Environmental Engineering Reference
In-Depth Information
mobile or transitional gas-water interface has to be taken into account (Crist et al. ,
2004; Lenhart and Saiers, 2002; Ouyang et al. , 1996 ; Wan and Tokunaga, 1997 ). While
the maximum size of mobile colloids will be limited by straining fi ltration and pore
velocity, concentration and size distribution of smaller colloids are controlled by
physico - chemical fi ltration. Altogether, subsurface transport of small (
100 nm),
individual colloids is limited mainly by the diffusion driven collision rate, whether
the transport of larger colloids or aggregates (
<
m) is limited by straining (if
colloid density equals fl uid density) or sedimentation (for colloid density
>
1
µ
>
fl uid
density).
4.7.1
Saturated Porous Media
There are many approaches available to describe the transport of colloids them-
selves or contaminants associated with colloids in saturated porous media. As
already pointed out, the reactions taking place in the porous medium can be sepa-
rated into the hydraulic part (the movement of the colloids with the water stream),
the collision part and the attachment/detachment part. The so-called classical fi ltra-
tion theory (CFT) provides adequate analytical solutions for clean bed fi ltration
under favourable chemical conditions. Other approaches developed the advection-
dispersion -deposition equation to account for charge heterogeneity and dynamic
processes during the fi ltration of colloids. For an extensive overview, the reader is
pointed towards Elimelech et al. (1995b) , Kretzschmar et al. (1999) and Ryan and
Elimelech (1996). Colloid transport in saturated porous media has been success-
fully described by the CFT. (Iwasaki, 1937) described fi ltration as a fi rst order
kinetic law:
CCe
P
=
(
−⋅
λ ∆
x
)
(4.14)
0
P
where C P is the colloid concentration at the travel distance x , C 0 P is the original
colloid concentration,
is the fi ltration factor in m − 1 . The colloid travel distance
until certain retention is reached can be expressed as the reciprocal value of the
fi ltration factor:
λ
(
)
C
R
(4.15)
1
=−
ln
P
λ
C
T
0
P
where R T is the colloid travel distance in metres at a given retention rate (e.g.
ln ( C P / C 0P ) = 6.9 for 99.9% colloid retention). The relation between the fi ltration
factor and travel distance is given in Figure 4.17.
Developed by Yao (1968) for clean bed fi ltration and extended by Rajagopalan
and Tien (1976), the CFT enables the calculation of the fi ltration factor (and thus
colloid transport prediction in saturated media). The equations by Yao (1968) to
quantify fi ltration (
) by the four different mechanisms of colloid fi ltration, that is
sieving/straining, sedimentation, diffusion and interception, neglected the infl uence
of adjacent collector grains and the hydrodynamic retardation (Tien and Payatakes,
1979). To account for these processes, (Rajagopalan and Tien, 1976) introduced the
Happel parameter ( AS ) to account for hydrodynamic retardation. It can be
described by the Happel sphere in cell model, in which the grains with the porous
λ
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