Pore‐Scale Flow Dynamics Control Capillary Pressure‐Saturation‐Interfacial Area Relations in Multiphase Porous Media

Abstract

Capillary pressure–saturation relationships are central to modeling multiphase flow in porous media, yet conventional formulations often neglect how pore‐scale flow organization and interfacial geometry evolve during displacement. Here, we investigate curvature‐derived capillary pressure during immiscible two‐phase displacement using microfluidic experiments and phase‐field simulations across ranges of wettability and viscosity ratio under low‐capillary‐number conditions. Microfluidic experiments provide benchmarks for invasion morphology and specific fluid–fluid interfacial area, while simulations provide access to interfacial curvature, capillary pressure, and pathway localization. The simulations reproduce the experimental magnitude, breakthrough interfacial area, and interfacial‐area generation efficiency of the A _wn – S _inv relationship, supporting their use for constitutive analysis. We introduce a front‐localized flow‐focusing index to quantify whether invasion is distributed across many pores or concentrated into a few active pathways. This index is positively correlated with the magnitude of the local capillary‐pressure curve slope, showing that stronger pathway localization is associated with steeper capillary‐pressure changes. Representative pore‐scale events show that burst‐like filling broadens the curvature distribution and promotes abrupt pressure changes, whereas cooperative advance maintains a narrower curvature distribution and smoother pressure evolution. By fitting the coupled effective saturation, capillary pressure, and interfacial‐area data for viscously unfavorable and neutral‐to‐favorable regimes, we obtain two regime‐specific S _e – P _c – A _wn surfaces. These results show that a single surface does not adequately represent both displacement regimes. Instead, interfacial area acts as a regime‐dependent geometric mediator between saturation and capillarity, while flow focusing diagnoses the pore‐scale organization that controls the form of the capillary‐pressure relation. This framework provides a physically grounded basis for improving constitutive models of multiphase flow in porous media.