Research and development on high-level radioactive waste in Korea was launched in 1997, and a deep geological disposal system for spent nuclear fuels, which was called KRS (KAERI Reference disposal System for spent nuclear fuels) was developed in 2007. It is expected that the amount of spent nuclear fuel will continue to increase as it is currently temporarily stored and accumulated at the nuclear power plant sites. Moreover, the operation of the nuclear power plant is required in accordance with the established basic power supply plan. The disposal site area for their safe management is thus also expected to increase significantly. Therefore, for efficient use of the national land and public acceptability, the improved disposal concepts, called KRS+ (the KAERI Reference disposal System Plus), were proposed to improve disposal efficiency by reducing the area of disposal site based on KRS concept .
There are two types of SNF generated in Korea: pressurized light water reactor (PWR) SNF and pressurized heavy water reactor (PHWR:CANDU) SNF. The safest technology for disposing high-level waste including SNF with current technology is a deep geological disposal technique that isolates high-level waste by applying the concept of a multibarrier in underground stable rock at a depth of 500 m.
The main factor that should be considered in the design of a deep geological disposal system is to maintain the integrity of the installed engineered barrier to ensure the safety of disposal. That is, when the temperature of the bentonite blocks around the disposal container exceeds 100℃ due to the decay heat emitted from the high-level waste in the disposal container, the bentonite performance as an engineered barrier decreases because of a change in physical properties [2, 3]. The thermal stability of the engineered barrier for ensuring the safety of a disposal system considering the decay heat from wastes loaded in the disposal container thus should be analyzed. Moreover, the distance between high-level wastes should be adjusted and placed so that the temperature limit of the bentonite blocks is not exceeded. In addition, the disposal container, which is a major component of the engineered barrier, must maintain structural integrity against hydraulic pressure and swelling pressure of the bentonite blocks in the deep underground disposal environment.
In advanced countries in the field of SNF disposal technologies such as Sweden, Finland and Canada, they carried out the analyses on the thermal stability of their own developed disposal system and on the structural integrity of their disposal container concept from early research stage [4-6].
In this paper, direct disposal of two types of SNF discharged from domestic nuclear power plants into deep geological bedrock in Korea was considered. The thermal stability of a bentonite buffer and the structural integrity of the disposal container of an improved disposal concept, called KRS+, that improved the disposal efficiency to suit the domestic environment based on existing disposal concepts, referred to as KRS [7,8], were analyzed. In other words, the thermal stability for the evaluation of compliance with the thermal requirements of the engineered barrier, which constitutes a major requirement for the design of the disposal system, and the structural stability of the disposal container against the hydraulic pressure and the buffer swelling pressure at the depth of disposal were analyzed.
2. Improved Geological Disposal System for SNF
2.1 Improved CANDU SNF disposal system
2.1.1 Reference CANDU SNF
The spent nuclear fuel generated from the CANDU NPPs, pressurized heavy water reactors developed in Canada, is loaded in baskets with capacity of 60 bundles and temporarily stored in concrete silos or dry storage facilities called Maxtor 400 at power plants sites. In the case of CANDU spent nuclear fuels, the initial concentration was 0.711%, and with advances in nuclear power generation technology, the burn-up was raised from 7,800 MWd/MtU to 8,100 MWd/MtU, which was reflected in the improved disposal system .
2.1.2 Improved CANDU SNF disposal system
The CANDU SNF disposal system was designed with the concept of loading the baskets into the disposal container, as the CANDU SNF is smaller than the PWR SNF and is currently loaded in a basket of 60-bundle capacity and stored in dry storage facilities. In addition, the disposal systems applied the concept of a traditional KBS-3 vertical type disposal and the concept of Canadian NWMO type disposal, which is a horizontal disposal concept as shown in Fig. 1 . Table 1 shows the comparison between existing system and improved systems and the improvement of the disposal density from about 30% to 70%.
2.2 Improved PWR SNF disposal system
2.2.1 Reference PWR SNF
In developing the improved PWR SNF disposal system, the system was designed for the SNF discharged from PWR type NPPs in Korea. In addition, the characteristics of the reference PWR SNF, such as the actual amount and specifications by the operation of the PWR type NPPs were considered. The characteristics of the high burn-up SNF, which were an initial concentration of 4.5wt% and burn-up of 55 GWD/tU were reflected and two reference SNFs were established for each specification as follows .
- S-SF (Short-Spent Nuclear Fuel) : 406 cm long spent nuclear fuel discharged from the early age of nuclear reactor such as Gori 1,2,3,4, Hanbit 1, and Hanul 1 and 2 plants.
- R-SF (Regular-Spent Nuclear Fuel): 453 cm long spent nuclear fuel other than the S-SF above.
2.2.2 Improved PWR SNF disposal system
Two types of disposal containers classified according to the characteristics of the PWR SNFs were developed and the amount of heat for each disposal container was established according to the disposal scenario described in reference 9. In other words, the cooling time of SNFs was set based on the time of SNF discharged from the domestic NPPs and the disposal scenario in accordance with the current national basic plan. Furthermore, the decay heat capacity acceptable to each type of disposal container was established based on this. For thermal stability analyses according to the requirements of the disposal system design and the decay heat capacity, the disposal container was set up and the disposal system was designed based on the concept of the disposal container as shown in Fig. 2. Table 2 shows the comparison between existing system and improved systems and about 20% improvement of the disposal density.
3. Thermal Stability Analyses of the Improved Disposal Systems
The concept of deep geological disposal on stable rock located at underground depth of about 500 m, which isolates the highly toxic and long-lived radioactive wastes including spent nuclear fuel from the human environment, is considered the safest and most feasible technology. This concept has a multiple barriers concept with engineered barriers consisting of disposal containers and buffer materials, and natural barriers, which are embedded rocks. One of the most important requirements for the design of this concept is to ensure that the temperature of bentonite, a buffer, does not exceed 100℃ in order to prevent corrosion of the disposal container and deterioration of the safety performance of the buffer [2,3]. Therefore, a thermal analysis should be performed for the improved disposal concept of spent nuclear fuel established in this study to ensure that the thermal design requirements are satisfied.
The thermal analysis is carried out at a unit cell scale. Once the spent fuels are disposed of in a disposal container, the heat transfer in the buffer and crystalline rock is mainly by a conduction, which is a somewhat conservative assumption. The schematic views of the calculation domain for each type of spent nuclear fuels are given in 3.1 and 3.2. The domains are for a quarter of one disposal container including the deposition hole and the disposal tunnel. The heat transfer is represented with the following three dimensional heat conduction equation :
where T is the temperature (℃), t is the time (s), ρ is the density (kg‧m-3), Cp is the specific heat (J‧kg-1℃-1), k is the thermal conductivity (W‧m-1℃-1), q(t) is the time-dependent volumetric heat source (W‧m-3).
In performing this thermal analysis, rock properties of KURT (KAERI Underground Research Tunnel) site, a small underground research facility, were applied on the assumption of a disposal site . Also, the properties of the disposal system components were shown in Table 3.
In addition, the computational program for these thermal analyses was ABAQUS ver. 2019 , a commercial code using the finite element method, which was reviewed and verified as a code for the design of a high-level waste disposal system .
3.1 Thermal stability of improved CANDU SNFs disposal system
3.1.1 Decay heat of CANDU spent nuclear fuel
The radioactive decay heat (W/tHM) of SNF, which affects the area around the deposition hole in the disposal system, originates from the fission products and the actinide elements. In the case of discharged burn-up of 8,100 MWD/ MTU-1 for CANDU SNFs, the decay heat P(t) according to the history of radio nuclide decay taking into account the cooling time after release from the reactor is expressed in the following regression formula, as shown in Fig. 3 and Table 4. This was calculated by deriving the reference spent nuclear fuel and analyzing the characteristics of the spent nuclear fuel  for the disposal of CANDU SNFs discharged from the current NPPs and those expected to be discharged in the future.
Here, P(t) is the decay heat (W) according to the time released from the reactor per unit weight (1 tU) of the reference CANDU SNFs and t is the time released from the reactor. y0, A1, A2, A3, t1, t2, and t3 are constants for each time range, and their values are shown in Table 4 below.
3.1.2 Scope and method of the thermal analyses
When a disposal container loaded with SNFs is disposed of at an underground repository, decay heat from the SNFs is transferred to the disposal container, bentonite block, backfill and rock and then spreads. At this time, since the disposal system is filled with backfill material and closed, the main method of thermal transfer is conduction, and thus convection and radiation can be ignored. For thermal stability analyses according to temperature requirements caused by radioactive decay heat in the improved CANDU SNF deep geological disposal system, a three-dimensional model was used. The basic assumption was that the disposal container and the engineered barrier were installed at the same time. The layout characteristics with many disposal tunnels and disposition holes placed at equal intervals were taken into account. Therefore, the one-quarter model was applied in the horizontal direction, considering one-half of the disposal tunnel interval and that of the deposition hole interval. The top-to-bottom boundary was considered from the ground surface to a depth of 1,000 m for sufficient distance to prevent impact of decay heat of emplaced SNFs in the deposition holes located at the depth of 500 m. The geometry of the models for thermal analyses of each disposal concepts are shown in Fig. 4.
Boundary conditions according to the symmetrical model for thermal analysis of the CANDU disposal system were set as adiabatic boundaries for both the vertical and bottom sides of the analytical model. For the initial condition of the temperature distribution, it was assumed that the temperature of the ground surface was 10℃, and the thermal gradient was 3℃/100 m [13, 18], and the temperature was 40℃ at the depth of 1,000 m.
3.1.3 Results of thermal stability assessment for improved disposal systems
The thermal stability analysis results for ensuring that the thermal requirement for the buffer material temperature by the decay heat of SNFs should not exceed 100℃ in a disposal environment for CANDU SNFs are shown in Figs. 5 and 6. As shown in the figures, in the case of the KBS- 3 type vertical disposal system, when the disposal tunnel and deposition hole space were 40 m and 5 m respectively, the surface temperature of the disposal container reached its highest value of 90.4℃ when 17 years had passed after disposal (Fig. 5), which satisfied the disposal system temperature limit requirement (< 100℃). In addition, in the case of Canadian NWMO-type horizontal disposal systems, the highest temperature of the buffer material(the surface of disposal container) for a disposal module interval of 2.6 m at a disposal tunnel interval of 30 m was 92.5℃ at 48 years after disposal (Fig. 6), which satisfied the temperature limits of the disposal system requirements.
3.2 Thermal stability of improved PWR type SNFs disposal system
3.2.1 Decay heat of PWR spent nuclear fuel
The SNFs released from a nuclear power plant emit high heat due to continuous decay of the radionuclides remaining inside. The regression formula described below showed the decay heat formula (W/tU) and the constant for each time range of the PWR SNF used on a high burnup basis (see Table 5), and the results of the decay heat calculation based on this are shown in Fig. 7. As shown in the figure, the history of decay heat with time was represented as follows [14,15].
Here, Y is the decay heat (W) according to the time released from the reactor per unit weight (1 tU) of the reference PWR SNFs and t is the time released from the reactor. x0, y0, A1, A2, A3, t1, t2, and t3 are constants for each time range, and their values are shown in Table 3.
3.2.2 Scope and method of analysis
The range of thermal analyses for thermal stability assessment of the PWR geological disposal systems is shown in Fig. 8. As shown in the figure, the analyses area was set from the ground surface to a depth of 1000 m, which was the range where the effects of decay heat from the disposal container are not significant. Considering the characteristics of continuous arrangement of disposal tunnels and deposition holes at regular intervals, a 1/4 model based on the center of the disposal tunnel and deposition hole interval was set, and adiabatic conditions were set for the side of the analytical model considering its symmetry. In addition, the thermal stability of the disposal system was assessed by fixing the disposal tunnel spacing at 40 m and adjusting the deposition holes interval according to the decay heat. Deposition holes interval for these analyses were set to 6.5 m, 7 m, and 7.5 m for S-SF and to 7 m, 7.5 m, and 8 m for R-SF.
The initial conditions, geothermal gradient and material properties by the research data from KURT, the KAERI Underground disposal Research Tunnel, were utilized for thermal analyses . As the initial conditions, the ground surface was 10℃ based on the ground water temperature of the surface area, and 3℃/100 m was applied to the geothermal gradient according to the depth. Therefore, temperatures at the top and bottom of the analytical model range were set to 10℃ and 40℃ respectively. In addition, the properties required for analyses, such as rock, buffer, backfill, density, thermal conductivity, and specific heat of the disposal system, are shown in Table 3.
3.2.3 Results of thermal stability assessment for improved disposal systems
Based on the existing geological disposal system of the SNFs, the concepts of improving disposal efficiency were derived by classifying the disposal containers into two types and establishing decay heat according to the cooling time at the time of disposal, considering the characteristics of SNFs discharged from domestic NPPs. For these improved disposal concepts, the thermal requirements of the disposal system should also be satisfied, and the results of the thermal analyses according to the range and the method set in the previous section 3.2.2 are shown in Figs. 9 and 10.
For the S-SF disposal system with short spent nuclear fuel of 406 cm length, the maximum temperature of the bentonite blocks was calculated to be 95.5℃ (Fig. 9) at 11 years after disposal, based on 50 years of SNF cooling time at the point of disposal. At this time, the distance of the disposal tunnel was 40 m and the interval of the deposition hole was 7 m, and it was confirmed that the disposal concept was suitable for the design requirements. In addition, in the case of R-SF disposal systems with a length of 453 cm, it was assessed that the design requirements were also satisfied with a maximum temperature of 95.3℃ (Fig. 10) at 11 years after disposal, when the disposal tunnel distance was 40 m and the deposition hole interval was 7.5 m.
4. Structural Stability Analyses for the Improved Disposal Container
In this study, it was assumed that only the cast insert maintained the structural integrity of the disposal container. The structural analyses were performed with the procedure of the two-step conditions for loading described below [5,11].
- Step 1: Analyses of heat stress for disposal container by heat transfer in a disposal environment
- Step 2: Structural analyses by applying hydraulic pressure and swelling pressure in the disposal environment with the initial condition of step 1 results
The material models for the canister materials are based on elastic-plastic behavior with isotropic linear elasticity and von Mises plasticity . This is a very common way to model structural metallic materials. The justification to use von Mises plasticity for copper is given in  and the justification for nodular cast iron is given in [18, 19].
The thermal property values of the materials used in the structural analysis for this assessment are shown in Table 1, and are the same as those used in the thermal stability analysis. The structural property values are given in Table 6 [5,21]. Three-dimensional structural analyses were performed on the half model of the disposal container as shown in Table 7, and the program used in these analyses used ABAQUS Ver. 2019, a commercial analysis tool using the finite element method .
4.1 Analyses model for the structural integrity of the improved disposal containers
The CANDU SNF disposal systems improved in this study were the KBS-3 type vertical disposal system and the Canadian NWMO type horizontal disposal system . In addition, the improved PWR SNF disposal systems were KBS-3 type vertical disposal systems, which established two types of disposal container concepts according to the length of the SNFs. The structural integrity of these containers was assessed. The structural integrity analyses models of disposal containers subject to hydraulic pressure and swelling pressure in the second step of the disposal environment according to the results of thermal load in the first step are shown in Table 7.
4.2 Results of the structural integrity analyses for disposal containers
4.2.1 Structural integrity of disposal container for CANDU SNFs
Structural analyses of the disposal containers in the event of a heat load caused by the decay heat of the SNFs, hydrostatic pressure at the depth of disposal, and added swelling pressure of the bentonite blocks in an environment in which CANDU SNFs were disposed of were performed as described in the previous section. Table 8 shows the results of structural analyses in the case of the KBS-3 type vertical disposal system and the NWMO type horizontal disposal system for CANDU SNFs.
As shown in the Table 8, the analyses results of structural stability in normal cases showed that the von-Mises stress values were 80.2 MPa and 66.01 MPa with a safety factor of 2.8 and 3.5, respectively. The required safety factor in the design load case can be justifiably set for the cast iron insert to 2.0 . Therefore, it was determined that thermal-structural stability of the improved CANDU disposal containers could be maintained in the deep geological disposal environment.
4.2.2 Structural integrity of the disposal containers for PWR SNFs
Structural analyses of the disposal container for PWR SNFs were also carried out in the event of thermal load, hydrostatic pressure and swelling pressure in the deep underground disposal environment, and the results are shown in Table 9.
As shown in the table, the calculated von-Mises stress of the S-SF disposal container was 71.01 MPa, and the stress of the R-SF disposal container was 76.6 MPa, which showed safety factors of more than 3.0 compared to 230 MPa yield strength of cast iron at 100℃. Thus, it was evaluated that the thermal-structural stability of the improved PWR disposal containers could be maintained in the deep geological disposal environment.
5. Conclusions and Future Plan
A deep geological disposal with a multiple barrier concept in a stable rock at a depth of about 500 m is considered the safest technology that isolates high-level wastes including SNFs for a long time from the human environment. The main requirements for this disposal system design are to arrange the disposal tunnels and the deposition holes for the temperature of the buffer material, which is an engineered barrier element, at less than 100℃, and to ensure the structural integrity of the disposal containers against the loads at the environment of the deep geological disposal.
In this study, thermal stability and structural integrity analyses in the disposal environment have been performed for the improved disposal concepts (KRS+) that reduced the disposal area and increased the disposal density for domestic PWR SNFs and CANDU SNFs that are being considered for direct disposal.
The results of the thermal stability assessment for the improved disposal system of the domestic SNFs are described below.
- The disposal system for CANDU SNFs was improved to the KBS-3 type vertical disposal system and the Canadian NWMO type horizontal disposal system. For the KBS-3 type vertical disposal system, two disposal containers that accommodate four baskets of 60 bundles capacity were emplaced in each deposition hole, and the maximum buffer temperature was 90.4℃ when the disposal tunnel and deposition hole distances are 40 m and 5 m, respectively. For the NWMO type horizontal disposal system, a module with four disposal containers accommodating one basket of 60 bundles was emplaced, and thermal stability was ensured at a maximum temperature of 92.5℃, when the disposal tunnel distance was 30 m and the modules interval was 2.56 m. The thermal stability of these two improved disposal systems was thus secured with satisfaction of the thermal requirements.
- The disposal system for PWR SNFs was improved to two types of disposal systems depending on the length of the SNFs. The S-SF disposal system, which had a short length of SNFs, had a 40 m distance between disposal tunnels and 7 m distance between the deposition holes. The R-SF disposal system, which had a longer length of SNFs, had distance of 40 m between disposal tunnels and distance of 7.5 m between deposition holes. In both cases, the thermal stability was maintained, as the maximum temperature of buffer was around 95.
The results of the analyses for the structural integrity of the disposal container in the disposal environment for the improved disposal system were described below.
- In the KBS-3 type vertical disposal system for CANDU SNFs, the von-Mises stresses of the disposal container by thermal and hydrostatic and swelling pressure loads in the disposal environment were 80.2 MPa, and the stresses of the disposal container by the same load in the NWMO type horizontal disposal system were 66.0 MPa. It was assessed that the structural integrity of the disposal container was secured with a safety factor higher than 2 compared to the yield strength of 230 MPa at 100℃
- For the improved disposal systems of PWR SNFs according to the length of SNFs, the von-Mises stress of the S-SF disposal container with short length SNFs for the loads in the disposal environment was 71.01 MPa. In addition, that of the disposal container for the R-SF disposal system with regular length SNF was 76.6 MPa for the same loads. It was assessed that structural integrity of the disposal container was secured with a safety factor higher than 2 to yield strength of 230 MPa at 100℃.
The results of thermal and structural stability assessment of the disposal systems and the disposal containers in this study can be used as a reference disposal system for empirical test for demonstration in the URL (Underground disposal Research Laboratory) and as basic data for establishing a domestic SNF management policy. In the future, in order to reduce uncertainty, more specific analyses and interpretation are required with accurate material data and site characteristics data.