RM-1927
RELEASABLE MEMORANDUM
REACTION AND DIFFUSION OF NATURAL HYDROCARBONS IN THE
ATMOSPHERE OVER FORESTS
by
Alan Eschenroeder
September 1974
GENERAL
RESEARCH ^O CORPORATION
P.O. BOX 3587, SANTA BARBARA, CALIFORNIA 93105
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September 1974
REACTION AND DIFFUSION OF NATURAL HYDROCARBONS IN THE
ATMOSPHERE OVER FORESTS
By
Alan Eschenroeder
General Research Corporation
P.O. Box 3587
Santa Barbara, California 93105
Contract No. 68-03-2034
Program Element 1AA006
Project Officer
Dr. Lawrence Raniere
National Ecological Research Laboratory
National Environmental Research Center
Corvallis, Oregon 97330
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
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ABSTRACT
This study investigates the internal consistency of natural hydrocarbon
emission estimates, reaction kinetic measurements from the laboratory,
and ambient concentration measurements from the atmosphere. A one-
dimensional steady state reactive diffusion analysis for ct-pinene and for
isoprene is carried out as the primary test. A closed solution is obtained
in modified Bessel's functions, and numerical substitution demonstrates
internal consistency of the estimates and measurements.
This report was submitted in fulfillment of Contract No. 68-03-2034 by
General Research Corporation under the sponsorship of the U.S. Environ-
mental Protection Agency.
ii
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CONTENTS
Page
Abstract ii
Sections
I Introduction 1
II Kinetic Assumptions for the Calculation 3
III Solution of the Governing Equation 5
IV Summary and Recommendations 12
V References 14
iii
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SECTION I
INTRODUCTION
Volatile organic materials emitted by vegetation have been investigated
1O O / C
by Went, ' Rasmussen and Went, and Rasmussen. ' They conclude that
plant species release considerable quantities of monoterpene and hemiter-
pene substances. In his 1960 paper, Went estimated that both sagebrush
and coniferous forests would produce approximately five tons of volatile
organic matter per square kilometer per year. More recently, Rasmussen
pointed out that worldwide terpene emission estimates varied anywhere
from 0.1 to 10 times Went's original estimate. Despite these comparisons,
however, Rasmussen comes to no conclusion regarding the best estimate to
use. He uses Went's figures for his own approximate calculations in
Ref. 5.
Most of the speculation regarding the fate of these naturally emitted
reactive hydrocarbon substances suggests that reaction mechanisms like
fi—8
photochemical smog are responsible for the removal. Ripperton, et al.
have carried out specific studies on the dark reactions of ozone with
ct-pinene in order to investigate both the removal of ot-pinene and the pro-
9
duction of blue hazes in the atmosphere.
It is the purpose of this note to examine analytically the consistency of
the emissions estimates and the kinetics measurements that have been taken
in light of the observed concentrations of the naturally emitted hydro-
carbons above forested areas. These three aspects of the problem have
been discussed separately in the literature; however, little if anything
has been done regarding the synthesis of these results into a reactive
diffusion model. The scenario chosen here will be relatively stagnant
conditions over a large forested area in which a balance is set up be-
tween the emission of natural reactive hydrocarbons from the forest, a
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diffusion upward by atmospheric mixing, and the subsequent reaction of the
hydrocarbons emitted with ambient ozone. Subsequent sections of this note
discuss the assumptions of the analysis, the solution of the governing
equation, and the recommendations for further research in this area.
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SECTION II
KINETIC ASSUMPTIONS FOR THE CALCULATION
For the kinetics of the naturally emitted hydrocarbon, a single step reac-
tion with ozone is assumed.
0 + HC ->• products (1)
This reaction is assumed to occur in an infinite bath of ozone-polluted
air. This is equivalent to assuming that the ozone concentration in the
air is unperturbed by reaction. Ripperton, Jeffries, and White observed
that the stoichiometry of hydrocarbon disappearance relative to ozone
disappearance suggests considerable regeneration of ozone. In the ambient
atmosphere, however, daytime conditions establish a photostationary state
(approximately) between ozone, nitric oxide, and nitrogen dioxide. It
will be assumed, tentatively, that this photostationary state is the
dominant mechanism for maintaining a level of ambient ozone concentration.
This assumption will be tested after the calculations are complete. The
photostationary state occurs in the following reaction cycle:
hv + N02 + NO + 0 (2)
0 + 02 + M •* 03 + M (3)
+ NO •*• N02 + 02 (4)
Stationarity is established by the balance between the oxygen atom produc-
tion from reaction 2 (which quickly leads to ozone formation via reaction
3) being counterbalanced by the reverse effect of reaction 4 which con-
sumes ozone and produces NO-. In urban areas of strong nitric oxide
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sources, this photostationary state may not obtain because of heterogenei-
ties in the mixture or competing reactions. However, for the purpose of
analyzing the air over forests, it is safe to assume that complete mixing
takes place when there is no intrusion of anthropogenically polluted air
and that no competing reactions interfere.
The rate constant for reaction 1 depends on the identity of the hydrocar-
bon reacting with ozone. Isoprene and a-pinene have been identified as
A 5
significant forest-type emissions into the atmosphere. ' For the rate
of ozonolysis of isoprene, the constants for 1,3-butadiene are employed
by analogy since isoprene differs from this compound only in one methyl
radical. An average between the reported rates ' is employed giving
the rate constant for the ozone-isoprene reaction as 0.011 ppm min
The reaction step of ozone attacking a-pinene is a much more efficient
process. The rate constant obtained by Ripperton, Jeffries, and White
is employed for this reaction: k = 0.50 ppm min . The background
ozone concentration to be used in the analysis is 0.03 ppm which is repre-
sentative of the range of measurements taken on the Piedmont by Ripperton,
12
Worth, and Kornreich. This level of background to ozone is consistent
with other published measurements of background levels.
The surface flux of terpene and hemiterpene compounds suggested by Went
sets the gradient of concentration at the surface which is used as a
boundary condition for the governing equation. Went's value converts to
-3 -2 -1
8.64 x 10 mg*m -min . This completes the set of input data needed
to specify the kinetics and the boundary conditions for the hydrocarbon
balance equation.
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SECTION III
SOLUTION OF THE GOVERNING EQUATION
The steady state reactive diffusion of the naturally emitted hydrocarbon
species is described by a one-dimensional form of the species balance
relationship. For steady state conditions under the assumptions outlined
in the previous sentence, the governing equation is
where c, = mass concentration of hydrocarbon species
k = reaction rate constant for reaction 1
X_ = ozone concentration in parts per million
3
For consistency in the calculations, the units of c, are taken to be
n
yg-HC/g-mixture.
In Eq. 5, the vertical diffusion is described by a gradient flux term with
a variable vertical diffusivity. Its value is denoted by "a" at the
2 -1
ground and it increases linearly at the rate of 1 m -min for each meter
of height increment. This profile of diffusivity is derived from the
lower portion of the neutral stability distribution plotted in Ref. 13.
Thus
D = a + z (6)
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where D = vertical diffusivlty
z = height above ground
a = ground value of vertical diffusivity (which equals
2 -1
60 m *min in the profile chosen from Ref. 14)
-3 -2 -1
The ground flux value of 8.64 x 10 mg-m «min (see previous section)
* -4 -i _i
gives a gradient of -1.2 x 10 ug*g *m from the expression:
flux = -D(8c/3z).
Substituting in Eq. 5 using the value of D from Eq. 6 and the selected
value of background ozone, we obtain the balance equation for hydrocarbon
concentration in the following form:
i- (a +,)l- bch = 0 (7,
where b = kxo
This equation is subject to the boundary condition obtained from Went's
surface flux:
dc, <{>, Ail
IT = D(OJ" ° -1'2 x 10 P8*g '» Ut z = 0) (8)
The gradient is expressed in units of mass concentration per unit length.
For convenience, we scale mass concentrations up by 10^, giving units of
pg«g~l for concentration and yg«g~l-m-l for concentration gradient.
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The boundary condition at z = °° should be vanishing hydrocarbon
concentration:
lim c = 0 (9)
h
Using the following change of variables
u(£) = c, (z) and ? = 2/b(a + z) (10)
n
we obtain the following expression for the transformation of Eq. 7.
•2u" + £u' - £2U = 0 (11)
where primes denote differentiation with respect to £ . The boundary
conditions from Eqs. 8 and 9 become
= -2 x 10~3 C/k (at ? = 2^b) (12)
and
lim u = 0 (13)
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Equation 11 is the hyperbolic form of Bessel's equation which has the
solutions I (C) and K (C) . Either of these solutions is multiplied
by an arbitrary constant C- . Applying the boundary condition at °°
expressed in Eq. 13, we find that K (?) is the one we should choose.
Consequently, the solution to Eq. 11 subject to the boundary condition at
» is
(14)
where K is one of the modified Bessel functions. The singular beha-
vior of K at £-*•() does not concern us because the transformation
o
expressed in Eq. 10 moves the ground boundary out to £ = 2t/ab~ . The
first derivative of the modified Bessel function of zeroth order is simply
the negative of the first order modified Bessel function. Consequently,
(15)
and using the boundary condition at z = 0 , we obtain for b = 0.03k
and a = 60
= (5.4 x !0"3)k1/2K^ao) (16)
for the arbitrary constant C . Thus the solution of Eq. 11 satisfying
both boundary conditions is
u = (5.4 x lo"3)k~1/2K~1(5o)Ko(O (17)
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where
= 2.7k
1/2
Figure 1 shows the solutions obtained by substitution in Eq. 17 for the
rate constant and the modified Bessel functions. For a-pinene and for
isoprene, the concentration units have been converted to ppb (parts per
billion) by the use of conversion factors depending on the molecular
weights of the compounds. It is gratifying to note that the measured
3
values for volatiles in the air for 16 days near West Plains in the
Ozark Mountains of Missouri for August 1-16, 1963 vary between 7 and 14
ppb, indicating rather good agreement with the average value curve esti-
mated for isoprene based on our solution of Eq. 11. Also in Ref. 3, pro-
duction of volatiles for a dense ground cover of juniper is recorded as
an ambient air concentration in the 3-6 ppb range. These results are
straddled by the a-pinene and the isoprene solution shown in Fig. 1. Much
of the work that has been reported in the literature deals with concentra-
tion measurements inside enclosures placed over the vegetation or on
plants or foliage contained in leaf assimilation chambers under irradiation
60
50
40
3°
20
10
la -PINENE
ilSOPRENE
34567
HYDROCARBON CONCENTRATIONS, ppb
10
Figure 1. Comparison of concentration profiles for two assumptions for the
chemical properties of naturally emitted hydrocarbon (solutions
of eq. 11)
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conditions. These results, of course, are not comparable with the pre-
dictions for the free atmosphere. In a subsequent paper, Rasmussen use
a value of 10 ppb as a nominal estimate of ambient concentration.
The separation between the isoprene curve in Fig. 1 and the a-pinene curve
is due to two factors: (1) a difference in rate constants, with a-pinene
reacting almost five times as fast as iosprene with ozone, and (2) the
molecular weight difference of approximately a factor of two. The con-
centration is inversely proportional to the molecular weight in the con-
version from mass units to mole units. Also, the atmospheric diffusion
coefficient profile varies widely according to wind instability conditions
as well as local values of surface roughness. The concentrations in the
solution vary inversely with the value of vertical diffusivity. Consider-
ing all of these uncertainties and the use of nominal values for both dif-
fusion and kinetic parameters, the agreement between the computed estimates
and the measurements of ambient concentration is rather good.
It is important now to recheck the assumption of an ozone concentration
that is unaffected by the reaction of hydrocarbon with ozone. To do this,
we postulate the background concentrations of ozone, nitric oxide, and
nitrogen dioxide based on the averaged measurements on the Piedmont reported
12
by Ripperton, Worth, and Kornreich. These measurements show that the
ozone concentration is approximately 0.03 ppm, the nitric oxide concentra-
tion 0.002 ppm, and the nitrogen dioxide concentration, 0.006 ppm. At a
nitrogen dioxide photodissociation rate of 0.25 min (which is typical
of midmorning or afternoon in the summer), we obtain an oxygen atom pro-
duction rate of 1.5 x 10 ppm-min . Consequently, this gives an ozone
production rate of this same value because reaction 4 produces ozone at
essentially the same rate that reaction 3 produces 0-atoms. The reverse
-3 -1
reaction (5) has an ozone consumption rate of 1.51 x 10 ppm-min
based on the concentrations stated above and on the rate constant for
14
reaction 5 measured by Stedman and Niki. Therefore, photostationary
equilibrium apparently occurs under these conditions.
10
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Now in order to check the perturbation of the photostationary state by
the ozone reactions of hydrocarbon, one can use a multiplier of up to 50
ozone molecules produced per hydrocarbon molecule consumed. This ratio
is suggested by the stoichiometry of the dark reaction of ozone with
hydrocarbon observed by Ripperton, Jeffries, and White. Using 0.001 ppm
a-pinene with the background ozone concentration of 0.003 ppm and the
rate constant of 0.5 ppm min along with the factor of 50, we obtain
-4 -1
a reaction rate of 7.5 * 10 ppm-min which is half the reaction rate
-3 -1
in the ozone photostationary cycle (i.e., 1.5 * 10 ppm'min obtained
in the previous paragraph). A similar calculation for the isoprene case,
which seems more likely representative of the observations, gives a reac-
-4 -1
tion rate of 1.32 x 10 ppm«min , still giving it the benefit of a
branching factor equal to 50 as obtained with the a-pinene observations.
Therefore, if the terpenes emitted have a molecular weight close to that
of isoprene and a reaction rate constant with ozone close to that of
1,3-butadiene, negligible interference of the hydrocarbon reaction should
be expected with the atmospheric ozone cycle under typical background con-
ditions. On the other hand, the much more active species like a-pinene
begins to approach some interference with the ozone balance. To carry
out a thorough investigation of this question, it would be necessary to
carry out computer simulations of the coupled non-linear atmospheric
processes. For our approximation, it would appear that the provisional
assumption of non-interference of the hydrocarbon consumption with the
ozone balance is acceptable.
11
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SECTION IV
SUMMARY AND RECOMMENDATIONS
A steady state reactive diffusion analysis for naturally emitted organic
substances based on nominal values of atmospheric diffusion parameters
indicates internal consistency among the following three estimates and
observations:
1. Estimates of terpene production in the form of atmospheric
emissions over vegetated areas
2. Laboratory determinations of rate constants for reactions of
ozone with hydrocarbon compounds
3. Concentrations of natural hydrocarbons measured in the
ambient atmosphere near vegetated regions of the earth's
surface
These results are sufficiently encouraging to indicate further measure-
ments and analysis. Vertical profile measurements of the naturally
emitted hydrocarbons hold the key to a direct determination of the com-
bined effects of reaction and diffusion over forested areas. More
detailed calculations should be carried out incorporating the atmospheric
reaction mechanisms involving oxides of nitrogen. Such mechanisms have
been extensively studied in connection with the urban photochemical smog
problem.
By the application of computer modeling, it is useful to consider the
temporal variations of the parameters. For example, the atmospheric
diffusion coefficient varies throughout the day depending on solar radia-
tion intensity. The photodissociation rate constants vary with sunlight
intensity in the ultraviolet. Likewise, the emission rates of the ter-
pene vary with illumination level. Diurnal measurements of ambient con-
centrations of the terpene substances are already available. A byproduct
12
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of these more detailed analyses will be a deeper insight into the inter-
ferences of the naturally emitted hydrocarbon substances with the ozone
cycle in the lower troposphere.
Ripperton and Vukovich have raised the question of the competition of
gas phase processes with surface processes as a major sink for tropospheric
ozone near the earth's surface. They conclude that the NO -0_ reactions
X J
are a significant sink for ozone. They devote some discussion to the
various terms in the ozone balance equation; however, their conclusions
are largely deductive, based on combined records of oxides of nitrogen
and ozone as measured in the atmosphere. This type of work should be
extended by the measurements of species in addition to the oxides of nitro-
gen and ozone. A concerted effort of these field measurements combined
with the analytical support described above will shed more light on the
fate of naturally emitted hydrocarbon substances as well as the natural
ozone balance in the atmosphere.
13
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SECTION V
REFERENCES
1. Went, F.W., "Organic Matter in the Atmosphere and its Possible Rela-
tion to Petroleum Formation," Proc. N.A.S., Vol. 46, pp. 212-221
(1960).
2. Went, F.W., "Blue Hazes in the Atmosphere," Nature, Vol. 187, No.
4738, pp. 641-643 (August 20, 1960).
3. Rasmussen, R.A., and Went, F.W., "Volatile Organic Material of Plant
Origin in the Atmosphere," Proc. N.A.S., Vol. 53, pp. 215-220 (1965).
4. Rasmussen, R.A., "Isoprene: Identified as a Forest-Type Emission
to the Atmosphere," Environmental Science and Technology, Vol. 4,
No. 8, pp. 667-671 (8 August 1970).
5. Rasmussen, R.A., "What Do the Hydrocarbons from Trees Contribute to
Air Pollution," Journal of the Air Pollution Control Association,
Vol. 22, No. 7, pp. 537-543 (July 1972).
6. Ripperton, L.A., White, 0., Jeffries, Harvey E., "Gas-Phase Ozone-
Pinene Reactions," American Chemical Society 154th Meeting, Chicago,
Illinois, September 10-15, 1967, Division of Water, Air, and Waste
Chemistry, paper 23.
7. Ripperton, L.A., Jeffries, H.E., and White, 0., "Formation of Aero-
sols by Reaction of Ozone with Selected Hydrocarbons," Photochemical
Smog and Ozone Reactions. R.F. Gould, ed. Advances in Chemistry
Series 113, American Chemical Society (Washington, 1972), pp. 219-231.
8. Lillian, D., "Formation and Destruction of Ozone in a Simulated
Natural System (Nitrogen Dioxide + a-pinene + hv)" in Photochemical
Smog and Ozone Reactions, R.F. Gould, ed. Advances in Chemistry
Series 113, American Chemical Society (Washington, 1972), pp. 211-218.
9. Went, F.W., "Blue Hazes in the Atmosphere," Nature, Vol. 187, No.
4738, pp. 641-643 (August 20, 1960).
10. Hanst, P.L., Stephens, E.R., Scott, W.E., and Doerr, R.C., "Atmos-
pheric Ozone-Olefin Reactions," paper at the 136th Meeting of the
American Chemical Society, Atlantic City, N.J. (1959).
11. Vrbaski, T., and Cvetanovic, R.J., Canadian Journal of Chemistry
38:1053 (1960).
14
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12. Ripperton, L.A., Worth, J.J.B., and Kornreich, L., "Nitrogen Dioxide
and Nitric Oxide in Non-Urban Air," Journal of the Air Pollution
Control Association. Vol. 20, No. 9, pp. 589-592 (September 1970).
13. Eschenroeder, A., Martinez, J.R., and Nordsieck, R.A., "Evaluation
of a Diffusion Model for Photochemical Smog Simulation," General
Research Corporation CR-1-273, p. 63 (October 1972).
14. Stedman, D. and Niki, H., "Kinetics and Mechanism for the Photolysis
of Nitrogen Dioxide in Air," J. Phys. Chem.. Vol. 17, pp. 2604-2609
(1973).
15. Ripperton, L., and Vukovich, Fred M., "Gas Phase Destruction of
Tropospheric Ozone," Journal of Geophysical Research, Vol. 76, No.
30, pp. 7328-7333 (October 20, 1971).
15
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