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6. Dispersivity under Partially-Saturated Conditions
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conditions, there is a reasonable agreement between the results obtained from
the pore-network model and experiments. The deviation between the two results
could be due to the simple geometries used within the network model,
together with the fact that we did not have detailed information on the pore
size distributions of the sand sample used by Toride et al. [2003]. Considering
the small size of the pore network compared to the experimental sample,
we believe that our network does not capture all heterogeneities present within
the real sample. However, the comparison shows the capability of pore-network
modeling to capture dispersion under unsaturated conditions.
Figure (6.11) compares the fraction of the mobile phase, β = θm θ , as of a function
of saturation, calculated by the MDPN model with that obtained through
experiment [Toride et al., 2003].
Figure 6.11: Comparison between fraction of the mobile phase calculated
using the MDPN model and the results based on experiments by Toride et al.
[2003].
Under saturated conditions, the number of immobile pores is very small and
the mobile fraction is close to unity. As a result the ADE model adequately
describes the BTC under saturated conditions. Padilla et al. [1999] and Toride
et al. [2003] observed the same for a saturated sand packing (e.g., β > 0.95).
The fraction of (practically) immobile water will increase as saturation decreases
up to some extent, and then it starts to decrease with further decrease
in saturation. This is also seen in Figure (6.11) in both the pore-scale modeling
and experimental results.
When the porous medium is at higher saturation, some pores (mostly percolating
saturated pores) have higher velocities creating the mobile phase. The rest
of pores (mostly drained pores) with much lower velocities create a relatively
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