A New Model of Trapping and Relative Permeability Hysteresis for All Wettability Characteristics

The complex physics of multiphase flow in porous media are usually modeled at the field scale using Darcy-type formulations. The key descriptors of such models are the relative permeabilities to each of the flowing phases. It is well known that, whenever the fluid saturations undergo a cyclic process, relative permeabilities display hysteresis effects. In this paper, we investigate hysteresis in the relative permeability of the hydrocarbon phase in a two-phase system. We propose a new model of trapping and waterflood relative permeability, which is applicable for the entire range of rock wettability conditions. The proposed formulation overcomes some of the limitations of existing trapping and relative permeability models. The new model is validated by means of pore-network simulation of primary drainage and waterflooding. We study the dependence of trapped (residual) hydrocarbon saturation and waterflood relative permeability on several fluid/rock properties, most notably the wettability and the initial water saturation. The new model is able to capture two key features of the observed behavior: (1) nonmonotonicity of the initial-residual curves, which implies that waterflood relative permeabilities cross; and (2) convexity of the waterflood relative permeability curves for oil-wet media caused by layer flow of oil.