Convenient formulae for determination of relative permeability from unsteady-state fluid displacements in core plugs

Convenient interpretation formulae are presented and demonstrated for determination of relative permeability from unsteady-state, two-phase fluid displacements in laboratory core tests under constant rate or pressure conditions. These formulae allow the effective processing of the after-breakthrough immiscible fluid displacement data by considering constant fluid and core properties, negligible gravity effect, and sufficiently high flow rates to overcome the capillary end-effects. The fluid mobility and characteristic parameters of immiscible displacement processes are related by means of Darcyʹs law and specially derived functions. Analyses of various experimental data demonstrate that the present analytic method uniquely and rapidly determines the relative permeability within the accuracies of the simplifying considerations, which may closely approximate the conditions of usual laboratory core tests.