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6. Dispersivity under Partially-Saturated Conditions
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3.0
var L var M
var H
vity [cm]
Dispersiv
2.0
1.0
0.0
0.0 0.2 0.4 S 0.6 0.8 1.0
w
Figure 6.9: The relation between dispersivity of the MIM model and the
wetting phase saturation (α − S w) for three networks shown in Figure (6.1)
The dispersivity values obtained using MIM (Figure 6.9) are lower than those
obtained using the ADE model (Figure 6.6). This result has been observed by
others [Toride et al., 2003]. The reason for lower dispersivities using MIM is
that the contribution of mass transfer between mobile and immobile domains
causes extra mixing.
Compared to the ADE model, the MIM model fits the BTCs better under
unsaturated conditions (results not shown). Functionally, the ADE model provides
mean transport characteristics, e.g. average velocity, necessary to predict
solute transport. ADE results will be appropriate provided it is possible to estimate
effective (or average) values for the transport characteristics. However,
under intermediate saturations, due to the high velocity variations, one single
average velocity (such as the one used in the ADE model) may not sufficiently
describe the mean advective flux within the system. Under such a condition,
the MIM model gives better results, since it divides the pore-scale velocities
into two groups, one with a non-zero average velocity and the other one with
a velocity of zero.
At saturated conditions the velocity field variation is narrower (i.e., with an
smaller value for c.v.), and transport may be described well using the ADE.
6.5.3 Case study
In this section, we use our pore-network model to simulate solute transport
within a real porous medium. We have chosen data reported by Toride et al.
[2003], who studied the hydrodynamic dispersion coefficient under unsaturated
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