Competitive Sorption and Transport - Transport and Fate of Chemicals in Soils: Principles and Applications - page 193

that account for their governing mechanisms. The one-dimensional reac-
tive-convective-dispersive transport equation is the most frequently used
model for describing the transport of dissolved chemicals in soils (Selim,
1992).

∂θ
∂

C
t

ρ ∂
∂

S
t

∂
∂

∂
∂

C
z

− ∂
∂

qC
z

i i i i

+ = θ D

( 7.1)

z

where S i is the amount of adsorption (mg kg -1 ), C i is the dissolved con-
centration (mg L -1 ), i indicates the i ith component in the system, D is the
dispersion coefficient (cm 2 h -1 ), θ is the soil moisture content (cm 3 cm -3 ),
ρ is the soil bulk density (g cm -3 ), z is distance (cm), and t is reaction time
(h). Retention reactions of a solute from the soil solution by the matrix of
soils and geological media is accounted for by the term (

∂
∂ ) in Equation
7.1 and can be quantified based on several approaches. A number of trans-
port models simulate heavy metal sorption based on the local equilibrium
assumption (LEA). Here one assumes that the reaction of an individual
solute species in the soil is sufficiently fast and that an apparent equilib-
rium may be observed in a time scale considerably shorter than that of
the transport processes. The local equilibrium assumption is the basis for
several commonly used models, including ion-exchange, surface complex-
ation, Freundlich, and Langmuir models. A discussion of the various mod-
els from the perspective of competitive sorption and transport is given in
subsequent sections. In contrast to the LEA, for most heavy metals time-
dependent retention in soils has been commonly observed, as discussed in
previous chapters. As a result, a number of formulations were introduced
to describe their kinetic sorption behavior in soils. Examples of kinetic
models include the first-order, Freundlich kinetic, irreversible, and second-
order models. Commonly used equilibrium and kinetic models are sum-
marized in Table 7.1.
Another class of models is that of the multireaction, multistep, or mul-
tisite equilibrium-kinetic models. Basic to multireaction and multisite
models is that the soil is a heterogeneous system with different constitu-
ents (clay minerals, organic matter, Fe and Al oxides, carbonates, etc.),
with sites having different affinities/energies for heavy metal sorption.
Therefore, a heavy metal species is likely to react with various constit-
uents (sites) by different mechanisms. As a result, a single equilibrium
or chemical kinetic reaction is unlikely to be the dominant mechanism
in heterogeneous soils, which are made of multiple sites having differ-
ent energies for heavy metal sorption. In subsequent sections, multire-
action and multisite models and simulations in competitive systems are
presented.

S
t i