Agriculture Reference
In-Depth Information
∂
c
i
∂
lim
x
=
0
i
=
1, 2, 3
x
→∞
7.4.6 Water Flow and Solute Transport in Heterogeneous Media
In macroporous heterogeneous soil, the classical water flow theory based on
Buckingham-Darcy law may not adequately describe the infiltration and redistri-
bution of water. Although these macropores may comprise only a small fraction of
the total soil volume, they can have a profound effect on the rate of infiltration and
redistribution of water. As a result, pollutants dissolved in water can reach deeper
soil layers and ground water tables much faster as could be expected assuming
homogeneous flow in the matrix.
Under such conditions, the two-domain concept or double-, dual-,
bi(multi)modal-porosity models, with macropores as a second domain next to
the less permeable micropore region, are nowadays widely accepted for modeling
water flow and solute transport in heterogeneous soils. Both regions are treated as
continua and the continuum approach is used to establish the flow and transport
equations in each region. Both equations are coupled by means of an exchange term
accounting for the mass transfer of water and solutes between both regions.
7.4.6.1 Dual Porosity Model for Solute Transport
In the mobile-immobile solute transport model, the soil water volume is split up
into a “mobile” and an “immobile” region. Solute transport in the mobile region is
described by the convective-dispersion equation, and solute exchange between both
regions is modeled by a first-order kinetic diffusion process:
2
C
m
∂
θβ
∂
C
m
∂
)
∂
C
im
∂
D
m
∂
v
m
∂
C
m
∂
+
θ
(1
−
β
=
θβ
−
θβ
(7.14)
z
2
t
t
z
)
∂
C
im
∂
θ
(1
−
β
=
α
(
C
m
−
C
im
)
(7.15)
t
where
β
is the ratio of the mobile water content,
θ
m
, versus the total water content;
1
-
;
C
m
and
C
im
are the
concentrations in the mobile and immobile phases;
D
m
is the dispersion coefficient
for the mobile region,
β
is the ratio of the immobile water content
θ
im
versus
θ
is the first-order mass exchange rate; and
v
m
the average
pore-water velocity in the mobile liquid phase.
α
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