Dissolution trapping of supercritical CO2 (ScCO2) in deep saline aquifers undergoes different stages such as ScCO2 mixing with brine, buoyant convection and slumping of CO2 rich brine. The effects of permeability and capillarity on these stages were previously studied for (i) uniformly injected ScCO2 at the top of the aquifer and (ii) spreading from a finite initial patch of CO2 or after short injection duration of CO2. In this paper we discuss the results of continuous injection of CO2 from a well that is screened inside the aquifer between caprock at the top and bedrock at the bottom. For this case, the injection pressure significantly influences the spreading of CO2 plumes. The injection pressure decreases with time for constant mass injection flux of ScCO2 (m˙). Injected ScCO2 flows upward and spreads laterally below the caprock. An evolving capillary transition zone is one of the main features of this study. Below the capillary transition zone, the diffusive boundary layer of dissolved CO2 becomes unstable depending on the injection pressure (PScCO2), permeability (k) and capillary entry pressure (Pc0). The evolution of ScCO2 and dissolved CO2 plume and injection pressure history are directly proportional to m˙/k. The evolution rate and the onset time of gravitational instability are inversely proportional to k. For very small and large m˙/k ratio, gravitational instability may not occur. Higher permeability yields more effective CO2 dissolution trapping and dissolution flux increases after onset of convection. For continuous injection case, the plume tip position varies as the power law of time tn where 0.6 < n < 0.85 where t is in years and plume tip position is in meter. © 2019 Elsevier Ltd