Pore-scale modeling extension of constitutive relationships in the range of residual saturations

A pore network model is used to describe constitutive relationships between saturation, capillary pressure, relative permeabilities, and interfacial a reas over the full range of saturations. We focus on residual nonwetting-ph ase saturations, that is, the saturation range between main drainage and pr imary drainage. Interphase mass transfer and dynamic miscible transport are modeled to generate the range of saturations over which the extended const itutive relationships are calculated. To accommodate all saturations in a c onsistent way, we define capillary pressure as the areal average of local c apillary pressures associated with each fluid-fluid interface. The extended constitutive relationships provide input for continuum-scale models coveri ng the entire saturation range and indicate that special care is needed in the general formulation of continuum-scale equations.