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7.3 Unsaturated flow modeling
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generation can be found in Chapter (2).
In this study, we have chosen to make a MDPN with an average coordination
number of 4.5. This value corresponds to the sand packing [Talabi and Blunt,
2010, Talabi et al., 2008]. The distribution of coordination number is given in
Figure (7.2).
0.25
Normalized frequency
0.2
0.15
0.1
0.05
0
1 2 3 4 5 6 7 8 9 10 11 12
Coordination number
Figure 7.2: The coordination number distribution of the MDPN model. The
mean coordination number is equal to 4.5.
7.2.4 Pore space discretization
To take into account the effect of limited mixing within the drained pores we
follow our approach which was explained in Section 6.2.4, i.e., under unsaturated
conditions, we consider each corner of the pore, occupied by the wetting
space, as a separate element with its own pressure and concentration. In addition,
since we take into account adsorption process, We also calculate separate
adsorbed mass concentration for each of these elements. Thus, for a cubic pore
body, 8 different corner elements exist with 8 different pressure and concentration
of solution and adsorbed mass assigned to them (see Figure 6.3a).
7.3 Unsaturated flow modeling
We wish to simulate drainage in a strongly water wet porous medium, initially
saturated with water. The non-wetting phase is assumed to be air, which can
flow under negligibly small pressure gradients. To simulate drainage in our
network, the displacing air is considered to be injected through an external
reservoir which is connected to every pore-body on the inlet side of the network.
The displaced water escapes through the outlet face on the opposite side.
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