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We study the role of the capillary number, $Ca$ and of the surfacewettability on the dynamics of the interface between an invading and adefending phase in a porous medium by means of numerical simulations. We employa hybrid phase field-immersed boundary approach to successfully model thecontact line dynamics over the solid objects. We map the three dominant modesgoverning the motion of the interface, namely, viscous fingering, capillaryfingering, and stable penetration, in the ($Ca$-$\theta$) plane, with $\theta$the static contact angle prescribed at the solid pores. Viscous fingering isdominant at larger capillary numbers irrespective of the contact angle.Capillary fingering dominates at lower values of $Ca$ and pores hydrophobic tothe invading phase, while stable penetration is observed on hydrophillicsurfaces. We also show that the pressure needed for the invading phase toadvance at constant flow rate decreases with the capillary number, andincreases with the contact angle at the lowest capillary numbers considered.The latter is due to a significant increase of the length of the interface inthe case of capillary fingering. Finally, we show that it is possible toidentify the different interfacial modes by measuring the penetration lengthand velocity during the medium filling.

The role of wetting on the flow of two immiscible fluids in porous media