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5.1 Introduction
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ber of six.
There exist many PNM studies investigating various geometrical and topological
properties of porous media and their effect on flow and transport in porous
media. They include: the effect of pore size distribution [Lindquist et al., 2000,
Jerauld and Salter, 1990], network structure and coordination number [Al-
Kharusi and Blunt, 2008, Sok et al., 2002, Mahmud et al., 2007, Arns et al.,
2004, Øren and Bakke, 2003a, Mogensen and Stenby, 1998], pore angularity
and shape factors [Sholokhova et al., 2009, Zhang et al., 2010, Patzek and Kristensen,
2001, Øren et al., 1998a], and correlation functions [Arns et al., 2003b,
Rajaram et al., Ferrand et al., 1994, Lymberopoulos and Payatakes, 1992, Jerauld
and Salter, 1990, Tsakiroglou and Payatakes, 1991, Renault, 1991, Ioannidis
et al., 1993]. In almost all of these studies, the selected pore size distributions
are such that most of the pore space is assigned to the pore bodies. In
such cases, the modeling of flow within pore bodies will be of major influence
on hydrodynamic properties of the network, certainly in the case of flow on
partially drained pore spaces. This issue, however, unlike the above-mentioned
properties of porous media has not been addressed in any pore-network study.
We will address this particular issue in this study.
5.1.3 Objectives and approach
Under partially-saturated conditions, much of a pore body is occupied by the
non-wetting phase, such that the wetting phase can only flow through the
edges, similar to the flow conditions within drained pore throats. Under these
conditions, the effect of resistance within the pore-bodies become important
and comparable to pore throats; taking this effect into account can improve
the result of k r − S calculations. This is, however, not possible within current
pore-network modeling approaches. In fact, this is one of the shortcomings
of pore-network modeling compared to other pore-scale modeling approaches,
such as lattice-Boltzmann method (LBM). LBM has the advantage that it fully
discretizes the space within each pore space. In PNM, however, the smallest
discretization unit is normally one pore body or pore throat. That is, in PNM,
only one (average) pressure (or one average concentration) is assigned to each
pore body. Thus, using pore body or pore throat discretization, one needs
to apply so-called effective parameters [Meile and Tuncay, 2006, Raoof and
Hassanizadeh, 2008, 2010b]. While this assumption may be acceptable for a
fully saturated pore body (considering the large size of a pore body compared
to pore throats connected to it), it is a crude approximation when the water
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