This project has developed a new procedure and a unique statistical and semi-analytical model to predict oil recovery at any water/oil ratio (WOR) and ultimate oil recovery for mature reservoirs under water injection. The new approach uses fractional flow, and multiple linear regressions. We have studied the linear portion of the commonly used plot of log WOR vs. recovery factor (RF) determining the boundaries of that straight-line zone (SLZ) in terms of initial and final RF and/or initial and final WOR numerically using mathematics rules. We also determined slopes and intercepts of this line as functions of commonly used rock and fluid properties values, such as relative permeability curves end-points, connate water saturations (Swc), residual oil saturations (Sor), mobility ratios (M) and Dykstra-Parsons coefficients (VDP). Characterizing this line helps us to determine the performance of a waterflood in terms of RF and pore volumes injected (PVI). We correlated the results from homogeneous and heterogeneous reservoirs by using a correction in terms of the VDP and mobility ratios. We validated the model using reservoir simulation and field cases. Limitations and assumptions are those derived from the application of the simplified fractional flow equation, including that no dip angle, no capillary pressure, and no gravity effects were considered. The model was tested and validated for waterfloods with relatively small initial gas saturation (Sg < 0.2). At higher gas saturations waterflooding process must be applied with extreme care to avoid displacing oil into the gas cap zone and reducing the remaining oil saturation (ROS).
Waterflooding is the most popular secondary recovery method used around the world because of the general availability of water, relative low costs, ease of injecting water into the formation, and the high efficiency of water displacing oil. Primary recovery leaves behind about 80% of the original oil in place (OOIP); while a minimum of 35 to 40% of remaining oil saturation (ROS) is considered good enough to start a waterflooding project (Thakur and Satter 1998; Cobb and Marek 1997; Taber et al. 1996). Waterflooding may improve ultimate recovery with an additional 10 to 30% of the original oil in place, which can make this process very attractive technically and economically.
Several studies using various linear relations to forecast waterflooding performance can be found in the literature. Jordan estimated ultimate recovery factor and economic limits as a function of WOR as early as 1958 successfully; Cobb and Marek(1997)estimated volumetric sweep efficiencies (fraction of the reservoir swept by the injected water) as a linear function of cumulative production (NP). Extrapolating a straight line in this kind of plot is useful, especially when dealing with production data and recovery factors (RF), but it also may be dangerous because it may overestimate reserves. Lo (1998) presented a linear relationship for the approach, using the log of the water-oil ratio (Log WOR) vs. cumulative production (Np) plot to estimate mature waterflood performance, and Kumar (2005) added material balance techniques to estimate areal pattern distribution of ROS in mature waterflooding projects. The methodology accounts for loss of water injected and progressive gas fillup.
Baker et al. (2003) criticized arbitrary use of decline curve analysis (DCA) to estimate waterflood performance and reserves, highlighting that a good understanding of the factors controlling the reservoir performance must be the base in the analysis. They established that DCA must be applied only in mature waterfloods, with specific parameters and recommended plots of log WOR vs. cumulative production to enhance decline curve interpretation. The arbitrary use of exponential decline for waterfloods is dangerous since the method will underestimate ultimate recovery when volumetric sweep efficiency is increasing.