An Analytical Equation to Predict Oil-Gas-Water Three-Phase Relative Permeability Curves in Fractures

Abstract

As fractures are the major flow channels for multiphase flow in naturally and hydraulically fractured reservoirs, the accurate prediction of multiphase flow in fractures is highly important. The oil-gas-water three-phase relative permeability relations in fractures define the hydrodynamics of multiphase fluids flow and are necessary for modeling of multi-phase flow in fractured reservoirs. In this work, a novel flow model based on the concept of shell momentum balance, Newton's law of viscosity, and the cubic law, is derived to determine analytic functions for the three-phase relative permeability curves versus phase saturation and viscosity in a single fracture. The results show that the equations describing three-phase relative permeability curves in a fracture are function of saturations and viscosities. Water phase relative permeability depends on water saturation, gas phase relative permeability depends on gas saturation when µg is much lower than µo and µw. However, oil phase relative permeability is function of all-phase saturations. The isoperms of water phase and gas phase are straight lines. However, oil phase isoperms are functions of all phase saturations and have significant curvature. The curvatures of oil phase isoperms increase with the increase of µo. Gas saturation decreases oil phase relative permeability with a given oil saturation, while the viscosity ratio increases it.