On Two-Phase Relative Permeability and Capillary Pressure of Rough-Walled Rock \nFractures

Abstract

This paper presents a con~eptual and numerical model of multiphase flow in fractures.The void space of real rough-walled rock fractures is conceptualized as a twodimensional heterogeneous porous medium, characterized by aperture as a function of position in the fracture plane.Portions of a fracture are occupied by wetting and nonwetting phase, respectively, according to local capillary pressure and accessibility criteria.Phase occupancy and permeability are derived by assuming a parallel-plate approximation for suitably small subregions in the fracture plane.For log-normal aperture distributions, a simple approximation to fracture capillary pressure is obtained in closed fonn; it is found to resemble the typical shape of Leverett's j-function.Wetting and non-wetting phase relative permeabilities are calculated by numerically simulating single phase flows separately in the wetted and non-wetted pore spaces.illustrative examples indicate that relative penneabilities depend sensitively on the nature and range of spatial correlation betWeen apertures.It is also observed that interference between fluid phases flowing in a fracture tends to be strong, with the sum of wetting and nonwetting phase relative permeabilities being considerably less than 1 at intermediate saturations.