The difference between steady-state and unsteady-state relative permeabilities

Abstract

In constructing simulations, it is commonly assumed that steady-state relative permeabilities can be used to describe displacements, which are unsteady-state flows. In order to test this assumption, a statistical structural model is used in the context of local volume averaging to examine the effects of interfacial tension, the interfacial viscosities, wetting and the viscosity ratio upon the capillary pressure and relative permeability functions in a displacement. The statistical structural model is a highly simplified idealization of the local pore structure, in which pores are randomly oriented in space, but no pore interconnections are recognized. While the statistical structural model is too simplified to give accurate descriptions of the relative permeabilities, it should be sufficient to determine whether significant qualitative differences between steady-state and unsteady-state relative permeabilities might be expected.