Constitutive relationships derived from pore-scale network models

We use a quasi-static pore-scale network model for fluid displacements to investigate specific aspects of new constitutive relationships at the continuum scale. We examine the underlying definition of capillary pressure at the macroscopic scale, showing why traditional definitions do not apply at the limits of residual saturations. We then investigate the conjecture that hysteresis between the capillary pressure and saturation is eliminated by extension of the capillary pressure-saturation relationship to include a third variable, namely fluid-fluid interfacial area or common line length. For a considered sample pore network, hysteresis was nearly eliminated with a physically plausible choice of model displacement rules. This observation has potentially important implications for two-phase flow models that incorporate hysteresis.