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CHAPTER 14
Plume Dispersion
Objectives:
Assess environmental impact of an emission
source in terms of legislated standards for:
• Toxicity, and
• Odour
In Ontario this constitutes regulation 419/05:
http:www.rwdi.com/regulation419/
Pg. 176 course notes
Our task is to estimate the impact of an
emission source from an industrial plant:
Plume dispersion occurs
in the y- and z-directions
Plume is convected
by the wind in the xdirection
Z-axis starts from ground level
Turbulent dispersion:
y-direction:
z-direction:
2




1
y




C  exp  


 2   y  
 1  z  2 
 
C  exp  - 

2


 z  
Where y and z are dispersion
parameters that must be estimated
Recall from our treatment of particle diffusion:
1 .2 5

where 
2
2Dt
D is the particle
diffusivity
D t = 1 /1 6
1 .0 0
C /Q
C
 1 y2 
exp  2 
2
 2  
Q
0 .7 5
D t = 1 /4
0 .5 0
Dt = 1
0 .2 5
0 .0 0
-5
-4
-3
-2
-1
0
1
2
3
4
5
y
Pg. 49-50 course notes
Diffusion mechanisms:
• Solute (gas or liquid) diffusion occurs by
random molecular motion.
• Particle diffusion occurs by random
Brownian motion.
• Plume dispersion occurs by random
turbulent motion.
Transverse
turbulent
dispersion


y and z must be estimated
Ground-level concentrations will
depend on …
Wind …
Wind rose shows
average direction
and magnitude of
the wind vector
Pg. 178 course notes
Atmospheric stability …
Dry adiabatic lapse rate (stable, neutral atmosphere)
dT
 - 1 C 100 m

dZ
dA
P
Natural balance
between hydrostatic
head,  g dA dZ, and
pressure forces
Pg. 179 course notes
dZ
P + dP
Super-adiabatic lapse rate:
H e gi h t
H e gi h t
S u p e ra d ai b a t ic
100
D ry A d ai b a t ic
L a p s e R a te
T
0
20
21
H e gi h t
T em p e ra tu re
22
L o o p ni g
H e gi h t
A “buoyant” atmosphere
N e u tra l
100
Pg. 180 course notes
20
He g
i h t 21
22
N e u t ra l
100
Sub-adiabatic lapse rate:
T em p e ra tu re
0
20
He g
i h t
100
T em p e ra tu re
22
21
Loop n
i g
He g
i h t
S ubad a
i b a t ic
T em p e ra tu re
0
He g
i h t
20
a 2tu re
2 1T em p e r2
C on n
i g
He g
i h t
100
Is o th e m
r a l
T em p e ra tu re
0
He g
i h t
20
He g
i h t
2 1T em p e r2
a 2tu re
Pg. 180 course notes
F ann n
i g
The Gaussian plume model:
The concentration of material downwind in the x-direction
varies as the inverse of the local transport velocity, i.e.,
C
1
U
A Gaussian type distribution is used in the y-direction:

 1  y
C  A exp  
2

 y




2




A
If we choose
1
2  y
The distribution will provide an integrated concentration of
unity across the transverse cross-section

1
2 y

-

 1  y
exp  
2

 y




2


 dy  1

… starting to look like a normal distribution!
Z- direction requires special treatment …
When the “edge” of the plume reaches the ground …
we assume perfect “reflection”!
C

1
 exp
2 

 1  z - H 2 
 1  z  H 2 
  exp  
 
 2    
 2  

z 
z 






(z - H) term accounts for the
above ground contribution
(z + H) term accounts for the
imaginary source below ground
Final form of the Gaussian plume model:
C  x, y, z, H  

  exp


Q
2   y z

 1  y
exp  
U
 2  y





2




2
2 


 1 z - H  
 1  z  H  
 exp - 
 
 2    
 2
z  
z 






• Product of the y- and z-direction distributions
• Q is the emission rate in mass per unit time
C  x, y, z, H 

  exp


2


Q
 1  y  

exp  


2   y z U
 2   y  
 1  z - H 2 
 1  z  H 2 
  exp  



 
 2  z  
 2   z  




Variation of C with x is contained in the behaviour
of y and z with downstream position, x, from the
emission source.
10000
1000
A
1000
 y, m
A
B
B
C
C
D
E
F
100
D
 z, m
E
100
F
10
10
0 .1
1
10
D o w n w in d d is ta n c e , k m
100
1
0 .1
1
10
100
D o w n w in d d is ta n c e , k m
Fig 6-14 and 7-14, pg. 184 and 185
Stability classes A - F
Table 1-14 pg. 186
Mathematical models for y
10000
y ax
1000
 y, m
A
B
C
D
E
F
100
10
0 .1
1
10
D o w n w in d d is ta n c e , k m
100
p
Mathematical models for z
z  bx
1000
A
• for class C, and
B
C
100
D
• piecewise (in x) for
other different classes
 z, m
E
F
10
1
0 .1
q
1
10
D o w n w in d d is ta n c e , k m
100
Pg. 187 course notes
But …
Pg. 188 course notes
1/--страниц
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