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Direct numerical simulations are used to elucidate the interplay ofwettability and fluid viscosities on immiscible fluid displacements in aheterogeneous porous medium.We classify the flow regimes based usingqualitative and quantitative analysis into viscous fingering (low $M$), compactdisplacement (high $M$), and an intermediate transition regime ($M \approx 1$).We use stability analysis to obtain theoretical phase boundaries between theseregimes, which agree well with our analyses. At the macroscopic (sample) scale,we find that wettability strongly controls the threshold $M$ (at which theregimes change). At the pore scale, wettability alters the dominantpore-filling mechanism. At very small $M$ (viscous fingering regime), smallerpore spaces are preferentially invaded during imbibition, with flow of films ofinvading fluid along the pore walls. In contrast, during drainage, burstsresult in filling of pores irrespective of their size. As $M$ increases, theeffect of wettability decreases as cooperative filling becomes the dominantmechanism regardless of wettability. This suggest that for imbibition at agiven contact angle, decreasing $M$ is associated with change in effectivewetting from neutral-wet (cooperative filling) to strong-wet (film flow).

Interplay of viscosity and wettability controls fluid displacement in porous media