Environmental Engineering Reference
In-Depth Information
is a first-order kinetic rate coefficient [T
−
1
]. Several other nonequilibrium
adsorption expressions have been used in the past (see Table 2 in Van Genuchten
and Šimunek
1996
), and are often referred to as one-site sorption models.
Because contaminant transport models assuming chemically controlled nonequi-
librium (one-site sorption) often did not lead to significant improvements in
predictive capability when used to describe column transport experiments, the
one-site first-order kinetic model was extended into a two-site sorption concept
that divides the available sorption sites into two fractions (Selim et al.
1976
;Van
Genuchten and Wagenet
1989
). Conceptually, sorption on one fraction (type-1 sites)
is assumed to be instantaneous, while sorption on the remaining (type-2) sites is
considered to be time-dependent. Assuming linear sorption, the two-site transport
model is given by (Van Genuchten and Wagenet
1989
):
where
α
κ
∂
(
f
ρ
b
K
d
+
θ
)
c
∂
∂
D
h
∂
c
−
∂
(
qc
)
∂
=
θ
−
φ
e
∂
t
z
∂
z
z
(18.57)
∂
s
k
∂
t
=
α
k
[(1
−
f
)
K
d
c
−
s
k
]
−
φ
k
where
f
is the fraction of exchange sites assumed to be at equilibrium [
−
],
φ
e
[ML
3
T
−
1
] and
φ
k
[MM
−
1
T
−
1
] are reactions in the equilibrium and nonequilibrium
phases, respectively, and the subscript
k
refers to kinetic (type-2) sorption sites.
When
f
0, the two-site sorption model reduces to the one-site fully kinetic sorp-
tion model (i.e., when only type-2 kinetic sites are present). However, if
f
=
1, the
two-site sorption model reduces to the equilibrium sorption model for which only
type-1 equilibrium sites are present.
=
18.3.3.3 Colloid-Facilitated Solute Transport
There is considerable evidence that many contaminants, including radionuclides
(Noell et al.
1998
; Von Gunten et al. 1988), pesticides (Kan and Tomson
1990
; Lindqvist and Enfield
1992
; Vinten et al.
1983
), heavy metals (Grolimund
et al.
1996
), viruses, pharmaceuticals (Thiele-Bruhn
2003
; Tolls
2001
), hormones
(Hanselman et al.
2003
), and other contaminants (Magee et al.
1991
;Mansfeldtetal.
2004
) in the subsurface are transported not only with moving water, but also sorbed
to mobile colloids. Because many colloids and microbes are negatively charged and
thus electrostatically repelled by negatively-charged solid surfaces, the process of
anion exclusion may occur. As a result, contaminant transport could be slightly
enhanced relative to water flow. Size exclusion may similarly enhance the advec-
tive transport of colloids by limiting their presence and mobility to the larger pores
(e.g., Bradford et al.
2003
). Sorption of contaminants onto mobile colloids can thus
significantly accelerate their transport relative to more standard advection-transport
circumstances.
Colloid-facilitated transport is a relatively complicated process that requires
knowledge of water flow, colloid transport, dissolved contaminant transport, and
colloid-contaminant interaction. This requires formulation of transport and/or mass
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