Investigating Relationship Between Capillary Pressure, Phase Saturation, and Interfacial Area in a Three-Phase Flow Water-Wet System

Immiscible fluid displacement in porous media is encountered in many applications, including waterflooding in oil reservoirs, carbon capture and storage, groundwater remediation, and underground hydrogen storage. Displacement is controlled by capillary forces which is typically assumed to be a function of saturation (S), although the relationship is known to be hysteretic, in that the capillary pressure (P_c) is different for displacement where the saturation is increasing or decreasing for the same rock sample. A thermodynamically based theory predicts capillary pressure is a function of both saturation and specific fluid-fluid interfacial area (a). Recent advances in X-ray micro-computed tomography (micro-CT) allow for the saturation, capillary pressure, and the fluid-fluid interfacial area to be measured directly in situ on three-dimensional images of the rock sample and fluids. In this study, we investigated the relationship P_c-S-a in a steady-state experiment conducted on a water-wet Bentheimer sandstone. In our three-phase system water was the most wetting phase, oil was intermediate wet, and gas was the non-wetting phase. We examine the effect of introducing the gas to the water-oil fluid pair and the theory for water-oil and oil-gas fluid pairs. The main findings were as follows. (1) Introducing gas will push the oil to intermediate-sized pores while the oil also forms spreading layers, which results in no oil trapping; hence P_c-S hysteresis is not observed for the water-oil fluid pair compared to two-phase flow. Trapping has a significant effect on hysteresis. (2) The P_c-S-a relationship eliminated hysteresis and produced a unique three-dimensional surface, for both fluid pairs for steady-state conditions.