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

Computational pore-scale network models describe two-phase porous media ̄ow 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 capillary pressure, saturation, and relative permeability. In addition, these models allow nontraditional porous media variables to be quanti®ed, 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 de®nition 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 ®nd that hysteresis can essentially be eliminated using a speci®c 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 ®nd that macroscopic measures of common line lengths behave similarly to ̄uid± ̄uid interfacial areas, although the functional dependencies on capillary pressure and saturation di€er to some extent. Ó 2001 Elsevier Science Ltd. All rights reserved.