Second-Order Transport Modeling - Transport and Fate of Chemicals in Soils: Principles and Applications - page 157

6

Second-Ord er Transport Modeling

In this chapter, an analysis is presented of a kinetic second-order approach
for describing mechanisms for retention of reactive chemicals in the soil
environment. The basis for this approach is that it accounts for the sites
on the soil matrix that are accessible for retention of reactive chemicals in
solution. The second-order approach will be incorporated into the non-
equilibrium two-site model for the purpose of simulation of the poten-
tial retention during transport of reactive chemicals in soils. As will be
described in a subsequent chapter, this second-order approach will be
extended to the diffusion-controlled mobile-immobile (or two-region)
transport model.
A main feature of the second-order model proposed here is the suppo-
sition that there exist two types of retention sites on soil matrix surfaces.
Moreover, the primary difference between these two types of sites is based
on the rate of the proposed kinetic retention reactions. It is also assumed that
the retention mechanisms are site specific, for example, the sorbed phase on
type 1 sites may be characteristically different (in their energy of reaction
and/or the identity of the solute-site complex) from that on type 2 sites. An
additional assumption is that the rate of solute retention reaction is a func-
tion not only of the solute concentration present in the solution phase but
also of the amount of available retention sites on matrix surfaces. Another
feature of the second-order approach is that an adsorption maximum (or
capacity) is assumed. For a specific reactive chemical, this maximum repre-
sents the total number of adsorption sites on the soil matrix. This adsorption
maximum is also considered an intrinsic property of an individual soil and
is thus assumed constant (Selim and Amacher, 1988).

6.1 Second-Order Kinetics
For simplicity, we denote S max to represent the total retention capacity or the
maximum adsorption sites on matrix surfaces. It is also assumed that S max is
invariant with time. Therefore, based on the two-site approach, the total sites
can be partitioned into two types such that:

= ( ) + ( )

S S S (6.1)

max ax max

1 2

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