Introduction

Small-modular reactors (SMR) and micro nuclear reactors (MNR) are defined as nuclear reactors ranging from 30 MWth to 1000 MWth and from 2 MWth to 40 MWth, respectively1,2. These advanced reactors have a significant potential to reduce carbon emissions, as well as to provide low-emission energy access to remote communities and industrial activities isolated from the main electricity grid3. They can also be used for industrial production, water desalination, hydrogen production, and other applications4. The leading reactor concepts include small pressurized water reactors (PWR), high-temperature gas cooled reactors (HTGR), heat-pipe reactors (HPR) and sodium-cooled fast reactors (SFR) with the fast-neutron spectrum2. These reactors have significantly more robust safety profiles, owing not only to their small power rating, but also to their passive safety systems, high thermal capacity in the core, new fuel forms such as TRISO, and (in some cases) low-pressure operation enabled by nonvolatile coolants such as sodium5.

As these technologies get closer to commercialization, their waste management is becoming an increasingly important topic. In 2023, the US National Academy of Science and Engineering raised concerns about waste management and disposal requirements related to SMR/MNRs6. In particular, the report highlights their potential to increase difficulties associated with the disposal of spent nuclear fuel (SNF). Today, about 88,000 metric tons of SNF from commercial reactors are stored in dry casks and pools at reactor sites in the US. Although there is a consensus that deep geological repositories are required to isolate SNF from the environment for an extended period, there is only one country, Finland, that has successfully constructed a repository.

Several studies have investigated SNF from SMRs/MNRs, reaching divergent and contradictory conclusions. Krall et al.7 concluded that SMRs would generate more SNF than conventional power plants and would exacerbate the challenges of nuclear waste disposal and management. Results obtained in Keto et al.8 are in agreement with Krall et al.7, even though their conclusion is less pessimistic. In fact, Keto et al.8 concluded that the low discharge burnup would facilitate final disposal, since the radioactivity and the decay heat would be lower compared to conventional reactors. Brown et al.9 also agreed with these two studies, noting that the reduction in the core size would increase neutron leakage, and hence would reduce the fuel utilization and discharge burnup. On the other hand, Kim et al.10 concluded that SNF from SMRs would not increase challenges compared with conventional reactors. Although they agreed that small-modular PWRs (SPWR) would slightly increase the SNF volume, they found that their radiotoxicity, decay heat, and radioactivity would be comparable to those of large PWR reactors. Such inconsistent conclusions have resulted in confusion within and beyond the nuclear community. Such confusion may ultimately distort public perception regarding the environmental impacts of SMRs/MNRs, and threaten their public acceptance (e.g.,11).

The objective of this study is to develop a multidisciplinary, open-source, reactor-to-repository framework for comparing SNF from different reactor technologies, with a particular focus on the final disposal conditions. Our framework (Fig. 1) includes (a) reactor physics models and post-discharge decay calculations using OpenMC12,13, (b) repository footprint models using NWPY14,15, and (c) SNF repository performance assessment (PA) models with explicit radionuclide release/transport simulations using PFLOTRAN16,17,18. All our codes are open sourced and freely available, which creates a transparent and more objective methodology for performing a comparative study.

Fig. 1
figure 1

Diagram summarizing the various inputs, steps, and models used in our framework. The red box represents the components typically included in the previous comparative analysis of SMR/MNR SNF; the rest is newly developed in this study. DCF is the dose conversion factor.

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Here our unique contributions—compared to previous studies—are the evaluation of not just the amount of waste but also the repository footprint and radiological risk associated with the SNF repository (Fig. 2). As noted by Apted et al.19, the conventional SNF metrics fail to include the repository conditions and the mobility of radionuclides, which greatly influence the size of the repository and the quantity of radionuclides that may be released to the biosphere. Even though previous studies have suggested the impact of decay heat on the repository footprint and acknowledged that radiotoxicity would not represent the environmental impact7, none of them included repository models that would quantify those aspects.

Fig. 2
figure 2

(a) A repository footprint model with the layout of a 3 × 3 repository package array, and  (b) a simplified performance assessment (i.e., radionuclide transport) model from a generic saturated-zone repository. In (a), the central package is modeled as a finite line source, while adjacent canisters and drifts are modeled as point sources. In (b), the repository parameters are from Stein et al.20.

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In the following sections, we first provide a systematic review and meta-analysis of the previous studies on SMR/MNR waste7,8,9,10. Qualitative and quantitative analyses are performed to resolve contradictions among those studies, and to explain why their conclusions diverged. We then demonstrate the new framework by comparing multiple SMR/MNRs with a reference PWR based on their generic reactor designs. We aim to investigate more granular differences than previous studies such as the one between fully ceramic microencapsulated (FCM) TRISO fuel and Uranium Oxycarbide (UCO) TRISO. We would note that some technologies such as SFRs are often used in conjunction with reprocessing, which is likely to have different radionuclide compositions and waste forms in the final waste. However, we consider a once-through fuel cycle only, which is considered to be the near-to-intermediate term choice in the US6.

Reactor-to-repository framework

In our framework (Fig. 1), OpenMC first simulates reactor physics, including neutronics, depletion analysis, radionuclide generation, and decay-chain calculations during the reactor operation and post-discharge periods. It provides the radionuclide composition of SNF at any given time, as well as the decay heat, activity, and radiotoxicity of each radionuclide. These can be converted to commonly used SNF metrics, including SNF mass (heavy metal equivalent) and volume as well as total activity, radiotoxicity, and decay heat (Sect. 6.1).

The repository footprint model (NWPY) then quantifies the repository area per package and per GWe.y given the thermal constraints14,15. It assumes a geological repository below the water table, which has been considered in Sweden, Finland, and France, as well as in the recent US generic PA models18,20. The repository includes engineered barrier systems (EBS), including waste forms, waste packages, and clay buffer for transport retardation. The temperature limit—for preventing the degradation of EBS—is assumed to be 100 deg-C in the clay geologic setting, which is the most stringent due to the low heat conductivity of clay.

Given the decay heat per package, NWPY solves analytical heat-conduction equations to determine the surface temperature of a waste package located at the center of a square array of N-by-N waste packages (Sect. 6.3: Fig. 2a), where the heat contribution from adjacent packages is the highest. The package at the center is modeled as a finite line source, while the remaining N2–1 packages are modeled as point sources. In addition, the drift spacing and the package spacing within the drift defines the minimum repository size. The area per package is calculated through an optimization algorithm to find the minimum area to satisfy the temperature constraint. In addition, we explore different package loading (i.e., the number of fuel elements per package) based on the previously studied package designs (Table S421).

Subsequently, the generic repository PA is developed (Sect. 6.4) to compute the release of radionuclides from the waste forms, their migration in the geosphere, and the peak dose rates over one million years22,23. Our conceptual model (Fig. 2b) is the simplified version of the generic clay model described in Stein et al.20, such that only the clay host rock and limestone aquifer below are considered. The release rates from the packages and repository—dependent on waste forms—are computed based on the analytical solutions developed by Ahn21. The release rates are then connected to the groundwater flow and reactive transport code PFLOTRAN, which has been extensively used for the repository PAs18. We focus on iodine-129 (I-129), which is typically the dominant dose contributor in the PAs7,18,23,24,25. We would note that rock properties can be changed, or different repository models can be coupled in this framework. For example, granitic host rock has been selected in Finland and Sweden15,26.

The peak dose rates are then computed based on the assumption that people use groundwater pumped from a well 10 km from the repository. The groundwater concentration is converted to the dose rate using the biosphere dose conversion factor used in the US Yucca Mountain (YM) assessment27. To compare our results with the current US regulatory standard (0.15 mSv/yr for the first 10,000 years) established for the YM repository, we multiplied the source terms to match the capacity of 70,000 metric tons (heavy metal equivalent). We would note that, for the real repository, the peak dose rates are not linear with the SNF amount, since the dose rates depend on the repository configuration and flow direction28. I-129 is not solubility-limited, so that such multiplication can be justified. This provides the conservative prediction of the dose rates.

Meta-analysis of previous comparative studies

To investigate the contradictions among the previous studies that compared the SNF from SMR/MNRs7,8,9,10, we first gather the data and assumptions from these studies, including reactor designs and their main parameters. Table 1 shows that these studies selected different reactor concepts and design parameters. In addition, the reference PWR burn-up (the key parameter determining the amount of SNF) is different among the studies, thus biasing their conclusions.

Table 1 SMR/MNR characteristics and technologies in the previous comparative studies. *Values calculated using the thermal efficiency. **Krall et al. (2022) did not perform depletion calculations; the results are from MOX-based fuel (Kuwagaki et al., 2020).
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The common SNF metrics (Sect. 6.1) are then compiled and discussed in the following subsections (Table 2). We note that Brown et al.9 and Krall et al.7 considered thermal energy as the comparison basis (thermal efficiency was neglected), while Kim et al.10 and Keto et al.8 used the electricity output. We re-calculated and re-scaled these metrics based on the electricity production (GWe.year).

Table 2 Selected SNF metrics studied for SMRs/MNRs. * re-calculated to convert from per GW-thermal-year to per GW-electric-year.
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Mass

We confirmed that the SNF mass (heavy metal equivalent) is inversely proportional to the burn-up and thermal efficiency for all the reactors. Overall, the reactors with high burnup and high thermal efficiencies (Natrium and X-1000) produce lower SNF mass. Krall et al.7 came to a pessimistic conclusion about SMRs, since their reference reactor had a relatively higher burnup, and they compared it to SMRs with relatively lower burnup. In contrast, the burn-up of 49.5 MWd/kgU for NuScale in Kim et al.10 leads to a SNF mass similar to the reference PWR.

Volume

The SNF volume is impacted not only by SNF mass but also by fuel types and densities. The two fast neutron-spectrum reactors (Natrium and 4S30) have consistently small volume in Krall et al.7 and Kim et al.10 because of the high-density metallic fuel. For Xe-100, the high volume-to-mass ratio of TRISO pebbles increases the volume by a factor of 12.3 compared to the reference PWR.

In addition, the SNF volume is significantly impacted by the methodology used in its calculation. Krall et al.7 considered the entire core, including the void space, while Kim et al.10 used the assembly/pebble volume-to-mass ratio. This is why Krall et al.7 estimated that SNF volume from NuScale was 2.5 times larger than the reference PWR, although in Kim et al.10 the difference was only 10%.

Decay heat

The decay heat at 100 years—affected by the amount of fission products and transuranic elements—is similar among the three studies for the reference PWR and NuScale. The higher burnup reactors result in increased decay heat per unit mass of initial uranium, although this figure is counterbalanced by a lower SNF mass generated per unit of electricity. There is a large discrepancy for the two fast reactors between 4S30 in Krall et al.7 and Natrium in Kim et al.10 such that 4S30 has 50% higher decay heat than the reference PWR, while Natrium has 50% lower decay heat. Krall et al.7 did not perform depletion simulations but took decay heat from the MOX-based fuel29, which has higher Pu than the U-Zr fuel that 4S30 plans to use. Kim et al.10 noted that the lower SNF decay heat of Natrium and HTGR is attributed to the high thermal efficiency. We note that while these papers mention the impact of decay heat on the repository area, none of them had repository models.

Activity/radiotoxicity

The SNF activity and radiotoxicity are governed by fission products in the first hundred years, and then afterwards by actinides. Since NuScale and the reference are both light water reactors with thermal neutron spectrums, their isotope composition is similar. The three studies7,9,10 are consistent, such that the NuScale’s activity and radiotoxicity are 5–15% higher than the reference PWR. Once again, the efficiency and the discharge burnup are the main drivers of the difference. Since the SNF from SFR has higher plutonium content with a fast neutron spectrum, the activity and radiotoxicity of one-through SFR SNF are significantly higher than the reference at 100–10,000 years. In contrast, HTGR has significantly lower activity and radiotoxicity, since more Pu is consumed during the operation.

Results from the reactor-to-repository framework

To demonstrate the framework, we have selected the following five relatively mature reactor concepts (Table 3) to represent the diversity of SMR/MNR designs2,30,31: small PWR, HTGR, HPR, HTGR with fully ceramic microencapsulated (FCM) TRISO fuel, and SFR, compared with the reference PWR of AP100032.

Table 3 Selected SNF metrics studied for SMRs/MNRs. *Re-calculated to convert from per GW-thermal-year to per GW-electric-year.
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Overall metrics

The SNF metrics are summarized in the radar chart (Fig. 3).

Fig. 3
figure 3

Radar chart comparing SNF from different reactor types normalized against the respective results for the large reference PWR reactor. The units shown are the computed values before normalization. The reactors with the same type of fuel are represented with the same line styles. Similar burnups are showed with the same markers.

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SNF mass and volume

Compared to the reference PWR, SPWR generates 3.3 times larger SNF mass due to its lower discharge burnup. On the other hand, owing to their high thermal efficiency and/or higher burnup, HTGR, HPR, and FCM-HTGR produce 40–50% less SNF mass. In addition, with 120 MWd/kgU burnup, SFR produces the lowest SNF mass (65% lower than the reference). We note that our SFR has higher burn-up (120 MWd/kgU) than SFR 4S30 used in Krall et al. (2022). The SNF volumes vary more significantly. The SNF volume from HTGR, HPR, and FCM-HTGR is 25–30 times higher than the reference, due to their use of low-density TRISO fuels. In addition, SFR shows the lowest SNF volume (30% lower than the reference).

Decay heat

At 50 years after the discharge, the decay heat ranges from 7.7 × 103 W/GWe.y for SFR to 16.8 × 103 W/GWe.y for FCM-HTGR. This difference results primarily from the variation in the fission products, Pu-238, and Am-241. Compared to the reference PWR, SPWR produces about 15% less decay heat. As the concentration of fission products is roughly proportional to the number of fissions and burnup, the observed variation is attributed to the actinide concentrations that depend on the fuel residence time and burn-up. The decay heat is similar for HTGR and HPR, which is 15% lower than the reference due to their high efficiency. The SFR decay heat is 45% lower than the reference, due to the lower concentrations of Pu-238 and Am-241 per GWe.y. There is a difference among the three TRISO-based reactors. FCM-HTGR has 20% higher decay heat than the reference owing to the higher uranium density in the fuel and increased production of actinides, even though we assume that FCM-TRISO reactors have the same burn-up as TRISO fuel-based HTGR.

Radiotoxicity

At 10,000 years after the discharge, the long-term radiotoxicity varies between 8.95 × 107 Sv/GWe.y for HTGR to 4.63 × 108 Sv/GWe.y for SFR. The radiotoxicity is dominated by Pu-239 and Pu-240, accounting for more than 90% of total radiotoxicity for all the reactor types. The SPWR radiotoxicity is 60% higher compared to the reference, which is associated with the increased Pu-239 per GWe.y due to lower burn-up. The radiotoxicity for HTGR is 10% lower than the reference owing to the higher burnup and thermal efficiency. The higher radiotoxicity of SFR (360%) is attributed to the Pu-239 and Pu-240 concentration resulting from the fast neutron spectrum.

Repository footprint

The minimum repository footprint was defined based on the fixed interim storage time of 50 years. The footprint ranges from 757 m2/GWe.y for SFR to 1472 m2/GWe.y for FCM-HTGR. Compared to the reference PWR, the repository footprint is 30% smaller for HTGR, and 16% smaller for HPR. FCM-HTGR is larger than the reference by 30%. More detailed results are shown in Sect. 4.2.

Peak dose rate

The peak dose rates from the 1GWe.y-equivalent SNF range from 2.2 × 10− 20 mSv/yr for HTGR to 2.2 × 10− 16 mSv/yr for SFR. The TRISO-based reactors (HTGR, FCM-HTGR, HPR) have the values ~ 4 orders of magnitude lower than the others. This large difference is primarily attributed to the waste form. More detailed results are shown in Sect. 4.3.

Repository footprint analysis

The required repository area per package decreases as a function of surface storage time (Fig. 4a only for HTGR as an example), because it allows the short-lived fission products to decay. As expected, the larger loading requires a larger area per package. However, the relationship is nonlinear: for the waste packages containing fewer elements and beyond a certain storage time, the decay heat is no longer constraining the spacing between the packages. The required area reaches the minimum defined by the package geometry and the drift radius.

Fig. 4
figure 4

Repository footprint analysis results: (a) the required area per package for HTGR SNF in a clay repository as a function of storage time and package loading (i.e., the number of fuel elements in each package), (b) the repository footprint per GWe.y as a function of storage time and package loading, and (c) the minimum footprint per GWe.y equivalent SNF for each reactor after the storage of 50 years. In (c), the number of fuel elements in each package achieving this minimum is indicated in the middle of the bars (n).

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The repository footprint is the area per package multiplied by the number of packages (Fig. 4b). Since the number of packages increases with smaller loading, the 6-element loading case results in the largest footprint, which does not depend on the storage time, since the area is determined by the tunnel geometry. In contrast, with a sufficient storage time, the repository footprint decreases with increasing the number of elements. Such nonlinear relationships and the trade-off between the area per package and the number of packages lead to the minimum repository footprint. The 42-element packages result in the smallest footprint for HTGR up to 50 years of storage time. For the minimum repository footprint with a fixed interim storage time of 50 years, the optimized loading varies significantly among the reactors, from 1 to 42 (Fig. 4c).

Repository performance assessment

The three waste forms—UO2, TRISO, and metallic matrix—have significantly different matrix dissolution rates (Fig. 5a). The metallic matrix completely disappears within 4000 years after package failure. UO2 is more resistant to degradation: it takes 800,000—8 × 106 years for the reference PWR and SPWR SNF to completely dissolve. TRISO performs the best, as the degradation is minimal for 107 years in both the low/high degradation cases.

Fig. 5
figure 5

Repository PA results: (a) the fraction of the waste form matrix remaining in the waste package after contact with groundwater (i.e., canister failure), (b) the cumulative release of I-129 from the package to the geosphere, (c) the I-129-associated annual dose rates from the repository of the 1GW.y equivalent SNF, and (c) the peak annual dose rate from I-129 from the repository with 70,000 MTHM (metric ton of heavy metal). In (a) and (b), the dot-dashed lines correspond to the high degradation rate, while the plain line corresponds to the low degradation rate. In (d), the Yucca Mountain standard (0.15 mSv/yr) corresponds to the horizontal red line.

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The cumulative I-129 release from the repository per GWe.y depends on both the initial inventory of SNF and the degradation rate (Fig. 5b). The degradation rate determines the timing, while the initial inventory of I-129 determines the total release. The release from the SFR SNF occurs the earliest due to its metallic waste form, and also becomes the highest due to the high inventory, since the I-129 fission yield is higher for Pu-239 (1.406%) than U-235 (0.54%). For the UO2-based reactors, the release increases around 10,000 years, reaching the full release around one million years. The TRISO-based reactors (HTGR, HPR, FCM-HTGR) have small releases compared to the other waste forms.

In addition to the waste form, the geosphere provides a natural barrier against radionuclide transport. The annual dose rates associated with I-129 from using the pumped well water at 10 km from the repository start to increase after 100,000 years (Fig. 5c), even for SFR with the fast-degrading metallic waste form. The dose rates at one million years vary by more than four orders of magnitude from the lowest (HTGR) to the highest (SFR). The TRISO-based reactors show the lowest concentrations compared to the other waste forms. The peak dose rates from the YM-equivalent capacity of 70,000 MTHM (metric ton of heavy metal) vary between 10− 14 and 10− 9 mSv/yr (Fig. 5d), which are smaller than the YM standard by a significant margin.

Discussion

In this study, we first synthesized the results from the previous studies that compared the SMR/MNR SNF7,8,9,10. Our analysis showed that different reactor types and parameters were selected, even though each study made sweeping conclusions about “SMR wastes.” In particular, thermal efficiency is not included in several studies, although it is an important parameter when we define the waste mass/volume per energy production. In addition, we found that there were differences in the methodology calculating the SNF volume, based on the core volume or the assembly/pebble mass-to-volume ratio. At the same time, the reference PWR was also different among the studies, which led to diverging conclusions. Finally, none of the studies included the repository models, although they implicitly related the decay heat to the footprint, and discussed the environmental impact. This is a significant omission, since the repository conditions and the mobility of radionuclides greatly influence the footprint and the quantities of radionuclides that leave the facility and enter the biosphere.

To overcome the subjectivity of previous studies and reflect realistic SNF disposal conditions, we have developed an open-source reactor-to-repository framework. It takes advantage of open-source code developments for both reactor physics (OpenMC) and repository assessments (NWPY, PFLOTRAN). Our framework takes the outputs from OpenMC and calculates various SNF metrics, and then connects the source terms to the repository footprint and radionuclide transport analyses. This framework would be useful for the industry and research communities, and valuable for educators. In particular, Wainwright et al.33 has highlighted the need for nuclear engineering students to know more about the mobility of radionuclides and disposal conditions, and to consider the impact of reactor designs on nuclear waste for improving the sustainability of energy systems.

The SNF mass and volume results in our study are consistent with Kim et al.10, driven largely by the burnup and thermal efficiency. The SPWR increases the SNF mass and volume compared to the reference PWR due to the lower burnup. On the other hand, the high burnup reactors have significantly lower SNF mass due to increased fuel utilization. However, the SNF volumes are significantly higher for reactors using TRISO fuel, which could lead to higher costs for handling, transportation, and storage of SNF.

Decay heat and radiotoxicity mostly depend on the fission products, plutonium and americium isotopes. Since the fission-product concentrations are nearly proportional to the energy generated, their difference is small among different reactors in the comparison. However, the thermal-spectrum reactors tend to have more Pu-238 and Am-241, which contribute significantly to the decay heat in the first 100 years34. On the other hand, the long-term radiotoxicity is higher for SPWR and SFR, because of the higher normalized Pu-239 content in SNF. In addition, FCM-HTGR has higher radiotoxicity and decay heat, because of its higher content of Pu-238 and Am-241. This is consistent with Lu et al.35 which has reported that the higher uranium density in the uranium nitrate fuel leads to higher Pu concentration than the UO2 fuel.

One of our significant findings is to show that the repository footprint is not linearly dependent on the decay heat, since it also depends on the thermal constraints of the repository and the decay heat per package. Particularly for HTGR, although the SNF volume is significantly larger than the reference PWR, the lower decay heat density allows for tighter spacing between packages and results in a reduced repository footprint. The repository footprint is smaller for the reactors selected in this study than for the reference, except for FCM-HTGR, which has higher decay heat. HTGR indeed has the smallest repository, even though it has a 30 times larger volume than the reference. This result highlights the importance of investigating the granular differences such as FCM-TRISO versus UCO-TRISO.

It has been known that radiotoxicity does not represent the environmental impact or human health risk from the SNF disposal, since the majority of radionuclides are relatively immobile in the geosphere7,19. Although Krall et al.7 mentioned that the mobile fission products are proportional to the number of fissions and hence to the energy generated, our analysis shows that there is a difference in the I-129 inventory between thermal and fast reactors, because of the significantly higher fission yield from Pu-239 than from U-235. In addition, our results highlight the importance of waste forms for repository performance, which is consistent with Atz et al.36. The robustness of TRISO in capturing mobile elements and its low degradation rate37 should considered in the SNF analysis. We would note that the metallic waste form from SFRs could be different in real deployment since SFRs are often considered to be coupled with reprocessing. We would also note that I-129 separation and transmutation are the active area of research38,39,39.

Overall, our results have emphasized the granularity and the specificities of each reactor type, highlighting that we should avoid making sweeping conclusions about SMR/MNRs. Each reactor and its waste management should be treated and evaluated differently. In addition, we need to recognize the trade-offs involved with each rector type. The TRISO-based fuel, for example, would increase the SNF handling cost owing to the large volume, but reduce the repository footprint and improve the repository performance.

We acknowledge that our study does not consider the secondary waste streams associated with these reactors. Concerns have been raised about the new waste streams of low-level waste produced by SMR/MNRs7. In this study, we focused on SNF as the first step, since SNF management and disposal are typically considered the most important barrier to nuclear energy expansion. In addition, uranium utilization should be included, since the front-end waste generates the largest environmental impact throughout the fuel cycle40.

Our framework can be extended in the future to consider such secondary waste, as well as the entire fuel cycle. The reactor safety metrics—for example, the accident tolerance of TRISO—could be included to discuss the tradeoff between reactor safety and waste volume. Furthermore, the environmental impacts should be compared with other energy systems that tend to create a large amount of effluents and hazardous waste41—waste that has been less rigorously managed over the short compliance period of 30 years42. Our reactor-to-repository framework aims to be a part of the effort to improve waste management and life cycle assessments, as well as to enhance the sustainability of energy systems.

Method

SNF metrics

The SNF metrics common across these studies7,8,9,10 are primarily form the reactor physics simulations: SNF mass and volume, SNF radioactivity, decay heat, and radiotoxicity.

SNF mass (ton-HM/GWe.y)

The SNF mass (heavy metal equivalent) includes all heavy metals and fission products derived from the initial fuel materials43. The SNF mass (MSNF) can be obtained directly with the following equation:

$$\:\begin{array}{c}{\text{M}}_{\text{S}\text{N}\text{F}}\left(\frac{\text{t}}{\text{G}\text{W}\text{e}.\text{y}}\right)=\frac{365\:(\text{d}/\text{y})}{\text{B}\text{u}\text{r}\text{n}\text{u}\text{p}\:\left(\text{G}\text{W}\text{d}/\text{M}\text{T}\text{U}\right)\text{*}\text{T}\text{h}\text{e}\text{r}\text{m}\text{a}\text{l}\:\text{e}\text{f}\text{f}\text{i}\text{c}\text{i}\text{e}\text{n}\text{c}\text{y}}\end{array}$$
(1)

This metric is relevant to evaluate SNF handling, storage, transportation, and final disposal. We would note that it only reflects the mass of heavy metal (uranium, actinides, and fission products) in SNF, and does not include other components of the core that are also stored in geological disposal, such as cladding materials for LWRs or graphite used as the fuel matrix for HTGR.

SNF volumes (m3/GWe.year)

There are multiple approaches to quantify SNF volumes. We present two methodologies used in the previous studies for completeness.

In Krall et al.7, the entire volume of the active core is used to estimate the SNF volume to be disposed with the following equation:

$$\:\begin{array}{c}SNF\:Volume\left(\frac{{\text{m}}^{3}}{\text{G}\text{W}\text{t}\text{h}.\text{y}\text{e}\text{a}\text{r}}\right)=\frac{\text{V}\text{o}\text{l}\text{u}\text{m}\text{e}\:\text{o}\text{f}\:\text{t}\text{h}\text{e}\:\text{a}\text{c}\text{t}\text{i}\text{v}\text{e}\:\text{c}\text{o}\text{r}\text{e}\:\left({\text{m}}^{3}\right)}{\text{T}\text{h}\text{e}\text{r}\text{m}\text{a}\text{l}\:\text{p}\text{o}\text{w}\text{e}\text{r}\:\left(\text{G}\text{W}\text{t}\text{h}\right)\text{*}\text{r}\text{e}\text{s}\text{i}\text{d}\text{e}\text{n}\text{c}\text{e}\:\text{t}\text{i}\text{m}\text{e}\:\text{o}\text{f}\:\text{t}\text{h}\text{e}\:\text{f}\text{u}\text{e}\text{l}\:\left(\text{y}\text{e}\text{a}\text{r}\right)}\end{array}$$
(2)

Taking the entire volume of the core induces not only the fuel matrix, claddings, and fuel unit materials (assembly or fuel block), but also the voids between the fuel elements. This approximation may lead to the overestimation of the SNF volume.

Kim et al.10 used the assembly or pebble volume-to-mass ratio (m3/MT) to compute the SNF volume in the following equation:

$$\:\begin{array}{c}{\text{V}}_{\text{S}\text{N}\text{F}}={\text{M}}_{\text{S}\text{N}\text{F}}*{\text{f}}_{\text{m}\text{a}\text{s}\text{s}}^{\text{v}\text{o}\text{l}\text{u}\text{m}\text{e}}\end{array}$$
(3)

where VSNF is the SNF volume in m3/GWe.year, MSNF is the SNF mass obtained in Eq. (1), and \(\:{f}_{mass}^{volume}\)is the assembly or pebble volume-to-mass ratio in m3/t (volume of an assembly divided by the heavy metal loading per assembly). In this calculation, the volume is obtained at the assembly (or pebble) level, and therefore does not consider the voids between the assemblies (or fuel blocks).

SNF activity (Bq/GWe.year)

The radioactivity in SNF (per gram of initial uranium mass, gU) can be calculated according to the following equation:

$$\:\begin{array}{c}Activity\:\left(\frac{\text{B}\text{q}}{\text{g}\text{U}}\right)=\sum\:_{\text{N}\text{u}\text{c}\text{l}\text{i}\text{d}\text{e}\:i\:\text{i}\text{n}\:\text{S}\text{N}\text{F}}{\text{C}}_{\:\text{i}}\:\times\:\frac{\text{ln}\left(2\right)}{{\text{t}}_{1/2,\:\text{i}}} \end{array}$$
(4)

where \(\:{C}_{\:i}\) is the concentration of the nuclide i in SNF (in atom/gU), and t1/2 i is the half-life of the nuclide (in s). The normalized activity per electricity generated is then obtained with:

$$\:\begin{array}{c}Activity\:\left(\frac{\text{B}\text{q}}{\text{G}\text{W}\text{e}.\text{y}\text{e}\text{a}\text{r}}\right)=Activity\left(\frac{\text{B}\text{q}}{\text{g}\text{U}}\right)\times\:{\text{M}}_{\text{S}\text{N}\text{F}}\left(\frac{\text{M}\text{T}}{\text{G}\text{W}\text{e}.\text{y}}\right)\times\:{10}^{6}(MT/g)\end{array}$$
(5)

The SNF activity during the first 100 years—mainly governed by fission products—is relevant to radiation safety and others during discharge handling, packaging, storage, and transportation. The activity in the 1000–100,000 year interval is relevant to the repository performance.

SNF radiotoxicity (Sv/GWe.year)

The radiotoxicity of SNF (Sievert) reflects the theoretical dose consequence of ingesting a particle of SNF, including all radionuclides present in SNF at a particular point in time. The radiotoxicity is defined as:

$$\:\begin{array}{c}Radiotoxicity\:\left(\frac{\text{S}\text{v}}{\text{g}\text{U}}\right)=\sum\:_{\text{n}\text{u}\text{c}\text{l}\text{i}\text{d}\text{e}\:\text{i}\:\text{i}\text{n}\:\text{S}\text{N}\text{F}}{\text{A}}_{\text{i}}\text{*}\text{D}\text{C}{\text{F}}_{\text{i}} \end{array}$$
(6)

where the Ai in Bq/gU corresponds to the activity of each radionuclide, and DCFi is the Dose Conversion Factor for each nuclide i (in Sv/Bq) from the International Commission on Radiological Protection (ICRP) publication44. It reflects the health impact of ingesting a specific radionuclide by a member of the public. It is then converted to the radiotoxicity per energy generated in the same way as Eq. (5).

In the first several hundred years, fission products are dominant contributors to the radiotoxicity of the spent fuel. In the long term (between 10,000 and 100,000 years), transuranic isotopes are dominant contributors to radiotoxicity. The radiotoxicity at 100,000 years is a relevant metric to assess the long-term toxicity of SNF in the geological repository.

SNF decay heat (W/GWe.year)

Similar to the radioactivity, the overall decay heat in SNF is the sum of decay heat from all the radionuclides:

$$\:\begin{array}{c}Decay\:heat\:\left(\frac{\text{W}}{\text{g}\text{U}}\right)=\sum\:_{\text{n}\text{u}\text{c}\text{l}\text{i}\text{d}\text{e}\:\text{i}\:\text{i}\text{n}\:\text{S}\text{N}\text{F}}{\text{D}\text{H}}_{\text{i}}\text{*}{\text{C}}_{\text{i}}\end{array}$$
(7)

where \(\:{DH}_{i}\) (in W/atom) is the heat generated by a specified radionuclide due to several reactions, and \(\:{C}_{i}\) is the concentration of the radionuclide in SNF (in atom/gU). It is then converted to the decay heat per electricity generated in the same calculation as Eq. (5).

The decay heat at 10–100 years is relevant for SNF handling, interim storage, transportation, and initial emplacement in the repository. Indeed, a surface storage time of 5 to 100 years is necessary before the final disposal to allow SNF heat to decrease.

Reactor designs and simulation setups

Reactors physics simulations determine the composition and the characteristics of SNF at various time points after the discharge. For each reactor, the simulations include core neutronics modelling, depletion analysis and the radioactive decay chain calculations in SNF. The key parameters are listed in Table 1, while the detailed designs for individual reactors are described in Text S1.

OpenMC is an open-source Monte Carlo neutron and photon transport simulation code recently developed at the Massachusetts Institute of Technology12,13. It has the Python programming interface, which facilitates the connection to the repository models as well as the interactive workflow in Jupyter. We used the ENDF/B-VII.1 library for cross sections, depletion chain and decay chains, including the thermal and fast neutron spectrums45. For the neutronics, this study uses 5,000 particles, with 200 active batches and 20 inactive batches. The CE/CM (constant extrapolation, constant midpoint) method is used for time integration. We assume that the effect of fuel shuffling and other in-core operations is captured in the discharge burn-up specified in Table 1.

The depletion calculation uses shorter depletion time steps at the beginning to accurately capture the build-up of xenon isotopes, and then longer depletion steps until the input burnup is reached. After the discharge from the reactor, shorter time steps are applied during the first hundred years to capture the decay of short-lived fission products. Then, longer time steps are applied up to 1,000,000 years after the disposal of SNF.

Repository footprint model

We follow the methodology developed by Atz14, which determines the canister spacing and repository footprint based on the decay heat generation and the repository conditions. The decay heat released from the waste packages could accelerate the degradation of EBS and the surrounding host rocks. To prevent such effects, a threshold temperature is typically set for the repository design, depending on the host rock and EBS properties. The approach in Atz14 primarily focuses on the peak temperature at the surface of the canister located at the center of the repository, assuming it is higher than temperatures at any other ___location in the repository. The limit is 100 deg-C in the clay geologic setting, which has the most stringent temperature constraint due to the low heat conductivity of clay. This temperature limit is applied to prevent the thermally driven alterations of the bentonite buffer, which can increase rigidity, promote fractures, and decrease sorption as well as the mineralogical changes and thermally driven processes in the clay host rock. We would also note that the extent and properties of clay-bearing rocks have been extensively studied in the US46.

In the footprint analysis, the canister designs are also important to determine the heat loading of each canister. The canisters usually consist of an inner canister, loaded with nuclear waste, and an overpack used to prevent corrosion. This work considers generic waste canisters and overpack designs (Table S4) specified in DOE47, in which the diameters were selected based on international accounts and previous conceptual design studies in the US. The TRISO-based SNF canisters are assumed to be loaded with prismatic fuel blocks containing TRISO particles. Even though the separation of the compacts from the graphite matrix is possible, this work assumes that the whole block is loaded in the canister. Although the canisters containing 78 and 114 fuel elements are not included in the previous studies, we explore increased loading, since the decay heat density of the TRISO-based SNF is relatively low. Finally, for SFR, we assume that the heavy metal loading is the same as the UO2 fuel elements with the assemblies of the ABR-1000 reactor.

For the repository design, we considered the clay repository design reported in Atz14 and Hardin et al.48. It is a horizontal disposal, with the initial drift spacing of 30 m. The containers with SNF are inserted into carbon steel overpacks and surrounded by bentonite buffer material. The emplacements drifts are then filled with clay buffer and back fill materials.

The footprint model is implemented in a Python library npwy developed by Atz14. Although the details are available in Atz14, we describe the model briefly for completeness. In the model, the temperature constraint is evaluated at the surface of a waste package located at the center of a square array of N-by-N waste packages (Fig. 2a), where the heat contribution from adjacent packages is the highest. The drift spacing (sd) and the package spacing within the drift (sp) defines the minimum size of the repository. The package at the center of the array is modeled as a finite line source, while the remaining N2-1 packages of the array are modeled as point sources.

The decay heat of each canister is given by \(\:{Q}_{wf}\left(t\right){n}_{wf}\), where \(\:{n}_{wf}\) is the number of fuel units/elements in each canister, and \(\:{Q}_{wf}\left(t\right)\) is the decay heat per fuel unit. With the uniform thermal conductivity κ and thermal diffusivity α, the changes in temperature at some distance r and time t due to the heat for a finite line source are given by the following analytical equation:

$$\:\begin{array}{c}\varDelta\:{T}_{fl}\left(r,\:t\right)={\int\:}_{0}^{t}\frac{Q\left(t\right)}{8\pi\:k\left(t-\tau\:\right){L}_{wp}}.{exp}\left(-\frac{{r}^{2}}{4\alpha\:\left(t-\tau\:\right)}\right).{erf}\left(\frac{L}{4\sqrt{\alpha\:(t-\tau\:)}}\right)d\tau \end{array}$$
(8)

The temperature increase due to the surrounding canisters (point sources) is given by:

$$\:\begin{array}{c}\varDelta\:{T}_{pt}\left(r,\:t\right)={\int\:}_{0}^{t}\frac{Q\left(t\right)}{8{\alpha\:}^{\frac{1}{2}}{\pi\:}^{\frac{3}{2}}k{\left(t-\tau\:\right)}^{\frac{3}{2}}}.{exp}\left(-\frac{{r}^{2}}{4\alpha\:\left(t-\tau\:\right)}\right)d\tau \end{array}$$
(9)

For all times, the contributions from heat sources are superposed at the interface between the host rock and the last EBS layer. Each source is supposed to be surrounded by an infinite and homogeneous media which allows to superpose analytical solutions14 for the impact of the surrounding N2-1 packages on the center package.

The area per package is calculated through an optimization algorithm to finding the minimum area to satisfy the peak temperature constraint. The variable parameters include the drift spacing (sd), the package space (sp), and the size of the array N. The drift radius (rd) and the package length (Lwp) are the fixed parameters of the repository design and the package loading. The algorithm minimizes the area per package, with respect to the constraints on the peak temperature and the minimum spacing requirements \(\:{s}_{p}\ge\:{L}_{wp}\:\)and\(\:{\:s}_{d}\ge\:{2r}_{d}\). It uses the optimize.minimize function in the Python scipy package with the COBYLA (Constrained Optimization BY Linear Approximation) algorithm49. Finally, the repository footprint is obtained by multiplying the area per package by the number of canisters that need to be placed in the repository.

In addition, we explore different surface cooling time before the disposal as well as the waste mass per package based on the previously studied package designs47. We define the number of fuel elements (assemblies or fuel blocks) in each package, which yield the corresponding heavy metal equivalent and volume.

Repository performance assessment model

In terms of the environmental impact of the waste disposal, the repository performance assessment (PA) quantifies the radionuclide transport through the geosphere and released to the biosphere50. After the canister failure, the waste form limits the release of radionuclides into groundwater. The main release modes are: (1) the instantaneous release mode in which noble gases (Kr and Xe) and other volatile fission products (such as I-129) are released instantaneously51, and (2) the congruent release mode in which the radionuclides are released at the same rate as the fuel matrix degradation. Radionuclides are then transported in groundwater and then potentially come in contact with humans, mainly through groundwater pumping and its use for drinking and irrigation.

Our framework includes a simplified PA model estimating the potential dose risk from a generic clay repository filled with SNF. We focus on I-129, because it is the highest dose contributor in previous assessments18,23 due to its high instantaneous release fraction, long half-life, unlimited solubility and lack of sorption. The model consists of three steps to quantify: (1) the I-129 inventory per canister, given the thermal constraint from the footprint analysis (2), the release from the waste form in the congruent and instantaneous release modes, and (3) the transport in the geosphere.

In Step 1, we estimate the I-129 inventory per canister, based on the canister loading that minimize the repository footprint after a given surface storage time. The waste form mass within each canister is computed based on different waste forms. In addition, we calculate the number of canisters required for the 1GWe.y electricity production.

In Step 2, we assumed different waste-form dissolution rates and instantaneous release fraction, depending on the waste forms. The ranges of the dissolution rates (g/m2.day) are [2.20E-03, 1.10E-02], [7.40E-08, 1.30E-06], and [1.57, 3.46] for the UO2, graphite, and metallic fuel matrix, respectively. We assume that the instant release percentage for the UO2 fuel is 2.5%, which is the value used in Mariner et al.18. We would note that this value is conservative, since it has been shown that for fuels with a burnup below 40 MWd/kgU the instant release fraction is under 1%. (Metz, 2012). For the TRISO and FCM fuels, the instant release fraction is supposed to be equal to 2.0 × 10− 452, since the volatile fission products are encapsulated into the TRISO particles. Finally, the instant release fraction for the metallic fuels is assumed to be equal to that of the UO2 fuel due to the lack of data.

The remaining I-129 fraction is released congruently with the fuel matrix. We would note that the congruent-release source term for non-solubility-limited radionuclides has also been used in the disposal assessment in Sweden and Finland as well53,54. In this study, we use the model developed Ahn22 for the UO2 and metallic fuel and Van der Akker and Ahn23 for the TRISO fuel to quantify the amount of I-129 released from a failed waste package in a geological repository. We would note that for TRISO particles, the major barrier preventing fuel degradation and radionuclide release is the graphite matrix of the fuel element, because the degradation rate of the graphite matrix is much lower than the one of PyC or SiC.

Here we describe the mathematical formulation of the congruent release for completeness, although the details were described in Ahn22 and Van der Akker and Ahn23. First, the geometrical transformation is applied for all matrix types to transform the fuel matrix into the sphere of the equivalent volume in a package. This approximation is then used to evaluate the evolution of the fraction of the matrix remaining in the canister. We assume a constant degradation rate.

For a sphere of radius r (in m) and density ρ (in kg/m3) with the degrading at a rate R (kg/m2/s), the rate of change of the radius is given as:

$$\:\begin{array}{c}\frac{dr}{dt}=-\frac{R}{\rho\:} \end{array}$$
(10)
$$\:\begin{array}{c}r\left(t\right)={r}_{0}-\frac{R}{\rho\:}t \end{array}$$
(11)

where ro is the initial radius of the sphere calculated from the initial matrix mass contained in a canister. Assuming that the density of the matrix is uniform and does not vary in time, the fraction of the matrix remaining in the waste package is determined by the following equation:

$$\:\begin{array}{c}{f}_{matrix}\left(t\right)={\left(1-\frac{R}{\rho\:{r}_{0}}t\right)}^{3} \end{array}$$
(12)

Assuming that the concentration of I-129 is constant and uniform in the waste package, the mass of I-129 released out of the waste package congruently with the matrix is given as:

$$\:\begin{array}{c}{m}_{\text{I}129}\left(t\right)={M}_{\text{I}129}\left(1-{f}_{\text{m}\text{a}\text{t}\text{r}\text{i}\text{x}}\right)*\left(1-\text{I}\text{R}\text{F}\right) \end{array}$$
(13)

where \(\:{m}_{\text{I}129}\left(\text{t}\right)\) is the mass of I129 released in the environment after time t, \(\:{M}_{\text{I}129}\left(\text{t}\right)\:\)is the mass of I-129 initially contained within the canister, and IRF is the instant release fraction.

In Step 3, we use a groundwater flow and contaminant transport simulator PFLOTRAN16,17, which has been extensively used in the SNF repository PA in the US18. Our conceptual model (Fig. 2b) is a simplified version of the generic clay model described in Stein et al.20, such that only the clay host rock and limestone aquifer below are considered. The main flow parameters are included in Fig. 2b. It does not include a bentonite buffer around each canister, because the key parameters, such as permeability, are comparable between the host rock and the buffer. Our grid spacing is 20 m by 20 m horizontally, and 10 m vertically. We assume that I-129 is a non-reactive species, which is consistent with previous studies (e.g., Mariner et al.18).

Because the repository footprint model shows that the 1GWe.y-equivalent footprint can fit within a few grid blocks, the source term is defined at one repository block based on the release rate from Step 2. Since the I-129 is not solubility limited, the concentration linearly increases with the number of canisters if they are arranged parallel to the groundwater flow55. If they are arranged perpendicular to the flow, the concentration does not depend on the number of packages. Since our focus is to compare SNF from different reactors, we consider that it is appropriate to consider the 1GWe.y-equivalent footprint without considering the repository configurations. As the performance metric, we consider the peak I-129 concentration in the well located 10 km from the repository, and associated annual dose rates. We convert the concentrations to the annual dose rates based on the biosphere dose conversion factor (for example, rem/yr divided by pCi/L) used for the Yucca Mountain (YM) assessment27. We would note that the YM assessment assumed a well 18 km away from the repository as well as the current population and water use. We assume that the distance of 10 km is compatible to this assessment. To compare the peak annual dose rates with the YM standard, we scale the dose rates from per GWe.y to the YM capacity of 70,000 metric tons of heavy metal.