EPA-650/4-74-040
NOVEMBER 1974
Environmental Monitoring Series
I
55
UJ
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EPA-650/4-74-040
MATHEMATICAL SIMULATION
OF SMOG CHAMBER
PHOTOCHEMICAL EXPERIMENTS
by
Thomas A. Hecht, Mei-Kao Liu, and David C. Whitney
Systems Applications, Inc. .
950 Norfhgate Drive
San Rafael, California 94903
Contract No. 68-02-0580
ROAP 2.1 AKC
Task 23
Program Element No. 1A1008
EPA Project Officer: MarcJaC. 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
November 1974
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This report has been reviewed by the Environmental Protection Agency
and approved for publication. Approval does not signify that the
contents necessarily reflect the views and policies of the Agency,
nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
11
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1i
CONTENTS
PREFACE v
ABSTRACT vi
ACKNOWLEDGMENT vii
LIST OF ILLUSTRATIONS viii
LIST OF TABLES xi
LIST OF ABBREVIATIONS xiii
I " INTRODUCTION 1
A. Investigating the Phenomenology of Smog Formation 1
B. Smog Chamber Experiments 2
C. Studies of Elementary Reactions 6
D. Kinetic Simulation 7
E. Mathematical Techniques Useful in Kinetic Simulation ... 8
PART 1THE PHENOMENOLOGY OF SMOG FORMATION 11
II DEVELOPMENT, ANALYSIS, AND APPLICATION OF THE KINETIC
MECHANISM 12
III EVALUATION OF THE GENERAL MECHANISM USING NAPCA DATA 15
A. Predictions for Propylene/N0x, n-Butane/NOx,
and Propylene/n-Butane/NO Experiments 16
X
1. Changes in the General Kinetic Mechanism 17
2. Results and Discussion 25
B. Simulation of a Multiparaffin/NO Smog Chamber
Experiment. 38
1. Choice of Rate Constants and Reaction Mechanism .... 40
2. Results and Discussion 41
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Ill EVALUATION OF THE GENERAL MECHANISM USING NAPCA DATA (Continued)
C. Simulation of a Multiolefin/NO Smog Chamber Experiment ... 46
1. Choice of Rate Constants for the Oxidant-Olefin
Reactions 53
2. Changes in the General Mechanism 53
3. Results and Discussion 60
IV SENSITIVITY AND UNCERTAINTY OF REACTIONS IN THE GENERAL
MECHANISM 69
A. The Mechanism Employed 70
B. Sensitivity Analysis 74
1. Criterion of Sensitivity 76
2. Procedure 78
. 3. Results 80
C. The Implications of Combined Sensitivity and Uncertainty
Data 82
1. Rate Constants That Should Be Determined with Great
Accuracy 82
2. Reactions That Can Possibly Be Eliminated From the
General Mechanism 85
D. Concluding Comments 86
V ANALYSIS OF UCR DATA
A. Characteristics of the Chamber System That Affect the
Chemical Kinetics 88
1. Light Intensity 88
2. Homogeneity of Reactants 93
3. Temperature 93
4. Water Concentration 93
5. Wall Effects 96
6. Analytical Methods and Dilution Due to Sampling 102
B. Simulation of UCR Propylene/NO Experiments 105
f\
PART 2METHODOLOGY 124
VI TECHNIQUES-FOR EVALUATING THF KINETIC MECHANISM 125
VII AN AUTOMATIC COMPUTER PROGRAM FOR EVALUATION OF KINETIC
MECHANISMS 126
A. Chamber Effects 127
B. Computational Aspects 129
C. Ease of Changing Reactions 130
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IV
VIII THE QUASI-STEADY-STATE ASSUMPTION OF CHEMICAL KINETICS 132
A. The Need for the Quasi-Steady-State Assumption 133
B. The Validity of the Quasi-Steady-State Assumption
When Applied to a Simple Kinetic Mechanism 134
1. Exact Solutions 136
2. Quasi-Steady-State Solutions ..... 137
3. Comparison of the Exact and the Quasi-Steady-State
Solutions 138
C. A General Theory on the Validity of the Quasi-Steady-State
Assumption 143
D. Some Numerical Experiments .Using the General Mechanism .... 149
E. Conclusions 151
IX TREATMENT OF COMPLEX MIXTURES OF ORGANIC REACTANTS IN THE
KINETIC MECHANISM 153
A-. Exact Solutions "'" 158
B. Approximate Solutions 162
PART 3OVERVIEW AND PROSPECT 170
X OVERVIEW AND PROSPECT 171
REFERENCES 174
EPA TECHNICAL REPORT DATA FORM 178
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PREFACE
As part of its program to clarify the roles of organic compounds
and oxides of nitrogen in the production of photochemical smog, the U.S.
Environmental Protection Agency (EPA) has supported and is continuing to
support the study of irradiation-induced air pollution in environmental
chambers and the determination of the rate constants and mechanisms of
elementary reactions thought to be important in smog formation. However,
experimental work cannot by itself lead to a complete understanding of
the smog formation process. Consequently, the EPA is sponsoring SAI's
work on the development of a chemical kinetic mechanism for photochemical
smog formation. The mechanism incorporates the experimentally measured
rate constants and is presently being tested in relation to data obtained
during smog chamber experiments. Ultimately, the mechanism should be
capable of predicting the kinetics of the chemical transformations that
take place in photochemical smog. Our initial efforts to formulate and
evaluate a kinetic mechanism for photochemical smog formation were
summarized in a detailed planning document (Seinfeld et al., 1973) and
in a 1973 final report (Hecht et al., 1973). In the present report, we
describe the results of our continued efforts to improve this kinetic
mechanism.
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VI
ABSTRACT
This report deals with the continued development and testing of a
general kinetic mechanism for photochemical smog formation. In line
with recent experimental measurements, several rate constant values were
updated, and simulations of several n-butane/NO , propylene/NO , and n-
f\ J\
butane/propylene/NO smog chamber experiments were repeated. The predictions
A
made vary in their agreement with experimental observations, but they
tend to be best at high ratios of initial hydrocarbons to NO . The
/\
mechanism also reproduced reasonably well the behavior of a complex
mixture of paraffins and NO , and of a mixture of six olefins and NO . A
X X
sensitivity analysis of the mechanism was carried out, and the results
were combined with uncertainty estimates of the rate constants to quantify
the importance of determining individual rate constants with greater
accuracy. Operating parameters of the University of California, Riverside,
(UCR) evacuable smog chamber were considered in detail; experimental
data from this chamber will soon be used to test the mechanism further.
Finally, the report discusses the validity of the steady-state approximation
in simulating smog chamber experiments and some techniques for mathematically
combining a number of similar organic species into general groupings.
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vii
ACKNOWLEDGMENT
We wish to express our appreciation to the individuals who contributed
to the computational aspects of this work. The sensitivity calculations
in Section II-B were carried out by John Overton of EPA; the other
computer runs used for the study were done by Gary Lundberg of SAI.
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V111
ILLUSTRATIONS
1 Results of Smog Chamber Simulation for Run EPA 306 26
2 Results of Smog Chamber Simulation for Run EPA 325 27
3 Results of Smog Chamber Simulation for Run EPA 329 27
4 Results of Smog Chamber Simulation for Run EPA 459 28
5 Results of Smog Chamber Simulation for Run EPA 307 29
6 Results of Smog Chamber Simulation for Run EPA 333 30
7 ' Results of Smog Chamber Simulation for Run EPA 348 31
8 Results of Smog Chamber Simulation for Run EPA 349 32
9 Results of Smog Chamber Simulation for Run EPA 352 33
10 Simulation of the Multiparaffin/N0x RunPredictions
for NO, N02, 03, and 2-Methyl-Pentane 43
11 Simulation of the Multiparaffin/NOx RunPredictions
for 2,2,4-Tri-Methyl-Pentane, n-Pentane, and Aldehyde 44
12 Simulation of the Multiparaffin/NOx RunPredictions
for Iso-Pentane, 2,4-Di-Methyl-Pentane, and PAN 45
13 Simulation of the Multiolefin/NOx Experiment Using
the Mechanism in Table 1--Predictions for NO, N02,
and 03 49
14 Simulation of the Multiolefin/NOx Experiment Using
the Mechanism in Table 1--Predictions for Aldehyde,
Cis-2-Butene, and Ethylene 50
15 Simulation of the Multiolefin/NOx Experiment Using
the Mechanism in Table 1--Predictions for PAN,
1-Butane, and 2-Methyl-2-Butene 51
16 Simulation of the Multiolefin/N0x Experiment Using
the Mechanism in Table 1--Predictions for 2-Methyl-
1-Butene and Propylene 52
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IX
17 Simulation of the Multiolefin/N0x Experiment Using
the Revised Mechanism (Table 8)--Predictions for
NO, N02, and 03 ........................ 64
18 Simulation of the Multiolefin/NOx Experiment Using
the Revised Mechanism (Table 8)--Predictions for
Formaldehyde, Aldehyde, Cis-2-Butene, and Ethyl ene ...... 65
19 Simulation of the Multiolefin/N0x Experiment Using
the Revised Mechanism (Table 8) Predictions for
PAN, 1-Butene, and 2-Methyl-2-Butane ............. 66
20 Simulation of the Multiolefin/NOx Experiment Using
the Revised Mechanism (Table 8) --Predictions for
2-Methyl-l-Butene and Propylene ................ 67
21 Base Case for the Sensitivity StudyRun EPA 329 ....... 75
22 Spatial Distribution of Light Within the Evacuable
Chamber Without a Reflector .................. 89
23 Water Concentration as a Function of Time for Run EC-11 ,
and Constant Value (Solid Line) Used for Simulating
This Experiment ........................ 94
24 Water Concentration as a Function of Time for Run EC-16,
and Constant Value (Solid Line) Used for Simulating
This Experiment ........................ 95
25 Simulation of Run EC-11 Using the Mechanism in Table 1--
Predictions for NO, N02, and PAN ............... 110
26 Simulation of Run EC-11 Using the Mechanism in Table 1--
Predictions for Olefin, Aldehyde, and 03 ........... Ill
27 Simulation of Run EC-12 Using the Mechanism in Table 1--
Predictions for NO, NOg, and PAN ............... 112
28 Simulation of Run EC-12 Using the Mechanism in Table 1--
Predictions for Olefin, Aldehyde, and^Os ........... 113
29 Simulation of Run EC-14 Using the Mechanism in Table 1--
Predictions for NO, N02, and PAN ............... 114
30 Simulation of Run EC-14 Using the Mechanism in Table 1--
Predictions for Olefin, Aldehyde, and 03 ........... 115
31 Simulation of Run EC-16 Using the Mechanism in Table 1
Predictions for NO, N02, and PAN ............... 116
32 Simulation of Run EC-16 Using the Mechanism in Table 1--
Predictions for Olefin, Aldehyde, and 03 ........... 117
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33 Simulation of Run EC-17 Using the Mechanism in Table 1~
Predictions for NO, N02, and PAN ............... 118
34 Simulation of Run EC-17 Using the Mechanism in Table 1--
Predictions for Olefin, Aldehyde, and 63 ........... 119
35 Simulation of Run EC-18 Using the Mechanism in Table 1--
Predictions for NO, N02, and PAN ............... 120
36 Simulation of Run EC-18 Using the Mechanism in Table 1
Predictions for Olefin, Aldehyde, and 03 ........... 121
37 Simulation of Run EC-21 Using the Mechanism in Table 1--
Predictions for Olefin, NO, N02, and Aldehyde ......... 122
38 Simulation of Run EC-21 Using the Mechanism in Table 1
Predictions for 03 and PAN .................. 123
39 Comparisons of the Exact and the QSSA Solutions for
Stable Species ........................ 138
40 Comparisons of the Exact and the QSSA Solutions for
the Reaction Intermediate ................... 140
41 The Rate Constant for HC + 0 ................. 167
42 The Rate Constant for HC + Os ................. 168
43 The Rate Constant for HC + OH ................. 169
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TABLES
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
A Lumped Kinetic Mechanism for Photochemical Smog
Formation
Validation Values of the Rate Constants and Their
Comparison with the Recommended Values of Other
Investigations
Initial Conditions Associated with Experimental
Chamber Data
Reactions That Can Be Eliminated from the General
. Mechanism Shown in Table 1
Values of T, H, and M Before and After Removal of the
Reactions in Table 4
Rate Constants for the 0 and OH Oxidation Reactions
Experimental Values for the Simulation of Oxidant-Olefin
Reactions
Revised General Mechanism Used To Simulate the Multiolefin/
NOx Experiment
The Kinetic Mechanism Used for the Sensitivity Analysis . . .
Sensitivity of the Reactions
Combined Sensitivity and Uncertainty of the Reactions ....
Reactions Participating in the Total Ozone Decay Process . . .
Physical and Chemical Parameters Measured
Initial Conditions for Experiments in the Propylene/
NOX Block
Error Resulting from the Use of the QSSA
Percentage Errors Incurred by Using the Quasi -Steady-State
Assumption
Percentage Errors Incurred by Using the Photostationary
State Assumption
19
22
25
37
38
42
48
61
71
81
84
99
103
109
141
150
152
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xii
18 Comparison of Hydrocarbon Consumption for Different
Lumping Schemes 161
19 Comparison of Ozone Production for Different Lumping
Schemes 161
20 Comparison of Hydrocarbon Consumption in the Multiparaffin
Run 163
21 Comparison of Ozone Production in the Multiparaffin Run . . . 163
22 Comparison of Hydrocarbon Consumption in the Multiolefin
Run 164
23 Comparison of Ozone Production in the Multiolefin Run .... 164
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xiii
ABBREVIATIONS
cc Cubic centimeters
EC Evacuable chamber
EPA Environmental Protection Agency
GC Gas chromatograph
NAPCA National Air Pollution Control Administration
NBS National Bureau of Standards
ppb Parts per billion
pphm Parts per hundred million
ppm Parts per million
SAI Systems Applications, Incorporated
SAPRC Statewide Air Pollution Research Center
SM Sensitivity measure
UCR University of California at Riverside
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I INTRODUCTION
In contrast to the two earlier documents describing a kinetic
mechanism for photochemical smog formation mentioned previously (Seinfeld
et al., 1973; Hecht et al., 1973), this report distinguishes between the
analysis of the phenomenology of the chemical process and the mathematical
and computational methodology used to carry out the simulations. This
chapter discussed the concepts of phenomenology and methodology as they
relate in general to the work described in this report. In addition,
this chapter briefly reviews the aspects of experimental investigations
of the smog formation process that are relevant to kinetic modeling.
Special consideration is given to the manner in which kinetic simulation
with a chemical mechanism complements smog chamber experiments and
reaction kinetics studies in investigations of the chemistry of smog
formation. We conclude this chapter with a discussion of the role of
kinetic simulation in understanding the nature of photochemical smog
formation and a summary of the uses of mathematical techniques for
kinetic simulation that have been developed during the reported work.
A. INVESTIGATING THE PHENOMENOLOGY OF SMOG FORMATION
In a system as complex as the atmosphere, isolation and character-
ization of the chemical processes that occur are virtually impossible.
Thus, two fundamental approaches have been'devised for controlled study
of the chemistry of smog formation: irradiation of known concentrations
of pollutants in a large reactor (smog chamber) and determination of the
rates and mechanisms of elementary reactions thought to occur in polluted
air. Data obtained during a smog chamber experiment include the concen-
trations of a limited number of reactants (N0?, NO, organics) and products
(NO-, Oo> PAN) with time. However, one is unable to gain insight into the
details of the chemical transformations taking place; only the macroscopic
effects of the overall chemical process are observed. On the other hand,
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detailed information concerning the rate and course of a single
reaction, such as that obtained in a reaction kinetics study,
reveals little concerning the nature of the overall smog formation
process. Indeed, one has difficulty knowing whether all the important
reactions have been identified.
Kinetic simulation provides a means of comparing the results of
these two experimental approaches for investigating the chemistry of
smog formation. Studies of several elementary reactions can be drawn
together, yielding a chemical mechanism. The mathematical rate equations
describing the mechanism can then be solved numerically to obtain predictions
of the concentrations of the reactants and products with time. In
principle, therefore, kinetic simulation takes the results of elementary
reaction studies as input data and produces results of a form identical
to the data obtained in smog chamber experiments as output. By comparing
the predictions of the mechanism with actual chamber data, one is able
to determine the degree of agreement between the two experimental approaches.
In practice, the comparison process is somewhat more complicated
than that just described. For example, it has been shown that the surfaces
of smog chambers can and do affect the overall rate of the chemical
transformations. This and other systematic effects must be included in
the kinetic simulation. Uncertainties in the values of experimentally
measured rate constants are equally perplexing. These can range from 20
per cent in the most favorable case to a factor of 5 or greater. The
major sources of uncertainty in both types of experimental data are
addressed here in detail, and the value and role of kinetic simulation
for understanding the chemistry of smog formation are examined in light
of these difficulties.
B. SMOG CHAMBER EXPERIMENTS
A smog chamber experiment is generally conducted in the following
manner. A reactor (ranging in size from a few liters to thousands
of liters) is charged with a known number of moles of organic compound(s)
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and NO in air. After the reactants are homogeneously distributed
^
throughout the chamber, the system is irradiated. During the irradiation,
the concentrations of various reactants and products are determined at
several points in time.
Replicate runs carried out in a particular environmental chamber
are generally reproducible to within a difference of 10 percent. When
the same experiment is carried out in different chambers, however, the
agreement between the observed concentration-time profiles is erratic.
The reasons for these "anomalies" have been discussed at some length by
Seinfeld et al. (1973), but the major causes are reviewed briefly here.
Some of the discrepancies can be accounted for simply in terms of
operating characteristics of the various chambers. For example, key
radical chain initiating reactions, such as the dissociation of N0? ,
are photolytic. Thus, depending on the magnitude of variations between
chambers, differences in the intensity and the spectral and spatial
distribution of the light can have a significant effect on the rate of
smog formation. The majority of reactions occurring in smog, however,
are thermal. Most of these are known to have small positive activation
energies (0 to 5 kcal/mole), although a few have small negative activation
barriers (0 to -2 kcal/mole). Smog chamber experiments are generally
.carried out at ambient temperatures. But, depending upon the placement of
the lights (outside or inside the chamber) and the adequacy of the air
conditioning available, temperatures within a chamber can rise to 50 C
during a six-hour irradiation. The variation of the rate of smog formation
with temperature has not yet been systematically investigated in chambers.
However, it is unlikely that a temperature rise of 25°C would have a
negligible effect on the kinetics. Fortunately, while variations in
light intensity and temperature can affect the observed rate of the
chemical transformations, these sources of uncertainty can largely be
eliminated through careful measurement, control, and chamber design
procedures.
Interactions of the walls or material on the walls with the reactants
and products in the gas phase are less easily quantified causes of dis-
agreement between chambers. Gay and Bufalini (1971) have shown that
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nitric acid accumulates on the walls of a small reactor when ppm levels
of organic and NO are irradiated. As a result, it is not possible to
X
account for all of the "nitrogen" introduced into the chamber in terms
of nitrogen-containing products measured in the gas phase at the end of
an experiment. Ozone, on the other hand, is known to decompose directly on
the walls. The loss rate varies from chamber to chamber, but the destruction
of 20 percent of an initial 0- charge over a six-hour irradiation of 0~
in air is not uncommon. The observed rate probably depends upon the
surface-to-volume ratio and the type of wall materials used in the
reactor (Jaffe, 1972).
In their study of the thermal oxidation of NO, Bufalini et al.
(1972) have shown that if NO and air are photolyzed in an unpurified
chamber, NO will be oxidized to N0? at a faster rate than one would
predict based on the thermal air oxidation reaction alone:
2NO + 02 * 2N02 .
They have suggested that this is due in part to the liberation of organic
contaminants from the walls of the reactor. If this occurs, the organics
then participate in a chain process resulting in the additional oxidation
of NO above that due to the thermal reaction. In a related experiment,
Bufalini et al. have also shown that if air containing a reactive organic
compound such as biacetyl is irradiated in a dirty chamber, small concen-
trations of GO will form. Presumably, this 03 forms as a result of a series of
cf reactions involving the organic compound and flO liberated from the
X
walls.
A final class of chamber uncertainties are those associated with
the analytical instrumentation. Errors clue to inaccurate calibration of
the instruments and chemical interferences in the measurements (lack of
specificity) are well known and need not be discussed here. A somewhat
more subtle source of uncertainty is attributable to the large volume of
sample gas that must be withdrawn from the chamber to obtain accurate
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measurements, thus leading to a continuous reduction in the concentrations
of both the reactants and the products over the course of an experiment.
For example, the analytical instruments commonly used for the measurement
of NO/NCL, 0.,, organics, PAN, and CO require samples to be withdrawn at
£. O
an average rate of about 1.5 liters/minute. Thus, during a six-hour
experiment, about 10 percent of the original molar charge of reactants
would, for example, be lost from a 5000 liter reactor. The percentage
of charge lost for a particular chamber depends on the following:
> The volume of the chamber
> The type and number of analyzers employed
> The periodicity of the measurements.
This so-called dilution effect (the volume withdrawn is normally replaced
by an equal volume of "clean" air to maintain a constant pressure in the
reactor) can be taken into account easily in the analysis of the chamber
results if the sampling rates and chamber volume are known. The magnitude
of the effect, however, demonstrates the need for the development and
application of in situ measurement methods for chamber studies.
Sources of uncertainties in the interpretation of smog chamber
datawhether due to imprecise measurements of light intensity, lack of
control over temperature, wall reactions, wall contaminants, or other
factorsare generally recognized by chamber scientists. In many cases,
the data quality can be strengihened simply by keeping careful records
of the operating conditions of the chamber, by calibrating instruments
with increasing frequency, and by modifying the system design. Unfortunately,
wall contamination problems and heterogeneous reactions remain very
difficult to characterize. In current programs, the rates of a few
particu1 ar effects attributable to the walls, such as ozone decomposition,
are determined periodically. A detailed chamber characterization study
is presently being carried out by Jaffe at Lockheed under contracts with
.the Coordinating Research Council and EPA. Hopefully, that work will
lead to a greater understanding of the magnitude and nature of surface
effects.
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C. STUDIES OF ELEMENTARY REACTIONS
The primary criterion used to decide whether a reaction involving
reactants present in photochemical smog should be included in a chemical
mechanism is the rate of the reaction. The speed at which an elementary
reaction proceeds is, of course, proportional to the product of the
concentrations of the reactants, and the proportionality factor is
usually called the "rate constant" of the reaction. In actual fact,
many of the rate constants of the nonphotolytic reactions in smog vary
with temperature, pressure, or both and with the concentrations of other
gases present. Thus, one must take care to note the conditions under
which a rate constant is measured. If necessary, suitable correction of
the value for the desired temperature and pressure must be made before
the rate constant is used for a kinetic simulation.
Unfortunately, the determination of many gas phase reaction rate
constants is extremely difficult because measurements must frequently be
carried out near the detection limits of the analytical apparatus. Thus,
even though investigators are generally able to achieve a high level of
precision in their measurements, the study of the same reaction in other
laboratories or by different experimental techniques often leads to very
different values of the rate constant, as shown later in this report.
To be sure, the complete kinetic analysis of a reaction entails
more than the measurement of the rate constant; the mechanism and
products of the elementary reaction must be determined as well. Certainly,
most of the reactions considered in this report are well characterized
in this regard, but there are some significant exceptions. For example,
the detailed fate of the various intermediates of the OH-propylene
reaction is still unclear. (Little is known about the behavior of the
OH-propylene adduct; for present purposes, the species has been assumed
to react in the same fashion as an alky! radical and has been included
in the R0? class.) The OH oxidation is the most significant chain
transfer step involving organics during a propylene-NO smog chamber
X
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experiment. Thus, the uncertainty as to the role of the adduct in smog
formation is particularly significant. Another weak link in the mechanism
involves the lack of knowledge of the products of the Og-olefin reaction.
These two deficiencies, however, are well recognized and are being
addressed in current research programs.
D. KINETIC SIMULATION
Smog chamber data constitute a standard against which the accuracy
of predictions of a kinetic mechanism can be measured. But because of wall
effects and other operating characteristics of the system, the observed
time-varying chemical distribution in the chamber cannot be accounted
for entirely in terms of the reactions occurring in the gas phase.
Thus, the use of chamber results as a standard or reference for judging
the accuracy of a mechanism must be carefully qualified.
As a collection of individual elementary reactions, a chemical
mechanism represents the chemistry that one would presumably observe in
an infinitely large reactor that is irradiated by a uniform source of
light and is maintained at constant temperature. Of course, a typical
smog chamber does not meet all of these criteria. Therefore, before
predictions and experimental results can be compared, terms must be
added to the mechanism to represent operating characteristics of each
particular smog chamber. The most important corrections involve the
following:
> Accounting for the dilution of rcactants and products
due to sampling.
> Specifying the rate of decomposition of 0^ and the
formation of HNO, on the walls.
O
> Expressing rate constants in the temperature-dependent
(exponential) format so that the effects of temperature
variations in a chamber on the rate of reactions are
properly represented.
In essence, then, the chemical kinetic mechanism actually is an integral
component of a mathematica1 model that simulates a smog chamber system.
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8
A major goal of the chemical and mathematical investigations of
smog formation is to gain a level of understanding sufficient to allow
prediction of the atmospheric photochemical process. As has been noted,
however, there are considerable uncertainties with which one must contend,
even in the prediction of the kinetics of a propylene-NO experiment.
A
Inaccuracies in measurements and unknown effects of walls and wall
contaminants on the gas phase chemistry create sources of uncertainty in
the chamber data. Similarly, large error bounds on the values of many
reaction rate constants and unknown reaction mechanisms provide a dis-
comforting number of degrees of freedom with which to "tune" the pre-
dictions of the model into agreement with the chamber data.
E. MATHEMATICAL TECHNIQUES USEFUL IN KINETIC SIMULATION
To obtain predictions of concentration as a function of time, for
comparison with smog chamber data, one must fulfill the following
requirements:
> The initial state of the system must be specified
(e.g., concentrations of all chemical species present,
temperature, and irradiation intensity and spectral
distribution).
> A rate constant value must be assigned to each reaction
in the mechanism.
> The chemical rate equations for each reactant, intermediate,
and product must be derived.
> The resultant differential equations must be solved.
The differential rate equations can be derived manually from the
mechanism, but the process is cumbersome. In this report, we describe a
computer program (MODKIN), prepared during this study, that automatically
formulates the rate equations that mathematically represent a chemical
mechanism. Reactions are submitted to this program in standard notation,
e.g.,
aA + bB -» cC + dD
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Since the addition (or deletion) of a single reaction of this ftrm
results in changes to four rate equations, the convenience of MODKIN
over manual coding is readily apparent.
Because the characteristic time scales of formation of the individual
reactants and intermediates in the mechanism usually vary greatly, the
*
resultant set of coupled differential equations are often "stiff."
When this is the case, small integration time steps are required to
obtain accurate solutions of the equations for the most rapidly varying
species. Recently, numerical integration routines have been developed
that automatically increase the integration time step as the stiffness
of the system of equations decreases, thereby reducing the computing
time required for a complete smog chamber simulation run. We have incorporated
such an algorithm, that of Gear (1971), in MODKIN.
Other mathematical techniques can also result in computer time or
storage savings. For example, by invoking the steady-state approximation
for cases in which it is valid, the pertinent coupled differential rate
equations can be replaced with algebraic equations. Such a change in
representation usually results in a reduction in the computing time
required for a simulation. However, the magnitude of the savings, if
any, depends on the degree to which the stiffness of the system of
differential equations is relieved and the number of iterations required
to solve the algebraic equations.
Computational time can also be shortened by employing "lumping"
techniques. Consider the simulation of a niultiorganic/NO /air experiment.
For this system to be represented exactly., each organic species would
have to bo assigned its individual rate equation. If the number of
organic species were large, a significant amount of computer core and time
would be required to obtain predictions of the behavior of the system.
Although computer storage needs are not of direct concern in the
*
A set of differential equations are called "stiff" when the magni-
tudes of the eigenvalues of the system differ by several orders
of magnitude.
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10
development of a chemical mechanism, the mechanism will ultimately be
applied to the atmosphere. Exact representation of the hundreds of
different reactive organic species at every "grid point" simulated by an
airshed model would tax even the largest computers. Consequently, a
means of combining or lumping a number of organic species that react in
similar ways into a single, fictitious species is needed. We discuss
one possible lumping scheme in this report.
-------
11
PART 1
THE PHENOMENOLOGY OF SMOG FORMATION
-------
12
II DEVELOPMENT, ANALYSIS, AND APPLICATION
OF THE KINETIC MECHANISM
A general kinetic mechanism for smog formation has several possible
uses. Such a model might be used to calculate the reactivity of individ-
ual organic compounds in terms of their ability to "form" smog. Or, im-
bedded in an airshed dispersion model, the chemical mechanism might be
instrumental in evaluating alternative emission control strategies and
in assessing the impact of planned urban growth. These uses, however,
are contingent upon the accuracy of the mechanism. Thus, the development
of a substantially complete and re-liable model is of considerable importance.
The qualitative natur^ of the smog formation process has been under-
stood for a number of years (Leighton, 1961). However, prediction of the
chemical process depends on detailed knowledge of both the pathways and
the rate constants of the reactions in the mechanism. During the past
decade, great progress has been made in measuring the rate constants of ga?
phase reactions involving short-lived or transient species. The rates
of many of the reactions thought to occur in smog have been measured for
the first time only recently. Even now, several heretofore speculative
reactions are being scrutinized, and the values of other rate constants
are being confirmed (e.g., H02 + NO -> OH + NO,,).
In such a dynamic scientific environment, it would be presumptuous
to suggest that any given set of reactions and rate constants is the
chemical mechanism for smog formation. Even this report reflects a con-
tinuous updating of the mechanism as new knowledge of reaction kinetics
become available; several similar forms of the general mechanism appear
in conjunction with the different tasks of the project. Only one formu-
lation of the kinetic mechanism (presented later in Table 1) has been
tested over an extensive r^nge of initial conditions and reactant ratios.
Further evolutionary changes in this mechanism, in the form of a more
-------
13
detailed treatment of aldehydes, 0_-olefin reaction mechanisms, and
reactions of PAN, were made when we simulated the behavior of a multi-
olefin-NO -air smog chamber experiment (these are presented later in
/\
Table 8). Similarly, before carrying out the sensitivity study reported
in Chapter IV, we modified the mechanism in Table 1 to augment the agree-
ment between the predictions and the data for the particular smog chamber
experiment that was simulated. The modified scheme is presented later
in Table 9. Because these latter sets of reactions are ad hoc formula-
tions that have not yet been tested extensively, we recommend, for the
time being, that prospective users of these general mechanisms select the
form in Table 1 for their applications.
Although the mechanism is presented in three forms, most of these
changes were made to replace overly general representations with more
detailed descriptions and to substitute sound experimental measurements--
as they became availablefor speculative estimates.
The development of the mechanism during this project followed two
complementary paths. The first approach involved testing the quality of
predictions in relation to smog chamber data. By adding, modifying, or
deleting reactions and then varying the values of rate constants within
their bounds of uncertainty, we sought to increase the accuracy of pre-
diction of the mechanism over a wide range of organic compound-to-NO
X
ratios. For these runs, we Devaluated many of the NAPCA propylene/NO ,
X
and propylene/n-butane/NO experiments that; we had reported previously
X
(Hecht et al. , 1973). In addition to those experiments, however, we
examined two multiorganic-NO smog chamber experiments. One of these
was conducted with five different paraffins present initially; the other
contained six different olcfins in the initial charge.* The results of
those chamber simulations are discussed in Chapter III.
* The niuiltiolcfin/NOw experiment was tho last set of data to be modeled
i\
during tho contract year. In attempting to simulate this run, we found
. it desirable to introduce several changes into the kinetic mechanism
to reduce discrepancies between predictions and observed concentration
time data. Though tested against only one set of experimental data,
the resulting mechanism shows promise and will serve as the springboard
for our analysis of UCR propylene-fiO experiments next year.
A
-------
14
The second approach focused on quantifying the influence of uncer-
tainties in the values of individual reaction rate constants on the
predictions of the mechanism. We first carried out a detailed sensitivity
analysis of the mechanism, calculating the change in the predictions of
the model with the change in each rate constant. The sensitivity values (S)
were then combined with uncertainty estimates (U) for each rate constant
to create a new index (S*U). The combined index reflects the importance
of obtaining more accurate rate constant measurements as a means of re-
ducing the uncertainties in the predictions of the model. In addition to
identifying reaction rate constants for which accurate measurements are
particularly important, we were able to point out insensitive reactions
that can possibly be deleted from the mechanism without significant loss
of accuracy. This effort is described in Chapter IV.
In Chapter V, we describe our work using data from the new UCR evacu-
able smog chamber. The exercises carried out thus far deal primarily with
our attempts to model the chamber characteristics properly, but they in-
clude simulations of the first seven UCR propylene/NO photochemistry
/\
experiments using the mechanism in Table 1.
Unfortunately, the photochemistry data arrived too late in the pro-
ject to permit us to begin a formal mechanism development and evaluation
program. These propyl^ne experiments, along with many more runs involving
n-butane and toluene that are yet to be carried out, will provide the
principal chamber data base for our model refinement work next year.
-------
15
III EVALUATION OF THE GENERAL MECHANISM
USING NAPCA DATA
During the past decade, the National Air Pollution Control Administra-
tion* (NAPCA) conducted an extensive experimental program to investigate
the rate of formation of secondary air pollutants (e.g., N0?, CL, PAN,
aldehydes) in an irradiated system initially containing organic reactants,
NO , and air. We used a number of these experiments involving the irradia-
s\
tion of propylene, n-butane, or both, in NO and air to test the general
X
kinetic mechanism in its initial configuration (Hecht et al., 1973). Since
our 1973 report discussed the experimental techniques and apparatus used,
the sources of experimental uncertainty, and the adequacy of these parti-
cular experiments as a data base for model evaluation, our comments in this
chapter focus chiefly on the continued development and testing of the
general mechanism with reference to the NAPCA chamber data.
As noted earlier, one of the principal goals of this project was to
refine the general mechanism so as to achieve greater accuracy and con-
fidence in prediction. Toward this end, we have kept abreast of current
kinetic and mechanistic studies of relevant elementary reactions, incor-
porating the results of these studies into the mechanism as soon as possible
Our progress in modeling photochemical smog has been, and will continue to
be, limited principally by the rate at which knowledge of uncertain rate
constants and elernontory reaction mechanisms is established experimentally,
A total of five different combinations of organic compounds were
represented in the eleven different NAPCA organic-NO -air irradiation
X
experiments that we used to evaluate the mechanism. The data base was
distributed as follows:
* Now part of EPA.
-------
16
System No. of Runs
propylene-NO 3
/\
n-butane-NO 1
x '
propylene/n-butane-NO 5
J\
n-pentane/iso-pentane/2-Me-pentane/
2,4-di-Me-pentane/2,2,4-tri -Me-pentane-NO 1
/v
ethylene/propylene/l-butene/cis-2-butene/
2-Me-l-butene/2-Me-2-butene-NO 1
J\
As previously noted, the propylene, n-butane, and propylene-n-butane
experiments were first considered during last year's mechanism development
program. Our interest in the multiolefin/NO and multiparaffin/NO exper-
A X
iments was twofold. First, these experiments provided an opportunity to
explore the generality of the mechanism, particularly with respect to re-
actions of general classes of organic molecules and free radicals. Second,
these experiments were well suited for testing our mathematical technique
for lumping (or combining) individual organic compounds into general classes
In this chapter, we restrict our comments to a discussion of changes
introduced into the general mechanism during the simulation of the NAPCA
experiments. The details and validity of the lumping techniques are con-
si dcjred in Chapter IX.
A. PREDTC1"TONS FOR PROPYLENE/NO , n-BUTANE/NO , AND PRPPYI.FNE/n-BUTANE/
NO EXPERIMENTS X X
X
Shortly after completion of the previous report, we learned that
three of the rate constants in the mechanism had been measured or estimated
to be significantly lower than the values we were usiny. These reactions
and their associated rate constants are tabulated as follows:
-------
17
New Value Old Value
Reaction (ppm" min ) (ppm~ min" )
k7
03 + N02 * N03 + 02 0.046 (Ghormley et al., 1973) 0.11
NO + HNO., -I2 N09 + HN09 2.5xlO"4 (Jaffee and 10.0
6 * * Ford, 1967)
HN02 + HN03 I3 2N02 + H20 0.2 (Westberg, 1973) 5.0
Two of the new rate constants, k-, and k,2, were of particular concern to us
because we had recently determined that these reactions influenced the pre-
dictions of the mechanism. Reaction 13 was unimportant, however, even when
the substantially higher "old" rate constant value was used in the simulations.
Decreasing k7 to its new value resulted in a 15 percent increase in the
magnitude of the N0? peak and an 18 percent reduction in the time before
the N0? peak was reached. Finally, a simulation of the experiment with all
three rate constants at -Their revised values resulted in predictions of un-
acceptably low peak N0? and 0^ levels and an unsatisfactorily premature time
before the N0? peak was reached when compared with the experimental data.
The general mechanism, as presented in the previous report, had been
"tuned" into good agreement with experimental data through the adjustment
of uncertain rate constants. The deterioration in accuracy of prediction
caused by the introduction of the new values of the three rate constants,
however, forced a serious reconsideration of the rate constants and reactions
in the kinetic mechanisn.
1. Chances in the General Kinetic Mechanise
In addition to the three rate constant modifications discussed above,
we altered three other rate constants and selected new products for two
other reactions.
-------
18
Reactions 38 and 39, formerly chain termination reactions
H02 + R02 + ROOM + 02
and
R02 + R02 -> ROOR + 02,
were modified to produce 01! and RO and two RO radicals, respectively,
rather than peroxides. This is in line with current thinking regarding
peroxy-radical/peroxy-radical reactions involving R09.
In addition to k-,, k-,9, and k^, the following rate constants were
revised:
Reaction New Value Old Value
03 + NO 3 N02 + 02 20.8 ppnf1 min"1 23 ppm"1 min"1
NO + N02 + H20 ^ 2HN02 2.1xlO"6 ppm"2 min ] 4.3xlO"6 ppm"2 niir
ALD + hv 29 0R09 + (2-B)H02 2.bxlO"3 min"1 2.0xlO"3 min"1
The rate of Reaction 3 was revised to the recently measured value of Ghoinfiey
et al. (1973). The rate constants for the heterogeneous formation of nitrous
acid and Lhe photcdissociation of aldehydes v,
-------
Table 1
A LUMPED KINETIC MECHANISM FOR PHOTOCHEMICAL SMOG FORMATION
19
N02 + hv + NO -f 0
+ 0 + M + 0 + M
NO
The N02-NO-03 Cycle
0 + NO + M -» N02 + M
0 + N02 + NO + 02
0 + N02 + M -»- N03 + M
°3 * N02 "*" N03 + °2
NO + NO + 2NO
i o
N2°5
^Or -i- H,0 -» 2H
2 5 c
N°2 + N03
Important Reactions of 0
>.*
with Inorganic Species
The Chemistry of
NoOr, and
NO + IlKO.
HN02
HN02 + HN03 -* H20 !- 2NC
Rear, 1.1 or>.s of HNOo with
Inorganic Species
15
16
2HN0
NO
HN02 + hv -» OH + NO
H20 \ Chemistry of HN02
-------
20
Table 1 (Continued)
OH + NO,
OH + NO + M
17
18
J9
HNO-
HN02 + M
OH + CO + (02) - C0£ + H02
.Important Reactions of
H with Inorganic Species
H02 + NO » OH + N02
hv f 20H
> Oxidation of NO by H02
Photolysis of
22
HC] + 0 -»
23
HC, + 07 *
1 3
HC1 + OH "
25
HC2 -f- 0 +
HC2 4- OH *
27
I!C340 +
ROO +
RCOO J
6
ROO +
ROO +
ROO +
ROO 4
aRCOC
0
^ RO H
HC4
OH
H2°
OH
) + (l-a)HO
t- HC4
20
HC3 + OH -» ROO -i- Hj>0
HCXl + hv -* $ROO + (2-3)HO,
*? c.
30
HC, + OH + BRCOO+ (l-B)f!09+ H90
4 ^ ^
0
Organic Oxidation Reactions
HC1 = Olefins
He.? = Arornatics
HC3 = Paraffins
HC = Aldehydes
-------
Table 1 (Concluded)
31
ROO + NO + RO + N02
RCOO + NO +(0?) " ROO + N0£ + C02
RCOO
ii
0
RO
RO + N02
33
3,
36
2
RCOONO
ii
0
HO 2
RONO,
, Reactions of Organic
)Free Radicals with NO,
M02, and 02
RO + NO -»- RONO
H02 + H02
37
38
H02 -;- ROO -* RO + on + o2
39
2ROO -> 2RO + 02
Other Peroxy Radical
Reactions
-------
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25
2. Results and Discussion
The results of nine smog chamber simulations are displayed graphically
in Figures 1 through 9. In all figures in this report, the experimental
data are represented by symbols, and the simulated results, by solid lines.
Except for the revisions in the mechanism and rate constants already noted,
these runs were carried out in the manner, and under the assumptions, de-
scribed in Chapter V of the previous report. The initial conditions asso-
ciated with the experimental chamber data are listed in Table 3.
Table 3
INITIAL CONDITIONS ASSOCIATED WITH
EXPERIMENTAL CHAMBER DATA
EPA Run
306 i-
325
329
459
307
333
348
3^9
352
(N02)0*
0.03
0.04
0.06
0.06
0.05
0.08
0.08
0.08
0.07
(NO)Q*
0.30
0.32
0.26
1.14
1.23
1.25
1.23
0.31
0.27
(n-Butane) *
1.60
3.06
3.41
3.39
3.25
3.29
(PropyleneK*
0.45
0.24
0.78
0.36
0.23
0.44
0.44
0.26
* Initial concentrations in units of ppm.
t 0.12 ppir, of aldehyde also present initially.
a. Analysis of Chamber Simulation Results
It is difficult to draw broad, general conclusions about the adequacy
and accuracy of the kinetic mechanism. Although many of the predicted
concentration-time profiles match the experimental data very well, other
profiles show poor agreement. Some of the discrepancies may be due to
-------
26
EPA 306
N-BUTANE
NO
N02
03
> ~_. ] ._ I _!
100 200 300
TIME (MINUTES)
FIGURE 1. RESULTS OF SMOG CHAMBER SIMULATION
FOR RUN EPA 306
400
-------
0.60
27
0-0.45
Q_
O
<0.30
h-
Z
LJ
O
O 0.15
O
0,
EPA 325
* PROPYLENE
a NO
°N02
* PAN
O
O
0 100 200 300
TIME (MINUTES)
FIGUR-E 2. RESULTS OF SMOG CHAMBER SIMULATION
FOR RUN EPA 325
400
0.45
EPA 329
* PROPYLENE
a NO
o N02
PAN
O
O
O
O
0
100 200 300
TIME (MINUTES)
FIGURE 3. RESULTS OF SMOG CHAMBER SIMULATION
FOR RUN EPA 329
400
-------
28
EPA 459
* PROPYLENE
0 RAN
D NO
o N02
o 03
0
0
200 300
TIME (MINUTES)
400
FIGURE 4. RESULTS OF SMOG CHAMBER SIMULATION FOR RUM EPA 459
-------
3.50
3.00
2.50
Q_
CL
g 2-°°
h-
o:
u '-50
o
O
O
1.00
0.50
EPA 307
* N-BUTANE
* PROPYLENE
a NO
o N02
o 03
o o
0 100 200
TIME (MINUTES)
FIGURE 5. RESULTS OF SMOG CHAMBER SIMULATION FOR RUN EPA 307
400
-------
30
3.50
3.00
2.50
Q_
0_
O 2.00
o:
h-
Ld 1.50
O
O
O
i.oo -
0.50
°0 "
EPA 333
N-BUTANE
PROPYLENE
NO
N02
03
_. J__.
100
T~»- __
20^0 ^" 300 400
TIME (MINUTES)
FIGURE 6. RESULTS OF SMOG CHAMBER SIMULATION FOR RUN EPA 333
-------
31
3.50
EPA 348
N-BUTAN'E
PROPYLENE
NO
N02
400
TIME (MINUTES)
FIGURE 7. RESULTS OF SMOG CHAMBER-SIMULATION FOR RUN EPA 348
-------
32
3.50
3.00
2.50
Q_
Q_
§2.00
cr
g°-75
o
O
O
0.50
0.25
0.
>D
EPA 349
N-BUTANE
PROPYLENE
NO
N02
s s
O
0
"" lOO" ~J200 ~l300
TIME (MINUTES)
400
FIGURE 8. RESULTS OF SMOG CHAMBER SIMULATION FOR RUN EPA 349
-------
33
3.50
3.00
2.50
Q_
Q_
O
(T
h-
^
LJ
O
O
2.00
0.80
0.60
0.40
0.20
EPA 352
* N-BUTANE
* PROPYLENE
a NO
o N02
o
o o
o
o
200
TIME (MINUTES)
300
400
FIGURE 9. RESULTS OF SMOG CHAMBER SIMULATION FOR RUN EPA 352
-------
34
inaccuracies or interferences in the chemical measurements or to incomplete
characterization of the chamber operating conditions (e.g., light intensity).
We considered these possibilities in some detail in the previous report and
shall not, therefore, discuss them here.*
Complete omission or inaccurate specification of products of key
reactions, along with inaccuracies and uncertainties in the values of many
rate constants, are probably the causes of a major portion of the disagree-
ment between predictions and experimental data. Resolution of these types
of uncertainties is a slow and painstaking process. In the absence of ex-
perimental measurements, provisional rate constant values can be estimated
and elementary reactions and reaction mechanisms can be hypothesized on
the basis of thermochemical principles (Benson, 1968). However, because
of the large uncertainty associated with most estimates, we depend mainly
on experimental studies to justify the changes introduced into the mechanism.
Analyzing the predicted coricentration-versus-time profiles for organics,
NO
. , 0.3, and PAN, as shown in Figures 1 through 9, we can make the following
A O
observations:
> The rates of oxidation of n-butane and propylene predicted
by the mechanism match the data uniformly well over the full
range of initial concentrations studied.
> The predicted rate of oxidation of NO and the time to the
N0? maximum agree well with the data. At initial concen-
trations of NO greater than 1 ppm, however, the rates of
X
* EPA's decision to support a new program of chamber experiments (see
Chapter V) was based in part on the poor characterization of many chamber
operating parameters in previous studies. Although early experiments
generally provided answers to many of the qualitative and semi quantitative
questions about the chemistry of smog formation, they were not performed
with model evaluation purposes in mind and are not, therefore, ideally
suited for use in such wor*.
-------
35
03 accumulation and NCL oxidation are predicted to be more
rapid than those observed (e.g., Figures 5 through 7). Under
these conditions, the predicted rate of accumulation of
N0? was lower, and the magnitude of the N0? maximum was
smaller, than the corresponding experimental values. Con-
ceivably, interferences by HNCL and HNCL in the NCL measure-
ments could have resulted in artificially high experimental
values for NCL. And as we have already noted, important
reactions may be missing from the mechanism, or rate constants
may be in error. Decreases in k-,-, and k-,? (heterogeneous and
homogeneous formation of HNOo) would slow the consumption of
NCL after the NCL peak, as would the introduction of other
reactions that consume OH (a reactant in Reaction 17)--or
genitors of OH--after the NCL peak. Another possible expla-
nation for the discrepancies is that reactions involving
nitrogen-containing products (such as HNCL and PAN) that lead
to NCL formation might be occurring. We considered one reaction
of this type, the reaction of NO + HN03 (k-jg). but it is too
slow to be important in the kinetics. Possible reactions of
PAN are discussed in Section III-C. As of this time, however,
it is not possible to pinpoint specific errorswhether they
involve experimental data, reactions, or rate constantsthat
lead to inaccurate predictions under conditions of high ini-
tial NO .
A
CL reached an asymptotic level in only five of the nine
experiments (Figures 1, 2, 3, 8, and 9). The predicted maxima
were somewhat lover than the measured values in each case, but
the technique used to determine 0- suffered from interferences,
as described in the previous report. In the four experiments
in which more thon 0.5 ppm NO was present initially, the 0~
concentration did not reach a plateau during the irradiation.
In most of those simulations, the predicted onset of 0, accu-
mulation was in good agreement with the data.
-------
36'
> Measurements of PAN were made in only three of the experiments
(see Figures 2 through 4). For the first two of these runs,
the predicted PAN concentrations are in good agreement with
the data. For Run 459 (Figure 4), however, the predicted
onset of PAN formation occurred too early and the levels
reached were too high compared with the data. We discuss
possible causes of high PAN predictions in Section III-C,
where we consider a reaction that may be important in con-
suming PAN.
b. Elimination of Insensitive Reactions from the General Mechanism
We have stated several times in this section that certain reactions
are insensitive and that varying particular rate constants has only a minor
effect on predictions. Because the general mechanism may ultimately be
used in complex atmospheric air pollution simulation models, the mechanism
should be as concise as possible to reduce the computing time required for
evaluation of the models. Roth et al. (1974) have carried out a detailed
sensitivity analysis of the mechanism presented in Table 1. -Since we have
included an analogous sensitivity study of a modified version of the general
mechanism in Chapter IV, we do not repeat the discussion by Roth et al.
here. Nevertheless, because of the importance of their results, which
show that the mechanism can, indeed, be simplified, we summarize their
findings in the following pages.
In the Roth study, reactions were considered to be "insensitive" if,
upon their removal from the mechanism, both individually and as a group,
the remaining set of reactions was able to predict the following within
10 percent of the values predicted by the complete mechanism;
> The time taken to reach the N0? peak (T)
> The height of the N02 peak (H)
> The magnitude of the ozone peak (M).
-------
37
These three scalars, all of which can be easily quantified, are of interest
because the onset of formation of many secondary products in the atmosphere
accompanies the peak concentration of NCL, and the intensity of smog is
often associated with the ozone and NCL concentrations. Thus, T, H, and M
constitute three major indicators of smog formation and severity. The de-
cision that the remaining set of reactions must be capable of predicting
these three sealers within 10 percent of the values generated by the total
mechanism was arbitrary. However, such a value is less than the uncertainty
bounds associated with the experimental chamber data used to evaluate and
"tune" the model. Thus, sucii a choice is reasonable.
Consideration of the sensitivity values associated with each rate
constant led to the selection of ten reactions for possible removal from
the mechanism. Of these, Roth et al . found that only six could actually
be eliminated based on the criteria cited above. These reactions are listed
in Table 4.
Table 4
REACTIONS THAT CAN BE ELIMINATED
FROM THE GENERAL MECHANISM SHOWN IN TABLE 1
Reactants Reaction _
0 + NO k4
0 + N00 + M kr
-------
38
As shown in Table 5, the values of T, H, and M after removal of
these six reactions are all within 10 percent of their previous values
for the three EPA runs that Roth et al. examined. A number of other re-
actions could have been removed for one or two of the EPA runs, but not
for all three. However, their elimination would limit the applicability
of the kinetic mechanism to a narrower range of initial concentrations
and ratios. Consequently, no other reactions can be dropped from the
general mechanism.
Table 5
VALUES OF T, H, AND M BEFORE
AND AFTER REMOVAL OF THE REACTIONS IN TABLE 4
Time T
Concentration
(ppm)
(minutes) Value of H Value of M
Run Before After Before After Before After
329 87 86 0.25 0.25 0.39 0.40
333 285 281 0.75 0.70 0.40 0.41
352 65 70 0.25 0.25 0.50 0.52
B. SIMULATION OF A MULTIPARAFFIN/NO SMOG CHAMBER EXPERIMENT
X
The chemical systems of greatest interest in the control of ambient
air pollution are considerably more complicated than the propylene/n-hutnne/
NO mixtures just discussed. In principle., the kinetic mechanism has been
X
formulated to be capable of simulating the behavior of complex mixtures of
organics in an irradiated system containing MO, and air. The ultimate
A
test of the mechanism in this regard will rest on its ability to predict
the chemical transformations occurring in a polluted air mass. But, before
the mechanism is applied to a system as complicated as the atmosphere, it
should be proven capable of simulating the chemical behavior of a simple
mixture of hydrocarbons under well-controlled laboratory conditions.
-------
39
In this section, we discuss a test of the generality of the mechanism.
We used the general kinetic mechanism to simulate a smog chamber experiment
in which five different paraffins and NO were irradiated in air. Al-
/\
though each paraffin was treated separately in this simulation (i.e., the
behavior of each paraffin w?s described by its own differential equation),
all five paraffins were assumed to react alike, in accordance with the
principles of formulation of the mechanism (Seinfeld et al., 1973).*
The multiparaffin/NO experiment was conducted in the same chamber that
/\
was used for the propylene and butane experiments discussed in the previous
section and in Hecht et al. (1973). No data relating chamber operating
characteristics were included with the concentration-time data; we therefore
assumed the same values of light intensity, relative humidity, and chamber
temperature as were supplied for the propylene and n-butane runs. We
-4 -1
further assumed the average dilution rate to be 4.06 x 10 min , which
is typical of other runs performed in the NAPCA chamber for which sampling
data were available. The concentrations of reactants at the beginning of
the exoeriment were as follows:
Concentration
Species (ppm)
iso~pentane 0.51
n-pentane 0.69
2-methyl-per.tarie 0.22
2,4-di-methyl-pentane 0.18
2,2,4-tri-methyl-pentano 0.17
N02 0.038
NO 0.458
* In Chapter IX, we present another simulation of this experiment in which
we lumped the five individual paraffins into one pseudo-species, or
general class.
-------
40
1. Choice of Rate Constants and Reaction Mechanisms
As a reaction framework for the simulation of this experiment, we chose
the formulation of the general mechanism in Table 1» except that the reac-
tions for olefins and aromatics (Reactions 22 through 26) were eliminated.
We then added reactions for the oxidations of each of the five paraffins
by 0 and OH. Assuming that these reactions proceeded by the same general
mechanism, we replaced Reactions 27 and 28 in Table 1 with five pairs of
reactions of the following form:
Paraffini + 0 -» ROO + OH , i = 1,5 ,
Paraffini + OH + ROO + H20 , i = 1,5 ,
where i denotes the individual paraffins. The peroxyalkyl radicals produced
by these reactions vary in structure, depending upon which hydrogen atoms
are abstracted from the hydrocarbons. We assumed, however, that all these
radicals react in the same general manner, and we lumped them into the
pseudo-species ROO.
Carrying out a simulation of this experiment necessitated specifying
the rate constants for the 10 new 0 and OH oxidation reactions. Herron
and Huie (1969) have measured the rate of reaction of 0 with three of the
five paraffins that were used in this chamber experiment: iso-pentane,
n-pentsne, and 2,2,4-tri-Me-pentanc. The rate constants are listed in
Table 6. However, we had to estimate the rate constants for the other
two 0-paraffin reactions. Because iso-pentane and 2-Me-pentane have nearly
identical structures (2-Me-pentano has an extra methylene group in its
carbon skeleton), we assumed that both compounds react at similar rates
with 0; we therefore estimated the 0-2-Me-pontanc rate constant to be
-1 -1
200 ppm min . Herron and Huie have also measured the rate of reaction
of 0 with 2,2-di-Me-pentane, a species somewhat similar in structure to
2,4-di-Me-pentane. We assumed that the latter two species react with 0
at the same rate, and we thus assigned the 0-2,4-di-Me-pentane reaction
-------
41
a rate constant value of 160 ppm~ min" . The rate constants of OH-paraffin
reactions can be calculated directly using the equations formulated by
Greiner (1970a). Values for the OH-paraffin constants calculated in this
manner are summarized in Table 6.
2. Results and Discussion
We carried out a simulation of this multiparaffin experiment after
modifying the mechanism in Table 1 in accordance with the foregoing dis-
cussion. (In performing the integration, v/e did not invoke the steady-
state assumption for any species.) Otherwise, the simulation procedure
was identical to that described for the propylene and n-butane experiments.
The predictions and experimental data are presented graphically in
Figures 10 through 12.
The predictions show good qualitative agreement with the experimental
data for all species. Although the rates of N0? formation, NO oxidation,
aldehyde formation, and PAN formation are all slower than those observed
experimentally, the predicted concentrations of 03 and the five paraffins
agree quite well with the data.
The discrepancies can probably be accounted for in several ways, in-
cluding the reasons given in Hecht et al. (1973) for the propylene and
n-butano simulations. In addition, several considerations pertinent to
the sinulation of this particular experiment might explain the inaccuracies
in the predictions. For example, we made several rather important assump-
tions concerning chamber operating conditions. If the light intensity,
relative humidity, or heterogeneous rate of HNO? formation were greater
than we assumed, the predictions for N0?s NO, aldehydes, and PAN would
improve cine! the predictions for other species would deteriorate in relation
to the experimental data. Also, we used calculated, rather than experi-
mentally measured, rate constant values for the important OH--paraffin
reactions. Although we believe that the technique employed to obtain
these values is sound, the rate constants are undoubtedly uncertain by a
-------
42
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46
factor of at least 1.3. Finally, the peroxyalkyl radicals produced in the
paraffin oxidation reactions are in many cases considerably larger and more
complicated structurally than the radicals produced as a result of propylene
and n-butane oxidations. Consequently, some of the free radical reaction
chains may not proceed in the manner or at the rate that was assumed in
the general mechanism.
Because we tested the mechanism for the multiparaffin case under only
one set of initial conditions, it is risky to draw even qualitative conclu-
sions about the merits of the model. The mechanism in Table 1, though for-
mulated and evaluated for paraffins chiefly in relation to n-butane, simulated
the chemical transformations occurring in the multiparaffin run surprisingly
well. This level of success encourages us about the intrinsic soundness
of using a general mechanism to model smog kinetics.
C. SIMULATION OF A MULTIOLEFIN/NO SMOG CHAMBER EXPERIMENT
A
We undertook the simulation of a multiolefin/NO smog chamber experiment
X
with the same objectives in mind as those pursued for the multiparaffin run:
> To examine the generality of the mechanism.
> To analyze a run with which we could further test our lumping
technique (Chapter IX).
This multiolefin experiment had been conducted in the NAPCA chamber at about
the same time as the multiparaffin run just discussed. Thus, all of our
comments in Section IH-B concerning assumptions as to chamber conditions
and sampling rates apply to our simulation of this run as well. The con-
centrations of the six olefins, NOS and NOp at the beginning of the run
are given on the next page.
-------
47
Concentration
Species (ppm)
1-butene 0.608
cis-2-butene 0.609
2-methyl-1-butene 0.464
2-methyl-2-butene 0.454
propylene 1.334
ethylene 3.039
N02 0.057
NO . 1.013
When we simulated this experiment using the mechanism in Table 1,
assigning individual differential equations to each olefin and using the
oxidant-olefin rate constants in Table 7 (the choice of these values is
discussed shortly), we found that predictions agreed moderately well with
the data up to the N0? peak, as shown in Figures 13 through 16. After the
peak (which occurred 20 minutes after the irradiation was begun), however,
the predicted N0? concentration decayed rapidly to a value of 0.00007 ppm
at 60 minutes. By 100 minutes into the run, the predicted N09 concentre-
j <-
tion was 10 ppm, compared with an observed concentration of 0.09 ppm.
Predictions for most other species also agreed poorly with the data. For
example, by 100 minutes, 0, had already peaked and decreased to a predicted
concentration level of less than 0.05 ppn. (At that point in the experiment,
the 0- concentration actually stabilized at about 0.55 ppm.) The maximum
observed concentration of PAN was one-fifth that predicted. The consumption
of the six olefins due to chemical reactions essentially ceased by 100
minutes, since the Oo had reached a very low level, the NO- had been depleted,
and the only substantial initiators of free radicals left were the aldehyde
and HNOp photolysis reactions.
In view of the extremely poor agreement between the predictions and
the experimental data, we decided to reexamine those reactions in the
general mechanism that became important after the N0? peak. As noted in
-------
48
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53
Chapter IV, the rate constants for many of the most rapid reactions after
the peak are uncertain by a factor of 2 or more. In fact, there is no
assurance that all of the important reactions are even included in Table 1.
Our efforts to improve post-NO?-peak predictions of the general mechanism
by testing new reactions and varying product distributions in uncertain
reactions are delineated in this section.
1. Choice of Rate Constants for the Oxidant-Olefin Reactions
We had to specify the rate constants for the reactions of 0, OH, and
DO with each of the six olefins present at the beginning of the experiments.
The rate constants for the reactions of propylene with the three oxidants
were required for simulations discussed in Section III-A and are listed in
Table 2. Of the other fifteen rate constants, all but two were measured
experimentally. The experimental values that we used to simulate this run
are listed in Table 7.
The rate constants for the 0 and OH oxidations of 2-Me-l-butene have
not yet been measured. Because 2-Me-l-butene is a branched external olefin,
it should be more reactive than the unbranched external olefin, 1-butene
(just as 2-Me-2-butene is more reactive than the unbranched olefin,
cis-2-butene). However, internal olefins are usually much more reactive
than external olefins (Morris and Niki, 1971), and so 2-Me-l-butene should
be less reactive than cis-2-butene. Consequently, we estimated that the
0 and OH rate constants for 2-!1e-l-butene foil about one-third of the way
between the respective 0 and OH rate constants for 1-butene and cis-2-butene
e.g.,
kO = kO + 3 j"0 " K0
2-Me-l-butene 1-butene \ cis-2-butenc 1-butene,
2 Changes in the General Mechanism
The results of the simulation of this experiment using the mechanism
in Table 1 point out the extreme and antithetical behavior of N02 and PAN.
-------
54
As already noted, the predicted disappearance rate of NCL and the appearance
rate of PAN, a species formed in a direct reaction involving NCL (Reaction 33
in Table 1), were both much greater than that observed in the experiment.
Also, the predicted concentration of NCL after its peak was much less than
the observed concentration, whereas the predicted PAN concentration was
much greater than the experimentally measured PAN value. We therefore
suspected that errors in reactions that either (1) produce PAN or its pre-
cursors or (2) consume PAN might account for a major portion of the dis-
crepancies in prediction.
a. Reactions That Produce PAN or Its Precursors
PAN is thought to form primarily as a result of a radical-radical
reaction involving peroxyacyl radicals (other than HCCL) and NCL:*
RCOO + NCL -* RCOONCL
II C- II C.
0 0
PAN
Since the chemistry of NCL is understood fairly well, we focused our atten-
tion on reac
predictions.
tion on reactions producing or consuming RCCL to explain the anomolous PAfJ
(Reactions Producing RCO.,. The principal sources of peroxyacyl radicals
in the general mechanism (Table 1) for a system involving olefins are the
* Hanst (1971) has suggested that PAN might alsoor alternativelyform
by the reaction
RCO + NCL * RCOONCL
II 3 II (.
0 0
Although neither this reaction nor the RCOo-NCL reaction has been observed
O f~
directly, to our knowledge, we have ruled out the RCO^-NO^ reaction for
conditions typical of irradiated smog chambers and the atmosphere because
of the rapid decomposition of acylate radicals to R- and CCL.
-------
55
(L-olefin reaction (Reaction 23) and the OH oxidation of aldehydes (Reactions
29 and 30). It is common knowledge that the reaction mechanism and elemen-
tary products of the 0.,-olefin reaction in the gas phase are extremely un-
certain. Chemists, however, feel reasonably certain about the OH-aldehyde
elementary mechanism. We treat each of these in turn.
Recently, O'Neal and Blumstein (1973) postulated a "new mechanism" for
the 03-olefin reaction. The mechanism, in fact, consists of many reaction
pathways for the biradical reaction intermediate and was formulated in part
on the basis of several 03-olefin reaction product studies. It is clear
that Reaction 23 in Table 1 is overly simplistic, in view of the large
number of reactions pathways that they proposed and defended. On the other
hand, one reaction mechanism described by Leighton (1961) approximates
many of the important aspects of their mechanism reasonably well. Leighton's
mechanism is
V /R3 initial , Rl , R3 + , Rlx, , R3V
C - C + 0, -* addition -*- ~ C = 0 + l- COO" + 1 tOO"+ ^ C - 0
^ \ J 2Rf * ^ 2 ^ 2 ^
(1)
followed by
K+ , ,0* , *o* 1111
COO * 1 R,OC t 1 P,2OC , 1 R,0- + 1 R2C- + 1 R20- + \ R,C- .
K2 2 Kl 0 0
(2)
-------
56
The Leighton mechanism and the O'Neal and Blumstein mechanism agree in the
following important respects:
> Both predict that aldehydes and ketones are formed in the
reaction.
> Both predict that free radicals are formed.
> Both predict that OH is formed if the olefinic carbon atoms
are not completely substituted with carbon chains.
The mechanisms differ chiefly in their level of complexity; the O'Neal and
Blumstein mechanism allows a much greater number of reaction pathways.
On one hand, Reaction 23 appeared to be inadequate as postulated in
Table 1; on the other hand, the O'Neal and Blumstein formulation seemed
overly complex (though by no means necessarily improper) for use in the
general mechanism. We therefore decided to test the Leighton 0~-olefin
mechanism in the general mechanism on a provisional basis. Reaction 23
in the mechanism was replaced by the following six reactions (one for each
olefin in the multiolefin/NO experiment):
0, + 1-butene -* 0.75 ALD + 0.50 FORM +"0.75 OH + H09 + 0.25 RCOO
O C. ||
0
o + cis-2-butene -> ALD + 0.50 OH + 0.50 110, + 0.50 RO + 0.50 RCOO
0 £ II
00 + 2-Me-l-butene -> 0.50 FOR!' + 0.50 OH + 0.50 H00 + 0.50 RO + 0.50 RCOO + 1 KE"
6 c. it I
0
00 + 2-Me-2-butene + 0.50 ALD + 0.25 OH + 0.25 H09 + 0.75 RO + 0.75 RCOO + 1 KET
6 L. II i
-------
57
03 + ethyl ene -* FORM + OH + H02
03 + propylene -> 0.50 ALD + 0.75 FORM + 0.75 OH + H02 + 0.25 RCOO
0
where FORM represents formaldehyde, ALD represents all aldehydes other than
formaldehyde, and KET represents ketones.
The other major source of RC03 was the OH oxidation of aldehydes other
than formaldehyde (Reaction 30). In our original formulation of the general
mechanism, both formaldehyde and higher aldehydes were lumped into the class
HC*. Consequently, to indicate the portion of total aldehydes that was not
formaldehyde, we introduced a fractional coefficient, g, into the reaction.
During the multiolefin/NO experiment, the concentrations of three aldehydes--
X
formaldehyde, acetaldehyde, and propionaldehyde-~were measured; formaldehyde
reached a level of over 2 ppm. As a result, the chromotopic acid determina-
tion of HCHO, which is often imprecise at HCHO concentrations less than
0.5 ppin, provided more reliable measurements than are usually possible
(see Seinfeld ot a!., 1973). Ihus5 before simulating this experiment, we
decided to separate the "total aldehyde" class into two classes, formaldehyde
and other aldehyces (which in this cose consisted of acetaldehyde and pro-
prionaldehyde). The coefficient 3 in Reactions 29 and 30 was eliminated as
a result of this change. We also included reaction pathways in the mechanism
for the photolysis of both classes of aldehydes to stable products (Calvert
et a'l. , 1972). Thus, Reactions 29 and 30 in Table 1 were replaced by
FORM > 2H02 ,
FORM -> H2 + CO ,
-------
58
ALD -* ROO + H02 ,
ALD -> PROD + H2 ,
OH + FORM -> H02 + H20 ,
OH + ALD » RCOO + H20 ,
0
where PROD is a stable product, usually a paraffin (methane when the alde-
hyde is acetaldehyde).
The separation of formaldehyde from the general aldehyde class neces-
sitated one additional change. He were forced to distinguish between
methoxy and higher alkoxy radicals, since the former leads to formaldehyde
formation, and the latter, to the formation of higher aldehydes:
CH30 + 02 -» HCHO + 02 ;
but, for example,
pu pij p, _i p. . pii pun j- iin
L/nQLtioU T u/j ~r (sti'^Lnv T n\Jn .
Thus, Reaction 34 in Table 1 was replaced with the reaction
RO + o2 -+ Y ALD + (I-Y)FORM + no2 ,
where Y is the fraction of RO that is not CH,,0. For this experiment, we
J
estimated that Y is about 0.25, based on d consideration of the various
elementary reactions involving olefins and aldehydes.
The coefficient Y is essentially a direct replacement for B. It, too,
could be eliminated if we were to introduce two new free radical species in
the general mechanism, QLO and CH-00. Then, RO would represent all alkoxy
radicals other than CH30, and R02 would contain all peroxyalkyl radicals
other than CH,,00. If we did this, however, we would also need to specify
-------
59
the fraction of aldehydes (ALD) that is not acetaldehyde, since the photolysis
of acetaldehyde leads to methyl radical formation and the photolysis of
higher aldehydes leads to the formation of alkyl radicals other than methyl.
When the chemistry is generalized in this manner, one parametric coefficient
must be introduced into the mechanism to close the reaction sequence.
A Reaction Consuming RCO-. Finally, we added one radical chain termi-
nation reaction to the mechanism to control the concentration of RC03 in
the absence of both NO and N02 (Reactions 32 and 33). This reaction is
RCOO + H00 -» RCOOH + 00 ,
II f- II C-
0 0
Peracid
for which we assigned a rate constant of 100 ppm" min~ by analogy to
Reaction 38.
b. Reactions That Consume PAN
PAN is known to be unstable. In 1969 Stephens reported that PAN de-
composes on the walls of a reactor, yielding a variety of products, including
CH3ON02, C02, and CH3COOH. Laboratory explosions involving droplets of PAN
have also occurred. A reaction between PAN and NO studied by Schuck et al.
(1972) involves a mechanism that is apparently complex and that has not yet
been established. The
the very slow reaction
2
been established. The reaction is, however, about 10 times faster than
2ND + 02 * 2N02 .
Since PAN absorbs light very weakly at wavelengths greater than
(Stephens, 1969), its photodissociation in the atmosphere can be ruled out.
The reported decomposition of PAN on the reactor walls could conceivably
be evidence of a slow PAN hydrolysis reaction. Thus, we hypothesized a
-------
60
direct reaction between PAN and water leading to the formation of acetic
acid, nitrous acid, and (L:
CH0COONCL + H00 -v CH-COH + HN00 + 00
o n £ d. 6 H c e.
Based on the tables in Benson (1968), we calculated that this reaction is
exothermic by 7 kcal/mole, and we assigned the reaction a rate constant of
2 x 10" ppnf min" . This value seems reasonable in relation to the rate
of the fLOr-H^O reaction (Reaction 11 in Table 1). One might expect an
alternate formulation of the PAN-hLO reaction leading to pernitric acid
formation to be even more exothermic:
CHQCOON00 + H00 + CI-LCOH + HOONO,
3n 21 3u 2
However, we have not yet pursued this possibility in depth.
3. Results and Discussion
The modifications and additions to the general mechanism and the re-
vised reactions and rate constants ore presented in Table 8. Using the
mechanism and rate constants in this table, we carried out a simulation of
the niultiolefin run. The results are depicted graphically in Figures 17
through 20.
As shown in those figures., the agreement betv/cen predictions and d?u?~-
up to the time of the N0? peek--using the mechanism in Table 1 is preserved
using the new Formulation of the mechanism. After the peak, however, the
N0? disappearance rate predicted by the new reaction scheme agrees more
closely with the observations. The predicted ozone asymptote agrees very
well with the data, although the mechanism fails to predict the 0~ peak
even qualitatively. The peak in the 0~ concentration-time profile may
have been due to N0? interferences in the experimental 03 measurements (see
Seinfeld et al., 1973). However, this hydrocarbon/NO system is extremely
A
reactive. It is not unreasonable to expect that 0~ would accumulate rapidly
-------
Table 8
REVISED GENERAL MECHANISM USED TO SIMULATE
THE MULTIOLEFIN/NOV EXPERIMENT
A
61
Number
Reaction
Rate Constant*
1 N02 + hv -» NO + 0
2 0+0, + M -» 0, + M
2 3
3 NO + 0, -* NO, + 0,
«5 t. C.
4 0 + NO + M + N02 + M
5 0 + N02 t- NO + 02
6 0 + N02 + M -> N03 + M
7 N02 + 03 H. N03 + 02
8 NO, + NO * 2KO,
3 2
9 NO, + NO, ->- N.,0,
O C. £. i)
10 N,0r -+ MO, + NO,
L. 0 ^- O
11 N,0r + H,0 -> 21-ii'tO,
L. 0 (L ^
12 NO + HN03 -> HN02 + NOp
13 HN02 + HN03 -v H20 + 2N02
14 NO + N02 + H20 + 2!!N02
15 2HN02 -+ NO + N02 + H,,0
16 HII02 + hv -*- OH + NO
17 0!! + NO, * IIDO,
C. h'N02
19 H02 + NO -> OH + N0?
20 H02 + H02 -» H202 + O^
21 H202 + hv + 20H
22 HC11 +0 -» ROO + 0.50 RCOO + 0.50 HO,
II £
0
23 HC12 + 0 * ROO + RCOO
II
0
2.23 x 10"1 min"1
2.00 x 10"5 ppm"2 min"1
2.08 x 101
3.50 x 103
1.38 x 104
2.20 x 103
4.65 x 10"2
1.50 x 104
4.50 x 103
2.70 x 101 min"1
1.00 x 10"5
2.50 x 10"4
2.00 x 10"1
2.10 x 10"6 ppm"2 min"1
4.50
1.30 x 10"2 min"1
1.50 x 104
1.20 x 104
7.00 x 102
5.30 x 103
1.06 x 10"3 min"1
4.70 x 103
3.10 x 104
-------
62
Table 8 (Continued)
Reaction ___^_ Rate Constant^
IIUI'IUCI
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
HC13 + 0
HC14 + 0
HC15 + 0
HC16 + 0
HC11 + 0,
o
HC12 + 03
HC13 4 03
HC14 + 03
HC15 + 03
HC16 + 03
HC11 + OH
HC12 + OH
HC13 + OH
HC14 + Oil
HC15 + OH
HC16 + OH
HCHO -t hv
HCHO + hv
ALD + hv
ALD + hv
OH + HCHO
OH + ALD
-» ROO + 0.50 RCOO + 0.50 H02
0
+ ROO + RCOO
It
0
* ROO + H02
* ROO + 0.50 RCOO + 0.50 HO,
II C
0
-»- 0.75 ALD + 0.50 HCHO + 0.75 OH + HO, + 0.25 RCOO
t ft
0
-> ALD + 0.50 OH + 0.50 H02 + 0.50 RO + 0.50 RCOO
0
» 0.50 HCHO + 0.50 OH + 0.50 HOg + 0.50 RO -t- 0.50 RCOO
0
-f 0.50 ALD + 0.25 OH + 0.25 H02 + 0.75 RO + 0.75 RCOO
0
-+ HCHO * OH + H02
+ 0.50 ALD H- 0.75 HCHO + 0.75 OH + H09 + 0.25 RCOO
C. II
0
-» ROO + HCHO
-* ROO + HCHO
+ ROO + HCHO
-v ROO * HCHO
-» ROO -! HCHO
-v ROO + HCHO
, 2H02
-> H2 + CO
-, R02 + H02
-» Alkane + H?
, H02+H20
* RCOO + H,0
1.30 x 104
6.00 x
7.60 x
6.80 x
1.30 x
4.10 x
1.60 x
4.30 x
3.10 x
1.60 x
6.00 x
9.00 x
7.00 x
1.30 x
7. HO x
2.50 x
2.50 x
2.50 x
2.50 x
2.50 x
2.30 x
2.30 x
104
102
103
ID'2
ID'2
ID'2
10"2
10"3
10"2
104
104
104
105
103
104
10"3 min"1
10"3 min"1
10"3 min"1
10"3 min"1
104
104
-------
63
Table 8 (Concluded)
Number
46
47
48
49
50
51
52
53
54
55
ROD + NO -»
°2
RCOO + NO *
II
0
RCOO + NO, -»-
it f-
0
RCOONO, + H,0 +
H C. L.
0
RO + 02 -»
RO + NO +
RO + N02 +
H02 + ROO -*
RCOO + H09 *
II f-
0
2ROO -*
Reaction
RO + N02
ROO + N02 + C02
RCOONO,
n (-
0
Acid + HN02 + 02
H02 +0.75 HCHO +0.25 ALD
RONO
RON02
RO + OH + 02
Peracid + 02
2RO + 02
HC11 = l-butcne.
HC12 = cis-2-butene.
HC13 = 2-Me-l-butene.
HCH = 2-Me-2-butene.
HO5 = ethyl one.
HC1C = propyleno,
* In units of ppm min unless othervrise indicated.
Rate Constant*
9.10 x 102
9.10 x 102
1.00 x 102
2.00 x 10"6
2.40 x 10"2
2.50 x TO2
4.90 x 102
1.00 x 102
1.00 x 102
1.00 x 102
-------
64
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-------
68
with N02 and then be consumed by the 0--N02 and CL-olefin reactions. For-
maldehyde measurements agree reasonably well with observations through much
of the run, but discrepancies become increasingly more serious after 200
minutes of the run. The predictions of the concentrations of other alde-
hydes are low throughout the simulation. PAN predictions, which were five
times greater than the observations when the Table 1 mechanism was used,
are in much better agreement with the data here, although the predicted
concentration is too low after about 150 minutes. Finally, the predictions
for all the olefins are vastly improved compared with those obtained using
the mechanism in Table 1.
We made several changes in the mechanism to simulate this particular
experiment. Although the results are encouraging, this exercise, by itself,
does little to substantiate the veracity of these modifications. The im-
provement in predictions can be attributed chiefly to the expanded treat-
ment of the 0~-olefin reactions and to the introduction of the PAN-H?0
reaction. Unfortunately, both of these reactions are speculative. The
latter, in particular, has never been studied explicitly in a laboratory,
though we understand that the rate constant for the reaction is to be deter-
mined soon at the University of California, Riverside.
Perhaps the only conclusion we can draw from this work is that the
formulation of the general mechanism in Table 1 is inadequate for the simu-
lation of post-NO? peak chemistry. The improved agreement between predic-
tions and experimental data using the reactions and mechanisms postulated
here does not necessarily prove that they arc the correct explanations for
the experimental observations. However, the change in agreement between
predictions and data was dramatic enough to make us feel that the mechanism
of the 0.,-olefin reaction and the rate constant and mechanism of the PAN-HLO
reaction merit further detailed experimental scrutiny.
As noted earlier, this set of data was the last that we simulated
during the contract year. The modified mechanism predicts this one multi-
olefin/NO experiment quite well and will be developed further next year
X
during the analysis of the UCR propylene/NO experiments.
X
-------
-------
69
IV SENSITIVITY AND UNCERTAINTY OF REACTIONS
IN THE GENERAL MECHANISM
The evaluation studies presented in Chapter III are chiefly a test of
the accuracy of the specific set of reactions and rate constants employed
in the general mechanism. We realize, of course, that other important re-
actions may have been omitted from the mechanism and that elementary mechan-
isms proposed for some reactions may be incorrect. However, the value of
every rate constant in the mechanism is uncertain to some degree. If a
newly measured or redetermined rate constant were to differ significantly
from the value used in our simulations, the predictions and, consequently,
the accuracy of the kinetic mechanism would be altered greatly. Therefore,
before the general mechanism is used for decision-making, it is important
to quantify the extent to which uncertainties in values of the rate constants
influence the prediction of photochemical smog formation. Toward this end,
we calculated the sensitivity (defined as 3p/8k-, the rate of change in the
predictions of the model with changes in the value of the i-th rate constant)
of every rate constant in the general mechanism.
A second factor, however, must be taken into account in judging the
effect of this sensitivity. Suppose that every rate constant were known with
absolute accuracy. Then, it would make little difference if predictions were
extremely "sensitive" to variations of the rate constant(s), since the pos-
sibility of a change in the rate constants would never arise. As we stated
above, and as we discuss in depth later in this chapter, every rate constant
in the general mechanism is uncertain to some degree. The magnitudes of
the individual uncertainties influence our interpretation or weighting of
the sensitivity value calculated for each constant. We therefore combined
the calculated sensitivity measures with estimates of the uncertainty
bound of each rate constant to create a new index that reflects the im-
portance of obtaining more accurate measurements of rate constants to
reduce the uncertainties in the model predictions. From the ranking of
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70
the reactions according to this index, we were able to identify (1) reactions
for which accurate measurements of the associated rate constants are needed
and (2) insensitive reactions that can possibly be eliminated from the
mechanism without a significant loss of accuracy.
A. THE MECHANISM EMPLOYED
When we carried out the sensitivity calculations, we used a slightly
modified version of the kinetic mechanism presented in Tables 1 and 2.
The changes had been implemented to augment the agreement between predic-
tions and experimental data for EPA Run 329: [N02]0 = 0.06 ppm,
[N0]0 = 0.29 ppm, [C3H6]Q = 0.24 ppm, and [H2o]Q = 10,000 ppm. We were
particularly interested in this experiment because the initial concentra-
tions were at values typical of polluted atmospheres and because ozone
accumulated to an asymptotic level during the experiment.
Although the mechanism used for the sensitivity analysis (see Table 9)
closely resembles the kinetic mechanism presented in Tables 1 and 2, some
minor differences are worth noting. In earlier simulations, v/e had shown
that Reactions 12 and 13 could be eliminated from the general mechanism
(Table 1) without affecting predictions. Also, since no CO, paraffins, or
aromatics were present in EPA Run 329, Reactions 19 and 25 through 28 were
not needed to carry out the simulation. However, the photolysis reaction
of aldehydes leading to stable products,
RCHO + hv -> Stable Products
had not been included in Table 1. Since we thought this reaction was of
moderate importance (Calvert et al., 1972), we included it in the modified
version of the mechanism.
Several rate constants were also changed within their bounds of un-
certainty to improve the predictions for EPA Run 329. The reactions so
affected, the values of the rate constants in Table 2, and the values of
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71
Table 9
THE KINETIC MECHANISM USED FOR THE SENSITIVITY ANALYSIS
Uncertainty
Number Reaction Rate Constant* Factor
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
N02 + hv -» NO + 0
o + o2 5 o3
03 + NO -> N02 + 02
0, + N09 -> N0~ + 09
O C. 0 C.
N03 + NO -» 2N02
H90
N00 + N00 4 2HNO,
23 3
M
0 + NO " N02
0 + N02 -»- NO + 02
0 + N09 9 NO,
L. O
NO + N02 2 2HN02
HN02 + HN02 + NO + N0? + H20
HN02 + hv -> OH + NO
OH + N09 -> HNOo
£, v)
OH + NO -> HN02
H02 -:- NO -> OH + N02
HOOH + hv -^ 20H
OLEF + 0 -» R02 + 0.5H02 + 0.5RC03
OLEF + OH -v RCHO + R02
OLEF + 0, t- RCHO + RCO. + OH
2.7 x 10"H
3.3 x 106§
2.1 x 101
4.6 x 10"2
1.5 x 104
4.5tt
2.5 x 103tt
1.4 x 104
3.0 x 103tt
1.5xlO-2tt
1.1
1.3 x 10"2t
6.0 x 103
4.8 x 103
7.0 x 102
1.5 x 10"3t
6.8 x 103
2.5 x 104
1.6 x 10"2
1.4
1.2**
1.3**
1.3**
5.0**
2.5**
1.2**
1.2**
1.6**
10.0
10.0
3.0
2.0**
2.0**
3.2**
3.0
1.2**
1.2
1.5
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72
Table 9 (Concluded)
Number
20
21
22
23
24
25
26
27
28
29
30
31
Reaction
RCHO + hv * Stable Products
RCHO + hv -» 0.5R02 + 1.5H02
RCHO + OH -> 0.5RC03 + 0.5H02
R02 + NO + RO + N02
RCO. + NO -> R09 + N09
O C. L.
RCOo + N09 -> PAN
*? C*
°2
RO 4- RCHO + H02
RO + N02 + RON02
RO + NO -*- RONO
H02 + H02 -> H202 + 02
R02 + H02 -» RO + OH + 02
R02 + R02 -^ 2RO + 02
Rate Constant*
2.5 x 10"3+
2.5 x 10"3t
2.3 x 104
3.0 x 103
1.5 x 103
5.0 x 102
5.0 x 103§
4.9 x 102
2.5 x 102
5.3 x 103
1.0 x 102
1.0 x 102
Uncertaint
Factor
3.0
3.0
1.3**
5.0
5.0
5.0
5.0
5.0
5.0
2.0**
4.0
10.0
* Second-order rate constants (in units of ppm~ rrn'n" ) unless otherwise
indicated.
t First-order reaction (in units of min" ).
§ Pseudo-first-order rate constant value.
** Garvin and Hampson (1974).
tt Pseudo-second-order rate constant value.
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73
the rate constants used in the improved prediction of EPA Run 325 are
tabulated below:
Rate Constant Used for
Rate Constant the Special Simulation
in Table 2 of EPA Run 329
Reaction (ppm-1 min-T) (ppm-1 min-1)
0 + 02 + 03 2.0 x 101* 1.65 x 101*
0 + NO + N02 3.5 x 103* 2.5 x 103*
0 + N02 3 N03 2.2 x 103* 3.0 x 103*
HN02 + HN02 * NO + N02 + H20 4.5 1.1
OH + N02 -* HN03 1.5 x 104 6.0 x 103
OH + NO * HN02 1.2 x 104 4.8 x 103
R02 + NO + RO + N02 9.1 x 102 3.0 x 103
RC03 + NO -*- R02 + N02 9.1 x 102 1.5 x 103
RC03 + N02 -> PAN 1.0 X TO2 5.0 x 101
There are several reasons why we did riot feel compelled to use the
mechanism and rate constants in Tables 1 and 2 for the sensitivity calcula-
tions. First, we carried out. the sensitivity analysis using a single set
of initial reactant concentrations. Although this automatically limited
the scope, or generality, of our results, the information that we obtained
was sufficient to answer the questions posed at the beginning of this project:
* Pseudo-second-order rate constants.
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74
(1) Which rate constants should be determined with greatest
accuracy and precision to reduce uncertainty in predictions
of smog formation?
(2) Which reactions can we possibly eliminate from the mechanism
without a significant loss of accuracy?
Because we were examining the sensitivity of the mechanism under only one
set of initial conditions, we wanted the predictions to be as good as pos-
sible for that case. If the predictions were not accurate to begin with,
the sensitivity results have little value.
Even aside from these considerations, there are many uncertainties
in the kinetic mechanism regarding reactions and rate constants. Thus,
although we tested the mechanism in Tables 1 and 2 over a range of initial
conditions and observed moderate accuracy in prediction, it is difficult
to state definitely that the mechanism in Tables 1 and 2 is intrinsically
more accurate (or inaccurate) than that given in Table 9. As shown in
Figure 21, the kinetic mechanism in Table 9 simulates EPA Run 329 with
very good accuracy.
In summary, the two mechanisms differ, but most of the changes are
minor. We realize, of course, that slightly different rankings of reactions
according to sensitivity might result using Tables 1 and 2 for the calcula-
tions. However, the general groupings of sensitive and insensitive reactions
for FPA Run 329 observed using Table 9 would almost certainly be similar to
those that would be obtained using Tables 1 and 2 (cf. the sensitivity
analysis of the mechanism in Tables 1 and 2 discussed in Roth et al. (1974)]
B. SENSITIVITY ANALYSIS
Central to the performance of a sensitivity analysis of a mathematical
model is the meaningful quantification of changes that perturbations of in-
put parameters cause in predictions of the model. The sensitivity, S., of
the i-th parameter, k., can be defined as
-------
75
00
\i i i
z
Cu OU-i
oor-
oo
D;
o
LU
(^)
cC
CO
CM
UJ
K
rD
CD
O
LO
O
CO
C\J
o
o
o
(Wdd)
-------
76
the rate of change of the predictions of the mechanism, p, with changes in
the parameter. Obviously, the calculated values of S, depend on the model
(mechanism) that is being tested, the initial conditions, and the base values
(which may not necessarily be the true values) of the rate parameters k..
1. Criterion of Sensitivity
The definition of sensitivity in Eq. (3) is somewhat stricter than that
needed to reach our objectives, which were stated in Questions 1 and 2 in
Section IV-A. For example, at every time step, integration of the kinetic
mechanism generates the concentrations of 19 different chemical species.
Yet, we are most interested in the concentration-versus-time behavior of
just four of these--NO, NCL, CL, and propylene--the species for which the
experimental measurements are most accurate. Thus, in calculating sensitiv-
ity in this study, we characterized the change in prediction, 3p, as the
change in predicted concentration of each of those four species.
Although strict adherence to Eq. (3) would require the use of a very
small perturbation of each rate constant, the large uncertainties of many
rate constants made that choice seem unrealistic for this investigation.
For example, many of the rate constants are poorly characterized, having
associated uncertainties of a factor of 5 or greater.* Even the best known
of the rate constants have uncertainty factors of l.,2. To facilitate com-
parison and ranking cf the sensitivities of the constants, we wished to
vary all parameters in turn by the same fixed percentage. An inspection
of the uncertainty factors in Table 9 suggested that 1.5 was a representative
uncertainty factorroughly t 50 percent. Therefore, we elected to use that
percentage as the magnitude of perturbation for the sensitivity calculations.
Because the precision bounds of the rate constant values for individual
* The manner in which the uncertainty estimates were made is discussed
in Section IV-C.
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77
reaction rate constants vary greatly, however, the choice of the "range
of perturbation" must be regarded as arbitrary. This factor of 1.5, or
50 percent, is significant only because it marks the approximate division
between the very uncertain and the less uncertain parameters (see Table 9).
One would, of course, expect the magnitude of the change in prediction,
3p, to depend on the degree of perturbation of the parameter (e.g., 10 per-
cent versus 50 percent). However, the values of the sensitivity measures
are not, in general, identical, even for plus and minus perturbations in a
given parameter, because the equations governing the kinetics are nonlinear.
For example, if we were to carry out sensitivity calculations for a single
parameter, k, varying it continuously from its nominal value to k+100 per-
cent and from k to k-100 percent, we might find that the sensitivity measure
(SM) changes in the following manner:
SM
-100
-50 0
k (percent)
+50
+100
(If predictions of the model were insensitive to the value of this para-
meter, the rise along the ordinate with perturbations in k would be slight.)
Carrying out such a detailed analysis of the sensitivity of each parameter
would be prohibitively expensive. Thus, our analysis was limited to deter-
mining two points on that curve--+50 and -50 percent. Since the calculated
sensitivity measures for positive and negative perturbations were in reasonably
-------
78
good agreement, we decided to average the two values for the ranking of
rate constants by sensitivity.
Equation (3) makes no reference to time. But, in simulating chemical
transformations with the kinetic mechanism, the concentrations of reactants,
intermediates, and products constantly change; these changes are reflected
in the rates of the various reactions and the sensitivities of the rate
constants. Since we are primarily interested in identifying the sensi-
tivities (or insensitivities) of the kinetic mechanism for the overall
prediction of smog, a mean value of S. over the period of integration
would be adequate for our needs. Because the mechanism has been used
primarily in the simulation of six-hour smog chamber experiments, 360
minutes appeared to be an appropriate period over which to determine the
mean sensitivity. We realize that the use of mean value sensitivity cri-
teria in the analysis of nonlinear systems can sometimes be misleading,
inasmuch as momentary periods of extreme sensitivity of a parameter might
be mashed or obscured by the time-averaging process. However, in view of
our application of the calculated sensitivity data, we believe that the
use of mean values is justified. This does not rule out the utility of
examining sensitivity as a function of time in the future. Furthermore,
in the subsequent discussion of the possible elimination of insensitive
reactions, we emphasize the need for additional detailed testing of the
reactions over a range of initial conditions and bounds of uncertainty
of the rate constant.
2. Procedure
The sensitivity analysis was carried out in the following manner.
Concentration-time profiles for propylene, NO, N0?, and 0~ were obtained
C, O
by integrating the governing rate equations with each rate constant at
its "standard" value (Table 9). One of the rate constants was then in-
creased by 50 percent of this value while all other rate constants were
held fixed. The equations were then integrated for this new rate-constant
setting. The concentration-time profiles obtained for each of the four
species at this setting were compared with the respective profiles obtained
-------
79
when all rate constants were at their standard value (Table 9). The area
of the absolute differences between these profiles was then calculated.
The standard value for the rate constant was decreased by 50 percent and
the process was repeated. The areas determined in this manner for each
species at the two rate-constant settings were averaged. This average
was then divided by the area under the curve obtained for the respective
species when all rate constants were at their standard values. This number
was multiplied by 100 to yield the normalized percentage change in the
average area resulting from the perturbation of this rate constant by
+50 and -50 percent. Finally, the percentage changes obtained for each
of the four species were averaged to yield the sensitivity of this rate
constant. This procedure »(as repeated for each of the 31 rate constants.
In summary, the criterion of sensitivity used in this study is given
by
t=o
jd^.t) - C..(k. - 50% k.,t)|] dt , (4)
where the variables and indices are defined as follows:
S. the sensitivity of the i-th rate constant
U. area under the concentration-time profile for the j-th species
J
C. concentration of the j-th chemical species
k. value of the i-th rate constant
j species index (N0p> NO, 03, and propylene)
-------
80
i reaction or rate constant number
t time.
3. Results
If the time history of a chemical species was greatly altered when a
given rate constant was perturbed, the value calculated according to
Eq. (4) for the sensitivity was small.
The results of the sensitivity study are given in Table 10. As this
table shows, the following rate constants display the greatest overall
sensitivity:
k-, the photolysis of N0?
ko the oxidation of NO by 0~
k-,0 the formation of HNO^ from NO, NO^, and H^O
k-jp the photolysis of HNO?
k-,0 the reaction of OH with N09
I O C-.
k^ the reaction of OH with NO
k-,r the oxidation of NO by H0?
k-jfi the oxidation of olefins by OH
k,q the oxidation of olefins by 0,,
k91 the photolysis of aldehydes to radicals.
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81
Table 10
SENSITIVITY OF THE REACTIONS
Rank Reaction Sensitivity
27.9
22.0
13.8
12.6
11.1
9.1
8.5
7.4
7.2
6.4
4.8
4.5
4.4-
3.2
2.4
2.4
2.0
1.9
1.8
1.1
0.8
0.6
0.5
0.4
0.3
0.3
< 0.1
< 0.1
< 0.1
< 0.1
< 0.1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
OLEF + OH
RCHO + hv -» Radicals
N02 + hv
03 + NO
OH + N02
OH + NO
HN02 + hv
OLEF + 03
H02 + NO
NO + N02 + H20
RCHO + OH
RC03 + N02
RC03 + NO
H02 + H02
RO + 02
0 + 00
i.
OLEF + 0
HN02 + HN02
RCHO + hv > Products
RO + N02
RO + NO
N02 + 0
N02 + 03
N03 + NO
HOOH + hv
N02 + N03
R02 + NO
R02 + H02
N02 + 0 + M
R02 + R02
0 + NO
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82
C. THE IMPLICATIONS OF COMBINED SENSITIVITY AND UNCERTAINTY DATA
The sensitivity results have additional meaning when assessed in
conjunction with the uncertainties of the rate constants used in this
study. If a rate constant is well known, little uncertainty is introduced
into the predictions, even though this rate constant may rank high on the
sensitivity scale. The same holds true if a rate constant is highly un-
certain but its sensitivity is negligible. Therefore, meaningful improve-
ment in the kinetic mechanism will be achieved if accurate values are de-
termined for those rate constants whose combined sensitivities and uncer-
tainties are high. To identify these major sources of uncertainty in the
model predictions, we formulated the following ad hoc index:
S*U = Sensitivity x Uncertainty
Values selected for the uncertainty of each rate constant are listed
in Table 9. The uncertainty is expressed in terms of a multiplicative
factor. Thus, the "true" value of k, might be within the range 1.3 x k~
to (1/1.3) x k-. Many of the uncertainty estimates, especially for the
inorganic reactions, are those of the National Bureau of Standards (NBS),
as referenced in Garvin and Hampson (1974). These estimates were deter-
mined in most cases through a critical evaluation of experimental methods.
The remaining values are our subjective estimates or those of Golden,
Hendry, and Mendenhall of Stanford Research Institute; Garvin end Hampsori
of the NBS, and Dodge of FPA.
1 Rate Constants That, Should ___Be Determined with Great Accuracy
The values of the S*U index calculated for each rate constant are
given in Table 11. Because of the subjective nature of many of the un-
certainty estimates, their relative order in this table has greater mean-
ing than their actual numerical rankings. Particular attention should be
directed toward those clusters of reactions ranking very high or very low
in the table. The reactions that rank highest include the following:
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83
k]0 the formation of HN02 from NO, N02, and H20
k,? the photolysis of HNCL
k,~ the reaction of OH with N02
k,r the oxidation of NO by HOp
k-,o the oxidation of olefins by OH
kp-i the photolysis of aldehydes to radicals
ky, the oxidation of NO by RCOo
k25 the formation of PAN from RC03 and NOg.
The uncertainty in predictions of the kinetic mechanism will be reduced
significantly if more reliable values for these rate constants are deter-
mined.
This list includes rate constants that must be measured in situ
(i.e., in smog chambers) as well as rate constants most easily measured
in independent laboratory experiments. Carefully executed chamber experi-
ments are a key ingredient in a successful kinetic mechanisn verification
program. It is generally recognized that, for the data to be of optimum
value, the experiment should be monitored accurately, and the chamber
should be maintained at constant conditions of temperature, humidity,
light intensity, wall activity, and the like. For some time, investiga-
tors have realized the importance of determining k-i, the photolysis rate
of HOr,. Yet, the results of this study indicate that because of their
combined sensitivities and uncertainties, the rate constants chosen for
the photolysis of nitrous acid (k-,n) and aldehydes (koi) to radicals
introduce even more unreliability into the predicted concentration-time
profiles. Unless our nominal values for these two rate constants are
gross overestimates, we feel that the photolytic dissociation rates for
aldehydes and nitrous acid must also be measured in future chamber
experiments.
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84
Table 11
COMBINED SENSITIVITY AND UNCERTAINTY
OF THE REACTIONS
Rank Reaction S*U Index
66.0
64.0
33.5
25.5
23.0
22.5
22.2
22.0
19.3
19.0
18.2
16.4
12.0
11.1
6.4
6.2
5.5
5.4
4.0
2.9
2.4
2.0
0.9
0.8
0.7
0.6
< 0.1
< 0.1
< 0.1
< 0.1
< 0.1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
?4
25
26
27
28
29
30
31
RCHO + hv -v Radicals
NO + N02 + H20
OLEF + OH
HN02 + hv
H02 + NO
RCO- + N00
3 2
OH + N02
RC03 + NO
N0? + hv
HN02 + HN02
OH + NO
03 + NO
RO + 02
OLEF + 03
H0? + H02
RCHO + OH
RO + N02
RCHO + hv -* Products
RO + NO
0 + 02
OLE.F + 0
N03 + NO
IIOOH -i- hv
N0? + M03
N02 + 0
N02 + 03
R02 + NO
R02 + H02
N02 + 0 + M
R02 + R02
0 + NO
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85
Other rate measurements that should be carried out involve OH, HOp,
and HNOp. The smog formation process is sustained to a significant degree
by reactions involving the interconversion of OH and HOp radicals. The
formation reaction of HNOp from NO, N0?, and HpO (Reaction 10) may con-
tribute significantly to the accumulation rate and maximum concentration
of nitrous acid in smog. Since OH is a photolysis product of HNOp,
Reaction 10 may, in fact, participate indirectly in the initiation of
ambient smog formation. The termination of OH chains through a reaction
with NOp (k-,3) and the OH-olefin chain transfer reaction (k-jo) strongly
influence the OH concentration and, hence, the rate at which the overall
chemical transformations occur in olefin/NO smog chamber experiments.
X
In addition, the accumulation of 03 as a result of disruption of the
Oo-NO-NOp equilibrium (Reactions 1 through 3) is attributable chiefly
to the oxidation of NO by HOp (Reaction 15). We strongly recommend that
these rate constants be reevaluated.
The '.'high sensitivity" list also includes two reactions for which no
experimental determinations of the rate constants have yet been made.
Should our estimated values be low, these rate constants may be more im-
portant than the sensitivity analysis indicates. Thus, we also recommend
that initial rate determinations for the RC03 + NO (k24) and RC03 + N02
(kpr) reactions be carried out.
2 Re a c t. j o n s That Can Possibly Be Eliminated Promthe General Hechanjsn^
In addition to the "critical" parameters in the model whose values
must be determined with certainty, the model contains some parameters
that are almost insensitive. These are parameters for which large varia-
tions in magnitude result in small changes in the predictions. By identi-
fying those reactions that contribute minimally to the total predicted
response, the sensitivity analysis forms the basis for eliminating reac-
tions from the mechanism, subject to further limited individual testing
of each reaction over a range of initial conditions and bounds of uncer-
tainty. The elimination of insignificant reactions results not only in
a clearer perception of the fundamental process by which smog forms, but
-------
86
also in a reduction in the amount of computer time necessary to carry out
a simulation.
Reactions with S*U values of less than 1.0 are auite insensitive,
their rate constants are known with certainty, or both. Thus, this study
indicates that reactions exhibiting both low sensitivity and low S*U indices
should be tested individually over a range of initial reactant concentrations
and rate.constant uncertainty bounds to evaluate the effect that their
elimination would have on predictions. As noted earlier, we have shown
that reactions ranking 28 through 31 can be eliminated from the general
mechanism without a significant loss of accuracy.
D. CONCLUDING COMMENTS
The results of the sensitivity analysis depend on the initial concen-
trations of reactants chosen for the test. If the calculations were re-
peated with half the initial hydrocarbon and twice the initial NO used in
A
the present study, we would expect the ordering of rate constants to be
somewhat different than that shown in Tables 10 and 11. However, based
on our experience in applying the general mechanism over a wide range of
initial conditions and in carrying out a similar sensitivity calculation
for another reactant system (n-butane-propylene-NO ) [Roth et al. (1974)],
v X
our feeling is that the rankings in the two tables represent the approxi-
mate order of parameter sensitivity fairly well.
The sensitivity values calculated in this study can be used quantita-
tively to facilitate model evaluation. They can also be used to establish
weighting factors for regression analyses or linear programming studies
that optimize the agreement betv.'een predictions and experimental data by
perturbing rate constants within their bounds of uncertainty. The ordering
of the rate constants in Table 11 can also be used as a guide to kineticists
in choosing reactions for future study. Kincticists might contribute most
directly and meaningfully to the understanding of air pollution by investi-
gating the rates of those reactions that have been shown to introduce
significant uncertainty into the predictions of the kinetic mechanism.
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87
V ANALYSIS OF UCR DATA
Under EPA sponsorship, the Statewide Air Pollution Research Center
(SAPRC) at the University of California, Riverside (UCR), is presently
carrying out an extensive series of experiments in the UCR evacuable smog
chamber. The intended use of these data is primarily for kinetic mechanism
evaluation, although UCR is also engaged in an effort to detect and quantify
the presence of "novel" (speculated but heretofore unmeasured) chemical
species. Special care is being taken in the program to assess quantita-
tively the magnitude of chamber parameters.
Although the determination of chamber operating properties is an on-
going process, a particularly extensive characterization was undertaken in
the first phase of the UCR project. A number of experiments were carried
out to measure the photolysis rate of N0?, the spatial distribution of
light, the time required for an initial charge of reactants to distribute
homogeneously within the chamber., the decomposition rate of ozone on the
walls of the chamber, and the like. The details of these experiments are
being transmitted to EPA by the SAPRC periodically. We deal with the re-
sults here on a provisional basis and only to the extent needed to sub-
stantiate our choices of chamber parameters for the simulation of UCR
photochemistry runs.
Because of the extent of the chamber characterization effort under-
taken, the results of the first photochemistry (propylene/NO ) experiments
suitable for mechanism evaluation were not available for use until the last
working month of this project. The short amount of time that was available
for mechanism development before the end of this year's work, along with
the scheduling of the majority of photochemistry experiments next (project
calendar) year, have led us to defer detailed discussion of these first
experiments until next year. In lieu of presenting a version of the
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88
mechanism tentatively revised in accordance with the results of the
propylene/NO experiments, we chose to simulate the runs using the mechan-
A
ism presented in Tables 1 and 2. Because no changes other than those ne-
cessary to describe physical and chemical parameters of the UCR chamber
have been introduced into the general kinetic mechanism, these simulations
can be viewed as a test of the accuracy of the model in making predictions.
A. CHARACTERISTICS OF THE CHAMBER SYSTEM THAT AFFECT THE CHEMICAL KINETICS
As we stressed in Chapter I, it is extremely important to account for
physical and chemical characteristics of smog chamber systems when using
chamber data for mechanism evaluation. In this section, we summarize the
bases for all chamber parameter values that we must specify in carrying
out simulations of the experimental runs.
1. Light Intensity
a Spectral Light Distribution
The evacuable chamber is irradiated by a "solar simulator" (Beauchene
et al., 1973) positioned at one end of the cylindrical reactor. The spectral
emission pattern of the lamp and the transmission characteristics of the
quartz windows and special filters enable the spectral light distribution
within the chamber to simulate sunlight at sea level.
b S£
-------
3.0-
o
>
T: 2.0-
£ 1.0-
89
SOLAR SIMULATOR
POWER = 20 Kl!
I
10
20
Distance from Flange Face (inches)
(a) Port Near Back of Chanber
I
30
Ql
t->
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4.0-,
3.0-
2.0-
l.Tr
0 ,
SOLAR SIMULATOR
POWER = 20 KW
I
20
30
Distance fron riange Face (inches)
(b) Port h'ofir Simulator
FIGURE 22. SPATIAL DISTRIBUTION OF LIGHT WITHIN THE
EVACUABLE CHAMBER WITHOUT A REFLECTOR
-------
90
Approximately 85 percent of the chamber volume is irradiated at full light
intensity, and 15 percent of the chamber (including the wall boundary
layer) is weakly illuminated.
Under these conditions, the following question arises: In carrying
out a mathematical simulation of the chemistry occurring in this chamber,
should spatial variations in the light intensity be treated explicitly,
or can an "average" light intensity value be used without a significant
loss of accuracy? The answer to this question depends on the rates of
the photolytic reactions and the time required for the reactants in the
weakly irradiated portions of the chamber to mix into the bulk gas.
For example, consider the change in the average concentration of N0?
with time in the chamber that is due only to the photolysis reaction
N02 H- hv + NO + 0
in two extreme cases: (1) instantaneous mixing between the boundary
layer (weakly irradiated portion) and bulk gas and (2) no mixing between
the two volumes. For the purposes of this calculation, we also assume
that 85 percent of the volume is exposed to the full value of k-, , and
15 percent, to k, =0. The concentration of N0? as a function of time
for Case 1 is given by
r- I j N r- -U.uO k-, t / r- \
C(t) = C e i (5)
For Case 2, the situation in which no mixing between the irradiated and
nonirradiated volumes occurs, the average concentration of NO,, in the
chamber is given by
C(t) = 0.15 C0 + 0.85 CQ e~klt . (6)
-------
91
At t = 0, these expressions predict that the MCL concentration is identical
for both cases, as one would expect. As time passes, however, the predicted
N02 concentration in the "well-mixed" case decreases much more rapidly than
it does in the "no-transfer" case. The ratio of the predicted N0? concen-
tration in the latter case to that in the former case is
Concentration -k,t
D = no transfer _ 0.15 + 0.85 e
Concentration -0.85 k,t
well mixed e
Assuming that k, = 0.2 (a typical value for this chamber), the ratio in-
creases rapidly with time, as shown by the tabulation below:
T
(minutes) R
0 1
1 1.003
5 1.08
10 1.45
25 11.12
If, for example, the gas in the boundary layer actually takes five minutes,
on the average, to exchange with or mix into the hulk gas, and if we assume
that the mixina is instantaneous, the actual N00 concentration would be
" C-
8 percent higher than we would predict with an otherwise correct model.
In fact, an experiment carried out in the evacuable chamber indicates
that, at a distance of one-half radius from the center of the chamber, the
characteristic mixing time is one minute or less. The use of an average
photolysis rate constant for N0? determined experimentally in the manner
-------
92
described by Holmes et al. (1973) (photolysis of N02 in Ng) would, therefore,
be in error by only 0.3 percent according to Eq. (7).
We are presently using spatially averaged photolysis rate constants in
our simulations of UCR chamber data. However, we recognize the need for the
characteristic mixing times to be determined in the boundary layer and at
the center of the chamber before such usage can be considered "well justified."
c. Photolysis Rate of NOp
To determine the photolysis rate of N00 experimentally, UCR uses the
method described by Holmes et al. (1973). For the photochemistry experiments
simulated in Section V-B, the value of k, was 0.223 min" . However, the
intensity of the solar simulator has been found to diminish slowly with time.
Consequently, UCR redetermines k, often, and the value of ..k, presented here
jshould not be applied indiscriminately for the simulation of future experi-
mental data.
d. Photolysis Rates of Other Photoabsorbers
Doyle and Winer (1974) have made preliminary estimates of the photo-
dissociation rates of other photoabsorbing species present during organic/
NO smog chamber experiments. The pertinent reactions and rate constants*
are as follows:
Rate Constant
Rejiction (min" )
HNOg + hv > OH + NO 0.0138
HCHO + hv -» H + CHO 0.0010
HCHO + hv » H2 + CO 0.0013
CH3CHO + hv -» CH3 + CHO 0.0011
CH3CHO + hv -> CH4 + CO 0.0003
* The values were calculated for a light intensity at which k, = 0.223 min"
-------
93
We used these provisional values in our simulations of evacuable chamber
experiments.
2. Homogeneity of Reactants
Experiments have shown that approximately 20 minutes are required
for a reactant charge introduced in one end of the chamber to distribute
uniformly throughout the volume. Consequently, a period of 30 minutes or
more is generally allowed between charging of the chamber and initiation
of the photolysis. Homogeneity is checked before every photochemistry ex-
periment by continuous monitoring of the NO concentration at a single loca-
tion within the chamber.
3. 'Temperature
The temperature within the chamber is controlled through adjustments
of a heating/cooling circulation system on the chamber walls. The temper-
atures of both the walls and the gas being withdrawn for analysis are
determined once every 15 minutes. In general, the temperature during a
photochemistry experiment is maintained within t 3°F of the mean value
(usually 84°F). For the simulations presented in Section V-B, we assumed
that the temperature remained constant throughout the experiment. In view
of the small temperature variations and the substantial uncertainties as
to the activation energies of the reactions in the general mechanism, we
feel that this assumption was justified.
4. Hater Cone en t r a t i o n_
The relative humidity within the chamber is determined every 15 minutes
using a Brady Array. The water concentration can then be calculated directly
from the temperature, relative humidity, and saturation water vapor pressure
at the given temperature and total chamber pressure (1 atmosphere). Con-
centration-time profiles of H?0 for two of the evacuable chamber (EC) runs
(EC-11 and EC-16) simulated are shown in Figures 23 and 24. Typically,
the total variation of water concentration was about 10 percent of the
-------
94
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-------
96
mean concentration. In Run EC-16, the variation was as large as 18 percent
but was exhibited in a manner suggesting a short-time-measurement anomaly.
In simulating the photochemistry experiments, we assumed that the
water concentration is constant and is equal to the average value observed
during an experiment. We realize that under these assumptions the rates
of reactions involving water may be understated or overstated at times.
However, the rate constants of reactions occurring in smog are, for the most
part, significantly more than 10 percent uncertain. Furthermore, to our
knowledge, the role of water in the overall smog formation process is ex-
perimentally unquantified. We recommend that a series of orgam'c/NO /air
A
experiments be carried out at various water concentrations to determine
what effect, if any, water has on the rate of formation and the observed
distribution of products. If such experiments were to show that large
variations in the water concentration affect the process only minimally,
the use of a constant average value in our simulation would be substantiated.
5. Wall Effects
Scientists have shown that the surface-to-volume ratio and surface
materials of a smog charber influence the overall chemical process observed
(cf. Seinfeld et al., 1973). The detailed nature and magnitude of the
effects of surfaces on the kinetics, however, are poorly understood. The
only wall reaction that has been considered extensively is the heterogeneous
decomposition of CL [see references in Seinfeld et al. (1973)] which can be
represented as
ko
03 +3 Wall
a. Heterogeneous Loss of Ozone
Scientists at UCR carried out several ozone decay experiments during
the first phase of the project to determine kn . The chamber preparation
U3
-------
97
for a kn experiment" was the same as that made for a photochemistry ex-
3
periment. First, the reactor was pumped to a few microns of mercury
pressure. Air containing about 1 ppm of CU was then rapidly introduced
into the chamber, and a total pressure of 1 atmosphere was achieved through
the addition of pure air. Subsequently, the time required for one-half of
the ozone to be consumed in the dark was determined. The half-life was
found to be about 8.35 hours.
If we assume that the loss of CL during a decay experiment is attri-
butable entirely to the reaction on the walls, the rate of CL decay is
given by
d03
dt~
The half-life of (k is related to the 03 decay constant as
from which we calculate that kn = 0.0014 min" . This value indicates, for
^
example, that the rate of 0, loss to the walls will exceed the rate of loss
due to reaction with propylene, should the.concentration of C^Hg in the
reactor be less than 0.08 ppm. (Two of the eight experiments in the propy-
lene experimental block considered in Section V-B have an initial C^H,-
o o i
concentration of 0.1 ppm.) Thus, the rate of 0- decay in the UCR chamber /
is significant, and the 0~ wall loss reaction must be included in our
simulations.
Ozone decay experiments were also performed under irradiated, rather
than dark, conditions, and the 0^ half-life was found to be about 4.25
hours. We believe that this decrease in the 0, half-life from that ob-
served in a dark chamber is due to a series of chemical reactions involving
On 0( D), H?0, free radicals, and light, rather than any intrinsic change
in the activity of the walls when the solar simulator is in operation.
-------
98
(Recall that the solar simulator has been focused so that it does not
shine directly on the cylindrical surfaces.)
We carried out a mathematical simulation of the August 15, 1973 light
decay experiment, which was similar in all ways, except for the presence
of light, to the dark decay experiments used to calculate k~ above. We
assumed that the 12 reactions in Table 12--in idd_ijtign_to the ,wall reaction--
participated in the total 0., decay process.
The 03 photolysis rates were based on the results of Demerjian et al.
(1974), who calculated the photolysis rates of N0?, 0,,, and many other
species for sunlight with z = 46°. Under those conditions, they calcu-
lated that the photolysis constant for NOp was 0.48 min" . Since the rate
of that reaction in the UCR chamber is 0.223 min" , we scaled Demerjian's
0~ photolysis constants by 0.223/0.48. He further assumed that the rate of
HpOp photolysis was 1/250 of the rate of NOp photolysis. This rate constant
is quite uncertain; we found that this reaction can be eliminated from the
mechanism without seriously affecting the reactions, and so the choice of
this rate constant is not critical. The rate constants of the other re-
actions are based on the recommended values of Garvin and Hampson (1974)
and Demerjian et al. (1974).
Integrating this mechanism and using the initial conditions for the
experiment ([03]Q = 1.15 ppm, [H20] = 2.0 x 104 ppm, [02]= 2.0 x 105 ppm,
and [ll] -- 1.0 x 10 ppm) resulted in a predicted 03 half-life of 4.48 hours.
The observed half-life for this particular experiment was 4.35 - 0.09 hours.
The results of this exercise are consistent with the following tenta-
tive conclusions. First, the "true" 0^ wall decay constant appears to be
that measured in the dark, rather than the illuminated, decay experiments.
Second, the 0~ photolysis reactions, which initiate reactions such as
1
0( D) + HpO, are an important sink for 0~ and should be considered in
future smog chamber simulations. In the simulations discussed subsequently,
we use the value of k~ determined in the dark. The sequence of reactions
initiated by the photolysis of 0~ will be included in the next formulation
of the kinetic mechanism.
-------
99
Table 12
REACTIONS PARTICIPATING IN THE TOTAL OZONE DECAY PROCESS
Number Reaction Rate Constant*
1
2
3
4
5
6
7
8
9
10
11
12
13
03 ->- Wall 1.38 x
03 + hv -» 0(1D) + 02 1.58 x
03 + hv » 0(3P) + 02 9.76 x
0(]D) + M + 0(3P) + M 8.70 x
0(3P) + 02 + M '+ Q3 + M 2.00 x
0(]D) + 0., -> 200 9.80 x
3 C
O^D) + H20 -> 20H 5.25 x
OH + 0, -*- H00 + 00 8.60 x
3 C. L.
H09 + 0, -> OH + 200 2.40
Co c.
H02 + H02 -> H202 + 02 8.40 x
H202 + hv -v 20H 8.90 x
OH + OH + H20 -* H202 + H20 3.25 x
Oil + OH + M -> H202 + M 6.50 x
10"3 min"1
10"3 min"1
10"3 min"1
104
-5 -2 -1
10 ppm min
io4
5
IO1
IO3
IO"4 min"1
-1 -? -1
10 ppm " min
-2 -2 -1
10 ppm min
* In units of ppm" min" unless otherwise indicated.
-------
100
b. Wall Off-Gassing
After several consecutive photochemistry experiments had been conducted
in the evacuable chamber, a study was made of the rate of wall off-gassing.
The reactor was evacuated, refilled with nitrogen, and irradiated for 5.5
hours. The maximum concentrations of the species monitored were as follows:
Maximum Concentration
Species (ppm)
HCHO None detected (less than 0.02)
CH-CHO 0.002
acetone 0.012
methyl ethylketone 0.0014
NO " 0.005
N02 0.004
03 0.028
The concentrations of the two aldehydes are of little concern, since
the formaldehyde and acetaldehyde concentrations observed in virtually
every experiment in the propylene photochemistry block exceeded the measured
background values by a factor of 10 or more because of off-gassing. Although
the acetone and MEK concentrations are a sizable fraction of the values ob-
served during the photochemistry experiments, neither of these species is
particularly reactive, especially at these concentrations.
The background N0? level due to off-gassing is much lower than that
observed in most propylene photochemistry experiments and probably need
not be considered further.
The measured NO concentration is more disturbing. In most of the
propylene-MO experiments discussed in the following section, the NO (after
J\
the N02 peak) stabilized at about 0.005 to 0.009 ppm--well within the range
of off-gassing levels observed in the irradiated chamber. Since the exact
-------
101
rate of NO off-gassing depends on the chamber operating history (e.g.,
was the previous experiment conducted at high initial NO levels?), it is
extremely difficult to account for this effect properly. Thus, we do
not now include a source term in the kinetic simulations for NO due to
wall emissions.
A very small amount of 03 was measured during the off-gassing experi-
ment. Because the investigation was conducted in a pure N?, rather than
an air, atmosphere, ozone formation due to the reaction
0
may have been suppressed. Consequently, the 03 produced as a result of
reactions involving off-gassed organics and NO may be understated. At
/\
present, we make no correction for this wall-related effect because its
true magnitude is still unclear.
c. Other Effects
Reactions such as
NO + N02 + H20 -> 2HN02
and
M n j. u r, . 9|-!i\jn
1 »rj w ^- ' I I Q V-1 f i~\.\\\\J Q
C- O ^_ v5
are thought to proceed more rapidly on surfaces than in the gas phase.
And PAN, like 0,,, may decompose on the walls. The PAN reaction, however,
is the only additional wall effect to be studied at present.
-------
102
6. Analytical Methods and Dilution Due to Sampling
a. Instrumentation
The accuracy, precision, and range of applicability of the analytical
techniques and instrumentation used in measuring the chamber conditions
and the concentrations of reactants and products are summarized in Table 13.
All of the chemical measurement techniques have been discussed extensively
in the literature, and synopses of the methods are presented in Seinfeld
et al. (1973). Instruments and techniques employed for the physical measure-
ments will be discussed in a forthcoming UCR report; we note here only that
instruments are recalibrated frequently to ensure accurate, precise measure-
ments.
b. Sampling and Dilution
Four chemical analyzers operate continuously throughout each experiment:
Dasibi 1003 for ozone, Mast for oxidant, Teco for NO and NO , and Beckman
A
6000 for CO. An additional continuous instrument, the Bendix, is used
occasionally to determine NO and NO . Samples for two other analyses--
A
organics using a gas chromatograph (GC), and formaldehyde (HCHO) using
the chromotopic acid methodare taken on a discrete (usually periodic)
basis. Together, these instruments abstract about 15 percent of the
original chamber volume during a six-hour experiment.
The timing of sample withdrawals for the CC and HCHO analyzers is as
follows. Five samples for GC measurements are taken at the beginning of
a run. Thereafter, one sample is withdrawn every 15 minutes for propy-
lenc, one every 30 minutes for PAN, and three additional every hour for
all organic species other Lhan HCHO; all GC samples are 200 cc. The dura-
tion of HCHO sampling symmetrically spans the recorded time.* Thus, if,
for example, the log shows a 30 liter HCHO sample at 1230, sampling was
begun at 1215 and was terminated at 1245.
* Except at t = 0, when the sample is taken in the 30 minutes prior to
the irradiation.
-------
103
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Because the GC and HCHO samples are taken at varying time intervals,
rather than continuously, the dilution rate fluctuates somewhat. The GC
sampling rate is small (less than 2 liters/hour) in comparison with the
continuous (typically 120 liters/hour) and HCHO (30 liters/hour) sampling
rates; the assumption of continuous sampling for GC introduces less than
1 percent average error in the instantaneous dilution rate. The HCHO
sampling cycle is normally 30 minutes on followed by 30 minutes off. Al-
though the instantaneous sampling rate for HCHO swings ± 25 percent about
the average HCHO sampling rate, we assumed that the sample for the HCHO
measurement is withdrawn at a continuous average rate. The total sample
loss due to HCHO analysis is small enough that no appreciable error results
from this assumption. The dilution constants for each UCR photochemistry
experiment considered in tuis report are listed with the initial conditions
in the following section.
As samples are withdrawn from the chamber, an equal volume of replace-
ment air is introduced to maintain the chamber pressure at 1 atmosphere.
The replacement gas is room air that passes through a canister containing
activated charcoal and Purafil for removal of hydrocarbons and MO , respect-
A
ively. Experiments have shown that the system is capable of reducing back-
ground MO in the air to 0.005 ppm, acetaldehyde to 0.001 ppm, acetone to
0.005 ppm, methyl ethylketone to less than 0.001 ppm, and CO to about 2.0
ppm. The background levels on any given day depend somewhat on the pollutant
concentrations in the outside air. Our concern v:ith those background levels
is essentially that stated in our discussion of off-gassing. Fortunately,
however-, must of the sir from the clean air system is introduced before an
irradiation is undertaken; so the concc-n1',rolion of any reactents present in
the background air are accounted for when the initial conditions of the cham-
ber (t = 0) are determined.
B. SIMULATION OF UCR PROPYLENE/NO EXPERIMENTS USING THE GENERAL MECHANISM
The data generated in the UCR evacuable chamber provide a reference
against which the predictions of the general mechanism can be measured.
Because the mechanism cannot predict the concentration-time histories of
many chemical species accurately over a wide range of initial reactant
-------
106
ratios, we seek clues to specific weak points in the mechanism by thoroughly
examining disagreements between data and predictions. In fact, our efforts
to reduce the discrepancies between predictions and data often result in
the introduction of new reactions into the mechanism and in the variation of
certain rate constants within their uncertainty bounds.
As a prelude to the utilization of the UCR data for the further develop-
ment of the general mechanism, we carried out simulations of the first seven
UCR propylene/NO photochemistry experiments. These simulations essentially
A
use the formulation of the general mechanism presented in Tables 1 and 2,
which was tested extensively in relation to NAPCA propylene/, n-butane/,
and propylene/n-butane/NO data. Only those reactions and rate constants
X
explicitly affected by characteristics of the UCR chamber were altered.
Specifically, the rates of photolysis of NOp, HNCL, and aldehydes were
changed in line with the discussion in Section V-A; and the reaction for
DO decay on the walls, using the constant determined in the darkened UCR
chamber, was included in the mechanism. No attempt was made to improve
the agreement between predictions and the UCR data (that, of course, is
the goal of next year's project). Consequently> these simulations can be
viewed as a test of the mechanism in Tables 1 and 2.
The initial conditions for the seven experiments, which are the first
of about fifty scheduled to be conducted in the evacuable chamber as part
of the EPA-UCR chamber program, arc listed in Table 14. Since two pairs
of experiments are essentially replicate runs (which differ enough that
they cannot bo compared diroclly), the seven experiments fill only five
positions in the following propylenc'/MO factorial block:
/\
-------
107
1.0
o
16
0,5
o
21
0.1
0.1
o
18
0.5
Propylene (ppm)
1.0
Predictions of the general kinetic mechanism and the experimental results
for the seven EC runs are presented graphically in Figures 25 through 38.
In some cases, severe discrepancies occur between the predictions and
the experimental observations. The time of the predicted M0? peak is, for
the most part, late compared with the data, and the predicted 0., level and
rate of propylcno oxidation are less than those observed for every run.
The predicted aldehyde maxima are in good agreement with the data for some
of the experiments but are low for the others. Finally, the quality of the
PAN predictions varies, but, in general, the predictions are low for runs
with [propylene^Q ----- 0.1 ppm and high for all of the other runs.
Many possible explanations can account for these discrepancies. First,
we suspect that the kinetic mechanism in Tables 1 and 2 may be "chamber
dependent." By this we mean that values of uncertain rate constants may have
unknowingly been chosen to compensate for effects attributable to the MAPCA
chamber system not explicitly included in the kinetic mechanism. As a result,
-------
108
while we thought we were modeling just the gas phase chemistry in the NAPCA
chamber, we may, in fact, have been tuning the reaction set in relation to
gas phase reactions and chamber effects. Second, the set of reactions in
Table 1 may be incomplete. In discussing the 03 wall decay constant, v/e
presented evidence to suggest that a reaction sequence involving the photol-
ysis of 03 and the oxidation of water by 0( D) may be important in the UCR
chamber. Other reactions may also be omitted from or misrepresented in the
general mechanism, as noted below:
> The reactions of the OH-olefin adduct are poorly understood
and may be oversimplified in Table 1.
> Formic acid is observed as a product in the UCR chamber but
is not predicted by the mechanism. Does it result from an
0,,-olefin reaction, from formaldehyde oxidation, or from
other sources?
> PAN may react with H?0 or other species found in a smog chamber.
No such reactions have been included in the general mechanism.
Finally, many of the rate constants may be in error. Garvin and Hampson
(1974) have recently evaluated the rate constant values of many of the
reactions in the general mechanism. Host of the values in Table 2 are
close or identical to their recommended values. However, the rate constants
in Table 2 of the two radical chain termination reactions, OH + N0? and
OH + [\05 are high (compared with the values of Garvin and Hampson) by a
factor of greater than 2. Other rate constant values not yet evaluated
by NBS may also be in serious error.
In the next phase of this project, we will pursue these and other pos-
sibilities. Many kinetics laboratories that were being used primarily for
the study of stratospheric reactions until recently are now being used in-
creasingly for the study of smog-related reactions. Consequently, we expect
that our knowledge of the elementary kinetics will continue to improve sub-
stantially in the forseeable future. We believe that the UCR evacuable
chamber is one of the best characterized in the country and that it is well
suited for the experimental study of complicated organic/NO /air reactant
X
systems.
-------
109
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PART 2
METHODOLOGY
-------
125
VI TECHNIQUES FOR EVALUATION THE KINETIC MECHANISM
Without methods for testing, analyzing, and proving the chemists'
conjectures, proposing kinetic mechanisms is an empty exercise in theoretical
chemistry. In this portion of the report, we present techniques that we
have developed to assist in the all-important task of evaluating a proposed
mechanism in light of the available experimental data.
Chapter VII discusses the types of analytical tools that are necessary
in this evaluation and describes a computer program that embodies these
tools. In addition, Appendix A (bound separately) is a complete user's
manual and programmer's guide to the computer program that was developed
under this contract.
Two of the tools useful in the analysis of chemical mechanisms, the
steady-state assumption and the "lumping" of similar species, are dealt with
in detail in Chapters VIII and IX, respectively. Both of these topics have
engendered controversy in the past, and, since both are present in our
analysis programs, we felt that an in-depth treatment of their justifica-
tion as a means of simplifying the calculation of chemical kinetics was
appropriate. In both cases, actual numerical examples are offered in
defense of the validity of the techniques.
-------
126
VII AN AUTOMATIC COMPUTER PROGRAM FOR EVALUATION
OF KINETIC MECHANISMS
Once a set of reactions for the formation of photochemical smog has
been proposed, it is necessary to demonstrate that the mechanism is correct;
i.e., it is able to account for, within experimental error, the actual con-
centration of each species present in the reaction mixture at any point
during the time span of the reaction. This evaluation process involves,
in its simplest form, the formulation and solution of the set of coupled
differential equations that describe the variation in the formation and
consumption of each species in the reaction mixture as a function of time.
This set of equations can be expressed as
dyi ^ f-
t J=l i,j k=l ci,k
where the following definitions apply:
Y. the concentration of Species i
t time
Rf the rate of formation of Species i in Reaction j of the
i,j set of J reactions that form Species i
R the rate of consumption of Species i in Reaction k of the
ci,k set of K reactions that consume Species i.
The concentrations thus calculated can be compared with those measured
experimentally in the reaction mixture.
Unfortunately, the real world presents experimental, computational,
and operational obstacles to the pursuit of this simple validation scheme.
First, for the integrity of the reaction mixture to be preserved, the
-------
127
mixture must be contained in some sort of reaction chamber, which in turn
gives rise to two side effects: leaks (intentional, as in sampling, or un-
intentional) and wall reactions. Second, when the most efficient computer
codes are used, the time needed to solve the coupled differential equations
increases as the square of the number of species. Moreover, certain sets of
rates lead all too often to sets of "stiff" equations, for which the solution
times can approach infinity. Finally, the urge always exists to "improve"
a reaction mechanism, no matter how closely it approximates the experimental
data; the computer code must allow these changes to be performed with a
minimum amount of effort. In dealing with these realities, the researcher
is called upon to display his mettle and to tax his ingenuity. The approaches
we used in this study are described in this chapter.
A. CHAMBER EFFECTS
With few exceptions, reaction chambers are not completely airtight.
Under normal operating conditions, this does not create a serious problem,
since almost all chambers are maintained at atmospheric pressure, and since
the small amount of interchange by diffusion can usually be ignored. How-
ever, a problem does arise when samples are removed from the chamber for
analysis. Since the species that comprise smog exist in the atmosphere
in minute (1 to 1000 ppb) concentrations, sample sizes on the order of a
few liters are commonly needed to obtain enough material for an accurate
analysis. Moreover, samples must be withdrawn fairly frequently during
the reaction to monitor species concentrations that are changing rapidly.
As a result, it is not unusual for 10 to 20 percent of the chamber volume
to be withdrawn through sampling procedures. The reaction simulation
technique must take this "dilution" of the reaction medium into account.
In the ideal case, the gas used for replacement of withdrawn samples
is inert with respect to the reaction (e.g., pure nitrogen in a smog
system), or it contains only reactive species whose concentrations are
so largerelative to the amounts consumed or produced by the reactions
that they can be assumed to be constant throughout the reaction (e.g., oxy-
gen or water vapor in "clean" air). In this case, it is sufficient to
-------
128
apply a "dilution factor" to the concentrations of all the species (inert
diluent) or to those that do not remain constant (clean air diluent). If
samples of more or less constant size are removed at reasonably uniform
time intervals, the dilution factor can be considered to be a constant,
Q, and the equation for the rate of change of the concentration of Species
i becomes
dy. J K
dt1 = E Rf - ZRC -YfQ - (9)
dt j=l Vj k=l Ci,k 1
In some chamber experiments, however, the incoming medium is just the
natural atmosphere in the laboratory, which may contain concentrations of
pollutant species as high as or higher than those being followed in the
reaction chamber. Moreover, it may be desirable in some cases to inject
pollutants or pollutant precursors deliberately into the chamber to simulate
the effect of fresh emissions on the reaction mechanism. As long as the
concentration of Species i, y. , in the incoming medium is known, the
effect of such inflowing species on the rate equation can be easily expressed:
dy. '0 K
dt1 = £Rf -E Rc - (y-j -yin)Q do)
dt j = l M,j k=l ci,k n in
Unfortunately, wall effects cannot be handled as neatly. Wall absorption
is best determined by placing the species in question. A, in a "nonreactive"
environment within the chamber and following its decay with time. One can
then include within the reaction mechanism an equation such as
A + Wall , k , (11)
a
with an appropriate rate constant.
Heterogeneous catalysis by the reactor walls is even more troublesome.
However, by determining reaction rates at several different surface-to-volume
-------
129
ratios for the reactor (e.g., through the use of "artificial" walls to par-
tition the chamber), the rate constants for the homogeneous and heterogeneous
reactions can be obtained, and both reactions can be included in the
mechanism:
A + B * C , kc , (12)
(Wall)
A + B -> C , kw . (13)
B. COMPUTATIONAL ASPECTS
As mentioned earlier, the computer time required to solve a set of dif-
ferential equations increases at least as the square of the number of equa-
tions to be solved (or, in the present case, as the square of the number of
distinct chemical species that appear in the reaction mechanism). Thus, any
techniques that can be used to decrease the number of species concentrations
that actually require coupled differential equations for their solution should
be applied. Such techniques include the assumption of constant concentra-
tion; the uncoupling of product-only species; the invocation of the steady-
state approximation; and the aggregation, or "lumping," of species that
yield similar products. Tl.e last two techniques are the subjects of ex-
tensive discussion in Chapters VIII and IX and are thus not treated here.
As mentioned earlier, certain species that appear in the reaction mech-
anism either are present, at truly constant concentrations (e.g., the reactor
walls) or heve concentrations so highrelative to the amounts of that spe-
cies formed or consumed during the reactionthat they remain essentially
constant with respect to time (e.g., oxygen). Since the change in concen-
tration for these species is only negligibly different from zero, they can
be excluded from the differential equation process.
A second category of species that need not be included in the set of
coupled differential equations is comprised of those species that appear
in the reaction mechanism only as products (e.g., CO,, or HNOO. The rate
C- O
of formation of these product species is, to be sure, represented by the
-------
130
following differential equation:
dt~ "
However, the presence of this species has no effect on the rate of formation
of any other species; thus, the differential equation describing its forma-
tion can be uncoupled from the set of all differential equations and solved
independently, at a significant savings in overall computer time.
C. EASE OF CHANGING REACTIONS
Most computer codes used in the simulation of reaction kinetics incor-
porate, in one form or another, the features described above. The major
advantage offered by the present program is the ease of preparation and,
particularly, the ease of alteration of the mechanism and its associated
species concentrations. The user need know nothing about computer program-
ing or the solution of differential equations, and very little about chem-
ical reaction mechanisms, to obtain meaningful results from the program.
On the first line of input, the user specifies the run identification,
the number of reactions in the mechanism to be studied, how many of these
are lumped reactions, the number of each of the various types of species
described in Section VII-B, and an indication as to whether the reaction
rates should be printed. The second line continues this specification of
parameters with an indication of the frequency of printout, the time step
sizes, and the dilution factor.
The user then submits his reaction mechanism, one reaction per line,
restricted only by one requirement on ordering: The lumped reactions must
appear last. Each reaction appears as an ordinary chemical equation, with
a list of reactants, a list of products, and a rate constant. The products
can have coefficients (either fractions or integers), but the reactants
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131
cannot--each reactant molecule must be entered separately. The user can
choose any four-letter mnemonic he wishes for the species names.
If there are any lumped reactions, the sets of individual reactions
comprising each "lump" are then entered. Their formulation is exactly the
same as that of the lumped reaction, except that the name of each species
that contributes to the composition of the lump appears in place of the
lumped species as the first reactant.
The user then provides the list of species and their initial concentra-
tionsone per line. The order of their types must be the same as that
given on the initial parameter line, but no particular order is required
within each species type.
Should any of the species be present in the gas flowing into the re-
action chamber, their concentrations in the inflowing stream and, if needed,
the time and new values of any change in this concentration are entered
next. Finally, the user can request concentration-time plots of any species.
If he so desires, these plots can contain experimental points with which
those points calculated by the proposed mechanism can be compared.
To change a rste constant or chemical reaction, the user need merely
alter the corresponding input line. New reactions can be added by insertion;
old ones can be removed by deletion. A similarly ear.y process can be used
to change an initial species concentration or to eJd or remove species names
from the list. Species can bo transferred among species types (e.g., dif-
ferential to steady state) by a single interchange of lines.
As previously noted5 a complete user's guide to the computer program
is included in Appendix A. This appendix (bound separately) provides de-
tailed information on each of the features described above, descriptions
and listings of all of the computer routines, and sample inputs and outputs.
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132
VIII THE QUASI-STEADY-STATE ASSUMPTION
OF CHEMICAL KINETICS
The use of the quasi-steady-state assumption (QSSA) is probably as old
as the theory of chemical kinetics itself. First developed by Bodenstein
in 1913, this method essentially replaces the differential equations by
algebraic ones in the rate equations for certain intermediate or transient
species (Benson, 1960). Consequently, it considerably simplifies the rate
equations, since the solution of differential equations is, in general,
more difficult than the solution of comparable algebraic equations. Thus,
the quasi-steady-state assumption has often been invoked not only in the
early stages of the development of kinetic models for photochemical smog
to simplify the complex system of rate equations (Westberg and Cohen, 1969;
Friedlander and Seinfeld, 1969; Hecht and Seinfeld, 1972), but also in the
literature (Smith and Urone, 1974).
With the recent development of increasingly high-speed digital com-
puters and with the availability of ingenious software packages designed
to solve systems of stiff ordinary differential equations [e.g., the Gear
method (Gear, 1971)], the desirability of invoking the quasi-steady-state
assumption has been questioned (Gelinas, 1972; Farrow and Edelson, 1974).
In view of this controversy, we review the QSSA in this chapter.
We first discuss the reasons why the quasi-steady-state assumption
must be invoked under certain specific situations. The reasons (or the
needs) for the QSSA obviously cannot alone justify its use if unacceptably
inaccurate or erroneous results are obtained by invoking the QSSA. The
rest of the chapter is devoted to a quantitative assessment of the validity
of the quasi-steady-state assumption.
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133
A. THE NEED FOR THE QUASI-STEADY-STATE ASSUMPTION
Regardless of its validity, the quasi-steady-state assumption is only
an approximation of the full set of differential equations. Thus, this
assumption should not be invoked without a legitimate reason. Although
the most compelling reason for using the QSSA is always its simplicity,
its applications in the past can be conveniently grouped into two categories
of uses: analytical solutions and numerical solutions.
For many complex problems, it is often desirable to obtain analytical
solutions, possibly at the expense of accuracy. In these cases, drastic
simplifications have to be made; the quasi-steady-state assumption, when
applicable, has been the most powerful tool available to simplify the
kinetic equations. An example of this type of application appears in the
analysis of laminar flames (Williams, 1965). In the so-called fundamental
approaches, the quasi-steady-state assumption has been invoked in a non-
isothermal system that involves molecular transport processes and multiple
chemical reactions. After other suitable approximations have been introduced,
closed-form solutions for the radical distributions and burning velocity
can be obtained from the simplified set of equations. This procedure has
proved to be extremely useful in the study of the ozone decomposition flame
(Von Karman and Penner, 1954), the hydrogen-oxygen flame, and the hydrogen-
bromi.ne flame (Milan and da Riva, 1962).
With the availability of high-speed digital computers, the number of
problems that are solved by directly seeking numerical solutions has been
rising. Although the use of the quasi-steady-state assumption in such
cases is not uncommon, its application is frequently suspect and has thus
been the subject of controversy. The major advantage of introducing the
quasi-steady-state assumption apparently lies in the savings in computa-
tional effort that can be realized because solving a system of algebraic
equations is, in general, easier than solving a comparable system of dif-
ferential equations. In cases where explicit solutions can be obtained
for species for which the quasi-steady-state assumption has been invoked,
the savings can be particularly substantial.
-------
134
For kinetic mechanisms, such as those employed to delineate the photo-
chemical transformations in urban atmospheres, which may involve as many
as 50 elementary reaction steps, a typical simulation requires only a few
tens of seconds of computing time on a modern computer, even when the full
set of equations is used. Since the savings in computational time resulting
from the use of the QSSA can amount to, at best, only a fraction of this
relatively small amount of computing time, the invocation of the assumption
is not justifiable per se in a kinetic study. However, studies of chemical
kinetics are often imbedded in a larger and more complicated system that
involves both physical and chemical processes. A superb example is the
role played by photochemistry in the study of urban air pollution. Since
the numerical solution of the entire problem requires considerably larger
amounts of computing time (for instance, the SAI airshed model presently
uses one hour of 360/165 computing time for a ten-hour simulation), the
savings achieved by invoking the quasi-steady-state assumption in the re-
peated solution of the chemical kinetics is by no means trivial. Preliminary
estimates indicate that a savings in comoutinci time of UD to 30 percent can be
realized if a moderately complex kinetic mechanism (involving, say, 50 ele-
mentary steps) is incorporated into the urban airshed model. Therefore,
the QSSA certainly ought to be an important consideration in the development
of a more complex kinetic model if the eventual application is to be coupled
with an urban airshed model.
B. THE VALIDITY OF THE QUASI-STEADY-STA'lE ASSUKPTION
WHEN APPLIED TO A SIMPLE KINETIC MECHANISM
In addition to its succnss when applied to short-lived intermediates
in straight-chain reactions, the quasi-steady-state assumption has been
shown to be a valid approach for many other cases that cannot be strictly
classified as chain reactions. However, the exact conditions under which
the quasi-steady-state assumption is valid have been extremely difficult
to delineate. To illustrate the major features that are involved in this
approach, we discuss here a simple example concerning the conversion of
ortho-hydrogen to para-hydrogen. The reaction mechanism for the initial
phase of the conversion can be described (Williams, 1965) by
-------
135
kl
+ X +' 2H + X , (15)
H + Ortho H2 + Para \\2 + H , (16)
h
2H + X v3 H2 + X . (17)
If we denote the concentrations of the following species by
[Ortho H2] - a
[Para H2] = 3
[H]
the rate equations for the product g and the intermediate y can be
written as
/-,0\
dt ' ' '
Jn Eo,. (19), the conservation law for hydroc;en is invoked:
[H21 - [Ortho I!2"J ^ [Para II,,] --- constant
(19)'
* We use k, and ki to represent the quasi-first-order and quasi-second-order
reaction rates for reaction Steps 1 and 3, respectively.
-------
136
Through a differentiation of this relationship, a rate equation for a can
be found:
(20)
We now consider Eqs. (18) through (20), subject to the following initial
conditions:
a = A (21)
U = 0 , (22)
Y = 0 . (23)
1. Exact Solutions
Analytical solutions for the system of equations posed above can be
obtained. By eliminating a and 3 from Eqs. (18) through (20) and by in-
voking the initial conditions given in Eqs. (21) and (22), we find that
^ = -2k^Y2 ^ 2k] A . (24)
This is a Riccati equation, the exact solution to which, subject to
Eq. (23), is the following (Kainke, 1971):
''exact - tan" 2'H 4 /t ' (25)
By substituting this solution for y in Eq. (20), we can obtain the exact
solution for a:
-------
137
aexact = A
cos h fzy
/ ' V ' A t I
\ 1 r\ n r\ c i
/
"24
(26)
2. Quasi-Steady-State Solutions
In this section, we seek the corresponding solutions for the system
of equations when the quasi-steady-state assumption is applied to the
reaction intermediate H. Thus, by setting the left-hand side of Eq. (19)
equal to zero, we immediately obtain the solution for y:
'QSSA
(27)
Using this solution in Eq. (18), we can easily find the quasi-steady-state
solution for a:
aQSSA
- A
(28)
These solutions [Eqs. (27) and (28] can then be compared with their counter
parts obtained above in Eqs. (?.5) and (26).
'
lt is quite clear from a comparison of Eos. (25) and (?6), as shown
in Figure 39, that differences betv.'een the two solutions depend upon the
relative magnitudes of the time of interest and a characteristic time T
defined by
T =
1
(29)
A
-------
138
1.0
0.5
Exoct
QSSA
= o.oi
T-= O.I
ki.
'=0.5
0
1.0
2.0
C.
o»
o
S-
o
03
X
CD
~= 0.5
A t
FIGURE 39. COMPARISONS OF THE EXACT AND THE QSSA
SOLUTIONS FOR STABLE SPECIES
-------
139
If the time of interest is considerably larger than this characteristic
time,
t » T
(30)
which is likely to occur if
_
A
(31)
then the analytical solution in Eq. (25) can be approximated by
VI-
t » T
(32)
which, of course, is the same as Eq. (27). Under the condition given in
Eq. (30), the exact solution for a [Eq. (26)] also reduces to
exact
A t
V2T3/
- A 2 6 e
A t
t » T
(33)
Comparing Eqs. (28) and (33), as illustrated in Figure 40, we find that
the error committed by the invocation of the quasi -steady-state assumption
in the calculation for a stable species is bounded by a constant. This
constant is dependent upon the ratio of the two rate constants k?
and
-------
140
-,-I-PO
1.0
0
,QSSA
1.0
2.0
0)
o
S-
GJ
CL
00
00
01
u
rd
X
o>
300 h
200 f-
100 &-
0
1.0
2.0
FIGURE 40. COMPARISONS OF THE EXACT AND THE QSSA
SOLUTIONS FOR THE REACTION INTERMEDIATE
-------
141
\2k' /
Error = 2 x J ' -1 , (34)
which tends to decrease to zero if
k'
f- » 1 . (35)
K2
For finite but large kVkp, the values of the error are tabulated in
Table 15. As Table 15 shows, for large values of kA/kp, the quasi-steady-
state solution is sufficiently accurate.
More insights can be gained if the above mathematical discussions are
translated into physical descriptions. The validity of the quasi-steady-
Table 15
ERROR RESULTING FROM THE USE OF THE QSSA
* Error
1.0 41.4%
0.5 18.9
0.1 3.52
0.01 0.35
0.001 0.035
-------
142
state assumption, according to this simple example, is always associated
with a very large rate constant* governing the consumption rate of the
intermediate in question [in the above example, k~ ; see Eqs. (31) and (35)].
Under this condition, the intermediate disappears as soon as it is formed;
thus, after a short time period, the validity of neglecting the time deri-
vative (i.e., justifying the invocation of the quasi-steady-state assumption)
is evident. The invalidity of the quasi-steady-state assumption during this
short time period, which might be called an "induction" period, is related to
the boundary layer feature of the problem; a small parameter (in the above
example, k?/ki) is associated with the highest derivative, a singular per-
turbation problem (Cole, 1968). Thus, the use of the quasi-steady-state
assumption can be viewed as a formal procedure to obtain the zeroth order
outer solution that is apparently invalid within the boundary layer (i.e.,
a short period of time). This aspect has been pointed out in a slightly
different context by Bowen, Acrivos, and Oppenheim (1963).
According to the above analysis, the error incurred by invoking the
quasi-steady-state assumption when it is valid remains constant or decays
with time, in contrast to other types of errors, such as numerical errors
due to finite differences, which generally grow with time because of accu-
mulation. In fact, this feature has not only been demonstrated by Giddings
and Shin (1961) for many other types of reaction mechanisms, but also it
* This large rate constant will, on the other hand, inevitably introduce
severe "stiffness" problems if the full set of equations is being used.
In the limiting case, when this rate constant is extremely large, the
invocation of the quasi-steady-state assumption is probably the only
means of obtaining solutions, since it is doubtful that even the Gear
method can reasonably deal with this situation.
-------
143
has been confirmed by two numerical experimentsone reported by Gelinas
(1972) and one carried out in the present study and discussed later.
C. A GENERAL THEORY ON THE VALIDITY OF THE QUASI -STEADY-STATE ASSUMPTION
Despite the conclusive results, the findings presented in the last
section are, rigorously speaking, applicable only to that specific mechanism;
furthermore, the procedure used in the analysis cannot always be duplicated.
This is particularly true for complex mechanisms where exact solutions are
impossible to obtain and where interactions are expected. Based on this
work, however, some of the logic involved in the derivation of the conclu-
sions can be generalized to a certain extent. This section describes our
preliminary efforts in this direction.
We consider the following general expression to be the full set of
rate equations for the kinetic mechanism:
dyi
dt1 = f.j(yl'y2'--"yN; e) ' i = 1,2,...,N . (36)
A small parameter e was included because we know, from the last section,
that an a priori condition for the validity of the quasi -steady-state assump-
tion is the appearance of a very large rate constant. The reciprocal of
this large number, properly nondirnansionalized and designated here as e ,
v/as chosen in accordance with conventions used in the perturbation theory.
Assuming that y,, is the species in the steady slate, the solutions to
Eq. (36) can be first expanded into power series in e :
(37)
* As pointed out by Bowen, Acrivos, and Oppenheim (1963), it may be necessary,
under complicated situations, to invoke a noninteger power series in e
However, for the sake of simplicity, it probably suffices to consider a
simple power series in the present study.
-------
144
Substituting Eq. (37) into Eq. (36) and equating the likely power of e ,
we formally obtain the following for the zeroth order:
i = 1,2,...,N-1
(38)
dy .
1 - -F
dt " Ti
o = fN
v(0) y(0) (0)
yl ' y2 ' ' ' ' ' YN
y(o) t y(o) t t y(o)
For the first order, we obtain
dy?1} N m m
1 _ v^ \ I) \ I)
where a', can be a function of y| ' , y^ »...,
(39)
Presumably, Eq. (38) will yield the quasi-steady-state solutions, and
Eq. (39) will represent the first-order correction. If we can establish
that the solutions to Eq. (39) are bounded, then we can conclude that the
error incurred by invoking the quasi -steady-state assumption is at most
on the order of ' e . With this objective in mind, we rewrite Eq. (39)
in matrix form:
dt
where Y is a column matrix with elements y. ' and A
solutions to Eq. (40) can be generally written as
(40)
. The
(1) _
Cije
(41)
-------
145
where A. are the eigenvalues of Matrix A, defined by,
J
Ul - Al = 0
(42)
Our objective, however, is not to seek the general.solutions of Eq. (40).
Rather, we are interested in knowing only certain behavior characteristics
of these solutionsparticularly, whether they will grow or decay. This
will, of course, depend on whether all of the characteristic roots have
negative real parts, i.e., whether Matrix A is a stability matrix. The
answer to this question is provided by the Hurwitz criterion (Bellman,
1960). According to this criterion, the condition for Matrix A being a
stability matrix is that the following sequence of determinants must be
positive:
bl '
1
0
b
(43)
The elements in these determinants are obtained from the characteristic
polynomial of A ,
- A| =
.N , , .N-l ,
A + b, \ +
(44)
To illustrate tfie use of the above theory, we again use the example
in Section VIII-B. First of all, recognizing that kA is relatively large
compared with the other two rate constants, we let
where k? is arbitrarily chosen to form a nondimensional parameter. To
create a proper balance of each term in Eqs. (18) through (20), the
following transformations are required:
-------
. _ r
« ~ . ~9
t =
Then, Eqs. (18) through (20) become
da _ .
By assuming that
0 -
r .
we obtain the following for the zeroth order
0 - 2kj k2 [a(0) + 3(0)] - 2k2r
(0)
2
146
(45)
re. , > (46)
H7= 2kjk2(a + 3) - 2k2r2 . (47)
F(0) a(0) (4P)
' \^ '
(49)
(50)
-------
147
These equations are identical to the set of equations obtained from a direct
invocation of the quasi-steady-state assumption for Eqs. (18) through (20).
Similarly, the equations for the first-order correction can be found:
_k r(0) (1) k (0) (1)
dT 2 r a ~k2 r
k r(0) a(1) + k a(0) r(T
dT 2 2
using a coefficient matrix A,
,(0)
A =
,r<°>
2kik2
0
,(o)
.(o)
-4k2r
(0)
The characteristic polynomial is then given by
XI - A
x + 4k2r<°>
4k|r«°> x - 4kjk| «
-------
148
Hence, the sequence of determinants, as expressed in Eq. (43), is
5k2r<°>
5k2r<°>
4l|r<0>'
Since both of these determinants are positive irrespective of the zeroth-
order solutions, we conclude that under all conditions the error incurred
by invoking the quasi-steady-state assumption is on the order of e . The
reader will recall that, according to the analysis presented in Section VII-B,
the error is given by
2\2/-i
In 2
-1
In 2
if e « 1
This confirms the conclusion we obtained above,
The application of the theory derived in this section to more complex
kinetic mechanisms is certainly possible. Although in principle there is
no limit to the number of equations, N, that can be treated using the
theory, algebraic manipulations can become extremely tedious if the number
of equations exceeds five. For this reason, we do not employ the theory
we derived above to assess the validity of the quasi-steady-state assumption
for intermediates in the mechanism discussed in Table 1. Rather, a set of
-------
149
"head-to-head" numerical experiments was carried out. Nevertheless, we
can demonstrate through these numerical experiments that phenomena and
conclusions obtained from the theoretical analysis still hold, albeit
qualitatively, in cases where more complex kinetic mechanisms are involved.
D. SOME NUMERICAL EXPERIMENTS USING THE GENERAL MECHANISM
In this section, we describe a set of "head-to-head" numerical ex-
periments we conducted to assess the validity of introducing the quasi -
steady-state assumption. Because of our familiarity with it, the general
kinetic mechanism (Table 1) was chosen for this test. The experiments,
also used by Gelinas (1972) for the same purpose, simply consist of two
sets of numerical simulations,* one that invokes the quasi-steady-state
assumption and one that does not. The conditions are otherwise identical.
Comparisons of the two sets of predictions yield information regarding
the errors incurred by invoking the quasi-steady-state assumption.
For the experiments, the following four species in the general mechanism
were chosen to test the validity of the quasi-steady-state assumption:
RCCL, RCL, 0, and CL. Initial conditions corresponding to EPA smog chamber
Run 325 were used (Hecht, Seinfeld, and Dodge, 1974). The differences, in
percentages, between the predictions calculated with and without the quasi -
steady-state assumption for each individual species are presented in
Table 16. The large deviation between the solution obtained through the
use of the quasi-steady-state assumption end the exact solution, as shown
in the last column of Table "16, clearly indicates that ozone is probably
not a good candidate for the application of the quasi-steady-state assump-
tion. This conclusion, however, should not be confused with the well-
known photostationary state assumption (Leighton, 1961; O'Brien, 1974)
in the study of photochemistry. The photostationary state assumption
postulates that an approximate balance exists between the photolysis of
nitrogen dioxide and the reverse reaction of nitric oxide oxidation by
* The Gear technique (1971) was used to integrate the system of ordinary
differential equations.
-------
150
Table 16
PERCENTAGE ERRORS INCURRED BY USING THE QUASI-STEADY-STATE ASSUMPTION
Species
Time
l I int.
(minutes)
0.2128
0.5128
1.013
4.013
9.413
18.92
28.92
43.92
53.92
63.92
78.92
93.92
108.9
123.9
138.9
163.9
188.9
213.9
RC03
-1.29
0.17
-0.40
0.01
0.02
0.18
0.14
0.11
0.15
0.17
0.20
0.08
0.05
0.01
-0.02
0.06
0.08
0.15
0
2.04
0.04
-0.04
0.01
0.01
-1.10
-1.32
-1.49
-1.42
-1.25
-0.87
-0.06
0.20
0.38
0.52
0.56
0.66
0.72
R02
-15.78
- 0.45
0.32
0.24
0.13
1.03
- 0.89
- 0.89
2.82
0.47
- 1.24
- 1.00
- 0.53
- 0.15
0.01
0.07
0.21
0.43
°3
27.77
7.72
4.61
4.67
5.19
5.42
6.78
11.10
16.81
33.87
400.33
384.76
193.31
119.51
81.50
45.02
18.26
-10.62
-------
T51
ozone. The differences (in percentages) between ozone concentrations calcu-
lated under the photostationary assumption and those resulting from the
exact solution in the same numerical experiment are shown in Table 17.
A comparison of Tables 16 and 17 shows that the photostationary state
assumption works quite well for the time span of interest.*
On the other hand, Table 16 shows that, for RCCL, 0, and R02» the
errors incurred by invoking the quasi-steady-state assumption are all
within 1 percent after an initiating time period, implying that the quasi -
steady-state assumption is apparently acceptable for this specific case.
Also, the errors for these three cases tend to decrease with time. This
verifies one of the key features we derived in the theoretical studies:
The quasi-steady-state solution, when applicable, will converge to the
exact solution. This same behavior has also been observed by Gelinas
(1972) in a similar experiment.
E. CONCLUSIONS
Although the quasi-steady-state assumption clearly should not be in-
voked indiscriminately, its use can be fruitful in certain cases. A
potential example is the application of the kinetic model to the urban
airshed model. In these cases, however, care must be taken to ascertain
that the species for which the quasi-steady-state assumption is invoked
are judiciously chosen and that their validities are thoroughly assessed.
* The accuracy of the photostationary state at later times can, of course,
be further improved if one includes the ozone-nitrogen dioxide and ozone-
hydrocarbon reactions.
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152
Table 17
PERCENTAGE ERRORS INCURRED
BY USING THE PHOTOSTATIONARY STATE ASSUMPTION
Percentage
Time
(minutes)
5.925
18.92
23.92
28.92
43.92
53.92
63.92
78.92
93.92
108.9
123.9
138.9
163.9
188.9
213.9
Error in Ozone
Concentrations
0.45%
0.76
0.92
0.97
1.35
1.82
2.81
7.19
12.47
13.55
14.02
14.44
15.24
16.06
17.17
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153
IX TREATMENT OF COMPLEX MIXTURES OF ORGANIC REACTANTS
IN THE KINETIC MECHANISM
One of the major difficulties in the study of photochemical air pollution
is that the contaminated atmosphere consists of a multitude of organic
species with widely varying capabilities of participating in photochemical
reactions. Because a kinetic model of reasonable size for atmospheric
applications cannot individually incorporate all organic species that parti-
cipate in the photochemical reactions, a means must be found to lump the
organics together. This chapter presents an analytic technique for approach-
ing this problem.
To illustrate the principles of the proposed technique, we chose the
general kinetic model (Table 1) as the basis for the following discussion.
In the kinetic mechanism, the reactive hydrocarbons are grouped into the
following four categories:
> HC, = olefins
> HC^ = aromatics
> HCo - paraffins
> HC. = aldehydes.
Since the atmosphere contains a variety of species having widely varying
rate constants and stoichiometric coefficients within each group, a scheme
is needed to evaluate the lumped rate constants and stoichiometric co-
efficients for these four lumped hydrocarbons.
To begin, consider as an example a mixture of M individual olefins,
denoted by OL-,, OLp, ..., OL^, and represented as one lumped olefin, HC-,.
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154
We assume that the concentrations (in moles), as well as the respective
rate constants and stoichiometric coefficients, are all known. The follow-
ing tabulation summarizes the characteristics of this example:
/* Stoichiometric
Species Concentration Rate Constants* Coefficient
J r22,l r23,l r24,l Ol
OL2 £OL2] r22j2 r23}2 r24j2 ^
[OLH] r22>M r23)M r24>M
The objective is to obtain lumped rate constants (r??, r?^, r?«) and a lumped
stoichiometric coefficient (a) for the lumped olefin whose concentration is
M
t^] " Z>Li^ - (5D
i=l
The pertinent chemical reactions for the olefins are
22
HC-j +0 * ROD + aRCOO + (l-a)HOp , (52)
0
HC. + 0, -v RCOO + RO + HC, , (53)
I O || li
23
F
0
HC, + OH -> ROD »- HCA . (54)
'1
* The numbers 22, 23, and 24 refer to reaction numbers in the mechanism
(Table 1).
-------
155
Consider the last reaction first. For each individual olefin, the
reaction steps can be expressed by
OL + OH
ROO + HC
OL2 + OH + ROO + HC4
(55)
OLM + OH + ROO + HC4
with the overall reaction step represented by Eq. (54). The rates of deple-
tion of olefins due to Eqs. (54) and (55) can be written, respectively, as
«[HC]
"~fiT
= -r24 [HCj] [OH]
(56)
6[OU]
6[OL
] [OH]
(57)
However, because other oxidants (0 and O^) are continuously in competition
with OH for depletion of the olefins [Eqs. (52) and (53)], these equalities
can hold only instantaneously. Therefore, we use a different symbol for
the time derivative, 6/6t, to emphasize this fact. Now, if we sum both
the left- and right-hand sides of Eq. (57) and invoke Eq. (51), we find
that
-------
156
M
Cjr24 ^OL.]/- [OH]
M .
(58)
Comparing Eqs. (56) and (58), we immediately obtain
M
r24 = r24,i Yi (59)
1=1
where Y.. denotes the mole fraction of OL-. One can similarly show that
for the reactions in Eqs. (52) and (53),
M
r22
1=1
M
r23
1=1
To obtain the lumped stoichiometric coefficient a in Eq. (52), we
can repeat the same procedures. The individual reactions can be written as
-------
157
+ 0
ROO + a, RCOO + (1-a,) HO,
I ii I <-
0
ROO
a2 RCOO
0
(62)
OLM + 0
ROO
RCOO
0
The rate equations for production of RCOO due to Eqs. (52) and (62) are,
respectively,
(63)
[0]
X t*)\
-^-[RCOO]^ = a?r59 9
ot I! c cc,^:
a
i-[RCOO]»" - Va>H
0
(64)
Again, if we sum both sides of Eq. (64) and use the identity
M
[RCOO] =
0
0
we finally find that
-------
158
M
oo - V22 1Yi * " >] ' (65)
22 1=1 1 "jl 1
1=1
Thus, we have obtained the desired formulas for computing the lumped rate
constants and stoichiometric coefficient for the olefins.
In appearance, Eqs. (59) through (61) are similar to the type of for-
mula first proposed by Jackson (1963), who used a linear summation of the
products of mole fractions and the corresponding rates of individual com-
ponent hydrocarbons to calculate the overall reactivity for the mixture.
In his calculation, reactivities were based on the initial mole fractions
of the reactants. He then assumed that the relative mole fractions of the
individual components remain constant as the reactions take place; this,
of course, is incorrect, except in the degenerate case when the reactivities
of all the various components are identical. In all other cases, as the
reactions proceed, the more reactive species are depleted at a faster rate.
Consequently, the influence of these species diminishes most rapidly with
time. Therefore, it is obvious that the straightforward linear summation
method tends to overpredict the overall reaction rate.
The essence of the present scheme lies in its recognition of the tem-
poral variations of the hydrocarbon concentrations. Two procedures, one
exact and one approximate, have been proposed to update the mole fractions.
A. EXACT SOLUTIONS
With a kinetic model available, the updating of the hydrocarbon mole
fractions can be achieved analytically. For example, the exact concentration
history of [OL.] can be shown as
[Ot,]t -
(66)
-------
159
We should emphasize that no assumption whatsoever has been used in deriving
Eq. (66). The application of this equation, however, requires the contin-
uous knowledge of the concentration levels of 0, 03, and OH. This can be
achieved approximately in the numerical kinetic model as follows.
Assume that the time steps used in the numerical model are, in
sequence,
At
-,,
At
o,
At.
(we have allowed for a variable step-size numerical scheme, such as the
one now being used). Then, using the initial concentrations (at the beginning
of time step Atn) of 0, 0^, OH, denoted by [0]/n\, [03]/n>
[OH]
interval, At , Eq. (66) becomes
[OL.]t = [OL.]0-exp
/ >
for the time
N
n=l
(67)
Or, more simply., the updating of [OL-]/ +-,\ can be accomplished by computing
At.
which can readily be implemented in the kinetic model.
(68)
To test the validity of the proposed scheme, we carried out the following
numerical experiment. Employing our kinetic model, we used three different
methods to treat the binary hydrocarbon mixture (propylene and ethylene):
-------
160
> Propylene and ethyl ene were modeled as two distinct olefins
(each represented by a different equation). This scheme
is, therefore, an "exact" means of modeling a binary hydro-
carbon system with the general mechanism.
> Propylene and ethyl ene were lumped together using the
linear scheme (Jackson, 1963).
> Propylene and ethylene were lumped together using the
proposed lumping scheme.
The initial conditions, identical for all three, are listed below:
Concentration
Species
NO
N02
Paraffin
Ethylene
Propylene
(ppm)
1.25
0.08
3.41
0.184
0.046
Comparisons of the predicted hydrocarbon consumption rates and ozone
production rates are presented in Tables 18 and 19. The accuracy of the
proposed scheme is demonstrated by the small deviations between it and
the exact schema: less than 0.3 percent after 375 minutes of simulation.
In contrast, during the same interval, the linear scheme overpredicted
(as expected) the hydrocarbon consumption by 4 percent arid the ozone
production by 15.2 percent.
As a further example, we also carried out tests for two kinetic
simulations discussed in Sections III-B and III-C. The first run in-
volved a group of five individual paraffins, and the second, six olefins.
Because of the large number of hydrocarbon species involved and the wide
disparity in reactivity (at least in the case of the olefins), these runs
provide a more severe test for our proposed lumping scheme.
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161
Table 18
COMPARISON OF HYDROCARBON CONSUMPTION FOR DIFFERENT LUMPING SCHEMES
Time Exact Scheme Linear Scheme* Present Scheme*
(minutes) (ppm) (ppm) (ppm)
0 0.2300 0.2300 0.2300
130 0.1949 0.1947 (0.1%) 0.1948 (0.05%)
300 0.1485 0.1459 (1.8%) 0.1482 (0.2%)
375 0.1292 0.1240 (4.020 0.1288 (0.3%)
* Percentages in parentheses indicate deviations from the exact scheme.
Table 19
COMPARISON OF OZONE PRODUCTION FOR DIFFERENT LUMPING SCHEMES
Time Exact Scheme Linear Scheme* Present Scheme*
jmijiutesl (pphm) jjiphm) (pphm)
00 0 0
130 0.2539 0.2550 (4.3%) 0.2539 (0%)
300 1.924 2.033 (5.7%) 1.926 (0.1%)
375 6.948 8.005 (15.2%) 6.970 (0.3%)
* Percentages in parentheses indicate deviations from the exact scheme.
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162
Tables 20 and 21 compare the predictions for the paraffins and ozone
derived from the exact scheme with those from the proposed scheme. The
maximum differences observed during a six-hour simulation were 0.53 per-
cent for ozone and 0.16 percent for the paraffins. The computational time
for the two runs was 1.524 seconds for the exact scheme and 1.420 seconds
for the lumping scheme. Thus, the lumping scheme results in a 7 percent
savings in computation time for the paraffin run.
Tables 22 and 23 present the results for the olefins. These data
again confirm the accuracy of the proposed scheme; the maximum differences
are 1.08 percent for ozone and 0.31 percent for the olefins for a six-hour
simulation period. The extremely small differences for the two predictions
for the olefins are particularly noteworthy because, at the end of six
hours, the five most reactive species were depleted by more than 99.9
percent! The wide range of rate constants for the six olefins is also
apparently responsible for the impressive savings of computing time; lumping
apparently reduced the stiffness of the system of equations. The computa-
tional times were 3,236 seconds for the exact scheme and 2.402 seconds for
the lumping scheme. Thus, the lumping scheme resulted in a 25.8 percent
savings in computing time.
B. APPROXIMATE SOLUTIONS
In the absence of a kinetic model, the lumped rate constant of a
hydrocarbon mixture can be obtained in the following manner. Consider as
an example the species OL-. If we invoke the steady-state assumption for
[o]5 [Oq]> [OH], which, for the time being, we interpret as
O
[0], [03], [OH] =« constant , (69)
we can write the solution for [OL.] as
'[OL.]t = [OL.]0e"M , (70)
with
ki = r22,i [°l + r23,i t°33+r24,i [OH] , (71)
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163
Table 20
COMPARISON OF HYDROCARBON CONSUMPTION IN THE MULTIPARAFFIN RUN
Time Exact Scheme Present Scheme Difference
(minutes) (ppm) (ppm) (percent)
0 1.770 1.770 --%
102.8 1.639 1.638 -0.06
202.8 1.457 1.455 -0.14
302.8 1.305 1.303 -0.15
362.8 1.235 1.233 -0.16
Table 21
COMPARISON OF OZONE PRODUCTION IN THE MULTIPARAFFIN RUN
Time
minutes)
0
102.8
202.8
302.8
362.8
Exact Scheme
(£phm)
0
0.5250
7.779
30.23
39.10
Present Scheme Difference
L), _ (per cent)
0 --%
0.5245 -0.10
7.738 -0.53
30.17 -0.20
39.05 -0.13
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164
. Table 22
COMPARISON OF HYDROCARBON CONSUMPTION IN THE MULTIOLEFIN RUN
Time
(minutes)
0
51.49
100.1
200.1
361.6
Exact Scheme
(ppm)
6.505
4.034
2.842
1.672
0.759
Present Scheme
(ppm)
6.505
4.028
2.845
1.675
0.757
Difference
(percent)
-0.15
+0.11
+0.18
-0.26
Table 23
COMPARISON OF OZONE PRODUCTION IN THE MULTIOLEFIN RUN
Time
(minutes)
0
51.49
100.1
200.1
361.6
Exact Scheme
pphiTi)
0
0.5649
0.5921
0.6686
0.7039
Present Scheme
(pphm)
0
0.5608
0.5857
0.6674
0.7061
Difference
(percent)
-0.73
-1.08
+0.31
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165
where [OL.]. is the instantaneous concentration of OL. at Time t and [OL.]n
I u 1 1 U
is the initial value. Thus, an expression for the time-dependent mole
fractions can be derived:
-k.t
[°LiV '
Yi -n kt - (72)
~lx v
J
Equation (72) takes care of only the "aged" olefins injected at Time 0;
any fresh addition of olefins at a subsequent time should, of course, be
included in computing this mole fraction.
As an illustration of the use of the approximate technique, consider
the following example. For a binary mixture of ethylene and propylene, we
have the following information:
Species (ppm molar) (ppnf min" ) (ppnf min ) (ppm min )
Ethylene 0.060 722 Ch004 2,500
Propylene 0.015 4,000 0.016 25,000
Using this information, we can calculate the lumped rate constants from
Eqs. (59), (60), (61), (71), and (72), provided that we know [o], [Oj],
and [Oil]levels. For example,
r22
-[Eth]0 e'kEtht.r22iEth+[ProP],
(73)
-------
166
where
kEth = r22,Eth -M + r23)Eth -[03] + r24jEth .[OH]
kProp = r22,Prop ' + ^S.Prop '°3 + r24sProp
Similar expressions can be derived from r?^ and r?». These results are
plotted in Figures 41 through 43. The time-dependent feature of these
rate constants is apparent.
-------
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PART 3
OVERVIEW AND PROSPECT
-------
171
X OVERVIEW AND PROSPECT
Our formulation of the general kinetic mechanism is limited in exact-
ness by uncertainties in the kinetics of elementary reactions, and the
thoroughness of our evaluation suffers from incomplete measurements in
smog chambers. For the many inorganic reactions in the mechanism that
have been studied by several different investigators over the years, there
is virtually no doubt about the nature of the reactants and products, and
the rate constants are "known" within a factor of 1.5 or less of the true
values. However, although the rate constants of many other reactions in
the general mechanism have been measured by at least one group, too often
little effort has been made to identify the products of the elementary
reactions (at times, because mechanistic studies are difficult or impossible
using the kinetic techniques employed). In such cases, we know the impor-
tance of the specific reactions as loss mechanisms for the reactants in-
volved, but we can only speculate as to the intermediates and subsequent
reactions of the intermediates. Finally, there are some reactions in the
mechanism that have never been studied experimentally. These are reactions
that should occur, according to thermochemical considerations, but have not
yet been observed directly. Thus, both the mechanism and the rate constants
are, at best, intelligent speculation.
The smog chamber data base possesses a similar mix of strengths and
weaknesses. If we specifically consider the UCR evacuable chamber system,
one of the newest and most technically advanced systems presently in use,
we can cite a long list of attributes, such as the following:
> Measurements of most organics, PAN, NO, NCL, and O^, with
an accuracy of better than ± 5 percent, even at pphm concentrations.
> Characterization of the rate of NCL photolysis.
-------
172
> Characterization of the rate of 03 decay on the walls.
> Control of the temperature within the chamber.
Yet, the magnitude and nature of many other chamber effects and operating
parameters are poorly characterized, and some of the most important chemical
species in the smog system, the free radicals, are not measurable routinely,
if at all.
Consequently, the development of a kinetic mechanism might be viewed
as a quest to piece together a puzzle showing a blurred and evolving pic-
ture, with some pieces that are rigid and well shaped, others that are
moldable, and still others (possibly) that are missing. Smog chamber
scientists are continually striving to improve the picture, kineticists
are adding and changing pieces, and the modelers are ordering and re-
arranging the pieces in new ways to complete the picture as much as pos-
sible. But every time that either our perception of the picture or our
set of pieces changes, the model may also have to be changed.
We are speaking of a picture as though there were only one. In fact,
we showed in Figure 21 that the model can predict the behavior of reactants
under a single set of initial conditions very well. If we-were interested
only in that one case, we would probably conclude that the general mechan-
ism is quite satisfactory.
But in actual fact our expectations and needs are broader, and every
smog chamber experiment that uses a different set of initial reactant
ratios provides a new and stiffer test for the kinetic mechanism. Once
we have shown that a particular formulation of the general reaction scheme
works well, we construct new ways to stress the model--to test the complete-
ness and accuracy of the reactions and the values of the rate constants.
As inadequacies appear, steps are taken to resolve the deficiencies, and
a new and stronger formulation of the general mechanism results.
We shall continue this type of development work next year. If predic-
tions do not appear to improve substantially from one year to the next,
-------
173
it is partly because the tests of the model are growing increasingly broad.
But new information is continually being introduced into the mechanism,
new reactions are being studied in kinetics laboratories, and new species
and effects are being measured in smog chambers.
In short, we are well along the path from ignorance to knowledge, and
the roots of the general mechanism are being based increasingly on fact
rather than speculation. We are confident that the combination of experi-
mental and theoretical research being performed will result in an accurate,
reliable mechanism for photochemical smog formation.
-------
174
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-------
175
Garvin, D., and R. F. Hampson, eds. (1974), "Chemical Kinetics Data Survey
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-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO. 2.
EPA-650/4-74-040
4. TITLE AND SUBTITLE
Mathematical Simulation of Smog Chamber
Photochemical Experiments
7. AUTHOR(S)
Thomas A. Hecht, Mei-Kao Liu, David C. Whitney
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Systems Applications, Inc.
950 Northgate Drive
San Rafael, California 94903
12. SPONSORING AGENCY NAME AND ADDRESS
U. S. Environmental Protection Agency
Office of Research and Monitoring
National Environmental Research Center
Research Triangle Park, N. C. 27711
3. RECIPIENT'S ACCESSION-NO.
5. REPORT DATE
November 1974
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NC
R74-9
10. PROGRAM ELEMENT NO.
1A1008
11. CONTRACT/GRANT NO.
68-02-0580
13. TYPE OF REPORT AND PERIOD COVERED
Final (June 1973 - June 1974}
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16. ABSTRACT
The continual development and testing of a kinetic mechanism for photochemical
smog is described. Several rate constant values were updated, in line with recent
experimental measurements, and simulations of several EPA smog chamber runs were
repeated. The predictions vary in their agreement with experimental observations
but tend to be best at high initial hydrocarbon-to-NO/ ratios. The mechanism
also reproduced the behavior of a complex mixture of paraffins and NOx and a
mixture of six olefins and NOX. A sensitivity analysis of the mechanism was
carried out. The results were combined with uncertainty estimates of the rate
constants to quantify the importance of determining individual rate constants
with greater accuracy. Preliminary modeling of smog chamber data collected at
the University of California, Riverside, was also undertaken.
This report was submitted in fulfillment of Contract No. 68-02-0580 by
Systems Applications, Incorporated under the sponsorship of the Environmental
Protection Agency.
17.
KEY WORDS AND DOCUMENT! ANALYSIS
DESCRIPTORS
Photochemical modeling
Chemical kinetics
Atmospheric chemical modeling
nr RS/opi~N ENDED TFRMS
COSAT!
13. DISTRIBUTION STATEML-NT
Unlimited
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
178
20. SECURITY CLASS (Thispage)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
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