A computer simulation of Earth's climate is used to study if marine carbon removal will lead to a reduced atmospheric carbon dioxide concentration, and if there are potential secondary impacts on marine life and chemistry. We find that for stationary carbon removal plants the ocean cannot supply sufficient carbon rich water to allow a meaningful reduction of atmospheric CO2. This also means that outside the location of carbon removal there is no noticeable impact on plankton concentrations. It can be speculated that putting carbon removal plants on ships would lead to a significant increase in removal efficiency, although the engineering and energy aspects of this approach would need to be investigated.