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

Computational pore-scale network models describe two-phase porous media flo w systems by resolving individual interfaces at the pore scale, and trackin g these interfaces through the pore network. Coupled with volume averaging techniques, these models can reproduce relationships between measured varia bles like capillary pressure, saturation, and relative permeability. In add ition, these models allow nontraditional porous media variables to be quant ified, such as interfacial areas and common line lengths. They also allow e xplorations of possible relationships between these variables, as well as t esting of new theoretical conjectures. Herein we compute relationships betw een capillary pressure, saturation, interfacial areas, and common line leng ths using a pore-scale network model. We then consider a conjecture that de finition of an extended constitutive relationship between capillary pressur e, saturation, and interfacial area eliminates hysteresis between drainage and imbibition; such hysteresis is commonly seen in the traditional relatio nship between capillary pressure and saturation. For the sample pore networ k under consideration, we find that hysteresis can essentially be eliminate d using a specific choice of displacement rules; these rules are within the range of experimental observations for interface displacements and therefo re are considered to be physically plausible. We find that macroscopic meas ures of common line lengths behave similarly to fluid-fluid interfacial are as, although the functional dependencies on capillary pressure and saturati on differ to some extent. (C) 2001 Elsevier Science Ltd. All rights reserve d.