Transitions of Fluid Invasion Patterns in Porous Media

Abstract Fluid invasion into porous media to displace a more viscous fluid exhibits various displacement patterns. For such unfavorable displacements, previous works overlooked the dynamic effect of viscous force on pattern transitions at low flow rates. Consequently, the crossover from compact displacement to capillary fingering under various wetting conditions remains unclear. Here, we establish a theoretical model to capture pattern transitions affected by wettability and flow rate. We rigorously quantify the dynamic effect of viscous force and find that critical contact angles for the crossover from compact displacement to capillary fingering decrease with capillary number. Our model also well describes transitions from capillary fingering to the crossover to viscous fingering. The predicted phase diagram exhibits good agreement with our pore‐scale simulations and microfluidic experiments and is highly consistent with existing experiments. This work extends the classic phase diagram under unfavorable conditions and is of practical significance in subsurface applications.