A model for hysteretic constitutive relations governing multiphase flow: 1. Saturation-pressure relations

In these companion papers, a general theoretical model is presented for the description of functional relationships between relative permeability k, fluid saturation S, and pressure P in two-or three-phase (e.g., air-water or air-oil-water) porous media systems subject to arbitrary saturation paths. A parametric description of hysteretic S-P relations is developed in paper 1 which includes effects of air and oil phase occlusion or “entrapment” during imbibition. Entrapped nonwetting fluid saturations at a given point along a saturation path are linearly interpolated between endpoints of primary imbibition scanning curves using maximum trapped saturations estimated by extension of the method of Land (1968). Arbitrary order scanning curves are predicted using an empirical interpolation scheme coupled with a scaling procedure which simplifies computations and minimizes the parametric complexity of the model. All model parameters are defined in terms of measurements which may be obtained from two-phase systems (air-water, air-oil, oil-water). Extension to three-phase systems is based on the assumption that fluid entrapment processes in three phase systems are similar to those in two-phase systems and that wettability decreases in the order: water to oil to air.