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Particle Formation and Growth in PowerPlant Plumes
Volume 1: Field Observations and TheoreticalStudies of the Evolution of Particles in the Plumes
From Coal-Fired Electric Power Plants
EA-3105, Volume 1Research Project 330-1
Final Report, May 1983
Prepared by
UNIVERSITY OF WASHINGTONCloud and Aerosol Research GroupAtmospheric Sciences Department
Seattle, Washington 98195
Principal InvestigatorsP. V. Hobbs
M. W. EItgrothD. A. HeggL. F. Radke
Prepared for
Electric Power Research Institute3412 Hillview Avenue
Palo Alto, California 94304
EPRI Project ManagerC. Hakkarinen
Environmental Physics and Chemistry ProgramEnergy Analysis and Environment Division
ORDERING INFORMATION
Requests for copies of this report should be directed to Research Reports Center(RRC), Box 50490, Palo Alto, CA 94303, (415) 965-4081. There is no charge for reportsrequested by EPRI member utilities and affiliates, U.S. utility associations, U.S. governmentagencies (federal, state, and local), media, and foreign organizations with which EPRI has aninformation exchange agreement. On request, RRC will send a catalog of EPRI reports.
Copyright (C) 1983 Electric Power Research Institute, Inc. All rights reserved.
NOTICEThis report was prepared by the organizaiion(s) named below as an account of work sponsored Oy the ElectricPower Research Institute, Inc. (EPRI). Neither EPRI, members of EPRI. the organizalion(s) named below, nor anyperson acting on behalf of any of them: (a) makes any warranty, express or implied, with respect to the use ofany information, apparatus, method, or process disclosed in this report or thai such use may not infringe private-ly owned rights; or (b) assumes any liabilities with respect to the use of, or for damages resulting from the useof, any information, apparatus, method, or process disclosed this report.
Prepared byUniversity of WashingtonSeattle, Washington
ABSTRACT
A parallel field study and theoretical investigation of particle size distributions
in the plumes of coal-fired power plants is described. The field studies, which
were carried out on a plant in Washington State and one in New Mexico, show that
the particles in the plumes fell into three distinct size modes characterized by
geometric mean volume diameters between 0.001-0.2 pm, 0.11-0.55 pm and 0.55-4.4 pm.
All three modes played important roles in the coagulation of particles in the
plumes. The concentrations of particles sometimes decreased with travel time in
the center of a plume while increasing at the edges of the plume. The concentra-
tions of particles of a certain size were often less in certain regions of a plume
than in the ambient air. Measured gas-to-particle (g-to-p) conversion rates were
on the order of 0.1% of SOn/hr for the Washington plant and 1% of SO^/hr for the
New Mexico plant.
A 3-D numerical model which allows for the effects on the particle spectra of
advection, diffusion, coagulation, gravitational settling, g-to-p conversion and
interactions with the ambient air, is shown to be capable of reproducing many of
the principal features of the observed particle spectra in the plumes. The model
predicts maximum g-to-p conversion rates at the edges of the plumes where the
predicted rates are comparable to the field measurements. Elsewhere in the plume
the predicted g-to-p conversion rates are about a factor of ten below the field
measurements.
111
EPRI PERSPECTIVE
PROJECT DESCRIPTION
Sulfur oxides and nitrogen oxides have been implicated as major contributors to
visibility impairment and acidic precipitation in the United States. Formation of
small particles that scatter light, producing "haze" and act as condensation nuclei
for raindrops has been reported to occur in the plumes of fossil-fueled power plants
as well as other locations. The studies described in this two-volume report in-
volved theoretical and field investigations of the rates of formation and size
distributions of particles in six coal-fired power plants in the midwestern and
western United States.
PROJECT OBJECTIVES
The objectives of the project, which spanned some five years, were to measure par-
ticle size distributions in coal-fired power plant plumes at various locations and
under a variety of meteorological conditions. In addition, a three-dimensional
numerical model was developed and refined for simulating particle formation and
growth in plumes.
PROJECT RESULTS
The measured rates of conversion of sulfur dioxide to particulate sulfate ranged
from 0 to 5.7% per hour. However, most observations fell within a narrower range of
0.1 to 1.0% per hour. Reaction rates were all found to depend on travel time from
the stack and ultraviolet light intensity. The PHOENIX model predictions of maximum
gas-to-particle conversion rates that occur near the edges of the plume are in
agreement with the measurements. Elsewhere in the plume, the model predictions were
about a factor of 10 lower than the measurements. The PHOENIX model has been
applied in recent years by other sponsors to the specific question of haze genera-
tion in western plumes.
Charles Hakkarinen, Project ManagerEnergy Analysis and Environment Division
ACKNOWLEDGMENTS
This work was supported by the Energy Analysis and Environmental Division of the
Electric Power Research Institute under Contract RP330. We wish to express our
thanks to Dr. C. Hakkarinen of EPRI for his help and interest, and to the Pacific
Power and Light Company and the Arizona Public Service Company for their cooperation
in this study.
v-n
CONTENTS
Section
BACKGROUND AND SCOPE OF STUDY
Background
Scope of Study
2 POWER PLANTS STUDIED AND AIRBORNE INSTRUMENTATION
Power Plants
Airborne Instrumentation
3 DATA ANALYSIS TECHNIQUES
Particle Spectra
Gas-to-Particle Conversion Rates
4 RESULTS OF FIELD MEASUREMENTS
Particle Spectra
Gas-to-Particle Conversion
5 A NUMERICAL MODEL FOR PLUMES
Introduction
Background
Description of the PHOENIX Model
Trace Gas Section of Model
Particle Section of Model
6 COMPARISON OF MODEL RESULTS WITH MEASUREMENTS
Introduction
Measurement-Model Comparisons
Centralia; March 30, 1976
Central ia; April 28, 1976
Centralia; October 19, 1976
Centralia; September 22, 1977
Four Corners; June 23, 1977
Four Corners; June 24, 1977
Four Corners; June 25, 1977
Discussion
ix
Section
7 SUMMARY AND CONCLUSIONS
Field Measurements
The PHOENIX Plume Model
8 REFERENCES
ILLUSTRATIONS
4-1 Fitted curves to particle number concentration distributions
4-2 Excess concentrations (dN/d log D) above ambient values of particlesin the plume from the Centralia Power Plant on October 19, 1978
4-3 Excess concentrations (dN/d log D) above ambient values of particlesin the plume of the Central ia Power Plant on March 16, 1976
4-4 Excess concentrations (dN/d log D) above ambient values of particlesin the plume of the Four Corners Power Plant on June 23, 1977
4-5 Excess concentrations (dN/d log D) above ambient values of particlesin the plume of the Centralia Power Plant on September 22, 1977
4-6 Excess concentrations (dN/d log D) above ambient values of particlesin the plume of the Centralia Power Plant on March 30, 1976
4-7 Excess concentrations (dN/d log D) above ambient values of particlesin the plume of the Central ia Power Plant on April 28, 1976
4-8 Excess concentrations (dN/d log D) above ambient values of particlesin the plume of the Four Corners Power Plant on June 24, 1977
4-9 Excess concentrations (dN/d log D) above ambient values of particlesin the plume of the Four Corners power plant on June 25, 1977
4-10 Excess concentrations (dN/d log D) above ambient values of particlesin the plume of the Four Corners Power Plant on June 29, 1977
5-1 Schematic of the processes considered in the PHOENIX plume model
5-2 Schematic of particle interactions by coagulation consideredin the PHOENIX plume model
6-1 Excess (i .e. above ambient) concentrations (dN/d log D) of particlesin the plume of the Centralia power plant on March 30, 1976,as predicted by the PHOENIX plume model
6-2 Homogeneous gas-to-particle conversion rates (in units of 0.1% ofSO^/hr) in the plume of the Centralia power plant on March 30, 1976,as predicted by the PHOENIX plume model
6-3 Comparisons of measurements with predicted values from thePHOENIX plume model of the Aitken nucleus concentrations andight-scattering coefficients through plumes along horizontal
traverses perpendicular to the direction of the wind.
6-4 Excess (i .e. above ambient) concentrations (dN/d log D;of particles in the plume of the Central ia power planton April 28, 1976, as predicted by the PHOENIX plume model
XI
6-5 Homogeneous gas-to-particle conversion rates (in units of0.1% of SOo/hr) in the plume of the Centralia power planton April 28, 1976, as predicted by the PHOENIX plume model
6-6 Excess (i .e. above ambient) concentrations (dN/d log U)of particles in the plume of the Central ia power plant onOctober 19, 1976, as predicted by the PHOENIX plume model
6-7 Homogeneous gas-to-particle conversion rates (in units of0.1% of SO^/hr) in the plume of the Central ia power planton October 19, 1976, as predicted by the PHOENIX plume model
6-8 Excess (i .e. above ambient) concentrations (dN/d log D)of particles in the plume of the Central ia power plant onSeptember 22, 1977, as predicted by the PHOENIX plume model
6-9 Homogeneous gas-to-particle conversion rates (in units of0.1% of SO^/hr) in the plume of the Central ia power planton September 22, 1977, as predicted by the PHOENIX plume model
6-10 Excess (i .e. above ambient) concentrations (dN/d log D)of particles in the plume of the Four Corners power plant onJune 23, 1977, as predicted by the PHOENIX plume model
6-11 Homogeneous gas-to-particle conversion rates (in units of0.1% of SO^/hr) in the plume of the Four Corners power planton June 23, 1976, as predicted by the PHOENIX plume model
6-12 Excess (i .e. above ambient) concentrations (dN/d log D)of particles in the plume of the Four Corners Power planton June 24, 1977, as predicted by the PHOENIX plume model
6-13 Homogeneous gas-to-particle conversion rates (in units of0.1% of S0;?/hr) in the plume of the Four Corners power planton June 24, 1977, as predicted by the PHOENIX plume model
6-14 Excess (i .e. above ambient) concentrations (dN/d log D) ofuncharged particles in the plume of the Four Corners powerplant on June 25, 1977, as predicted by the PHOENIX plume model
6-15 Excess (i .e. above ambient) concentrations (dN/d log D) ofcharged particles in the plume of the Four Corners power planton June 25, 1977, as predicted by the PHOENIX plume model
6-16 Homogeneous gas-to-particle conversion rates (in units of0.1% of SO^/hr) in the plume of the Four Corners power planton June 25, 1977, as predicted by the PHOENIX plume model
6-17 Total particle concentrations (in units of 10 cm" acrossthe Centralia plume at a distance of 2 km downwind predictedthe PHOENIX model for April 28, 1976.
xn
TABLES
Table
2-1 Electrical outputs of the power plants during theperiods of measurements discussed in this report
2-2 Specifications on research instruments on theUniversity of Washington’s B-23 aircraft
4-1 Modal parameters for particle distributions in the plumesfrom the Centralia power plant and the ambient air
4-2 Modal parameters for particle distributions in the plumesfrom the Four Corners power plant and in the ambient air
4-3 Ranges of values for the geometric mean diameter D and its
geometric standard deviation a p. for the three particle modes
4-4 Rates of change of the fraction (fy .) of the total volume ofparticles in mode i
4-5 Summary of gas-to-particle (g-to-p) conversion ratesdeduced from the field measurements
5-1 Trace gas reactions included in the PHOENIX plume model
5-2 Ranges of concentrations of trace gases in the ambient airused in the PHOENIX plume model runs discussed in this report
6-1 Particle input data for case studies discussed in this report
xm
SUMMARY
RESULTS OF THIS STUDY
Gas-to-particle (g-to-p) conversion rates have been measured in the plumes of six
coal-fired power plants situated in the West and Midwest of the United States.
The conversion rate was estimated from measurements of the changes in the total
volume of particles in the plume, the production rate of Aitken nuclei and three
different particulate filter analysis techniques (flash vaporization. X-ray fluor-
escence and ion-exchange chromatography) Comparison of sulfate concentrations
derived from X-ray fluorescence and ion-exchange chromatography showed fair agree-
ment-indicating that most of the particulate sulfur is sulfate. Comparison of
g-to-p conversion rates estimated from the changes in total particle volume with
those derived from particulate filter data showed, in general that the major
portion of the g-to-p conversion product was sulfate. However, in some instances,
the g-to-p conversion rate based on total particle volume was higher than the rate
based on particulate filter analysis; this suggests that conversion products other
than sulfate may sometimes be formed in power plant plumes.
One possible conversion product, other than sulfate, which has been postulated to
be produced in power plant plumes, is nitrate. To evaluate this hypothesis some
nitrate measurements were made in the plumes. The data suggest that nitrate forma-
tion, in general was of ittle importance during the flights in which measurements
were obtained. An estimate of the NO -to-m’trate conversion rate was made for one
of the cases studied at the Big Brown (Texas) power plant and was found to be
’"^0.4%/hr for distances of 4.8 to 43.2 km. The S0,,-to-su1fate conversion rates,
measured simultaneously, ranged from 0.7 to 2.8%/hr and increased with travel time
from the stack.
The rates at which new particles were nucleated in the plumes were evaluated and
the ratio of this nucleation rate to the rate of formation of new particle volume2 5
was calculated. The ratio was found to range from 2.7 x 10 to 3.9 x 10 particles
pm with a mean value of 7.4 x 10 +/- .2 x 10 particles pm This ratio is
S-1
indicative of the fraction of g-to-p conversion product which forms new particles
--the remainder of the conversion product condensing directly onto already existing
particles. The large variation in this ratio, some of which is attributable to
differing plant locale, suggests regional differences in the g-to-p conversion
process. Results from the PHOENIX plume model suggest that it should be possible
to predict this ratio on the basis of a modified version of the theory of McMurry
(27) The PHOENIX model outputs suggest the importance of the above ratio in
determining the light-scattering coefficient and visibility degradation.
Further analysis was made of the relationship between the rates of formation of
new particle surface area and new particle volume. The data were found to be in
fair agreement with the theoretical relationship of McMurry and Friedlander (64)
in which the particle surface area varies as the rate of formation of new particle
volume raised to the 3/5 power. This suggests that the size distribution of the
particles in the plume becomes self-preserving.
The SOp-to-particulate sulfate conversion rates were found to range from 0 to
5.7%/hr--the higher rates generally occurring in the Southwest. This range is in
agreement with previous studies conducted both in the Eastern United States and
at the Four Corners power plant in New Mexico. The SO? g-to-p conversion rate
was also found to depend on travel time from the stack and UV ight intensity.
Both the physics and the chemistry of the g-to-p conversion process(es) suggest
that the dominant (though not necessarily the sole) conversion mechanism in the
plumes studied is the oxidation of SO? by OH radicals. A significant correlation
(r 0.9) was found between the conversion rates and a parameter indicative of
this reaction.
The results of this study have suggested several areas in which further efforts
might yield valuable information.
While the data collected in this study suggest that the SOp-to-sulfate conversion
process is predominantly SO? oxidation by OH radicals, this has not been conclu-
sively demonstrated. An extension of the present work would be to correlate
measured g-to-p conversion rates with actual measurements of OH concentrations.
Furthermore, this study was conducted preferentially in fair weather when free
S-2
radical reactions would be at their maximum importance. More data should be
gathered under cloudy weather conditions when aqueous processes might dominate.
The question of the source of the variation in the fraction of new particle volume
that appears as new particles has not been fully answered by this study. More
precise data on particle surface area, volume formation rates, collision frequen-
cies, and particle nucleation rates are necessary to determine possible relation-
ships between these parameters and the fraction of new particle volume that forms
new particles. The use of a refined version of the theory of McMurry (27) in the
PHOENIX plume model appears to be a potentially useful tool in attacking this
question.
Further data are needed on nitrate concentrations in power plant plumes in order
to evaluate more fully the importance of nitrate formation to the overall g-to-p
conversion process. In view of the low nitrate concentrations that we measured,
much larger sample volumes will be needed than those obtained in this study; vol-
umes as high as 2000 liters may be necessary. Analysis for particulate organics
should also be carried out together with a more detailed analysis of background
hydrocarbons to identify possible particulate organic precursors.
The results of this study suggest that regional differences may exist in the
g-to-p conversion process. Sufficient data should be gathered at each of several
different locales to allow parameters such as the ratio of particle nucleation
rate to particle volume formation rate to be determined with great statistical
precision at each site. Statistically meaningful intersite comparisons could
then be made.
S-3
Section
BACKGROUND AND SCOPE OF STUDY
BACKGROUND
Although the dispersion of industrial plumes has been studied for many years, it
is only recently that much attention has been paid to the complex physical and
chemical processes which can take place within them.
A subject of particular concern in recent years has been the conversion of SOo into
sulfate particles in the plumes from coal-fired power plants. In an extensive
review of this subject in 1976, Levy et a1 (1) concluded that only minimal success
has been achieved in the understanding of this subject. Since then, three
important studies of gas-to-particle (g-to-p) conversion in the plumes from coal
power plants have been reported. In the first of these studies, Forrest and Newman
(2) describe simultaneous measurements of the concentrations of SOo and particulate
sulfate at various ranges downwind from the stacks of four coal-fired power plants
located in the eastern United States. Both particulate sulfate and SOo were
measured by the filter pack method [Newman et a1 {3}]. Forrest and Newman
concluded that the rates of oxidation of SOo to particulate sulfate in the plumes
were in the range of 0.5 to 5%/hr. No distinct correlations of g-to-p rate with
travel time, temperature, relative humidity, time of day, or atmospheric stability
were discernible from this study.
Another study of g-to-p conversion in a coat power plant plume was reported by
Gillani et a1 (4_) who obtained measurements on two occasions in the Labadie power
plant near St. Louis. SOo oxidation rates were again deduced from simultaneous
measurements of the total gaseous sulfur and particulate sulfur at the various
points in the plume; gaseous sulfur was measured with a Meloy flame photometric
detector and particulate sulfur (assumed to be SO^" was determined by the flash
volatilization technique [Husar et a1 (5j]. It was concluded that the g-to-p
conversion rate was less than 3%/hr on both days, with the highest rates occurring
at peak sunlight hours and the ratio of particulate to total sulfur being linearly
related to the total solar radiation dose experienced by the plume.
1-1
Finally, Whitby et a1 (6) and Cantrell and Whitby (7) deduced g-to-p conversionrates by measuring (indirectly) the changes in the total particulate volume in theplume with travel time and attributing these changes to g-to-p conversion. Basedon two sets of measurements in the Labadie power plant plume, Whitby et a1deduced a g-to-p conversion rate of less than 0.5%/hr at 2 km downwind from thestack and 4.9%/hr at 45 km downwind. Cantrell and Whitby analyzed another threesets of measurements from the Labadie plant. Two of these measurement sets showedan increase in g-to-p conversion with travel time, the rates varying from 0.41 to.12%/hr; the third set of measurements produced a g-to-p conversion rate of about
0.45%/hr which did not increase significantly with travel time.
G-to-p conversion is only one of many processes which can affect the sizes,
concentrations and nature of the particles in the plume from a power plant.Primary stack emissions are also modified by the diffusion, coagulation and
gravitational settling of particles. Measurements of the size spectra of
particles at various distances downwind of coal power plants are even scarcer thang-to-p conversion measurements, mainly because the necessary instrumentation
(particularly for particles less than a few tenths of a micrometer) has only very
recently become available. The only reasonably comprehensive measurements of thesize spectra of particles in power plant plumes which have been previously
presented are those of Whitby et a1 (8) and Cantrell and Whitby for the Labadie
Plant.
SCOPE OF STUDY
For the past three years we have been engaged in a detailed study of power plant
plumes. In a previous EPRI report [Hegg et a1 (9)~\ and a published paper
[Hegg et a1 (10)] we have described our studies of the reactions of ozone and
nitrogen oxides in power plant plumes. The present report is concerned with
observational and theoretical studies of the evolution of particles in the plumesof coal-fired electric power plants. We describe first the results of airborne
measurements of particle size distributions and g-to-p conversion rates in the
plumes from two large coal-fired power plants. We then describe a sophisticated
3-D numerical model designed to simulate the principal physical and chemical
processes occurring in the plumes from coal power plants which affect the
concentrations and size distributions of particles. Finally, the predictions of
this model are compared with our field measurements.
1-2
Section 2
POWER PLANTS STUDIED AND AIRBORNE INSTRUMENTATION
POWER PLANTS
The two coal-fired electric power plants which have been studied are the Centralia
Plant in Washington State and the Four Corners Plant in New Mexico.
The Centralia power plant is situated in an east-west oriented river valley about
125 km south of Seattle in the western portion of Washington State. It is subject
to the prevailing rainy weather characteristic of Western Washington and occasion-
ally, when the winds are from the north, to fairly high ambient levels of pollution
from the Seattle-Tacoma urban-industrial area. The plant burns coal with an ash
content of ^15%, sulfur content ^0.5%, and an average heat content of ^1 .83 x 10
J kg"1 (7900 Btu 1b"1 ). The flue concentrations of SO^ and N0^ are both about
500 ppm. Direct particle emissions from the stack are relatively low due to the
use of two electrostatic precipitators (a Kopper and a Lodge-Cottrell in series
which have a 99"’"% efficiency in removing particulate mass. Consequently, the
plume from the power plant stack is essentially invisible. The Centralia power
plant is rated at about 1400 MM electrical output at full load; the electrical
outputs during the fl ights to be discussed in this report are listed in Table 2-1
The Four Corners coal power plant is situated in a relatively arid region near
Farmington, New Mexico, far from any major urban or industrial centers. The plant
burns coal with an ash content of ^22.5%, sulfur content of 0.7% and an average
heat content of ^2.09 x 107 J kg"1 (9000 Btu Ib’t The flue concentrations of
SOo and NO from the Four Corners Plant are similar to those at Centralia. How-
ever, the particle mass loading of the flue gas at Four Corners is considerably
higher than at Central ia; this is due, in part, to the somewhat less efficient
(97%) electrostatic precipitators on the two larger generator units and, pre-
sumably, to the higher ash content of the coal used at Four Corners. Most of the
particulate mass in the emissions from the Four Corners Plant is in relatively
small numbers (^102 cm" of large particles (5-20 pm in diameter) The plume
from the Four Corners Plant is generally visible. This is due both to the
2-1
particulate loading and to the relatively low rates of mixing of the plume with
the ambient air under the stable atmospheric conditions which are common in the
Four Corners area, particularly in the early hours of the morning when our
measurements were made. The Four Corners power plant is rated at about 2100 MW
electrical output at full load; the electrical outputs during the flights to be
discussed in this report are listed in Table 2-1
Table 2-1
ELECTRICAL OUTPUTS OF THE POWER PLANTS DURINGTHE PERIODS OF MEASUREMENTS DISCUSSED IN THIS PAPER
Electrical OutputDate Power Plant of Plant (MU)
October 31 1975 Centralia 640November 5, 1975 400March 16, 1976 630March 30, 1976 600April 28, 1976 1050October 8, 1976 844October 19, 1976 1323September 22, 1977 1227October 18, 1977 H85October 20, 1977 622
June 23, 1977 Four Corners 2050June 24, 1977 2075June 25, 1977 1310June 29, 1977 1200
AIRBORNE INSTRUMENTATION
All of the measurements to be described in this report were obtained aboard the
University of Washington’s B-23 research aircraft. A complete ist of the
instruments on this aircraft is shown in Table 2-2. Since the details on the
instruments and methods of on-board sampl ing have been given by Hobbs et a1 (1_1_)only a summary wilt be given here.
2-2
Table 2-2
SPECIFICATIONS ON RESEARCH INSTRUMENTS ON THE UNIVERSITY OF WASHINGTON’S B-23 AIRCRAFT
point"
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hard-copy
2-3
In order to obtain essentially point measurements of the size spectra of the
particles and the masses of participate sulfate and total aerosol in a plume,"grab samples" of plume air were sucked into large bags in the aircraft (at a
rate of 100 A s~ for the particulate sulfur measurements and 4 a s~1 for theparticle size spectra measurements). These samples were then passed immediatelyinto the appropriate instruments (TSI 3030 and 3205, Royco 202, and the Pallflexfilters) and the data from these instruments (except for the filters) were fedinto an on-board computer. The computer generated hard-copies of the data (andvarious derived parameters) as well as storing them on a floppy disk for
subsequent detailed analysis. "Grab samples" were generally taken in regions of
a plume where the continuously measured variables (e.g. gaseous sulfur, NO 0-,0
and Aitken nuclei indicated the plume to be most pronounced. Each plume was
generally sampled at a number of different altitudes (at least three) at variousdistances downwind from the stack.
In most cases, each measurement presented in this report was obtained from one
aircraft pass through the plume. However, on all flights a few repeat passes weremade through the same part of a plume in order to check reproducibil ity of thedata. Measurements obtained at plume center in these repeat passes agreed towithin 10%, but near the edges of a plume the variabil ity increased to 100%. Thevariability of the ambient air samples over short time intervals (<10 min) was
less than 10%. On some flights however particle loading in the ambient air in-
creased or decreased with time. For the g-to-p conversion estimates based on thetotal aerosol volumes, the "grab samples" taken at each range were averaged in thevertical (for the g-to-p estimates based on Aitken nuclei formation, plume averageconcentrations were also employed). The Pallflex filters, from which g-to-pconversion rates were also deduced, were exposed only to the "grab samples" takenat the altitude where the SOn reached a maximum value.
On some occasions pilot balloons were released and tracked from the ground toobtain wind measurements, however, this was not essential since continuous wind
measurements (as well as many other meteorological variables see Table 2-2)were measured aboard the aircraft.
*Prior to being passed into the particle size measuring instruments the airsamples were either heated or passed through a diffusion drier. Consequently,the particle sizes referred to in this report are those at which the particlesare tn equilibrium at low (S40%) relative humidities.
2-4
Section 3
DATA ANALYSIS TECHNIQUES
PARTICLE SPECTRA
The particle size spectrum measurements are processed by a ground-based computer
to give particle number (dN/dlog D) particle surface area (dS/dlog D) and
particle volume (dV/dlog D) concentration distributions (N, S and V are the total
particle number, surface area and volume concentrations and D the effective
particle diameter). Up to three log-normal particle number concentration
distributions are then fitted to the measured distributions using a ^-m^mmzat-ionscheme [Bevington (TJ?)] which uses an algorithm given by Marquardt (1_3) the number
of distributions used to fit the data is determined objectively. Each log-normal
distribution describes a "mode" of the particle size distribution. Willeke and
Whitby (M_) refer to these modes as "Aitken nuclei", "accumulation" and "coarse
particle" modes; we will refer to them as modes 2 and 3, respectively, and
indicate them, when necessary, by the corresponding subscripts.
The particle size distributions generated by the fitting routine described above
are used in our numerical model of power plant plumes which employs particle
volume (rather than diameter) as the independent variable, thus a transformation
from diameter to volume has to be made. In this case the transformed experimental
data (dN/dlog v versus v) are fitted to the following function:
3 N.
^ ^ ^^exp in2 v
2 ^Svz ^(3-1
where v is the volume of a particle of diameter D, N the number concentration of
particles in mode i and a the geometric standard deviation of the geometric^v^ th
mean particle volume v_ of the i mode. After the data have been fitted togi
Eq. 3-1 volume parameters may be transformed back to diameter parameters.
3-1
For example:
1/3
gNz \ v vg^
\Si W^ ^"W ^"gVz ^ ^P I,3 1n\Qi
(3-2)
where, D ^, D (^ and D y^ are the geometric mean diameters with respect to thenumber, surface and volume concentrations, respectively, of mode i. The geometricstandard deviation a
^of the geometric mean diameter is the same whether it is
evaluated with respect to the number, surface or volume concentration; for the
i mode it is given by:
\1/3"gDz "gVi (3-3)
It should be noted that unlike Cantrell and Whitby, who make various assumptionsabout the distributions (e.g. they assume that the geometric standard deviation
o p. of the geometric mean diameter of the "Aitken nuclei" mode is .5 +/- 0.1
we place no a priori restrictions on the modal parameters.
GAS-TO-PARTICLE CONVERSION RATES
Three methods are used in this paper to deduce gas-to-particle (g-to-p) conversion
rates in plumes. The most direct method used for determining the rate of g-to-pdue to sulfur oxidation alone was to measure the ratio of particulate sulfur togaseous sulfur at various points in the plume. We used the flash volatilization
technique described by Roberts (1 5) and Husar et a1 (5J to measure particulate
sulfur. However, since we have only recently refined this method to adequate
precision, only limited results from this technique are available.
G-to-p conversion rates are also determined from the changes in the total
volume of particles in the plume with travel time. The change with time in the
volume concentration V of particles in an expanding plume, assuming an expanding
3-2
Lagrangian box model is given by:
dVdt
-3(1n V
---t ^- MA) + R (3-4)
where V is the volume of the plume, Vn the volume concentration of particlesP
in the ambient air, and R (which is assumed to be constant) is the rate of
production of particle volume by g-to-p conversion in a unit volume of the plume.
Also, we may write:
9(1n Vp)8t
(3-5)
where a is a diffusion parameter which can be determined by either the downwind
change in the cross-sectional area of the plume or the change with travel time
in the mean concentration of a conserved species in the plume [Hegg et a1 (9j].
Noting also that:
^-^ dVdt dt
(3-6)
and combining Eqs. 3-4 through 3-6, we obtain;
dA a
^ t ^ R (3-7)
where <j) V-V,,.
The solution of Eq. 3-7 is:
Rt /, ^o \ t \ "c^TT^o crrrAt-/’ (3-8)
(t,).where (}> ()> Solving Eq. 3-8 for R we obtain:
^ JL_ t" v n+ \a + At. Y
3-3
(3-9)
G-to-p conversion rates were calculated from Eq. 3-9 using both the particle
volumes determined from the raw data and from the fitted particle volume dis-
tributions described above.
The third method which we have used for calculating g-to-p conversion rates is
based on measurements of the rates of production of Aitken nuclei in the plume.
Based on the work of Luria et a1 (J_6) we assume that all of the Aitken nuclei
produced by g-to-p conversion are 0.0072 \im in diameter and consist of sulfuric acid,
The rate of production of Aitken nuclei N in the plume, employing the plume model
of Gelinas and Walton (J_7) is given by:
^ -K^ ^N N^ S (3-10)
where N,, is the concentration of Aitken nuclei in the ambient air, K a coagulation
coefficient, and S the rate of production of Aitken nuclei by g-to-p conversion.
The solution of Eq. 3-10 is in the form of imaginary Bessel functions, and since
S appears in the argument of the Bessel function it cannot be solved for explicitly.
An asymptotic solution to Eq. 3-10, given by Hegg et a1 (9), is of the form:
(1 + f)V (3-11
While S can readily be obtained from Eq. 3-11 the values are only applicable at
large t (^200 mins). For the shorter travel times appl icable to our data,
NN and Eq. 3-10 may be written as:
d^ ^ N2 ? + ST ^ ^ (3-12)
also 6P_ aP_dt t
where P is the concentration of a conserved species in the plume (again assuming
PP^ for short travel times). In this study we have chosen SOo as the conservative
tracer, since the amounts by which its concentration changes are negligible over
the short travel times with which we are concerned, and we have assumed that the
3-4
rate of production of Aitken nuclei by g-to-p conversion is proportional to the
concentrations of SO^, so that S S’P. From Eqs. 3-12 and 3-13:
iK?) -o ^ (3-14)
or,
^ K^ ^ + S- (3-15)
where ^ N/P and we have assumed that N may be approximated by the average
Aitken nucleus concentration N over the relatively short time intervals with
which we are dealing.
The solution to Eq. 3-15 is:
^ -^ + (^o -^ ^P f- ^ N ^-^lK N \ K N / L o O Jo o
uhprp ill ilift } Frnm Fn. .?-1fi"where V ^(t ). From Eq. 3-16:
^ ^ofr ^P [- ^ ^^o^s- ----L-0----^------ (3-17)exp [- Kp N (t-ty)]
and the rate of production of Aitken nuclei is given by S ST" where P is the
average concentration of SO? over the travel time considered. This method
requires a knowledge of the coagulation coefficient K We assume that most of
the loss in the number concentrations of particles is due to coagulation among
the smaller particles (mode and determine (from the particle size distribution
fi ts) the val ues of F, ( ) and -o where r -?
K is then determined from [Fuchs (18)]:
y 2 kT"o 3 ~^ + r [^^^^^[-J.^ - (9 - A^ (3-18)
where k is Boltzmann’s constant, T the absolute temperature, n the viscosity of
air, 1 the mean free path of air molecules and A is the constant which we have
3-5
taken to be equal to .12 [Fuchs (18)]. Clearly, this method for calculating
g-to-p conversion contains several approximations and may therefore be expected
to yield cruder estimates than the other two methods.
It should be noted that the first method described above measures only sulfur
oxidation whereas the other two methods should measure g-to-p conversion rates
due to all chemical species in a plume.
3-6
Section 4
RESULTS OF FIELD MEASUREMENTS
PARTICLE SPECTRA
Shown in Figure 4-1 are the fitted particle number distributions based on
measurements made at points close to the centers of plumes from the Central ia
and Four Corners power plants. (The center of a plume in a horizontal traverse
was taken to be the point where the SO? concentration reached a maximum value.
No spatial averaging or extrapolations of the measurements have been made. This
differs from the technique used by Mhitby et a1 (8) who calculated total particle
volume fluxes on the assumption that a direct correlation existed between the
light backscattering coefficient and particle volume. Our data show that in the
case of the plume from the Centralia power plajit this assumption would not be
valid, since most of the variations in the total volume of particles in the plume
occur in mode and the particles in this mode are too small to cause appreciable
variations in the backscattering coefficient.
Complete istings of the modal parameters derived from our measurements at the
Central1a and Four Corners power plants are given in Tables 4-1 and 4-2. The
parameters associated with the three particle modes fall within fairly distinct
ranges, as illustrated by the values shown in Table 4-3. Modes 2 and 3 sometimes
appeared and disappeared with travel time in the plume: we attribute this to these
two modes occasionally overlapping one another.
The differences in the number concentrations of particles in mode 3 in the Four
Corners and Central ia plumes are clearly evident from the results shown in
Fig. 4-1 The concentrations of 0.5-1 .0 ym particles in the Four Corners plume
were one to two orders of magnitude greater than in the Centralia plume. This
appears to have been due primarily to the different stack emission rates of these
large particles. At Centralia, mode 3 never contributed more than 12% to the total
volume of particles and only 0.01% to the total number of particles. At Four
Corners, on the other hand, mode 3 contributed up to 50% to the total volume and
0.2% to the total number of particles.
4-1
Figure 4-1 Fitted curves (from Eq. 3-1 and 3-2) to particle number concentrationdistributions for:
November 5, 1975. The wind speed was 35 km hr~1.March 16, 1976. The wind speed was 39 km hr-1.March 30, 1976. The wind speed was 17 km hr~1.April 28, 1976. The wind speed was 9.3 km hr~1.October 8, 1976. The wind speed was 19 km hr"1.September 22, 1977. The wind speed was 8.0 km hr-1.
(a)(b)(c)(d)(e)(f)
CentralCentraliaCentralCentralCentralCentral
ia
iaiaiaia
plumeplumeplumeplumeplumeplume
onononononon
4-2
D(,um)
PFigure 4-1 (continued)
(g) Central ia plume on October 19 1976.(h) Centralia plume on October 20 1977.(i Four Corners plume on June 23 1977.(j) Four Corners plume on June 24 1977.(k) Four Corners plume on June 25 1977.(1 Four Corners plume on June 29 1977.
The wind speed was 15 km hr~’The wind speed was 4.8 km hr~’The wind speed was 11 km hr~1.The wind speed was 14 km hrThe wind speed was 6.0 km hr~1The wind speed was 14 km hr~1.
4-3
Table 4-1
MODAL PARAMETERS FOR PARTICLE DISTRIBUTIONS IN THE PLUMES FROM THECENTRALIA POWER PLANT AND IN THE AMBIENT AIR. SEE TEXT FOR KEY TO SYMBOLS
(a) General information for each data set, indicated by tine number
Line Number
89
1011
12131415
161718
1920212223
24252627
282930
Date/Local Time
November 5, 1975125913381304
March 16, 19761203122113361320
March 30, 19761212122313051145
April 28, 19761307132013391408
October 8, 1976134114291344
October 19, 197611071139105111491151
September 22, 19771348142014351438
October 20, 1977123513231345
Plume (P) orAmbient (A)
AirAltitude(m, MSL)
244457335
533457610549
488396457457
457457457457
640640640
549671671671671
9141070914914
640701701
Distancefrom Stack
(km)
0.99.3
4.69.3
25.9
2.88.316.7
5.613.020.0
0.91.9
1.99.313.019.0
7.413.020.0
2.815.0
Table 4-1 (cont)CENTRALIA
(b) Mode (for general information on each data set, indicated by a line number, see (a) above)
Line Number
23456789
10
-^ n12131415161718192021222324252627282930
(Numbe.04.13
3.279.662.79.66
4.132.385.482.375.575.522.733.672.287.759.277.148.182.215.87.07.82
2.666.16.43
8.20.05
4.05.74
^ -"^ir cm"x 107x 107x 106x 104x 104x 104x 105x 10x 105x 104x 106x 104x 104x 104x 10"x 103x 103x 103x 105x 105x 105x 105x 104x 104x 103x 104x 103x 105x 104x 104
gN1(in units of
10-3 urn)
0.795.11.34
18.522.62.792.14.06
2.2919.20.368
23.222.123.8
.3462.814.847.35.95
15.510.613.132.622.022.828.428.822.120.16.88
^(pm- cm-3)27842019325011591 .873.0
15310783.511228215219812019230.6
12566064993629819912333.2
10640.3
52720112.9
"gsi(in units of10-2 ym)
.06
.06
.404.445.806.312.63.93
2.725.84.73
7.008.017.23.24
12.87.100.1184.326.034.776.77
10.76.717.538.295.447.207.863.43
(pm30
0.8132
0
0
0423040379
1054
0
0830
v!cm-3).944.31
.30
.41
.18
.597
.02
.905
.07
.846
.33
.79
.16
.431
.90
.536
.11
.80
.16
.8
.08
.77
.82
.563
.91
.428
.50
.70
.11
D,(in ui
10
334699989
10110003
1815180000
191113147
13157
gvinits of-2 urn).90.28.55.88.30.50.19.22.39.2.9.121.152.126.78.4.5.7.116.119.101.154.4.7.7.2.48.0.6.65
gD13.122.892.96.94.99.90
3.063.333.0422.1084.0072.102.232.112.87.83
2.42.97
2.712.282.382.472.162.112.172.08.76
2.162.282.45
Line Number (Number cm"-)0.534
2 0.5123 0.3964 32.45 0.9816 .087 0.6778 0.8679 0.804
10 .5211 0.82812131415 29.216 8.4617 0.79218 6.5919202122232425 39126 228627 1088282930 47.0
h(Number cm~^)
0.5340.5120.396
32.40.981.08
0.6770.8670.804.52
0.828
29.28.460.7926.59
gN2(in pm)0.5110.5170.5280.2270.5020.4970.5240.5210.5220.4570.504
0.3170.4950.5080.500
S2(pm^ cm~^)
0.4490.4400. 3575.270.7900.8820.5960.7580.700.18
0.667
10.86.710.6465.21
^(in pm)
0.5240.5290.5430.2280.5100.5250.5350.5340.5310.540.0.508
0.3710.5100.5120.503
^(urn" cm"3)0.0400.0390.0320.2010.0670.0780.0540.0680.0620.1110.057
0.6930.5750.0550.437
"9V2(in \im)0.5300.5350.5500.2290.5150.5400.5410.5410.5350.5880.510
0.4010.5180.5140.505
aD2.12.11.12.05.10.18.11.12.10.34.06
.32
.13
.06
.06
0.1900.1070.203
0.1690.1020.068
37.977.432.8
0.1820.1050.141
.18
.370.926
.22
.12
.83
0.283 14.3 0.343 0.3780.861 .36
Line Number
23456789
101112131415161718192021222324252627282930
^(Number cm~^)0.0380.1950.0920.7500.1810.1360.0770.1560.154
0.1560.2300.5960.2350.1540.7630.1230.4960.4100.2240.3110.1130.0900.0300.0360.0770.087
0.0940.285
"9N3(in pm)
.01
.110.9600.5150.851.02.05.04.03
.020.9660.6400.8130.985.00.00
0.991.20.15.10.04.51.16.06.04
2.09
.35
.10
h9 ^(pnr cm -)’0.2980.8430.2870.6510.5300.4600.2840.5580.548
0.5300.882.14
0.9000.4202.480.393.60.85
0.942.23
0.4070.7760.1420.1310.271.96
0.6191 .20
gS3(in pm)
.06
.24
.030.537.10.06.11.10.10
.06
.270.952.497
0.993.03.01.03.20.16.14.10.81.28.10.08
3.43
.56
.22
V3(pm^ cm~^)
0.0530.1790.0500.0590.1030.0820.0530.1030.102
0.0950.1990.2000.2610.0780.4310.0660.2780.3700.1840.2360.0760.2450.0310.0240.049.27
0.1670.248
D^(in
0.
2.
.98
.35
.12
.104.39
.68
.28
/3pm)
0831075492508141313
084516030005020620171713
gD3.16.26.21.16.43.15.18.18.19
.14
.44
.56
.74
.06
.14
.08
.15
.05
.09
.15
.18
.35
.25
.14
.15
.64
.31
.25
(e)(for general inform
Line Number
23456789
101112131415161718192021222324252627282930
Fraction (fy,ation on each
^10.9100.8570.9080.8980.8920.8810.8480.8560.8460.9070.8500.9560.9330.9230.3580.8300.8160.8130.9550.9800.9790.9850.9510.9830.3190.5740.163.000
0.9570.090
Table 4-1 (cont)CENTRALIA
of the total particle
data set, indicated by
^20.0390.0250.0360.0780.0420.0580.0770.0570.0580.0930.057
0.5760.0970.0840.114
0.6670.4110.353
8.500.043
0.706
volume
a line
^30.0510.1170.0560.0230.0650.0610.0750.0870.095
0.0950.0440.0670.0760.0650.0730.1000.0730.0450.0200.0210.0150.0490.0170.0140.0150.483
0.203
in mode i
number, see (a) above)
Total V(pm3 cm-3)
.04
.530.8952.56.58.34
0.704.19.07.18.00
4.532.993.42.20
5.910.6573.838.169.35
11 .065.155.02.85.76
3.332.62
3.87.22
Table 4-2
MODAL PARAMETERS FOR PARTICLE DISTRIBUTIONS IN THE PLUMES FROM THEFOUR CORNERS POWER PLANT AND IN THE AMBIENT AIR. SEE TEXT FOR KEY TO SYMBOLS
(a) General information for each data set, indicated by line number
Line Number
10n1213
14151617
Date/Local Time
June 23, 19771124094510510947
June 24, 197712081052101909571055
June 25, 19771052101609221217
June 29, 19770822081507471019
Plume (P) orAmbient (A)
AirAttitude(m. MSL)
2290226019802130
21601980183019801980
2060190017501980
1707182917371890
Distancefrom Stack
(km)
.97.413.0
.97.413.028.0
5.6II .017.0
5.611 .122.2
Travel Timefrom Stack
(hrs)
0.140.57.00
0.130.530.932.00
.002.003.00
0.400.79.59
Line Numbe
234
56789
10111213
14151617
r (Numb.
3.974.283. 108.52
2.98.75
4.025.684.45
.243.26.80
8.92
3.163.573.867.39
^er cm’3)x 103x 103x 104x 103
x 105x 105x 104x 105x 103
x 107x 10x 10"x 103
x 103x 103x 103x 103
^(in ur10-
75.7113.25.
3.7.
12.2.
27.
0.0.
32.
88.76.7122.
3N1n’ts of-3 \im}
.5269
7569831
897985237
6547
^? ^(urn cm -^120111no57.7
16819410112439.1
33320917271 .8
10798.892.132.9
9’(in ur
10-2
12.118.8.
4.4.6.2.
10.
0.2.2.7.
12.1110.6.
51n’ts of
urn)
863432
785924903
956074683
23626
3 ^ 3(urn- cm"")
2.922.422.42.07
2.522.32.56.13
0.940
0.960.54.49.17
2.362.00.80
0.442
"gvi(in units o10-2 um)
16.614.820.714.9
17.011 .213.810.320.2
3.129.49
11 .012.1
14.313.712.910.4
\a auuvti;
faDl.67.64
2.592.15
3.082.572.443.082.27
2.973.443.40.94
.49
.55
.562.04
10111213
14151617
Table 4-2 (cont)
FOUR CORNERS
(c) Mode 2 (for general information on each data set, indicated by a tine number, see (a) above
Line Number
M"2(Number cm"3)
14.54.304.912.55
10.74.704.88.257
535
13.82.664.070.904
4.103.403.460.403
"9N2(in units of
10-3 pm)
0.5310.5030.5110.504
0.5370.5350.5040.5070.115
0.3520.5060.5080.499
0.5130.5100.5200.514
^(ym cm"3)
13.33.474.072.05
9.984.353.92.02
25.0
6.902.163.330.71
3.492.853.030.341
^(in units of10-2 pm)
0.5490.5110.5160.509
0.5510.5500.5070.5110.129
0.4540.5100.5120.503
0.5280.5220.5370.523
^(ym3 cm"3)
.230.2970.3510.174
0.9230.4010.3320.0870.554
0.5560.1840.2840.060
0’.3090.2490.2740.030
gV2(in units of
10-2 urn)
0.5590.5150.5190.511
0.5580.5570.5090.5130.137
0.5160.5120.5140.505
0.5360.5280.5450.528
gD2
.14
.09
.07
.07
.12
.12
.06
.06
.28
.43
.07
.06
.06
.13
.11
.14
.10
Line Number
10111213
14151617
Table 4-2 (cont)FOUR CORNERS
(d) Mode 3 (for general information on each data set, indicated by a ine number, see (a’) above
N3
(Number cm’3)
8.272.042.50.40
5.412.322.200.4280.402
.66
.432.350.494
2.062.13.68
0.402
"a(in u
1G
0.
0.
0.
0.0.
N3nits ofi~3 pm)
02830604
0104980811
07009104
9759270111
S
(pm2
29.5.9.6.40
18.8.8.
6.5.8.2.
7.7.6.3.
3cm-3)
99695
869247765
44606320
47311914
D
(in
2
gS3units of0-2 pm)
.13
.12
.20
.40
.10
.15
.22
.22
.18
.15
.25
.28
.36
.18
.18
.16
.24
V"3
(pm3 cm-3)
5.80.19
2.05.61
3.54.71.77
0.3710.329
.261 .232.000.533
.54
.52
.24
.39
gv(in un
10-
3.
3its o12 ^")
20292762
1521363021
19405155
30332418
0gD3
.26
.46
.28
.47
.23
.26
.39
.28
.18
.21
.40
.51
.44
.36
.41
.30
.81
Table 4-2 (cont)
FOUR CORNERS
(e) Fraction (f^ of the total particle volume in mode i
(for general information on each data set, indicated by a tine number, see (a) above)
Line Number VI ^2Total V
^3 (pm3 cm-3)
10111213
14151617
0.2930.6180.5020.376
0.3620.5240.4250.7100.516
0.3460.5220.3940.663
0.5610.5310.5430.237
0.1230.0760.0730.061
0.1320.0900.0910.0550.304
0.2000.0620.0750.034
0.0730.0660.0830.016
0.5830.3060.4250.563
0.5060.3860.4840.2300.180
0.4540.4160.5300.303
0.3660.4030.374.0.747
9.953.914.822.85
6.984.443.66.58.82
2.772.963.78.76
4.213.773.31.86
Table 4-3
RANGES OF VALUES FOR THE GEOMETRIC MEAN DIAMETER D (WITH RESPECT TO VOLUME)AND ITS GEOMETRIC STANDARD DEVIATION o
^FOR THE THREE PARTICLE MODES
Mode {i}
i
i 2
i 3
"gV-i {vm}
0.001 0.02
0.11 0.55
0.55 4.4
gDz
.5 4
.8
.8
4-14
The existence of the third particle mode appears to have a substantial effect
on the mechanics of the overall particle size distribution in power plant plumes.
This can be seen from Table 4-4 which lists the rates of transfer of particle
volume from mode to mode, in terms of the fraction of the total particle volume.
For travel times less than about 15 min the third mode in the Centralia plume
gains fractional volume, whereas modes and 2 lose volume (November 5, 1975,
March 16, 1976 and October 8, 1976). Since the total particle volume also
increased on the November 5 flight, all of the new particle mass must have been
going into the third mode. The large decreases in the total volume of particles
in the Central ia plume on March 16 and October 8, 1976, were probably due to
plume diffusion close to the stack. However, since the fractions of the particle
volumes in mode 3 were increasing, coagulation or g-to-p conversion via condensa-
tion into this mode was also taking place. Unfortunately, we do not have any
measurements at Four Corners from which we can deduce changes in particle volumes
for travel times less than 15 min. However, at Four Corners the fractional
particle volume in the third mode increased for travel times between about 1/2 hr
on June 23, 1977, June 24, 1977 and June 29, 1977, and on June 25, 1977 it in-
creased between 2 and 3 hrs of travel time.
The flights of June 23 and 25, 1977 at Four Corners also show that the third
mode was absorbing the largest part of the total increase in particle volume.
df,,~y^en was positive, a pg or N3 (or both) also increased with time; this suggests
that in addition to g-to-p conversion, inter-modal particle coagulation was respon-
sible for the increase in the volume of particles in mode 3. Since the rate of
increase in the fraction of the total volume of particles in mode 3 is positive,
it seems likely that the most important inter-modal coagulation rates in the plume
were those due to particles in mode 3 coagulating with particles in modes 2 and
However, after about 5 min travel time at Centralia, or to 3 hrs at Four
Corners, the coagulation of particles with mode 3 should become negligible due to
the dilution in the concentrations of particles in mode 3.
4-15
Table 4-4
RATES OF CHANGE OF THE FRACTION (fy .) OF THE TOTAL VOLUME OF PARTICLES IN MODE -L.
THE RATE OF CHANGE OF THE TOTAL VOLUME V OF THE PARTICLES IS ALSO LISTED.
Date
November 5, 1975
March 16, 1976
March 30, 1976
April 28, 1976
October 8, 1976
October 19, 1976
September 22, 1977
October 20, 1977
June 23, 1977
June 24, 1977
June 25, 1977
Tune 29, 1977
Power Plant
Centralia
Four Corners
Age (hr)at startof measurStart
0.03
0.160.32
0.150.45
0.601.40
0.05
0.120.610.85
1.01.75
0.50
0.140.57
0.130.530.93
1.02.0
0.400.79
of plumeand endement
End
0.26
0.320.89
0.450.90
1.402.20
0.10
0.610.851.22
1.752.75
2.67
0.571.00
0.530.932.0
2.03.0
0.791.59
^Vldt
-0
0
-0
-00
-0-0.012
-0.28
-0-00
-00
-0
0-0
0-00
0-0
-00
(hr-1
.23
.037
.019
.038
.14
.029
.051
.004
.016
.89
.26
.020
.76
.27
.40
.25
.27
.18
.13
.077
.015
^hr-1-^(hr-0.061
-0.2250.028
0.0030.78
-0.26
0.89-0.26
-0.11-0.007
-0.100.003
-0.03
-0.140.013
-0.0440.021
^3,-d^0.
0.-0.
0.-0.
0.0.
0.
-0.0.
-0.
-0.0.
0.
-0.0.
-0.0.
-0.
0.0.
0.-0.036
hr-129
262008
02721
029012
54
051004016
004001
020
6528
302524
0411
23
dV / ym3 \dt W hj
2.1
-6.1-0.42
-0.400.24
-1.90.54
-110
2.47.1
-5.9
-0.121.6
-2.13
-142.1
-6.3-1.91.9
0.190.82
-2.8-0.57
Hence in our model for particle interactions in plumes [unl ike whitby et a1 {8)~\we allow particles in mode 3 to coagulate with particles in modes and 2. If
such coagulation is ignored particulate formation rates for travel times up to
3 hrs from the stack will in general be underestimated.
To illustrate more directly the variations in the concentrations of particles of
different sizes with travel time in a plume, the reader is referred to Figs. 4-2
through 4-10. These figures show the values (in excess of ambient) of dN/d(1ogD)
in the plumes at various distances from the stacks for particles 0.024 and 0.55 pm
in size. The isolines shown in the figures were extracted and drawn by hand.
Measurements of 0.024 pm sized particles in the Centralia plume on October 19, 1976
showed decreasing concentrations with increasing distance from the stack (Fig.
4-2a). However, in the upper regions of the plume, the 0.55 pm particles increased
in concentration beyond 15 km (^1 hr travel time) from the stack (Fig. 4-2b). In
the lower regions of the plume, at a travel distance of about 10 km (^40 min
travel time) the concentration of 0.55 pm particles was actually less in the plume
than in the ambient air (Fig. 4-2b)
The data for March 16, 1976, at Centralia (Fig. 4-3) are similar to those for
October 19, 1976. The 0.024 pm particles decrease in concentration with travel
time, but in this case they decrease below ambient values (Fig. 4-3a) The 0.55 pm
particles are present in concentrations above ambient values in the upper part of
the plume and below ambient values in the lower portion of the plume (Fig. 4-3b).
Again these particles increase in concentration after hr travel time.
As we shall see later, our plume model shows that the increases in the concentra-
tions of 0.55 pm particles beyond 15 km is attributed to the coagulation of the
large numbers of small particles (e.g. 105 cm’3 of 0.024 pm particles on October
19). Although the concentrations of 0.024 pm particles in the plumes decrease
with travel time, the decreases are much slower than would be produced by their
diffusion and coagulation; this is due to g-to-p conversion increasing their
numbers. The deficits in the concentrations of 0.55 pm particles at about 10 km
(^0 min travel time) on October 19 and between about 10 and 25 km (^15-38 min
travel times) on March 16 can also be explained by g-to-p conversion with
coagulation rapidly shifting particles of this size into larger-sized particles
(see Section 6).
4-17
5 10 15
DISTANCE FROM STACK (km)
(0)
5 10 15 20
DISTANCE FROM STACK (km)
(b)
Figure 4-2.. Excess concentrations (dN/d log D) above ambient values ofparticles in the plume of the Centralia Power Plant on October 19, 1976.The wind speed was 15 km hr-1.(a) Particles 0.024 \im in equivalent diameter (concentrations in units of 104 cm"3),(b) Particles 0.55 pm in equivalent diameter (concentrations in units of cm-3)
4-18
15 20 25 30 35DISTANCE FROM STACK (km)
(a
900
800
in
700
600o
500<
400
^0 5 10 15 20 25 30 35
DISTANCE FROM STACK (km)
(b
Figure 4-3. Excess concentrations (dN/d log D) above ambient values ofparticles in the plume of the Centralia Power Plant on March 16, 1976.The wind speed was 39 km hr ".
(a) Particles 0.024 pm in equivalent diameter (concentrations in units of 104 cm"(b) Particles 0.55 pm in equivalent diameter (concentrations in units of cm-3)
4-19
3 4 5 6 7 8 9
DISTANCE FROM STACK (km)
a
3 4 5 6 7 8 9
DISTANCE FROM STACK (km)
b)
Figure 4-4. Excess concentrations (dN/d log D) above ambient values ofparticles in the plume of the Four Corners Power Plant on June 23, 1977.The wind speed was 11 km hr ".
(a) Particles 0.024 pm in equivalent diameter (concentrations in units of 104 cm"3)(b) Particles 0.55 pm in equivalent diameter (concentrations in units of cm-3)
4-20
<
1300
<n
1200
100
^ lOOOh-
900
800 6 8 10 12 14 16
DISTANCE FROM STACK (km)
(a
w
E
Q 1000
<
6 8 10 12 14 16
DISTANCE FROM STACK (km)
(b)
Figure 4-5. Excess concentrations (dN/d log D) above ambient values ofparticles in the plume of the Centralia Power Plant on September 22, 1977.The wind speed was 8.0 km hr-1.(a) Particles 0.024 \m in equivalent diameter (concentrations in units of 10^ cm ")(b) Particles 0.55 ym in equivalent diameter (concentrations in units of cm-3).
4-21
-1.0
-0.64 -2.32
-0.32
5 10 15
DISTANCE FROM STACK (km)20
(a
5 10 15DISTANCE FROM STACK (km)
(b
Figure 4-6. Excess concentrations (dN/d log D) above ambient values ofparticles in the plume of the Central ia Power Plant on March 30, 1976.The wind speed was 17 km hr ".
(a) Particles 0.024 pm in equivalent diameter (concentrations in units of 104 cm"3),(b) Particles 0.55 pm in equivalent diameter (concentrations in units of cm"3)
4-22
(/)
700
600
< 400
300,
0 500J336 4.2C/ 1.68
0
0.68
5 10 15 20
DISTANCE FROM STACK (km)
(a
25
<n
700
600
^ 500
< 400
0.69
3000 5 10 15 20 25
DISTANCE FROM STACK (km)
(b
Figure 4-7. Excess concentrations (dN/d log D) above ambient values ofparticles in the plume of the Centralia Power Plant on April 28, 1976.The wind speed was 9.3 km hr ’.
(a) Particles 0.024 pm in equivalent diameter (concentrations in units of 104 cm"3).(b) Particles 0.55 pm in equivalent diameter (concentrations in units of cm"").
4-23
2000
</i
2c 1900
Q3
< 1800
17006 9 12 15 18 21
DISTANCE FROM STACK (km)
(0)
2000
V)
c 1900
Q=)
< 1800
^^O 3 6 9 12 15 18 21DISTANCE FROM STACK (km)
b)
Figure 4-8. Excess concentrations (dN/d log D) above ambient values ofparticles in the plume of the Four Corners Power Plant on June 24, 1977.The wind speed was 14 km hr ’.
(a) Particles 0.024 pm in equivalent diameter (concentrations in units of 104 cm"3)(b) Particles 0.55 pm in equivalent diameter (concentrations in units of cm-3).
4-24
2200
21 00
2000
1900h-
1800h-
1700
3 4 5 6 7 8 9DISTANCE FROM STACK (km)
a )
3 4 5 6 7 8 9DISTANCE FROM STACK (km)
b)Figure 4-9. Excess concentrations (dN/d log D) above ambient values ofparticles in the plume of the Four Corners Power Plant on June 25, 1977.
(a) Particles 0.024 pm in equivalent diameter (concentrations in units of 104 cm"3)(b) Particles 0.55 pm in equivalent diameter (concentrations in units of cm-3)
4-25
5 10 15 20 25 30
DISTANCE FROM STACK (km)
( a )2000
en900
LJQ isooK/o
< 700
’^O 5 10 5 20 25 30DISTANCE FROM STACK (km)
( b )
Figure 4-10. Excess concentrations (dN/d log D) above ambient values ofparticles in the plume of the Four Corners Power Plant on June 29, 1977.(a) Particles 0.024 \im in equivalent diameter (concentrations in units of 104 cm"3)(b) Particles 0.55 pm in equivalent diameter (concentrations in units of cm"3)
4-26
The data from June 23, 1977 at Four Corners show quite a different situation
(Fig. 4-4). In this case, the 0.024 pm particles are present in relatively low
concentrations (^5 x 10 cm"-) and show an increase in concentration about 13 km
(<1 hr travel time) downwind of the stack (Fig. 4-4a) white the 0.55 pm particles
reach a peak concentration at about 2 km (^10 min travel time) from the stack
(Fig. 4-4b). As we have seen, the relatively high concentrations of particles in
the second and third modes in the Four Corners plume enhance the rate of coagulation
of the small particles. As the concentration of 0.55 pm particles decreases,
primarily by dilution, the 0.024 \im particles begin to increase in concentration
due to g-to-p conversion. The latter increase is more evident at Four Corners than
at Central ia, because of the lower concentrations of the smaller particles in both
the Four Corners plume and in the ambient air.
The data from Central ia on September 22, 1977 (Fig. 4-5) exhibit yet another
situation. Here both the 0.024 pm and 0.55 pm particles decrease in concentration
with distance from the stack in the center of the plume but, near the top and
bottom of the plume, and at travel distances in excess of 12 km M-1/2 hr travel
time) the concentrations of these particles increase with distance from the stack.
This implies that g-to-p conversion in the plume was limited by the rate of
diffusion into the plume of an ambient species (e.g. OH, as suggested by Forrest
and Newman [2]). A diffusion-l imited process may also have been at work at
Centralia and Four Corners on October 19, 1976 and June 23, 1977, respectively,
since the peaks and deficits in particle concentrations seem to be largest at the
upper and/or lower regions of the plume (Fig. 4-2 and 4-4) Hegg et a1 (10)
have shown that reactions involving ozone and nitrogen oxides in power plant plumes
may also be controlled by the rates at which the plumes mix with the ambient air.
More complicated situations are evident on March 30 and April 28, 1976 (Figs. 4-6
and 4-7). On March 30, 1976, the concentrations of 0.024 urn particles in the
plume very close to the stack were below ambient, but after about 10 min travel
time they reached peak values (Fig. 4-6a). The concentrations of both the 0.024
and 0.55 pm particles were below ambient between about 5 and 17 km downwind from
the stack (^20 min to hr travel times) However, beyond 17 km M hr travel
time) both sized particles were present in concentrations above ambient values at
the top and bottom of the plume (Fig. 4-6a, b) The data for April 28 (Fig. 4-7)
also show several changes in the concentration of particles in the plume, with
values sometimes above and sometimes below ambient concentrations.
4-27
The data obtained in the plume from the Four Corners plant on June 24 and 25, 1977
(Figs. 4-8 and 4-9) show similar trends. The 0.024 \im particles exhibit a peak
concentration downwind (^6 km) of the stack. The 0.55 pm particles show lobes of
peak concentrations above and below the center of the plume. On June 24 the 0.024
and 0.55 urn particles reached peak values at about 30 and 80 mins travel times,
respectively, from the stack (Fig. 4-8) while on June 25 the peaks in the concen-
trations of both the 0.024 and 0.55 pm particles occurred at a travel time of
about hr (Fig. 4-9). By contrast, on June 29, 1977, the concentrations of both
the 0.024 and 0.55 pm particles in the plume of the Four Corners power plant
decreased with increasing travel time (Fig. 4-10)
It is clear from the measurements shown in Figs. 4-2 through 4-10 that the concen-
trations of various sized particles in plumes can vary in a variety of ways. In
Section 6 we will present the results of numerical model calculations for several
of the fl ights described above in an attempt to unravel in more detail the mech-
anisms responsible for the observed variations in the particle spectra in the
plumes.
GAS-TO-PARTICLE CONVERSION
Gas-to-particle conversion rates deduced from our field measurements, using thethree techniques described in the previous section, are summarized in Table 4-5.As might be expected, the values obtained from the various techniques sometimes
disagree by quite large amounts. Some of these variations may be real (e.g. dueto the different spatial averaging of the measurements; also the flash volatiliza-tion technique measures only sulfur oxidation, while the total aerosol volume
technique measures the total rate of g-to-p conversion and the Aitken nuclei
method measures only conversion products which form new particles) However,the discrepancies are also within the range of the experimental errors since we
estimate the uncertainties in computing g-to-p conversion rates by the filter-
flash volatil ization technique to be +/-100%, by the aerosol volume technique torange from less than a factor of two up to a factor of five, and by the Aitken
nucleus production rate technique to be an order of magnitude. In the last
case, the error is largely due to the uncertainties in our derived values of thecoagulation coefficients, which we estimate to be a factor of five.
If we assume that the conversion rates deduced from the measurements of the changesin the volume of particles in the plume are upper limits for g-to-p conversion,
it can be seen from Table 4-5 that this conversion rate is generally equivalent
4-28
Table 4-5
SUMMARY OF GAS-TO-PARTICLE (g-to-p) CONVERSION RATES DEDUCED FROM THE FIELD MEASUREMENTS
Date
October 31,
5, 1975
March 16, 1976
30. 1971iro1^3 8, 1976
19, 1976
September 22. 1977
18,
20, 1977
23, 1977
24. 1977
29, 1977
Power Plant
8.1
Hater VaporPressure
(nib)
8.3
7.6
10.9
6.2
7.0
5.4
9.1
9.7
DiffusFactor
0.2
2.3
2.9
1.8
0.9
ion(")
RelativeHumidity
(I)
71
83
66
60
66
63
56
50
25
38
33
U1
(J
2.15
7.2
travadiam-2
43.0
30.0
35.8
8.6
.8
63.1
12.0
iolctfinnS-1)
Travel TimeFrom Stack
(min)
33
28
18
55
45
72
85
88
52
Dedu<CoaguliCoeffl.
(cm31.2
1.4
1.5
3.7
2.3
.0
4.4
6.8
1.5
2.0
~editioii:ientS-1).
10-10-810-810-810-910-8in-910-910-9
10-810-910-9
g-to-pConversion Ratefrom Filters and
Flash VolatilizationTechnique( S0,/hr)
0.9
0.008
0.014
g-to-Conversiorfrom ChancParticle VolumeUsing Raw Data
(I SO^/hr)*
.4
0.19
0.2
0.08
0.11
0.08
0.03
5.4
2.2
1.8
PRatein
g-to-pConversion Ratefrom Change in
Particle Volume UsinqFitted Volume Distrib.
(i SO^/hr)
0.19
0.19
0.03
0.34
Productionof Aitken(number
19
65
W
20
26
189
14
Rateuclei
s-1)
g-to-pConversion RaBased Aitki
Nuclei Product(t S0;/;,r)
0.008
0.04
0.002
0.12
0.03
0.008
0.03
0.06
0.007
0.02
te
ion
These conversion rates based the assumption that the g-to-p conversion product is sulfurc acid formed from SOg oxidation.
to a few tenths of one per cent of SO^/hr (or less) in the plume from Central ia
power plant, but at the Four Corners power plant it is generally on the order of
a few per cent per hour. These values are comparable to those measured by
Forrest and Newman (2J Gill am et a1 (4_) and Cantrell and Whitby (_7). However,we wish to stress that the actual magnitudes of the conversion rates shown in
Table 4-5 are quite sensitive to the assumption that the excess aerosol volume
produced in the plume is H^SO^. If it is partially composed of nitrates or
organics, the actual SO^ conversion rate (as distinct from the equivalent SO?conversion rate shown in Table 4-5) will be substantially lower. Even if the
g-to-p conversion products were (NH,)?S(L rather than H?S(L the g-to-p conversion
rates would be lower by ^25%.
It is tempting to attribute the higher g-to-p rates at Four Corners compared toCentralia to the greater intensities of ultraviolet light in New Mexico comparedto Washington State: however, our measurements of the g-to-p conversion rates atCentralia show no correlation with UV intensity. Furthermore, it should be notedthat the particle emission rate from the Four Corners plant is about 3.3 x 103
-1 ?kg hr while that from the Central ia plant is only 6 x 10 kg hr Forrest and
Newman have suggested that higher particulate loadings might produce higher g-to-pconversion rates. Clearly, however, neither our data set nor those of other
workers are yet large enough to determine with any certainty which factors are
primarily responsible for controlling the g-to-p conversion rate in lower plant
plumes.
4-30
Section 5
A NUMERICAL MODEL FOR PLUMES
INTRODUCTION
In Section 4 of this report we have presented the results of airborne measurements
of particle size distributions and gas-to-particle (g-to-p) conversion rates in
the plumes from two large, coal-fired, electric power plants. These measurements
reveal a number of important features concerning the evolution of particles with
travel time in power plant plumes; they also demonstrate the complexity and
variability of this evolution. In this section we describe a numerical model
(referred to as PHOENIX) designed to simulate many of the physical and chemical
processes which play a role in determining the evolution of particle size distri-
butions in power plant plumes.
BACKGROUND
Most efforts at modeling power plant plumes have been concerned with trace gas
reactions [e.g. Tesche et a1 (19); Lusis (2^) Hegg et a1 (TOh Gillani (21)to mention only a few]. To our knowledge, no models have been described in the
literature in which an attempt is made to simultaneously and quantitatively
simulate particle interactions, qas-to-particle conversion and gas reactions in a
power plant plume as it interacts with the ambient air.
Several workers have considered particle interactions in the "natural atmosphere
and in urban plumes. For example, Friedlander (22) considered a one-dimensional
model in which the size distribution of particles in the atmosphere was determined
by coagulation and gravitational settling. The results of these calculations pro-
vided a theoretical basis for Junge’s power law distribution [Junge (23j] and the
basic similarity in time and space of the shapes of particle size distributions
in the atmosphere. Middleton and Brock (24_) developed a fairly complex one-
dimensional model which considered the effects of coagulation, homogeneous
nucleation and heterogeneous condensation on an initial particle size distribution.
Homogeneous nucleation was assumed to be produced by a single equivalent chemical
species. The effects of the various processes on changing the particle size
distribution could be seen in the 20 min of model time for which the calculations
were performed.
5-1
Sheih (25) formulated a three-dimensional model which considered the effects of
coagulation, gravitational settling and diffusion on particles in an urban plume.The ambient concentration of particles was assumed to be zero. This model con-
siders the concentrations of six discrete sizes of particles ranging from 0.001
to 100 urn in diameter. The results of the calculations revealed the importance
in the coagulation process of particles larger than pm interacting with small
(<0.01 urn) particles. Finally, Peterson and Seinfeld (26) derived a solution to
the analytical steady-state three-dimensional diffusion equation for particles
and gases in a plume. This model included the gravitational settl ing of particles
but not coagulation, except as a first-order term which created particles from a
gas species; the effect of this conversion on changing the total concentration of
particles was also considered. The size distribution of particles was not con-
sidered in this model and the ambient particle concentration was assumed to be zero.
DESCRIPTION OF THE PHOENIX MODEL
Our three-dimensional numerical model of power plant plumes allows for the effectsof g-to-p conversion, advection, diffusion, coagulation, gravitational settl ing
and interactions with the ambient air, on the evolution with time (or travel
distance) of the particle size distribution in a plume. The model provides
predictions of the size distributions of particles and the concentrations of tracegases in a plume as a function of travel time from the stack.
We give here a relatively brief description of the main features of the model for
a detailed description the reader is referred to Eitgroth (27). The model consists
of two main sections: one is concerned with trace gases and the other with
particles. An overview of the processes considered in these two sections, and
the interactions between them, is shown in Fig. 5-1
Trace Gas Section of Model
The steady-state concentration c. of a trace gas i at any point in a plume is
determined from the continuity equation:
3 3c 3 3 r 9c. -i
s/^ ^ z 1 4 b,^j (^-Dm=\ w=1 j=1
where Xp x^ and x., are the three Cartesian coordinates (x-, along the axis of the
plume, x^ perpendicular to x-, and in the horizontal plane, and Xo the vertical
5-2
GAS SECTION PARTICLE SECTION-A^
^TRACE GASAT TIME(22 OF THEM)
fADVECTION INIX-DIRECTION
( PLUMEI DIFFUS ION
/HETEROGENEOUS/ GAS-TO-
1-^ PARTICLE\ CONVERSION\^ (S02 ONLY)
^
HOMOGENEOUSGAS-TO-PARTICLE
CONVERSION(SOg ONLY)
/REACTIONS WITH\I OTHER GASES_}
MONO-DISPERSED(UNCHARGED)H2S04DROPLETS(0.014 ^mDIAMETER)
t= +
1--^
((
c
At
AMBIENT(UNCHARGED)PARTICLESAT TIME
(3 LOG-NORMALSIZE
DISTRIBUTIONS)
"ADVECTION IN^\^X-DIRECTION )
PLUME ^\DIFFUSION J^1;RAVITATIONAL\SETTLING )
COAGULATION \.
MEASURABLE PROPERTIES(SIZE DISTRIBUTION, b, ETC.)OF CHARGED AND UNCHARGEDPARTICLES AT TIME At
(
UNCHARGED ORCHARGED
PARTICLES FROMSTACK AT TIMEt(3 LOG-NORMAL
SIZEDISTRIBUTIONS
\^ADVECTION IN ^X-DIRECT10N
f PLUME
^ DIFFUSION
\
/GRAVITATIONAL^
^ SETTLING ^
"^COAGULATION’
)
)
+
AMOUNT OFSOOT SURFACEAREA AVAIL-ABLE FORHETEROGEN-EOUS GAS-TO-PARTICLECONVERSION
At
/TRACE GAS AT\TIME * At
Figure 5-1 Schematic of the processes considered in the PHOENIX plume model
coordinate), Vi and Vo are the horizontal components of the windspeed and V-, is
the vertical windspeed (i .e. updraft) R. the rate of change of c due to chemical’2’ "^,
transformations, and k the eddy diffusivity coefficients.t/"’
Since the plume is aligned along the direction of the horizontal wind, V? 0.
In our case studies we have also assumed that Vo is zero, since the atmospheric
stabilities were neutral to stable. Hence, the only component of V in Eq. 5-1
is the horizontal wind V-, at the height of the plume (which can be determined by
tracking a pilot balloon or from measurements aboard an aircraft)
Determination of the eddy diffusivity coefficients is based on the theoretical
work of Brutsaert (28) who found that when the mean wind is along Xi the non-zero
components of the eddy diffusivity tensor are k^ k-^ k.p k^ and k,. and that
these coefficients can be expressed in terms of the vertical eddy diffusivity
coefficient (k^, or k^ in the simpler, conventional terminology) In all of the
case studies presented in this paper we have taken values of k given by Ageeet a1 (29) for a neutral to stable atmosphere.
The concentration of a trace gas at any point in the initial grid is determined
by adding the "plume" concentration (which is assumed to fall off exponentially
from a maximum concentration at the center of the plume to essentially zero
concentration at the edges of the plume) to the "ambient" concentration (which is
assumed to fal off exponentially from a maximum concentration at the edges of
the plume to essentially zero concentration at the center of the plume)
The source (or sink) term R. in Eq. 5-1 is due to in situ production (or destruction)’?/
of the chemical species i. Up to twenty-seven trace gases and thirty-seven
chemical reactions are considered in the PHOENIX model These are listed, together
with current best-estimates of the rate constants, in Table 5-1 Trace gases may
be converted into particles by heterogeneous and homogeneous reactions. The only
heterogeneous reaction presently included in our model involves SOn reacting on
the surfaces of soot particles (Fig. 5-1 Based on data given by Novakov (30)and Rosen (31 we assume that 25% of the available surface area of sub-micron
particles emitted from the stack of a power plant is active in this respect, and
that the reaction is quenched as this surface area is progressively used up by the
deposition of sulfate. In all of the cases described in this report the g-to-p
conversion rates due to this heterogeneous mechanism were less than 0.001% of SOnper hour. Particles (actually droplets) are also allowed to be produced by
5-4
Table 5-1
TRACE GAS REACTIONS INCLUDED IN THE PHOENIX PLUME MODEL
Input Trace Sas Species: SO;. OH, H;0, NO, UNO;, NO;,, Og, N03, HO,
H;SO,, N;05, SO,’, HC, 0, (Hydrocarbon radical, e.g. Wy CH^CO),
RO;, RO, RONO, RO*, H, H;0;
Reaction
SO; OH M HS03 M
OH NO M HNO; H
HNO; h NO OH
NO, OH M HNOj M
HNO, hu NO; OH
KNO; OH HO; H;0HNO, OH N03 H;0NO 03 NO; 0;
NO; 03 N03 0;
NO, HO; HNOj 0;
KO N03 2NO;
NO; N03 N N;0g M
SO; Ap SO;’ (Ap 251 of
surface of sub-micronparticles emitted from stack)
HC 03 HC’
Rate Constant
4.4 10’32 cm6 s’1 no1ec-
9.2 10’31 cm6 s’1 molec"25.0 10"4 s"1 ( <485 nm)
1.5 10’30 cm6 s"’ molec-23.4 )0"7 s"1 U <546 nm)
10’12 cm3 s’1 molec"18.9 10’14 cm3 s" molec’
1.5 )0-14 cm3 s’1 mo1ec’13.1 10’17 cm3 s’1 mo1ec"’
10’12 cm3 no1ec-
7.4 10-12 cm3 s"1 mo1ec"12.8 10-30 cm6 s-1 mo1ec-210-’6 10-20 cm-2 s-’ mo1ec-
10-’6 10-20 cm3 s-1 mo1ec-1
Reference
Calvert et al. (32)8au1ch pt a1. (33)Crutzen (34)
Baulch et al. (35)Crutzen (34)Demerjian et al. (36)
Margltan et al. ( 3
Hampson (38)Hampson and Garvin (39)
Oeraerjian et a1. (36)Demerjian et a1. (36)Baulch et_ a]_. (35)Derived from Novako<(30)Rosen (31) and ForreTC"and NeAian-(2)Huie and Herron (40)Stedran and Niki FT^Y)
HC 0 HC’
HC OH HC’
0; RO;
RO; 0; RO 03RO NO RONO
RONO hv RO* NO
RO* 0; R’O HO;
HO; HC R’O R;CO
0; M HO; H
HO; NO OH NO;^0; 0; RO 503’’’SO; HO; OH S032HO; H;0; 0;20H H H;0; H
20H H;0RO NO; RONO;
RO; RO; XXX (non-reactie)
RO SO; ROSO;+ROSO; hv S03RO; NO NO; RO
H;0; hu 20H
10-1210-12
10
10-1610
10-6-1.6
10-’55.5
1.7
4.4
8.7
3.1
2.5
1.7
1(
3.3
10’15 cm3 s’1 mo1ec’1Fast
II
3.3
10-’5 cm3 s-1 molec-110-15 cm3 s-1 molec-’
-13 en,3 s-’ mo1ec-1cm3 s-1 nolec-’ (?)
r3 cm3 s-1 mo1ec-110-13 s-1 (?)
10-17 cm3 s-1 molec-1cm3 s"1 molec-110-32 cm6 s-1 mo1ec-210-13 cm3 s-’ molec-’10’15 cm3 s-1 mo1ec’110-16 cm3 s-1 nolec-1)0’12 en3 s-’ nolec-210-31 en6 s-1 mo1ec-210-12 cm3 s-’ motec-1)-13 cnV mo1ec-110-’3 cm3 s-1 mo1ec-1
D-’3 cm3 s-’ nolec-110-6 s-’ (i <536 mi)
Herron and Huie(42)Atkinson and Pitts (43)Denerjian et a1. (36)
Oemerjian et a1. (36)
Demerjian et a1. (36)Demerjian et a1. (36)Hampson and Garvin (39)
Lloyd (44)Walter et a1. (45)Payne et a1. (46)Lloyd (44)Trainor and Rosenberg (47)Baulch et a1. (33)Denerjian et a1. (36)Parkes et a1. (48)Calvert et a1. (32)
Crutzen (34)Crutzen (34)
These the first steps in the homogeneous reactions leadingto the production of H,SO,. The next txo steps
503 H;0 (vapor) "S03 (fast)
HS03 H;SO, (complex process, but fast)
5-5
homogeneous reactions involving SOn to produce HpSO^,. Based on the laboratorystudies of Luria et a1 (16) and Kocmond and Yang (49J we assume that these
reactions produce monodispersed HpSCL-solution droplets 0.014 pm in diameter which
are in equilibrium with the ambient relative humidity and temperature. Possible
g-to-p conversion reactions involving trace gases other than SO,, are not considered
in the model
Particle Section of Model
In considering the evolution of the particle size spectrum in a plume, the
diffusion and advection of the particles are treated in the same way as for thetrace gases. In addition, the particles are allowed to coagulate and to settleout under gravity (see Fig. 5-1 The general equation for the number density of
particles n [= dN/d(1nv) where dN is the total concentration of particles with
volumes between In v and In v + d (In v)] is therefore:
8n ^ 3(v^ n) ^s n) ^ ^ fr ^ r a -i l"n \ m s r c /c i\
^+ L ~^- -^x- c + s + ^ 2.j 37- k \w^\ r ^-^m-\ m 3 m=1 j=1 \\_ wj L jJ
where Vg is the gravitational settl ing speed (or sedimentation velocity) for a
particle of volume v, C the rate of change in the number density of particles of
volume v due to coagulation, S the rate of generation of particles of volume v
due to g-to-p conversion, and the other symbols are as previously defined.
In order to solve Eq. 5-2 without excessive use of computer time, and for
mathematical simplicity, it is helpful to use an assumed particle size distribution
function. Then by integrating Eq. 5-2 over all particle volume v, the equation
becomes a set of equations for the moments of the particle size distribution
functions, rather than for n. These moments are functions of time and position
in the plume. An inversion technique can be used to obtain n from the moments.
The Particle Size Distribution Function. Eq. 5-2 contains five independent
variables (x-, x^, x-,, v and t) We now write:
n (x^, v, t) =Z^ ^ (v; o^, ^. y^) (5-3)
where 6. is the particle size distribution function and the parameters a., @. and1- t’
y. (which are functions of x and t) depend on the exact forms of the particleTTl
size distributions which contribute to (j)"Z/
5-6
We have seen in Section 3 that the particle size distribution can be described by
three modes (indicated by i 2 and 3) each of which is described by a log-
normal distribution. In this case a. is the natural logarithm of the geometric
standard deviation, @. the geometric mean particle volume (v ) and y. the totalth
number concentration of particles N for the i mode. Hence:’z’
^ (v; "z’ h- ^N.i,
^\ Ct.Vi.
exp r ?
^ ^vv-)gz /(5-4)
+h
The r moment of the -i mode is defined by:
/*
Y^ (r) v’" (t^(r)dvJo(5-5)
from which it can be seen that N is the zeroth moment y. (0) of the i mode.7/ "^
From Eqs. 5-4 and 5-5:
^ (r) N.
^ Ct.’L-f/ v*"" exp
9 2Za.z
,^ ( v )1\i l\ dv (5-6)
By substitution of variables (u In v) and completing the square of the argument
of the exponent in Eq. 5-6, we obtain:
/c^ r2\ (>") N v^ exp (5-7)
Substituting r and 2 in Eq. 5-7 and solving for a. and v yields:f g’z-
a. Inz,
N, \ WY,2 (1 )^
(5-8)
v-___^ ^V_.
^ N .3/2 ^2 (2)^i- ’t-
5-7
(5-9)
From Eqs. 5-6 5-9:
2
Y, (r) (N,)1 ^ ^ Y, (1
2r r2 r -)
k (2).
l ^2 r-2 r 2
(5-10)
Eqs. 5-8 5-10 may be used to determine a., v_ and the r moment of the particle’2’ y1’
size distribution function if the first three integer moments of the distribution
are known. The latter are obtained as follows. Eq. 5-2 is multiplied by v and
integrated over v from 0 to ; using Eq. 5-5 for r 0, and 2 el iminates the
particle volume v dependence. Each particle mode is then described by three
equations, which can be used to determine y .{r) for r 0, and 2. It should be7/
noted that we integrate v from o to instead of over a finite interval however,
this assumption introduces an error of less than 5% in y for each mode.
In order to integrate Eq. 5-2 over v, the form of V V S, C and k must betj’11
restricted. The restriction we apply is that:
P(x^. v, t) ^yP^ P(x^, t; r) (5-11
where P represents V^, V^, S, C or k.^
and p(r) is the power of v for the r^term. The parameters which are represented by Eq. 5-11 are, in fact, modeledfairly realistically if an appropriate number of terms in the expression of the
right-hand side of Eq. 5-11 are used.
Dropping x and t in the notation, using the fact that V is not a function of vm mbut only of x and t, and defining:
V,(v) Z ^a{r) V^(r)Sz
k (v)= V v^^k (r)^(^l3m’ ^ 3-m’
(5-12)
(5-13)
Eq. 5-2 becomes
nM . y 8V. "^ y ^Mv^^v)s"(xi + yat t-’^t ~.i 8^ z" 8X3(5-14)
3 3 ,c(r),C(v) - S(v) . Z Y Z k, (r) ^-^
r .=1 ,-1 9X. P"5-8
sx.
For further ease" in calculation, two more assumptions are made. We assume the
plume is in a steady-state condition, so that:
9n(v]3 t 0 (5-15)
and that the air is incompressible:
I 9V_m
^ 9xm=\ m
0 (5-16)
If we define:
/S(r) =/ ^ S(v)dv
J
C(r) =/* ^ C(v)dv’
(5-17)
multiply Eq. 5-14 by v^ (5. 0, 2) and integrate over v and use Eq. 5-5,
we obtain:
3 9y, W 9V (r)y, [&+a(r)]V v v ----\---- c. <0 + s .(&)
^ w 9x ^ 8X3 z’ i’
m=1 r(5-18)
3 3+ y y y 9 k (r)L L L 37- jw’
r m+1 j=1 m
9Y^ |>c(k)]
9x-z,
where A 0, 2 for each i mode.
Now the moments of the ^th mode can be found by solving the three equations
defined by Eq. 5-18 and these moments can then be used to determine the parameters
N a. and v., for each mode.i -z- gi
The PHOENIX model solves Eq. 5-18 for i 2, 3 and A 0, 2 for both the
ambient and plume particles. This gives a total of 18 equations to be solved at
each grid point in the plume.
5-9
The following sections give brief descriptions of the terms in Eq. 5-18.
Advection. The windspeed is along the axis of the plume. Also the windspeed is
assumed to be constant in speed and direction. Therefore, the advection term in
Eq. 5-18 is simply:
9^ W’~\ 9X^ (5-19)
Sedimentation. The sedimentation velocity V is found from the use of Stokes’
formula together with the Cunm’ngham correction factor [see, for example, Fuchs
OS)]:
Vs -t^ Cu (5-20)
where, p is the particle density (assumed to be 3 g cm g the acceleration due
to gravity, D the particle diameter, n the viscosity of the air, and Cu the
Cunm’ngham correction factor which is given by
Cu + ^- [l .23 + 0.41 exp (- 0.44 ^-)1 (5-21
where X is the mean free molecular path. We use values for n and \ from the U.S.
Standard Atmosphere. Eq. 5-21 is expanded in order to express V as a polynomialt-h
of the form of Eq. 5-12. The number of terms in the polynomial for the z modeis determined by the values of a. and v
T/ >yu
Generation of Particles. The rate of generation of particles by g-to-p conversion
is inputted into the particle section of the model from the trace gas section as
described in the Trace Gas Section above.
Diffusion. The concentration of particles at any point in the initial grid is
determined in a similar manner to that described previously for the trace gases,
namely, by adding "plume" and "ambient" particle concentrations. Since the eddy
diffusivity tensor is assumed to be independent of particle size, r in Eq. 5-13
has a value of and c(r) 0.
5-10
Coagulation. A schematic of the particle interactions by coagulation which are
considered in the model is shown in Fig. 5-2. Particles in each of the three
modes, both in the plume and the ambient air, are allowed to coagulate with
particles within their own mode and with particles in the other two modes.
The gain in number density of particles of volume v in the z mode due to
coagulation with particles of volume u in the 3 mode is given by:
-vG. .(v) 6. .(u,v-u)*.(u)0 .(v-u)du (5-22)t3 J Q
where B. is the coagulation coefficient, which satisfied the relations:’Z-J
B.,(u,v) f5, ,(v,u) B ., (v,u) l 0 (5-23)t-tV "<1
and, for uncharged particles [Fuchs (18)3:
"1 + A 2^_ + ^2A_
^,(u,,) ^ (D, . D,) -^ .-^ , (5-24)
where D-, and Or, are the diameters of particles of volumes u and v in the i and
3th distribution, A is .23 (from the Cunningham correction factor) and 6 is the
correction factor, given by Fuchs, which is a function of D^ and D^. The S factor
has a value of between ^0.25 to for particles with diameters larger than ^0.01 urn.In our model calculations we assume that 2<5 is unity. Since 6 approaches for
the larger (Q\) particles, this simpl ification will result in an underestimate
of the effects of coagulation for these particles. For D 0.01 pm, & 0.5 and
our simplification is, in fact, accurate. For D 0.01 pm, 6 10" however, the
number concentration of particles of this size falls off very rapidly when a log-
normal distribution is used to describe the particle spectrum. Hence, the effect
of these very small particles on coagulation is negl igible anyway. In our studies,
the average geometric mean diameter of the peak concentration of mode particles
was 0.006 pm which is in the region where 26 ^
The decrease in the number density of particles of volume v in the i mode due to
coagulating with particles of volume u in the 3 mode is given by:
L .(v) /* B. .(u,v) (b.(v)(b .(u)du (5-25)ij / o
5-n
THREE LOG-NORMAL SIZE DISTRIBUTIONSFOR BOTH PLUME AND AMBIENT AIR AT X. Y. Z
/ COAGULATION OF(MODE WITH MODE 2V PARTICLES
/ COAGULATION OF( MODE WITH MODE 3V PARTICLES
/ COAGULATION OF( MODE 2 WITH MODE 3\. PARTICLES
/ COAGULATION OF \MODE PARTICLES
\ WITH EACH OTHER /
/COAGULATION OF ^MODE 2 PARTICLES\WITH EACH OTHER /
/^COAGULATION OF ’\( MODE 3 PARTICLES )\WITH EACH OTHER/
SIZE DISTRIBUTIONOF MODE PARTICLES
(D ^ 0.01/zm)
SIZE DISTRIBUTIONOF MODE 2 PARTICLES
(0.01/Am^. D S, l^m)
SIZE DISTRIBUTIONOF MODE 3 PARTICLES
D ^, l^.m)
Figure 5-2. Schematic of particle interactions by coagulation considered in the PHOENIX plume model
If @. .(u,v) is expressed as a polynomial of the form of Eq. 5-11 G .(&) and’z’j
L. .(&) are defined as:1-3
G. .(&) [ ^ G .(v) dv ^-^^3 J Q ^3
/L. .W } ^ L .(v) dv (5-27)
-t-3 J Q -z-J
and use is made of Laplace transforms and the convolution theorem, both G^ .(^)
and L .(&) can be expressed in terms of the function M, .[f(u,v)] which is defined
by:
r rM. .[f(u,v)] / f(u,v) B. .(u,v) 4) .(v) ((>,(u)dudv (5-28)1^3 / / ^3 3
The function of M. .[f(u,v)] is symmetrical hence:t’3
M^.[f(u,v)] M^[f(v,u)] (5-29)
The coagulation term C in Eq. 5-2 for the three particle modes may now be written
as:
C^ (v) \ G^ (v) L^ (v) L^(v) L^(v) (5-30)
C^v) ^ G^(v) + G^(v) L^ (v) L^(v) L^(v) (5-31
C3(v) ^ G33(v) + G^(v) + G^(v) 1-3^) i^(v) 1-33^) (5-32)
In the case of charged particles from the stack, the charge q acquired by a
particle of diameter D in passing through a field Ep in an electrostatic precipi-
tator is given by [White 50)]
q ^ E,D2 (5-33)
5-13
For charged particles the coagulation coefficient P. given by Eq. 5-24 is
multiplied by:
^12^TT^ {^e \c.
for particles with like charges, and by:
A12-^12
^12E ---^To (5-35)
e
for partic les with unl ike charges, where
2lq^ q
’12 (D/+ D^k^12 (D. + DjkT (5-36)
k being the Boltzmann constant and T the temperature. In the case of coagulationbetween a charged (plume) particle and an uncharged (ambient) particle, the ambientparticle is assumed to acquire the image charge of the plume particle.
Inputs and Outputs for the Model
General Inputs. General inputs to the model include an atmospheric sounding ofhorizontal winds, temperature and humidity, and the eddy diffusivity coefficientin the vertical which is determined by atmospheric stability [see Agee et a1 (29)].The number of grid points in the vertical and horizontal planes and the farthestdistance downwind for which computations are required must also be specified.
Trace Gas Section. The input parameters required for the trace gas section arethe concentrations of the trace gases emitted from the stack and in the ambientair. For the case studies described in this report, the stack source strengths of
SO^, NO, N0^ and H^O (vapor) were deduced from airborne measurements of the totalfluxes of those gases measured in the plume at about km downwind of the stack(they could also be obtained from in-stack measurements, if available) None ofthe other trace gases listed in Table 5-1 were assumed to be emitted by the powerplants. Trace gases in the ambient air (which are held constant for each particularrun of the model are mixed into the plume through the eddy diffusivity coefficientsin Eq. 5-1 In our case studies the ambient concentrations of SOo, NO, NO,,, 0-,
and H^O (vapor) measured from the aircraft were used as inputs to the model theambient concentrations of the other trace gases isted in Table 5-1 were assumedto be within the ranges listed in Table 5-2.
5-14
Table 5-2
RANGES OF CONCENTRATIONS OF TRACE GASES IN THE AMBIENT AIRUSED IN THE PHOENIX PLUME MODEL RUNS DISCUSSED IN THIS REPORT
Range of ConcentrationsTrace Gas (molecules cm’3) Reference
OH 106 107 Crutzen (51), Davis (52)
HNOo 2 x 107 3 x 108 Crutzen (51)
HNO. 106 2 x 1010 Crutzen (51)0
NO. 0 2 x 1010 Spicer {53), Bach (54,)
HO. 3 x 106 4 x 108 Crutzen (51)
H SO. 0 2 x 1010 Tanner et a1 (55)
N.Oc ^ 1010 2 x 1012 Heicklen (56)C. 3
SO" 0 6 x 1010 Bach (54)
HC ^ 6 x 1013 Bach (54)
0 10"2 (for O1^) Levy {57)
R 0
RO 102 Harrison (58)
RO 0 1012 Heicklen {56)
RONO 0
RO* 0
H 0
H o 106 5 x 1010 Crutzen (51)
5-15
The output from the model consists of the concentrations of each of the tracegases listed in Table 5-1 at various points in the plume.
Particle Section. A representation of the size distribution of particles at a
known point at the center of the plume and close to the stack must be inputted tothe model In our case, these measurements were obtained from the aircraft flyingin the plume at about km downwind, however, a particle size distribution could
also be obtained from measurements made in the stack. The size distribution is
represented by the total number concentration of particles (N .) the square of thenatural logarithm of the geometric standard deviation (a.) an^ the geometric meanvolume (v^) of each mode [i 2, 3) If there is an electrostatic precipitatorin the plant, the applied electric field should be inputted to the model Theparticle size distribution in the ambient air at the altitude of the plume mustalso be inputted. In addition, a scale height (i .e. the height required for adecrease by a factor of e in the number concentration) for the ambient particlesin each mode must be specified.
Outputs from the particle section of the model consist of the size distributionsof particles (represented by total number, geometric standard deviation and
geometric mean volume of each mode) and g-to-p conversion rates at various pointsin the plume. Other properties of the plume, which depend on the particle dis-tribution, may also be outputted. For example in the next section we show valuesof the iqht-scatterinq coefficient (at a wavelength of 550 nm) at various pointsin the plume.
The general formula for the light-scattering coefficient b is [van de Hulst (59^)]:
^ -r ^cat "(D) 4- dD/ 0
(5-37)
where Q^g^ is the scattering efficiency of particles of diameter D. In thepresent version of the model all particles are assumed to be non-absorbers and
^scat is 9^" by’
^cat 2 ^ sin p + -\ (1-cos p) (5-38)
where
p2DTT lp-1
(5-39)
5-16
where p is the refractive index of the particles (assumed to be .5) and \ the
wavelength of the radiation. Absorption of radiation by the particles could be
taken into account in the model if their imaginary indices of refraction were
known.
Solution Techniques
Eq. (5-18) is highly non-linear and each of the eighteen equations of the type of
(5-18) which must be solved at each point in the grid is coupled to the other
equations through the coagulation term. This degree of non-linearity and coupling
is difficult to solve by any elegant scheme. The technique used in the model is
the simplest available, namely, that of finite differences. Except for the ad-
vection term, all the terms in Eqs. (5-1 and (5-18) are evaluated at each point
iin the plume. This gives an equation of the form:
SY, WV T"1 9x^
(5-40)
where the left-hand side is just the advection term and the right-hand side is the
sum of all the other terms in (18) Simple finite differencing then gives
T Ax,
[Y, W\ [y, W\ ^ -^-(5-41
where the subscripts 0 and n represent respectively the old and new values of
y. (&) and AXi is the distance downwind of the stack traveled by the plume in at’
time step At.
The time steps used in the calculations discussed in this paper were checked for
stability by running parts of the program with quarter time steps. There was no
appreciable difference in the outputs from the different time steps.
The minimum time step allowed is 0.5 s and the maximum is 300 s. The time step
for the next downwind grid is determined by keeping the magnitude of the largest
rate of change of all the y. (&) ’s to less than one quarter of Y^ (&) pe^ time
step. The maximum increase in time step is a factor of 2 between any one grid
and the next.
5-17
Section 6
COMPARISON OF MODEL RESULTS WITH MEASUREMENTS
INTRODUCTION
In this section we compare the predictions of the PHOENIX plume model with the
airborne measurements of particle size distributions, g-to-p conversion rates,
light-scattering coefficients and total concentrations of particles in several of
the plumes described in Section 4. Apart from one of the case studies presented
below (Four Corners, June 25, 1977) the model predictions were essentially the
same whether or not the particles in the plume were considered to be uncharged or
charged.
The input data for all of the case studies to be described are given in Table 6-1
The table is presented in a form which aids comparison with the parameters given
in Tables 4-1 and 4-2. The parameters in Eq. 5-4 are related to those in Table
6-1 by:
a, 1n a (6-1z. g-z-
TT 3^gi 6" gNz (6-2)
MEASUREMENT-MODEL COMPARISONS
Central ia; March 30, 1976
Shown in Fig. 6-1 are the excess (above ambient) concentrations (dN/d log D) in
the plume of particles 0.024 and 0.55 pm in diameter predicted by the PHOENIX
model for March 30, 1976, at the Central ia coal power plant. The corresponding
airborne measurements for this case are shown in Fig. 4-6.
Close to the stack (^2 km) the model predicts that the concentrations of 0.024 ym
particles in the plume are less (by ^104 cm"3) than the concentrations of these
sized particles in the ambient air (Fig. 6-1a) This is in good agreement with
the measurements (see Fig. 4-6a). The measurements show the concentrations of
the 0.024 pm particles reaching maximum values (of ^10 cm" above the ambient
va"iues at about 3 km downwind; the model results showed similar maximum values,
6-1
Table 6-1
PARTICLE INPUT DATA FOR CASE STUDIES DISCUSSED IN THIS REPORT’
Plume
Mode
Ambient Hide
Mode
Plume Mode
node
Node
Ambient
Mode
node
Plune Mode
Mode
Mode
Ambient Mode
Mode
Mode
Plume
Mode
Ambient
Mode
Mode
",
(a)
2.795 10’2.527
3.812 10"’
2.075 1051.500
2.004 10"’
(b)
1.159 1071.826 10’2.172 10’’
5.823 1042.306
5.424 10"2
(c)
7.937 1051.524 10’3.909 10"’
3.602 1044.219 10’3.393 10’’
(d)
5.316 I051.430 10’7.066 10"’
3.946 1033.779 1024.697 10’2
a0.
Central la
1.710
1.149
1.357
2.860
1.116
1.176
Central la;
2.918
1.313
1.223
2.392
1.072
1.128
CentraUa
2.441
1.146
1.146
2.310
1.272
1.158
Centralia;
2.059
1.204
1.190
1.988 2.992
1.484
1.104
Power Plant;
4.333
5.060
3.957
4.896
1.014
April 28.
1.476
3.475
4.848
1.164
October 19. 1976
8.365
4.368
1.054
1.074
7.599 10"’1.030
September
1.720
4.382
1.038
1.422
1.127
qNi
10-210-’10-’
10-310-’
1976
10-310-’10-’
l0-210-’
l0-310-’
in-2
22, 1977
10-210-’
10-210-’
1.161 0.4702
5calc Heigh’,.
"o,. (.a)
30, 1976
1.028 10-’5.361 10-’1.130
1.087 10"’ 1.001
5.076 10"’ 2.283
1.097 4.261
4.605 10"24.341 10-’1.116
1.281 10"’ 20.45
4.919 10"’ 5.691
1.216 0.8857
9.122 10-24.618 10-’1.114
8.796 10-2 0.9339
9.040 10"’ 1.218
1.099 1.093
8.225 10"24.859 10-’1.137
1.233 10-’ 1.294
2.269 10"’ 1.086
"i
(e:.
Plume Mode 6.339 103Mode 1.015 10’Mode 2.230
Ambient Mode 3.501 103Mode 6.471 10-2
1.089
Plume Mode 5.020 104Mode 1.603 10’Mode 9.223
Ambient 5.174 103Mode 1.093 103Mode 1.875 10-’
(g) Four Corners; June 25, 1977
Plume Mode 5.049 10s7.993
Mode 5.198
Ambient Mode 4.257 103Mode 9.753 10-’Mode 1.147 10-’
*N. total concen
"sDl S’201"6^1’10
"gNz geometric
moment and Dgv-z,
volume moment, of
g0i "in,
Four Corners Power Plant; June
2.814 2.379 10-21.011 5.667 10"’1.143 1.094
2.784 7,515 10-31.162 5.467 10-’1.200 1.096
2.328 1.666 10"21.137 5.439 10"’1.252 1.076
2.290 2.124 10"21.138 1.093 10-’1.187 1.103
3.14] 2.750 10"31.121 5.368 10"’1.272 1.029
1.831 4.103 10"21.095 5.038 10"’1.366 1.012
tration of particles (cm
standard deviation of particles,
mean diameter of
geometric mean
the i mode.
Scale Height
9i (x>)
23. 1977
5.902 10"25.669 10-’1.154
1.745 )0-’ 2-578
5.850 10-’ 0.5444
1.211 0.3546
1.419 10-’5.715 10-’1.252
10-’ 0.4096
1.149 10-’1.205 -0.6081
1.400 10"’5.582 10"’1.224
1.230 10"’ 0.5509
5.164 10"’ 1.589
1.355 0.6084
the zeroeth
diameter of the
en2
LJQ3
<
700
600
500
400
3005 10 15
DISTANCE FROM STACK (km)
(o
CO2E"
Q=)
<
700
600
500
400
3000 5 10 15 20
DISTANCE FROM STACK (km)
(bFigure 6-1 Excess (i .e. above ambient) concentrations (dN/d log D) of particlesin the plume of the Central ia power plant on March 30, 1976, as predicted by thePHOENIX plume model
(a) Particles 0.024 pm in equivalent diameter (concentrations in units of 10 cm"
(b) Particles 0.55 ym in equivalent diameter (concentrations in units of cm" ).
For corresponding measurements see Figure 4-6.
6-3
but they occurred between about 5 and 15 km downwind. The model results are in
excellent agreement with the measurements at 15 to 20 km downwind in showing0.024 ym particles in concentrations above and below the ambient concentrationsin different regions of the plume.
For the 0.55 pm particles the model predicts excess concentrations above ambient
values (up to a maximum of about 4 cm" out to about 17 km from the stack (Fig.6-1b). The measurements show above ambient concentrations of these sized particles
0
(up to about 6 cm" close to the stack, but between about 7 and 20 km downwind
there were regions in the plume where the concentrations of the 0.55 urn particleswere below the ambient concentrations (see Fig. 4-6b) the model results also showsome below ambient concentrations between about 18 and 20 km downwind.
The homogeneous g-to-p conversion rates predicted by the PHOENIX model for this
case are shown in Fig. 6-2 (the heterogeneous g-to-p conversion rates predictedby the model were essentially zero in all cases) The g-to-p rates are highestat the edges of the plume where they reach a few tenths of per cent of SOo/hr,which is in good agreement with the measured values at Centralia (see Section 4)elsewhere in the plume the predicted values are lower (by about one order ofmagnitude) than the values which we derived from our measurements.
Shown in Fig. 6-3a are the measured and computed values of the Aitken nucleus(i .e. total particle) concentrations at three distances downwind of the plant.It is interesting to note that at 16.7 km downwind both the measured and computed
concentrations are lower at the center of the plume than just to either side of
the center; this is due to the rate of g-to-p conversion (which creates smallparticles) at the center of the plume being limited by the rates at which ambient
trace gases (e.g. OH, OJ can be transported into the plume. The measured and
calculated values of the light-scattering coefficient (b are compared in Fig.6-3b; in this case the agreement between the predicted and measured b ’s is verypoor. The values predicted by the model are high in the ambient air (due to the
high concentrations and the large spread in sizes of the small mode particles)and decrease with time in the plume. The reason why the calculated values of b
are much higher than the measured values is that the particles are assumed to be
non-absorbers; this suggests that the particles in mode are optically absorbing.The decrease of b with time in the plume is due to decreases in the particle
concentrations in mode produced by coagulation of ambient and plume particles
and diffusion of the particles.
6-4
DISTANCE FROM STACK (km)Figure 6-2. Homogeneous gas-to-particle conversion rates (in units of D-1^ 0^^^^ 1n the
plume of the Central ia power plant on March 30, 1976, as predicted by the PHOENIX plume
model (The calculated heterogeneous g-to-p conversion rates were essentially zero.
518 m 457 m0.49 hrs 0.98 hrs8.3 km 16.7 km
ALTITUDE 488mTRAVEL TIME 0.16 hrs
DISTANCE DOWNWIND 2.8 km2.5 x 10^2.5 x 10-’
(a
ALTITUDE 488 mTRAVEL TIME 0.16 hrs
DISTANCE DOWNWIND 2.8 km
2.5 x l0-4.
0(b)
ALTITUDE 457 mTRAVEL TIME 0.19 hrs
01 DISTANCE DOWNWIND 1.8 km
2.5 x 10"4
0(c)
ALTITUDE 671 mTRAVEL TIME 0.12 hrs
DISTANCE DOWNWIND 1.8 km
2.5 x 105
300
300
^y<- ^’^- -^ ~-"
\J
/ ’’- ’/\-;
.^/ ..,
’’
CENTRALIA,
518 m0.49 hrs8.3 km
~\
\\ ;
’^
CENTRALIA,
457 m0.40 hrs3.7 km
/ \
CENTRALIA,
671 m0.25 hrs3.7 km
,-T\~~-
MARCH 30, 1976,
457 m0.98 hrs16.7 km
\\\\
/
MARCH 30, 1976,
457 m 457 m0.60 hrs 0.80 hrs5.6 km 7.4 km
r\\
/ \
APRIL 28, 1976,
671 m0.62 hrs9.3 km
^.-^s^’" ^
AITKEN NUCLEUS CONCENTRATIONS
LIGHT SCATTERING COEFFICIENTS (bg)
457 m 457 m 457 m 457m 457m1.00 hrs 1.40 hrs 1.80 hrs 1.99 hrs 2 19 hrs9.3 km 13.0 km 16.7 km 18.5 km 20.4km
LIGHT SCATTERING COEFFICIENTS (bs)
671 m 671 m0.87 hrs 1.23 hrs13.0 km 18.5 km
-^ ^>
(d) CENTRALIA, OCTOBER 19, 1976, AITKEN NUCLEUS CONCENTRATIONSFigure 6-3 (a-d) Comparisons of measurements (solid lines) with predictedPHOENIX plume model (dashe- lines) of the Aitken nucleus concentrations andcoefficients through plumes along horizontal traverses perpendicular to thethe wind.
values from thelight-scatteringdirection of
ALTITUDETRAVEL TIME
DISTANCE DOWNWIND
2.5 x 10’4
0^
ALTITUDETRAVEL TIME
DISTANCE DOWNWIND2.5 x 105
300
ALTITUDE 1006mTRAVEL TIME 0.23 hrs
DISTANCE DOWNWIND 1.8 km 3.7 km
2.5 x 10’4
0’--
ALTI TUDETRAVEL TIME
DISTANCE DOWNWIND2.5 x 105
/L.
-^-
671 m0. 12 hrs1.8km
1006 m0.23 hrs1.8 km
’ft’^J ^
2134m0.08 hrs0.9 km
-^"^
e)
g) CENTRALIA,
2134m0.67 hrs7.4 km
671 m0.25 hrs3.7 km
CENTRALIA,
1006 m0.46 hrs3.7 km
,-f\-^.-1 \-Ji
CENTRALIA,
1006 m0.46 hrs
-^^
670.69.3
OCTOBER
1006 m0.46 hrs3.7 km
,-fw-U V- s’
SEPTEMBER 22, 1977,
1006m0.46 hrs3.7 km
SEPTEMBE
2134 m0.67 hrs7.4 km
m2 hrskm
19, 1976, Ll(
914 m0.46 hrs3.7 km
i y u
914m0. 46 hrs3.7 km
:R 22, 1977,
2134 m1. 18 hrs13.0 km
.."--^’-
671 m0.87 hrs13.0km
3HT SCAT
1067m0.93 hrs7.4 km
\ J
AITKEN NUCLEUS CONCENTRATIONS
1067 m0.93 hrs7.4 km
LIGHT SC
213^1.1813.0
^-.---~
TE
\^
1.63 hrs
:AT1
f mhrskm
’i ^-^*^’
6
^ING CC
101.613.
1067 m
13.0km
TERING COEFFICIENTS (bs)
71 m23 hrs8.5 km
)EFFICIENTS (bg)
67m 1067m3 hrs 2.55 hrs0 km 20.4 km
-/^-’ w\/~\^
1067 m2.55 hrs20.4 km
(h) FOUR CORNERS, JUNE 23, 1977, AITKEN NUCLEUS CONCENTRATIONS
Figure 6-3 (e-h) Comparisons of measurements (solid lines) with predicted values from thePHOENIX plume model (dashed lines) of the Aitken nucleus concentrations and light-scatteringcoefficients through plumes along horizontal traverses perpendicular to the direction of the wind,
ALTITUDETRAVEL TIME
DISTANCE DOWNWIND
2.5x 10’4
ALTITUDETRAVEL TIME
DISTANCE DOWNWIND2.5 x 105
300
ALTITUDETRAVEL TIME
DISTANCE DOWNWIND
E 2134 m^E 0.08 hrsW 0.9 km
,"’~’’’-~.
(i)
7E 1905 mIE O.I3 hrsID 1.8 km
(j
IE 1905 m<fE 0.13 firsND 1.8 km
FOUR
19a7.
~~-’"y
FOUR
1905 m0.53 hrs7.4 km
2134m0.67 hrs7.4 km
CORNERS,
05 m53 hrs4 km
CORNERS,
2134 m0.67 hrs7.4 km
JUNE 23, 1977,
1905 m0.93 hrs13.0 km
’^^s "-^JUNE 24, 1977,
1905 m0.93 hrs13.0km
213I.13.
LIGHT
1905 m32 hrs
18.5km
AITKEN
190t1.3218.5
^4 m 2134 m9 hrs 18 hrs0 km 13.0 km
SCATTERING COEFFICIENTS (bs)
1905 m1.99 hrs27.8km
// ^NUCLEUS CONCENTRATIONS
? m 1905 mhrs 1.99 hrskm 2>7.8 km
2.5 x 10-4
ALTITUDETRAVEL TIME
DISTANCE DOWNWIND
2.5 x 10’4
(k FOUR CORNERS, JUNE 24, 1977, LIGHT SCATTERING COEFFICIE
E 1829 m 1905m 1829 m 1829 mE 1.85 hrs 1.85 hrs 2.78 hrs 4.63 hrsD ll.l km ll. km 16.7km 27.8 km
FOUR CORNERS, JUNE 25, 1977, LIGHT SCATTERING COEFFICIENTS (bg)Figure 6-3 (i-5,) Comparisons of measurements (solid lines) with predicted values from thePHOENIX plume model (dashed lines) of the Aitken nucleus concentrations and light-scatteringcoefficients through plumes along horizontal traverses perpendicular to the direction of the wind,
Central ia; April 28. 1976
PHOENIX model predictions for this case are shown in Figs. 6-3c, 6-4 and 6-5. (In
this case, no Aitken nuclei measurements were available for comparison with the
model results, therefore, the latter are not shown.
The model results show the concentrations of 0.024 pm particles to be greater than
those in the ambient air at all points in the plume out to 23 km downwind, with
peak concentrations within 3 km of the stack and at about 6 km and 17-23 km from
the stack (Fig. 6-4a) Very similar oscillations with increasing distance from
the stack were measured on this day (see Fig. 4-7a) Both the model results and
the measurements for the 0.55 \im particles show peak concentrations at about 8 and
18 km downwind of the stack, although the peak concentrations predicted by the
model are about an order of magnitude lower than the measurements.
The predicted g-to-p conversion rates (Fig. 6-5) are similar to those for March 30,
1976, with the highest rates at the edges of the plume and a slow increase in the
rate of g-to-p conversion with travel time at the center of the plume.
The ight-scattering coefficients predicted by the model are in reasonable agree-
ment with the measurements in the ambient air, but not with the measurements in
the plume,for travel times up to 0.6 hr (Fig. 6-3c) This is because there were
large numbers of mode particles in the plume (see Table 6-1 which must have
been optical absorbers. However, for travel times greater than about 0.6 hr, the
concentrations of mode particles decreased significantly (due to coagulation
and diffusion) consequently the model results are in much better agreement with
the observations.
Central ia; October 19, 1976
PHOENIX model predictions for this case are shown in Figs. 6-3d, 6-3e, 6-6 and 6-7,
The model results show the concentrations of the 0.024 ym particles in the plume
decreasing steadily with distance from the stack, with no significant local peaks
or concentrations below ambient values (Fig. 6-6a) These predictions are in very
good agreement with the measurements (see Fig. 4-2a) It is interesting to note
that the measured concentrations in this case were about an order of magnitude
larger than is common at Central ia and this is reflected nicely in the model
results.
6-9
800L-0*69 1*88 2*52 2.36 2*73 2*30 2*69 2*54 2*58 2*64 2*76 2*87 3*104
\" ^-*^_* / \ /^ ^" S ~^V)
h-7.544.69^/3.83 /4.51 \ 2.79 M.93 4.89 4.71 4.54 4.18 4.07 4.0N4700^^4.67 / __^
t^. .600h-29.62fl4* 3*63 4*13 2*54 4*71 4*76 4.">5 4"52UJ03
Li 500ha*l 5.’57 *,)3’9ol4.’34/ 3*32 V.4’61 4.41 4*24 4.*>7 4*59 4*51 4*48< L---’4-05 >^y ^.-.----,_________ <4
400 0.302.29 2.44 2.53 2.18 2*46 2*48 2*50 2*50 2*30 2*51 2*682.72
300,0 5 10 15 20
DISTANCE FROM STACK (km)
(a
25
V)
LUQ3
i|-0.01-0.07 -0.03 -0.15 0*t7 0*32 0.24 0*4 0’06
\ 1 /^~^\ \. / /" \-1.24\0.85 0.43 -~-0.03 f2.01\ 0.59 0.29 0.16 0.08
500h
400h3J04
600k.73
<
3000 5 10 15 20
DISTANCE FROM STACK (km)
(b)
25
Figure 6-4. Excess (i .e. above ambient) concentrations (dN/d log D) of particlesin the plume of the Central ia power plant on April 28, 1976, as predicted by thePHOENIX plume model
(a) Particles 0.024 \im in equivalent diameter (concentrations in units of 104 cm’3)(b) Particles 0.55 pm in equivalent diameter (concentrations in units of cm"3)For corresponding measurements see Figure 4-7.
6-10
900
800
/ 03 \. 1 . . . . . .\ . . . . . . . . . . . . . .\ .12.6 0.44 0.26 0.22 0.20 0.29 028 0.45 0.39 036034 032 037 Q43 0.46 0.51 0.56 059 0.66 0.77 0.94 1.14
C/") I ^ -.^ -7nn 0-02 0.070.08 0.090.100.18 0.18 0.360330,32031 0290270.29r0.280.280290.30030Q30031 0.32uu <----^ <^E’Ld 600 *0 0>0 0>0 Q01 ^1 Qo’ 0^2 0102 0102QD2 0<02002^0<S 003 0>03 0<04 OD4 004 0-05 0-05
500 ~0.02 0.07 0^)8 O’lOO’lO O^ O.T9 D37 0.35 033032 0*31 031 033032 033 033 0*34034034035 5.36< -^ /^\. . . /. . . . . . . . . . . ^r~~’
400 "^ 0.38^)250.230,220320320.480.41 Q380.42 0.50 Q56 0.63 0.68 0.750.86 1.04 1.22 1.43 1.68 1.98
) 03
3000 5 10 5 20 25DISTA NCE FROM STACK (km)
Figure 6-5. Homogeneous gas-to-particle conversion rates (in units of 0.1% of S02/hr) in theplume of the Central ia power plant on April 28, 1976, as predicted by the PHOENIX plume model(The calculated heterogeneous g-to-p conversion rates were essentially zero.
C/)
SE"
o=)
800
700
< 600
5005 10 15
DISTANCE FROM STACK (km)
(a
800
CO2E"700
LdQ=3h;h<
600
5000 5 10 15
DISTANCE FROM STACK (km)
(b)Figure 6-6. Excess (i .e. above ambient) concentrations (dN/d log D) of particlesin the plume of the Central ia power plant on October 19, 1976, as predicted by thePHOENIX plume model
(a) Particles 0.024 pm in equivalent diameter (concentrations in units of 104 cm"3)(b) Particles 0.55 pm in equivalent diameter (concentrations in units of cm"For corresponding measurements see Figure 4-2.
6-12
800h(/)
2E"LJQ=)
h:<
700
600
500
D ISTANCE FROM STACK (k m)Figure 6-7. Homogeneous gas-to-particle conversion rates (in units of 0 1% of S02/hr)m the plume
of the Centralia power plant on October 19, 1976, as predicted by the PHOENIX plume mudel (The
calculated heterogeneous g-to-p conversion rates were essentially zero.)
The measurements for the 0.55 pm particles (see Fig. 4-2b) show three main zones:high concentrations out to about 5 km from the stack, concentrations significantlybelow ambient concentrations near the lower region of the plume between about 7and 18 km from the stack, and above ambient concentrations near the top of theplume at about 18 km from the stack. The model results for the 0.55 pm particles(Fig. 6-6b) show high concentrations close to the stack which decrease with travel
time out to about 16 km and then increase again near the top and bottom of theplume at 19 km downwind. Thus, the trend with travel distance of the predictedconcentrations is in agreement with the observations, but the model does not showthe below ambient concentrations which were observed between 7 and 18 km from thestack.
The g-to-p conversion rates predicted by the PHOENIX model range from about 0.04to 0.3 per cent of SO^/hr at the edges of the plume to 0.001 to 0.01 per cent of
SO^/hr along the center of the plume (Fig. 6-7) The value of 0.3 per cent of
SO^/hr is the highest g-to-p conversion rate which the PHOENIX model has yetpredicted for the Centra1 ia plume.
The predicted Aitken nucleus concentrations and ight-scattering coefficients arein excellent agreement with the measurements in this case (Fig. 6-3d, 6-3e)
Centralia; September 22, 1977
PHOENIX model predictions for this case are shown in Figs. 6-3f, 6-3g, 6-8 and 6-9.
The model results for the 0.024 urn particles show decreasing concentrations with
increasing distance from the stack, but the concentrations of particles in the
plume are everywhere above the ambient values (Fig. 6-8a) The measurements showsimilar trends with travel distance (see Fig. 4-5a). The model results for the
0.55 \im particles also decrease in concentrations with travel distance and show
above ambient concentrations everywhere in the plume (Fig. 6-8b). The measurementsof the 0.55 pm particles, on the other hand, show a more complex pattern with
concentrations below ambient around 5 km downwind (see (Fig. 4-5b).
The model predictions for the g-to-p conversion rates are similar to the casestudies described previously with higher rates at the edges of the plume and
increasing rates with increasing distance from the stack (Fig. 6-9)
The Aitken nucleus concentrations predicted by the model are in rather good agree-ment with the measurements, except that the predicted widths of the plume are
6-14
< 900
21.66 2*44 2.78 2.63 2.41 2.22 204 2.0;
V) "^2E
^ 10003
3.85 3.54 3*25 2.95 2*72 2*55 2*42 2*35 2*26 2*18 2.*! 2*11
-< ) .\ .\19.8 10.1’ 6.05 4.25 3.86 3.53 3.20 2.93 2.73 2.57 2.47 236 2.27 2.19 2.18
I- 7.40 &36 4*83 3.69 3.38 3*10 2.85 2.66 2*51 2*39 2*32 224 2*16 2*10 2*11
2./2.072.78 2.89 2.58 234 2.21 2.15 2.09 2.07 2.02 1.98 1.94 1.91 1.89 1.88
800.0 5 10 15
DISTANCE FROM STACK(km)
(a
20
120Q
036088 1*2\. 0.98 0*84 0.68 O57 0.* O.*t0 0*33 0.*;4 0*9 0*5 0.*2 0*09
^/ v / ^5. ^/
(n
2
E
LJQ3(^L]<
100
1000
900h4-493-90
^O 5 10 15DI STANCE FROM STACK (km)
(b)Figure 6-8. Excess (i .e. above ambient) concentrations (dN/d log D) of particlesin the plume of the Central ia power plant on September 22, 1977, as predicted bythe PHOENIX plume model
(a) Particles 0.024 urn in equivalent diameter (concentrations in units of 10 cm"_l
(b) Particles 0.55 ym in equivalent diameter (concentrations in units of cm"For corresponding measurements see Figure 4-5.
6-15
en2
E
LdQ=>h:t:<
OJv^/ 0^01 ^^^--;---^-^ \^.71 O."05 *^&."03 QOT 0*03 0.53 0.03 O.W 0.06 0.07 0.59^0.11 O.T2 O.W 0.^8
^02^ . . . . . . T0’?3---^a/100
0.52 * 0.52 0*02 0.01 0"02 0.52 0.^2 0.02 0.52 0*02 0.02 0.03 003 0.03 0*05
0.010. 001 0.01 0.01 0.02 0.02 002 0*02 OSX. 0.02
10000.02 0.02/).03 0.03 0.04
0.02
90Or0-02 a02 a02 0-01 0-02 0-02 a02 0-02 0.02’6.03 0.03 0.03 0.03 0.04 0.06
0.11’0.05 0.04 0.05 Q04 0.05 0.08 ,0.10 0.13 0*15 0.18 0*21 0*24 0.29 0.*>5^_______\___________\L800
5 10 15DI STANCE FROM STACK ( km)
0 20
Figure 6-9. Homogeneous gas-to-particle conversion rates (in units of 0.1% of SO^/hr) in the plumeof the Central ia power plant on September 22, 1977, as predicted by the PHOENIX plume model (Thecalculated heterogeneous g-to-p conversion rates were essentially zero.
greater- than the measured widths (Fig. 6-3g) The predicted values of the light-
scattering coefficient are lower than the measured values (probably due to the
neglect of Rayleigh scattering) but they show similar variations to the measure-
ments (Fig. 6-3g)
Four Corners; June 23, 1977
PHOENIX model predictions for this case are shown in Figs. 6-3h, 6-3i 6-10 and
6-11 The model results show the concentrations of 0.024 pm near the center of
the plume.decreasing out to about 4 km and then increasing at greater distances
downwind (Fig. 6-IOa). These predictions are in excellent agreement with the
measurements near the center of plume, both in trend and absolute values; the
measurements show decreasing concentrations for the first few kilometers and much
higher concentrations at about 12 km downwind (see Fig. 4-4a) The trends of the
model results for the 0.55 pm particles (Fig. 6-IOb) are also in good agreement
with the measurements (see Fig. 4-4b) Both- the calculations and the measurements
show peak concentrations at about 2 km downwind, although the concentrations
predicted by the model are about twice the measured values.
The calculated g-to-p conversion rates for this case (Fig. 6-11 are very low,
except in the lower and upper regions of the plume very close to the stack.
The computed and measured Aitken nucleus concentrations are in reasonable agree-
ment (Fig. 6-3h) The computed light-scattering coefficients show similar trends
to the measurements but are about two to three times higher (Fig. 6-3i). The
latter discrepancy is directly attributable to the predicted concentrations of
the 0.55 pm particles being about twice as high as the measured concentrations.
Four Corners; June 24, 1977
PHOENIX model predictions for this case are shown in Figs. 6-3j, 6-3k, 6-12 and
6-13. The principal feature of the model results for the 0.024 ym particles is
an elongated region of relatively high concentrations extending from about 13 to
25 km downwind (Fig. 6-12a) The measurements, on the other hand, show peaks in
concentrations at about 8 and 28 km downwind (see Fig. 4-8a) The winds at Four
Corners on this day were light and variable, but a constant windspeed was used in
the model calculations. It appears that the windspeed which was used in the model
was too light by about a factor of two, since doubling the windspeed used in the
model calculations puts the onset of the predicted peak in the concentrations of
the 0.024 urn particles close to the observed peak at 28 km downwind. The model
6-17
2 4 6 8 10 12 14DISTANCE FROM STACK (km)
(a
2 4 6 8 10 12 14 16DISTANCE FROM STACK (km)
(bFigure 6-10. Excess (i .e. above ambient) concentrations (dN/d log D) of particlesin the plume of the Four Corners power plant on June 23, 1977, as predicted by thePHOENIX plume model
(a) Particles 0.024 um in equivalent diameter (concentrations in units of 104 cm"3)(b) Particles 0.55 um in equivalent diameter (concentrations in units of cm"3)For corresponding measurements see Figure 4-4.
6-18
Figure 6-10. Excess (I .e. above ambient) concentrations (dN/d log D) of particles
in the plume of the Four Corners power plant on June 23, 1977, as predicted by the
PHOENIX plume model
-3,(b) Particles 0.55 ym in equivalent diameter (concentrations in units of cm" ).
2400
2300V)
2E" 2200
LJ
21 00
^^ 2000
0.01 0*09 0*32 0.52 0.82 1*)01*18 1*33 1.68 1.86o.
1900h- o. 0.04 0.19 0*53 0*85 1*29 1.54 17.7 1*97 2*39 2.59
0 2 4 6 8 10 12 14 16
DISTANCE FROM STACK (km)
(b)
Figure 4-4. Excess concentrations (dN/d log D) above ambient values of
particles in the plume of the Four Corners Power Plant on June 23, 1977.
The wind speed was 11 km hr ".
(b) Particles 0.55 vm in equivalent diameter (concentrations in units of cm--’)
3 4 5 6 7 8 9
DISTANCE FROM STACK (km)
b)
JenSE"LJQZ)h-
Lj<
2400
2300
2200
2 100
2000
1900
0.
/^ 5f
3.W0.03/
0.
^S\2.00^0.02
\ ^\ . \0 06y
^rQ/
0.
\.
i
0.517
0*02
0.
^0.02
O.F2
,0.07
0.01
0.
,OJOI
0.02
0.02
",--0.06
6.01
0.
,0.01
,0.04
0*01
0.
,0.01
0.01
,0.03
0*01
0.
,0.01
0.01
0.04
0*01
0.
0.01
0.01
0.02
0.01
0.
0.01
0.01
0.02
0*01
0.
0.01
0.01
0 2 4 6 8 10 2 14 16DISTANCE FROM STACK (km)
Fiqure 6-11 Homogeneous qas-to-particle conversion rates (in units of 0.1% of SO^/hr) in the plume
of the Four Corners power plant on June 23, 1976, as predicted by the PHOENIX plume model (Thecalculated heterogeneous g-to-p conversion rates were essentially zero.)
<n
2000
1950
^ 1900
<1850
1800
9 12 15 18 21 24 27 30DISTANCE FROM STACK (km)
(a
9 12 15 18 21DISTANCE FROM STACK (km)
b
Figure 6-12. Excess (i .e. above ambient) concentrations (dN/d log D) of particlesin the plume of the Four Corners power plant on June 24, 1977, as predicted by thePHOENIX plume model
(a) Particles 0.024 pm in equivalent diameter (concentrations in units of 104 cm"3)(b) Particles 0.55 pm in equivalent diameter (concentrations in units of cm"3)For corresponding measurements see Figure 4-8.
6-20
2000
950
7 005 ^o.*9 o.<b6>"^b5 o.o4 o*)4 ^ o’o8 0.08 o.")8 o.’be o.os o.o8/ 0.09
^ d05 o !o90.05 o.oi
0.01 0.01" 0.01 0.03 0.03 10.07 0.08 0.08 0.08 0.08 Y0.09 0.09
0.09
y 1900
1850
1800
0.01 0.02 0.03 0.07 0.08 0.08 0.08 I 0.09 0.09 0.09 0.09
0.01
0.01 0.01 OJ02 0.03 0.03 0*07 0.08 0.08 0.08 0.08\ 0.09 0.09
0.05^^|~ 0.09 N’040*04 0*04 |0*04 O.*08 0*08| 0*08 0.08 O.|08 ’0.09| O.TO
3 6 9 12 5 8 2 24 27DISTANCE FROM STACK ( km)
Figure 6-13. Homogeneous gas-to-particle conversion rates (.in units of 0.1% SO^/hr) in theplume of the Four Corners power plant on June 24, 1977, as predicted by the PHOENIX plume model(The calculated heterogeneous g-to-p conversion rates were essentially zero.
results for the 0.55 \sm particles show a general decrease in concentration with
travel distance from the stack (Fig. 6-12b) The measurements also show decreasingconcentrations with travel distance but with two higher lobes of concentrationnear the top and bottom of the plume at about 18 km downwind (see Fig. 4-8a)
In this case the predicted g-to-p conversion rates are fairly uniform in the
vertical over the plume but increase with increasing distance from the stack
(Fig. 6-13).
Both the predictions of the Aitken nucleus concentrations and the ight-scatteringcoefficient are in fair agreement with the observations (Figs. 6-3j and 6-3k)
Four Corners; June 25, 1977
Model results for this case are shown in Figs. 6-3A, 6-14, 6-15 and 6-16. This
was the only case study in which the model predicted significantly different
concentrations of particles depending on whether they were assumed to be unchargedor charged as they left the stack. The sensitivity to charge in this case was
due to the large numbers of particles greater than 0.5 pm in diameter. Shown in
Figs. 6-14a and 6-15a are the model results for the concentrations of 0.024 pm
uncharged and charged particles, respectively. For the uncharged 0.024 ym particles
the concentrations initially increase with increasing distance from the stack,
reach peak concentrations near the top and bottom of the plume at about 6 kmdownwind, and then decrease in concentrations at greater distances (Fig. 6-14a)Between and 7 km downwind the concentrations of 0.024 urn uncharged particles in
the plume are less than those in the ambient air, due to their rapid coagulation
with larger particles (Fig. 6-14a). The model results for the charged 0.024 ym
particles also show below ambient concentrations of particles at km from the
stack, but the concentrations then increase steadily with increasing distance
downwind (Fig. 6-15) The measurements for the 0.024 pm particles (see Fig. 4-9a)are in better agreement with the model predictions for the uncharged particles in
that they reach a peak concentration at about 5.5 km downwind.
The model results for the uncharged 0.55 ym particles also show below ambient
concentrations within 2 km of the stack (and at the extreme lower and upper edgesof the plume at longer distances downwind) and two lobes of peak concentrations
at about 5 km downwind (Fig. 6-14b) However, the model results for the charged0.55 ym particles show predominantly below ambient concentrations throughout the
plume. Again, the model results for the uncharged particles are in good agreement
6-22
4 6 8
DISTANCE FROM STACK (km)
a
2 4 6 8 10
DISTANCE FROM STACK (km)
(b)Figure 6-14. Excess (i .e. above ambient) concentrations (dN/d log D) of uncharged
particles in the plume of the Four Corners power plant on June 25, 1977, as predicted
by the PHOENIX plume model
(a) Particles 0.024 \im in equivalent diameter (concentrations in units of 10 cm
(b) Particles 0.55 urn in equivalent diameter (concentrations in units of cm"
For corresponding measurements see Figure 4-9.
6-23
4 6 8
DISTANCE FROM STACK (km)(a
4 6 8
DISTANCE FROM STACK (km)
(bFigure 6-15. Excess (i .e. above ambient) concentrations (dN/d log D) of chargedparticles in the plume of the Four Corners power plant on June 25, 1977, aspredicted by the PHOENIX plume model
(a) Particles 0.024 pm in equivalent diameter (concentrations in units of 104 cm"3)(b) Particles 0.55 vm in equivalent diameter (concentrations in units of cm"3).For corresponding measurements see Figure 4-9.
6-24
2100 ^ 3.83 l.*2 ’l 13 1.16 1.24 1.30 1.36 1.36
/1.33 1.36 1.3’n
-J 2000en2
1900LJ0
L 1800t;<
1700
0.28 0.42 0*29 0.24 0*22 0*21 0.*!! 0.**! 0*21 0.23 0.23 0.24
0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
0*26 0.36 O."i5 0."’2 0.21 0.20 0.20 0.20 0.21 0.23 0*23 0.23
1.96 0.92 0.86 0.84 0.78 0.72 0.68 0.63 0.64 0.62
2 4 6 80 10
DISTANCE FROM STACK (km)Figure 6-16. Homogeneous gas-to-particle conversion rates (in units of 0.1% of SO^/hr)in the plume of the Four Corners power plant on June 25, 1977, as predicted by thePHOENIX plume model (The calculated heterogeneous g-to-p conversion rates wereessentially zero.
with the measurements which also show two lobes of peak concentrations for the0.55 \im particles at about 5 km downwind (see Fig. 4-9b).
The calculated g-to-p conversion rates are shown in Fig. 6-16. Although the ratesat the center of the plume are essentially zero, at the edges of the plume thiscase produced the highest values for the g-to-p conversion rate at Four Cornerspredicted by the PHOENIX model (^0.4% of SO^/hr)
Aitken nucleus concentrations were not measured on this flight. The computed and
measured ight-scattering coefficients are shown in Fig. 6-3&. The values in theambient air are in good agreement with the measurements but in the plume the cal-culated values are much too high. As in the case of April 28, 1976 at Central ia(see above) the concentrations of mode particles and the spread in their sizes(see Table 6-1 were too high in this case; as mentioned previously, this indicatesthat the mode particles are optically absorbing, which has not been allowed forin our calculations of the light-scattering coefficient.
DISCUSSION
It is clear from the above case studies that the PHOENIX model is capable ofreproducing many of the significant features associated with particle size distri-
butions in the plumes from coal-fired power plants. In particular, the peaks anddeficits (with respect to the ambient air) in the concentrations of particles ofvarious sizes at different points in the plume are often depicted well by the model
The model also provides insights into the mechanisms responsible for the observedparticles size distributions. The peaks in the concentrations of the 0.024 pm
particles originate primarily from the coagulation of smaller particles producedby g-to-p conversion. The model predicts that the homogeneous g-to-p conversionof SO^ to sulfuric acid is greatest near the edges of a plume, where the concen-trations of OH radicals from the ambient air are greatest. Very small particlesproduced by g-to-p conversion in these regions diffuse into the plume (as well asout into the ambient air) and coagulate to form larger particles. Consequently,the concentrations of the 0.024 pm particles are often highest near the centersof the plumes (see, for example. Figs. 6-1a, 6-6a, 6-IOa and 6-12a) The higherg-to-p conversion rates at the edges of a plume also explain why the concentrationsof a certain size particle at the edges of a plume sometimes increase with in-creasing distance from the stack, while the concentrations of the same size
particle at the center of the plume decrease with travel time.
6-26
When the concentrations of particles in modes 2 and 3 (0.1 to 0.5 \im and ^0.5 pm,
respectively) are sufficiently high they may coagulate with the 0.024 urn particles,
causing the latter to decrease in concentration near the center of plume (e.g.
Figs. 6-4a and 6-14a) Hence, both inter- and intra-modal coagulation can be
important in controll ing particle size distributions in plumes. This is demon-
strated by the fact that the concentrations of 0.55 ym particles often increase
with increasing distance from the stack while, at the same time, the 0.024 ym
particles decrease in concentration. See, for example, the model results described
above for Central ia March 30, 1976, April 28, 1976, October 19, 1976, and for
Four Corners June 23, 1977 and June 25, 1977.
The homogeneous rates of g-to-p conversion of SOo to sulfuric acid predicted by
the model (^0 to 0.4 per cent of SOo/hr) are generally lower than the values
(^.01 to 7 per cent of SOn/hr) we have derived from our measurements. The model
predicts that g-to-p conversion due to heterogeneous reactions on soot particles
is negligible.
The differences in the g-to-p conversion rates determined directly from field
measurements and those predicted by the model could be due to several factors.
Firstly, in the PHOENIX model it is assumed that the particles created by g-to-p
conversion are a mixture of H;)SO^ and water in equil ibrium at the ambient temper-
ature and humidity. In deriving g-to-p rates from the field measurements, on the
other hand, it is assumed that the particles are pure H^SO. These differences
could result in the predicted g-to-p conversion rates being up to about a factor
of two less than the g-to-p conversion rates deduced from the field measurements.
Secondly, since g-to-p conversion seems to be diffusion imited in the model the
values chosen for the eddy diffusion coefficients have a great effect on the
computed g-to-p rates. In the model calculations we have used eddy diffusivity
coefficients corresponding to stable or neutral atmospheres. In several cases at
Centralia, the eddy diffusivity coefficients at particular altitudes determined
in this way were similar to the values determined from the airborne measurements.
In these cases, the g-to-p conversion rates predicted by the model were in reason-
able agreement with the values determined directly from the field measurements.
By contrast, the values of the eddy diffusivity coefficients used in the model
for the Four Corners plume were generally considerably lower than the values
measured from the aircraft and in these cases the g-to-p conversion rates pre-
dicted by the model were lower than the directly measured rates. Since the g-to-p
conversion appears to be diffusion limited, if the the values of the eddy diffusion
6-27
inputted into the model are underestimated the g-to-p conversion rates, predicted
by the model will be too small Thirdly, the approximation of the 6 factor in
Eq. 5-24 to 0.4 probably leads to underestimates of the g-to-p conversion rates.Finally, we note that to accurately determine g-to-p conversion rates from the
field measurements, the concentrations of both particles and gases are required
throughout the plume. In practice, average values of particle and gas concentra-tions across the plume at various distances downwind are deduced fr(R)m ’limited
point measurements in computing g-to-p conversion rates from the field measure-
ments. As can be seen from Fig. 6-17, the PHOENIX plume model indicates that the
concentrations of particles across a plume may vary quite markedly, the region of
highest particle concentrations being contained in an annulus around the center
of the plume. Clearly, there could be quite large (but essentially random) errors
involved in deducing average values of particle concentrations across the plume
from a few point measurements; there errors, in turn, would produce (random)errors in the estimates of g-to-p conversion rates.
6-28
DISTANCE FROM PLUME CENTER (km)
Figure 6-17. Total particle concentrations (in units of 10 cm" across the Centraliaplume at a distance of 2 km downwind predicted by the PHOENIX model for April 28, 1976.The shaded area indicates the ring of highest particle concentrations.
Section 7
SUMMARY AND CONCLUSIONS
FIELD MEASUREMENTSIn the first part of this report we described the results of detailed field
measurements of particle size distributions and gas-to-partice (g-to-p) conversionrates in the plumes from two coal-fired power plants (Centralia, WA, and FourCorners, NM) These measurements revealed the complexity and variability of theevolution of the particle size spectrum with travel time in power plant plumes.
The particles in the plumes which were studied generally fell in three distinctsize ranges, which we have referred to as mode (with geometric mean particle
diameters with respect to volume. D p in the range 0.001 0.2 ym) mode 2
(Dgy^ in the range 0.11 0.55 pm) and mode 3 (D 3 in the range 0.55 4.4 pm)Modes 2 and 3 sometimes overlap.
The concentrations of particles in mode 3 emitted by the Four Corners plant weretypical ly 1-2 orders of magnitude greater than those emitted by the Centralia plant.Due to their role in the coagulation of particles produced by g-to-p conversion,mode 3 particles had important effects on the evolution of the particle spectra inthe plumes for travel times up to at least 15 min for the Centralia plume and 3 hrfor the Four Corners plume. The principal effect of high concentrations of mode 3particles was to rapidly deplete the concentrations of particles in modes and 2(the depletion by coagulation being even more rapid than depletion by diffusion)Consequently, the concentrations of particles of a particular size in the plumessometimes fell below the corresponding concentrations in the ambient air. In thisrespect, a plume may be ikened to a Swiss cheese with "holes" in it. Also, the
concentrations of particles of a certain size sometimes decrease with travel time
in the center of a plume but increase with travel time at the edges of the plume.
Three techniques (flash volatil ization, the change in the total volume of particles,
and the production of Aitken nuclei have been used to measure g-to-p conversion
rates near the centers of the plumes. The upper limit to the g-to-p conversion
rates in the Centralia plume is equivalent to a few tenths of one per cent of
SOo/hr; in the Four Corners plume the upper limit is a few per cent of SO^/hr.
7-1
THE PHOENIX PLUME MODEL
In Section 5 of this report we have described a sophisticated three-dimensional
model of power plant plumes (called PHOENIX) which considers the effects of ad-
vection, diffusion, gravitational settling, coagulation, g-to-p conversion, andinteractions with the ambient air, on the evolution with time (or travel distance)of the particle size distribution in a plume.
The case studies presented in Section 6 show that the PHOENIX model can reproducemany of the principal features of the evolution of particle size distributions in
power plant plumes (including the’Swiss cheese"nature of the plume) over the
travel distances (up to 30 km) considered so far. The only inputs required for
the model are specifications of the ambient conditions (trace gases, winds and
atmospheric stabil ity) and of the plume constituents at one point close to (or in)the stack.
The model results indicate that the homogeneous g-to-p conversion of SO., to sul-
furic acid is greatest at the edges of a plume, where the concentrations of OHradicals from the ambient air are greatest. The model predicts that g-to-pconversion due to heterogeneous reactions on soot particles is negligible. The
model predictions of g-to-p conversion rates at the edges of the plumes approach
the average values deduced from field measurements, but elsewhere in the plumes
the predicted values are about an order of magnitude lower than the measurements.
The PHOENIX model could be improved if diffusion were handled more realistically
and if a time and space varying wind field were used. With these improvements,
and further testing against comprehensive data sets such as those presented in
this study, the model might eventually be valuable as an operational tool for
forecasting particle size distributions and g-to-p conversion downwind of coal-
fired power plants.
7-2
Section 8
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8-4
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describing the major subject area covered in the report
CDDcmParticle Formation and Growth in Power PlantPlumes Volume 1: Field Observations and Theoretical
Studies of the Evolution of Particles in the Plumes FromCoal-Fired Electric Power Plants
Contractor: University of Washington
Volume describes a parallel field study and theoretical investigation of par-ticle size distributions in the plumes of coal-fired power plants. The discov-
ery of three distinct size modes of particles, characterized by geometricmean volume diameters, is discussed. In addition, the significance of the
size in the coagulation of the particles is analyzed. 114 pp.
EPRI Project Manager: C. Hakkarinen
Cross-References:1. EPRI EA-3105, Volume 2. RP330-1 3. Environmental Physics and Chemistry Program4. Air Pollution
ELECTRIC POWER RESEARCH INSTITUTEPost Olfice Box 10412. Palo Alto, CA 94303 415-855-2000
EPRI EA-3105, VOLUME 1 EDOerrParticle Formation and Growth in Power PlantPlumes Volume 1: Field Observations and TheoreticalStudies of the Evolution of Particles in the Plumes FromCoal-Fired Electric Power Plants
Contractor: University of Washington
Volume describes a parallel field study and theoretical investigation of par-
ticle size distributions in the plumes of coal-fired power plants. The discov-
ery of three distinct size modes of particles, characterized by geometricmean volume diameters, is discussed. In addition, the significance of the
size in the coagulation of the particles is analyzed. 114 pp.
EPRI Project Manager: C. Hakkarinen
Cross-References:1. EPRI EA-3105, Volume 2. RP330-1 3. Environmental Physics and Chemistry Program4. Air Pollution
ELECTRIC POWER RESEARCH INSTITUTEOffice Box 10412. Palo Alto, CA 94303 415-855-2000
RP330-1 CpCbJ 1
Particle Formation and Growth in Power PlantPlumes Volume 1: Field Observations and TheoreticalStudies of the Evolution of Particles in the Plumes FromCoal-Fired Electric Power Plants
Contractor: University of Washington
Volume describes a parallel field study and theoretical investigation of par-ticle size distributions in the plumes of coal-fired power plants. The discov-
ery of three distinct size modes of particles, characterized by geometricmean volume diameters, is discussed. In addition, the significance of the
size in the coagulation of the particles is analyzed. 114 pp.
EPRI Project Manager: C. Hakkarinen
Cross-References:1. EPRI EA-3105, Volume 2. RP330-1 3. Environmental Physics and Chemistry Program4. Air Pollution
ELECTRIC POWER RESEARCH INSTITUTEPost Oflice Box 10412, Palo Alto, CA 94303 415-855-2000
