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Macroscopic capillarity and hysteresis for flow in porous media

R. Hilfer
Institut für Computerphysik, Universität Stuttgart, 70569 Stuttgart, Germany
Institut für Physik, Universität Mainz, 55099 Mainz, Germany

A macroscopic theory for capillarity in porous media is presented challenging the established view that capillary pressure and relative permeability are constitutive parameter functions. The capillary pressure function in the present theory is not an input parameter but an outcome. The theoretical approach is based on introducing the residual saturations explicitly as state variables (as in Phys.Rev.E 58, 2090 (1998)). Capillary pressure and relative permeability functions are predicted to exist for special cases. They exhibit hysteresis and process dependence as known from experiment.

Key words and phrases:
porous media, multiphase flow, immiscible displacement PACS: 47.55.Mh, 47.55.Kf