A total pressure-saturation formulation of two-phase flow incorporating dynamic effects in the capillary-pressure-saturation relationship

摘要

New theories suggest that the relationship between capillary pressure and saturation should be enhanced by a dynamic term that is proportional to the time rate of change of saturation. This so-called dyamic capillary pressure formulation is supported by laboratory experiments, and can be included in various forms of the governing equations for two-phase flow in porous media. An extended model of two-phase flow in porous media may be developed based on fractional flow curves and a total pressure - saturation description that includes the dynamic capillary pressure terms. A dimensionless form of the resulting equation set provides an ideal tool to study the relative importance of the dynamic capillary pressure effect. This equation provides a rich set of mathematical research questions, and numerical solutions to the equation provide insights into the behavior of two-phase immiscible flow. For typical two-phase flow systems, dynamic capillary pressure acts to retard infiltration fronts, with responses dependent on system parameters including boundary conditions.