Understanding the dissolution kinetics of CO2 in brine is important for efficient management of cycled CO2 in underground salt caverns. The kinetics is strongly influenced by natural convection, which is caused by density changes related to the concentration of dissolved gas as well as thermal changes driven by CO2 cycling and the effects of the geothermal gradient. Based on a novel non-dimensional model that couples cavern thermodynamics with the dissolution mechanisms, this study investigates how the natural convection related to mass and thermal changes impacts dissolution kinetics. The numerical model is validated using laboratory measurements, and thereupon upscaled to typical dimensions of a salt cavern. Although our simulations show that the total dissolved mass is relatively minor compared to the initial stored mass/cycled mass, it is nevertheless important to quantify other loss phenomena, particularly gas permeation into the host rock salt. The developed model can also be adapted easily to study the kinetics of dissolution of other gases, such as hydrogen and methane.