We investigate the potential of a specific geoengineering technique: the carbon sequestration by artificially enhanced silicate weathering via the dissolution of olivine. This approach would not only operate against rising temperatures but would also oppose ocean acidification. If details of the marine chemistry are taken into consideration, a new mass ratio of CO2 sequestration per olivine dissolution of about 1 is achieved, 20% smaller than previously assumed. We calculate that this approach has the potential to sequestrate up to 1 Pg of C per year directly, if olivine is distributed as fine powder over land areas of the humid tropics, but this rate is limited by the saturation concentration of silicic acid. These upper limit sequestration rates come at the environmental cost of pH values in the rivers rising to 8.2 in examples for the rivers Amazon and Congo. Open water dissolution of fine-grained olivine is an alternative option, which might rise the sequestration potential further. The secondary effects of the input of silicic acid connected with this approach leads in an ecosystem model to species shifts aways from the calcifying species towards diatoms, thus altering the biological carbon pumps. In summary, the secondary effects on the marine biology might lead to carbon sequestration rates which are higher than the theoretical limits given by the carbonate chemistry alone. We finally investigate open ocean dissolution rates of up 10 Pg olivine per year corresponding to geoengineering rates which might be of interest in the light of expected future emission (e.g. A2 scenario with emissions rising to 30 PgC/yr in 2100 AD). Those rates would still sequestrate only less than 20% of the emission until 2100, but would require that the nowadays available shipping capacity of tankers and bulk carriers is entirely used for olivine dissolution ten times a year.