REPORT
ON
NATURAL PRECIPITATION WASHOUT
OF SULFUR DIOXIDE
M. T. Dana, J. M. Hales and M. A. Wolf
TO
ENVIRONMENTAL PROTECTION AGENCY
DIVISION OF METEOROLOGY
BNW-389
February 1972
ATMOSPHERIC SCIENCES DEPARTMENT
BATTELLE-PACIFIC NORTHWEST LABORATORIES
RICHLAND, WASHINGTON 99352
-------
NOTICE
This report was prepared as an account of work sponsored by the United States Government. Neither
the United States nor the United States Atomic Energy Commission, nor any of their employees, makes any
warranty. express or implied, or assumes any legal liability or responsibility for the accuracy, completeness
or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would
not infringe privately-owned rights.
PACIFIC NORTHWEST LABORATORY
operated by
BATTELLE
for the
U.S. ATOMIC ENERGY COMMISSION
Under Contract A T(45-1 )-1830
-------
REPORT
ON
NATURAL PRECIPITATION WASHOUT OF SULFUR DIOXIDE
M. T. Dana, J. M. Hales and M. A. Wolf
TO
ENVIRONMENTAL PROTECTION AGENCY
DIVISION OF METEOROLOGY
BNW-389
February 1972
ATMOSPHERIC SCIENCES DEPARTMENT
BATTELLE-PACIFIC NORTHWEST LABORATORIES
RICHLAND, WASHINGTON 99352
-------
FOREWORD
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 Project Officer was Mr. Francis Pooler, Jr., Chief, Field
Investigations Branch, Division of Meteorology, Raleigh, North Carolina.
The principal investigators were Mr. M. T. Dana, Dr. J. M. Hales and
Mr. M. A. Wolf.
Mr. D. W. Glover was responsible for the design and
fabrication of the field generation and sampling equipment. Other
personnel of Battelle, Pacific Northwest Laboratories who contributed
significantly to the investigations were:
O. B. Abbey
M. C. Miller
A. G. Dunbar
J. W. Sloot
V. T. Henderson
S. L. Sutter
F. D. Lloyd
R. E. Wheeler
The authors especially want to acknowledge the contributions of the
following persons to the success of the field investigation:
Mr. Ronald Pretti, Director, Washington State Aeronautics Commission,
Seattle, Washington
Mr. Clarence Davis, Manager, Ouillayute State Landing Field, Forks,
Washington
Mr. Donald Carte, Meteorologist-In-Charge, National Weather Service,
Forks, Washington
-i-
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FOREWORD
LIST OF FIGURES
LIST OF TABLES
NOMENCLATURE
SUMMARY
CHAPTER I
CHAPTER II
CHAPTER III
CHAPTER IV
CHAPTER V
CHAPTER VI
CHAPTER VII
REFERENCES
APPENDIX A
APPENDIX B
APPENDIX C
TABLE OF CONTENTS
NATURAL PRECIPITATION WASHOUT OF SULFUR DIOXIDE
INTRODUCTION
WASHOUT MODELING
S02 SOLUBILITY MEASUREMENT
FIELD EXPERIMENTS IN WASHOUT
ANALYSIS OF RESULTS
ISOLATED DROP EXPERIMENT
EVALUATION AND CONCLUSIONS
TABULATIONS OF MEASURED S02 CONCENTRATIONS
IN PRECIPITATION
RESULTS OF PEAK-TO-MEAN ANALYSIS
COMPARISONS OF MEASURED WASHOUT CONCENTRATIONS
WITH PREDICTIONS BY THE NONLINEAR, NONFEEDBACK
MODEL
-iii-
Page
i
v
ix
xi
xiii
1
3
23
33
55
83
89
95
99
III
129
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FIGURE
2.1
2.2
2.3
3.1
3.2
3.3
4.1
4.2
4.3
4.4
4.5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
LIST OF FIGURES
TITLE
Schematic of Volume Element in Space
Elements of Washout Rate Calculation
Simplified Schematic of Computer Program -- Nonlinear,
Nonfeedback Model
Solubility Measurement Apparatus
Solubility Cell
Solubility of Dilute S02 in Water
Location of Field Experiment Site
Quillayute Grid System
Special Grid System
at 25.1 °c
Composite of Field Study Equipment
Comparison of Observed and Calculated S02
Concentrations in Air
Comparison of Predicted and Measured Washout
Coefficients as a Function of Rainfall Rate
Comparison of Observed Washout Rates with Those
Predicted from Washout-Coefficient Analysis
Solubility Relationship for S02 in Water at 10°C,
pH = 5.5
Time-Averaged S02 Concentrations in Rain Based Upon
Equilibrium with Ground-Level Plume Concentrations --
Mean Plume on IS-Second Incremental Analyses
Time-Averaged S02 Concentrations in Rain Based on
Equilibrium with Ground-Level Plume Concentrations --
Mean Plume and Peak-to-Mean Analyses
Comparison of Observed Washout Rates with Those
Predicted from Peak-to-Mean Analyses
Comparison of Observed Washout Rates with Those
Predicted on Basis of Equilibrium with Average
Plume Concentrations at Ground Level
Comparison of Observed Washout Rates with Those
Predicted by Nonlinear, Nonfeedback Model
Comparison of Observed Washout Rates with Those
Predicted by Linear, Nonfeedback Model
-v-
PAGE
5
8
15
26
27
29
34
36
37
40
53
58
59
62
64
66
67
68
73
74
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FIGURE
5.10
5.11
5.12
6.1
7.1
B.l
B.2
B.3
B.4
B.5
B.6
B.7
B.8
B.9
B.lO
B.ll
B.12
B.13
B.14
B.15
TITLE
Predictions by Nonlinear, Nonfeedback Model for
Time-Average and IS-Second Incremental Analyses
Computed Concentrations in Drops as a Function of
Vertical Position - Run 4WB, Gas-Phase Limited
Computed Ground-Level S02 Concentrations in Rain as a
Function of Drop Size -- Run 4WB, Gas-Phase Limited
Schematic of Suspended-Drop Apparatus
Suggested Research Program
Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run IE
Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run lW
Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run 2E
Predicted
Comparison of Observed Values with Those
by the Peak-to-Mean Analysis Run 2W
Comparison of Observed Values with Those
by the Peak-to-Mean Analysis Run 3
Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run 4E
Predicted
Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run 4w
Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run 5E
Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run 5W
Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run 6W
Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run 7E
Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run 7W
Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run 8E
Comparison of Observed Values with Those
by the Peak-to-Mean Analysis Run 8W
Comparison of Observed Values with Those
by the Peak-to-Mean Analysis Run 9E
Predicted
Predicted
-vi-
PAGE
76
78
80
88
90
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
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FIGURE TITLE PAGE
B.16 Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run 9W 128
C.l Predictions of Nonlinear Model for Run IE 131
C.? Predictions of Nonlinear Model for Run lW 132
C.3 Predictions of Nonlinear Model for Run 2E 133
C.4 Predictions of Nonlinear Model for Run 2W 134
C.5 Predictions of Nonlinear Model for Run 3E 135
C.6 Predictions of Nonlinear Model for Run 3W 136
C.7 Predictions of Nonlinear Model for Run 4E 137
C.8 Predictions of Nonlinear Model for Run 4w 138
C.9 Predictions of Nonlinear Model for Run 5E 139
C.lO Predictions of Nonlinear Model for Run 5W 140
C.ll Predictions of Nonlinear Model f or Run 6E 141
C.12 Predictions of Nonlinear Model for Run 6W 142
C.13 Predictions of Nonlinear Model for Run 7E 143
C.14 Predictions of Nonlinear Model for Run 7W 144
C.15 Predictions of Nonlinear Model for Run 8E 145
C.16 Predictions of Nonlinear Model for Run 8W 146
C.17 Predictions of Nonlinear Model for Run 9E 147
C.18 Predictions of Nonlinear Model for Run 9W 148
-vii-
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TABLE
3.1
3.2
4.1
4.2
4.3
4.4
4.5
5.1
6.1
A.l
A.2
A.3
A.4
A.5
A.6
A.7
A.8
A.9
LIST OF TABLES
TITLE
PAGE
Solubility Parameters from Work of Johnstone and
Leppla
Experimental Measurements of Solubility of S02 in
Water Solution
25
30
Concentration Run 1
44
46
47
49
52
71
86
101
102
Run Summary
Raindrop Size Frequency Distributions
Rainfall Characteristics Summary
S02 Washout Summary
Data Summary
Input to Nonlinear, Nonfeedback Model
Isolated Drop Experiments
Precipitation Sample S02
Precipitation Sample S02
Precipitation Sample S02
Precipitation Sample S02
Precipitation Sample S02
Precipitation Sample S02
Precipitation Sample S02
Precipitation Sample S02
Precipitation Sample S02
Concentration Run 2
Concentration Run 3
Concentration Run 4
103
104
105
106
107
108
109
Concentration Run 5
Concentration Run 6
Concentration Run 7
Concentration Run 8
Concentration Run 9
-ix-
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NOMENCLATURE
a
Raindrop radius, £
A
2
Bucket area, £
c
3
Liquid-phase concentration, moles/£
Diffusion coefficient, £2/t
D
f
Raindrop probability-density function
F
Fractional depletion of plume
H
3
Henryls-law constant for undissociated 802' ~ /mole
hI
Functional form for partition coefficient
Partition coefficient, £3/mole
HI
J
Rainfall rate, £/t
Liquid-phase mass-transfer coefficient, mOles/£2t
k
y
k
y
K
Y
M
Gas-phase mass-transfer coefficient, moles/~2t
Overall mass-transfer coefficient, mOles/£2t
Downwind washout rate, moles/£t
m.
1.
Moles of 802 collected in individual sampler
Moles of 802 released during sampling period
m
o
NA
N
o
Flux of 802
2
from drop surface, moles/£ t
3
Total raindrops in a unit volume element, drops/£
Q
3
802 release rate, moles/t or £ /t
r
3
Radius of collector, £; also reaction rate, moles/£ t
t
Collection time, t
11
Wind velocity at stack height, £/t
vA
Velocity vector of pollutant in gas phase, £/t
Vt
Velocity vector of raindrop, £/t
-xi-
-------
w
x
y
z
z
o
11
I1Y
A
p
CJ.
1-
A
b
e
x
~
y
Volumetric washout rate, moles/£3t
Downplume distance, £; also liquid-phase mole fraction
Crossplume distance, £; also gas-phase mole fraction
Vertical distance, £
Datum height, £; taken to be infinite in this report
Difference operator
Spacing between collectors, £
Washout coefficient, lit
Density, m/ £ 3
Standard deviation in the i direction, units of i
SUBSCRIPTS
Pollutant A
Bulk
Equilibrium
Average value in total liquid phase
Average value in drop
Average value in gas phase
-xii-
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SUMMARY
This report presents recent results in the continuing investigation of 802
washout by precipitation from plumes of large, coal-fired power plants.
The research consisted of three phases:
a washout modeling effort, a
laboratory investigation of solubility and mass-transfer behavior in the
802/water system, and an experimental field program.
The modeling effort resulted in the creation of two washout models.
The
first of these is based on linear theory and provides a relationship that
can be used for hand-calculated estimates of washout provided that the
implicit assumption of vertical rainfall is not violated significantly.
The second model can account for nonlinear behavior and is not restricted
to vertical rainfall, but necessitates computer calculation to predict
washout values.
The general washout models reduce asymptotically two limiting cases.
One
of these describes washout totally in terms of rate processes (irreversible
washout of the classical washout-coefficient approach); the other describes
washout totally in terms of equilibrium phenomena (equilibrium washout).
An additional derivation from the theory of reversible washout is the
criterion for the approach of real systems to the limiting case of equi-
librium washout.
This criterion suggests that under the conditions of
the recent experiments true equilibrium washout does not occur.
Both of the general washout models utilize the bivariate-normal plume
equation for the description of airborne 802 concentration.
for the washout models are derived from field measurements.
Input data
The extent
to which these measurements are representative of the pertinent factors
determines to a large degree the validity of the results.
The computer algorithm for the general nonlinear model computes the
partition coefficient for 802 between air and water in accordance with
-xiii-
-------
a previously derived solubility equation.
Solubility experiments conducted
in the laboratory show that the behavior of the SOZ/water system at low
concentrations is predicted reasonably well by that solubility equation.
The field-study program was conducted on the Olympic Peninsula of Washington
state to examine the washout of S02 in an unpolluted atmosphere. S02 from
commercial gas cylinders was released at various heights on a 30.5 m tower
during rainfall.
Precipitation samples were collected on downwind arcs at
distances to 122 m and analyzed for their 802 content. Support data were
collected during the experiments to relate the washout to atmospheric para-
meters. Of the 20 experiments conducted, useful data were obtained from 16.
The observed S02 concentrations and the derived washout rates, which are the
arcwise integrated quantities of S02 deposited per unit time and unit distance,
were compared with the washout models and with their asymptotic limits.
Irreversible washout was shown to be untenable, as was suggested earlier in
the report of the S02 washout investigation conducted at the Keystone Gene-
rating Station. Although the asymptotic expressions of the general models
do not necessarily correspond to extrema in washout rates, this limiting
case does provide a virtual upper limit to washout rates observed at
Quillayute.
On the other hand, observed washout rates were found to fall
close to those predicted on the basis of equilibrium behavior, noted excep-
tions being data from experiments conducted at short distances downwind from
the source.
Predictions from the nonlimiting washout models were found to agree well
with experiments in a majority of cases, including those corresponding to
short downwind distances. In addition the models predict that the observed
proximity to equilibrium of S02 in ground-level rain results more from a
decrease of plume concentration with height at ground level than from fast
mass-transfer responsiveness of the rain.
This, therefore, resolves the
apparent conflict between observation and the prediction of the equilibrium-
washout criterion.
The general-model ability to predict washout behavior at
that these models will be useful in future analyses of SO
2
Quillayute su~gests
-xiv-
-------
washout from power-plant plumes.
The possibility that the observed proximity to equilibrium behavior is
caused by rapid absorption and desorption of 802 by rain on the sampler
collection surfaces was considered. Although the present results indi-
cate that this effect is minimal, additional experimentation will be
required to resolve this question completely.
-xv-
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CHAPTER I
INTRODUCTION
Research described in this report was undertaken to elucidate several
important aspects of S02 washout which were identified in a previous
(1)
study. The results of that study, conducted at the Keystone Generating
Station in western Pennsylvania, indicated very low washout of S02 from
the power plant plume. The nature of the source, however, raised doubt
as to the amount of sulfur present in the plume as S02' An observed
increase in sulfate washout beneath the plume suggested that chemical con-
version of S02 had occurred. However, the high level of contamination in
the atmosphere in the vicinity of the Keystone Station and the high back-
ground of sulfur dioxide from numerous sources in the area made the results
inconclusive.
A concurrent development of gaseous washout theory indicated that reversi-
bility of the process of S02 absorption in rain should be responsible for
the low washout rates observed. It was recognized that certain properties
of the S02' the precipitation and the atmosphere were necessary considera-
tions in the washout determination. The need for detailed knowledge of
their interactions led to the present work, which consists of model devel-
opment, laboratory experiments and controlled field experiments.
This report documents the work performed during the latter half of FY-197l
and outlines the continuing effort to provide a general means for the cal-
culation of sulfur dioxide washout.
Chapter II describes the results of
the washout-modeling effort.
Solubility measurements, which are required
to facilitate use of the models presented in Chapter II are described in
Chapter III.
Chapter IV describes the controlled field experiments which
were conducted to clarify the washout behavior of S02'
techniques are discussed and the data are summarized.
Data reduction
-1-
-------
The three phases of the research described in Chapters II through IV are
brought together in Chapter V which is an analysis of the data resulting
from the field experiments relative to irreversible and reversible theories.
A remaining area of uncertainty in the washout model, S02 mass transfer
rates, is discussed in Chapter VI. Chapter VII examines additional prob-
lems in the formulation of a general S02 washout model applicable to power
plant plumes.
Dimensional units are expressed in the metric system throughout this report.
Insofar as practicable the centimeter-gram-second-degree Kelvin system is
used to provide a consistent set of units to facilitate the use of equa-
tions and computer routines described herein.
-2-
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CHAPTER II
WASHOUT MODELING
The previous report(l) on S02 washout dealt extensively with microphysical
aspects of gas-raindrop interactions, including the effects of mixing,
solubility, and chemical reaction on washout by drops and ensembles of
drops falling through pollutant clouds of arbitrary distribution.
The
present analysis will emphasize macrophysical aspects, combining microphys-
ical factors into models to compute total washout from atmospheric plumes
under stated conditions of rainfall, mixing, and pollutant release.
Although rather general in nature, this analysis is devoted primarily to
an examination of the March-April 1971 Quillayute field results, which will
be described in a later chapter.
The present effort is initiated by a formulation of the general material
balance relationships of importance to the overall scavenging process.
Establishing these relationships is an essential first step in defining
washout in the context of other, competing processes for transport and
removal in the atmosphere.
These relationships are important also in
providing a standard of assessment for all scavenging models, which are
necessarily based upon these more general equations of conservation.
Subsequent effort has been devoted to the creation of a progression of
washout models in order of increasing sophistication.
these models will be described in this chapter.
The first two of
MATERIAL BALANCE RELATIONSHIPS
Pollutants may be transported through and removed from the atmosphere by
a number of competing mechanisms.
Because of such competition, any complete
analysis of contaminant removal by scavenging must take stock of possible
interactions with other processes.
Such an analysis may be accomplished
through the traditional approach of performing material balances about a
-3-
-------
volume element, fixed in the atmosphere, as shown in Figure 2.1.
The over-
all material balance for the element may be separated into individual
balances for the gas and liquid phases.
Thus:
Pollutant material balance for rain in volume element (liquid-phase):
time rate of change of mass of pollutant in rain (liquid-phase)
within volume element
time rate of gain of pollutant mass in liquid phase by flow of
pollutant-containing rain through walls of volume element +
time rate of gain of pollutant mass in liquid phase by uptake
from gas phase within the volume element +
time rate of gain of pollutant mass by liquid-phase
reaction within the volume element.
(2.1)
Pollutant material balance for air in volume element (gas-phase):
time rate of change of mass of pollutant in air (gas phase)
within volume element
time rate of gain of pollutant mass in gas phase by gas-phase
input through walls of volume element +
time rate of gain of pollutant mass in gas phase by release
from the liquid phase within the volume element +
time rate of gain of pollutant mass by gas phase reaction
within the volume element.
(2.2)
Total pollutant material balance for the volume element:
time rate of change of total mass of pollutant within
volume element
time rate of gain of pollutant mass in liquid phase by flow
of pollutant-containing rain through walls of the volume
element +
time rate of gain of pollutant mass in gas phase by gas phase
input through walls of volume element +
time rate of gain of pollutant mass by liquid phase reaction
within the volume element +
-4-
-------
I
VI
I
z
x
Figure 2.1
!u
Schematic of Volume Element in Space
-------
time rate of gain of pollutant mass by gas phase reaction
within the volume element.
(2.3)
Equations (2.1)-(2.3) form the basis for the partial differential equations
of conservation of pollutant in the rain-air system.
The restricted case
wherein spherical, noninteracting raindrops fall with static size distri-
bution may be represented by:
ap Ax - 47fNo
at - - ~
(vo f
3 -
a f(a) Vt 0Ax
(a) da)
+ w + rAx
(2.la)
ap Ay -
at - - (v. PAy vA) - w + rAy
(2.2a)
and
ap A -
at -
47fN
o
--
3
(vo [
3
a f(a) vt(a) 0Ax
(a) da)
-(V. PAy vA) + rAx + rAy'
(2.3a)
w, for the stipulated conditions, is given in accordance with Reference (1)
as:
w
=
- 47fN
o
f
2
a f (a)
NAo da
=
47fN
o
1000
a2f(a) Ky(a) (YAb - YAe) da
(2.4)
-6-
-------
Other nomenclature is defined as follows:
K
Y
N
o
t
VA
Vt
YA
°Ax
p
a
drop radius
probability density function for drops existing in the
volume element
f
=
overall mass transfer coefficient
number concentration of drops in volume element
time
velocity vector for pollutant A in gas phase
raindrop velocity vector
gas phase mole fraction of pollutant A
mass of A in a drop/drop volume
density based on total space in volume element
subscripts
e equilibrium
x average value in total liquid phase
~ average value in drop
y = average value in gas phase.
One should note that Equation (2.3a) is simply the continuity equation for
pollutant A in a "binary" solution, (2) including an additional term for
depletion by washout.
Formulation of general conservation equations such
as the ones above may be viewed as somewhat academic, since in many washout
situations a majority of the terms are negligible.
For general purposes,
however, the significance of each of the included terms must be considered,
and such a breakdown is necessary to provide a meaningful definition of
the washout process.
One should note in particular that Equation (2.3) is obtained by adding
Equations (2.1) and (2.2): the uptake-release terms, which serve to couple
the equations, simply cancel one another.
Coupling of the differential
equations constitutes a rather severe complication to their rigorous solu-
tion, and necessitates an iterative or "feedback" approach as shown schema-
tical1y in Figure 2.2.
The two models described in the following sections
-7-
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PRECI PITATION
CHARACTER I STICS
(PHY S I CAL)
,~
POSTUlA TED
PLUME - MASS - TRANSFER
CHARACTER I STICS - RElA TI ONSH IPS
a (l I NEAR OR NONl I NEAR)
. I'
MATERIAL PRECIPITATION
~ CHARACTERISTICS
BALANCES ~
(CHEMICAL)
~~
.,
I NTERFAC I AL
CONDI TIONS
p
DEPOS 1 TI ON
Figure 2.2
Elements of Washout Rate Calculation
-8-
-------
attempt to overcome this problem by assuming that plume geometry under
precipitation conditions is known; thus only Equation (2.1) (or a simpli-
fied version of it) need be solved. Future study, which will concentrate
more directly on plume redistribution through washout processes, will
involve solutions wherein this coupling is allowed to remain intact.
LINEAR, NONFEEDBACK MODEL
The objective of the initial modeling effort was to create a washout
equation based upon linear solubility and transport relationships.
This
was accomplished in conjunction with a similar effort in the analysis of
trl'tl'um washout. (3) S. SO 1 b'l't d t t t
lnce 2 so u 1 1 Y an ranspor parame ers are
nonlinear, the result of this effort can be applied for S02 only after
a suitable linearization is performed. Errors in this application, accord-
ingly, will reflect the extent of deviation from linearity.
The assumptions employed by this model are summarized as follows:
1.
Nonfeedback, i.e., the plume is defined under precipitation
conditions, or alternatively, it is assumed that the precipi-
2.
tation has negligible effect on geometry of the plume.
Linearity; i.e., Henry's law is obeyed and the mass-transfer
3.
coefficient is independent of concentration.
Rainfall is vertical and of constant size-distribution and
4.
5.
intensity.
Plume is expressible in terms of normal-distribution parameters.
The precipitation is composed of spherical, noninteracting elements.
Upon solving Equation (2.2) subject to these stipulations and to appro-
priate boundary conditions, one can obtain the well-known equation for a
bivariate-normal plume.
Equation (2.1) need not be solved completely.
since the objective of this effort is simply to determine washout fluxes
at ground level. This may be accomplished by performing material balances
on drops of different sizes as they fall through the plume to determine
their concentration at ground level, and then evaluating the fluxes after
distribution over the drop size spectrum.
-9-
-------
. (1)
Material-balance considerations have been used prevlously to
ground level concentration in an a-radius drop to be given by
show the
cAo(a)
3K
-.:L
vta
1000
(3K HIZ)
exp y
vta
Y Ab dz
(2.5)
When YAb is supplied by the bivariate normal equation this may be integrated
to give
3QK F exp (- 2 22)
cAo(a) y --Y-- + O"z 1;;
2 n:;;:- 0" u vta 20" 2 2
Y Y
[ (2) ]
-0" 1;;-h
exp (1;;h) 1 - erf 0": 12 + (2.6)
exp (-1;;h) [ Cz2C+h)]
1 - erf
0" 12
z
3K HI
1;; = y (2.7)
vta
Here the nomenclature is consistent with that used previously and that in
the treatment by Gifford(4). If units are expressed in the cgs system of
3
measurement, then the "source strength" Q will have units of cm S02/sec,
The dimension-
measured at ambient conditions of temperature and pressure.
less variable F represents the fractional depletion of the plume at the
downwind distance of interest. For the physical situations described in
this report F is close to unity. F will be defined in terms of overall
washout in the following development.
-10-
-------
Computations for large distances from the source may be accomplished
somewhat more conveniently using the following asymptotic approximation
to (2.6);
c Ao (a)
-3 Q K 0 F
Y z
(_L
20 2
y
exp
2rr 0
y
u v a
t
-0
z
1
2
t;-h
( )2
o
1 - z
-Oz2 t;-h
1
-0 2 t;+h
z
( )2
o
1 - z
-Oz2 t;+h
L)
20 2
z
+
+
( )4
120
o 2 z . (2.8)
o t;-h
z
of".
The final term in (2.8) is a truncation-error estimate, 0 denoting "order
Downwind washout rate, defined as the amount of material washed out
per unit time per unit downwind distance can be calculated with the use of
(2.6) or (2.8) by integrating over the crosswind distance and then distri-
buting according to the rain spectrum.
given by
Thus the downwind washout rate is
J foo 3 c (a) v (a) f(a) da
a
cross t (2.9)
M 0
ioo 3 v (a) f(a) da
a
t
-11-
-------
where J denotes rainfall rate and ccross' defined by
c
cross
= foo
-00
cAo(a) dy
(2.10)
is obtained by formal integration of (2.6) or (2.8); thus
-3 Q Ky F exp (cr/ 1;;2)
2 u vta 2
~p (,h) [1- erf (-::2~h)] +
[1 - erf C:: 2~h) ] I
c
cross
exp (-1;;h)
(2.11)
is the expression for c corresponding to (2.6) and
cross
c
cross
-3 cr Q K F
z Y
v'27T u v a
t
exp ~:2" z 2)
1 [1 - c:~ ,-h)]
2 +
-cr 1;;-h
z
1 [1 - c:~ ,+h) 2]
2 (2.12)
-cr 1;;+h
z
-12-
-------
is that corresponding to (2.8).
In the event that there is appreciable depletion of the plume by washout
F may be calculated from the expression
F
1
1--
Q c
y
lX
M
dx
(2.13)
c denoting the total molar gas concentration at ambient conditions of
y
temperature and pressure.
Depending upon how the raindrop statistics are
treated the previous equations may reduce to explicit forms upon incor-
porating (2.13), or they may be implicit in nature, necessitating iterative
or numerical approximations to their solutions.
Although this linear, nonfeedback model is admittedly an approximate one,
it is significant in that it is the first model to give a satisfactory
qualitative description of some observed gas washout behavior, particu-
larly the capability for desorption of pollutant from the rain.
This model
is also somewhat appealing because it is simple enough for hand calculation,
if necessary.
This model is evaluated by comparison with actual field
results in a later chapter.
NONLINEAR, NONFEEDBACK MODEL
The second washout model developed as a part of this study differs from
the previous model in that it allows for nonlinearities in both the mass
transport and solubility parameters.
It also allows for the downward
passage of raindrops through arbitrary trajectories.
This model is expected
to provide a realistic calculation of washout from low elevation sources,
and is intended primarily for use in analysis of the Quillayute results.
This model, in contrast to the one described previously, cannot be expressed
in the concise mathematical form exhibited by Equation (2.6).
Rather, it
-13-
-------
takes the form of a general computer program, which solves the nonlinear
differential mass-balance equation, (cf., [1]).
d cAb (a)
dz
3Ky h' (cAb)
vta
cAb (a)
(2.14)
3K
-Y
va y~
t
(h' K variable),
, y
while calling on various subroutines to supply information concerning YAb'
K , and h'.
y
Operation of the computer program is illustrated in Figure 2.3. It consists
of a rather general calling program which coordinates subroutines, enabling
a modular replacement should increased sophistication become desirable.
Subroutines are listed as follows:
1.
Terminal velocity routine (V) -- Computes fall velocity of radius-a
drop from the equation
Vt = -8710.9
+ 18029.7
2
a
+
3
a
32184.5
(2.15)
a
2.
which is a polynomial fit to the data of Gunn and Kinzer. (5)
Wind velocity routine (WIND) -- Computes wind velocity as a function of
3.
height (assumed to be constant at present).
Gas-phase concentration routine (CONC) -- Computes gas phase concentra-
tion over trajectory of drop as determined by the wind speed and the
fall velocity.
4.
Gas phase mass transfer coefficient routine (GK) -- Computes K (a) using
y
5.
the Frossling equation (cf., [2]).
Solubility routine (HPRlME) -- Computes partition coefficient for 802
between air and water in accordance with the solubility equation derived
in Chapter III and the parameters of Johnstone and Leppla. (8)
Differential-equation solving routine (ITER) -- Computes overall mass
transfer coefficient and solves (2.14) for ground level concentration,
cAo' Solves for gas phase limited, stagnant drop, linearized stagnant
6.
-14-
-------
READ I NPUT DATA
Q,u,h,T, P,oe'0(j)'x,y, [H~X]
RAIN SPECTRA
CONTROL VARIABLES
~
SET UP COMPUTATION GRI D
PICK INITIAL DROP SIZE IN SPECTRUM
~
DETERMINE TRAJECTORY AND PLUME
CONCENTRATION OVER THI S TRAJECTORY
(EMPLOY SUBROUTINES V, WIND, AND
CONC)
.
CALCULATE GAS-PHASE MASS-TRANSFER
ADVANCE TO COEFFI C lENT
NEXT DROP
SIZE (EMPLOY SUBROUTI NE GK)
f +
SOLVE (2.14) FOR GROUND LEVEL
INCOMPLETE CONCENTRATION I N DROP
(EMPLOY SUBROUTI NES ITER, V, HPRI ME)
~
TEST FOR COMPLETION OF
CALCULATIONS FOR SPECTRA
I
COMPLETE
D I STR I BUTE OVER DR OP
SPECTRUM TO COMPUTE
WASHOUT FLUXES
PRINT RESULTS
Figure 2.3
Simplified Schematic of Computer Program
-- Nonlinear, Nonfeedback Model
-15-
-------
drop, or arbitrary input values of K , depending upon control variables
y
read in as data.
Euler's method(6) is used in ITER as the algorithm for approximating the
solution to (2.14). This approximation is characterized by a truncation
error of the order of the size of increment spacing chosen for the computa-
tional grid. This relatively simple algorithm was chosen over the more
accurate and sophisticated techniques (higher-order Runge-Kutta methods)
owing to the greater versatility that it offers for solving with various
types of mass-transfer models. In addition Euler's method was judged to
give results well within the limits of accuracy required by the present
investigation.
Results from this nonlinear, nonfeedback model have been applied exten-
sively in the analysis of field data and are presented with these data in
Chapter V.
LIMITING BEHAVIOR OF WASHOUT EQUATIONS
It is emphasized that the general washout models presented in this chapter
reduce asymptotically to limiting cases, which have been treated previously
in more restricted theories of washout.
Two cases of specific interest may
be described as follows:
1)
washout is describable totally in terms of rate phenomena;
considerations of equilibria are of no importance, and
washout is describable totally in terms of equilibrium
phenomena; rate processes are so fast that their consid-
2)
eration is unimportant.
The first of these cases has been referred to as "irreversible" washout, and
has been treated previously using the classical washout-coefficient approach.
The second limiting case occurs directly as a consequence of reversible
behavior, and shall be referred to here as "equilibrium" washout.
-16-
-------
The general linear washout Equation (2.6) can be used directly to illus-
trate the ability of the general models to describe asymptotically the
above limiting types of behavior.
This can be accomplished for the
irreversible washout case by noting that "total solubility" corresponds
to 1;;=0.
In this event (2.6) reduces to
cAo(a)
3 Q K
Y
F
2 2
exp (- y /2 cr )
y
(2.16)
ili cr
y
u v a
t
which is easily shown to be the product of 3K /v a and the integral
y t
exposure to a drop falling through a normally-distributed plume; i.e..
cAo
=
~ foo
v a
t 0
Y Ab dz
(2.17)
Equation (2.17) may be distributed over the drop-size spectrum to obtain
the average concentration collected at ground level;
£00 Y Ab dz
100
o
2
4TIa N f(a) K
o y
da
c
Avg
(2.18)
J
Conventional definition of the washout coefficient. on the other hand. may
be given by
w
fl..
l
Y Ab c y
(2.19)
-17-
-------
c being the total gas concentration and w denoting, as before, the rate of
y
removal of material from a unit volume of atmosphere by washout. Summing
over all volumes encountered during passage to the ground, one may obtain
the following expression for CAvg:
A.
l.
Cy ioo
J
Y Ab dz
c
Avg
(2.20)
From previous work (1, 10) in classical washout theory
be given by
Ai may be shown to
fl.
l.
1
100
o
2
4TIa N f(a) K
o y
da
(2.21)
c
y
Applying this relationship to (2.20) results in an expression that is ident-
ical to (2.18) which was derived as a special case of the general linear
theory; thus it is demonstrated that the washout-coefficient approach is
simply a special case of the more general treatment discussed in this
chapter, and may be derived directly from it.
Conditions leading to equilibrium washout are typified by large values of S.
Applying s=oo to Equation (2.8) results in the limiting form
TI a
y
a
z
U HI
exp (
2
y
2 a 2
y
- h2)
2 a 2
z
(2.22 )
cAo
QF
-18-
-------
which is simply the expression for ground-level concentration of a
bivariate-normal plume, modified by the solubility parameter, H'.
One
should note here in particular the lack of dependence of rain concentra-
tion on drop size, and also the independence of washout on plume concen-
trations other than those at ground level.
Criteria for equilibrium-washout conditions can be established by utilizing
the linear theory to analyze behavior of a drop as it falls through a plume
and approaches ground level.
This can be accomplished describing a simple
"plume" in terms of a concentratiun at ground level which increases steadily
with vertical distance, thus
YAb
y Abl
ground level
+
z
d Y Ab
dz
(2.23)
Substitution of this into the material-balance expression (Equation [2.14])
for a single vertically falling drop and integration gives
YAb I
~j ground level
H'
v a
t
3K H,2
Y
dy Ab
(2.24)
cAo
=
dz
Since the equilibrium state is represented by
cAo
yAbl
~ ground level
H'
(2.25)
-19-
-------
it follows directly that the criterion for equilibrium washout should be
given by
vta
3K HI
Y
~
dz
YAbl
ground level
« 1
(2.26)
Inequality (2.26) may be used as a conservative criterion for equilibrium
washout from plumes where concentration does not necessarily increase
linearly with height by taking IdYAb/dzl to be the maximum gradient experi-
enced by the drop during its fall to the ground. For a bivariate-normal
plume this maximum is given by
dy Ab
dz
2'TT U 0
Y
o
z
2
exp
(- t)
(2.27)
Q
which, in conjunction with (2.26) provides the following criterion for
equilibrium washout from a bivariate-normal plume:
-3K HI 0
Y z
1/2
e
vta exp (h2/20z2)
» 1
(2.28)
-20-
-------
It should be emphasized that general application of (2.28) must pertain to
the total ensemble of collected drops; hence the properties chosen for
insertion into this criterion must be those corresponding to the largest
drop of importance to the system.
It also should be stressed that (2.28)
is applicable to isolated, normally-distributed plumes only.
If additional
sources or background effects are present this criterion should not be
employed.
Limiting behavior has been investigated here using the linear equations
for washout, owing to their matbematica1 simplicity.
It should be recog-
nized, however, that the nonlinear model is simply a generalized version
of the linear analysis.
This model also, therefore, may be reduced to the
limiting forms, and is capable of computation for either irreversible or
equilibrium washout conditions.
These asymptotic situations will be
examined in more detail in Chapter V in the context of the field results.
-21-
-------
CHAPTER III
S02 SOLUBILITY MEASUREMENT
. (1) h h. d h
The previous report on S02 scavenglng as emp aSlze t e importance of
solubility on washout behavior, and has indicated that rain acidity should
be an important influence in this regard.
The models presented in Chapter
II provide an additional demonstration of how S02 solubility should affect
its macroscopic washout behavior. Unfortunately there exist few data in
the previous literature which pertain to the low concentration levels of
interest, the only real contribution being the results of Terraglio and
Manganelli, (7) which are rather limited in extent and give no specific
information regarding the influence of acid-forming impurity.
Because of the need for knowing solubility behavior accurately prior to
utilizing the models for washout calculations, a laboratory investigation
was conducted to examine and quantify the relationships between S02 solu-
bility, concentration, and hydrogen-ion impurity at levels normally
encountered in the atmosphere.
The previous report(l) has suggested that if S02 dissolution progressed
according to the scheme,
S02g + H20 t H20 + S02aq
(3.1)
+ -
S02aq + H20 t H30 + HS03
(3.2)
(second ionization negligible)
then the concentration of dissolved S02 could be expressed in terms of
airborne concentration and solution acidity by the form
-23-
-------
cso = [S02]aq + [HSO;]
2
= [S02]g
H
-[H 0+] + ~[H30+]L + 4Kl[S02] /H
3 ex ex g
+
2
(3.3)
where the bracketted terms denote concentrations in moles/liter and [H30+]
ex
is the concentration in solution of hydrogen ions donated by sources other
than Reaction (3.2). Hand Kl are the Henry's-law and dissociation constants,
respectively, for Reactions (3.1) and (3.2):
[S02]
H = [S02]g
aq
(3.4)
K =
1
- +
[HS03] [H30] 1
tota
[S02]
aq
(3.5)
Precise measurements of Hand Kl have been obtained by Johnstone and
( 8)
Leppla The results of these authors, summarized in Table 3.1, were
acquired under conditions involving gas-phase concentrations corresponding
to 270 ppm and above.
Use of these values in conjunction with Equation
(3.3) to predict solubility under atmospheric conditions, therefore,
represents an a priori extrapolation of over four orders of magnitude,
and indicates a need for supporting experimental measurements.
-24-
-------
TABLE 3.1
*
SOLUBILITY PARAMETERS
FROM WORK OF JOHNSTONE AND LEPPLA
Temperature Kl H
oC moles/l
0 0.0232 0.0136
10 0.0184 0.0196
18 0.0154 0.0270
25 0.0130 0.0332
35 0.0105 0.0445
50 0.0076 0.0673
*Defined in Equations (3.4) and (3.5).
The apparatus employed herein to test solubility behavior and the validity
of Equation (3.3) is shown schematically in Figures 3.1 and 3.2. Diluent
gas from a regulated cylinder source was passed through a humidifier and
a rotameter, and finally into a 25.1oC thermostatic water bath containing
a heating coil, a permeation tube S02 source, and the solubility cell.
Upon emerging from the solubility cell the gas was passed through a wet
test-meter for final accurate flow measurement.
The solubility cell is shown in detail in Figure 3.2.
Constructed of
Pyrex glass, this cell was designed so that the dilute gas stream was in
contact with glass only, during its passage between the permeation tube
and the absorbing liquid.
Access ports were provided for optional inser-
tion of pH and conductivity probes to monitor progress toward equilibrium.
An experimental run was initiated by charging the solubility cell with a
given quantity of absorbing solution (usually 7 ml).
The cylinder valve
was then turned on and gas was allowed to bubble slowly through the
solution until sufficient time had elapsed to bring the system to a point
where it would be almost at equilibrium under the final flow conditions
-25-
-------
I
N
0-
I
o
o
o
o
o
2
3
1. REGULATED DILUENT GAS SUPPLY
2. HUMIDIFIER
3. ROTAMETER
4. CONSTANT-TEMPERATURE BATH
5. STAINLESS STEEL HEATING COIL
6
5
8
9
4
6. S02 PERMEATION TUBE SYSTEM
7. BYPASS STOPCOCK
8. STANDARD TAPER JOINTS
9. TEST CELL
10. WET TEST METER
Figure 3.1
Solubility Measurement Apparatus
1 0
-------
I
N
......
I
SIDE VIEW
Figure 3.2
FRONT VIEW
Solubility Cell
-------
anticipated for the run. The gas floww~ then turned up to a point where
the desired gas concentration was attained, and the system was allowed to
proceed to its final solubility equilibrium.
Gas-phase concentration was determined directly from known permeation
rates of the calibrated permeation tubes, in conjunction with diluent
flow measurements obtained from the wet test meter.
Liquid-phase con-
centration was measured by removing aliquots from the solubility cell and
analyzing them using the modified T'!est 1"nd Gaeke !1lethod. (9) A Technicon
Autoanalyzer was employed for this purpose. Approach to final equilibrium
was noted by removing aliquots at various intervals of time which were
comparable to the relaxation times expected for the system (usually 6 -
15 minutes).
The few experiments for which equilibrium was not attained
during the sequence of aliquot
removal and measurement were discarded
and then repeated to obtain more reliable results.
Grade A helium supplied by the Bureau of Mines was used as a diluent gas.
Helium was ultimately chosen as a diluent after severe difficulties were
encountered arising from impurities in the prepurified grade nitrogen
.
employed during preliminary tests. Liquid absorbing solution was com-
posed of water, triple distilled from permanganate solution, and adjusted
to the desired pH by addition of standard HCl. Three types of absorbing
-4 3
solution, containing 0, 1.00 x 10 , and 1.00 x 10- moles HCl per liter
(pH 7,4, and 3), were employed.
Experimental results are shown in Table 3.2 and Figure 3.3, in conjunc-
tion with deviations from solubility behavior predicted from Equation
(3.3) and the values of Hand Kl given by Johnstone and Leppla. These
deviations, which range from 0.7 to 21.2 percent are noted to increase,
in general, with decreasing S02 concentration. Such a trend should be
expected, owing to the increasing errors of measurement as the lower
limit of the analytical method (in the neighborhood of 2 x 10-7 moles/t
H20), is approached.
-28-
-------
10-3
e::: 10-4
w
I-
c:(
3:
e:::
w
I-
-1
--
C\J
a
U'J
I
N U'J
\0 w
I -1
a
~ 10-5
10- 6
10-9
TRIPLE-DISTILLED WATER ~
~~.
r1' .
[H;J = 1:/\
[H~xJ = 10-3
10-8
MOLES SOZ/LITER AIR
(= PPM/2.45 X 107)
Figure 3.3
. EXPERIMENTAL POINTS
D DATA OF TERRAGLIO
AND MANGANELLI
10-7
10-6
Solubility of Dilute S02 in Water at 25.1 °c
-------
TABLE 3.2
EXPERIMENTAL MEASUREMENTS OF SOLUBILITY OF S02 IN WATER SOLUTION
Moles/£' HCl
In Test Liquid
"Excess"
pH
Moles/£. S02
In Gas
x 106
o
o
o
o
7
7
7
7
0.00178
0.00247
0.0135
0.0397
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
4
4
4
4
4
4
0.00182
0.00183
0.00400
0.0144
0.0328
0.1075
0.001
0.001
0.001
0.001
3
3
3
3
0.00437
0.0126
0.0333
0.1075
Moles/£. S02
In Liq~id
x 10
Percent Deviation
Above Predicted*
Value
29.4
33.5
74.0
133.0
10.2
6.9
1.4
5.5
8.4
8.5
15.2
43.8
81. 6
168.8
20.2
21.2
8.6
7.3
9.2
2.7
2.2
5.4
14.5
43.9
18.2
1.9
4.1
0.7
*
Predicted using Johnstone-Leppla values for 25°C in Table 3.1
in conjunction with Equation (3.3).
T~e good reproducibility exhibited by the experiments in addition to the
obvious high trend of the results, however, indicates that some nonrandom
factor is present.
This factor could have arisen either from a systematic
error in the experiment or, more likely, from an increasing inability of
Equation (3.3) to represent true behavior as concentration is lowered.
An analysis of the experimental procedure shows that a random error of
about 3 to 7 percent (depending on concentration) should be expected,
owing to individual errors in sampling and analysis.
Systematic errors
-30-
-------
could have arisen from a number of sources; these~ however, were all
considered to be too small to account for the effects observed.
Per-
meation-tube characteristics were checked by both chemical and gravi-
metric ana1yses~ and were known to within about + 1 percent.
Systematic
errors arising from impurities in the diluent gas were severe during
some of the preliminary tests using prepurified nitrogen; these~ however,
were shown to be inconsequential after the nitrogen was replaced with
high-purity helium.
The possibility of error arising from sparging of
HCl from the absorbing solutions was checked by monitoring pH during
the courses of several experiments.
No loss of HCl could be measured in
any of these tests, demonstrating this effect to be a negligible source of
systematic error.
Temperature depression of the absorbing solution by
exposure to partially-humidified diluent was checked and found~ under the
most extreme circumstances, to be less than one degree centigrade.
From
Equation (3.3) and Table 3.1 one can predict that solubility will increase
by about 3 percent per degree; thus this error source, while possibly
approaching the expected random error under extreme conditions, cannot
account for the total deviations shown.
The most plausible explanation of the nonrandom discrepancy between
Equation (3.3) and the experimental results is simply the approximate
nature of the equation itself, which neglects the effects of the second
ionization,
HS03 + H20 t SO; + H30+
(3.6)
and the formation of other species such as pyrosulfites and hydrates.
All
of these effects could reasonably be expected to contribute to positive
deviations from Equation (3.3), becoming increasingly significant as
concentration is lowered.
-31-
-------
In view of the large extrapolation from previous data and its approximate
nature, Equation (3.3)'s ability to predict low-concentration solubility
behavior is considered to be remarkable.
The positive trend of the deviation between experiment and Equation (3.3)
might tempt one to adjust the values of Hand Kl to obtain a more satis-
factory agreement. This should be discouraged, since the discrepancy is
most likely to have arisen from the equation itself rather than from errors
in the parameters.
Adjusting these parameters, therefore, would amount to
an empirical curve-fitting procedure wherein Hand Kl would be stripped of
much of their theoretical significance. Any future endeavor to refine the
agreement should begin, therefore, by attempting to formulate a more sat is-
factory solubility equation.
-32-
-------
CHAPTER IV
FIELD EXPERIMENTS IN WASHOUT
OBJECTIVES OF FIELD STUDY
The necessity for controlled field experiments was recognized during the
course of sulfur dioxide washout studies involving the Keystone Generating
Station plume. (1) Here the apparent low washout of plume sulfur dioxide
emphasized the influence of background sulfur dioxide in obscuring the
experimental results.
Uncertainties concerning the amount of sulfur
as sulfur dioxide in the power plant plume further complicated the
analysis. A revised theory of sulfur dioxide washout, which was developed
in those studies, showed the importance of plume geometry and precipita-
tion properties on the washout process.
Adequate definition of these
factors on the scale of the Keystone experiment was not feasible because
of the plume height an~ the spatial and temporal nonuniformity of the
atmosphere and precipitation on that scale.
A controlled field experiment at a properly selected site, it was
reasoned, could circumvent the disadvantages of operation at the Keystone
site while retaining the reality of natural precipitation in the actual
atmosphere.
Furthermore, suitable measurements could be taken to define
adequately the plume and precipitation characteristics on this limited
scale.
Control would be exercised on the height, the rate, and the
duration of the sulfur dioxide release and on the distance to the
samplers.
It was intended that a large number of experiments be con-
ducted so that a variety of atmospheric and precipitation conditions
could be sampled for each control configuration.
It was therefore
necessary to select a site with abundant rainfall.
Such a site is the
Quillayute State Landing Field near Forks, Washington, which has been
utilized for washout studies by Battelle-PNL during recent years.
EXPERIMENT DESIGN
The Quillayute site, located west of the Olympic Mountains on the
Olympic Peninsula of Washington, as shown in Figure 4.1, receives
-33-
-------
PACIFIC
OCEAN
I
W
P.
I
BRITISH COLUMBIA
------._-
---------
BELLINGHAM
SEATTLE
SPOKAN E .
. TACOMA
.
OLYMPIA
I --
I ---........ ,,"'-
'_/ ,--,---
OREGON
\
I
I
,
I
I
I
I
I IDAHO
I
I
I
I
,
\
\
- -- -------
Figure 4.1
Location of Field Experiment Site
-------
approximately 250 em of precipitation per year. From October through
March the precipitation, which is principally rain, falls during 20 or
more days of each month for monthly totals in excess of 25 em.
The
rainfall is usually continuous and of moderate intensity over periods of
several hours.
Wind speeds also are moderate and a southerly wind direc-
tion remains quite steady during most periods of precipitation. The
southerly flow assures a low pollution background since the upwind tra-
jectory is over the ocean or sparsely inhabited coastal regions.
The landing field is located 5 km inland from the coast on a broad plain
and is relatively free of obstacles for extended distances.
Winter clo-
sure of the field precludes interference from normal airport traffic.
The
National Weather Service has maintained a first class weather station at
the site since 1966.
Thus standard surface and upper air data are avail-
able for the site.
Teletype circuits at the station provide information
on the movement of storms.
At the Quillayute site, two trailer-mounted towers which could be extended
from 7.6 to 30.5 m were installed approximately 215 m apart in a line
roughly normal to the mean wind direction during precipitation. Three
sampling arcs were established from 3050 to 0600 at distances of 30.5, 61
and 122 m from each tower.
These arcs were staked out at 50 intervals for
positioning of the precipitation and air samplers. These two grids, desig-
nated "East Grid" and "West Grid" ,are shown in Figure 4.2. Also shown in
this figure is the location of a trailer-mounted 8.5 m tower, which was
positioned about 150 m north of the West Grid tower to measure sulfur
dioxide concentrations in the air with a vertical array of samplers.
Figure 4.3 depicts the special grid that was utilized on one occasion when
precipitation occurred with northerly flow.
The sulfur dioxide metering systems were located on the trailers at the
tower bases. Each consisted of an insulated box containing two 9.1 kg mani-
fold-connected cylinders of sulfur dioxide.
The box temperature was regul-
ated with a thermostatically controlled electric heater to maintain adequate
-35-
-------
WEST GRID
EAST GRID
00000000
0°22 25 24 000
00~9 31 00
0016 34 00
o 0
01 3 37
o
o
o 10
o
000000000 g7
00 22 25 28 000
0019 3100
o 34 0
o 16 0
00 ~ 370
o 1 3,- "b
g 10 I ~
g I (
07
8.5m TOWER.
I
v..>
C)\
I
. W
Figure 4.2
E
Quillayute Grid System
t
N
-------
WEST GRID
EAST GRID
. w
. E
J
VJ
-...J
I
1 7
0000 1 3
00 9
°00
0005
00 1
00
o
I
N
o 1 7
o
000000000000000
13 9 5 1
Figure 4.3
Special Grid System
-------
cylinder pressure for constant emission rate.
Valves and flowmeters on
the box exterior permitted the operator to maintain a predetermined sulfur
dioxide flow.
Pressure and temperature sensors monitored the flowmeter
conditions for accurate determination of the total emission.
Polyethylene
tubing carried the sulfur dioxide to the top of the tower where it was
vented to the atmosphere.
Additional equipment at the top of each tower consisted of a three-dimensional
Gill anemometer and a solenoid-activated device for the ignition of red
smoke grenades.
The Gill system was the primary instrumentation for docu-
mentation of both the mean and fluctuating wind conditions at the source.
Additional detail concerning this system is contained in the discussion of
the tape recorder, which follows.
The smoke grenades were provided as a
back-up system with time exposure photography to define the vertical plume
spread.
Recording of the Gill system output was provided with a 20 channel digital
magnetic tape recorder (Brush #DL 620 A). With 18 channels available for
recording the u, v and w wind components from each tower (two channels were
used for identification of the run and for timing), each parameter was
sampled 7.2 times per second. Mean wind speed and direction and angular
standard deviations, 0e and 0~, for the duration of the sulfur dioxide
generation period were determined subsequently from these.
The recording system was housed in a 4.6 m house trailer located midway
between the two towers.
This trailer also housed recorders for a surface
wind set and a fast response rain gauge.
Operation control was exercised
from this location by the field director who was in contact with the tower
operators by citizen-band radio.
The field director and his assistant had
the additional duties of smoke plume photography and documentation of the
raindrop size spectra using a Battelle-PNL developed ozalid image spectro-
meter.
-38-
-------
Each precipitation sampler consisted of a rigid polypropylene funnel,
supported by an ordinary office-type waste basket, with a polyethylene
bottle attached at the neck by a perforated screw cap. The bottle con-
tained 5 ml of tetrachloromercurate (TCM) solution to assure retention
of the sulfur dioxide in the precipitation. Twenty-four samplers were
spaced at 5° intervals on each of the active arcs. Except when the special
grid was employed, two arcs were activated on each grid for all runs.
Deployment or recovery of the sample bottles on the two arcs of each grid
was accomplished in ten minutes or less with two men.
Five bubbler-type air samplers were operated at a sampling rate of 500 ml
per minute on each active arc to ascertain the near-surface sulfur dioxide
concentration in the air.
One was located along the expected plume center-
line and it was flanked by the others at angular distances of 15° and 45°.
An additional five bubblers were logarithmically spaced in the vertical on
the 8.5 m tower.
These units, self-contained in plastic lunch boxes, are
operated by minature, battery-pack powered pumps.
Chemical assay of the precipitation was performed in the Battelle labora-
tory trailer, which was located in a hanger at the air field.
Complete
analysis of the precipitation and air samples could be accomplished in
about three hours using two Technicon Autoanalyzers.
The sulfamic acid
variation of the well-known West and Gaeke method was used.
Precipitation
volumes were measured prior to discarding the samples into carboys follow-
ing the analysis.
disposal.
The carboys were returned to Battelle-PNL for safe
Figure 4.4 is a composite showing the various equipment described above.
CONDUCT OF EXPERIMENTS
The runs typically were conducted in the following manner. The field
director determined the tentative run configuration, (i.e., release heights,
-39-
-------
- \ 'r.J 1..r 1
,I .. \ I ~
I~-
-
- -,
. .
~
a
..
~l
.,. I
-...... I
, . ... I
~~'~
-J., ~,,,;J
" ~~
~ -: i!t~
\ ~~ ; "~.~
~ ,"'d'j.'-!
.., ,
~
,
,'."..
'"'
.
.
#,
I ...... #'p..
I. ,.
'.
... .,
. " ~
~' ~. ..,-.' -.-
. {"
.".'!~'..'~~
";' it.
. t:~ ,
1 ..,~' . .
. .- ..."" ......
. I, t.1' jI
j~ .
~.' I
. ~ "'. . :..:.I!.
r~,,;~~~~ ,t't
*~~~
'.'-::t
.
AI
" .
t
~"
~
4' ."
...~..,
. """.';
~ I'~~;~
i I "..si
;!.'; . ~. ".~:
I . ""-..'.4.."
.~,!-. "'=',..,~,!
f!1!!?t "~:~\~~
~~:~~,.!-*-~~
c
b
..,.....
-:-
. .
1- -
1_-
-
d
Figure 4.4 Composite of Field Study Equipment. (a) S02 release
system, (b) Gill anemometer and smoke grenade rack on tower, (c)
Fast-response rain gauge, (d) Precipitation collector.
-40-
-------
'"'f
e
>.
.r
'.
. r{t~ I
. ~'s.';.'
,
L '
f
'.
.~
. "'~~
...,.(~Jo.J;1
(...'~' ~~
:\c~' P.'~i{~
.- ~ ~~~~.
- . D>-.W
- ~ - "i
---:
-<'
- ...t";"';o", {i' ,.. - ....-
- ~
~.:
g
Figure 4.4 (continued). (e) S02 analysis system,
(f) S02 bubbler boxes, (g) Raindrop size spectrometer.
-41-
}.,
'>-"\'~'.-:"........
- --
-------
release rates, and sampling arcs to be employed), based
requirements and existing wind conditions measured on a
to the control trailer. Towers were raised and release
on preestablished
3 m mast adjacent
height winds observed
to verify the run configuration.
Air samplers and the precipitation sampling
funnels, contained in plastic bags, were deployed.
Smoke releases from each
tower were photographed before final run readiness which was completed by
attaching the collection bottles to the funnels, placing the funnels in
their supports and starting the air sampling pumps.
Tower operators noti-
fied the field director when all preparations on their respective grids were
completed.
A brief countdown assured concurrent emission of sulfur dioxide
on the two grids.
The tape recorder was activated at the same time.
Raindrop size spectra were obtained periodically during the runs.
Sulfur
dioxide flow rates were maintained by the tower operators, and the wind
velocity and rainfall rates were carefully monitored by the field director
to assure run acceptability.
The run was terminated at the discretion of
the field director either after the prescribed run period had elapsed or
when large changes in wind velocity or precipitation intensity threatened
to compromise the acceptability.
Immediately following each run the sample bottles were recovered, capped,
and returned to the laboratory trailer. The air samplers, deactivated
during bottle recovery, were gathered and returned to the laboratory for
sample removal and renewal of their sampling capability.
A 2.5 ml aliquot
of each sample was withdrawn using an individual syringe, and transferred
to a cup on the carousel of the Autoanalyzer. When weather conditions were
suitable, subsequent runs were conducted during the period of chemical
analysis, which could be completed automatically upon loading the samples
and activating the Autoanalyzer.
The field period extended from March 8 to April 9, 1971 with grid layout
and equipment installation requiring about five days as a consequence of
persistent, and often heavy, rains. The following week was dry and no
runs were conducted until the third week in the field when 14 sulfur
-42-
-------
dioxide releases were made.
Another week went by before the weather
became suitable for the final controlled releases.
The extended dry
periods and showery nature of the rain after mid-March were evidence that
the ideal washout-studies weather, typical of Quillayute, had passed.
As
a consequence fewer runs were made than were planned, and there were few
repetitive releases with the same configuration to observe the influence
of atmospheric and precipitation parameters.
A summary of the runs is presented in Table 4.1. Rainfall ranged from
-1
0.8 to 5.7 mm hr and release-height wind speeds were between 2.2 and 7.6
-1
m sec
-1
min at heights of 7.6 to 30.5 m.
Rates of sulfur dioxide emission were between 0.38 and 5.66 moles
The selection of sampling arcs and
release heights was tempered by the wind speed and the degree of atmospheric
mixing.
High mixing with a low release height was expected to result in
high surface air concentrations of sulfur dioxide close to the source and,
perhaps, give an erroneously high indication of washout as a result of S02
absorption on the wet funnels. A high elevation release in a high-wind
condition could result in low observed washout on the inner arcs owing to
sampled precipitation having blown in beneath the plume.
Consequently,
there is a bias toward release from midtower levels and sampling on the
two outer arcs.
The plumes of sulfur dioxide were contained on the sampling arc (that is,
they passed over active samplers) on 19 of the 20 releases.
Data from all
support instrumentation were complete.
However, four of the releases did
not result in meaningful washout distributions.
Runs IE and lW did not
result in S02 concentration measurements sufficiently above the analysis
threshold to define the washout distribution. This was attributed to a
loss of S02 from the samplers prior to analysis arising from insufficient
TCM in the fixing solution. Runs 10E and lOW encountered an apparent mal-
function of equipment during the analysis which resulted in only partial
definition of the S02 distribution.
omitted from further consideration.
Consequently, these four runs are
-43-
-------
TABLE 4.1
RUN SUMMARY
Release
Run Rainfall Rate Temp. Height Wind Speed Release Rate S amp liny
-1 4 (emX10-3) -1 -2 -1 2
No. Date Time (em-see X10) oK (em-see X10 ) (moles-see X10) Are(l
IE 3/22/71 1440-1455 0.28 282 2.14 5.2 4.96 B,G
1W 2.14 4.3 5.11 B,G
2E 3/23/71 1018-1027 0.42 282 1. 68 6.2 9.44 B,G
2W 1.68 5.4 .63 B,G
3E 3/26/71 0954-1016 0.28 277 2.14 5.4 4.93 (2)
3W 1. 22 4.9 4.86 (2)
I 4E 3/27/71 1011-1020 loll 280 1. 22 2.2 4.86 B,G
~ 4W 3.05 2.3 5.31 B,G
~
I
5E 3/28/71 0812-0828 0.67 282 0.76 5.5 4.90 B,G
5W 1. 68 6.3 5.40 B,G
6E 3/28/71 1028-1040 1.58 282 1. 22 7.6 .95 B,G
6W 1. 22 7.0 5.41 B,G
7E 3/28/71 1344-1410 0.42 282 1. 22 6.4 2.70 B,G
7W 0.76 5.9 3.03 B,G
8E 4/06/71 0854-0901
0904-0911 0.22 282 0.76 3.5 8.17 A,G
8W 3.05 4.0 8.17 A,e
9E 4/07/71 0938-0952 0.75 279 1.22 3.0 4.41 A,B
9W 1.22 3.2 .97 A,B
10E 4/07/71 1450-1453 0.42 282 1. 22 5.7 .63 A,B
lOW 1. 22 5.8 4.49 A,B
(1) Arc distances were: A, 100 ft; B-. 200 ft; G, 400 ft.
(2) Special grid shown in Figure 4.3.
-------
DATA REDUCTION
The basic field data consists of measurements describing the source and
sampling configuration, the meteorology (including description of the
precipitation), the concentration of S02 in the air and the S02 content of
the precipitation; the former three being necessary in explanation of the
latter. Many of the data can be utilized in initial form, but other
data require additional processing.
Such is the case with the raindrop
size spectra, the S02 concentrations and the wind data from the three-
dimensional anemometers.
Raindrop size spectra were determined from the raindrop images on ozalid
paper which was exposed for a measured period during rainfall. Reduction
of these data relies upon previous calibration of the images of various
sized raindrops falling at terminal velocity. The frequency distribution
of drop sizes for each run are presented in Table 4.2. A summary of other
characteristics of the rainfall appear in Table 4.3.
Included are several raindrop spectrum parameters.
Among the various runs,
the number median raindrop diameter varied from 0.035-0.093 em, and the
flux varied over a factor of ten (.083-.87 cm-2 see-I). The quantity a is
defined as TI F D;/4, where D2 is the area mean raindrop diameter. This
number is important in classical washout theory, where
A
aE
(4.1)
E being the average collection efficiency of the raindrop spectrum for the
material.
Moreover, the great number of raindrop size spectra collected
at Quillayute over the years has shown that a is proportional to the rain-
fall rate J. for prefrontal continuous rain - the proportionality constant
being about 1.2.
This parameter helps to indicate the type of rainfall
experienced during the experiments noted in Table 4.3, the shower rain
generally having a higher value for a/J. In this light, it is seen that
the experiments included considerable variability in the rainfall character,
and ostensibly in its washout ability.
-45-
-------
TABLE 4.2
RAINDROP SIZE FREQUENCY DISTRIBUTION
Run Diameter (cm)
No. .0249 .0299 .0360 .0430 .0515 .0615 .0740 .0900 .107 .129 .154 .169 .186 .209 .215 .229 .279
---------
1 .007 .084 .122 .146 .092 .122 .240 .172 .014
2 .030 .073 .253 .453 .161 .015 .015 .005
3 .135 .184 .198 .090 .081 .062 .049 .186
4 .093 .127 .211 .201 .083 .054 .030 .059 .059 .035 .040 .010
5 .115 .082 .097 .094 .061 .097 .130 .106 .133 .058 .004 .010
6 .085 .128 .191 .102 .045 .052 .056 .042 .045 .112 .095 .055 .009
7 .100 .123 .105 .241 .173 .073 .054 .023 .050 .027 .028 .005
I
.p.. 8 .101 .136 .169 .129 .154 .103 .125 .040 .011 .015 .015 .004
(j\
I
9 .113 .117 .172 .140 .113 .091 .063 .046 .037 .045 .032 .032 .055
10 .016 .082 .126 .121 .098 .099 .055 .077 .082 .121 .082 .038 .005
NOTE:
Tabulated values are the proportion of raindrops contained in the interval between the
diameter of that entry and the preceding diameter.
-------
TABLE 4.3
RAINFALL CHARACTERISTICS SUMMARY
-~-
Raindrop Size Spectrometer Data
Median Raindrop Rainfall (2) a/J
Run Rain Sample Diameter -2Flux Rate, J a
-1 103) , -1
No. ~ Type(l) No. (cm x 102) (cm sec-l) (cm sec-l x 104) (sec x (cm )
1 6.6 S 1 6.9 0.22 0.46 0.86 .186
2 5.7 0.30 0.38 0.86 .227
2 6.4 S 1 3.7 0.87 0.28 1.03 .362
3 (3) C 1 3.5 0.13 0.33 0.43 .130
4 5.3 S 1 3.8 0.27 0.52 0.81 .154
2 4.7 0.33 0.54 0.93 .171
I 5 4.7 S 1 7.2 0.11 0.35 0.53 .151
~
" 2 5.7 0.26 0.59 0.97 .163
I
6 5.0 C 1 9.3 0.19 1.12 1. 41 .125
2 4.2 0.25 1. 21 1.39 .114
3 3.8 0.62 2.34 2.80 .120
7 5.1 C 1 4.1 0.16 0.22 0.39 .174
2 3.6 0.26 0.71 0.88 .124
8 5.1 S 1 4.0 0.21 0.22 0.45 .199
9 5.3 S 1 3.9 0.17 0.43 0.59 .137
10 5.4 S 1 5.5 0.08 0.36 0.46 .128
(1) Rain Type: S, shower; C, continuous (generally prefrontal).
(2) 2
a = 'IT F D2/4; DZ' area mean raindrop diameter.
(3) Not recorded.
-------
pH of the rain was measured using a conventional pH meter.
These results,
however, were rather inaccurate owing to meter instability which was attri-
buted subsequently to a faulty electrode.
Fortunately, pH of the collected
rain was in a region where its variations were insignificant in determining
solubility behavior; thus these experimental errors were of no consequence
to the related modeling effort. 802 concentrations of the collected preci-
pitation samples were measured in the field laboratory and then corrected
for dilution by precipitation which was collected before and after the
period of 802 emission. Therefore, the precipitation concentration of 802
was calculated by dividing the quantity of 802 contained in a sampler 'by
the precipitation collected during 802 emission, which was determined from
the precipitation rate measured with the fast response rain gauge.
Table 4.4 shows the total amount of 802' Lmi' recovered from the samplers
of each arc and the total amount deposited in one cm of downwind distance
during a one-second emission (downwind washout rate, cf. pg. 11).
latter quantity, M, is approximated by the relationship,
The
M
Lm, ~y
1
At
(4.2)
(cf. Equation [2.9]) where ~y is the sampler separation along the arc, A
is the sampler collection area and t is the duration of 802 emission. A
third column gives the washout per cm of downwind distance as the percent
of 802 released. The maximum value is approximately 4 percent per kilo-
meter. Precipitation concentrations of the individual samplers are tabu-
lated in Appendix A.
Concentrations of airborne 802 were measured with bubbler-type samplers
which were operated throughout the emission period. The recovered mass,
determined in a manner similar to that for the precipitation samplers, was
divided by the volume of air which was sampled during the emission period
to give the average air concentration.
-48-
-------
TABLE 4.4
S02 WASHOUT SUMMARY
Lm. Deposition, M M/Q
Run 1
8 -1 10 -1 x 105)
No. Arc (moles x 10) (moles [em see] x_10 ) (percent em
IE *
1W*
2E B 0.88 9.90 0.10
C 2.04 44.40 0.47
2W B 0.07 0.78 0.12
C 0.18 4.00 0.63
3E 14.76** 65.10 1.30
3W 7.51 26.30 0.54
4E B 14.00 153.00 3.20
C 8.55 186.00 3.80
4W B 5.23 56.80 1.10
C 2.89 63.00 1. 20
5E B 13.61 83.40 1. 70
C 7.78 95.30 1. 90
5W B 0.29 2.19 0.04
C 0.38 5.66 0.10
6E*
6W B 8.71 71.10 1.30
C 9.23 150.80 2.80
7E B 4.66 17.70 0.65
C 4.63 34.90 1.30
7W B 17.89 67.80 2.20
C 9.77 73.60 2.40
8E A 8.75 30.80 0.37
C 8.82 127.50 1. 50
8W*
9E A 7.98 28.00 0.64
B 7.84 55.00 1. 20
9W A 2.19 7.70 0.79
B 1. 62 11.40 1. 20
10E*
10W*
*Undefined
**Incomp1ete1y contained
-49-
-------
The three-dimensional anemometers were oriented with their propellers
facing upward, to the east and to the south.
From the wind speed components
thus obtained, mean and turbulent airflow parameters were calculated using
the following relationships:
u
1/2
l: ([u2+v2] )
N
(4.3)
-1 u
l: (tan -)
8 1800 - 57.3 v (4.4)
N
{ -1 U 2 1 U r t2
08 l: ([ tan N v] ) ["
u
where u, v and ware the easterly, southerly and upward wind components,
respectively. u and e are the mean resultant wind speed and direction,
Ow is the standard deviation of the wind speed in the vertical, and 08
and Oct> are the standard deviations of wind direction and wind inclination,
respectively. N is the number of data points contained in the summation.
With the exception of 8, all airflow parameters were used in the calculation
of the concentrations of 802 in the near-surface air.
were performed using the relationship
These calculations
-50-
-------
Q exp - 1:. [(h/0)2 + (y/0 )2]
2 Z Y
x
(4.8)
'IT U a
y
o
Z
where the concentration adjacent to the surface at a location displaced a
lateral distance y from the plume axis is determined by the rate of 802
emissio~, the height of release, the mean wind speed at release height and
the standard deviations of the plume in the lateral and vertical direction
Evaluations of 0 and 0 at downwind distance x were accomplished. using the
y z
relationships
o
Z
0q,X
o
y
=
0eX
(4.9)
which are appropriate when the standard deviation of wind inclination and
wind direction are evaluateg with sampling times equal to the duration of
sulfur dioxide emission and averaging times which are equal to one-fourth
the travel time from the source to the sampling arcs. (10) The standard
deviations can be obtained by taking the square root of the difference of
the squares of the standard deviations determined for sampling times -equal
to the emission duration and one-fourth the travel time.
The utilization of the airflow.parameters for air concentration calculations,
therefore, defined the manner in which the data were reduced.
Table 4.5
contains the data appropriate to the Quillayute runs.
Figure 4.5 shows the
degree of agreement between observed and calculated values of 802 concen-
tration in the near-surface air. While there is considerable scatter in
the data pairs, it is markedly reduced when only the observed data for which
-51-
-------
TABLE 4.5
DATA SUMMARY
QUILLAYUTE 3-D ANEMOMETERS
"--
Turbulence Parameters
Mean Wind Velocity 1st Arc (A or n) 2nd Arc (B or C)
Run HeighE3 Sp~rd -2 eYe eY~ eYe eY~
No. (crnXI0) Dir(Deg) (em see XI0 )
IE B,C 2.14 176.4 5.2 .1330 .1058 .1214 .0944
lW B,C 2.14 176.9 4.3 .1730 .1086 .1594 .0971
2E B,C 1. 68 186.5 6.2 .1722 .0976 .1659 .0884
2W B,C 1. 68 190.6 5.4 .1969 .1091 .1919 .0960
3E 2.14 008.6 5.4 .0997 .0582
3W 1. 22 007.5 4.9 .1337 .0653
4E B,C 1. 22 160.8 2.2 .3799 .1294 .3639 .1175
4W B,C 3.05 163.3 2.3 .3343 .2022 .3111 .1598
5E B,C 0.76 166.6 5.5 .1882 .0828 .1771 .0737
5W B,C 1. 68 168.1 6.3 .2156 .1127 .1877 .1018
6E B,C 1. 22 176.0 7.6 .1320 .0845 .1260 .0795
6W B,C 1. 22 176.8 7.0 .1540 .0958 .1462 .0892
7E B,C 1. 22 207.3 6.4 .2133 .0885 .2069 .0799
7W B,C 0.76 212.6 5.9 .2568 .0873 .2433 .0775
8E A, C 0.76 170.9 3.5 .1935 .0811 .1798 .0656
8W A,C 3.05 172.1 4.0 .1671 .1026 .1505 .0839
9E A,B 1. 22 203.1 3.0 .2010 .1005 .1965 .0943
9W A,B 1. 22 205.4 3.2 .2117 .0884 .2061 .0816
10E A,B 1.22 175.7 5.7 .1714 .0841 .1676 .0785
lOW A,B 1. 22 183.7 5.8 .2229 .1042 .2206 .0994
-52-
-------
10-10
(V')
E
u
-
(/)
W
--I 10-11
C)
::E:
z:
0
........
I-
c::c:
~
I-
z:
w
u
Z
I C)
VI U
W
I 10-12
o
w
:>
~
w
(/)
ro
C)
10-13
10-14
x DENOTES DATA FOR WHICH
THE BUBBLER SOLUTION S02
CONCENTRATION >10-9 MOLES-cc-1
8 DENOTES BURBLER SOLUTION
S02 CONCENTRATION >10-9 MOLES-cc-1
FOR RUNS EXHIBITING ~UASI-NORMAL
GROSS-ARC DISTRIBL!TIONS
.
.
.
.
.
4P
. x
.
x
.
.
.
10-10
10-13 1n-12 10-11
CALCULATED CONCENTRATION, MOLES/cm3
Figure 4.5
Comparison of Observed and Calculated 802 Concentrations in Air
-------
the bubbler solution concentration
for which the analytical method is
-9
of 802 exceeded 10
reasonably accurate)
-1
mole-cc (those
are considered.
The
scatter is further reduced by limiting these more reliable data to those runs
for which the observed distribution of 802 concentrations in precipitation
were approximately Gaussian. Finally, the even distribution around the
line which denotes a one-to-one relationship, demonstrates the basic agree-
ment of the calculated and observed values and establishes the validity of
calculated 802 concentrations.
Although the concentration of 802 in the air apparently can be defined
adequately in the preceding manner, it must be recognized that the
resulting values are averages for the period of emission. It has been
demonstrated previously(l) that washout is related directly to the time-
averaged definition of a plume only when the process is linear.
Chapter
III has shown, however, that the solubility relationship between 802 and
water is nonlinear under the conditions of interest. Consequently, long-
period average air concentrations may be inappropriate for the definition
of washout concentration.
The influence of nonlinear behavior on the
resultant washout is discussed in the following chapter.
-54-
-------
CHAPTER V
ANALYSIS OF RESULTS
A large number of factors apparently influence the washout of S02' It is,
therefore, extremely difficult to relate the observed washout variability
to specific factors without the aid of some prescribed analysis technique
which attempts to represent the influences of the pertinent variables to
the total system.
Accordingly it is convenient to evaluate the field
observations by comparing them with predictions resulting from the analyses
described in Chapter II.
If these techniques are sufficiently valid to
permit grouping of results they should enable greater insight into washout
mechanisms and allow further refinement of the analysis.
It should be emphasized at the outset, however, that deviations between
theory and experiment may arise from three basic causes, which are listed
as follows:
1.
intrinsic shortcomings of the analyses, for example, the use of an
idealized plume model for mathematical description of the actual plumes;
2.
utilization of input data that is not completely representative of
the system, such as employing raindrop size spectra obtained over
short time periods to represent conditions during an entire emission
period;
and, to a lesser extent,
3.
inadequate precision in measurements, for example, S02 measurements
which, in some cases, were inaccurate because of sensitivity limits
of the technique.
If deviations caused by the last two factors are significant, they will
tend to mask systematic deviations caused by the first and thus reduce
the effectiveness of the analysis.
-55-
-------
This chapter will consider first the comparison of experimental results
with predictions of the two simple asymptotic cases discussed in Chapter
II (the washout coefficient and the equilibrium washout approaches). It
is emphasized here that although these cases constitute opposing limits in
the sense that they pertain, respectively. to transport-controlled and
equilibrium-controlled behavior (s=o and s=oo) they do not necessarily
define upper and lower limits of washout rates.
Comparison of these
limiting cases is followed by similar comparisons of the general models.
Discussion of behavior exhibited by individual experiments is presented in
the context of the examination of these techniques.
WASHOUT COEFFICIENT ANALYSIS
As shown in Chapter II, the traditional washout coefficient approach repre-
sents the limiting situation wherein washout is totally a kinetic phenomenon,
and considerations of equilibria are unimportant to the analysis. This
implies that the system is irreversible. Under such conditions it can be
shown(l) that the washout coefficient, as defined by Equation (2.19), can
be determined from experimental data using the relationship
II
Em, !c,y u
1
m A
o
(5.1)
Here Emi is the total amount of 802 recovered from the samplers on an arc,
!c,Y is the sampler spacing along the arc, u is the mean wind speed at release
height, IDO is the total amount of 802 released, and A is the collection
area of a sampler. Upon application of Equation (4.2), Equation (5.1)
reduces to
II
Mu
Q
(5.2)
-56-
-------
where Q is the 802 emission rate in moles/sec. From this it is observed
that the M/Q values in Table 4.4 differ from A only by the factor u.
As shown by Engelmann(ll) ,the washout coefficient also may be estimated
theoretically, assuming gas-phase limited behavior, by employing Equation
(2.21) in conjunction with typical rain spectra. The curve for 802 wash-
out coefficient as a function of rainfall rate defined by this relationship
is plotted in Figure 5.1.
The experimental points calculated by Equation
(5.2) from the field data are also plotted on this graph.
From this com-
parison it is seen that few data points approach the washout coefficients
predicted by the irreversible washout theory. These data have been
expressed as downwind washout rates and plotted versus values predicted
from the Engelmann curve in Figure 5.2.
This will be useful in comparing
with predictions from other models later in this chapter.
It is apparent from Figures 5.1 and 5.2 that low elevation releases of 802
generally produce higher experimental washout coefficients. Also, higher
coefficients tend to be observed at greater distances from the source.
The Run 5 results demonstrate the effects of source elevation and sampling
distance.
Emission from 16.8 meters, on the west grid, results in coeffi-
cients that are more than an order of magnitude lower than the emission on
the east grid from an elevation of 7.6 meters.
In addition, the washout
coefficient on Arc C of the west grid is more than double the value on
Arc B.
The smaller difference between washout coefficients on Arcs Band
C of the east grid apparently results from more rapid diffusion into the
near-surface layer from the lower-elevation emission.
Consequently, there
is a slight decrease in the air concentration of 802 between the arcs of
the east grid, whereas a substantial increase occurs in concentration
between the arcs of the west grid.
The washout coefficient determined theoretically for Run 5 from the
measured raindrop size spectrum using the relationship by Engelmann(ll)
is shown as an asterisk in Figure 5.1 for comparison with the experi-
mentally determined washout coefficients of that run.
This point is
-57-
-------
AT' RUN S
'*
10-4 0 Q)SEC
. -m
[I] SE~ .(D
-m
I
u
Q)
V1 . rn .m
~ Q) - .rn
z CD
I..LJ . .@
u [TI. &. ern
l.1...
l.1...
I..LJ &.
C)
u
~
~
C)
:r:
VI
c:( 10- S
3:
,W
[I]
. Q) SWC
. QJ SWB
SAMP LI NG
ARCS
L A
o B
o C
OSPECIAL
( 3 E )
EMISSION
HEIGHTS
(METERS)
1. 7.6
2. 12.2
3. 16.8
4. 21.4
S. 3'1. S
10- 6
~
10-J
10-4
10-3
RAINFALL RATE, cm-sec-1
Figure 5.1 Comparison of Predicted and Measured Washout
Coefficients as a Function of Rainfall Rate.
-58-
-------
10
ARC
t::t.A
XB
8C
co
0 8 4E
6W
x X 4E
u 8
<1J 5E / 8E
III v~
E
u
....... X6~J 84W
III
<1J X 4W
7W X 9E
o
E 82E
L.J.J 7E 8 t::t.8E
I-
ex: X 3W t::t. 9E
c:r:
I-
=>
0 X 7E
:I:
V>
ex:
3:
Q X 9W
L.J.J O. 1 X 2E
>
c:r: t::t. 9W
L.J.J
V>
co 8 5W
0
82W
X 5W
0.01
0.01
0.1
10
PREDICTED WASHOUT RATE, moles/em see x 108
Figure 5.2 Comparison of Observed Washout Rates With
Those Predicted From Washout-Coefficient Analysis
-59-
-------
seen to lie above Engelmann's general curve, which was calculated with a
generalized raindrop spectrum. The agreement within approximately a factor
of two between the theoretical and experimental values for the 7.6 meter
emission elevation emphasizes the importance of S02 desorption in the case
of the higher elevation emission, where low concentrations of the gas occur
beneath the plume centerline near the source.
The possibility that some of the collected rain passed into the system
along trajectories below the S02 source was investigated. Obviously, such
an effect would lead to the observance of lower washout for higher plumes
and smaller downwind distances.
An analysis of the rain trajectories for
these experiments, however, has shown that such "blow under" effects were
of small importance except for a few circumstances where rather severe
conditions were encountered.
These experimental results, therefore, are
considered to be a strong confirmation of the occurrence of reversible
sorption in S02 washout, and of the previous speculation that the washout
coefficient is of reduced value for gases in general, which do not exhibit
irreversible behavior except under rather specialized circumstances.
EQUILIBRIUM WASHOUT ANALYSIS
Chapter II has demonstrated that "equilibrium" washout poses a limiting case
which is opposite to that characterized by washout coefficient theory. The
usefulness of the limiting case can be tested, initially at least, simply
by comparing measured S02 concentrations in rain with those predicted to
occur if the rain were in diffusional equilibrium with S02 at the ground
level plume concentrations present. In performing such a comparison,
however, the question of the significance of plume fluctuations emerges as
an important factor in the analysis. This question is a special case of a
problem described previously(l), regarding errors arising from calculating
washout in nonlinear systems on the basis of time-averaged concentrations
of a fluctuating plume.*
For the special case of true "equilibrium"
---
*It should be noted that this problem did not arise in
using washout-coefficient theory, owing to the linear
of analysis.
the previous analysis
nature of this type
-60-
-------
washout this problem is simplified, since only the non1inearities in the
solubility relationship must be considered; furthermore, only the plume
fluctuations at ground level are important to the analysis,
since concen-
trations aloft have no direct bearing on S02 concentrations in rain at
ground level, if equilibrium conditions prevail.
The effect of plume fluctuations on equilibrium washout may be demon-
strated by referring to Figure 5.3, which is a solubility plot for S02 in
water calculated for typical Oui1layute conditions from the relationships
given in Chapter III.
Since this plot is given on logarithmic scales, it
is observed that any deviation from a slope of unity represents a nonlinear
equilibrium relationship. To provide an example of this effect one can
observe from this plot that a constant S02 concentration in air of 10-11
-1
moles cc will result in an equilibrium precipitation concentration
- 7 -1 . . f 1 0-11 1
about 10 moles cc . If the mean alr concentratl0n 0 mo es
of
-1
cc
were attained through precipitation exposure to an air concentration of
10-10 moles cc-1 for one-tenth of the sampling period and to clean air
for the remainder of the time, however, the resultant S02 concentration
in the sampled precipitation would be about 3.3 x 10-8 mo1es-1 - a devia-
tion that arises totally as a consequence of the nonlinear behavior shown
by Figure 5.3.
Consequently, time-averaged air concentrations are not
totally appropriate in the determination of washout based on equilibrium
with the surface air concentrations.
Owing to the complexities of actual plume fluctuations, an exact compen-
sation for this effect would be extremely difficult.
One way to partially
correct for this behavior, however, is to break the description of the
plume into individual descriptions for small time increments, thereby
attempting to provide a more "instantaneous" definition of plume behavior.
This was performed for conditions corresponding to one of the Oui11ayute
experiments (Run 4E) using anemometer data for consecutive 15-second inter-
vals to compute ground-level plume and equilibrium rain concentrations.
Average rain concentrations for the entire experiment were obtained by
-61-
-------
10- 6
N
C>
U1
l.J...
C>
:z::
C>
....... 1 0 - 7
~
c:I:
a:: r-
~ I
:z:: u
w u
U I
:z:: U1
C> W
U ~
C>
I :z:: :E:
0\ C>
N
I ....... 10-8
~
c:I:
~
.......
0....
.......
U
W
a::
0....
10-9
10-14
Figure 5.3
10-13
10-12
10-11
AIR CONCENTRATION OF 502' MOLE5-cc-1
Solubility Relationship for S02 in Water at IOce, pH = 5.5
10-10
10-9
-------
adding the l5-second contributions distributed across the arc according to
the individual l5-second mean wind directions.
These results are shown in Figure 5.4, which is a plot of ground-level
rainborne S02 concentration as a function of crosswind distance.
'/
the equilibrium concentration predicted from the above incremental
analysis, plotted as a solid line, i8 compared with that based on the
Here
simple time-averaged plume (plotted as circular points).
concentrations are shown as vertical bars for comparison.
Actual measured
The magnitude
of the deviation between predictions based on time-averaged and fluctuating
plume models is striking; obviously plume fluctuations give rise to a
first-order effect in this instance.
It is interesting to observe that
although the peak values are in close agreement, the predicted width of
the washout distribution is greater than observed.
peak is apparent in the calculated washout as well.
The observed secondary
While there may be merit in this incremental analysis, it must be recog-
nized as only a first-order approximation to instantaneous plume behavior.
The associated calculations are rather laborious, and the choice of any
fixed increment in time (e.g., 15 seconds) is arbitrary.
An additional technique for estimation of near-surface air concentrations
appropriate for calculations of equilibrium washout in fluctuating plumes
involves the use of "peak-to-mean" ratios.
Some insight into the variabi-
lity of instantaneous air concentrations relative to the mean concentra-
tion is provided by Hinds(12) and Ramsdell and Hinds(13) who measured
short-term mean air concentrations (5 seconds and 38.4 seconds, respectively)
during ground level emissions of 10 to 20 minutes.
Their work indicates
that the ratios of short-term to long-term mean air concentrations should
vary from about 4 to 10 between the mean plume centerline and its edges.
For elevated emissions, still greater rates are to be expected, owing to
increased separation from the mean plume centerline.
They show, further-
more, that short-term concentrations tend to be constant over a substantial
crosswind region about the mean plume centerline. This suggests that the
-63-
-------
120
. MEAN PLUME ANALYSIS
- 15-SECOND ANALYSIS
.
.
.
.
.
100
.
.
.
.
. .
80
C1\
0
><
u . .
u
-.....
(/)
w
-'
0
:i:
60 . .
z
0
f--
c1:
cr:
f--
z . .
w
u
z
0
u
40
. .
.
.
20 . .
. .
. .
. .
.
o 360 020 040
260 280 300 320 340
AZIMUTH, DEGREES
Figure S.4
Tune-Averaged S02 Concentrations in Rain Based
Dpon Equilibrium With Ground Level Plume Concen-
trations -- ~ean Plume on IS-Second Incremental
Analyses.
-64-
-------
mean distribution arises largely from the frequency distribution of the
instantaneous plume centerline location on the sampling arc. The peak-
to-mean ratios, in conjunction with the mean air concentrations over the
period of emission, can be used to define the peak concentrations in air at
all crosswind arc positions and may be taken as the inverse of the proba-
bility of occurrence.
Peak-to-mean ratios extrapolated from the results of Ramsdell and Hinds(13)
for short-term periods on the order of 5 seconds were applied to the calcu-
lated mean ground-level air concentrations for the periods of emission to
obtain the peak air concentration values at each crosswind position.
Equi-
librium precipitation concentration values were then obtained using the
solubility relationships of Chapter III (cf., Figure 5.3).
These peak
precipitation concentration values were divided, in turn, by the peak-to-
mean ratios to obtain the mean precipitation concentrations of 802.
Comparison of the results with observed values for Run 4EB is shown in
Figure 5.5.
The distributions are compared by superposing the peak values
since this technique, unlike the previous one, does not account for the
instantaneous wind direction.
It is observed that the peak-to-mean
analysis predicts equilibrium rain concentrations comparable to those
predicted by the time-increment analysis, both analyses giving results
that are close to those measured experimentally.
The peak-to-mean analysis was applied to all runs and the results are
presented in Appendix B.
These results are summarized in Figure 5.6,
which is a comparison of observed washout rates with those that would
occur if the rain were in equilibrium with the ground-level concentration
as defined by the peak-to-mean relationship.
It should be noted that the
generally wider distribution of the predicted washout leads to calculation
of washout rates higher than those observed, although predicted peak con-
centrations are generally lower than those measured experimentally.
A
similar plot, comparing observed washout with that which would occur with
the rain in equilibrium with the time-averaged ground level concentration
is given in Figure 5.7 for comparison. The measured washout rates are
-65-
-------
120
.
MEAN PLUME ANALYSIS
PEAK-TO-MEAN ANALYSIS
.
.
.
.
.
100
.
.
.
.
. .
80
0'\
a
x
u . .
u
---
V)
W
-J
a
::;: 60
. .
:z:
a
......
I-
c:(
a::
I-
:z: . .
w
u
z:
a
u
40
. .
.
20 .
.
.
.
.
0
260 280 300 320 340 360
AZIMUTH, DEGREES
.
.
.
.
.
020
040
13'igure 5.5
Time-Averaged 802 Concentrations in Rain Based
on Equilibrium wlth Ground-Level Plume Concen-
trations -- Mean Plume and Peak-to-Mean Analyses
-66-
-------
co
0
x'
U
QJ
VI
E
u
.......
VI
QJ
0
E
w
f-
c:t:
a::
f-
:::;)
0
::I:
VJ O. 1
c:t:
3:
0
w
:>
a::
w
VJ
c:>
0
ARC
AA
X B
8 C
8 4E
A 9E
A 8E
88E
SE
7 W '~7 W
X /.X
4W -?S< 6W
~:2E
X 7E
2E/X 9W
X
84W
8sw
8 2W
X SW
0.01
0.01
0.1
10
8
PREDICTED WASHOUT RATE, moles/em see x 10
Figure 5.6
Comparison of Observed Washout Rates With
Those Predicted from Peak-to-Mean Analyses
-67-
-------
10
ARC
l:J. A
X B
. C
OJ
0
)(
~
I
U
Q)
VI
I
E
u
VI
Q)
0
E
UJ 9E
I-
«: l:J.
0::
I-
=>
0
:I:
V)
«:
3:
c 0.1
UJ
>
0:: l:J. 9W
UJ
V)
a>
0
Figure 5.7
X 7E
X 9W
2E X
. 2W
X 5101
.8E
SEX
7 W 7 W8 X 6 W
X
9E XX 4W
.2E
87E
. SW
4E
6W .
.5E
4W
.
0.01
0.01
0.1
PREOICTED WASHOUT RATE, moles (em see)-1 x 108
10
Comparison of Observed Washout Rates with Those Predicted on
Basis of Equilibrium with Average Plume Concentrations at
Ground Level
-68-
-------
observed to fall much more closely to the peak-to-mean curve than to that
obtained from the time-average analysis.
The criterion for equilibrium washout developed in Chapter II (Equation
2.26 and 2.28) predicts that for the conditions encountered at Quillayute,
all falling raindrops should approach the ground at diffusional equilibrium
only at downwind distances much greater than those at which sampling was
performed.
This apparent conflict with the findings of the peak-to-mean
analysis requires further elaboration.
behavior are listed as follows:
Some possible explanations of this
1.
The Chapter II criterion is in error, and mass transfer to and from
the drops is much faster than has been assumed by this analysis;
2.
The Chapter II criterion is not necessarily erroneous, but some arti-
fact of the field sampling procedure (such as absorption or desorption
of S02 by the fallen rain during its residence on the sampler-funnel
surface) has distorted the measurements so that they tend to reflect
3.
some process other than washout; and,
The Chapter II criterion is essentially correct, but some effect not
accounted for by these analyses occurs to make the observations coin-
cide.
An example of the last explanation is simply that the rain is falling at
diffusional disequilibrium, some drops being subsaturated with respect to
the ground-level concentration while others are supersaturated.
They then
mix in the sample collectors to give an ensemble-average concentration
close to the predicted equilibrium value.
These possibilities will be
examined in detail after presentation of results from the general models
of S02 washout.
GENERAL MODELS OF GAS WASHOUT
The nonlinear model described in Chapter II has been utilized to calculate
washout concentrations and downwind washout rates from input data corres-
ponding to each of the Quillayute field tests.
The input data and their
-69-
-------
sources are summarized in Table 5.1.
As discussed previously, the most
important deficiencies of this model are:
1)
2)
3)
4)
time fluctuations in plume concentration are ignored,
time fluctuations in rainfall rate and direction are ignored,
redistribution of the plume is assumed negligible, and
the bivariate-normal plume distribution is assumed valid.
In addition it should be noted that this model accounts for S02 removal EY
washout only. Any dry deposition or reentrainment of S02' as mentioned
previously, could alter the model's capability to predict natural behavior.
Predictions of the distributions of S02 concentrati9ns in precipitation are
compared in Appendix C with the observed results on each sampling arc for all
runs (Figures C.l - C.18).
These curves pertain to the general model predic-
tions based on gas-phase limited mass transfer and on the opposite limiting
case of stagnant-drop behavior (cf., [1]). The predictions are compared with
measured concentrations (represented by vertical bars) and with concentrations
of S02 that would exist if the sample were in equilibrium with the calculated
average ground-level gas phase concentration (denoted by circles). The
results are "centered" by aligning the highest experimental values with the
midpoints of the computed distributions. Stagnant drop mass-transfer coeffi-
cients for these computations were estimated using the linearized equation(16)
k
x
5 D Ax Cx
(5.3)
a
rather than solving the complete diffusion equation presented in the previous
report(l). This simplification was utilized in the face of excessive compu-
tation time required by the more exact alternative procedure.
It is expected
that this measure was of little consequence in influencing the final computed
results.
-70-
-------
TABLE 5.1
INPUT TO NONLINEAR NONFEEDBACK MODEL
Reference
Physical Parameters
Source Parameters:
Height, Strength
Wind Parameters:
Velocity, 0~, 08
Precipitation Parameters:
Rate, Size Spectra
Receptor Parameters:
x,y,z
I
......
I-'
I
Solubility Parameters
Transport Parameters:
S02 Diffusivity in Air
S02 Diffusivity in Water
Kinematic Viscosity of Air
Values Used in Model
Table 4.1
Table 4.5
Tables 4.1 and 4.2
Bucket Locations
Solubility Equation of
Chapter III
2
.136 cm /sec
9 x 10-6 cm2/sec
.133 cm2/sec
(14)
(15)
(14)
-------
d . 1 (1) I' . t' t'
As discusse prevl0us y lml lng cases represen lng the extreme mass-
transfer coefficients should bracket washout behavior. Limiting values of
mass-transfer coefficients do not necessarily correspond to limiting washout
concentrations; however, they should provide reasonable estimates of these
limits under present circumstances.
Provided the model and test data are
valid, therefore, measured washout concentrations might reasonably be
expected to fall somewhere between the solid and dashed lines in the
figures.
Figures C.l - C.18 provide point concentrations which may be integrated
across the plume to obtain washout rates, as defined by Equation (2.9).
A comparison of these values is shown in Figure 5.8, which is a plot of
predicted versus observed washout rates.
As in the previous integration
of the equilibrium concentration distribution, the excessive. width of the
distribution tends to increase the calculated washout rate values.
Here
the limits on the tielines pertain to gas-phase limited and stagnant drop
behavior as calculated using the nonlinear model.
It is also of interest to compare the results with the predictions of the
simpler linear model, which was described in Chapter II. This model has
the advantage of being amenable to hand calculation, provided that the
raindrop size distribution is simplified in some acceptable manner.
Here
the mass-mean drop size was assumed, rather arbitrarily, to characterize
the rain spectra.
The linearized solubility parameter H' was chosen, again
rather arbitrarily. as the mean between the centerline and ground level
values beneath the plume axis at the downwind distance of the ground level
receptor, as calculated using the procedures of Chapter III.
The results
are shown in Figure 5.9, a scatter diagram similar to that used previously
to evaluate the more sophisticated nonlinear model.
The results exhibited
by this figure, as expected, are somewhat more scattered than those shown
for the nonlinear model.
The agreement is still rather good, however, in
view of the related assumptions and the potential for uncertainty in the
input data.
-72-
-------
10
/
co
0
x
u 6WC
CII
III 8EC
E SEC
u 6WB
...... ,SEB
'"
0
VI lWB 4WC
VI 4WB
L.U ZEC I
--' '/ '/
0
::E
lEC
L.U 19EA
f-
c:(
0::
f- lEB
=>
0
:z:: /
VI
c:( 9WB ZEB
:3 0.1
I
0
L.U / t 9WA
:>
0::
L.U I SWC
VI
co
0 ZWC
/
/ ISWB
0.01 ,/
0.01 0.1 10
PREDI CTED WASHOUT RATE, MOLES SOZ/em see x 108
Figure 5.8
Comparison of Observed Washout Rates With
Those Predicted by Nonlinear, Nonfeedback Model
-73-
-------
10
/
co /
C)
4EC
x 6WC
u 8EC 4EB
OJ
V1
E 5EC
u 5EB
....... 7WC 6WB
N 4WC
C) 7WB
I./) 9EB 4WB
I./)
w
--'
C) lEC
::;: EA
w
t-
ex:
ex: 7EB
t-
:::>
C) /
::I:
I./) 1/ 19WB
ex: 0.1 / ......-12 E B
:3
0 /
w
:> 15WC
ex: /
w .r
I./) 2WC
co
C)
/ I 5WB
0.01
0.01
0.1
PREDICTED WASHOUT RATE, MOLES S02/em see x 108
10
Figure 5.9
Comparison of Observed Washout Rates With
Those Predicted by Linear, Nonfeedback Model
-74-
-------
Comparison with Figures 5.1 and 5.6 indicates that the general model pre-
dictions show much better agreement than those of the washout-coefficient
analysis, and in most cases agreement that is comparable to that given by
the peak-to-mean analysis of equilibrium washout.
In comparing with the
equilibrium-washout analysis, however, it must be noted that this technique
attempted to compensate for the effects of plume fluctuations.
Since the
general models are based upon time-averaged plume concentrations such a
comparison is questionable, at least until some indication is given regard-
ing the adequacy of the mean-plume assumption for modeling purposes.
Applicability of the mean-plume assumption to the general washout models
was tested using the results for Run 4E, attempting to approximate instan-
taneous plume behavior by subdividing the experiment period into 15-second
increments as described previously.
Calculation for these individual time
increments with subsequent recombination for the total run resulted in the
predicted S02 concentration distributions shown in Figure 5.10. As shown
by this diagram, the calculated concentrations based on the 15-second
approximation to the fluctuating plume do not deviate markedly from those
based on the average plume - a somewhat surprising outcome in view of the
large deviations in the corresponding equilibrium curves (Figure 5.4).
This undoubtedly is due in part to the complete dependence of the equili-
brium analysis on air concentrations immediately above the sampler, whereas
for the model the entire plume depth influences the washout.
Thus while
the lateral plume shift modifies the model prediction, it is less sensitive
than the equilibrium analysis to large changes in the vertical distribution.
Owing to the large amounts of computer time involved, similar analyses were
not completed for the other Quillayute tests.
It was concluded on the basis
of Figure 5.10, however, that the mean-plume assumption was reasonably
appropriate for comparison of the general models under present circumstances.
All computations presented thus far have pertained to ground-level elevations.
For a general appreciation of the washout process it is of interest to
observe also the predicted concentrations of pollutant in rain at different
-75-
-------
0) 80
CJ
><
I
U
U
---.....
(/)
w
~
CJ
::;::
I Z
"'-.I 0
0'\ .......
I I-
c:{
ex:
I-
z
w
u
z
CJ
u
100
RUN 4E ARC B
MEAN PLUME ANALYSIS!
+ GAS-PHASE CONTROLLED
. STAGNANT DROP
15-SEcorw ANALYSIS l-GAS-PHASE CONTROLLED
) --STAGNANT DROP
+
+ +
60 + +
+
+
40 +
+
+ I
20 . .
+ . +
.
. +
. +
.
.-.-- +
.-
0
270 240 310 330 350 010 030
AZIMUTH, DEGREES
Figure 5.10
Predictions by Nonlinear, Nonfeedback Model for Time-Average and IS-Second
Incremental Analyses
-------
elevations during its fall through the plume.
As mentioned in Chapter II,
the algorithm for the nonlinear model computes these values enroute to
obtaining final ground-level results. Such values, computed from the non-
for Run 4WB, are shown for three different drop sizes in
Here the S02 concentration in the drops is plotted (as solid
height of the drop above ground. The dotted lines denote
the concentration that a drop would have if it were in continual equili-
linear model
Figure 5.11.
lines) versus
brium with the ambient mean gas-phase concentration, giving a representa-
tion of the gas-phase concentration experienced by the drop during its fall.
The dotted lines are different for each drop size, of course, owing to the
different trajectories of fall.
Observing the curves for the smallest (.0299 cm diameter) drop one should
note the relatively rapid response of the drop as it attempts to approach
diffusional equilibrium. During the drop's fall its concentration first
increases with plume concentration (absorption) and then decreases (desorp-
tion) until it reaches the ground, almost in equilibrium with the ground-
level plume concentration. The curves for the intermediate (.107 cm
diameter) drop indicate considerable lag between the plume and drop
concentrations; here, however, the drop has absorbed sufficient S02 so
that is unable to lose enough by desorption to approach equilibrium condi-
tions at ground level.
It therefore approaches the ground appreciably
supersaturated with respect to the ground level plume concentration.
The curve for the largest (.186 cm diameter) drop illustrates a prediction
of the general washout models which is likely to be important in explaining
some of the observations of the Quillayute experiments. Namely, this model
predicts that a drop does not necessarily have to be highly responsive to
mass transfer in order to approach the ground in a state close to equili-
brium.
As seen from the curve, the drop responds to the gas phase concen-
tration in a sluggish manner, but the fact that the plume concentration
decreases in the vicinity of the ground actually brings the two curves
close together at ground level, that is, a near "psuedoequilibrium" washout
condition is predicted.
-77-
-------
5000
E
u
0
z:
::::> 4000
0
0::
t!J
w
:>
0
a:::>
I «
-...J 3000
ex> I-
I :J:
""
W
:J:
2000
-- LIQUID SO CONCENTRATION IN
EQUILIBRIDM WITH AMBIENT AIR
COMPUTED S02 CONCENTRATION
IN DROP
1000
--(----
----
--
0.186 em DIAM DROP ----
\ ",,-
, ""'-
"
-- .......
-- .......
----- ,
---- "'-
r---" "
DIAM DROP ............, \
'"
6000
0.0299 em DIAM DROP
o
10-10
10-9
10-8
CONCENTRATION. MOLES/em3
10-7
10-6
Figure 5.11
Computed Concentrations in Drops as a Function of Vertical Position -
Run 4HB, Gas-Phase Limited
-------
Predicted ground-level concentration is shown as a function of drop size
in Figure 5.12, which pertains to gas-phase limited conditions for Run 4WB.
From this it is seen that, according to the nonlinear model, the concen-
trations can vary considerably above and below the average of the ensemble,
which may fall close to the equilibrium value.
One can easily explain the
reason for the maximum concentration value at intermediate drop size and
the approach to equilibrium from Figure 5.10.
The peculiar dip in concen-
tration at small drop sizes occurs primarily because of the slight exposure
to the plume by drops drifting in at small angles.
It is emphasized that the curves in Figures 5.11 and 5.12 pertain to
specific hypothetical conditions, and curves for other rain-plume condi-
tions may vary widely.
In particular, the situation visualized to develop
the equilibrium washout criteria (where all drops are sufficiently respon-
sive to achieve true equilibrium conditions), would be characterized by a
concentration curve lying exactly on the equilibrium line, rather than
displaced above and below as shown in Figure 5.12.
An examination of the computer output for the experiments wherein both the
nonlinear model and the peak-to-mean equilibrium analysis agree well with
experiment shows that a combination of the above two effects contributed
significantly in creating a prediction of near-equilibrium conditions in
the mixed samples.
Thus it may be concluded that, under conditions where
this agreement exists, there is no real conflict between the final results
and the precepts of the nonlinear model, or indeed, those of the equili-
brium washout criterion.
DISCUSSION
The overlap in predictions by the general model and the equilibrium analysis
limits the extent of any meaningful conjecture concerning the effects of
absorption or desorption of S02 by rain on the collector surfaces. Obviously.
if the incoming rain is close to equilibrium, little driving force will exist
to encourage this process.
Some information in this regard, however, may be
-79-
-------
1 .0
r--.
a
x
u 0.8
u
.........
(/)
W
-l
a AVERAGE COr~CENTRATION
L
- --
CL 0.6
a
c.:::
0
z:
I .......
00
0 z:
I a EQUILIBRIU~1 CO N C Ern RA T ION
....... 0.4
I- ---
c:::(
c.:::
I-
z:
w
u
z:
a
u 0.2
N
a
(/)
o
o
0.025
0.050
0.075
0.100
o . 125
0.150
0.175
0.200
RAINDROP DIAMETER, em
Figure 5.12
Computed Ground-Level S02 Concentrations in Rain as a Function of Drop
Size - Run 4WB, Gas-Phase Limited
-------
obtained by examining the few data points in Figure 5.6 where poor agree-
ment between the equilibrium analysis and experiment occurs.
In particular,
experiments SEA, 9EA, and 9WA provide washout rates that are much greater
than predicted by the peak-to-mean equilibrium analysis.
Ostensibly this
is explained by the short downwind distance of arc A, which results in
relatively low ground-level concentrations. The drops entering the
collectors apparently have brought down sufficient quantities of 802 from
aloft to be substantially supersaturated at ground level. This conjecture
is reinforced by noting that the general model (cf., Figure 5.8) predicts
washout rates that are in reasonable accordance with those observed for
these experiments. Apparently desorption of 802 at the funnel surfaces
was not sufficient to cause an appreciable effect in these instances.
Experiments 5WB and 5WC provided results that agree poorly with both the
general model and with the equilibrium analysis.
The reason for this is
unclear, although measured gas-phase concentrations were also low for this
experiment, indicating a failure to describe the plume in a satisfactory
manner.
Regardless of this, the discrepancy appears to arise from a factor
common to both analyses and cannot, therefore, be attributed to pertur-
bations at the collector surfaces.
In a final analysis it is concluded that, for the most part, the field
observations are predicted reasonably well by both the general models and
the equilibrium analysis.
The general models provide an explanation for
this virtual overlap in prediction, and tend to give more satisfactory
results for the few experiments where conditions leading to overlap did not
exist.
The relatively good agreement between the general models and experi-
ment suggests that these models will be useful as basis for analysis of
future experiments involving power-plant plumes.
The experimental results of the present study have enabled the conclusion
that washout of 802 is indeed a reversible phenomenon, and that the washout-
coefficient approach is generally invalid for these conditions. Although
the results indicate that absorption and desorption on the collector surfaces
-81-
-------
is an unimportant factor in most cases, these data are insufficient to resolve
this question completely; direct experimental confirmation is needed prior to
drawing final conclusions in this regard.
-82-
-------
CHAPTER VI
ISOLATED DROP EXPERIMENT
Because of its basic importance to washout, an experiment has been designed
to measure the overall mass-transfer coefficient, K. Such data, if avail-
y
able, could be used with the models to compute washout rates directly.
rather than applying the presently used technique of "patching" solutions
by definition of limiting behavior.
The major effort on this project so far has been the selection and design
of the experiment.
Experiments involving sprays and supported drops were
ruled out immediately because of difficulties with unnatural perturbations
in such systems.
The decision between employing a falling drop experi-
ment or an experiment wherein the test drop would be suspended by an up-
ward flow of air was more difficult.
Both types of experiments share the
advantage of maintaining the drops under near-natural conditions; they
do, however, have some rather critical disadvantages as well.
The major question concerning the suspended drop type of experiment is
whether or not the upward flow of suspending air exhibits flow (particu-
larly shear and/or turbulence) properties which may cause behavioral
deviations between the experimental drop and a natural raindrop.
Such
effects apparently do occur if the drops are suspended in a vertical,
tapered tube (a rotameter tube, for instance) wherein the dimensions of
the drop and the tube diameter are similar. Kinzer and Gunn(17) found
that water evaporation rates measured with such an experiment did not
compare well with known values unless the ratio of the tube bore to the
drop diameter exceeded two.
This should obviously preclude any future
use of tapered tube support columns under conditions where this ratio is
low. Situations involving higher ratios are also suspect if liquid-phase
phenomena are being observed. Kinzer and Gunn's study involved the trans-
port of water from the drop surface to the ambient atmosphere, and was
therefore essentially a gas-phase experiment. The present experiment,
-83-
-------
which is devoted primarily to the investigation of liquid-phase phenomena,
is expected to be more sensitive to distortions in gas-flow behavior.
This
may be seen intuitively by noting that there is a distinct velocity profile
across the bore of a tapered support tube - if this is a small tube the
profile will be nearly parabolic. A drop suspended on such a flow will
tend to fall to one side of the tube to a region of lower velocity, result-
ing in a spin-inducing shear across the drape By virtue of this spin, the
Magnus effect will tend to counteract the force inducing the drop toward
the wall, and ultimately a rather complex force equilibrium will exist.
Since internal circulation of the drop is dependent directly upon exterior
flow behavior it is probable that liquid-phase mass-transfer coefficients
measured in tapered tube experiments will tend to deviate markedly from
natural values. This becomes especially apparent when it is observed that,
owing to the low magnitudes of liquid molecular diffusion coefficients, any
perturbation in convection behavior will have a marked effect upon modifying
mass transfer rates.
This contrasts to the gas-phase situation, where diff-
usion coefficients are usually about four orders of magnitude higher and
reduce the relative effects of any changes in flow pattern.
Suspended drop experiments involving vertical wind tunnels of large cross
sections are more attractive than the tapered tube type of experiment.
These maintain the drop in the vertical flow of air by creating a "well"
in the velocity profile near the center of the system. The shear field in
the well region is much less intense than that in a small diameter tube,
resulting in more nearly natural conditions. The question of perturbations
to the drop by tunnel-induced turbulence is not completely resolved at
present. It appears, however, that the turbulence can be maintained at
levels low enough such that its effect is negligible, particularly if the
spectra are not characterized by large powers at amplitudes of the order of
the drop size or less. This has been substantiated in part through the
. (18)
work of Garner and hlS coworkers, who photographed oscillitory behavior
of drops suspended in such systems.
-84-
-------
A practical difficulty with suspended drop experiments is their small
sample size, which makes the problem of analysis a rather difficult one.
-5 3
A 0.03 cm drop, for instance, has a volume of about 10 cm, and would
necessitate an S02 concentration of 0.1 moles/£ to be detectable by
conventional methods. Since concentrations of present interest range
-4
between 0 and 2 x 10 moles/£, some rather elaborate means of measure-
ment would be required.
Such a difficulty could be counteracted in part by catching multiple drops
and combining them for analysis. Although this can be accomplished with
a suspended drop apparatus, multiple drop samples can be acquired in a more
natural way using an isolated, falling drop type of experiment.
Falling
drop experiments are attractive also because they allow the drops to fall
under near natural conditions, avoiding the aforementioned problems with
external flow conditions.
The major problem with falling drop experiments insofar as liquid phase
measurements are concerned is simply their size.
Because of nonlinear
responses, measurements of gas mass-transfer coefficients must be acquired
for all stages'of concentration buildup; for the larger drops this may
require fall distances of the order of hundreds of meters, not including
the several meters of fall necessary to stabilize the drops and allow them
to approach terminal velocity prior to their exposure to the test atmosphere.
The largest drop experiment reported in the literature is that of Kinzer
and Gunn, which involved a vertical drop tube 200 meters in length. All
other reported experiments have been smaller in scale, and, accordingly,
have been of limited value insofar as liquid-phase mass-transfer measure-
ments are concerned. A summary of the pertinent literature on suspended
and isolated falling drop experiments is given in Table 6.1.
The preceding considerations indicate that a vertical wind tunnel sus-
pended drop system, rather similar to the one employed in the studies by
Garner and his coworkers, is most appropriate for present purposes.
Shown
-85-
-------
Type of Experiment
Suspended drop, 1n ver-
tical wind tunnel.
Suspension Times:
2 - 2000 aec
TABLE 6.1
ISOLATED DROP EXPERIMENTS
Drop Composition and
Size RanRe
Method
Of Analysia
Author(a)
Gas Composition
Water, Dekalin, Ker-
osene, Mentor 28
(fuel oil) Trans-
former oil,
0.5 mole-fraction C02 in air
Chemical
Garner and
Lane [18]
Glycerol, propylene
glycol, ethylene
glycol
2.9 - 5.9 mm
Controlled H20 vapor at 80 -
1l0°F in air.
Refractro-
metric
Suspended drop in
tapered tube
Suspension Times:
15 - 2500 aac
Water
1.2 - 1.5 mm
DHO - H20, saturated in air
at room tem."erature
Friemnan~ Machta,
Soller [19]
Mass-
spectro-
scopic
Suspended drop, in
tapered tube,
and on 'lfre~"
support.
Water
Air
Gravimetric
Kinzer and
Gunn [17]
0.4 - 4.5 mm
Suspended drop in
vertical wind
tunnel.
Suspension Times:
o - 600 aec
Water
Air, THO
Scintilla-
tion
counter
Mensing and
Schiigerl [20]
Drop Tube,
Approx. 50 cm long
Drop tube,
200 cm long
Drop tube,
165 cm long
Drop tube, 200 cm 1008
with 800 cm acceleration
column
Drop tubes,
200 cm 10ng and
800 cm long
Drop tube,
70 cm long
Drop tube,
168 cm long
Drop tube,
52 cm long
Water NIl) Chemical Hatta and
Babba [21]
Water .95 mole fraction C02 in air Chemical Dixon,
4-6mm et 81. [22, 23]
Water Pure CO~ Chemical Hughes and
2.5 5mm Gilliland [24]
Water .06 mole fraction NH3 in air, Chemical Shabal1n [25]
2.2 4.2 mm pure C02
Water, saturated Air Chemical Guyer, et al. [26]
with C02
Various amines and .05 to 1 mole fraction C02 Differential Goodridge [27, 28]
amine-water solu- in air pressure
tions, 1. 3 - 1. 6 mm
Solutions of Chemical J ohne tone and
H2S04, .015 - .031 M.F. NIl) Williams [29]
NaOR, .022 - .026 M.F. S02
.018 - .021 ]of.F. RCl
and .021 .048 M.F. C02
NaOR R202 .021 - .029 ]of.F. R2S
In Water In Air
2.6 6.0 mm
Wate.r Pure C02 Chemical Whitman, Long, and
2.7 2.g mm .43 .49 M.F. NIl) Wang [30]
in 8i r
.0007 .0030 M.F. H2S in air
Air Gravimetric, Kinzer and Gunn [17]
photographic
Pure C02 Shabal1n [25]
Drop tube J 20,000 cm long
(evaporation of drops)
Water
.04 - 1.0 mm
Drop tube. 200 em long with
1,000 em adjustment height
Water
4mm
-86-
-------
in Figure 6.1 this system utilizes a circulating flow driven by an
internal blower.
Temperature of the gas is controlled precisely by a
compact heat exchanger, located just downstream of the blower.
From
this region the gas progresses through various turbulence control
devices up to the tapered test section containing the drop formation
and catching equipment. From this point the gas recirculates through
flow control and metering devices, and finally back to the blower intake.
802 will be injected into the system through the ports as shown. Humidity
will be controlled at saturation.
Experimental runs would begin by suspending a drop in clear air for a
period of time until stabilization is complete. The 802 would then be
turned on and the drop allowed to experience a simple function (e.g.,
a "step" or a "ramp") of concentration in time.
Drops will be removed
and analyzed after varying exposures to assess mass-transport behavior.
The most important problem involved with this experiment is that of
analysis.
It was first anticipated that this would be overcome by
employing a radioactive tagging method; this, however, was discouraged
because of severe associated difficulties including the large complexity
and expense involved with the rather high levels of radioactivity required.
Accordingly, it appears advantageous to employ a chemical microanalytical
technique. At present the techniques of chemical conversion and analysis
by microcoulometry or electron capture are under investigation, and it is
expected that one of these will be developed for ultimate use with the
experiment.
It was expected initially that construction of the experiment would be
begun immediately. Recent findings from the modeling component of this
project, however, suggest that it may be more beneficial to postpone this
work until a later date, thereby allowing a total effort to be placed on
field work and modeling in the immediate future.
For this reason the
isolated-drop experiment will be held at the present stage until future
field tests are completed and interpreted.
-87-
-------
VENTURI SECTION
MANOMETER OUTLETS
VENTURI AND BUTTERFLY
SECTIONS STAINLESS.
ALL OTHER RETURN LINES
PRE-MADE GLASS
SECTIONS 3" DIA
ALL OVER-RUN
LI NES I NDI CATE
FLANGE JOINTS
OPENING FOR
DR) TUBES
"
I'
I
I
I
I I
"
I I
: I
WORKING
SECTION
~
ALL SECTIONS FROM BLOWER TO
WORKING SECTION TO BE
STAINLESS STEEL WITH EPOXY
COATING
, '~;:f>::~,----"-
DAMPING ---
SCREENS ---,
Figure 6.1
Schematic of Suspended-Drop Apparatus
-88-
-------
CHAPTER VII
EVALUATION AND CONCLUSIONS
In evaluating the accomplishments described in this report it is appro-
priate to review the total washout program conducted to-date, indicating
its direction and objectives, and describing briefly suggested plans for
the continuing study. The perspective of the program is indicated by the
chart in Figure 7.1, which shows portions of the program that have been
completed as well as those that are in progress or suggested for the near
future.
As shown by the chart, each of these segments is related to the
ultimate objective of establishing reliable models and correlations for
calculating atmospheric scavenging of sulfur compounds under general
atmospheric conditions.
The progress chart in Figure 7.1 begins with the initial Keystone washout
study, which provided experimental results leading to a revision of the
previously accepted theories of gas washout.
This revised theory, while
qualitatively in accord with experimental findings, indicated that inter-
actions between various atmospheric phenomena were so complex that simpler
studies were required for verification.
For this reason, the current pro-
gram consists essentially of three parts, including a modeling component,
a laboratory component involving measurement of the basic physical para-
meters of interest, and finally, a field component consisting of controlled
experiments conducted under natural atmospheric conditions.
Tentative plans for future work are shown schematically in the remainder
of the chart.
These are itemized in the following discussion.
1.
The modeling program will continue in its development, and (at a later
date), mass-transfer parameters will be measured using the single drop
2.
experiment.
A program will be initiated to investigate in more detail the signifi-
cance to scavenging of the interaction between stack and cooling tower
plumes.
-89-
-------
rO"R-IGTN,.TKEYsf~E1
ilFIElD EXPERIMENTS J
---.---
SIGNIFICANT DEVIATIONS FROM PREDICTED BEHAVIOR
IMPORTANCE OF DEPENDENCE DISPROPORTIONATE IMPORTANCE OF
REVERSIBILITY LIQUID-PHASE ON OTHER EFFECT OF lOW SO REACTION OTHER
ALTITUDE SO~ 2 l
r--l- - - ----- __T~::l~: ---- - -- :~l~r~:~___--_F::~_O~:l ~~-_C:: - - - - - -- --_J_- ---- -- ------ ----,
CREATION OF REVISED THEORY Of GAS WASHOUT ;
------ --------- -- n______- ----- --.------------ ----______n- __n__- - ______n.J
:-- CR-EAT i~-Of PR-OORAM-i 0"-:
~ EVALUATE SIGNIFICANCE:
: OF CDa.1 NG-TOWER PLUMES:
~~ ~-~~:~-~~i~-~~~~---~ ~~~~
, DESIGN OF lOW-BACKGROUND:
i INDUSTRIAL FIELD TESTS'
L.. --"£~'"-"f~~!....._J
MODI FrCATI ON
r- DESIGN-(j:-ADDi"ri ~AC:
, CQNTRCUED FIELD TESTS:
L- ----~~~~~ ~~~~)--"--j
.'- - PERFORMANCE"OF-FIELD -TESTS-:.. r
, ,
AND EVALUATION WITH MODELS n
;--;;;I~~~~;-:;l~~~~~~~u~~~~~
: FI ElD TESTS :
, (KEYSTONE) :
~------~~~~~~~I~~~~~~~~~~~~: MODEL MODIFICATIONS
.-..--::::':,,~:!r:~~~'~~~: ~__m- I
i ESTABLISHMENT OF FINAL MODELS AND ~
, CORRELATIONS FOR PREDICTING ATMOSPHERIC:
: SCAVENGING OF SULFUR COMPOUNDS I
: UNDER GENERAL ATMOSPHERIC CONDITIONS'
L... ---- -- ------ ------ ------ - ---- - - ------_J
Figure 7.1
Suggested Research Program
-90-
-------
3.
Future field tests at Quillayute and at the Centralia, Washington
power plant will be designed and conducted.
The additional tests at
Quillayute will be conducted for the purpose of increasing the volume
and reliability of data and to obtain measurements at greater distances
from the source.
The Centralia experiments will be conducted for the
following reasons:
a.
To measure washout from power plant plumes under low background
conditions, and to compare the measurements with theoretical
b.
predictions.
To evaluate in more detail the washout of sulfate and the rate
of its formation.
An automated means for sulfate analysis will
c.
be employed to facilitate this part of the study.
To measure amounts of trace metals in the precipitation, and to
d.
attempt to relate these measurements to sulfate formation.
To initiate investigations of the consequences to scavenging of
the cooling tower plume interaction.
4.
Results of the total Quillayute tests and those from Centralia will be
analyzed, and the models and correlations will be revised accordingly.
A first effort for incorporating sulfate formation in the scavenging
model will be made.
5.
The final field study of the Keystone Plant will be planned.
These
experiments will be conducted primarily for the following reasons:
a.
To verify and correct the refined model of sulfur compound washout.
To examine sulfur dioxide washout in more detail at greater dis-
b.
tances from the source.
c.
To examine sulfate formation in highly polluted atmospheres during
precipitation as a function of
(i)
(ii)
(iii)
(iv)
(v)
802 concentration
rain acidity
background ammonia concentration
trace metals concentration, and
cooling tower interactions.
-91-
-------
d.
To evaluate the significance of cooling tower-stack plume interactions
to the problem of scavenging by post-emission precipitation.
6.
The field study of the Keystone Plant will be conducted in accordance
with the previously described plans.
Information from the total investigation will be compiled and evaluated
7.
to provide final models and correlations of sulfur compound scavenging
rates.
The results described in this report constitute a significant contribution to
accomplishment of the objectives shown in Figure 7.1. Measurements of 802
washout have been performed which confirm the existance of reversible sorption
behavior. Two models of 802 washout have been formulated. Based on reversible
absorption theory these models differ primarily in degree of sophistication,
one being a linearized version of the other, more general treatment.
Utilization of these models in conjunction with average plume geometry calcu-
lated using the bivariate-normal distribution has shown encouraging agreement
with measured values.
The nonlinear washout model, when applied with a fluc-
tuating plume analysis, gives somewhat different predictions for the conditions
encountered at Ouillayute.
Optimism concerning the applicability of the general
models to washout calculation is tempered somewhat by our present inability to
provide a precise estimate of the mass-transfer coefficient.
Measured washout
rates, however, were generally observed to fall between those predicted on
the basis of limiting conditions.
An additional factor tempering optimism is the rather close agreement between
measured washout and that predicted on the basis of simple equilibrium with
ground-level 802 in a fluctuating plume. This agreement is consistant with
general-model predictions, but it also raises the question of the relative
importance of factors such as dry deposition of 802 on collector surfaces.
The field results suggest that these factors are of minor importance: more
measurements are required, however, to confirm this completely.
-92-
-------
Laboratory measurements of 802 solubility in water have been performed,
and an equation has been presented which describes these measurements
satisfactorily under the low concentrations of present interest.
This
solubility equation has been used extensively in formulation of the general
washout models used for data evaluation.
It is expected that the solubility equation and the general washout models
described in this report will be used extensively in the ongoing program,
both as tools for evaluation of washout from industrial plumes and as bases
for formulation of more refined expressions to be used as ultimate means
for washout calculation.
-93-
-------
REFERENCES
1.
J. M. Hales, J. M. Thorp and M.
Sulfur Dioxide Washout from the
Plant by Natural Precipitation.
Protection Agency. Air Pollution
CPA 22-69-150, Battelle Memorial
Laboratory, March, 1971.
A. Wolf. Field Investigation of
Plume of a Large Coal-Fired Power
Final report to Environmental
Control Office, Contract
Institute, Pacific Northwest
2.
R. B. Bird, W. E. Stewart, and E. N. Lightfoot.
Wiley Co., New York, 1960.
Transport Phenomena.
3.
J. M. Hales and L. C. Schwendiman. "Precipitation Scavenging of
Tritium and Tritiated Water," Pacific Northwest Laboratory Annual
Report for 1970 to the USAEC Division of Biology and Medicine,
BNWL-155l, Part 1, p. 82, Battelle, Pacific Northwest Laboratories,
Richland, Washington, June, 1971.
4.
F. A. Gifford. "An Outline of Theories of Diffusion in the Lower
Layers of the Atmosphere," Meteorology and Atomic Energy 1968,
D. H. Slade, Ed., U.S.A.E.C., 1968.
5.
R. Gunn and G. D. Kinzer. "The Terminal Velocity of Fall for Water
Droplets in Stagnant Air," J. Meteor., ~, 246, 1969.
6.
B. Carnahan, H. A. Luther and J. O. Wilkes.
Methods. Wiley Co., New York, 1969.
Applied Numerical
7.
F. P - Terraglio and R. M. Manganelli. "The Absorption of Atmospheric
Sulfur Dioxide by Water Solutions," J. Air Poll. Control Assoc., ..!.Z.,
403, 1967.
8.
H. F. Johnstone and P. W. Leppla. "Solubility of S02 at Low Partial
Pressures - Ionization Constant and Heat of Ionization of H2S03,"
J. Am. Chem. Soc., ~, 2233, 1934.
9.
F. P. Scaringelli, B. E. Saltzman and S. A. Frey. "Spectrophotometric
Determination of Atmospheric Sulfur Dioxide," Anal. Chem., ~, 1709,
1967.
10.
F. Pasquill.
Atmospheric Diffusion, Van Nostrand Co., London, 1962.
11.
R. J. Engelmann. The Calculation of Precipitation Scavenging, BNWL-77,
Battelle-Northwest, Pacific Northwest Laboratory, Richland, Washington,
July, 1965.
12.
W. T. Hinds. "Peak-to-Mean Concentration Ratios from Ground Level
Sources in Building Wakes," Atmospheric Environment, 1., 145, 1969.
-95-
-------
13.
J. V. Ramsdell and W. T. Hinds. "Concentration Fluctuations and Peak-
to-Mean Concentration Ratios in Plumes from a Ground Level Continuous
Point Source," Atmospheric Environment, i, 483, 1971.
14.
R. C. Reid and T. K. Sherwood. The Properties of Gases and Liquids,
McGraw-Hill Co., New York, 1958.
15.
S. Lynn, J. R. Straatemeier and H. Kramers. "Absorption Studies in
the Light of Penetration Theory," Chern. E. ScL, i, 49, 1955.
16.
J. M. Hales. "Fundamentals of the Theory of Gas Scavenging by Rain,"
submitted to Atmospheric Environment, November, 1971.
17.
G. D. Kinzer and R. Gunn. "The Evaporation, Temperature and Thermal
Relaxation Time of Freely Falling Water Drops," J. Met., ~, 71, 1951.
18.
and J. J. Lane. "Mass Transfer to Drops of Liquid
a Gas Stream," Part II: Experimental Work and Results,"
Chem. Engrs., ~, 162, 1959.
F. H. Garner
Suspended in
Trans. Inst.
19.
I. Friedman, L. Machta and R. Soller. "Water Vapor Exchange Between
A Water Droplet and its Environment," J. Geophys. Res., g, 2761, 1962.
20.
W: Mensing and K. Schugerl. "Stoffaustausch-Messungen an schwebenden
Tropfen," Chemie. Ing. Techn., 42, 837, 1970.
21.
S. Hatta and A. Babba. "The Absorption of Ammonia by a Water Drop,"
J. Soc. Chern. Inc., (Japan) 38, 546B, 1935.
22.
B. E. Dixon and A.A. W. Russel. "Absorption of Carbon Dioxide by
Liquid Drops," J. Soc. Chem. Ind., (London) ~, 284, 1950.
23.
B. E. Dixon and J.E.L. Swallow. "Use of Liquid Films in the Study of
Absorption of Gases by Drops," J. App1. Chem., i, 86, 1959.
24.
R. R. Hughes and E. R. Gilliland.
Ser.,2!, 16, 1955.
"The Mechanics of Drops," CEP Symp.
25.
K. Shabalin. "Absorption of Gas by a Drop of Liquid," Zhur. Prik1.
Khim., Leningr., 13, 412, 1940.
26.
A. Guyer, B. Tobler and R. H. Farmer.
cation," Chem. Fabrik., ~, 5, 1936.
"The Principles of Degasifi-
27-
F. Goodridge. "Kinetic Studies in Gas-Liquid Systems, I," Trans. Far.
Soc., 51, 1703, 1955.
28.
F. Goodridge. "Kinetic Studies in Gas-Liquid Systems, II," Trans.
Far. Soc., 49, 1324, 1953.
-96-
-------
29.
H. F. Johnstone and G. C. Williams.
Droplets," 1. E. C., l!., 993, 1939.
30.
W. G. Whitman, L. Long and H. Y. Wang:
Liquid Drop," 1.E.C., 18, 361, 1926.
-97-
"Absorption of Gases by Liquid
"Absorption of Gases by a
-------
APPENDIX A
TABULATIONS OF MEASURED
S02 CONCENTRATIONS IN PRECIPITATION
-99-
-------
TABLE A.l
PRECIPITATION SAMPLE S02 CONCENTRATION RUN 1
-1 9
(Values are in units of moles cc x 10 )
EAS T GRID
Arc B Sampler No. Arc C
.76 14 .16
~72 15 .44
1.36 16 .60
1. 24 17 .32
.76 18 .32
1.40 19 .48
.42 20 0
1. 20 21 .16
.40 22 .28
.92 23 .20
1. 84 24 .20
1. 04 25 .12
1.44 26 0
1. 68 27 .04
1.08 28 .12
1.12 29
1.08 30 .20
WEST GRID
Arc B
Sampler No.
Arc C
.16
.24
20
23
-101-
-------
TABLE A.2
PRECIPITATION SAMPLE S02 CONCENTRATION RUN 2
-1 9
(Values are in units of moles cc x 10 )
EAST GRID
Arc B
Sampler No.
Arc C
4.00
1. 42
4.26
4.53
3.42
4.71
10.35
4.22
2.31
21
22
23
24
25
26
27
28
29
10.44
14.57
15.94
22.60
18.34
6.62
18.66
WEST GRID
Arc B Sampler No. Arc C
14 .28
.19 17 .64
.23 20 .28
o 23 0
.24 24 0
.54 25 1. 70
.22 26 2.42
o 27 .90
o 28 .18
.20 29 .69
.10 30 .44
o 31 .21
.32 32 .20
o 33 .24
.36 34
.45 35
.19 36
-102-
-------
TABLE A.3
PRECIPITATION SAMPLE S02 CONCENTRATION RUN 3
-1 9
(Values are in units of moles cc x 10 )
EAST GRID
Special
Arc
Sampler No.
27.1
34.4
29.1
26.1
43.6
33.7
32.75
31.35
26.3
22.55
22.3
24.15
20.7
10.25
7.93
8.64
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
WEST GRID
Special
Arc
Sampler No.
8.86
23.9
39.8
51.3
40.5
22.7
13.4
3.69
7
8
9
. 10
11
12
13
14
-103-
-------
TABLE A.4
PRECIPITATION SAMPLE S02 CONCENTRATION RUN 4
-1 9
(Values are in units of moles cc x 10 )
EAST GRID
Arc B
Sampler No.
Arc C
1.07
6.94
6.65
9.90
11.3
24.6
36.2
33.0
28.5
15.6
26.1
18.5
12.2
2.78
13
14
15
16
17
18
19
20
21
22
23
24
25
26
2.98
8.51
14.2
27.6
28.8
18.8
15.7
19.1
6.81
WEST GRID
Arc B Sampler No. Arc C
4.79 17 .23
6.89 18 .55
11.11 19 4.06
19.96 20 9.66
18.25 21 10.00
13.66 22 10.31
8.64 23 9.56
3.62 24 3.06
25 .63
-104-
-------
TABLE A.5
PRECIPITATION SAMPLE S02 CONCENTRATION RUN 5
(Values are in units of moles cc-1 x 109)
EAST GRID
Arc B Sampler No. Arc C
16.1 19 2.74
37.4 20 30.3
58.6 21 41.1
56.5 22 31. 9
28.8 23 15.5
14.4 24
.83 25
WEST GRID
Arc B Sampler No. Arc C
17 .20
20 .62
2.53 21 3.31
.23 22 .22
.19 23 .78
.20 24 missing
.47 25 .22
.23 26 .58
.19 29
.47 32
--105-
-------
TABLE A.6
PRECIPITATION SAMPLE S02 CONCENTRATION RUN 6
-1 9
(Values are in units of moles cc x 10 )
EAST GRID
Arc B Sampler No. Arc C
.46 14 0
.30 17 .12
o 20 0
o 21 0
.45 22 0
o 23 .17
o 24 0
o 25 0
o 26 .13
o 29 .22
.084 32 0
o 35 0
WEST GRID
Arc B Sampler No. Arc C
7.72 21 3.58
14.9 22 13.8
19.2 23 17.8
16.25 24 32.2
18.3 25 13.6
26
-106-
-------
TABLE A. 7
PRECIPITATION SAMPLE S02 CONCENTRATION RUN 7
-1 9
(Values are in units of moles cc x 10 )
EAST GRID
Arc B Sampler No. Arc C
27 2.04
1.00 28 3.60
4.25 29 5.43
13.0 30 14.0
17.1 31 16.1
16.0 32 17.1
14.8 33 9.87
5.65 34 6.50
WEST GRID
Arc B Sampler No. Arc C
5.98 28
19.5 29 8.24
21. 5 30 22.7
43.8 31 26.0
49.4 32 31.4
58.8 33 33.8
36.5 34 17.4
38.4 35 10.7
1. 20 36
-107-
-------
TABLE A.8
PRECIPITATION SAMPLE S02 CONCENTRATION RUN 8
-1 9
(Values are in units of moles cc x 10 )
EAST GRID
Arc A Sampler No. Arc C
0.9 17 0
0.7 18 0.5
3.5 19 9.3
16.1 20 10.8
30.8 21 26.9
32.3 22 50.2
56.7 23 46.7
48.4 24 66.8
54.0 25 74.9
54.5 26 61.0
50.1 27 25.7
22.4 28
WEST GRID
Arc A
Sampler No.
Arc C
-108-
-------
TABLE A.9
PRECIPITATION SAMPLE 802 CONCENTRATION RUN 9
-1 9
(Values are in units of moles cc x 10 )
EAST GRID
Arc A Sampler No. Arc B
.63 26 .86
3.40 27 5.02
9.70 28 12.4
28.2 29 16.5
34.5 30 27.2
27.5 31 26.1
13.0 32 18.6
9.72 33 15.4
34 2.37
35
WEST GRID
Arc A Sampler No. Arc B
3.40 28
9.52 29 6.43
11. 4 30 4.71
7.58 31 5.98
1. 64 32 6.45
1.19 33 2.21
--109-
-------
APPENDIX B
RESULTS OF PEAK-TO-MEAN ANALYSIS
Plots of measured concentrations (vertical bars) versus those predicted
from peak-to-mean analysis (dots).
-111-
-------
ARC C
16
CT\
<=>
x 12
.
I
U
U
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<=>
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V)
ARC B
.
4 . .
. .
2
. .
. .
0
310 320 330 340 350 0 010 020
AZIMUTH ANGLE. DEGREES
Figure B.l Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run IE.
-113-
-------
ARC C
16
.
. .
0'>
0
X
I 1 2
u . .
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N ARC B
o
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4
.
. .
. .
. .
. .
0
310 320 330 340 350 0 010 020
AZIMUTH ANGLE, DEGREES
Figure B.2 Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run lW.
-114-
-------
'"
0 1 2
x
I
U
u 8
I
f.I1
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.
I .
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20
16
6
2
340
10
20
30
350
o
Figure B.3
AZIMUTH ANGLE, DEGREES
Comparison of Observed Values with Those
by the Peak-to-Mean Analysis Run 2E.
Predicted
-115-
-------
ARC C
.
. .
6
0'>
a
x
.
I
U
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u
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a
VJ
.
. .
2 .
.
.
.
0
350 0 010 020 030 040 050 060
AZIMUTH ANGLE, DEGREES
Figure B.4 Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run 2W.
-116-
-------
0'1
a
x
I
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U
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w
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a
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60
40
20
o
40
20
o
165
Figure B.5
EAST GRID
1.
.
.
.
.
.
.
WEST GRID
I
.
.
170
185
190
195
200
205
175
180
AZIMUTH ANGLE, DEGREES
Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run 3.
.-117-
-------
0'1
0
>< 20
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I
U
U
I
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W
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.
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.
I-
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20
o
300
310
010
320
330
340
350
360
Figure B.6
AZIMUTH ANGLE, DEGREES
Comparison of Observed Values with Those
by the Peak-to-Mean Analysis Run 4E.
Predicted
-118-
-------
0">
a
>< 10
I
U
U
,
V1
L.U
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a
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-
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. .
.
. .
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o
300
340
350
o
010
330
Figure B.7
AZIMUTH ANGLE, DEGREES
Comparison of Observed Values with Those
by the Peak-to-Mean Analysis Run 4W.
Predicted
-119-
-------
20
0"1
0
><
.....
I
U
U
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-
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. .
-
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~ . .
. .
.....
I I
o
330
340
350
o
010
020
Figure B.B
AZIMUTH ANGLE. DEGREES
Comparison of Observed Values with Those
by the Peak-to-Mean Analysis Run 5E.
Predicted
-120-
-------
0'1
a
x
I
U
U
I 10
V)
W
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.
.
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.
I I . . . . . . I I I
o
320
020
060
330
o
040
340
350
Figure B.9
AZIMUTH ANGLE. DEGREES
Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run SW.
-121-
-------
20
a'o
a
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.
. ~
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-
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10
o
340
350
o
010
020
Figure B.10
AZIMUTH ANGLE, DEGREES
Comparison of Observed Values with Those
by the Peak-to-Mean Analysis Run 6W.
Predicted
-122-
-------
0'1
C>
x 10
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o
010
030
040
020
Figure B.ll
AZIMUTH ANGLE, DEGREES
Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run 7E.
-123-
-------
0'1
a
x 20
.--
I
U
U
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. .
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20
o
010
020
030
040
050
060
Figure B.12
AZIMUTH ANGLE, DEGREES
Comparison of Observed Values with Those
by the Peak-to-Mean Analysis Run 7W.
Predicted
-124-
-------
ARC C
80
I
C'\ I .
a I
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X
I I
u . .
u 40
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ex:
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w
u
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a
(J')
20
.
.
330 340 350 0 010
Figure B.B
AZIMUTH ANGLE, DEGREES
Comparison of Observed Values with Those
by the Peak-to-Mean Analysis Run 8E.
Predicted
-125-
-------
ARC C
0"1 80 -
0
X
I -
U
U
I
V1
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0
u
N
0 I-
V1
20
-
1 1 1 1 1 1
330 340 350 0 010 020
AZIMUTH ANGLE, DEGREES
Figure B.14 Comparison of Observed Values with Those Predicted
by the Peak-to-Mean Analysis Run aw.
-126-
-------
40
0'1
a
x
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U
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ARC A
-
-
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I - .
o
o
040
010
020
030
Figure B.15
AZIMUTH ANGLE, DEGREES
Comparison of Observed Values with Those
by the Peak-to-Mean Analysis Run 9E.
Predicted
-127-
-------
C'>
a
x 4
I
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f--
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8 8
8 8
~
8
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~
I-
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-
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8-8-8-8-8-8
4
o
010
020
030
040
050
Figure B.l6
AZIMUTH ANGLE, DEGREES
Comparison of Observed Values with Those
by the Peak-to-Mean Analysis Run 9W.
Predicted
-128-
-------
APPENDIX C
COHPARISONS OF MEASURED WASHOUT CONCENTRATIONS
WITH PREDICTIONS BY THE NONLINEAR, NON FEEDBACK MODEL
-129-
-------
80
H
Q
U
RUN lE ARC C
21.3 M
0.0417 MOLES/SEe
5.2 M/SEC
.
EQUILIBRIUM
GAS-PHASE CONTROLLED
STAGNANT DROP
10 METERS
--
I.........J
60
40
.
0'>
0
x 20
. .
u
u
-.
V)
LLI . .
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A
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0 RUN lE ARC B
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r-
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a::
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LLI
W
:z
0
w
60
. .
40
o
.
.
20
.
.
. .
Figure C.1
CROSSWIND DISTANCE BENEATH PLUME
Predictions of Nonlinear Model for Run IE
-131-
-------
80
0'\
0
x 20
u
u
.......
V)
W
-I
0
::E: 0
Z
0
......
I-
«
et:
I-
Z 80
w
u
Z
0
u
60
60
40
40
20
o
H
Q
U
RUN 1 W ARC C
21 .3 M
0.0512 MOLES/SEC
4.3 M/SEC
EQUILIBRIUM
GAS-PHASE CONTROLLED
- - STAGNANT DROP
L....-...J 10M E TE R S
.
/:\
. .
.
/..---..'"
/ "-
--/ '--
.
.
RUN 1 W
ARC B
Figure C.2
.
.
.
.
.
.
.
CROSSWIND DISTANCE BENEATH PLUME
Predictions of Nonlinear 110del for ~.un lW
-132-
-------
80
RUN 2E ARC C
H = 16.8 M
Q = 0.0943 MOLES/SEC
U = 6.2 M/SEC
EQUILIBRIUM
GAS-PHASE CONTROLLED
--- --- STAGNANT DROP
~ 10 METERS
.
60
I~\
40 / \
0\ / \
0 . / \ .
x 20
u / \
u . .
.......
V)
L.LI
...J .
0
::E: 0
Z
0
f- RUN 2E ARC B
~
cr::
f-
~ 80
u
z
0
u
60
40
20
o
.
.
Figure. C. 3
CROSSWIND DISTANCE BENEATH PLUME
fre.dictions of Nonlinear Model for Run 2E
-133-
-------
RUN 2W ARC C
H=16.8M
Q = 0.0063 MOLES/SEC
U = 5.4 M/SEC
EQU I LI BRI UM
GAS-PHASE CONTROLLED
- - STAGNANT DROP
~ 10 METERS
.
80
60
40
0\
0
x 20 .,...........-...
u
u . .
.......
V> . .
W
....J . .
o . .
::E 0
z:
0 RUN nJ ARC B
I-
-------
0-
o
x
u
u
......
V1
W
--'
o
::E
z
o
~
<:(
0::
~
Z
W
U
Z
o
U
EQUILIBRIUM
GAS-PHASE CONTROLLED
--- --- STAGNANT DROP
~ 10 METERS
90
H
Q
U
RUN 3E
21. 3 M
0.0493 MOLES/SEC
5.4 M/SEC
.
80
70
60
.
.
.
.
.
.
.
.
50
.
.
.
40
30
-
-
20
,,-
-
",..
..........
........
"
10
"
o
CROSSWIND DISTANCE BENEATH PLUME
Figure C. 5
Predictions of Nonlinear Model for Run 3E
-135-
.
.
.......
-------
200
180
H
Q
U
RUN 3W
12.2 M
0.0487 MOLES/SEC
4.9 M/SEC
160
140
0'1
0 120
~
x
u
u
.......
(,/)
I..LJ
-I 100
0
::IE:
z
0
t-
c(
a:
t- 80
z
I..LJ
U
Z
0
u (\
60
I \
40
20
.
o
o
EQUILIBRIUM
GAS-PHASE CONTROLLED
- - STAGNANT DROP
L...-...I 10M E TE R S
.
\
Figure C. 6
CROSSWIND DISTANCE BENEATH PLUME
Predictions of Nonlinear Model for Run 3W
-136-
-------
80
RUN 4E ARC C
H=12.2M
Q = 0.0487 MOLES/SEC
U = 2.2 M/SEC .
.
. . .
.
.
.
. EQUILIBRIUM
GAS-PHASE CONTROLLED.
-- STAGNANT DROP
~ 10 METERS .
.
.
60
.
40
0'1
0
>< 20
u
u
......
t/')
LLI
...J
a
~
z:
0
I--
-------
80
RUN 4W ARC C
H 30.5 M
Q - 0.0532 MOLES/SEC
U 2.4 M/SEC
.
EQUILIBRIUM
GAS-PHASE CONTROLLED
- - STAGNANT DROP
L--I 10 METERS
60
.
.
.
.
.
.
.
40
.
.
a'I
o
.
x
20
.
.
.
u
u
.......
VI
.....
...J
o
:E:
-----
-----~ ---
----- -.........."-.
o
z:
o
I-
-------
. .
RUN 5E ARC C
H 7.62 M
U = 5.5 M/SEC
80 . .
. EQUILIBRIUM
GAS-PHASE CONTROLLED
-- STAGNANT DROP
60 L..--J 10 METERS
. .
40 . .
0'1
o
. .
x 20
u
u
........ . .
V')
.......
.oJ
0
~ 0
z
0 RUN 5E ARC B
I-
c(
c::
I-
z 80
.......
u . .
z
0
u
60
. .
40
. .
20
. .
. .
. .
0
CROSSWIND DISTANCE BENEATH PLUMf
Figure C.9 Predictions of Nonlinear Model for Run SE
-139-
-------
RUN 5W ARC C
H=16.8M
Q = 0.0540 MOLES/SEC
U = 6.3 M/SEC
.
EQUILIBRIUM
GAS-PHASE CONTROLLED
STAGNANT DROP
10 METERS
--
80
L.....-...J
.
60 . .
. .
40
. .
0\ . .
O
x 20
u . .
u
......
V) .
UJ .
-J
0
::E 0
.
z
0 RUN 5W ARC B
.....
I-
co::
ex:
I-
z 80
UJ
u
z
0
u
60
o
.
.
40
20
.
.
.
.
.
CROSSWIND DISTANCE BENEATH PLUME
Figure C.10
Predictions of Nonlinear Model for Run SW
-140-
-------
RUN 6E ARC C
H = 12.2 M
Q = 0.0095 MOLES/SEC
U = 7.6 M/SEC
EQUILIBRIUM
GAS-PHASE CONTROLLED
- - STAGNANT DROP
~ 10 METERS
.
80
60
40
.
. .
0'1
a
20 . .
x
u
u
........ . .
V)
I..LI
--J
o . .
::E 0
z: RUN 6E ARC B
a
I-
c:(
C<:
I-
z: 80
I..LI
U
z:
a
u
60
40
.
20
.
.
.
.
.
.
.
.
o
Figure. C. 11
tROSSWIND DISTANCE BENEATH PLUME
Predictions of Nonlinear Model for Run 6E
-141-
-------
80
60
40
0'1
C>
x
u
u
.......
V)
W
...J
C>
::IE:
z:
C>
I-
ex:
et:
I-
z:
w
u
z:
o
u
80
40
RUN 6W ARC C
H=12.2M
Q = 0.0542 MOLES/SEC
U . 7.0 M/SEC
.
20
.
.
.
o
RUN 6W
ARC B
60
20
.
o
.
[Q U I LI B R I U M
GAS-PHASE CONTROLLED
- - STAGNANT DROP
L........-I 10M E TE R S
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Figure C.12
CROSSWIND DISTANCE BENEATH PLUME
Predictions of Nonlinear Model for Run 6W
-142-
-------
100
RUN 7E ARC C
H 6.4 M
Q = 0.0270 MOLES/SEC
U = 6.4 M/SEC
EQUILIBRIUM
GAS-PHASE CONTROLLED
- - ST AGNANT DROP
~ 10 METERS
.
80
60
.
. .
40 . .
. .
0'1
o
. .
x 20
u . .
u
........
(/') .
L.IJ .
-'
0
::;:
0
z:
0
I- RUN 7E ARC B
ex:
ex:
I-
z
L.IJ 80
u
z
0
u
60
40
o
.
.
20
.
.
.
.
.
.
.
CROSSWIND DISTANCE BENEATH PLUME
Figure. C.13
Pre.dictions of Non1ine.ar Mode.l for Run 7E
-143-
-------
100
RUN 7W ARC C . EQUILIBRIUM
H = 7.6 M GAS-PHASE CONTROLLED
80 Q = 0.0303 MOLES/SEC -- STAGNANT DROP
U - 5.9 M/SEC '-----' 10 METERS
.
. .
60
. .
. .
40
. .
. .
0\
a
x 20 . .
u
u
........
In
W
-'
a
:::;: 0
z
a RUN 7W ARC B
......
I-
c(
c::: .
I- . .
z 80
w
u
:z: .
a .
u
. .
60
. .
40 . .
. .
20 . .
. .
. .
. .
o
CROSSWIND DISTANCE BENEATH PLUME
Figure C.14 Predictions of Nonlinear Model for Run 7W
-144-
-------
CTI
0
X
U
U
........
V)
U.J
-'
0
:E 0
z
o
f-
e:(
cr:
f-
~ 200
<..>
z
C>
<..>
200
100
100
RUN 8E ARC C
H = 7.62 M
Q = 0.0816 MOLES/SEC
U = 3.5 M/SEC
EQUILIBRIUM
GAS-PHASE CONTROLLED
- - STAGNANT DROP
L...-.-J 10 METE RS
.
.
.
.
.
.
.
.
.
.
.
.
.
RUN 8E
ARC A
f\
t~
.
.
.
.
.
.
o
CROSSWIND DISTANCE BENEATH PLUME
Figure C. 15
Predictions of Nonlinear Model for Run 8E
-145-
-------
200
100
0'1
o
x
u
u
.......
VJ
\..U
-I
o
::E
:z:
o
.....
f-
-------
200
100
0\
o
x
u
u
'-
V)
W
....J
C>
::E
z
C>
......
t-
c:x:
ex:
t-
z
w
u
z
C>
u
200
100
RUN 9E ARC B
H=12.2M
Q = 0.0442 MOLES/SEC
U = 3.0 M/SEC
EQUILIBRIUM
GAS-PHASE CONTROLLED
--- --- STAGNANT DROP
L--J 10 METERS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
o
RUN 9E
ARC A
o
CROSSWIND DISTANCE BENEATH PLUME
Figure C .17
Predictions of Nonlinear Model for Run 9E
-147-
-------
200
RUN 9W ARC B
H=12.2M
Q = 0.0097 MOLES/SEC
U = 3.2 M/SEC
EQUILIBRIUM
GAS-PHASE CONTROLLED
--- -- STAGNANT DROP
L.........-J 10M E TE R S
.
100
en
0
x
u
u
.......
V')
UJ .
-' . .
o . .
::E 0
:z RUN 9W ARC A
o
I-
~
cr:
I-
:z 200
UJ
u
:z
0
u
100
o
Figure C.18
CROSSWIND DISTANCE BENEATH PLUME
Predictions of Nonlinear Model for Run 9W
-148-
------- |