Modeling Relative Permeability Variations in Three-Phase Space

Abstract

AbstractThree-phase relative permeability can vary greatly from two-phase relative permeability as mechanisms such as flow coupling, double displacement, and layer drainage flow regime play a role in three-phase flow. These are on top of the dependency of three-phase relative permeability on two saturations and saturation path/history. The net result is that it is difficult to model/predict relative permeabilities in three-phase space. In this work, we present three-phase oil relative permeability data measured along 11 saturation paths, in a water-wet consolidated (Berea sandstone) and unconsolidated (sandpack) porous media. These saturation paths cover a wide swath of the three-phase saturation space, providing a better physical understanding of the complete three-phase phase space. Three different oils (crude oil, mineral oil, and n-octane) are used in the experiments; the varying viscosities, spreading coefficients, and composition of the oils allows us to investigate the effect of different drainage mechanisms on relative permeability curves. Our data show that there are significant variations between the curves depending on the media, final water saturation, and fluids. In particular, when the media and fluids are held constant, oil relative permeability can vary an order of magnitude at the same oil saturation, depending on the initial condition and water saturation. We find that within each media, all the curves represent a similar shape, but reach to a different residual saturation. This suggests that residual oil saturation is the key parameter in observed relative permeability differences along different saturation paths. We examine this hypothesis with the most common three-phase relative permeability models, i.e. Saturation Weighted Interpolation, Stone I and II, where we vary residual oil saturation to fit the experimental data. We find that if residual oil saturation is used as a fitting parameter, the models predict experimental data well. Otherwise, without varying residual oil saturation, these relative permeability models perform poorly in predicting experimental data.