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AIR POLLUTION
CONCENTRATION
MODELS
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Air pollution concentration models
Allows prediction of concentration from a
specific set of pollutant emissions
For any specified meteorological conditions
At any locations
For any time period
There are may types of models from simple to
complex. But all models are not ideal.
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BOX MODELS
Conservation of mass principle applied to relatively large
scale systems such as an urban airshed
INPUT - OUTPUT + GENERATION - CONSUMPTION = ACCUMULATION
Steady state rarely of interest, we are usually interested
in modelling, explaining, predicting, preventing severe
air pollution episodes of a transient nature
Wind, emission, and ambient monitoring data required
for meaningful modelling work
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Fixed-Box Model
Simple box model of a rectangular city. 8 assumptions (see text book)
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SIMPLE FIXED-BOX MODEL OF A CITY
boxleavingairinionconcentratpollutant=
speedwind=
heightmixing=
windofdirectioninboxoflength=
source)(areacityin theareaunitper
rateemissionmasspollutant=
airenteringinionconcentratpollutant"background"=
6.7)eqn(
c
u
H
L
q
b
uH
qLbc
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Example 6.1 (page 122)
A city has the following description: W= 5 km, L = 15km, H = 1000 m. The wind velocity u = 3 m/s (at
direction L) , the background concentration of CO is b =
5 g/m3. The emission rate per unit area q = 4 10-6
g/sm2. Determine the CO concentration over the city.
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uH
qLbc
Directly substitute into
the equation 6.7;
3m
g25205
10003
1500045
c
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Example 6.2 (page 123)
For the city in Example 6.1, the meteorologicalconditions (u = 3 m/s, H = 1000 m) occur 40% of the
time. For the remaining 60%, the wind blows at right
angles (in W direction) at velocity 6 m/svand at the
same mixing height. What is the annual averageconcentration of CO in this city?
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Find the concentration at 60% of the time:
3mg33.833.35
10006500045
c
Sum up the values from previous example:
Annual average concentration = 25(0.4) + 8.33(0.6) = 15 g/m3
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To apply this eqn to find situation in which highest
conc occur., we need to know the worst case for all
the parameters (wind speed, mixing height, etc. ) Larsen proposed a simpler form by holding u, L & H
constant, we get a linear graph like Fig 6.2.
If for example the concentration c1 with emissionrate q1, then to reduce conc to c2, we can find q2.
8
bc
bc
q
q
L
uHbcq
1
2
1
222 or
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Fractional reduction in emission rate
If the current pollutant conc exceeds the
standard guideline, then we must make c2 &
q2 (the new conc) lower than c1 & q1.
Fractional reduction in emission rate can be
computed using:
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bc
cc
bc
bc
qqq
1
21
1
2
1
2
1
21
1
1rateemissionin
reductionFractional(Eqn 6.11)
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Example 6.3 (page 125)
The ambient air quality standard for particulates (TSP) in USAin 1971 was 75 g/m3. In 1970, annual average particle
concentration measured at one monitoring station was 190
g/m3. The background concentration was estimated to be 20
g/m3
. By what percentage would the emission rate ofparticulates have to be reduced below the 1970 level in order
to meet the 1971 ambient air quality standard?
10
bc
cc
1
21
rateemissionin
reductionFractional
67%or67.020190
75190
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MULTIPLE BOX MODEL OF A CITY
THE URBAN AIRSHED MODEL - UAM
Mass balances (including generation and
consumption terms) written for many boxes of
typically 2-5 km square and ~ 102 meters high.
Each box is considered to be well mixed.
Boxes can have mass fluxes to/from all adjacent
boxes.
Inputs are time variant emission and wind patterns
as well as solar flux (for ozone photochemistry)
Outputs are time variant concentrations of pollutant
in each box.
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Figure 6.10 de Nevers
UAM scheme
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What is Dispersion?
Dispersion: The act or process to drive off or
scatter in different directions
Key parameters:
Diffusion due to concentration gradient
Mean air motion that transport pollutants
downwind
Turbulent velocity fluctuations that disperse
pollutants in all directions
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DIFFUSION MODELS
It is possible to estimate the air contaminant
levels with higher degree of reliability the=anthe fixed-box model.
With knowledge of meteorological
phenomena & variables in weather systems. Can be used as basis for devising air pollution
prevention & abatement programs.
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The Gaussian Plume Idea
Based on material balance.
Consider a point source such as a factory
smokestack and attempts to compute the
downwind conc resulting from this point
source.
Figure 6.3 (page 126) describes the schematic
diagram of this model.
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The Gaussian Plume Idea
Origin of coordinatesystem is the base of
stack.
X axis aligned in the
downwind direction. Plume rises, then
levels off to travel in
the x-direction, and
spreads in y and z
directions.
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Gaussian dispersion - describes the transport and diffusion of a
gas (or particle) from a source to a receptor according to stability
class and other parameterized characteristics of the atmosphere.
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Dispersion Models:
Point Source Gaussian Plume Model
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Effective Stack Height
Plumes normally rise upwards
first because they are normally
emitted at higher T than atm T
and with a vertical velocity. H is the effective stack height.
H is the sum of physical stack
height and plume rise.
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H = h + h
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2-D STEADY DISPERSION MODEL
Solution for windspeed of u m/s and continuous release of
Q g/s of pollutant at : x = y = 0 (stack location) andz = H (the effective stack height)
H = h +h
h : physical stack height,
h : plume rise due to buoyancy
6.27)(eqn2
)(2
exp2 2
2
2
2
zyzy
HzyuQc
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Example 6.4
A factory emits 20 g/s of SO2 at height H. The
wind speed is 3 m/s. At a distance of 1 km
downwind, the values ofy and z are 30 m
and 20 m, respectively. What are the SO2 concat the centreline of the plume, and at a point
60 m to the side of and 20 m below the
centreline?
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Horizontal & Vertical dispersion
coefficients, y and z
To use the Gaussian plume eqn, need to have
y and z values.
These can be obtained from Fig 6.7 & 6.8
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Horizontal dispersion
coefficient
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Vertical dispersion
coefficient
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Example 6.5
Estimate the values ofy and z at a point 0.5
km downwind from pollutant source on a
bright summer day with a wind speed greater
than 6 m/s.
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Pasquill Stability Classes
Table 3-1 Wark,
Warner & Davis
Table 6-1 de Nevers
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Stack Design
Meteorological data are necessary for
expressing dispersion equations
For optimum stack design local variables
must be considered
Local variables
Mechanical turbulence from nearby buildings
Irregular terrain
Using different criteria for short-term releases,
explosions, for instantaneous release of
nuclear fission products28
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102.681.5 3-
s
ass
T
TTPD
u
DVh
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Hollands equation and Davidson &
Bryant
Where h = rise of plume above the stack, m
= stack gas velocity, m/s
d = inside stack diameter, m
u = wind speed, m/s
p = atmospheric pressure, millibarsT = stack gas temperature minus air
temperature, K (Ts Tair)
Ts = stack gas temperature, K
H = h + h
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Davidson & Bryant
Not a very reliable eqn.
Where h = rise of plume above the stack, m
= stack gas velocity, m/s
d = inside stack diameter, m
u = wind speed, m/s
T = stack gas temperature minus air
temperature, K (Ts Tair)
Ts = stack gas temperature, K
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Plume Rise Example 6.9
Estimate the plume rise for a 3 m diameter
stack whose exit gas has a velocity of 20 m/s
when the wind velocity is 2 m/s, P = 1 atm
(1013 milibars) , Ts = 100C, Ta = 15C.
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DISPERSION COEFFICIENTS
Ky and Kz approximately proportional to wind speedKy/u and Kz/u approximately constant
y and z should vary approximately with x(1/2)
Field observations show more complex variation (Figures6.7 and 6.8 de Nevers)
Wind speed and solar flux combine to give stability classes
A - F (Table 6.1 de Nevers)
zzK x
u 2y
yK xu
2
St bilit Cl
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Stability Classes
Table 3-1 Wark,
Warner & Davis
Table 6-1 de Nevers
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Maximum Ground Level
Concentration
Maximum ground level conc occurs when z =
0.707H, provided z/y are constant with
downwind distancex
(Source: Meteorological Aspects of Air Pollution,
Air Pollution Training Program, U.S. Dept.
H.E.W. Division of Air Pollution, Cincinatti,
Ohio. 1962.)
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Ground level burning
If the effective stack height is zero,
zyu
Qc
2
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Other topics
Building wakes
Aerodynamic downwash (Mountainous areas)
Transport distances
Initial dispersion
EPA recommended models: Includes manyfactors into the basic plume model.
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