Modeling Relations Among Relative Permeabilities, Fluid Saturations, and Capillary Pressures in Mixed-Wet Porous Media: Model Testing and Application to Oil-Water Systems

A critical component of all multiphase flow codes is how relationships among relative permeabilities, fluid saturations, and capillary pressures (i.e., k-S-P relations) are described. Models that are able to mimic fundamental fluid-flow processes to predict k S-P relations are preferable than extrapolating measured data points to estimate k-S-P relations because they may have greater utility and may be more consistent. Furthermore, different saturation-path histories may be simulated with a computer code than those measured in the k-S-P experiments. Because the geometry of the pore spaces in natural porous media is very complex and will likely never be precisely known to predict k-S-P behavior from fundamental relationships, k-S-P models are largely empirical. In this paper, an empirical model based on theoretical considerations is developed to predict hysteretic k-S-P relations in porous media in which the smaller pores are water-wet and the larger pores are oil-wet, i.e., mixed-w et. At high oil-water capillary pressures, the water saturation is modeled to approach the residual water saturation. At low oil-water capillary pressures (i.e., negative), the oil saturation is modeled to approach the residual oil saturation. Relative permeabilities are predicted using parameters that describe main-drainage S-P relations and accounting for the distribution of water andmore » oil in the pore spaces of mixed-wet porous media. The proposed algebraic expressions are easy to implement in multiphase flow codes and can be used to predict k-S-P relations for any saturation-path history. In addition, the model is relatively easy to calibrate to porous media.« less