The anisotropic properties of clay-rich porous media have significant impact on the directional dependence of fluids migration in environmental and engineering sciences. This anisotropy, linked to the preferential orientation of flat anisometric clay minerals particles, is studied here on the basis of the simulation of three-dimensional packings of non-interacting disks, using a sequential deposition algorithm under a gravitational field. Simulations show that the obtained porosities fall onto a single master curve when plotted against the anisotropy value. This finding is consistent with results from sedimentation experiments using polytetrafluoroethylene (PTFE) disks and subsequent extraction of particle anisotropy through X-ray microtomography. Further geometrical analyses of computed porous media highlight that both particle orientation and particle aggregation are responsible of the evolution of porosity as a function of anisotropy. Moreover, morphological analysis of the porous media using chord length measurements shows that the anisotropy of the pore and solid networks can be correlated with particle orientation. These results indicate that computed porous media, mimicking the organization of clay minerals, can be used to shed light on the anisotropic properties of fluid transfer in clay-based materials.