“Relations between Seepage Velocities in Immiscible, Incompressible Two-phase Flow in Porous Media”
The paper from A. Hansen, S. Sinha, D. Bedeaux, S. Kjelstrup. M. Aa. Gjennestad and M. Vassvik on “Relations between Seepage Velocities in Immiscible, Incompressible Two-phase Flow in Porous Media” has become the most downloaded paper ever in Transport in Porous Media, the main journal in porous media research, since 1986.
We demonstrate in the paper how certain easily overlooked symmetries in immiscible two-phase flow in porous media lead to new equations constraining how the two fluids move. (A symmetry is a property that is unchanged after transforming the system.) The ultimate goal of this work is to be able to present a complete theoretical description of immiscible two-phase flow in the limit where the porous medium may be seen as a continuum, i.e. the scales where relative permeability theory today reigns
Abstract: Based on thermodynamic considerations, we derive a set of equations relating the seepage velocities of the fluid components in immiscible and incompressible two-phase flow in porous media. They necessitate the introduction of a new velocity function, the co-moving velocity. This velocity function is a characteristic of the porous medium. Together with a constitutive relation between the velocities and the driving forces, such as the pressure gradient, these equations form a closed set. We solve four versions of the capillary tube model analytically using this theory. We test the theory numerically on a network model.