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5. Pore-Network Modeling of Two-Phase Flow
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We show that the resistance to the flow within these filaments of fluids is comparable
to the resistance to the flow within pore throats. The resulting saturation-relative
permeability relationships show very good agreement with measured curves.
While our computations have been restricted to relative permeability curves, they
demonstrate the significance of this formulation of pore-network modeling to predict
other transport properties such as dispersivities and mass transfer coefficients,
through including limited mixing within the pore bodies. We will address this issue
in Chapter 5.
5.1 Introduction
5.1.1 Pore-network modeling
Understanding of multiphase flow and transport in porous media is of great
importance in many fields, including contaminant cleanup and petroleum engineering.
Modeling multiphase fluid flow in porous media requires specification
of the capillary constitutive properties of the porous medium. Examples are i)
the relationship between the capillary pressure, P c (the difference between the
pressures in the nonwetting and wetting fluids) and the fluid saturation, S, ii)
the relative permeability, k r , as a function of either the saturation or capillary
pressure, and iii) the relationship between dispersivity and saturation in solute
transport processes.
The relative permeability of a fluid is a measure of the conductance of the
porous medium for that fluid at a given saturation. Relative permeability
measurements on field samples are difficult and time consuming. In general,
experimental determination of the P c − S relationship is easier than measurement
of relative permeability. For this reason, empirical relationships, such as
those of Brooks and Corey [Brooks and Corey, 1964] and Van Genuchten [van
Genuchten, 1980], are often used to model the dependence of relative permeability
on capillary pressure or saturation.
Another approach for obtaining multiphase constitutive properties is to use
Pore-Network Models (PNMs). One of the early attempts to estimate relative
permeability was using a bundle-of-capillary-tubes model. This was based on
the assumption that a porous medium may be modeled as bundle of capillary
tubes of various diameters. However, such models ignore the interconnected
nature of porous media and often do not provide realistic results. PNMs, first
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