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5.2 Network Generation
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to relate it to the radii sizes of the two terminating pore bodies, as suggested
by Raoof and Hassanizadeh [2010b]. By equating the area of the triangle to
the area of the equivalent circle we fully specify the triangular cross-section.
Similarly, for rectangular pore-throats, the rectangle area is obtained from the
area of the equivalent circle. Knowing the area and the shape factor, we can
calculate the dimensions of the rectangle by solving a quadratic equation.
5.2.3 Coordination number distribution in MDPN
One of the main features of the MDPN is that pore throats can be oriented not
only in the three principal directions, but in 13 different directions, allowing
a maximum coordination number of 26, as shown in Figure (2.1). To get a
desired coordination number distribution, we follow an elimination procedure
to rule out some of the connections. The elimination procedure is such that a
pre-specified mean coordination number can be obtained. A coordination number
of zero means that the pore body is eliminated from the network, so there
is no pore body located at that lattice point. A pore body with a coordination
number of one is also eliminated except if it is located at the inlet or outlet
boundaries (so it belongs to the flowing fluid backbone). Thus no dead-end
pores are included in the network. Details of network generation can be found
in Chapter 2.
Since in many pore-network modeling studies, a fixed coordination number of
six is employed, we chose to generate a stochastic network with the coordination
number ranging from zero to 16, but with a mean coordination number
of six. However, we shall also present results for networks with other mean
coordination numbers, related to some real porous media. The distribution of
coordination number and a representative domain of the network used in this
study are given in Figure (5.2).
5.2.4 Pore space discretization
Flow in both pore bodies and pore throats arises from pressure gradients. The
conductivity of a flow path is dominated by the narrowest constriction along
the path. Under saturated conditions, considering the larger sizes of pore bodies
compared to pore throats, one may safely neglect the resistance to the flow
within pore bodies (thus assuming zero pressure gradient within a pore body)
and assign conductances only to the pore throats. This has been the common
practice in almost all pore-network models. However, under unsaturated con-
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