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Raoof, A. and Hassanizadeh S. M., “A new formulation for pore-network modeling of
two-phase flow”, accepted for publication at Water Resources Research, 2011.
CHAPTER 5
A NEW FORMULATION FOR PORE-NETWORK
MODELING OF TWO-PHASE FLOW
The question is not what you look at, but what you see.
Henry David Thoreau
Abstract
Pore network models of two-phase flow in porous media are widely used to investigate
constitutive relationships between saturation and relative permeability
as well as capillary pressure. Results of many studies show discrepancy between calculated
relative permeability and corresponding measured values. Often calculated
values overestimate the measured values. An important feature of almost all porenetwork
models is that the resistance to flow is assumed to come from pore throats
only; i.e., the resistance of pore bodies to the flow is considered to be negligible
compare to the resistance of pore throats. We contend that this simplification may
considerably affect the magnitude of the relative permeability curves.
In this study, we present a new formulation for pore-network modeling of two-phase
flow, which accounts for the resistant to the flow within the pore bodies. In a quantitative
investigation, we have shown the significance of this effect under primary
drainage conditions. The pore space is represented by cubic pore bodies and parallelepiped
pore throats in a MDPN. model, which allows for a distribution of coordination
numbers ranging between zero and 26. This topological property, together
with geometrical distributions of pore sizes are used to mimic the microstructure of
real porous media. Under unsaturated conditions, the wetting fluid is considered to
fill only spaces along edges of cubic pore bodies.