EPA-R3-73-047
June 1973
Ecological Research Series
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EPA-R3-73-047
NATURAL PRECIPITATION WASHOUT
OF SULFUR COMPOUNDS
FROM PLUMES
by
M. Terry Dana, J. M. Hales,
W. G. N. Slinn, and M. A. Wolf
Atmospheric Sciences Department
Battelle, Pacific Northwest Laboratories
P. 0. Box 999, Richland, Washington 99352
Interagency Agreement No. IAG-025 CD)
Program Element No. 1A1009
EPA Project Officer: Herbert Viebrock
Meteorology Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S.ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
June 1973
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This report has been reviewed by the Environmental Protection Agency and
approved for publication. Approval does not signify that the contents
necessarily reflect the views and policies of the Agency, nor does men-
tion of trade names or commercial products constitute endorsement or
recommendation for use.
11
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CONTENTS
Page
ABSTRACT iv
LIST OF FIGURES v
LIST OF TABLES ix
ACKNOWLEDGMENTS xi
SECTIONS
I. CONCLUSIONS 1
II. RECOMMENDATIONS 3
III. INTRODUCTION 5
IV. PROGRESS IN WASHOUT MODELING 17
V. SECOND-SERIES QUILLAYUTE EXPERIMENTS 24
VI. CENTRALIA EXPERIMENTS 63
VII. FURTHER ANALYSES OF KEYSTONE RESULTS 121
VIII. RECOMMENDED APPLICATIONS OF THE EPAEC MODEL FOR
ENVIRONMENTAL IMPACT ANALYSES 126
IX. REFERENCES 131
X. NOMENCLATURE 134
XI. APPENDICES 139
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ABSTRACT
A model has been developed for prediction of the reversible washout of S09
emitted from power-plant plumes and other sources. Predictions of this
computer-code model compare favorably with washout measurements made dur-
ing fifteen controlled-source experiments and four power plant experiments.
An application of the model to previous experimental conditions of high
background rain acidity shows that "negative washout" can and has occurred
as a result of desorption of SO from the rain below the S0~ plume. The
resulting washdown effect was analyzed mathematically, and shown to be not
a significant pollution problem on the distance scale of current interest,
but could be important for gases that are more strongly dissolved than SCL.
The effect of dry deposition upon the experimental results of the study
appears to be unimportant for rainfall rates over about one mm hr~^.
Sulfate washout measurements were made during the power plant study, and
an approximate reaction-washout analysis indicates that a rapid initial
oxidation occurs, which slows at increasing downwind distance. The sulfate
washout coefficient appears to be about 0.05 hr~l for background pH > 5.2,
but could be much smaller for more acid rains.
This report was submitted in fulfillment of work specified in proposal No.
300A00585 (BNW-389), Amendment 2, by Battelle, Pacific Northwest Labora-
tories under the sponsorship of the Environmental Protection Agency. Work
was completed as of July, 1972.
^v
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FIGURES
Page
1. Chronological Summary of Major Segments of the
EPA-Sponsored Washout Program 6
2. Schematic of Keystone Rain Sampling Network 7
3. SC>2 Washout Concentrations at Keystone - Run 9,
February 10, 1970 9
4. S(>2 Washout Concentrations at Keystone - Run 18,
April 24, 1970 10
5. SC>2 Washout Concentrations at Keystone - Run 4,
November 2, 1969 11
6. Quillayute Sampling Network - First Series 14
7. Predicted and Measured S02 Concentrations at Quillayute,
First Series - Typical Run, Dashed and Solid Curves
Show Model Predictions 16
8. The Redistribution of an S02 Plume Caused by Washout 23
9. Quillayute Sampling Network - Second Series 26
10. 30.5 m S02 Release Tower - Quillayute Second Series 28
11. Portion of the West Sampling Arcs - Quillayute
Second Series 29
12. Measured and Calculated SC>2 Concentration in Rain - Run 11 .. 36
13. Measured and Calculated S02 Concentrations in Rain -
Run 12 W 37
14. Measured and Calculated SC>2 Concentration in Rain -
Run 12 E 38
15. Measured and Calculated SC>2 Concentration in Rain -
Run 14 W 39
16. Measured and Calculated SC^ Concentration in Rain -
Run 14 E 40
17. Measured and Calculated SC>2 Concentration in Rain -
Run 15 W 41
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Page
18. Measured and Calculated SC>2 Concentration in Rain -
Run 15 E 42
19. Measured and Calculated SC>2 Concentration in Rain -
Run 16 W 43
20. Measured and Calculated SC>2 Concentration in Rain -
Run 16 E 44
21. Measured and Calculated SC>2 Concentration in Rain -
Run 17 45
22. Measured and Calculated 862 Concentration in Rain -
Run 18 46
23. Measured and Calculated SC>2 Concentration in Rain -
Run 19 47
24. Measured and Calculated SC-2 Concentration in Rain -
Run 20 48
25. Measured versus Predicted SC>2 Washout Rates -
Quillayute Second Series 50
26. Error in Washout Concentration Measurements,
as a Result of Dry Deposition 61
27. Map of Centralia Steam Plant Area 64
28. Centralia Sampling Network 66
29. Centralia Steamplant with Rawinsonde Antenna
at Control Center in Foreground 68
30. Centralia Sampling Location: SO^ and S02 Samplers,
Left; pH and SC>2 Bubbler Box, Right 69
31. Measured SC>2 Concentrations in Air - Run C-l 73
32. Rawinsonde Data - Run C-2 74
33. Measured SC>2 Concentrations in Rain - Run C-2 7,-
34. Predicted S02 Concentrations in Rain - Run C-2
EPAEC Model Calculations Based on Gas-Phase
Limited Transport and an S02 Reaction Decoy
Half-Life of 15 Minutes 76
35. Measured SC>2 Concentrations in Air - Run C-2 77
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36. Measured Sulfate Concentrations in Rain - Run C-2
(Background Corrected) 78
37. Measured Free Hydrogen-Ion Concentrations - Run C-2
(From pH Measurements, Background Corrected) 79
38. Rawinsonde Data - Run C-3 80
39. Measured SC>2 Concentrations in Rain - Run C-3 81
40. Predicted S02 Concentrations in Rain - Run C-3
EPAEC Model Calculations Based on Gas-Phase
Limited Transport and an S02 Reaction Decay
Half-Life of 15 Minutes 82
41. Measured SC>2 Concentrations in Air - Run C-3 83
42. Measured Free Hydrogen-Ion Concentrations - Run C-3
(From pH Measurements, Background Corrected) ..... 84
43. Measured SC>2 Concentrations in Rain - Run C-4 85
44. Predicted SC>2 Concentrations in Rain - Run C-4
EPAEC Model Calculations Based on Gas-Phase
Limited Transport and an S02 Reaction Decay
Half-Life of 15 Minutes 86
45. Measured SC^ Concentrations in Air - Run C-4 87
46. Measured Sulfate Concentrations in Rain - Run C-4
(Background Corrected) 88
47. Measured Free Hydrogen-Ion Concentrations - Run C-4
(From pH Measurements, Background Corrected) 89
48. Measured SC>2 Concentrations in Rain - Run C-5 90
49. Predicted SC>2 Concentrations in Rain - Run C-5
EPAEC Model Calculations Based on Gas-Phase
Limited Transport and an S02 Reaction Decay
Half-Life of 15 Minutes 91
50. Measured SC>2 Concentrations in Air - Run C-5 92
51. Measured Sulfate Concentrations in Rain - Run C-5
(Background Corrected) 93
v^^
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52. Measured Free Hydrogen-Ion Concentrations - Run C-5
(From pH Measurements, Background Corrected) 94
53. Schematic of Idealized Plumes Employed by EPAEC Model
for Centralia Calculations 101
54. Rain-borne SC>2 Concentrations at Ground Level as
Function of Raindrop Size 105
55. Schematic of Features of Reaction/Washout Process 110
56. Washout Coefficient as a Function of Particle Size 112
57. Solutions to Equation (28) For Run C-2 116
58. EPAEC Model Calculation for Keystone Run 4, Arc A,
Using Data of Table 23 122
59. Representation of Simplified Film Theory 173
60. Superficial Flow Diagram of EPAEC Model 177
61. Sub-Routine Hierarchy in EPAEC Model 177
62. Pictorial Bases for EPAEC Model 179
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TABLES
1. Basic Data Used for Washdown Calculation 21
2. Release and Sampling Parameters - Quillayute, Second Series . . 25
3- Times, Temperatures and Rainfall Rates - Ouillayute, Second
Series 31
4. Raindrop Size Frequency Distributions - Quillayute Second
Series 32
5. Wind Parameters Calculated from Anemometer Data - Quillayute
Second Series 33
6. Measured Washout Rates - Ouillayute Second Series -<-
7. Summary of Dry Deposition Results 57
8. Transport Parameters for Dry Deposition Tests 59
9. Calculated Incident Rain Concentrations for Dry Deposition
Runs Dl and D3 60
10. Centralia Steam-Elertric Plant Statistics
(February-March, 1972) 65
11. Run Data - Centralia -,,
12. Raindrop Size Frequency Distributions - Centralia 72
13. Summary of Washout Measurements - Centralia 72
14. Trace Metals Analysis - Centralia Run C-4 97
15. Average Wind Data from Anemometers - Centralia 98
16. First-Order Rate Constants for S02 Decay Used in Centralia
Model Calculations 100
17. Effective Stack Heights and Loft Velocities Used in Applying
the EPAEC Model to the Centralia Results (After Briggs13) . . . 102
18. EPAEC Calculations of S02 Washout Concentrations -
Centralia, Run C-5 , 103
19. Extreme Limits of Sulfate Washout Coefficients and
Reaction Rate Constants 113
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Page
20. Revised Extrema of Sulfate Washout Coefficients and Reaction -
Rate Constants 114
21. Solutions to Equation (28) for Applicable Centralia Sampling
Line Pairs 117
22. Comparison of Sulfate Washout Rates: Observed versus Those
Calculated Using Equations (28) and (29) 120
23. Keystone Run 4 Base Data 125
24. Results of Application of Sulfate Washout Model to Keystone,
Run 4, Arc A Data 125
25. Summary of Required Input Data for the EPAEC Code, and
Recommended Values for Initial Use 127
26. Example Input Data Format for EPAEC Code 130
27-35. Measured SC^ Concentrations - Quillayute Second Series .... 141
36-49. Measured S02 Concentrations - Centralia 149
50-58. Measured SO^ and H Concentrations - Centralia 161
59. Computer Nomenclature 185
x
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ACKNOWLEDGMENTS
This research was conducted by scientific and technical personnel of the
Atmospheric Sciences Department of Battelle, Pacific Northwest Laboratories
under related services agreement BNW-389 with the Richland Operations
Office, U. S. Atomic Energy Commission for the Environmental Protection
Agency.
The principal investigators were. M. Terry Dana, Jeremy M. Hales, W. G. N.
Slinn, and M. A. Wolf. Special appreciation is due D. W. Glover, who
directed and performed much of the design and development of special field
equipment. Other Battelle, Pacific Northwest Laboratories personnel who
contributed significantly were:
R. E. Kerns J. Mishima
R. N. Lee J. W. Sloot
M. C. Miller W. A. Stone
We are expecially grateful for the contributions of the following persons
and organizations, whose assistance was valuable in the success of the
field effort:
The management of the Centralia Steam Plant, particularly:
Pacific Power and Light Company
Washington Irrigation and Development Company.
Washington State Aeronautics Commission, Seattle, Washington
Mr. Clarence Davis, Manager, Quillayute State Landing Field
Mr. Donald Carte, Meteorologist-In-Charge, National Weather
Service, Forks, Washington
Professor Donald Adams, Washington State University.
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SECTION I.
CONCLUSIONS
A method of calculating S0_ washout from plumes has been developed. This
method is based upon reversible gas absorption phenomena, and is applicable
to circumstances involving power-plant plumes emitted from tall stacks, as
well as for less complicated situations. It can be employed for predicting
washout of pollutant gases other than SO. upon substitution of the appro-
priate physical properties.
The washout calculation procedure is accomplished in terms of a model given
in FORTRAN IV computer code, which is listed and documented in an appendix
to this report. The basic precepts of the model—reversible behavior and
negligible plume distortion by washout—were checked theoretically and ex-
perimentally and found to be valid under the conditions of present interest.
Field experiments conducted during this program showed that S09 concentra-
tions in rain often can be calculated to within a factor of two of observed
values, although the predictive capability is reduced for near-source con-
ditions, and complicated by the occurrence of chemical reaction. The
accuracy of the present model, moreover, is improved, compared to that of
previous calculation procedures; the latter predict results high by several
orders of magnitude under circumstances involving tall stacks. Additionally
the washout model predicts behavior consistent with earlier measurements
near the Keystone plant, which appeared anomalous at the time. These model-
verified observations include;
1. Washout of SO from a concentrated, high-elevation plume can be
obscured by the presence of low-elevation, low-concentration
background levels.
2. The acidity of rain strongly influences its SO -scavenging poten-
tial.
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3. "Negative" washout of S0_ occurs under appropriate circumstances—
that is, rain that has passed through a power plant plume often
contains less S07 than that which has not.
Sulfate washout from power plant plumes was measured during this study: the
results indicate that the rate of sulfur removal via sulfate washout is from
one to five times more rapid than that via S0? washout. A definitive model
of sulfate washout was not developed during this study; however, the field
results applied to an approximate analysis lead to a conclusion that the
reaction process occurs rapidly near the source, and decreases with distance
downwind. The overall reaction-rate constant—for all sampling distances—
derived from this analysis is in the neighborhood of 5 hr~*, with corres-
ponding sulfate washout coefficients ranging below about 0.07 hr"1.
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SECTION II.
RECC)W^ENDATK)N_S
The computer model developed by this project is recommended for use in en-
vironmental impact analyses of fossil-fuel power plants, as well as for
assessments of washout of gases from plumes of other tvpes. Selected local
wind, rain, and pollutant-source characteristics, plus physical properties,
background levels, and topography can be applied to the model to calculate
concentrations of pollutant in rain as a function of distance from the
source.
The simplified plume description, assuming a bivariate-normal distribution
with spread parameters given by the equations of Smith and Singer, and loft
given by the equations of Briggs. is recommended for use with the washout
model for impact-analysis purposes. More specialized calculations may re-
quire other models of plume behavior; these can be easily incorporated
within the overall washout model at the user's option.
The washout model developed during this study is focused pritnarilv on re-
moval of SO . Sulfate washout is an additional important aspect of the
overall sulfur-removal process in power-plant plumes; accordinglv, an ex-
tension of the present model to provide for sulfate washout calculations is
desirable. Such an extension is complicated by a lack of knowledge of the
microphysics of sulfate formation and removal. Through a modest effort,
however, the present washout model can be extended to provide a macroscooic
calculation procedure. This would provide a computational framework which
would accept (in subroutine form) any given microphysical model of sulfate
formation within plumes and proceed to perform corresponding washout compu-
tations. This extension is useful for testing of microphysical models under
practical conditions" it is also desirable because it will yield an improved
environmental impact analysis tool once the appropriate microphysical models
have been established. For these reasons the development of an extended
washout model is recommended as a limited addition to the present work.
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With the exception of the microphysics of sulfate formation and washout, a
majority of the processes leading to sulfur removal from plumes are now
fairly well understood. Improvements in our ability to estimate washout
rates, therefore, can be expected to stem directly from future improvements
in our ability to describe the features required for model input. Such
features are categorized below, in order of expected importance in improv-
ing our existing ability to compute sulfur compound washout from power plant
plumes.
1. Sulfate formation and washout-rate phenomena.
2. Plume description ("diffusion" model considerations).
3. Dry deposition processes and their effect on plume description.
4. SCL absorption microphysics.
If future research is sponsored by the Environmental Protection Agency on
washout of sulfur from power plant plumes, we recommend that specific areas
be given priority in the order listed above.
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SECTION III.
INTRODUCTION
In October, 1969, Battelle-Northwest began field studies of precipitation
washout of sulfur compounds from coal-fired power plant plumes under
sponsorship of the Division of Meteorology, Environmental Protection Agencv
(then the National Air Pollution Control Administration). At that time,
we conducted an initial series of field experiments in the vicinity of the
Keystone Generating Station in western Pennsylvania. Subsequent years'
investigations included controlled-release S0? washout experiments at Quill-
ayute airfield, Washington, and a return to power plant effluent wash-
out experiments at the Centralia, Washington Steam Plant. (Figure 1
summarizes the locations and times of the field efforts under this program.)
Results of the Keystone and early Quillayute experiments have been docu-
mented previously (Hales, Thorp, and Wolf:1 Dana, Hales, and Wolf2). These
references will be cited often in the present report, and we shall refer to
them hereafter as "HTW" and "DHW" for convenience. The purpose of this re-
port is to describe results from additional Quillayute experiments and from
Centralia, and to focus subsequent conclusions of these into the context of
the total EPA washout program. The remainder of this introduction provides
an overall perspective on the program by summarizing briefly the design and
findings of the Keystone and early Quillayute work, and by outlining the
bases of the investigations to be reported in later chapters.
KEYSTONE
The precipitation washout study at Keystone consisted basically of obtaining
chemical analyses of precipitation samples collected at various locations
beneath the power plant plume. Although SO was the compound of primary in-
terest, we also measured the concentrations of other species—N0_, NO , F ,
SO,—in specific samples. Figure 2 is a lavout of sampling locations with
respect to the Keystone power plant.
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LEGENDS
^K flRC fl STRTIONS
0 RRC 8 STHTI0NS
« RRC C STRTI0NS
K DENQTES PLHNT L8CRTI0N
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= 1 MILE
FIGURE 2. SCHEMATIC OF KEYSTONE PAIN SAMPLING NETWORK.
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Measured S0« levels in the collected rain did not follow behavior predicted
at the time; in fact, it was exceedingly difficult to determine the in-
fluence of the plume on the SO content of the precipitation. At times the
spatial distribution of S0~ concentration levels in the rain showed a
relatively high S02 content but indicated no relationship to plume location
whatsoever (cf. Fig. 3); other distributions, such as that shown in Figure
4, showed little S0_ in precipitation collected at any location. Still
other experiments, such as that shown in Figure 5, indicated an inverse
relationship between SO content and plume position—a paradoxical "negative
washout" effect.
These results, in combination with additional findings described in HTW,
led to the following conclusions:
C-l. Washout of S02 from high-elevation plumes is an inefficient process,
at least at distances within a few miles from the source. Washout
rates are less than those predicted from classical washout theory,
and never amount to more than a fraction of one percent of the source
per mile at the Keystone plant.
C-2. Washout of background SO from low elevations is usually sufficient
to obscure contributions from the Keystone plume.
C-3. Free hydrogen-ion concentrations (obtained from pH measurements) cor-
relate somewhat with plume location, at least when background levels
are low.
C-4. Measured sulfate content of the rain correlates somewhat with plume
location, although background levels tend to obscure this relation-
ship.
C-5. S0_ content of the rain shows a strong inverse correlation with rain
acidity.
In addition to these conclusions the following speculations were made as
proposed explanations of the observed behavior:
S-l. SO- absorption by the falling raindrops must be a reversible process,
with significant amounts of captured S0_ desorbing during the rain
drops' fall beneath the more concentrated regions of the plume.
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LEGENDS
* flRC fl STRTI8NS
< RRC B STHTI0NS
& flRC C STflTIQNS
K DENOTES PLRNT LGCRTIQN
SCRLES
I 1- 1 MILE
= 10 MICR0MOLES/L
FIGURE 3. SO WASHOUT CONCENTRATIONS AT KEYSTONE - RUN 9, FEBRUARY 10, 1970.
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* RRC n STRTIONS
< flRC B STRTIQNS
« flRC C STflTlQNS
K DENQTES PLflNT LGCflTIQN
N
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I 1 = 1 MILE
= 10 MICROM0LES/L
FIGURE 4. S02 WASHOUT CONCENTRATIONS AT KEYSTONE - RUN 18, APRIL 24, 1970.
10
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LEGENDS
* RRC fl STRTIQNS
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S-2. S09 solubility is strongly dependent on rain acidity, with this de-
pendency forming the basis for the strong correlation between pH and
washout. The negative washout effect shown in Figure 5 is a conse-
quence of the rain increasing its acidity by scavenging nonvolatile
acid-forming materials from the plume, causing SO- to desorb to con-
centration levels below those reflecting background concentrations in
rain collected at surrounding locations.
S-3. If the desorption effect (S-l) is valid, then a redistribution of the
S09 plume takes place as a result of the descent of the rain, lower-
ing the altitude of the plume with increasing distance from the source.
This effect will be referred to as "washdown" in the succeeding text.
S-4. The validity of S-l also requires that an exact description of the
plume be used to calculate washout rates. This is in contrast to a
consideration of particulate plumes, where only a total mass term is
required. Also, if nonlinearities exist in the microphysical rela-
tionships dictating washout of S0«, then fluctuations of the plume
with time may become an important consideration.
S-5. There is a rapid initial oxidation of S0« to SO, in the plume near the
source; this reaction proceeds at a much slower rate at greater dis-
tances .
Speculation S-5 is based on measurements of sulfate in rain collected at
various downwind distances from the plant. It is questionable for two
reasons, these being the inherent noise in the measurements (turbidimetric),
and the fact that washout measurements provide a rather indirect means of
assessing in-plume behavior. This speculation is in accord, however, with
many of the more direct attempts to study in-plume oxidation processes.
The speculations pertaining to reversibility and the influence of acid-
forming impurity provided a basis for performing more valid calculations of
S0« washout. Subsequently, this approach has been generalized to apply to
all gases, and has been described in a separate publication.3
Additional field research was necessary to test the validity of the above
postulates. We felt that a relocation of sites of field studies to areas low
in pollution background would be advantageous, owing to the noted interference
12
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effects. Moreover, we believed that controlled field experiments—employing
releases of pure SO—would be valuable for direct testing of the desorption
mechanism. Information obtained from these tests plus results of another
power plant study could then be employed in a final analysis of washout from
power plant plumes.
INITIAL QUILLAYUTE STUDY
The site chosen for the controlled release experiments was the Quillayute
airfield, located on the Olympic Peninsula in western Washington State.
This location is characterized by near-zero S0_ background concentrations,
and ample rainfall. S09 was released simultaneously from two towers (ad-
justable heights from 0 to 30 m) and was analyzed in rain collected on
surrounding arcs, as shown in Figure 6. Comparison of washout concentra-
tions resulting from different release heights enabled us to observe the
desorption effect. In addition to the field experiments, laboratory studies
were conducted to evaluate quantitatively the relationship between SO.
solubility, concentration, and rain acidity. Also, an attempt was made to
model SO- washout based upon the postulated reversible behavior.
The SO., solubility measurements were successful in extending quantitative
knowledge of SO--H 0 interactions down to ambient concentrations of the
order of parts per billion. They demonstrated conclusively the strong in-
fluence of rain acidity on solubility under these conditions, verifying
partially the above speculation S-2 (cf. DHW, pg. 29).
Two models of reversible gas washout were developed; one was a computer
model, and the other a simplified linear version amenable to hand calcula-
tion. The first of these is described in detail in Appendix C of this re-
port. The second has been documented in former reports (DHW; Males'4), and
in the open literature.5 The basis for these models is summarized in
Appendix B. As expected, the Quillayute SO- washout results did not exhibit
the anomalous behavior observed at Keystone. The absence of background im-
purities and non-volatile acid-forming plume constituents allowed the cross-
wind concentration distributions to assume even, well-defined patterns, re-
flecting the quasi-Gaussian form of the plume. In addition, we observed the
13
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measured concentrations to compare reasonably well with predictions of the
newly-derived models. Figure 7 is an example of such a comparison.
Conclusions of the initial Quillayute series can be itemized as follows:
C-6. S09 washout is indeed a reversible phenomenon and desorption can and
will occur under appropriate circumstances, which readily exist in
the natural atmosphere.
C-7. Solubility of SO in rain depends strongly on rain acidity, and can
be accounted for quantitatively.
C-8. The reversible-absorption-based models of washout provide a fairly
accurate means of SO- washout prediction—at least under the ideal
conditions exemplified by the Quillayute studies.
Other aspects of the problem, such as the influence upon washout of time-
fluctuations of the plume, were not elucidated adequately by these experi-
ments. In addition, the relative effect of dry deposition was brought into
question, and not resolved. To further examine these complications, x^e
felt that an additional series of experiments at Quillayute would be bene-
ficial to the program. These were conducted immediately prior to the power
plant runs, which were held at Centralia, Washington, early in 1972. The
remaining sections of this report provide a detailed description of these
studies.
-------
CTl
O
80
60
40
20
80
60
40
RUN 4E ARC C
H = 12.2 M
Q = 0.0487 MOLES/SEC •
- U = 2.2 M/SEC •
RUN 4E ARC B
EQUILIBRIUM
GAS-PHASE CONTROLLED
STAGNANT DROP
10 METERS
CROSSWIND DISTANCE BENEATH PLUME
FIGURE 7. PREDICTED AND MEASURED S02 CONCENTRATIONS AT QUILLAYUTE - FIRST
SERIES. TYPICAL RUN - DASHED AND SOLID CURVES SHOW MODEL PRE-
DICTIONS .
16
-------
SECTION IV.
PROGRESS IN WASHOUT MODELING
INTRODUCTION
The washout modeling activities of this program, as indicated in Figure 1,
have been in progress since the latter stages of the Keystone field series.
We have described modeling during earlier phases of this project (DHW)•
accordingly, this section will concern only modifications of these earlier
models, and related progress since the time of the previous report.
MODEL MODIFICATIONS
The nonlinear washout model utilized by the previous study to calculate S0?
scavenging rates at Quillayute has been modified substantially to increase
its versatility, applicability: and numerical accuracy. Additional changes
have been made to gain greater simplicity by eliminating features which, at
this stage of development, do not appear necessary for the provision of re-
liable results. A complete description of the nonlinear model is given in
Appendix B, and the final version of the computer code (EPAEC) is provided
in Appendix C. Modifications of the previous model to formulate this final
version are itemized as follows:
1. The Euler algorithm for solution of the basic differential equation
for concentration response of a falling drop was replaced by a
fourth-order Runge-Kutta technique, resulting in a substantial in-
crease in computational accuracy.
2. The code has been rewritten in terms of a master subroutine (MASTED)
enabling an overall program to be written rapidly for a particular
plant, topographical situation, and computational requirement. One
simply writes a calling program that reads the required data, com-
putes results by the command "CALL MASTER, ' and prints the results
as desired. Alternatively, one can employ the general calling pro-
gram (EPAEC) listed in Appendix C. and supply appropriate data in
the formats required.
17
-------
3. Equilibrium washout was investigated using the previously-derived
criteria (DHW, pg. 20). In terms of a Gaussian plume superimposed
on a constant background level, this may be expressed by the form
-6nK H'ua a2y, (ground level
7,— f~i T~TT~~T\ > constant. (1)
vtaQ exp(-% - % y2/a2) v '
Here, a = drop radius,
H" = modified Henry's law constant,
h = release height,
K = overall mass transfer coefficient,
y
-------
6. Chemical-reaction decay of SO is incorporated into the model by
assuming a quasi -first-order gas-phase reaction. Various reaction
rates can be accommodated by adjustment of the rate constant, which
is read as input data.
7. Background SCL influences are accounted for. The background SO,
concentration is supplied as input data.
As indicated by the documentation and flow chart given in Appendix C. this
model retains the advantages of modular construction, so that various com
ponents may be replaced easily, if desired. The Pasquill-Gif ford plume
model6 used here, for example, can be replaced by a more sophisticated
counterpart, simply by replacing the subroutine YAB. Similarly, the wash
out of gases other than S0~ may be calculated with this model upon supply-
ing the appropriate input data after replacing the solubility subroutine
HPRIME, which applies specifically to the system SO_-H 0. Additional
aspects of the washout computer code are discussed in detail in Appendix C.
RAINDROP MICROPHYSICS
Previous calculations of mass transfer to stagnant drops performed during
this project have been based upon a linearization of the liquid-phase mass
transfer coefficient,3
5D c
where D is the diffusivity of SO in water, and c is the total liquid
AX L X
phase concentration (nominally 1/18 moles/cm3 for water). Equation (2) is
based upon the concentration response of a stagnant drop experiencing a
linear increase of gaseous pollutant concentration in time. Since raindrops
do not generally experience linear increases, however, Equation (2) is onlv
an approximation to actual stagnant-drop behavior. A rigorous solution for
these circumstances was presented in HTW on page 40; use of this result in
the washout model however, requires knowledge of an interfacial concentra-
tion and necessitates time-consuming iterative calculations.
19
-------
The above problems can be avoided by deriving a rigorous drop-response
equation that is based on the bulk gas concentration rather than that ex-
isting at the drop surface. This was accomplished in the present study by
combining the equation for mass transport through the gas phase
N. = -k (y., - Hx. ) , (3)
Ao y Ab Ao
with the equation expressed in HTW, page 40, subject to step-function con-
centration forcing, and applying Duhamel's theorem.7 The result is
- ^ [{[ (t - T) - Hx ] Z ex (-aMr!-+ ^ " ^
Ab H I Ab Ai ., n a.2 H
1 n=i n
o
sin a [—5- sin a -- cos a ] }dT + x, . , (4)
n a2 n a n Ai
n n
where H = Henry's law constant, (see Nomenclature)
N. = flux of S0~ from the drop surfaces,
Ao 2
k = gas-phase mass transfer coefficient,
x., = bulk mole fraction of A in liquid,
Ab
x = initial mole fraction of A in liquid,
Al
x = interfacial mole fraction of A in liquid,
AO
y , = bulk mole fraction of A in gas ,
AD
t = DA • time/a2
Ax
a = roots of aaCotaa + a[3 - 1 = O,8
p = Hak /c D.
r y x Ax
The assumption of constant H has entered into the derivation of (4). This
constraint can be eliminated in numerical applications, however, simply by
recalculating a "constant" H as numerical computation proceeds .
PLUME WASHDOWN
Lowering of altitude of a gaseous plume by virtue of the uptake-release
action of falling rain has been examined to determine the importance of this
effect insofar as practical scavenging calculations are concerned. Assess-
ment of this effect requires solution of the coupled conservation equations
20
-------
for pollutant in the rain and in the gas phase;3 it presents a more complex
approach than that taken in previous modeling, which was based essentially
upon the assumption that the rain had no effect on the position of the plume.
A number of alternative mathematical approaches to this problem were con-
sidered. We finally found, however, that the most fruitful approach was to
combine the coupled, linearized conservation equations, apply repeated
Fourier and Laplace transformations to remove all differential forms, and
then invert to obtain the solutions.
Inversion of the transformed equations was performed to give, for the gas-
eous plume,
" (h ~ W
vAb(t,y.z) --_
I2rir ua
(2na
'
(5)
which posesses a characteristic ''washdown velocity" given by w = JH(c /c ).
J being the rainfall rate and c and c being the total molar concen-
trations of matter in the gas and liquid phases, respectively. 5 is a
characteristic length parameter defined in Appendix D.
A detailed description of the derivation of (5) is given in Appendix D, and
it will suffice here to provide an example to indicate the predictions of
this analysis insofar as practical modeling aspects are concerned. For
this example we have chosen a rain-plume situation characterized by the
parameters given in Table 1, which are representative of actual rains and
SO- characteristics. For reasons of simplicity, we have chosen a plume"
TABLE 1. BASIC DATA USED FOR WASHDOWN CALCULATION.
Rain Rate, J
Raindrop Diameter, a
Terminal Velocity, v
Mass-transfer Coefficient, K
y
Effective Henry's Law Constant, (H
10 ^ cm/sec
.03 cm
-300 cm/sec
8.2 moles/cm sec
3.3 x 103
21
-------
with zero diffusion for this example, which is sufficiently realistic for
illustrative purposes.
Solutions of Equation (5) for the above conditions are shown in Figure 8,
where the concentration of the gaseous SO- plume is plotted versus height
for a number of discreet transit times (t = x/u). In this plot the initial
plume (an impulse function at t = 0) is seen to spread out in a downward
direction as it is washed down by the rain.
The primary result of this analysis is the indication that, although the
gaseous plume is indeed "washed down," this effect is not a highly signifi-
cant one for SC>2 plumes over the time and distance scales of interest to
this project. The "nonfeedback" aspect of the EPAEC model (i.e., the
assumption that the rain does not affect the plume's shape), is therefore
justifiable under these circumstances.
A word of caution, however, is in order about the application of these re-
sults to other gases. The source of concern is in the use of handbook
values for H obtained at high concentrations of the gases. In some cases,
e.g., NO, CH., tritium compounds, krypton, etc., for which simple solutions
of the gases are formed, this is probably acceptable and the results predict
that such plumes would fall orders of magnitude more slowly than an S0~
plume. For other gases which are strongly dissolved, the washdown effect
can be appreciable. Ammonia gas, for example, is about ten times as soluble
in water as SO , resulting in an order-of-magnitude increase in the washdown
effect. This could indeed be a significant factor for the assessment of the
environmental impact of an NH plume.
22
-------
O
I
T -j-..
O
oo
§
o
t—
<
§ 5
o
2
O
S ^
o" 1/1
s
C3
C3
<=5
O
ffl
Q
W
<;
u
CxJ
O
to
H
Pi
H
CO
M
Q
W
oo
w
o
'NOI1VA313 3All\H3y
23
-------
SECTION V.
SECOND-SERIES QUILLAYUTE EXPERIMENTS
INTRODUCTION
The second series of controlled-release SO washout experiments conducted
at Quillayute during November-December, 1971, was designed to supplement
knowledge gained during the initial series. This design involved an expan-
sion of the sampling array to overcome some physical difficulties experi-
enced earlier, and thus provide more cases of well-defined desorption be-
havior (higher release heights in contrast with low-level releases) for
further testing of the washout models. More distant sampling was also de-
sired, in anticipation of a closer approach to equilibrium washout behavior.
Special measurement techniques were added to evaluate the contribution of
dry deposition to S0_ concentrations measured in collected rain. We ex-
pected also that an additional series of experiments would expand the range
of natural conditions—as they pertain to washout—against which to test
the models.
Realization of chest; objectives required additional sampling equipment and
a slightly modified procedure; these changes will be described below. In
general, however, the basic methods are the same as those reported in detail
previously, (DHW); accordingly, a repetition of the complete collection and
analysis procedure will not be given here.
EXPERIMENTAL METHOD
Sulfur dioxide was released from two independent regulated systems, utiliz-
ing polyethylene tubes for its transfer to the tops of portable telescoping
towers. In general, the tower releases were at different heights, and were
conducted simultaneously to ensure identical meteorological conditions.
The flow rate of S0_ was controllable, but previous results indicated that
use of different release rates for the two sources added little to the sig-
nificance of the results. Therefore, for all washout experiments in the
series, a convenient S0~ flow rate of 0.04 gram-moles/sec was used.
24
-------
During the previous Quillayute series, the full release height of 30.5 m
was not generally usable because the wind speeds encountered (usually above
5 m/sec) caused the raindrops to fall at such an angle that those which
entered the collectors would have undercut the plume. Thus for this
series, we modified the earlier grid (shown in Figure 6) to include a
sampling line at a greater distance from the source on the east grid. The
west grid was left as before. The new sampling arrangement is shown in
Figure 9. The more distant line (Line D), whose samplers averaged 290 m
from the source, was placed such that the maximum release height of 30.5 m
could be used with nearly all observed wind speeds. Line D was situated,
for convenience, along the existing warming apron and taxistrip configura-
tion of the airport.
The behavior of plumes originating lower than 30.5 m was investigated
earlier; the experience led us to choose a convenient west grid release
height which would be sufficiently different from that of the east grid to
reflect the influence of reversibility. The choice was 16.8 m. Table 2
lists sampling geometry and release parameters which apply to all the wash-
out runs of the current series.
TABLE 2. RELEASE AND_ SAMPLING P.ARAMETERS_~QUI_LLAYUT_E SECOND SERIES .
Grid Tower Height, m Operative Arcs S00 Release Rate Q, mole/sec
--. ^
East 30.5 C, D 0.04
West 16,8 A, B, C 0.04
a
A arc - 30.5 m
B arc - 61.0 m
C arc - 122 m
D line - 290 m (average)
The rain samplers—the locations of which are shown as points in Figure °—
consisted of waste basket-mounted funnels attached to 250 ml plastic bottles.
The bottles were precharged with a small amount of tetrachloromercurate (TCM)
solution for fixing of the S0_ in the rain water. Air concentration measure-
ments with simple bubblers were deleted from the procedure for the regular
25
-------
o
o 2
o
o
o
o
o
o
0$
o
o
/-!*>
OcM
o
o
O
O
O2>
O
O <£
O
O f>
o
o?,
O 10
o
o_
o
O
o
o
O
O Q
O
o
I
t-
co
<
ui
•
o
o
0 =
o,
2
*
o
Ooo
o
o
oSJ
o
O
CO
w
M
Ctf
W
CO
Q
Z
O
o
w
CO
o
H
W
2
O
53
CO
w
3
nJ
nJ
M
:=>
ex
CTv
W
PCS
>oo y
oo
ort«
OO O
26
-------
sampling arcs because past experience has shown these measurements to be
nearly in agreement with concentrations calculated from a bivariate-normal
diffusion model. Bubblers were used on Line D, however, since such measure-
ments had not been made at that distance before. Sulfur dioxide concentra-
tions in the sampled rain and the bubbler fluid were analyzed as before
using Technicon Autoanalyzers in the mobile laboratory at the site.
Wind data were collected by Gill three-component anemometers, mounted at
the S0_ release points. A third such anemometer, located atop a small
tower midway between the release towers, was added to the current study.
The height of the third Gill was 8 m; thus, for all the dual SO release
experiments, complete wind data were collected at heights of 8, 16.8 and
30.5 m.
Additional supporting equipment included a raindrop size spectrometer (rain-
drops sized by image sizing of spots from water sensitive paper) and a fast-
response rain gauge. These, plus the translators and magnetic recorder for
the Gills, were located at the control trailer, midway between the release
towers. Figures 10 and 11 are photographs showing the experimental layout
and equipment.
A typical dual-release experiment proceeded as follows: the source towers
were raised to their appropriate heights, and the mean wind speed and direc-
tion were determined. If the direction was suitable for sampling on both
grids (wind approximately normal to the tower baseline) and the rain was
sufficiently steady, the sampling funnels were deployed and the S0~ genera-
tors made ready. Upon signal from the field director, the bottles and
bubblers were set out, with S0« releases following immediately. During the
releases, the Gill recorder was operated and monitored by the field director.
The usual release time was ten or twenty minutes, shortened at the discretion
of the field director, as dictated by wind and rain conditions. At the con-
clusion of the release, the bubblers and rain samples were returned to the
laboratory, where analysis generally commenced immediately. On all occasions,
the chemical analyses were completed within 24 hours of the experiment.
27
-------
FIGURE 10. 30.5 m SO RELEASE TOWER - QUILLAYUTE SECOND SERIES.
28
-------
w
w
Q
S3
O
C_>
w
CO
w
H
H
o-
I
u
ft!
55
M
n4
W
EC
H
§
O
29
-------
EXPERIMENTAL RESULTS—WASHOUT MEASUREMENTS
During the field period November 29-December 17, 1971, fifteen S0_ releases
were made for the purpose of washout measurement. These consisted of five
dual-releases and five single releases. The latter were the result of
several different situations. The first run, Run 11 (Runs 1-10 are the
experiments of the initial Quillayute series in March-April, 1971), was
conducted on the east grid only because of a temporary shortage of SO-
cylinders. Run 17 was conducted on the west grid only so that concurrent
dry deposition measurements could be made, using personnel normally assigned
to the east grid. Runs 18-20, all on the same day, were also west grid only
because the wind direction was not favorable for using both grids. This
opportunity, however, was utilized to make dry deposition measurements on
the west grid during these runs. Table 3 lists pertinent run conditions.
The dry deposition experiments, which will be described later in this
chapter, are included in this table for chronological placement.
The rainfall encountered during the experimental period was mainly of the
continuous pre- or near-frontal passage type, which is characteristic of
the site during the winter muulat>. Wii.ii lew exceptions—namely Runs 13 and
20, which were probably convective showers and occured near the end of
storms—the rain was continuous and of remarkable constancy in rainfall
rate. A number of raindrop size spectra were collected and one or two from
each run were sized using a Zeiss particle counter. Table 4 is a listing
of the raindrop spectra selected from these data, which were deemed typical
of the runs. The spectra are consistent in character with pre-frental con-
tinuous rain spectra observed in the past at Quillayute. The exceptions,
the spectra for Runs 13 and 20, were typical convective shower spectra, con-
sisting mainly of relatively small raindrops.
Data obtained from the Gill anemometers were processed by translating the
Metrodata tapes to IBM-compatible tapes using a special-purpose computer.
These new tapes were then processed on a UNIVAC 1108 system to produce mean
and short-term wind speeds and directions, and standard deviations (a and
a.) for a variety of sampling and averaging times. The computer program
D
employed for this purpose utilized the following equations:
30
-------
TABLE 3. TIMES. TEMPERATURES, AND RAINFALL RATES-QUILLAYUTE SECOND SERIES.
Run No.
11 E
12 E
12 W
13 E
13 W
D1S
D2a
D3a
14 E
14 W
15 E
15 W
16 E
16 W
17 Wb
18 WC
19 W
20 W
Date
12-4-71
12-8-71
12-8-71
12-8-71
12-8-71
12-9-71
12-11-71
12-11-71
12-11-71
12-11-71
12-11-71
12-11-71
12-13-71
12-13-71
12-13-71
12-16-71
12-16-71
12-16-71
Time, PST
1355-1407
1039-1058
1039-1058
1438-1445
1438-1445
1155-1215
1122-1133
1154-1205
1329-1349
1329-1349
1502-1521
1502-1517
1321-1337
1321-1337
1513-1523
0940-0950
1108-1118
1512-1522
Rainfall Rate, mm/hr
1.5
2.7
2.7
1.7
1.7
1.3
1.8
1.8
1.1
0.88
2.2
2.2
2.5
3.1
3.2
1.1
Temperature, °C
4.4
5.0
5.0
9.4
9.4
2.2
2.2
2.2
2.2
2.2
2.2
2.2
8.3 .
8.3
8.3
a
HDry deposition run
Includes dry deposition run D4
£
Includes dry deposition run D5
31
-------
TABLE 4. RAINDROP SIZE FREQUENCY3 DISTRIBUTIONS-QUILLAYUTE SECOND SERIES.
Run No.
11
12
13
14
15
16
17
18
19
20
.024
.22
.135
.22
.27
.16
.17
.25
.272
.11
.60
.030
.14
.16
.13
.167
.155
.19
.23
.32
.19
.15
.038
.105
.275
.07
.157
.215
.17
.21
.241
.29
.12
Diameter, cm
.046 .060 .074
.085
.11
.07
.107
.12
.11
.20
.106
.24
.05
.105
.095
.11
.093
.11
.13
.04
.018
.06
.02
.095
.080
.12
.07
.09
.09
.06
.017
.03
.02
.094
.095
.065
.08
.05
.065
.06
.01
.017
.02
.04
.118
.075
.045
.13
.043
.055
.06
.009
.05
.148
.045
.03
.07
.027
.025
.02
.01
.190
.035
.005
.016
.005
Tabulated values are the proportion of raindrops contained in the inter-
val between the diameter of that entry and the preceding diameter.
=
(EV)2)% f
'1 -)
9 = 180° - 57.3 - — — , (7)
Z(tan
• (10)
where N is the number of discrete data points sampled and the remaining
terminology, as defined in Section X, takes its usual significance.
Average values of the wind parameters obtained from the anemometer data in
the above manner are given in Table 5; the values of a and afi given
32
-------
TABLE 5. WIND PARAMETERS CALCULATED FROM_ANEMOMET ER_DATA-
OJJILLAYUTE SECOND SERIES
-» Arc Aa Arc Ba Arc Ca Line D3 VERT° Run Time,
o
-------
here are based on sampling and averaging times equal to the SO- release
times and one-fourth the transit times, respectively; values actually used
for EPAEC computations are underlined. Standard deviations calculated for
additional combinations of sampling and averaging times were utilized for
various exploratory analyses of the washout data; these will be described
later in this section.
Results of the S0« analyses of collected rainwater are shown in Figures 12
through 24, which are distribution plots of rainfall concentration versus
wind direction. The solid bars represent the observed concentrations; the
lines show the results of EPAEC model calculations, which will be discussed
in the analysis section. The lower figure in each case is the deposition
for the inner sampling arc and the upper figure is the more distant arc
(line). The distributions are essentially complete, indicating containment
of the plume by the deployed collectors. Run 13 is not included in these
figures, because of an early termination of the shower. Very little rain
fell during the actual release time, which led to severe dilution of the
SO- content by the previous heavier rain; thus, little detectable S09 was
present. Inactive sampler regions are indicated by cross-hatching. In
most of the dual-release runs, some SCL from the west source was deposited
on Line D, which was outfitted with collectors to receive east-grid S0_.
Thus, the distributions for the west source on Line D are not complete, and
concentrations are indicated there only for Runs 12 and 16, where suitable
sampling and separation occurred. Complete rain concentration data are
tabulated in Appendix A.
The total deposition of SO. for each arc was determined, and washout rates
(the amount of SO- deposited per unit distance downwind per unit time) cal-
culated using the approximation
Zm. Ay
M ^ —-— fn ^
M ~ AT ' U±;
where Zm. is the total amount of S0_ collected on the arc, Ay is the
distance between collectors on the arc, A is the area of one precipitation
collector (1000 cm2), and T is the time of the release. These washout
rates are listed in Table 6, in terms of both absolute values and percent-
ages of the emission rate.
34
-------
TABLE 6. MEASURED WASHOUT RATES
QUILLAYUTE SECOND SERIES
M, (pioles/sec cm )xlQ10 M/Q,
25.9
56.0
41.4
99.5
8.22
0
2.54
0.71
0.94
66.5
143
30.5
60.6
10.3
85.4
18.6
58.4
29.0
146
119
41.0
b
9.86
189
103
214
31.0
127
14.6
53.9
(percent /cm ) x 10 5
0.65
1.40
1.04
2.49
0.21
0
0.06
0.02
0.02
1.67
3.58
0.76
1.52
0.26
2.14
0.46
1.46
0.73
3,65
2.98
1.03
b
0.25
4.72
2.58
5.35
0.78
3.18
0.37
1.35
Run Arc
HE C
D
12 W B
C
E C
13a E B
C
W C
D
14 W B
C
E C
D
15 W A
C
E C
D
16 W A
C
D
E C
D
17 W A
C
18 W B
C
19 W B
C
20 W B
C
Due to early stop of generation, concentrations measured marginal. Non-
zero values of M represent measurable rain concentration in only one
sampler.
Overlap plumes from two sources occured.
35
-------
12
°^0
pr\
I
CO
id
O
O
<
S
o
z
o
o
20
10
RUN HE LINED
GAS-PHASE CONTROLLED
STAGNANT DROP
\
N
11 13 15 17 19 21
RUN HE ARCC
FIGURE 12.
13 15 17 19 21 23 25
SAMPLE POSITION NUMBER
MEASURED AND CALCULATED S02 CONCENTRATION IN RAIN - RUN 11.
36
-------
20
10
0
30
20
10
RUN 12W LINE D
RUN 12WARCC
o
x
f\
i
^
O
O
z"
o
RUN 12W ARC B
50
8 40
z
19 21 23
—-- GAS-PHASE CONTROLLED
— STAGNANT DROP
cc
30
20
10
17 19 21
SAMPLE POSITION NUMBER
FIGURE 13. MEASURED AND CALCULATED SO CONCENTRATION IN RAIN - RUN 12 W.
37
-------
GAS-PHASE CONTROLLED
STAGNANT DROP
17 19 21
SAMPLE POSITION NUMBER
FIGURE 14. MEASURED AND CALCULATED SC>2 CONCENTRATION IN RAIN - RUN 12 E.
38
-------
60
40
rr,
I
o
LU
O
s
s
o
z"
o
O
z
o
CJ>
20
0
60
40
20
0
RUN 14W ARC C
GAS-PHASE CONTROLLED
STAGNANT DROP
V
15 17
19
RUN 14W ARC B
15 17 19 21 23
SAMPLE POSITION NUMBER
FIGURE 15. MEASURED AND CALCULATED S02 CONCENTRATION IN RAIN - RUN 14 W.
39
-------
I
S 20
X
^
^
£ 10
LjJ
O
0
e>
z"
o
i—
<
40
20 —
RUN 14E LINED
GAS-PHASE CONTROLLED
STAGNANT DROP
12 14 16 18 20
RUN 14EARCC
17 19 21 23
SAMPLE POSITION NUMBER
FIGURE 16. MEASURED AND CALCULATED SC>2 CONCENTRATION IN RAIN - RUN 14 E.
40
-------
20 22
GAS-PHASE CONTROLLED
STAGNANT DROP
14 16 18 20 22 24
SAMPLE POSITION NUMBER
FIGURE 17. MEASURED AND CALCULATED SO CONCENTRATION IN RAIN - RUN 15 W.
41
-------
o
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20
10
o
(—
<:
t—
UJ
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10 —
RUN 15E LINE D
RUN 15EARCC
GAS-PHASE CONTROLLED
STAGNANT DROP
V
SI
11 13 15 17 19
14 16 18 20 22
SAMPLE POSITION NUMBER
FIGURE 18. MEASURED AND CALCULATED SO CONCENTRATION IN RAIN - RUN 15 E.
42
-------
o
CO
o
o
O
O
RUN 16W LINE D
10 12 14 16 18 20
RUN 16W ARC C
27 29
GAS-PHASE CONTROLLED
STAGNANT DROP
RUN 16W ARC A
.- 120 -
80
40 -
21 23 25 27 29
SAMPLE POSITION NUMBER
FIGURE 19. MEASURED AND CALCULATED SO CONCENTRATION IN RAIN - RUN 16 W.
43
-------
40
20
o
(/I
a
o
0
<
Of.
o
1
40
20
RUN 16E LINE D
RUN 16E ARC C
GAS-PHASE CONTROLLED
STAGNANT DROP
22 24 26 28 30
23 25 27
SAMPLE POSITION NUMBER
FIGURE 20. MEASURED AND CALCULATED SO CONCENTRATION IN RAIN - RUN 16 E.
44
-------
o
en
a
o
o
o
t—
-------
80
40 —
°b
0
I 12°
i
t—
UJ
O
O
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GAS-PHASE CONTROLLED
STAGNANT DROP
26 28 30 32 34
SAMPLE POSITION NUMBER
FIGURE 22. MEASURED AND CALCULATED SC>2 CONCENTRATION IN RAIN - RUN 18.
46
-------
80
S 40
X
»>
I
S
CJ>
uj
O
O
o
z
O
80
40
RUN 19WARCC
GAS-PHASE CONTROLLED
STAGNANT DROP
RUN 19W ARC B
31 33 35 37
SAMPLE POSITION NUMBER
FIGURE 23. MEASURED AND CALCULATED SO CONCENTRATION IN RAIN - RUN 19.
47
-------
80
40
°b
O
a o
o
on
s
o
z 80
40
RUN 20W ARC C
GAS-PHASE CONTROLLED
STAGNANT DROP
RUN 20W ARC B
30 32 34 36
30 32 34
SAMPLE POSITION NUMBER
FIGURE 24. MEASURED AND CALCULATED S00 CONCENTRATION IN RAIN - RUN 20.
48
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ANALYSIS OF WASHOUT RESULTS
The experimental results presented in the previous sections were analyzed
by comparison with predictions of the EPAEC model, based on the input data
given in Tables 2 through 5. As noted previously, these calculations were
performed using plume-spread parameters based on sampling and averaging
times of the S0~-release time and one-fourth the source-receptor travel
time, respectively, indicating the tacit assumption of mean-plume behavior.
These calculations were based on assumptions identical to those of the
analysis of previous Quillayute data (DHW); aside from the improvements in
the numerical algorithms of the EPAEC code, therefore, the calculations are
similar and are directly comparable. As seen from the comparisons of re-
sults given in Figures 12 through 24, the computed values generally tend to
be close to those observed, although the agreement does not seem to have
improved from that found in the previous study. Values tend to fall be-
tween the well-mixed drop—stagnant drop limits, and worse agreement between
the computed and observed values is found, generally, for near-source sampling
Arcs A and B. These characteristics also can be observed from Figure 25,
which is a plot of observed washout rates (M from Table 6) versus those
computed from the EPAEC model. In Figure 25, the limits of the tie lines
pertain to gas-phase limited and stagnant drop behavior.
The experimental results, similar to those observed previously, reflect the
presence of reversible washout. This effect is shown much more clearly and
dramatically by the Centralia results in the following section, however, and
discussion of this effect will be limited here. The observations at the
new, more distant sampling line (Line D) conform with model predictions in
an acceptable manner, giving further evidence of applicability of the wash-
out model and its basic precepts.
The relatively poor agreement between observed and calculated washout rates
at close downwind distances is thought to be primarily a consequence of plume
"undercutting" by the rain, combined with poor definition of the plume near
the source resulting from the point-source approximation. The EPAEC model
provides for the possibility of plume undercutting by the raindrops; however,
the resulting trajectories are strongly dependent on raindrop size and any
49
-------
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£0.10
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U8WC
U9WC
I I18WB
14ED, i
15ED|-—M
4WB
I20WC
0.1
1
10
PREDICTED WASHOUT RATE, (GRAM-MOLES/CM SEC) x 10
,8
FIGURE 25. MEASURED versus PREDICTED SCL WASHOUT RATES - QUILLAYUTE SECOND
SERIES.
50
-------
degree of non-representation of true conditions by the measured spectra will
seriously affect the resulting calculations. This is particularly true for
showery rain conditions (Runs 13 and 20), where the rain spectra are charac-
terized by smaller raindrops, and are quite variable over short time periods.
Additionally, the extremely high concentrations predicted by the plume model
at distances near the source (°° at (0,0,h)) are unrealistic and cause in-
accuracies in the numerical computations. If an incoming drop, as envisioned
by the model, just clears the release point and encounters the "plume," a few
centimeters, say, downwind from the source, it will experience an extremely
high concentration for a short time period. The computer code will recover
itself from the resulting perturbation—at the expense of numerical accuracy,
however. These aspects lead to the conclusion that although the EPAEC code
leaves much to be desired insofar as near-source calculations are concerned,
the noted lack of agreement does not at all challenge the validity of its
basic precepts, particularly with regard to reversibility. An additional
noteworthy point in this regard is the possibility of SO desorption from
rain during its time of residence on the funnel surfaces of the samplers.
The fact that the washout model consistently overestimates observed concen-
trations on the inner arcs suggests that such an effect may indeed have been
present; the discrepancy between observed and predicted results may have
arisen more from an inability to measure washout precisely under these con-
ditions than from any shortcomings of the model. This possibility will be
reviewed in greater detail in a later section where the dry deposition
measurements of this project are discussed.
During this program we applied a number of variations of the basic EPAEC
model in attempts to improve agreement with the experimental results. Each
of these variations falls into one of the following two classifications:
1. Attempts to improve the raindrop-microphysics component of the
EPAEC model;
2. Attempts to improve the spatial and temporal definition of the
plume-model component of the EPAEC model.
After rather extensive investigation we concluded that such elaborations did
not improve washout predictions sufficiently to warrant their incorporation
51
-------
into the basic computer code. For this reason we will not provide the de-
tailed results of these investigations here; rather, we will only itemize
and summarize them in the following paragraphs.
Stagnant Drop Response
As discussed in Section IV, the stagnant-drop option of the EPAEC code — as
it exists presently — is based on the quasi-steady-state, linearized mass-
transfer coefficient
5D c
the more rigorous relationship being given by Equation (4) . Equation (4)
can be incorporated into the EPAEC code at the expense of additional compu-
ter time and complexity, an interpolation or search routine for the roots
a being required. Test solutions employing Equation (4) however, were
found to approach those corresponding to Equation (2) closely under practi-
cal conditions. In view of this finding, and in view also of the magnitudes
of deviations caused by other features of the model, we have concluded that
incorporation of this more rigorous equation is not desirable under present
circumstances. As a consequence, the stagnant-drop option of the computer
listing in Appendix C is presented in terms of the less exact approach.
Equilibrium Washout
On the basis of the previously developed washout theory, equilibrium washout
(S0? concentration in rain in equilibrium with that in air at ground level)
should occur under conditions satisfying the criterion of Equation (1) . The
Quillayute test conditions do not, in general, satisfy this criterion. In
the previous report (DHW) , however, we observed that in many cases experi-
mental washout concentrations were near those calculated assuming equilib-
rium conditions in conjunction with a fluctuating (peak-to-mean) plume de-
scription. At that time it was apparent that this behavior occurred pri-
marily because of a coincidental overlap of predictions based on equilibrium
behavior and that assumed by the EPAEC model. This behavior also suggested
two possible additional explanations, however. The first of these was that
dry deposition and desorption of SO- from rain on the sampler surfaces is
extremely rapid, and tends to mask the effects of washout.
52
-------
Further dry deposition tests and the experimental results from Centralia,
both to be described later in this report, provided evidence contrary to
the two alternative explanations given above. In view of these findings we
terminated further application of equilibrium-based theory to the Quillayute
results.
Lofting-Plume Modification
Anemometer data from the Quillayute tests indicated a vertical component of
average wind velocity that ranged between -.25 and +.57 meters per second
with positive values predominant. The exact cause of this non-zero compo-
nent is unknown, although it probably resulted from upwind orographic com-
plexities. If this trend continued for long distances downwind, it could
effectively loft the SO plumes and consequently affect washout behavior.
This possibility was tested by supplying appropriate loft velocities (VERT
in the computer code) to the EPAEC model. The results of these tests showed
washout rates to be rather insensitive to loft in the ranges possible at
Quillayute, hence further analysis of this effect was abandoned. The loft
provision of EPAEC, however, was utilized extensively for near-source cal-
culations at Centralia. Further discussion of this feature will be presented
in Section VI.
Fluctuating-Plume Modifications
The disadvantages of applying mean-plume models for calculating gas washout
from actual, fluctuating plumes have been discussed previously (HTW, p. 207;
DHW, p. 61; Hales3). It is sufficient here to note that the generally non-
linear equilibrium relationship between gas-phase and liquid-phase concen-
trations of a species requires that the time-fluctuating concentrations en-
countered by the raindrop as it falls through the plume be represented
accurately. The importance of this requirement to the washout calculation
depends on the solubility and mass-transfer relationships of the particular
species. We suggest, therefore, that the performance of the EPAEC model in
its application to S0_ washout might be improved by replacing the original
mean-plume submodel with one accounting for time fluctuations of concentra-
tion in a more realistic manner.
53
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The peak-to-mean analysis, used previously for equilibrium washout calcula-
tions (DHW) , is unsuitable to the EPAEC model which requires knowledge of a
complete distribution of pollutant concentration along the raindrop trajec-
tory. A means for defining concentration distributions in instantaneous
plumes which is compatible with the EPAEC model was suggested by Pasquill9
and is based on the method of Smith and Hay10 for defining the concentration
of a puff. This method, which applies basically to homogeneous, isotropic
turbulence, was extended empirically to actual atmospheric conditions.
Pasquill indicates that the standard deviations of the vertical and lateral
dimensions of the instantaneous plume (a and a , respectively) should be
related to their respective components of the total intensity of turbulence,
i and iQ, by the following relationships:
, (12)
ay = 3ix . (13)
The Quillayute results were analyzed using this approach. This analysis was
performed by computing turbulence intensities (i and i ) from the anemom-
cp y
eter data, which were employed in conjunction with Equations (12) and (13)
to obtain the instantaneous spread parameters a and a . The spread
parameters thus obtained were utilized with the washout model to provide
estimates of the "instantaneous" washout patterns, which were superimposed
over the observed distribution of wind directions to arrive at estimates of
time-average washout behavior.
The instantaneous-plume approach was found to produce results that were in
somewhat better agreement with the observations than those based on time-
averaged plume behavior. This improvement, however, was not sufficient to
justify the additional complexity and computer time necessary for these cal-
culations. For this reason, we did not proceed with further examination of
this aspect of the investigation. It should be noted, however, that although
the instantaneous plume approach did not appear practical in this series of
experiments, it may prove worthwhile for the washout of gases having differ-
ent transfer rates and solubilities or if the (low frequency) wind-direction
variability is of greater amplitude. In view of the associated theoretical
54
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complexities, however, additional investigation is necessary to develop a
sound technique for applying the instantaneous plume approach.
EXPERIMENTAL RESULTS AND ANALYSIS - DRY DEPOSITION
All previous experimental analyses of washout under this program have been
based on the tacit assumption that dry deposition of S0~ on collected rain
is an unimportant source of error in washout measurements. This assumption
is undoubtedly valid insofar as deposition on rain in sample-collection
bottles is concerned; the narrow constriction of the bottle neck essentially
eliminates any gas-phase transport of S0_. Deposition to (or desorption
from) rain during its residence on funnel surfaces, however, is less well
understood. During the Keystone experiments we performed tests wherein
S0_-containing water drops were allowed to fall from a syringe through
clean air onto a rain collector. Analysis of SO contents of the collected
drops and the original solution showed perturbations caused by the drop-
funnel interaction to be insignificant. These tests were conducted in con-
fined atmospheres, however, and some questions remain with respect to be-
havior under field sampling conditions where increased ventilation of the
sampler surfaces may occur. Because of this uncertainty and because of the
expected importance of dry deposition to natural surfaces as a sink of S0_,
we conducted several tests of this effect during the Quillayute series.
The Quillayute dry deposition tests involved the use of special dry deposi-
tion samplers. These consisted of normal washout collectors which were
shielded to prevent natural rainwater from entering, but open to the ambient
air concentration of S0_. The "rain" provided to the funnels consisted of
drops of either distilled water or a dilute TCM solution, issued by hypo-
dermic needles. The needles were mounted on rotating arms so that the en-
tire areas of the funnels could be covered by the water enroute to the
bottle. The rate of dripping from the needles (rainfall rate) could be
varied to approximate that of the ambient rain. In a given dry deposition
experiment, two of these samplers were placed side-by-side. These were
identical except that one employed distilled water and the other used TCM
solution as the dripped liquid. Also nearby was a normal washout sampler.
In terms of fluxes of SO- through the top openings of the funnels, these
55
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three samplers allowed the following measurements:
Flux 1. Due to rain, containing washed-out SO^, impacting the funnel
naturally and draining into the bottle where the SO- is fixed
(normal collector);
Flux 2. Due to distilled water, impacting the funnel, absorbing S0_
while residing there, and draining into the bottle where the
S09 is fixed (artificial rain dripper and shielded funnel);
Flux 3. Due to TCM solution, impacting the funnel, absorbing SCL
while residing there, and draining into the bottle (artificial
TCM rain dripper and shielded funnel).
Seven experiments were performed during which these three samplers were used.
In most cases, a bubbler air sampler was also included for concentration
measurement at the approximate level of the funnel surface. Three of the
experiments were conducted independently from washout experiments (identi-
fied as Dl, D2, and D3—cf. Table 3), and four were conducted along with
washout Runs 17-20. Of the latter, two (19 and 20) led to null results as
the collectors were not properly located with respect to wind direction.
Table 7 presents experimental details and results of the tive successful dry
deposition experiments. Incompleteness due to technical difficulty and
meteorological phenomena are noted. Gas-phase concentrations are presented
here, for convenience, as corresponding equilibrium values in the liquid
phase. Deposition fluxes may be determined from the concentrations listed
in this table by multiplying by the rain rate J.
Interpretation of dry-deposition behavior from the Quillayute results is
complicated by a number of factors. An approximate analysis can be per-
formed, however, by applying an extension of the reversible mass-transfer
theory employed for scavenging calculations. It should be noted in this
regard that the deposition velocity concept, which is based on the assump-
tion of irreversible behavior, is not applicable for these purposes.
56
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TABLE 7. SUMMARY OF DRY DEPOSITION RESULTS
Normal TCM Equilibrium H20/Natural/TCM Source Sampling
H20 Drip Rain Drip With "Rain" Rates, Height Distance
Run Sampler Sampler Sampler Ambient Air (cm/sec) * 105 m m
Dl
D2
D3
D4f
D5b
52
29
24
I
0
38
No Rain
43
3.2
4.2
72
76
50
0
.04
214
159
140
No Measure
59
2.5/3.6/11.1
7.0/ 0 /27.8
8.3/7.9/7.9
4.2/6.9/1.7
4.2/8.7/7.0
3
8.5
8.5
16.8
16.8
30.5
61
61
30.5
61
Q
Concurrent with Run 17
Concurrent with Run 18
It is convenient to begin by considering the inner surface of a funnel being
used as a rain collector. The rain impinging on this surface will be ex-
posed to the ambient air for a short time before running into the collection
bottle. Because of this, a certain area a* of water will be exposed to
the ambient air in the form of drops, rivulets, or films, providing a sur-
face for interphase transfer of SO,,, a* is expected to depend in a com-
plex way on a number of factors, including the surface properties of the
collector; it should increase with rain rate, (roughly) approaching the
collector surface area A* as the rate becomes large.
The rate of S0_ transport to the surface water on a collector depends upon
both a* and the concentration driving force. This relationship can be
expressed in a semi-empirical manner as follows:
w K a*
F, = — = ~-(c - c ) , (14)
d A c A eq avg
where F is the flux, w (moles/sec) is the rate of SO transport to the
surface water by the dry deposition mechanism, c is the concentration of
SO- in the deposited water that would exist at ambient air concentrations
under equilibrium conditions, and c is the total liquid-phase concentra-
X
tion (nominally 1/18 moles/cm3, preserved in the equation to provide a
definition of the mass-transfer coefficient K consistent with the
x
57
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treatment throughout this report). A denotes the area of the funnel mouth
and c is some representative average concentration of S0_ in the sur-
face water. We will estimate c in the present treatment by assuming
that
Cavg = %(cr + Cf} ' <15>
where c is the concentration of S0? in the rain impinging on the surface
and cf is that of the water collected in the sampler bottle.
K is similar in concept to the mass-transfer coefficient used for washout
x
calculations except that it is based, for convenience, on the liquid-phase
driving force. K will vary in a complex manner with air ventilation of
X
the sampler, surface water configuration, and rain rate. Neither K nor
a* can be predicted a priori. One can proceed, however, using the well-
known chemical-engineering technique of lumping these variables together
and proceeding on a semi-empirical basis.
If one assumes that the Quillayute data arising from the covered, distilled-
water drip sampler characterizes behavior from incoming rain at zero concen-
tration, then c = 1/2 c and K a*/c A can be calculated. As indicated
avg r xx
by the results shown in Table 8, the relationships between K a*/c A and
X X
rain rate or wind speed is not totally clear. The zero value for D5 is ex-
pected to have arisen primarily from low concentration measurement error,
and probably can be excluded for present purposes; the other values are
centered reasonably closely around 10~5 cm3/sec, suggesting that this value
of K a*/c A might be utilized for order of magnitude estimates of dry
X X
deposition behavior. In proceeding, one should note that data from the
rotating syringe apparatus provides only approximate values of K a*, since
X
both the mass-transfer coefficient and the surface area might be expected
to vary for natural rain, which encounters the surface with a variety of
drop sizes and impact velocities. The present values are expected to be
reasonable first estimates of natural behavior, however, and will be employed
in the subsequent analysis of deposition phenomena.
Equation (14) can be extended to allow prediction of dry deposition condi-
tions by defining fluxes for separate mechanisms. Thus if a total flux F
58
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Run
Dl
D2
D3
D5
"Rain" Rate,
(cm/sec) x 105
2.5
5.5
6.3
4.2
u,
cm/sec
149
253
230
188
TABLE 8. TRANSPORT PARAMETERS FOR DRY DEPOSITION TESTS
K a*/c A,
x x
(cm/sec) x 1Q5
.69
1.41
1.55
0
is defined as the net rate of SO- (washout + dry deposition) passing through
the top end of the collection funnel divided by the area of the opening,
then
Ft - Fr + Fd - V '
where F = c J and F, = (c,. - c )J are the fluxes for washout and dry
r r d f r J
deposition to the funnel surface. Incorporating Equations (14) and (15)
one obtains
(Gf - Cr> ' l(ceq - *
-------
TABLE 9. CALCULATED INCIDENT RAIN CONCENTRATIONS FOR DRY DEPOSITION RUNS
Dl AND D3.
Concentrations of S02 In Liquid,
(moles /cm3) x 109
Measured From Rain Sampler Calculated Incident
Dl 38 0.72
D3 43 17.7
Equation (14) can be used to apply the results of the dry deposition tests
to estimate errors in the washout measurements arising from dry deposition.
Provided the group K a*/c A is known, this equation can be applied to de-
X X
termine the ratio of the incident-to-measured concentrations, c /cf, for
any set of values of the rain rate and the ratio c /cf. Choosing
K a*/c A = 10~5 cm/sec (as suggested by the above dry deposition results),
X X
one obtains error curves such as those shown in Figure 26, where the con-
centration ratio is expressed as a function of the rain rate for parametric
values of c /c .
eq t
The curves in Figure 26 illustrate several important aspects of dry deposi-
tion errors and of the limits of this analysis. Rain impinging on the
collectors in a state subsaturated with respect to its surroundings
(c /c.. < 1) will result in measured concentrations below those of the in-
eq f
cident rain because of desorption; conversely, situations involving
c /c,_ > 1 will exhibit positive deviations. Whenever c /c. is close
eq f eq t
to 1, of course, there will be little deviation owing to the absence of any
driving potential for mass transfer.
It is evident that the Qui1layute-type samplers provide an extremely poor
measure of washout whenever rain rates are low. This measurement capability
improves with increasing rain rate, approaching an ideal situation (c - cf)
as the rain rate becomes large. Fortunately, the Quillayute experiments in-
volved rain rates greater than 2 x 10~5 cm/sec (0.9 mm/hr), and values of
c /c ranging between zero and approximately two. Corresponding estimates
eq t
of sampling errors, then, range from zero to on the order of thirty percent.
Such sampling errors are not considered to be serious in view of the noted
deviations between experiment and the washout model. Applying the indicated
60
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61
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corrections does improve the agreement between predicted and experimental
results, especially for the near-source arcs where high estimates from the
washout model have been noted. The magnitude of this correction, however,
is often insufficient to bring the experimental values to within the pre-
dicted range. It is also evident that the previously mentioned problems
with undercutting and near-source plume modeling play a prominent role in
distortion of the predicted results.
The rather odd behavior of the Figure 26 curves at low rain rates should be
noted. This is an outcome of the assumption of a constant value of
K a*/c A, which becomes more invalid as the rain rate decreases, until mass
xx
conservation is violated and prediction of negative concentrations results.
Since a* must tend toward zero for very small rain rates, actual behavior
should follow approximately that indicated by the dashed lines in this
region. Such behavior is immaterial to the present situation, which in-
volves rain rates in the region where deposition measurements were made
(that is, always above the dotted-line region). It is still important to
note, however, the strong qualitative evidence that the Quillayute type of
sampler provides an extremely poor measurement method whenever rain rates
are very low.
Finally, the results from the dry deposition samplers utilizing TCM solution
in their rotating needles should be noted. Since this solution was expected
to act as a total sink for SO immediately after it contacted the liquid
phase, these samplers provided a measure of gas-phase resistance to mass
transfer in the dry deposition process. Corresponding calculations of
K a*/c A for these experiments showed this group to be about twice as large
X X
as that obtained for the pure water experiments, indicating an approximately
equal importance of gas-phase and liquid-phase influence on the dry deposi-
tion process. Such behavior, in addition to providing an explanation for
the previously mentioned finding of low desorption rates from non-ventilated
samplers, further illustrates the complexities of this problem. In view of
these factors, any application of the deposition results of this section for
sampling conditions outside the observed range of wind speeds and rain rates
should be performed with caution.
62
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SECTION VI.
CENTRALIA EXPERIMENTS
INTRODUCTION
The recent construction of the first major coal-fired power plant in the
Pacific Northwest at Centralia, Washington, provided a convenient site for
further study of the washout of power plant effluents. In addition to the
economic attractiveness of the site—it is located essentially midway be-
tween Hanford and Quillayute—it also provided the chance to examine atmos-
pheric effects of a power plant in a region that is new to such sources,
possessing low background levels of the pollutants of primary interest.
The Centralia study represents an intermediate situation between the rela-
tively ideal controlled-release, zero-background study of Quillayute and a
study of a large power plant—such as Keystone—in a heavily polluted area.
In contrast with our Keystone experience, we were able to isolate the
effects of the effluent plume with rain-concentration measurements and de-
termine the effect of the plant on local levels of SO-, SoT» and H in pre-
cipitation. The results of the measurements and model calculations provided
a good test of the EPAEC model's effectiveness in a situation more real than
that of Quillayute, but still having less uncertainty with regard to back-
ground levels and distinction of source.
The Centralia steam plant is located in Hanaford Valley, about five miles
northeast of Centralia, Washington. The first of two generating units went
into operation shortly before our field research began in February, 1972.
Pertinent plant operation data with outputs at that time, are listed in
Table 10. Precipitator testing was underway during the period of our ex-
periments, and as a result the firing rate of the plant varied considerably,
as is noted later in Table 13.
As indicated by the map in Figure 27, the plant is located in a wide valley.
Surrounding hills rise to about 300 feet above the valley floor and thus to
within about 200 feet of the top of the stacks.
63
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H
CO
H
£3
H
CJ
CM
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64
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TABLE 10. CENTRALIA STEAM-ELECTRIC PLANT STATISTICS
(February-March, 1972)
Generating Capacity 700 megawatts
Stack Height 470 feet
Coal Type Subbituminous, 8100 BTU/lb
Sulfur Content (Average) 0.55%
Firing Rate (Average) 300 tons/hr
Cooling Towers Forced-draft
EXPERIMENT DESIGN
Precipitation was collected on the sampling array shown in Figure 28. Line
A (inset) was set up on power plant property, flanking the location of the
experiment control center. Lines B-D were situated along existing state
and county roads in mostly open valleys downwind of the plant. Line B is
fragmentary because of impassability of a portion of one road in the area.
Additional collection sites were located at a greater distance behind the
resulting gap, providing more dense coverage in the expected downwind sector.
Each rain collector consisted of a 20 cm diameter funnel, supported by a
steel rod and laboratory support. A 500 ml plastic bottle, capable of hold-
ing 1.5 cm of rainfall (enough for several hours of rainfall normally) was
attached to each funnel. A collector containing TCM solution sampled rain-
borne SO- at each active collection site, and a separate collector contain-
ing hydrogen peroxide sampled rain for subsequent sulfate analysis. Actu-
ally, the latter sampler indicated total sulfur, as it converted S0_ to
sulfate—the sulfate concentrations were derived later by subtraction of
the SO- as measured from the TCM-doped collectors. At every third site an
additional collector sampled untreated rainwater for pH and trace-metal
measurement. Air concentrations of S02 were also measured at these sites
using battery-driven bubbler boxes.
Supporting instrumentation was essentially the same as for the Quillayute
studies, except that pilot balloons were flown to determine mean wind direc-
tion and speed prior to runs, and a portable rawinsonde unit was used to
obtain wind, temperature and dew-point information during runs. The rawin-
sonde unit was located at the control center on Line A, as were raindrop
sizing equipment (calibrated water sensitive paper), and the fast response
rain gauge.
65
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A Gill three-dimensional anemometer was operated atop a 30.5 m portable
tower, which was erected on a hilltop approximately 3 km downwind from the
plant site on Line B. The elevation of the Gill was about 140 feet below
the level of the top of the active stack. Figures 29 and 30 are photo-
graphs of relevant installations.
Analyses of the samples (with the exception of trace metals) were performed
on site at the Battelle portable air pollution laboratory. Technicon Auto-
analyzers were used to determine sulfate and SO,, concentrations; analyses
were usually completed within 24 hours of sampling.
S09 analyses were conducted using the modified West and Gaeke method, which
was employed for previous field studies under this program (HTW, DHW).
Sulfate analyses were performed using the methylthymol blue methodology de-
scribed by Lazrus, et al.11 The accuracy of these methods can be stated
approximately using the following expression for expected analytical error:
E '=* ±(s + Bcf) . (18)
Here, s is the sensitivity limit of the technique, B is an accuracy param-
eter, and c, is the sample coucentj.ai-J.oa. For the S0_ analysis, B was
about 0.05 and s was in the neighborhood of 0.1 micromoles/liter; for
sulfate these values were about 0.1 and 0.2 milligrams per liter, respec-
tively.
The field crew consisted of three sampling teams of two persons each, and a
field director. When a suitable rainstorm was anticipated, these persons
assembled at the control center, where initial pilot balloons were released
to determine the suitability of the wind direction, and the appropriate
sampling positions. The wind speed at plume level, thus estimated, aided
in the decision as to which three of the four available sampling lines would
be used (winds faster than about 10 miles per hour were deemed too fast for
sampling on Line A because of plume undercutting). These matters settled
(and in the event of continuing rain), collector setout was begun. When
all samplers were in place, crew members monitored the wind system and oper-
ated other supporting instrumentation. Radio communication was maintained
between the control center, the sampling lines, and the wind tower to
67
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monitor rain conditions and wind direction. Since the setout usually took
about 1 1/2 hours, several hours were generally allowed for sampling in
order to collect sufficient rain for analysis and to smooth somewhat the
effects of rain showers and short-term wind shifts.
EXPERIMENTAL RESULTS
Five experiments were performed during the February-March, 1972 field
period. Four of these involved significant collections of precipitation;
S0_, sulfate and pH measurements of the samples were performed (owing to
analytical difficulties Run C-3 did not include sulfate measurements). SO-
air concentration measurements were made at selected sites during all runs.
Basic experimental data are provided in Tables 11 through 13; complete con-
centration data are given in Appendix A. In addition, the processed con-
centration and sounding data are shown graphically in Figures 31 through 52.
These figures indicate concentration as a function of sampling location
using radial lines extending outward from the sampling points. Points with
no lines denote active sampling sites producing results too small to show
on the figures. Rain concentrations shown in these plots have been correc-
ted for background by subtraction of background concentration levels ob-
tained from off-plume samples. Sulfate background levels ranged between
0.2 and 0.6 milligrams per liter, while free hydrogen-ion background levels
(as determined from pH measurements) ranged from 0.7 to about 16 micromoles
per liter. S0~ did not appear in background rain samples in significant
concentrations. Figures 31 through 52 are presented in the following para-
graphs in the context of individual descriptions of meteorological condi-
tions for each of the experiments.
Run C-l (February 27)
An energetic storm dropped over one inch of rain on the area the night of
February 26-27. Precipitation decreased in the morning and stopped com-
pletely shortly after sampler deployment. Strong winds continued throughout
the sampling period. Although no significant rain was collected, air-
concentrations of SO^ were measured: these are shown as a function of sam-
pling location in Figure 31.
70
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Run C-2 (February 29)
A filling surface low off the Washington coast, moving northeast, created
southwesterly flow of moist and unstable air over the area. Aloft, the
Jetstream was also southwest-to-northeast and very strong, bringing the
liklihood of considerable precipitation. The freezing level was quite
high (7500 feet) in the early morning and dropped to 4000 feet as the storm
passed. Rainfall totalled 1.27 inches at Centralia; rainfall amounts
collected by our samplers (averages for the sampling lines) are shown in
Table 11. The lower-level temperature and dewpoint profiles, as well as
winds recorded by the rawinsonde flight, are shown in Figure 32. Measured
rain concentrations of S0_ are shown in Figure 33, and for comparison, in
Figure 34 is a plot of the concentrations calculated by the EPAEC model.
This comparison and comparisons for the other runs will be discussed sub-
sequently in the analysis section. Figures 35, 36, and 37, are plots of
S02 air concentration, and SO, and H rain concentration measurements,
respectively.
Run C-3 (March 1)
This was a situation of a weakening storm; a warm front on the coast at
1300 PST was occluded by the time of its passage over the Centralia area
at 2200. The surface flow of air was southerly, cold and moist, but aloft
it was southwesterly below 10,000 feet and westerly above. The Jetstream
was weak overhead. The freezing level was near 3000 feet in the morning
and dropped slightly by the next day. The precipitation in Centralia was
only 0.37 inches during the day, commencing as snow. The snow changed to
sleet near noon, and finally rain at the surface at about 1400. The wind
direction at the plant throughout the morning was unsuitable for sampling
(easterly), but changed to southerly near 1400, when setout began. Rawin-
sonde, SO , and H concentration data are shown in Figures 38, 39, 41, and
42, with the corresponding EPAEC computations in Figure 40. The generally
small volumes of rain collected created a problem for the sulfate analysis;
the quantity of hydrogen peroxide pre-added to the sampler bottles proved
to be too great in relation to the rain volume collected, resulting in the
previously-noted obscuration of the sulfate levels. Despite later efforts
95
-------
to separate the sulfate by other methods, these data were not acquired for
Run 3. (On later runs, a smaller amount of peroxide was pre-added, and no
such problems were encountered.)
Run C-4 (March 5)
An occluded front passed the area near 0400 PST, and another front was near
the coast at 1300. Southwesterly flow of warm, moist air continued through-
out the sampling period. The freezing level was near 8000 feet in the morn-
ing, and dropped sharply after sampling was completed. Centralia recorded
1.76 inches of rain during the day, but the amounts varied considerably on
our sampling network, as Table 11 indicates. The run was, in fact, termi-
nated early because of heavy rain on the outer sampling lines.
The rain rate was variable at the plant, and totalled only a moderate amount.
The winds were gusty, and an attempt to launch a radiosonde package—unfor-
tunately during a heavy rain period—failed. The SC- , SO,, H results are
shown in Figures 43, 44, 45, 46, and 47.
Run C-5 (March 9)
An occluded front passed the area near 1800 PST. Warm and moist south-
westerly flow occured over the area ahead of the front. The freezing level
was high, near 10,000 feet in the morning. This run was unique among those
conducted at Centralia, in that there had been no precipitation during the
previous two days. Those days were calm and unusually warm, with a notice-
able buildup of low-level visible smoke. This last run was conducted after
the BNW tower had been removed, and was manned by a reduced crew of five
persons; thus only two sampling lines were used. The rawinsonde flight
failed. The rainfall, which totalled 0.21 inches at Centralia, was light
and essentially occured entirely during the sampling period. SO-, S0~, and
4- ^4
H data are shown in Figures 48, 49, 50, 51, and 52.
As mentioned previously, some limited measurements of trace metals in the
rainwater were performed. These were obtained by acidifying selected rain
samples, freezing, and shipping back to the Battelle laboratories for
analysis using an atomic absorption spectrophotometer. These results, shown
in Table 14, appear to reflect the presence of the plume, although the high
96
-------
TABLE 14. TRACE METALS ANALYSIS - CENTRALIA, RUN 4.
Concentration, (g/cm3) x 1Q9
Sample Fe Mn Ni Cr Cu S02, (moles/cm3) x 1Q9
BKG3 b 2.0 0.76 0.55 2.5 0.0
BIO 94 2.3 0.39 0.32 1.8 0.0
B13 225 3.0 0.52 0.74 1.7 2.5
B16 380 25.5 0.87 0.72 2.8 13.0
B20 170 2.2 0.46 0.36 1.4 0.0
Fe
b
94
225
380
170
130
120
260
98
96
104
240
Mn
2.0
2.3
3.0
25.5
2.2
2.2
2.3
5.5
2.3
1.8
2.2
5.8
Ni
0.76
0.39
0.52
0.87
0.46
0.26
0.35
0.46
0.36
0.57
0.62
0.57
Cr
0.55
0.32
0.74
0.72
0.36
0.32
0.68
0.37
0.31
0.24
0.21
0.50
Cu
2.5
1.8
1.7
2.8
1.4
2.1
1.4
1.0
1.7
1.1
4.5
1.1
C23 130 2.2 0.26 0.32 2.1 1.9
C26 120 2.3 0.35 0.68 1.4 12.0
C28 260 5.5 0.46 0.37 1.0 5.9
C31 98 2.3 0.36 0.31 1.7 0.0
D28 96 1.8 0.57 0.24 1.1 3.2
D29 104 2.2 0.62 0.21 4.5 6.5
D35 240 5.8 0.57 0.50 1.1 0.0
3.
Background sample.
No measurement.
values in the "background" sample, obtained just upwind from the power plant,
introduce some definite questions in this respect. These measurements were
performed in hopes of elucidating catalytic effects of trace metals in the
SOy oxidation reaction; much more extensive measurement is needed, however,
before any significant features can be evaluated in this manner.
The Gill anemometer data were recorded on magnetic tape, translated, and
processed to provide short- and long-term average velocities, wind direc-
tions, and dispersion parameters using procedures similar to those employed
for the Quillayute experiments. Table 15 gives the average velocities and
directions for approximately half-hour intervals during Runs C-2 through
C-4. The long-term averages for run C-5 appearing in the table were esti-
mated from data from the plant-operated tower, since the BNW tower was re-
moved before this run took place.
It was intended originally that the Gill anemometer results would be employed
to calculate dispersion parameters for use with the washout modeling program.
It was extremely difficult, however, to apply the resulting values to obtain
reasonable or reliable estimates. The major problem in this regard arose
because of the large range of times and distances involved. CT values
97
-------
TABLE 15. AVERAGE WIND DATA FROM ANEMOMETERS - CENTRALIA
Run
Approximate
Time Span
(PST)
1230-1311
1315-1344
1348-1417
1421-1450
1454-1523
1527-1549
1510-1538
1540-1610
1612-1642
1644-1705
0919-0959
1004-1034
1039-1109
u,
cm/sec
747
418
509
578
475
444
430
531
538
754
741
770
911
5b 1230-1545 400 187
wind direction expressed in degrees from true north.
These are averages of the 15 min. averages reported by wind instrumenta-
tion on the plant-operated tower.
calculated from anemometer data were in a reasonable range for receptors on
sampling Lines A and B; they became troublesomely small, however, as the
transit time (and thus the averaging time) became longer, thus filtering out
most of the higher-frequency contributions of the turbulence. In addition,
the corresponding sampling times became so long that they often exceeded the
length of record of the anemometer data.
In view of the above difficulties we decided to apply one of the simpler,
more realistic estimates of the dispersion coefficients. For this purpose
we chose the expressions of Smith and Singer12
a = 0.36 x'86 , (19)
a = 0.33 x'86 , (20)
z
where x is the downwind distance in meters.
98
-------
These are somewhat unsatisfying dimensionally, but they have been shown to
represent true behavior reasonably well out to fairly large distances. In
addition, these expressions represent Smith and Singer's findings for neu-
tral atmospheres, which we have deemed most typical of frontal-type rain-
fall conditions at Centralia. The following section discusses application
of these expressions in conjunction with the EPAEC model to provide S0_
washout estimates.
ANALYSIS OF RESULTS: S02 WASHOUT
A striking feature of the Centralia SO- washout measurements is their regu-
lar appearance, reflecting the presence of the plume in a well-behaved,
quasi-Gaussian manner. This is in sharp contrast to the Keystone results
exemplified by Figures 3 through 5, where extremely complex behavior is in-
dicated. Such features are a strong confirmation of earlier speculations,
listed in Section III, with regard to the influence of reversibility and
background effects. An additional noteworthy point is the difference be-
tween Runs C-2 and C-3 in Line A S0_ concentration levels. Run C-3,
characterized by rather small raindrop sizes (cf. Table 12), showed virtu-
ally zero S0_ washout, while Run 2, characterized by abnormally large rain-
drop sizes and essentially the same wind speed as Run 3, indicated signifi-
cant washout rates. This is totally in accord with the assumption of re-
versible washout behavior, and is considered to be strong evidence on its
behalf.
The S0? washout measurements were examined by employing the EPAEC model in
conjunction with input data from the previous section. The pH for each
station was estimated from available data (cf. Appendix A) by linear inter-
polation. Calculations were performed for each experiment using the five
different S0_ reaction rate parameters shown in Table 16.
The values given in Table 16 pertain to the first-order reaction
(21)
99
-------
TABLE 16. FIRST-ORDER RATE CONSTANTS FOR S02 DECAY
USED IN CENTRALIA MODEL CALCULATIONS.
Rate Constant k, Corresponding SC>2 Half-Life,
Hours"1 Hours
0 °° (no reaction)
.35 2
.69 1
1.39 0.5
2.77 0.25
In the probable event that the actual reaction rate does not follow first-
order kinetics, reaction (21) can be viewed as a linearization approximation
to true behavior. The rate constants in Table 16 fall in the range of ex-
pected behavior from actual plumes, corresponding to observed S0_ half-lives
on the order of a few minutes up to the order of hours.
The Centralia results were computed using a special calling program in con-
junction with the EPAEC model. This program memorized the topography and
arrangement of the sampling stations and, in conjunction with the wind
direction, calculated sampling station coordinates relative to the plume
centerline. The EPAEC algorithm was then executed and resulting washout
concentrations were printed in the usual manner.
Plume loft was calculated using the procedure recommended by Briggs.13 For
the purpose of modeling washout at the Line A stations, the plume was assumed
to loft linearly with distance downwind from the stack exit. Calculations
for other lines were performed, assuming that the plume had attained its
ultimate loft height, by incorporation of an effective stack height with
zero loft velocity. These provisions for plume loft can be interpreted
visually by referring to Figure 53; effective stack heights and loft veloci-
ties employed for EPAEC calculations are given in Table 17.
EPAEC calculations based on gas phase limited behavior and an SO- reaction
half-life of fifteen minutes are presented in the computer plots shown in
Figures 34, 40, 44, and 49. These particular results were chosen for ex-
amples primarily because these conditions appeared to provide the best
agreement with observation. Lowering the reaction rate in the washout
model does not affect the Line A predictions significantly, but influences
100
-------
60
o
W
t-4
P
U
U
w
o
.J
§
g
o
PP
w
>H
s
w
w
H
3
W
H
H
W
8
CO
ro
O
H
Pn
101
-------
TABLE 17. EFFECTIVE STACK HEIGHTS AND LOFT VELOCITIES USED IN APPLYING THE
EPAEC MODEL TO THE CENTRALIA RESULTS (After Briggs13).
Loft Velocity (VERT), Effective Stack Height
Run/Arc cm/sec at Source, m
2/A 216 143
2/B 0 484
2/D 0 484
3/A 215 143
3/B 0 480
3/D 0 480
4/B 0 366
4/C 0 366
4/D 0 366
5/A 230 143
5/D 0 636
the outer line results increasingly with distance of the receptor from the
source. Stagnant drop calculations tend to overestimate washout close to
the source, and converge with gas-phase limited calculations as equilibrium
washout conditions are approached (cf. criterion of Equation (1)).
An example of the effects of varying the mass-transfer coefficients and re-
action rate constants is given by Table 18 which presents the total calcu-
lated results for Run 5. From these it is evident that—within the limits
of comparison of calculated and observed values—varying the chemical re-
action rate over the range shown does not affect the quality of the compari-
son strongly, except for the extreme cases on the outer sampling line. Here
variation of the reaction half-life between fifteen minutes and infinity
results in a corresponding change in SO washout concentrations by approxi-
mately a factor of five.
Variation of mass-transfer behavior from gas-phase limited to stagnant-drop
conditions, in addition to providing higher estimates, results in a more
peaked concentration distribution in the crosswind direction. Although the
concentrations themselves are less in agreement with measured values, the
shape of the stagnant drop based distribution is more in conformity with
observed behavior in this case.
102
-------
TABLE 18. EPAEC CALCULATIONS OF SO2 WASHOUT
CONCENTRATIONS - CENTRALIA,
RUN C-5
Gas-Phase Controlled
Line
A
D
A
D
A
D
Position
Number
18
19
20
21
22
23
24
28
29
30
31
32
33
34
18
19
20
21
22
23
24
28
29
30
31
32
33
34
18
19
20
21
22
23
24
28
29
30
31
32
33
34
Concentration, gm moles/cm"3
k - 2.77 hr-1
1.58
14.6
23.3
26.1
25.6
16.2
2.01
1.15
1.99
2.32
2.74
3.36
3.75
3.85
.15
4.36
54.4
142.
40.6
4.55
.23
.51
1.03
1.26
1.61
2.05
2.32
2.37
2.95
112.
1852.
9619.
1050.
76.8
3.54
11.1
28.4
40.6
63.1
73.7
72.8
62.5
k - 1.35
1.61
14.7
23.4
26.1
25.6
16.3
2.04
2.97
5.18
6.10
7.46
8.88
9.61
9.63
.15
4.42
54.9
143.
41.0
4.62
.23
1.J5
2.67
3.30
4.24
5.18
5.68
5.68
3.00
115.
1875.
9700.
1065.
78.0
3.61
27.8
71.6
103.
164.
191.
188.
162.
hr"1 k = .69 hr"1
1.62
14.8
23.4
26.2
25.6
16.3
2.06
4.68
8.09
9.57
11.8
13.8
14.7
14.5
Stagnant Drop
.16
4.46
55.1
144.
41.2
4.66
.24
2.18
4.16
5.12
6.73
8.14
8.82
8.76
Irreversible
3.02
115.
1887.
9741.
1072.
78.7
3.64
44.2
114.
165.
266.
310.
304.
262.
x 109
k = .35 hr"
1.62
14.8
23.4
26.2
25.6
16.4
2.07
5.82
10.0
11.8
14.7
17.0
17.9
17.7
.16
4.47
55.2
144.
41.4
4.68
.24
2.70
5.15
6.37
8.41
10.1
10.9
10.8
3.03
116.
1892.
9762.
1076.
79.1
3.65
55.6
144.
209.
339.
393.
333.
70.2
1 k = 0
1.63
14.8
23.4
26.2
25.7
16.4
2.08
7.2
12.3
14.6
18.2
20.8
21.8
21.4
.17
4.48
55.3
145.
41.5
4.69
.25
3.37
6.41
7.93
10.6
12.5
13.4
13.2
3.05
116.
1899.
9783.
1080.
79.4
3.67
70.2
182.
265.
434.
504.
493.
426.
Observed
0
0
2.5
5.5
3.5
0
0
0
0.4
1.6
4.8
6.2
2.0
0
0
0
2.5
5.5
3.5
0
0
0
0.4
1.6
4.8
6.2
2.0
0
0
0
2.5
5.5
3.5
0
0
0
0.4
1.6
4.8
6.2
2.0
0
103
-------
A comparison of observed and predicted SO distributions for runs C-2
through C-5 shows that the EPAEC model tends to overpredict on the inner-
most sampling line. Because of the complexity of the situation involved,
it is difficult to speculate meaningfully on the various reasons for this
behavior. This sampling line, which was only 300 meters downwind from the
source, experienced a considerable plume undercutting effect. Consequently,
the EPAEC model encountered the same difficulties with near-miss of a point
source by the raindrops as those which were mentioned previously in the
context of the Quillayute analysis. The approximate treatment of the loft-
ing plume undoubtedly introduced further inaccuracies in the treatment.
Moreover, the longer experiment times at Centralia made it exceedingly
difficult to designate representative spectra to characterize rain condi-
tions. The extreme consequences of any non-representativeness in chosen
raindrop spectra for Line A calculations is indicated in Figure 54, which
is a plot of rain-borne SO concentrations at ground level versus drop size.
For outer-arc conditions (note the curve for Line D) this drop-size depend-
ence is not nearly so pronounced, and here less refined estimates of drop
spectra can be tolerated without severe consequences. In addition to the
above factors, the Line A computations were found to be extremely sensitive
to rain pH. Consequently, any errors in pH measurement caused large corres-
ponding errors in predictions by the model.
Finally, the potential for rain sampling errors arising from S0~ desorption
from the funnel surfaces should be mentioned. If the values of K a*/c A
x x
determined from the Quillayute deposition experiments are applicable to the
present situation, then for the rain rates experienced at Centralia, corres-
ponding sampling errors could be as great as sixty percent (cf. Table 8 and
Figure 26) in extreme cases. Moreover, this situation may have been
worsened by an increase of the actual values of K a*/c A under Centralia
J xx
conditions, which involved higher acidity levels in the rain. This effect
can be explained in terms of the following relationship between the overall
mass-transfer coefficient and the gas- and liquid-phase coef f icients : 11+
(22)
k Hk
x y
104
-------
o
of
w
M
Pi
§
O
M
H
CO
hJ
w
0 g
D_ O
§ IS
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2 M
< §
0£. H
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CO
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o
PQ
I
a
evi
gOI x £WO/SJ10W
Nl
OS
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fe
105
-------
The Quillayute experiments indicated that deposition on (or desorption from)
the surface water of the samplers is influenced by both the gas- and liquid-
phase stages of SCL transport; that is, k is of the same order of magni-
£ X
tude as Hk . Therefore, a decrease in solubility (increase in pH) will
cause a corresponding increase in K .
X
Since owing to the higher acidity of the Centralia rain the solubility of
SO was indeed decreased, higher values of K a*/c A would be expected
t, X X
under these circumstances. It is impossible to give a quantitative esti-
mate of this effect on the basis of available data. In view of these argu-
ments, however, it appears reasonable to expect a large sampling error in
the Line A measurements under low rain-rate conditions; it is entirely
possible that the EPAEC model predicted values closer to reality than those
indicated by the samplers under such circumstances.
Despite the relatively poor quantitative agreement between calculated and
observed values for Line A, some of the more qualitative trends provide en-
couraging evidence in favor of EPAEC model assumptions. In particular, the
previously mentioned difference in Line A values between Runs C-2 and C-3
is reflected strongly by the EPAEC estimates—this correspondence is further
strong evidence on behalf of the basic EPAEC assumptions. Further dramatic
evidence in this regard is given by the final portion of Table 18, which
pertains to calculations based on irreversible theory. These values were
obtained by altering the solubility function in the EPAEC model to predict
total solubility (H* = 0) under all conditions. The corresponding results,
orders of magnitude higher than both the experimental and reversible theory-
predicted values, are considered to be conclusive evidence in favor of the
existence of reversible behavior in the case of S0_ washout.
From the general results, it is apparant that the Smith-Singer12 equations
for plume dispersion provide an adequate description for present purposes.
This leads to their recommendation for use in conjunction with the washout
model for applied impact analyses. This recommendation is tempered somewhat
by the comparatively wide washout distributions observed in a number of the
experiments. Much of this behavior, however, was caused by wind shifts dur-
ing the experiments. These were especially prevalent in Run C-2 (note Table
106
-------
15). Such behavior could have been modeled more accurately by sequential
computations which accounted for the time-variation of plume position.
Owing to the complications posed by the fact that each sampler was set out
for a different (but overlapping) time period, however, such calculations
were not attempted.
The reasonable agreement of the experimental and EPAEC-predicted results
for SO- washout demonstrated by this study leads us to recommend the use of
the EPAEC model, under the conditions indicated, to predict S0? washout
from large as well as moderate and small plumes under clean-background con-
ditions . Application of this model to contaminated-background conditions
will be discussed in Section VII.
ANALYSIS OF RESULTS; SULFATE WASHOUT
The sulfate measurements obtained at Centralia, as shown by the preceeding
figures and by the numerical data of Appendix A, distinctly indicate the
presence of the power plant plume. As with the SO- measurements this be-
havior is in sharp contrast to that observed at Keystone, and is primarily
a consequence of the relative background pollution levels at these two
sites.
From the Centralia washout results it is apparent that an appreciable frac-
tion of the plume-borne sulfur existed in the form of sulfate. It is also
interesting to note that samples collected on sampling line A showed sig-
nificant amounts of sulfate (and free hydrogen ions) being washed out—even
under circumstances where extremely small quantities of rain-borne S0? were
detected. From past considerations it is evident that this is a direct
consequence of below-plume desorption of SO-.
Assuming emission primarily as S0?, the observation of substantial sulfate
concentrations in Line A rain indicates a significant, rapid reaction to
sulfate near the stack. An additional point of interest is the breadth of
the sulfate washout patterns relative to those for S0?. Several explana-
tions for this effect, involving specific non-linearities in the chemical-
reaction/washout process, are possible; none of these, however, has been
investigated sufficiently to warrant any specific conclusions in this regard
at the present time.
107
-------
Past inventories15 have indicated that sulfur leaving power plant stacks is
released almost totally in the form of SO-. The bulk of sulfate washed out
of the Centralia plume must, therefore, have been formed by chemical conver-
sion between the source and the receptors. Under conditions where the ex-
tent of conversion is small the fact that SO is depleted rather than gen-
erated by chemical reaction within the plume permits its washout to be esti-
mated using a rather casual approach to reaction kinetics. In the computer
calculations of the previous section, for example, we varied the reaction
rate between zero and rather large finite values; although the corresponding
changes in predicted washout behavior were indeed noticeable, they were not
excessively large compared with the deviations between the experimental and
predicted results.
Owing to the fact that sulfate is generated rather than depleted within the
plume, its washout should be expected to be much more critically dependent
on chemical reaction behavior. Varying the reaction rate from zero to any
positive value will, in contrast to similar treatment for SO , result in an
infinite relative change in predicted sulfate washout. Any truly adequate
theoretical assessment of sulfate washout, therefore, must attempt to treat
reaction behavior in a more rigorous manner.
Determination of S0_-sulfate reaction kinetics is not a goal of the present
project; in a field study of this type, one cannot expect to describe ex-
plicitly the microphysics of the sulfate conversion and removal process.
Because of the noted dependence on reaction behavior, however, the sulfate
washout results of this study provide a number of important inferences with
regard to SO oxidation. The following subsections are addressed to the
analysis of sulfate washout in this context.
Limiting Values of Washout and Reaction Parameters
There are a number of processes by which sulfate can be formed in, and sub-
sequently removed from, industrial plumes. Formation can occur through
liquid-phase reaction processes where SO is converted to sulfate inside
raindrops, or in the cloud-size (~ 10u) water droplets which are likely to
exist in such plumes in rainy weather. Gas-phase reaction processes may
108
-------
lead to free particles of sulfate whose sizes cover the range of the natural
aerosols. Subsequent removal mechanisms, then, cover a corresponding range
of possibilities including irreversible gas washout, aerosol washout, and
cloud droplet nucleation processes.
In spite of these complexities, one can provide some insight into the prop-
erties of the overall process by expressing sulfate formation in terms of
an equivalent first-order gas-phase reaction. By applying this approach in
conjunction with the Centralia data, upper and lower limits for the reaction-
rate constants and washout coefficients can be established. The fact that
measurable sulfate was indeed washed out at Centralia precludes at the out-
set the choice of zero as a lower limit for either the pseudo first-order
reaction constant or the washout coefficient. There is nothing initially
obvious, however, that rules out the choice of infinity as the upper limit
of one or the other of these parameters; the observed washout rates could
be attributed, for instance, to a very fast (essentially infinite) reaction
rate, with a finite washout rate being the rate-controlling step of the
process.
Assuming that the upper-limit reaction rate is indeed infinitely fast, one
can estimate a corresponding lower-limit washout coefficient. The well-
known expression
A - ^ . (23)
can be modified for this purpose, upon making the conservative assumption
of zero upwind removal of material in the plume, to obtain the following
form for the lower-limit washout coefficient:
. M'u ,_.,
Ak=» = Q^- ' (24)
In the above expressions M' is the molar rate of sulfate deposition (moles/cm
sec) at a given downwind distance x , and Q' is the molar flow rate of
sulfate across the plane defined by x.. . M' can be estimated from the
Centralia measurements by crosswind integration of the amounts collected at
the individual sampling positions. Figure 55 provides a schematic indica-
tion of the significance of the various entities employed in this discussion.
109
-------
X
II
X
X
c/o
«=t
o
I/}
o
:i
X
en
CO
w
u
§
O
ffi
H
U
PC;
o
CO
W
ffi
O
CO
w
ptj
110
-------
In a parallel sense, the lower-limit reaction-rate constant (corresponding
to an infinite washout coefficient) can be obtained. Since in this event
sulfate is assumed to be washed out the instant it is formed by reaction,
the washout rate equals the reaction rate. Again assuming negligible de-
pletion of SOy upwind from the receptors, a material balance on a volume of
atmosphere defined by a vertical slice of thickness dx in the proximity
of x provides the following expression for the lower-limit, pseudo first-
order reaction-rate constant:
*A--f •
The similarity of Equations (24) and (25) is not surprising in view of the
fact that they both result from attempts to express washout in terms of
first-order irreversible processes.
The extreme upper and lower limits of the rate constants and the washout
coefficients obtained by applying the above analysis to the Centralia data
are shown in Table 19. The actual ranges of washout coefficients, however,
can be restricted further by replacing the infinite upper limit with more
realistic limits obtained from washout theory. The semi-empirical analysis
of Slinn16 for example, can be used for this purpose. In his analysis
Slinn presents the washout coefficient as a function of particle size, as
shown in Figure 56; these curves are observed to approach upper limits as
aerosol size is increased. The curve for a mean raindrop-radius of 0.2 mm
represents a conservatively high estimate for the rains experienced at
Centralia, and can be used in conjunction with the normal assumption of
proportionality of A to the rainfall rate to obtain the revised upper
limits of the washout coefficients shown in Table 20. For this estimation,
a rainfall rate averaged for all sample lines is used to represent that of
each run.
Corresponding lower limits of the washout coefficients could be obtained
using the minima in Figure 56 in a similar manner. This proves to be im-
practical, however, since the resulting values are lower than those esti-
mated using the Centralia results in conjunction with Equation (24), and
therefore do not result in any further restriction in the ranges of the
extrema.
Ill
-------
10
,-2
10
-3
O
10
r4
<••' c
E 10"5
o
o
to
a: /
10'6
i
-------
TABLE 19. EXTREME LIMITS OF SULFATE WASHOUT COEFFICIENTS
AND REACTION RATE CONSTANTS*
Run/Sampling Line Lower-Limit Parameters, hr
A, or k.
k=<*> A=°°
-1
C-2 A .0062
B .033
D .058
C-4 B .048
C .035
D .043
C-5 A .00061
D .0049
Upper limit values for k and A are infinite.
The problem of estimating lower-limit rate constants based on these revised
estimates of upper-limit washout behavior is not a trivial one. It can be
approached in a somewhat superficial sense by formulating a simplified model
of the washout process and calculating values of the rate constants from the
corresponding equations. Thus, if one begins by assuming oxidation to be
the primary mechanism for plume-borne S0? removal (dry deposition and wash-
out of S0~ negligible), then the molar flow rate of S09 in the plume at any
downwind position x1 is described in terms of the expression
^ = -kQ; Q = QQ at x = 0 , (26)
where k is the reaction-rate constant. If sulfate is assumed to be pro-
duced only by reaction (26) and removed only by washout, the corresponding
equations
|3- = -AQ' + kQ; Q' = 0 at x = 0 , (27)
are obtained.
Combination of the above expressions, integration, and substitution of
Equation (23) results in the form
AkQ
M1 = -(A °_ k)[exp(-kt) - exp(-At)] , (28)
113
-------
which can be utilized in conjunction with the Table 20 values to obtain
estimates of the limiting reaction-rate constants.
The rate constants thus calculated are shown in Table 20, which provides
revised estimates of the extrema in k and A. Interpretation of these
values, of course, must be weighted in view of the numerous linearizations
and other simplifying assumptions used in their derivation.
TABLE 20. REVISED EXTREMA OF SULFATE WASHOUT COEFFICIENTS
AND REACTION-RATE
CONSTANTS .
Washout Coefficients
Run/Sampling Line
2
4
5
A
B
D
B
C
D
A
D
A.
k=°°
.00622
.033
.058
.048
.035
.043
.00061
.0049
A*
4.
4.
4.
7.
7.
7.
2.
2.
, hr-1
a
8
8
8
0
0
0
2
2
Reaction
j
0
0
0
0
0
0
0
0
Rate
^ul
.065
.061
.063
.086
.044
.046
.006
.006
Constants,hr 1
V
00
00
00
oo
00
00
00
00
*Based on analysis of Slinn assuming A is proportional to average rain-
fall rate for all sample lines of run.
In spite of the restrictions of parameter ranges obtained here, the extrema
shown in Table 20 are still too widely separated to be of quantitative use.
Further extension of this simplified analysis, however, can be employed to
provide some insight pertaining to absolute values within these extrema.
Such an extension is described in the following subsection.
Non-Limiting Values of Washout and Reaction Parameters
Equation (28) expresses the washout rate M' as a function of the two
parameters k and A. Since the Centralia experiments provided for measure-
ment of more than one value of M' during each run (one value for each
active sampling line), it is possible to express corresponding forms of
Equation (28) as simultaneous equations, and solve for "absolute" values of
k and A directly. Such a treatment presupposes that k and A are in-
variant with distance downwind from the source—an assumption that was used
previously in the formulation of Equation (28).
114
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Such calculations may be performed most conveniently by constructing plots
of A versus k, as dictated by Equation (28), corresponding to the meas-
ured values of M'; points of intersection of any two curves then denote
solutions for appropriate combinations of k and A. An example of such
a determination is shown in Figure 57, which presents the solutions to
Equation (28) for measured results from three sampling lines of Run C-2.
This figure illustrates an unsettling aspect of this method: the fact that
Equation (28) is symmetric with respect to k and A permits two possible
solution pairs (A, k) for any two curves. Accordingly, solution pairs for
all of the applicable Centralia runs, listed in Table 21, are presented in
terms of the two possibilities with subscripts "high" and "low" indicating
the alternative cases.
Examination of the numerical results in Table 21 yield the conclusion that
the solutions corresponding to large A and small k (A , , k ) can be
excluded on the basis of previous findings. The reaction rate constant,
for example, is observed to fall in the vicinity of 0.05 hr or less, which
corresponds to S0~ half-lives in the neighborhood of 15 hours or greater.
Such lifetimes are more than an order of magnitude greater than those ex-
pected on the basis of numerous previous measurements of in-plume S09 oxi-
dation behavior by other investigators.17""21
In addition, the high values of A, about 5 hr , are unrealistic. Although
washout coefficients of this magnitude are certainly not impossible on the
basis of Figure 56, they do pertain to near-optimal conditions, involving
washout of either extremely large or extremely small particles. Finally,
the computed SO- washout results from the previous subsection provide some
further (albeit weak) evidence in this regard. The observation of superior
agreement between experimental and computed SO,, washout rates using higher
reaction-rate constants in the model appears to indicate that the low reac-
tion rates predicted by the solution set (A, . , , k, ) are inappropriate
high low
for present purposes.
The alternative solution pair (A.. , k, . , ) , appears to conform with ex-
pected behavior in a more acceptable fashion. The washout coefficients, on
the order of 0.05 hr , correspond with those for particles in the neighbor-
-3
hoods of 10 and 1 micron (cf. Figure 56). The reaction-rate constants
115
-------
10.00
1.00
0.10
0.01
2B
2D
(klOW AHIGH'
0.01
0.1
A, HR
"1
10
FIGURE 57. SOLUTIONS TO EQUATION (28) FOR RUN C-2.
116
-------
Table 21. SOLUTIONS TO EQUATION (28) FOR APPLICABLE
CENTRALIA SAMPLING LINE PAIRS
Run
2
2
2
4
5
Sampling Lines
A, B
A, D
B, D
C, D
A, D
A, , hr 1 1
low'
0.056
0.063
0.064
0.048
0.005
, -1
CT. • i. > hr
5.7
5.1
4.7
5.7
4.1
A, . , , hr
high'
5.7
5.1
4.7
5.7
4.1
k, , hr l
low
0.056
0.063
0.064
0.048
0.005
from the pair (A.. , k, . , ), about 5 hr , compare reasonably well with
previous measurements17"20 in view of the increases in reaction rate ex-
pected under high-humidity conditions.22 Because of these considerations
we shall proceed on the assumption that the most appropriate solution sets
are (A, , k, . , ), and shall focus all subsequent discussion on these
low high ^
values.
It is interesting to note that values of A and k are obtained which
approximately satisfy all three sample lines for Run C-2, and these are
close to those found for Run C-4, Lines C and D. (Run C-4, Line B deposi-
tion data were fragmented due to the gap in th*3 campling array; M' and t
are very inaccurate for this line, and estimated values for them do not
lead to a solution with either Line C or Line D.) This agreement, while
somewhat encouraging, is probably rather fortuitous and cannot be cited as
a strong argument on behalf of the precepts leading to formulation of
Equation (28). In addition the Run C-5 results, while indicating a rate
constant comparable to the previous runs, suggest that the washout coeffi-
cient should be an order of magnitude lower. Other than the observation
that the pH of the background rain was significantly lower for Run C-5 than
for the preceeding runs (4.7 versus about 5.5), there is little that is
obvious to explain this reduction in washout rate.
A relationship between pH and sulfate washout rate could be used also as a
plausible explanation for the observation of relatively wide crosswind dis-
tributions of this species in rain. Unfortunately there are insufficient
data from this study to permit an adequate evaluation of the effect of
background pH on sulfate washout rate. There is, however, ample evidence
117
-------
from laboratory investigations22 28 to indicate that a lowering of M'
with pH should indeed be expected. Beilke, et al.,26 for example, shows
that the sulfate-formation rate should be approximately proportional to the
inverse square of the free hydrogen-ion concentration over the pH ranges
encountered at Gentralia. This is certainly in qualitative accordance with
our Centralia findings, although on this basis one would expect the reduc-
tion in M' to be caused primarily by a reduction in k, rather than A
as implied in Table 21. Further sulfate washout data with simultaneous pH
measurements would do much to elucidate this behavior.
The predicted reaction-rate constants in Table 21, while in fair conformity
with expectations from previous studies, are insufficient to explain total
behavior observed at Centralia. Corresponding S09 half-lives are about ten
minutes or less, and are probably too short to explain the airborne SO-
levels actually observed on the outer sampling lines. In a retrospective
analysis of the preceeding considerations it seems apparent that the in-
plume SO- oxidation process proceeds very rapidly as the plume leaves the
source and attenuates as distance downwind increases, leaving higher amounts
of SO. at larger distances than would be predicted on the basis of linear
kinetics in conjunction with the given rate constants.
In view of its simplistic interpretation of the sulfate washout process it
is difficult to state just how far Equation (28) should be utilized in in-
terpreting these field results. From previously mentioned studies in the
laboratory and in the field it is strongly apparent that the assumption of
first-order reaction kinetics is useful only as a first approximation.
Moreover, it is evident that the effective washout coefficient used in
Equation (28) is strongly cross-correlated with reaction phenomena, and the
simple explicit behavior implied by this equation is not actually followed.
Thus changes in reaction kinetics will be accompanied by corresponding
changes in the apparent washout coefficient, and any microphysical interpre-
tations using Equation (28) become of doubtful validity. In addition, in-
exact analysis of field behavior arising from plume undercutting, non-
vertical rainfall, and approximate cross-plume integration of washout fluxes,
present additional complications in this respect.
118
-------
Additional direct measurements of in-plume S0_ oxidation rates would ob-
viously be of high interest in this regard. Also, a more refined analysis
procedure which could calculate sulfate washout for a more realistic model
of rain-plume conditions would be beneficial—both as a method of diagnosing
suggested models of sulfate-formation microphysics and as a future tool for
related applied impact analyses. The EPAEC model can, with a reasonably
modest effort, be updated for this purpose; this modification is recommended
as a topic of continued research.
Application of Sulfate Washout Results
In spite of the noted shortcomings of the approximate model of sulfate wash-
out given in this subsection, it still may be applied for empirical estimations
of sulfate washout behavior under relatively high background pH conditions
(pH £ 5.2). For this purpose we recommend the application of Equation (28)
using a reaction rate constant of 4.16 hr (SCL half-life = 10 minutes).
This value is suggested because it is in approximate conformity with a
majority of the experimentally observed behavior. Owing to the insensitiv-
ity of washout to the reaction constant in this range (cf. Figure 57), the
deviations between this value and those in Table 21 do not result in any
appreciable deviation in A. Insertion of this value in Equation (28) and
solving for observed washout rates for Runs C-2 and C-4 yields the follow-
ing expression for the sulfate washout coefficient:
A ~ 0.026 J (hr'1) , (29)
where the rainfall rate J is in units of mm hr . The constant in this
case represents an average of the values of A/J as derived from the
Equation (28) curves for Runs C-2 and C-4.
Application of this set of values for A and k in conjunction with
Equation (28) results in the washout rates given in Table 22. As seen from
the comparison of measured and fitted values, this procedure provides a
fairly consistent order of magnitude method for sulfate washout prediction
and is recommended for impact analyses of sulfate washout in the vicinity
of fossil-fueled power plants under "clean" background conditions. This
recommendation is tempered by the noted deficiencies of the analysis, and
119
-------
by the realization that plant-to-plant variations in plume properties and
meteorological situations are likely to result in considerable deviations—
especially with regard to chemical reaction behavior. In view of the lack
of more comprehensive results, however, the washout rates calculated using
the above procedure are expected to constitute the most reliable estimates
presently available under these circumstances.
Present results indicate that sulfate washout, under conditions where the
background rain pH is of the order of 4.7, can be described in terms of
Equation (28) using the same reaction rate constants and a washout coeffi-
cient of 0.005. The Run C-5 data providing this indication however are
insufficient to warrant any recommendations for Equation (28)'s use under
these conditions.
TABLE 22. COMPARISON OF SULFATE WASHOUT RATES: OBSERVED VERSUS THOSE
CALCULATED USING EQUATIONS (28) AND (29) - CENTRALIA
Washout Rates, gm-moles_/m_ hr
Run/Sampling Line Observed Calculated [Eq. (29)]
C-2 A 0.0107 0.011
B O.G560 O.U58
D 0.1000 0.092
C-3 A a 0.004
B a 0.019
D a 0.052
C-4 B 0.0971b 0.050b
C 0.0713 0.115
D 0.0856 0.227
C-5 A 0.00206 0.012b
D 0.0165 0.109
NO measurement
Uncertain, see text
120
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SECTION VII.
FURTHER ANALYSES OF KEYSTONE RESULTS
The washout analyses described in this report have been applied in Sections
V and VI to situations involving plumes in low-background environments. A
more severe test of their predictive capability is in their application to
the complex environment of the Keystone plant. This section presents
comparisons of EPAEC-predicted and measured washout behavior under such
conditions. Also presently considered is an application of the first-order
washout and reaction rate analysis of Section VI, for comparison with Key-
stone sulfate measurements.
Because of the lack of comprehensive support data, particularly pH measure-
ments, the comparisons of this section will be limited to one case. The
case chosen for this purpose is Run 4 of the original Keystone series (cf.
HTW), whose 50 washout distributions were presented in Figure 5 of this
report. Additional information regarding this run is summarized in Table
23. Run 4 was chosen as a test example because it exhibits many of the
apparent anomalies that were observed during the Keystone field series. In
particular, the "negative washout" etfect is highly apparent here, and it
is of interest to determine the behavior of model predictions under these
circumstances.
SO WASHOUT
EPAEC model predictions for S0~ washout corresponding to Run 4, Arc A, were
obtained by executing computer runs using data given in Table 23. Computa-
tions were carried out for each station on the sampling line using pH values
obtained by interpolating between the centerline and off-plume measurements.
A first-order reaction-rate constant corresponding to a 15 minute SO,, half-
-l L
life (k = 2.77 hr ) was employed for these computations. The results are
shown in Figure 58, with the computed values depicted by the superimposed
curve, and the measurements denoted by radial bars. The fact that the
computed values do indeed conform with measurements in indicating a negative
washout is considered to be rather dramatic evidence on behalf of the basic
precepts employed by the EPAEC model.
121
-------
LEGENDS
* f\KC fl STflTIQNS
< flRC B STflTIONS
O flRC C STRTIONS
K DENOTES PLflhr L0CHTIQN
SCflLES
= 1 MILE
= 10 MICROM8LES/L
FIGURE 58. EPAEC MODEL CALCULATION FOR KEYSTONE - RUN 4, ARC A, USING DATA
OF TABLE 23.
122
-------
This application of the model can be criticized on the basis of the fact
that it employs some rather uncertain base data in its computations, par-
ticularly with regard to pH values and reaction rates. These are admittedly
only best estimates used in lieu of more comprehensive measurements. The
fact that these reasonable estimates of basic properties can be employed to
predict the complex behavior exhibited in Figure 5, however, is still strong
confirmation of the practical utility of the computational procedure. It
leads to our recommendation for its use in applied washout analysis under
high background conditions as well as for less complete atmospheric circum-
stances. The final section of this report describes a recommended procedure
for application of the EPAEC model in this respect.
SULFATE WASHOUT
The semi-empirical sulfate washout equation of Section VI was applied to the
Keystone Run 4 results to assess predictive capabilities in a manner similar
to that used above to test the S0~ washout model. This is a somewhat diffi-
cult comparison, since the high sulfate background levels and scattered data
characteristic of the Keystone sulfate measurements permit only rough esti-
mates of the corresponding washout rates. On the basic of previous consid-
erations (HTW, pp. 101-103) this rate for Run 4, Arc A, at Keystone can be
estimated to be roughly 0.01 gm-moles/m hr.
Predictions from Equation (28) for the conditions of Run 4 are shown with
the measured washout rate value in Table 24. From this comparison it is
apparent that the sulfate washout parameters corresponding to high pH
Centralia conditions (Runs C-2 and C-4) substantially overpredict the wash-
out observed at Keystone during Run 4. Washout parameters obtained from
the low pH, Run C-5 results agree with the Keystone measurements in a more
acceptable manner. Since the background pH's at Keystone were relatively
low (5.1 or less) this is considered to be additional evidence of the nega-
tive effect of acidity on sulfate washout.
An additional factor to be considered is the higher sulfur-compound concen-
tration existing in the Keystone plume. It seems likely that the resulting
increases in acidity may have contributed rather substantially to the lower-
ing of washout efficiency under these circumstances. In view of these
123
-------
complexities we cannot recommend the use of Equation (28) under low pH con-
ditions at the present time, except as an order-of-magnitude approximation.
As future washout data are acquired, however, limits on k and A should
become more well established, and this equation could possibly become more
valuable as a practical means of sulfate washout estimation. Additional
field measurements taken under a wide variety of circumstances would be an
important contribution in this regard.
CONCLUDING REMARKS
Although all quantitative aspects of this field of study are not presently
defined in a totally satisfactory manner, the factors discussed in this and
the previous sections lend to the significant qualitative conclusion that
precipitation scavenging of both S0_ and sulfate from power plant plumes
becomes less efficient when concentration levels of these species are in-
creased. In addition, since dry deposition processes share a number of
mechanisms with those of precipitation scavenging, one can reasonably specu-
late that similar nonlinear behavior occurs for dry deposition as well.
These findings imply that (over meso- and larger scales of distance), ambi-
ent levels of SCL and sulfate originating from a power plant will not, gen-
erally, be linearly proportional to the strength of their source. Doubling
the sulfur compound output from a power plant, for instance, would be ex-
pected to more than double its original ambient pollution contribution at
some point located, say, ten miles downwind. Conversely, a given decrease
in source strength can be expected to result in a more favorable resultant
modification in ambient levels than would be expected on a strict^ propor-
tional basis.
Such behavior is of significance in the context of control policy considera-
tions; it suggests that control policies such as the well-known "linear-
rollback" approach may be rather lacking, at least when mesoscale and larger
distances are involved. In view of these findings we suggest that evolving
control policy plans, in order to achieve optimal benefit, should be designed
to account for such nonlinearities in atmospheric response, and should be
sufficiently flexible to incorporate additional aspects of atmospheric be-
havior as such features become known and validated through future studies.
124
-------
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125
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SECTION VIII.
RECOMMENDED APPLICATIONS OF THE EPAEC MODEL
FOR ENVIRONMENTAL IMPACT ANALYSIS
The purpose of this section is to outline a procedure for application of
the EPAEC SO washout model to general environmental impact analysis. The
complete model is listed in Appendix C; we present here salient points re-
garding recommended input parameters and sub-models. In general, these
recommendations derive from the experimental knowledge gained from this
project; for example, the plume loft and diffusion parameters considered
reflect continuous, frontal-type rainfall conditions (~> neutral stability).
However, by example, we expect that it will be clear what modifications
are required for other situations. The following may be considered a typi-
cal procedure; features of the approach which are variable, depending on
the user's situation, are noted.
BASIC INPUT
The basic input to the model includes the following entities: plant operat-
ing characteristics and site factors; physical constants related to the
pollutant gas, rain, and air; diffusion and other plume parameters; site
meteorological parameters. The first two categories include various user-
specified terms and known physical constants. These are summarized in
Table 25. The latter two categories involve greater sophistication regard-
ing choice of terms; our recommendations follow.
Plume Parameters
Briggs ' revised formulae133 for power plant plume rise under neutral atmos-
pheric conditions are given by
!
Ah = 1.6
and
Ah = 1.6 F3x3/u (x < 3.5 CD F8) , (30)
is
II 1
Ah = 1.6 F3(10 h)3/u (x > 3.5 CB F8) , (31)
D
where F ^ 3.7 x 1CT5 Qu, mVsec3
n
Q = rate of heat emission from the stack to the atmosphere, cal/sec
H
126
-------
TABLE 25. SUMMARY OF REQUIRED INPUT DATA. FOR THE EPAEC CODE,
AND RECOMMENDED"VALUES FOR INITIAL USE
Input Parameter
Computer Symbol
A. Plant and Site Characteristics
Receptor location
XBUK,YBUK,ZBUK
(cm)
Grid-spacing parameters DELTAY,DELTAZ
(cm)
S02 release rate
Temperature
B. Physical Constants
Diffusivity of S02 in
water
Diffusivity of S02 in
air
Kinematic viscosity of
air
Atmospheric pressure
C. Plume Parameters
Excess hydrogen-ion
concentration
Effective release height
S02 reaction-rate constant
moles/sec
T
DAX
cm2/sec
DAY
cm2/sec
XNU
cm2/sec
P
atm
HEX
molar
H
RK
sec
-l
Plume-dispersion param- SIGPHI,SIGTHE
eters cm
S02 background
BKG
mole fraction
D. Meteorological (Climatological) Factors
Raindrop spectrum
parameters N,D(I),F(I)
numb er,cm,cm"*
Rain rate
Loft Velocity
XNT
cm/sec
VERT
cm/sec
Value and/or Source
Set XBUK as dictated by user;
Set YBUK and ZBUK equal to
zero (see text)
Set equal to zero
Plant characteristics
As dictated by user
9 x 1Q~6 cm2/sec2
0.136 cm2/sec2
.0133 cm2/sec2
1 atm.
3.16 x 1G~^ molar or as dictated
by user
Equations (30) and (31)
0.00077 sec"1
Equations (32) and (33)
Zero or as dictated by user
Representative values (see text)
As dictated by user
See Appendix C
127
-------
h = stack height, m
x = distance of interest downwind, m
u = wind speed, tn/sec
c^. = Briggs1 constant: = 14 m for F < 55 mVsec3, = 34 m for
B
F > 55 m4 sec3
The separation into two equations reflects an approximate description of
the bending over of the plume at distance; thus, the effective stack height
H = h + Ah is obtained through a choice of Equation (30) or (31) depending
on the distance of interest to the user.
The Smith-Singer relationships,12 as discussed in Sections VI and VII, pro-
vide a reasonably adequate estimate of diffusion parameters on a power plant
siting study scale of distances. The parameters for neutral stability
(which are not greatly different from those for unstable conditions), given
in Equations (19) and (20), may be written in terms of the model's input
requirements, as:
a = 0.36 x--14 , (32)
u
a = 0.33 x~-lk . (33)
On the basis of behavior observed from this study, a reaction-rate constant
pertaining to a 15-minute SO half-life (k = 2.77 hr"1) is recommended for
use with power plant calculations. Insertion of SO background levels and
excess hydrogen-ion concentrations will depend on the information available
to the user. If these levels are unknown, the use of a zero S0? background
level and a hydrogen-ion concentration of 3.16 * 10~6 molar (corresponding
to a pH of 5.5) will result in conservatively high washout predictions.
Meteorological Parameters
Certain meteorological parameters (or more properly, climatological, when
dealing with year-round impact) are required, including wind speed and
direction, rainfall rate, and raindrop size characteristics. The problem
posed by variations in meteorological conditions and the corresponding
difficulties in interpreting long-term washout behavior can be addressed by
proceeding through the sequence of steps listed below:
128
-------
1. Obtain wind and rain frequency records for the proposed plant
location. Divide the wind speeds into three or more ranges, and note asso-
ciated frequencies of occurence and directions.
2. From the rain records, divide the rain rates into three or more
ranges and note associated frequencies of occurence.
3. Obtain representative drop-size spectra for each discreet rain in-
tensity. These can be acquired from local measurements if available; if
not, generalized spectra29'30 can be employed.
4. Employ the EPAEC model under the conditions specified in this sec-
tion to obtain cross-plume washout distributions for each chosen set of
wind-velocity-rain conditions.
5. Combine the computed washout distributions according to the pre-
viously acquired synoptic records to obtain estimates of long-term washout
behavior.
INTRODUCTION OF DATA
The physical data necessary for calculations involving the EPAEC code are
summarized in Table 25. These are read using the general-purpose main pro-
gram listed in Appendix C; an excerpt of this program showing the data-read-
ing sequence is given below;
100 READ (5,320) N,J1,J2,J3,J4,JOPT,JP,JEND
IF (Jl.EQ.l) GO TO 110
READ (5,330) (D(I),I=1, N)
READ (5,330) (F(I),I=1, N)
110 IF (J2.EQ.1) GO TO 120
READ (5,340) DAX,DAY,HEX,XNU,P,T,XNT,RK
120 IF (J3.EQ.1) GO TO 130
READ (5,350) SIGTHE,SIGPHI,U,H,Q,VERT,BKG
130 IF (J4.EQ.1) GO TO 140
READ (5,360) XBUK,YBUK,ZBUK,DELTAY,DELTAZ
The first READ statement reads the number of steps in the discrete raindrop-
size spectrum (N) (cf. Table 12), in addition to a series of control vari-
ables. If these are set as follows:
129
-------
J1-J4 = 0
JOPT = 1 for gas-phase limited conditions. JOPT = 0 for
stagnant-drop conditions.*
JP =1
JEND = 0 ,
then the program will proceed to calculate a distribution of washout con-
centrations about the plume's centerline, and integrate to provide a wash-
out rate for the specified physical conditions of the problem.
Input formats for a typical application are shown in Table 26. For
further details regarding formats, options, and extensions of the EPAEC
model's capabilities, the reader is referred to the comprehensive de-
scription in Appendix C.
TABLE 26. EXAMPLE INPUT DATA FORMAT FOR EPAEC CODE
5000011
.01 .02 .03 .04 .05
.05 .10 .25 .45 .15
9.E-6 1.36E-1 3.16E-6 1.33E-1 l.OEO 1.3E-4 1.16E-3
.062 .056 5.13E2 1.17E4 3.7EO
3.0E5
*Gas-phase limited conditions recommended for impact analyses.
130
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SECTION IX.
REFERENCES
1. Hales, J. M., J. M. Thorp, and M. A. Wolf. Field Investigation of
Sulfur Dioxide Washout from the Plume of a Large Coal-Fired Power Plant
by Natural Precipitation. Battelle, Pacific Northwest Laboratories.
Richland, Washington. BNW-389. March 1971. 214 p.
2. Dana, M. T., J. M. Hales, and M. A. Wolf. Natural Precipitation Washout
of Sulfur Dioxide. Battelle, Pacific Northwest Laboratories. Richland,
Washington. BNW-389. February 1972. 148 p.
3. Hales, J. M. Fundamentals of the Theory of Gas Scavenging by Rain.
Atm. Environment j6:635-659, 1972.
4. Hales, J. M. Scavenging of Gaseous Tritium Compounds by Rain. Battelle,
Pacific Northwest Laboratories. Richland, Washington. BNWL-1659.
April 1972. 35 p.
5. Hales, J. M., M. A. Wolf, and M. T. Dana. A Linear Model for Predicting
the Washout of Pollutant Gases from Industrial Plumes. A.I.Ch.E. J.
_19:242-247, March 1973.
6. Turner, D. B. Workbook of Dispersion Estimates. Environmental Protection
Agency. U. S. Government Printing Office, Washington, D.C. Publication
Number AP-26. 1971.
7. Churchill, R. V. Operational Mathematics. New York, McGraw-Hill, 1958.
p. 229.
8. Carslaw, H. S. and J. C. Jaeger. Conduction of Heat in Solids. Oxford,
Clarendon Press, 1959. p. 233.
9. Pasquill, F. Atmospheric Diffusion. London, Van Nostrand, 1962. 297 p.
10. Smith, F. B. and J. S. Hay. The Expansion of Clusters of Particles in
the Atmosphere. Quart. J. Roy. Meteorol. Soo. ^7:82-101, 1961.
11. Lazrus, A., E. Lorange, and J. P. Lodge. New Automated Microanalysis for
Total Inorganic Fixed Nitrogen and for Sulfate Ion in Water. In: Trace
Inorganics in Water. ACS Advances in Chemistry Series Number 73.
Washington, D.C., American Chemical Society, 1968.
12. Smith, M. E. and I. A. Singer. An Improved Method of Estimating Con-
centrations and Related Phenomena from a Point Source Emission. J. Appl.
Meteorol. 5:631-639, 1966.
131
-------
13. Briggs, G. A. Plume Rise, AEC Critical Review Series. USAEC Division
of Technical Information, Oak Ridge, Tennessee. 1969.
13a. Briggs, G.A. Some Recent Analyses of Plume Rise Observation. Proc. ?.nd
Int. Clean Air Congress. Washington, B.C. 1970.
14. Bird, R. B., W. E. Stewart, and E. N. Lightfoot. Transport Phenomena.
New York, Wiley, 1960.
15. Smith, W. S. and C. W. Gruber. Atmospheric Emissions from Coal
Combustion - An Inventory Guide. U.S. Public Health Service Publication
Number 999-AP-24. 1966. 112 p.
16. W.G.N. Slinn. Numerical Explorations of Washout of Aerosol Particles.
In: Pacific Northwest Laboratory Annual Report for 1970 to the USAEC
Division of Biology and Medicine, BNWL-1551, Volume II, Part 1. Battelle,
Pacific Northwest Laboratories, Richland, Washington. June 1971. p. 75-81.
17. Baldwin, R. D., L. Cohen, J. Forrest, B. Manswitz, L. Newman, M. E. Smith,
M. Sternberg, and W. D. Tucker. The Atmospheric Diagnostics Program at
Brookhaven National Laboratory. Second Status Report, BNL-50206. 1969. 42 p.
18. Arin, M. L., C. E. Billings, R. Dennis, J. Drescall, D. Lull, F. A. Record,
P. Warneck, and J. E. Wilder. Study of Reactions of Sulfur in Stack Plumes.
GCA Corporation, Bedford, Mass. Report No. GCA-TR-69-12-6. 85 p.
19. Foster, P. M. The Oxidation of Sulfur Dioxide in Power Plant Plumes.
Atmos. Environ. _3:157-175, 1969.
20. Stephens, N. T. and R. 0. McCaldin. Attenuation of Power Station Plumes
as Determined by Instrumented Aircraft. Environ. Sci. Tech. _5:615-621, 1971.
21. Weber, E. Contribution to the Residence Time of Sulfur Dioxide in a
Polluted Atmosphere. J. Geophys. Res. 75:2909-2914, 1970.
22. Cheng, R. T., J. 0. Frohliger, and M. Corn. Aerosol Stabilization for
Laboratory Studies of Aerosol-Gas Interactions. J. Air Poll. Cont. Assoo,
21:138-142, 1971.
23. Junge, C. E. and T. G. Ryan. Study of the S02 Oxidation in Solution and
Its Rate in Atmospheric Chemistry. Quart. J. Roy. Meteorol. Soo.
jJ4:46-55, 1958.
24. Miller, J. M. and R. G. DePena. The Rate of Sulfate Ion Formation in
Water Droplets with Different Partial Pressures of S02. In: Proceedings,
Second International Clean Air Congress. New York, New York, Academic
Press, 1971. p. 375-380.
25. Van Den Heuvel, A. P. and B. J. Mason. The Formation of Ammonium Sulfate
in Water Droplets Exposed to Gaseous Sulfur Dioxide and Ammonia. Quart.
J. Rou. Meteorol. Soa. 89:271-275, 1963.
132
-------
26. Beilke, S., D. Lamb, and J. M. Miller. Neure Untersuch ungen zur Oxidation
von Schwefaldioxid in Gegenwant van FlUssigwasser. Bericht des
Sonderforschungsberich 73 Deutchforschungnogemernshaft, 1973.
27. Johnstone, H. F. and D. R. Coughanour. Absorption of Sulfur Dioxide in
Air, Oxidation in Drips Containing Dissolved Catalysts. Ind. Eng. Chem.
.50:1169, 1958.
28. Matteson, M. J., W. Stober, and H. Luther. Kinetics of the Oxidations of
S02 by Aerosols of Manganese Sulfate. Ind. Eng. Chem. Fund.. 8:677-687, 1969.
29. Mason, B. J. The Physics of Clouds. London, Oxford University Press, 1957.
p. 356.
30. Engelmann, R. J. The Calculation of Precipitation Scavenging. In:
Meteorology and Atomic Energy, Slade, D. H. (ed.). Oak Ridge, USAEC
Division of Technical Information Extension, July 1968. p. 208-221.
31. Johnstone, H. F. and P. W. Leppla. Solubility of S02 at Low Partial
Pressures - lonization Constant and Heat of lonization of H2S03. J. Am.
Chem. SOG. .56:2233, 1934.
32. Gunn, R. and G. D. Kinzer. Terminal Velocity of Fall for Water Droplets
in Stagnant Air. J. Meteorol. 6_:246, 1949.
33. Carnahan, B., H. A. Luther, and J. 0. Wilkes. Applied Numerical Methods.
New York, Wiley Co., 1969. 604 p.
133
-------
SECTION X.
NOMENCLATURE
Units: £ = length; t = time; none = dimensionless
a Raindrop radius, £
a* Area of precipitation collector covered by water, £2
A Horizontal area of precipitation collector, £2
A* Total area of precipitation collector surface, £2
B Accuracy parameter for chemical analysis
C
avg Representative average concentration of S02 in water on
precipitation collector surface, moles/£3
c Concentration in collected rainwater that would exist at
" ambient air concentration under equilibrium conditions,
moles/£3
cf Concentration of S02 in the rainwater collected in the
sampler bottle, moles/£3
c Concentration of S02 in the rain impinging on the precipitation
collector surface, moles/£3
c Air concentration of S02 used in rate expression, moles/£3
oU2
c Total concentration of liquid phase, moles/£3
X
c Total concentration of gas phase, moles/£3
C Concentration of pollutant in rainwater collected during
release (Quillayute) or sampling period (Centralia), moles/£3
D , D Diffusivity of S02 in water, in air, £2/t
D , D Effective diffusivities of S02 in liquid, gas phases, £2/t
£>x Cj'y
D , D , D Effective eddy diffusivities in x, y, z directions, £2/t
x y z
E Error in chemical analysis
F Plume depletion factor to account for upwind washout
134
-------
F , , F Flux of SC>2 to precipitation collector by dry, wet processes,
d r moles/£2t
F Total flux of S(>2 to precipitation collector by dry and wet
processes combined, moles/£2t
h Stack height, £; functional equilibrium relationship
H Effective stack height due to plume, £,; Henry 's-law constant,
H = (y.v/x.,) -i ., .
'Ab Ab equilibrium
H "True" Henry 's-law constant for undissociated SCL in water
H° =
H' Modified Henry 's-law constant
H' = H/c , £3/mole
X
H* Modified Henry 's-law constant, H* = H(c /c )
y ^
i., i. Total intensity of turbulence in 6,
-------
t Time, t
T Time of pollutant release, t
t Dimensionless time parameter
u Wind velocity in x direction, &/t
u Mean wind speed, £/t
v Wind velocity in y direction, £/t
v Terminal fall velocity, £/t
w Wind velocity in z direction, £/t; washdown velocity, £/t
w. Rate of transport of S02 to precipitation sampler by dry
processes, moles/t
x Downwind distance, I
x , Interfacial mole fraction of pollutant A in liquid phase
x . Initial mole fraction of pollutant A in liquid phase
x Interfacial mole fraction of pollutant A in liquid phase
A.O
y Crossplume distance, £
y.. Mole fraction of pollutant A in gas phase
y. Gas phase mole fraction that would coexist in equilibrium
with the mixed mean mole fraction in the liquid phase x.,
AD
z Vertical dimension, I
a Parameter defined in Equation (55) et seq.
a Parameter defined in Equation (4) et seq.
n
Parameter defined in Equation (4) et seq. ; Parameter defined
in Equation (55) et seq.
Diffusion film thickness, £; also length parameter defined
in Appendix D.
136
-------
A Distance between precipitation collectors, £
e Radius of region on Bromwich contour
£ Fourier transform parameter
6 Mean wind direction, degrees
A Sulfate washout coefficient, t"1
u Kinematic viscosity of air, £2/t
£, Fourier transform parameter
a Standard deviation of vertical wind velocity, £/t
a , a Plume dispersion parameter in y, z direction, £
OQ, CT Plume dispersion parameter in azimuthal, elevational direction,
radians
2m. Total mass of SC>2 collected on sampling line, moles
i Time-integration variable, t
X Measured air concentration of 862, moles/£3
SUBSCRIPTS
a Aqueous
A Pollutant A
b Bulk
d Dry deposition
e, eq Equilibrium
ex Excess
E Effective
f Final
g Gaseous
137
-------
i Initial
o Plume origin or surface condition
r Rain
t Total
w Vertical component
x Liquid phase in x direction
y Gas phase in y direction
z z direction
0 Azimuthal direction
6 Elevational direction
138
-------
SECTION XI.
APPENDICES
A. Tabulations of Measured Concentrations ............. 140
B. A Synopsis of the Washout Modeling Procedure .......... 170
C. Description of Computer Code for the EPAEC Nonlinear
Nonfeedback Washout Model ................... 176
D. Redistribution of a Gas Plume Caused by Reversible
Washout ............................ 197
139
-------
APPENDIX A.
TABULATIONS OF MEASURED S02 CONCENTRATIONS,
QUILLAYUTE SECOND SERIES AND SQ2, SOij, H+ CONCENTRATIONS,
CENTRALIA
In the following tables, the position numbers correspond with those of
Figure 9 for Quillayute, and Figure 28 for Centralia.
Missing data indicate no measurement made or measurement lost.
The lower limit S02 air concentrations relate to the approximate minimum
measurement capability.
The columns of data are aligned to indicate the approximate radial align-
ment of the sampling positions (cf. Figures 9 and 28).
C is the concentration of the material in rainwater collected during the
R
release (Quillayute), or during the time of sampling (Centralia; cf. Table
11).
140
-------
TABLE 27.
MEASURED SO,, CONCENTRATIONS - RUN 11
* -3
(Units: gm-moles cm
In Rainwater
West Grid East
Arc Arc Arc C
Pos. I CR GR Pos. * CR
(No Release) 10-14 0
15 0.384
16 3.20
17 8,21
18 13.6
19 11.7
20 10.0
21 7.04
22 4.44
x 109)
Grid
i
Line D
Pos. /)
10
11
12
13
14
15
16
17
18
19
20
21
22
23
• CR
0
3.14
7.57
10.0
11.2
9.94
9.94
9.54
11.3
11.6
3.8
0.77
0
0
In Air
(East) Line D
Pos. I x
10 < 0.1
13 < 0.1
16 < 0.1
19 < 0.1
22 < 0.1
25 < 0.1
28,31,34,36 < 0.1
141
-------
TABLE 28.
MEASURED S02 CONCENTRATIONS
In
(Units : gm-moles cm 3 x
Rainwater
West Grid
Pos. #
10,13-14
15
16
17
'18
19
20
21
22
23
24-25
28,31,33
Arc B
CR
0
2.02
6.29
11.7
20.8
22.7
18.4
14.7
3.28
0
0
0
Arc C
CR
0
1.38
6.16
14.5
25.0
23.5
27.6
18.3
6.10
0.369
0
0
25
- RUN 12
109)
East Grid
Arc C
Pos. #
10
11
12
13
14
10
11
12
13
14
15
16
17
18
19
20
21-22
,28,31,33
CR
0
0
0
0
0
0.342a
0
0
0
0
0
0
0
5.77
3.90
0.463
0
0
Line
Pos. #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19,22
D
CR
13. 9a
19. 5a
10. 7a
0.6143
0
0
0
0
0.764
4.53
—i n i
i . zj.
6.00
4.84
0.463
0
Q
S02 from west source.
In Air
(East) Line D
Pos. # X
0.74a
0.318a
10 <0.1
13 <0.1
16 0.508
19,22,25 <0.1
142
-------
TABLE 29.
MEASURED S02
CONCENTRATIONS - RUN 14
(Units: gm-moles cm 3 x 109)
In Rainwater
Pos. #
10,13
14
15
16
17
18
19
20
21
22
23
24
25
28,31,33
West
Arc B
CR
0
1.51
13.1
34.8
37.6
44.6
44.0
29.6
27.5
16.1
4.85
0
0
0
Grid
Arc C
CR
0
1.61
10.3
22.4
43.1
48.0
53.1
43.4
27.8
16.6
6.33
0
0
0
Pos.
10
11
12
13
14
15
16
17
18
19
20
21
22
23
25,28,31
East
Arc C
# CR
0
0
0
0
0
0
2.90
6.80
12.7
12.2
10.8
6.97
4.88
0.958
0
Grid
Pos.
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
25
Line D
1 CR
4.40a
0
0
0.3903
0
0
0.628
3.44
5.19
10.0
12.7
12.4
10.6
9.67
6.28
4.60
3.52
1.53
0.247
0
In Air
(East) Line D
Pos . # x
4 < 0.1
7 < 0.1
10 < 0.1
13 0.64
16 0.32
19 < 0.1
22 0.64
25 < 0.1
S02 from West source.
-143-
-------
TABLE 30.
MEASURED S02 CONCENTRATIONS - RUN
15
(Units: gm-moles cm 3 x 109)
In Rainwater
West
Arc A
Pos. //
10-12
13
14
15
16
17
18
19
20
21
22
23
24
25
28
31
Grid
Arc C
CR
0
1.
3.
10.
19.
22.
26.
33.
24.
10.
2.
0.
1.
0.
0.
0.
66
02
2
4
2
9
8
3
9
74
525
07
443
446
716
0
2
7
25
32
55
58
48
44
27
19
6.
0
0
0
0
CR
.91
.05
.4
.0
.0
.8
.5
.6
.6
.8
49
East
Arc C
Pos. #
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
28,31
CR
0
0
0
0
0.438
1.37
7.80
11.6
15.8
12.1
8.74
3.09
0.564
0
0
0
0
Grid
Line
Pos. #
4
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
25
D
5
0
0
2
11
14
16
18
17
15
14
11
6
4
0
0
0
0
In Air
„ (East) Line D
R Pos. # X
.72a (all < 0.1)
.338a
.94
.0
.9
.5
.9
.2
.7
.6
.8
.70
.54
S02 from West Source
-144-
-------
TABLE 31.
MEASURED S02 CONCENTRATIONS - RUN 16
(Units: gm-moles cm ^ x 10^)
In Rainwater
West Grid
East Grid
Arc A Arc C Arc C
Pos. # CR CR Pos. #
10,13,16,19 0 0
20 1.40 1.08
21 6.25 1.80 10
22 12.8 12.8
23 21.6 26.1
24 25.7 43.2 13
25 24.3 36.2 14
26 28.2 35.2 15
27 19.5 29.0 16
28 16.2 23.0
29 15.8 15.8
30 8.93 3.03 19
31 0 0 20
21
22
23
24
25
26
27
28
29
31
Line D
CR Pos. #
3.95a
5.40a
4.96a
3.77a
3.92a
0
0
0
1.90
6.14
11.5
16.8
18.6
6.34
2.42
0
0
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
CR
12. 2a
20. 2a
13. 2a
14. 9a
24. Oa
11. 2a
10. 4a
8.55a
8.16a
5.25a
5.093
6.413
3.85
3.97
7.11
12.9
17.4
21.0
18.9
16.6
9.38
5.37
0.73
0
In Air
(East) Line D
Pos. # x
(No Measurements)
S02 from West source.
-145-
-------
TABLE 32.
MEASURED S02 CONCENTRATIONS - RUN 17
(Units: gin-moles cm 3 x 109)
In Rainwater In Air
Pos. //
10-16
17
18
19
20
21
22
23
24
25
26-33
West
Arc A
CR
0
0.462
1.78
6.44
13.0
12.5
12.3
5.15
1.24
0
0
Grid East Grid
Arc C Arc C Line D
CR Pos. # CR Pos. # CR
0
10.9 (No Measurement)
19.0
38.6
43.6
52.4
38.6
31.1
19.3
0.44
0
(East) Line D
Pos . # x
(No Measurement)
-146-
-------
TABLE 33.
Pos. #
14
17
20
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
West
Arc B
CR
1.47
1.32
1.10
1.49
2.16
4.26
9.90
20.9
46.2
36.7
30.0
21.2
16.8
16.4
11.3
2.18
1.20
1.86
MEASURED S02 CONCENTRATIONS - RUN 18
(Units: gm-moles cm 3 x 109)
In Rainwater In Air
Grid East Grid
Arc C Arc C Line D f
c c C vtast; Line D
R Pos. # R Pos. # R Pos. # x
0.765 (No Measurement) (No Measurement)
0.903
0.903
1.18
1.08
3.24
19.3
26.9
42.0
32.2
25.3
23.8
23.4
17.7
12.3
2.92
1.57
1.37
-147-
-------
TABLE 34.
MEASURED S02 CONCENTRATIONS - RUN 19
(Units: gm-moles cm 3 x 109)
In Rainwater
Pos. #
22-30
31
32
33
34
35
36
37
West
Arc B
CR
0
1.73
3.72
10.9
10.7
14.5
12.4
10.8
Grid East Grid
Arc C Arc C Line D
CR Pos. # CR Pos. # CR
0
8.04 (No Measurement)
12.3
23.8
30.0
26.8
24.8
9.36
In Air
Pos. #
Line D
X
(No Measurement)
TABLE 35.
MEASURED S02 CONCENTRATIONS - RUN 20
(Units: gm-moles cm 3 x 109)
In Rainwater
Pos. #
19,22,25,
30
31
32
33
34
35
36
37
40
West
Arc B
CR
28 0
2.44
9.49
24.2
29.8
20.2
2.77
0
0
0
Grid East Grid
Arc C Arc C Line D
CR Pos. # CR Pos. # CR
0
8.03 (No Measurement)
29.0
38.9
56.4
26.4
3.82
2.68
0
0
In Air
(East) Line D
Pos. # x
(No Measurement)
-148-
-------
TABLE 36.
S02 CONCENTRATIONS - RUN Cl, LINE A
(Units: gin-moles cm"3 x 109)
Sample Position
19
22
28
34
In Rainwater
Concentration
a
a
a
a
In Air
Concentration
< 10-5
2.4-3.9b
187
82-102b
No rainfall.
Uncertainty due to loss of bubbler fluid.
Sample Position
17
20
23
26
29
TABLE 37.
S02 CONCENTRATIONS - RUN Cl, LINE B
(Units: gin-moles cm"3 * 109)
In Rainwater
Concentration
a
a
a
a
a
In Air
Concentration
< 10-5
102
300-600b
25.2
< 10~5
wo rainfall.
Uncertainty due to loss of bubbler fluid.
149
-------
TABLE 38.
S02 CONCENTRATIONS - RUN Cl, LINE C
(Units: gm-moles cm 3 x
In Rainwater In Air
Sample Position Concentration Concentration
32 a < 10~5
35 a < 10~5
38 a 169
41 a 266-332b
44 a lll-222b
47 a 19.2
TJo rainfall.
Uncertainty due to loss of bubbler fluid.
150
-------
TABLE 39.
S02 CONCENTRATIONS - RUN C2, LINE A
(Units: gm-moles cm"3 * 109)
In Rainwater In Air
Sample Position C on cent r at ion Concentration
11 0
12 0.3
13 0.4 < 10~5
14 0.9
15 0.7
16 2.1
17 9.4
18 12.5
19 15.8 0.004
20 14.7
21 9.8
22 6.9
23 6.1
24 7.9
25 7.2 < 10~5
26 5.3
27 2.0
28 0.3 0.0111
29 0.2
30 0
151
-------
TABLE 40.
SO2 CONCENTRATIONS - RUN C2, LINE B
(Units: gm-moles cm~3 x 109)
In Rainwater In Air
Sample Position Concentration Concentration
5-7 0
8 0 0.0824
9 0
10 0.9
11 2.5 0.0159
12 5.3
13 9.7
14 11.3 0.113
15 6.4
16 4.3
17 4.7 0.0368
18 5.6
19 3.2
20 2.7 0.0834
21 2.0
152
-------
TABLE 41.
S02 CONCENTRATIONS - RUN^ C2, LINE D
(Units: gm-moles cm~3 * 109)
In Rainwater In Air
Sample Position Concentration Concentrat ion
21-22 0
23 0 < 10~5
24 0
25 2.6
26 0.5 0.010
27 0.7
28 1.6
29 2.6
30 2.7
31 4.0
32 2.8 < 10'5
33 2.1
34 1.8
35 1.0 0.021
36 0.8
37 0.5
38 0.5 < 10*5
39 0.4
41 0
153
-------
TABLE 42.
S02 CONCENTRATIONS - RUN C3, LINE A
(Units: gm-moles cm"3 x 109)
In jlainwater In Air
Sample Position Concentration Concentration
11-17 0 (all < 1CT5)
18 1.0
19 0.9
20-30 0
TABLE 43.
S02 CONCENTRATIONS - RUN C3, LINE B
(Units: gm-moles cm~3 x 109)
In Rainwater In Air
Sample Position Concentration Concentration
5-9 0
10 9.2
11 13.9 0.088
12 23.2
13 21.5
14 15.5 0.031
15 4.8
16 0
17 0
18 0
19 0
20 0 < 10~5
21 0
154
-------
TABLE 44.
S02 CONCENTRATIONS - RUN C3, LINE D
(Units: em-moles cm"3 x 109)
In Rainwater
In Air
Le Position Concentrati
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
0
0.2
4.0
6.6
11.1
13.3
9.6
7.1
8.1
7.0
7.0
4.0
3.6
0.2
0.3
0
0
0
0
0
0
Concentration
< 10~5
0.030
0.043
0.026
< 10
,-5
< 10
,-5
< 10
-5
155
-------
TABLE 45.
S02 CONCENTRATIONS - RUN C4, LINE B
(Units: gin-moles cm"3 x 109)
Sample Position
10-12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
In Rainwater
Concentration
0
2.5
15.2
7.4
13.0
4.3
0.3
0.0
0.1
0
0
0
0
0
0
In Air
Concentration
1.24
0.070
< 10~5
< 10
-5
< 10
-5
156
-------
TABLE 46.
S02 CONCENTRATIONS - RUN C4, LINE C
(Units: gm-moles cm"3 * 109)
In Rainwater In Air
Concentration
Le Position
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
Concentration
1.9
3.5
9.3
12.0
10.2
5.9
2.8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.386
0.088
0.017
< 10'
0.0064
0.0044
157
-------
TABLE 47.
S02 CONCENTRATIONS - RUN C4, LINE D
(Units: gin-moles cm"3 x 109)
In Rainwater In Air
Sample Position Concentration Concentration
26 0
27 0.1
28 3.2 0.262
29 6.5
30 9.3
31 11.5 0.116
32 7.4
33 1.1
34 0 < 10"5
35 0
36 0
37 0 < 10"5
38 0
39 0
40 0
41 0 < 10~5
42 0
43 0 < 10~5
44 0
45 0
158
-------
TABLE 48.
Sample Position
11
12
13
14
15
16
17
18
19
2C
21
22
23
24
25
26-30
S02 CONCENTRATIONS - RUN C5,_ LINE A
(Units: gm-moles cm"3 * 109)
In Rainwater
Concentration
0
0
0
0
0
0
0
0
0
2.5
5.5
3.5
0
0
0
In Air
Concentration
0.0011
0.0047
0.0138
10-5
< 10
-5
159
-------
TABLE 49.
SQ2 CONCENTRATIONS - RUN C5, LINE D
(Units: gm-moles cirf^ x 109)
In Rainwater
Sample Position
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
Concentration
0
0
0
0
0
0
0
0.4
1.6
4.8
6.2
2.0
0
0
0
0
0
0
In Air _
Concentration
0.009
0.014
0.0010
0.0301
< 10~5
10
- 5
160
-------
TABLE 50.
SO, and H CONCENTRATIONS - RUN C2, LINE A
4 -39
IN RAINWATER (Units: gin-moles cm x 10 )
Sample Position Concentrations - Less Background
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
S°I H+
0
0
0 0
0
0
2.1 3.2
11.5
28.1
24.0 33.3
24.0
20.8
11.5 15.6
11.5
19.8
18.8 13.6
14.6
13.5
11.5 5.0
1.0
3.1
Background 6.3 2.2
161
-------
TABLE 51.
SQ^ AND H+ CONCENTRATIONS - RUN C2, LINE B
IN RAINWATER (Units: gm-moles cm"3 x 1Q9)
Sample Position Concentrations - Less Background
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Background 6.3 2.2
SO^
2.1
0
2.1
2.1
3.1
4.2
7.3
7.3
15.6
22.9
14.6
30.2
13.5
12.5
8.3
6.3
6.3
H+
1.0
2.8
4.7
16.4
9.0
8.3
162
-------
TABLE 52.
AND H+ CONCENTRATIONS - RUN C2, LINE D
IN RAINWATER (Units: gm-moles cm~3 x 1Q9)
Sample Position Concentrations - Less Background
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41 4.2
Background 6.3 2.2
— _L
cr\ "u
OUi4. "
1.0
3.1
8.3
4.2
15.6
5.2
8.3
8.3
7.3
6.3
9.4
9.4
9.4
6.3
7.3
6.3
4.2
5.2
6.3
2.8
5.0
6.7
6.1
5.7
4.9
163
-------
TABLE 53.
AND H+ CONCENTRATIONS - RUN C3, LINES A, B, D
IN RAINWATER (Units: gm-moles cm"3 x 1Q9)
Sample Position Concentrations - Less Background
SO" H+
A 13 (1) 0
16 4.2
19 21.6
22 0.7
25 0
28 0.2
B 8 0
11 48.2
14 32.3
17 0
20 0
D 23 11.2
26 30.8
29 14.7
32 6.0
35 2.4
38 0.6
41 0.1
Background 0.8
(1) No measurement - Analytical difficulties arising from low sample volumes,
164
-------
TABLE 54.
AND H+ CONCENTRATIONS - RUN C4, LINE B
IN RAINWATER (Units: _ gm-moles_cm~3_ x 1()9)
Sample Position Concentrations - Less Background
H+
10 0
11 3.1 1.8
12 3.1
13 15.6
14 34.4 48.1
15 17.7
16 52.1
17 11.5 23.1
18 10.4
19 6.3
20 3.1 2.8
21 3.1
22 0 1.3
23 0
24 0
25 0 0.8
26 0
27 0
Background 2.1 3.2
165
-------
TABLE 55.
Sample Position
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
S04 AND H+ CONCENTRATIONS - RUN C4, LINE C
IN RAINWATER (Units: gm-moles cm~3 x 109)
Concentrations -
SO"
7.3
7.3
16.7
19.8
15.6
13.5
8.3
6.3
4.2
3.1
2.1
0
0
0
0
0
0
0
0
0
0
Less Background
H+
27.7
18.2
11.9
1.7
1.0
0.6
Background 2.1 3.2
166
-------
TABLE 56.
Sample Position
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
S04 AND H+ CONCENTRATIONS - RUN C4, LINE D
IN RAINWATER (Units: gm-moles cm"3 x 109)
Concentrations -
Less Background
SO^ H+
3.1
4.2
8.3
10.4
13.5
14.6
11.5
10.4
3.1
0
0
0
0
0
0
0
0
0
0
16.8
23.1
4.7
0
0
1.6
Background 2.1 3.2
167
-------
TABLE 57.
Sample Position
11-12
13
1A
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
SOU AND H+ CONCENTRATIONS - RUN C5, LINE A
IN RAINWATER (Units: gm-moles cnT3 x 109)
Concentrations -
so"
0
0
0
0
0
1.0
5.2
5.2
15.6
24.0
14.6
7.3
2.1
0
0
0
0
0
2.1
Less Background
H+
0
0
34.0
19.0
12.0
Background 6.3 VL6.0
168
-------
TABLE 58.
AND H+ CONCENTRATIONS RUN C5, LINE D
IN RAINWATER (Units : gm-moles cm"3 x 1Q9)
Sample Position Concentrations - Less Background
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
Background 6.3
0
0
0
2.1
2.1
3.1
5.2
5.2
6.3
9.4
9.4
4.2
0
0
0
0
0
20.0
6.4
12.0
18.0
6.4
1.8
169
-------
APPENDIX B.
A SYNOPSIS OF THE WASHOUT MODELING PROCEDURE
The reversible gas washout calculations described in this report are based
upon an approach that has been developed over the duration of Battelle's
involvement in the EPA washout studies. This appendix provides a short de-
scription of the fundamentals of this approach, and should suffice to pro-
vide a basic understanding of the theory involved in this report. For a
more detailed description the reader is referred to the previous reports
and publications on this subject.1-i+
The basis for all washout calculations utilized herein is the property that
a gas will be absorbed or desorbed depending upon whether the concentration
driving force is to or away from the falling raindrop. Mathematically,
this may be expressed by the form
\o - -Ky <3«>
where, as shown in the Table of Nomenclature N is the flux of pollutant
Ao
A away from the drop at its interface. The subscripts A and o denote
"pollutant A" and "interface," respectively, in a manner consistent with
terminology used throughout this text; the subscript b denotes "bulk,"
indicating that the entity being described is an average or "mixed-mean"
value; y is the mole fraction of A in the local gas phase, y is
the mole fraction of A in the liquid phase expressed in gas-phase terms
to allow incorporation with y as a driving force; it is, more precisely,
the gas phase mole fraction that would coexist in equilibrium with the
mixed-mean mole fraction in the liquid phase x .
AD
The above equilibrium relationship can be expressed by the functional form
^Ae = h(xAb> ' (35)
In the event that the gas-phase fraction is linearly dependent on the liquid-
phase value, the above equation reduces to
y = Hx * (36)
170
-------
where H is the Henry's-law constant. This may be expressed in terms of
liquid-phase concentration by the essentially equivalent form
y* = H'CAU
Ae Ab
where H' = H/c is a modified Henry's-law constant, c being the total
X Q X
liquid-phase concentration (nominally 1/18 moles/cm ).* Nonlinear behavior
in the equilibrium relationship is accounted for in the numerical model
simply by applying the form (37) and varying H' as the computation pro-
gresses .
S09 solubility in water is known to depend upon concentration in a highly
nonlinear fashion. Our previous laboratory measurements have shown this
relationship to be given approximately by the form (cf. DHW, pg. 24),
] + [HSOJ
clu J
H°
(38)
where the bracket ted terms denote concentrations in moles/liter and
[H_0 ] is the concentration in solution of hydrogen ions donated by
J GX
sources other than the SO- ionization reaction. H and K.. are the
("true") Henry 's-law and dissociation constants, respectively, for Reactions
(39) and (40):
'
K tHSO"3"H30+]
Ki = — isoT~ - • (40)
2. aq
Here it is important to note that [SO ] denotes dissolved, undissociated
^_ 3.Q
SO , while the total dissolved SO is denoted by c .
L. Z. OU~
*0wing to the variety of definitions of the Henry's-law constant that occur
in the literature, one must take care to insure correct application.
171
-------
The flux N in Equation (34) is defined as the moles of material leaving
the drop per unit area per unit time; whether the process is one of absorp-
tion or desorption, therefore, depends on the sign of the term (y., - y ).
Ab Ae
Thus if a raindrop contains sufficient dissolved pollutant gas to render it
supersaturated with respect to its surroundings (y > y ), then the sign
Ae
'Ab'
will be negative and desorption will occur. Conversely, if a relatively
clean raindrop finds itself in an environment where y is large, then
AD
the driving-force sign will be positive, indicating an absorption process
is taking place.
The overall mass-transfer coefficient K can be estimated by expressing
it in terms of "film resistances" on the gaseous and liquid sides of the
raindrop interface. For present purposes this relationship can be written
as
K
H_
k
(41)
where k and k
x J
defined as
and
y x y
respectively are the liquid- and gas-phase mole fractions
NA = -k (XA - x..)
Ac x Ao Ab
N
Ao
- yAo}
(42)
(43)
Here
x
Ao
and y are the mole fractions of pollutant A existing pre-
cisely at the gas-liquid interface. The rationale for this procedure may
be shown superficially, at least, in terms of the schematic of Figure 59.
This drawing represents a close-up view of a raindrop interface; pollutant
gas is being transferred to the drop (absorption) and the corresponding con-
centration gradients are established. By assigning film thicknesses and
effective diffusivities to the gaseous and liquid regions, one can apply
Pick's law of diffusion to formulate Equations (39) and (40), where
and
k =
k =
x
(44)
(45)
172
-------
O
w
IT
H
s
H-l
Q
W
C/D
En
O
Z
O
H
2
W
CO
w
a!
PH
W
O
173
-------
The situation depicted by the above analysis, obviously rather simplistic
in nature, has found extended practical application. Continuing with this
approach, one may employ the well-known Froessling equation to determine
the gas-phase mass-transfer coefficient. This equation, given in dimension-
less form as
2k a -2av 1 1
> (46)
has been validified for a wide range of conditions and is expected to pro-
vide an excellent estimate of k for falling raindrops.
The method of estimating the liquid-phase mass-transfer so efficiently is
not so straight forward, and involves a number of inevitable assumptions.
The approach utilized here is to assume that the lower limit of mass tran-
fer will occur if the raindrop is stagnant. In this event (if we treat this
situation as one of pure "physical absorption" (cf. HTW, DHW)), one can
solve the equation of continuity for diffusion into a sphere to determine
corresponding mass-transfer rates (HTW, p. 40). Normally this results in
variable mass-transfer coefficients; however, if one calculates for the
special case of a linearly increasing gas concentration, the expression
5D c
k = ** x , (47)
X ct
is obtained. This equation can be used in conjunction with (39) to provide
a linearized mass-transfer expression, if desired. Alternatively, one can
employ the combined gas-liquid expression derived during this project and
given in Section IV to provide a less direct but theoretically more satisfy-
ing means of estimation.
To calculate washout concentrations using the above approach one must re-
write (34) in terms of the liquid-phase concentration, c . The result is
AD
dC 3K
*v - A,
dz v a wAb Ab
(48)
where v is the terminal fall velocity of the raindrop, and the gas-phase
concentration field y ,(x,y,z) must be furnished prior to calculation of
A.D
174
-------
numerical results. At the present time this procedure uses the Pasquill-
Gifford bivariate-normal plume equation, modified to account for pseudo
first-order chemical reaction and background, to fulfill this purpose. This
is given as
y z
Execution of the EPAEC model consists simply of solving Equation (47) numeri-
cally in conjunction with Equation (48) for a number of selected drop sizes,
and then distributing the results according to the raindrop spectrum to ob-
tain average concentrations. The computer code described in Appendix C
performs this function and allows for a number of sophistications including
nonlinear solubility behavior, lofting plumes, and nonvertical rainfall.
If these sophistications are not included, the above problem can be solved
analytically, the result being given by
CAb(a'o) =
AD
3QFk r
—
2V2n a uv a
y t
6Xp(~
2a
-a
- h
{expCOOerfc(
a V2
z
exp(-£h)erf c(
-a \
+ h
where r = exp(-kx/u) and
= 3K H'/v a.
a V2
z
bkg
/H'
(50)
175
-------
APPENDIX C.
DESCRIPTION OF COMPUTER CODE
FOR THE EPAEC NONLINEAR NQNFEEDBACK WASHOUT MODEL
The computer code can be described, in a somewhat superficial sense, in
terms of the flow chart shown in Figure 60. This figure demonstrates that
washout calculations may be performed using the code simply by employing a
main program that performs the following functions: 1) reading of appro-
priate input data; 2) execution of algorithm by the statement CALL MASTER;
3) printing of resulting computed values. MASTER is a master coordinating
subroutine which employs all of the program functions to calculate washout
as indicated in Figure 61.
The utility of the above arrangement is that it allows the code to be
applied generally for a variety of specific purposes; one simply writes a
main program designed to fulfill his particular requirements, and employs
the statement CALL MASTER to execute the basic algorithms required. The
Centralia computations described in Section VI, for example, were executed
using a main program that memorized the topography of the surrounding area,
computed relative distances based on the plume location, and then calculated
corresponding washout concentrations by the statement CALL MASTER.
A generalized main program can be employed to perform the above functions,
if desired. Use of such a program will provide results identical to those
computed using customized main programs, the major disadvantages being
probable increased inconvenience in data input and less control over output
formats. An example of such a generalized program is shown on the pages
immediately following Table 59, which defines the computer nomenclature.
Named EPAEC, this program employs a common statement to facilitate exchange
of information with the subroutine MASTER. The following EXTERNAL statement
designates the function subroutines V, HPRIME, and YAB to be used internally;
this statement is essential to the operation of any main program for this
purpose.
Reading of input data proceeds, governed by the control variables J1-J4
which allow the bypass of designated READ statements if desired. Finally,
176
-------
READ INPUT DATA
RAINDROP SIZE SPECTRUM AND RATE (N, F, D, XNT);
MOLECULAR TRANSPORT PROPERTIES (DAX, DAX, XNU)
REACTION RATE CONSTANT (RK);
PRESSURE, P; TEMPERATURE, T; EXCESS HYDROGEN ION CONCENTRATION, HEX;
PLUME PROPERTIES (SIGTHE, SIGPHI, U, H, Q, VERT, BKG);
RECEPTOR LOCATION (XBUK, YBUK, ZBUK);
CONTROL VARIABLES (OOPT, ...)
±
CALL MASTER
PRINTING OF COMPUTED WASHOUT CONCENTRATIONS
CGRND (I), CAVG, CEQ
AND/OR
STORAGE FOR SUBSEQUENT COMPUTATION
FIGURE 60. SUPERFICIAL FLOW DIAGRAM OF EPAEC MODEL.
MASTER
SOLVE
>
RUNGE |
i
>
t
1 MTC 1
1
±
S
[YAB
f
HPRIME
FIGURE 61. SUBROUTINE HIERARCHY IN EPAEC MODEL.
177
-------
an optional, internally-generated receptor spacing (DYDUM) is calculated.
This provides for performance of subsequent calculations at 5-degree in-
creasing cross-plume distances.
Upon printing the input data, MASTER is called. Execution of this sub-
routine pertains to a single receptor location. Upon completion of the
calculations controlled by MASTER, appropriate printing is performed, in-
cluding that of REF, which is the variable denoting height above the source
passed by individual raindrops at x = 0.
At this point, depending upon the current value of the control variable
JEND, the program has two options. It can either proceed to the adjoining
cross-plume location, perform subsequent computations, and integrate to
provide (ultimately) a downwind washout rate (WORATE) or it can read new
input data and proceed to calculations for other conditions. In the event
that cross-plume integrations are performed, the program terminates when
relatively low concentrations are encountered on the edges of the plume,
and the downwind washout rate is printed.
The program is terminated completely whenever no additional data cards are
found, or when the control variable JEND is set equal to 1. An example
data set for use with EPAEC has been given previously in Section VII.
DESCRIPTION OF BASIC COMPUTATIONAL ALGORITHM
Exclusive of the input-output functions governed by the main program, the
basic computational algorithm can be described by the hierarchy of sub-
routines shown in Figure 61. The primary function of this algorithm is to
solve the drop-response equation
dc., 3K
- H'c ..) , (48)
..
dz v a'Ab Ab
which was given previously in Appendix B. The calculations performed by
the computer listing given here envision a rain-plume situation as shown in
Figure 62. In this visualization a single raindrop of radius R falls
through the plume to a receptor over a linear trajectory determined by the
wind speed U and the terminal fall velocity V. A computational grid is
set up along the trajectory, and Equation (48) is solved numerically using
178
-------
179
-------
a Runge-Kutta finite-difference approximation to obtain the value of c
Ab
(CGRND in the computer code) at the receptor location. This procedure is
repeated for all drop sizes in the discretlzed spectrum and the results are
averaged to obtain a final mixed-mean concentration (CAVG) for that location.
y , values along the trajectory are furnished by a plume model in the form
of a subroutine (YAB). At present this subroutine is written to accomodate
the Gifford-Pasquill Bivariate-Normal plume model,6 modified to account for
quasifirst-order chemical reaction, plume loft, and ambient background. De-
scriptions of the subroutines shown in Figure 61 are given individually in
the following text. Listings of these subroutines are provided at the end
of this appendix.
Subroutine V provides the terminal fall velocity dz/dt, as a function of
raindrop radius R. This internal function is simply an empirical poly-
nomial fit to measured terminal velocity data.31
Subroutine HPRIME utilizes Equation (38) or appropriate variations thereof,
to determine values of the apparent Henry's-law constant appropriate to the
current value of either c , or y , depending on the value of the control
variable LGOPT. If LGOPT is set equal to 1 in the calling sequence, cal-
culation is based on the value of y.y.; otherwise the current value of c ,
is employed.
Upon being initiated, HPRIME first computes the dissociation constant
(EQCON) and Henry's-law constant for undissociated SO- (HANK), as defined
by _ +
[HSO ][H 0 1
EQCON = [so ] ' (moles/liter) (51)
2 aq
YAb
HANK = rgn "— , (liters/mole). (52)
LS°2Jaq
This is done in accordance with Johnstone and Leppla's^2 measured values as
interpreted in our previous analysis (DHW, p. 23 et seq.).
Upon computing EQCON and HANK the subroutine branches, depending on the
value of LGOPT, to computations based on liquid or gas-phase concentrations.
Each of these branches tests for low-concentration conditions and applies an
180
-------
asymptotic approximation to the solubility expression if these conditions
are satisfied. If low-concentration conditions do not exist, the complete
solubility equations are employed for final assessment of the return value
of the apparent Henry's-law constant,
^AK •}
HPRIME = _-,,.-,—. gn , (cm /mole). (53)
total dissolved SO
3
Conversion from units of liters to cm is completed within the subroutine
prior to returning to the calling routine.
Subroutine MTC computes the overall mass-transfer coefficient K . It be-
gins by calculating the gas-phase coefficient using Equation (46). Then,
if the control variable JOPT has been set equal to 1, (gas-phase limiting),
the overall coefficient is returned as the gas-phase value. Otherwise, a
liquid coefficient is calculated using Equation (47), and the gas and liquid
coefficients are combined using Equation (41) to obtain the corresponding
stagnant-drop values.
Subroutine RUNGE, in conjunction with subroutine SOLVE performs the numeri-
cal integration of Equation (48), SOLVE supplying RUNGE values of the de-
rivative dc ,/dz (F in the computer code) and RUNGE returning values of
A.D
c . RUNGE is a fourth-order Runge-Kutta algorithm which has been adapted
from a previous work.33 This algorithm is rather complex and will not be
discussed in detail here, except to state that its expected errors are of
the order of the fractional grid spacing to the fourth power. For a com-
plete discussion of this method the reader is referred to the work of
Carnahan, et al. 33
Subroutine YAB, as mentioned previously, provides values of the gas-phase
mole fraction of pollutant as a function of spatial location x, y, and z.
Equation (49), which is the Gifford-Pasquill Bivariate-Normal equation,
modified for quasifirst-order gas-phase chemical reaction, is employed for
this purpose. The subroutine computes values of the dispersion parameters,
and proceeds directly with a solution of Equation (49) to provide the re-
turn value YAB. H in this subroutine is a virtual value, and depends upon
the value of emission height supplied by the calling program.
181
-------
Subroutine SOLVE performs the function of establishing the computational
grid and implementing RUNGE to obtain the solutions to Equation (47). The
routine begins by initializing variables and then testing for the occurrence
of equilibrium scavenging. This is accomplished by calculating a virtual
emission height (HSTAR) and an appropriate dispersion parameter (SIGMAZ).
This is followed by determination of an effective Henry's-law constant,
which is employed in conjunction with the criterion of Equation (1) (GROUP
> 15) to determine whether or not equilibrium scavenging occurs. If equi-
librium conditions are indeed predicted, the scheme bypasses the solution
of Equation (47) and simply returns the equilibrium washout concentration
value.
In the event that equilibrium conditions are not predicted, the routine in-
itializes the concentration of pollutant in the drop, C(l), to its appro-
priate above-plume value, and proceeds to establish a computation grid. In
performing this function it first tests for plume undercut by the raindrop
(REF < 0). In the event that undercutting occurs, the grid network is es-
tablished by dividing the vertical distance between the sampler and the
height at which the drop crosses X = 0 into thirty equally-spaced measure-
ments .
If plume undercutting does not occur, a "normal" grid spacing is established.
This is accomplished by finding an appropriate vertical spread parameter
SIGMA) for early stages of the drop-plume encounter and (rather arbitrarily)
beginning numerical computations at an elevation equal to the effective
release heights plus three times the computed spread (HSTAR + 3 * SIGMA).
Grid spacing is set at one-sixtieth of the vertical distance between the
receptor and the point where calculations are initiated.
A final modification of the computation grid structure is performed if the
raindrop encounters a plume having a low degree of spread ("compact plume").
This is done simply by testing for whether the current spacing is less than
one-fourth the computed spread parameter SIGMA. If not, a top grid spacing
(TDZ) is set equal to SIGMA/4 (SIGMA/8 if SIGPHI is greater than 0.5). If
"compact" plumes are encountered, this finer grid spacing is employed for
25 increments, and the original grid spacing, DELTAZ, is employed thereafter.
182
-------
The choices of grid spacings described above were arrived at after experi-
mentation with various arrangements. This system provides for general
stability and accuracy of the algorithm, with reasonable economy in execu-
tion time.
As described earlier, numerical solution of the object equation is accom-
plished using subroutine RUNGE. This subroutine is called repeatedly, and
control is transferred between it and the calling subroutine SOLVE, which
updates the downwind distance (x) and effective release height HSTAR.
SOLVE also updates the derivative function F(l) and supplies this value
to RUNGE, which in turn provides calculated values of the concentration
Calculations continue until the receptor location is encountered. Then the
value of the ground-level rain concentration (COBJ) is calculated and re-
turned with other pertinent variables in the calling sequence.
Subroutine MASTER coordinates calculations for the ensemble of drops in the
descretized spectrum, and combines the resulting concentration values to
obtain mixed-mean levels. MASTER simply calls subroutine SOLVE for each
raindrop size in the spectrum, saves the individual concentrations in the
array CGRND(I), and averages according to the equation
N 3
I, F(I)D(I) CGND(I)
CAVG = - - - - — - . (54)
1
Control is then transferred to the main program for subsequent printing
operations.
MODIFICATION OF THE COMPUTER CODE
The modular form of the general computer code enables it to be modified
easily for use in other applications. Such modifications can be categorized
into two types, depending on whether they are meant to improve the accuracy
of the calculations or to adapt the algorithm for use with substances other
than SO .
183
-------
The first type of modification—an incorporation of an improved plume
model for instance—can usually be accomplished by modular replacement of
one or more subroutines in a straight-forward manner. The second type of
modification usually can be accomplished easily, depending on the materials
of interest. If this material is a nonreactive gas, one simply must re-
place the solubility function HPRIME with one appropriate to the gas in
question. Other routines are generally applicable, and corresponding
modifications are accomplished automatically by changes in the physical-
properties input data. Scavenging of a totally soluble gas, for instance,
can be calculated simply by modifying the function HPRIME to return a zero
value whenever it is called.
184
-------
TABLE 59.
COMPUTER NOMENCLATURE
Symbol
AA
B
BKG
C
CAVG
CAVGCL
CCUM
CDUM
CEQ
CGRND
CLAST
COBJ
CSET
CTEST
D
DAX
DAY
Units
2
cm
gm moles /liter
dimensionless
gm moles /cm
gm moles /cm
gm moles /cm
gm moles /cm
2
gm moles/ (liter)
gm moles /cm
gm moles/cm
gm moles /cm
gm moles /cm
gm moles /cm
gm moles /cm
cm
cm /sec
2.
cm /sec
Definition
Summing variable for calculation of average
concentration
Dummy variable in subroutine HPRIME used for
storage of sum of the equilibrium constant
and the excess hydrogen ion concentration
Mixing ratio of pollutant in gas phase back-
ground (moles/mole)
Mixed-mean concentration of pollutant in a
specific raindrop
Mixed-mean concentration of pollutant in a
collected rain sample
Mixed-mean concentration of pollutant in rain
sample collected beneath plume centerline
Cumulative concentration used for integration
across the plume to calculate washout rate
Dummy variable used in HPRIME
Concentration of pollutant in rain in equilib-
rium with ground-level gas-phase concentration
Mixed-mean concentration of pollutant in a
specific raindrop at receptor
Dummy variable used for performing cross-plume
integration
Mixed-mean concentration of pollutant in a
specific raindrop at receptor
Mixed-mean concentration of pollutant in a
specific raindrop used for calculation of
mass-transfer coefficient in subroutine TKY
Dummy variable used to test for cross-plume
integration termination conditions; also used
to establish compact plume characteristics in
SOLVE
Raindrop diameter
Molecular diffusivity of pollutant in air
Molecular diffusivity of pollutant in water
185
-------
TABLE 59 (Cont'd.)
Symbol
Units
Definition
DELTAY cm
DELTAZ cm
DYDUM cm
DZ cm
DZTST cm
EQCON gm moles/liter
HEX
HSTAR
HTEST
I
ICP
IGRND
IS
-3
cm
GR dimensionless
GROUP dimensionless
H cm
HANK liters/gm mole
gm moles/liter
HPRIME cm /gm mole
cm
cm /gm mole
Cross-plume spacing of calculation points
Vertical grid spacing employed under non-
compact plume conditions
Cross-plume spacing of calculation points
generated by computer if no value is entered
as data
Vertical grid spacing
Test variable for assessing compact plume
conditions
Equilibrium constant for first dissociation
of SO (cf. Equation (40))
Probability-density function for raindrops of
size R in a distributed system; also denotes
derivative used in subroutines SOLVE and RUNGE
(gm-moles/cm^)
Dummy variable used in subroutine SOLVE
Dimensionless group used to evaluate equilib-
rium scavenging conditions (cf. Equation (1))
Effective emission release height
Henry's-law constant for undissociated S0_ in
water (cf. Equation (39))
Hydrogen ion in rain other than that contrib-
uted by dissolved S0~
Effective Henry's-law constant for total
dissolved SO in water
Plume height, or effective release height
Effective Henry's-law constant used for
evaluation of equilibrium scavenging conditions
Index integer
Internal control variable in subroutine SOLVE
providing for grid spacing modifications in the
case of a compact plume
Internal control variable in subroutine SOLVE
providing for termination of the algorithm as
the raindrop encounters the receptor
Internal control variable communicating status
of solution between subroutines SOLVE and RUNGE
186
-------
TABLE 59 (Cont'd.)
Units
Definition
J
Jl
J2
J3
J4
JEND
JOPT
JP
LGOPT
M
N
P
PHI
Q
R
RE
REF
RK
S
a tin
gm moles/sec
cm
dimens ionles s
cm
sec
-1
Internal control variable providing a runaway
trap on cross-plume integration sequence
Index integer
Read control variable providing for optional
reading of raindrop size distribution data
Read control variable providing for optional
reading of physical properties data
Read control variable providing for optional
reading of plume data
Read control variable providing for optional
reading of grid data
Program termination control variable
Mass-transfer coefficient option control
variable (JOPT = 1 gives gas-phase controlled
coefficient; JOPT = 0 gives stagnant-drop
contribution)
Print control variable (JP set equal to 1
suppresses printing of individual raindrop
data
Control variable for gas (= 1) or liquid (= 2)
based solubility calculations
Internal/external control
Integer for RUNGE and SOLVE
Number of discreet drop sizes in descretized
spectrum; also number of simultaneous equations
in RUNGE
Ambient pressure
Internal computation variable in RUNGE
Source strength of plume
Raindrop radius
Reynolds number for falling drop
Height above release point where raindrop
passes x = 0
First-order reaction constant for decay of
pollutant in plume
(Integer) status variable used in subroutine
RUNGE—counterpart of variable IS in subroutine
SOLVE
187
-------
TABLE 59 (Cont'd.)
Symbol
Units
Definition
SAVEY
SC
SIGMA
SIGMAY
SIGMAZ
SIGPHI
SIGTHE
SIGY
SIGZ
T
TDZ
TEST1
TRY
TDZ
U
V
VERT
WORATE
X
XBUK
XCL
XK
XNT
Y
YAB
YBUK
YK
Z
ZBUK
dimensionless
dimensionless
cm
cm
cm
radians
radians
cm
cm
°K
cm
liter/gm mole
gm moles /cm sec
cm
cm/sec
cm/sec
cm/sec
gm moles /cm
cm
cm
cm
gm moles /cm sec
cm/sec
cm
dimensionless
cm
gm moles /cm sec
cm
cm
Mixing ratio of pollutant in gas phase at
receptor
Schmidt number for falling drop
Internal estimate of plume spread in z-
direction—utilized when compact plumes are
encountered
Plume spread in y-direction
Plume spread in z-direction
Plume spread in cp-direction
Plume spread in 6-direction
Plume spread in y-direction at receptor
Plume spread in z-direction at receptor
Ambient temperature
Compact plume grid spacing
Test variable for asymptotic dilution conditions
Overall mass-transfer coefficient (cf. Eq. (41)
Grid spacing for compact plume
Mean wind velocity
Terminal fall velocity of raindrop (fall in +z
direction)
Plume loft velocity
Downwind washout rate
Downwind distance from source
Downwind distance of receptor from source
X position where drop falls across release
elevation
Liquid-phase mass-transfer coefficient
Rainfall rate
Crosswind distance from source
Mixing ratio of pollutant in air (moles/mole)
Crosswind distance of receptor from source
Gas-phase mass-transfer coefficient
Distance above stack base
Distance of receptor above stack base
188
-------
PROGRAM EPAEC,REF
1F(JEND.EQ.3) GO TO 100
C TESTING FOR WHETHER RECEPTOR IS ON CENTERLINE
189
-------
180 IF (lY.EQtO) GO TO 190
IF (JENO.E0.2) GO TO 20U
C TEST FOR OFF-PLUME CONDITIONS
CTEST=l,-(CAVGCL«CAVG)/eAV6CL
CCUMaCCUM*(CAVG*CLAST)
IF (CTEST.LT,,001) GO TO 210
GO TO 200
190 CAvGCLaCAVG
200 YBUK=YBUK*OELTAY
IYaIY+1
IF UEND.EQ.2) GO TO 100
IF (IY.GT.35) GO To 220
CLAST=CAVG
C CALCULATION AND PRINTING 0*- DOWNPLUME WASHOUT RATE (MOLES/CM SEC)
WORATE=CCUM*DELTAY*XNT
GO TO 150
210 WRITE <6»300) WORATE
IF (JEND.NE.l) GO TO 100
220 CAt L EXIT
C
230
24C
250
260
270
280
290
300
310
320
330
340
350
360
FORMAT (lHl//,10Xt"PRECIPITATION WASHOUT ESTlMATES»i//»5X,
1"VALUES GIVEN IN GM-MOLE - CM - SEC UNITS UNLESS SPECIFIED OTHERWI
2SE»»///i20X. "INPUT DATA")
FORMAT (1H »"DAX »
-------
SUBROUTINE MASTER
C SUBROUTINE FOR CALCULATION OF WASHOUT CONCENTRATIONS IN RAIN
C AT GROUND LEVEL USING GENFHALIZED NONLINEAR MODEL. IT ACCEPTS
C INPUT DATA FROM MAIN PR8GRAM THROUGH THE COMMON STATEMENT AND
C THFN PROCEEDS TO CALCULATE RAINDROP CONCENTRATIONS BY CALLING THE
C RFfJUIHED SUBROUTINES. IT THEN CALCULATES THE AVERAGE
C CONCENTRATION IN THF RAIN SAMPl.e, AND R!TTU!0.
C COMPUTATION OF AVERAGE CONCENTRATIOJ 8Y DISTRIBUTION OVER DROP SIZES
DO 110 I=liN
110 AA*AA«F(I)*D(I)**3
DO 1?0 1 = 1.N
CAvG«CAVG + F(I> «CGRND(I)»D tli**3
CAVGcCAVG/AA
RETURN
F.ND
191
-------
SUBROUTINE SOLVE (R.COBJ,JOPT.PAX.pAr>HEX>XNU»P»T.SlGTHE.SIGPWl,U
lH,QrX8UK.Y«ZBUK,SAVEY»RKtbKG.VFRTtC6Q)
C SUBROUTINE FOR CALCULATION OF INDIVIDUAL RAINDROP CONCENTRATIONS,
C PROGRAM SETS UP APPROPRIATE COMPUTATION GRID FOR NUMERICAL
C SOLUTION OF THE FIRST-ORD6H, ORDINARY DIFFERENTIAL EQUATION
C DESCRIBING DROP RESPONSE. IT THEN CALLS THE RUNQE-KIJTTA
C ALGORITHM REPEATEDLY. PROGRESSING FROM THE TOP OF THE
C COMPUTATION GRID TO GROUNO LEVEL.
DIMENSION C(l) ,F(1)
C INITIALIZATION OF VARIABLES
ICPaO
M*i)
IGRNDsO
C(l)=0
1*1
C BYPASS TEST FOR EQUILIBRIUM SCAVENGING CONDITIONS
HSTAR=H«VERT*XBUK/I)
SIGMAYcSIGTHE*XBUK
SIGMAZ=SIGPHI*XBUK
SAVEY=YAB(T,PtU.HSTAR.Q,XBljK,Y,ZBUK,SIGTHEtSIGPHI»RK.BKG)
HTEST=HPRIME(SAVEY,HEX,T.P.I)
IF(HTEST.LE.O,) GO TO 100
CTFSTaSAVEY/HTEST
CALL MTC(R.DAX»DAY,XNU,T,P.JOPT,CTESTtHTEST.TKY)
GR«18.9*TKY»HTEST«U*SIGMAY*SI6MAZ**2*EXP(.5*.5»Y*Y/SIGMAY**2>
GR«-GR/(V(R)»R)
GROUPaGR*SAVEY/(82,*Q*T/P)
CORJ=CTEST
CEG=CTEST
IF(3ROUP.GT,15.) GO TO 190
C CALCULATION OF INITIAL RAINDROP CONCENTRATION
C(l )=BKG/HPRIM.E(BKG»HEXtT*^»l)
C TEST FOR PLUME UNDERCUT
TOO REFs-X8UK*V(R)/U»ZRUK-H
Z»RE.F*H
IF (REF.GT.O.) GO TO 120
C SPACING FOR UNDERCUT GRID
DELTAZ*-XBUK*V(R)/(U*30,")
GO TO 13"
C SETTING OF NORMAL GRID SPACING
120 XCL=XBUK*U*(H-ZBUK)/V(R)
SIGMA=SIGPHI*XCL
HSTARsH»VERT*XCL/U
ZlsHSTAR*3.*SIGMA
IF (Zl.LT.Z) Z»ZJ
DELTAZ»Z/60.
C TEST FOR COMPACT PLUME
nZTST»SIGMA/4,
IF(SIGPHI.GT..5) DZTSTsQZTST/2,
IF(DZTST.GT.DELTAZ) GO TO 130
C SETTING OF COMPACT GRID SPACING
TDZ-DZTST
ICP«1
C START OF NUMERICAL INTEGRATION LOOP
130 IF (ICP.NE.1.0R.I.GT.25) GO TO HO
DZ.-TDZ
192
-------
60 TO 150
Ho DZ«-DELTAZ
C INITIATION OF RUNGE-KUTTA
ISO CALL RUNGE ( 1 f C »F . Z iDZ. IS ." )
IF(CU).LT.O.) C<1)«0.
IF (IS.NE.t) GO TO 160
X«XBUK*U*(Z-ZBUK)/V(R)
HSTAR«H+VERT*X/U
C CALCULATION OF MASS-TRANSFfcR COEFFICIENT
CALL MTC -i
1KG)-HPRIME(C(1> »HEX,T«Pt2)»C(l)l
GO TO 150
C TEST FOR APPROACH TO GROUMJ
160 ZTEST»Z*DZ-ZBUK
IF(ZTEST.LT.100.I GO TO ITu
GO TO 130
170 IF (IGRND.EQ.l) GO TO 180
IGRND«1
DZsZ8UK-Z
GO TO 150
180 COBJ«C(1>
190 RETURN
END
SUBROUTINE MTC IR»OAX,DAY.XNU.T,P,JOPT.CSET.HEX,TKY)
C SUBROUTINE FOR MASS-TRANSftR COEFFICIENT CALCULATION.
C GAS COEFFICIENT BASED ON FNOESSLING EGUATION. LIQUID
C COEFFICIENT IS BASED ON CONTINUITY EQUATION SOLUTION FOR
C RESPONSE TO RAMP CONCEKTRaTION FORCING FUNCTION.
C
C CALCULATION OF GAS-PHASE COEFFICIENT
RE«-2.*R*V(R)/XNU
SC.XNU/DAY
YK«(l.«,3*RE**.5*SC»*.333»*OAY*P/tR»T«fl2,057)
TKY«YK
IF (JOPT.EGI.l) GO TO 100
C CALCULATION OF LIQUID-PMASt COEFFICIENT
XK«.2778*DAX/R
TKY*l/(HPRIME(CSET.HEXtTiPt2)/XK*l/YK)
100 RETURN
END
193
-------
FUNCTION YABlT.P.U.H.QtX.Y.Z.SIGTHE.SIGPHI.RK.BKG)
C SUBROUTINE FOR CALCULATING MOLE FRACTION OF POLLUTANT IN GAS PHASE
C PASQUILL-GIFFORD BIVARUTF-NOHMAL EQUATION IS MODIFIED TO ACCOUNT
C FOR POSSIBLE BACKGROUND CONTRIBUTIONS AND FIRST-ORDER, GAS PHASE
C REACTION.
IFJX.LE.O.) YAB=BKG
IF (X.LE.O.) GO TO 100
SIGMAY«SIGTHE«X
5tGMAZsSlGPHI»X
YAB=»13.059ft*Q*T*EXP(-Y*«2/<2»SIGMAY««2))*
-------
FUNCTION HPRlME(C.HEXiT«P.LGQPT)
C SUBROUTINE FOR CALCULATING APPARANT HENRY"S-LAW CONSTANT USING
C JOHNSTONE-LEPPLA PARAMETERS.
IF(C.GT.-1.) GO TO 110
HANKaEXP(9.94-3040./T)/P
EQCON=EXP<-10.3*1780./T)
C TRANSFER POINT FOR LIQUID- OH GAS-PHASE BASED CALCULATIONS
IFfLGOPT.EQ.l) GO TO 100
R*EQCON*HEX
Cr>UMsEQCON*1000.*C
r TEST FOR LOU-CONCENTRATION CONDITIONS
TESTl34.*CDUM/B**2
C ASYMPTOTIC EXPRESSION FOR LOW-CONCENTRATION CONDITIONS
HPRIME=1000.*{HANK-HANK*EQCON/8)
IF(TEST1.LT..001) GO TO 11"
C SOLUTION OF TOTAL SOLUBILHY EQUATION
r!PRIML = HANK«f l.-(-R*SQRT(H«»?»4.*CDUM) )/(2000. *C) 1*1000.
GO TO 110
C TEST FOR LOW-CONCENTRATION CONDITIONS
100 DUMMY=HEX*HEX«HANK/(4*EQCOrv*C)
IF(DUMMY.LT,1000.) GO TO 105
C ASYMPTOTIC EXPRESSION FOR LOW-CONCENTRATION CONDITIONS
HPRIMEslOOO.*HANK*HEX/(NEX*EQCON)
GO TO 110
C SOLUTION OF TOTAL SOLUBILITY EQUATION
105 CTEST=(C/HANK*(-HEX*SORT(HtX**2*4*C*EOCON/HANK))/2)/lOOQ.
HPRlMExC/CTEST
C RETURN VALUE OF HPRIME HAS UNITS OF CENTIMETERS CUBED PER MOLE
110 RETURN
END
195
-------
SUBROUTINE RUNGE .PHItl),F(l),YU)
INTEGER S
GO TO (100,110,130,150.170), M
100 S«l
GO TO 190
110 DO 120 JsliN
SAVEYIJ)-Y(J)
PHI (J)»F(J)
120 Y(J)«SAVFY(J)*.5«H«F(JI
X«X*.5*H
S»l
GO TO 190
130 DO 140 J»ltN
PHnJ)apHI(J)*2,*F(J)
140 Y(J)aSAVEY(J)*.5*H*F(J)
S«l
GO TO 190
150 DO 160 J«1,N
PHI (J)»PHI (J)*2.«F(J>
160 Y(J)»SAVEY(J)»H*F(J)
X«X*,S*H
GO TO 190
170 DO 180 J*1,N
180 Y(J)=SAVEY(J)*(PHI (J)*F(J) )«H/6.
MaQ
s«?
190 CONTINUE
RETURN
END
196
-------
APPENDIX D.
REDISTRIBUTION OF A GAS PLUME CAUSED BY REVERSIBLE WASHOUT*
In Section IV we presented an expression (Equation (5)), for concentration
in a plume modified by the sorption-desorption action of rain; this appendix
presents a derivation of that equation. In proceeding with this derivation
we start by assuming the rain to be composed of homogeneous, vertically-
falling drops. As discussed elsewhere,5 this assumption can be used to
approximate actual conditions reasonably well under most practical circum-
stances .
Having made this assumption, one can focus attention on any single drop of
rain falling through a gaseous plume. As the raindrop traverses the plume,
sorption will occur and the drop's concentration will approach a saturation
value with respect to the concentration in the plume. It then can emerge
from the plume with a concentration, supersaturated with respect to that of
its surroundings, and desorption of the gas may occur. This can result in
an effective lowering of the plume with an increased dosage to low-level
receptors as well as a modified washout pattern.
We proceed with the further assumption that mass-transfer and solubility
behavior can be linearized (invariant mass-transfer coefficient and Henry's-
law constant). In addition, we utilize a majority of the assumptions neces-
sary for derivation for the Pasquill-Gifford plume equation, i.e., neglect
of longitudinal diffusion, constant effective eddy diffusivities in the
vertical and crosswind directions, negligible wind shear, and a point-source
release.
With the above assumptions the coupled equations of conservation for pollu-
tant in the gas (air) and liquid (rain) phases set forth in previous pub-
lications reduce to mathematically tractable forms. In presenting these
equations here it is convenient to drop some of the subscripts used in
previous nomenclature, since the following derivations are rather cumber-
some, and since there is no danger of ambiguity at present. Thus we will
*The work of this section was sponsored in part by Battelle Institute,
Physical Sciences Program.
197
-------
denote the mixed-mean gas- and liquid-phase concentrations of pollutant A,
c and c. , simply by the symbols X and c, respectively.
Ay Ax
With the above assumptions, the conservation equations become
(55)
3y 3z
and
-J |J = aX - pc , (56)
where a = - 3JK /ac v and B = - 3JK /aH*c v . Here the nomenclature is
y x t r y x t
consistent with our previous usage; H* is a modified, apparent Henry's-law
constant defined by the relationship
X = H*c at equilibrium . (57)
CASE 1: IGNORING DIFFUSION
We look first at the simpler case for which diffusion of the plume can be
ignored. In this case, if we let t = x/u, then Equations (55) and (56)
simplify to
|| = pc - aX , (58)
and
-J |^ = aX - PC . (59)
If c is eliminated between Equations (58) and (59) we obtain an equation
describing only the plume:
ax _aj ax , J a2x ,,AN
"5T ~~cF~ TT "*" o ->„->«. • (.ou;
To solve Equation (60), a Laplace transform (parameter s) is taken in time.
Solving the resulting ordinary differential equation in z, subject to the single
boundary condition X(z -> °°,s) = 0, gives
X (z,o) ^ >z
X(z,s) = „ , „ +
(s + a)'
198
-------
where A = ({3/J)(s/(a+ s)). Inverting the first term on the right hand side of
Equation (61) is trivial. It leads to an exponential decay of the initial plume
profile: X (z,o) exp(-at).
The second term is a little more difficult. The integral to be evaluated
is the integral on the Bromwich contour:
1 f A(z - £) st
I = ~ - — - f— ds . (62)
2ni JB.C. (s + a)2
Point -a in the complex s plane is an essential singularity because of the
s dependence of A. If near s = -a we take s = e - a, then the expansion
of the integrand for small e leads to
A(z - £) + st ( .2
2 - = ±2 exP*j *1 ~ at>[1 + 5t + 2! + '"]
(s + a) e
where T] = £ - z. By collecting all terms of the coefficient of e , and
identifying the resulting series as uiat for a first order modified Bessel
function, we obtain the residue
|^ expf^r] - atJI^q) , (64)
2 8
where q = 4at *•:(¥, - z). The solution is then obtained from Equation (61) to
J
be
X(z,t) - Xo(z)e + ir e dij XD . _ g) - qlj(q) . (65)
•^ z
Into Equation (65) can be substituted any initial plume concentration, including,
for example, a plume which has diffused to any realistic provile downwind of the
stack.
A particular case for Equation (65) is quite informative. If initially the plume
is a delta function at the height h, then subsequently, X = 0 for z > h, and
for z 5 h,
-at R qI1 (q)
X(z,t) = 6(z - h)e at + % exp{-at - f(h - z)} -~ - r- , (66)
J \j\-z)
199
-------
9 B
with q = 4at -"^(h - z). A plot of this solution is given in Section IV. The
J
large q behavior of Equation (66) can be found using the known asymptotic
expansion of I, (q) and leads to
X(z,t) ~- \ ()% exp{-[(at)%-
To obtain the concentration in the rain, we return to the original equation,
Equation (59), and obtain
4« r -4^
c(z,t) - ^ eJ X(£,t)e J d£ . (68)
J z
In particular, if the Green's function (66) is substituted into Equation (68),
and if known integrals of Bessel functions are utilized, then for z 5 h,
c(z,t) = -7 I (q) exp{-at - -|(h - z)} . (69)
ij O J
THE "WASHPOWN" VELOCITY
It is of interest to obtain an estimate of the rate at which the plume is
"washed down" by precipitation. One way to evaluate this is to determine the
centroid of the plume as a function of time. If the centroid is taken about the
top of the stack, then for the case of a delta function initial plume Equation
(66) yields
«
-at
ql(q) = - ^ t . (70)
The "washdown" velocity of the plume is then
d oJ
w =
dt p
(71)
GENERAL CASE; INCLUDING DIFFUSION
We now return to the general case given by Equations (55) and (56). In this
case, when the effects of diffusion are included, some approximations will be
made. These will be justified using the results of the previous section. If
the liquid phase concentration is eliminated between Equations (55) and (56),
there results the single equation for the gas-phase concentration
200
-------
2222 3
3X 3X 1C.3X . ~ 3 X 3X _ 3 X OTX 3 X /->^\
—~ = w T— + 5 -r-r— + D —^ + D —r- - 5D r- - 5D r- , (72)
at Bz 3t3z y ^ 2 z.2 y _ .2 z - 3
J 3y 3z J 3z3y 3z
where w = aJ/p is the washdown velocity and 6 = J/(3 is a characteristic
length which for the example shown in Figure 8 is about 5.5 m. Equation (72)
is to be solved subject to the boundary and initial conditions: X(t -> o,y,z)
= X 6(y)6(z - h) ; X(t,y -> ±°°,z) = 0 ; and X(t,y,z -> ±°°) = 0. These con-
ditions correspond to the case downwind (t = x/u) of a stack of height h
and source strength X , for those situations when the influence of the ground
can be ignored.
To solve Equation (72), the method of multiple transforms will be used. Taking
first a Laplace transform in time (parameter s), then infinite Fourier trans-
forms in y (parameter rj) and z (parameter £), leads to the algebraic
equation which contains the boundary conditions:
X e"
+ T] D + CD - -t£(w + 6D T] + 6D ^ )]
Inverting the Laplace transform is trivial since there is only one simple-pole
in the complex s-plane. Next, the simple r)-Fourier transform is inverted.
Finally, the ostensible inversion of the ^-transform leads to
1 Xo 2
x(t'y'z) =
wt
The integral in Equation (74) is rather difficult to evaluate. It converges
only in the region | Im£ | < |Re£|; there is an essential singularity at £ = --c/5;
in order to find paths of steepest descent it is necessary to find the roots
of the obvious cubic in £. Rather than pursue the interesting mathematics
involved in evaluating Equation (74), we attempt to simplify the last term in
the exponential for the cases of practical interest. From the previous section
201
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we notice that for the washdown of S0«, 6 ~ 5.5 m. On the other hand, the
largest £ value that will contribute significantly to the integral is seen
i.
from the first term in the exponential to be ~ (tD ) . Thus £ is small
-1 2 2
compared with 6 provided t » 5 /D . This condition is satisfied, for
2 _f
the case with D as small as 1 m sec and for the S00 plume considered in
Z L.
the previous section, provided only that t » 1 minute. This is not at all
a serious restriction. Then expanding the last term in the exponential
according to
(75)
and performing the simple integral, we obtain
r
exp{
2 -[z - (h - wt)]2,
4t(D +w6)
X(t,y,z) = X - -- 5 - - f (76)
° (4ntD )5 [4nt(D + w6)P
y z
which was presented earlier (in the form of mixing ratios) in Section IV.
Thus in the general case (for the approximations stated), the influence of the
reversible scavenging by rain is that the plume diffuses about the effective
plume height (h - wt), where w = JH* is the washdown velocity, and the
diffusivity is slightly enhanced by the factor w6.
202
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BIBLIOGRAPHIC DATA
SHEET
1. Report No.
Keport No.
EPA-R3-73-047
2.
3. Recipient's Accession No.
4. Title and Subtitle
Natural Precipitation Washout of Sulfur Compounds
from Plumes
5. Report Date
June 1973 .
6.
7. Author(s)
M. Terry Dana, J. M. Hales, W.G.N. Slinn, M.A. Wolf
8. Performing Organization Rept.
No.
9. Performing Organization Name and Address
Battelle, Pacific Northwest Laboratories
Atmospheric Sciences Department
Battelle Boulevard
Richland, Washington 99352
10. Project/Task/Work Unit No.
BNW 389 / B46621
11. Contract/Grant No.
EPA-IAG-0104 (D)
12. Sponsoring Organization Name and Address
EPA Division of Meteorology
Research Triangle Park
North Carolina 27709
13. Type of Report & Period
Covered
Final Report
14.
15. Supplementary Notes
16. Abstracts
This report describes field measurement and modeling of the washout of
SOT and sulfate from plumes. Field measurements of precipitation washout
were conducted in conjunction with both controlled test sources and actual
power plant plumes. A primary achievement of this work has been the formu-
lation of an SC>2 washout model, which predicts rain-borne SC>2 concentrations
that agree favorably with those observed. An approximate theoretical analysis
of sulfate washout in conjunction with field observations indicates that
sulfate formation and scavenging exhibit a strong inverse dependence on
acidity levels in the background rain.
17. Key Words and Document Analysis. 17a. Descriptors
Washout
so
Sulfate
Plumes
Power Plants
17b. Identifiers/Open-Ended Terms
17c. COSAT1 Fie Id/Group
18. Availability Statement
19. Security Class (This
Report)
UNCLASSIFIED
20. Security Class (This
Page
UNCLASSIFIED
21. No. of Pages
214
22. Price
FORM NTIS-35 (REV. 3-72)
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