Hydrodynamic dispersion in heterogeneous anisotropic porous media: A simple model for anomalous diffusion emergence

Anomalous transport processes in porous media have become a central physical issue due to the increasing amount of processes and applications where it appears, ranging from contaminant transport in aquifers and oil recovery to anomalous diffusion in biological membranes. In all these cases, the existence of strong heterogeneities and anisotropies make proper physical and mathematical modelling a complicated problem, leading to simplified models where these spatial features and their implications for transport and diffusion are treated separately. In this work we propose a simple model for transport in porous media that includes anisotropy and strong heterogeneities. We show that depending on how strong the medium heterogeneities are, different regimes of superdiffusive transport emerge, going from superdiffusion due to long-range correlations to Lévy walks and ballistic diffusion.