R. Hilfer and F. Doster
Institute for Computational Physics, Universität Stuttgart, 70569 Stuttgart, Germany
Abstract.
The concepts of relative permeability and capillary pressure
are crucial for the accepted traditional theory of two phase
flow in porous media. Recently a theoretical approach was
introduced that does not require these concepts as input
[25, 26].
Instead it was based on the concept of hydraulic percolation
of fluid phases.
This paper presents the first numerical solutions of the
coupled nonlinear partial differential equations introduced
in [26].
Approximate numerical results for saturation profiles
in one spatial dimension have been calculated.
Long time limits of dynamic timedependent profiles are
compared to stationary solutions of the traditional theory.
The initial and boundary conditions are chosen to model the
displacement processes that occur when a closed porous column containing
two immiscible fluids of different density is raised from a horizontal
to a vertical position in a gravitational field.
The nature of the displacement process may change locally in space
and time between drainage and imbibition.
The theory gives local saturations for
nonpercolating trapped fluids near the endpoint of the displacement.
