.jpg)
1. Introduction
The containment of highly radioactive waste, including spent nuclear fuel, in stable rock of deep geological formations is recognized as the safest way to isolate this waste from the human and natural environment. The host rock for such disposal can be selected from various rock types, such as sedimentary and crystalline rock, depending on the conditions in each country. Deep geological disposal systems incorporate a multibarrier consisting of an engineered barrier and the natural barrier of the host rock system. The key components of the engineered barrier are the disposal container and the buffer material. The disposal container must be able to contain radioactive waste through its specified performance period. If a crystalline rock is selected as the host rock, a buffer material is essential to prevent groundwater inflow through rock fractures, resulting in corrosion of the disposal container and radionuclide outflow.
The thickness of the buffer material is an important consideration when designing the engineered barrier of a deep geological disposal system. Buffer materials serve to (1) prevent the intrusion of corrosive oxidants, such as oxygen, from the outside and suppress the spread of nuclides that may leak from the disposal container, (2) effectively dissipate the decay heat generated in the disposal container to the outside, and (3) protect the disposal container from physical shocks, such as external tectonic movements [1]. If the buffer material is too thick, there will likely be inadequate dissipation of the decay heat, and the cost of installation increases with buffer thickness. If the buffer material is excessively thin, the function of limiting the transfer of nuclides is reduced, and the physical buffering effect is insufficient.
In this study, the performance goal and the safety function of bentonite buffers were reviewed. Subsequently, the requirements or factors necessary to determine the appropriate thickness of the bentonite buffer for a vertical disposal concept—which is an important component of engineered barriers—were identified, and the required thickness for each side of the disposal container was calculated. In addition, a double-layered emplacement method for buffer materials was proposed to improve the disposal efficiency in terms of thermal management.
To confirm that these results can be applied to waste disposal system design, additional detailed analysis, applying actual disposal site data, is required. In addition, in the case of horizontal disposal, the super container concept that integrates the disposal container and bentonite buffer material is applied, so a separate analysis is required later on regarding the thickness of the buffer material for horizontal disposal.
2. Safety Functions and Performance Goal of Buffer Material
The main safety function of the disposal system is to safely isolate high-level waste loaded into the disposal containers from the surface environment for a long period of time by directly or indirectly protecting and preserving the safety function of the barrier system. The disposal container and the buffer material are the main components of an engineered barrier system. The buffer material is typically natural clay, containing swelling substances, that surrounds the disposal container and fills the space between the disposal container and the wall of the host rock in a deposition hole. When selecting and implementing buffer materials, the main performance goal is to maintain and preserve the radionuclide containment function by limiting the transport of corrosive materials as well as corrosion on the surfaces of disposal containers. To preserve the containment performance of the disposal container, a buffer material should be designed based on the structural soundness of the disposal container. If the disposal container is damaged, the buffer material must contribute to the retention of radionuclides and delay their diffusion into the environment [2, 3]. The specific functions of the buffer, which can be quantified and assessed are:
-
limit advective mass transfer,
-
limit microbial activity,
-
colloidal filtration,
-
protect disposal containers from harmful structural loads, such as rock shear and pressure loads,
-
deformation resistance,
-
maintain disposal containers in place,
-
maintain sufficient mass throughout the life cycle.
With respect to its ability to maintain these safety functions, clay-containing swelling material was chosen as a buffer between the disposal container and the rock wall. These clay materials have an additional function: to retain radionuclides and retard their dispersion, and to sorb radionuclides if the containment of the disposal container is breached.
The first three safety functions listed above are mainly related to hydraulic conductivity, swelling pressure and density [4]. In this paper, the next four safety functions, which are mainly related to the thickness of the buffer, are considered in the following sections.
3. Consideration Factors for the Bentonite Buffer Thickness
Deep geological disposal involves loading a disposal container with spent nuclear fuel and placing it in a deposition hole drilled vertically into the floor of a disposal tunnel excavated. The space between the disposal container and rock wall of the deposition hole is filled with bentonite buffer material, and the disposal tunnel is backfilled and sealed. The thickness of the bentonite buffer material is determined by the need to maximize both the radiological safety and thermal stability of the disposal system and also depends on the size of the deposition hole. In other words, the thicker the bentonite buffer material, the greater the disposal safety. However, with increasing thickness, the thermal stability decreases and a larger disposal hole is required for the disposal container and buffer, which becomes costly. The thicknesses of the material around, above and below the canister will, together with the dimensions of the canister, determine the buffer volume. Therefore, it is necessary to set an optimized thickness to ensure maximum disposal safety as well as sufficient thermal stability and cost effectiveness.
The requirements for bentonite buffer of deep geological disposal [4] indicate that the buffer thickness—that is, the distance between the canister and the deposition hole wall—should be at least 0.3 m, and the thickness of the buffer below and above the canister should be at least 0.5 m.
The functions of the buffer material that should be considered when setting the optimized thickness of the bentonite buffer material are as follows.
-
Prevent the intrusion of corrosive oxidants, such as oxygen, from the outside and suppress the spread of nuclides that may leak from the disposal container to the external environment.
-
Dissipate the decay heat emitted from the radioactive waste contained within the disposal container as effectively as possible.
-
Protect disposal containers from physical shocks, such as external tectonic events.
-
Support the disposal container and seals the area of the floor of the disposal tunnel that was disturbed during excavation.
For each function of the bentonite buffer material described above, an appropriate thickness must be set to maintain its long-term performance.
3.1 Optimal Buffer Thickness Based on the Nuclide Release Rate
When a disposal container is damaged and loses its function, radionuclides diffuse through the buffer material into the groundwater flowing out into the bedrock around the disposal site. Considering the geometric structure of the disposal site, the outflow of radionuclides through the buffer material can be simulated by modeling a two-dimensional diffusion movement that takes into account radioactive decay. The rate of radionuclide outflow, Ri, defined as the total cumulative flux of radionuclides through the cross-section of the buffer material at the buffer-rock interface, can be expressed by the following equation [5]:
where θ is the porosity of the buffer material, Dp is the pore diffusion coefficient of the nuclide, Ci is the concentration in the solution of nuclide i, and A is the cross-sectional area where the nuclide diffusion outflow occurs at the buffer material-rock interface.
The Korea Atomic Energy Research Institute (KAERI) evaluated the leakage rate through a buffer of 12 radionuclides known to be important nuclides for assessing the safety of high-level waste disposal [6]. The total release rate of radionuclides over time after the closure of the disposal site was calculated as a function of the radial thickness of the buffer material. As can be seen in Fig. 1, the total release rate of radionuclides decreases rapidly until the radial thickness of the buffer increases to 0.25 m and then decreases gradually, up to a buffer thickness of 0.5 m. However, an increase in buffer thickness beyond 0.5 m has little additional effect on reducing radionuclide outflow. Thus, the appropriate thickness can be said to be between 0.25 and 0.5 m.
Fig. 1
Total radionuclide release rate according to the radial thickness of the buffer material over 1,000 years after repository closure.
3.2 Optimal Range of Buffer Thickness Based on Rock Shear Displacement
In deep geological environments, the bentonite buffer must provide a physical buffer against tectonic movement. Table 1 shows the criteria for shear movement that can withstand the disposal containers set by JAEA, SKB and KAERI [7, 8, 9]. This is an important evaluation factor in countries, such as Japan, that experience frequent earthquakes and should also be considered in Korea, a country that is not completely safe from earthquakes. These criteria predict the maximum shear movement that can occur at sufficiently large geological depths. In this study, the maximum shear distance was set as 100 mm.
Table 1
Tectonic fault movement parameters as criteria in the design of disposal containers
| Item | Japan, JAEA [7] | Sweden, SKB [8] | Korea, KAERI [9] |
|---|---|---|---|
|
|
|||
| Shear displacement | 100 mm | 50 mm | 100 mm |
| Shear rate | 1.0 m·sec−1 | 1.0 m·sec−1 | 1.0 m·sec−1 |
When the disposal container is emplaced within the buffer material, the rotation angle owing to the rock shear movement passing through the center of the disposal container is calculated as follows:
where θ is the rotation angle of the disposal container, δ is the shear distance, and L is the length of the disposal container [10].
The possible shear displacements and rotational angles depending on the thickness of the buffer material are shown in (A)–(D) in Table 2. The rotational movement of the disposal container is illustrated in Fig. 2. As shown in the figure, when the actual shear distance was 100 mm, the collision between the disposal container and rock was prevented, even if the buffer material thickness reached from 500 to 100 mm. However, when the thickness of the buffer material reaches 100 mm, the clearance between the disposal container and the rock almost disappears; therefore, in order to achieve a sufficient safety factor, the thickness of the buffer material must be at least 200 mm.
Table 2
Estimated shear movement and rotational angle of bentonite buffer based on buffer thickness
| No. | Canister length (L, mm) | Buffer thicknes (t, mm) | Shear movement (δ, mm) | Rotational angle (θ, °) |
|---|---|---|---|---|
|
|
||||
| (A) | 4,778 | 500 | 100 | 1.20 |
| (B) | 4,778 | 500 | 950 | 11.47 |
| (C) | 4,778 | 200 | 350 | 4.20 |
| (D) | 4,778 | 100 | 160 | 1.92 |
3.3 Optimal Buffer Thickness Based on Thermal Conductivity
Typically, the thermal conductivity of a bentonite buffer material is lower than that of rock. Therefore, when a buffer material surrounds the disposal container, the surface temperature of the container increases. In most countries, the temperature of a bentonite buffer at the interface with a disposal container is set at 100°C or lower [11]. When the thickness of the buffer material with low thermal conductivity increases, the temperature of the disposal container increases, which is thermally disadvantageous; therefore, prior to completing the disposal system design, it is necessary to estimate the surface temperature of the disposal container based on the thickness of the buffer material.
In a deep geological repository, the decay heat of spent nuclear fuel loaded in a disposal container diffuses to the disposal container, buffer material, and host bedrock. This transfer of heat occurs mainly by conduction rather than convection or radiation when the repository is closed [12]. Therefore, the heat transfer energy through conduction can be expressed by Fourier’s law of heat conduction, as follows:
where Q is the heat flux, k is the thermal conductivity, A is the heat transfer area, and is the temperature gradient in each direction [13].
As shown in the equation, the heat transfer rate is proportional to the thermal conductivity and the area through which heat is transmitted and inversely proportional to the thickness of the area through which the heat is transmitted.
In this study, thermal analyses using ABAQUS ver. 2019, a commercial computational program for the finite element method [14], were carried out to evaluate the temperature of the bentonite buffer material with respect to its thickness. The basic conditions used in the calculations are as follows. The rock temperature was set to 25°C (=surface temperature of 10°C + geothermal gradient of 30 °C·km−1 × depth of 500 m), an internal heating value of 2,000 W, a rock thermal conductivity of 3.2 W·mK−1, a buffer thermal conductivity of 0.8 W·mK−1, container radius of 0.5 m and container length of 4.8 m [15].
The calculation results are shown in Fig. 3. When the thickness of the buffer material reaches 0.5 m, the surface temperature of the container exceeds 100°C which is currently the temperature limit in the design of deep geological repositories [9]. Because this calculation is simple with several assumptions, an accurate value must be confirmed through detailed analyses with real disposal site data. However, in the preliminary design stage, a basis for a buffer material thickness not exceeding 0.5 m was obtained.
Fig. 3
Temperature history and maximum temperature of disposal container (subfigure) as a function of thickness of bentonite buffer.
3.4 Buffer Thickness Above and Below the Disposal Container
As mentioned in Section 3, the buffer thickness above and below the disposal container should be at least 0.5 m. In addition, the excavation damaged zone (EDZ) of the disposal tunnel above the deposition hole and the corrosion of the disposal container lid by sulfides in the backfill should be considered for the buffer thickness above the disposal container.
In Table 3 are shown the EDZ extent values based on excavation method [16]. As shown in the table, the maximum extent of the EDZ was less than 2 m in the GTS (Grimsel Test Site) using the blasting method. Given the EDZ extent, the thickness above the disposal container should be 2.5 m. If a smooth blasting method or TBM (Tunnel Boring Machine) is used to excavate the disposal tunnel, the extent of the EDZ can be less than 1 m. Therefore, the buffer thickness above the disposal container can be reduced to 1.5 m.
Table 3
Extent of EDZ at various sites [14]
| Country | Experiment site | Excavation method | EDZ extent (m) | Depth (m) | Rock type |
|---|---|---|---|---|---|
|
|
|||||
| Sweden | ASPO-Access tunnel | Normal blasting Smooth blasting | 1.7 | 80 | Crystalline rock |
| ASPO-ZEDEX | TBM | 0.3 | 420 | Crystalline rock | |
| ASPO-TASQ | Smooth blasting | 0.3 | 450 | Crystalline rock | |
| ASPO-TASS | Smooth blasting | 0.25 | 450 | Crystalline rock | |
| Stripa | Smooth blasting | <0.8 | 340 | Crystalline rock | |
|
|
|||||
| Canada | URL-Room2009 | Smooth blasting | 0.3 (floor) | 240 | Crystalline rock |
| URL-Mine by tunnel | Smooth blasting | 0.2–0.3 | 420 | Crystalline rock | |
| URL-Tunnel sealing | Smooth blasting | <1.0 | 420 | Crystalline rock | |
|
|
|||||
| Finland | ONKALO | Drilling & blasting | 0.3 | 500 | Crystalline rock |
|
|
|||||
| Switzerland | Mont terri | Blasting | 0.2–1.5 | 400 | Opalinus clay |
| GTS | Blasting | <2.0 | 450 | Crystalline rock | |
|
|
|||||
| Japan | Mizunami | Smooth blasting | 1.0 | 500 | Crystalline rock |
|
|
|||||
| France | Meuse/Haute-Marne | TBM blasting | 1.0 | 490 | Clay |
|
|
|||||
| Belgium | Hades-URF | TBM | 0.6–1.0 | 230 | Clay |
|
|
|||||
| Germany | Asse URL | Blasting | 1.5 | 800 | Salt |
|
|
|||||
| Korea | KURT | Smooth blasting | 0.6–1.5 | 100 | Crystalline rock |
In Fig. 4 are shown the results of the reevaluation of the buffer thickness above the disposal container [17]. As shown in the figure, even with a buffer thickness of 1 m, the lifetime of the disposal container due to corrosion with varying buffer thicknesses is much longer than the minimum requirements (>10,000 years) by the NSSC (Nuclear Safety and Security Commission) Notices, “General criteria for Deep Geological Facilities of High-Level Radioactive Wastes” in Korea.
3.5 Results of Buffer Material Thickness Analyses
When considering the buffering effect of shear movement of the buffer by the rock movement and the effect of suppressing the radioactive nuclide outflow rate according to the hydraulic conductivity among the factors related to determine the thickness of the side buffer material for disposal container, consequently, a minimum buffer thickness of 0.25 m was required. As a result of considering the thermal diffusion effect, it was judged to be disadvantageous if the thickness of the buffer is 0.5 m or more. Therefore, it is reasonable to conclude that a buffer thickness in the range of 0.25 to 0.5 m will satisfy these factors. In fact, the published national standards require a minimum thickness of 0.3 m [4]. Adding a margin of 20%, a buffer of 0.36 m would be optimal. This is similar to the buffer thickness of 0.35 m required in the design requirements set in Sweden and Finland [18].
The buffer thickness below and above the disposal container, according to the requirements, should be at least 0.5 m. The thickness above the disposal container should be greater than 2 m, considering the EDZ of the disposal tunnel excavated using the normal blasting method. However, if the smooth blasting or TBM methods are applied for the excavation of the disposal tunnel, the buffer thickness above the disposal container can be between 1 m and 1.5 m.
4. A Proposal of a Double Layered Buffer Installation for Thermally Effective Disposal
As previously explained, when placing a disposal container in a deposition hole, 0.36 m was considered the optimal thickness of the bentonite buffer around the container. In this study, a more efficient buffer installation method for thermal management was proposed. In other words, because the minimum thickness required to prevent leakage of radionuclides was 0.25 m, pure bentonite (thermal conductivity of 0.8 W·mK−1) was used for this first layer. An additional layer, 0.11 m thick, should be made of improved bentonite, with a thermal conductivity of 2.0 W·mK−1 [19].
In Fig. 5 was shown the temperature history over time for the three cases.
-
Case 1) Existing pure bentonite buffer material, thickness of 0.36 m;
-
Case 2) Two-layer buffer, consisting of 0.25 m of standard bentonite and 0.11 m of improved bentonite (improved thermal conductivity) installed on the side of the disposal container,
-
Case 3) Two-layer buffer (same as in Case 2) installed on the side of the host rock wall.
As shown in Table 4 and Fig. 5, when the buffer material with improved thermal conductivity was installed on the disposal container side (Case 2), the maximum temperature was 89℃, which was lower than the maximum temperature in the existing system (Case 1, 96.2℃). Therefore, this buffer installation method (Case 2) was the most effective in terms of thermal management.
Table 4
Double layered buffer installations and maximum temperature
| Description (installation) | Max. Temp | |
|---|---|---|
|
|
||
| Case 1 | Pure bentonite 0.36 m | 96.2℃ |
|
|
||
| Case 2 | Pure bentonite 0.25 m: rock wall side | 89℃ |
| Improved bentonite 0.11 m: container side | ||
|
|
||
| Case 3 | Pure bentonite 0.25 m: container side | 91.7℃ |
| Improved bentonite 0.11 m: rock wall side | ||
5. Conclusions
In deep geological disposal of radioactive waste, a multi-barrier is utilized, consisting of an engineered barrier and the natural barrier of the host rock system. The key components of the engineered barrier are the disposal container and buffer material. The disposal container loaded with spent nuclear fuel is placed in a disposal hole drilled vertically at the bottom of a disposal tunnel excavated at an appropriate depth underground, and the space between the disposal container and the rock wall of the disposal hole is filled with bentonite buffer material. The thickness of the bentonite buffer material is determined by criteria for radiological safety as well as the thermal stability of the disposal system and the size of the disposal hole.
In this study, we carried out quantitative analyses to determine the optimal thickness of bentonite material to ensure reasonable disposal safety. A number of factors were considered, including the published design standards, radionuclide release rate, shear displacement, thermal conductivity, and corrosion lifetime of disposal container.
Based on the results of these analyses, the optimal range of the thickness of the buffer material was determined. It was found that 0.36 m is the appropriate thickness of the bentonite buffer surrounding the disposal container and that the thickness of the buffer above the disposal container should be determined based on the EDZ depth and excavation method. In terms of improving thermal management of the disposal system, double layers of bentonite buffer, consisting of 0.25 m of standard bentonite (thermal conductivity 0.8 W·mK−1) and 0.11 m of improved bentonite (thermal conductivity 2.0 W·mK−1) was the best choice.
The results of this study can be used as a reference when designing and implementing deep geological disposal systems to contain high-level radioactive waste, including spent nuclear fuels. The results give some flexibility in disposal system design, depending on the site parameters. In the future, to confirm the validity of these results and their applicability in Korea, further analysis, using data obtained from actual disposal sites, is required. In addition, analysis on the gaps between the disposal container and the bentonite blocks to emplace the disposal container, and between the blocks and the deposition hole wall to install the bentonite blocks is also required.
