Modeling multicomponent flows in porous media is important for many applications relevant to energy and environment.

Advances in pore-scale imaging, increasing availability of computational resources, and developments in numerical algorithms have started rendering direct pore-scale numerical simulations of multiphase flow in pore structures feasible.  This talk presents recent advances in the numerical solution of phase-field models for systems of two-phase flows. Spatial discretization is based on interior penalty discontinuous Galerkin methods. Time discretization uses either a fully implicit method or a decoupled splitting approach. Both theory and application of the proposed methods to model flows in porous structures are discussed.