  Immiscible fluid-fluid displacement in porous media is of great importance in
many engineering applications, such as enhanced oil recovery, agricultural
irrigation, and geologic CO2 storage. Fingering phenomena, induced by the
interface instability, are commonly encountered during displacement processes
and somehow detrimental since such hydrodynamic instabilities can significantly
reduce displacement efficiency. In this study, we report a possible adjustment
in pore geometry which aims to suppress the capillary fingering in porous media
with hierarchical structures. Through pore-scale simulations and theoretical
analysis, we demonstrate and quantify combined effects of wettability and
hierarchical geometry on displacement patterns, showing a transition from
fingering to compact mode. Our results suggest that with a higher porosity of
the 2nd-order porous structure, the displacement can keep compact across a
wider range of wettability conditions. Combined with our previous work on
viscous fingering in such media, we can provide a complete insight into the
fluid-fluid displacement control in hierarchical porous media, across a wide
range of flow conditions from capillary- to viscous-dominated modes. The
conclusions of this work can benefit the design of microfluidic devices, as
well as tailoring porous media for better fluid displacement efficiency at the
field scale.
