A new methodology is proposed for the acceleration of CO2 dissolution to lower the risk of CO2 leakage for carbon capture and storage (CCS) technology. It is called ex situ dissolution because CO2 is being dissolved at a surface before it is injected underground. This new approach reduces or eliminates possible leakage of CO2 from underground formation. To achieve full underground dissolution of injected pure supercritical CO2 or gaseous CO2 may take thousands of years because of the absence of strong mixing (convective-diffusion dominated processes). Dissolving CO2 in brine before injection significantly increases the security of geological sequestration. The mass transfer from CO2 droplets into brine during cocurrent (CO2-brine) horizontal pipe flow is studied mathematically to investigate the effectiveness of the proposed method. The dissolution rate of the CO2 droplets is correlated to the variation of mean droplet diameter versus time, because the mass transfer causes shrinkage of the droplets. Empirical correlations based on Sherwood numbers were employed in the example for calculation of mass-transfer coefficients for droplets of CO2 in the fluid flowing through a pipe.