In a series of laboratory waterfloods, we investigate the extent of mixing of injection water and connate water, connate-water mobility, and connate-water banking during water injection for enhanced oil recovery (EOR). Local dynamic water saturations of connate water and injected water were imaged individually by use of a nuclear-tracer technique. The connate water was displaced from the pore space by the injected water and accumulated downstream in a connate-water bank that advanced toward the production end. The connate-water bank significantly reduced the contact between the injected water and mobile oil. During capillary displacement - i.e., during spontaneous imbibition without a viscous pressure drop - the connate water was also mobilized and accumulated downstream in the core. During viscous displacement - i.e., with a pressure gradient as small as 0.3 mbar/cm - the accumulated connate water was mobilized in a miscible displacement and produced from the core. Only a small mixing zone was observed between the injected and connate waters, even with fully miscible conditions by use of identical brine compositions. The results of the displacement mechanisms experimentally visualized in this work are important for water-based EOR techniques, including low-salinity-water and polymer injections, as well as any tertiary oil recovery method based on chemical injection.