Environmental Engineering Reference
In-Depth Information
concentration (
C
i,sat
) of a contaminant in water (e.g. at the NAPL/water-interface)
can be described by the Raoult's law:
C
i
,
sat
=
χ
i
,
o
γ
i
,
o
S
i
(19.1)
γ
i
,
o
[dimensionless] and
S
i
[M L
−
3
], denote the molar
fraction of contaminant
i
in the organic contaminant mixture, the activity coeffi-
cient of
i
and the aqueous solubility of the individual contaminant
i
(pure substance)
[M L
−
3
], respectively.
For mass transfer into groundwater a film diffusion model can be used to describe
the dissolution rates
F
b
[M L
−
2
T
−
1
] from NAPLs trapped as blobs or ganglia in a
porous medium (Grathwohl
1998
):
where
χ
i
,
o
[dimensionless],
D
aq
δ
F
b
=
(
C
0
−
C
)
(19.2)
where
D
aq
is the aqueous diffusion coefficient [L
2
T
−
1
],
is the film thickness [L],
C
is the contaminant concentration in the aqueous phase and
C
0
is the contaminant
concentration at the interface. The ratio
D
aq
/
δ
is often indicated as mass transfer
coefficient
k
[L T
−
1
]. This parameter is generally unknown and empirical corre-
lations are often used to estimate it based on dimensionless constants such as the
Sherwood, Schmidt and Reynolds numbers (e.g. Imhoff et al.
1993
; Miller et al.
1990
). The overall dissolution rate also depends on the interfacial area of the NAPL.
Generally the length of mass transfer zones in groundwater flowing through areas
with residual NAPL existing as blobs or ganglia is rather short in the range of cen-
timeters and decimeters indicating that equilibrium contaminant concentrations in
this scenario are reached very rapidly.
For NAPL entrapped as connected free phase on top of low permeability lay-
ers and impervious formations (“DNAPL pools”) or floating on the water table
(“LNAPL pools”) the dissolution rates depend on the contact time between the
aqueous and coherent organic phases, the pool dimensions and the transverse verti-
cal dispersion. In a first approximation the dissolutions rate can be described as (see
Grathwohl
1998
for further detail):
δ
D
π
·
F
p
=
2
C
0
n
t
c
L
p
B
p
(19.3)
where
C
0
is the equilibrium concentration at the interface between organic and water
phase, n is the porosity through which the water can flow,
D
[L
2
T
−
1
] is the vertical
transverse dispersion coefficient,
t
c
[T] is the contact time and
L
p
and
B
p
[L] are the
pool length and width, respectively.
Because of the less favorable surface to volume ratio, contaminant dissolution
rates from NAPL pools are significantly lower that the ones from disconnected
NAPL blobs resulting in longer time and higher resistance to remediation.
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