Transport of Reactive Contaminants - Contaminant Geochemistry - page 265

k ¼ 3

2 ð 1 n Þ L d c a c g ;

ð 11 : 6 Þ

where n is the porosity, L is the length of the porous medium column, d c is the
median grain size diameter (Rajagopalan and Tien 1976 ), a c is the collision effi-
ciency (an empirical, fitting constant), and g is the collector efficiency (estimated
by various means, as discussed by Logan et al. ( 1995 ) and Tufenkji and Elimelech
2004 . The CFT assumes homogeneity of particles and the porous matrix and leads
to an expected fast exponential concentration decay along the colloid travel path.
The CFT can be modified to account for the occurrence of nonideal behavior, for
example, by combining Eq. ( 11.5 ) with a model for a first-order, rate-limited
adsorption-desorption process (Eq. 11.1 ) (Toride et al. 1995 ).
A major problem with these approaches, however, lies in the complexity and
nonuniqueness involved with identification of parameterizations for processes of
particle straining, deposition, and detachment. An alternative to CFT-based the-
ories is given by Amitay-Rosen et al. ( 2005 ), who suggest a simple phenomeno-
logical model of particle deposition and porosity reduction that avoids these
difficulties.
As noted by Cortis et al. ( 2006 ), CFT and modifications of standard filtration
models invariably predict an exponential decay of the colloid concentration with
distance. However, similar to the discussion of non-Fickian transport in Sect. 10.3 ,
power-law tails in breakthrough curves are observed frequently in experiments (e.
g., in the context of bacterial ''biocolloids,'' see Albinger et al. 1994 ; Martin et al.
1996 ; Camesano and Logan 1998 ; Baygents et al. 1998 ; Bolster et al. 1998 ;
Redman et al. 2001 ). Cortis et al. ( 2006 ) propose a generalized model based on
CTRW theory that captures these power-law tails, together with the full evolution
of breakthrough curves. The CTRW filtration model is found to be controlled by
three parameters, which are related to the overall breakthrough retardation (R), the
slope of the power-law tail (b), and the transition to a decay slower than t -1 .

11.3 Dissolving and Precipitating Contaminants

Dissolution and precipitation can occur as contaminants travel from the land
surface to groundwater aquifers. These processes can affect water chemistry, and
they can significantly modify the physical and chemical properties of porous media
(Lasaga 1984 ; Palmer 1996 ; Dijk and Berkowitz 1998 , 2000 ; Darmody et al.
2000 ). Under some conditions, large quantities of mass can be transferred between
the liquid and solid mineral phases.
A number of experimental and theoretical studies analyzed the influence of
dissolution processes on the physical and chemical properties of soluble porous
matrices (Fogler and Rege 1986 ; Daccord and Lenormand 1987 ; Hoefner and
Fogler 1988 ; Daccord 1987 ; Daccord et al. 1993 ). Similarly, several theoretical