EPA-R4-73-030c
July 1973
ENVIRONMENTAL MONITORING SERIES
SSilSJE:*:
$$i$i!8S^
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EPA-R4-73-030c
URBAN AIR SHED PHOTOCHEMICAL
SIMULATION MODEL STUDY
VOLUME I - DEVELOPMENT AND EVALUATION
Appendix IB - Generalized Mechanism for Describing
Atmospheric Photochemical Reactions
by
T.A. Hecht
Systems Applications, Inc.
9418 Wilshire Boulevard
Beverly Hills, California 90212
Contract No. 68-02-0339
Program Element No. 1A1009
EPA Project Officer: Herbert Viebrock
Meteorology Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
July 1973
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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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ACKNOWLEDGMENTS
We wish to thank Dr. Marcia Dodge of E.P.A. for many helpful
discussions concerning modeling of the auto exhaust data, particu-
larly with regard to establishing the hydrocarbon concentrations
and definitizing the roles of particles and carbon monoxide. We
also acknowledge Dr. S. L. Kopczynski of E.P.A. for his aid in
clarifying a number of experimental and analytical details related
to the data base.
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CONTENTS
Page
I. PURPOSE OF WORK B-l
II. THE KINETIC MECHANISM B-3
A. The Treatment of HNO B-3
B. Hydrocarbon Mixtures B-9
C. Reactions Involving Particles B-10
D. Dilution Effects B-10
E. The Constancy of Stoichiometric Coefficients B-ll
F. The Reaction Rate Constants B-ll
III. THE DATA BASE AND SOURCES OF EXPERIMENTAL
UNCERTAINTY B-12
A. The Data Base B-12
B. Light Intensity B-14
C. Water Vapor in Chamber B-15
D. Walls Effects B-15
1. NO and NO2 B-16
2. NO B-16
3. HNO- B-18
4. Other Chemical and Catalytic Effects
of the Walls B-18
5. Conclusions B-19
E. Estimates of Experimental Error B-19
1. The Accuracy of the Analytical Instruments . . . B-20
2. The Repeatability of Experimental Runs B-21
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CONTENTS (Continued)
Page
IV. VALIDATION OF THE MECHANISM B-24
A. Estimation of Parameters B-24
1. The Rate Constants B-24
2. Generalized Stoichiometric Coefficients B-27
3. Sensitivity of the Model to Variations in
the Magnitudes of Parameters B-29
B. The Validation Results B-32
1. Toluene-NO Validation B-32
x
2. Toluene-n-Butane-NO Validations B-35
x
3. Propylene-Ethane-NO Validations B-47
A
4. Auto Exhaust Validations B-55
V. CONCLUDING COMMENTS B-75
REFERENCES B-79
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LIST OF TABLES
Page
1. The Generalized Photochemical Kinetic
Mechanism B-4
2. Mathematical Representation of the Kinetic
Mechanism B-6
3. Initial Conditions Associated with
Experimental Chamber Data B-13
4. Precision Bounds (90% Confidence Levels) for
Toluene-NO and Toluene-n-Butane-NO Data B-22
5. Sensitivity of the Model to Light Intensity,
Water Concentration, and Initial N02 Concentration . . B-31
6. List of Figures B-33
7. Key to Figures B-34
8. Validation Parameters for Toluene-NO
Experiments B-36
9. Validation Parameters for Toluene-n-Butane-NOx
Experiments B-48
10. Validation Parameters for Propylene-Ethane-N0x
Experiments B-56
11. Values of Base Parameters Used to Calculate Rate
Constants and Stoichiometric Coefficients for
Complex Hydrocarbon Mixtures B-68
12. Validation Parameters for Auto Exhaust Experiments
(Unequipped Chevelle) B-71
13. Validation Parameters for Auto Exhaust Experiments
(Equipped Chevelle) B-72
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I. PURPOSE OF WORK
The main purpose of the current contract effort is the development
and valideition of a simulation model for estimating ground level concen-
trations of photochemical pollutants. A major component of the model is
a generalized kinetic mechanism capable of describing atmospheric chemi-
cal reactions. Before a kinetic mechanism can be included in an airshed
simulation, however, its validity must be established by comparing its
predictions with concentration/time profiles observed under controlled
laboratory conditions; i.e., smog chamber experiments.*
During the first phase of model development, under Contract CPA
70-148, we undertook to identify an existing kinetic mechanism, or, if
necessary, to develop a new mechanism, capable of meeting the following
requirements for inclusion in an atmospheric simulation: relative sim-
plicity (in the interest of minimizing requisite calculations), sufficient
generality to include all major gaseous contaminant species (aerosols
were not considered in the study), and acceptable accuracy in the pre-
diction of smog chamber data over a range of values of HC/NO ratios
and for a variety of hydrocarbons. Initially, we carried outxan assess-
ment of existing mechanisms, and we concluded that a "better" model was
needed. At about that time, a program to develop such a model was being
initiated under the aegis of Prof. John H. Seinfeld at the California
Institute of Technology. It became clear at an early stage of that work
that the mechanism being formulated at Caltech represented a significant
advance in the field. We adopted the new mechanism and carried out a
series of validation runs which are detailed in Seinfeld, et al. (1971).
The results demonstrated that this model is capable of predicting with
acceptable accuracy the concentration/time behavior of smog chamber
experiments for propylene, isobutylene, n-butane, and a mixture of pro-
pylene and n-butane at initial NO to hydrocarbon ratios of 1/3 to 1.
The mechanism was also shown to simulate accurately the effect on photo-
oxidation rates of variations in CO concentration, as well as the in-
hibitory effect of high initial concentrations of nitric oxide on the
maximum concentration of ozone obtained.
* The attainment of acceptable validation of the model using smog cham-
ber data does not necessarily imply that the mechanism is capable of sim-
ulating cictual atmospheric processes. Certain physical and chemical attri-
butes of the atmospheric mixture are not simulated in laboratory studies.
In particular, aerosols and particulates found in the atmosphere undoubtedly
influence chemical processes. As their density, number and size distribu-
tion and chemical composition remain highly uncertain, their effect on rate
processes remains unknown.
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Despite the generally favorable character of the results of this
study, further work was needed. We wished to modify the treatment of
nitrous acid in the mechanism, to include additional categories of lumped
hydrocarbons and their reactions, and to improve means for estimating
the genercilized stoichiometric coefficients. Most importantly, however,
we wished to assess more fully the mechanism's validity. It was the
purpose of this effort to carry out validation of the mechanism, as mod-
ified, for a variety of reactive systems, including single hydrocarbons,
binary mixtures, and auto exhaust. If validation were adjudged "successful",
the mechanism could then be considered for incorporation into the urban
airshed model. We herein report the results of this study.
B-2
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II. THE KINETIC MECHANISM
The kinetic mechanism, given in Table 1, has been discussed in
detail in Seinfeld, et al. (1971). The mechanism consists of fifteen
reactions involving ten chemical species. The mathematical represen-
tation includes four differential equations to permit prediction of the
change in concentration with time of NO , N02 , ozone, and hydro-
carbons. Five of the species, all radicals, react rapidly to establish
equilibrium concentrations and can thus be represented by algebraic
equations. These species are 0 , OH , H02 , R02 and N03 . The tenth
species HNO2 has been treated as if the steady state approximation
were valid for its reactions, although this is known not to be the case.
We will discuss the basis for this assumption later in this section.
Thus, four differential equations and six algebraic equations, given
in Table 2, embody the complete mathematical statement of the mechanism.
As noted, we have discussed the mechanism fully in our previous
report. We thus limit the discussion of this section to a description
of modifications of the original formulation.
A. The Treatment of HN02
The original formulation of the kinetic mechanism [Hecht and
Seinfeld (1972)] included a differential equation to describe the
variation in HN02 concentration with time. This species, how-
ever, is not of major importance in the urban airshed model, is
not measured in the atmosphere, and is not, in fact, listed among
those pollutants for which air quality standards have been written.
The urban airshed model, as formulated, requires the integration
of the coupled, time-dependent, partial differential equations of
conservation of mass for NO , N02 , ozone, and hydrocarbon. In-
clusion of a fifth equation for HN02 would increase computing
time by 20 to 25% and would also increase computer storage
requirements.
While we were well aware of the fact that HN02 concentration
varies with time, we thought it would be worthwhile to explore the
possibility of introducing the artifact of a steady-state assumption
in describing the concentration of this species, achieving the nec-
es;sary scaling by suitably modifying the reaction rate constant.
Two questions immediately arise: (1) Is such an assumption justi-
fiable?, and (2) If it is justifiable, is it warranted?
The justifiability of the assumption can be argued on two
grounds. First, the term dcHNO /dt is quite sensitive to changes
in the magnitude of kg and water concentration in the reaction
6
NO + NO,, -> 2HNO,,
B-3
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TABLE 1. The Generalized Photochemical Kinetic Mechanism
The Basic 15-Step Mechanism
NO + hv -> NO + 0
O+O+M + O
O, + NO -*- NO + O
<3 ft £,
°3 + N°2 ~" N°3 + °2
5
NO + NO -»- 2
6
NO + NO *Q 2 HNO
2
HN02 + hv -> OH + NO
8
CO + OH ± C02 + HO
9
HO + NO -> OH + NO
10
11
HC + O +
12
HC + OH -* gRO
13
HC + 0
lit
R02 + NO -» N02 + eOH
15
RO + NO -* PAN
B-4
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TABLE 1. (Continued)
Additional Reactions Considered in This Study
16
I- O -»
17
OH -»
HC2 + °3
19
NO. + PARTICLE -> NITRATE
B-5
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TABLE 2. The Mathematical Representation of the Kinetic Mechanism
Rates of the Reactions:
rl
r2
r3
r4
5
r6
r7
r8
r9
r
10
= k1 ' N02
t
= k2 0
= k3 03 NO
' k4 ' °3 * N02
tt
- k5 N03 N02
tt
= k NO N0_
b 2
~ 7 2
= = kg ' OH f
= kg ' H02 NO
- k . HH un
~ 10 "U2 U2
ril ' kll
r!2 * k!2
r!3 ' k!3
r!4 = k!4
r = k
15 15
r!6 = k!6
r!7 = k!7
r = k
t ft 1 Q
J.O J.O
r!9 - k!9
HC
HC '
HC
R02
RO
2
" HC2
' HC2
HC2
' N°2
0
OH
°3
NO
. NQ
0
OH
* °3
Differential Equations:
d
- r
!0
- r
!5
dNO
.dt
y* T" + y ir i*
1 3 6 7 9 r!4
dt
r
!3
dHC_
dt
~ r
!3
" r
!8
t pseudo first order reaction
tt pseudo second order reaction
B-6
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TABLE 2. (Continued)
Algebraic Steady State Equations:
(NO.) = r2- (0.)
C
k,(N00)
(0) = rr^
(HC) + k.,(HC
Xb
(RO DF - EB
2 eEk14(NO) + CF
where B = 2k. (NO) (NO^)
b 2
C = ~
D = -[ak(HC) (0)
n
(0)
E =
F = k12(HC)
2k (NO) (NO ) + ek (RO ) (NO)
_ = _ * - _
k!2(HC) + kl7(HC2}
k (OH')
(HO ') =
2 fc0
-------
and to k_ in. the reaction
7
HNO + hv -» OH + NO
k has not yet been accurately determined, water concentration
was not controlled with care during the experimental program,
and k^ , which depends on light intensity, is not well known.
Thus, dcuNOo/^ can ^e determined only with considerable uncer-
tainty. (This does not, however, imply that its magnitude is
negligible.) Second, there are absolutely no measurements of
HNO;> ; thus, there is no way to verify predicted values of HN02
concentration.
In light of these considerations and due to our desire to
avoid the inclusion of an additional partial differential equation
in the airshed model, we decided to investigate the effects of in-
voking the steady-state assumption for HN02 . In particular:
(a) if the assumption were made, what effect would it have
on predicted concentration/time profiles for NO, NO
ozone, and hydrocarbon?
(b) Assuming the effect were small, what modifications, if
any, in the value of k6 would be needed? Would it be
possible to establish a value, p = (£5AS) » where kg
is the pseudo rate constant that yields HN02 vs. time
profiles under the steady-state assumption that closely
match the profiles computed when the differential equa-
tion for HN02 was included in the formulation?
If the NO , N02 , 03 , and hydrocarbon concentration/time profiles could
be duplicated, or nearly duplicated, under the steady-state assumption by
adopting a rate constant, k = pkg , which was invariant, or nearly so,
for the various reaction systems of interest, we felt that the steady-
state assumption was then both justifiable and warranted.
In order to investigate the appropriateness of the steady-state
assumption we carried out validation runs at different HC/NOX ratios
for the reactants, n-butane and n-butane-toluene. We also undertook
validation for n-butane at one HC/NOX ratio with 100 ppm of added
CO . We carried out two runs for each reactant system, one including
B-8
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the differential equation for HNO2 in the model, with k6 =
.004 ppm-lmin~l , and one assuming HNC>2 to be in steady state,
with kg = 1/8 k6 (p = 1/8). Virtually identical profiles for
NO , N02 , 03 and HC were obtained in the two calculations over
the six hour integration for each reactant. For example, for the
n-butane-toluene system, the NC>2 peak occurred at 116 minutes
with HN02 concentration variations described by a differential
equation, and at 113 minutes with HN02 in steady state. (This
reflects the low sensitivity of the model to nitrous acid (see
Section IV)). In view of these results we have elected to intro-
duce the steady-state artifact into the formulation of the mech-
anism in the interest of easing the computational burden associa-
ted with the urban airshed model. We do believe, however, that
the; inclusion of a differential equation for HNO2 will eventually
be desirable.
B. Hydrocarbon Mixtures
In order to better account for the potentially wide range of
reactivity of hydrocarbon mixtures, we have introduced a modifica-
tion to the basic 15 step mechanism of Table 1. The mixture is
represented by two lumped hydrocarbons, a low reactivity hydrocarbon
(HC) and a high reactivity hydrocarbon (HC2) . The inclusion of
HC2 creates the need for three additional reactions
0 -*
17
HC + OH -» 60RO
£ £ £.
HC2 + °3 Y2R°2
and a fifth differential equation
d(HC2)
~dt (r!6 + r!7 + ri8>
HC2 includes all olefins, while HC is comprised of aromatics
(other than benzene), acetylenes (other than C2H2 ), and C+
paraffins. C., to C paraffins, acetylene and benzene are taken
to be unreactive. The representation of reactive hydrocarbons in
this way enhances the accuracy of the model, especially with respect
to the NO oxidation and hydrocarbon consumption rates. The
division of hydrocarbons by class and the assignment of rate con-
stants and stoichiometric coefficients is discussed further under
Auto Exhaust in Section IV.
B-9
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C. Reactions Involving Particles
As we suggested earlier, aerosols and particles have a large
influence on atmospheric chemical processes [Wilson, W.E., Jr., (1972)]
Unfortunately, little is known about the physics and chemistry of
the pertinent phenomena. We do know, however, that cognizance must
be given to these phenomena in order to account for the loss of NOX
prior to the N02 peak that is observed when particles are present
in the smog chamber. We have thus included the reaction
19
NO + particle * nitrate
in the basic mechanism. We discuss this rate step in greater detail
under Auto Exhaust in Section IV.
D. Dilution Effects
The loss of material due to sampling during experimentation
is often considerable, up to 20 to 25% of the original charge. To
account for this, we have included a loss term in each differential
and algebraic equation. The term is of the form
F
- vci
where P = volumetric flow rate
v = volume of chamber
c. = concentration of species i
Thus, each differential equation is of the form
1,2,. . . ,n
B-10
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Note that while samples are drawn at approximately regular
intervals, with no withdrawal between sampling periods, this
formulation assumes continuous withdrawal at a uniform rate.
This assumption was necessary, as exact information concerning
withdrawal rates and periods is unavailable. The error intro-
duced by this approximation is, however, negligible.
E. The Constancy of Stoichiometric Coefficients
In earlier validation studies of propylene-NOjj and isobutylene-
NOX we included a Stoichiometric coefficient in the mechanism that
varied with, the ratio, (HC)/(NO) . We have since learned that
the need for this variable coefficient was attributable to biases
introduced into the observed results as a result of "chamber effects".
As data were collected in different chambers, the "chamber effects"
differ among the data sets. Also, initial conditions in many of
the runs were poorly defined. In contrast, all data used for vali-
dation purposes in the current study were collected in the same
smog chamber with better defined initial conditions.* In carrying
out validations using these data, we have been able to establish
fixed values for all Stoichiometric coefficients, independent of
the HC/NOX ratio.
F. The Reaction Rate Constants
We have adopted literature values of rate constants for all
inorganic reactions (with the exception of reaction 4), where these
constants are known. Similarly, we have used literature values
of rate constants for individual hydrocarbon reactions when possible.
Specifically, we have done so for the reactions of toluene, n-butane,
propylene, and ethylene with OH and ozone.* However, we have assumed
values for the 0-hydrocarbon reaction that are higher than those
reported in the literature.
Literature values of rate constants for the inorganic reactions
are given in Table B-4 of Seinfeld, et al. (1971), for the hydrocarbon
reactions, in Table B-5. Constants not available in this reference may
be found in Johnston, et al. (1970). Where values other than those
reported in the literature have been adopted, the reasons for this
selection of "new" values are given in Section IV.
* This, of course, suggests that a "chamber effect" may be incorporated
into the estimated values of model parameters, and thus predictions of the
validated mechanism may not compare as favorably with data collected in
another chamber. Its applicability in the atmosphere would also be
lessened due to such a bias. We discuss chamber effects in some detail
in Section III of this report, and in still greater depth in a report being
written under EPA Contract 68-02-0580.
** Toluene and n-butane are essentially unreactive in the presence of ozone.
B-ll
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III. THE DATA BASE AND SOURCES OF EXPERIMENTAL UNCERTAINTY
The significance of the validation results for a kinetic mechanism
is to a large degree dependent upon the diversity and reliability of the
experimental data base. We were fortunate in being able to obtain cham-
ber runs for this study involving both low and high reactivity hydro-
carbons, as well as simple mixtures and auto exhaust. Moreover, the
ratio of HC/NO was varied over a wide range for each reactant system.
In this section we describe the data base provided by the Division of
Chemistry and Physics of EPA for validation purposes. We examine in
some detail the importance of accurately specifying certain experimental
variables, notably light intensity and water vapor concentration. We
discuss the degree to which wall effects may influence observed chamber
results. Finally, we comment on the accuracy and specificity of the
analytical instrumentation used to monitor pollutant concentrations
and present estimates of the precision with which concentrations were
determined.
A. Data Base
The data base used in this validation study is that supplied '
by the Division of Chemistry and Physics of EPA. It is comprised
of four hydrocarbon-NOx systems:
Toluene-N0x at five different HC/NOX ratios
Toluene-n-butane-NOx at three different HC/NOX ratios
Propylene-ethane-NOx at four different HC/NOX ratios
Auto Exhaust at two different HC/NOX ratios
All of the chamber runs were made between June 1966 and March 1967
by the staff of the Chemical and Physical Research and Development
Program at the National Center for Air Pollution Control in Cincinnati,
Ohio [Altshuller, A.P.,et al. (1967a, 1967b, 1969, 1970)]".
The experiments are best specified by a statement of initial
conditions, as given in Table 3. Duplicate runs were carried out
for all but two sets of initial conditions, these sets both being
for the propylene-ethane-NOx system. In general we chose to vali-
date the model using that experimental run in each replicate pair
B-12
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TABLE 3. Initial Conditions Associated with Experimental
Chamber .Data
PA NO.
300
258
250
272
271
251
253
257
318
325
321
329
222
231
HC Type
Toluene
Toluene
Toluene
Toluene
Toluene
n-Butane
toluene
n-Butane
toluene
n-Butane
toluene
Propylene
Propylene
Propylene
Propylene
Auto Exhaust
Auto Exhaust
(N02)*
.02
.05
.04
.04
.05
.07
.08
.07
.06
.04
.10
.05
.12
.23
(NO)*
o
1.25
.35
1.17
.55
.32
1.10
.53
.27
1.12
.35
1.31
.26
1.95
2.80
(HO*
o
3.22
2.88
1.53
1.67
1.20
4.62t
4.91f
4.26t
.51
.45
.275
.24
2.21#
.61#
* initial concentrations in ppm
t combined total of n-butane and toluene
# combined total of all hydrocarbons in the auto exhaust
B-13
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having the smoother concentration time profiles and the lesser
loss of NOjj prior to the N02 peak. Experimental results dis-
playing such anomalies as the concentration of NO exceeding that
of NOo at the time of the N02 peak or the N02 peaking at a time when
only 2/3 of the NO had been oxidized were rejected for validation purposes.
B. Light Intensity
Radiation intensity is one of the most important parameters
in a smog chamber experiment, for it governs the photolysis rate
of N02 (reaction 1), the reaction which initiates and sustains
the smog formation process. Irradiation of the smog chamber was
carried out through the use of two banks of externally mounted
fluorescent lamps, 148 lamps of three different types. Under nor-
mal operation, these lamps have an expected lifetime of 1000 hours,
but throughout the program they were operated at a 25% overvoltage
to increase radiation intensity. Overload operation results in a
more rapid deterioration of the lamps; consequently, approximately
1/7 of the lamps were replaced after every 100 hours of operation.
The average first order "rate constant" for N02 disappearance
in nitrogen, k^* , was determined by the experimenters to be 0.40
minutes"^, but was not redetermined during the ten-month period
over which the data provided to us were taken. We have assumed, in
accordance with the results of Schuck, et al. (1966) , that k^ ,
the overall photolysis rate of N02 , is equal to 2/3 k
1 a
k = photolytic absorption rate constant
cl
<{> = dissociation efficiency
k2
and 0 + N02 + M -» NO + M
0 + NO -» NO + 0
^ £
Thus, kfl is , in essence, a lumped parameter representing the combined rates
of all N02 reactions in an oxygen-free atmosphere. Unfortunately, the use
of kg leads to difficulties in presenting the kinetics, as the combined
reaction which it represents is not first order. However, since the only
available data for light intensity in these chamber experiments are based on
the validity of k^ as a rate constant, we use it here to estimate k^
B-14
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C. Water Vapor in Chamber
Another parameter which is thought to be important in smog
chamber runs is the water concentration. Water enters into the
smog kinetics via reactions 5 and 6, nitric and nitrous acid
production. The latter is particularly important since photolysis
of nitrous acid produces OH radicals which, in turn, initiate
further reactions. The humidifier control of the inlet air stream
to the chambers was set to generate 50% relative humidity at 75°F,
but, during very cold, dry weather, relative humidities of only 30%
were achieved. The humidity of the inlet air stream was checked only
once or twice during the ten-month study. Because of the uncertainty
in the water concentration for these runs, we have lumped the rate
constant for reaction 6 and the water concentration into a pseudo-
second order rate constant, kg .
In order to assess the effect of uncertainties in kg and/or
water concentration on predicted concentration/time profiles, we
carried out three sensitivity runs. The results of these runs
showed that an assumed uncertainty of +_ 25% in kg , in the water
concentration, or in the lumped rate constant (all are equivalent)
leads to a change of +_ 4 minutes in the time to the NO2 peak,
which occurred at 112 minutes.* These reults are discussed more
fully in Section IV.
In the future, it would be desirable to obtain more exact
measurements of the water concentration. If such measurements be-
come available, it would be meaningful to dispense with the lumped
rate constant, treating k& and the water concentration individually.
D. Wall Effects
An effect of particular concern in smog chamber studies is the
influence of surfaces on chemical dynamics, and thus on observed
reaction kinetics. Of major importance in this regard is the possi-
bility of direct loss of material to the walls. Of lesser concern
is the possibility of chemical interactions occurring between pollu-
tants on the walls and material in the gas phase. Although it is
possible that some low reactivity organics such as carboxylic acids,
aldehydes, and ketones can be found on the walls as a result of
hydrogren bonding with adsorbed water, we focus our attention in this
discussion on species which have been clearly identified on the walls
of a small smog chamber fGay and Bufalini (1971)J --nitric acid,
nitrates, and nitrites. We begin then by discussing the reactions of
the most important oxides of nitrogen, NO and NO- , and examining
the possibility of the interaction of each with the walls. In the
process we also give attention to various mechanisms that might
account for the appearance of HNO_ on the walls.
* Westberg (1972) has raised doubts concerning the accuracy of the only
determination of kg [Johnston, et al. (1970)]. We have, therefore,
treated the pseudo rate constant kg1 = kg(H20) as an adjustable parameter
in our validation studies, and the low sensitivity of the time to the N02
peak with variations in kg1 is a reflection of our choice.
B-15
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1. NO and NO
Even in so-called dry systems it is reasonable to assume
that an adsorbed layer of water, will be found on the walls of
the smog chamber. This is certainly the case for the experi-
ments under consideration in this study, as the chamber was
intentionally humidified during all runs. Thus one possible
explanation for the appearance of nitrate and nitrite on the
walls would be dissolution of NO and NO- in the adsorbed
water layer. Nitric oxide can be eliminated in this regard
because of its extremely low solubility in water; N02 , how-
ever, dissociates in water by the following reactions [Hill, (1971/J
6NO + 3H 0 «- 3HNO + 3HNO
£2. J £,
3HN02 HNO + 2NO + H 0
The rate of loss of NO- in this manner is dependent
upon the amount of water adsorbed, the rate of dissolution
of NO2 / and the magnitude of rate constants for the disso-
ciation reactions. In the experiments under consideration,
however, N02 losses via this mechanism can be neglected be-
cause, within experimental error, all of the NOX initially
present can be accounted for at the time of the NO- peak
as N02 , NO , and NO and N02 lost by sampling and dilution
up to the time of the peak. We might then conclude that no
significant amounts of NO or NO2 were lost directly to
the walls during the smog chamber experiments.
2. N205
After the N02 peak occurs, and as 03 begins to accumu-
late, N20g forms by the reactions
B-16
-------
NpO will undergo hydrolysis to form nitric acid by the
reaction
NO + HO 2- 2HNO
^ 3 ^ O
If the hydrolysis takes place in the adsorbed layer of water
on the wall, HNO^ will form directly on the walls. However,
both the water concentrations in smog chambers (63% relative
humidity (RH) at 25°C is equivalent to 20,000 ppm H20) and the
rate constants for the primary reactions in nitric acid forma-
tion in the gas phase* are large enough that the loss of NOX
after the N02 peak may be fully ascribed to the formation of
nitric acid in the gas phase.
It remains unclear, however, as to whether ^05 hydro-
lyzes in the gas phase or on the walls. As we have noted, the
water concentration during these chamber runs was quite high.
As the stationary state concentration of nitric acid** would also
have been high, actual HN03 concentrations in these experiments were
always far from saturation. Thus there would have been a strong
tendency for ^Og , whether it were found in the gas phase or
on the wall, to hydrolyze rather than to decompose, forming
N02 by the reactions
N2°5 * N°2 + N°3
NO + NO -> 2ND
«J £
However, even if these reactions were favored due to the forma-
tion of N20_ , the rate of formation of NO2 would still be
low since No is depleted at this stage of the smog reactions.
Thus, in light of the various considerations presented, we con-
clude that reactions involving N^Og at the walls would have
little if any effect on the course of the overall smog reactions.
* See Johnston, H.S.,et al. (1970) for estimates of these rate constants
** Leighton (1961), p. 193, calculates that the stationary state concentra-
tion of HNO3 is 3,000 ppm for initial conditions of 0.10 N02 ,
0.10 03 , 0.01 NO , and 63% RH at 25°C.
B-17
-------
3.
Nitric acid is very soluble in water because of strong
hydrogen bonding. Thus, it is highly likely that a nitric
acid molecule in the gas phase that is involved in a collision
with the wall would dissolve. The rate of loss of HN03 from
the gas phase, then, is probably transport-limited and will
depend to some degree on the rate of stirring in the chamber.
Unfortunately, detection of HN03 in the gas phase has until
now proven to be a difficult task, perhaps because the acid
is lost to the walls of the sampling tubes.
4. Other Chemical and Catalytic Effects of the Walls
It would be highly beneficial to gain some insight into
the degree to which interactions occur between pollutants on
the walls and material in the gas phase. Unfortunately, our
knowledge concerning such phenomena is limited, and we can
only speculate. We thus offer-the following comments:
It is expected that, for a chamber having a small
surface to volume ratio, such as the one employed
in the experimental studies utilized in this effort,
the influence of the walls on NO oxidation rates
is small. The effect would be additionally reduced
in reactant systems for which the time to the N02
peak is relatively short (i.e., two hours or less).
As we concluded earlier, we expect that the presence
or absence of wall effects would result in no
detectable differences in the rate of formation of
HN03 , largely because of the strong tendency of
N20g to hydrolyze. Similarly, whether HN03 is
formed in the gas phase, subsequently migrating to
the wall, or whether it is formed directly on the
wall, it is unlikely that the site of hydrolysis will
have much of an effect on the observed chemistry.
While nitric acid is commonly used as an oxidant
when concentrated (60%) in the liquid phase (bodt,
et al.(1956)] , it is ineffective as an oxidant
at low concentrations. The highest attainable
concentration of HN03 during the chamber runs is
a value that is numerically equal to the initial NOX
concentration, which never exceeded 4 ppm.
B-18
-------
5. Conclusion
We conclude, based on the preceding discussion,
that no significant amounts of NO and NC>2 are lost
directly to the walls and that the loss of ^05 and
HN03 to the walls should not alter the observed photo-
chemistry. However, it is not possible at this time to
ascertain the degree to which the walls might accelerate
the oxidation of NO . Wall effects, then, probably do
not have to be taken into account in our validation efforts.
Nonetheless, it is highly desirable that experimenters
undertake to establish the magnitude of wall effects under
a wide variety of experimental conditions, and that they
do so in the near future. Until this is done, the possi-
bility that such effects may be of consequence will remain
an open issue.
E. Estimates of Experimental Error
Before comparing model predictions with experimental observa-
tions, it is desirable to establish both the accuracy and the pre-
cision of the measurements. Accuracy refers to the extent to which
a given measurement agrees with the true but unknown value of the
parameter being measured. Precision refers to the extent to which
a given set of measurements agrees with the mean of the observations.
Thus, if in a given experiment we observe yi and the true and
unknown value of the observed quantity is rii » then we might state
that
y. = n. + b. + e.
1111
where b. is a bias that impinges upon the experiment and e.
is a random error, which we will assume to be normally distributed
with mean zero and variance a2 (or e(0 , a2 )). If b^ is
large relative to n^ , we say that y. is inaccurately determined.
If a is large, with the result that er^ is large, we say that
yi is imprecisely determined.
Inaccuracies in determination of concentrations are largely
attributable to lack of specificity or accuracy in analytical
procedures, particularly in the instrumentation used to monitor
concentrations during the course of an experiment. Imprecision
is detected through the poor repeatability of an experiment, the
results of which may or may not be accurately determined. There
may be a wide variety of causes of imprecision, some of which are
also attributable to instrumentation problems.
B-19
-------
1. The Accuracy of the Analytical Instruments
The four pollutant species of primary importance in
our modeling efforts, NO2 , NO , 03 , and hydrocarbons,
were all measured using standard instrumentation and
techniques.
Hydrocarbons were determined individually by
gas chromatography; the accuracy of these
measurements is estimated to be +_ 10% at a
concentration level of 1 ppm.
Oxidants were measured using two independent
techniques: the Mast Ozone Meter and neutral
KI analysis. Corrections to KI readings
were required to account for interferences
due to PAN and N02 . Despite the corrections
the KI measurements exceeded the Mast readings
by an average of 50%. As Dr. S.L. Kopczynski
of the Division of Chemistry and Physics is
of the opinion that the KI technique is the
more accurate of the two procedures, we have
validated our model using the results of the
KI analyses.
Oxides of nitrogen were sampled manually into
fritted bubblers containing Saltzman reagent.
Nitric oxide was oxidized to form NO2 by
reaction with sodium dichromate. Dr. Kopczynski
has estimated that this conversion is almost
100% efficient. Absorbance was read on a Beckman
DU spectrometer reading 2ppm at full scale.
In general, the accuracy of these various measurements
is a function of the concentration level of the pollutant
being measured. Accuracy is poorest over the low concentra-
tion range. As most pollutants are present at low concen-
trations at some time during the course of a reaction,
questions of accuracy will inevitably arise with regard to
chamber studies. For example, at concentrations of N02
below 0.15 ppm, concentrations can be determined no more
accurately than +_ 50%. At the higher concentrations en-
countered as the reaction proceeds, the accuracy of the
readings improves substantially. Unfortunately, no recali-
bration of the oxidant or the nitrogen oxide analyzers
was performed during the ten-month study.
B-20
-------
2. The Repeatability of Experimental Runs
Because replicate runs were made for the toluene-NOx
system at five different sets of initial conditions and
for the toluene-n-butane-NOx system at three sets of
initial conditions, we have been able to estimate the pre-
cision of the hydrocarbon, NO , and N02 measurements in
those systems by calculating pooled standard deviations
[Hunter (I960)] .
The equations used to calculate the pooled standard
deviation, sp , are as follows:
N.
and
(y - y)2
2 _ i=lvyi Y'
Sj - N. - 1
V
- 1)
where NJ is the number of observations made at time t ,
j is the index representing a given set of replicates, y^
are the observed concentrations at time t , and y" is
the average of the observations made at time t . The
pooled standard deviation is then simply the square root
of the pooled variance s^ . The error bounds calculated
at the 90% confidence level (±tV)o.-90Sp) are listed in Table
4 for the specific times indicated. Bounds may be indica-
ted graphically by shading the regions of uncertainty. In
Figures 1 and 6, we display the uncertainty bounds for the
toluene-NOx and the toluene-n-butane-NOx validations
respectively.
Our impression of the chamber data is that, in spite
of the lack of recalibration of the light intensity and
chemical analyzers, the data are in general reproducible,
were carefully taken, and are as suitable as any currently
available for validation purposes. Although the data were
taken in 1966 and 1967, at a time prior to the development
of photochemical kinetic mechanisms for atmospheric reactions,
the investigators did exercise sufficient care in quantifying
those parameters important in validation of these models.
B-21
-------
TABLE 4. Precision Bounds (90% Confidence Levels) for
Toluene-NO and Toluene-n-Butane-NO Data
x x
SYSTEM: TOLUENE-NO
x
TIME (MINUTES) SPECIES UNT *° AT
80
160
240
320
50
100
80
160
240
320
SYSTEM:
80
160
240
320
50
80
160
240
320
NO-
2
NO,,
2
NO
2
N0_
2
NO
NO
HC
HC
HC
HC
TOLUENE-n-BUTANE-NO
x
NO,,
2
N02
NO,,
2
NO,,
2
NO
HC
HC
HC
HC
5
4
3
2
5
3
4
4
4
4
3
3
3
3
3
3
3
3
3
v**
5
4
3
2
5
3
4
4
4
4
s t
P
0.76
0.94
0.16
0.07
0.07
0.11
0.24
0.23
0.22
0.18
ui^wijfs.xn.j.iN J. i j
90% CONFID]
±.15 ppm
±.21
±.37
±.21
±.13
±.26
±.50
±.49
±.48
±.37
0.14 ±.34 ppm
0.12 ±.28
0.07 ±.17
0.02 +.04
0.03 ±.07
0.22 ±.53
0.17 ±.40
0.21 ±.50
0.16 ±.37
* Calculated as ±t - nns , where t ...... is the Student t statistic
v,0.90 p v,0.90
with v degrees of freedom
** Degrees of freedom
t Pooled standard deviation
B-22
-------
For example, dilution rates and the rate of conversion
of NO to N02 in the absence of hydrocarbons were
measured for all reactant systems. Probably the greatest
weakness in the chamber data with regard to their use in
validation is the lack of precise knowledge of the light
intensity. As will be shown in Section IV the magnitude
of light intensity has a substantial effect upon the time
to the N02 peak predicted by the model.
B-23
-------
IV. VALIDATION OF THE MECHANISM
Validation of the kinetic mechanism consists in
obtaining estimates of the various parameters in the
mechanism the reaction rate constants and the generalized
stoichiometric coefficients and establishing, when appropriate,
how these parameters vary with changes in the species and com-
position of hydrocarbons in the reactant mixture
carrying out sensitivity studies for these parameters, i.e.,
establishing the effect of controlled variations in the
magnitudes of the various parameters on the concentration/
time profiles for NO, N0_, O_ and hydrocarbon
generating concentration/time profiles for the various
reactant mixtures using specified initial conditions.
These predictions are then compared with experimental
results to assess the "goodness of fit".
In the first part of this section, we discuss the basis for selection
of some of the more uncertain parameters, notably the rate constants
for the hydrocarbon oxidation reactions (with 0, 0.,, and OH) and the
generalized stoichiometric coefficients a, 3, y, and e . in the
second portion of the section, we present the validation results for
each of the four hydrocarbon systems studied. Results are summarized
as a series of plots displaying both predicted and measured concentra-
tions. We would remind the reader that the results reported represent
the second validation effort involving the present model. Previous
validation studies are described in detail in Seinfeld, et al. (1971).
A. Estimation of Parameters
1. The Rate Constants
While the kinetic mechanism is both general and compact,
we have striven to formulate it in such a way that the
majority of rate constants may be taken from the literature
dealing with the study of individual reaction steps. How-
ever, due to the generalized nature of the model, some rate
constants, of necessity, are artifacts, notably those
specified for reactions 6, 11, 12, 13, and 15. All other
rate constants have been estimated from the results of experi-
ments reported in the literature; their magnitudes and
sources are given in Seinfeld, et al. (1971).
As described in Section II, kfi was selected such that a
model based on four differential equations, with HNO_ in
steady state, gave predictions comparable with those of a
model in which a differential equation for HNO was included.
In the remainder of this section we discuss the r>asis for
estimating the four remaining rate constants, k.... , k..- ,
B-24
-------
k , and k.. 5 , those associated with the hydrocarbon
oxidation reactions and the RO--NO. reaction.
The results of early validation runs indicated that
the literature values of k (0 + HC) , as given by
Johnston, et al. (1970), are too low to account for the
observed early oxidation rate of hydrocarbons and the
oxidation of NO to N0_ . A number of reactions were
excluded from the mechanism for the sake of compactness,
notably the oxidation of hydrocarbons by alkyl, oxy, and
peroxy radicals. The omission of one or more of these
"reactions of lesser importance" might account for the
apparent "smallness" of k . While the hydrocarbon-
radical reactions cited do not, in general, result in a
rapid increase in the number of free radicals, the
radicals produced may be of higher reactivity than those
present originally. The overall reactivity of the smog
system may thus increase with time.
As an example, consider hydrogen abstraction from n-
butane by a peroxymethyl radical.
(This type of reaction is discussed by Leighton (1960),
p. 217.) One hydrocarbon molecule is consumed in this
reaction, and a 2-butyl radical is formed in exchange
for the peroxymethyl radical. Several reactions now
become likely. First, the 2-butyl radical may react
with oxygen to form a hydroperoxyl radical and an olefin.
CH3CH=CHCH3
or
This reaction is of interest because a low reactivity
paraffin is replaced in the system by a highly reactive
olefin, which then participates in further chain propaga-
tion reactions. In addition the hydroperoxide formed when
the peroxymethyl radical reacts with butane photolyzes
readily, leading to still further chain branching.
CH3OOH + hV-» CH30« + -OH
The overall result of the peroxymethyl oxidation, then, if
it in fact occurs to a significant degree, is the formation
of an olefin and three free radicals.
B-25
-------
The reactions between hydrocarbons and alkyl, oxy,
and peroxy radicals, although not thought to be parti-
cularly rapid, probably still play an important role
early in the smog forming process because 1) they
compete with 0 atom attack on hydrocarbons, a reaction
which itself is not very fast due to the low 0 concentra-
tion and 2) the concentration of radicals increases
rapidly until the steady-state level is achieved. However,
these reactions are not included in the mechanism because
there is a dearth of kinetic data for the radical-hydro-
carbon reactions and because knowledge of the magnitude of
the radical populations is lacking. Consequently, values
of k11 higher than those reported in the literature have
been adopted to account for the early loss rate of hydro-
carbon observed experimentally. We note, however, that the
influence of other reactions, such as the OH-hydrocarbon
reaction, become relatively greater as the smog reactions
proceed. The contribution of the radical-hydrocarbon
reaction to the overall hydrocarbon loss rate thus becomes
less significant with time.
In the future it will be desirable to investigate the
possibility of adding a radical-hydrocarbon reaction to the
mechanism to account for the rapid early loss rate of hydro-
carbon and ' NO observed. It might also be possible to
employ literature values of k^ by modifying the values
of the stoichiometric coefficients, thus avoiding the addi-
tion of other reactions. These possibilities will be
explored in the near future when an extensive sensitivity
analysis of the model is completed.
k12
hydr
In general, we were able to use literature values for
and k,3 , the rate constants for the OH and 03
ocarbon oxidation reactions , for the validation runs
[Johnston, H.S., et al. (1970); Morris, E.D., Jr., et al.
(1971) ] . In cases where 03 does not react directly with
the hydrocarbon, a small residual value of k13 has been
assigned to account for the reaction of ozone with hydrocarbon
oxidation products. For example, in the case of n-butane,
it is possible that various butenes form subsequent to 0
or OH attack on the hydrocarbon. The reaction of these
butenes with 03 is accounted for through the artificial
increase in k.., .
Finally, the value of k-^5 was selected so that, on a
qualitative basis, the predicted concentration/time profiles
of organic nitrates and pernitrates formed as reaction
products conformed with expected behavior. The observed
rate of loss of N02 after the N02 peak was also taken
into account in estimating the magnitude of this constant.
B-26
-------
2. Generalized Stoichiometric Coefficients
Stoichiometric coefficients are those parameters intro-
duced into each individual reaction step to satisfy the
requirement of conservation of mass. While these coefficients,
in general, are easily established by carrying out a mass
balance for all elements appearing in the reaction expression,
a problem arises in the treatment of vaguely defined species
such as the generalized hydrocarbon, HC. We cannot specify
the exact number of atoms that comprise this fictitious species,
and thus it is impossible to derive or compute appropriate
coefficients. To skirt this problem, we introduce flexible
parameters, termed "generalized" Stoichiometric coefficients,
such as a in the reaction, HC + 0 M- aR02 These
generalized coefficients must be established through deductive
procedures such as "chemical" arguments and trial and error
calculations. In the discussion that follows, we present
the rationale for selecting the generalized coefficients,
a , 3 , y , and e introduced in the new mechanism. See
Seinfeld, et al. (1971) for an earlier discussion of this
same topic.
We first consider the selection of a value of a , the
number of radicals formed in the reaction of hydrocarbons and
atomic oxygen. This choice is of prime importance, as a
strongly governs the chain length of the reaction, and the
hydrocarbon-atomic oxygen reaction itself is critical in
determining the rate of oxidation of NO to N02 . As we
mentioned in Section II, in earlier validation studies we
have treated this parameter as a function of the NO/HC
ratio over the course of the reaction, rather than as a con-
stant. However, we have considered the need for a functional
relationship between a and NO/HC to be a weakness in the
formulation. We have found in the current validation studies
that a could indeed be taken as a constant for a particular
hydrocarbon and we have done so throughout. We attribute the
earlier need for a variable a to weaknesses in the data
base used at that time. Unfortunately, we have not as yet
discovered a procedure for obtaining a priori estimates of
a . Values of a used in validation were established by
comparison of predicted and observed concentrations of NO
and hydrocarbon.
The Stoichiometric coefficient y is determined by com-
paring predicted and observed concentrations of a reaction
system in which an olefin is the principal reacting hydro-
carbon. The magnitude of the coefficient is selected so as
to minimize discrepancies between the predicted and observed
hydrocarbon loss rate after the NO peak and between the
maximum predicted and observed ozone levels ultimately
attained. An olefin reaction is desirable because ozone
B-27
-------
reacts directly and rapidly with hydrocarbons of this
class. This reactant system will thus give a good
indication of the effect of the 0,-HC reaction on the
NO. decay curves. Because most three carbon and greater
hydrocarbons can form olefins as degradation products,
the value of y is the same for all hydrocarbon systems.
The stoichiometric coefficient 3 in reaction 12 is
analogous to a and y , in that it governs the number of
RO* radicals formed due to reaction of hydrocarbons
in this instance, with hydroxyl radicals. As in the case
of the other generalized stoichiometric coefficients, 3
is treated as a constant for a given hydrocarbon system.
In general we expect that 3 will be about one, since
likely products of the HC-OH- reaction are one free
radical and an aldehyde (in the case of olefins) or water
(in the case of paraffins) . Accurate estimation of e ,
the number of moles of OH formed per mole of RO2 that
reacts with NO , is important in simulation of the effect
of CO .
In order to estimate e , along with 3 , we require
experimental data for reaction systems in which the initial
charge of CO varies from zero to some substantial concen-
tration, for the product of B and e will to a large
degree determine the amount by which the time to the NO
peak is shortened for a given increase in CO concentration.
This point can be seen by inspection of the algebraic steady
state equation for the RO radical, given in Seinfeld, et al.
p. B-18 (1971). In particular, note that in this equation
the ROy concentration is inversely proportional to
- 3e) k12k14(HC)(NO) + k12k15(HC)(N02)
Since NO is oxidized by both HO" (formed in reaction 8) and
RO' , changes in the product 3e will affect the concentration
of the RO* radicals and consequently the relative contribution
of RO* to the total NO oxidation rate. Thus, for a fixed
value of 3e , the time to the NO peak will decrease as the
initial CO concentration increases, because the NO loss
rate will become more negative. In general observed reductions
in time to the N02 peak are greatest in the presence of CO
when the hydrocarbon components of the system are of low reac-
tivity and least when reactant systems consist primarily of
highly reactive olefins [Dodge, et al. (1972)].
In addition to making these qualitative observations, we
can also specify quantitative limits for the product 3e .
Since OH* attacks both HC and CO and since the products
of both reactions are radical species capable of oxidizing
B-28
-------
NO to N02 (RD2' in the former case and HO2- in the
latter), it is necessary that the number of H02* radicals
formed in the CO-OH* reaction (always equal to one) ce
greater than the number of R02* radicals formed in the
HC-OH- reaction in the presence of CO . If the product
Be were greater than one, CO would effectively inhibit
the rate of NO oxidation. This effect would be attributable
to the scavenging of OH- radicals by CO , thereby diminish-
ing the supply of OH- available for possible reaction with
HC , a reaction capable of generating more radicals than the
single H0_- produced in the CO-OH- reaction. This point
can also be verified by inspection of equation B-2b in Sein-
feld, et al. (1971). If Be > 1 , the negative terms (1 - Be)
in the denominator become positive, d(NO)/dt is then also
positive, and NO is not converted to NO- . Thus, we
require that Be < 1 . Finally, the value of e must be less
than one, as all RO are actually HO if e is equal
to one.
A final consideration in the selection of the value of B
is that the magnitude of this coefficient strongly influences
the NO decay and hydrocarbon consumption rates in the vicin-
ity of (NO) = 1/2(NO) . During that time reaction 12 is
the most important factor in the loss of HC and NO . Thus
the shapes of the HC and NO decay curves in that region
depend upon the proper choice of B .
3. Sensitivity of the Model to Variations in the Magnitudes
of Parameters
We have carried out a large number of validation runs
during both this study and that reported in Seinfeld, et al.
(1971). Many of these runs involved the investigation of the
effect of varying the magnitude of a parameter on the predicted
concentration/time profile. These efforts can thus be viewed,
in part, as an informal sensitivity study of the current
version of the kinetic mechanism. Through the experience
gained, we have acquired a fairly good "feeling" for the
extent to which variations in the rate constants, stoichio-
metric coefficients and initial conditions alter the predicted
concentration profiles. However, we have not as yet carried
out a formal sensitivity analysis. It is anticipated that we
will undertake such a study for EPA as a part of our efforts
under contract 68-02-0580.
In place of the full and formal study that we have
suggested is eventually needed, we carried out a more limited
investigation of model sensitivity. We examined the effect
of variations in four parameters k. (light intensity)* ,
*
The uncertain variable in the reaction of interest is noted in parentheses.
B-29
-------
kfi (water concentration) , k_ (light intensity) , and
initial NO concentration lN02)0on predicted time
to the NO- peak, T . These parameters have been
identified in previous studies as being the parameters
whose variations would likely have a substantial influence
on predictions. The variable T was selected as the
decision variable because it had been observed previously
that it is particularly sensitive to variations in the
parameters cited, because other key variables such as
time to the onset of 0, formation are closely linked
to it, and because it can be conveniently expressed as a
scalar.
The sensitivity calculations were performed for the
toluene-n-butane system for various initial concentrations.
The four parameters were varied within the limits of their
estimated uncertainty bounds and the effects of these changes
on T were noted. Typical results are presented in Table
5. The mechanism is clearly quite sensitive to variations
in the N02 photolysis rate and initial NO- concentrations,
but is insensitive to variations in HN02 production and
photolysis rates. Unfortunately, both k., and NO I are
subject to considerable experimental uncertainty.
In carrying out the validation runs that are reported
in the following section, we calculated concentration/time
profiles using, first, base values of all parameters and,
second, base values of the parameters with k^^ and NO I
varied within their limits of uncertainty so as to minimize
the discrepancy between prediction and experiment. In this
way one can compare the paired results and "get a feeling"
for the degree of variation:(really, improvement) in
predicted values to be expected as a result of parameter
variation for the limited, yet perhaps highly indicative,
case of varying two "sensitive" parameters. Viewed another
way, we demonstrate how lack of accuracy in certain measure-
ments, in this case initial N0? concentration and light
intensity, can affect predictions, and thus our ability to
properly assess the validity of the mechanism.
B-30
-------
TABLE 5. Sensitivity of the Model to Light Intensity, Water Concentration,
and Initial NO Concentration
Base Values of Parameters:
NO I
2|o
NO I
0.07 ppm
1.10 ppm
hydrocarbon
(toluene + n-butane)
4.62 ppm
.266 min
5x10 ppm min
3 -i
5x10 min
NO peak occurs at 112 minutes for these settings of the base parameters
Variation in Parameter
k - 0.10
Resultant Change in
Time to NO « peak (minutes)
+57
k + 0.10
-28
- 25%
+ 4
k, + 25%
b
- 4
- 50%
k? + 50%
- 50%
+21
N°
2'o
-12
B-31
-------
B. The Validation Results
In this section we present validation results for the
mechanism shown in Table 1 for the following reactant systems:
Reactant System Number of Sets of Experimental Data
toluene-NO:. 5
toluene-n-butane-NO 3
propylene-(e thane)-NO 4
auto exhaust 2
14
As we have discussed, for each set of data we carried out a
validation using base values of the parameters and a validation
using base values of all parameters except k and NOJ , which
were varied within their limits of uncertainty to obtain improved
(but not necessarily optimal) predictions. We thus report the
results of two computer simulations for each data set, "mean
value" predictions and "improved" predictions. These pairs are
labeled using the same figure number, with an "A" designating
the "improved" concentration profiles. Figure numbers, EPA
experiment identification number, initial conditions, dilution
rates, and variations in k and NO | are given in the List
of Figures , Table 6 . A key to reading the figures is given in
Table 7.
In carrying out the simulations in which parameters were
varied from their base values, no attempt was made to minimize
the discrepancy between prediction and experiment. A qualitative,
"experience-based" judgment was made as to what variations in
and
~ i
and the "improved" simulation was carried out. We do believe,
however, that these results are of value in assessing the
suitability of the mechanism for describing the chemistry. Yet
it is likely that still greater improvements in fit could have
been obtained if other parameters (rate constants, stoichiometric
coefficients, and/or initial conditions) were also varied within
their uncertainty limits. We did not feel, however, that in
light of the uncertainties in the experimental results such
simulations were warranted. Optimization studies are of interest
at a time when more precise experimental data become available.
1 . Toluene-NO Validations
Validation runs for the toluene-NO experiments were
performed using the rate constants listed in Table 8. Note
B-32
^ d NO I , within their limits of uncertainty [k =
0.266 ± 0.10 min~l , NO i ± 50%], would reduce the discrepancy,
-------
TABLE 6. List of Figures
[CURE
1
1A
2
2A
3
3A
4
4A
5
5A
6
6A
7
7A
8
8A
9
9A
10
10A
11
11 A
12
12A
13
14
EPA NO.
300
300
258
258
250
250
272
272
271
271
251
251
253
253
257
257
318
318
325
325
321
321
329
329
222
231
HC TYPE
Toluene
Toluene
Toluene
Toluene
Toluene
Toluene
Toluene
Toluene
Toluene
Toluene
n-Butane
Toluene
n-Butane
Toluene
n-Butane
Toluene
n-Butane
Toluene
n-Butane
Toluene
n-Butane
Toluene
Propylene
Propylene
Propylene
Propylene
Propylene
Propylene
Propylene
Propylene
Auto Exhaust
Auto Exhaust
(N02)*
.02
.02
.05
.075
.04
.04
.04
.06
.05
.075
.07
.035
.08
.04
.07
.07
.06
.06
.04
.04
.10
.05
.05
.075
.12
.23
(NO)*
1.25
1.25
.35
.35
1.17
1.17
.55
.55
.32
.32
1.10
1.10
.53
.53
.27
.27
1.12
1.12
.35
.35
1.31
1.31
.26
.26
1.95
2.80
o
3.22
3.22
2.88
2.88
1.53
1.53
1.67
1.67
1.20
1.20
4.62
4.62
4.91
4.91
4.26
4.26
.51
.51
.45
.45
.275
.275
.24
.24
2.21*
.59**
k^ AVG. OIL. RATE
.266
.216
.266
.200
.266
.200
.266
.300
.266
.366
.266
.166
.266
.266
.266
.366
.266
.166
.266
.366
.266
.266
.266
.366
.166
.266
5.50
5.50
4.63
4.63
5.48
5.48
5.40
5.40
5.74
5.74
5.85
5.85
5.90
5.90
4.65
4.65
5.75
5.75
6.95
6.95
7.13
7.13
6.85
6.85
5.37
5.75
* Units of ppm
t Units of minutes
tt Units of liters minutes"
B-33
HC-L = 1.15, HC2 = 1.06
HC^ = 0.20, HC2 =0.39
-------
TABLE 7. Key to Figures
EXPERIMENTAL
RESULTS:
I
1
A
O
O
NO
NO
OXIDANT
HYDROCA
PREDICTIONS:
NUMBERED FIGURES ARE CALCULATED USING MEAN VALUE OF kj_ AND
INDICATED INITIAL CONCENTRATION OF NO2 .
NUMBERED "A" FIGURES ARE IMPROVED PREDICTIONS BASED ON CHOICES
OF kx , AND/OR (N02)o AS INDICATED IN THE LIST OF FIGURES.
SHADED REGIONS INDICATE PRECISION BOUNDS BASED UPON POOLED
STANDARD DEVIATION AT 90% CONFIDENCE LEVEL.
B-34
-------
that the value of kj^ adopted is about sixty times greater
than the literature value of the constant. This substantially
elevated value was required if discrepancies between hydro-
carbon and NO predicted and experimental values were to be
acceptably small during the early portion of the experimental run.
(See Section III for a more detailed justification of this
assumption.) The value of k^2 is an estimate based on measure-
ments made by Morris, E.D., Jr., et al. (1971) for the xylene-OH
reaction. A value of k^3 was adopted that is less than that
employed by us for n-butane in previous validation studies. This
decrease in k^ takes into account the fact that aromatics
typically react to form acetylenes as oxidation products in
preference to olefins. Thus, the use of this reduced value
permits more accurate description of the post-NC^-peak hydro-
carbon oxidation.
Turning now to the stoichiometric coefficients, the value
of a selected was based on the rate of loss of NO observed
early in the irradiation. Because toluene and n-butane are
both low reactivity hydrocarbons, carbon monoxide might be
expected to affect the toluene-NO system in a manner similar
to the n-butane-NO system. Consequently, 3 and E were
given the same value for toluene as they were for n-butane, as
reported in Seinfeld, et al. (1971). The value of y is the
same as that used for the propylene system, which will be dis-
cussed shortly.
Plots of predicted and experimental values of concentra-
tions with time are shown in Figures 1 through 5; improved
predictions, obtained by varying either k or (NO ) , or
both, are given in Figures 1A through 5A. °
2. Toluene-n-Butane-NO Validations
As toluene and n-butane are hydrocarbons having similar
reactivities, a mixture of these species will remain in approxi-
mately constant proportion throughout the course of a reaction.
We thus elected to combine the two species, for modeling
purposes, into a single "lumped" hydrocarbon. The rate con-
stants and stoichiometric coefficients for this "lumped"
species were estimated by computing the weighted average of
the constants for the individual species, the weights being
the initial mole fraction of each hydrocarbon. Because the
ratio of toluene to n-butane remained approximately constant
throughout the course of the reaction, it was not necessary
to update the rate constants during the integration. Rate
constants and stoichiometric coefficients for this system are
listed in Table 9.
As in the case of toluene, the value of the 0-n-butane
rate constant was taken to be sixty times greater than the
literature value. The literature value for the OH-n-butane
B-35
-------
TABLE 8. Validation Parameters for Toluene-NO Experiments
Rate Constants
12
E13
C14
C15
0.
2.
21
0.
0.
5.
5.
1.
10
6.
1.
7.
1.
30
266
76
.8
X
106
006
1
0
0
8
.0
0
5
5
8
.0
X
X
X
X
X
X
X
10
10
10
10
10
10
10
-4
-3
3
3
4
-5
3
-1
min
min
-1 .
ppm min
ppm min
ppm min
ppm min
min
-1 .
ppm mm
-1 .
ppm mm
-1
-1
-1
-1
-1
-1
-1 . -1
ppm mm
-1 .
ppm mm
-1
-1 . -1
ppm mm
ppm min
-1 ,
ppm mm
-1
-1
Stoichiometric Coefficients
a
6
Y
e
6.0
1.2
4.0
0.61
B-36
-------
FIGURE 1, EXPERIMENT #300, TOLUENE,
RERCTI3N TIME (MINUTES)
-------
FIGURE IA, EXPERIMENT #300, TOLUENE,
SCflLE FflCTOR = 10
0.0 0.400 0.800 1.200 1.600 2.000 2.400
RERCTIGN TIME (MINUTES)
2.800
3.200
3.600
-------
FIGURE 2, EXPERIMENT #258, TOLUENE,
SCflLE FflCTOR = 10
0.0 0.1400 0.800 1.200 1.600 2.000 2.400
REflCTION TIME (MINUTES)
2.800
3.200
3.600
-------
FIGURE 2A, EXPERIMENT #258, TOLUENE,
SCflLE FRCTOR = 10
0.0 0.400 0.800 1.200 1.600 2.000 2.400
REflCTION TIME (MINUTES)
2.800
3.200
3.600
-------
o
o
LO
CO
^ O
a. co
Q_
in
£~
oc
o
m
FIGURE 3, EXPERIMENT #250, TOLUENE,
SCflLE FiCTOffc= 10
0.0 0.400 0.800 1.200 1.600 2.000 2.400
REflCTION TIME (MINUTES)
2.800
3.200
3.600
-------
o
o
LO
CO
21 C3
Q_cn
Q_
0§
(X
QC
O
DO
I
FIGURE 3A, EXPERIMENT #250, TOLUENE,
0.0 0.400 0.800 1.200 1.600 2.000 2.400
REflCTIGN TIME (MINUTES)
2.800
3.200
3.600
-------
o
o
LO
CO
-8
in
CM
CC
CJ
o
o
o
o
o
in
o
»
o
FIGURE 4, EXPERIMENT #272, TOLUENE,
O
O
o
SCflLE FflCTOR = 10
0.0 0.400 0.800 1.200 1.600 2.000 2.400
REflCTION TIME (MINUTES)
2.800
3.200
3.600
-------
o
o
I/)
*
CO
§
cn
LO
QC
s
CJ
O
O
O
O
O
tn
CO
*>.
O
O
FIGURE IA, EXPERIMENT #272, TOLUENE,
O
O
O
O
0.0 0.400 0.800 1.200 1.600 2.000 2.400 2.800
REflCTIGN TIME (MINUTES)
3.200
3.600
-------
o
o
in
(O
21 CD
Q-co
Q_
08
LO
oc
CJ
o
o
LO
tn
£>
(Jl
FIGURE 5, EXPERIMENT #271, TOLUENE,
SCflLE FHCT8R = 10
I
0.0 0.400 0.800 1.200 1.600 2.000 2.400 2.800
REflCTION TIME (MINUTES)
3.200
3.600
-------
o
o
LD
CO
o
o
o
OS
O
O
o
o
o
in
o
o
FIGURE SA, EXPERIMENT # 271, TOLUENE,
0.0 0.400 0.800 1.200 1.600 2.000 2.400
REflCTION TIME (MINUTES)
2.800
3.200
3.600
-------
rate constant has been used, and, as before, we have assigned
a small residual value for the ozone-n-butane reaction.
Because n-butane should not fragment as greatly as toluene
when under attack by 0 atoms, we have adopted a slightly
smaller value of a for the former reaction (a = 5) than for the
latter. Equal values of all other stoichiometric coeffi-
cients have been assigned for each of the two species (i.e.,
6toluene = 3n-butane " etcj' simulation results for this
system are presented in Figures 6 to 8 and 6A to 8A.
3. Propylene-Ethane-NO
X
During our preliminary examination of the propylene-ethane-
NO data we found that the disappearance of ethane over the
course of a six hour chamber run could be accounted for as
losses due to sampling and dilution alone; the loss of ethane
through photochemical reactions was not significant. Conse-
quently, we treated these data as a propylene-NO run, con-
sidering ethane to be inert over the course of a six-hour
irradiation. Values of the rate constants and stoichiometric
coefficients for this system are given in Table 10.
As before, it was necessary to use a larger value for k
than that reported in the literature in order to account for trie
loss rate of hydrocarbon and NO during the first few minutes
or irradiation. In the case of propylene we adopted a value
ten times greater than the literature value. Literature values
were used for the rate constants for the reactions of propylene
with OH and O_ , reactions that account for the vast majority
of propylene consumed.
When propylene undergoes attack by oxygen radicals, it
splits into two organic free radicals, an acyl and an alkyl
radical.
0 + CH3CH = CH2 * CH3C. +
\
CH,CH_- + HO
3 2
This is in contrast to the 0-toluene reaction, which initially
yields an alkyl radical
+ 'OH
B-47
-------
TABLE 9. Validation Parameters for Toluene-n-Butane NO Experiments
Rate Constants
Run 251
Run 253
Run 257
k.
1
k0
2
k3
k4
*
k5
*J
\
k.
7
k
8
k9
kio
k
k!2
k!3
JL
-------
w
1
£
VO
FIGURE 6, EXPERIMENT #251, N-BUTANE-TOLUENE,
/o
0.400
0.800
1.200
1 .600
2.0
P
)00
2
o
!
.400
TS~
2
"- .
!
.SCO
SCEUL
q onr>
>j . t- '_' w
FRCTC3 =
*""" -. i
'-, PP
\ 'u> 'W
10 2
!0
REHCTION T1HE (MINUTES)
-------
o
o
to
o
o
o
o
o
FIGURE GA, EXPERIMENT #251, N-BUTANE-TOLUENE,
o
o
LO
CO
O
O
O
cr>
O
O
O
o
o
LO
CM
SCflLE FflCTOR = 10
0.0 0.400 0.800 1.200 1.600 2.000 2.400
REflCTIGN TIME (MINUTES)
2.800
3.200
3.600
-------
FIGURE 7, EXPERIMENT #253, N-BUTANE-TOLUENE,
O
G
O
O
0.400
0.800
1.200 1.600 2.000 2.UOO
RERCTIGN TIME (MINUTES)
2.800
3.200
FflCTOR = 10
A [A
3.600
-------
FIGURE ZA, EXPERIMENT #253, N-BUTANE-TOLUENE,
O
O
0.0 0.400 0.800 1.200 1.600 2.000 2.400
RERCTIGN TIME (MINUTES)
2.800
3.200
3.600
-------
FIGURE 8, EXPERIMENT #257, N-BUTANE-TOLUENE
0.400
0.800
1.200 1.600 2.000 2.400 2.800
REflCTIGN TIME (MINUTES)
3.200
3.600
-------
FIGURE SA, EXPERIMENT #257, N-BUTANE-TOLUENE,
O
O
O O
0.400
0.800
1.200 1.600 2.000 2.400
REflCTIGN TIME (MINUTES)
2.800
SCflLE FflCTOR = 10
IA A I
3.200 3.600
-------
Significantly, the time to termination of a chain initiated
by an acyl radical is longer than the time to termination
of one initiated by an alkyl radical. This is due to the
fact that the alkyl radical is a decomposition product of
the acyl-initiated NO oxidation.
02 NO -C02
CH,C- * CH.COO- -» CH,CO' -» CH_
3II 3I 3i 3
NO
Thus, the 0 atom-initiated NO oxidation chain for pro-
pylene is much longer than for toluene. We have estimated
that in this case, a = 16 .
As we discussed earlier, the values for (3 and e
are determined largely by studying the effect of CO on
predicted concentrations. We established values for g
and e for isobutylene in earlier work [Seinfeld, et al.
(1971)] and have used these same values for propylene. The
two olefins are of similar reactivity and would thus be ex-
pected to react similarly in the presence of CO .
The value of y was established by observing the predicted
oxidant formation rate and the N02 decay rate after the
NO2 peak. Since ozone reacts directly with propylene, the
data provide a sound basis for estimation of y We have
used this estimate of y for all hydrocarbon systems studied
thus far.
The validation results for the propylene-ethane system
are presented in Figures 9-12 and 9A-12A.
4. Auto Exhaust
The auto exhaust data consist of two pairs of replicate
runs obtained by irradiating auto exhaust diluted to levels
approximately equal to those observed in the Los Angeles Basin.
B-55
-------
TABLE 10. Validation Parameters for Propylene-N0x Experiments
Rate Constants
10
13
'14
0.266
6
2.76 x 10
21.8
0.006
0.1
, -4
5.0 x 10
3
5.0 x 10~°
1.8 x 103
10.0
4.0 x 104
2.5 x 104
0.016
1.8 x 103
3.0
-1
min
-1
min
-1 . -1
ppm nun
-1 . -1
ppm nun
-1 . -1
ppm nun
-1 . -1
ppm nun
-1
min
-1 . -1
ppm nun
-1 . -1
ppm min
-1 . -1
ppm nun
-1 . -1
ppm min
-1 . -1
ppm mm
-1 . -1
ppm min
-1 . -1
ppm nun
Stoichiometric Coefficients
a
e
Y
e
16.0
0.2
4.0
0.22
B-56
-------
o
o
LO
»
CO
FIGURE 9, EXPERIMENT #318, PROPYLENE,
08
cc
DC
UJO
CJ
o
o
LO
Ofl
A
A
0.0 O.UOO 0.800 1.200 1.600 2.000 2.400
REflCTION TIME (MINUTES)
2.800
3.200
3.600
-------
o
o
LD
tn
o
o
CE
DC
o
CJ
o
o
in
FIGURE QA, EXPERIMENT #3is, PROPYLENE
w
tn
00
0.1400
0.800
1.200 1.600 2.000 2.1400 2.800
REflCTIGN TIME (MINUTES)
3.200
3.GOO
-------
o
o
in
CO
Q-co
Q_
0§
»«LO
cc
QC
C\J
o
o
o
o
o
o
in
CO
I
un
O
o
FIGURE 10. EXPERIMENT #325, PROPYLENE,
0,0
0.40C
0.800
1.200 1.600 2.000 2.400
REflCTIGN TIME (MINUTES)
2.800
3.200
3.600
-------
o
o
CO
FIGURE 10A, EXPERIMENT #325, PROPYLENE,
-8
^ o
Q-co
Q_
CM
o
o
o
O
o
o
in
o
o
o
o
o
in
03
O
k
O
O
SCflLE FftCTOR = 10
I
0.0
1.200 1.600 2.000 2.400
REflCTION TIME (MINUTES)
2.800
3.200
3.600
-------
o
o
in
CO
-8
Zio
Q-co
Q_
in
£~
QC
I
UJO
o
o
in
FIGURE 11, EXPERIMENT #321, PROPYLENE,
I
A
D
O
D
SC
A
D
D
FflCTOR = 10
10
0.0
0.400
0.800
1.200 1.600 2.000 2.400
REflCTION TIME (MINUTES)
2.800
3.200
3.600
-------
o
o
in
co
FIGURE HA, EXPERIMENT #321, PROPYLENE,
-8
"
08
CM
OC
CJ
o
o
in
0.0 0.400 0.800 - 1.200 1.600 2.000 2.400
REflCTION TIME (MINUTES)
2.800
3.200
A
D
D
FflCTOR = 10
|O
3.600
-------
o
o
in
CO
FIGURE 12, EXPERIMENT #329, PROPYLENE,
Q-cn
Q_
08
cr
GC
I
UJO
zr
0«
CJ
o
o
LO
O
O
O
O
O
en
Ul
0.0
0.400
0.800
1.200 1.600 2.000 2.400
RERCTION TIME (MINUTES)
2^800
3.600
-------
o
o
in
co
FIGURE 12A, EXPERIMENT #329, PROPYLENE,
-8
jr o
9-co
in
GC
o
o
CJ
o
o
in
o
o
o
o
o
in
CO
I
0.0 0.400 0.800 1.200 1.600 2.000 2.400
REflCTION TIME (MINUTES)
2.800
3.200
3.600
-------
One set of data was obtained by employing as a reactant
the exhaust of a Chevelle equipped with air pollution
control devices. Exhaust taken from an "uncontrolled"
Chevelle constituted the reactant in the second experi-
ment. The cumulative effect of the emissions control
devices was to reduce hydrocarbon and CO emissions by
a factor of nearly four and to increase NOX emissions
slightly. No measurements were made of the particulate
emissions from the two cars, although loss of NOX prior
to the NO2 peak upon irradiation indicates that the
particles present significantly influenced the chemical
dynamics.
The hydrocarbons in the auto exhaust were analyzed
in detail prior to dilution using gas chromatography.
After injection into the chamber and subsequent dilution,
but prior to irradiation, the hydrocarbons were analyzed
again. The results of these two determinations were in
poor agreement. The discrepancies observed are probably
attributable to the fact that the diluted hydrocarbon
species in the chamber were present at concentrations
lower than those that can be accurately measured. Al-
though it.is still possible to estimate the initial hydro-
carbon concentrations for these runs from the analyses
made prior to dilution, hydrocarbon analyses carried out
for samples collected during a chamber run are of questionable
value. The hydrocarbon decay profiles shown on the valida-
tion figures have been estimated by Dr. Marcia Dodge of
the Division of Chemistry and Physics. Analyses for NO ,
NO2 , and oxidant were performed in the manner described
earlier.
One notable difference between the irradiation results
for the auto exhaust gases and those for the "pure" systems
such as toluene-NOx was that in the exhaust runs a sub-
stantial amount of NOX was lost before the NO2 peak.
Because exhaust contains a large amount of particulate matter
it has been suggested that nitrate formation might occur
on particle surfaces. This is consistent with the results
of Lee,et al. (1971) , who found that the nitrate content
of particulate matter in exhaust that had been irradiated
through the region of sharp decrease in NO and increase
in NO2 was 175 times that of the particulate matter in
unirradiated exhaust. Other chamber studies of synthetic
auto exhaust [Wilson, (1972)] have shown that the loss of
B-65
-------
NO prior to the NO peak is not observed in the
absence of paxticulate matter. Consequently, we have
included in the mechanism the additional reaction
19
NO + PARTICLE -> NITRATE
While the exact chemical details of early NOX loss are
not yet known, inclusion of this type of reaction aids in
accounting for the effect observed.
For the purpose of validating the exhaust data we
elected to segment the hydrocarbons into two reactivity
classes. Ct paraffins and aromatics, excluding benzene,
comprise the first reactivity class, ethylene and other
olefins, the second reactivity.class. C^ to C3 paraffins,
benzene, and acetylene were considered to be unreactive.
We further assumed that the reactivities of Ct paraffins
are equal to that of n-butane, that the reactivities of
aromatics are equal to that of toluene, that ethylene is
best treated individually*, and that the reactivities of
all other olefins are equal to that of propylene. Although
these assumptions obviously are subject to some question,
they allow us to base our estimates of group reactivity on
values established in validation runs performed previously.
Moreover, the uncertainties in the hydrocarbon data do not
justify a further refinement in the rate constants and
stoichiometric coefficients at this time.
In order to carry out validation runs using the data
described, it was first necessary to calculate the rate
constant for PAN formation and the rate constants and
stoichiometric coefficients for the reactions of 0 , OH ,
and 03 with each class of hydrocarbons. As in the case
of toluene-n-butane, the lumped rate constants and stoichio-
metric coefficients were calculated as the weighted average
* The 0-ethylene rate constant was taken to be ten times the liter-
ature value, whereas all the stoichiometric coefficients were assumed
to be the same as those established for propylene.
B-66
-------
of the parameter values estimated for a pure system,
weighted in proportion for the composition of the
mixture. All of the lumped rate constants were cal-
culated using the equations
where k^ refers to the reaction rate constant for
hydrocarbon species i (for example, isobutane) and
reaction j (for example, HC + 0 ). The stoichio-
metric coefficients, e and a , were calculated using
the equations
C'i1tuci
The remaining stoichiometric coefficients are not a function
of the hydrocarbon composition of the reaction mixture. The
base values of the rate constants and stoichiometric coeffi-
cients may be found in Table 11.
B-67
-------
TABLE II. Values of Base Parameters Used to Calculate Rate Constants and Stoichiometric
Coefficients for Complex Hydrocarbon Mixtures*
C PARAFFINS
4
0
1920
OH
5720
.0001125
PAN
1.2
.61
ARDMATICS
(excluding benzene)
6420 15000 .000075
30
1.2 4 .61
7
o>
00
ETHYLENE
OTHER OLEFINS
7720 2500 .00287
40000 25000 .0165
16 .2
16 .2
.22
.22
-1 -1
* Reaction rate constants are given in ppm min
-------
Estimates of the rate constants for the lumped
hydrocarbon and PAN formation reactions were based
on initial compositions of the reactant mixture. How-
ever, samples were drawn from the chamber during the
course of the experiment and were analyzed chromato-
graphically to determine their hydrocarbon composition.
As a result, we were able to calculate updated estimates
of the high reactivity hydrocarbon reaction rate constants
at two times
the time at which half of the initial NO had
disappeared
the time at which the N02 peak occurred.*
The effect of updating the high reactivity rate constant
at the two times was to lower the reactivity of the class
since ethylene, having a lower reactivity than the other
olefins, increased in its percentage composition with
time. The reactivity of the low reactivity hydrocarbon
class appeared to remain essentially constant throughout
the period of irradiation.
We assumed for the purposes of validation that the
concentration of CO was constant throughout each run.
Losses of CO are incurred, however, through reaction
with OH radicals and as a result of sample withdrawal.
Also, CO is formed when formyl radicals and other products
decompose. Carbon monoxide enters into the chemical dy-
namics most prominently between the times when irradiation
commences and when the N©2 peak occurs. The loss of CO
during this period was probably less than 10 percent.
Attempts at validating the model for exhaust obtained
from the unequipped Chevelle revealed that our estimated,
a priori values of the stoichiometric coefficients were too
high, that is, the NO oxidized too rapidly. In order to
* Due to suspected uncertainties in the chromatographic analyses
we did not attempt to continuously update the estimates of the rate
constants. Also, as such a calculation depends upon having knowledge of
the measured values, it is not a particularly desirable procedure.
B-69
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obtain improved validation results we found it necessary
to use values of a , 0.2 i 6 / $2 an<^ Y that are twenty
percent lower than those originally calculated. Experimen-
tally, the slower loss of NO might have occurred because
the presence of particles enhanced the rate of chain ter-
mination, thus reducing radical chain length. It is also
possible that the CO is not treated properly in the model.
Finally, we assumed that the value of k, was at the lower
end of the uncertainty range, or 0.166 min. .
In carrying out validation runs for exhaust collected
from the equipped Chevelle, we used the mean light intensity
and the a priori values of the stoichiometric coefficients.
Reasonably good predictions were obtained for the NO loss
and N02 production rates, but the hydrocarbon disappeared
much too rapidly. A twenty percent reduction in the radical
chain lengths and a lower light intensity would have resulted
in a better hydrocarbon validation but much poorer results
for the NOX . Because the hydrocarbon data are of doubtful
accuracy, especially in this run, we chose not to make the
20% reduction. Also, it is not possible to assess the
accuracy of assuming shorter radical chain lengths or loss
of N©2 to particles, as no characterization of the particles
was attempted experimentally (i.e., the number and size dis-
tribution of the particles, the chemical composition of the
particles, and the magnitude of light scattering due to the
particles). Making the assumptions cited, however, constitutes
one means of obtaining improved validations and, as a result,
perhaps merits further investigation experimentally.
The rate constants used for auto exhaust simulation
runs are listed in Tables 12 and 13, and the validation results
are presented in Figures 13 and 14.
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TABLE 12. Validation Parameters for Auto Exhaust Experiments
(Unequipped Chevelle)
Rate Constants
k.
Run 222
10
12
!4
!5
!6
l8
k19
Stoichiometric Coefficients
a
3
Y
e
a2
32
Y2
At a time half way to the NO0 peak, the following changes were made:
k.
0.166
2.76 x 106
21.8
0.006
0.1
5 x 10"4
5 x 10"3
1.06 x 104
1.8 x 103
10.0
3.83 x 103
9.51 x 103
9.8 x 10"5
1.8 x 103
10.6
2.54 x 104
1.48 x 104
0.01
5 x 10"3
4.56
0.96
3.20
0.415
12.8
0.16
3.2
min
min
-1 . -1
ppm min
-1 . -1
ppm mm
-1 . -1
ppm mm
-1 . -1
ppm mm
min
min
-1 . -1
ppm mm
-1 . -1
ppm mm
-1 . -1
ppm min
-1 . -1
ppm mm
-1 . -1
ppm mm
-1 . -1
ppm mm
-1 . -1
ppm mm
-i . -i
ppm mm
-1 . -1
ppm mm
-1 . -1
ppm mm
min
16
k!7
At the time of
k!6
k!7
2.5 x 10
-1 . -1
ppm mm
1.45 x 10 ppm min
the NO peak, the following changes were made:
4-1-1
2.12 x 10 ppm min
, . ,,.4 -1 . -1
1.19 x 10 ppm mm
o r ,o-3 -1 . -1
8.5 x 10 ppm mm
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TABLE 13. Validation Parameters for Auto Exhaust Experiments
(Equipped Chevelle)
Rate Constants
Run 231
-1
10
12
C13
C14
17
'18
Stoichiometric Coefficients
a
0
Y
e
a2
B2
Y2
0.266
2.76 x 106
21.8
0.006
0.1
5.0 x 10~4
5.0 x 10~3
3
2.4 x 10
1.8 x 103
10.0
3.96 x 10
9.9 x 103
9.6 x 10~5
1.8 x 103
8.24
2.18 x 104
1.23 x 104
5.0 x 10"3
, -3
5.0 x 10
5.73
1.20
4.00
0.352
16.0
0.2
4.0
min
min
-1 . -1
ppm nun
-1 . -1
ppm mm
-1 . -1
ppm man
-1 . -1
ppm mm
min
-1
min
-1 . -1
ppm nun
-1 . -1
ppm nun
-1 . -1
ppm nun
-1 . -1
ppm nun
-1 . -1
ppm nun
ppm min
-1 . -1
ppm nun
ppm min
-1 . -1
ppm nun
-1 . -1
ppm mm
. -1
mm
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FIGURE 13, EXPERIMENT #222, AUTO EXHAUST
SCflLE FRCTOR = 10
0.0 0.400 0.800 1.200 1.600 2.000 2.UOO 2.800
RERCTIGN TIME (MINUTES)
3.200
3.600
-------
o
o
in
CO
8
og
-------
V. CONCLUDING COMMENTS
The data base provided for the validation studies fulfills many
of the important requirements that one would wish to place on it.
The concentration levels of the hydrocarbons, nitrogen oxides, and
oxidants are representative of those observed during smoggy days
in Los Angeles. Initial conditions for the runs covered a. broad
range of hydrocarbon to nitrogen oxide ratios. This is a particularly
important property of the data base if the validated mechanism is
to be part of an airshed model which will be used to evaluate proposed
alternative control strategies. On the whole, the accuracy and pre-
cision of the measurements is adequate, although there are a number
of important exceptions, which we will mention shortly.
An important aspect of the data base is the variety of hydrocarbon
systems included. High, intermediate and low reactivity hydrocarbons
were represented, as were single reactants (toluene and propylene) and
a binary mixture. Moreover, a complex and highly realistic mixture,
auto exhaust, is included, serving as an important test of the model.
A useful addition to the four reactant systems studied would be a binary
mixture of high and intermediate or low reactivity hydrocarbons, per-
haps propylene and toluene.
While the data base possesses many desirable attributes, its
shortcomings must be noted as well, for these determine the limits
within which the model may be tested. Consider, for example, a data
base for which concentrations have been determined with only passable
accuracy. Wide ranging sets of parameters could easily produce pre-
dictions all of which fall within the broad limits of experimental
uncertainty. Under such circumstances, it is not possible to satis-
factorily test the adequacy of the mechanism to represent the data.
We have mentioned the most notable deficiencies of the data base
at one point or another in earlier sections. We summarize them here,
with some comments.
Inaccuracy in measurement and in analytical procedure.
As noted earlier, Mast and KI readings were badly dis-
crepant, initial N02 was imprecisely determined, and
light intensity was not known with sufficient accuracy.
Also NO and N02 determinations were inaccurate at
low concentrations, and hydrocarbon analyses prior to
and subsequent to injection into the chamber were in
poor agreement. We recommend the use of chemiluminescent
techniques for NOX and 03 analyses in future studies,
the careful determination of k., by an accurate technique
[see, for example, Holmes, et al. (1972)] , and determination
of the cause of discrepancies in hydrocarbon analyses.
B-75
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Lack of measurement of certain species, both in the gas
phase and on the wall. It would be of value to monitor
nitric and nitrous acid concentrations in future studies.
Determination of wall concentrations of these species is
also desirable.
Lack of control of water concentration.
Lack of controlled variation of CO concentration. CO
was present only in the auto exhaust runs; its influence
on rate processes is best determined by allowing it to
vary over a broad range in concentrations in simple hydro-
carbon systems.
Complete lack of characterization of particles in the auto
exhaust experiments. Information concerning size, number
and chemical composition is needed. Also, we would wish
to determine the degree to which size and number distribu-
tion of the exhaust are altered due to deposition and ab-
sorption on the sampling container, and, after injection
into the chamber, during the chamber sampling procedure.
Turning now to the results of the validation efforts, we make
a number of observations. First, we have been able to demonstrate
that, in general, there is acceptable agreement between predicted
and measured concentrations. In making this statement, we must em-
phasize that substantial uncertainties exist in the magnitude of
light intensity and initial NO2 concentration, as well as in the
values of measured concentrations of HC , NO , N02 and 03 , thus
limiting the possibilities for critically testing the adequacy of the
model. More specifically, the mechanism has shown good qualitative
and quantitative agreement with observed values of the time to the
N02 peak and final ozone levels reached for a wide range of hydro-
carbon to NOX ratios. This agreement was achieved using fixed
values of rate constants and stoichiometric coefficients (except
where these constants are known to vary with composition) for all
validation runs for a given reactant system.
Prior to undertaking the validation runs we carried out a limited
and informal sensitivity study. The results of the study indicated
that k^ and N02| had a large effect on predicted concentrations.
As the uncertainty in the magnitude of these parameters was considerable
B-76
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= 0.266 + .10 min.""1
NO.| = measured value ^ 50% ,
we elected to carry out simulation runs using both (1) base parameter
values and (2) base parameter values, with k., and/or NC^Io varied
within their uncertainty limits in such a way as to improve the pre-
dicted concentration/time profiles. In general, discrepancies between
predicted and observed concentrations were reduced considerably when
"improved" values of k^ and NC>2lo were used. The sensitivity of
the model to these parameters highlights the need for more accurate
and precise determination of key experimental variables and parameters
if the adequacy of the mechanism is to be critically evaluated.
The grouping or "lumping" of hydrocarbons in complex reactant
systems is a topic which will require further study. How many
groupings are needed? How shall they be segmented? How shall we
estimate the "lumped" rate constants and stoichiometric coefficients?
As the number of hydrocarbon groupings in the model, and thus the
level of detail and complexity, increases, so does the opportunity
for more accurate representation. But with the increase in complexity
there is an increase in computation and storage requirements and in
the amount and quality of data needed. In this study we have chosen
to divide the hydrocarbons into three classes:
(1) high reactivity hydrocarbons consisting of olefins
(2) low reactivity hydrocarbons consisting of 4 paraffins
and all aromatics except for benzene
(3) non-reactive hydrocarbons consisting of C-± to 3
paraffins, benzene and acetylene.
For extremely complex systems, such as actual atmospheric mixtures,
usually relatively little is known concerning the hydrocarbon com-
position and its variation in space and time. Moreover, emissions
rates and composition, and their spatial and temporal variations,
are usually poorly determined. In such cases there would be little
advantage in dividing the hydrocarbons in this manner. Rather, one
might lump all reactive hydrocarbons into a single reactivity class,
leaving only those species that are essentially unreactive to be
included in a second grouping.
B-77
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Once the three groupings of hydrocarbons were selected it was
necessary to establish values of "lumped" parameters. We assumed
throughout that the "lumped" rate constants and stoichiometric
coefficients could be estimated quite simply as weighted averages
of the individual parameters, the weights being equal to the fraction
of each species present in the hydrocarbon mixture. The validation
results suggest that this procedure is quite satisfactory, given the
limitations in accuracy of the data. However, future validation
studies, involving more precise data, will provide a better test of
this assumption.
To conclude, we believe that the validation results reported
here indicate that the mechanism provides an adequate, perhaps good,
description 6f smog chamber kinetics. In particular, the model
appears capable of predicting the concentration/time behavior of a
variety of reactant systems over a wide range of initial conditions.
The few auto exhaust simulations performed indicate that the mech-
anism displays promise for describing the complex mixtures that exist
in the atmosphere. The guidelines established for estimating rate
constants and stoichiometric coefficients also have proven to be quite
adequate. However, a considerably more accurate and complete data
base is required if the adequacy of the model is to be critically
evaluated. We recommend that a carefully conceived experimental
program be undertaken for the sole purpose of providing the data
needed to carry out such an evaluation.
With regard to the status of the present model, it would perhaps
be useful to carry out further validation studies using existing data,
if these data fill a gap in the data base that has been employed thus
far. For example, it would be valuable to perform simulations for a
mixture of high and low reactivity hydrocarbons. It may also be use-
ful to carry out validations for reactant systems similar to those
studied by us, but where the experiments were performed in smog
chambers having different configurations, sizes, wall materials, etc.
However, we do not believe that is is appropriate to undertake addi-
tional validation studies for "fine tuning" of the model; existing
data cannot support such an effort. More accurate and complete data
bases are required for this purpose, data bases that do not suffer
from the deficiencies listed earlier in this section.
B-78
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REFERENCES
Altshuller, A.P., Kopczynski, S.L., Lonneman, W.A., Becker, T.L.,
Slater, R., Environ. Sci. Tech., 1_, 889 (1967a).
Altshuller, A.P., Kopczynski, S.L. Lonneman, W.A., Sutterfield,
F.D., Wilson, D.L., Environ. Sci. Tech., 4_, 44 (1970).
Altshuller, A.P., Kopczynski, S.L., Lonneman, W., Wilson, D.,
J. Air Pollution Control Assn., 17, 734 (1967b).
Altshuller, A.P., Kopczynski, S.L., Wilson, D., Lonneman, W.,
Sutterfield, F.D., J. Air Pollution Control Assn., 19,
791 (1969).
Dodge, M.C., Bufalini, J.J., "The Role of Carbon Monoxide in
Polluted Atmospheres," Environmental Protection Agency,
Research Triangle Park, North Carolina 27711 (1972).
Gay, B.W., Jr., Bufalini, J.J., Environ. Sci. Tech., 5_, 422 (1971).
Godt, H.C., Jr., Quinn, J.F., J. Am. Chem. Soc. 78, 1461 (1956).
Hecht, T.A., Seinfeld, J.H., Environ. Sci. Tech., 6^, 47 (1972).
Hill, A.C., J. Air Pollution Control Assn., 21, 341 (1971).
Holmes, J.R., O'Brien, R.J., Crabtree, J.H., Hecht, T.A.,
Seinfeld, J.H., "Measurement of Ultraviolet Radiation
Intensity in Photochemical Smog Studies," Submitted
to Environ. Sci. Tech. (1972).
Hunter, J.S., "Some Applications of Statistics to Experimentation,"
Chem. Eng. Prog. Symp. Series, No. 31, Vol. 56, p. 10 (1956).
Johnston, H.S., Pitts, J.N., Jr., Lewis, J., Zafonte, L.,
Mottershead, T., "Atmospheric Chemistry and Physics,"
Project Clean Air, Vol. 4, Univ. of Calif., Sept. 1, (1970).
Lee, R.E., Jr., Patterson, R.K., Crider, W.L., Wagman, J.,
Atmospheric Environment, Jj/ 225 (1971).
Leighton, P.A., Photochemistry of Air Pollution, Academic Press,
New York, N.Y., (1961).
B-79
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REFERENCES (Continued)
Morris, E.D. , Jr., Niki, H. , J. Phys. Chem., 75^ 3640 (1971).
Schuck, E.A., Stephens, E.R. , Schrock, P.R., J. Air Pollution
Control Assn., 3£, 695 (1966).
Seinfeld, J.H., Hecht, T.A., Roth, P.M., "A Kinetic Mechanism
for Atmospheric Photochemical Reactions," App. B of
"Development of a Simulation Model for Estimating Ground
Level Concentrations of Photochemical Pollutants",
71-SAI-9, Systems Applications Inc., Beverly Hills, Calif.
(May 1971).
Westberg» K., Private Communication (1972).
Wilson, W.E., Jr., Private Communication (1972).
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