It is well known that relative permeabilities (RPs) can vary depending on the flow configuration and are lower during counter-current flow as compared to co-current flow.

In this paper we use a novel two-phase momentum-equation approach to generate effective RPs where this dependence (and others) is well captured whereby the fluids transfer momentum due to fluid-rock interaction and fluid-fluid interaction.

During co-current flow the faster moving fluid accelerates the slow fluid, but is itself decelerated, while for counter-current flow they are both decelerated.

We investigate recovery of oil from a matrix block surrounded by water due to a combination of gravity drainage (GD) and spontaneous imbibition (SI), relevant for fractured reservoirs.

In capillary-dominated systems the flow is counter-current and viscous coupling can result in increased time scale of the recovery process.

During gravity-dominated flow it is more co-current and applying co-currently measured relative permeabilities from the lab becomes a better assumption.

Using one set of parameters the momentum-equation approach is thus able to model the behavior of blocks of different operating at different Bond numbers in the reservoir.


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