The role of phase interference in steady-state two-phase flow in porous media

When two fluids flow simultaneously in a porous medium at a low flow rate, known as steady-state two-phase flow, the total pressure drop deviates from a linear relationship with the Darcy flux. This deviation is primarily caused by the capillary pressure drop induced by interphase interference at pore throats. This study aims to estimate the capillary pressure drop based on fluid–fluid interfacial area at the pore scale. Recognizing that steady-state two phase flow typically exhibits discontinuous behavior, we proposed a simple equation to explain the relationship between total pressure drop, viscous pressure drop, and capillary pressure drop. Experiments were conducted in transparent micromodels to investigate the effects of flow rate, average viscosity and pore structure under both drainage and imbibition conditions. The results indicate a linear relationship between capillary pressure drop and the specific interfacial area of the moving wetting and moving non-wetting phase. Additionally, the slope of the capillary pressure drop-specific interfacial area curve is only related to the flow rate. Moreover, we established and verified the relationship between the specific interfacial area and relative permeability. This study provides new insights into the nonlinear relationship between Darcy flux and pressure drop in two-phase flow.