Unified relative permeability model and waterflooding type curves under different levels of water cut

Understanding the relative permeability of multiphase flow in porous media is crucial for the efficient development of waterflooding reservoirs. The semi-log linear relationship between oil-water relative permeability ratio (kro/krw) and water saturation (Sw) has been commonly used to derive waterflooding type curve-an empirical and practical tool for the forecast of production performance. However, recent experiments suggest that owing to the highly dispersed oil in water phase, the kro/krw vs Sw correlation deviates from a straight line in a semi-log plot at high water-cut stage (>90%). Considering the linear model of ln(kro/krw) vs Sw fails to describe the multiphase flow behavior for average water saturation greater than ~65%, we present a unified mathematical model to account for different water saturations and develop two type curves to predict the waterflooding performance. Data from previous literatures, numerical simulations, and actual oilfields are employed to examine the capability of the proposed method. In comparison with traditional Type-A and -B curves, in which the correlation of ln(kro/krw) vs Sw is linear, the proposed model provides remarkably accurate results. Although the nonlinear relationship occurs only at high water saturations, neglecting this feature of the relative permeability curve can cause a significant error in the prediction. This work provides a comprehensive model of ln(kro/krw) vs Sw and new Type-A and -B curves for reservoirs at high water-cut stage, which are beneficial for accurate performance forecasts for the entire duration of waterfloods.