Transport and Dispersion of Air Pollutants

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CHAPTER 19 Transport and Dispersion of Air
Pollutants
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Wind Direction The direction of transport of
pollutants emitted from sources depends on wind
direction (WD). WD is the most important
parameter affecting dispersion of pollutants
particularly from point sources. It is also
important for dispersion from mobile sources, but
not as much as in the case of stationary point
sources.
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WD should be handled very carefully in the
models, because it is the only way to assess the
impacts of emissions from more than one source in
the study domain. In order to determine the
dispersion of pollutants we must be able to
assess how wind direction changes with altitude.
Because, meteorological measurements are
generally conducted at standard 10 m altitude.
But, pollutants are emitted and subsequently
transported at the top of the stack which can be
up to 300 m high.
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Wind direction change with altitude, which is
called wind shear. At the ground level, surface
friction cause the wind to turn clockwise with
altitude. This process is called veer. Beyond
certain altitude thermal structure (horizontal
temperature variations) dominates over the
friction. And the direction of the wind is
determined by this thermal structure. It is very
common that winds that shift clockwise due to
veer, shifts counterclockwise beyond a certain
altitude.
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Wind Speed Wind speed generally increase with
height. Most of the wind measurements are carried
out at 10 m standard altitude. But most of the
emissions occur at higher altitude (exact
altitude depends on the stack height).
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Wind at the stack height can be calculated using
the wind measurements at 10 m with the following
power relation. U(z) u(za) (z/za)p u(z) wind
speed at altitude z u(za) measurement height
(generally, but not necessarily 10 m) p exponent.
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The value of p is very important in wind
extrapolation. It generally takes values between
0.1 and 0.4 and depends on surface roughness,
stability of the atmosphere, and depth of the
layer. The value that is most widely used for p
is 1/7. (If you do not know anything about
surface roughness and stability use 1/7)
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Figure 19-1 shows measured and calculated (using
the above formula and 1/7 as the p) wind profiles
in different places in the USA. The general theme
of the figure is that measured and calculated
profiles do not always match well. This is
generally true for most of the calculations in
the atmosphere.
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The wind speed is important in atmospheric
dispersion, because it dilutes pollutants as soon
as they are emitted from the source. Figure 19-2
is a nice example. At wind speed of 6 m s-1 there
are 1 unit of pollutant between each line
(separated by 1 m). At wind speed of 2 m s-1
there are 3 units of pollutant. Dilution occurs
at the emission point. Because of this, in
modeling wind speeds calculated for the top of
the stack are used in calculations.
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• In addition to dilution, wind speed also effects
• Travel time between the source and receptor
  (double the wind speed half the time)
• Plume rise (higher the wind speed lower the
  plume rise)

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TURBULANCE Turbulence is the irregular motion of
the wind. Usually there is a mean wind flow and
these irregularities are superimposed onto that
flow. The irregularities which we call turbulence
are usually in the form of swirls and
eddies. Eddies are very important in the
plume-dilution process, because they move
pollutants outside the plume and brings fresh air
(unpolluted) into the plume.
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• Turbulence is generated by two mechanisms
• Mechanical turbulence is generated when wind
  passes around objects.
• Thermal turbulence is generated by the rising air
  parcel.
• Air close to the surface of the earth heated and
  rise. Colder air around these rising parcels
  moves down to replace them. But usually the
  downward movement of cold air is slower than
  upward movement of heated air parcels.
  Consequently, heated air parcels move fairly fast
  in a slowly descending air. This generates
  turbulence.

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You can feel the turbulence by gusts. When you
look at the wind records turbulence can be
observed as rapid changes in wind direction or
temperature. Eddies generated by thermal
turbulence are more irregular and larger. You can
see these in Figure 19-3.
Thermal turbulance
Mechanical turbulance
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The most common mixing process in the atmosphere,
which results in the dilution of pollutants in a
plume, is called eddy diffusion. The swirling
action in the plume removes polluted parcels from
the plume and brings unpolluted air parcels into
it. The net result is diffusion of the plume and
its dilution. Eddies are more efficient in
diluting the plume if the scale of the eddy is
similar to the plume that is diluted.
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The eddies smaller than the plume, can only
remove pollutants at the edges of the plume. The
eddies that are larger than the plume can
transport the plume as a whole, rather than
diluting it. As a result of the turbulence
(eddies) plume widens and dispersed, and
pollutants diffuse away.
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The effect of the eddies on the expansion of the
plume depends on the temperature profile in the
atmosphere. The expansion and the shape of a
plume under three different temperature profiles
and their combinations are given in Figure
19-4 The level of turbulence is a measure of the
dispersive capacity of the atmosphere.
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ESTIMATING CONCENTRATIONS FROM A POINT SOURCE The
equations, which form basis to calculate
concentrations from a point source in a
3-dimensional axis system are commonly, called
Gaussian Plume Model. The coordinate
system x-along the plume y-across the
plume z-height 0-at the ground
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• The model assumes that the concentration of a
  pollutant at any point in the plume is
• proportional to emission rate,
• diluted by the wind at the point of emission with
  a rate inversely proportional to wind speed,
• concentration across the plume and vertically in
  the plume are described by a Gaussian
  distribution.

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• The standard deviations of concentrations across
  the plume and vertically in the plume increase
  with
• Turbulence
• Distance from the source
• The magnitude of the standard deviation both in y
  and z directions shows the expansion of the plume
  (diffusion of the pollutants).

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• Additional assumptions in Gaussian plume model
  includes
• No chemical reactions of pollutants
• No scavenging processes
• It is assumed that when the plume touches to the
  ground or top of the mixing layer it reflects
  back to the plume centerline.
• Characteristics of the Gaussian Model are shown
  in Figure 19-5.

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For stable conditions or unlimited vertical
mixing, concentration of a pollutant (g m-3) at a
point (x, y, z) from a point source located at
(0, 0, H) is given by X Q (1/u)g1/(2?)0.5
?yg2/(2?)0.5 ?z (19-2)
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For y 0 (plume centerline) For z 0 (ground
level) For z and H 0 this equation is
simplified. For unstable or neutral conditions
where ?z gt 1.6L the following equation is used
(when the plume is well mixed in the vertical
direction) X Q(1/u)g1/(2?)0.5 ?y(1/L)
(19-3)
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Note that When you use this equation ?z gt 1.6L.
?z is a measure of how much the plume is
expanded in the vertical direction. ?z gt 1.6L
means that the plume expanded so that it touches
the top of the mixing layer and ground. Then,
eddy reflection repeatedly occurs in both both
boundaries. The net result is that plume is well
mixed in the vertical direction.
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For unstable or neutral conditions where ?z lt
1.6L (which means that the plume is fairly
narrow) the following equation is used X
Q(1/u)g1/(2?)0.5 ?yg3/(2?)0.5 ?z
(19-4) Where G3 ? exp -0.5(H z
2NL)2/?z2 exp -0.5(H z 2NL)2/?z2 This
series converges fast. Evaluation of N between 4
and 4 is usually enough. Computers can calculate
these series fairly easily. When you do the
calculations by hand in practice it is enough to
apply equation 19-2 until ?z 0.8 L
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Note that Eqn 19-4 is for a narrow plume which
is the case close to the emission point Eqn 19-3
involves expanded plume and multiple reflections
from the mixing height and ground which occurs as
you go away from the source. In order to describe
the whole plume you must combine the equations
describing both situations (equations 19-3 and
19-4)
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What would be the maximum concentration in the
plume? Integrate equation 19-2 and set it equal
to zero Xmax (2Q/?ueH2)(?z/?y) This maximum
concentration occur at the distance where ?z
H/(2)0.5
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Alternate coordinate systems for the Gaussian
equations The coordinate system described in the
previous section 0 at the bottom of the stack z
vertical y crosswind x downwind The results will
be identical if you put coordinate system at the
bottom of the receptor, x upwind, z vertical and
y crosswind. You can also use map coordinates or
east north, or polar coordinate systems. The
results do not change.
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Determination of Dispersion parameters Dispersion
parameters in the Gaussian Plume Equation are
important as they determine how much the plume is
dispersed as it travels. True determination of
dispersion parameters require measurement of wind
fluctuations, because these fluctuations
determine how much the plume is dispersed. But
the measurement of fluctuations every time a
modeling is performed is not practical. Because
of this usually dispersion parameters ?y and ?z
are determined from the stability of the
atmosphere.
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There are various estimates of these parameters,
but the most widely used ones are based on
Pasquill stability classes. Pasquil have
developed a scheme to estimate ?y and ?z if there
are no wind fluctuation measurements (which is
usually the case). Later Gifford modified these
to be used in Gaussian Plume equations. The ?y
and ?z estimated from Pasquill Gifford method
are fairly broad estimates
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• In this method you need three parameters to
  determine the stability of the atmosphere
• Wind Speed
• Insolation (solar flux)
• Cloudiness
• These are standard parameters regularly measured
  in met stations.

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Six classes of stability are defined depending on
wind speed and the strength of the sunlight
(insolation and cloudiness) (from class A to
class F) These are given in Table 19-3 Classes A,
B and C corresponds to unstable conditions, Class
D corresponds to neutral condition and classes E
and F correspond to stable conditions of the
atmosphere. Usually for overcast conditions,
neutral class D should be used no matter what the
wind speeds are.
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Once the stability class of the atmosphere is
established, ?z and ?y are determined using
charts given in Figure 19-6. Note that units of
?z and ?y in this figure are meter and they
change with distance from the source. That is why
they represent spreading of the plume. This type
of ? calculation is performed for every hour by
models.
?z (m)
?y (m)
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• Example of Dispersion Calculation
• A point source releases 0.37 g s-1 of a
  pollutant. (Q)
• Effective height (H) 40 m
• Wind speed (u) 2 m s-1
• Stability class B
• What is the approximate distance where the
  maximum concentration occurs?
• What is the maximum concentration?

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The maximum concentration occurs when ?z
H/(2)1/2 ?z 40/(2)1/2 28.3 m for ?z 28.3 m
from figure 19-6. x 0.28 km this is where the
maximum concentration occurs. for x 0.28 ?y
49.0 m Xmax (2Q/?ueH2)( ?z/?y) Xmax 1.56 x
10-5 g m-3 15.6 ?g m-3
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• Now let us see if the calculated ground level
  concentration is indeed the maximum.
• We have to calculate concentration (x) using
  equation 19-2 first
• Note that this is the ground level concentration
  and it occurs on the plume centerline (y 0, z
  0)
• If you set y and z to 0 in equation 19-2 you will
  obtain
• X Q//?u?y?zexp-0.5(H/?z)2)
• Note that the x at 0.28 km from the stack was
  15.6 ?g m-3

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• Let us calculate x at 0.26 km and at 0.30 km
• First we must find ?y and ?z for these distances.
• From figure 19-6
• For 0.26 km ?y 45.9 m and ?z 26.2 m
• For 0.30 km ?y 52.2 m and ?z 30.1 m
• Plug these values into above equation
• X 1.53 x 10-5 at 0.26 km from the stack
• And
• X 1.55 x 10-5 at 0.30 km from the stack
• Both of these concentrations are lower than the
  maximum concentration we have calculated.

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Figure 19.1. Wind variation with height- measured
(solid lines) and one-seventh power law (dashed
lines).
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Figure 19.2. Dilution by wind speed.
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Figure 19.3. Examples of turbulence on wind
direction records (a) mechanical, (b) thermal
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Figure 19.4. Vertical expansion of continuous
plumes related to vertical temperature structure.
The dashed lines correspond to the dry adiabatic
lapse rate for reference.
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Figure 19.5. Two cross sections through a
Gaussian plume (total mass under curves conserved)
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Figure 19.5. Two cross sections through a
Gaussian plume (total mass under curves conserved)
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Table19.3. Pasquill Stability Categories
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Figure19.6. Pasquill-Gifford ?y (left) and ?z
(right)
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49.0 m
0.28 km
0.28 km
Figure19.6. Pasquill-Gifford ?y (left) and ?z
(right)