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121
collection, and provide heuristic guidelines for impact evaluation. Toward
this end, the kinetic mechanism provides a basis for conclusions, strengthens
arguments, and tests hypotheses. Although the mechanism has been validated
for a restricted number of hydrocarbons, by using it as a "laboratory" we
have obtained results that hopefully have broad significance.
The purpose of this study was not to provide absolute quantification
of hydrocarbon reactivity. Such quantification, if it is possible, must be
obtained from well-controlled laboratory experiments. Extensive tabulations
of laboratory results can be found in Heuss and Glasson (1968), Glasson and
Tuesday (1970), and an MSA Research Corporation report (1972).
c. Procedure
By inputting desired initial conditions and integrating the appropriate
kinetic equations, we obtained concentration-versus-time curves for a given
hydrocarbon-NOx-air system. It was then necessary to select the relevant
points, such as peak concentrations or times of peaks, from the computer
output to determine values for the various reactivity measures. More de-
tails on what these points were and how they were used are given in subse-
quent sections.
2. Measure Study
a. Criteria for the Evaluation of Measures
While criteria for a good measure are basically intuitive, it is worth
mentioning a few of them here. Ideally, a measure of a given hydrocarbon's
reactivity would be independent of initial reactant concentrations. Unfor-
tunately, because of the complexity of smog systems, such independence is
not realizable. However, some measures will show less variability than
others. If the inevitable variations show a consistent trend, it may be
possible to specify their functional dependence and, hence, to develop a
very useful predictive ability. Within this report, a measure that shows a
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122
small predictable trend is termed "self-consistent." Aside from being self-
consistent, satisfactory measures must also be consistent with each other
and not widely disparate with accepted reactivity values.
Three pragmatic requirements we have imposed are that the measure be
(1) directly related to the production of harmful smog components,
(2) clearly defined, and (3) easily and accurately measurable. Without
these properties, the applicability of the measure would be severely
limited. Other criteria will be developed as needed.
b. Normalization
The results from a study of the measures defined in Table 15 are tabu-
lated in Table 16, and the initial conditions for the experiments reported
are shown in Table 17. The entries in Table 16 were normalized by the reac-
tivity of propylene; i.e., they are in units of propylene equivalents. P.ro-
pylene simulations were carried out at initial NO, N02> and hydrocarbon con-
centrations corresponding to each row, and the times, concentrations, and
rates corresponding to each column were determined. These were then used to
normalize values obtained for other olefins. Since the rate constants are in-
versely proportional to time, for the time scales, an inverse ratio was used,
in which the relative reactivity of a given hydrocarbon (HC) is given by the
ratio Tpropylene^HC' wfiere T is t^ie appropriate time scale. For other measures,
a direct ratio was used.
c. The Elimination Process
The data in Table 16 do not provide a sufficient basis for choosing
the best measure of reactivity without additional considerations. But an
inspection of these data does permit a rapid elimination of three of the
criteria. The % HCt=ioo obviously fails the self-consistency test because
it produces a wide range of values at various initial concentrations.
While showing self-consistency, N02(max) and 03(max) are quite inconsistent
with other measures. In fact, they are so close to unity that, in light of
model inaccuracy, the differences in reactivity between the various olefins
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123
Table 15
DEFINITIONS OF REACTIVITY MEASURES*
Reactivity Measure
HCt=100
03 (max)
Scaling
N02 rate
conversion
Definition
conversion (°r
100 x HC(t=loO min)/HCo
Peak concentration of N02
Peak 03 concentration or asymptotic
concentration
Reciprocal of the HC concentration
required to obtain a Tj^fmax) equal
to that of 1 ppm C^\s
N02(max)/TN02(max)
Time for the N02 concentration to
reach the value [N0210 + 1/2[NO]0
Time to the N02 peak
Time when [HC] = 0.75[HC]0
* Reactivities relative to C3Hs are given by the reciprocal ratio of
time scales and direct ratio of all other measures.
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124
Table 16
RESULTS OF THE MEASURE STUDY: REACTIVITIES* RELATIVE TO PROPYLENE
Experiment*
1
2
3
4
5
6
7
8
9
10
11
12
G&TS
A&B**
ASCtt
% HC10Q
0.12
0.10
0.16
0.27
0.29
0.18
0.06
0.17
N02(max)
--
0.91
0.93
0.95
0.96
0.92
0.91
0.84
Q
3(max) Scaling
< 0.25
0.25
0.89
0.90
0.90
0.90
0.27
1.16
1.12
1.10
1.09
N02 rate
0.23
0.23
0.28
0.28
0.28
0.27
0.23
(H NO conversion)
0.25
0.22
0.20
0.21
0.25
0.29
0.24
0.49
N02(max)
0.25
0.25
0.29
0.29
0.30
0.30
0.27
1.45
3.27
1.83
3.98
0.36
0.23,0.31
\ HC
* 0.2
0.23
0.23
0.24
0.26
0.24
0.24
0.26
1.68
3.84
2.11
5.23
0.48
The reactivity measures are defined in Table 15.
** Altshuller and Bufalini (1970) values for ethylene.
t The Initial concentrations are given in Table 16.
tt Altshuller and Cohen (1953) values for ethylene.
5 Glasson and Tuesday (1971) values for ethylene.
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125
Table 17
INITIAL CONCENTRATIONS FOR EXPERIMENTS LISTED
IN TABLES 16 AND 18
Experiment
1
2+
3
4
5
6
7
8
9+
10+
11 +
12+
13+
14
15
16+
17
[NO]Q
0.4
0.4
0.4
0.4
0.4
0.2
0.48
0.5
0.4
0.4
0.4
0.4
0.4
0.3
0.48
0.4
0.4
[NOJ
* 0
0.1
0.1
0.1
0.1
0.1
0.05
0.02
0.1
0.1
0.1
0.1
0.1
0.1
0.075
0.02
0.1
0.1
[HC]Q
0.5
1.0
2.0
3.0
4.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.6
Initial HC Composition
HC5*
HC5
HC5
HC5
HC5
HC5
HC5
HC5
HC1
HC,
£.
HC3
HC4
0.2 each HC] , HC2, HC3> HC4, and HCg
0.2 each HC] , HC2, HC3, HC4> and HCg
0.25 each HC2, HC4, HCg, and HCg
0.25 each HC2, HC4> HCg, and HCg
0.15 each HC0, HC., HCC, and HCC
£. <\ 0 D
* In this study H^ s 1-butene; HC2 = cis-2-butene; HC3 = 2-me-l-butene;
HC4 s 2-me-2-butene; HCs = ethylene; HC6 = propylene.
t These initial conditions are defined as "standard." Experiments 2 and
9 through 13 provided data for the mixture study.
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126
are insignificant when they are based on either W^fmax) or 03(max). The
investigators who successfully used 03(max) probably defined it either as
a peak or, when no peak occurred, as the concentration of 63 at the end of
a time-limited experiment; they are usually not clear on this point. The
entries omitted from Table 16 correspond to experiments in which 03 had
reached neither a peak nor an asymptotic value by the end of 400 minutes.
In these omitted cases, the final value indicated a reactivity significantly
less than one. Thus, the definition of 03(max) varies, depending on whether
a peak is reached. The values of reactivity obtained will thus depend on the
length of the experiment; they are neither clearly defined nor consistent.
We surmise that 03(max) and N02(max) are insufficient measures.
As shown in Section 5, scaling can be demonstrated to be equivalent
to TUJ. Their theoretical equivalence is borne out by experimental evidence,
as shown in Table 16.
Relative reactivity based on the N02 rate is defined as NOaCmax) times
TJJ, (it is multiplicative because of the inverse normalization of time scales)
Since the N02(max) values are all close to unity, the difference between Tm
and the N0£ rate should be small. The added complexity in rate determina-
tion hardly seems worthwhile. Because it is a "combined spatio-temporal"
measure, the error in determination of the N02 rate is the sum of errors of
its component parts. Clearly, if one of these components is a good measure,
accuracy as well as simplicity can be gained by using it alone. A last, and
possibly undesirable, property of the N02 rate is that it is a difference
approximation to the rate of N02 formation. Therefore, it does not repre-
sent the actual rate at any point on the NOg curve; it is instead an average
value.
conversion ">s a widely used measure, usually appearing in the
guise of "NO photooxidation rate," defined as NOo/2T^ (c.f. , Glasson and
Tuesday, 1970). Since, in the present study, relative reactivities were
computed at a given NOg, this column in Table 16 could just as easily have
been labeled "R(NO photooxidation)"- Interpreted as such, \ also has the
possible shortcoming of being a difference approximation, although it is a
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127
very good one when the induction period is negligibly short. Ti^NO conversion*
as defined in Table 15, is not the half-time for N02 formation, rather it
falls somewhere between the half-time and peak time of N02- Its location
relative to the time of product formation is therefore ill defined. Thus,
the most objectionable quality of \ is its lack of direct correlation with
03 production or other harmful smog constituents. In the application of
reactivity criteria to pollution control, this is indeed a serious shortcoming.
TN02(max) and Tj,HC conversion' the on^ measures left, are the measures
we have selected for use. Because of their importance to the present study,
they are discussed in detail in Section 3.
The results of other investigations are also included in Table 17 for
the purpose of indicating the need to eventually combine the work contained
in this report with laboratory investigations. Meaningful comparisons of
our values with those of the other investigators cannot be made now because
experimental conditions generally differ considerably.
3. The Measures Selected
a. Practicality
The measures found to be most conducive to the quantification of smog
effects are the time of the N02 peak, TNo2(max) (hereafter denoted as Tm) ,
and the time required for one-quarter of the initial hydrocarbon to be oxi-
dized (Tjj). In the terminology introduced in Section A, these are temporal
measures. By being one dimensional, they avoid the increased measurement
error inherent in the combined concentration and temporal measures. Both
are simply and clearly defined. Although the N02 peak may not be sharply
resolved in practice, interpolation methods along with extremum theory pro-
vide for its accurate determination. A parabolic curve fit can be used for
this purpose.
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128
As shown by the results of Experiments 1 through 5 in Table 16, the
relative reactivity of ethylene based on Tm (hereafter abbreviated RR-j-J
varies by about 15 percent as the initial hydrocarbon concentration (HCg)
is changed by a factor of 4. There is a visible trend toward increasing
RRj with increasing HCg. Although any variability is undesirable, the fact
that it is small indicates that the RRTm, measured as a single HCQ, may be
applicable throughout a wide range of HCo's (at fixed N00 and N02Q). !t may
even be possible to capitalize on the consistency of the trend to estimate
the accuracy of a constant value in this range.
At fixed HCQ, increasing N0o/N020 by a factor of 6 caused an increase
in RRj of almost 20 percent (see Experiments 2 and 7). In Section 5, this
behavior is shown to be attributable to induction period effects. Because
of its role in determining RRjm, further study of the induction period would
be useful.
As shown by the data in Table 17, RRT% exhibits the same trend with
increasing HCg as that observed for RRTm. But variability with N0o/N020
is almost absent. An increase in this ratio by a factor of 6 caused vir-
tually no change in RRTj,. The slightly erratic behavior shown in Experi-
ment 8 is most probably caused by inaccuracy in this experiment. (Unfortu-
nately, the need to incorporate an interpolation scheme did not become ap-
parent until the late stages of this study.) \ is therefore partially in-
consistent with Tm. The apparent absence of induction period effects on
RR-|> is interesting and deserves further investigation. It is probably due
to the smaller initial slope of the hydrocarbon curve.
b. Usefulness
Aside from considerations of simplicity and consistency, a useful
measure must ultimately be related to objectionable pollution effects.
Dimitriades et al. (1970) have discussed this issue and concluded that,
while no one index is fully satisfactory, "...there is evidence that the
over-all [sic] level of activity in the photosimulated hydrocarbon/NOx
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129
system is reflected in the pattern of N02 formation." It is well known
that the N0£ peak is correlated with the formation of 03 and PAN, two haz-
ardous components of smog. In any "time-limited" system, such as an urban
airshed with a characteristic residence time, the amount of 03 present due
to chemical reaction is directly related to Tm. Aldehydes also contribute
to the deleterious effects of smog. Because aldehyde appearance is comple-
mentary to hydrocarbon disappearance, 1% is an indication of their importance
in a time-limited system. T^ is also useful for evaluating the magnitude
of synergistic effects in mixture reactions. Altshuller and Bufalini (1971)
define a synergistic effect as "...one in which the reactivity or the amount
of product produced by a given compound is affected by the presence of a
second." Since, in general, the oxidation of several hydrocarbons in a par-
ticular mixture will lead to the same or similar products, synergism is not
easily determined from product measures. A much simpler means, particu-
larly when using a numerical model, is to monitor the rate of hydrocarbon
disappearance. For a given hydrocarbon, the change in TV from its value
in an individual hydrocarbon-NOx reaction system to that in a multihydrocarbon-
NOX reaction system provides an indication of interactive effects.
c. Measurability
Because laboratory techniques must ultimately be used either to mea-
sure reactivity or to obtain empirical constants needed for its prediction,
a satisfactory measure must have the additional property that accurate and
reliable instrumentation be available for its determination. N0£ and hydro-
carbon concentrations are routinely monitored in smog chamber experiments
with reasonable accuracy. Hydrocarbon concentration can be measured with
as little as 1 percent error by gas chromatographic methods. In contrast,
N02 is obtained from the difference between NOX (after conversion to NO) and
NO concentrations. These are measured by chemiluminesence with about 95
percent accuracy. When N02 concentrations are low, the percentage error in
the difference of these values may be large. When [NOel is at its peak and,
consequently, [NO] is low, the error in the difference will be at a minimum.
The accuracy in [N02] at the peak should therefore be close to 95 percent.
-------
130
Of course, only the temporal location (Tm), not the peak value itself is
used. The cycling time for NO measurement is only a minute or two; so a
high density of points and, hence, sharp resolution of Tm can be obtained.
With reasonably accurate values of concentration and the time of measurement
of each point well known, an accurate determination of Tm should be possible.
4. Mixture Study
a. Mixtures Used
Reactivities were computed for five different olefin-NOx mixtures at.
the initial concentrations indicated in Table 16. Experimental and pre-
dicted results are shown in Table 18. The reactivities are all relative to
that of propylene at standard initial conditions (N0o=0.4, N020=0.1, HCo=1.0).
The olefin mixture used in Experiments 13 and 14 is composed of the five most
reactive olefins studied and is a typical "highly reactive" mixture. A
second mixture, used in Experiments 15 through 17, contains the two most
reactive and the two least reactive olefins and is characteristic of a wide
reactivity range mixture.
b. Results
The first row of entries for each experiment in Table 18 is labeled
"mixture." In Columns 3 and 5 (Tm and Tj, measured) of this row, relative
reactivities of the olefin mixtures are measured. Tm, as before, is the
time of the NOg peak. Tj. is now the time required for the total olefin con-
centration to drop by 25 percent. Below the \ entry are the time for each
component olefin to reach 75 percent of its initial concentration. As
before, all results are normalized by propylene experiments at the given
initial concentrations.
c. Predictions
There are also three prediction columns in Table 18. These are pre-
dictions of mixture reactivity computed by the "linear summation" method,
defined by:
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131
Table 18
RESULTS OF THE MIXTURE STUDY: MIXTURE REACTIVITIES RELATIVE TO PROPYLENE
Tm
Experiment Hydrocarbons Simulated LSM
13 Mixture 2.42 2.31
HC,*
HC2
HC3
HC4
HC6
14 Mixture 2.64
HC,
HC2
HC3
.HC4
HC6
15 Mixture 1.54
HC2
HC4
HC5
HCfi
16 Mixture 2.16 2.13
HC2
HC4.
HC5
HC6
17 Mixture 1.26 1.28
HC2
HC4
HC5
"6
LSM
Uneorrected
Simulated Prediction
2.86 2.77
2.30
3.42
2.71
4.27
1.37
2.71 -
2.15
3.39
2.53
4.44
1.21
1.94
2.33
2.83
0.44
1.20
2.58 2.56
3.58
4.31
0.47
2.58
1.98 1.54
2.52
3.15
0.44
1.20
\
Simulated
Reactivity of
Hydrocarbons
In Mixture
1.68
3.84
2.11
5.23
1.0
1.68
3.84
2.11
5.23
1.0
3.84
5.23
0.23
1.0
3.84
5.23
0.23
1.0
3.84
5.23
0.23
1.0
Prediction
Corrected for
Synerqlsm
2.81
2.76
1.70
2.73
1.83
In this study. HC] i 1-butene; HC2 i cit-2-butene; HC3 i 2-oe-l-butene; HC4 a 2-me-2-butene; HC5 i ethylene;
HC( i propylene.
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132
RLS ' E C1R1
where
RLS = mixture reactivity by linear summation,
n = number of organic mixture components,
cj = initial concentration of the ith hydrocarbon,
R-j = reactivity of the ith hydrocarbon.
The linear summation technique has been discussed by Glasson and Tuesday
(1971) and Dimitriades et al. (1970).
The values of R-j, based on either Tm or T^, were obtained from the
experiments in Table 16 as follows: R-j comes from Experiment 9, R2 from
Experiment 10, R$ from Experiment 11, R4 from Experiment 12, R$ from Experi-
ment 2, HC5 is the reference olefin (propylene) with a reactivity defined
to be 1. (Note, from the definitions of HCs 1 through 6 in the footnote to
Table 17, that R-j increases with increased substitution at the double bond.
Column 4 of Table 18 gives the mixture reactivity based on Tm as com-
puted by the linear summation method. The values shown agree very well
with observations. Experiments 14 and 15 were done under nonstandard ini-
tial NO and N02 values, and, therefore, no predictions could be made.
Although the initial olefin concentration in Experiment 17 was not the
standard value of 1 ppm, prediction could be made by "scaling." This pro-
cedure consists simply of multiplying RLS by the ratio of the initial
hydrocarbon concentration to its standard value (in this case the RRLS of
Experiment 16 times 0.6). Hence, the slower rate at lower hydrocarbon con-
centrations is compensated for multiplicatively. Justification for the
application of the scaling technique to RRTm is given in Section 5. Its
application to RRj^ is not really justifiable because the approximately
exponential hydrocarbon decay rate indicates a nonlinear dependence of
on HCg. This explains the low value listed.
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133
d. Synergism
Columns 6 and 7 of Table 18 show both the linearly predicted reactivity
of the mixtures and the standard reactivities of their components. The lat-
ter were copied from Table 16. Comparison of the standard reactivities in
Column 7 with the observed values in Column 5 indicates the presence of
synergistic effects. It is evident that in all cases the two most reactive
olefins, HC2 and HC4, experienced a decrease in relative reactivity, whereas
the less reactive olefins experienced an increase. This behavior can be ex-
plained qualitatively in the following manner. The competition for available
oxidant between higher and lower reactivity olefins depressed the reaction
rate of the former. At the same time, the high rate of oxidant production
by HC2 and HC4 accelerated the consumption of less reactive olefins.
Linear summation was also applied to the synergistically modified values
of T^J (Tjj measured). The resulting mixture reactivities are listed in the
last column of Table 18. Although these predictions are close to observed
values, we cannot state that they are always an improvement over the unmodi-
fied predictions.
Another inconsistency between Tm and Tjj is contained in Table 18.
Whereas decreasing NOXQ from Experiment 13 to the value used in Experiment
14 increased RRr , it decreased RRT. . Many explanations of this behavior
'HI. "Z
can be offered, including the changed 03 production and the radical-
scavenging ability of N02. It is the complex interaction of all these ef-
fects that leads to the discrepant behavior.
5. Derivation of Some Properties of Tm
a. Derivation
In this section, the analytical solution for the dependency of Tm on
Initial hydrocarbon and NO concentrations is obtained through a consideration
of simplistic photochemical smog kinetics. Kinetic equations and empiricism
based on the observed shape of smog profiles are used toward this end.
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134
O'Brien (1974) has demonstrated that, except in the late stages of the
photolytic hydrocarbon-NOx-air reaction, the concentrations of NO, 03, and
N02 are related by the approximation
k,
[N02] *f- [N0][03] , (IV-D
where k-| and k3 are rate constants for the reactions
i
N02 + hv !*- NO + 0 (1)
k-
NO + 03 i- N02 + 02 . (3)
Existence of the photostationary state, expressed by Eq. (IV-1), in smog
profiles computed using the Hecht-Seinfeld-Dodge kinetic model has been
demonstrated by Liu (1974).
In addition to Reaction (3), the conversion of NO to NOg is accomplished
through the reaction
R0£ + NO ^RO- + N02 , (42)
where R is usually an alkyl group or hydrogen atom. Hence, in the period
before the N02 peak, the rate of NO production and consumption is governed
by Reactions (1), (3), and (42). Thus,
j - k3[NO][03] - k42[R02][NO]
Equation (IV-1) can be used to simplify Eq. (IV-2):
-------
135
This expression represents the perturbation to photos tationarity introduced
by free radical oxidation.
In a completely generalized mechanism, ROg includes all free radical
oxidation products of hydrocarbons. It is formed in the following reaction
where Ox represents a general oxidant (primarily OH- in the time prior to
the N02 peak), HC-j a hydrocarbon, and ct^ an appropriate stoichiometric co-
efficient (see Hecht and Seinfeld, 1972).
Using Reactions (IV-4), (42), and the steady-state assumption for R02
leads to the following equation:
O x]
x
*
Substituting for RO^ in Eq. (IV-3) and using Reaction (IV-4) gives
d[HC.]
The rate terms in Eq. (IV-5) can be used to relate Tm to HCg and NOg
through the use of empirical observation. Figure 59 is an illustration of
a typical, through idealized smog profile at initial NO and N02 concentra-
tions for which there is a very short induction period. It is apparent
that the curves labeled NO and hydrocarbon are approximately linear during
the early stages of the reaction. Good approximations in this linear
period are
* Liu (1974) has demonstrated that this assumption becomes valid within a
few seconds of reaction initiation. The neglect of termination reactions
1n the steady-state expression is valid early in the reaction.
-------
136
Hydrocarbon
50
100
Minutes
150
FIGURE 59. TYPICAL SMOG PROFILE
-------
137
m
and
[HC.] . [HC.] (1 - b.t) , (iv-7)
where b^ is a constant related to the slope;
The introduction of HCQ. as a multiplicative factor can be justified
by a direct integration of the hydrocarbon rate equation derived from
Reaction (IV-4):
[HC.] = [HC.] exp |"-/k0 [Ox] dtj * [HC.] /I - / kQ [Oxl dt) ; t < t,
U 1» X. -J U > X« /
(IV-8)
Comparison of Eq. (IV-8) with Eq. (IV-7) shows that bj can be related to
the average oxidant concentration,
but such an interpretation is not essential to this derivation. There is
no reason to believe that ^ will be independent of N00, N02o, or HCi
Furthermore, the evidence indicates that bl is proportional to light inten-
sity (Niki et al., 1972; Glasson and Tuesday, 1970). Other factors not
considered may also influence ty. However, the dependence on N0xn and HC0
1s assumed to be negligible.
Substituting Eqs. (iv-6) and (IV-7) in Eq. (iv-5) and rearranging
gives
-------
138
[N0]fl
Tm a b' [HC.l ; bi ~= aibi
1 0
b. Verification and Application
At a fixed initial NO concentration, Eq. (IV-10) states that the time to
the N02 peak should be inversely proportional to the initial hydrocarbon con-
centration. In Figure 60, the observed values of Tm are plotted as a func-
tion of HC-JQ for HCi = propylene at one NOg value and HCi = ethylene at two
values of NOg. All curves can be fit by the form a/HC0. From Eq. (IV-10),
a = N00/bj. For propylene, the curve fit has been drawn in, whereas for the
two ethylene curves it has only been indicated. When the two values of a
for ethylene are divided by the corresponding values of NOg, the results are:
a/NOo = 500 and a/NOn. = 496. Therefore, b\ for ethylene is 2 x 10'3.* The
data presented in Figure 60 thus confirm Eq. (IV-10).
Equation (IV-10) can be used to predict reactivity relative to propylene
RRT - Tm prop _ bi HCJ
- "
Once RR-rm has been determined at one HCiQ, it can be predicted at other
HCig's by applying Eq. (IV-11). Recall that this is exactly the procedure
(called "scaling") used to predict the mixture reactivity in Experiment 17.
The equivalence of scaling and Tm as reactivity measures can be shown
as follows: Equation (IV-11), with Tm HC. = Tm propylene and [prop]0 = 1 ppm,
states that
K)"1
bi
B1 (IV-12)
prop
* As an order of magnitude check using Eq. (IV-9) and taking Ox as OH-,
0.75 x 104 ppm-1 min-1, OH- = 1.5 x 10-7 ppm; thus
1 x 10-3 min'1 (^ is then 2).
-------
139
250 -
Experimental Conditions
0.1
N00 = 0.5, N02_ = 0.1
N00 = 0.4, N02()
Curve
Fit
HCg (ppm)
FIGURE 60. Tm AS A FUNCTION OF INITIAL HYDROCARBON CONCENTRATION
-------
140
This, by definition (Table 15), is the scaling reactivity of HCj. Because
RRTn) is normalized, HC1(J = [prop]0. Thus, from Eq. (IV-11),
The equivalence of RRTm and scaling follows directly.
The derivation of Eq. (IV-10) can be extended to multihydrocarbon
smog systems by summing over the index 1 from Eq. (IV-4) onward. Equation
(IV-10) then becomes (upon inversion)
HCb
where n is the number of hydrocarbons. Assuming the values of b] are those
obtained in individual hydrocarbon simulations, the linear summation method
results directly. In light of this required assumption, it is surprising
that synergistically modified predictions (Table 18) are not better than
unmodified values. However, the modified values were based on RRT
'%
whereas the above derivation is based on Tm and is not rigorously applicable
to Tjj.
c. The Induction Period
It is worth reiterating that Eqs. (IV-6) and (IV-7) are valid only if
induction period effects are negligible. For this condition to hold, the
initial HC/NOX and N02/N0 ratios must be relatively high (lower bounds have
not been established but 2 and 0.1, respectively, seem reasonable). In
addition, the individual values of HC0, N00, and N02g may themselves be
important.
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141
A striking, and possibly disconcerting, feature of Eq. (IV-10) is the
absence of explicit dependence on N02Q. Dimitriades (1972) found that, for
irradiated auto exhaust with an N02o/N00 ratio of about 0.1, the rate of NO
photooxidation was independent of N02Q as long as N02Q was above 0.03 ppm.
The major effect of low values of N02o is to cause a nonnegligible induction
period. It seems reasonable to speculate that an induction period of length
TI will simply cause a shift in the start of the "linear period" by Tj.
Tm can then be replaced by
where T° is given by Eq. (IV-10). RR-^ is defined as follows:
T1 T° + T
, s = - , }
°
mi Ira1 T 'Ij
I prop
m
where Tj/TJjj « 1 has been assumed. If hydrocarbon i is less reactive
than propylene (RRQ < 1) and has an induction period about equal to that
m
or propylene, the correction to RRjO will be positive.* Conversely, for
more reactive hydrocarbons (RR-j-jj) > 1), the correction will be negative.
The induction period, therefore, always has the effect of shifting the
relative reactivity toward unity. The increase in RRTm with decreasing
initial [N02] from a value of 0.25 in Experiment 2 (Table 17) to 0.30 in
Experiment 7 can be cited as evidence of this tendency.
Since atmospheric concentrations include the range of NOg, N02n, and
HC0 for which there is an induction period, methods for predicting TI are
needed. Apparently, an inverse dependence on N02Q is indicated.
* Under these conditions, RRT. % RRTm + (Ti/TJj.) (1 - RRTo)
m Q \ v m
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142
C. RELATION OF THE ABOVE CONSIDERATIONS TO OZONE PRODUCTION
The preceding discussion of the issue of relative hydrocarbon reac-
tivity has shown that indices directly related to ozone production are in-
adequate for reactivity assessment. The production of ozone entered only
indirectly through its relation to Tm. In the following discussion, this
relationship is explored in greater detail. As a prefacing note, the dis-
tinction between individual hydrocarbon reactivity (at a fixed NOX concen-
tration) and hydrocarbon-NOx system reactivity (with both hydrocarbon and NOX
being variable) should be emphasized. From a control strategist's point of
view, this distinction is between emissions composition and total emissions.
For the former, which was the topic of the previous section, net ozone pro-
duction is not a sufficient characterization, whereas for the latter, ozone
production (as shown below) is a distinct characteristic.
1. Ozone Isopleths
Isopleths relating the concentration of 03 and the time of the NO?
peak, Tm, to initial hydrocarbon and NO concentrations at various reaction
times are shown in Figures 61 through 66.* These figures are based on the
same computer output used to generate the isopleths contained in the final
report for the first contract year (Hecht et a!., 1973). The initial con-
ditions were as follows:
> [HC]0 = 75 percent n-C^io and 25 percent C3H6
> [N0}0 = as stated on each figure
[N02]Q = 0.1 [NOX]
= 0.35 mlrr1.
As might be expected from the derivation in the preceding section of this
report, the lines of constant Tm (Figure 66) are nearly straight, and their
slope increases as Tm decreases.
* The dashed portions of these figures have been obtained by extrapolation.
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143
2.0
i.
a.
o
o
10
4J
O
1.6
1.2
0.8
0.4 -
FIGURE 61. LINES OF CONSTANT 03 (IN PPM) AFTER 1 HOUR OF SIMULATION
-------
144
0.5 0.4
20
o.
o.
o
o
10
0.8
FIGURE 6.2. LINES OF CONSTANT 03 (IN PPM) AFTER 2 HOURS OF SIMULATION
-------
145
i.
o.
(O
4->
O
0.4 -
0 L
FIGURE 63. LINES OF CONSTANT 03 (IN PPM) AFTER 5 HOURS OF SIMULATION
-------
146
a.
a.
o
o
as
4->
o
.0
0.9
FIGURE 64. LINES OF CONSTANT 03 (IN PPM) AFTER 8 HOURS OF SIMULATION
-------
147
O
O
re
to
P
FIGURE 65. LINES OF CONSTANT 03 (IN PPM) AFTER 9 HOURS OF SIMULATION
-------
148
o
o
x.
to
4->
O
240
360
540
N00 (ppm)
FIGURE 66. TIME OF THE N02 PEAK (IN MINUTES)
-------
149
In Figures 61 through 65, there are two characteristic regions. A
line drawn along the ridge line of the surface represented by the set of
isopleths in each of these figures would divide these regions. In the re-
gion to the right of the ridge line, the isopleths are fairly straight, and
the super-imposition of Figure 66 would indicate that, especially at earlier
times, they are nearly parallel to the lines of constant Tm. The line
dividing the regions is also nearly a line of constant Tm. The region to
the left is characterized by almost vertical isopleths, though in Figures
64 and 65 they curve back on themselves noticeably.
The features of these figures are not at all surprising; they simply.
reflect the characteristics of 03-versus-time profiles observed in smog
chambers (see, for example, the UCR profiles contained in this report).
The empty space in the lower right-hand corner of Figures 61 through 65
(03 < 0.1 ppm) reflects the finite time that elapses before 03 begins to
build up. At Tm, 03 begins to accumulate almost linearly with timehence,
the closely spaced isopleths that parallel lines of Tm = constant (Figure 66),
Eventually, [03] approaches an asymptotic level. Correspondingly, the
spacing of isopleths widens, and they turn to the vertical. The reactions
N02 + 03 * N03 + 02 , (5)
N03 + N02 * N205 , (7)
N205 + H20 -> 2HN03 , (9)
and
03 + HC * Products
along with photolysis and destruction on surfaces, cause 03 depletion late
in the reaction, resulting in the backward curvature of the isopleths.
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150
2. Chemical Dynamics
These observations indicate that the characteristics of Figures 61
through 65 are prescribed by the chemical dynamics of smog formation. In
the atmosphere, where chemistry interacts with the mechanical processes of
dispersion and transport, a consideration of dynamics is essential to con-
trol strategy planning. For example, consider the upper region in the 8-
hour isopleths (Figure 64). Figure 62 indicates that, at a fixed level of
NO, a reduction in [HC]0 would have very little effect on 03 production.
The results presented previously show that maximum 03 levels (at fixed NOX
concentrations) are also almost independent of hydrocarbon reactivity (for
a set of olefins). However, an examination of Figure 66 (and the data in
Section B above) shows that a reduction in [HC]0 (or HC reactivity) has a
significant effect on increasing Tm. Thus, a reduction in [HC]0 could slow
down 03 production, even though this decrease may have little effect on the
expected net yield. In the atmosphere, where pollutants can be rapidly dis-
persed, the predicted maximum yield, based on simulations of smog chamber
experiments, may never be realized. The peak 03 level achieved is therefore
closely related to the expected Tm.
From the preceding results, one can conclude that both HC and NO must
be taken into account when attempting to select optimum 03 abatement strate-
gies. However, because of the complex interaction of mechanical and chemi-
cal processes in the atmosphere, it is difficult to extrapolate such results
as those presented in this report directly to atmospheric emissions. To
evaluate the effect of control strategies directly, one would need to imbed
the kinetic mechanism in an airshed model that takes atmospheric conditions
into consideration. In isolation, the kinetic mechanism can only provide
"rules of thumb."
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151
V CONCLUDING REMARKS
In closing, some mention should be made of the implications of our
findings on air pollution modeling. First, we briefly summarize these
findings.
Kinetic mechanisms for the chemical transformations occurring in irra-
diated propylene, butane, toluene-NOx, and propylene-NOK-S02 systems were
postulated and used to simulate smog chamber data. Varying degrees of cor-
respondence between predicted and observed profiles were obtained. In general,
the propylene-NO and propylene-NQX-S02 mechanisms were the most successful.
For the most part, their predictions of propylene, 03, NO, N02, and S02 were
reasonably good. Although the accuracy was not very good, the propylene
mechanisms were still able to follow the behavior of each species. The
butane mechanism predicted too rapid NO oxidation and the toluene mechanism
predicted insufficient oxidation of toluene. Butane oxidation products con-
taining structures of two or more carbon atoms were apparently produced in
greater quantity than the mechanism indicated; the low carbon recoveries in
the UCR butane runs support this conclusion. However, more kinetic and smog
chamber data are needed before the toluene mechanism can be assessed and
revised.
We demonstrated that uncertainty in the magnitude of surface reactions
and light source spectrum decay, as well as other chamber effects, could ac-
count for a great deal of the discrepancy between data and theory, although
erroneous rate constants and reaction mechanisms contributed also. Instrument
error, a topic barely touched upon here, is another ever-present source of
ambiguity.
Unlike purely gas-phase thermal reactions, surface and photolytic reac-
tions are chamber-dependent; furthermore, for a given chamber they may vary
from experiment to experiment. Their proper treatment would require a con-
siderable and continuous effort toward chamber characterization. Thus, smog
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152
chamber experiments, which are meant to clarify the kinetics by eliminating
some of the complexities present in the atmosphere, have introduced their
own problems, although they are not as complex as those in the atmosphere.
We are not denying the value of smog chamber experiments; instead, we are
emphasizing the intricacy of this analysis.
Upon being confronted with the important role chamber effects play in
the laboratory, one cannot help wondering whether atmospheric counterparts
exist, and if so, how to incorporate them into an airshed model. Heterogen-
eous (pseudo-gas-phase) rate constants are functions of surface-to-volume
ratio, as well as the surface's catalytic efficiency, both of which are not
known for the urban environment. Solar irradiation depends on the state of
the upper atmosphere, as well as on meteorological conditions, and has a di-
urnal and seasonal periodic variation. Hopefully, parametric representation
of the variability of the solar spectrum will make the characterization of
the spectrum feasible. Clearly, the spectrum itself affects numerous reac-
tions, and the variation of a single rate constant (such as k]) cannot ade-
quately account for the effects of spectrum variability.
The approach to modeling heterogeneous chemistry used in the present work
was to represent local surface reactions as pseudo-gas-phase reactions. The
pattern of N02 formation was shown to reflect the value assigned to rate con-
stants for heterogeneous (HNOX) chemistry. Capitalizing on this relation-
ship, we determined heterogeneous rate constants by "tuning" to the N02
curve. When applying the mechanism to the atmosphere, one can take a simi-
lar approach. In the absence of requisite kinetic data, tuning to atmos-
pheric N02 data may be possible. Assuming gas phase kinetics are accurately
represented, this approach would provide a practical means of evaluating the
heterogeneous reactions.
The mechanism's applied utility was demonstrated, in Chapter IV, in a
study of hydrocarbon reactivity and ozone formation.* Thus, the kinetic
mechanism can be a useful tool to investigators of photochemical air pollution,
either in the explicit form or in the streamlined, generalized format.
* There the issue of chamber effects was avoided by presenting results on a
relative.basis.
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153
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-------
TECHNICAL REPORT DATA
(I lease read Inunctions on the reverse before completing)
EPA-650/4-75-026
4. TITLE AND SUBTITLE
Mathematical Modeling of Simulated
Photochemical Smog
3. RECIPIENT'S ACCESSION-NO.
5. REPORT DATE
June 1975
6. PERFORMING ORGANIZATION CODE
Paul A. Durbin, Thomas A. Hecht, and Gary Z. Whitten
8. PERFORMING ORGANIZATION REPORT NO
EF75-62
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Systems Applications, Inc.
950 Northgate Drive
San Rafael, CA 94903
10. PROGRAM ELEMENT NO
1A1008
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
U. S. EPA
Office of Research And Development
National Environmental Research Center
Trianglg Park, M r. 977H
68-02-0580
13. TYPE OF REPORT AND PERIOD COVERED
Final (June'74 -June '75)
14. SPONSORING AGENCY CODE "*
15.
JOTES
16. ABSTRACT
The continued development and testing of a kinetic mechanism for photochemical
smog formation is described. Detailed mechanisms containing the individual
chemical reactions occurring in irradiated propylene, n-butlne. toluene-
Nh^h^dHpropylfn!:NY5?2 ?ystems were Postulated and used to simulate smog
chamber data A theofetieal evaluation was made of the contribution of such
chamber effects as light source spectrum decay and surface reactions ?n tho
reactivity of the chamber mixture. The applicatl of kineti? s mu at on to
reactlvi^ and ozone production in smog systems is
17.
_. T
3.
DESCRIPTORS
KEY WORDS AND DOCUMENT ANALYSIS
Photochemical Modeling
Chemical Kinetics
Atmospheric Chemistry
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I. SECURITY CLASS I This page)
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21. NO.OF PAGES
160
22. PRICE
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