Mathematical model and constitutive formulations for frictional pressure drop of oil-water-air three-phase flow in horizontal pipes

This work deals with a review of the relevant theoretical and experimental work for oil-gas, oil-water two-phase flow and oil-water-gas three-phase flow through horizontal straight tubes. Flow patterns of three-phase flow are then classified for horizontal straight circular tubes. Based on the two-phase two-fluid model, a series of simplified models for every flow pattern can be proposed while correlation for the predicting frictional pressure drops can be deduced. Constitutive formulations involving of void fraction, and holdup, are suggested.