The injection and storage of freshwater in saline aquifers for the purpose of managed aquifer recharge is an important technology that can help ensure sustainable water resources. As a result of the density difference between the injected freshwater and ambient saline groundwater, the pressure field is coupled to the spatial salinity distribution, and therefore experiences transient changes. The effect of variable density can be quantified by the mixed convection ratio, which is a ratio between the strength of two convection processes: free convection due to the density differences and forced convection due to hydraulic gradients. We combine a density-dependent flow and transport simulator with an ensemble Kalman filter (EnKF) to analyze the effects of freshwater injection rates on the value-of-information of transient pressure data for saline aquifer characterization. The EnKF is applied to sequentially estimate heterogeneous aquifer permeability fields using real-time pressure data. The performance of the permeability estimation is analyzed in terms of the accuracy and the uncertainty of the estimated permeability fields as well as the predictability of breakthrough curve arrival times in a realistic push-pull setting. This study demonstrates that injecting fluids at a rate that balances the two characteristic convections can maximize the value of pressure data for saline aquifer characterization.