Quantification of Sor Reduction during Polymer Flooding Using Extensional Capillary Number

Since the introduction of viscous/capillary concepts by Moore and Slobod (1956), several modifications and advancements have been made to the capillary number (N-c) so that it could have a better correlation with residual oil saturation (S-or) during enhanced oil recovery (EOR). In subsequent years, laboratory-scale studies have indicated that the viscoelastic polymers can influence the S-or reduction at relatively higher fluxes and N-c. Although the flux rate of at least 1 ft/D is reported to be needed for viscoelastic polymers to reduce S-or to a noticeable extent, significant S-or reductions were reported to occur only at higher fluxes that are likely to be seen in the reservoir closer to the wellbore. At similar levels of flux and N-c, the polymer solutions with significant elastic properties have shown higher S-or reduction than viscous polymer of similar shear rheology. However, the existing models used for correlating the polymer's viscoelastic effect on S-or reduction relies on either core-scale N-c and/or the oscillatory Deborah number (De). De also has limitations in quantifying the polymer's viscoelastic effects at different salinities. In this paper, a modified capillary number called an extensional capillary number (N-ce) is developed using the localized pore-scale extensional viscosity. For viscoelastic polymer solutions, pore-scale apparent viscosity dominated by localized extensional viscosity is calculated to be significantly higher than core-scale apparent viscosity. We provide rheological insights using the variable-strain-rate concept to explain why and when the pore-scale apparent viscosity could become significantly higher, even at a flux of approximately 1 to 4 ft/D, and why it will not be reflected on the core-scale apparent viscosity or pressure drop. An exponential correlation was developed between N-ce and S-or using the extensive coreflood experimental data sets extracted from various literature. Performance of N-ce for predicting the viscoelastic polymer's residual oil recovery is compared with conventional N-c, De, and a recent correlation. The results show that newly developed N-ce can predict the S-or during polymer flooding for a wide range of operational and petrophysical conditions, including brine-salinity effects.