A Viscous Coupling Model for Relative Permeabilities in Fractures

Abstract

Abstract Two-phase flow properties are required for modeling fluid flows and pollutant transport through fractured media. Several laboratory experiments have been reported in the literature but so far there is no general model to predict the two-phase conductivity of a fracture for a given pair of flowing fluids. In this paper we propose a simple model based on viscous coupling between two fluids flowing simultaneously in a single fracture. This viscous coupling model leads to simple analytical relationships between the relative permeabilities (Kr) and either saturation or fluid velocities. This model also explains the dependence of the non-wetting fluid Kr on the viscosity ratio. Results obtained with this model were compared to several series of data available in the literature with air and water. The fit between predicted and measured Kr is good when the ratio of flow rates is used as variable (Lockhart-Martinelli parameter). For use in numerical simulations, the saturation can be derived from the flow rates using the same model. The proposed model can improve the relative permeability curves that are used in the numerical simulations. P. 253