86
G. Langergraber et al.
The volumetric water content E>(h) and the unsaturated hydraulic conductivity
function K(h) are strongly non-linear functions in terms of the pressure head. Pairs
of empirical soil-moisture characteristic curves are used to describe these relationships. Soil-moisture curves can be described in analytical form, e.g. using the van
Genuchten relationships (van Genuchten 1980). The expressions of van Genuchten for volumetric water content E>(h) and unsaturated hydraulic conductivity K(h)
are given by
h
e s
h~O
and
(3)
where m = 1 -lin, n > 1, Ks = saturated hydraulic conductivity (dm3w.dm-2s.h-l),
and Se = the effective water content defined as
8-8
S =
r
e
8-8 s
r
(4)
Equations (2) and (3) contain five independent parameters: E>r and E>s = the residual and saturated water content, respectively (dm 3 w.dm- 3 s); a (dms-l) and
n (-) = empirical coefficients; and .e (-) = pore-connectivity parameter (estimated
to be about 0.5).
Solving the Richard' s equation (1) in the region under consideration results in
the distribution of the pressure head. Knowing the pressure head, the vector of the
Darcy velocity can be calculated as follows:
~
v=-K(h) ·Vh.
(5)
Equation (5) is the main link between the flow model and the transport model.
2.3 The Transport Model
The transport of migrants in the subsurface proceeds by molecular diffusion, convection or advection, and hydrodynamic dispersion. Convection is the transport of
solutes due to the average velocity of the water. Transport processes due to molecular diffusion occur independently of convection. Hydrodynamic dispersion,
G. Langergraber et al.
The volumetric water content E>(h) and the unsaturated hydraulic conductivity
function K(h) are strongly non-linear functions in terms of the pressure head. Pairs
of empirical soil-moisture characteristic curves are used to describe these relationships. Soil-moisture curves can be described in analytical form, e.g. using the van
Genuchten relationships (van Genuchten 1980). The expressions of van Genuchten for volumetric water content E>(h) and unsaturated hydraulic conductivity K(h)
are given by
h
e s
h~O
and
(3)
where m = 1 -lin, n > 1, Ks = saturated hydraulic conductivity (dm3w.dm-2s.h-l),
and Se = the effective water content defined as
8-8
S =
r
e
8-8 s
r
(4)
Equations (2) and (3) contain five independent parameters: E>r and E>s = the residual and saturated water content, respectively (dm 3 w.dm- 3 s); a (dms-l) and
n (-) = empirical coefficients; and .e (-) = pore-connectivity parameter (estimated
to be about 0.5).
Solving the Richard' s equation (1) in the region under consideration results in
the distribution of the pressure head. Knowing the pressure head, the vector of the
Darcy velocity can be calculated as follows:
~
v=-K(h) ·Vh.
(5)
Equation (5) is the main link between the flow model and the transport model.
2.3 The Transport Model
The transport of migrants in the subsurface proceeds by molecular diffusion, convection or advection, and hydrodynamic dispersion. Convection is the transport of
solutes due to the average velocity of the water. Transport processes due to molecular diffusion occur independently of convection. Hydrodynamic dispersion,