Approaches to a new theory on multiphase flow in porous media
The commonly used constitutive theory for multiphase flow in porous media on macroscopic scales -- the extended Darcy theory -- has several drawbacks regarding hysteresis and residual saturations. Experimental evidence shows that the fundamental parameter functions of the theory, i.e. capillary pressure and relative permeabilities are process dependent and hence are not parameter functions.
Within this talk I will present a new theory on multiphase flow in porous media which addresses some of these challenges. The resulting
equations of motion allow to describe flow processes where drainage
and imbibition processes occur simultaneously. To study the dynamics
of systems governed by these equations of motion, we develop an
implicit finite volume algorithm in one dimension. The numerical
studies of the Buckley Leverett problem and a comparison to the analytic solution are presented. A measurement of capillary pressure by measuring saturation profiles in porous column in the gravity field is carried out numerically. We show that the second drainage and imbibition processes can be simulated without adjusting parameters.