Geoscience Reference
In-Depth Information
2 Approach and Methods
2.1 General Description of Contaminant Transport
in Groundwater
In this chapter, the final 2D advection-dispersion equation resulting from the
transport continuity equation has been used for describing the groundwater con-
taminants transport with consideration of the instantaneous nonlinear reversible
sorption term (for inorganic chemicals) (Chiang
2005
):
2
C
2
C
@
@
C
@
þ
m
@
S
u
x
@
C
D
x
@
D
y
@
1
þ
x
¼
x
2
þ
(1)
t
@
C
@
@
y
2
where:
C
the solute concentration in flowing groundwater in aqueous phase (in
the local equilibrium conditions);
S
¼
the mass of the solute species adsorbed on
the grounds per unit bulk dry mass of the porous medium (in the local equilibrium
conditions);
u
x
¼
¼
component of the so-called pore groundwater velocity in pore
space along the
x
axis;
D
x
,
D
y
¼
components of the longitudinal and transverse
dispersion coefficients along the
x
and
y
axes that depend on the longitudinal and
transverse dispersivity
ða
L
; a
T
Þ
;
r ¼
the bulk density of the porous medium;
m
¼
the effective porosity of
the porous medium;
t
¼
coordinate of
time;
(
x, y
)
¼
Cartesian coordinates of the assumed reference system; and
½
1
þðr=
m
Þ
ð@
the retardation factor, constant in time, resulting from sorption pro-
cess (Seidel-Morgenstern
2004
).
The reason for using the above-mentioned form of equation, along with detailed
description of all the parameters being considered in it (
u
x
;
S
=@
C
Þ ¼
m
; r
,
D
x
ða
L
Þ;
D
y
ða
T
Þ
)is
given in Aniszewski
(
2009
).
In the nonequilibrium state analyzed further
on (
0), for the mathematical description of sorption models, the kinetic
time-dependent models should be always used as the reversible first-order or
N-order models of kinetics. Among many different kinetic models presented in
the literature, the first-order kinetic sorption models (the nonlinear and linear
kinetic equations) were chosen for further analysis. These kinetic models are also
widely adopted in practice (Travis and Etnier
1981
; Seidel-Morgenstern
2004
;
Chiang
2005
).
The first-order kinetic sorption model (the nonlinear kinetic equation) can be
written in the form:
@
S
=@
t
6¼
@
S
@
m
r
C
N
t
¼
k
1
k
2
S
(2)
where:
k
1
¼
the rate constant of adsorption process (the so-called forward adsorption
rate constant);
k
2
¼
the rate constant of desorption process (the so-called backward
