EPA-650/4-74-011
July 1973
REGION TIT LIBRARY
ENVIRONMENTAL PROTECTION AGEHC1
Environmental Monitoring Series
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EPA-650/4-74-011
MATHEMATICAL SIMULATION
OF ATMOSPHERIC PHOTOCHEMICAL REACTIONS
MODEL DEVELOPMENT, VALIDATION,
AND APPLICATION
I1 * F- ; nrr'i-'ial Pwtectiw Agancy
f ..i .. ; ;-\cruation Rewurc*
C .:.ru:."E2)
by
Thomas A. Hecht, Philip M. Roth, and John H. Seinfeld
Systems Applications, Inc.
950 Northgate Drive
San Rafael, California 94903
Contract No. 68-02-0580
Task No. 10
Project No. 26AAD
Program Element No. A11008
EPA Project Officer: Marcia C . Dodge
Chemistry and Physics 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
July 1973
^iLIpltia, PA 19107 ^
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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.
11
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ACKNOWLEDGEMENTS
We wish to acknowledge the contributions of Dr. Charles Wells,
Dr. Robert Shainker, Dr. David Stepner, and Mrs. liana Siegall of
Systems Control, Inc. of Palo Alto, California. Under a subcontract
to their firm, they carried out the digital and analog sensitivity
studies reported in Chapters II and III and in Appendix A, and were
the authors of Appendix A and a portion of Chapter II.
111
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Abstract
The results of a number of individual tasks involving the development,
evaluation, exercise, and analysis of kinetic mechanisms for photochemical
smog are described in this document. First, we have carried out a sensitivity
analysis of the simplified Hecht-Seinfeld (HS) mechanism. The mechanism was
then used in the planning of a number of smog simulation experiments for the
University of North Carolina outdoor chamber program. Major aspects of this
study were the simulation of the chemical dynamics of proposed experiments
under conditions of varying temperature, light intensity, and
ratios. While these two tasks were in progress, we were also preparing a
detailed planning document focusing on experimental and observational areas
of inquiry in which further work is vital to the understanding of smog for-
mation and the development of mathematical models. That report has been
submitted to EPA as a separate document EPA-R4-73-031; thus, we only briefly
review its contents here.
Results of the sensitivity study of the HS mechanism and our analysis
of kinetic mechanisms in the planning report demonstrated deficiencies in
the HS mechanism. We therefore undertook the development of an improved
kinetic mechanism. The new mechanism, which treats the inorganic reactions
in substantial detail and the organic reactions in general terms, has been
formulated to strike a balance between accuracy of prediction and compactness
of representation. The results of the initial evaluation of the new mechanism
using n-butane/NQ , propylene/NO , and n-butane/prcpylene/NO smog chamber
/» A /»
data are included.
IV
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TABLE OF CONTENTS
List of Figures vi
List of Tables vi
I. .Introduction 1
II. Sensitivity Analysis of the Hecht and Seinfeld Kinetic
Mechanism 6
A. Analog Studies 15
B. Digital Studies 18
C. Conclusions 30
III. Planning of Outdoor Chamber Experiments 33
A. Effect of Initial NOY Concentration on Maximum Oxidant 34
A
B. Effect of Diurnal Light Intensity Variations on N02
and 03 Maximums and Dosages 37
C. Effect of Temperature Variations on N0£ and 03 Maxima
and Dosages 40
D. Conclusions 44
IV. Preparation of a Recommendations Report, "Existing Needs
in the Observational Study of Atmospheric Chemical Reactions" 46
V. Development of an Improved General Kinetic Mechanism 51
A. The Data Base ind Sources of Experimental Uncertainty 59
B. Evaluation of the 39-Step Lumped Mechanism 70
C. Concluding Consents 118
VI. Summary and Prospects 131
References 135
Appendix A. Analog and Digital Sensitivity Analysis Techniques
as Applied to the Hecht-Seinfeld Mechanism 137
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LIST OF FIGURES
1. Sensitivity Analysis 11
2. Effect of Initial NOX Concentration on Maximum Oxidant 35
3. EPA Run 306 84
4. EPA Run 314 87
5. EPA Run 345 90
6. EPA Run 318 93
7. EPA Run 325 96
8. EPA Run 329 98
9. EPA Run 459 99
10. EPA Run 307 101
11. EPA Run 333 104
12. EPA Run 348 107
13. EPA Run 349 110
14. EPA Run 352 113
15. EPA Run 457 116
16. Isopleths of Maximum Ozona Concentration Achieved During an 8-
hour Irradiation of Various Mixtures of n-butane, Propylene and
NO. (N02 initially at 0.1 ppm.) 124
17. Surface of Maximum Ozone Concentrations Achieved During an 8-
hour Irradiation of Various Mixtures of n-butane, Propylene and
NO. (N02 initially at 0.1 ppm.) 125
18. Maximum Ozone Concentration Achieved During an 8-hour Irradia-
tion of an Initial Mixture of [HC] = 0.80 ppm, [NO] = 0.40 ppm,
and [N02] = 0.10 ppm, for Various Initial Mixtures of n-butane,
and Propylene 127
LIST OF TABLES
1. The HS Kinetic Mechanism 7
2. Base Values of Parameters for the Toluene-N0x System 19
3. Effects of Parameters Variations on Time to N02 Peak and on
Magnitude of Asymptotic 03 Concentration (or Concentration at
400 Minutes ) for the Toluene-N0x System 20
4. Rank Order of Parameters: Sensitivity of "Time to N02 Peak"
to Parameter Variations of +_ 5% for the Toluene-NO System. ... 22
^ /\
vi
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5. Rank Order of Parameters: Sensitivity of "Asymptotic Ozone Con-
centration, or Ozone Concentration at 400 Minutes" to Parameter
Variations of +_ 50% for the Toluene-N0x System 23
6. Base Values of Parameters for the Propylene-N0x System 24
7. Effects of Parameter Variations on Time to N02 Peak and on Magni-
tude of Asymptotic 03, Concentration (or Concentration at 400
minutes) for the Propylene-N0x System 25
8. Rank Order of Parameters: Sensitivity of "Time to N02 Peak" to
Parameter Variations for the Propylene - NOX System 26
9. Rank Order of Parameters: Sensitivity of "Asymptotic Ozone Con-
centration, or Ozone Concentration at 400 Minutes," to Parameter
Variations for the Propylene-N0x System 27
10. Results of Limited Sensitivity Study Carried Out on the Digital
Computer for the Toluene-N0x System 29
11. Effect of Diurnal Light Intensity Variations on the HS Reaction
Model 39
12. Activation Energies of the Reactions in the HS Mechanism 42
13. Effect of Changes in Temperature on NOg and 03 Concentrations . . 43
14. A Lumped Kinetic Mechanism for Photochemical Smog 52
15. Initial Conditions Associated with the Experimental Chamber Data . 62
16. Validation Values of the Rate Constants and their Comparison with
the Recommended Values of Other Investigations 73
17. List of Figures 83
vn
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I. INTRODUCTION
The goal of the project about which we report here, "The
Mathematical Modeling of Photochemical Smog", was the develop-
ment and validation of a kinetic mechanism capable of describ-
ing atmospheric photochemical reactions. The project itself,
however, involved a series of tasks, most of which are related
to mechanism evaluation, but each being a separate and distinct
piece of work. In reporting on the accomplishments of the year,
we have elected to discuss each undertaking on an individual basis
and in the order carried out. The four main tasks were the fol-
lowing:
1. Exercise and analysis of a simplified kinetic mechanism,
as developed by Kecht and Seinfeld (1972), the "best"
available mechanism as of the inception of the project.
2. Consultation in the planning of experiments to be carried
out in twin 6000 cubic foot outdoor chambers located on
the campus of the University of North Carolina.
3. Preparation of a detailed planning document concerned
with appraising the current state of knowledge in atmos-
pheric photochemisLy and pinpointing specific areas of
inquiry in which further experimental work is vital to
the advancement of knowledge.
-1-
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4. Evaluation of an improved, lumped, 39-step kinetic
mechanism. Data used for validation were provided
by EPA.
It had been clear for some time that there was no kinetic
mechanism available, as of mid-1972 that was truly adequate for
describing the dynamics of atmospheric reactions. Each mechanism
that had been proposed suffered some obvious deficiency (or defi-
ciencies) that required rectification. Furthermore, it was apparent
that available smog chamber data were not suitable for use in criti-
cally evaluating the capabilities of existing mechanisms. Thus, we
were faced at the outset with inadequacies in both models and data.
Given these circumstances, we entered into discussions with Dr. M.
C. Dodge of EPA, the project officer, in an effort to define an
appropriate course of action. As a consequence of these discussions,
the following plan was adopted:
To carry out sensitivity analyses using the Heoht-Seinfeld
(HS) mechanism. While we were aware of the weaknesses of
the mechanism, we felt it important to gain some under-
standing of the sensitivity of predicted concentration-
time profiles to variations in the magnitudes of the
parameters of the mechanism, the reaction rate constants
and the stoichiometric coefficients. Such analyses were
expected to provide further insight into model defici-
encies, as well as information helpful in identifying
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parameters which should be most accurately determined.
In addition, these studies afforded us an opportunity
to experiment with both the analog and digital computers
in integrating the coupled, first order differential
equations. This work is discussed in Chapter II.
To use the. HS mechanism to simulate the dynamics of
chemical reactions in the outdoor1 charfoer, in response
to temporal variations in temperature and radiation
intensity. In particular, after consultation with
Dr. B. Dimitriades of EPA and Dr. H. Jeffries of the
Univeristy of North Carolina, we carried out the following
calculations for the toluene system (the "best" surrogate
for atmospheric hydrocarbon mixture of the various re-
active systems we had studied to date).
1. Determined maximum oxidant levels as u function
of initial NO for constant initial hydrocarbon
rt
at 0.1, 0.5, 1.0, 2.5 and 5.0 ppm. Range of
NOY was 0 to 1 ppm.
A
2. Determined the effect of variations in light
intensity on maximum N0£ and 0, and on dosage of
both for five light intensity profiles. This
calculation was carried out for several pairs
of initial conditions of HC and NOX, where
initial conditions within each pair differed
only in terms of HC concentration.
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3. Determined the effect of temperature on maxi-
mum NCL and 03 and on dosage of both. This calculation
was carried out over a wide range of ambient
temperature levels for four pairs of initial
HC and NOX conditions, as above.
The results of this effort are presented in Chapter III.
To prepare a recommendations document for the Chemistry and
Physics Laboratory (CPL) that will serve as an aid in plan-
ning for the support of future contracts and grants in
experimental and observational aspects of atmospheric
chemistry. The core of the report focuses on laboratory
studies concerned with the kinetics and mechanisms of
individual reactions, on smog chamber studies, and on pro-
grams involving atmospheric observations. Also included
is a thorough review of the status of modeling of photochemical
reaction processes in both the presence and absence of
transport-limiting phenomena. This report, "Existing
Needs in the Experimental and Observational Study of
Atmospheric Chemical Reactions: A Recommendations Report",
by J. H. Seinfeld, T. A. Hecht, and P. M. Roth, (EPA-R4-73-031),
has been submitted to EPA as a separate document. We will thus
only briefly review its contents in this report (Chapter IV).
To develop and evaluate an improved photochemical kinetics
mechanism. Development of the improved mechanism, which
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was documented originally in the planning report,
was taken to completion more rapidly than was originally
anticipated, thus allowing time for a relatively ex-
tensive validation effort. The model and the
validation results are described in detail in
Chapter V. We would note here only that the results
are quite favorable.
We conclude the report (Chapter VI) with an evaluation of the
work carried out to date and a summary of future needs.
-5-
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II. Sensitivity Analysis of the Hecht and Seinfeld Kinetic
Mechanism.
Chemical kinetics mechanisms of varying degrees of complexity are
presently being developed for inclusion in urban scale air pollution simu-
lation models. These models, in turn, may be used in the planning and
development of air pollution abatement and control strategies. The degree
of confidence that one can place in the predictions of such simulation
models depends, among other considerations, on the uncertainties associated
with the parameters of the model (for example, the reaction rate constants).
More important, however, is the sensitivity of the model's predictions to
variations in the magnitudes of inaccurately known parameters. Thus, an
important step in the development of an accurate, as well as compact kin-
etic mechanism for photochemical srr.og is the determination of the sensitivity
of concentration-time profiles predicted by the mechanism to variations in
each of the various input parameters, rate constants, parameterized stoichio-
metric coefficients, and initial reactant concentrations. By carrying
out such studies, those: parameters can be identified which must be accurately
determined to insure reliable prediction of pollutant concentrations.
A promising generalized kinetic mechanism (see Table 1.), formulated
by Seinfeld et al, (1971) and further developed by Hecht (1972), was,
chosen as the subject of a detailed sensitivity analysis carried out by
us as a part of Lhis umtratl effort. This mechanism was selected for
the study bf-cause, in comparing it with other mechanisms that have been
developed, we judged it "best" in terms of accuracy and reliability. The
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TABLE 1. The HS Kinetic Mechanism
NO + hv -» NO + 0
Oj + NO N02 + 02
03 + N02 * NOj + 02
5
N03 + NO -* 2N02
H20
N03 + N02 6 2HN03
H20
NO + N02 -> 2HN02
8
2HN02 > NO + N02
9
HN02 + hv * OH + NO
°2
CO + OH Y* C02 + H02
11
H02 + NO + OH + N02
12
H02 + N02 + HN02 + 02
13
0 + HC + aR02
l«f
OH + HC -* BR02
IS
03 + HC * YR02
16
R02 + NO -> N02 * eOH
17
R02 + N02 + PAN
18
0 + HC2 - a2R02
19
OH + HC? -* 32R02
20
HC2
21
N02 + WALL OR PARTICLE
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mechanism, termed by us the HS mechanism, has been evaluated for
several hydrocarbons and for a wide range of values of the HC/NOX ratio
(see references cited). In this section we report on the sensitivity
analysis, the design of the study,and the results of the work.
Simultaneously with our carrying out the sensitivity analysis, we
undertook development of a more detailed mechanism, with the intent of
eliminating a number of deficiencies in the HS mechanism. During the
course of this development work, it soon became apparent that the new
mechanism, which we present in Chapter V, represented a substantial im-
provement over the HS mechanism. Thus, the sensitivity results to be
reported here are of limited interest in the sense that the HS mechanism
has been substantially improved upon since the task was carried out.
Nevertheless, we have elected to fully disclose the results of the work
here because
it is the first such sensitivity study performed
the methods employed are generally applicable
the HS mechanism contains the same general chemical
dependencies c:s thp improved kinetics, so that the
results are of interest and value for making quali-
tative sensitivity judgements concerning the new
rrochanism
the task itself was a clearly defined portion cf the
overall effort.
l.'c would note, however, that the sensitivity study itself was limited to
a detailed aiie.lysis cf en HC-f!Ox systcn. of low reactivity and a partial analysis
of a more reactive hydrocarbon-IIO system, particular attention being given
A
to those parameters which wore different for the two systems. This scope
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of work, in our judgment, provided a reasonable approach, limiting the
expenditure of effort in light of the limited value of the results.
There are several points to be noted about the HS mechanism as we
used it. First, reactions 5 and 8, although a part of the mechanism as
originally formulated, were found to be unimportant in subsequent vali-
dation work (Hecht, 1972) and are now deleted from the mechanism. Re-
actions 10 to 12 apply only when CO is present initially. To facilitate
the interpretation of the results we chose to study only single hydro-
carbon reactions systems. As a consequence of this simplification, we
were able to delete four additional reactionsreactions 18 to 21. Re-
actions 18 to 20 are needed when simulating the behavior of binary
hydrocarbon mixtures. Reaction 21 is included to account for the observed
behavior of auto exhaust when irradiated in sir.og chambers. To summarize,
because we did not consider binary hydrocarbon mixutres, auto exhaust,
or systems containing CO in this sensitivity study, the mechanism which
we ultimately examined consisted of only of twelve reactions: 1-4, 6, 7,
9, 13-17.
The sensitivity analysis was carried out in the following manner.
For the tvo hydrccarbon-NO systems evaluated in the current project,
A
nominal (or base) values for all parameters were taken to be those reported
in Hecht (1972). Ease concontration-tine profiles for hydrocarbon, NO, K02,
03 were obtained by integrating the governing ratt equations with each
parameter at its nominal vdlue. One of the pararrsters was then increased
and decreased by a fixed percentage, with all other parameters held at
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their nominal values. The equations were then integrated twice, once for
each of the two new settings (+x% and -x%) of the selected input parameter.
This process was repeated for each parameter of interest. Thus, for n
parameters, integrations were carried out for a base case and 2n parameter
variations. Finally, for each of the 2n+l integrations, values of "decision
variables" were determined. The magnitudes of the decision variables for
each variation in a parameter were compared with those computed for the
base case, and rankings of sensitivities of the parameters were obtained
by tabulating the magnitudes of the differences.
It is appropriate to corr,ment at this point about what constitutes a
decision variable. By a decision variable, we have in mind any measure
that can be constructed or derived from the predicted responses (in this
case, concentration) that is of use in characterizing the sensitivity
of the model or mechanism to changes in the magnitudes of the parameters.
Measures that are simply calculated include, as noted before, the maximum
ozone concentration n.easured, the time to the N02 peak, and the time of
"cross-over" of the NO and N02 concentration profiles. In none of these
simple cases, however, is the decision variable suggested a measure of
sensitivity over the entire time period of the integration for each species
determined experimentally. Instead of adopting a simple measure, then,
we have had to construct one that meets our needs.
Consider the following. Assu.ne that the solid line in Figure 1 is
the time history of species y- (i being one of m species present)
for a set of nominal reaction rate constants, k, , . . . , k . Assume
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time
FIGURE 1, SENSITIVITY ANALYSIS
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further that one of the reaction rate constants k. (j representing
one of n rate constants, stoichiometric coeffecients, or initial con-
ditions) is altered by a small, fixed percentage. The time history of
all the reaction constituents will be altered in some manner in response
to this change. For example, the change in y. , y. + 6y.j , may be shown
by the dotted line. The vertical distance between the lines is the value
of <5y.(t) at each time point t, and the shaded area is a measure of the
effect that a small change in k. has on the time history of y.. The
w
total change in y^, using squared values to allow for both positive and
negative differences, is given by
(1)
If this same operation were performed for the m constituents, the total
effect (squared) of a small change in k. is given by
m t
£ /(^(t))2 dt (2)
1=1 o
This is clearly a measure of the sensitivity of the constituent values to
variations in the rate constant k.. If the time histories are greatly al-
tered, indicating a large sensitivity to that particular rate constant,
then the expression in equation (2) will have a large value. If the sen-
sitivity is small, there will be very little change in the time histories
of constituent values, and the expression in equation (2) will also be small
A measure of sensitivity such as that described can be easily calculated
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using a digital computer. However, if an analog computer is used to carry
out the analysis, then only more limited (or simpler) measures of sensi-
tivity can be used, as they must be observed visually.
For the purposes of the present study, we elected to employ an analog
computer to carry out the necessary calculations. This decision was
based on several factors. First, the experimental data from which the
nominal values of the rate constants and stoichiometric coefficients
were derived [see Hecht (1972)] were corrupted by error to a large
enough degree that the base concentration-tirr.e profiles were subject to
greater than desirable levels of uncertainty. Second, experimental
concentration-time profiles were determined only for four of the eleven
chemical constituents in the mechanism; thus, the value of a complete
sensitivity analysis for each species over the course of the entire ir-
radiation is limited. Third, a digital sensitivity analysis based on
equation (2) is extremely expensive to carry out. Given these various
considerations, we did not feel that the use of the digital computer
was justified. The digital computer was therefore used primarily as
a means for checking the results of the analog computations (although
wo did perform a few sensitivity runs on the digital computer to demon-
strate the potential pc-./er of this approach).
The availability of a previously wired circuit board also influenced
our decision to a degree. As part of the contract effort, we had, at
an earlier staqe, programed the HS Mechanism for analog usage. As the
render may be aware, analog programing requires a substantial expenditure
of effort; once the circuits have been wired, however, the analog provides
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virtually Instantaneous "turn around" time at a very low cost. Aside
from rapid and direct response, other advantages of analog computation
include flexibility in use and the opportunity the device provides for
"getting a feel" for the effect that varying the parameters has on pre-
dicted concentrations. However, only four place accuracy is available
on the analog, scaling of variables can, under certain conditions, be a
serious problem, and personnel are required for operation at all times.
Despite these latter shortcomings, the analog seemed to be the
wisest choice for the work at hand.
As we noted earlier, the selection of the analog for use limited our
choice of decision variables to those scalars which can be observed
visually, i.e., the variables, time to the N02 peak, T, and the magni-
tude of the 03 maximum, M. These are logical choices inasmuch as the
onset of smog symptoms, as characterized by the time to the NOp peak,
and the intensity of smog, as generally evidenced by th° (L concentration,
are often taken as two major indicators of smog formation and severity.
Further, both of these variables are quite sensitive to variations in the
values of the input parameters. If consideration is limited to a six
hour simulation, as was done in this study, T occurs most often between
the first and third hours of irradiation and M between the third and
sixth hours. During the first hour the principal occurrence is the oxi-
dation of NO to N02> which in turn is reflected in T. Thus, except for
the first hour (the "induction" period), T and M serve as sensitive and
explicit indicators of the course of the experiment.
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In this chapter we present the results of the sensitivity study
of the HS mechanism. We examine the parameters displaying the greatest
sensitivity, exploring the reasons for the uncertainties associated with
each. We then conclude by discussing the basis for our decision to develop
the new kinetic mechanism presented in Chapter V. Should the reader be
interested, a detailed description of the mathematical representation
of the HS mechanism and the techniques used for carrying out both the
analog and digital sensitivity analyses can be found in Appendix A.
A. Analog Studies
Use of a large, powerful EAI 8800 analog computer was provided at no
cost by the NASA Am2s Research Center. The 8800 at Ames is one of the
largest analog computers in existence. As such, it has far greater capacity
than is required to integrate the governing equations. -The computer also
has rcany features which ease programming and debugging. For example,
potentiometers can be set directly from the control panel, and the components
are versatile enough to allow the programming of coupled differential
equations whose individual scales differ by many orders of magnitude. (For
this particular application voltage ranges had to be scaled over eleven
orders of magnitude.) It also has two attached CRTs, an X-Y plotter, 16
strip chart recorders, and a ciiqital printer for permanently recording
integrator initial condition? and pot settings. In short, we found it
to be very suited for our use.
In using the analog, special consideration had to be given to the
form of the governing equations. In particular, in order to avoid the
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need for solving nonlinear algebraic equations, the steady-state assumption
was not Invoked for any of the species. Thus, Instead of employing
five differential equations and six steady-state algebraic equations
to describe the kinetics (the complete set of equations for this repre-
sentation can be found in Seinfeld et al, 1971), we solved the full set
of eleven differential equations. Equipment requirements for integration
of the equations embodying the mechanism were the following: 11 integrators,
15 multipliers, approximately 50 pots, and 65 summing amplifiers. Following
initial preparations, the 11 differential equations were time and amplitude
sealed, based on the peak amplitudes of the 11 state variables obtained from
a digital simulation of the kinetic mechanism using the rate parameters.
A low and a high reactivity hydrocarbon-NO system were evaluated
A
in this sensitivity study, with toluene and propylene, respectively,
serving as representative hydrocarbons. These hydrocarbons were chosen
because extensive validation studies have been carried out for each over
a range of initial hydrocarbon to NO ratios (Hecht, 1972) and because
A
they demonstrate behavior typical of the low and high "reactivity" organic
species that participate in atmospheric reactions.
1. Toluene
We carried out a comprehensive sensitivity study
on the analog computer for the rate constants and stoichio-
metric coefficients associated with the toluene-NOv system.
A
Parameters were varied ± 50:.: from their tiase values end
predicted values of T, the time to the NOp peak, and M,
the asymptomatic 03 level, were noted. Base values of
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the parameters are tabulated in Table 2; effects of para-
meter variations on T and M are shown in Table 3. In
Tables 4 and 5, respectively, we have "rank-ordered" the
parameters in terms of the magnitude of change in T and
M observed as a result of the ±50% variations in rate con-
stants and stoichiometric coefficients. T is most sensitive
to variations in 6 , e , a , k, , k2 , and k,-., M to
variations in B , e , a , and k,. In addition, decreases
in k~ and k. significantly increase M, while a decrease
in k,- causes a large decrease in M.
2. Propylene
The kinetic mechanism and rate parameters were the same
for the propylene-NO system as for the toluena-NO system;
A A
except for changes in the stoichiometric coefficients, in the
rates of the hydrocarbon oxidation reactions, and in the rate
of PAN formation. We began the analysis of the propylene-NO
A
system by examining the sensitivities of k, , k~ , k, , and
k.,g , parameters whose nominal values are identical in both
systems, and found that their sensitivities followed the same
"rank ordering" observed for the toluene-NO system. For this
reason and the reasons already outlined in the introduction to
this chapter, we limited the sensitivity runs for the propylene
system to eight of tho input rate constants and one of the
initial conditions.
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Base values of the parameters used in the propylene
sensitivity runs are presented in Table 6. Effects of para-
meter variations on T and M are shown in Table 7. In Tables
8 and 9, respectively, we have "rank-ordered" the parameters
examined in terms of the magnitude of change in T and M
that have resulted from the indicated variations in rate
constants. Both T and M are most sensitive to variations
in k, and k2 . In addition, a 50% decrease in k,- results
in a large decrease in T and M , and a 50% increase in k^5
results in a substantial decrease in M. Formal evaluation of
the sensitivity of the stoichiometric coefficients was not
performed. From our experience with this system, however, we
can conclude that a , 6 , and e are extremely sensitive
parameters, as was the case for the toluene system.
B. Digital Studies
Our principal interests in digital computation techniques are in
performing routine validation experiments, such as those presented in
Chapter V, and in estirating the ir.cgnitude and uncertainty (i.e. variance)
of "sensitive11 parameters through the analysis of experimental data. However, we
have also used the digital computer in what amounted to a pilot study, to
carry nut a limited sensitivity analysis of the toluene-NO system. Speci-
A
fically, we examined the effect on predicted concentration-time profiles
of varying the magnitude of four parameters--^ , k^ , k^ , and k-jg.
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TABLE 2.. Base Values of Parameters for the Toluene-NO System
Rate Constants *
kl
7
C9
C12
C13
C15
0.266 min'l
ppm"1 mi
mn
"^
2.76 x 106 min'l
21.8 ppm-lmin"
0.006 ppm'lmin"
0.1
5.0 x
5.0 x
1.8 x
10.0
6.0 x
1.5 x 10 ' ppm~'mi n"
7.5 x 10 ppm"lmin"l
1.8 x 10^ ppm'lmi n"'
ppm'lmi i
ppm"'mi i
ppm'lmi i
30.0
ppm" mi n
Stoichionetric Coefficients
a
e
Y
e
6.0
1.2
k.Q
0.61
Oilution
0. = 5.^ liters/min.
*
k
k8 k!0
-19-
18 through 21
0.0
-------
TAB4.E 3. Effects of Parameters Variations
On Time to NO- Peak and On Magnitude of
Asymptotic 0? Concentration (or Concentration at 400 Minutes)
for the Toluene-NO System
/%
Parameter Varied, Time to CQ, max (in ppm)
and Magni tude of
Varied Parameter
Base Values
k, = .133
k, = .399
k2 = 1.38 x 106
k2 = 2.07 x 106
k2 = 4.14 x 106
k3 = 10.9
k} = 32.7
kk = .003
k,, = .009
k/, = .06
k6 = .05
k6 = .15
k? = .00025
k? = .00075
kg = .0025
kg = .0075
kj = 3000
k,3 = 9000
k,/, = 7500
k)/4 = 22500
k15 = 3.75 x 10"15
k)5 = 1.125 x lO'1"
k,6 = 900
ku = 2700
N02 Peak
162
278
119
94
128
224
164
160
162
160
148
162
160
162
162
162
158
286
118
163
160
161
160
186
151
or
CQ, @400 min
.24
.11
>.3
>.3
.27
.19
>.3
.205
.28
.21
.09
.24
.24
.24
.24
.24
.24
.14
.28
.24
.24
.2.4
.24
.17
.29
-20-
-------
TABLE 3. (Continued)
Parameter Varied, Time to CQ, max (in ppm)
and Magnitude of N02 Peak or
Varied Parameter
Base Values
k,7- 15
kl? " *5
a = 3
0 = 9
6 = .6
3 = 1.8
Y = 2
Y = 6
£ = .305
e = .915
(N02)0 = .02
(N02)0 = .04
(N0)0 = .45
(N0)0 = .65
(03)Q = .05
(HC)0 = 1.34
(HC)0 = 2.00
162
163
161
300
114
360
48
160
160
336
56
186
142
158
165
124
194
136
Cg, e tuu mm
.24
.29
.21
.12
.30
.09
>.3
.24
.24
.12
>.3
.24
.24
.23
.25
.25
.20
.27
-21-
-------
TABLE A. Rank Order of Parameters: Sensitivity of "Time to
NO, Peak" to Parameter Variations of ± 50% for the
Tofuene-NO system.
THOSE CHANGES CAUSING GREATEST DELAY IN TIME TO N02 PEAK
Parameter Chanqe '
6 - 50%
e - 50%
a - 50%
k,3 - 50%
k, - 50%
k2 + 50%
k]6 - 50%
ki - 50%
kT/. - 50%
k,7 - 50%
No Effect: k^ - 50%
k6 - 50%
k? + 50%
k^ - 50%
THOSE CHANGES CAUSING GREATEST
Parameter C'r.anoe
B + 50f:
e + 50%
k2 - 50 x
a + 50%
kn + 50%
k, + 50%
kl6 + 50%
kg + 50%
V.\ + 50%
kj + 50%
k, + 50%
k,^ + 50%
k15 + 501
Y - 501
Y + 50%
k,, - 50%
k 7 + 50C.:
360
336
300
286
278
22k
186
164
163
163
REDUCTION IN TIME TO N02 PEAK
T
48
56
Q u
1 1 *J
118
119
151
158
160
160
160
160
160
160
160
161
161
-22-
-------
TABLE 5. Rank Order of Parameters: Sensitivity of "Asymptotic
Ozone Concentration, or Ozone Concentration at 400
Minutes" to Parameter Variations of + 50% eor the Toluene-
NO system.
x\
THOSE CHANGES CAUSING GREATEST INCREASE IN 0^ LEVELS (at <<00 Minutes)
k2 - 50%
k3 - 50%
6 + 50%
e + 50%
a + 50%
kl6 + 50%
k,7 - 50%
k/, - 50%
k13 + 50%
.3
.29
.29
.28
.28
THOSE CHANGES CAUSING GREATEST DECREASE IN Oj LEVELS C»00 Minutes)
0 - 50%
k, - 50%
o - 50%
e - 50%
kn - 50%
- 50%
k, + 50%
k, + 50%
kL + 50%
LI7
+ 50%
.09
.11
.12
.12
.14
.17
.19
.205
.21
.21
-23-
-------
TABLE 6. BASE VALUES OF PARAMETERS FOR THE PROPYLENE-NO
SYSTEM x
Rate Constants*
kl
k2
k3
k4
k6
k?
kg
kll
k!2
k^
k!4
k!5
k!6
k!7
Stoichiometric
a
6
Y
c
0.266
2.76 x 106
21.8
0.006
0.1
5.0 x 10"4
5.0 x 10"3
1.8 x 103
10.0
4.0 x 104
2.5 x 104
0.016
1.8 x 103
3.0
Coefficients
16.0
0.2
4.0
0.22
-24-
min"
min
ppm" min"
ppm" min"
ppm min
ppm" min"
min"
ppm min
ppm" min
ppm min
ppm min
ppm min
ppm min
ppm" min"
r\i 1 1,4- -i
U J. J. U U J.
Q =
1
1
1
l
1
1
1
1
1
1
1
r\
, U
6
kg = k,Q = k,g through k7, = 0.0
-------
TABLE 7. EFFECTS OF PARAMETER VARIATIONS ON TIME TO N02
PEAK AND ON MAGNITUDE OF ASYMPTOTIC 03 CONCENTRATION
(OR CONCENTRATION AT 400 MINUTES) FOR THE PROPYLENE-
NOX SYSTEM.
c« max (in ppm)
or
Parameter Varied;
Value of Parameter
Base Values
ka = .133
kj = .312
k2 = 1.38 x 106
k2 = 4.14 x 106
k3 = 10.9
k3 = 32.7
k13 = 20,000
k13 = 60,000
k14 = 12,500
k14 = 37,500
kis = .%024
k^6 = 900
kl6 = 2700
k1? = 1.5
k17 = 4.5
(N02)Q = .02
(N)2)Q = .06
Time to
N02 Peak
130
250
114
66
194
142
124
260
88
130
130
134
128
130
130
130
164
112
0*a HUU iiij.ii
ff
3
.47
.25
.51
>.58
.36
.48
.47
.24
.58
.48
.47
.30
.46
.48
.48
.46
.46
.49
-25-
-------
TABLE 8. RANK ORDER OF PARAMETERS: SENSITIVITY OF "TIME
TO NO, PEAK" TO PARAMETER VARIATIONS FOR THE'
PROPYtENE-NOv SYSTEM
Those Changes Causing Greatest Delay in Time to N02 Peak
Parameter Change j_
k13 - 50% 260
k1 - 50% 250
k2 + 50% 194
(N02)Q - 50% 164
k3 - 50% 142
k15 + 50% 134
Those Changes Causing Greatest Reduction in Time to N02 Peak
Parameter Change j[
k2 - 50% 66
kl3 + 50% '88
(N02)0 + 50% 112
kx + 25% 114
k3 + 50% 124
k,, - 50% 128
lo
No Effect k,4 +_ 50
klfi + 50
k - 50
* Changes and ordering nbout the same as for toluene, with
exception, of k-, ^ , \:hich is less sensitive for propylerie
-26-
-------
TABLE 9. RANK ORDER OF PARAMETERS: SENSITIVITY OF
"ASYMPTOTIC OZONE CONCENTRATION, OR OZONE
CONCENTRATION AT 400 MINUTES",TO PARAMETER
VARIATIONS FOR THE PROPYLENE-NO SYSTEM
Those Changes Causing Greatest Increase in 0, Levels
(Maximum or at 400 Min., Whichever is Greatest)
Parameter Change J_
k2 - 50% >.58
kj + 25% .51
(N09) + 501 .49
L O
k3 - 50% .48
k14 -^50%% .48
k16 + 501 .48
k17 - 50% .48
Those Changes Causing Greatest Decrease in 0, Levels*
k13 - 50% .24
kL - 50% .25
k15 + 501 .30
k2' + 501 .36
kl6 - 50% .46
k1? + 50% .46
(N02)Q - 50% .46
No Effect k3 + 50%
k14 + 50%
* Effects about the same as for toluene, except that, for
propylcne systcn, k^ - 50% causes greater reduction in
Oj than kj_ - 50?, . The effect occurs, however, because
N02 peak has boon delayed.
-27-
-------
Details of the methods employed can be found in Appendix A.
The measure of sensitivity employed for the digital studies was the
"root sum square" criterion, equation (2), which can be expressed in the
expanded form,
. V2
(t) - yj (t))2 dt
l_ 1= I O
B
where y. = predicted concentration of the i species using
base values of parameters
V ..
y^ = predicted concentration of i species using base
values of all parar.eters, except one. This parameter
was varied ]% in magnitude.
t = time at which simulation was terminated
j = index of parameter that was varied
The summation is carried out over the integrated, squared, predicted
differences for 11 speciesNO, N02, 03, HC, HC2> R02, OH, 0, HN02§ N03>
and H02. The results cf the analysis are shown in Table 10. As we noted
in the introduction this measure of sensitivity v;ould have been of greater
significance if all the chenical constituents had been determined experi-
mentally, [uring the exparirients only NO, ;,09, 0,, and HC were monitored.
b 3
Comparison of these results (Table 10) with those in Tables 4 and 5, hov.ever,
shows that the resultant "rank-ordering" of the digital and analog sensitivity
r2ti ods agree.
-28-
-------
TABLE 10. Results of Limited Sensitivity Study Carried Out
On the Digital Computer for the Toluene-N0v System
Reaction Rate k K.**
Constant- » J
k, 1.46
kl6 0.271
k 0.256
* In decreasing order of sensitivity
** K: is defined in text. The criterion Kjkr is derived from
KJ: x (k? - kV) , where k? - kV = .Oik? =J.6]k: . Thus, the
JJJ J J A J J
tabulated values are .OlkjKj x 10^ , or k:K-
-29-
-------
C. Conclusions
In the analysis of the HS mechanism that we have described, we
found the concentration predictions to be most sensitive to changes
1n the same rate constants and stoichiometric coefficients, where T
and M have been employed as decision variables. These input para-
meters are k-j , k2 , k^3 , 0,3, and e . The only major dif-
ference in behavior observed between the two systems is that variations
in the rate of the ozone-hydrocarbon reaction (reaction 15) affect the
ozone concentrations predicted for the propylene system, but not for
the toluene system. This, of course, reflects the fact that ozone does
not react with aromatics at a significant rate; hence, changes in k^5
for this system have virtually no effect. Nevertheless, individual
variations in each of the input parameters results in some observable
change in the concentration-time profiles for at least one of the
hydrocarbon-NOY systems. As a result, one may conclude that the HS
A
mechanism cannot be made more compact without having a deleterious ef-
fect on the quality of description.
The fact that several parameters are "sensitive" does not imply that
predictions of the mechanism are necessarily uncertain. Nor is the un-
certainty in prediction related in a simple manner to the completeness
of thr kinetic representation or to the accuracy with which input
parameters are known. Rather, it is uncertainty in sensitive parameters
or,for that matter, in the mechanism itself which results in uncertain
predictions. Thus, the uncertainty in prediction associated with one of
the sensitive rate constants, k~ , is very low because good agreement
-30-
-------
exists among the many experimental determinations of the rate constant,
and the stoichiometry of the elementary reaction is well known. As for
the other parameters, the following recommendations can be made. Careful
measurement of the light intensity in future studies will substantially
reduce the uncertainty associated with k^. The magnitudes of the stoichio-
metric coefficients and k,_ , however, have been established by means
of model fitting procedures, as there is no a priori technique presently
available for determining these parameters. Rather, their magnitudes must,
in the future, be based on values established in successfully completed
validation studies. Thus, the uncertainty in k,- , a , 6 . and e
will decrease as the number of different systems for which successful
validation studies are carried out increases. While parameter estimation,
as opposed to parameter determination, is not particularly desirable, it
is a necessary consequence of adopting a compact, generalized mechanism.
Finally, we might note V-.at, despite the high probability that the
new kinetic mechanism (Chapter V) alluded to in the introduction will prove
to be more reliable a predictor, the sensitivity study performed here using
the HS mechanisn is still of value for the following reasons:
Both rochanisrrs contain the Seme skeleton of important
eleirentary reactions, so that "patterns of sensitivity"
in the HS rrechanism may well be similar to patterns of
sensitivity observed using the larger rrechanism.
In addition to characterizing patterns of sensitivity,
we have been able to identify several parameters for which
it is important to reduce uncertainties in the future both
in and through experimental studies.
-31-
-------
For example, in reviewing the plans for the U.C. Riverside chamber
studies that were initiated this summer, we have been guided by the
results of the sensitivity studies in suggesting that emphasis be placed
on accurate determination of both k^, and the initial NOg concentration,
parameters that in the past have not been controlled with precision. More-
over, we have recommended to the staff of CPL that work be supported
that would lead to more accurate determination of the sensitive rate
constants including that for the ROg-NO reaction.
In summary, then, while the sensitivity studies that we carried
out are surely not of long range or lasting value, they have provided
both information and insights that have been of use. Furthermore,
the techniques explored in this work will prove to be of considerably
greater use when they are applied in a future study of the new, expanded
mechanism.
-32-
-------
III. PLANNING OF OUTDOOR CHAMBER EXPERIMENTS
A novel type of smog chamber has recently been constructed out-of-
doors in a rural community near Research Triangle Park, North Carolina.
This structure, an A-frame covered with transparent Teflon film, is
divided by a membrane into two 6,000 cubic foot reactors. In carrying
out an experiment, these reactors are filled with ambient air (the pollutant
content of which is typically quite low) and charged with varying amounts
of hydrocarbons and NO . Chemical reactions are then allowed to proceed
/\
under conditions of natural sunlight, temperature, and humidity. The
initial concentrations of reactants for these experiments are chosen so
as to demonstrate the changes in "air quality" which may result from various
pollution control strategies presently under consideration.
We have participated in the planning of these experiments through
the simulation of the proposed chamber runs using the simplified HS
mechanism (Table 1). At the request of Dr. B. Dimitriades of EPA and
Dr. H. Jeffries of UNC, we undertook the following calculations.
. (i) computed maximum oxidant as a function of initial
NO for constant initial hydrocarbon at 0.1, 0.5,
A
1.0, 2.5, and 5.0 ppm. The range of NO concentrations
n
is 0 to 1 ppm.
(ii) determined the effect of variations in light intensity
*
on maximum NOp and 0., and on dosage of both for five
light intensity profiles. This calculation was carried
* All dosage calculations were based on an irradiation time of 1000
minutes.
-33-
-------
out over a wide range of ambient temperature levels
for four pairs of initial conditions for HC and NOX.
(iii) determined the effect of temperature on maximum NOg and (K
and on dosage* of both. This calculation was carried out
over a wide range of ambient temperature levels for four pairs
of initial conditions for HC and NO .
A
We selected toluene as a surrogate for the atmospheric mixture for the purposes
of this calculation because, of the various hydrocarbons for which-we have
carried out validation studies, it has a reactivity most similar to that of the
observed hydrocarbon mix in the atmosphere. While we are aware that the HS
mechanism may provide uncertain predictions for reactant systems for which
evaluative studies have not been undertaken, our success in validating the
toluene-NO system for a large variety of initial conditions lends a reasonable
/\
degree of credence to the predictions of the mechanism for this particular
system. In this chapter we report the results of each of these three tasks
using the toluene-NOY system as a model of the atmospheric hydrocarbon mixture.
A
A. Effect of Initial NO Concentration on Maximum Oxidant
r*
The purpose of this calculation was to generate plots of maximum oxidant
as a function of initial NO for fixed hydrocarbon levels. The rate constants
/\
determined for toluene in previous validations were used in generating the
required predictions. The input parameters for these simulations are shown in
Table 2. In addition, a dilution rate of 5.4 liters/second, necessitated by
the sampling procedure, was assumed. In order to minimize computer time and
decrease the probability of numerical instabilities, the free radical eciui-
*A11 dosage calculations were based on an irradiation time of 1000 minutes.
-34-
-------
ts
'.3
u
-o
I
S3
.2
.1
^ ^FIGURE 2. EFFECT OF INITIAL NO
rrhr~: CONCENTRATION ON MAXIMUM
,2 .3 .4^ .5 .6 .7 .8 .9 1.0
NO at Initial Condition, ppm
-35-
I 1
-------
.' ! ''.. . .' I 'i
11.00
.1.00
: 0
- Figure ^2 Continued..
10.00
9.00
'
8.00
,7.00
1
6.00
5.00
4.00
3.00
2.00
i
i
n :
f .
0 '
fH
,x .
C
0
u
rt
M
c '
V
U '
e
o
o
v :
C
O :
N ;
o ;
r
.(. .
)-
£- KJ « 10 10 JMr
-------
librium assumption was made. Invocation of this assumption reduces the
number of differential equations to be integrated from eleven to four.
The results of 50 executions of the model are plotted on Figure 2.
In this figure, the maximum ozone concentrations over a six hour inte-
gration period is plotted versus initial NOX concentration. The initial
NO concentration is fixed at a NO/NO- ratio 13.7/1.0 and varies from
A Cm
0 to 1.0 ppm. A family of five curves representing constant initial
hydrocarbon concentrations are plotted. It is evident that negligible
03 is generated -..han the initial HC is less than 0.1 ppm. However,
as the initial HC level increases to approximately 0.5 ppm, the oxidant
level becores reasurable, although it still does not show a great depen-
dency on initial ?,0 concentration. At and above an initial HC concen-
A
tration cf 1.0 ppr, however, the maximum ozone level displays narked
dependency on imtiel NO concentration, first increasing with increasing
A
NO , then going thrc-jgh a iraxirLir., and finally decreasing as the NO is
x x
increased still further.
B. EiTec: cf Ciuv:! Light I.-ransity Variations on NOp and 0., Max i munis
and fosages.
Th£ cbjccti'.i c" this u^-. v.as to investigate the effect of varying
light intc-rsities en the r:3.\i om values of N02 and 0, , and on their
respective c'csoces, fo»- bcth si,r..-.er and './inter conditions. To simulate
the effect of the diurnal variation of light intensity on the reaction
f,02 + hv NO + 0 ,
-37-
-------
It was assumed the k-. Is related to time, t , 1n the following
manner (see Leighton (1961), p. 163):
k, = a. f Summer
kl = ai ' fw Winter
2
where f = 1.0 - 0.694r and is ^0.0 for all T
f, = 0.774 - 1.07t2 and is > 0.0 for all T
w ^
and
t - 12
0 < t < 24
Note that t is in units of hours past midnight. The peak light
intensity occurs at 12:00 hours and the ratio of the peak winter in-
tensity to peak si:rr.mer intensity of 0.774/1.000, as given in Leighton.
lie carried cut diurnal light intensity simulations for three values of
the coefficient a. for both summer and winter conditions as given in
the first column to Table 11. These values correspond roughly lo high
average, and low sunlight intensity conditions which might occur at noon
on clear days at about the time of the summer solstice, the vernal and
autumnal equinoxes, and the winter solstice, respectively, at the lati-
tude of North Carolina.
The simplified mechanism was modified to include variations of k.
-38-
-------
TABLE 11. EFFECT OF DIURNAL LIGHT INTENSITY VARIATIONS
ON THE HS REACTION MODEL
SUMMER
WINTER
al
.37
.37
.37
.37
.266
.266
HC
2."
.8
.5
.24
.5
3.
t
1
.166
.166
.166
.286
.286
.24
.5
.8
.24
.5
.286 { .8
.286
.206
.206
1.
.5
3-
i
.128
.24
.128 ' .5
.]28
.8
J
NO
X
. 3
.35
.35
.35
.35
.5
.35
.35
.35
.35
.35
. 55
.5
.35
.5
.35
.35
.35
0.. max
.34914
.2435
0358
.007027
.00378
.34171
.001912
.00895
.00567
.00318
.00361
.0531
.08795
.00351
.2189
.00112
.001974
.00295
NO 2 max
,31393
.2467
1416
[07358
.05687
.31485
.05373
.12571
.10993
.05454
.10518
.1620
.2453
.0778
. 2722
.0412
.0837
.1109
O^ dosage
100.833
36.819
8.3486
3.4108
2.585
233.915
.8112
2.3651
1.936
1.189
1.900
6.981
17.986
1.69
44.816
.722
.916
1.034
N09 dosage
165.597
132.27
54.102
56.744
136.702
38.542
81.216
69.601
39.494
51.193
74.336
126.229
57.928
136.633
48.827
56.372
57.057
-39-
-------
with time, as described by the expressions for kj for summer and
winter given earlier. The observed 0, and N(L maxima and dosages for
six values of a. (three each for summer and winter) and for several
sets of initial conditions for toluene and NO are reported in Table 11.
In general, the magnitudes of each of the four responses decreased as
light intensity (a-|) decreased. An exception to this behavior, however,
was an increase in the NOp dosage with decreasing light intensity for
hydrocarbon to NO ratios below 1.5. This behavior results from a
n
reduced rate of oxidation of NO as a result of low ambient hydrocarbon
concentrations and from a reduced rate of conversion of NOg to products.
C. Effect of Temperature Variations on N02 and 03 Maxima and Dosages
Host of the. reactions contributing to smog formation are thermal r&ther
than photolytic. Because me rates of thermal reactions depend on the tem-
perature of the reaction system, it is reasonable to expect that variations
in temperature will result in a change in the rate at which srr.og forms.
In the US mechanism, for example, all the reactions except the first
and ninth (photolysis of NOg and HMOg, respectively) are thermal.
In this task it was our goal to evaluate the effects of temperature
variations on bclecled resronses, notably N02 and ozone maxima and dosages.
To evaluate the effect of changc-s in temperature on the predictions of the
US rrcthanir.;!, cr/: r:'jsji. f'irbi, dci;rminr tl-c octivdtion energy (r.«) or Lhrnnal
dependency cf each reaction. The activation energies for several of the
reactions in the US mechc-nism have been determined experimentally (Johnston
et al., 1970), and v;e hi.ve useo these values wherever possible. For those
-40-
-------
cases in which no experimentally determined value if E^ is available,
we either estimated or approximated the activation energy by analogy
with similar reactions for which activation energies have been measured.
The activation energies which we used for the temperature varying cal-
culations are presented in Table 12. In view of uncertainties in the
mechanism and our estimates of unmeasured activation energies, the results
which follow probably have an uncertainty of about ±50%.
The temperature range considered in our study was 264°K to 315°K. This
range spans the majority of temperature conditions which might be encoun-
tered during the year-round operation of the outdoor chamber in North
Carolina. The temperature effects were studied for four sets of initial
reactant concentrations:
Toluene (ppm) NOY (ppm)
A
1)0.6 0.35
2) 0.8 0.35
3) 1.0 0.50
4)1.7 0.50
In Table 13 we present the i,'0? and (L maxima and dosages for each of these
cases.
In surveying the results of the simulations, we observed the following
general trends:
(i) As the temperature increases, the peak NO^
concentration increases. The effect of changes
-41-
-------
TABLE 12: ACTIVATION ENERGIES OF THE REACTIONS
IN THE HS MECHANISM
REACTION
E(kcal/mole)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
0
2.1
2.5
7.0
0 (est.)
0
1.08
1.0 (est.)
8.0 (approx.)
3.0 (approx.)
8.0 (approx.)
1.0 (approx.)
0
0
Source of activation energies: Project Clean Air
-42-
-------
TABLE 13: EFFECT OF CHANGES IN TEMPERATURE ON N02 AND 03 CONCENTRATIONS
SYSTEM
(NOY)n = 0.35 ppm
X 0
(Toluene). = 0.6 ppm
0
(NOV). = 0.35 ppm
X 0
(Toluene) = 0.80 ppm
u
(NO ) = 0.5 ppm
X 0
(Toluene). = 1.0 ppm
o
(NO ) = 0.5 ppm
X 0
'(Toluene). = 1.7 ppm
* u
TEMP.
264°K
279°K
288°K
301°K
311°K
273°K
290°K
305°K
315°K
273°K
290°K
305°K
315°K
264°K
279°K
288°K
301°K
311°K
°3
PEAK
(ppm)
0.018
0.047
0.075
0.095
0.100
0.076
0.131
0.143
0.145
0.140
0.174
0.180
0.177
0.251
0.296
0.303
0.298
0.288
N02
PEAK
(ppm)
0.092
0.144
0.171
0.201
0.219
0.156
0.203
0.231
0.244
0.266
0.321
0.353
0.368
0.295
0.343
0.362
0.382
0.394
°3
DOSAGE*
(ppm min)
10.5
29.0
40.9
90.0
113.73
25.6
113.9
121.1
125.5
54.6
143.7
153.3
141.5
170.5
230.2
248.5
286.4
350.6
N02
DOSAGE*
(pprr. min)
87.7
175.7
172.3
234.6
217.5
121.6
246.5
160.6
126.3
211.9
276.4
187.9
141.5
310.7
234.7
185.6
125.1
94.96
^Dosage calculated over a 1000 minute simulation.
-43-
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1n temperature on the peak Nt^ concentration
is proportionately greater at lower temperatures
than at higher temperatures.
(ii) The NC^ dosage goes through a maximum; the
temperature at which the maximum occurs depends
on the HC/NOV ratio.
A
(iii) The peak 0-, concentration increases sharply when
the temperrture is raised form 264°K to 290°K.
Further increases in the temperature however,
have little effect on the peak concentration.
(iv) The 0-j dosage also increases substantially when
the temperature is raised from 264°K to 290°K.
But, as is the case of the peak ozone concentration,
further increases in temperature affect the ozone
dosage only slightly.
These results suggest that extreme caution must be exercised in inter-
preting and compering the results of smog chamber experiments performed
under different temperature conditions, especially for the range, 264°K
to 290°K.
D. Conclusions
Using the simplified mechanism we have demonstrated that, for toluene
(a surrogate for the atmospheric hydrocarbon mixutre), variations in light
intensity and temperature substantially influence the predicted N02 and 0., maxima
-44-
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and dosages. We have also shown that the predicted maximum ozone level
Is quite sensitive to the initial hydrocarbon concentrationmuch more
so than to the initial NO concentration. Finally, while influences
A
on the N02 and CL maxima and dosages due to variations in light intensity
and temperature are not at all unexpected, the calculations presented here
suggest the magnitudes of the changes that might be expected.
The study of snog formation in an outdoor chamber results in some
obvious disadvantages, namely lack of control over light intensity,
temperature, and humidity. With these three parameters uncontrolled, it
is not possible to truly replicate experiments. If, however,
the non-linear changes in the concentration-time behaviors of the pol-
lutants resulting from variations in these three parameters can be properly
accounted for, it may still be possible to compare runs which are other-
wise identical (i.e. same initial concentrations, etc.). One means of
analyzing the data is to program the observed diurnal temperature and
light intensity profiles into a kinetic mechanism, comparing the predicted
profiles for the "replicate" runs with those profiles which were observed
in the experiments. Such an approach may still be inadequate in the sense
that variations in other experimentally undetermined parameters may sub-
sequently be shown to be important. But, without some type of mathematical
analyses, no quantitative evaluation of the reproducibility of the outdoor
chamber experiments will be possible.
-45-
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IV: PREPARATION OF A RECOMMENDATIONS REPORT, "EXISTING NEEDS IN
THE OBSERVATIONAL STUDY OF ATMOSPHERIC CHEMICAL REACTIONS"
A great many experimental and observational programs have been
carried out over the years in an effort to increase our knowledge
of atmospheric chemical reactions. Carefully conceived laboratory
experiments have provided the basis for estimation of individual
rate constants. Smog chambers studies have served as an important
aid in establishing a qualitative understanding of the overall smog
formation process. Atmospheric observations have also proven valu-
able in this respect and, in addition, in the identification of
pollutant species. Within the last four years, however, advances
in the development of mathematical descriptions of the photochemical
reaction process have created a need for refined experimental and
observational programs, programs geared to yielding information
either of ir.uoh greater accuracy than seemed necessary five or ten
years ago or of a typa or kind that has rarely been collected in the
past.
Two major "breakthroughs" have spurred the interest in increas-
ingly corrplex. and sophisticated experimentation in the field of
atrospheric c(-.cr,istry--
' the development of photochemical kinetics mechanisms
capable of describing the concentration-ti.72 behavior
of major reactants and products, as monitored in a smog
%
chamber, l.'nils the ccrp?risons between prediction and
-46-
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observation have often been good for experiments having a
variety of initial conditions, the hydrocarbon reactant
has generally been a single species or binary mixture.
' the development of mathematical models capable of predic-
ting the concentrations of photochemical pollutants as a
functions of location and time over a region of the order
of two to five thousand square miles (i.e., a major metro-
politan airshed). The spatial resolution of such models is
typically of the order of one to two miles.
While development of both types of models has proceeded rather
smoothly and swiftly over the past three years, it became apparent
at an early stage that t'f.sre presently zzis^s no data base of suf-
ficient accuracy and detail to properly support model validation
studies. As a part of this contract effort we have prepared a sep-
arate report, "Existing Needs in the Experimental and Observational
Study of Atmospheric Chemical Reactions", in which we made detailed
recommendations for data collection programs that might be carried
cut in order 1.0 rect 2 brood spectrum of nseds.
but the collection of d.'te for rrodel validation purposes alone
S'jcgcsls c. r&ther nerrcw horizon, l-'e see as a primary value cf model
development :r,c codification of knowledge in the field of study, the
"pulling together" of the many bits and pieces in an attempt to gain
-47-
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an 'expanded understanding of the whole. When viewed in this way,
the mounting of an experimental program with a model, models, or
modeling as the structural foundation for the pursuit is a major
step forwardfrom gaining knowledge in a piecemeal fashion (and
understanding often with long delays) to gaining knowledge effi-
ciently, in quantity, and in a coordinated manner.* It is the
purpose of the recommendations report to discuss future needs in
the measurement and observation of atmospheric reaction processes
with the broader perspectivewith the unifying element of the
mathematical model, our best descriptor of the dynamic processes
that we are attempting to understand.
If we are to deal with the subject of atmospheric reactions
in a unified manner, it is necessary to discuss mathematical model-
ing at an early stage. In Chapter II of the report, we examine
the nature of the photochemical mechanism (i.e., its mathematical
structure, the c'egree of detail it incorporates, etc.) and present
a short history of model development. We then discuss the need
for lumping of hydrocarbon and radical species and suggest a nech-
anicin ( presu tly beinfj subjected to vcrif icafior.--sce
Chnpu'r 5 of tl.ic rope: 0 ttvit has strong potential
* The notion of coordi-iatinr) all elements of an experimental and
observation:! progrufi1 is of qrcat. in'portjncc. For example, if
the concentration-tiir.2 predictions of a validated kinetic mech-
anism are relatively insensitive to the magnitude of a particular
rate constant, there is little point in expending effort to im-
prove the accuracy of its estinated value. Science is better
served by concentrating efforts in areas in which an increase
in knowledge pays a greater reward. The model serves admirably
as a tool for identifying such efforts.
-48-
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for accurately describing the concentration-time behavior of all
measurable species (except, of course, those that are lumped). Model
assumptions are carefully stated and the validation procedure is
described. Finally, we outline the alterations that must be made
in any kinetic mechanism if it is tc be incorporated into an urban
airshed model.
In Chapter III, we present a full discussion of the two major
classes of urban airshed modelsthe Eulerian and the Langrangian.
Fundamental equations are presented and applied forms of the equa-
tions are derived so that the assumptions on which the latter are
based can be clearly discerned. The two commonly applied types of
modelsthe grid and the trajectoryare detailed, and their advan-
tages and shortcomings are discussed. Levels of uncertainty associ-
ated with input variables to these modelsemissions and meteoro-
logicalare presented. The chapter concludes with a section sum-
marizing possible avenues of pursuit for improving the present
generation of models.
\
The remaining three chapters, IV, V, and VI, are, in many ways,
the core of the report. They deal, respectively, with laboratory
studies concerned with the kinetics and mechanisms of individual
reactions, smog chamber studies, and atmospheric observations. In
each, we discuss existing deficiencies in knowledge, examine in detail
-49-
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the types of studies needed, and recommend specific studies and/or
general programs. Thus, these three chapters, taken as a whole,
constitute a comprehensive review, analysis, and diagnosis of needs
in experimentation and observation of the atmospheric chemistry of
contaminants.
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V. . DEVELOPMENT OF AN IMPROVED GENERAL KINETIC MECHANISM
In the two years since simplified mechanisms-such as that of
Hecht and Seinfeld (1972) (Table 1) were developed, signficant ad-
vances have been made in our knowledge of the mechanisms and rate
constants of the individual reactions contributing to smog forma-
tion. These advances have set the stage for the development of a
new kinetic mechanism, one which does not suffer many of the defi-
ciencies of the three existing mechanisms. In particular, a new
mechanism should be rigorous in its treatment of inorganic reactions
(because of their importance), sufficiently detailed to distinguish
between the reactions of various classes of hydrocarbons and free
radicals, f»ee of poorly defined adjustable parameters, and as com-
pact as possible. In Chapter II of the recon-mendations report,
"Existing Needs in the Experimental and Observational St'jdy of
Atmospheric Chemical Reactions", we have presented a new formulation
which meets the requirements; it is restated in Table 14.
-51-
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TABLE 14
A Lumped Kinetic Mechanism for Photochemical Smog
N02 + hv -*- NO + 0
0 + 02 + M
0 + NO
03 + M
>The N02-NO-03 Cycle
0 + NO + M - N02 + M
0 + N00 -t NO + 00
0 + N02 + M * N03 + M
Important Reactions of 0
'with Inorganic Species
N0
N03 + NO -> 2N02
3
NO, + N00 -» N90.
J <- C. 3
2HN0
The Chemistry of NO,
, and H!;
NO + HN03 UNO
l!f,'0
H20 + 2f!02
Reactions cf UNO, with
Ir.oiganic Species
NO
2O,
HN02 + hv
NO + NO, + H-0
i. t
Che-.iistry of HN02
OH + f'O
-52-
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TABLE 14 (Continued)
OH + N0
OH + NO + M
OH + CO + (02)
H02 + NO
hv
IB
19
20
21
22
HNO.
HN02 + M
C02 + H02
OH + N0
20H
Important Reactions of
' with Inorganic Species
Joxi
dation of NO by H02
>Photolysis of H90
2U2
HC
HC]
HC]
HC
HC
HC
HC3
HC4
HC4
1+0
+ 03
+ OH
2 + 0
2+OH
3 + 0
+ OH
+ hv
+ OH
-»-
23
"*"
->
25
+
26
->
27
>
28
->
29
-*
30
->
ROO +
RCOO
5
ROO +
ROO +
ROO +
ROO +
ROO +
3ROO
3RCOO
n
0
aRCOO + (l-a)H09
n f-
0
+ RO + HC4
HC4
OH
H20
OH
H20
+ (2-B)H02
t (1-B)HO,+ H00
c. c.
ROO + NO
RCOO + NO
n
0
31
32
Hydrocarbon Oxidation
Reactions Where
HC1 = olefins
HC2 = aromatics
HC, = paraffins
HC4 = aldehydes
33
RCOO + N02 -
6 3,
RO + 00 -»
RO + NO2
ROO + N02 + CO.
RCOO::O,
II
0
H0
,
L
HC
4
Reactions of Organic
Free Radicals with NO,
N02, and 02
-53-
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TABLE 14 (Continued)
RO + N02 * RON02
RO + NO
36
RONO
H0
37
H02 + ROD
38
39
ROOM +
2ROO - ROOR + 02
iPeroxy Radical Recombina-
tion Reactions
-54-
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There are two points to be noted regarding this mechanism. First,
the unspecified stoichiometric parameters, a and 0, can now be estimated
a priori with a high degree of confidence, a is the fraction of
carbons attached to the double bond in a mono-olefin which are not
terminal carbons on the chain. Consider, for example, the 0-HC1 re-
action for propylene and 2-butene which contain, respectively, external
and internal double bonds.
0 + CK3CH =
|CH3CK2CH*
CHO
CH3CCK3*
0 + CH3CH = CHCH3
-» CK,C- + CH.
CH3C- + CH3CH2
If we asstr.e that al'.yl and acyl radicals react rapidly with 02 and
that the Ci.O ceccr, ':scs into CO + H02 in the presence of CL, these
reactions cr.n be rewritten in our generalized notation as
0 + CH.CH -- CH9
o 2
RCOO-
and
0 + CH3CH = CHCH3 1 R02- + RCOO-
-55-
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If we now further assume that 0 will react with equal probability
at either carbcn attached to the double bond, a = 1/2 for propylene
and a=l for 2-butene. By the same reasoning a can be shown to
be zero for ethylene.
B is the fraction of total aldehydes which are not formaldehyde.
During smog chamber studies of the propylene-NO system, equal quan-
A
titles of formaldehyde and higher aldehydes are observed to form;
thus, B = 1/2. In the case of toluene, Altshuller et al. (1970)
have observed that only 15% of the aldehydes are formaldehyde; there-
fore, 3 - .85 in this case.
Second, as in earlier studies, we have exercised care in selec-
ting those species v/hose concentration-time (c-t) behavior is to be
described by a differential equation and those whose c-t behavior is
to be described by algebraic equations. The most complete mathematical
representation of the kinetics of this mechanism v.-ould be a description
of the time-varying Lehavior of each reactant and product (exclusive
of Op, COp, end !-!~0, v.nich ere not follov;ed) '.,'ith a differential
equation. But ^accuse Uie computing tiirs required to integrate the
governing equations nun.oncally increases at a rate proportional to
the square of the number of differential equations*, we are interested
* We have ussrl the technique of Gear (1971) to solve the system
of coupleJ differentia1
-56 -
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1n minimizing that number. One way of accomplishing this is to apply
the steady-state approximation for those species which reach their
equilibrium concentrations on a time scale short relative to that
of the majority of reactants and products. Mathematically, this
means that the concentration-time behavior of those species assumed
to be in steady-state is described by an algebraic rather than a
differential equation.
In our validation experiments we have assumed four species to
be in pseudo steady-state: 0, OH, RO and N03. The validity of
this approximation for the first three species has been established
by comparing the concentrations predicted when the approximation is
invoked to those predicted when the species are represented by dif-
ferential equations. We have found in these comparisons that agree-
ment is excellent, maximum discrepancies in concentration being on
the order of 0.01% over a 400 minute simulation. This test shows
conclusively that the steady-state approximation is accurate for
0, OH, and RO. V.'hen we tried to perform an identical test for N03,
we found that the concentration predicted by a differential equation
was negative at startup**- Thus, a meaningful test as to the
validity of the slcedy-statc approximation could not be made. We
This ro fleets the fact th?t NO., forms chiefly after the ML
peak by reaction 7. As there is no 0- present initially,
numerical roundoff error at the first time step results in
negative NO- concentrations.
-57-
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are, however, reasonably confident that the approximation is "good"
in this case as well.
In this chapter we devote our attention to a discussion of the
first phase of an evaluation study of the 39-step mechanism. For
this portion of the validation program we have used smog chamber
data obtained !y the Division of Chemistry and Physics of EPA; we
begin, then, with a description of the data base and sources of
experimental uncertainty. Next, we present validation results for
the mechanism using data from three different hydrocarbon-NO systems:
A
n-butane-NO , propylene-f.'O, , and n-butane-propylene-NO . We
A A A
conclude witii a discussion of the results, including predictions
of the effect of initial hydrocarbon and NOV reactant concentrations
X
on peak ozone formation.
-58-
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A, The Data Base and Sources of Experimental Uncertainty
The significance of the validation results for a kinetic mechan-
ism is to a large degree dependent upon the diversity and reliability
of the experimental data base. We were fortunate in being able to
obtain chamber runs for this study involving both low and high reacti-
vity hydrocarbons, as well as a simple mixture. Moreover, the ratio of
HC/NO was varied over a wide range for each reactant system. In this
A
section we describe the data base provided by the Division of Chemistry
and Physics of the Environmental Protection Agency (EPA) for validation
purposes. We examine in some detail the importance of accurately speci-
fying certain experimental variables, notably light intensity and water
vapor concentration. We discuss the degree to which wall effects may
influence observed chamber results. Finally, we comment on the accuracy
and specificity of the analytical instrumentation used to monitor
pollutant concentrations and on the reproducibility of the experiments.
1. Data Base
The data base used in this validation study is that supplied by
the Division of Chemistry and Physics of EPA. It is comprised of three
hydrocarbon-NO systems:
n
(i) n-Butane-NO at three different HC/NO ratios
A A
(ii) Propylene-NO at four different HC/NO ratios
A A
(iii) n-Butane-Propylene-NO at six different HC/NO ratios
A X
-59-
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All but two of the chamber runs were made between February and May of
1967 by the staff of the Chemical and Physical Research and Development
Program at the National Center for Air Pollution Control in Cincinnati,
Ohio (Altshuller et al., 1967,1969; Bufalini et al., 1971). The remain-
ing two runs (457 and 459) were carried out in March 1968. The initial
conditions for the experiments are given in Table 15.
2. Light Intensity
Radiation intensity is one of the most important parameters in a
smog chamber experiment, for it governs the photolysis rate of NOp
(reaction 1), the reaction which initiates and sustains the smog forma-
tion process. Irradiation of the smog chamber was carried out through
the use of two banks of externally mounted fluorescent lamps, 148 lamps
of three different types. Under normal operation, these lamps have an
expected lifetime of 1000 hours, but throughout the program they were
operated at a 25% overvoltage to increase radiation intensity. Over-
load operation results in a more rapid deterioration of the lamps; con-
sequently, approximately 1/7 of the lamps were replaced after every
100 hours of operation.
The average first order "rate constant" for N02 disappearance in
nitrogen, k*j , was determined by the experimenters to be 0.40 min ,
but was not redetermincd during the ten-month period over which the
It can be shown that
k
1 k2(M) + k.
where
k, = pliotolytic absorption rate constant (continued)
a
-60-
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data provided to us were taken. We have assumed, in accordance with
the results of Schuck et al. (1966), that k] , the overall photolysis
rate of NC^j is equal to 2/3 k^ , or 0.266 min~ . Finally, we have
estimated that, due to inaccuracies in the determination of k . , in
the factor of 2/3 relating k. to k, , and in the estimation of
irradiation intensity, k, has an uncertainty bound of ±0.10 min .
3. Water Vapor in the Chamber
Another parameter which is thought to be important in smog
chamber runs is the water concentration. Water enters into the smog
kinetics via reactions 11 and 14, nitric and nitrous acid production.
The latter is important since photolysis of nitrous acid produces OH
radicals which, in turn, initiate further reactions. The humidifier
control of the inlet air stream to the chambers was set to generate
50% relative humidity at 75°F, but, during very cold, dry weather,
relative humidities of only 30% were achieved. The humidity of the
inlet air stream was checked only once or twice during the eleven-
month study.
(Continued)
= dissociation efficiency
k2
0 + NO, + M + NO., + M
k
0 + N02 +3 NO + 02
Thus, k. is, in essence, a lumped parameter representing the combined
rates old!! NO? reactions in an oxygen-free atmosphere. Unfortunately,
the use of k^" leads to difficulties in presenting the kinetics, as
the combined reaction which it represents is not first order. However,
since the only available daca for light intensity in these chamber
experiments are based on the validity of k. as a rate constant, we
use it here to estimate k .
-61-
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TABLE 15
Initial Conditions Associated with the Experimental
Chamber Data
PA Run
**
306
314
345
318
325
329
459
307
333
348
349
352
457
(N02)*
0.03
0.02
0.12
0.06
0.04
0.06
0.06
0.05
0.08
0.08
0.03
0.07
0.05
(NO);
0.30
0.29
1.28
1.12
0.32
0.26
1.14
1.23
1.25
1.23
0.31
0.27
1.11
*
(n-Butane)Q
1.60
3.17
3.40
3.06
3.41
3.39
3.25
3.29
3.29
(Propyli
0.51
0.45
0.24
0.78
0.36
0.23
0.50
0.44
0.26
0.81
Initial concentrations in units of parts per million (ppm)
**
0.12 ppm of aldehyde also present initially
-62-
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4. Wall Effects
An effect of particular concern in smog chamber studies is the
influence of surfaces on chemical dynmaics, and thus on observed re-
action kinetics. Of major importance in this regard is the possibility
of chemical interactions occurring between adsorbed pollutants and
material in the gas phase. Although it is possible that some low
reactivity organics such as carboxylic acids and ketones can be
found on the walls as a result of hydrogen bonding with adsorbed
water, we focus our attention in this discussion on species which
have been clearly identified on the surfaces of a small smog chamber
(Gay and Bufalini, 1971)--nitric acid, nitrates, and nitrites. We
begin, then, by discussing the heterogeneous reactions of the most
important oxides of nitrogen, NO and KOp. In the process we also
give attention to various mechanisms that might account for the ap-
pearance of HN03 as 2 product of these reactions.
a. NO and NO,
Even in so-called dry systems it is reasonable to assume that
an adsorbed layer of water will be found on the walls of the smog
chamber. This is certainly the case for the experiments under con-
sideration in this study, as the chamber was intentionally humidified
during all runs. Thus one possible explanation for the appearance of
nitrate and nitrite on the walls would be dissolution of NO and N02
in the adsorbed water layer. Nitric cxide can be eliminated in this
regard because of its extremely low solubility in water; IKL, hov/ever,
-63-
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dissociates in water by the following reactions (Hill, 1971):
6N02 + 3H20 J 3HN03 + 3HN02
3HN02 * HN03 + 2ND + H20
The rate of loss of N02 in this manner is dependent upon the amount of
water adsorbed, the rate of dissolution of N02> and the magnitude of
rate constants for the dissociation reactions. In the experiments
under consideration, however, N02 losses via this mechanism can be
neglected because, within experimental error, all of the NOX initially
present can be accounted for at the time of the N02 psak as N02, NO,
and NO and N0« lost by sampling and dilution up to the time of the
peak. We might thus conclude that no significant amounts of NO or N02
were lost directly to the walls during the smog chamber experiments.
b. N205
After the N02 peak occurs, and as 03 begins to accumulate, NJD,-
f.orms by the reactions
N03
NpOc will undergo hydrolysis to form nitric acid by the reaction
N205 + H20 - 2HN03
If the hydrolysis takes place in the adsorbed layer of water on the
wall, HN03 will fonn directly on the walls. However, both the water
concentrations in sniog chambers (63* relative humidity (RH) at 25°C is
-64-
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equivalent to 20,000 ppm HgO) and the rate constants for the primary
reactions in nitric acid formation in the gas phase (Table 6) are
large enough that the loss of NO after the N02 peak may be fully
ascribed to the formation of nitric acid in the gas phase.
It remains unclear, however, as to whether NJ3,- hydrolyzes in
the gas phase or on the walls. As we have noted, the water concentra-
tion during these chamber runs was quite high. As the stationary
*
state concentration of nitric acid would also have been high, actual
HNO-, concentrations in these experiments were always far from satura-
tion. Thus there would have been a strong tendency for NpO,-, whether
it were found in the gas phase or on the wall, to hydrolyze rather
than to decompose, forming N02 by the reactions
N03 + NO +
However, even if these reactions wore favored due to the formation of
Og, the rate of formation of NO^ would still be low since NO is
depleted et this stage of the smog reactions. Thus, in light of the
various considerations presented, we concluds that reactions involving
NpQr at the walls would have little if any effect on the course of tho
overall snog reactions.
Leighton (19G1), D. 193, calculates that tha stationary state concen-
tration of HuO-j is 3,000 pom for initial conditions of 0.10 NOo ,
0.10 03 , 0.01 NO , and 63; RH at 25°C.
-65-
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c." HN03
Nitric acid Is very soluble in water because of strong hydrogen
bonding. Thus, It Is highly likely that a nitric acid molecule in
the gas phase that is involved in a collision with the wall would
dissolve. The rate of loss of HN03 from the gas phase, then, is
probably transport-limited and will depend to some degree on the rate
of stirring in the chamber. Unfortunately, detection of HNO, in the
gas phase has until now proven to be a difficult task, perhaps because
the acid is lost to the walls of the sampling tubes.
d. Other Chemical and Catalytic Effects of the Walls
It would, of course, be highly desirable to expand our understanding
of the degree to which interactions occur between adsorbed pollutants
and material in the gas phase. Unfortunately, our knowledge concerning
such phenomena is limited, and we can only speculate. We thus offer
the following comments:
(i) We expect that the rate of heterogeneous oxidation of NO
in chambers is small. For example, in one chamber charac-
terization experiment, 1.6 ppm of NO was irradiated in air
for six hours. At the end of that period it was found
that 19% of the initial NO had been oxidized to N02. We
believe that this figure represents an upper limit for the
rate of non-photochemical oxidation of NO. The effect
would be additionally reduced in reactant systems for
which the tiiie to the NOg peak is relatively short (i.e.,
two hours or less).
-66-
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(ii) As we concluded earlier, we expect that the presence or
absence of wall effects would result in no detectable
differences in the rate of formation of HN03, largely be-
cause of the strong tendency of hLCL to hydrolyze at the
water concentrations used during these experiments. Simi-
larly, whether HN03 is formed in the gas phase, subsequently
migrating to the wall, or whether it is formed directly on
the wall, it is unlikely that the site of hydrolysis will
have much of an effect on the observed chemistry. While
nitric acid is corcmonly used as an oxidant when concentrated
(60%) in the liquid phase (Godt and Quinn, 1956), it is
ineffective as an oxidant at low concentrations. The high-
est attainable concentration of H.'IOj during the chamber
runs is a value that is numerically equel to the initial
NO concentration, which never exceeded 1.5 ppm.
J\
We conclude, based on the preceding discussion, that no signifi-
cant amounts of flO and K02 are adsorbed on the walls and that the
possible adsorption of I'pOr and HN07 should not alter the observed
piiotochcnistry. !L',.:ver, u is not possible at this tin to ascer-
tain the degree to which the presence of surfaces might accelerate the
oxidcticn of NO. Bv-ced on these tentative conclusions, \s have not
taken wall effects into c-.ccount in our velidaticr, effcnts.
-67-
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5. Estimates of Experimental Error
Before comparing model predictions with experimental observations,
it is desirable to establish both the accuracy and the precision of the
measurements. Accuracy refers to the extent to which a given measure-
ment agrees with the true but unknown value of the parameter being
measured. Precision refers to the extent to which a given set of
measurements agrees with the mean of the observations. Inaccuracies in
determination of concentrations are largely attributable to lack of
specificity cr accuracy in analytical procedures, particularly in the
instrumentation used to monitor concentrations during the course of an
experiment. Imprecision is detected through the poor repeatability of
an experiment, the results of which may or may not be accurately deter-
mined. There may be a wide variety of causes of imprecision, some of
which may also be attributable to instrumentation problems.
a. The Accuracy of the Analytical Instruments
The four pollutant species of prirr-ary importance in our modeling
efforts, NOp, MO, CL, and hydrocarbons, were all measured using standard
instrumentation and techniques.
(i) Hydrocarbons '..'ere determined individually.by gas chroirato-
graphy: the accuracy of these measurements is estimated to
be ±10?; at a concentration level cf 1 ppn.
(ii) Oxiaants were r.easured using two independent techniques:
the Mast Ozone f-'eter and neutral KI analysis. Corrections
to KI readings ware required to account for interferences
-68-
-------
due to PAN and NO,,. Despite the corrections the KI
measurements exceeded the Mast readings by an average
of 50%. As Dr. S. L. Kopczynski (1972) of the Division
of Chemistry and Physics, who was in charge of executing
the smog chamber experiments used in this validation
study, is of the opinion that the KI technique is the
more accurate of the two procedures, we have validated our
model using the results of the KI analyses.
(iii) Oxides of nitrogen were sampled manually into fritted
bubblers containing Saltzrcan reagent. Nitric oxide was
oxidized to form N02 by reaction with sodium dichromate.
Dr. Kopczynski has estimated that this conversion is alnost
100% efficient. Absorbance was read on a Beckman DU
spectrc~et=r reccing 2 ppm at full scale.
In general, the accuracy of these various measurements is a
function of the concentration level of the pollutant being measured.
Accuracy is poorest over the low concentration range. As most pol-
lutants are present at low concentrations at some time during the
course of a reacticn, questions cf accuracy will inevitably arise
with regard to cherbar studies. For example, at concentrations of
N02 below 0.15 ppn, concentrations can be determined no more accurately
than ±50':. At the higher concentrations encountered as the reaction
proceeds, the accuracy of the reading ir.proves substantially. Un-
fortunately, no recalibraticn of the oxidant or the nitrogen oxide
-69-
-------
analyzers was performed during the eleven-month study.
b. The Repeatability of Experimental Runs
Because replicate runs were made for only four of the experi-
ments used for our validation studies, we have been unable to calculate
a meaningful statistical measure of the reproducibility of the ex-
periments. But, in those few instances for which a replicate run was
available, the agreement jetween the two sets of data was quite good.
Our impression of the chamber data is that, in spite of the lack of
recalibration of the light intensity and chemical analyzers, the data
are in general reproducible, were carefully taken, and are as suitable
as any currently available for validation purposes. Although the data
were taken in 1967 and 1968, at a time prior to the development of
photochemical kinetic mechanisms for atmospheric reactions, the in-
vestigators did exercise sufficient care in quantifying most of those
parameters important in validation of these models. For example,
dilution rates and the rate of conversion of NO to NOp in the absence
of hydrocarbons i\ere measured for all reactant systems. Probably the
greatest weakness in the chamber data with regard to their use in
valuation is the Icick of precise knowledge of the light intensity.
As will be shov;n in Section Dl, the magnitude of light intesity has a
substantial effect upon the tiire to the N02 peak predicted by the model.
B. Evaluation of the 39-Step Lumped Mechanism
Evaluation of the lumped kinetic mechanism in Table 14 consists
of
-70-
-------
(1) obtaining estimates of the various input parameters to
the mechanismthe reaction rate constants, parameterized
stoichiometric coefficients a and B, initial concentra-
tion of reactants, and average dilution rate constants.
(ii) carrying out sensitivity studies for these parameters;
I.e., establishing the effect of controlled variations
in the magnitude of the various parameters on the concen-
tration-time profiles for NO, NOg, 0,, and hydrocarbon,
and
(iii) generating concentration-time profiles for the various
reactant mixtures using the specified initial conditions.
These predictions are then compared v/ith experimental
results to assess the "goodness of fit".
In the first part of this section we discuss the basis -for selection
of the input parameters. In the second part, we present the valida-
tion results for each of the three hydrocarbon systems studied. Re-
sults are summarized as a series of plots displaying both predicted
and measured concentrations.
1. Estimation of Par?meters
Prior to obtaining kinetic information from the lumped nechsnism
all known parameters must be specified and uncertain parameters esti-
mated. The input parameters to this ir.echanism include the rate con-
stants, parameterized stoichiometic coefficients, initial reactant
concentrations, and average loss rates of the reactants-and products
due to sampling.
-71-
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a. The Rate Constants
While the kinetic mechanism is written in a general fashion, we
have striven to formulate it in such a way that all important features
of the detailed chemistry are retained. Thus, our goal has been to
include each elementary reaction thought to contribute to the overall
smog kinetics. A reaction has been judged unimportant only if its
Inclusion in the mechanism results in no significant changes in the
predictions of the decision variables, namely, the rate of oxidation
of NO, the time to the N02 peak, and the rate of accumulation and
maximum levels of O*. By virtue of the mechanism's detail we are able
to use directly as input experimental determinations of the rate con-
stants for the individual reactions in every case for which measure-
ments have been made. [One problem associated with the adoption of
simplified mechanisms (e.g., HS and EM mechanisms) was that their
highly compact nature precluded strict adherence to the use of ex-
perimental values of pertinent rate constants. ]
Several papers have been published in the past three years which
review the vast literature dealing with kinetic studies relevant to
the reactions now thought to be important in smog formation. These
include the detailed modeling study of Demerjian et al. (1973), the
atmospheric chemistry and physics assessment in Project Clean Air
(Johnson et al., 1970), and the detailed modeling study of propylene
conducted by Niki et al. (1972). Their recommended values for the
rate constants of the individual reactions incorporated in the lumped
-72-
-------
TABLE 16
Validation Values of the Rate Constants and Their Comparison with the Recommended
Values of Other Investigations
ction
1
2
3
4
5
6
7
8
9
10
11
12
13
t
14
15
16
17
18
Validation*
Value
.266 min
2.0*10 ppm" min
2.3X101
_O _l) 1
3 . 5x1 0 ppm mi n"
1.38xl04
2.2xlO~3ppm~2min~1
l.lxlO"1
1.5 xlO4
j
4.5xlOJ
1 .5x10 min"
l.OxlO"5
l.OxlO1
5.0
COT
4.3x10 ppm min
4.5
1/10 k,min~]
1.5x10^
4**
1.2x10^
Demerjian
et al. (1973)
DEPENDS ON
2.0x!0"5
2.3X101
_}
3.4x10 J
S.lxlO3
2.2xlO"3
0.48-l.lxlO"1
0.66-1.47x 104
3
6.8xlOJ
l.SxlO1
2.5xlO"3
<4.3xlO~6
14.5
l/4xk1
>1.5xl04
0.8 ki/.
Johnston
Niki
et al. (1970) et al . (19
EXPERIMENTAL SYSTEM
2.3xlO~5
2.9X101
_!
2.5x10 J
S.lxlO3
l.lxlO"1
1.5xl04
s
4.5xlOJ
1.4X101
3.0xlO"3
6.9xlO"6
l/10xk.
1.5x10^
2.2xlO"5
2.9X101
l.lxlO"1
1.5xl04
i
4.4xlOJ
1.4xlO]
l.SxlO"6
3.6xlO"8
2.8xlO"2
1/2000 k]
6.0xl03
0
2-lxlO-3
Others
1.38x10
,4 t
-------
TABLE 16 (Continued)
K'Mction
19
20
?}
??
,j
;'4
V5
26
11
28
29
30
31
32
33
34
3b
36
V;il id-.il ion*
Vnluo
2.5HO''
7.0'M)''
_1
I/2MI k.min
]
j i
!.(,.! (}~V
2.1, H)/l
i.n/ n/
bxl()3
G.b'IO1
3.H-I01
_ -i _ i
'i* <1() " in in
- j,!^
^i-iof
9.1,102
1.0- 10^
2.4,10"''
4.9'K)''
2. ,,)(/
Donu;rjian
ct. al. (1973)
2.5*102
2.0-102
1/1GO k,
6.8 103
1.0 10"2
9.4-103
3.2X101
3.8>103
_T
0.4-2.5x10 J
2.2xl04
9.1xl02
4.7X102
4.9--102
2.4-5.6xlO"2
3.0-4.9''10L>
2.0-2.5xl02
Johniton Niki
ct nl. (1970) et al.(197J
2.2X102 2.6xl02
2.9-102
3.7-4.4-103 4.4x10''
0.9-l.f. !()"? 1.7-1()"?
2 'Ml/1
1.07-in2
0.16-f>.!»<101
5.7-in1
1/1000 k
2.3M04
2 gxlf)?
l.BxlO3
2.2xlO]
,i-3
2/h-lO3
9.9xl02
Others
1t
l/2r.O
6.0xl0
3 tttt
-------
1
01
Reaction
37
38
39
*
Value
5.3xl03
2
1.0x10^
>
1.0x10--
-1 -1
TABLE 16 (Continued)
Validation* Demerjian Johnston Niki
et al. (1973) etal.(1970) etal.(1972)
5.3xl03 5.3xl03 5.3xl03
l.OxlO2 5.3xl03
l.OxlO2 4.4xl03
Units of ppm min unless indicated to the contrary
** i
Pseucio second order value
f Schuck et al., 1966
tTDavis, et al., 1972
TTTDodge, 1973
"TtTMcrris and Niki, 1S71
-------
mechanism, as well as more recent or different determinations, are
presented in Table 16, along with the values which we used in our
validation studies. Note that, for each reaction, the validation
value of the rate constant is within the range of values recommended
by these three groups or other individuals. For some reactions a
considerable span exists between the lowest and highest "best" esti-
mates of the rate constants (e.g., the formation of PAN by reaction
33). This generally indicates that the rate constant has not yet
been precisely determined experimentally. In such instances para-
meter values have usually been estimated by analogy to similar re-
actions with known rate constants. In Chapter IV of the recommenda-
tions report, "Existing Needs in the Experimental and Observational
Study of Atmospheric Chemical Reactions", we have discussed in detail
the reactions for which considerable uncertainty in either the value
of the rate constant or the nature of the elementary mechanism still
remains and have made recommendations for further important experi-
mental investigations.
b. Parameterized Stoichionstrie Coefficients
As we noted in the introduction to this chapter, two parameter-
ized stoichiometric coefficients must be specified. Since the only
olefin which we are considering in this validation study is propylene,
a terminal olefin, a is always equal to 1/2. The value of 6
depends upon the fraction of total aldehydes formed during an irradi-
ation which is not formaldehyde. The approximate values of 6 for
-76-
-------
the three systems validated are
System _§_
n-Butane-NOx .75
Propylene-NO .50
A
n-Butane-Propylene-NO .63
A
The accuracy of these values is probably no better than ±20% because
(i) the ratio of formaldehyde to higher aldehydes fluctuates
somewhat during an irradiation,
(ii) all the higher aldehydes may not have been detected with
the analytical instruments, and
(iii) the accuracy of the analytical techniques used to deter-
mine aldehydes in this study is poor.
This uncertainty, however, introduces no substantial impediment to the
validation effort since variation in B over the extremes of the un-
certainty bounds have little effect on the predictions of the decision
variables, T and M, first defined in the sensitivity study of the Hecht
Seinfeld mechanism (Chapter II).
c. Initial Concentrations of Reactants
The initial concentrations of the reactants were not always
determined at T = 0.0 minutes, that is, the instant at which the
lights were turned on. In those cases for which measurements at
zero time were unavailable, we have estimated the initial concentra-
tions by interpolating between the last measurement before and the
-77-
-------
first measurement after the irradiation was begun.
d. Average Dilution Rate
In carrying out chemical analyses of reactants and products,
large volumes of gas were drawn from the chamber during an experi-
ment. Removal of such large samples for analysis was necessary in
order to obtain accurate determinations of contaminant concentrations.
Because a volume of clean air, equal in volume to the amount of
gas removed for sampling, was added to the chamber to maintain the
total chamber pressure at 1 atmosphere, dilution gene-ally amounted
to 20-25% of the initial concentrations of reactants during a 6-hour
irradiation. In order to determine the amount of dilution, ethane,
a hydrocarbon which is virtually unreactive in photochemical smog,
was added to the reactant mix as a tracer gas. If ethane is assumed
to be chemically inert, its loss from the chamber can be attributed
entirely to sampling and dilution, carried out at an average rate
given by:
- kc
dt kc
The "rate constant" for the reaction is then
2.3 Iog(c0/cf)
k
V'o
where o and f are the beginning and ending times of the irradiation,
The <;verage dilution rate constants for the experiments used for
-78-
-------
validation were:
EPA Run
306
314
345
318
325
329
459
Sensitivity of
k x 10H(rmn )
7.5
8.5
7.5
8.2
8.5
8.9
4.C
Kinetic Mechanisms
EPA Run
307
333
348
349
352
457
to Variations
k x 10H(min~')
9.5
10.0
7.9
9.3
9.5
6.9
in the Magnitudes
of Parameters
We have carried out a large number of validation runs during
this study, many of which involved the investigation of the effect of
varying the magnitude of a parameter on the predicted concentration-
time profiles. These efforts can thus be viewed, in part, as an
informal sensitivity study of the lumped kinetic mechanism. We have
also completed a detailed formal sensitivity analyses of the simplified
Hecht and Seinfeld (HS) mechanism (Chapter II). In comparing the HS
mechanism wi Lh the new lurr.ped kinetic mechanism we find the most
striking difference to be that a large number of stoichiometric co-
efficients having a poor correspondence to actual stoichiometries must
be specified in the simple mechanism. Otherwise, with the exception
of the obvious difference in detail of chemical description, the two
mechanisms present the same basic features of the smog formation pro-
cess. A sensitivity analysis of the HS mechanism thus provides a
-79-
-------
useful indication of the sensitivity of parameters in the lumped
mechanism.
Among those parameters that are imprecisely known, the predictions
of the HS mechanism are most sensitive to variations in the rate of
photolysis of N02, k-j, the initial concentration of N02> and the
stoichiometries of the OH-HC and R02-N0 (which involves regenerat-
ing OH) reactions. Variations of ±50% in the water concentration,
however, have virtually nc effect on the predictions. In one sensi-
tivity study, using a set of data from the toluene-NO system in
/\
which the N02 peak reoccurrec! at 162 minutes, +50% changes from the
base values of (N02)Q, k^, B , and e caused the following changes
in the time to the peak T.
Parameter Change Change in T (minutes)
B - 50% + 198
E - 50% + 174
k1 - 50% + 116
(N02)Q - 50% + 24
6 + 50% - 114
e + 50% - 106
k] + 50% - 43
(N02)0 + 50% - 20
B and e both govern the rate of NO oxidation due to the OH-
hydrocarbon oxidation reaction. As it is this reaction which is pri-
marily responsible for the hydrocarbon loss rate observed in smog,
-80-
-------
and as the rate constant of the reaction correlates most closely
with the photochemical reactivity of hydrocarbons in smog chambers,
one would expect changes in the stoichiometries of reactions involved
in the production or loss of OH to have an impact on the predictions
of kinetic mechanisms. In terms of the lumped mechanism, we would
expect changes in the stoichiometries of the reactions of OH with the
four classes of hydrocarbons and changes in the termination rate of
OH through reaction with N02 and NO (reactions 17 and 18) to have a material
effect on the predictions. We would also expect variations in the two
experimental parameters, k-| (light intensity) and initial NO- concen-
tration, to perturb the predictions of the lumped mechanism. During
validation of the mechanism we have qualitatively confirmed these
expectations.
2. The Validation Results
In this section we present validation results for the lumped
mechanism (Table 14) for the following reactant systems:
Reactant System Number of Sets of Experimental Data
n-Butane-NO 3
A
Propylene-iJOv 4
A
n-Butane-Prcpylene-NOx 6
The input parameters to the mechanism ere those presented in Section
VB1. The results are depicted as a series of figures. Figure numbers,
-81-
-------
EPA experiment identification number, and initial concentrations of
reactants are given in the List of Figures, Table 17. Predictions of
the mechanism are represented by solid lines, and the experimental
data points are coded according to
D NO
A N02
O 03
O Propylene
# n-Butane
X Pcroxyacyl nitrates
a. n-Butane-NOx
Plots of the predicted and experimental values of concentrations
with time are shown in Figures 2 through 4. The (n-butane)0/(NOx)0
ratios span a range from 2.4 to 10.4.
b. Propylene-N0x
The propylens-NO validation results are presented in Figures
5 through 8. For this system the (propylene)Q/(NO )Q ratios for the
four experiments vary between 0.4 and 1.3.
c. n-Butana-Propylene-N0x
The validation results for this binary hydrocarbon system are
displayed in Figures 9 through 14. The hydrocarbon/NO ratios for
A
the experiments considered here span approximately the same range as
those used for the validations of the single hydrocarbon system. The
-82-
-------
TABLE 17
List of Figures
Figure
3a,b,c
4a,b,c
5a,b,c
6a,b,c
7a,b
8a
9a,b
lOa.b.c
lla.b.c
12a,b,c
13a,b,c
14a,b,c
.15a,b
EPA Run
3061"
314
345
318
325
329
459
307
333
348
349
352
457
0.03
0.02
0.12
0.06
0.04
0.06
0.06
0.05
0.08
0.08
0.03
0.07
0.05
(NO)Q
0.30
0.29
1.28
1.12
0.32
0.26
1.14
1.23
1.25
1.23
0.31
0.27
1.11
(n-Butanek
1.60
3.17
3.40
3.06
3.41
3.39
3.25
3.29
3.29
(Propylene)Q
0.51
0.45
0.24
0.78
0.36
0.23
0.50
0.44
0.26
0.81
Initial concentrations in units of parts per million (ppm)
f
0.12 ppm of aldehyde also present initially
-83-
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CO
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SCflLE FflCTOR = 10
1.000
2.000
TIME (MINUTES)
3.000
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Figure 3a. EPA Run 306
-------
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Q_
EPfl 306
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in
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0.0
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Figure 4b. EPA Run 314
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Figure 5a. EPA Run 345
-------
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Figure 5b. EPA Run 345
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3.000
4.000
Figure lla. EPA Run 333
-------
I
_J
o
I
0.0
Pfl 333
1.000
2.000
TIME (MINUTES)
3.000
11.000
Figure lib. EPA Run 333
-------
I
o
O
O
LO
CO
O
O
O
CO
Q_
Q_
en
UJ
z°
o§
o
o
0.0
I
EPR 333
SCflLE FflCFOR = 10
1.000
2.000
TIME (MINUTES)
3.000
U.OOO
Fiqure lie. EPA Run 333
-------
o
CD
U)
EPR 3148
o
^i
i
0.0
1.000
2.000
TIME (MINUTES)
3.000
u.ooo
Fiqure 12a. EPA Run 348
-------
o
00
c
c?
LO
'Or-
0.0
EPfl
1.000
2.000
TIME (MINUTES)
3.000
u.ooo
Figure 12b. EPA Run 348
-------
o
vo
i
O
O
LO
ro
o
o
o
n
CL
Q_
§§
>* LO
I
CE
01
UJ
o
o
LO
o.o
EPR 3U8
x
I
SCflLE FflCTOR = 10
I
1.000
2.000
TIME (MINUTES)
3.000
_J
4.000
Figure 12c. EPA Run 348
-------
FIGURE 13a.
o
I
EPfl 349
in = 10
j
1.000
2.000
TIME (MINUTES)
3.000
u.ooo
Figure 13a. EPA Run 349
-------
o
a
o
a
in
r-
Q_
n_
c:
cc
LJ
o
I
o
0.0
o
0
I
EPfl 349
1.000
2.000
TIME (MINUTES)
SCflLE FflCTOR = 10
3.000
.000
Figure 13b. EPA Run 349
-------
o
o
LO
EPfl 349
o
o
m
OL_
Q_
ro
i
\
Q-CM
cn
LU
O
O
0.0
I
1.000
2.000
TIME (MINUTES)
SCflLE FflCTOR = 10
I
3.000
I
u.ooo
Figure 13c. EPA Run 349
-------
co
0.0
EPfl 352
1.000
2.000
TIME (MINUTES)
3.000
J
4.000
Figure 14a. EPA Run 352
-------
-£»
I
EPR 352
1.000
2.000
TIME (MINUTES)
3.000
4.000
Figure 14b. EPA Run 352
-------
O
O
LO
CO
EPfl 352
O
O
O
II
00
Q_
0_
in
i
in
CE
OC
UJ
o
o
1/7
i
SCflLE FHCTOR = 10
I
_J
u.ooo
0.0
1.000
2.000
TIME (MINUTES)
3.000
Figure 14c. EPA Run 352
-------
EPfl 457
SCflLE FACTOR = 10 2
1.000
2.000
TIME (MINUTES)
3.000
4.000
Figure 15a. EPA Run 457
-------
a
o
LO
CO
o
o
o
CO
Q_
CL
in
cr
cc
UJ
08
o
o
LO
0.0
EPfl 457
SCflLE FflCTOR = 10
I
1.000
2.000
TIME (MINUTES)
3.000
4.000
Figure 15b. EPA Run 457
-------
(n-butane)Q/(NOx)0 ratio ranges from 2.4 to 9.7 and the (propylene)Q/
(NOX)0 from 0.2 to 1.3.
C. Concluding Comments
The data base provided for the validation studies fulfills many
of the important requirements that one would wish to place on it. The
concentration levels of the hydrocarbons, nitrogen oxides, and oxi-
dants are representative of those observed during smoggy days in Los
Angeles. A variety of hydrocarbon systems have been studied; high
and low reactivity hydrocarbons are represented in the data base, as
are single reactants (n-butane and propylene) and a binary mixture.
Initial conditions for the runs cover a broad range of hydrocarbon to
nitrogen oxide ratios. This is a particularly important property of
the data base if the validated mechanism is to be part of an airshed
model which will be used to evaluate proposed alternative control
strategies. On the whole, the accuracy and precision of the measure-
ments 1s adequate, although there are a number of important expec-
tations, which we will mention shortly.
While the data base possesses many desirable attributes, its
shortcomings must be noted as well, for these determine the limits
within which the model nay be tested. Consider, for example, a data
base for which concentrations have been determined with only passable
accuracy, Hide ranging sets of parameters could easily produce pre-
dictions which fall within the broad limits of experimental uncer-
tainty. Under such circumstances, it is not possible to satisfactorily
-118-
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test the adequacy of the mechanism.
Vie have mentioned the most notable deficiences of the data base
at one point or another in earlier sections. We summarize them here,
with some comments.
(i) Inaccuracy in measurement and in analytical procedures.
As noted earlier, Mast and KI readings were badly discrepant,
initial NC^ was imprecisely determined, and light intensity
was not known with sufficient accuracy. Also, NO and NOg
determinations were inaccurate at low concentrations.
(ii) Lack of measurement of certain species, both in the gas phase
and on the wall. It would be of value to monitor nitric and
nitrous acid concentrations in future studies. Determination
of wall concentrations of these species is also desirable.
1. Discussion of the Chamber Validation Results
Turning now to the results of the validation efforts, we make a
number of observations. First, we have been able to demonstrate that,
in general, there is good agreement between predicted and measured
concentrations. In making this statement, we must emphasize that sub-
stantial uncertainties exist in the magnitude of light intensity and
initial NCL concentration, as well as in the values of measured con-
centrations of HC, NO, N02 and O.j, thus limiting the possibilities
for critically testing the adequacy of the model. More specifically,
the mechanism has shown good qualitative and quantitative agreement
-119-
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with observed values of the time to the N02 peak and of final ozone
levels reached for three different hydrocarbon-NOx systems and for a
wide range of hydrocarbon to NO ratios.
A
The predictions of the lumped mechanism agree most closely with
the experimental data when the initial NO concentration is less than
^ <
about 0.5 ppm~a condition typical of polluted atmospheres. At initial
concentrations of NO greater than 1 ppm, the rates of oxidation of NO
A
and accumulation of N02 predicted by the mechanism continue to agree
well with the data; however, the rates of 03 accumulation and N02 oxi-
dation after the peak are more rapid than those observed experimentally.
In many of the experiments the high initial concentrations of NO suffi-
ciently delayed the attainment of the N0« peak that a maximum level
of ozone was not achieved before the end of the irradiation (usually
375 minutes). As a result, while it is apparent that, under the condi-
tions stated, the onset of 0, accumulation predicted is somewhat pre-
mature, it is still not possible to fairly evaluate the accuracy of
the simulated 0^ maximum. In those experiments during which ozone
reached a maximum asymptotic level (e.g., runs 306, 325, and 349} the
agreement between the data and the predicted ozone maxima are good. The
rates of oxidation of propylene and n-butane predicted by the mechanism
match the data uniformly well over the full range of initial concen-
trations and hvHvoo.rLjn/NO ratios studied. PAN validation data were
avail?!:."e for only three sets of experiments, runs 325, 329, and 459.
.cor the first two of these runs the predicted PAN concentrations are
in good agreement with the data; for run 459, however, the predicted
-120-
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onset of PAN formation occurs too early and the levels reached are
unacceptably high, when compared with the data.
Earlier we noted that two of the experiments being used in our
validation program were performed ten months after all the other data
were obtained. In our attempts to validate the lumped mechanism against
each of these experiments, runs 457 and 459, we have found that the
predicted course of reaction, as displayed in the concentration-time
traces, preceded that observed by about 80 minutes. Because, in at
least one of these cases (run 459), the hydrocarbon/NO ratio is not
X
appreciably different from that of another system successfully vali-
dated (run 329), it is possible that chamber conditions might have
changed significant! ' during the 10 month interim period. In par-
ticular, the radiation intensity might have decreased substantially.
While there is no way of checking, a posteriori, what changes, if any,
occurred in the operating conditions of the smog chamber, this experi-
ence demonstrates the importance of continuously and accurately moni-
toring all the operating parameters of smog chambers.
As is apparent from the results, the data and predictions are
not always in good agreement for all species over the full period of
the irradiation. These discrepancies can be attributed to at least
four possible sources of uncertainty:
(i) The mechanism may be incomplete. It has been our intent
to include every reaction presently thought to be impor-
tant to explaining smog formation in the lumped mechanism.
In the future, new reactions may be discovered and/or
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previously unsuspected products of elementary reactions
may be found. Furthermore, reactions and products presently
included in the mechanism may be shown to be unimportant
(although this is unlikely).
(ii) The lumping process may introduce error. For example, we
have assumed that the CH,qHCH90,,- radical (product of the CH-
JOH ^ *
propylene reaction) to react in the same fashion as the
CH3CH2CH202- radical. To the extent that their reactivities
are different error will be introduced into the predictions.
(iii) There are uncertainties in the experimental data used for
validation.
(iv) Chamber effects (such as surface effects) which are not
accounted for in the model are potential sources of dis-
crepancy.
(v) Not all of the rate constants are known with a high degree
of certainty. Indeed, for a few of the reactions no experi-
mental determination has yet been made of the rate constants.
For the cases of those reactions for which several determina-
tions of the rate constants have been carried out, there is
often poor agreement between the various estimated values.
As a consequence of these uncertainties, we have not yet reached the
point in model evaluation where we are in a position to quantitatively
assess the "goodness" of the proposed mechanism or, for that matter, to
draw unequivocal qualitative conclusions regarding its merits. Yet,
the mechanism appears capable of predicting the concentration-time
behavior of a variety of reactant systems over a wide range of initial
-122-
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conditions. Clearly, however, a considerably more accurate and complete
data base is required if the adequacy of the lumped mechanism is to be
critically evaluated. We thus recommend that a carefully conceived
experimental program be undertaken for the sole purpose of providing
the data needed to carry out such an evaluation.
2. Effect of Initial Reactant Ratio on Ozone Formation
A well-documented characteristic of the photochemical smog system
is that, for a series of experiments in which the ratio of initial hydro-
carbon to NO (NO + N0?) is continually decreased, either at fixed
/\ £
initial hydrocarbon or NO concentrations, the maximum concentration
A
of ozone attained in each experiment increases, goes through a maximum,
and then decreases (Hamming and Dickinson, 1966; Korth, 1966; Altshuller
et al. 1967; Dimitriades, 1970; Glasson and Tuesday, 1970). While this
phenomenon has been verified in many experimental smog chamber programs,
no kinetic mechanism has to date been shown to be capable of predicting
this behavior. Therefore, as a test of the mechanism, we undertook a
study of the effect of variation in initial reectant mixtures on ozone
formation.
Isopleths of maximum ozone concentration predicted by the mechan-
ism given in Table 14 as a function of total initial hydrocarbon con-
centration and initial NO concentration are shown in Figure 16. The
hydrocarbon mix consisted initially of 75% n-butane and 25% propylene.
Further, 0.10 ppm of NOp was present initially in each case, so that
the total initial NO is the sum of the indicated NO concentration
A
-123-
-------
»»
Q_
Q_
0
0.4 0.5
NO (PPM)
Figure 16. Isopleths of maximum ozone concentration achieved during an
8-hour irradiation of various mixtures of n-butane, propylene
and NO. (N02 initially a't 0.1 ppm.)
-------
1.2
HC (PPM)
7 0.85
NO(PPM)
Fiqure 17a. Surface of maximum ozone concentrations achieved during an
8-hour irradiation of various mixtures of n-butane, propylene
and NO. (NO-, initially at 0.1 ppm). Note that the axes do
not correspond to the origin of the NO-HC coordinate system.
The smallest values of [NO] and [HC] are in the lower left
hand corner of each figure.
-125-
-------
0.1
1.0 HC(PPM)
NO(PPM)
Figure 17b. Same as Figure 17a. except that axes have been rotated,
-126-
-------
0.125
0.25
0.375
0.50
Figure 18.
PROPYLENE FRACTION OF INITIAL
HYDROCARBON MIXTURE (PROPYLENE
PLUS n-BUTANE)
Maximum ozone concentration achieved during an 8-hour irradi-
ation of an initial mixture of [HC] = 0.80 ppm, [NO] = 0.40 ppm,
and [N02] = 0.10 ppm, for various initial mixtures of n-butane
and propylene.
-127-
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and 0.10 ppm. Viewed in three dimensions (Figures 17a and 17b), the
predicted surface of peak ozone levels has a maximum both at fixed
initial hydrocarbon and increasing initial NO and at fixed initial NO
and increasing initial hydrocarbon, a result which is in qualitative
agreement with the experimental results cited above. The maximum ozone
ridge on the surface follows a line of constant [HC]o/[NOx]Q = 2.5 for
the hydrocarbon mix and the range of concentrations studied.
The ozone values indicated in Figures 15 and 16 are the maximum
values reached in eight simulated hours of irradiation. For all cases in
which [HC] /[NOXJ0 < 6, tne maximum ozone concentration occurred at the
end of the eight hour irradiation. Thus, in these cases, the ozone
levels reached after, say, ten hours of irradiation would be somewhat
higher than those shown. The smallest ozone maxima are reached either
under conditions of low initial hydrocarbon and high initial NO (not
N02), or under conditions of high initial hydrocarbon and low inital
NO. In the former case, high initial levels of NO inhibit the form-
ation of ozone over the long incubation period during which NO is
oxidized to NOo; in the latter case, high levels of ozone cannot ac-
cumulate since the NQ*, which is necessary for ozone production, is
rapidly consumed to form stable products. The general behavior de-
picted in Figures 16 and 17 matches closely that of eye irritation as
a function of initial hydrocarbon and NO (Hamming and Dickinson, 1966;
A
Los Angeles County Air Pollution Control District, 1971). In addition,
Figures 16 and 17 exhibit the seme behavior observed in a number of
experimental programs (Altshuller et al., 1967; Dimitriades, 1970;
Glasson and Tuesday, 1970), although precise quantitative comparison
is not possible because different systems were studied.
-128-
-------
As noted, the results shown in Figures 16 and 17 are based on
the study of an initial hydrocarbon mixture of fixed composition,
75% n-butane and 25% propylene. However, it is also important to
determine the effect of altering the composition of the initial
hydrocarbon mixture on the quantity of ozone formed. Figure 18
shows the maximum ozone concentration attained over an eight hour
irradiation as a function of the composition of an initial hydror
carbon mixture of n-butane and propylene at [NO] = 0.40 ppm and
[ML] =0.10 ppm. We see that reduction in the olefin fraction
of the mixture results in a substantial decrease in the amount of
ozone formed. The reduction in ozone level is particularly effec-
tive between 0 and 10% olefin. Levy and Miller (1970) experimentally
investigated this same issue through the study of organic solvent-
NO mixtures and observed general behavior similar to that shown
A
in Figure 18. In their study, n-octane and m-xylene were used as
the low and high reactive species, respectively. They found that
a reduction in the m-xylene to 3% of the solvent mixture resulted
in a 32% reduction in the amount of ozone formed from that for a
50-50% mixture. Increasing the m-xylene fraction to 8% resulted in
a sharp increase in the ozone level to 92% of that in the 50-50%
mixture.
Point A on Figures 16 - 18 indicates the approximate composi-
tion of the Los Angeles atmosphere in 1969. At that time the
ozone levels lay close to the "ridge" of observed maximum
-129-
-------
values. While reductions in either or both of the hydrocarbon and NO
emission levels can be expected to result in decreased ozone levels,
it appears that hydrocarbon reductions will be more effective in reduc-
ing ozone formation since the surface of ozone levels declines more
steeply in the direction of decreasing hydrocarbons at fixed NO than
in the direction of decreasing NO at fixed hydrocarbon. Furthermore,
a simultaneous reduction in both hydrocarbon and NO emissions will
not be as effective as either of these other two routes. Finally,
we see that reduction in the olefin (high reactivity) fraction in the
atmosphere may also provide an attractive abatement strategy.
Based upon our results (Figures 3-16) and the principles of
formulation, the kinetic mechanism developed here appears to hold
substantial promise for incorporation in airshed models. The mechan-
ism describes the important inorganic chemistry in detail, yet mini-
mizes the overall number of reactions by taking advantage of the
general behavior of specific groupings of similar hydrocarbons
and free radicals. Further, the mechanism is free of arbitrarily
assignable stoichiometric coefficients. Thus, the new lumped mechan-
ism represents a reasonably rigorous, yet manageable, description of
the photochemistry of air pollution.
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VI. SUMMARY AND PROSPECTS
During the course of this project we have completed a multi-
plicity of tasks concerned with the mathematical modeling of photo-
chemical smog. First, we have carried out an extensive sensitivity
study for the simplified Hecht-Seinfeld mechanism. In this work
we exposed the most notable shortcomings of simplified general mech-
anisms, the principal one being the strong dependence of predictions
on the magnitudes of parameters which cannot be specified, with cer-
tainty, a priori. We then applied the simplified mechanism as an
aid in planning a series of smog chamber experiments which are to
be conducted this year in an outdoor chamber near Research Triangle
Park, North Carolina. Specifically, we examined the effects that
variations in the initial hydrocarbon to NO ratio, light intensity,
A
and temperature have on such decision variables as the N02 and 03
maxima and dosages. This work is noteworthy inasmuch as it marks
the first time that a kinetic mechanism has been used to aid in
planning an experimental program concerned with the study of air
pollution. Third, we prepared an exhaustive recommendations docu-
ment dealing with existing needs in the experimental and observa-
tional study of atmospheric chemical reactions. That document,
which both appraises the current state of knowledge and identifies
specific issues requiring further investigation, should be considered
as a companion volume to this report. Finally, we have developed
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and begun validation of a rigorous, yet general, lumped kinetic
mechanism for photochemical smog. In the first phase of validation
we have simulated the photo-oxidation of n-butane -NO propylene -NO
^ A
and n-butane - propylene - NO mixtures when irradiated in an air-
n
filled smog chamber. The results of this work are presented herein.
In reviewing the work carried out during the past year, we
have concluded that the area of inquiry most likely to produce
fruitful results is continued development of the 39-step lumped
kinetic mechanism. We envision that the development program will
be comprised of three groups of tasks:
(1) The validation of the mechanism using data for an
aromatic-NO reactant system. To date we have evalu-
J\
ated the mechanism using an olefin, a paraffin and an
olefin-paraffin mixture as reactants. However, aromatics
constitute a significant percentage of the atmospheric
hydrocarbon mix. It would, therefore, be extremely valu-
able to simulate aromatic, and aromatic-.olefin-paraffin re-
actant systems, especially if the mechanism is ultimate-
ly to be applied in simulating atmospheric reactions.
(ii) The further validation of the mechanism using data
presently being obtained at the new smog chamber re-
search facility of the Statewide Air Pollution Research
Center, University of California, Riverside. These
data are being collected expressly for the purpose of
-132 -
-------
model validation and, as a consequence, should be
subject to considerably less uncertainty, due to
omissions and imprecisions in the data base, than
have previous data.
(iii) The development of the mechanism for use as a plan-
ning tool. In Chapter II we demonstrated the utility
of the simplified HS kinetic mechanism for this pur-
pose. When satisfactorily validated, the new mechan-
ism should prove even more useful in this regard. Be-
fore using the lumped mechanism as a planning aid, how-
ever, two tasks must be completed:
A full sensitivity analysis of the
mechanism must be made so that con-
fidence bounds can be placed on the
predictions.
The mechanism must be extended so
that variations in temperature,
light intensity, and humidity can
be accounted for.
It appears likely that, in the near future, the lumped kinetic
mechanism will be incorporated into airshed models for use in pre-
dicting the concentrations of pollutants in urban areas. Before am-
bient smog can be accurately modeled, however, and,thus, before cur-
rently existing mechanisms are so used, the composition and reactivity
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of the atmospheric organic mix must be carefully determined. The
organic species in the atmosphere can then be rationally segmented
into a number of mathematical "lumps". So that rational separation
can be carried out, we recommend that
the concentration distribution of organics in polluted
air be determined from existing data
alternative lumping techniques both for chamber and
atmospheric applications be investigated
the physical reasons for observed synergisms*be explicated.
To summarize, in this project we have demonstrated the short-
comings and limitations of simplified kinetic mechanisms and made
progress in determining the level of complexity required in kinetic
mechanisms in order to produce accurate predictions. A very promis-
ing kinetic representation has been developed, and with further work,
this mechanism may well be of use both in planning experimental
studies to be carried out in, and as part of, airshed simulation
models which will ultimately find use in the evaluation of alter-
native emission control strategies.
* Synergism in this case refers to the change in the rate of
oxidation of KO observed when mixtures of two or more hydro-
carbons are irradiated in a system of NO and air relative to
the rate which occurs when an I10x-air system containing a single
hydrocarbon is irradiated.
..l 34 _
-------
References
Altshuller, A. P., Kopczynski, S. L., Lonneman, W. A., Becker, T. L.,
Slater, R., Environ. Sci. Technol., 1_, 899 (1967)
Altshuller, A. P., Kopczynski, S. L., Lonneman, W. A., Sutterfield, F.
D., Wilson, D. L., Environ. Sci. Technol., 4_, 44 (1970)
Altshuller, A. P., Kopczynski, S. L., Wilson, D., Lonneman, W.,
Sutterfield, F. D., J. Air Pollut. Contr. Assn., ]9_, 791 (1969).
Bufalini, J. J., Gay, B. W., Jr., Kopczynski, S. L., Environ. Sci.
Technol., 5_, 333 (1971).
Davis, D. D., Wong, W., Payne, W. A., Steif, L. F., "A Kinetics Study
to Determine the Importance of H02 in Atmospheric Chemical
Dynamics; Reactions with CO," presented at the Symposium on
"Sources, Sinks, and Concentrations of CO and Cfy in the
Earth's Environment," St. Petersburg Beach, Fla., August 1972.
Demergian, K. L., Kerr, J. A., Calvert, J. G., The Mechanism of
Photochemical Smog Formation, in press (1973).
Dimitriades, B., "On the Function of Hydrocarbon and Nitrogen Oxides
in Photochemical Smog Formation," U.S. Department of the
Interior, Bureau of Mines, Report 7433, 1970.
Dodge, M. C., private communication, Environmental Protection Agency,
Research Triangle Park, N. C., 1973.
Eschenroeder, A. Q., Martinez, J. R., Advances in Chemistry, 113, Am.
Chem. Soc., Washington, D.C., 1972
Gay, B. W., Jr., Bufalini, J. J., Environ. Sci. Technol., 5_, 422 (1971).
Gear, C. W., Coirmun. of the Ass. for Computing Machinery, 14, 176 (1971).
Glasson, W. A., Tuesday, C. S., Environ. Sci. Technol., 4^ 37 (1970).
Godt, H. C. Jr., Quinn, J. F., J. Am. Chem. Soc., 78., 1461 (1956).
Hamming, W. J., Dickinson, J. E., J. Air Pollut. Contr. Assn., 16, 317
(1966).
-135-
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Hecht, T. A., "Further Validation of a Generalized Mechanism Suitable
for Describing Atmospheric Photochemical Reactions," Report 72-SAI-
26, Systems Applications, Inc., 9418 Wilshire Blvd., Beverly Hills,
Calif., 1972.
Hecht, T. A., Seinfeld, J. H., Environ. Sci. Technol., 6_, 47 (1972).
Hill, A. C., J. Air Pollut. Contr. Assn., 21_, 341 (1971).
Johnston, H. S., Pitts, J. N., Jr., Lewis, J., Zafonte, L., Mottershead,
T., "Atmospheric Chemistry and Physics," Project Clean Air, Task
Force Assessments, Vol. 4_, Univ. of California (1970).
Kopczynski, S. L. private communication, Environmental Protection Agency,
Research Triangle Park, N. C., 1972.
Korth, M. S., "Effects of the Ratio of Hydrocarbon to Oxides of Nitrogen
in Irradiated Auto Exhaust," U.S. Department of Health, Education
and Welfare, Cincinnati, Ohio (1966).
Leighton, P. A., Photochemistry of Air Pollution, Academic Press, New
York, N.Y., 1961
Levy, A., Miller, S. E., "Role of Solvents in Photochemical Smog Formation,"
Report 799, Battelle Memorial Institute, Columbus, Ohio, 1970.
Morris, E. D., Jr., Niki, H., J. Phys. Chem., 75_, 3640 (1971).
Niki, H., Daby, E., Weinstock, B., Advances in Chemistry, 113. Am. Chem.
Soc., Washington, D.C., 1972.
"Profile of Air Pollution," Air Pollution Control Distric, County of
Los Angeles, Los Angeles, Calif. (1971).
Schuck, E. A., Stephens, E. R., Schrock, P. R., J. Air Pollut. Confr. Assn.,
16_, 695 (1966).
Wayne, L. G., Weisburd, M., Danchick, R., Kokin, A., "Final Report--
Development of a Simulation Model for Estimating Ground Level
Concentrations of Photochemical Pollutants," Technical Memorandum,
System Development, Corporation, Santa Monica, Calif., 1971.
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APPENDIX A
Analog and Digital Sensitivity Analysis
Techniques as Applied to the Hecht-Seinfeld
Mechanism
R. Schainker
D. Stepner
C. Wells
Prepared by*
Systems Control, Inc.
260 Sheridan Avenue
Palo Alto, California 94306
for
Systems Applications, Inc.
950 Northgate Drive
San Rafael, California 94S03
*Minor editing carried out at SAI
-137-
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I. INTRODUCTION
This report summarizes the work accomplished under Phase I of
Contract No. SAI-72-7, between Systems Applications, Inc., and Systems
Control, Inc., dated July 15, 1972.
The two major objectives of Phase I were (l).to determine the
feasibility of using an analog computer to assist in the estimation of
photochemical reaction rate parameters, and (2) to evaluate the feasi-
bility of, develop a methodology for, and perform sensitivity analyses
for the H-S kinetic mechanism using the digital computer.
In the following sections of this appendix, the model used, the analog
sensitivity experiments, the digital sensitivity methodology, and the
digital sensitivity experiments are discussed and conclusions and recom-
mendations are presented.
II. PHOTOCHEMICAL SMOG MODEL
The Hecht-Seinfeld (Seinfeld et al., 1971; Hecht and Seinfeld, 1972)
kinetic mechanism for describing photochemical smog formation was used as
the basis for the feasibility studies performed in Phase I. This mechanism
was used because it appeared to be the best available at the time at which
this work was undertaken. The complete mechanism is summarized in Table I
of Chapter II. The kinetic and sloichiometric parameters for the toluene-NO
J\
and propylene-IIOx reactant systems, for which the studies reported here
were carried out, can be found in Tables 2 and 6 of Chapter II.
The following assumptions were made in formulating the mass continuity
-138-
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equations for the reaction mechanism:
1. Smog chamber is well mixed
2. Volumetric loss rate due to sample withdrawal is constant
3. Initial concentration of reactants are known with certainty
The resulting eleven unsteady-state mass balances that represent the kinetic
model are given below:
Symbols used
y} = N02 y6 = OH-
y2 = NO y? = H02-
y3 - 03 y8 = R02-
y4 = HC1 yg = HN02
y5 = HC2 y]0= N03
yn = o
-139-
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Unsteady-state mass balances
(1) K02
*1 " ' Rl + *3 * R4 + 2R5 - R6 - *7 + *8 + *!! * *12 ' *17
(2) NO
- ~ 3
(0)
(9) UK
(10) K
(11) 0
~ R - R - ^ 4 *8 + R9 -
(3) 03
^3 = R2 " *3 - R4 ' *15 " "20 - Qy3
(A)
(5) nc2
- *20 -
(6) OH'
*6 C "~ ^0 "!" R9 + \1 ~ ?14 " R19+ e R16
(7) 110,-
' P12 "
CR13
2R7 - 2R8 - R9 + R12
Rl - R2 - ?13 - R18 - Qyll
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Rate functions
BK3
"ll" ^11 ' 72 ' y7
yl *12 - "12 ' y7 ' yl
yll "13
y2 ' y8
R6 * ^6 ' yl ' y!0 ^7 " ^7 ' yl ' y8
y5 * y6
y9 ^0 = BK2Q y3 y5
10 y6 *21 = ^21 ' yl
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Two methods of solution of these reaction equations were investi-
gated in Phase I, one involving use of the analog computer, the second
involving use of the digital computer. In both cases the purpose was to
determine the feasibility of performing sensitivity calculations using
the device in question.
In past work it has been standard practice to assume that the free
radical reactions (reactions 6-11) are always in an equilibrium state
(Seinfeld, et al, 1971; Hecht and Seinfeld, 1972). If this assumption
is made, the set of eleven differential equations reduces to a set of
four differential equations (for a single hydrocarbon system) and six
non-linear algebraic equations. However, analog computers are not well
suited to solving non-linear algebraic equations. It was thus decided
to solve equations (1-11) as a set of eleven simultaneous differential
equations. In the course of this work it was shown that there is no
appreciable difference between the simulated time histories of the measur-
able chemical species using the free radical equilibrium assumption and
the time histories generated from the solution of the full set of un-
steady-state material balances.
In the following sections the analog and digital sensitivity results
are outlined. Working wiring diagrams and pot setting sheets for the
analog computer runs have been furnished directly to EPA.
III. ANALOG SENSITIVITY RUNS
The NASA Ames EAI 8800 Hybrid computer was used on a no-cost contract
basis to solve the eleven differential equations describing photochemical
A-5
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reaction kinetics.
Analog Computer System Description
The EAI 8800 computer is one of the largest and most accurate analog
computers built. It is in nearly constant use at NASA Ames and undergoes
daily preventive maintenance and calibration. The analog portion of the
machine consists of the following analog computer hardware: 240 precision
potentiometers, 60 high gain amplifiers, 60 integrating amplifiers, 60
summing amplifiers, 48 multipliers, and numerous additional analog computer
components, e.g., resolvers, clocks, logic circuits, etc. The computer
has an accuracy of 1 part in 10,000, which is essential in developing
a valid solution to the H-S Photochemical Smog Model. Time scaling
capacitor logic of 0.01, 0.1, 1.0, 10, 100, 1000 is also available.
The computer system has several integral output devices including:
X-Y plotter, 4 variable CRT display, and multiple strip chart recorders.
In addition, potentiometer settings can be made through the digital com-
puter portion of the hybrid system.
Programming the H-S Photochemical Smog Model
Time and amplitude scaling are basic difficulties inherent in pro-
gramming analog computers. Time scaling is relatively straightforward
and is attained simply by multiplying the right hand side of the differ-
ential equations by the appropriate scaling factor. Amplitude scaling,
however, must be performed on the output of each amplifier. Amplitude scaling
can be accomplished by normalizing the differential equations by the maximum
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voltage level of the particular machine. In the H-S Photochemical Smog
Model normalization factors were obtained directly from the digital
computer solutions. Without this information, a successful simulation
of the mechanism would have been much more difficult to obtain.
Criteria Used in Sensitivity Runs
The analog computer was time scaled to produce a solution to the
H-S mechanism in from 0.4 to 40 seconds, depending on the integration
speed settings on the operator's panel. The 40 second runs were used
for producing a solution on the X-Y plotter. The 0.4 second runs were
used to display the solution on the CRT in high speed repetitive operation.
The objective of the analog computer experiments was to display a
solution to the photochcmist so that, based on his judgment, parameters
could be adjusted to obtain the best possible fit to experimental data.
After several iterations in this mode of operation, it was apparent that
some form of goodness-of-fit criterion should be selected to compare dif-
ferent solutions.
The major element of the criteria finally selected was the time
to the N02 peak, T. Other elements in the criteria included maximum 0^
values, and the time at which the NO and NOg concentrations were equal
(toluene system only).
The utility of using phase plane plots to display characteristics
of the solution was examined. A phase plane plot is a cross plot of one
dependent variable versus another, for example NO versus NOp. The time
axis is represented parntnetcrirally along the trajectory which begins at
A-7
-------
the initial condition (I.C.) and ends at the equilibrium condition (E.G.).
The location of the maximum NO- is readily apparent in this type of display
and, in cases where flat peaks occur in the time domain plots, the phase
plane plot often-greatly sharpens the peak. An example of a phase plane
plot for (N02, NO) is shown below:
I.C.
NO (I.C.) = .55 ppm
N02 (I.C.) - 0.04 ppm
HO, ppm
.1 .2 .3 .4 .5
max NO,
NO (E.G.) = 0.00 ppm
NO (E.G.) = 0.13 ppm
ppm
Figure 1. Phase Plane Plot of N0/N02 (Toluene System)
In this figure the trajectory begins at the initial condition I.C.
point (0.04, 0.55) and terminates at the equilibrium condition E.G. (0.13,
0.00). The location of maximum predicted N02 could be used as a sensitive
indicator when compared with experimentally measured values of (NOo, NO).
This type of plot is frequently used in the study of non-linear
systems and, in particular, is used extensively in the development of
control systems for non-linear systems. Phase plane trajectory analysis
could prove useful in the preliminary validation of smog chamber experi-
ments. The phase plane diagram based on the measured data from a smog
chamber run could be plotted and the model outputs compared in the phase
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plane Instead of the state-time plane.
In this task of Phase I It was shown that the H-S photochemical smog
model could be solved on the analog computer for two HC species, namely
toluene and propylene. For both systems analog sensitivity studies were
performed. Time history plots of the four measured variables, NOo, NO,
Og, and HC, were obtained for perturbations about nominal rate constant
values and for different initial conditions. The resulting plots were
forwarded to Systems Applications, Incorporated for further analysis.
IV. DIGITAL SENSITIVITY RUNS
Task II of Phase I of the contract included -the development of the
digital sensitivity functions for subsequent use in the SCI maximum likeli-
hood identification program. The toluene system was used as the test case.
As indicated earlier, a solution to the set of 11 differential equations
was required in order to scale the analog computer program. For this
reason, all 11 differential equations were solved simultaneously on the
digital computer. Several integration programs were examined for possible
use in obtaining solutions to the system of equations. The Fourth Order
Runge Kutta method and the Adams Moulton predictor-corrector methods
proved to be unsuitable for this model because of numerical instabilities.
The original GEAR and the modified GEAR (provided by Systems Applications,
Inc.) were used to obtain an accurate solution of the equations. It was
found that an initial transient occurred in the solution for the free radical
species because of the mismatch between equilibrium concentrations and the
assumed zero concentrations of these chemical species. Computation times
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were thus slightly lengthened due to the small time step required during
the first several milliseconds of the simulation.
Basis for Sensitivity Calculations
The sensitivity equations, as defined herein, are the partial derivatives
of the dependent variables with respect to the unknown parameters. Para-
meters include rate constants, stoichiometric coefficients, and initial
conditions. There are 11 dependent variables and up to 25 parameters
requiring up to 275 sensitivity equations.
Symbolically, the reaction and sensitivity equations may be written
as a set of coupled nonlinear first order differential equaitons. In the
vector-matrix notation these can be summaried as
y = f (y,p)
3 f_ 3 f_ 3 y
3~p" a~y ' 3 p
where y = (11 x 1) vector, p = (25 x 1) vector, f = (llxl) vector
function, (3y_ /a ) = (11 x 25) matrix of sensitivities, and 31/3p =
(11 x 25) matrix of first order partial derivatives (Jacobian). The
Jacobian is an integral part of the SCI Maximum Likelihood Identification
program. The simultaneous integration of Eq. (1) and Eq. (2) generates
the time histories of the sensitivities.
The sensitivity ot any time means little when compared to the overall
"shape" of the solution for any specified set of parameters. A useful
measure of the overall sensitivity, as derived in the following section,
is based on the "Information" contained in the output data with respect
to the unknown parameters. The "Information" is defined as,
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(3)
where T denotes transpose. The "Information" is a quantitative measure
of degree of certainty with which we can estimate the individual parameters
contained in a set of equations.
In order to illustrate the method of sensitivity analysis outlined
below, five parameters were selected. These were: RK,, RKi-,, RKici RK3,
RK^. For this set of parameters sixty-six equations were needed to calculate
sensitivities, the original 11 differential equations plus 55 sensitivity
equations. Twenty-five additional equations were integrated to generate
the Information Matrix. A summary of the sensitivity analysis that was
carried out is outlined below.
Digital Sensitivity Analysis
Although analog computer simulation of the smog mechanism is a flexible
tool for allowing visual, qualitative sensitivity studies, the precise
ordering of the reaction coefficients must be done on a digital computer,
and with specialized alogrithms. The relative importance of the reaction
coefficients is found by computing the sensitivity of the time histories,
over a specified length of time and for all eleven reaction constituents,
to a fixed percentage change in each of the reaction coefficients, in
turn. At the heart of this analysis is the computation of the information
matrix, from which the reaction coefficient sensitivities are easily deter-
mined.
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For small changes in a given rate constant, RK., with all the other
J
rate constants fixed, the variation in the concentration of species y^
at a given moment in time from that observed at the same time in the inte-
gration with all input parameters at their base values, 6y^,is given by
3yi
6RKJ
and the total squared variation for all 11 constituents, integrated over
the total reaction time, is
u / 2 " /M2 2 /yv^y 2
^ / (6y,)Zdt = 2: / (6RKiTdt = / L[ (6RK.Tdt
i=l oj 1 i=l./\3RKi/ J * 1=1\ 3RK. / J
Q\J/ U \J/
A convenient measure of the sensitivity of the constituent level to RK.
J
is the root sum square variation given by
ll /.
E J (6yi
)2dt
1=1 0
6RK- = M. (5RK, (4)
j j J
the appearance of the value of the change in the j rate constant,
j,
J
in this equation is extremely important since this acts to normalize the
sensitivity of the constituent's level with respect to the magnitude of
the rate constants. Clearly, a change of 1 (unit) for each Rl
-------
order partial derivatives, -r^r Multiplying these first order
J
partials by a fixed percentage of the values of the rate constants (e.g.,
6RK. = 1% of RK-) provides a normalized measure.
J J
The quantities, MI, . . . , M^, can all be computed simultaneously
through the use of the information matrix. This matrix, presented as a
function of time, is given by
(5)
where y is a vector of the 11 reaction constants and RK is a vector
of the 21 rate constants. The first order partial ay is an (11 x 21)
sRK
matrix. Each concentration-time history is given by a differential
equation
^(yj) = fj (y, RK) . i = 1. n
For example, for y1Q (N03)
A ^lO5 = RK4 yly3 ' RK5y2y10 " RK6yly10
Differentiating with respect to RK^ yields
H /'W-(n\ **{ 9y3 / 3y10 3y2 \
u l_ Lr. I = u v 4- Rl^ v + Rl^ v - PK I v + 1- v
7TT l^iJi' / "K^ NA aRtf J^ RNd^l aBI^ R \y ?al?k aRK I 'in
d.t \3KiM / I -' '* 3KK.,, J H I dKN/i 3 I tdKN/i dKN>ln/ IU
3y10 3yl \
0/
~RK6 yl iRl + affi ' y!0
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Inspection of equation (5) shows that a diagonal element of the infor-
mation matrix, I, is identically the square of one of the M.'s of Eq. (4).
J
Therefore, to determine the sensitivities of the reaction constituents
to any set of rate constants, the information matrix for the first order
partials is computed. After a fixed length of integration time, the
square roots of the diagonal elements are calculated and the sensitivities
are found via Eq. (4).
As an illustrative example, the sensitivities of the constituents
with respect ot the five rate constants RK^, RK,,, RKig, RK^, and RK^
were computed. These five rate constants were selected because of their
broad range in magnitude and, thus, the potential for numerical instability
problems. In this example, all other rate constants remained constant,
and thus their sensitivities were not evaluated. As we have noted, even
this simple example involves the solution of 66 simultaneous differential
3y.
equations (11 for yi y^ , and 55 first order partials for v4 ,
oKr\
J
j = k,3,4,11,16 and i « 1 11). The noninal values for the rate
constants were those used for the toluene base case. The square roots
of the diagonal elements of the information matrix were computed to be:
RKjtS.64), RK11(1.37xlO"18), RKlg(l.50xlO"4), RK3(1.17xlO"2), RK4(24.05)
The sensitivities for these constants are:
RK, : (5.64)(2.66 x 10"3) = 1.46 x 10"
RKn: (1.37 x 10"18)(18) = 0.0
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RK]6: (1.56 x 10~4)(18) = 2.71 x 10"3
RK3 : (1.17 x 10"2)(.218) = 2.56 x 10"3
RK4 : (24.05)(6 x 10"5) = 1.44 x 10"3
The importance of these five rate constants can be ordered as (from most
to least important)
ie» "3» °'M » 11*
The results of this experiment indicate that digital sensitivities
can be generated using the H-S model and the modified GEAR program. It
is estimated that up to 15 simultaneous sensitivity analyses may be per-
formed without excessive accumulation of computer time. Because this
method of sensitivity analysis is an integral part of the maximum likeli-
hood estimation procedure, it can be used to order the parameters to
be identified in terms of thier relative sensitivity.
V. DISCUSSION AND CONCLUSIONS
Discussion
In phase I of this study, two different approaches to the problem of
determining the sensitivity of photochemical smog reaction parameters were
evali:. tod. The analog computer was used to study the effect of large
parameter changes that often result when a new set of experimental smog
chamber data is being validated. The analog computer produces accurate
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results for any desired parameter values as long as the amplitude scaling
for the parameter has been properly carried out in programming the solu-
tion. In our first attempt at solving the reaction model on the analog
computer, the ranges allowed for the parameter changes were far too
limited, and, consequently, solutions for small changes in parameter
values often required several hours of program modification. This prob-
lem can be avoided by allowing for larger ranges of parameter variations
in the inital amplitude scaling.
Peripheral devices, used as aids in plotting, display, and other func-
tions, have proven to be valuable tools in the photochemical smog model
validation studies. The CRT and the use of cross (phase plane) plots
were also helpful in guiding the sensitivity studies.
One major advantage of the anlog computer over the digital computer
is that of stability of the solution procedure. If amplitude scaling is
correctly carried out, the analog computer will always produce valid inte-
gration of the equations, whereas roundoff error and numerical stability
problems can result in inaccurate solutions on a digital computer.
The digital computer provides a means for quantitatively determining
a measure of the sensitivity of parameter values. A method of simultaneously
solving the sensitivity equations was developed, and an example of a means
for rank ordering the parameters was given for the toluene system. The
sensitivity calculations arc required in Lhe maxin:i:in likelihood identifica-
tion program, and consequently the sensitivities are determined automatically
when parameter estimation is carried out.
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The major problem in using a digital computer for sensitivity studies
1s that of achieving valid integrations. The modified GEAR program does
not always yield an accurate solution, even when the error function test
1s successful. Each solution should be tested for convergence using cer-
tain options available in the program. In the results contained herein,
only those solutions that result in FLAG = 1 were considered successful.
A major advantage of the digital computer is that its use, on the
average, minimizes the time required to obtain new results. However, as
indicated above, caution should be exercised in drawing conclusions from
the digital solution unless convergence is assured.
Recommendations
We recommend that, in future sensitivity studies, the digital computer
be used as the basic tool for the experimental planning activities because
of the lower manpower requirements. We further recommend that the analog
and digital computers continue to be used in a complementary manner to in-
sure that accurate integrations are obtained.
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REFERENCES
1. Hecht, Thomas A. and John H. Seinfeld, "Development and
Validation of a Generalized Mechanism for Photo-
chemical Smog," Environmental Science and Technology,
8, 47. (1972).
2. Seinfeld, John H., Thomas A. Hecht, and Philip M. Roth,
"A Kinetic Mechanism for Atmospheric Photochemical
Reactions," Appendix B of Report 71-SAI-9 , Systems
Applications, Inc., Beverly Hills, California, under
Contract CPA 70-148, May (1971).
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1 RtPORTNO
EPA-650/4-74-011
3 RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
Mathematical Simulation of Atmospheric Photochemical
Reactions: Model Development, Validation and
Application
5 REPORT DATE
July 1973
6. PERFORMING ORGANIZATION CODE
7 AUTHOR(S)
Thomas A. Hecht, Philip M. Roth, John H. Seinfeld
8 PERFORMING ORGANIZATION REPORT NO
R73-28
9 PERFORMING ORGANIZATION NAME AND ADDRESS
Systems Applications, Inc.
950 Northgate Drive
San Rafael, California 94903
10. PROGRAM ELEMENT NO
26AAD, Task 10
11 CQNTRACT/GRANT NO.
68-02-0580
12 SPONSORING AGENCY NAME AND ADDRESS
Environmental Protection Agency
Office of Research & Monitoring
National Environmental Research Center
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16 ABSTRACT
The development and evaluation of a kinetic mechanism, for use in air quality
simulation models to describe photochemical smog formation, is described. The
mechanism, which treats inorganic reactions in detail and organic reactions in
general terms, was formulated to achieve a balance between accuracy of prediction
and compactness of representation. The results of the evaluation of this
mechanism using n-butane/NO , propylene/NOx, and n-butane/propylene/NO smoq
chamber data are included.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b IDENTIFIERS/OPEN ENDED TERMS |c. COSATI Field/Group
Computer Modeling
Chemical Kinetics
Photochemistry
Atmospheric Chemistry
8 DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (ThisReport/
Unclassified
21. NO. OF PAGES
156
20 SECURITY CLASS (Thispage)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
156
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