download pdf version of PhD book - Universiteit Utrecht

6. Dispersivity under Partially-Saturated Conditions
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
efficient, D, since water content and average pore-water velocity are known
from the pore-network mode. The dispersion coefficient (and thus dispersivity)
at a given saturation is determined by optimizing the analytical solution of
the ADE to the computed BTCs of average concentration at the outlet of the
network at that saturation.
Figure (6.6) shows the resulting relationship between dispersivity and saturation
(α − S w curve) for the three networks described in Section 6.2.3.
4.0
var L
var M
var H
vity [cm]
Dispersiv
3.0
20 2.0
1.0
0.0
0.0 0.2 0.4 S 0.6 0.8 1.0
w
Figure 6.6: The relationship between dispersivity (based on the ADE model)
and wetting phase saturation computed from the MDPN model for the three
networks whose pore size distributions are shown in Figure (6.1).
From Figure (6.6), it is clear that there is a strong relation between dispersivity
and saturation. The relation is non-monotonic, with the maximum dispersivity
(α max ) occuring at an intermediate saturation, S cr . This non-monotonic behavior
has been observed in laboratory experiments [Bunsri et al., 2008, Toride
et al., 2003]. To explore this non-monotonic behavior, we have analyzed various
pore-scale properties of the pore-network model under different saturations.
It is well known that dispersion in porous media is a result of velocity variation
within different pores. Under unsaturated conditions, velocity variations
depend on saturation, which may not be a simple relationship. While, under
saturated conditions the whole cross-section of a pore is available for the flow of
wetting phase (resulting in a high conductance), under unsaturated conditions,
the wetting phase flows only along the pore edges (which have less conductance
to flow) with much lower velocities. This means that the variation of
conductance is much larger under unsaturated conditions, leading to a larger
variations of velocities. We have calculated the coefficient of variation, c v , of
146