References

Steady-state two-phase ow in porous media has received very little at-tention compared to the instabilities that occur in connection with ooding, i.e., when the porous medium is initially saturated with one of the uids whereafter the other uid is injected into it displacing the rst. Steady-state ow, on the other hand, occurs e.g. in a representative volume element (RVE) of a porous medium when statistically the ow leaving the RVE is the same as that entering it. At low ow rates, steady state ow essentially consists of one uid being held in place by capillary forces whereas the other uid ows. However, at higher ow rates, both uids will move and there will be a incessant breakup and merging of uid clusters. In this regime, the ow settles into a state which is independent of the initial conditions and determined only by the ow parameters. This opens for a statistical description of the ow which is closely related to that of statistical mechanics and thermodynamics [1]. We discuss this approach, based on a numerical model [2], both from a general point of view and using specic examples [3, 4, 5, 6]. In particular we will discuss the stability of the interface between two immiscible uids owing in parallel in a porous medium [7]