  We report and discuss, by means of pore-scale numerical simulations, the
possibility of achieving a directional-dependent two-phase flow behaviour
during the process of invasion of a viscous fluid into anisotropic porous media
with controlled design. By customising the pore-scale morphology and
heterogeneities with the adoption of anisotropic triangular pillars distributed
with quenched disorder, we observe a substantially different invasion dynamics
according to the direction of fluid injection relative to the medium
orientation, that is depending if the triangular pillars have their apex
oriented (flow-aligned) or opposed (flow-opposing) to the main flow direction.
Three flow regimes can be observed: (i) for low values of the ratio between the
macroscopic pressure drop and the characteristic pore-scale capillary
threshold, i.e. for p0/pc < 1, the fluid invasion dynamics is strongly impeded
and the viscous fluid is unable to reach the outlet of the medium, irrespective
of the direction of injection; (ii) for intermediate values, 1 < p0/pc < 2, the
viscous fluid reaches the outlet only when the triangular pillars are
flow-opposing oriented; (iii) for larger values, i.e for p0/pc > 2, the outlet
is again reached irrespective of the direction of injection. The porous medium
anisotropy induces a lower effective resistance when the pillars are
flow-opposing oriented, suppressing front roughening and capillary fingering.
We thus argue that the invasion process occurs as long as the pressure drop is
larger then the macroscopic capillary pressure determined by the front
roughness, which in the case of flow-opposing pillars is halved.
