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5. Pore-Network Modeling of Two-Phase Flow
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Figure (5.6) show that, for a given cross section type, with increasing the
corner angle, the cross section changes from a regular hyperbolic polygonal cross
section to a regular polygonal cross section, and the shape factor increases. In
practice, the choice of cross section type is based on the measured shape factor
distribution of the pore throats acquired by image analysis [Joekar-Niasar et al.,
2010].
Integrating dimensionless velocity field over the flow domain, we calculated
dimensionless conductance for each domain. Figure 5.7 shows the relation
between dimensionless conductance and shape factor and number of vertices.
Figure 5.7: relation between dimensionless conductance, g ∗ , and shape
factor, G, and number of vertices, n.
Figure (5.7) shows that dimensionless conductance decreases with increase in
number of vertices and decresae in shape factor.
Figure (5.8) shows the relation between dimensionless conductance and ϕ for
polygons with different number of vertices. As shown in Figure (5.8), with
increasing of number of vertices, the maximum value of shape factor, possible
for a specific type of polygon, increases. The value of g ∗ decreases with increase
in corner angle, ϕ.
5.3.4 Calculation of relative permeability curves
To calculate relative permeability, we need to solve for fluid flow within all pores
simultaneously. The governing system of equations is obtained by writing the
volume balance for each and every corner element of all pore bodies. A corner
element i is connected to three other corner elements in the same pore body
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