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Contaminant Hydrogeology V

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Гидрогеология Загрязнений
и их Транспорт в
Окружающей Среде
Yoram Eckstein, Ph.D.
Fulbright Professor 2013/2014
Tomsk Polytechnic University
Tomsk, Russian Federation
Fall Semester 2013
Air-Water Gas
Exchange of
Chemicals
Thin-Film Model
Water-side control
J = -Dw(Cw – Ca/H)/Zw
where Zw is the thickness of the water film
if
Ca = 0
J = -DwCw/ Zw = -kw Cw
Thin-Film Model
Air-side control
J = -(Da/Za) (CwH - Ca)
or
J = – (Da - H/Za ) (Cw - Ca /H)
where Za is the thickness of the air film
Thin-Film Model
for H ≈ 0.01
= −
1


+



 −

Estimating gas exchange
coefficient
k
k
A
B
D
D
A
B
MW
B
MW
A
Estimating gas exchange
coefficient
In absence of a tracer with
a known gas exchange
coefficient models are
constructed empirically
for each gas, e.g. the four
models for kO2 :
K O2 24 . 94 1 N u
K O2
V 1 . 92 d Neglescu & Rojanski, 1969
K O2 23 . 2 V
d
0 . 73
1 . 75
Owens et al., 1964
*
d
Thackston & Krenkel, 1969
0 . 85
K O2 103 V
0 . 413
d
w
0 . 273
1 . 408
Bennet & Rathbun, 1972
Estimating gas exchange
coefficient
Similarly, gas exchange
coefficients for slowly flowing waters, lakes or
estuaries are approximated empirically:
for slowly flowing or stagnant waters:
kw[cm/sec] ≈ 4·10-4 + (4·10-5·u2w10)
or
ka[cm/sec] ≈ 0.3 + (0.002·uw10)
Using gas exchange
coefficient
The air-water flux
density is proportional to the difference
between a chemical concentration in water
[Cw] and the corresponding equilibrium
concentration [CwH].
Therefore:
C ( x ,t ) C o e
k r t
Thin-Film of Air Model Above
a Slick of NAPL
C a
P
RT
MW while Za is the thickness of
the stagnant air film above
the slick, the velocity of gas
transfer (vaporization) is
proportional to Da of that gas
J Da
Za
Ca
Thin-Film of Air Model Above a
Slick of NAPL
the velocity of gas transfer (vaporization) is
also dependent on the size of the slick
v=
-0.11
-0.67
0.029·uw10·L ·Sc
where:
uw10 wind velocity 10m above the slick [m/hr]
L is the slick diameter [m]
Sc is the Schmidt number
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