CO2 injection into underground formations involves the flow of CO2 in subsurface rocks which already contain water. The flow of CO2 into the target formation is governed mainly by capillary forces, viscous forces and interfacial interactions. Any change in subsurface conditions of pressure and temperature during injection will have an impact on the capillary and viscous forces and the interfacial interactions, which, in turn, will have an influence the injection, displacement, migration, and storage capacity and security of CO2. In this study, an experimental investigation has been designed to explore the impact of fluid pressure (74–90 bar), temperature (33–55 °C), and injection rate (0.1–1 ml/min) on the dynamic pressure evolution and displacement efficiency when supercritical CO2 is injected into a water-saturated sandstone core sample. The study also highlights the impact of the capillary forces and viscous forces on the two-phase flow characteristics and shows the conditions where capillary forces or viscous forces become dominant. The authors are not aware of similar experimental studies conducted in the literature so far. The results revealed a moderate to considerable impact of the parameters investigated on the differential pressure profile, cumulative produced volumes, endpoint CO2 relative (effective) permeability and residual water saturation. The extent of the impact of each parameter (e.g. fluid pressure) was a function of the associated parameters (e.g. temperature and injection rate). Increasing fluid pressure caused the differential pressure profile of supercritical CO2-water displacement to transform to the likeness of liquid CO2-water displacement, while, increasing temperature transforms it to the likeness of gaseous CO2-water displacement. Increasing fluid pressure caused a considerable reduction in the maximum and quasi-differential pressures, an increase in the endpoint CO2 relative permeability (KrCO2) and a reduction in the residual water saturation (Swr) and cumulative produced volumes. Overall, the impact of temperature is opposite to that of fluid pressure. However, with increasing temperature, the KrCO2 showed a declining trend at high-fluid pressures (90 bar) but an increasing trend at low-fluid pressures (75 bar). Increasing injection rate caused a considerable increase in the maximum and quasi-differential pressures, a rise in the KrCO2, a reduction in the Swr, and an increase in the cumulative produced volumes. The Swr was in range of 0.34-0.41 while KrCO2 was less than 0.37, depending on the operational conditions. Changing the operational conditions caused a higher impact on KrCO2 than that on Swr. The results indicate that capillary forces dominate the multiphase flow characteristics as fluid pressure and temperature are increased.