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| Fig. 1: Fission of U-235 in a Light Water Reactor. [8] (Source: Wikimedia Commons) |
Small Modular [Nuclear] Reactors (SMRs) are emerging from myriad companies to provide flexible amounts of energy generation to all areas of the world. Their output is defined as being 10-300 MWe, compared to the output of conventional nuclear reactors around 1 GWe. As of 2020, there were 72 different SMR concepts in various stages of development. [1] The SMRs closest to commercial development will produce the same amounts of energy and High-Level Waste (HLW) per kilogram of uranium consumed as a conventional nuclear reactor. If the use of SMRs is to expand, the amount of fuel required and waste produced must be accounted for.
The 2021 world production of nuclear energy was 25.31 × 1018 Joules out of a total primary energy consumption of 595.15 × 1018 J, or 4.25%. [2] If we assume constant global energy consumption and the expansion of SMR use to cover the global energy market, 23.5 times the amount of fuel would be required and 23.5 times the amount of HLW would be produced.
Conventional nuclear reactors and SMRs both run off fission (Fig. 1): bombarding a uranium core with neutrons to cause atoms to split, yielding:
Heat (used for electricity generation).
More neutrons to perpetuate the nuclear chain reaction.
Spent fuel. Of note, any highly radioactive solid and liquid material after spent fuel is reprocessed is defined as HLW. [3]
Low-Level Waste (LLW), which is broadly categorized as any waste that is not high-level (this was the U.S. Nuclear Regulatory Commission's understanding of the law's definition in 1985). [4] Most structural materials that become irradiated by neutrons in varying degrees are LLW. [5]
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| Fig. 2: Nuclear Fuel Cycle. [6] (Courtesy of the NRC) |
The only natural fissile isotope for use in nuclear reactor fuel is U-235. When separated from the ore after mining, natural uranium is 0.7% U-235 and 99.3% U-238. Nuclear fuel is "enriched" to increase U-235's mass percentage. Enrichment ensures sufficient neutron activation to perpetuate the chain reaction, thus producing the desired amount of heat. U- 235 is typically enriched to around 4% for the fuel used in conventional Light Water Reactors (LWRs), the most common reactor type. [6] Nuclear fuel in SMRs can consist of various elemental/chemical mixes and shapes/designs depending on the reactor. However, the most mature SMR concepts closest to commercial deployment are of a LWR design, having similar fuel composition to conventional reactors. [1] For these reactors, enriched uranium is processed into UO2, formed into fuel pellets, and assembled into fuel rods. [6]
Throughout a reactor's operation, neutrons are absorbed by both the fissile (U-235) and non-fissile (U-238) material within the fuel. Most of the U-235 splits into varying radioactive daughter atoms, such as barium and krypton. Some of the U-238 transmutes to become Pu-239, a fissile isotope of plutonium. This process is referred to as "breeding." Some of this "breeded" Pu-239 then absorbs neutrons and fissions itself, accounting for roughly one third of the energy generated by a LWR. [6]
To determine the amount of uranium fuel required for SMRs to cover the global energy market, one first looks at the fission reaction of a single U-235 atom. Atomically, this reaction can proceed in various ways according to the generic equation below:
| U-235 + neutron → fission products + neutrons + ~200 MeV [6] |
200 MeV of released binding energy per U-235 atom is a good average across the numerous possible fission reactions. With a third of the energy generation from LWRs coming from the breeded plutonium, U-235 only accounts for two thirds of the current world nuclear energy output, or 16.87 × 1018 J. One then calculates the number of U-235 atoms necessary to provide this energy:
| 16.87 × 1018 J 200 × 106 eV atom-1 × 1.602 × 10-19 J eV-1 |
= | 5.27 × 1029 atoms U-235 |
Converting the number of atoms into a weight, using the molecular weight of U-235, yields:
| 5.27 × 1029 atoms
× 0.235 kg mol-1 6.02 × 1023 atoms mol-1 × 1000 kg tonne-1 |
= | 206 tonnes U-235 |
Since U-235 accounts for 0.7% the mass of naturally occurring uranium, the amount of naturally occurring uranium required to be mined is:
| 206 tonnes U-235 0.007 |
= | 2.94 × 104 tonnes uranium |
Extrapolating from published amounts for 2021, the actual amount of uranium mined in 2022 was around 6.2 × 104 tonnes. [2,7] The difference between the theoretical and actual amounts can be understood by the desired energy release of the nuclear fuel. Some of U-235's fission products are neutron "poisons," or parasitic absorbers. After a certain amount of burnup, the fuel no longer generates the desired amount of energy and is replaced. Therefore, not all U-235 undergoes fission. [6] For the purposes of this paper's calculations, I assume complete fission of all the U-235 within the nuclear fuel before replacement. This assumption gives the absolute minimum quantity of uranium required. In practice, the quantity would be higher.
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| Fig. 3: Spent fuel pool at Idaho National Laboratory. (Courtesy of the DOE) |
To cover the global energy market, 23.5 times the 206 tonnes U-235 would be required, or 4,834 tonnes. Additionally, 23.5 times the amount of naturally occurring uranium would be required, or 6.91 × 105 tonnes. The amount of mined uranium is separate and distinct from the mass of nuclear fuel required. Since U-235 accounts for approximately 4% the mass of uranium in the fuel (and ignoring the oxygen in the fuel's composition), the annual total mass of nuclear fuel required would be 1.21 × 105 tonnes.
To ensure constant energy generation by a reactor at desired levels, roughly one third of the fuel is replaced every 12-18 months. [8] A global energy market covered by the SMRs closest to commercial deployment would thus require 4.03 × 104 tonnes of nuclear fuel to be serviced to all SMR locations every 12-18 months.
The amount of nuclear fuel required for SMR global energy production is the same amount that would become HLW. As all Spent Nuclear Fuel (SNF) is highly radioactive, it meets the definition of HLW and requires the most stringent disposal. [9] For this reason, the terms SNF and HLW will be used synonymously below. The direct relationship between fuel required and waste produced is due to the lack of global reprocessing facilities and inability of most reactor designs to accommodate reprocessed fuel. [7]
In theory, SNF could be reprocessed to extract still-usable elements. In practice, reprocessing U-238 (which accounts for >90% of the spent fuel's mass), is expensive and accounts for <1% of projected world fuel requirements. The remaining Pu-239 could also be used as the main fissile element in the form of Mixed Oxide (MOX) fuel. In practice, only 5% of the world's reactor fleet can utilize MOX. [7] As of 2020, the Nuclear Energy Institute stated that no developers with advanced reactor designs (such as SMRs) plan to use reprocessed fuel in the short term (10-20 years). [10] For the majority of SNF in Fig. 2, the process is linear (vice cyclical) and ends with the "storage" phase at the right side of the image.
Since SNF/HLW has nearly the same molecular weight as the original fuel that underwent the fission, this equates to a volume of:
| 1.21 × 105 tonnes HLW | × | 1 m3 19.05 tonnes |
= | 6,344 m3 HLW |
This volume equates to roughly 2.5 Olympic-sized swimming pools of solid HLW. Of note, this calculation gives the absolute minimum volume of HLW generated. It assumes complete U-235 fission and ignores the dioxide in the SNF. In practice, the incomplete U-235 fission and inclusion of dioxide would increase the calculated volume. Of additional note, the increased amount of neutron leakage of SMRs over conventional LWRs could generate up to 35 times the amount of LLW. [5] This volume is beyond the scope of my analysis but would also require proper disposal.
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| Fig. 4: Dry cask storage at Idaho National Laboratory. (Courtesy of the DOE) |
Initially, HLW is extremely hot and must be stored in spent fuel pools (Fig. 3) for at least five years. [6,11] These pools conduct heat away from the HLW during its initial radioactive decay and prevent its liquification. In conventional reactors, SNF/HLW is typically moved from the reactor along the bottom of water canals to adjacent pools. [9] These pools are incorporated into the original plant design. The HLW must always remain under at least 20 feet of water to ensure proper radiation shielding for workers. [9] Additionally, the HLW must be adequately separated to prevent it from spontaneously creating a criticality. [9] Therefore, the combined volume of the actual pools required for initial HLW storage would be orders of magnitude more than 2.5 Olympic-sized pools. In a global energy market covered by SMRs, the immediate wet storage of HLW produced during every refueling would be a logistics problem that must be accounted for.
After sufficiently cooled, the HLW can be placed in longer term wet or dry storage. Dry storage is typically done in dry casks - steel canisters to hold the HLW surround by steel or concrete and steel designed to cool the HLW and shield its radiation. [11] An example of dry cask storage can be seen in Fig. 4. As the 6,344 m3 of HLW produced could not be safely stored as a densely packed volume within dry casks, a much larger storage volume would be required. The final fate of HLW is placement in a permanent geologic repository. Of note, there is no approved geologic repository in the United States. [11] The long-term storage of HLW produced in a global energy market covered by SMRs must be accounted for.
© Peter Slye. 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] "Small Modular Reactors: Challenges and Opportunities," Nuclear Energy Agency, NEA No. 7560, 2021.
[2] "BP Statistical Review of World Energy 2022," British Petroleum, June 2022.
[3] "Assessment of Deparment of Energy's Interpretation of the Definition of High-Level Radioactive Waste," Federal Register, 86 FR 72220, 21 Dec 21.
[4] "Nuclear Regulatory Legislation: 112th Congress, 2nd Session," Nuclear Regulatory Commission, NUREG-0980, Vol. 1, No. 10, September 2013.
[5] L. Krall et al., "Nuclear Waste from Small Modular Reactors," Proc. Natl. Acad. Sci. [USA] 119, e2111833119 (2022).
[6] P. Breeze, Nuclear Power (Elsevier, 2017).
[7] "Uranium 2022: Resources, Production and Demand," Nuclear Energy Agency, NEA No. 7634, 2023.
[8] "Nuclear Energy," University of Michigan, Pub. No. CSS11-15, July 2023.
[9] "Radioactive Waste: Production, Storage, Disposal," U.S. Nuclear Regulatory Commission, NUREG/BR-0216, Rev. 2, May 2002.
[10] M. Doane, "Discontinuation of Rulemaking - Spent Fuel Reprocessing," Nuclear Regulatory Commission, SECY-21-0026, March 2021.
[11] "Commercial Spent Nuclear Fuel: Congressional Action Needed to Break Impasse and Develop a Permanent Disposal Solution," U.S. Government Accountability Office, GAO-21-603, September 2021.
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