Page 96 - Percolation Models for Transport in Porous Media With
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Chapter 5
Percolation Model of
Non-Steady State
Two-Phase Flow in Porous
Media
5.1 Immiscible Displacement of a Viscous Fluid
by a Non-Viscous One
At present, the description of non-steady state flow of immiscible fluids is carried
out using equilibrium phase permeabilities and a capillary pressure curve. The
mentioned functions are determined by the saturation of porous media with any
of the phases and do not depend on time and space coordinates. In this case
the phase permeabilities are determined by the results of laboratory experiments
on steady state two-phase flow, and the Leverett's function is found from the
porometric curve.
However experimental data [14, 23] indicate the relaxational nature of inter-
phase equilibrium attainment in non-steady state fluid flow. Considering this
effect, a phenomenological model was suggested in [24] for the description of two-
phase flow. This model includes time-dependent phase permeability with charac-
teristic time of relaxation towards the equilibrium value. However, experimental
determination of these dependencies encounters great technical difficulties.
In this study, for the description of two-phase flow in micro heterogeneous
porous media a model of "forest growth" was proposed. It is a percolation model
which permits to take into account the non-equilibrium effects of such fluid flow.
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