Injection of carbon dioxide (CO2) in the ocean has been proposed as an option for accelerating the natural net flux of CO2 from the atmosphere into the ocean. Liquid CO2 released as droplets at depths <3000 m will create an ascending plume of droplets and entrained water. As the CO2 droplets dissolve, carbon is transferred into the plume water, yielding increased density and a lowered pH value of the plume water. As ambient water entrains the CO2-enriched water by mixing, the density difference disappears and the injected CO2 follows the ocean dynamics as a dynamically passive tracer. Here we report on numerical experiments performed with a two-phase Navier Stokes solver. The effects of different droplets sizes, background currents, and injection rates are examined. The numerical experiments show that the droplet size and the background current are key parameter for predicting the vertical distribution of the plume water, the associated reduction in the pH field, and the increase in the plume water density. If rapid dilution of the CO2-enriched water is the objective (leading to modest reduction in the pH value), large initial droplets and high background currents are preferable. On the other hand, if the objective is to increase the density of the plume water in order to generate a sinking plume (yielding enhanced residence time of the released CO2), CO2 injection with small droplets in a stagnant water column is optimal.