Modelling support of functional relationships between capillary pressure, saturation, interfacial area and common lines

Computational pore-scale network models describe two-phase porous media flow systems by resolving individual interfaces at the pore scale, and tracking these interfaces through the pore network. Coupled with volume averaging techniques, these models can reproduce relationships between measured variables like capilary pressure, saturation, and relative permeability. In addition, these models allow nontraditional porous media variables to be quantified, such as interfacial areas and common line lengths. They also allow explorations of possible relationships between these variables, as well as testing of new theoretical conjectures. Herein we compute relationships between capillary pressure, saturation, interfacial areas, and common line lengths using a pore-scale network model. We then consider a conjecture that definition of an extended constitutive relationship between capillary pressure, saturation, and interfacial area eliminates hysteresis between drainage and imbibition; such hysteresis is commonly seen in the traditional relationship between capillary pressure and saturation. For the sample pore network under consideration, we find that hysteresis can essentially be eliminated using a specific choice of displacement rules; these rules are within the range of experimental observations for interface displacements and therefore are considered to be physically plausible. We find that macroscopic measures of common line lengths behave similarly to fluid-fluid interfacial areas, although the functional dependencies on capillary pressure and saturation differ to some extent.