A KINETIC MECHANISM FOR ATMOSPHERIC
PHOTOCHEMICAL REACTIONS
Appendix B
of
Development of a Simulation Model
for Estimating Ground Level Concentrations
of Photochemical Pollutants
Prepared hy
Systems Applications, Inc.
Beverly Hills, California 90212
for the
Air Pollution Control Office
of the Environmental Protection Agency
Durham, North Carolina 27701
-------
A KINETIC MECHANISM FOR ATMOSPHERIC
PHOTOCHEMICAL REACTIONS
Appendix B
Of
Development of a Simulation Model
for Estimating Ground Level Concentrations
of Photochemical Pollutants
John H. Seinfeld
Thomas A. Hecht
Philip M. Roth
Report: 71SAI-9
May 1971
Prepared by
Systems Applications, Inc.
Beverly Hills, California 90212
for the
Air Pollution Control Office
of the Environmental Protection Agency
Durham, North Carolina 27701
under Contract CPA 70-148
-------
CONTENTS
INTRODUCTION B- 1
I. SURVEY OF PREVIOUSLY PROPOSED MECHANISMS B- 3
II. A NEW SIMPLIFIED MECHANISM B-13
A. Inorganic reactions ............... B-13
B. Organic reactions B-15
C. A Mathematical Representation
of the New Mechanism B-17
III. PARAMETERS OF THE NEW MECHANISM B-19
A. Reaction Rate Constants B-20
B. Generalized Stoichiometric Coefficients B-23
IV. NUMERICAL INTEGRATION OF THE REACTION RATE EQUATIONS. . B-24
V. VALIDATION OF THE NEW SIMPLIFIED MECHANISM B-27
VI. ADAPTATION OF THE NEW MECHANISM FOR INCORPORATION
INTO AN URBAN AIRSHED MODEL B-40
A. The Effects of Solar Radiation on Rates
of Photolysis B-43
B. Variations in Reactivity of Atmospheric
Hydrocarbons B-48
REFERENCES B-51
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INTRODUCTION
The quantitative description of the rates of chemical reaction of
atmospheric contaminants is a vital ingredient in the formulation of a
model capable of predicting accurately ground level concentrations of
gaseous pollutants. That this is true is evident from an inspection of
the governing equations of the model, the equations of continuity:
+ K (K
c2, ...,cp) + S± (B-l)
i = 1, 2, ..., p
where x,y = horizontal coordinates
z = vertical coordinate
vx» vy vz = three components of average wind velocity vector
ci = time-smoothed concentration of species i
Kx, Ky, K2 = turbulent eddy dif fusivities
S^ •• rate of emission of species i from elevated sources,
a repetition of equations (2) in the main text. The reaction rate
term, R^, represents the rate of production of species i and is
commonly expressed as the algebraic sum of the rates of production of
species i over all chemical reactions in which species i participates.
Thus ,
n n
where a . = -1 il species i is a reactant in reaction j, +1 if a product,
3 0 if not present.
and c -i c 2 ~ reactant concentrations in reaction j, assumed to involve two
^ ' •* species (c - = 1 if reaction j involves one species) .
32
Not only does Ri (cj_, c^, ...» cp) appear in each of the partial differential
equations that comprise the equations of continuity, but the common argument
of all R^, i = 1, 2, ..., p, links (or couples) these equations in such a
way that their solution must be simultaneous. Thus, the successful development
of a comprehensive airshed model depends heavily on the accuracy of description
of reaction rate processes.
The formulation of a kinetic mechanism of general validity is an endeavor
beset by several inherent difficulties. First, there is a multiplicity of
stable chemical species present in the atmosphere". Most of these exist at
very low concentrations, thereby creating major problems in detection and
analysis. A number of atmospheric constituents, in fact, remain unidentified.
Second, the large variety of highly reactive, short-lived intermediate species
and free radicals further complicates the picture. Finally, when we consider
the enormous number of individual chemical reactions that these species undergo,
the barrier to understanding becomes clear. However, while we must admit
B-l
-------
to only a limited knowledge of atmospheric reaction processes, it remains
essential that we attempt to formulate quantitative descriptions of these
processes which are suitable for inclusion in an overall simulation model.
The formulation and development of a kinetic mechanism that is to
be incorporated in any airshed model is both delicate and exacting, an
undertaking requiring a blend of science, craftsmanship, and art. Such
a mechanism must not be overly complex,.as computation times for integration
of the continuity equations in which the mechanism is to be imbedded are
likely to be excessive. On the other hand, too simplified a mechanism may
omit important reaction steps, and thus be inadequate to describe atmospheric
reaction processes. A major issue in this regard is the requirement that the
mechanism predict the chemical behavior of a complex mixture of many hydro-
carbons, yet do so with a paucity of detail.* Thus, the formulator must
strike a careful balance in postulating a mechanism—between compactness of
form and accuracy in prediction.
The kinetic mechanism, once developed, must be validated. This procedure
is commonly conceived as consisting of two parts: validation in the absence
of transport processes and validation in their presence. In practical terms
we are speaking, respectively, of comparison of the model's predictions with
data collected in smog chamber experiments and with data collected at actual
contaminant monitoring stations situated in an urban airshed. When we speak
of validation of a kinetic mechanism in this section, we are referring to the
comparison between predictions and experiment based on smog chamber studies.
The second and more complex of the two parts, validation of the kinetic
mechanism in the presence of transport processes (convection and turbulent
diffusion) is the primary undertaking of this project and is described in
the main text.
Only the most intrepid of readers can have been exposed to the warnings
and qualifications that highlight this discussion, and have emerged with
faith undiminished. Yet one final caveat is necessary. Smog chamber
experiments may be considered valid simulations of the atmosphere only under
the following conditions: (1) wall effects are eliminated or are negligible,
(2) contaminant concentrations are at levels found in the atmosphere,
(3) the initial charge to the chamber is representative of urban source
effluents and (4) the spectral distribution of the radiation is the same as
that found in the atmosphere. It is unlikely that many smog chamber studies
satisfy all these requirements.
As a part of the current contract effort, 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 simplicity, sufficient generality to include all major
gaseous contaminant species (aerosols were not considered in the present
study) and acceptable accuracy in the prediction of smog chamber data over
*Most mechanisms have been developed to simulate the photo-oxidation of .a
single hydrocarbon species, even though the model may include a general
hydrocarbon as a reactant. It is important to note that the behavior of a
mixture may be very different from the average behavior of unmixed hydro-
carbons .
B-2
-------
a range of values of NOx/HC and for a variety of hydrocarbons. In Section I
of this Appendix, we present an assessment of existing mechanisms, arriving
at the conclusion that a "better" model was needed. Included are the results
of the validation study for one of the more promising existing mechanisms
and a discussion of the deficiencies of this and other formulations. In
Section II, we present a new kinetic mechanism, one developed by Thomas A.
Hecht and John H. Seinfeld of the California Institute of Technology. The
results of recent validation studies, which are detailed in Section V,
demonstrate 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 propylene and n-butane at initial
NOx to hydrocarbon ratios of 1/3 to 1. The mechanism has also been shown
to simulate accurately the effect on photo-oxidation rates of variations
in CO concentrations, as well as the inhibitory effect of high initial
concentrations of nitric oxide on the maximum concentration of ozone obtained.
Finally, in Section VI, we discuss the adaptation of this validated mechanism
for use in an urban airshed model.
I. SURVEY OF PREVIOUSLY PROPOSED MECHANISMS
It is only in the last ten years that investigators have postulated
general kinetic mechanisms to describe the rates of chemical reactions in
the atmosphere.* The mechanisms that have been proposed can be classified
as follows:
Class 1. Highly simplified mechanisms (fewer than ten reaction steps)
Friedlander and Seinfeld (1969) general**
Eschenroeder (1969) general
Behar (1970) general
Class 2. Simplified mechanisms (ten to twenty-five reaction steps)
Wayne and Earnest (1969) propylene
Behar (1970) propylene
Class 3. Complex mechanisms (more than twenty-five reaction steps)
Westberg and Cohen (1969) isobutylene
Wayne, et al. (1970) general
(There are, in addition, several mechanisms under development or recently
completed that have not been reported. These include a Class 2 mechanism
of Eschenroeder and Class 2 and 3 mechanisms of Hecht and Seinfeld. As
we have adopted the Class 2 mechanism of Hecht and Seinfeld for use in
the development of our airshed model, we discuss this mechanism in
Section II of this Appendix.)
* This is in contract to the very considerable efforts that have been
expended by scores of investigators over the past two decades in the study
of individual atmospheric reactions. Since the literature in this field
is voluminous, the interested reader is referred initially to reviews and
articles. Particularly recommended are the reviews by Leighton (1961) ,
Altshuller and Bufalini (1965, 1971), and Johnston, et al. (1970).
**Refers to the hydrocarbon species for which the mechanism was developed.
B-3
-------
At the outset of this project, we vrere faced with the choice of
adopting an existing mechanism or developing a new mechanism. What
follows is a synopsis of the arguments leading to our eventual decision—
the development of a new mechanism.
* Class 3 mechanisms were ruled out for three reasons.
First, while the aim of those developed thus far has been
completeness of description, this thoroughness has been
achieved through the inclusion of a number of reaction steps
that involve free radicals. Unfortunately, knowledge of the
rates of these reactions is imprecise. Furthermore, when
several free radical reactions are included in a mechanism,
the flexibility in the choice of rate constants is increased,
as each imprecisely known parameter can be varied independently
in the process of matching prediction and experiment. To the
extent that Class 3 mechanisms possess this flexibility in
parameterization, the validity of comparison of prediction
and experiment is diminished.*
Second, computation time is a limiting factor in the solution
of the coupled partial differential equations that comprise the
overall airshed model. The inclusion of a Class 3 mechanism in
such a model greatly increases the computational burden and is
to be avoided if at all possible.
Finally, the decision to develop and implement a Class 3 mechanism
implies tire desire to represent reaction processes as accurately
as is feasible. Thus, a relatively large number of reaction steps
must be incorporated in a description of the dynamics of
consumption of a pcrticid-ar' hydrocarbon, such as propylene.
Reaction dynamics will, however, vary for the many hydrocarbon
species present in the atmosphere. If, for example, thirty to
*A statistical analogy is useful in illustrating this point. It is well
known that the sum of a linear combination of n normally distributed,
independent random variables is also normally distributed, with variance
equal to n times the variance of each individual variable (assumed equal).
n n
Thus, if n = I a^, V(n) = £ *| V(aJL). Further, if VCa^ •=...= V (an) ,
n
V(n) = nVCa^ I x*. Finally, if xt - x2 « ... « XR - 1, V(n) » nVfa^.
Hence, the variance of the predicted value n (or the uncertainty associated
with prediction) is proportional to n, the number of terms in the original
equation.
Consider now that the reaction rate constants, k , have associated with them
a measure of uncertainty, V(k.). We can now argue, in an analogous manner,
that the greater the number of reaction steps that are included in a mechanism,
the larger will be the uncertainty associated with the prediction of concentration,
which is a complex function of the k^, i = 1, 2, ..., n. Thus, parsimony in
parameterization is a desirable attribute in a kinetic mechanism.
B-4
-------
Run
1
2
3
4
5
forty steps are required to describe propylene kinetics, and
fifty hydrocarbon species, each having unique dynamics, are
believed to exert a significant impact on atmospheric reaction
processes, one is faced with an intractable representation of
the system. Alternatively, adoption of a detailed representation
of the reactions of a single species (for example, propylene)
which may, upon development, be applied to a single, generalized
hydrocarbon is tantamount to constructing a mechanism having
many of the representational deficiencies of a Class 1 or Class 2
kinetic scheme and, in addition, introduces a substantial
parameter estimation problem. For these reasons, we turned
to Class 1 and Class 2 mechanisms.
We had hoped, for obvious reasons of simplicity and convenience,
that it would, be possible to employ a Class 1 mechanism in the
overall airshed model. We thus undertook a validation study
for one of the three Class 1 mechanisms cited, that of Eschenroeder
(1969). (It is unnecessary to study the Class 1 mechanisms of
Friedlander and Seinfeld and of Behar, as it can be shown that
Eschenroeder1s mechanism, slightly modified*, is substantially
the same as, or superior to, the other two (see Table B-l for
details of this mechanism.)**
Five computer runs were carried out to test the accuracy of
prediction of the modified mechanism when compared with smog
chamber studies for propylene.
Pata Source
Gulf Research CRC-3
Gulf Research CRC-3
Gulf Research CRC-311
Gulf Research CRC-311
California State Air
Resources Board
Propyleno/NO
1.93
1.93
5.35
5.35
0.91
Rate Constants*** Figure
Original
Revised
Original
Revised
Original
B-l
B-2
B-3
B-4
B-5
Calculated values and experimental data for the five runs are
plotted in Figures B-l to B-5 respectively. While the results
shown in Figure B-2, employing revised rate constants, demonstrated
a distinct improvement over the results of Figure B-l, based on
Eschenroeder's original published constants, these revised constants
did not bring about a similar improvement in accuracy of prediction
for a Gulf data CRC-311 (see Figures B-3 and B-4). Also, the
mechanism was unable to predict NO2 and 03 concentration behavior
+ 02 -> RO- + C03 was eliminated because of its
*The reaction
endothermicity .
**The Friedlander and Seinfeld and the modified Eschenroeder mechanisms differ
in that the assumption of pseudo-steady state (or quasi-equilibrium) is
invoked for ozone in the former. The Behar and- Eschenroeder mechanisms are
at variance only in the choice of stoichiometric coefficients.
***See Table B-2 for a summary of original and revised reaction rate constants.
Figures B-l to B-5
and Tables B-l and
B-2 follow
B-5
-------
CO
I
cr»
c.
O-
Predicted Values
(original rate
constants)
ulf Research Data
0,0 100 120 140
:^;\CTIC?! TI::E (IIIHUTES)
FIGURE B-l. VALI^TION CF TS!E MCDiriZD ESCiSEfUCEDER MECHAHISH - RUH 1
160 ISO 200
-------
Predicted Values
(revised rate
constants)
Gulr Research Data
(CRC 3)
80 100 120 140
REACTION TI;;E (KINUTES)
FIGURE 3-2. VALIDATION OF THE ;:CDIFIEP ESCMENROEDER I'ECHANISM - RUN 2
-------
00
00
3.5
3.0
2.5
°- 2.0
1.5
E
Q.
O.
UJ
O
•zz.
O
O
1.0
0.5
0.0
Predicted Values
(original rate
constants)
Gulf Research Data
(CRC 311)
20 40
60
FIGURE B-3,
30 100 120 140
REACTION TIME (MINUTES)
VALIDATION OF THE MODIFIED ESCHENROEDER MECHANISM - RUN 3
160 180 200
-------
C-
£3.
LU
3.5
3.0
2.5
2.0
1.5
1.0
0.5 • —
0.0
Predicted Values
(revised rate
constants)
Gulf Research Data
(CRC 311)
20 40 60 30 100 120 140
REACTION TIME (MINUTES)
•FIGURE B-4. VALIDATION OF THE MODIFIED ESCMINROEDER MECHANISM - RUN 4
130 200
-------
CO
O
a
O-
Ci.
3.5
3.0
2 K
C. • ^
2.0
1.5
1.0
0.5
0.0
Predicted Values
(original rate
constants)
California State Air
Resources Doard Data
40
60
160
SO TOO 120 140
REACTION TIKE (MINUTES)
FIGURE 3-5. VALIDATION OF THE MODIFIED ESC'IENROEDER MECHANISM - RUN 5
180 200
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TABLE B-l. The Modified Class 1
Mechanism of Eschenroeder (1969)
NO2 + hv—-—> NO + 0
0 + 02 + M-—> 03 + M
03 + NO-^—> NO2 + 02
HC + 0-^—» bKD« + cRCHO
HC + 03-^—> bRO' + cRCHO
NO-»—> N02 + R0«
RO + 0- - > d0 + RO«
2 2- - 3
aPAN
Steady state assumed for atomic oxygen and RO*.
B-ll
-------
TABLE B-2. Reaction Rate Constants and Stoichiometric
Coefficients for the Modified Eschenroeder Mechanism (Propylene)
i (units)
Original* Revised
1 (min"1) 0.40 0.37
2 (min"1) 2.76 x 106 2.0 x 106
. 1
3 (ppm'1 min"1) 21.8 21.8
4 (ppm"1 min"1) 4.97 x 101* 4.97 x 101*
5 (ppm"1 min"1) .18 0.05
6 (ppm"1 min"1) 50.0 50.0
7 (min"1) 6.285 6.285
8 (ppm"1 min"1) 3.0 3.0
Stoichiometric Coefficients
b 2.5 2.5
d 0.5 0.7
*Eschenroeder (1969)
B-12
-------
for the Air Resources Board data (see Figure B-5). We therefore
dismissed the possibility of employing this mechanism, and thus
all available Class 1 mechanisms/ in the overall airshed model.
• The two Class 2 mechanisms that have been postulated, those of
Wayne and Earnest (1969) and Behar (1970), were found to be
Unsatisfactory for two reasons. First, both mechanisms omit
certain reaction steps which are now thought to be significant
(as, of course, do the simpler Class 1 mechanisms) and which
have been incorporated into the newly developed model discussed
in Section II. These steps are the formation of nitric acid,
the formation of nitrous acid and its photolysis to form OH'
radicals, the acceleration of N02 and 03 formation (due indirectly
to the reaction of CO with the OK' radical), and the oxidation of
hydrocarbon species by OH*radicals. Second, both models include
reaction steps, primarily involving free radicals, about which
little is known. This situation is similar to that described
earlier in the discussion of Class 3 mechanisms, in which a
model can be manipulated to fit what data exist.
These, then, are the arguments that led to the development of a new
mechanism, which is described in the following section.
II. A NEW SIMPLIFIED MECHANISM
Let us first briefly review the necessary attributes of a kinetic
mechanism that is to be a part of an urban airshed model. A suitable
mechanism mustt (1) describe reaction rate phenomena accurately over
a specified range of concentrations, (2) be a parsimonious representation
of the actual atmospheric chemistry, in the interest of minimizing
computation time, and (3) be written for a general hydrocarbon species,
with the inclusion of variable stoichiometric coefficients to permit
simulation of the behavior of the complex hydrocarbon mixture that actually
exists in the atmosphere. In short, an acceptable mechanism must
exhibit a balance between accuracy of prediction and ease of computation.
We present in this section a new, simplified (or Class 2) mechanism for
describing the rates of atmospheric chemical reactions that we believe
satisfies these requirements.
At this point we direct the reader to Table B-3 for a complete
statement of the new mechanism; reference should be made to this table
throughout the discussion that follows. Description of the mechanism
is facilitated by splitting the presentation into three parts—a brief
discussion of the reactions of inorganic species, a more detailed discussion
of hydrocarbon reactions, and a presentation of the mathematical equations
associated with the mechanism.
A. Inorganic reactions
The major inorganic species that participate in atmospheric
chemical, reactions are NO, NO0, 00, 0,, CO, and H_0. The reactions
£, £. O £-
Table B-3 follows
B-13
-------
Table B-3. The New, Simplified Mechanism
1
NO2 + hv— — >NO + 0
M
3
NO - >N02
03 + 2NO, >2HNO, *
d . H 0 3
2
NO + NO. »2HNO0
2 H 0 2
2
HNO + hv - > OH' + NO
7
CO + OH' -- *"CO + HO'
0 2 2
8
HO *+ NO - >HNO + 0
22 22
9
HC + 0
10
HC + 03
HC + Oil • - >6RO2' + eRCHO
12
R02- + NO -- > N02 + 60H'
13
R02- + NO^ - > PAN
H02' + NO - > N02 + OH'
*Reaction 4 is a composite of the three reactions,
03
NO, + N00.t>-t?>N)>0,
3 2 2 5
N2°5+ H2°-^£>2HN03
Thus, it is not necessary to retain NO, in the mechanism.
0
B-14
-------
of these five species are represented by reactions 1 through 8 and
reaction 14 in Table B-3. In particular, these nine reactions
account for the following experimentally observed phenomena:
1. the primary inorganic reactions in the formation of
photochemical pollutants (reactions 1 to 3)
2. formation of nitric acid (reaction 4)
3. formation and photolysis of nitrous acid (reactions 5, 6 and 8)
4. the reaction of CO and OH' radicals (reaction 7)
Reactions 5 and 6 have been included to account for the importance
of HNO, as a source of OH« radicals in the presence of water. In a
dry system, reactions 4 and 5 will be omitted. Reaction 8 is included
to provide for the consumption of HO2" when NO1 has been depleted.
The importance of these phenomena has been demonstrated in recent
smog chamber experiments reported by Stedman, et al. (1970), Holmes (1970),
and Westberg, et al. (1971).
B« Organic reactions
In the development of a simplified mechanism, it is helpful to
introduce a general hydrocarbon species, denoted HC, which may 'be
taken to represent a single hydrocarbon or a mixture of hydrocarbons.
In explaining the development of the mechanism, however, we classify
individual hydrocarbons as belonging to one of three groups — olefins,
aromatics, and paraffins. (The reactions of oxygenated hydrocarbons
have been ignored) . We can then consider the reactions of atomic
oxygen (0), ozone (03) , and the hydroxyl radical (OH«) with hydrocarbons
belonging to each of the three groups.
The reaction of atomic oxygen with an olefin results in the production
of two free radicals, generally an alkyl and an acyl. For example, the
reaction of atomic oxygen with ethylene produces CH3« + HCO; with propylene,
CH3' + CH3CO or C,H • + HCO; with isobutylene, (CH,) CH« + HCO or
<; 5 i 2
CjH • + CH-CO. These alkyl and acyl radicals, in turn, react rapidly with
molecular oxygen to form peroxyalkyl and peroxyacyl radicals. The reactions
of atomic oxygen with aromatics is in some cases also rapid (Leighton (1961,
p. 146)). While peroxides, acids and alcohols have been observed as
final products of the reaction chain initiated by the attack of atomic
oxygen on aromatics (Eventova and Prytkova, (I960)); Kemula and Grabowska,
(1960) ) , the initial products are not well known. The main reaction of
atomic oxygen with paraffins is most probably RH + 0 — »R* + OH- (Leighton
(1961, p. 142)). This reaction is relatively slow, although the
reaction rate increases significantly with molecular weight.
In summary, the main result of the reaction of atomic oxygen with
hydrocarbons is the formation of free radicals, usually two in number.
We represent this step in the mechanism as
9
HC + 0™ >
B-15
-------
v;here RO2* is a lumped radical species (in general, a peroxyalkyl or
peroxyacyl radical) and ct is the stoichioraetric coefficient, i.e., the
number of radicals produced in this reaction. It should be noted that
RO2' represents the total population of oxygen-containing free, radicals
which are capable of oxidizing NO to NC>2. However, RO2- is merely
symbolic of these radicals; some may not contain exactly two oxygen
atoms (for example, peroxyacyl radicals).
Vie now consider the reactions of ozone with hydrocarbons. The
initial products of the olefin ozone reaction are an aldehyde and a
zwitterion. The number of free radicals formed depends on the subsequent
zwitterion reaction. For three cororaon olefins, the result of 0 attack
is:
ethylene HCHO + Cl!202
propylene HCHO + C2HU°2 or
' CH CHO + CH 0
3 22
isobutylenc HCHO + (CH3)2CO2 or
) co + aio
The reaction of ozone with alkanes and aromatics is slow and can probably
be neglected. Thus, the initial reactions of hydrocarbon with ozone
can be summarized as
10
HC + o3 ----- > PRO • H- yr.cKo
where (3 and' Y are stoichionetric coefficients whose values depend on
the composition of the hydrocarbon mixture.
Vie now consider the reactions of OH* with various hydrocarbons.
Hecht and Seinfeld (1971) have proposed three possible mechanisms
for the propylene/OK. reaction. In the first two, aldehydes and free
radicals are the products, and, in the third, the chain reaction is
terminated by the formation of the allyl radical and water. The alkane/
OH« reaction has been recently considered by Greiner (1970) . He postulates
that the principal products of this reaction are a free radical and
water. We might also expect that the branched aroratic/OH- reaction
would yield similar products. Taking into account each of these possible steps
we include in the mechanism the general hydrocarbon/CK' reaction,
HC + OH ' — --> 5 R02 • + e RCHO
where the stbichioraetric coefficients 6 and £ are again a function of
the particular hydrocarbon mixture. Since aldehyds formation occurs only
through. the reaction of olefins (and possibly aromatics) , e will be
less than one.
The remaining organic reactions in the simplified mechanisn describe
the oxidation of NO to NO2 by peroxy radicals and the formation of PAN.
12
RO2' + NO ---- > K02 + 6OH*
13
RO2* -f N02 --- > PAN
B-16
-------
It is important to note that, if CO and ^0 are present, we treat
H02* and R02» as separate species. In the absence of CO and H^O, however,
we consider only the single species R02*, which must now include H02* since
reactions 5-8 and reaction 14 are omitted. In this case, 6 represents
the fractional product of OH. from reaction 12, that is, the fraction of
HO *in the total lumped radical species RC>2* .
Certain classes of reactions have not been included in the postulated
mechanism. For example, the formation of organic nitrates can be treated
as a part of reaction 13 and thus has not been considered separately.
Aldehyde decomposition is not included, but this may be accounted
for through the adjustment of y and e. PAH decomposition and radical-
radical recombination reactions have been neglected because of their
relative unimportance. Host notable, however t is the complete omission
of aerosols in this treatment.
C. A Mathematical Representation of the New Mechanism
The simplified mechanism consists of reactions 1 to 14 in
Table B-3 and includes the following species: NO, NO2 , 03, HC, 0,
OH', HO2. , R02« , KNO2, HN03, RCHO, PAN. Differential equations are
required for the first four species, steady state relations for
the next five. The last three species are products and may also
be represented by differential equations. In this section, we
present the algebraic expressions for each of the fourteen reaction
steps, the five steady state relationships, and the four coupled,
first order, ordinary differential equations that constitute the
mathematical representation of the reaction dynamics.
The individual reaction rate expressions may be written directly
from Table B-3 and arei
r = Ck(0)(M)](0) = k(0)
r = k (0 ) (NO)
3 33
r = [k (H 0)](NO)(NO ) = k1 (NO) (NO )
3 b i i ^ ^
r = k (HNO )
662
r? «= [k?(co)(02)](OH.) - k'?(OH.)
re
rg = kg(HC) (0)
ri
-------
rm"kn,(H02)(NC))
The constants k^» kg, and k' are each defined as the product of
the individual rate constant and concentration of a species present
in sufficiently large concentrations that k', kl and k^ nay be
considered invariant.
Now applying the steady state assumption to the species
0, OH', HOJ, ROJ, and UNO , we have:
0: r - r - r «= 0
UNO,: 2r_ - r + r « 0
2 568
OH*: r - r - r + 0r, + r, =0
6 7 11 . 12 l«t
R02': ar9 + Pr,fl + 6r - r.? - r,, «= 0
Substituting the individual reaction rate expressions into these five
equations , we have:
k,(N02)
(0) -
kj + K9(HC)
(OHO = [2k5'(NO)(N02){k1?(NO) + kn(N02)}
+ 6k12(NO){ak9(HC) (0) +• Bk10 (HC) (03)}]/B
(HO •) = ..... k7(OH°
2
(HNO
2 k8(N02)
(NO,)
2
(R02.) = [kn(HC){ak9(HC)(0) +
+ ?6k^kn (HC) (NO)
where B » kn (HC) {k^ (NO) + k13(M02)} - ^k^,, (NO) (HC)
The differential equations expressing the rate of formation
of KC, NO, NO2, and 03 can be written directly fron the reaction
steps shown in Table B-3.
. = (B-2a)
dt 9 10 11
B-18
-------
(B-2b)
d(N02)
*•*• •»-•••• y- v»y + v •» 9 ** — y *-i* + r* — v
dt "l r3 ^r»t r5 r8 r!2 r!3
- r2 - r3 - r,, - r10 (B-2d)
By substituting into these four differential equations the fourteen
individual reaction rate expressions, we have a set of equations that is
a function of the concentrations of the four species, HC, NO, NO2, and
03, and also a function of the steady state concentrations of 0, HNO2,
OH*fR02«, and HO2«. Given initial concentrations of NO, NO2, CO, 03
and HC, these four differential equations may be integrated numerically
(see Section IV) to predict the concentration/time behavior of the four
components for which the equations are written. Note, however, that
at each time step it is necessary to calculate new steady state
concentrations of 0, HNO , OH«, RO2*, and H02» as a function of the
most recent values of NO, NO , 0 and HC.
Finally, if we wish to compute the concentration of products as a
function of time, we add three differential equations to the original
set of four:
d(RCHO) _ „ .
_ r10
d(HN03)
dt H
cUPAN)
where (PAN) indicates all of the organic nitrate termination products
of reaction 13.
III. PARAMETERS OF THE NEW MECHANISM
Prior to validation, it is necessary to establish values for the
two classes of parameters that appear in the mathematical statement of
the new kinetic mechanism—the reaction rate constants and the
stoichiometric coefficients. For the most part, values of the rate
constants can be estimated from the chemical literature. However, the
values of certain rate constants, particularly those associated with the
reactions of the generalized species, HC and RO^' raust be deduced from
data available for individual species. Furthermore, there is a sacrifice
of chemical detail inherent in the adoption of generalized species, a loss
in the ability to associate the rate constant values with particular
reactions. Thus, the rate constants in the simplified mechanism are more
-------
a quantitative assessment of. the relative rates of competing reactions
than a reflection of the exact values for particular reactions. Similar
difficulties are encountered in establishing values for the generalized
stoichiometric coefficients that are included in the mechanism, as it
is not possible to write a balanced reaction expression for a lumped
hydrocarbon species.
In general, "base" values of rate constants that appear in the
kinetic mechanism will be derived from published values. It should be
kept in mind, however, that final values, established during validation
of the mechanism, will in some cases differ from these base values. The
rationale for selection of final values of parameters is presented in
Section V. In this section we present the arguments for assigning base
values to both the rate constants and the stoichiometric coefficients
of the mechanism.
A. Reaction Rate Constants
We present in this section the base values of the reaction rate
constants of the new mechanism. These values are summarized in
Tables B-4 and B-5. The rate constants, kj and k&, which depend on
irradiation conditions, are treated separately in part A of Section VI,
The selection of certain rate constants requires some comment.
Reaction 4 is a composite of three reactions:
Reaction 4 a will be rate controlling, as NO reacts rapidly with
NO,. Reaction 4c will also proceed rapidly in the presence of water
at concentrations typically found in the atmosphere. However, if the
concentration of water is low, this reaction may compete witn 4a. We
thus regard the base value of k. as an upper limit for k. . Similarly,
reaction 7 is a composite of two reactions:
CO + OH- — Ia_»c02 + H«
H- + 0 — Z
In this case, however, we assume that 7b is instantaneous, so that the
rate of reaction 7 may be taken as that of 7 a.
The values of rate constants presented in Table 3-5 are for the
reactions of representative hydrocarbon species. Thus, they have not
been adopted directly. Rate constants for reactions 12 and 13 are
not generally available.
Tables B-4 and B-5
B-20 follow
-------
TABLE B-4. Base Values of Reaction Rate Constants for the Inorganic Reactions Included
in the Simplified Mechanism
Reaction Units
Specific VP.IUP. or
Ran«e of Vp.lu/js
2
3
4a
w
£ 4b
4c .
*'
7a
8
14
min"1
ppm"
ppm"1
ppm"1
ppm
ppm~*
ppm"
ppm"
ppm"
(pseudo first order)
min"1
min"1
min"1
min"1
min"1
min"1
min"1
min"1
2.76 x 106
21.3
0.0405
5.41 x 103
2*94 x ID"3
4.3 x 10"6
200
10
2.94
Preference
\
Kaufnan, et al. (1967)
Clyne, et al. (1964)
Ford, et al.(1957)
Schott and Davidson (1958)
Zafonte (1970)
Wayne and Yost (1951)
Baulch, et al. (1968)
No reported values. Value given
estimated by authors.
Johnston, et al. (1970).
-------
TASLS B-5. Reaction Rate Constants .for Individual Organic Species*
Reaction Species t Rate Constant (ppr."1 r.ir."1)
9 ethylene 770
propylene 6850
n-butane 32
acetaldehyde 545
w 10 ethylene 4 x 10"3
M
10 propylene 1.6 x 10"z
isobutylene 3.4 x 10~2
t ,
trans-2-butane • 0.63
11 n-butane 5.7 x 103
ethylene • 7.5 x 103
formaldehyde 150
ecetalclehyde 25
^Values taJcen from Zafonte (1970).
-------
B. Generalized Stoichiometric Coefficients
Stoichiometric coefficients are those parameters introduced into each
individual reaction step to satisfy the requirement of conservation of
mass. For example, in the reaction NO3 + N02 + II20—§» 2HN03, the "2"
preceding HNOg is a Stoichiometric coefficient. 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*-^—>aRO2. 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, B, Y, <5, e, and 6, introduced in the new
mechanism.
We first consider the selection of a value for a, the number
of radicals formed in the reaction of hydrocarbon 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.
Extensive validation studies have shown that in some cases a is
most realistically treated as a function of the NO:HC ratio over the
course of the reaction, rather than as a constant. Since a governs
the chain length, this parameter should reflect the inhibitory effect
of large NO:HC ratios on the formation of ozone. It was therefore
decided that the instantaneous value of a a should depend on the
NO:HC ratio as it changes with time. We would expect the values of
a to lie between 2 and 10, depending on the particular hydrocarbon
mixture and the NOsHC ratio.
The stoichionetric coefficient 8, represents the number of oxygen-
containing radicals produced as a result of the reaction of hydrocarbons
with ozone. This coefficient is approximately two for olefins and
somewhat less for mixtures of olefins and paraffins. We have treated g
as a constant, as it is not necessary that both a and 3 vary with NO:HC
ratio. Thus $ is less than two and is a function of the composition
of the hydrocarbon mixture.
The Stoichiometric coefficient 6 in reaction 11 is analogous to a
and B, in that it governs the number of R02• radicals formed due to
reaction of hydrocarbons—in this instance, with hydroxyl radicals.
As in the case of 6 and for similar reasons, we have chosen to keep
6 cbnstant. The basic values of 6 are not as tightly constrained,
and thus less certain than those of $, because less is known about
*Chain length is defined as the average number of free radical reactions
(or propagation steps) that occur as a result of each initiation reaction.
B-23
-------
hydrocarbon/hydroxyl radical reactions than about hydrocarbon/ozone
reactions. We expect, however, that 6 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).
The coefficients y and E determine the amount of aldehyde
formed as a result of reactions 10 and 11. Neither of these
coefficients should exceed one, with reasonable values lying between
0.5 and 1.0. In the validation studies to be described we did not
compute aldehyde concentrations; thus the specification of y and
e was not necessary.
The generalized coefficients 6 (for R02« in the HC/OH* reaction)
and 6 (for OH" in the RC>2*/NO reaction) are important in simulating
the effect of CO. Since OH« attacks both HC and CO and since the
products of both reactions are radical species capable of oxidizing
NO to N02 (RO2* in the former case and H02« in the latter), it is
necessary that the number of H02* radicals formed in the CO/OH-
reaction (always equal to one) be greater than the number of RO2 •
radicals formed in the HC/OH• reaction in the presence of CO. If
the product 66 were greater than one, CO would effectively inhibit
the rate of NO oxidization. This effect would be attributable to
the scavenging of OH« radicals by CO, thereby diminishing the supply
of OH' available for possible reaction with HC, a reaction capable
of generating more radicals than the single H02. produced in the
CO/OH, reaction. This point can also be verified by inspection of
equation B-2h. If 1, the negative terms (1-66) in the denominator
become positive, d(NO)/dt is then also positive, and MO is npt
converted to M02, Thus, we require that 66< 1. Finally, the value of
6 must be less than one, as all R02* are actually HO2« if 6 is equal
to one. Unfortunately, there is little more that can be said about
this coefficient.
IV. NUMERICAL INTEGRATION OF THE REACTION RATE EQUATIONS
In general, the rate equations for a system of chemical reactions
among n species can be written in the form
f^ (cj , ..., cn) i = 1, 2, ..., n
€^(0) = c.
0
In the case of the kinetic mechanism we have adopted, given by
equations B-2, n is equal to four when the five steady state equations
are substituted in the right hand sides. These rate equations take the
form:
B-24
-------
(CNO' CN02' CHC'
dcN0
= fHC (CNO' CN02' CHC' C03)
(CNO'
Since the four f^ are nonlinear, equations B- 3 must be integrated
numerically, usually on a digital computer.
There are a large number of techniques available for the numerical
solution of coupled, first-order, ordinary differential equations. Selection
of an appropriate technique depends to a large extent on the nature of the
system that is represented by the differential equations. Chemically
reacting systems, for example, often consist of individual reaction steps
having widely disparate time constants (or characteristic reaction times) .
This is particularly true when fast free radical reactions and much
slower initiation and termination reactions are occurring simultaneously.
Mathematically, when such a situation exists, the associated system of
ordinary differential equations is characterized by eigenvalues* which
vary greatly in magnitude. Such a system of equations, termed a "stiff"
system,** often presents substantial difficulties in the selection of a
numerical integration technique.
To illustrate the problems associated with the integration of stiff
differential equations, we consider the linear ordinary equations/
±1 - .nCl +a12c2 , Cl(0) - 2
-------
where
S21 a22
-500.5 499.5
499.5 -500.5
The solution of these equations is
Cl = 1.5e-fc + 0.5
C2 = l.Be-* - 0.5
where the eigenvalues of A are Xi =-1000 and
Both c, and c have
1
a rapidly decaying component, corresponding to Xlf which very quickly becomes
insignificant. After a brief initial phase of the solution in which the X,
component is not negligible, we would like to proceed, if we were
integrating the equations numerically, with a step length At which is
determined only by the X« solution component.
The conditions for stability of most numerical integration procedures
take the form
|X At) <_ a
i = 1,2, ..., n
where a is of the order 1 to 10. If, for example, we wished to use the
fourth order Runge-Kutta method (for which ct = 2.785) for the solution
of equations B-4, a necessary condition for ensuring stability is
|lOOOAt| <_ 2.785
The maximum allowable At, therefore, is 2.785 x 10~3, which corresponds to
nearly 2000 integration steps for a five-second time interval. Thus, although
the component of the solution associated with Xj = -1000 disappears early in
the integration, we are constrained to use an unacceptably small time step
to preserve stability, with the result that computation time is far too
large.
. A number of techniques for integrating stiff systems of ordinary
differential equations have recently been proposed, and these methods
are summarized by Lapidus and Seinfeld (1971). The objective of each is
to permit the use of a time step that is sufficiently large to ensure
economical integration times, while simultaneously maintaining stability.
One of the most recent, and most promising, of these methods has been proposed
by Gear (1969, 1971). The basic procedure is of the predictor-corrector type,
in which one proceeds from the value of c(t) at t = (n-l)h (where h = At) to
the value at t «= nh by computing a first approximation of c
(0)
c +
n-i
c1 +
i n-l
hf?PCn-p
where p = number of prior values of concentration used to compute c ,
B-26
-------
then iteratively correcting c by applying for formula
c> w 11 = c 4- hgn f(c (m\t ) + hB* y1 + ... + h6 * y1
n n~i « n n 1 n-i p-i n-p+1
for m = 0, 1, 2, ... until the computed sequence converges.
(The notation c corresponds to c(t ), with t = nh. cn^°' *s termed
the predicted value of c , cn^m+1^ the corrected value.) The g. and $^*,
which vary for different methods, also assume various values depending
on the order of the method used, the order being equal to the number of
terms included in the Taylor series approximation of the function c(t) at any point
t . It is thus necessary that values of these parameters be taken from tables.
Gear's method is based on this predictor-corrector format. The
coefficients 3. and BJ* are chosen so that values of h can be used which
i i i
are compatible with the non-stiff components of the solution, i.e., those
associated with the smaller eigenvalues. The computer program we employed
to integrate the reaction rate equations is a slightly modified version
of that reported by Gear (1971). Both step size h and order are selected
automatically, with the order chosen so as to maximize step size while
maintaining stability. The method and program have proven extremely
efficient for the solutions attempted thus far, a typical computing time
being about three seconds for a 3'j hour smog chamber simulation, using an
IBM 360/75 computer.
V. VALIDATION OF THE NEW SIMPLIFIED MECHANISM
Having considered the selection of reaction rate constants and
stoichiometric coefficients and the problems encountered in the numerical
integration of the coupled ordinary differential equations, we turn now
to validation of the kinetic mechanism. Validation was undertaken for four
hydrocarbon systems:
Reactant Data Source
1 propylene Gulf Research Corp. (Strickler (1970))
State of California Air Resources
Board (Wayne, et al. (1970))
2 isobutylene Aerospace Corporation and Stanford
Research Institute (Westberg, et al.
0-971))
3 n-butane Battelle (Wilson (L971))
4 propylene/n-butane
mixture Battelle (Wilson CL971))
B-27
-------
The selection of each hydrocarbon (or mixture of hydrocarbons) served
a particular purpose. In the case of propylene, data were available for
two initial HC:NOX ratios; ability to represent smog chamber data for
various HC:NOX ratios is an important attribute of a mechanism. The isobutylene
data were valuable, as the experiments in which they were obtained were carried
out both in the presence and absence of CO; the capability of the model to
represent the effects of CO could thus be studied. While both propylene and
isobutylene are olefins and are thus characteristic of highly reactive
hydrocarbons, n-butane, the third hydrocarbon studied, is a less reactive
species. It was thus of interest to determine if the mechanism could
approximate the concentration/time behavior of smog chamber experiments
for this paraffin. Finally, the study of mixed hydrocarbon systems is a
critical step in achieving adequate representation of the reaction
characteristics of the highly complex mixture of hydrocarbons found in
the atmosphere. We were fortunate to obtain data for the propylene/n-butane
system, a mixture of two hydrocarbons having widely differing reactivities.
In this section, we present validation results for each of the four
hydrocarbon systems and conclude with a discussion of the effect of
initial NOX concentrations on ozone formation.
t
Propylene
The major objective of this study was to evaluate the ability of the
mechanism to predict concentration/time behavior for different initial
ratios of hydrocarbon to nitrogen oxides. Initial conditions and selected
values of stoichiometric coefficients and rate constants for the
validation are given in Table B-6.* Predicted concentrations and experi-
mental data are shown in Figures B-6 and B-7.
The comparison between prediction and experiment for the two
validation runs are, in general, favorable. Experimentally measured
NO- peaks occur at 75 minutes and 85 minutes as compared with predicted
peaks of 68 minutes and 103 minutes respectively. While there are
significant differences between prediction and experiment for N02i
propylene, and ozone at various instances in time, similar trends are
apparent.
In the case of propylene, a was taken to be
!2,45 [NO]/[HC] i,
we would expect a to decrease with an increase in"the ratio, as peak ozone concen-
trations decrease over this range. The values of 2.45 and 9.8 have no signifi-
cance other than the fact that they give good validation for the experiments shown.
*In the presentation of validation results for each of the four hydrocarbon
systems, only the values of rate constants that differ from base values are
given in Table B-6. See Table B-4 for values of the remaining constants.
B_28 Figures B-6 and B-7 and Table B-6 follow.
-------
TABLE B-6. Parameters and Initial Keactant Concentrations Used in Validation of the
New, Simplified Mechanism
Hydrocarbon
For validation results,
see Figure
Initial Concentrations
[HC] ppm
jo
[NO ] ppm
o
[N02 ] ppm
[co] ppm
[KC]O /[NOX]O
Propylene
Stride ler
(1970)
B-6
3.29
1.612
0.088
0
1.95
Wayne, et al.
(1970)
B-7
1.0
1.0
0.1
0
0.91
Stoichionetric Coefficients
o
8
6
6
see eq. (B-5)
1.7
0.8
0.02
Isobutylene
Westberg, et al.
(1971)
B-8
3.0
1.5
0.04
0
1.95
Westberg, et al.
(1971)
B-9
3.0
1.5
0.04
100
1.95
see eq. (B-5)
1.9
0.2
0.22
n-Butane
Wilson
(1971)
B-10
3.05
0.49
0.106
0
5.1
Wilson
(1971)
" B-ll
3^05
0.50
0.106
100
5.1
5.0
0.5
1.2
0.61
Propylene/
n-Butane
Wilson
(1971)
B-12
0.56/3.4
0.48
0.098
0
6.8
3.0
0.67
1-2 .
0.53
T
M
vo
(continued on next page?
-------
TABLE B-6 (continued)
a
U)
o
Hydrocarbon
For validation results,
see Figure
Reaction Rate Constants*
k
6
k9
kio
k
11
k^a-
k<*bcf
k5
k!2
k!3
klU
i
Propylene
Strickler
(1970)
B-6
*
0.
0.
5.0
0.
1.0
4
•
1800
10
1800
Wayne, et al.
(1970)
B-7
37
037
x 101*
0075
x 103
006 ^,
1
0025
Isobutylene
Westberg, et al.
(1971)
B-8
3.
1.
Westberg, et al.
(1971)
B-9
0.355
0.0355
1 x 101*
0.017
0 x 101*
n-Butane
Wilson
(1971)
B-10
Wilson
(1971)
B-ll
0.40
0.04
2.0 x 103
0.001
6.0 x 103
Propylene/
n-Butane
Wilson
(1&71)
B-12
0.40
0.04
see eq. (B-6]
see eq. (B-6
see eq. (B-6
> Same for all validation runs
*Photolysis rate, as reported by experimenter.
**The unit of kj^ and kg are min'1, all other rate
constants, ppm~l min~l.
t Rate constant for reactions 4b and 4c combined.
-------
w
Experimental Data
Strickler (1970)
0.0
20
40
60 CO 100 120 140
REACTION Tli'.E (MINUTES)
FIGURE B-6. VALIDATION OF THE HE1.-.' "ECiiANISM - PROPYLENE
-------
I
U)
to
3.5
3.0
2.5
i. 2.0
CL
O
UJ
o
O
O
1.5
0.5
0.0
Experimental Data
Wayne, et'a'1. (1970)
Predicted Values
20
40
60
FIGURE B-7,
SO 100 120 140
REACTION TIME (MINUTES)
VALIDATION OF THE NEW MEGHANISIi - FRCPYLENE
180
200
-------
Isobutylene
The objectives of this portion of the study were to examine the ability of
the model to represent the effect of CO on reaction rates and to evaluate the
mechanism using a second olefin. See Table B-6 for initial conditions
and values of selected parameters, Figures B-8 and B-9 for validation
results and experimental data.
Comparison of prediction and experiment are quite good for both of
the isobutylene experiments, at zero and 100 ppm carbon monoxide. In
particular, the model predicts earlier peaking of NOX (by 32 minutes,
in accord with experiment), accelerated accumulation of 03, and more rapid
oxidation of the olefin in the presence of CO than in its absence. The
only significant deviation between prediction and experiment is that
which occurs for isobutylene after 100 minutes in the absence of CO.
Finally, note that a was treated in the same manner as in the propy?ene
validation.
;l
n-Butane
The purpose of this portion of the study was to investigate the ability of the
mechanism to describe the reaction dynamics of a species less reactive
than the two olefins studied thus far, with alterations being made in only the
hydrocarbon rate constants and the stoichiometric coefficients. The values
of these parameters are given in Table B-6, the validation results in
Figures B-10 and B-ll. It should be noted that the simulations in these
figures are for six hours, nearly double that for the previous olefin
simulations. Comparisons between prediction and experiment are
excellent.
A few comments may be helpful regarding the treatment of three
parameters in this validation. First, in contrast .to the variable a
used in the propylene and isobutylene studies, a constant value of this
parameter was employed for n-butane because of its low reactivity relative
to olefins. Secondly, non-zero values of both k10 and B were used even
though ozone does not react with n-butane to any appreciable degree. This
is necessary because olefins probably are some of the first stable products
to appear as a result of the reaction of O and OH* with n-butane, and
their formation must be accounted for. A possible reaction scheme for
the generation of olefins is
CH3CH.,CH2CH2« - > C2H5* + CH2 «=. CH2
CH3CH2CHCH3 + 02 - > (CH3)2C «=• CH2 + HO^
The formation of isobutylene in the butane oxidation may be evidenced by
the fact that several products observed in the butane photo-oxidation
for example, acetone and PAN (Altshuller (1969)) — are the same as those
found in isobutylene photo-oxidation.
Figures B-8 to B-ll follow
B-33
-------
OS
I
Experimental Data
Westberg, et al. (1971)
— Predicted Values
80 100 120 140 160 180 200
REACTION TIME (MINUTES)
FIGURE B-S. VALIDATION OF THE NEV HECKANISK - ISCDUTYLENE (NO CARBON MONOXIDE)
-------
U)
Experimental Data
Westberg, et al. (1971)
20
FIGURE G-9.
80 100 120 140 160 180 200
REACTION TIME (MINUTES)
VALIDATION OF THE NEW MECHANISM - ISOBUTYLENE (100 ppm CARBON MONOXIDE)
-------
U)
3.0
2.5
Q.
OL
UJ
O
^—
O
O
2.0
1.5
1.0
0.5
0.0
CtfH10
Experimental Data
Wilson (1971)
_ Predicted Values
40
80
120 ICO 200
REACTION TIME (MINUTES)
240
230
320
FIGURE B-10. VALIDATION OF THE NEW MECHANISM - N-BUTANE (NO CARBON MONOXIDE)
-------
U)
3.0
2.5
2.0
Q.
OL.
O 1.5
= 1.0
o
0.5
0.0
NO
C H
10
Experimental Data
Wilson (1971)
— Predicted Values
40
FIGURE B-TI,
80
280
320
120 1GO 200
REACTION TliiE (I1INUTES)
VALIDATION OF THE NEU MECHANISM - N-BUTANE (TOO pptn CARBON MONOXIDE)
-------
Propylene and n-Butane
We now consider the photo-oxidation of a mixture of propylene and
n-butane, carried out experimentally by Wilson (1971). The purpose of
this portion of the validation effort was to explore the possibility of
deriving rate constants and stoichiometric coefficients for the mixture
from values established previously for the pure hydrocarbons species.
As a first step, both types of parameters were calculated for the mixture
of propylene and n-butane as linear combinations of values established
for the pure components, weighted in proportions to the fraction of each
in the initial mixture. Thus,
kj_ <= f ^ + (1-f) ^
mixture P b (B-6)
where k. «= rate constant for reaction i for propylene
P
k. «= rate constant for reaction i for n-butane
b
f «= fraction of propylene in the initial reaction mixture
This method of deriving rate constants for hydrocarbon mixtures is similar
in nature to the "combined rate" approach used by Glasson and Tuesday (1971).
In initial validation runs, we found that the combined rate approach
predicted a greater oxidation rate than was observed experimentally, a
phenomenon also reported by Glasson and Tuesday. However, by altering
the value of kJ3 from the combined rate value of 96 to a new value of 45,
we obtained the results shown in Figure B-12. Aside from this one
alteration, all parameters were computed using equation B-6 and values
of pure hydrocarbons shown in Table B-6. (Note that a is again treated
as a constant). As can be seen in Figure B-12, adoption of the "combined
rate" method results in close agreement between prediction and experiment.
However, much more study of this approach is needed.
NOx Inhibition
Extensive experimental evidence indicates that, after a certain point,
an increase in the initial concentration of NOX will result in a decrease
in the maximum concentration of ozone observed (Glasson and Tuesday (1970)).
One of the key requirements that a simplified mechanism must satisfy
is that it demonstrate this inhibitory effect of NOX on peak ozone
concentration. In this closing section, we explore the capability of the
new mechanism to satisfy this requirement. Before presenting the results
of this study, however, we wish to comment on the type of data needed in
order to investigate this effect adequately.
Figure B-12 follows,
B-38
-------
7
w
vo
c.
o.
o
o
4.0
3.5
3.0
z- 2.5
o
Experirental Data
Wilson (1971)
Predicted Values
1.0
0.5
0.0
-C..H10 + C3H6
40
FIGURE B-12,
80
280
120 160 200
REACTION TIME (MINUTES)
VALIDATION OF THE NEW MECHANISM - PROPYLENE/N-BUTANE
320
-------
It is not unusual that the results of smog chamber experiments be
presented in the form of ozone concentration after a fixed time of
irradiation (say two hours) as a function of (or plotted against) initial
concentration of NO at a fixed initial hydrocarbon concentration.
However, information of this type is useless because the time to the
N02 peak and the time at which Oa appears are dependent on the individual
concentrations of NO and NOZ, not -only on the NOX concentration. Individual
NO and NO/ concentrations must also be reported. To demonstrate this
point, we carried out two simulations, in each of which [HC] :[NOX]O = 2:1.1.
In the first case, the NO was composed of 0.1 ppm N02 and 1.0 ppm NO,
in the second, 0.4 ppm NO2 and 0.7 ppm NO. In the first case NO^, peaked
at 94 minutes, in the second, at 57 minutes. Although the concentration
of ozone ultimately reached about the same maximum level in both cases,
after two hours the two concentrations were 0.424 and 0.634 ppm, respectively.
The peak ozone formation rate, defined and and reported by Glasson and Tuesday (1970)
as Loa] /2ti , where ti is the time required for the attainment of one-
half the peak ozone concentration, is also highly dependent on the
composition of NO and WO2 in the initial reaction mixture. These points are
illustrated in Table B-7, in which the simulated results of three runs
are reported. In each run the initial concentration of NOX was 1.1 ppm,
but the initial NO concentration was varied. It is clear from these
results that if smog chamber data are reported in terms of either [0,] .
[03J /2tj^ , both the initial NO and NO^, concentrations must be reported."
Having warned the reader about the xxse of data in which nitrogen
oxides are Iximpecl together, we proceed to use such data anyhow, largely because
.the desired type of data were unavailable. Altshuller, et al. (1967) have
reported results pertaining to oxidant concentration as a function of [NO
at fixed [c3H6]Q. Even though the individual [NO] and [N02] were not
reported, the irradiation time for each run was six hours, insuring that
the peak 03 level had been reached. Their results are shown by the solid
curve in Figure B-13. Note a sharp inhibition at initial NOX concentrations
greater than about 2.5 ppm for experiments involving initial propylena
concentrations of 2 ppm. We have simulated these runs using the new simplified
mechanism with [N02]0 =0.1 ppm. The results are shown by the dashed curve
in Figure, B-12. It is important to realize that NO inhibition is reflected
in the model by the choice of ct, so that Figure B-13 demonstrates only that
the choice of a is consistent with observed behavior.
VI., ADAPTATION OF THE NEW MECHANISM FOR INCORPORATION
INTO AN URBAN AIRSHED MODEL
We have to this point focused our attention on the development and
validation of a kinetic mechanism capable of describing atmospheric
photochemical reactions. As has been noted, validation refers to the
comparison between predictions of the mechanism and experimental results
Table B-7 and Figure E-13
follow
B-40
X °
-------
TABLE B-7. Effect of Initial NO and N02 Concentrations on
the Time of Appearance of 03
[c3H6]o » 2 ppm,
l.l ppm
[N02]Q
ppm
0.05
0.10
0.40
[NO]O
ppm
1.05
1.00
0.70
C^max
ppm
0.734
0.741
0.789
^
min
127
113
77
t°3^2hrS
ppm
0.311
0.424
0.634
tS^nax/2^
2.89 x 10~3
3.28 x 10"3
5.12 x 1C-3
B-41
-------
a
i
*»
to
s.
CL
UJ
o
o
§
1.2
1.0
0.8
0.6
0.4
0.2
——— Experimental Data
Predicted Values
Propylene =2.0 ppm
NO (assumed)= 0.1 ppm
FIGURE B-13,
INITIAL N0¥ CONCENTRATION (ppm)
rt
RELATIONSHIP BETWEEN INITIAL NOX CONCENTRATION
AMD PEAK OXIDANT CONCENTRATION
4.0
4.5
-------
based on smog chamber studies. However, smog chamber experiments are not
directly representative of atmospheric reaction conditions. Specifically,
such experiments are commonly carried out at constant intensity of radiation
(and fixed spectral distribution) and for hydrocarbon reactants consisting
of a single species, a simple mixture, or a complex mixture "representative"
of atmospheric contaminants. Before we can incorporate the new, simplified
mechanism into an urban airshed model, it is necessary to account for
temporal variations in intensity of incoming radiation and for variations
in the reaction rate of the generalized hydrocarbon species, HC, and its
associated free radical, RO£, due to overall changes in the composition
of the mixture of hydrocarbons in the atmosphere.
A. The Effects of Solar Radiation on Rates of Photolysis
The sun, the sky, and the surface of the earth are all sources
of the radiation that is received by the lower atmosphere. The
quantity (or intensity) of radiation received is dependent on the
magnitude and spectral .distribution of the radiant flux density outside
the atmosphere, the amount of scattering, absorption, and reflection
by the atmosphere, the albedo of the earth's surface, and the solar
zenith angle. The amount of radiation absorbed by a particular species
is primarily a function of the spectral distribution and the intensity
of incoming radiation, but is also a function of concentration and
specific physical and electronic properties of the species in question.
Of particular interest to us is the influence of incoming solar
radiation on the rates of decomposition (or photolysis) of NO2 and HNO2,
the two species considered in the mechanism upon which solar radiation
has a significant effect.
Accounting properly for the effects of these many variables on the
intensity and distribution of incoming solar radiation is an extremely
complex undertaking. We have incorporated some of the variables into
our treatment, and not others. In particular, the effect of zenith
angle on radiation intensity is included by relating the reaction rate
constants, ki (for NO/) and k^ (for HN02), to latitude, time of the
year, and time of day. We have not attempted to deal with the effects
of cloud cover, as days on which high concentrations of photochemical
pollutants occur are days of virtually cloudless skies over the
Los Angeles Basin. In addition, we have not accounted for the effect
on kj and k6 of variations in aerosol concentration (due to absorption
and scattering) either as a function of time or as a function of
elevation above the ground. We believe that considerably more must
be known about the scattering and diffusion of radiant energy due to
the presence of aerosols before these effects be properly incorporated
into our model, and that, in any case, our current level of knowledge
of atmospheric reactions is insufficient to merit the inclusion of
such detailed phenomena.*
* See Leighton (1961, Ch. 2) for a discussion of the nature of solar
radiation and its absorption in the polluted layer of the atmosphere.
B-43
-------
We have accounted for variations in k and k rather simply.
i b
First, consider kj. Leighton (1961) presents a plot, reproduced in
Figure B-14, of (k./k )* as a function of time (PST) for both summer
and winter solstice conditions in Los Angeles. This plot is applicable
to the latitude of Los Angeles and may be used as the basis for
representing variations in kj with time of year and time of day for
cloudless days and for atmospheres relatively free of particulates.
To derive this relationship:
(1) We interpolated between the summer and winter solstice
curves in Figure B-14 to obtain a curve representative of
our validation period, late September. This is the dashed
line in the figure.
(2) Using values of k3 from Johnston and Crosby (and given
on page 154 of Leighton) that are based on estimates of
temperature as a function of time for the validation days
of 29 and 30 September 1969, we calculated (k^/ij)) as a
function of time (see Table B-8).
(3) We normalized ki/<|> by dividing it by the largest hourly
value achieved during th.a dety, which occurs at 11 a.m. The
normalized variable f ranges from zero to one.
(4) Finally, our estimated relationship between k^ and time
for the late September validation period is derived by
multiplying f by 0.37 minutes"1, the value of kj that is
typical of conditions of maximum intensity.
The derived curve is shown in Figure B-15 and is given by the quadratic
equation,
f = 1.017 - .068T - 1.076T2 (B- 7)
where T = T " 12
o
t = time in hours (PST)
and 0 <_ t _<_ 24
(Note: This equation represents a fit to the curve in Figure B-15 , and
is applicable only to the two validation days stated, since a specific
temporal distribution of temperature is assumed. However, we will
generalize this relationship in future work to include ambient temperature
and time of year as independent variables.) \
The photolysis 'Of HNO2 has not been investigated as thoroughly as
has the photolysis of NO2. In the absence of more pertinent data, we
have assumed that the temporal variation of kg is the same as that of
kj, given by Equation B- 7. Thus, kg = (kg) f, for the validation days,
29 an<3 30 September, 1969, where (kg)max is tt^en to be 0.1(kj)max or .037 min""1.
(Johnston, et al. (1970)).
*<(> is the fraction of photolytically excited NO2 molecules which actually react.
Figures B-14 and B-15 and Table B-8 follow.
B-44
-------
,
(pphm)
X
un
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Interpolated for
late September
Summer
Solstice
0400 0600
0800
1000 . 1200
TIME PST
FIGURE B-14. DIURNAL VARIATION IN k1/<|.k3 FOR LOS ANGELES
1400
1600
1800
2000
-------
03
JL
1.2
1.0
0.8
n
u.
J -?
^ I*:
0.4
0.2
0.0
Computed in Table B-8
__ Computed using Equation B-7
0400 0600 0800 1000 1200 1400 1600 1800
TIME PST
FIGURE B-15. DIURNAL VARIATION IN f FOR LOS ANGELES FOR 29 and 30 SEPTEMBER 1969
2000
-------
TABLE B-8. Determination of f and k} as a Function of Time of Day
for 29 and 30 September 1969
Time
of day
(PST)
6 AM
7
8
9
10
11
Noon
1 PM
2
3
4
5
6
*
kl
•jjp- (pphm)
.06
.43
.76
1.02
1.16
1.20
1.18
1.15
1.05
.86
.59
.26
zero
Estimated**
Temperature
62
66
70
78
85
88
90
90
90
90
86
82
75
k (pphm-1hr~'1)
tt
1L 1 k (min"1)
15.3
15.7
16.2
17.4
18.3
18.7
19.0
19.0
.19.0
19.0
18.4
17.8
16.9
.918
6.751
12.312
17.748
21.228
22.440
22.420
21.850
19.950
16.340
10.856
4.628
zero
.041
.301
.549
.791
.946
1.000
.999
.974
.889
.728
.484
.206
zero
* Taken from the dashed curve in Figure B-14.
** Estimated average hourly temperatures for the days 29 and 30 September 1969.
t Interpolated values, taken from k3 vs. temperature given by Johnston and
Crosby (see Table 44, p. 154, Leighton (1961)).
Figure B-15 for a plot of the function.
B-47
.015
.111
.203
.293
.35
.37
.37
.36
.33
.27
.18
.076
zero
-------
B. Variations in Reactivity of Atmospheric Hydrocarbons.
We have demonstrated in Section V that the new, simplified
mechanism is capable of simulating the important features of hydrocarbon
photo-oxidation reactions observed in the laboratory. However, as has
been pointed out, it is not clear that the smog chamber and the
atmosphere are equivalent reaction systems. By incorporating the
validated mechanism into the overall airshed, we are in effect assuming
that phenomena characteristic of smog chamber experiments, such as
NOX inhibition and CO acceleration, are also characteristic of atmos-
pheric reactions. This assumption is a fundamental premise in the
formulation and development of the airshed model.
We will employ two lumped hydrocarbons, an unreactive species
HC and a reactive species HCr, in the overall airshed model. The
unreactive species will include only those hydrocarbons which do not
undergo appreciable reaction during the course,.of a day. Individual
hydrocarbons are classified as reactive or unreactive according to the
hydrocarbon reactivity scale of Bonamassa and Wong-Woo (1966), shown
in Table B-9. We have chosen to include in the category HCU only
those hydrocarbons, with the exception of propane, having zero reactivity
on this scale. Propane is treated as reactive, since the rate constant
for the propane/OH« reaction is much closer to that of butane than
that of ethane. Thus, the lumped hydrocarbon HCU will consist of ethane,
benzene, acetylene, and methylacetylene and will be treated as an
inert substance in the simulation. The species HCr represents the
reactive mixture, composed of all other hydrocarbons, and is identical
to the species HC in the new, simplified mechanism.
While the assignment of individual hydrocarbons to specific
reactivity groups is unambiguous, a consistent procedure has not yet
been developed for the estimation of rate constants and stoichiometric
coefficients for reactions occurring in the atmosphere. There are
a number of reasons for this. The density of pollutant emissions
vary over space and time. The more reactive species (those in reactivity
classes 5 through 9) may be consumed with sufficient rapidity that the
composition of the hydrocarbon mixture in the atmosphere, and thus its
reactivity, declines during the course of the day. (However, Eschenroeder
and Martinez (1970), in analyses of Los Angeles contaminant data collected
at two sites, were unable to detect variations in reactivity). Furthermore,
even though we have assumed that the behavior of a mixture of hydrocarbons
may be similar to the average behavior of the individual species (see
Section V, validation of the propylene/n-butane system), the generality
of this assumption has not been established. Finally, by virtue of our
inclusion of a generalized hydrocarbon in the mechanism, it is not
possible to distinguish in the simulation among the various reactive
species that constitute HCr.
*Methane is present in the atmosphere in large quantities relative to other
hydrocarbons. As it derives predominantly from natural sources, is inert,
and is a ubiquitous atmospheric constituent, it will not be included
in HCU or treated in the model.
Table B-9 follows.
B-48
-------
TABLE B-9. Scale of Relative Reactivities for Hydrocarbons*
Reactivity** Representative Hydrocarbon Species
0 methane, ethane, propane, acetylene,
methylacetylene, benzene
1 butanes and higher paraffins, cycloalkanes
3 toluene
4 ethylene
5 ethylbenzene, m- and p-xylene
6 o-xylene, tri- and tetramethylbenzenes,
propadiene
7 1-alkenes
8 2-alkenes
* Proposed by Bonamassa and Wong Woo (1966)
** Based on product yield and biological effects when
hydrocarbons are irradiated in the presence of oxides of nitrogen.
B-49
-------
As of this writing, we plan to pursue the following course.
We will select constant values of reaction rate constants and
stoichiometric coefficients (except for o) so as to obtain the
best overall prediction during the course of the day. Values of
certain parameters—notably kg, kig, kjj, a, (3, and 6—will likely
be modified from values established in smog chamber studies (and
reported in Table B-6) during initial validation, in order to account
for characteristics of the atmospheric system that are at variance
with those observed in the laboratory. Should this approach prove
inadequate, we will investigate the possibility of dividing HCr into
two or more categories to represent more precisely the reactivity of
the atmospheric hydrocarbon mixture. This approach may also be an
aid in detecting spatial and temporal variations in reactivity, as
Eschenroeder and Martinez considered only the average reactivity of
a single lumped species in their study.
B- 50
-------
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B-53
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