We encounter three-phase flow in porous media within a range of settings, such as enhanced oil recovery, geologic CO2 sequestration, and groundwater remediation. While an abundance of studies has been performed on the behavior of two fluid phases (e.g. oil/water or air/water) in porous media, relatively little information exists for three-phase flow systems (e.g. oil/water/air). This work explores the relationships between capillary pressure (Pc), saturation (S) and fluid-fluid interfacial area (a) for water-wet three-phase flow systems where water is the wetting phase, oil is the intermediate-wet phase, and air (or gas) is the non-wetting phase. Specifically, we examine whether the Pc-S-a relationships exhibit hysteresis during drainage and imbibition cycles. We present data collected via x-ray microtomography resulting in high-resolution three-dimensional images of the fluid configurations for varying degrees of saturation. Among the findings of the study (based on the available data), we highlight that (1) the Pc-S-a relationship is non-hysteretic for both the oil-water fluid pair, and the air-oil fluid pair, and (2) that this same relationship is independent of the initial water saturation at the point of air injection. This finding suggests that both the oil-water and air-oil fluid pairs in a three-phase system can be adequately described by the thermodynamics-based theory originally proposed by Hassanizadeh and Gray (1993), as is the case for the equivalent two-phase system. 

Rebecca Paustian, Linnéa Andersson, Johan Olav Helland, Dorthe Wildenschild,”On the Relationship Between Capillary Pressure, Saturation, and Interfacial Area for Three-Phase Flow in Water-Wet Porous Media”, Advances in Water Resources, 2021, 103905, ISSN 0309-1708, abstract 

Schematic of the sample holder.