Geoengineering is a proposed action to manipulate Earth's climate in order to counteract global warming from anthropogenic greenhouse gas emissions. We investigate the potential of a specific geoengineering technique, 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, because it influences the global climate via the carbon cycle. If important details of the marine chemistry are taken into consideration, a new mass ratio of CO(2) 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. In our calculations for the Amazon and Congo river catchments, a maximum annual dissolution of 1.8 and 0.4 Pg of olivine seems possible, corresponding to the sequestration of 0.5 and 0.1 Pg of C per year, but these upper limit sequestration rates come at the environmental cost of pH values in the rivers rising to 8.2. Open water dissolution of fine-grained olivine and an enhancement of the biological pump by the rising riverine input of silicic acid might increase our estimate of the carbon sequestration, but additional research is needed here. We finally calculate with a carbon cycle model the consequences of sequestration rates of 1-5 Pg of C per year for the 21st century by this technique.