Variational formulations of multiphase flow and transport models in the subsurface are established. Specifically, incompressible and compressible Darcian single-phase flow, as well as miscible and immiscible two-phase flow, are considered. Further, compositional multiphase flow is treated as a more complex physical model, elaborating, in particular, on the triphasic water-oil-gas multicomponent flow. For qualitative analysis, mixed variational modeling is performed, determining existence results on the basis of composition duality principles. Also, for parallel computing, macro-hybrid variational reformulations are addressed.

multiphase flow and transport through porous media, mixed and macro-hybrid variational modeling, primal and dual evolution variational problems, composition duality methods and principles, existence analysis.