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The induced seismic hazard of future large-scale CCS projects remains unknown. Here, we develop a seismogenic index model describing and projecting seismicity triggered by CO2 injection into underground aquifers or reservoirs that are pre-saturated with water. The model considers the multiphase physics of fluid flow in porous rocks and capillary effects. Using reported seismicity and injection data of CO2-storage projects, including Quest (CA), Decatur (USA), In-Sahla (Algeria), Otway (AUS) and Gorgon (AUS), we compute the seismogenic index for CO2 storage based on our new formulation. We compare it to case studies of seismicity induced by water-disposal and find that CCS operations are characterized by a significantly lower seismogenic hazard compared to water disposal of the same scale. Using estimates of CO2 volumes for future large scale CCS projects we show how to quantify and forecast magnitude exceedance probabilities. We propose recommendations that follow from our model to reduce, and control induced seismic hazard for future large-scale CCS operations.