An advanced constitutive law in multiphase flow model for simulations in compressible media

The purpose of this investigation is to implement a new constitutive law of saturation-capillary pressure into a fractional flow-based multiphase flow model to simulate compressible subsurface flow problems. Using the new constitutive law to describe the saturation-capillary pressure relations alleviates an undue constraint on pressure distributions inherent in a widely used law. This makes the present model able to include all possible solutions of pressure distributions in subsurface flow modeling. Finite element methods (FEM) are used to discretize the three governing equations for three primary variables-saturation of water, saturation of total liquid, and total pressure. Four examples with different pressure distributions are presented to show the feasibility and advantage of using the new constitutive law. The results verify the feasibility and capability of the present model for subsurface flow systems to cover all possible pressure distributions.