Multiple-Reaction Approaches - Transport and Fate of Chemicals in Soils: Principles and Applications - page 147

the rate coefficients and m is the reaction order associated with S 2 , and k 5 and
k 6 are the reaction parameters associated with S 3 . In the absence of the con-
secutive reaction between S 2 and S 3 , that is, if S 3 = 0 at all times ( k 5 = k 6 = 0),
Equation 5.8 reduces to:

∂
∂

Θ
ρ

S
t

2

=

m

−

k C k S 3 4 2

(5.10)

Thus, Equation 5.10 for S 2 resembles that for S 1 except for the magnitude of
the associated parameters k 3 , k 4 , and m .
The sorbed phases ( S e , S 1 , S 2 , S 3 ) may be regarded as the amounts sorbed
on surfaces of soil particles and chemically bound to Al and Fe oxide sur-
faces or other types of surfaces, although it is not necessary to have a pri-
ori knowledge of the exact retention mechanisms for these reactions to be
applicable. These phases may be characterized by their kinetic sorption and
release behavior to the soil solution and thus are susceptible to leaching in
the soil. In addition, the primary difference between these two phases not
only lies in the difference in their kinetic behavior but also in the degree of
nonlinearity as indicated by the parameters n and m . The sink/source term Q
is commonly used to account for irreversible reactions such as precipitation/
dissolution, mineralization, and immobilization, among others. We express
the sink term as a first-order kinetic process:

=ρ ∂

S
t

3

Q

∂ =Θ

C

k s

(5.11)

where k s is the associated rate coefficient (h -1 ). The sink term Q is expressed
in terms of a first-order irreversible reaction for reductive sorption or pre-
cipitation or internal diffusion as described by Amacher et al. (1986) and
Amacher, Selim, and Iskandar (1988). Equation (5.11) is similar to that for the
diffusion-controlled precipitation reaction if one assumes that the equilib-
rium concentration for precipitation is negligible.
This model is multipurpose in nature, which accounts for linear as well
as nonlinear reaction processes of the reversible and irreversible types. The
capability of the model is not limited to describing commonly measured
batch-type sorption data (following a specific reaction time, e.g., 1 day)
but also in describing changes in concentration with time of reaction dur-
ing sorption as well as desorption. Therefore, the uniqueness of this model
is that its aim is to describe the reactivity of solutes with natural systems
versus time during sorption or desorption. In contrast, for most models, for
example, the simple linear, Freundlich, Langmuir, DDRM (double-domain
reaction model), and TDRM (treble-domain reaction model), two distinct
sets of parameters are obtained, one for adsorption and one for desorption
(Weber, McGinley, and Katz, 1992; Lesan and Bhandari, 2003). Moreover, the