Transport - Environmental Modeling - page 63

1E+02

1E+01

1E+00

Luckner and Schestakow
(1986)
Schröter (1984)
Gelhar et al. (1985), in:
Appelo and Postma (1993)
Beims and Mansel (1990)
Häfner et al. (1992)

1E-01

1E-02

1E-03

1E+00 1E+01 1E+02 1E+03

Pathlength [m]

Fig. 3.3 Scale dependency of longitudinal dispersivity in porous media, as observed by different
authors

where in the diffusivity D different contributions have to be considered: from the
molecular scale, from tortuosity or from dispersion at the regional scale. Similar
formulae can be stated for the flux components in y - and z -direction. In vector
notation results:

j ¼ D rc þ v c (3.15)

Here, the coefficient is written as a matrix in order to account for the general
case, as described above.
Now it is time to use this result to replace the flux terms in the mass conservation
(2.4). The result in one dimension is:

y @c

@t ¼ @

D @ c

@x y @x vc

þ q (3.16)

In case of constant velocity one obtains the most common formulation of the
transport equation:

yv @ c y @ c

@t ¼ @ @x yD @ c @x þ q

(3.17)

@x