  Porous media with hierarchical structures are commonly encountered in both
natural and synthetic materials, e.g., fractured rock formations, porous
electrodes and fibrous materials, which generally consist of two or more
distinguishable levels of pore structure with different characteristic lengths.
The multiphase flow behaviours in hierarchical porous media have remained
elusive. In this study, we investigate the influences of hierarchical
structures in porous media on the dynamics of immiscible fingering during
fluid-fluid displacement. By conducting a series of numerical simulations, we
found that the immiscible fingering can be suppressed due to the existence of
secondary porous structures. To characterise the fingering dynamics in
hierarchical porous media, a phase diagram is constructed by introducing a
scaling parameter, i.e., the ratio of time scales considering the combined
effect of characteristic pore sizes and wettability. The findings present in
this work provide a basis for further research on the application of
hierarchical porous media for controlling immiscible fingerings.
