Environmental Engineering Reference
In-Depth Information
Under assumed simple diffusion controlled release, Fick's second law may be
fit to cumulative release data to calculate an observed diffusivity,
D
obs
[m
2
/s], using
either of the following two simple equations for semi-infinite media:
2
⎡
⎤
a
n
⎢
⎢
⎢
⎢
⎥
⎥
⎥
⎥
2
2
⎡
⎣
⎢
⎤
⎦
⎥
⎡
⎣
⎢
(
)
⎤
⎦
⎥
A
t
V
S
1
2
obs
o
D
=
π
Δ
t
+
t
(10.4a)
()
n
n
−
1
n
⎣
⎦
where
a
n
/
A
o
is the fractional release [-] during the time interval
(
Δ
t)
n
[s] from
t
n-1
to
t
n
;
V
is the volume of the solid phase [m
3
]; and
S
is the solid surface area in contact with the leachant [m
2
].
2
⎛
⎞
M
Ct
⎜
⎜
⎟
⎟
obs
D
=
π
(10.4b)
(
)
2
⋅
−
t
⎝
⎠
o
n
n
−
1
where
M
is the cumulative release [mg/m
2
] during the time interval from
t
n-1
to
t
n
[s];
ρ is the density of the solid phase [kg/m
3
]; and
C
o
is the leachable content at the start of leaching [mg/kg].
Equation 10.4a was developed in concert with the ANSI/ANS-16.1-2003 proto-
col for radionuclide release,
204
while Equation 10.4b was developed for heavy metal
and matrix constituent release using NEN 7345.
222
Both of these equations are based
on the same diffusion model assuming (i) a homogenous solid matrix, (ii) constant
release parameters, (iii) constant driving force for diffusion (i.e., zero concentration
at the boundary), (iv) no depletion of the constituent at the core of the matrix, and
(v) less than 20% of the initial content is leached (allows use for finite media of the
solution for semi-infinite media given in the equations).
10.5.2.3
Changes in Mass-Transport Behavior
The condition of a solid matrix after long-term environmental leaching often is
simulated by subjecting the matrix to extremely aggressive leachants over a much
shorter time interval under the assumption that the same conditions would apply to
the matrix in the long term. Thus, the research of acid attack of cement materials
showed that the chemical and morphological characteristics are greatly affected by
contact with aggressively acidic leachants (see Section 10.2.2.3.1). Several other
long-term leaching studies have shown dual release regimes (i.e., a period of fast
release kinetic followed by a slower, residual constituent flux), indicating that the
behavior of mass-transport-based release from cementitious matrices may change
with time or with constituent concentration.
223,224
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