1. Introduction

As of the first quarter of 2020, 24 units of nuclear power plants were operating in Korea [1] and the stockpile of spent nuclear fuels (SNFs) was 19,632 assemblies from Pressurized Water Reactors (PWRs) and 465,828 bundles from Canada Deuterium Uranium (CANDU) reactors [2]. The total amounts of SNFs are expected to be about 62,400 PWR SNF assemblies and 664,000 bundles CANDU SNF by 2082 when all 30 nuclear power plants will be shut down. Because SNFs contain huge amounts of long-lived toxic radionuclides, the Korea Atomic Energy Research Institute (KAERI) has been conducting R&D programs on deep geological disposal for the safe management of SNFs since 1997. In 2007, KAERI developed a conceptual design of a deep geological disposal system for SNFs called KAERI Reference disposal System for spent nuclear fuel (KRS), which is similar to the Swedish KBS-3 disposal concept. Thereafter, KAERI has focused on R&D programs for advanced fuel cycles based on pyro-processing technology and fast reactors to reduce the toxicity and volume of highlevel radioactive waste (HLW) and reused valuable fissile materials. Accordingly, the Advanced KAERI Reference disposal System for advanced fuel cycle (A-KRS) has been developed for safe disposal of radioactive waste from the pyro-processing of PWR SNFs in 2011.

In May 2016, the Basic Plan for High-Level Radioactive Waste Management is announced by the Korean Ministry of Trade, Industry, and Energy (MOTIE). According to the basic plan, a deep geological repository for SNFs will be constructed and operated until the 2050s and predisposal storage and a site-specific underground research laboratory will be constructed in the repository site. The Moon administration, however, declared reappraisal of the previous government’s national plan on SNF management in August 2017.

Although the national SNF management policy is under reexamination, direct disposal of spent nuclear fuel seems to be the most feasible way considering the current technology readiness level of the back-end nuclear fuel cycle. The necessity of design improvement of existing KRS is growing as policy on spent fuel management is materialized. In particular, enhancing disposal efficiency is the primary purpose of system improvement considering the narrow territory and high population density in Korea.

In compliance with this demand, KAERI has been developing the improved KAERI Reference disposal System for SNFs (KRS⁺) since 2018. The KRS⁺ disposal concept is a package of feasible conceptual disposal system options. Disposal systems for PWR SNFs that are similar to the Swedish KBS-3 vertical (KBS-3V) disposal concept were designed. Two PWR disposal containers are suggested to accommodate two kinds of SNFs, which are categorized according to fuel length and disposal scenario. Two kinds of CANDU disposal concepts that are similar to the KBS- 3V concepts and NWMO-type horizontal disposal concept are proposed in KRS⁺. Since new disposal concepts and systems are suggested in the KRS⁺, it is necessary to assess the criticality and radiation shielding safety of each disposal system. In particular, critical and shielding analyses are indispensable, since the NWMO-type disposal concept for CANDU SNF was proposed for the first time.

This paper provides an overview of the scoping calculation results on criticality and radiation shielding of two KBS-3V type PWR SNF disposal systems and one NWMO- type CANDU SNF disposal system. The effective multiplication factors (k_eff) of three disposal systems were evaluated to verify the criticality safety of the KRS⁺ system. The effect of cooling time of PWR SNFs and nuclides set for criticality calculations was investigated. Combinations of initial fuel enrichment and discharge burnup for safe loading are examined for the R-SNF disposal system as a representative. The absorbed dose rates in the bentonite of three disposal systems were also evaluated for clarifying the shielding performance to prevent the radiolysis of porewater in bentonite. For the NWMO-type disposal system, the minimum thickness of the canister necessary for shielding was evaluated.

2. Methodology and Materials

2.1 Design Basis Fuels and KRS⁺ Disposal System

In this study, two types of PWR SNFs and one CANDU SNF are considered. According to Cho et al. [3], PWR spent nuclear fuels could be categorized into Westinghouse-type and Korean-type considering fuel array types, assembly dimensions, ²³⁵U enrichment, discharge burnup, and cooling time. In this study, PLUS7 with 4.5wt% ²³⁵U enrichment, discharge burnup of 55 GWd/MtU, and cooling time of 45 years was considered as a design basis fuel for Korean-type SNFs (R-SNF). KOFA with 4.5wt% ²³⁵U enrichment, 55 GWd/MtU discharge burnup, and cooling times of 50 years was considered for the Westinghouse-type SNFs (S-SNF). For CANDU SNFs, CANDU6 fuel, which has discharge burnup of 8,100 MWd/MtU and cooling time of 30 years, was considered.

In the KRS⁺ concept, disposal containers for PWR SNFs are deposited in a typical tunnel-type repository with vertical deposition holes similar to the KBS-3V concepts. Disposal containers for SNFs consist of two major components: a corrosion-resistant copper shell and a massive cast iron insert canister that provides mechanical strength for keeping a fixed-configuration and radiation shielding. Four PWR assemblies are placed in individual channels in a PWR container. The diameter of the cast iron insert is 93 cm and the outer copper thickness is 5 cm for the PWR containers. The total length of the container is 431 cm for the S-SNF container and 478 cm for the R-SNF container, respectively. The space between the disposal container and the deposition hole is filled with bentonite blocks. The thickness of the bentonite buffer was set to 36 cm at the side of the container, 50 cm at the bottom, and 250 cm at the top of the container. The tunnel inside is assumed to be backfilled with bentonite blocks or mixtures of bentonite and crushed rock. For the PWR SNF disposal system, the spacing between disposal containers is 7 m for the S-SNF container and 7.5 m for R-SNF with 40 m disposal tunnel spacing.

For the NWMO-type CANDU disposal system, disposal containers are deposited in buffer boxes and these buffer boxes are stacked in 2 by 2 layers along a deposition tunnel. A cast iron-copper double-layered disposal container is adopted and one basket containing sixty CANDU SNF bundles is accommodated in a CANDU container. The size of the CANDU SNF container is 128 cm in diameter and 98 cm in height. The thickness of the copper coating is 1 cm for the CANDU container [4]. The size of the buffer box is 168 cm in length and depth, 138 cm in height. The disposal tunnel spacing is set to 30 m, and the center to center distance of the disposal containers is set to 2.56 m for the NWMO-type disposal system [4].

The unit volume of each disposal system for criticality and shielding calculations was set based on these tunnel and hole distances. The disposal depth is assumed to be 500 m below the ground and the host rock is assumed to be crystalline rock for every disposal system. Fig. 1 and Fig. 2 show the concept and geometry of the PWR disposal systems and NWMO-type CANDU disposal system, respectively.

Fig. 1

Concept and geometry of the KRS⁺ disposal systems for PWR SNFs [4].

Fig. 2

Concept and geometry of NWMO-type disposal system of the KRS⁺ for CANDU SNFs [4].

2.2 Design Requirements for Criticality and Shielding Calculations

Although some standards and guidelines shall be adopted for exact evaluation, simple criteria for criticality and shielding were considered in these scoping calculations. The basic criterion for criticality adopted in this study is that the k_eff should not exceed 0.95. To maintain the subcritical condition, the k_eff of the system including uncertainties must not exceed a defined upper safety limit (USL) [5]. In this scoping calculation study, USL is set to 0.95 assuming a conservative margin of 5% without considering bias and uncertainty terms [6]. Another criterion for shielding is that the absorbed dose rate must be below 1 Gy‧hr^-1 in the bentonite to limit the effect of radiolysis of the pore water or moisture in bentonite, which can accelerate canister corrosion [7,8].

2.3 Computational Models

Criticality and shielding calculations were performed using MCNP6. Geometries of the KRS⁺ systems described in section 2.1 are modeled. The actual geometry of the active fuel region and disposal system was implemented in the computational model without change except for the bottom-end and top-end fuel structural components that were homogenized. The effective fuel area is assumed to be composed of UO₂ fuel rods, claddings, and guide tubes, not considering mid-grid components. Table 1 and Table 2 show major parameters for the design specifications and chemical compositions of each disposal system material [4, 9-12]. Cross-sectional views of the MCNP models for criticality and shielding calculations are depicted in Fig. 3 to Fig. 5.

Fig. 3

Cross sectional view of the R-SNF assembly and R-SNF container model.

Fig. 4

Cross sectional view of the S-SNF assembly and S-SNF container model.

Fig. 5

Cross sectional view of the CANDU SNF bundle and container model.

The isotopic composition of irradiated fuel is necessary for criticality and shielding calculations. To calculate the isotopic composition according to burnup, ORIGEN-S in SCALE 6.1 code was used. The built-in libraries for Westinghouse and CANDU fuels and the PLUS7 library generated by KAERI were used. Because SNFs contain more than thousands of actinides, fission products, and activation product isotopes, a limited set of importance isotopes should be selected. In this study, two nuclides sets listed below are considered for the criticality calculation [13]. The first nuclides set contains actinide-only burnup-credit nuclides and the second nuclides set contains actinide and fission product nuclides.

To calculate the absorbed dose in bentonite, source term evaluations for gamma and neutron sources generated from SNFs were carried out. Primary gamma rays emitted from the disintegration of fission products and actinides from SNFs and neutrons generated from spontaneous fission and (α, n) reaction of fissile materials are calculated using ORIGEN- S. The secondary gamma rays generated from (n, γ) reactions of fissile and non-fissile nuclides were calculated during the shielding analysis. Gamma and neutron sources used in the shielding calculations are listed in Table 3 and Table 4 respectively.

The isotopic inventory of irradiated fuel and total neutron and gamma sources emitted from SNFs are calculated for various combinations of enrichment and discharge burnup for determining the possible loading area. To evaluate depletion, initial enrichment from 2.0wt% to 5.0wt% of ²³⁵U and discharge burnup from 0 GWd/MtU (fresh fuel) to 60 GWd/MtU are considered.

For the criticality assessment, favorable conditions for reactivity were assumed as bounding conditions, such as water-filled containers and wetted bentonite for more moderation by water. To consider the most reactive configuration, fuel assemblies are assumed to be located toward the center of the canister. Infinite arrays of the unit volume for each disposal system are assumed. The neutron crosssection libraries at room temperature were applied because the temperature of the disposal system is maintained within several tens of degrees. The ENDF/B-VII is applied for most of the nuclides and ENDL92 is applied for some nuclides.

For shielding calculations, an air-filled container and dry bentonite were considered because water molecules act as a shielding material. Configurations that are identical to the criticality analysis model were used. The absorbed dose rate was evaluated using the F6 tally to reflect the influence of bentonite material. A cylindrical ring-type tally was applied at the side of the container and a cylindrical disctype tally was applied at the bottom and the top of the con-tainer. Relatively large tally regions are applied for efficient calculation. The tally regions used for shielding calculations are depicted in Fig. 6 for the S-SNF disposal system and NWMO-type CANDU disposal system.

Fig. 6

Vertical cross sectional view of the PWR and NWMO-type CANDU model and tally regions for radiation shielding calculations.

3. Results and Discussion

3.1 Criticality Safety Assessment Results

Criticality safety assessment results for the KRS⁺ are discussed in this section. For the R-SNF disposal system, the effects of nuclides selection and cooling time were analyzed and the preliminary loading area was investigated. The calculated k_eff values are shown in Table 5, demonstrating that all PWR and CANDU disposal systems are subcritical. If the container is filled with air assuming an intact container, the evaluated k_eff is much lower than 0.95. Moderation by the water condition, which means a damaged and flooded container, is a conservative and bounding assumption. The k_eff of the CANDU system is much lower than that of the PWR system due to the use of natural uranium fuel.

The time evolution curves of k_eff for the R-SNF container with two kinds of isotopic composition sets are shown in Fig. 7. The criticality of the R-SNF container changes along with decay and ingrowth of actinides and fission products in SNFs. Until 100 years, k_eff decreases due to the decay of fissile ²⁴¹Pu (half-life of 14.4 years [14]) and ²³⁸Pu (half-life of 87.7 years [14]). Ingrowth of ²⁴¹Am from decay of ²⁴¹Pu causes further diminution of k_eff. Between 100 years to 30,000 years, k_eff increases because of the decay of the neutron absorber ²⁴⁰Pu (half-life of 6,564 years [14]) to ²³⁶U and ²⁴¹Am (half-life of 432.2 years [14]) to ²³⁷Np. After tens of thousands of years, k_eff will decrease as a result of the decay of fissile ²³⁹Pu (half-life of 2.41×10⁴ years [14]). Maximum k_eff occurs in tens of thousands of years. The isotopic composition change of irradiated R-SNF over time is presented in Fig. 8.

Fig. 7

Time evolution of k_eff for R-SNF disposal system calculated with actinide-only nuclides (set1) and actinides with fission product nuclides (set2).

Fig. 8

Isotopic composition of actinides of R-SNF.

As shown in Fig. 7, the calculated k_eff using nuclide set1 is much higher than that using nuclide set2. This is because nuclide set2 contains much more neutron-absorbing elements such as Sm, Eu, and Gd. These results indicate that criticality calculations under cooling time of about 20,000 to 30,000 years and using actinide-only nuclide set are bounding calculation conditions for k_eff. The evaluated k_eff of the R-SNF container assuming 30,000 years of cooling and an actinide-only composition is much below critical.

For safe loading of SNFs in the container, loading curves or feasible loading area should be defined. In this study, the possible loading area for the R-SNF container is determined as a representative. Four identical R-SNFs are assumed to be inserted in a container and evaluated compositions of irradiated fuels having various enrichment and discharge burnup are applied. The evaluated k_eff depending on the initial enrichment and discharge burnup is presented in Table 6. The k_eff of a container filled with fresh fuel having enrichment over 2wt% ²³⁵U exceeds the limit for criticality. However, it is very unlikely that the disposal container will be filled only with nuclear fuel having extremely low burnup and very high enrichment, considering the SNF stockpile in Korea [15]. Most SNFs can be encapsulated in the R-SNF disposal container without any concern for the perspective of criticality.

3.2 Radiation Shielding Calculation Results

Results of radiation shielding calculations for the KRS⁺ are described in this section. In these scoping calculations, the absorbed dose rates in bentonite for each disposal system are evaluated and the effect of loading is investigated. For determining the optimum container thickness for the NWMO-type CANDU disposal system, the absorbed dose rate in the bentonite depending on the thickness of the cast iron canister is evaluated. Evaluated absorbed dose rates of the R-SNF, S-SNF, and CANDU-SNF disposal system are summarized in Table 7. The calculated maximum absorbed dose rates are 1.59×10^-2 Gy‧hr^-1 for the R-SNF disposal system, 2.00×10^-2 Gy‧hr^-1 for S-SNF, and 6.42×10^-2 Gy‧hr^-1 for the CANDU disposal systems, which are far below the design criterion for shielding (< 1 Gy‧hr^-1). The highest absorbed dose rate occurs at the side of the container for every disposal system. The absorbed dose rate at the side of PWR systems is much lower than that of the CANDU system, owing to the effective thickness of the cast-iron inner canister. The absorbed dose rate at the top of the R-SNF system is lower than that of S-SNF because of the longer top-end structure of R-SNF. In contrast, the absorbed dose rate at the bottom of the R-SNF system is higher than that of R-SNF due to higher total source strength. The evaluated absorbed dose rate may have been underestimated because of the use of a large tally area. Considering the substantial margin, however, underestimation caused by the tally region size will not have a significant impact on compliance of design requirements.

The evaluated absorbed dose rate depending on fuel enrichment and discharge burnup for the R-SNF disposal system is presented in Table 8. Absorbed dose rates are calculated by simply multiplying the source strength from SNFs having various enrichment and burnup by unit absorbed dose rate per container. The calculated absorbed dose rate increases as the discharge burnup and enrichment increases. It is identified that PWR SNFs can be loaded in KRS⁺ without a shielding issue, given that the evaluated absorbed dose rate of the R-SNF container accommodating SNF with various initial enrichment and discharge burnup values does not exceed the design limit.

The assessment for determining the minimum thickness of the cast iron canister for radiation shielding was conducted because the NWMO-type CANDU disposal concept is suggested for the first time. Fig. 9 shows the absorbed dose rate in bentonite depending on the thickness of the cast-iron canister. According to the right graph of Fig. 9, the absorbed dose rate decreases linearly on the log scale depending on the container thickness. The solid square line shows the absorbed dose rate according to the change of side thickness. The minimum thickness of cast iron at the side of the container is evaluated to be about 4 cm to satisfy the radiation shielding criterion. The solid circle line and solid triangle line show the absorbed dose rate depending on the top and bottom thickness change. Since the absorbed dose rate at the top and bottom is sufficiently low, the thickness of the top and bottom container is not an important design factor from a radiation shielding perspective. Therefore, it can be confirmed that the container thickness applied to the current KRS⁺ design has been conservatively determined.

Fig. 9

Absorbed dose rate in bentonite of NWMO-type CANDU SNF disposal system depending on container thickness.

4. Conclusions

The aim of this study is to evaluate the criticality safety and radiation shielding performance of the current design of KRS⁺. It is confirmed that the evaluated effective multiplication factor (k_eff) and absorbed dose rate in bentonite of two KBS-3V type PWR SNFs disposal systems and one NWMO-type CANDU SNFs disposal system satisfy design criteria. Assuming the flooded container is surrounded by wet bentonite and rock, fuel composition only considering actinide-only nuclides and time after disposal between 20,000 to 30,000 years are the bounding conditions for criticality calculation. According to the evaluated preliminary possible loading area, some SNFs with high ²³⁵U enrichment and low burnup should consider mixed loading with SNFs having lower enrichment and higher burnup for compliance of the criticality criterion.

Also, it is ascertained that every disposal system of KRS⁺ complies with shielding criteria for preventing the radiolysis of water or moisture in the bentonite. The entire R-SNFs having different enrichment and discharge burnup can be accommodated in the KRS⁺ container without any shielding issue. The container thickness applied to the current KRS⁺ design appears to be sufficient considering the minimum thickness of the NWMO-type container for satisfying the shielding criterion.

There are some limitations in the scoping calculations. Some material data used in this study are based on past design data. There may be a relatively large error in the results of the shielding calculation caused by large tally regions. For a rigorous calculation, the use of updated data and a detailed analysis using a fine tally are necessary for detailed analysis. Additionally, uncertainty and bias assessments based on international codes and standards should be performed. Since the effect of burnup is very large, detailed evaluations such as adopting axial burnup profiles should be fulfilled under the basis of international standards for burnup credit in the near future.