EPA-650/2-74-045

June 1974
                              Environmental Protection Technology Series
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55
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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

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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

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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)].

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        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:

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       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

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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 (
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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

-------
                          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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 Bartok, W. and Engleman V. S. (1972).  Definition of the Mechanism and
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 Barton, S. C. and Dove, J. E. (1969). Can. J. Chem. 47, 521.

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 Bell, A. W., Devolo, N. B., Breen, B. P., Bagwell, F. A., and Rosenthal, K.
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Benson, S. W.  and Fueno, T. (1962).  Mechanism  of Atom Recombination by
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Benson, S. W., Golden,  D. M., and Shaw, R. (August 1973).  SRI Interim
       Annual Report, Project PYU-2009.

 Blackman, V. H. (1956). Vibrational Relaxation in Oxygen and Nitrogen,
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                                 72

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Boden, J. C. and Thrust,  B. A. (1968).  Proc. Roy.  Soc. A305. 107.

Bortner, M. H.  (August 1963).  General Electric Missile and Space Division
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Bowman, B. R., Pratt, D. T., and Crowe, C. T. (1973).  Effects of Turbulent
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Bowman, C. T.  (1970). An Experimental and Analytical Investigation of the
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Bowman, C. T.  (1971). Investigation of Nitric Oxide Formation Kinetics in
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Bowman, C. T.  (1973). Kinetics of Nitric Oxide Formation in Combustion
       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-
       tion Systems (W. Cornelius and W. G. Agnew, Eds.), Plenum Press,
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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/
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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
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Frey, H. M. and Nickerson, G. R.  (1970). Two-Dimensional Kinetic Nozzle
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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

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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

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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

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                            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

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       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

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                            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

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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

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                                 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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