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| Fig. 1: An Olympic-size swimming pool has dimensions of approximately 50m x 25m x 2m, corresponding to a volume of about 2400 m3. Uranium metal has a density of about 19 tonnes m-3, so the approximately 65,000 tonnes of natural uranium consumed annually by the world's nuclear reactors would occupy roughly 3400 m3 as solid metal. This corresponds to about one and a half Olympic-size swimming pools. (Source: Wikimedia Commons) |
Commercial nuclear reactors generate electricity through the fission of uranium fuel. In most reactors this fuel is uranium enriched to several percent in the fissile isotope U-235. The fission process releases energy that heats water to produce steam, which drives turbines that generate electricity. A natural question is how much uranium must be consumed each year in order to sustain global nuclear electricity production. This quantity determines the scale of uranium mining and enrichment required to supply the nuclear fuel cycle.
International surveys of the nuclear fuel market estimate that the world's nuclear power industry consumes roughly 60,000 tonnes of natural uranium per year. [1] This report examines whether this number is reasonable by comparing it with the total electricity produced by nuclear reactors worldwide and the known energy released in nuclear fission.
This relationship between electricity production, thermal energy generation, and nuclear fission determines the number of uranium nuclei that must undergo fission each year.
According to the International Energy Agency, nuclear power plants generate approximately 2,600 terawatt-hours (TWh) of electricity each year worldwide. [2] Nuclear power plants do not convert all nuclear energy into electricity. The thermal efficiency of a typical light-water reactor is approximately 33%. [3] This means that producing 2,600 TWh of electricity requires about three times as much thermal energy in the reactor core. Thus the total thermal energy produced by nuclear fission annually is
Converting this to joules, we obtain
This represents the total nuclear energy released by fission in reactors worldwide each year.
Each nuclear fission releases approximately200 × 106 eV × 1.602 × 10-19 J eV-1 = 3.20 × 10-11 J. The number of fissions required to supply this much energy is thus
| 2.84 × 1019 J 3.2 × 10-11 J fission-1 |
= | 8.86 × 1029 fissions |
Each fission consumes one atomic nucleus of mass 235 × 1.627 × 10-27 kg = 3.82 × 10-25 kg. The total mass of U-235 fissioned is then
| 8.86 × 1029 fissions × 3.82 × 10-25 kg fission-1 | = | 3.38 × 105 kg |
or 340 tonnes of uranium nuclei.
Natural uranium contains only about 0.7% of the fissile isotope U-235. If 340 tonnes of U-235 nuclei undergo fission annually, the total mass of natural uranium required to supply this amount of fissile material can be estimated by dividing by the natural isotopic abundance
This calculation assumes that all of the U-235 present in natural uranium is successfully transferred into reactor fuel and completely consumed. In reality this is not the case. Enrichment processes discard some uranium, and reactor fuel is removed before all fissile material is burned. In addition, some energy in reactors comes from plutonium-239 bred from uranium-238. These effects partially cancel, so the simple estimate above gives a result of the correct order of magnitude.
Although only a few hundred tonnes of uranium nuclei undergo fission each year, reactors require much larger quantities of uranium fuel. This is because natural uranium contains only 0.7% U-235, and reactor fuel must be enriched to several percent U-235 before it can sustain a chain reaction. Furthermore, nuclear fuel is removed from reactors before all the uranium can be consumed. Typical reactor fuel burnup corresponds to only a few percent of the heavy nuclei undergoing fission before the fuel is replaced. As a result, the total amount of natural uranium required to supply reactor fuel is much larger than the mass that actually undergoes fission. International surveys of the nuclear fuel cycle indicate that the world's nuclear reactors require approximately 60,000 to 65,000 tonnes of natural uranium per year. [1] This number accounts for enrichment losses and the incomplete burnup of reactor fuel.
Global nuclear reactors generate approximately 2,600 TWh of electricity per year, corresponding to roughly 2.8 × 1019 joules of nuclear energy released through fission. Using the known energy released per fission, this energy production requires on the order of 1029 nuclear fissions annually, corresponding to roughly 350 tonnes of uranium nuclei actually undergoing fission.
This simple estimate suggests that tens of thousands of tonnes of natural uranium must be processed each year in order to supply the fissile material consumed in reactors. International surveys of the uranium market indicate that the world's nuclear power industry consumes roughly 60,000 to 65,000 tonnes of natural uranium each year. This number defines the scale of uranium mining and enrichment needed to sustain global nuclear electricity generation.
© Patrick Flanagan. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] "Uranium 2022: Resources, Production and Demand," Nuclear Energy Agency, NEA No. 7634, 2023.
[2] "World Energy Outlook 2023," International Energy Agency, October 2023.
[3] "The Future of Nuclear Power," Massachusetts Institute of Technology, 2003.
