An Empirical Model for Three-Phase Relative Permeability

Summary We present an empirical model for three-phase relative permeability. We allow for changes in hydrocarbon composition, different saturation paths, and the trapping of oil, water, and gas. The model is based on saturation-weighted interpolation between the two-phase relative permeabilities. By writing the relative permeabilities as unique functions of a flowing saturation, the model predicts the behavior for any sequence of saturation changes and accounts for trapping. Layer drainage allows the oil relative permeability to be extrapolated to low saturation. The formulation for water-wet media, including layer drainage and trapping, is tested against experimental three-phase data.