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5.3 Modeling flow in the network
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dimensionless to obtain a formula for the dimensionless conductance, g ∗
g ∗ = gµ
r 4 c
∫
=
A ∗ v ∗ zda ∗ (5.13)
We have performed this calculation for corner half-angles ranging from 5 to 75
degrees. The resulting graph is shown in Figure (5.5).
Figure 5.5: The dimensionless hydraulic conductance versus corner half-angle.
The line shows the result of this study and circles show the result obtained by
Patzek and Kristensen [2001] after rescaling the dimensionless groups used in
their study.
Patzek and Kristensen [2001] have also calculated the dimensionless conductance
for drained triangular cross-sections. In their work, they used the side
length (shown as b in Figure 5.4b) as the reference length. Since r c and b are
related (r c = b × tan(α)), we can convert the results to each other. Their
results are shown as solid circles in Figure (5.5). It is clear that there is an
excellent agreement between the two results. However, there is an advantage in
choosing r c as the reference length. Under quasi-static conditions, the capillary
pressure and, therefore, the radius of curvature of all interfaces are the same
in the network (for all pores). Thus, at any given saturation (or any given
capillary pressure) a single curve can be used for all pores. This will not be the
case if b is used as the reference length. Also, using b as the reference length,
the relation between dimensionless conductance and corner half-angle will be
non-monotonic (see Patzek and Kristensen [2001]), while, as shown in Figure
(5.5), using r c as the reference length, we get a monotonic relation.
An important conclusion can be drawn from Figure (5.5) regarding the significance
of conductance of edges of pore bodies invaded by the non-wetting
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