Role of Pore‐Scale Disorder in Fluid Displacement: Experiments and Theoretical Model

The flow of multiple immiscible fluids in disordered porous media is important in many natural processes and subsurface applications. The pore‐scale disorder affects the fluid invasion pathways significantly and induces the transitions of displacement patterns in porous media. Extensive studies focus on pattern transitions affected by disorder under quasistatic or dynamic conditions, but how the disorder controls the pattern transitions from capillary‐dominated regime to viscous‐dominated regime is not well understood. Here, we combine microfluidic experiments and theoretical analysis to investigate the role of disorder in fluid displacement. We perform drainage experiments with four different disorders under six flow rate conditions and show that increasing disorder destabilizes displacement fronts for all flow rates considered. Based on the scaling analysis of pore‐filling events, we propose a theoretical model that describes the pattern transitions from compact displacement to capillary to viscous fingering as functions of disorder and capillary number. The effects of disorder on both capillary and viscous forces are quantified within the theoretical model. The phase diagram predicted by this model agrees well with our experimental results. We further elucidate the role of disorder in fluid displacement via energy conversion and dissipation. We find that increasing disorder enhances the capillary instabilities and induces more energy dissipated in a capillary‐dominated regime, with the dissipation ratio increasing from 28.3% to 56.7%. Our work extends the classic phase diagram to consider the effect of disorder and provides a better understanding of the impact of the disorder on flow behaviors by energy dissipation. Key Points We propose a theoretical model to describe the transitions of displacement patterns as functions of disorder and capillary number Effects of disorder on both capillary and viscous forces are considered in the model and the phase diagram agrees with experiments Higher disorder destabilizes fronts and dissipates more energy, with the dissipation ratio increasing from 28.3% to 56.7%