Page 65 - Percolation Models for Transport in Porous Media With

Chapter 4

Percolation Model of

Steady State Multiphase

Flow in Porous Media

Description of multi-phase transport in actual rocks is based on the determination
of the effective macroscopic properties for micro heterogeneous media. In prac-
tice these properties are determined mostly through direct experiments which are
rather cumbersome and time consuming. At the same time, simple theoretical
models, like that of infinite cylindrical pores, are too inaccurate and insufficient to
describe and explain many of the experimental data. To develop a more adequate
theoretical description of multiphase transport at the micro-level, one should use
the network models of the pore space structure and the percolation methods for
analysis of these models, including the necessary calculations.

4.1 Steady State Flow of Immiscible Newtonian

Fluids

Up to a fairly recent period, the majority of theoretical studies of two-phase flow
was mostly dedicated to phenomenological models of Buckley - Leverett and Rap-
poport - Leas (57, 58). Attempts made towards analyzing the said phenomenon
at the micro-level were reduced to the simulation of the medium by a bundle of
parallel capillaries with different radii. These attemts, however, bound to fail,
since the sum of phase permeabilities for such a model is constant, while all the
known experiments indicate otherwise.
Studying two-phase flow in heterogeneous media by means of numerical simu-

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