Leakage of CO2 through fractures in saline formations will increase the CO2brine interface and promote CO2 dissolution. We use a 2D, finite difference MATLAB model to simulate dissolution rates from a vertical fracture, with CO2 flowing through it, in a secondary storage formation. The instigation of convection currents increases dissolution rates leading to higher dissolution in higher Rayleigh number systems. Comparison of our results with fracture flow rates shows that for typical fracture apertures dissolution from a fracture is small relative to the amount of CO2 flowing through the fracture. Temporal and spatial variations in fracture permeability may reduce fracture flow rates and increase the relative amount of CO2 dissolved from the fracture compared to the CO2 flowing through the fracture. Further work on CO2 dissolution in relation to fracture heterogeneity, flow of CO2 within fractures and the interaction of multiple fractures will improve our ability to predict CO2 dissolution rates for site characterisation.