A parametric model for constitutive properties governing multiphase flow in porous media

Abstract

A parametric model is developed to describe relative permeability‐saturation‐fluid pressure functional relationships in two‐ or three‐fluid phase porous media systems subject to monotonic saturation paths. All functions are obtained as simple closed‐form expressions convenient for implementation in numerical multiphase flow models. Model calibration requires only relatively simple determinations of saturation‐pressure relations in two‐phase systems. A scaling procedure is employed to simplify the description of two‐phase saturation‐capillary head relations for arbitrary fluid pairs and experimental results for two porous media are presented to demonstrate its applicability. Extension of two‐phase relations to three‐ phase systems is obtained under the assumption that fluid wettability follows the sequence water > nonaqueous phase liquid > air. Expressions for fluid relative permeabilities are derived from the scaled saturation‐capillary head function using a flow channel distribution model to estimate effective mean fluid‐conducting pore dimensions. Constraints on model application are discussed.