Flows in highly heterogeneous porous media are found in many practical fields, such as hydrology, petroleum engineering, and chemical engineering. The case of two-region heterogeneous media (fractured media, catalytic beds, etc.) plays a fundamental role. The different questions associated with this specific case are illustrated in this paper for two different kinds of transport: (i) flow of a slightly compressible fluid, (ii) dispersion of a tracer. Many different theoretical models are implemented using COMSOL Multiphysics™. These models correspond to direct simulation and macro-scale or large-scale models such as fully averaged models or mixed models.