W2 L2 Air Pollution Concentration Models

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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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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.

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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

qq

qqq

1

21

1

2

1

2

1

21

1

1rateemissionin

reductionFractional(Eqn 6.11)


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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?

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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

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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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W2 L2 Air Pollution Concentration Models

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