POTENTIAL
DISPERSION
OF PLU MES
FROM L ARC E
POWER PLANTS
-------
POTENTIAL DISPERSION
OF PLUMES
FROM LARGE POWER PLANTS
Francis Pooler, Jr.
U.S. Weather Bureau Research Station
Robert A. Taft Sanitary Engineering Center
U. S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFARE
Public Health Service
Division of Air Pollution
Cincinnati, Ohio
1965
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Public Health Service Publication No. 999-AP-16
GPO 822-190-2
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ABSTRACT
Expected ground-level concentrations resulting from emissions
from large power plants are discussed for three meteorological
situations considered to be most likely to result in significant air
pollution concentrations. These situations are (1) high wind; (Z) in-
version breakup; and (3) limited mixing layer with a light wind.
Effects of increasing stack height are discussed for each situation.
Numerical examples based on calculations included as an appendix
are shown.
-------
POTENTIAL DISPERSION OF PLUMES
FROM LARGE POWER PLANTS
Dispersion of effluent from large power-generating plants must be
considered on the basis of individual plants. Although diffusion formulae
for comparatively small sources have been at least partially checked
against actual dispersion, similar extrapolations from existing data
probably cannot be applied to estimates of pollutant emissions from plants
in the range of 1000- to 5000-megawatts capacity. Plants of such sizes
emit heat at a rate equivalent to the net heating by the sun over an area
many hundreds or thousands of meters in diameter; it is evident that
such a source •will set up its own circulation pattern in the air, at least
in the immediate vicinity of the plant. Most of the time the effluent plume
will rise far above the ground, and its only influence on air quality will
be to increase the surface concentrations of pollutants in the air mass
downwind by some rather small amount. If significant background pol-
lution levels exist, however, even a small addition to the background
concentration could introduce a pollution problem.
It is assumed that any new plant -will be designed to meet two en-
gineering criteria to prevent pollution in the immediate vicinity of the
plant. First, the stacks will be tall enough to prevent aerodynamic
downwash caused by large obstacles to the air flow. This criterion can
be met by following the "2-1/2" rule, which states that a stack should be
at least 2-1/2 times the height of any nearby obstacles to the flow. Be-
cause a large power plant requires a large building, the minimum stack
height imposed by this criterion alone will be several hundred feet. Sec-
ond, the exit speed of gases from the stack and designof the chimney top
should be adequate to prevent entrainment of effluent into the turbulent
wake of the stack. Generally, an exit speed in excess of the wind speed
will minimize this problem. Since both criteria evolve from aerodynamic:
considerations, the adequacy of the plant design can be tested by -wind-
tunnel models.
If it is assumed that these engineering criteria are met, then es-
timating potential pollution from large plants narrows to a consideration
of relatively infrequent weather conditions (conditions that do occur,
however) that can bringabout ground-level fumigations: high winds, in-
version breakup, and a limited mixing layer with light winds. The fre-
quency of these adverse conditions will determine the magnitude and
frequency of the potential pollution.
The following discuss ion of these threetypesof fumigation is illus-
trated numerically in Figures 1 through 3. The calculations on which
these figures are based are included as an appendix. The models of
plume dispersion used werp based on the experience of and data col-
lected by TVA personnel (.Gartrellet al. 1964), as well as on the author' s
personal observationof the behavior of plumes .from large heat sources.
These models were first used in conjunction with climatological data
1
-------
of the Oak Ridge, Tennessee, area (Holland, 1953) as an informal cross-
check on calculations then being made by TVA personnel to determine
the stack height required for a proposed new generating plant (Thomas
et al. , 1963). The conclusions regarding required stack height were
the same for both methods of calculation. The exact assumptions used
to obtain the numerical values shown by the figures are not critical in
this discussion; the principal purpose here is to suggest the meteorolog-
ical factors that influence dispersion and should be considered in loca-
tion and design of large power plants.
HIGH-WIND FUMIGATION (Figure 1)
High-wind fumigation occurs when the dilution of effluent by mo-
tions in the air--longitudinal dilution due directly to wind speed, and
transverse dilution by eddies, the magnitude of which is a function of
•wind speed--is sufficient to overcome the tendency for a heated plume
to accelerate upward as the result of buoyancy forces. With sufficiently
rapid dilution, the plume continuously decelerates vertically, and an ef-
fective plume rise can be computed. The larger the source, the greater
the wind speed necessary to cause this vertical deceleration throughout
the entire plume volume. Although a precise relationship between plant
5000-Mw PLANT
0.06 0.08 .0.10
059 '0.100 0132 X 0.157
0. 62 / 0115 / 0 161 /O 201
I
O
UJ
I
u
400
0|0 0.20 0.30 0.40
I
I 0.10 I'015
5 10 15 20
WIND SPEED, meters/sec
0 5 10 15 20
WIND SPEED, meters/sec
Figure 1,
Estimated ground-level SC>2 concentrations (ppm) in high-wind, neutral
stability conditions. (Sulfur content of coal is assumed to be 1%; for
other sulfur contents, value would be changed proportionately. Values
represent 1/2 hour averages. To approximate 3-minute average, multi-
ply by 2.5; to approximate 2-hour average, multiply by 0.5.)
POTENTIAL DISPERSION OF PLUMES
-------
capacity and this "critical" wind speed is not known, it is probable that
the critical speed for a 1000-Mw plant would be about 25 mph (13
meters/sec), and for a 5000-Mw plant, about 40 mph (20 meters/sec),
if all emissions are assumed to come from a single stack. At wind
speeds less than critical, an increasing proportion of the plume should
rise at a. rate determined principally by buoyancy forces; the dilution
of this part of the plume is determined by its upward motion as much
as by ambient turbulence. Plume rise with such a divergent plume
is difficult to define, and the concept of a coherent plume should
probably be discarded in favor of a formulation in which the stabilized
portion of the plume is considered, rather than the rising portion.
The particular f o r mu la t i o n s for "plume rise" and plume dispersion
were selected only because they are widely used; the numerical
results probably do show reasonable trends, even though they should
be valid, if at all, only for wind speeds in excess of "critical. " The
implicationis that for plants of large enough capacity, the concentrations
in a high-wind fumigation probably depend only on stack height and emis-
sion conditions, and thus maximum concentrations froma 5000-Mw plant
would be only slightly above those from a. 1000-Mw plant (with all emis-
sions from a single stack).
INVERSION-BREAKUP FUMIGATION (Figure 2)
Although inversion-breakup fumigation is likely to produce the
highest concentrations at ground level, the area fumigated is likely to
be_.a long, narrow ribbon-like formation with its closest point a num-
ber of miles away; therefore, the chances of detecting fumigations of
this type are very slight unless the same area is fumigated repeatedly
because of topographic restraints. This type of fumigation occurs when
effluent is emitted into a stable layer so that the plume moves off as an
elevated flat ribbon. A surface-based mixing layer subsequently de-
velops, builds up to include the plume, and stirs the effluent down to
ground level. The resultant ground-level concentration is inversely
proportional to plume height, horizontal spread, and wind speed at plume
height. The plume rise above the top of the stack is determined by the
wind speed and the degree of stability in the inversion layer. Since wind
speed generally increases through this layer while intensity of the inver-
sion decreases, these factors tend to counteract each other so thatplume
rise is not strongly dependent on stack height; thus increasing the stack
height increases height of the plume above the ground by a like amount.
With a taller stack, the plume is likely to be transported away by a strong-
er flow, and the horizontal spread of the plume will be greater because
a longer time is required for the mixing layer to develop to plume height.
Thus, tall stacks are fully as important for minimizing this kind of fumi-
gation as for a high-wind fumigation. In addition, since the plume from
a sufficiently tall stack may rise above the top of a nocturnal inversion,
the frequency of inversion-breakup fumigations is reduced with taller
stacks. Under inversion conditions an increase of plant size will result
ina proportionately smaller increase of plume rise than under high-wind
conditions; thus, the maximum concentrations should increase as plant
capacity is increased, but at a less than linear rate.
FROM LARGE POWER PLANTS
-------
o-
LLJ
X
< 400
0 50 040 0.30
0.60
\
_L
0 25 50 7.5 100 [25
WIND SPEED, meters/sec
WIND SPEED, meters/sec
Figure 2. Estimated ground-level SC>2 concentrations ( ppm) in inversion-breakup
fumigation. (Sulfur content of coal is assumed to be 1%; for other sul-
fur contents, values would be changed proportionately. Values repre-
sent 1/2- to 1-hour averages.)
FUMIGATION IN A LIMITED MIXING LAYER
WITH LIGHT WINDS (Figure 3)
Fumigation in. a limited mixing layer with light •winds occurs when
effluent is contained within too small a mixing volume. Under these cir-
cumstances, the plume will rise to the top of the surface-based mixing
layer (up to the base of the inversion), which may be up to thousands of
feet deep, and then diffuse and subside to ground level at a rate deter-
mined bythe rate of convective overturning brought about by solar heat-
ing of the ground. Stack height has essentially no effect on fumigations
of this kind. The ground-level concentration after some time will be
given by emission rate divided, by the product of mixing height, mean
wind speed, and cross-wind spread. The time after which such a com-
putation becomes meaningful is that required for the effluent to mix and
subside to ground level. With a relatively small plant, this subsidence
begins almost immediately after the plume has risen to the top of the
mixing, layer; with increasing plant size, a greater fraction of the plume
will still be warmer and therefore less dense than the air through which
it rose, and thus will stabilize at some short distance above the mixing
POTENTIAL DISPERSION OF PLUMES
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§
o
M
hd
O
3
H
fO
TJ
H
en
2500 -
ID
2000
o
>
z
o
o
1000
500
0
1 I
1000 -Mw PLANT
0.30 \\ \\
\ .0227 X.O.C
~ 0.70
^.0.362 +0226 ^.0.159
V 0.15
L20
I
_I.Op9 \ \+0.480 \0.305
n635\ 10.416
\ > '
1.40 |VDO °'80 O-60 "0.50
I I
2 3 4
WIND SPEED, meters/sec
0
234
WIND SPEED, meters/sec
'Figure'3. Estimated gr o u n d-l e v e I SC>2 concentrations ( ppm) in lightrwind, limited-mixing-
depth conditions. (Sulfur content of coal is assumed to be 1%; for other sulfur con-
tents, values would be changed proportionately. Values represent 1/2- to 1-hour
averages. To approximate 3-minute average, multiply by 1.75; to approximate 2- to
3-hour average, multiply by 0,75.)
-------
layer or within the capping stable layer. The plume will be released in-
to the mixing layer as that layer develops greater depth, thus introducing
a time-delay factor, which increases with increasing plant size. Incon-
sequence, the maximum ground-level concentration with this kind of
fumigation increases with plant size at a less than linear rate, but the
area fumigated increases in direct proportion to plant size.
The experience of the TVA with their many steam-generating
plants illustrates some of these situations. As plants of increasingly
larger capacity have been built, -with correspondingly taller stacks, the
fumigations have shifted from the high-wind type, with which many people
are most familiar, to the light-wind type. Although tall stacks can be
built to minimize the high-wind and inversion-breakup fumigations, the
total pollution discharge of the larger plants becomes a problem when
the limited capacity of the mixing layer prevents adequate dilution. Thus,
the other element that determines concentrations, the pollutant source
strength, must be controlled if such large plants are to be built in parts
of the country where this type of fumigation occurs with any appreciable
frequency. Although conditions of this type are most frequent in Southern
California, no section of the country can consider itself immune from
such problems if the pollution sources are present.
LOCAL EFFECTS
Local factors may exert some influence on each of these types of
fumigation. Since large power plants are built adjacent to sources of
cooling water, there are invariably some topographic complications that
must be considered. With both high-wind and inversion-breakup fumiga-
tions, the more elevated points in the areas affected will experience
higher concentrations than would be found over flat terrain. For the
high-wind fumigation comparatively large-scale topographic features,
such as a small mountain upwind or an extensive water s.urface down-
wind, can create a mean downflow that lowers the plume as it moves
downwind. For the inversion-breakup fumigation, large-scale channel-
ling such as found with the Trail, B.C., smelter (Hewsonand Gill, 1944)
may confine the plume to a selected path and lead to repeated local fumi-
gations. In other areas a stable layer may flow over a much warmer
region, e.g., from water to land in the summer or from the outskirts
of a large city over the city itself, and lead to an inversion-breakup
fumigation because of a spatial transition of the flow. For the light-
wind fumigation a. large, cool surface, such as a lake, will always be a
favored region for subsidence, so that the downwind shore may experi-
ence more frequent and severe fumigations than any surrounding areas.
The dispersionpotential fora large power plant must be calculated
from a consideration of the locale into which the plant is to be fitted,
and thus the details of location and design must be treated individually.
Meteorological control of plant operations may be required when poten-
tial pollution cannot be minimized by any other methods.
POTENTIAL DISPERSION OF PLUMES
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APPENDIX
Formulae and Numerical Values Used
in Calculating Maximum Ground-Level Concentrations
(All symbols and numerical values are listed and defined in Table Al. )
Atmospheric pressure of 1000 mb and temperature of 15°C were
assumed for all calculations. The emission rate of heat to the atmos-
phere was assumed to be 15 percent of the plant generating capacity,
with an emission temperature of 140°C and a stack efflux speed of 20
meters per second. From mass continuity with these assumptions, the
stack diameter for a 1000-Mw plant is 9.565 meters. With an assumed
coal consumption rate of 3,83 tons per hour for a 1000-Mw plant, with
full conversion of the sulfur to SO2 and its emission to the atmosphere,
the SO2 emission rate is 1. 932 x 10^ p grams per second. For a 5000-
Mw plant, the heat and SO2 emission rates were multiplied by 5, and
the stack diameter by 5l/2 2.236. All calculations were for p 1 per-
cent; the concentrations shown in Figures 1, 2, and 3 should be multi-
plied by p for other sulfur contents.
HIGH WIND, NEUTRAL FUMIGATION (Figure 1)
Plume rise was calculated from Holland's formula,
1. 5Vsds + 0.409 x 10"4QH
u
and the maximum ground-level concentration from Button's equation,
2Q
Xm~'reuh2 "so2
Calculations were made for four -wind speeds 5, 10, 15, and 20
meters per second; and for three stack heights 200, 400, and 600
feet. Concentrations at intermediate values were obtained by graphi-
cal interpolation.
INVERSION BREAKUP FUMIGATION (Figure 2)
A formula for plume rise was developed from dimensional consid-
erations :
1/2
jApgdj vsTa
4p3. T- u(u + vs)
2
(3)
It was assumed that the effluent plume rises some distance through
the inversion layer and becomes stabilized with the .plume centerline a
distance Ah above the top of the stack. Thereafter, as the plume moves
downwind, it widens with downwind travel but the depth is constant. It
was assumed that the maximum ground-level concentration occurs when
the plume elements emitted at the time that a surface-based mixing layer.
-------
has developed just to stack-top level are later mixed to ground level as
the mixing layer builds up to plume level, resulting in the minimum time
after emission for plume travel within the inversion layer. It was as-
sumed that the mixing layer would have to develop to the top of the plume,
defined here as 2az above the plume centerline (see Figure Al). The
'i;VU- PLUME" CENTERLINE'.;
(B)
(A) Temperature profile at time of emission, (t = o)
(B) Temperature profile at time of fumigation, (t = tm)
Figure Al.
net amount of heating of the mixing layer required (proportional to the
area enclosed between curves A and B) is given by
-------
where xv =
2
i-n
at t 0. Values of C
y
0. 05'657 m
1/8
and n = 0.. 25
were assumed. Initial plume widths were represented by assuming
-------
stabilization above the inversion base of any plume element will be pro-
portional to the excess temperature of the element, and inversely pro-
portional to the stability of the layer. The maximum penetration AH will
thus be given by
The effluent will be uniformly distributed in the layer from H to (H + AH).
For the plume elements at (H + AH) to become re-incorporated into
the mixing layer, the mixing layer must increase in depth by an amount
AH, or the temperature of the mixing layer must be increased by Tm.
If AH is small compared to H, the required heating per unit area of sur-
face is given by
q = HpacpATm (9)
Also q = Rt . Hence,
16ZQH
R 7T3uHR
It was further assumed that, once released, the plume elements subside
and mix back to ground level according to a vertical velocity distribution
dz
dt 0.5+0. 00 Iz. Integrating, the subsidence time tg is given by
ts 1000 ln(l + 0. 002H) (11)
The maximum ground-level concentration -when the total plume is
stirred back to ground level is given by
["i Z-n
u(tr + ts) + xvj 2 ; values of Cy- 1.00m1'4, n= 0. 50
Z-n
were assumed, whence xv ("-u)1'^
Calculations of Xm were made for -wind speeds of 1, 2, 3, and 4
meters per second, and mixing layer depths of 500, 1000, 1500, and
2000 meters. Concentrations at intermediate values "were obtained by
graphical interpolation.
The maximum (centerline) ground-level concentrationXj. for a time
of travel t other than (tr + tg) as a fraction of the maximum concentra-
tion is given by
Xt = (t-tg) U(tr + tg) + Xy
Xm tr [ Ut + Xy J
Xt U(tr + tg) + Xy °"
Xm L ut + xv J
0. 75
for ts (tr + ts) (13b)
Xt 0 for t < ts (13c)
10 POTENTIAL DISPERSION OF PLUMES
-------
These equations could also be expressedinterms of distance
through the equality x ut. Togetherwith Equation (12), these equations
show that for a given set of meteorological conditions (u, H, and R), the
ground-level concentration initially increases with travel time t at the
same rate for all plant sizes; however, the larger the plant, the longer
the travel time over which ground-level concentration increases, and
hence the higher the maximum concentration.
TableAl. DEFINITIONS AND DIMENSIONAL UNITS OF SYMBOLS AND
NUMERICAL VALUES
Cp specific heat of air at constant pressure, 0.240 cal g °K" .
n
Cy horizontal diffusion coefficient, (meters)2.
ds stack diameter, meters.
e base of natural logarithms, 2.71828....
g acceleration of gravity, 9. 806 m sec .
h (=hs + Ah) plume height above ground, meters.
hg stack height, meters.
Ah plume rise, meters.
H depth of mixing layer, meters.
AH increase in depth of mixing layer, meters.
n dimensionless exponent related to distance-dependence of diffusion
rate.
p percentage sulfur in coal.
q net heating of an air column, cal m .
Q emission rate of SO2, g sec" .
QTT emission rate of heat, cal sec.
R net rate of sensible heating of an air column by solar radiation,
assumed constant equal to 0.4 Langleys min 66.67 cal m"^
sec" .
t travel time, seconds.
tm time required for mixing layer to develop to top of plume, seconds
(for inversion breakup).
tr time required for mixing layer to develop to topof plume, seconds
(for light wind).
ts time required for plume elements to descendfromtop of mixing
layer to the surface, seconds (for light wind).
Ta ambient air temperature, assumed constant at 15°C = 288. 16°K.
ATm maximum temperature difference b et w e e n plume elements and
surroundings, °C (for light wind).
u wind speed, m sec" .
vs stack exit speed, m sec .
FROM LARGE POWER PLANTS 11
-------
x travel distance, meters.
xv virtual travel distance to represent initial plume spread, meters.
6_6 vertical potential temperature gradient, °C m; assumed constant
6z at 1. 96 x 10~2 °C m"1 for inversion breakup.
TT constant, 3. 14159. . . .
"a ambient air density, assumed constant at 1.209 x 10 g m .
£p density difference between stack effluent and ambient air, assumed
constant at 0. 3658 x 103 g m"3.
*SO density of SC>2 at ambient conditions, assumed constant at 2. 671 x
10"3 g cm"3.
•jj vertical and crosswind standard deviations of plume distribution
at height H, meters (for light wind).
*y crosswind standard deviation of plume distribution, meters.
«TZ vertical standard deviation of plume distribution, meters.
\rn maximum ground level concentration, ppm (vol).
Xt centerline ground level concentration at travel time t, ppm (vol).
12
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REFERENCES
Gartrell, F. E. , Thomas, F. W. , Carpenter, S.B., Pooler, F. Jr.,
Turner, D. B. , and Leavitt, J.M. (1964) Full-Scale Study of Dis -
persion of Stack Gases A Summary Report. Tennessee Valley
Authority, Chattanooga, Tennessee.
Hewson, E. W. , and Gill, G. C. (1944). Meteorological Investigations
in Columbia River Valley near Trail. Part II of Report Submitted
to the Trail Smelter Arbitral Tribunal, U. S. Bureau of Mines
Bulletin 453. Government Printing Office, "Washington.
Holland, J. Z. (1953) A Meteorological Survey of the Oak Ridge Area,
ORO-99. U.S. Atomic Energy Commission, OakRidge, Tennes-
see.
Thomas, F. W. , Carpenter, S. B. , and Gartrell, F. E. (1963) Stacks-
How High? Journal of the Air Pollution Control Association 13:
198-204.
GPO 822—190—3 13
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BIBLIOGRAPHIC: Pooler, Francis Jr. Potential dis-
persion of plumes from large power plants.
PHS Publ. No. 999-AP-16. 1965. ,13pp.
ABSTRACT: Expected ground-level concentrations re-
sulting from emissions from large power plants
are discussed for three meteorological situations
considered to be most likely to result in signifi-
cant concentrations. These situations are (1) high
wind; (2) inversion breakup; and (3) limited mixing
layer with a. light wind. Effects of increasing
stack height are discussed for each situation.
Numerical examples based on calculations included
as an appendix are shown.
ACCESSION NO.
KEY WORDS:
BIBLIOGRAPHIC: Pooler, Francis Jr. Potential dis-
persion of plumes from large power plants.
PHS Publ. No. 999-AP-16. 1965. 13 pp.
ABSTRACT: Expected ground-level concentrations re-
sulting from emissions from large power plants
are discussed for three meteorological situations
considered to be most likely to result in signifi-
cant concentrations. These situations are (1) high
wind; (2) inversion breakup; and (3) limited mixing
layer with a light wind. Effects of increasing
stack height are discussed for each situation.
Numerical examples based on calculations included
as an appendix are shown.
BIBLIOGRAPHIC: Pooler, Francis Jr. Potential dis-
persion of plumes from large power plants.
PHS Publ. No. 999-AP-16. 1965. 13pp.
ABSTRACT: Expected ground-level concentrations re-
sulting from emissions from large power plants
are discussed for three meteorological situations
considered to be most likely to result in signifi-
cant concentrations. These situations are (1) high
wind; (2) inversion breakup; and (3) limited mixing
layer with a light wind. Effects of increasing
stack height are discussed for each situation.
Numerical examples based on calculations included
as an appendix are shown.
ACCESSION NO.
KEY WORDS:
ACCESSION NO.
KEY WORDS:
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