Impact of Displacement Direction Relative to Heterogeneity on Averaged Capillary Pressure-Saturation Curves

The capillary pressure-saturation relation is one of the key constitutive equations used for modeling multiphase (or partially saturated) flow in porous materials. It is known that this empirical relation depends strongly on dynamic conditions, but the impact of a heterogeneity interface on this relationship has been studied less. The present study employed optical imaging to visualize two-phase drainage under different injection rates and two flow directions, in a heterogeneous micromodel. By analyzing the curvatures of the fluid-fluid interfaces, the averaged capillary pressures for the coarse and fine sections of the micromodel, and the entire micromodel were estimated. Results show that the capillary pressure-saturation relation in the vicinity of a heterogeneity interface does not follow the conventional models proposed in the literature. The averaged capillary pressure over the entire micromodel for the fine-to-coarse (FtC) direction shows decreasing capillary pressure with decreasing wetting phase saturation. However, in the coarse-to-fine direction, a non-monotonic trend was observed. These initial findings highlight the gaps in the knowledge of upscaling capillary pressure in heterogeneous porous materials. Moreover, discontinuity in saturation was clearly more pronounced for the FtC direction, as a result of lower entry capillary resistance against the flow in the coarse section.