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Carbon capture and storage (CCS) can help nations meet their Paris CO2 reduction commitments cost-effectively. However, lack of confidence in geologic CO2 storage security remains a barrier to CCS implementation. Here we present a numerical program that calculates CO2 storage security and leakage to the atmosphere over 10,000 years. This combines quantitative estimates of geological subsurface CO2 retention, and of surface CO2 leakage. We calculate that realistically well-regulated storage in regions with moderate well densities has a 50% probability that leakage remains below 0.0008% per year, with over 98% of the injected CO2 retained in the subsurface over 10,000 years. An unrealistic scenario, where CO2 storage is inadequately regulated, estimates that more than 78% will be retained over 10,000 years. Our modelling results suggest that geological storage of CO2 can be a secure climate change mitigation option, but we note that long-term behaviour of CO2 in the subsurface remains a key uncertainty.