Upward displacement of brine from deep reservoirs driven by pressure increases resulting from CO2 injection for geologic carbon sequestration may occur through improperly sealed abandoned wells, through permeable faults, or through permeable channels between pinch-outs of shale formations. The concern about upward brine flow is that, upon intrusion into aquifers containing groundwater resources, the brine may degrade groundwater. Because both salinity and temperature increase with depth in sedimentary basins, upward displacement of brine involves lifting fluid that is saline but also warm into shallower regions that contain fresher, cooler water. We have carried out dynamic simulations using TOUGH2/EOS7 of upward displacement of warm, salty water into cooler, fresher aquifers in a highly idealized two-dimensional model consisting of a vertical conduit (representing a well or permeable fault) connecting a deep and a shallow reservoir. Our simulations show that for small pressure increases and/or high-salinity-gradient cases, brine is pushed up the conduit to a new static steady-state equilibrium. On the other hand, if the pressure rise is large enough that brine is pushed up the conduit and into the overlying upper aquifer, flow may be sustained if the dense brine is allowed to spread laterally. In this scenario, dense brine only contacts the lower-most region of the upper aquifer. In a hypothetical case in which strong cooling of the dense brine occurs in the upper reservoir, the brine becomes sufficiently dense that it flows back down into the deeper reservoir from where it came. The brine then heats again in the lower aquifer and moves back up the conduit to repeat the cycle. Parameter studies delineate steady-state (static) and oscillatory solutions and reveal the character and period of oscillatory solutions. Such oscillatory solutions are mostly a curiosity rather than an expected natural phenomenon because in nature the geothermal gradient prevents the cooling in the upper aquifer that occurs in the model. The expected effect of upward brine displacement is either establishment of a new hydrostatic equilibrium or sustained upward flux into the bottom-most region of the upper aquifer.