The simulation of CO2 injection into deep saline aquifers provides challenges to reservoir modellers. Estimates of storage and trapping of CO2 must be made for large-scale aquifers for planning purposes, and these simulations are generally undertaken on coarse models with grid cells of several 100m in length. However, some of the physical processes which arise during CO2 storage can only be represented on finer grids. In this work, we used a variety of 2D models to study the effect of grid resolution on a range of processes which take place when CO2 is injected into a saline aquifer. A reasonably fine grid is required to model the buoyant rise of the CO2 plume and the migration under the caprock. Cell sizes of several meters in the horizontal and approximately 1m in the vertical are adequate. However, an even finer grid is required to limit the effects of numerical dispersion and correctly simulate the dissolution of CO2 in brine. When CO2 dissolves in brine, the brine becomes more dense and convection may take place, enhancing the dissolution. Estimates of time to onset of convection and critical wavelength have been determined by a number of people with variable results, but for a typical aquifer, a grid resolution of less than 1m may be required. If the cell size is too large, the amount of convection will be underestimated, and therefore the amount of dissolution will be underestimated. However, our results showed that the error in the amount of CO2 dissolved was greater at the end of injection than at the end of the simulation (100 years after injection ceased), due to numerical dispersion. On the other hand, our simulations showed that the grid resolution had little effect on the build-up of pressure, which indicates that coarse grids may be sufficient for initial assessments of storage potential.