We present an efficient numerical model for compositional three-phase flow in complex fractured media in 2D and 3D. The capillary effect is included in the simulations. The algorithm accounts for one aqueous phase and two hydrocarbon phases. CO2 is assumed to be soluble in the aqueous phase. We extend the fracture cross-flow equilibrium to three phases for the first time. The cubic plus association (CPA) equation of state describes the aqueous phase. To avoid small time steps in fracture elements we adopt an implicit time scheme discretization in the fractures. Capillary pressure gradients are computed at the element level. The phase fluxes are evaluated with the hybridized form of the mass conservative mixed finite element (MFE). A finite volume (FV) discretization is used in the mass balance equations in the fractures and the discontinuous Galerkin (DG) method is used in the matrix with an explicit time scheme. Pressure is implicit in the whole domain. Our algorithm accounts for different types of grids in 2D and in 3D.