Leaching of Contaminants to Groundwater - Dealing with Contaminated Sites: From Theory Towards Practical Application - page 811

The above pore-scale dispersion processes lead to an overall (macroscopic)
hydrodynamic dispersion process that can be described mathematically in approx-
imately the same way as molecular diffusion using Fick's first law. Adding the
dispersion and diffusion processes leads then to:

D h ∂

c

D ) ∂

c

J h =− θ

c =− θ

( D m + (18.31)

∂ ∂ z

where D h is the hydrodynamic dispersion coefficient [L 2 T − 1 ] that accounts for both
molecular diffusion and mechanical dispersion (Fetter 1999 ), D m is the mechani-
cal dispersion coefficient [L 2 T − 1 ], and D is the liquid phase diffusion coefficient
[L 2 T − 1 ]. The mechanical dispersion coefficient in one-dimensional systems has
been found to be approximately proportional to the average pore-water velocity v
( )[LT − 1 ], with the proportionality constant generally referred to as the (lon-

gitudinal) dispersivity

= q / θ

(Biggar and Nielsen 1967 ). The discussion above holds for
one-dimensional transport; multi-dimensional applications require the use of a more
complicated dispersion tensor involving longitudinal and transverse dispersivities
(e.g., Bear 1972 ).
Dispersivity is a transport parameter that is often obtained experimentally by
fitting measured breakthrough curves with analytical solutions of the advection-
dispersion equation (discussed further below). The dispersivity often changes with
the distance over which contaminants travel. Values of the longitudinal dispersivity
usually range from about 1 cm for relatively short, packed laboratory columns, to
about 5 or 10 cm for field soils. Longitudinal dispersivities can be significantly larger
(up to hundreds of meters) for regional groundwater transport problems (Gelhar
et al. 1985 ). If no other information is available, a good first approximation is to
use a value of one-tenth of the transport distance for the longitudinal dispersivity
(e.g, Anderson 1984 ), and a value of one-hundred of the transport distance for the
transverse dispersivity when multi-dimensional applications are considered.

λ

18.3.1.3 Advection

Advective transport refers to contaminants being transported with the moving fluid,
either in the liquid phase ( J lc )orthesoilgas( J gc ), i.e.:

J c = qc (18.32)

where we now use a more general notation by omitting the subscripts l and g.
Advective transport generally is dominant in the liquid phase. Advective transport
may also occur in the gaseous phase, but is often neglected since its contribution is
generally negligible compared to gaseous diffusion.
The total contaminant flux density in both the liquid phase and soil gas is
obtained by incorporating contributions from the various transport processes into
Eq. ( 18.27 ) to obtain