A numerical study of capillary and viscous drainage in porous media

This paper concentrates on the flow properties
when one fluid displaces another fluid
in a two-dimensional (2D) network of pores
and throats. We consider the scale where
individual pores enter the description and
we use a network model to simulate the displacement
process.
We study the interplay between the pressure
build up in the fluids and the displacement
structure in drainage. We find
that our network model properly describes
the pressure buildup due to capillary and
viscous forces and that there is good correspondence
between the simulated evolution
of the fluid pressures and earlier results
from experiments and simulations in slow
drainage.
We investigate the burst dynamics in
drainage going from low to high injection
rate at various fluid viscosities. The bursts
are identified as pressure drops in the pressure
signal across the system. We find that
the statistical distribution of pressure drops
scales according to other systems exhibiting
self-organized criticality. We compare our
results to corresponding experiments.
We also study the stabilization mechanisms
of the invasion front in horizontal 2D
drainage. We focus on the process when
the front stabilizes due to the viscous forces
in the liquids. We find that the difference
in capillary pressure between two different
points along the front varies almost linearly
as function of length separation in the direction
of the displacement. The numerical
results support new arguments about
the displacement process from those earlier
suggested for viscous stabilization. Our arguments
are based on the observation that
nonwetting fluid flows in loopless strands
(paths) and we conclude that earlier suggested
theories are not suitable to drainage
when nonwetting strands dominate the displacement
process. We also show that the
arguments might influence the scaling behavior
of the front width as function of the
injection rate and compare some of our results
to experimental work.