Dispersion for Point Sources - Air Pollution - Lecture Slides, Slides of Ecology and Environment

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Dispersion for point sourcesDispersion

for point sourcesCE 524

February 2011February 2011

1

ConcentrationConcentration

•^

Air pollution law in most industrial countriesbased on concentration of contaminants– NAAQS in USN

d

th d t

di t

t^

ti

t

•^

Need method to predict concentrations at anygiven location– Any given set of pollutant

Any given set of pollutant

• Meteorological conditions– At any location– For any time period -^

But even best currently available concentrationmodels are far from ideal

2

models are far from ideal

Factors that determine Dispersion

• Physical nature of effluents• Chemical nature of effluents

Chemical nature of effluents

• Meteorology

L

i^

f h

k

• Location of the stack• Nature of terrain downwind from the stack

4

Stack EffluentsStack

Effluents

•^

Gas and particulate matter

-^

Particles < 20

μ

m behave same as gas

• Low settling velocityP^

ti l

h

i^

ifi

t^

ttli

l^

it

•^

Particle > 20

μ

m have significant settling velocity

•^

Only gases and Particles < 20

μ

m are treated in

dispersion modelsdispersion models

-^

Others are treated as particulate matter

-^

Assumes effluents leave the stack with sufficientAssumes effluents leave the stack with sufficientmomentum and buoyancy– Hot gases continue to rise

5

Gaussian or Normal Distribution

• Gaussian distribution model

Gaussian distribution model

• Dispersion in y and z directions uses a

double gaussian distribution

plumes

double gaussian distribution -- plumes

• Dispersion in (x, y, z) is three-dimensional• Used to model instantaneous puff of

emissions

7

Gaussian or Normal Distribution

• Pollution dispersion follows a distribution

function

• Theoretical form: gaussian distribution

functionfunction

8

Gaussian or Normal Distribution

What are some properties of the normaldistribution?distribution?

10

f(x) becomes concentration, maximum at center of plume

Gaussian or Normal distribution

•^

of the area fall within 1 standard deviation of

the mean

(μ

σ

f^

f ll

i hi

d

d d

i^

i^

f

•^

of area fall within 1.96 standard deviation of

the mean

(μ

σ

•^

of the area fall within 3 standard deviations

•^

of

the area fall within 3 standard deviations

of the mean

(μ

σ

11

Gaussian Dispersion Model

-^

For localized point sources – stacks

-^

General appearance

-^

Plume exits at height, h

s

-^

Rises an additional distance,

Δ

h

-^

buoyancy of hot gases

-^

buoyancy of hot gases

-^

called plume rise

-^

reaches distance where buoyancy and upward momentum cease E it

l^

it^

V

-^

Exit velocity, V

s

-^

Plume appears as a point source emitted at height

H =

hs

Δ

h

-^

Emission rate Q (g/s)

-^

Assume wind blows in x direction at speed u

u is independent of time elevation or location (not really true)

13

-^

u is independent of time, elevation, or location (not really true)

Gaussian Dispersion Model

14

Gaussian Dispersion Model

Z-axis through stack

Y

**- axis is transverse Y

• axis**

is transverse

to wind

X-axis indirection of winddirection of wind

16

As distanceAs

distance increase so doesdispersion

17

Image source: Cooper and Alley, 2002

Point Source at Elevation H

•^

Assumes no interference or limitation todispersion in any directiondispersion in any direction

d^

l^

i^

f^

li^

f^

l

x^0

and z

are location of centerline of plume 0

y^0

taken as base of the stack z^0

is H Q = emission strength of source (mass/time) – g/su = average wind speed thru the plume – m/sC = concentration – g/m

3 (

Notice this is not ppm)

19

y

and



are horizontal and vertical standard deviations in metersz

Wind Velocity ProfileWind

Velocity Profile

• Wind speed varies by height• International standard height for wind-speed

g

p

measurements is 10 m

• Dispersion of pollutant is a function of wind

p

p

speed at the height where pollution isemitted

• But difficult to develop relationship

between height and wind speed

20