the existence and the rates of the following reactions:
25
-------
(56) CH3 + H
(57) CH.+HO = CH0+HnO
1) concentrations were essentially unchanged, which
means that NO formation and CH. oxidation are insensitive to the CH —» CHO
path under these conditions. Nevertheless, the three methylene reactions
(56), (57), and (39) are singled out as being potentially important in pyrolysis of
methane. Furthermore, when additional reactions of the form R + N0 -»RN + N
£»
are added to the 134-reaction set, CH2 may become important (see Chapter
VII). The explanation of measured NO and CHN in jet-stirred reactors at 0>i
also indicates that CH? may be important.
3. Controlling Reaction Set
The subset of reactions controlling the fuel-rich stirred reactor contains
21 reactions in 16 species. These are shown in Table 4.5.
Table 4.5
SCREENED REACTION SET (21 REAX)
FOR FUEL-RICH STIRRED REACTOR [WSR ( > 1)]
036 «JHU + M = UU + H + M 04« CHO + H = CO + H2 083 H + HO - H2
077 CO2 + M - CO + O + M 046 CH2O + O = CHO + HO 085 H + HO2 « HO
084 H20 + M = HO + H + M 047 CHO + HO = CO + H2O 088 HO + H2 - H + HZ
099 H+O+M -HO + M 052 CHO + O - CO + HO 091 HO + N - H + NO
101 H + O2 +M = HO + H +M 059 CH3 + O = CH2O + H inn HO + O - H + Q2
HO+HO -H20 + 0-
N + NO »N2 + 0
CHO+ 02 -CO + H02
26
lar Reactions
CHO + M =CO + H+M
CO2 + M =CO + O + M
H2O + M =HO + H+M
H+O+M =»HO + M
H + O2+M = HO + H+M
Bimolecular Reactions
044
046
047
052
059
065
066
070
CHO + H
CH2O + O
CHO + HO
CHO + O
CH3 +O
CH4 + H
CH4 + HO
CO +HO
= CO + H2
= CHO + HO
= CO + H2O
- CO + HO
= CH2O + H
= CH3 + H2
- CH3 + H20
= CO2 + H
083
085
088
091
100
117
125
143
-------
4. Critical Paths in Methane Oxidation
The differences in the methane breakdown scheme between 1 and
0=1 can be seen in Figures 4.3 vs. 4.1. We observe the following:
1. The fuel rich conditions rule out the initiating reaction
CH. + O = CH., + HO and causes a substantial shift from reaction
(66f (CH4 + HO = CH3 + H20) to reaction (65) (CH4 + H = CHg + H2).
2. The methylene path is favored over the formaldehyde path. A larger
percentage of CH~ goes to CH- in preference to CH^O. The main
path to CHO in the fuel rich case is through the reaction
CH2 + CHoO = CH + CHO, rather than by reaction (46).
However, XUH andthe methylene path were arbitrarily deleted
for reasons described above.
3. The remainder of the chain is essentially the same, the
principal reactions being
(36) CHO + M
(70) CO + HO
— CO + H -
- C02+H
5. Critical Paths of NO Formation
The NO-formation reactions are even simpler than in the stoichiometric
case. The oxygen-deficient conditions cause a slow rate of formation of NO
and the second Zeldovich reaction
(133) N + O2 = NO + O
is screened out upon application of the 5%/10% screening criterion. Likewise
the reaction
(135) N2O + O — NO + NO
producing only .16% of the NO, is screened out for the rich case. Just as in
the WSR ( = 1) case, NO is formed from N at a rate comparable to the
Zeldovich rate (in this case in 1:3 proportions) but all NO returns to N9 via
£t £»
N O + H [reaction (98)].
27
-------
COMPLETE MECHANISM
(Based on 134 reactions)
INPUT
FROM
CH2O +CH2
Figure 4.3
METHANE OXIDATION PATHS FOR
FUEL-RICH STIRRED REACTOR [WSR (<£ > 1)]
TO CH,
to
OB
10
Rate numbers based on
100 mole/sec production
of (CO + C02)
SO
OUTPUT
SIMPLIFIED MECHANISM
(Based on 21 Reactions)
100
(CH20
i+O 100
+M
-------
Thus, essentially all of the NO is formed by the two reactions
(125) O+N2 = NO+N
(91) HO + N = NO+H
It should be emphasized that these results are only as valid as the original
134-reaction set. In Chapter VII we suggest additions to the set of the form
R + N2 -» RN + N which seem needed to explain fuel-rich NO data, for which
the altered Zeldovich mechanism [(125), (91)] is entirely inadequate.
C. FUEL LEAN (0=0.8) PERFECTLY STIRRED REACTOR
1. Application of Screening Criteria
The residence time of this adiabatic stirred reactor is again taken at
2 msec. The reaction screening reduced the original 134-reaction set to 48
reactions. The reaction
(99) H+O + M = HO + M
was restored to the set as an important source of heat release, even though
the 5%/10% screening criteria indicated it had less than a 5% influence.
2. Elimination of Insignificant Species
Following the procedures of the 0 = 1 and <£ >1 well-stirred reactors,
the eight species CH, CH0, CH0O, CHN, CN, HN, HNO, and NO_ were
i. O £•
eliminated, thus resulting in 23 reactions. In this case N2O must be retained
as explained below in paragraph 5.
3. Reduced 2 3-Reaction Set for WSR (0 < 1)
The resultant set of 23 reactions is shown in Table 4.6.
29
-------
Table 4.6
SCREENED REACTION SET (23 REAX)
FOR FUEL-LEAN STIRRED REACTOR [WSR ( < 1)]
Termolecular Reactions
036 CHO +M=CO + H + M
077 CO2 + M = CO + O + M
084 H2O + M = HO + H + M
099 H + O + M = HO + M
101 H + O2 + M = HO2 + M
140 N2O + M -N2 + O+M
Blmolacular Reactions
046 CH2O + O = CHO + HO
052 CHO + O = CO + HO
059 CHS + O = CH2O + H
063 CH4 + O = CHS + HO
065 CH4 + H = CHS + H2
066 CH4 + HO - CH3 + H2O
070 CO + HO = CO2 + H
085 H + HO2 = HO + HO
088 HO + H2 = H + H2O
091 HO+N =H+NO
098 H + N2O = HO + N2
100 HO + O = H + O2
117 HO +HO = H2O +O
125 N + NO =N2+O
133 N + O2 = NO + O
135 N2O + O = NO + NO
143 CHO + O2 =* CO + HO2
4. Critical Paths for Methane Oxidation
The methane breakdown scheme in the lean case is shown in Figure 4.4
The results obtained here are not unlike those obtained for the 0= 1 case.
The following observations are made in comparing the lean with the
stoichiometric case:
1. In the lean case, the high oxygen concentration leads to
an increased importance of the oxygen-bearing species
in the initiation reactions (CH4 + O and CH4 + OH).
30
-------
COMPLETE MECHANISM
(Based on 134 reaction set)
FROM
CH20+CH2
Figure 4.4
METHANE OXIDATION PATHS FOR
FUEL-LEAN STIRRED REACTOR [WSR (oi> < 1)]
TO CH3
Rate numbers based on
100 moles/sec net pro-
duction of (CO + CO2)
OUTPUT
SIMPLIFIED MECHANISM
(BasedMDn 23-reaction set)
100
100
OUTPUT
-------
2. The methylene (CH2) reactions are suppressed by the rapid
consumption of CH3 by the reaction CH3 + O = CH2O + H.
Unlike the 1 cases, one need not overrule
the numerical computation in discarding the CH2 reactions.
The remainder of the scheme is approximately the same as the stoichiometric
and fuel-rich cases.
5. Critical Paths to NO Formation
The major path to NO is through the conventional Zeldovich mechanism,
with N + OH providing 19% of the fast second step (as opposed to 78% at 0 > 1):
(125) O +N2 -^ NO +N
(133) N + O2 -^ NO + O (81% of N)
(91) N + OH ^ NO + H (19% of N)
86% of net NO
In addition, an NO mechanism provides the remaining 14% of the NO.
£+
It was found that reaction (140), the recombination of N + O + M —N O + M,
is four times as active as reaction (125). Although 96% of the NO returns to
£
N2 (via N2O + H), the remaining N-O can lead to increased NO by the follow-
ing competing reaction:
(135) N2O + O -^NO + NO .
Since the rate of reaction (140) is unknown, this result should be explored
with further studies. The nitrous oxide reactions are unimportant in the
stoichiometric and fuel-rich cases because the NO-producing step
N2O + O—NO + NO is less important in their O-atom deficient atmospheres.
The importance of reactions involving N9O in lean systems has also been
£i
suggested by Pratt and Malte (1973).
D. SIMPLIFICATIONS TO THE METHANE OXIDATION MECHANISM
Consider the following mechanism for CH -*-CHO conversion:
O
32
-------
Path 1: Direct
Two-Step Through
CH20
Path 2: Parallel
Through CH_
£
Path 3: Formalde-
hyde Bypass
Step 1: Consume CH3
CH +O= CH2O + H
CH3+H = CH2+H2
CH3 + OH = CH2 + H2O
Step 2: Form CHO
CH O + O = CHO +H
CH2 + CH2O = CHO + CH3
Single Step CHg to CHO
CH3 + O = CHO + H2
In the conversion of CH3 to CHO, the direct two-step route through formaldehyde
gives over to the parallel route through methylene (CH_), as the equivalence ratio
is increased. Nevertheless it appears permissible to use simpler path (1) instead
of path (2) without incurring error. Both path (1) and path (2) are presumably
equal in terms of radical generation. In both cases we notice that the Step 1
reactions are all chain terminating (one radical product for two radical reactants) /
while the Step 2 reactions are all chain branching (two radical products for one
radical reactant).
Compare paths (1) and (2) with what might be called the formaldehyde-
bypass reaction (path 3), which is an alternative route from methyl to formyl,
viz.,
(144) CH + O = CHO + H
This reaction goes directly from methyl to formyl, omitting the intermediate
CH9O, and is probably not elementary. It has been used to simplify methane
£*
oxidation schemes because the second step of the two-step process CH + O—»
O
CH O + H —»CHO + H is fast. This reaction is chain terminating, as opposed
Z £
to the net chain carrying effect of the two-step routes discussed. The effect
of using the bypass reaction was to reduce the O-atom concentration and
hence reduce the NO. However, in substituting path (1) for path (2), no such
difficulties accrue.
33
-------
V.
A.
1.
RESULTS FOR PYROLYSIS. IGNITION. AND POST-FLAME REACTIONS
PYROLYSIS AND IGNITION AT STOICHIOMETRIC (0 = 1)
Application of the Screening Criterion
We attempted to simulate the ignition conditions of a combustor,
wherein the premixed reactants are visualized to mix with hot products of
combustion just before ignition (see Figure 5.1). For the purpose of this
computation, this ignition condition was represented by a 70/30 mixture of
reactants to equilibrated combustion products at a mixed temperature of
1200 K. These figures are, of course, arbitrary, but it is hoped that they
are representative of the actual situation.
Figure 5.1
SCHEMATIC OF IGNITION MODEL
Mixture of reactants
to products in 70/30
ratio at 1200°K
Hot combustion products
at 2000°K
As in the plug flow simulation of the post-name region, the screening
criterion is applied continuously during the ignition process. Again, experi-
ence demonstrated that the reaction screening criteria could be relaxed from
5%/10% to 5%/25%. Two regimes are readily apparent:
34
-------
• Pyrolysis (1200 - 1500°K)
• Combustion (T >1500°K)
In the combustion regime, once the incubation period is complete, what is
important is the species histories during the ignition phenomenon. However,
the ignition delay is of great interest in the pyrolysis regime.
The reaction screening on the original 134 reactions brings the set to
69 reactions in 25 species.
2. Elimination of Insignificant Species
As a first try at species screening, it was decided to follow the
example of the other screening cases and eliminate seven species: CH, CHN,
CN, HNO, HN, NO , and NO. This brought the set to 27 reactions/18
Lt £A
species. The predicted temperature and concentration histories were in fair
agreement. For combustion conditions (T > 1500°K), it was possible to eli-
minate five more reactions and one more species (CHgO) and still reproduce
the ignition profiles. This 22 reaction/18 species mechanism is given in
Table 5.2, p. 40.
However, at low temperatures (T < 1500°K), five other reactions had
to be added, otherwise the set predicted excessive CH.O and reduced igni-
tion delay.
3. Special Reactions for Pvrolvsis (T < 1500 K)
Some detective work was necessary to correct the excessive CHgO and
short ignition delay. As a result the following five reactions were added:
(41)
(60) CH0 + O- = CH_O + HO
32 £•
(64)
(58) CH, + O9 = CH9O + O
£+ u £*
(61) CH +H+M = CH + M
O T
However, none of the seven species (CH, CHN, CN, HNO, HN, NO2, or N2O)
needed to be restored. In what follows we present the details of the analysis.
35
-------
a. Adjustments to Recover Reference CH O Profile
£
CH2O builds up to huge concentrations prior to ignition, as can be
seen in Figure 5.2 where it is compared with the correct result (from the
69 reaction/25 species set). With respect to this early buildup of CH O,
there were five reactions containing CH2O which were deleted from the*
reaction set. Of these,we restored the reaction
(41) CH 0 + CH, —CHO + CH
£ o 4
which is an important destroyer of CH2O at early times, accounting for as
much as 95% of the term d(CH2O)/dt. The improvement from this change
[combined with restoring reactions (58), (60), (61), and (64) discussed in
c. below] is apparent from Figure 5.2.
Figure 5.2
COMPARISON OF FORMALDEHYDE PROFILES
FOR IGN (0 = 1)
.040
Incorrect Simple Solutlo
Scaled down x lo"1
(27 Reax/17 Species)
Reference Solution
(69 Reax/25 Species)
Final Solution
(32 Reax/17 Species)
.045 .050 .055 .060
Dimenslonless Distance, X
.065
36
-------
b. Additional Reactions Added for Pyrolysis (T < 1500°K only)
There are additional reactions whose omission could increase the
ignition delay by suppressing early radical buildup. We restored the reaction
(60) CH. +0. = CH.O + HO
O £• f'
which as a chain carrier is responsible for 32% of the production rate of
CH O at small times. Its inclusion should reduce the chain terminating
effect of reaction (59) , CH3 + O = CH2O + H, and thus reduce the ignition
delay. We also restored the reaction
(64)
which affects O at small times .
£*
There is still room for some improvement; with (41), (60), and (64),
ignition occurs too early, though the main criticism of the previous screen-
ing, the formaldehyde production, has been corrected. Seeking an even
better reaction set, the following reactions were restored to the set:
(58) CH2 + O2 = CH2O + O. At very small times, this
reaction accounts for only 1.1% of the production
of CH2O, but its omission changes the sign of the
net production of CH^O. Its inclusion should
improve both CH2 and CH2O, as well as O-production
rates .
(61) CH3 + H + M = CH4 + M. Omission of this reaction
was determined to be responsible for a methyl des-
truction rate which was too low.
The effect of the above-described corrections is seen for formalde-
hyde, Figure 5.2, based on a set of 32 reactions/17 species. The results
compare favorably.
An additional path for methyl decomposition is the formation and
subsequent dehydrogenation of ethane, which is known to exist at tempera-
tures as high as 1500°K in methane flames [Dryer (1974)]. In this case, the
scheme would be CH3 + CH3 + M - C^ + M, followed by C^ - C^-*
r H -» CH . Since ethane was not considered in the species list for the
24 2
present study, the significance of this ethane path was not explored.
37
-------
c. Effect of Methoxyl (CH3O) on Ignition Delay
In searching for mechanisms for increasing the ignition delay to its
reference value, it was decided to examine, in particular, the effect of the
species methoxyl (CHgO) on the ignition. It had originally been suggested
by Benson and co-workers (1972) that this species was potentially important
in methane combustion in the temperature and stoichiometry range of interest.
In fact, methoxyl had been screened out of every other case [i.e., WSR for
all 0and PFR (0 = 1)]. m the ignition case, however, the reaction screening
output indicated that the reaction
(148) CH +0. — CH00 + O
ot 3
is a marginal producer of O-atoms (responsible for as much as 7% of d[O]/dt)
at low temperatures and so can have a small but measurable effect on the
ignition delay interval. The effect of the species CH3O on the ignition pheno-
menon are shown in Figure 5.3. In this figure are plotted the temperature and
C-atom concentration as a function of distance for the 69-reaction screened
set and the same set less the two reactions containing methoxyl, viz.,
(148) CH3+02 —CH30 + 0
(149) CH30+M — CH20 + H+M
As can be seen in the figure the effect of the methoxyl is very small
indeed. There is a slight shift in the ignition but if the curves were over-
layed it would be seen that the O-atom concentration curves are identical
while the temperature profiles are identical for T > 1400°K. There is a
slightly larger gradient for T < 1400°K when the methoxyl is present. On the
basis of this comparison and the previous screening studies it seems reason-
able to conclude that methoxyl-containing reactions are not of importance in
methane combustion for temperatures in excess of 1500°K. Nevertheless
these reactions are included at low temperatures (T < 1500°K) and fuel-rich
conditions.
38
-------
Figure 5.3
EFFECT OF METHOXYL (CHgO) ON IGNITION DELAY [IGN (<£ = 1)]
(Temperature and Oxygen Mass Fraction)
E
0
a
e
0)
H
2600
2400
2200
2000
1800
1EOO
MOO
1200
CH-O Retained (69 reax)
CH3
°-05
CH30
Retained
(69 reax)
CH30
Deleted
(67 reax)
Dimensionless Distance, X
.011) .04$ .
-------
4' Controlling Reaction Sets for Ignition (22 Reax) and Pvrolvsis (33 Ra
With these reactions we have a set of 32 reactions in 17 species ,
listed in Table 5.1. The results are essentially indistinguishable from the
baseline case (69 reactions/25 species) .
TABLE 5 . 1
CONTROLLING REACTION
SET (22 REAX/15 SPECIES) FOR
IGNITION CASE [IGN (0= 1)]
(Sufficient for T > 1500°K)
Termolecular Reactions
/ 36
/ 77
/ 84
1 99
I 101
CHO + M
CO2 +M
H2O + M
H + 0 + M
= CO + H + M \
= CO + O + M
= HO + H + M
= HO + M
H + O2 + M = HO2 + M
Bimolecular Reactions
44
46
47
52
' 59
63
65
66
70
83
88
91
100
117
125
\ 133
\ 143
Pyrolysis
39
41
56
57
58
60
61
64
148
149
CHO + H
CH2O + O
CHO + HO
CHO +O
CHS + O
CH4 + O
CH4 +H
CH4 + HO
CO +HO
H +HO
HO +H2
HO + N
HO + O
HO +HO
N + NO
N + O2
CHO + O2
Reactions
CHO + CHS
CHO + CH4
CHS +H
CHS + HO
CH2 + O2
CHS + O2
CH4 +M
CHS + HO2
CHS + O2
CH3O + M
= CO + H2
= CHO + HO
= CO + H2O
= CO + HO
= CH2O + H
= CHS + HO
= CHS + H2
= CHS + H2O \
= C02 + H \
= H2 +O
= H+H2O /
= H + NO /
= H + 02 /
= H2O + O /
= N2 + 0 1
= NO + O 1
= CO + HO2
= CH2 + CH2O
= CH20 + CHS
- CH2 + H2
= CH2 + H2O
= CH2O + O
= CH2O + HO
= CH3 + H + M
= CH4 + O2
= CH3O + O 1
= CH2O + H + M /
CONTROLLING REACTION
SET (32 REAX/17 SPECIES) FOR
METHANE FYROLYSIS
(Needed to describe ignition
delay, T S1500°K)
40
-------
It is worthwhile noting that ten of the reactions discussed above are
important only at small times, i.e., at low temperatures. As such, these may
be classified as pyrolysis reactions which may be discarded for temperatures
in excess of 1500°K. In order to verify this, a special set of 22 reactions in
16 species was extracted from the 32 reaction/17 species set by eliminating
the pyrolysis reactions [including those involving CH2 which were discussed
in connection with the WSR (0 > 1) case]. This reaction set is shown in
Table 5.1 and appears to be valid to describe ignition following, ignition
delay. The agreement found for the temperature and each of the species
concentrations is good to excellent, for temperatures greater than 1500 K.
Of course, the ignition delay predicted by the smaller reaction set is meaning-
less.
5. Critical Paths of Methane Oxidation
The methane breakdown mechanism is shown at three specific times
during ignition (in Figure 5.4). Bearing in mind the purpose of this investi-
gation is to characterize the heat release and pollutant formation. We have
analyzed processes at ignition, at maximum O-atom concentration and at
maximum rate of nitric oxide formation. Notice that the times involved differ by
only a fraction of a millisecond, yet this time difference is larger than the
chemical runaway time. One important feature which distinguishes ignition
from the stirred reactor and post flame cases is the recombination of CO + H
to form CHO:
(36) CO + H+M -* CHO + M
This is probably attributable to the high CO-overshoot which occurs with the
runaway, arising because the main CO2-producing reactions are too slow to
keep up with the rapid production of CO.
A qualitative picture of the ignition phenomenon can be gained by
examining the history of key heat release constituents (CO and H2O), radicals
(HO and O), pollutant (NO), and hydrocarbon intermediate (CH2O, chosen
because it is the only stable molecule in the sequence). The results are
shown in Figure 5.5. The temperature and O-atom concentration profiles
41
-------
Figure 504
METHANE OXIDATION PATHS FOR IGNITION (= 1)
AT 86NITIOM jt = Qn I658°K)
NET CONSUMPTION
, i TO CH3
FROM CH2O4-CH2 ' ' ~ '
FROM
CHj+CHjO
WET
PRODUCTION
AT MAXIMUM O-ATOM CONCEMTRATIOiSi
(* = oOl msec, I8^°:<)
NET CONSUMPTION
NET
CONSUMPTION
'63
AT MAXIMUM RATE OF FORMATION OF NO
(8 = 024msec, 2I53°K)
All rate numbers based
on 100 mole/sec net
production of (CO + CO2)
NET
CONSUMPTION
100
100
PRODUCTION
CONTROLUNG MECHANISM
(22-REACTICN SZT)
NET CONSUMPTION
too
PRODUCTION
-------
have already been seen in Figure 5.3. The radicals behave in the same way
as CO, exhibiting a very sudden rise and overshoot then gradually relaxing
to equilibrium. The water behaves much like the temperature, rising monoto-
nically to its equilibrium value. The formaldehyde comes into existence
suddenly during the runaway and disappears as quickly as it appeared.
Figure 5.5
MASS FRACTION PROFILES FOR IGNITION
[IGN (0= 1)]
o
fi
w
(0
(0
.10
.04)
.041
•'*
.01
3-
.01
H20
CH20
.090 .099 .040 .361 .070 .071
Dimensionless Distance, X
(a) Carbon Monoxide and Hydroxyl Histories
.040 .04! .090 .OU .0*0 .0*1 .OH
Dimensionless Distance, X
(b) Water and Formaldehyde Histories
.070
6.
Critical Paths for Nitric Oxide Formation
Thus far, we have confined our attention in this case IGN (0= 1) to the
hydrocarbon sequence and no mention has been made of NO. Figure 5.6 shows
the NO concentration for the 69 reaction/25 species case, which allowing
for differences in the ignition delay, is reproduced faithfully by the controlling
22-reaction set. This brings up the question of prompt NO which is currently
of interest.
43
-------
In spite of an oxygen atom overshoot of 11 times equilibrium/ there is
negligible prompt NO formed. The NO-formation actually begins after the run-
away/ if we interpret the runaway to occur during the rise and fall of formal-
dehyde .
Figure 5.6
NITRIC OXIDE PROFILE FOR IGNITION
OF PREHEATED REACTANTS ( = 1)
.30 -i
.25
O
E
S .is
4>
•o
o .10
5
.05
Ignition spike
location
.040 .045 .050 .055 .060
Dimonsionless Distance, X
.065
.070
In fact/ while the NO-formation rates themselves are potentially very nigh during
the O-atom overshoot, the temporal duration is so short and the temperature is
so low as to preclude the possibility of forming substantial NO. Figure 5.7 shows
a blow-up of the runaway. The O-atom overshoot duration is only 150 microseconds
(O)/(O) has fallen to 1.5 before the temperature reaches 2000 K/ the temperature
eq
at which the NO-formation rate becomes significant. NO production from O-atom
overshoot cannot be ruled out in real flames, however/ since with backmixing the
high O-atom concentrations would be free to diffuse to adjacent high temperature
regions.
44
-------
An alternate possibility for prompt NO is the reaction R •+• N2 -* RN + N,
For example, if R is CH, RN is CHN. Indeed CHN has been observed in flat
flames [Eberius et al. (1973)]; however, none is predicted for the present 134-
reaction master set. Chapter VII describes how CHN and "prompt" NO would
be predicted if the reaction CH2 + N2 •* CHN + N were added to the 134-
reaction set.
Figure 5.7
DETAILED STRUCTURE OF IGNITION RUNAWAY
10
10
-2
X
10
-3
s
o
(0
2 -
O
ii. >- Coincide exactly
(si iuwa'separately ior clarity)
10
10
-7
2400
2200
2000
1800^
o
*
O
u
2
Ii
o
a,
1600 £
1400
1200
48.5
1000
49.0
49.1
45
-------
B.
POST-FLAME REACTIONS AT STOICHIOMETRIC (0 « 1)
1.
Application of Screening Criterion
A plug flow case was set up to represent the after-burning region of
a combustor, where the hot products such as CO equilibrate on longer time
scales than the main heat release zone. The initial composition was specified
as the WSR (= 1) output, and the case was constrained to be adiabatic.
The reaction screening on 134 reactions reduced the number to 61,
and the histories of key species and temperature are shown in Figure 5.8.
i
Figure 5.8
PROFILES FOR POST-FLAME CASE
(Plug Flow, 0=1)
.707
.10-
o-t
0
—i 1—— 1 1 I
.010 .020 .030 .040 .050
Dimensionless Distance. X
2400
-2350
-2300
-2200
-8150
"2100
2050
.060
.070
.080
46
-------
2. Elimination of Insignificant Species
Following the examples suggested by the stirred reactor runs, it was
found that the nine species CH, CH2, CHN, CH3O, ON, HN, HNO, NO2<
and N_O could be eliminated.
Ct
3. Reduced Reaction Set for PF (<£= 1)
This resulted in 23 reactions in 16 species; these are shown in Table
5.2. The predictions of this set compared favorably with the 61-reaction
set. Table 5.2
SCREENED REACTION SET (23 REAX) FOR
ADIABATIC PLUG FLOW REACTOR (0=1)
Termolecular Reactions
36 CHO + M = HO + H + M
77 CO2 +M = CO + O + M
84 H2O +M =HO + H+M
99 H+O + M =HO+M
101 H + O2 + M = HO2 + M
Bimolecular Reactions
44 CHO + H =CO + H2
46 CH2O + O = CHO + HO
47 CHO + HO =CO + H2O
52 CHO + O =CO + HO
59 CH3 + O = CH2O + H
63 CH4 + O = CH3 + HO
65 CH4 + H = CH3 + H2
66 CH4 + HO = CHS + H2O
70 CO + HO = CO2 + H
83 H + HO =H2 + O
85 H + HO2 = HO + HO
88 HO + H2 - H + H2O
91 HO + N =H+NO
100 HO + O = H + 02
117 HO + HO =H2O + O
125 N+NO = N2 + O
133 N + O2 = NO + O
143 CHO + O2 = CO + HO2
47
-------
4. Critical Paths of Oxidation
Oxidation paths are shown in Figure 5.9 for various elapsed times in
the simulated post flame region. Oxidation of the intermediates CH.O and
It
CHO in the earliest stages is somewhat artificial because of the initial con-
dition (in a real combustor the post-flame region would not start literally
with such a nonequilibrium WSR case). Therefore we direct the analysis to
the oxidation mechanisms occurring no sooner than 2 msec after the initial
condition. After 3 milliseconds, the methane, methyl, and formaldehyde are
totally consumed, and the main phenomenon is conversion of CO to CO. by
£t
reaction ( 70 ), CO + OH — CO + H, sustained by exchange reactions with
o
CO. The temperature has gone up from 2064 to 2251 K.
After 64 milliseconds, the CO has all been converted to CO,, and the
£*
temperature is equilibrated to a value 216°K above the starting condition.
Also the radicals O, H, and OH have equilibrated. For the remainder of the
residence time in the reactor only the slower NO-formation reactions are still
active and NO is being produced at a uniform rate (NO concentration increas-
ing linearly with time) j as shown in Figure 5. 10..
5. Paths of Nitric Oxide Formation
Because of the large residence time (60 msec) and the high adiabatic
temperature, cumulative NO was relatively high compared to the WSR cases.
Jt
In fact the N-O reactions were the only reactions significantly out of equili-
brium for t > 10 msec. But since products quickly cool by turbulent entrainment
in a real boiler, no inference can be made about the actual relative NO produc-
tion in primary vs. post-flame.
48
-------
Figure 5.9
METHANE OXIDATION MECHANISMS
IN SIMULATED POST FLAME CONDITIONS
PFR (0= 1)
(t = 0)
Same as WSR ( = 0
T = 2064°K
NO = 24 ppm
Rates w 10
mole/cc-sec
INPUT
TOCH3
OUTPUT
RELAXATION (t = 3.3 msec)
T = 2251°K
NO = 8° PPm
Rates « 10"7 mole/cc-sec
Rate numbers based on
100 mole/sec production
of (CO + CO2)
NET CONSUMPTION
RAiE
/IOO
OUTPUT RATE
(t - 64.5 msec)
•£ = 2280°K
NO = ?12 PPm
pates «10"10 molc/cc-sec
NET CONSUMPTION
RATE
100
-------
The O + N_-» mechanism [reaction (125)] controls N_ break up in the
2 ^
plug flow region, as shown in Figure 5. 10,
Four paths compete for the N-atoms produced by this NZ break up:
(133) N +O
NO + O
NO + H
HN + OH
(73) N +CO2 ->NO + CO
(91) N + OH
(104) N + HO
NO
32%
26%
26%
6%
The N O + O -* NO + NO path is of minor importance. Presumably if heat
loss had been simulated, NO -* NO0 would have been observed at lower
Li
temperatures.
Figure 5.10
NITRIC OXIDE MECHANISM IN SIMULATED POST FLAME CASES
PFR \ = 1)
•KOj 41
.^^ »
Elapsed Time 64 msec 48
NO = 712 ppm
O = 353 ppm
T = 2280°K
OUTPUT
O consumed to provide O atoms:
ITS TO
ZELOOVICH
50
-------
VI. SYNTHESIS OF THE SCREENED REACTION SET
A. UNION REACTION SET FOR FIVE TEST CASES
Because limiting cases have been included, the union of the five
reaction sets obtained in the sections IV and V hopefully represents most
of the reactions necessary and sufficient to describe methane combustion
and pollutant formation under the conditions
p = 1 atm
1500°K< T <2500°K
0.8 < <#>< 1.25
The reactions are summarized in Table 6.1, where the union is seen to consist
of 26 reactions in 16 species. Of these, 12 are related to the methane break-
down, 8 are in the O-H chain, and 6 are related to the pollutant formation
(i.e., nitric and nitrous oxide). Table 6.2 compares this union set with
reactions selected by previous investigators.
B. CORROBORATION WITH THREE NEW CASES
To confirm the predictive validity of the reaction set, the following
cases were run using the 134-reaction master set and then repeated with the
26 reaction set:
IGN (0 > 1): Ignition of methane/air at an equivalence
ratio of 1.25 . As with IGN (0< 1). a 70/30
ratio of reactants to equilibrated products was
permitted to ignite at 1200°K.
PFR (0< 1): The output concentration from a well-stirred
reactor at 0 = 0. 8 was permitted to approach
equilibrium adiabatically.
PFR (0> 1): The output concentrations of a stirred reactor
at 0 = 1.25 was permitted to approach equili-
brium through a region with a T4 heat loss.
51
-------
Table 6.1
UNION OF CONTROLLING REACTION SETS
# -n - E/RT
Rate Coefficients k = A T e
Conditions for
Reaction
Number Reaction
CH4 Partial Oxidation
036 CHO +M=CO *H *M
044 CHO *M =CO *H2
046 Cn20»0 =CHO *HO
047 CnO +HO =CO *H«£0
052 CHO +0 =CO + HO
059 Cn3 »0 =CH20*H
063 Cn4 *0 sCn3 *HO
065 Cn4 »H =CH3 *H2
066 CH4 + HO =CH3 *H«JO
143 CHO *02 CCO *H02
CO Oxidation
070 CO *HO =C02 *H
077 C02 +M*CO *0 +M
O-H Reactions
083 H «HO =H2 *0
084 H?0 tM = HO »H »M
085 H *H02 =HO *HO
088 HO «H2 =H »HSO
099 H *0 tM = HO +M
100 HO *0 srt »0<*
101 H *0?+M=HO? +M
117 HO «HO =H20 *0
NO Formation
091 HO *N *H *NO
098 H *N?0 eMO • *N«J
125 N *NO sN2 *0
133 N *02 s,^o *0
135 N?0 «0 =NO +MO
140 N?0 +M sN2 *0 tM
Low Temperature Pyrolysls
039~ CHO »Cn3 =CH2 *CH?0
041 CnO *Cn.4 =CH20+CriJ
056 CH3 »M =CH2 *HcT
057 Cn3 *HO *CH^ *H«iO
058 C^2 *02 =0^20*0
060 CH3 *0? =CHiJO*Hf>
061 CH4 -»M =CH3 *H «M
064 CH3 »r»02 cCH4 *()2
148 Cn3 *02 *CH30»0
149_ CH30 *M=CH20»H «M
A
?.-iO!:*20
3.00E>10
?« PDF *i i
3.00E'*10
3.00E*11
2.00K*12
l.OOf *10
<5.00E*10
1. 00^*1 3
fl.OOE*12
4,OOE*09
1.00E*15
8.00E*09
3.00E*15
2«50E*14
?.50E*13
?!50E*13
1 »50E*15
6.00E*12
6.00E*11
P.OOE*13
1.50F.+ 13
6.00F.*09
1.00E#14
1.00£»1»
1.50E*11
8.00F.»11
?.OOE*11
6.00E*U
5. OOF* 1 1
3.00E*13
?.OOF»17
1.00F*11
2.50E«09
4.00E»40
n
1.5
1.
1.
1.
1.
.5
1.
1.
,0
,0
- .5
0,
- 1.
.0
- .0
* .0
.0
• .0
.0
- .0
.5
.0
.0
1.
.0
.0
• .7
- .6
- .7
- .7
• .5
• .0
.0
- .5
-1.
7.5
E
16.8
0.
*.* .
0.
,5
- .3
8.
10.
5.
0.
0.
100.
7.
105.
1.9
5.2
0.
0.
1.
1.
8.
15.
0.
6.3
H8.
50.
*.
9.
3.
2,
7.
30.
88.
6.
2fl.5
22.6
1
Reference
BENSONU973)
BENSONt 1973)
BENSONU973)
BENSON! 1973)
BENSONI1973)
MORR1SU973)
WESTENBERGU969)
WALKER (196B)
W1LSONI1972)
PEETERSU973)
ENGLEMAN(I973)
CLARK (1971)
BAULCHU973)
BAULCHU972)
BAULCH(19?2)
BAULCHU972)
SCOFIELOU973)
8AULCH(1972)
BAULCH(1972>
8AULCH(1972)
BENSONt 1973)
BAULCHU973)
BAULCH(I973)
BAULCHII973)
BAULCH(1973)
ENGLEMAN1I973)
TUNOER(1967)
TUNDEP(1967)
TUNOER(1967I
TUNPERU967)
TUNDER ( 1V67)
BENSON! 1973)
HARTIG(1971)
TUNDER 11967)
BENSONU973)
BENSON (1973)
Which Reaction
is Needed
All
$< 1
All
< 1
All
All
0 < 1
All
All
All
All
All
0— 1
All
IGN
All
All
All
All
All
All
-------
Table 6.2
COMPARISON OF CONTROLLING REACTION SET
WITH THOSE OF PREVIOUS INVESTIGATORS
APPLICATION
REACTION!!
CH3 + H -CH2
CH3 + KO • CK2 * K2O
CH2 * O2 - CH2O » O
61 CH4 » M « Cti3 » H » M
02
148 CHJ » O2 « CKiO * O
20-H «M
(3 CH4 » O • C!I3 » KO
6S CH4 » H - CH3 + Hi
CH20 + C • CliO ' KO
CH20+H-CHO'K2
36 CHO + M • CO + K * M
44 CHO + H > CO * S
47 CHO » HO - CO * H^O
S2 CHO + O - CO + KO
13 CHC » "» - '"^ » '-'<"'
CO * HO - CC2 + H
H +HO-H2 + 0
H + HO2 • HO » HO
86 H + H02 - K2 * 02
88 HO»H2 - H + H2O
100 HO + 0 » H + C2
116 H2 » O2 - KO * HO
118 HO + HO2 - H2O - C2
L22 HOZ *O * H
79 H2 » M - K + H * M
14 H20 + M-HO*H»M
$9 H+O»M-HO
101 H +O2 +M -H02 *M
142 O + O + M-02* M
NA H + OH » H2C - K20 » HIO
CJ » H2O
91 HO » K • K * NO
124 N * N »M -:12 * M
12$ O + N2 - SO + N
132 NO * M - N * O » M
133 N + OZ • t.'O » 0
134 NO * '.:o * r.2 * 02
N2 * CM
127 N » NC2 " NO « NO
129 N * KC2 " N2 » O2
136 NO « NO2-J.20+C2
138 NO2 * M - MO * O * M
139 NO2 + O • NO « O2
IA. tiQ2 * M - n: • v • M
98 H » N2O ' !.O • N2
13S N2O * O « MO > NO
137 NO
MO N2O » M - .'i2 • I) • M
rt:o
•Olinsyittmi I'yiulyriia l".ic«lon«
53
-------
For the ignition case, IGN (0> 1), an additional run was made with the
union reaction set plus the ten pyrolysis reactions (for a total of 36 reactions
in 18 species). In all cases the comparisons were made graphically and
the results were generally excellent. A few exceptions did occur and these
are discussed below.
In the case IGN (0>1), the complete set with ten additional pyrolysis
reactions gives excellent agreement at low temperature, whereas the 26
reaction/16 species set exhibits gross misrepresentations (e.g., formaldehyde)
during preignition. It was also observed that HO radical concentrations were
about 50% greater with the 26-reaction set than with the more complete one.
The reference solution for PFR (0> 1) with heat loss predicted NO
slightly decreasing downstream, whereas with the reduced set NO tends to
remain constant. (See Figure 6.1) The change in NO concentration, amounting
to about 1% of original NO in 20 msec, was determined to be due to the
following reaction sequence
CHO + NO - CO + HNO -* CO. + HN
which was screened out of the 26 reaction set, and apparently only occurs
under peculiar conditions of heat loss and composition. This numerical
result suggests that NO may be reduced by injection of formaldehyde (a
stable hydrocarbon which readily goes to formyl) into the post flame zone.
Such scavenger techniques for reduction of NO have received only modest
attention in the literature to date. This result must be treated as speculative
because (a) the rates used in the calculation are unknown, (b) fuel rich
conditions are rare in post flame regions of real combustors, and (c) the
behavior may level off at a 2-3% reduction upon depletion of CHO.
It is felt that this agreement confirms that the union reaction set
of 26 reactions in 16 species to be as good as the original 134-reaction
set at describing methane combustion in the conditions previously stated.
54
-------
.30
.28-
-.26-
*• 24 -
It, •*••* \
tfl
Iff
O
•8
x .22
O
.20 -
.18
Figure 6.1
NITRIC OXIDE DECOMPOSITION
OBSERVED FOR PFR ( 1)
26 Reax (Controlling Set)
.
133 Reax (Master Set)
—I 1 1 1—
,005 .010 .015 .020
Elapsed Time (msec)
.025
,030
55
-------
VII. EVALUATION OF REACTION SET AGAINST STIRRED REACTOR DATA
A. PURPOSE
In the foregoing sections, a kinetic model describing CH./air combus-
tion was synthesized from a master set of 134 reactions with assigned rates.
It was found that 26 reactions are necessary and sufficient to duplicate to +5%
the predictions of the master set for .80«£< 1.25, 1500°K< T < 2500°K, and
P = 1 atm. The validity of this 26 reaction subset obviously depends on the
accuracy of the original 134-reaction set in two crucial aspects:
(1) That no significant reaction was inadvertently omitted.
(2) That rate constants selected for each of the 134 reactions
sufficiently describe the actual rate. Here it is recog-
nized that the three numbers characterizing a given rate
(A, n, E) are not exclusive. It is also recognized that the
more significant a reaction is , the more accurately its rate
must be known.
With regard to item (1) , the probability of overlooking a significant
reaction is not negligible, because the CHON system can support over 400
bimolecular reactions* of which only 134 have been included. With regard to
item (2), whereas the rate uncertainty can be as low as a factor of X2 for well-
studied reactions, some 85 of the 134 reactions had not been related to experi-
mental measurements and required rate approximation techniques accurate in
3
most cases to no better than X 10 .
Given these compounded uncertainties, any numerical screening without
compaiison to measured data could easily result in a subset which is partially
or completely fictitious. The purpose of the comparison reported herein was to
test the predictive ability of the 26-reaction subset against measurements of
CH /air combustion systems. The system selected as a data base was the well
stirred reactor, because of the ease with which it can be modelled due to mini-
mum mixing effects; other idealized combustion systems of interest for further
comparison are the shock-tube and the flat name.
Considering bimolecular collisions and only triatomic, diatomic, and atomic
species; in addition, one includes certain more complex molecules such as
CHa, CH O, and CH3 and these replace unlikely smaller molecules such as
C2°' C2^' andHN2*
56
-------
The stirred reactor data reported by Bartok and Engleman (1972) on the
CH /air system was selected because their Longwell reactor is rate limited,
exhibiting residence times of less than 2 msec, in contrast to other devices
requiring longer residence times because of greater "unmixedness" [e.g.,
Pratt and Malte (1973)]. This data is more reliable than the earlier data of
Bartok et al. (1971) because of the use of a chemiluminescent NO analyzer in-
Jt
stead of the electrochemical device which is suspect under fuel-rich conditions.
In the following sections we describe how the Kinetic Analysis Program (KAP)
was adapted to model the Longwell reactor, present the comparison with the
numerically screened set, and finally suggest specific explanations which
could be considered to bring data and theory into agreement:
(1) Revised reactions and rates
(2) Experimental errors due to probe and analyzer phenomena.
(3) Model deficiencies due to imperfect mixing or inadequate
representation of heat loss.
B.
REPRESENTATION OF EXPERIMENTAL CONDITIONS WITH KAP
The jet-stirred reactor shown in Figure 7.1 and described by Bartok
and Engleman (1972) is represented by a perfectly stirred (homogeneous) reactor
using the KAP program (see Appendix A).
1/4" dia. Pre-Mixed
Air and Fuel Inlet
1/2" dia. Lower
Hemisphere Drilled
with 40 Radial Holes
0.021" dia.
0.10" dia.
Perforations (40)-"'
1/2" Fire Brick
1/8" dia.
Water-Cooled Probe
Figure 7.1
JET-STIRRED REACTOR
[Bartok and Engleman (1972)]
57
-------
Needed as input to KAP are the inlet temperature, pressure, and reactant
concentration, heat loss coefficient (cal/sec-°K), reactor volume, and mass
throughput rate (gm/sec). These were taken as follows [Bartok and Engleman
1972)]:
Yo,
2
\
YCH4
To
P
H
V
m
Fuel Rich
(0 = 1.41)
.215
.709
.076
n
375 F
1 atm
.028 cal/sec°K
3
14.5 cm
1.22 g/sec
Stoichiometric
(0 = 1)
.220
.725
.055
f)
375 F
1 atm
.028 cal/sec°K
3
14.5 cm
1.20 g/sec
Fuel Lean
(0= .79)
.233
.733
.044
o
375°F
1 atm
.028 cal/sec°K
3
14.5 cm
1.19 g/sec
In accordance with the experimental data, variations in fuel/air ratio were
obtained by holding air flow constant and varying fuel flow. This accounts
for the slight increase in m with 0, and resulted in a slight variation in resi-
dence time.
3
Because the reported 14.5 cm reactor volume is slightly larger than the
volume calculated from the dimensions in Figure 7.1 [Bartok and Engleman (1972)
O
seem to have neglected the injection hemisphere of 0.6 cm displacement], we con-
sider the volume of the reactor to be uncertain to about +5%. This uncertainty
carries over into residence time and therefore significantly affects the kinetic
predictions.
Perhaps the most critical uncertainty lies with the heat losses to which
the kinetics predictions are sensitive. The heat transfer coefficient was esti-
mated from four supporting calculations:
58
-------
(a) From the discrepancy between calculated adiabatic
flame temperature, T d, and measured flame tempera-
ture, T, Bartok and Higleman (1972) derived a value
of H for each run from the energy balance:
(T ' T)
where T is the temperature of the surrounding air.
The authors recommend a value H (averaged over all
runs) of .025 cal/sec°K.
(b) Past studies of the Longwell reactor near the blowout
limit have shown the heat loss to be about 10% of the
chemical heat release. For the jet-stirred system
operating on CO/air, this amounts to
H = 0.1 mr7Q/(T - T^) w .028 cal/sec°K
where m = 1 g/sec, r) = .67 (conversion of CO to CO2),
Q = 701 cal/g-mixture, and T - T00«1700°K.
(c) Direct calculations of the rate of heat transfer through
a 1-1/2" thick hemispheric firebrick shell were carried
out using the expression
27rr rn
Q = -T-^T k^
-------
(d) Parametric studies of the KAP stirred reactor model
with CO/air reactants were compared with corres-
ponding data of Engleman et al. (1972). The results
at = 1 gave a best fit value between .015 and .030
cal/sec°K, as shown in Table 7.2 below:
Table 7.2
Predicted • H (cal/sec°K)
Measured
(unknown H)
T
NO
O0
2
TJ
2080 + 50°K
90 + 10 ppm
3.2+0.5%
.78
H=0
2131°K
180 ppm
4.2%
.72
H=.015
2085°K
117 ppm
4.1%
.73
H=0.30
2037°K
75 ppm
3.9%
.74
— ../
H=0.45
1993°K
45 ppm
3.8%
.75
Based on (a) - (d), the value of H= 0.28 cal/sec K was adopted for the
CH./air calculations. It is recommended that in future experiments the heat
loss be measured directly at several locations using thin film gages.
C. PREDICTIONS BASED ON SCREENED REACTION SET
The 26-reaction set of Table 6.1 predicts concentration levels of NO which
are much lower than measured values, as shown in Figure 7.2. The measured
values are about X 2.5 higher in the lean and stoichiometric cases and about
X40 higher in the rich case. This discrepancy exists despite rather good agree-
ment of temperature and O2 values, as shown below:
Case
£=1.00
6=1.41
T,°K
Measured
1900 + 60
2050+60
1900 + 60
T,°K
Predicted
1880
2065
1971
O2,%
Measured
5.0+0.5
1.4 + 0.5
not avail .
O2,%
Predicted
4.5
1.6
not avail.
Edelman also obtained underpredictions of NO for the same stirred reactor fueled
with propane [see Engleman et al. (1973)]; again the discrepancy was a factor
of twenty on the fuel rich side.
60
-------
Figure 7.2
COMPARISON OF EXPERIMENTAL DATA
FROM JET-STIRRED REACTOR WITH PREDICTIONS
BASED ON VARIOUS REACTION SETS
100,
80
60
40
20
.-.10
O
z
1
-.9
Stirred Reactor
CH4/Air
P = 1 atm
T = 375°F
o
ra 2msec
D
Measurements [Bartok and Engleman
(1972)]
Predicted with Unmodified 2 6-reaction
set
Predicted with Modification to
CO + OH — only
Predicted with Modified Rates for
Two Reactions:
O +N2—NO + N
CO+OH-CO2 +H
Predicted with 33-Reaction Set
including
R + N —-..—NO
I
I
.8 1.0 1.2
Fraction Stoichiometric Air
1.4
61
-------
D. KINETIC REVISIONS TO RECONCILE THEORY WITH DATA
1. Rate Adjustments for Lean Combustion
The rates of two key reactions were increased:
Reaction k (orig) k (revised)
CO + OH
N + NO
k
k
co2-
N2 '
f- H
H O
Q n T
4.00 x 103T *°
1.50 x 1013
5.6 x 1011 exp (-
6.31 x ID11!0'
1.08.
RT '
5
Both revised rates were taken from the Leeds critical assessment of Baulch et al.
(1970). At 0 = 1 (T = 2065°K), these two changes increase the predicted NO con-
centration by factors of 1.23 and 1.85, respectively, as shown in Figure 7.2.
Although factors of x 2 are not usually argued by kineticists, it may be useful to
comment briefly on these rates.
The CO/air data of Engleman et al. (1973) support an increase in the
CO + OH rate, because the measured "conversion" fraction, rj sXco ^
(X + XCo2)' is «78 compared to .73 predicted without revising the
CO + OH rate. The revised value for CO + OH is based on Drysdale and
Lloyd (1970) and agrees with the recent review by Smith and Zellner (1973)
at 2000°K.
With respect to the Zeldovich fixation step (O + N2~*)' clearlv
k (re vised) A (orig) « 2 at 2000°K. Which rate is correct? With respect to
the rate of Baulch et al. (1970), all of the NO predictions by Bartok et al.
(1971), Newhall (1968), Bell etal. (1971), lanes (1970), and Martinez (1970)
are underestimates by a factor of 2. The slower rate k(orig) quoted by these
workers can be traced to shock tube studies by Click et al. (1957) and Duff
and Davidson (1959), which were later confirmed by Wray and Teare (1962).
The key to this puzzling discrepancy may lie in the energy modes of
the nitrogen molecule. Of the three modes, translational, rotational, and
vibrational, it can safely be assumed that the first two are in local equili-
brium (T and T are identical to the local temperature, T). Equilibration
w" v trans rot
of the vibrational mode is somewhat more sluggish, and this can markedly
62
-------
affect the rate of any chemical reaction involving nitrogen: If the nitrogen
is vibrationally "cold" (nonequilibrium, T .. «T), the rate is much smaller
vib
than if N. is vibrationally "hot" (T , = T). In the latter case, the extra
vibrational energy helps push the reaction over the activation threshold EI .
The consensus of many engineers (who are not chemical kineticists)
was to adopt the shock tube data of Glick et al. (1957), and Duff and Davidson
(1959). However, this shock-tube data describes the rate of vibrationally
"cold" nitrogen reacting with oxygen atoms:
kf
O + N0 (cold) i± NO + N
2 !
kf = 6 x io13 exp (-EJ/RT)
Wray et al. (1970) re-examined the shock-tube data and determined that N_
was indeed at least 75% out of vibrational equilibrium. However, Wray et al.
concluded that the translational energy of the collision is sufficient to over-
come the endothermicity of the reaction O + N_ + 3.3 eV -» NO + N and have
that reaction occur with essentially the same rate as has been measured for
it when T = T . That is, the authors suggest that if N. had been vibration-
ally "hot", the rate of NO production would not have been considerably
larger.
By way of contrast, the Leeds evaluation assumed complete vibra-
tional equilibration and recommended a value for the following reaction:
kf
O + N_ (hot) z: NO + N
L k
k = 18 x IO13 exp (-E^RT)
Under vibrational equilibrium k, = K k, where K is the equilibrium con-
stant. In their determination of k,, the Leeds group used this relation and
exhaustive data on the reverse rate k (which has been studied much more
thoroughly than k,). Unfortunately, the k data was obtained at low temperature
63
-------
so that a lengthy extrapolation was required. The fact that the Leeds rate
is three times larger may be due to this extrapolation; however/ it is more
likely due to participation of the vibratlonal modes. The Leeds group
regards the shock tube data with considerable suspicion, advising that "in
themselves they cannot be regarded as very accurate."
In our Judgment N, is more likely to remain equilibrated throughout
an industrial flame than behind a shock wave because of the slower thermal
transients to which an element of fluid is exposed. That is, the NO forma-
tion process is system dependent. In the industrial flame, heat transfer
occurs by turbulent mixing and radiation so that characteristic times are in
the range 10"1 to 10"3 sec rather than the 10* to 10" sec range as charac-
teristic of the sudden passage of a shock wave. The characteristic vibrational
relaxation time for N.-N- collisions is about 150 ^sec [Blackman (1956)] under
b fL
typical boiler conditions, and since unlike-pair collisions are up to 100 times
more efficient [Vincent! and Kruger (1965)], the relaxation time in a mixture
involving O , HQO, and CO- may be on the order of 10 sec. Thus, the
L tt *•
Leeds rate data is to be preferred as a tentative best guess for NO formation
in practical combustion equipment. The rate of NO formation may be different
for shock tubes than for combustion equipment; i.e., the process is system
dependent.
2. Revisions for Fuel-Rich Combustion
Original-set predictions of NO on the fuel-rich side were about a factor
of 50 lower than measured values. Two lines of reasoning were pursued: (a)
Since, in the 26-reaction set, Zeldovich fixation (O + NZ—) governs NO forma-
tion, rate adjustments were sought to increase the O-atom concentration; (b)
alternate paths to NO (via R + N^) were sought.
(a) Attempts to Increase O-Atom Concentration
Both O9 and O-atoms far exceed equilibrium CHON levels (by factors
of 600 and 240, respectively) because of the intense backmixing of the perfectly-
stirred reactor. The predicted O-atom and O2 concentrations were 147 ppm and
64
-------
589 ppm, respectively, which constitutes an (O) /O2 value 100 times over equi-
librium at this temperature. The superequilibrium level of O-atoms needed to
make Zeldovich fixation sufficient was on the order of 0.4%, fully X7000 over
the CHON equilibrium value. Although 0.4% of free O-atoms was quite impro-
bable under fuel-rich conditions, nevertheless a number of rate adjustments
were attempted as shown in Table 7.3. Assuming a constant partial equili-
brium value of (O )(H)/(OH)(O) » 7 at 2000°K/ which was confirmed for many test
cases, rate adjustments were sought to decrease (OH), increase (OJ, or increase
(H). None of these measures increased O-atom levels more than a factor of 3.
Table 7.3
RATE REVISIONS INTENDED TO BOOST O-ATOM LEVELS
Case
Results
X
O
T,°K
Deeded to reconcile Zeldovich theory with
with measured rate
Original 26-reaction set (no revision)
4000 ppm 1900+50 35+5 ppm
147 ppm 1976 0.7 ppm
,ean revisions iCO + OH-M, see above
IO+N2 -I
Attempt to boost O-atoms:
Replace CH2O + O by 3-reaction
pyrolysis route:
+ H j* CH« + Hn
+ OH
6
CHO + CH.
CH,, + CHnO
Attempt to boost O2 by removing HO2
reactions
Also attempt to boost H by removing
(CHO + H-«) path
Same as above, except CH. + H-» removed
to boost H-atom concentration
153 ppm 1990 1.6 ppm
207 ppm 1985 1.9 ppm
430 ppm 1934 2.4 ppm
446 ppm 1935 2.5 ppm
65
-------
(b) Alternate Paths to NO
A number of reactions conceivably could produce nitrogen-bearing radi-
cals as an alternate to the O + N. -» NO + N path. A partial list is given in
Table 7.4 with selected comments.
Table 7.4
CANDIDATE R + N0- R • N + N REACTIONS
Listed in
Original
134-Reacdon
Set?
No
No
No
No
No
No
Yet
Yei
No
Yet
Reaction
CH2 + Nj •* HCN > NH
C2 + N2 -• CN + CN
C + N2 -• CN + N
HO2 •»• Nj •* HNO + NO
CH + N2 •» HCN * N
H2 + N2 •* HN + HN
CO + N2 •» CN + NO
H + N2 •• HN + N
OH * N2 •» HN + NO
OH*K2 ^N2O.H
Endothenuic ty
(kca I/mole)
at 300°K
20.2
23.0
53.1
40.4
3.3
160
159
140.9
92.2
62.3
Order of Magnitude
Concentration of
Species "R" in
CH./Air Flame
—
~
io-6
ID'7
io-2
io-2
ID'2
!0-2
io-2
Comments
N, breakup by CH. Is possible
because CH. is quite energetic.
4-center, probably not elemen-
tary; may go through CH-N
intermediate. Dlscussea by
Stemling and Wendt (1972).
Leads to CHN which has been
observed [Bachmaler et al (1973)]
Four-center. C. (Swan) band
emission obserred In hydro-
carbon flames at S16S A.
C less likely than Cj as
gaseous species
Sterlcally Improbable (four-
center). Also would be largest
in lean Instead of rich case.
Spin-forbidden, proposed by
Fenlmore (1971). CH ei^sslon
bands observed at 43 IS A.
Sterlcally improbable (four-
center). Also highly endothermlc
Highly endothermlc, four center.
Highly endothermlc.
Sterlcally improbable (four-
center). Bowman (1973)
suggests k » 10$ to 10°.
Endothermlc
The reaction selected was CH2 + Ng — CHN + HN, which was followed
by five reactions hypothesized to complete the path to NO:
66
-------
NH + O -» NO + H (later screened out)
NH + OH -N + H O
£t
HCN + OH - ON -l- HO
CN + O. - CO + NO
Lt
CN + O -» CO + N (later screened out)
Two of the five reactions were later screened out as relatively unimportant, as
noted. It will be more realistic in future studies to provide and screen addi-
tional reaction paths whereby HCN, NH, and CN can form molecular nitrogen,
thereby giving less than 100% conversion efficiency of these species to NO.
In order to provide the CH0 needed for the key CH,, + N. reaction, two
It It £t
pyrolysis reactions were considered:
CH + OH - CH + HO (screened out)
O It I*
CH_ + H - CH. + H,
O L» £t
Including these reactions is by no means arbitrary since the screening runs
at 0= 1.25 indicated their importance (see Chapter III). It was found that H
was eight times more effective than OH in producing CH2 for the 0=1.4 case.
Competing with the CH. + N sink for CH radicals were two key pyrolysis
i. £• 6
reactions previously shown to be important by the screening (again, see
Chapter III) :
CH0 + O- -+CH O + O (screened out)
Z L &
O -» CHO
It was found that CH + O0 could be screened out for the present conditions.
£t £*
The rate of the key reaction CH- + N9 -* CHN + HN was selected by
L* £t
adopting the activation energy based on 28% of bond energy (41 .7 kcal) . Then
a parameter study was conducted on predicted NO and CHN, as shown in
Figure 7.3. The rates selected for all six reactions are listed below:
67
-------
10
a
£
a> g
•8
O
i
10
Figure 7.3
PARAMETER STUDY ON THE RATE OF THE REACTION CH2 +
-CHN + HN
Conditions
TQ = 375°F
0 = 1.41
P = I atm
CH4/alr
Stirred Reactor
T st 2 msec
NO level measured in
jet-stir red reactor
Rate listed by Sternllng
and Wendt (1972) as
"maximum"
10
8
II
10" 10
Forward Rate at 2000°K of CH£ + Ng-* CHN + HN
(cc/mole-sec)
10
12
10
-------
k = A T~n exp (- B/RT)
A n 1
CH0 production
2 11
CH3+H = CH2+H2 2x10 -0.7 3.0
CHN and HN production
13
CH + N = CHN + HN 2.04x10 0 41.7
£» Lt
CH0 destruction
11
CH0 + CH O = CHO+CH 1.50x10 -0.7 4.0
22 «J
CHN and HN conversion to NO
CHN + OH = CN + H O 2x10 -0.6 5.0
11
CN + O0 = CO + NO 3x10 0 0
11
NH + OH = N + H9O 5x10 -0.5 2.0
£»
With this set the fuel-rich predictions are brought into reasonable agreement
with the data as shown in Figure 7.2. It is not claimed that the mechanism
adopted is unique or corresponds to reality. However some non-Zeldovich
path to NO (R + N -*R- N + N) appears mandatory for fuel-rich conditions.
£•
Iverach et al. (1973) and Fenimore (1971) have reported higher NO concentra-
tions for fuel-rich flames than can be attributed to the Zeldovich mechanism.
Bachmaier et al. (1973) measured substantial quantities of HCN (e.g. 8 ppm
at >= 1.3) for fuel-rich methane/air flames.
What has been shown above is that the jet-stirred results of Bartok and
Engleman (1972) corroborate these observations. The kinetic mechanism hypo-
thesized above may indicate one conceivable explanation for all of these
discrepancies between the Zeldovich mechanism and fuel-rich NO data.
3. Summary of Kinetic Revisions
Table 7.5 presents the 33-reaction set which results from forcing
agreement to the jet-stirred data of Bartok and Engleman (1972).
69
-------
Table 7.5
EMPIRICALLY ADJUSTED 33-REACTION SET
FOR CH./AIR WITH REVISIONS TO TABLE 6.1 NOTED (*)
A n —R/RT
Rate Coefficientsv k = A T e
Reaction
Number
36
77
84
99
101
140
Reaction
Termolecular
CHO . .
CO2
H2O
H + O
H +O2
H2O
Reactions
= CO
= CO
= HO
= HO
= HO2
= N2
+
4-
4-
4-
H
O
H
O
2
I
3
8
I
I
A
.50E+20
.OOE+15
.OOE+15
.OOE+15
.50E+15
.OOE+14
n
B
1.5 16.8
0 100.
0 105.
0 0
0 1.
0 50.
Reference
Benson (1973)
Benson (1973)
Baulch (1972)
Scofield (1973)
Baulch (1972)
Estimate
Bimolecular Reactions
44
46
47
52
59
63
65
66
70
83
•85
88
91
98
100
117
125
133
135
143
49
56
39
104
32
68
CHO
CH2O
CHO
CHO
CH3
CII4
CH4
CH4
*CO
H
H
HO
HO
H
HO
HO
*N
N
N20
CHO
*CH2O
*CH3
*CHO
*CH2
*HN
*CHN
*CN
4-
+
4-
+
+
1
4-
4-
4-
4-
+
4-
4-
4-
4-
+
+
+
+
+
4-
4-
4-
+
+
+
4-
H
O
HO
0
O
Q
H
HO
HO
HO
HO2
H2
N
N2O
O
HO
NO
O2
O
02
HO
H
CH3
N2
HO
HO
O2
= CO
= CHO
= CO
= CO
= CH2O
_ /•"•TT1
= CHS
= CHS
= CO2
= H2
= HO
= H
= H
= HO
= H
= H2O
= N2
= NO
= NO
= CO
= CHO
- CH2
= CH2
= CHN
= H2O
= CN
= CO
4-
4-
+
4-
4-
+
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
4-
H2
HO
H2O
HO
H
no
H2
H2O
H
O
HO
H2O
NO
N2
02
O
O
0
NO
HO2
H2O
H2
CH2O
HN
N
H2O
NO
3
2
3
3
2
i
5
3
5
8
2
2
6
8
2
6
6
6
1
8
1
2
1
2
5
2
3
.OOE+10
.OOE+11
.OOE+10
.OOE4-11
.OOE+12
Anr« j i r>
.OOE+10
.OOE+13
.60E+11
.OOE+09
.50E+14
.50E+13
.OOE+11
.OOE+13
.50E+13
.OOE+12
.31E+11
.OOE+09
.OOE+14
.OOE+12
.OOE+14
.OOE+11
.50E+11
.04E+13
.OOE+11
.OOE+11
.OOE+11
-1.
-1.
-1.
-1
- .5
X
-1
0
0
-1
0
0
- .5
0
0
0
- .5
-1.
0
0
0
- .7
- .7
0
- .5
- .6
0
0
4.4
0
.5
-.3
8.
10.
5.
1.08
7.
1.9
5.2
8.
15.
0
1.
0
6.3
28.
0
0
3.
4.
41.7
2.
5.
0
Benson (1973)
Benson (1973)
Benson (1973)
Benson (1973)
Morris (1973)
V/G stcnbcr" '1969^
Walker (1968)
Wilson (1972)
Baulch (1969)
Benson (1973)
Baulch (1972)
Baulch (1972)
Benson (1973)
Baulch (1973)
Baulch (1972)
Baulch (1972)
Baulch (1969)
Benson (1973)
Baulch (1973)
Peeters (1973)
Benson (1973)
Tunder (1967)
Tunder (1967)
Mod Stemling (1972)
(see Fig. 7.3)
Tunder (1967)
Tunder (1967)
Basco (1965)
Units: cc, mole, sec, K, kcal
70
-------
The set is not unique, and the model of perfectly stirred combustion
does not precisely apply to the data of Bartok et al. Nevertheless it would
appear from the analysis of this chapter that further study is warranted in the
following areas:
(1) Determination of the rate of the O + N -» NO + N
reaction to better precision, especially under con-
ditions permitting the vibrational state of N2 to be
well characterized.
(2) Rescreening the total 134-reaction set with the addi-
tion of Zeldovich bypass reactions such as CH2 + H2~*
CHN + HN. Of the ten reactions listed in Table 7 .4,
five were discarded as unlikely by Engleman et al.,
three were within the set of 134 recommended reactions,
and two were not considered by Engleman et al.
(3) Rates of the following two reactions appeared to have
been underestimated by x2 and x20, respectively, in
the original 134-reaction set: CO + OH -» CO2 + H,
CH2O + OH -» CHO + H2O. Again a rescreening is
called for.
71
-------
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Nitric Oxide and the Detection of HCN in Premixed Hydrocarbon-
air Flames at 1 Atmosphere, Comb. Sci. Tech. 7_ 77.
Bahn, G. S. (1973). Approximate Thermochemical Tables for Some C-H and
CHO Species, NASA CR-2178.
Bartok, W. and Engleman V. S. (1972). Definition of the Mechanism and
Kinetics of the Formation of NOX and Other Pollutants in Combustion
Reactions, EPA Contract No. 68-02-0224, Status Report, p. 87-117.
Bartok, W., Engleman, V. S., de Valle, E. G. (1971). Laboratory Studies
and Mathematical Modeling of NOX Formation in Combustion Processes,
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Barton, S. C. and Dove, J. E. (1969). Can. J. Chem. 47, 521.
Basco, N. (1965). Proc. Roy Soc. A283, 302.
Baulch, D. L., Drysdale, D. D., and Home, D. G. (July 1970). Dept. of
Physical Chemistry, The University, Leeds, England, High Temperature
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Baulch, D. L., Drysdale, D. D., Home, D. G., and Lloyd, A. C. (1972).
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Bell, A. W., Devolo, N. B., Breen, B. P., Bagwell, F. A., and Rosenthal, K.
(1971). Combustion Control for Elimination of Nitric Oxide Emissions
from Fossil Fuel Power Plants, 13th Symposium (International) on Com-
bustion, The Combustion Institute, Pittsburgh, p. 391.
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Annual Report, Project PYU-2009.
Blackman, V. H. (1956). Vibrational Relaxation in Oxygen and Nitrogen,
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Boden, J. C. and Thrust, B. A. (1968). Proc. Roy. Soc. A305. 107.
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Bowman, C. T. (1970). An Experimental and Analytical Investigation of the
High-Temperature Oxidation Mechanisms of Hydrocarbon Fuels, Comb.
Sci. Tech. 2, 161.
Bowman, C. T. (1971). Investigation of Nitric Oxide Formation Kinetics in
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Processes, 14th Symposium (International) on Combustion, The Com-
bustion Institute, Pittsburgh, p. 729.
Bowman, C. T. and Seery, D. J. (1972). Emissions from Continuous Combus-
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Brown, F. and Crist, R. (1941). J. Chem. Phys. 9_, 840.
Chinitz, W. and Bauer, T. (1966). An Analysis of Nonequilibrium Hydrocarbon/
Air Combustion, Pyrodynamics j4.
Clyne, M. A. A. and Thrush, B. A. (1962). Disc. Faraday Soc. .33, 139.
Dean, A. M. and Kistiakowsky, G. B. (1971). J. Chem. Phys. .54, 1718.
Dryer, F. (1974). Private Communication, Princeton University.
Duff, R. E. and Davidson, N. (1959). J. Chem. Phys. 3J., 1018.
Eberius, K. H., Hoyerman, K., and Wagner, H. Gg. (1973). Structure c_:
Lean Acetylene-Oxygen Flames, 14th Symposium (International) on
Combustion. The Combustion Institute, Pittsburgh, p. 147.
Edelman, R. B. and Fortune, O. F. (1969). A Quasiglobal Chemical Kinetic
Model for the Finite Rate Combustion of Hydrocarbon Fuels with Appli-
cation to Turbulent Burning and Mixing in Hypersonic Engines and
Nozzles, AIAA Paper No. 69-86.
73
-------
Engleman, V. S. and Bartok. W. (1973). Definition of the Mechanisms and
Kinetics of the Formation of NOX and Other Pollutants under Normal
and Combustion Modification Conditions, Progress Report No. 1
EPA Contract No. 68-02-0224, Modif. #1.
Engleman, V. S., Edelman, R. B., Bartok, W., and Longwell, J. P. (1973)»
Experimental and Theoretical Studies of NOX Formation in a Jet-Stirred
Combustor, 14th Symposium (International) on Combustion, The Com-
bustion Institute, Pittsburgh, p. 755.
Fenimore, C. P. (1964). Chemistry in Premixed Flames, Topic 19: Gas
Kinetics, Vol. 5, McMillan, New York.
Fenimore, C. P. (1971). Formation of Nitric Oxide in Premixed Hydrocarbon
Flames, 13th Symposium (International) on Combustion, The Combustion
Institute, Pittsburgh, p. 373.
Fenimore, C. P. (1972). Formation of Nitric Oxide from Fuel Nitrogen in
Ethylene Flames, Comb. Flame 19., 289-296.
Frey, H. M., Nickerson, G. R., and Tyson, T. J. (1970). One-Dimensional
Kinetic Nozzle Analysis Reference Computer Program, Dynamic Science
Report No. CS-1-9/70.
Frey, H. M. and Nickerson, G. R. (1970). Two-Dimensional Kinetic Nozzle
Analysis Reference Computer Program, Dynamic Science Paper No.
CS-12-70-1.
Fristrom, R. M. and Westenberg, A. A. (1965). Flame Structure. McGraw
Hill, New York.
Click, H. S., Klein, J. J., and Squire, W. (1957). J. Chem. Phys. 27, 850.
Hammond, D. C. Ir. and Mellor, A. M. (1973). Analytic Predictions of
Emissions from and Within an Allison J-33 Combustor, Comb. Sci.
Tech. 6, 279-286.
Hampson, R. F. (ed) (1972). NBS Report 10-692.
Hartig, R., Troe, I. and Wagner, H. Gg. (1971). Thermal Decomposition
of Methane Behind Reflected Shock Waves, 13th Symposium (Inter-
national) on Combustion, The Combustion Institute, Pittsburgh, p. 147.
Hirschfelder, J. O., Curtiss, C. F., and Bird, R. B. (1954). Molecular
Theory of Gases and Liquids, Wiley, New York.
Iverach, D., Basden, K. S., and Kirov, N. Y. (1973). Formation of Nitric
Oxide in Fuel-Lean and Fuel-Rich Flames, 14th Symposium (Inter-
national) on Combustion, The Combustion Institute, Pittsburgh, p. 767.
74
-------
James, D. E. (1970). A Boiler Manufacturer's View on Nitric Oxide Formation,
Presented to the Fifth Technical Meeting, West Coast Section of APCA.
JANAF Thermochemical Tables (1971). U.S. Dept. of Commerce, National
Bureau of Standards Publication NSRDS-NBS 37, second edition.
Johnston, H. S. (1968). NSRDS-NBS 20.
Kaufman, F. and Kelso, J. R. (1955). J. Chem. Phys. 23, 602.
Kliegel, J. R., Gold, P. I., and Weekley, C. T. (1968). Chemical Species
and Chemical Reactions of Importance in Nonequilibrium Rocket Engine
Performance Calculations, Pyrodynamics J5.
Kretschmer, C. B. and Petersen, H. L. (1963). J. Chem. Phys. 39_, 1772.
Leonard, P. A., Lester, T. W., Clancy, M. G., Laurendeau, N. M., and
Mellor, A. M. (1973). Nitric Oxide Formation in Hydrocarbon Flames,
TACOM Propulsion Systems Laboratory Technical Report No. 11816.
Lin, M. C. and Bauer, S. H. (1969). J. Chem. Phys. JJO, 3377.
Lloyd, A. C. (1971). NBS Report 10 447.
Mayer, S. W., Schieler, L., and Johnston, H. S. (1967). Computation of
High-Temperature Rate Constants for Bimolecular Reactions of Com-
bustion Products, llth Symposium (International) on Combustion, The
Combustion Institute, Pittsburgh, p. 837.
Martinez, P. (1970). Formation of NO in Hydrocarbon-Air Combustion, Comb.
Sci. Tech. !_, 461.
Mellor, A. M. (1972). Current Kinetic Modeling Techniques for Continuous
Flow Combustors, Emissions from Continuous Combustion Systems,
Plenum Press, New York, 22-53.
Morris, E. D. and Niki, H. (1973). I. J. C. K. J5, 47.
Newhall, H. K. (1968). Kinetics of Engine Generated Nitrogen Oxides and
Carbon Monoxide, 12th Symposium (International) on Combustion.
The Combustion Institute, Pittsburgh, p. 603.
Olschewski. H. A., Troe, J., and Wagner, H. Gg. (1967). Studies of Uni-
molecular Reactions of Triatomic Molecules, llth Symposium (Inter-
national) on Combustion. The Combustion Institute, Pittsburgh, p. 155,
75
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Peelers, J. and Mahnen, G. (1973). Reaction Mechanisms and Rate Constants
of Elementary Steps in Methane-Oxygen Flames, 14th Symposium (Inter-
national) on Combustion, The Combustion Institute, Pittsburgh, p. 133.
Penner, S. S. (1957). Chemistry Problems in Jet Propulsion, Pergamon Press,
New York.
Phillips, L. F. and Schiff, H. I. (1965). J. Chem. Phys. 42., 3171.
Pratt/ D. T. and Malte, P. C. (1973). Formation of Thermal and Prompt NO
in a Jet-Stirred Combustor, Paper No. 34b, 75th National AIChE Meeting.
Pratt, D. T. and Malte, P. C. (1974). Measurement of Atomic Oxygen and
Nitrogen Oxides in Jet-Stirred Combustion, WSS/CI Paper 74-8,
Pullman, Washington, Western States Section/The Combustion Institute.
Reid, R. C. and Sherwood, T. K. (1966). The Properties of Gases and Liquids--
Their Estimation and Correlation, McGraw-Hill, New York, 2nd ed.
Ripley, D. L. and Gardiner, W. C. Jr. (1966). J. Chem. Phys. 44., 2285.
Schofield, K. (1967). Planetary Space Sci. J_5, 643.
Shaw, R. (1973). Private communication.
Seery, D. J. and Bowman, C. T. (1970). An Experimental and Analytical
Study of Methane Oxidation Behind Shock Waves, Comb. Flame 14,
37-48.
Stemling, C. V. and Wendt, J.O.L. (1972). Kinetic Mechanisms Governing
the Fate of Chemically Bound Sulfur and Nitrogen in Combustion,
Final Report, EPA Contract EHS-D-71-45, Task 14.
Tunder, R., Mayer, S., Cook, B., and Shieler, L. (1966). Compilation of
Reaction Rate Data for Nonequilibrium Performance and Re-entry
Calculations Programs, Aerospace Corporation.
Tunder, R., Mayer, S., Cook, E., and Schieler, L. (1967). Aerospace
Report No. TR-1001 (9210-02)-!, Aerospace Corporation Thermochem-
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Tyson, T. J. and Kliegel, J. R. (1968). An Implicit Integration Procedure for
Chemical Kinetics, AIAA 6th Aerospace Sciences Meeting, Paper No.
68-180.
76
-------
Vincenti, W. G. and Kruger, C. H. Jr. (1965). Introduction to Physical Gas
Dynamics, J. Wiley, New York, p. 204.
Walker, R. W. (1968). J. Chem. Soc. (A) 1968, 2391.
Westenberg, A. A. and Dehaas, N. (1969). J. Chem. Phys. 50, 2512.
Wilde, K. A. (1969). Comb. Flame L3, 173.
Wilson , W. E. (1972). J. Phys. Chem. Ref. Data I, 535.
Wray, K. L., Feldman, E. V., and Lewis, P. F. (1970). Shock Tube Study
of the Effect of Vibrational Energy of N2 on the Kinetics of the O + N,
-« NO + N Reaction, J. Chem. Phys. 53.* 4131. [See also Wray, K. L.
and Teare, J. D. (1962), Shock-Tube Study of the Kinetics of Nitric
Oxide at High Temperatures, J. Chem. Phys. .36., 2582.]
77
-------
APPENDIX A
DESCRIPTION OF THE NUMERICAL PROGRAM
1. BACKGROUND
The computer program used in this study is based on analysis carried
out previously at Ultrasystems for the purpose of predicting delivered specific
impulse, including the effect of kinetic losses, for liquid propellant rocket
engines. These applications were reported by Tyson and Kliegel (1968) and
Frey et al. (1970). The method of solution consists of integrating the one-
dimensional conservation equations in a form such that gas phase chemical
reactors of a general type can be included. This computer program also per-
mits input of functions defining mass, momentum, and energy addition. Both
pressure defined and area defined chemically reacting systems may be analyzed,
Solid or liquid phase products are not considered.
A special screening option permits evaluation of the contribution of
each chemical reaction on the production or destruction of any specified
species at each integration step. The program will automatically delete any
reaction whose contribution to the net production or destruction of the parti-
cular species is less than a specified amount. The calculation is then
repeated if desired, to see the effect of the deleted reaction(s).
In the course of the present research effort some improvements were
made to the numerical program. In particular, an improved truncation error
control procedure was derived and implemented to allow for more efficient
control of the integration step size.
A version of the program compatible with IBM equipment was pre-
pared by Ultrasystems (the original was designed for CDC equipment) and
set upon EPA computers in Research Triangle Park, North Carolina.
78
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2. CONSERVATION EQUATIONS
The conservation equations governing the inviscid flow of reacting gas
mixtures have been given by Hirschfelder et al. (1954), Penner (1957), and
others. The following basic assumptions are made in the derivation of these
equations.
• Addition rates for mass (m), species (s) , momentum (M),
and energy (H) are defined for the system.
• The gas is inviscid.
• Each component of the gas is a perfect gas.
• The internal degrees of freedom of each component of the
gas are in equilibrium.
• The flow is one dimensional.
Based on these assumptions, the conservation of species/ mass,
momentum, and energy for the system can be expressed by Eqs. (I), (2),
(3) and (4) below*:
(1)
dJT (1 + m) = m (2)
(3)
~ (1 + m) h 1 = H, where h = £ c h + V2/2, (4)
L XJ i=i x x
CA are mass fractions, w. are net production rates, and h are specific enthal-
pies of species i. Equations (1) - (4) can be written as
dCi s.-mCi o^r*
dx ~ 1 -f m + pV (5)
dV _ id- mV 1 dP
dx 1 + In ~ pV dx ^6)
*The independent variable, x, is tajcen as unitless with r* as the conversion
factor to units. The quantity 1 + m represents the streamtube mass flux normal-
ized by the initial streamtube mass flux, i.e., 1 + m = (pVa)/(pVa)
79
-------
dT_ -L.
dx~ C_
H-mh
1 + m
"T V(M-mV) , IdP
" ~
dc,
1 + m P dx i=i idx
dx Pdx Tdx R \i=l i dx
(7)
(8)
where
C "
h. =
R.
(9,10)
(11,12)
The perfect gas relation
P = pRT
has been used to obtain the above equations.
3. CHEMISTRY
The method by which the net species production rate, G^, is deter-
mined is described below.
A chemical reaction can be written in terms of its stoichiometric coef-
ficients (v.. and v ) as
(13)
th
where M represents the i"1 chemical species name and j represents the j
reaction.
Given a system of chemical reactions, the net species production rate
cj for each species (component) is calculated from
1 £„
4—1
Here mw. is the molecular weight, where
(14)
80
-------
The reaction rate, k , is from right to left (reverse) in Equation (13)
and is represented by the Arrhenius form
where
-n.
k = a T J exp(-b /RT)
a. is the pre-exponential coefficient
n is the temperature dependence of the pre-exponential factor
b is the activation energy.
The equilibrium constant, K, , is
where
K = exp (-AF/RT) (RT) J
il fi "ij - il fi "l
and the integer, A., is determined for a given reaction from the stoichiometric
coefficients
The term M in Eq. (15) is provided so that the reaction rate can be modified for
individual third body species by calculating the general third body term (M ) as
M = £? an/an c. for reactions requiring a third body (16)
J 1 J. 1J KJ 1
M = 1 for all other reactions
where the a, 's are the individual pre-exponential coefficients.
81
-------
4. SOLUTION OF THE WELL-STIRRED REACTION EQUATIONS
IN KINETIC ANALYSIS PROGRAM
The conservation equations discussed in the previous section can be
manipulated through appropriate choice of the mass, momentum, species, and
energy addition functions to give the well-stirred reactor solution In the steady
limit of the one-dlmenslonal flow. Conceptually, one starts with a vessel con-
taining reactants In any concentration and adds into the vessel (at each time
increment) reactants having a composition, c^ , and energy hT , corresponding
to the stirred reactor inlet conditions. At the same time, fluid products are
removed at the same rate as the input (m= 0) so that as we proceed in time the
conditions in the vessel approach more closely the conditions In a stirred
reactor. For rn = 0 (no mass accumulation), M = mV, H = mh^, s = me,1 and
dP/dx = 0, equations (5)- (8) then become:
dci <*
i
n
In the limit as d/dx-*0, i.e., steady state:
i V*
where V = constant
m (h1 - h) =0
p - constant
For reference, the stirred reactor residence time is r= r /mV.
82
-------
5. NUMERICAL METHOD
It has been shown [Tyson and Kliegel (1968)] that explicit methods of
numerical integration are unstable when applied to relaxation equations [such
as Eqs. (5), (6), (7), and (8)] unless the integration step size is of the order
of the characteristic relaxation distance. Since in the near equilibrium flow
regime the characteristic relaxation distance is typically many orders of magni-
tude smaller than the characteristic physical dimensions of the system of interest,
the use of explicit methods to integrate relaxation equations often result in excess-
ively long computation times . An implicit integration method which is inherently
stable in all flow situations (whether near equilibrium or frozen) is therefore used
by the computer program. With this method, step sizes which are of the order of
the physical dimensions of the system of interest can be used/ reducing the com-
putation time per case several orders of magnitude when compared with conven-
tional explicit integration methods .
Equations (5) -(8) constitute N first order simultaneous differential equations
dy
— = f. (x, yit .... yN) i = 1, 2, .... N
with known partial derivatives (i.e. , the Jacobian for the system)
*
Ct =
The following implicit difference equations are used by the computer program
to determine the y. (the subscript n denotes the ntn integration step)
h = x ' Xn
where the Ay increment Ay^n+1 is solved implicitly from one of the following
three recipes " N
*The computer program uses analytic expressions for calculation of the partial
derivatives a., ft These may be printed with the output, if desired
83
-------
for the initial step and for restart (first order) ,
N
(f
i.n
for equal steps (second order with h = previous h)
(2h
h ) - h
n n
. n + (fi,n + ai/n hn+l
-h (hn«+hn)]
i
j
for unequal steps (second order with h ^ previous h) .
If the flow is frozen, the explicit form of the above equations can be
used (a =0, /? =0), i.e. the implicit difference equations given above are
each reduced from an NXN system of linear simultaneous equations to N explicit
equations (N = 3 + no . of species) .
Control of the integration step size, h, is provided by calculating esti-
mates for the truncation error and comparing these to an input criterion, 6. The
step size is halved if for any i = l,2, ...,N: E > 6 . The step size is doubled
if for all i - 1, 2, . . . , N: E < 5/10
where
Ei •
i.n
A
The above expression for E. is derived in Ref. 2.
84
-------
APPENDIX B
APPROXIMATION TECHNIQUES FOR ARRHENIUS RATE COEFFICIENTS
When no other resources are available for rate determination, the
following estimates prove to be useful. For rate constants represented by an
Arrhenius equation,
k = AT~nexp (-B/RT)
where T is the absolute temperature, R is the gas constant, B is the activation
energy, and N determines the pre-exponential temperature dependence,
approximations have been made as follows:
(1) Exothermic, termolecular reactions
B + C+Mf*BC + M , k = 3 x 1016 T~°*5
(2) Exothermic, bimolecular reactions with triatomic transition states
B + CD n BC + D , k = 5xl011T°*5 exp (-B/RT)
where E = 5.5% of the CD bond
energy
(3) Exothermic, bimolecular reactions with transition states of more
than three atoms
BC + DE J=? BCD + E , k = 1 x 1011 T°'5 exp (-B/RT)
where E = 5.5% of the DE bond
energy
(4) Exothermic, bimolecular, binary exchange reactions
BC + DE i=f ED + CE , k = lxl010T°*5 exp (-B/RT)
where B = 28% of the sum of the
BC and DE bond energies.
85
-------
The above method of estimating exothermic reaction rates are similar
to those used by Tunder et al. (1966).
The bond dissociation energy, D, for molecule BC was taken as
D = (AHf° of B) + (AHf° of C) - (AHf° of BC)
where the heats of formation are at 298.15 K. These AH, are given in Table
B .1 for the species used in this study. The species are listed in alphanumeric
order. The heat of reaction is taken as the sum of the AH * of the products
o 298
(RHS) minus the sum of AH r of the reactants (LHS). Thus, if the sign is
298
positive then the reaction is endothermic left to right, while if the sign is
negative then the reaction is exothermic left to right. The heats of formation
used in this study were taken from the JANAF Tables (1971).
Table B.I
BOND DISSOCIATION ENERGIES
Estimates from JANAF
(D kcal/mole)
DH-H
DN-H
DN-N • 226'°
DN-0
D0-H = 102.3
D0-0
86
-------
APPENDIX C
THERMQCHEMICAL PROPERTIES OF METHOXYL. CH O
o
The thermochemical properties of methoxyl (CHLO, free radical on the
o
O-atom) are not tabulated in the JANAF Tables (1971) , nor are they in the more
recent compilation by Bahn (1973) . The necessary data can all be computed from
the specific heat which can be calculated from the Meghreblian, Crawford, and
Parr method [Reid and Sherwood (1966)] from the equation
C° = 4R + Zq. CVi +
3n-6-£q.
= A + BT + CT
where
= ideal-gas heat capacity at constant pressure
R, cal/gm-mole°K
4R
n
qi
= 3/2R (for translation) + 3/2R (for external rotation) + R
= number of atoms in the molecule
= number of bonds of the itn type
2 x x 2
Cv,, Cfl. = Einstein function, i.e., RX e /(e -1)
X
h
v
d
k
T
or
-34
= Planck's constant, 1.58x 10 cal-sec/molecule
= characteristic frequency for stretching vibrations, sec
= characteristic frequency for bending vibrations, sec
—29 o
= Boltzmann's constant, 3.29 x 10 cal/molecule K
_i
= Temperature, K
The following data are taken from Table 5-3 of Reid and Sherwood (1966):
Bond
i
C-H
C-O
q for
CH3O
3
1
u) „ , wave l
number, cm
3000
1030
Stretching, j
A
-0.139
-0.458
BxlO3
0.168
3.722
?fi — _
CxlO6
0.447
-1.471
U6 , wave l
number, cm
1050
1120
Rpndinn. HIJ —
A
-0.579
-0.665
BxlO3
3.741
3.757
CxlOb
-1.471
-1.449
87
-------
With these values we find
A = 4.0705
x 10"
.-6
B = 22.951 x 10"3
C = -7.4575 x 10
The representation for the specific heat
r\
C = A + BT + CT
P
is valid only up to some value T* determined from
1*\ /•» m*
dC°
= o —»> T = —
dT Vi '
C° =A -
pmax
For T > T* we have C = C° (fully excited, electronic contributions are not
~ p p max
included). For methoxyl,
T* = 1539°K
C° = 21.729 cal/gm-mole°K
pmax
Once the specific heat is determined, the enthalpy, entropy, and free energy
functions are determined from classical thermodynamics, viz.,
T
-S° = S°
s STO
F° = H°-TS°
88
-------
These equations can be interpreted and expressed in terms of the parameters
A, B, and C and finally tabulated in the same fashion as presented in the JANAF
Tables (1971). (This form is necessary for inclusion in the KAP program.)
The results are shown in Table C.I.
Table C.I
THERMODYNAMIC FUNCTIONS FOR METHOXYL
„ o cal _.o ..o kcal /r,o
T,°K
TT° TT°
mole-°K 29 8 'mole
cal
A
mole°K
JOO
?oo
300
400
500
600
700
noo
900
in on
1100
l.ioo
1*00
1*00
1600
IV 00
l«t)0
2100
rrr-o
5*7 no
?'»no
3PPO
3:»00
3*00
3!>oo
3'-00
3VOO
• AIHIQ
A 100
*?.no
*700
AJIPO
«90C
5000
6.2910
8.3624
70.2130'
20.0729
SI.3fi3A
?l.7?un
21.7?H6
;-s. .vi1"
rl,7?UK
?1.7?HH
?1.7i»HO
?i.7?oe
2l.7;:tic
?1 .7?HH
?1.7?HO
2l.7?WU
?.
4.b373
in. 6.600
\ A. 3022
16.3863
1H.«
74.1^80
J7.0407
3?. 7323
411.1) /Ml)
4B.7f.p6
63.979B
77.f)J7l
79,1000
PI.3620
P3.5357
S6.b7.lO
S5.1S96
•J9.6430
6?. 2073
03.3930
65.2037
67.8231
b8.)700
6B.5207
60.8731
6Q.2P60
7o.201b
70.b30*
70.^771
72.3377
72.b70
7?,V99
73. j;.'
74.5060
7*.906^
75,2121
89
-------
TECHNICAL RF.I'ORT DATA
(J'lcasc rcatl /miriiftii?i/>k'linx)
1. HCPOHT NO.
EPA-650/2-74-045
2.
3. RECIPIENT'S ACCESSION-NO.
TITLE ANDSUBTITLE
Kinetic Mechanism of Methane/Air Combustion
with Pollutant Formation
5. REPORT DATE
June 1974
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
C. H. Waldman, R. P Wilson, Jr. , and K. L. Maloney
8. PERFORMING ORGANIZATION REPORT NO
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Ultrasystems, Inc
2400 Michelson Drive
Irvine, CA 82664
10. PROGRAM ELEMENT NO.
1AB014; ROAP 21ADG-10
11. CONTRACT/GRANT NO.
68-02-0270
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
NERC-RTP, Control Systems Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
Y NOTES
The report gives results of the evaluation of a large set of chemical reactions
describing methane/air combustion to determine the significant reactions at
atmospheric pressure at temperatures of 150--2500K, and at equivalence ratios
nlf ™~f v?V f revtact,lons1w.ere SCI>eened to eliminate: reactions with negligible
net contribution to heat evolution or pollutant formation, species with no discernible
effect on major species or temperature, and groups of reactions constituting only
species exchange loops. A set of 26 reactions/17 species was derived which can
duplicate within 5 percent the predictions of the 134-reaction/25-species master set.
Ten additional pyrolysis reactions are cited for low-temperature and fuel-rich
applications The Zeldovich mechanism is the principal route to NO for stoichiometric
combustion, but under lean conditions, a path to NO involving N2O is also active
For fuel-rich conditions , comparison with stirred reactor data suggests that NO*
formation cannot be explained by the Zeldovich mechanism alone- an alternate
path involving species of the type RN may be of importance. Finally prompt NO
arising from oxygen-atom overshoot was not predicted for an idealized plug flow
ignition case.
7.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Air Pollution
Mathematical Models
Combustion
Nitrogen Oxide (NO)
Nitrogen Oxide (N2O)
Methane
Reaction Kinetics
Air Pollution Control
Methane/Air
Chemical Heat Release
13B, 07D
12A
21B
07B
07C
DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
102
20. SECURITY CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
90
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