Controls on the stability of immiscible fluid displacement: Interplay between wettability, dynamics and heterogeneity

We study the coupled effects of wettability, flow rate and pore-scale heterogeneity on immiscible displacement of a viscous fluid. We present a discrete, pore-scale model that captures the spatiotemporal nonlocality associated with the rapid interface advancement and consequent readjustments and screening effects, and the disparate timescales of pore filling and bulk flow. Our simulations capture the transition between three invasion regimes: (i) viscous fingering with thin fingers and highly-irregular interfaces at high injection rates; (ii) capillary fingering with multiple trapped clusters in slow drainage (low contact angle θ); and (iii) stable, compact front in slow imbibition (high θ), despite a large, unfavorable viscosity ratio, in agreement with experiments. We show that increasing the wettability of the invading fluid (the contact angle) promotes cooperative pore filling that stabilizes the invasion, and that this effect is suppressed as the flow rate increases due to viscous instabilities. Stability increases in samples with lower disorder and porosity. We use scaling analysis to derive two dimensionless numbers that predict the mode of displacement.