Coupling of Origen2.1 and Top-Mc for the Simulation and Experimental Validation of Spent Nuclear Fuel Cask Shields
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MohammadAminKiani1✉Emailma.kiany.ch@gmail.comMohammadOutokesh1
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SeyedJavadAhmadi2MahdiRezaeian2
BehzadKhosrowpour2
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Department of Energy EngineeringSharif University of TechnologyTehranIran2
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Nuclear Fuel Cycle Research SchoolNuclear Science and Technology Research InstituteTehranIranMohammad Amin Kiani a,*, Mohammad Outokesh a, Seyed Javad Ahmadi b, Mahdi Rezaeian b, Behzad Khosrowpour b
a Department of Energy Engineering, Sharif University of Technology, Tehran, Iran
b Nuclear Fuel Cycle Research School, Nuclear Science and Technology Research Institute, Tehran, Iran
*Corresponding Author: Mohammad Amin Kiani
Email Address of the Corresponding Author: ma.kiany.ch@gmail.com
Abstract
This study presents a combined computational-experimental approach to the design of radiation shields for dual-purpose casks in dry storage systems. The shield performance was simulated using Origen2.1 and Top-Mc software and validated against laboratory experiments and MCNP simulations. Initially, using the ORIGEN2.1 code, the neutron and gamma fluxes resulting from nuclear mechanisms were calculated at different cooling time. The results indicate that Cm-244 element after 5 years from discharge, accounts over 98.2% and 29.9% and 97.6% of the spontaneous fission, (α,n) reaction mechanism and total neutron source, respectively. To evaluate and select the optimal radiation shield, dry storage casks containing 12 spent fuel assemblies were simulated using the Top-Mc software. By incorporating the radioactivity data obtained from ORIGEN2.1 calculations, a suitable composite shield for the transportation and dry storage of spent fuel was developed. The simulations demonstrated that a 10 cm-thick composite shield containing 20% boron carbide reduces the surface dose of the cask to 1.98 mSv/h, complying with the radiation safety requirements of SSR-6 standards. For benchmarking purposes, the designed neutron shield was fabricated and experimentally tested in the Tehran Research Reactor (TRR) against a thermal neutron spectrum. The shield achieved 99.69% thermal neutron absorption at a thickness of 0.99 cm. Furthermore, SEM imaging and elemental mapping analysis of the fabricated nanocomposite confirmed the uniform dispersion of filler particles within the polymer matrix. Experimental results were also simulated using MCNP code, revealing a maximum deviation of less than 7% between simulated and actual test conditions.
Keywords:
Dual-purpose cask
Polymer
Spent nuclear fuel
Radiation shielding
Neutron
Gamma
Neutron shield
Composite
1. Introduction
The global emphasis on sustainable development has elevated Health, Safety, and Environmental (HSE) considerations to paramount importance across industrial sectors. In the nuclear industry, ensuring comprehensive protection for personnel, infrastructure, and public represents an absolute operational imperative. This commitment to HSE is especially vital in the handling and storage of nuclear materials, where the potential for radiation exposure necessitates stringent safety measures. The safe and secure handling of spent nuclear fuel (SNF), in particular, presents a principal challenge that demands innovative and highly effective solutions for radiation shielding to mitigate risks and ensure the well-being of all stakeholders.1–3 The safe management of SNF from nuclear power plants necessitates advanced shielding solutions to effectively attenuate high-energy neutron and gamma radiations4. As outlined in IAEA technical documents, contemporary approaches for interim SNF storage increasingly employ dual-purpose casks (DPCs) that integrate storage and transport functionalities. Within these containment systems, neutron shielding constitutes a fundamental safety element due to the particularly hazardous nature of neutron radiation - characterized by both penetration capability and radiobiological impact.5 Effective neutron shielding materials function through a two-stage mechanism: initially moderating fast neutrons to thermal energies, followed by efficient absorption of the thermalized neutrons.6,7 Polymer-based composite materials gained significant attention as particularly effective neutron shielding solutions, primarily due to their substantial hydrogen content. This hydrogen-rich composition facilitates superior neutron moderation through elastic scattering processes, which effectively convert fast neutrons to thermal energy ranges.8 Beyond their fundamental neutron attenuation capabilities, polymeric materials offer several distinct advantages: their inherently low density reduces overall shielding weight, while their chemical stability ensures long-term performance reliability. These combined characteristics make polymer composites exceptionally suitable for critical applications across aerospace9,10, medical technology11, and nuclear engineering sectors12, where material weight and durability are paramount considerations.
Recent investigations have identified several high-performance polymer matrices for shielding applications, including high-density polyethylene (HDPE)13–18, polypropylene19–21, polyimide 22–24, polyurethane 25, Polyester 26–28 and epoxy resins 29,30. These materials demonstrate an optimal combination of mechanical integrity and hydrogen concentration, making them particularly attractive for advanced radiation shielding composites.8 To enhance the thermal neutron absorption capacity of these polymer matrices, various filler materials with high macroscopic neutron absorption cross-sections are incorporated 31. The most commonly studied neutron-absorbing elements include boron26, lithium32, cadmium 33–35, gadolinium 36,and rare earth elements 13,37,38. Boron-based fillers have emerged as particularly effective due to their exceptional thermal neutron capture capability through the ¹⁰B(n,α)⁷Li nuclear reaction. A wide range of studies have investigated the use of boron compounds, such as boron carbide (B4C) and boron nitride (BN), demonstrating a significant improvement in shielding performance 39–41. Gadolinium and cadmium, with their extremely high thermal neutron absorption cross-sections, have been incorporated into various polymer matrices to create highly effective shields, particularly for applications requiring thin, yet potent, absorbers. 31,42
The development and optimization of radiation shielding systems represent a sophisticated engineering challenge that necessitates an integrated approach combining computational simulations with empirical validation.
Monte Carlo simulation codes, such as MCNP 43, Top-Mc44 and FLUKA 45, have been extensively used to model neutron and gamma transport through various materials and predict shielding effectiveness. These simulation tools allow for the rapid and cost-effective evaluation of different material compositions and geometric configurations without the need for extensive physical testing.
However, a critical gap exists in the literature about neutron shielding materials of DPCs, where studies tend to focus on either computational modeling or empirical testing in isolation.46–48 The complex and dynamic nature of SNF requires a more integrated and comprehensive approach. The isotopic composition of SNF changes over time due to decay and transmutation, which significantly affects the emitted neutron and gamma spectra.
This research addresses this gap by introducing an innovative dual-methodology approach that combines computational modeling with experimental validation.
The research framework establishes a direct coupling between ORIGEN2.1 49 and Top-Mc simulation codes, creating an integrated computational platform for precise evaluation of radiation shielding performance of polymer composites.
The methodology begins with a detailed source term calculation using ORIGEN2.1 to model the time-dependent isotopic inventory of SNF. The resulting source term is then used as a precise input for the Top-Mc code to simulate neutron attenuation through the designed polymer composite shield. Furthermore, to provide empirical validation, the novel polymer composite was fabricated and experimentally tested at the Tehran research reactor 50. The experimental results were then rigorously compared with the values obtained from the simulation. This integrated research methodology - combining advanced coupled simulations (ORIGEN2.1/ Top-Mc) with empirical validation - represents a substantive advancement in radiation shielding design. The demonstrated concordance between theoretical and experimental results not only validates our modeling approach but also establishes a robust framework for developing next-generation shielding materials.
2.Methodology
The design of a DPC requires comprehensive thermal and structural analyses (e.g., impact resistance from accidental drops and fire scenarios), alongside the evaluation of shielding materials to attenuate neutron and gamma radiation. Radiation shielding analysis is performed to ensure compliance with safety standards (IAEA SSR-6) and for personnel and environmental protection.
To optimize material selection and address experimental constraints (e.g., material availability, cost, and time), computational modeling is prioritized. Simulations enable the assessment of filler materials, layer sequencing, and optimal thicknesses for target shielding efficiency before fabrication.
Using the ORIGEN2.1 nuclear code, spent fuel assemblies are simulated to calculate neutron/gamma fluxes and radioactivity levels for a burnup period and varying cooling times. These results define the neutron and photon sources for shielding design.
Using the Top-Mc software, the results obtained from ORIGEN2.1 were simulated to evaluate the neutron shielding performance of the DPC. Based on simulations, a polymeric nanocomposite shield with boron carbide (B₄C) is optimized, fabricated via direct mixing (followed by degassing and sonication), and tested against a thermal neutron beam at the TRR. For benchmarking, the experimental setup is replicated in MCNP simulations, and results are cross-validated with empirical data.
3. Source Term Simulation and Computational Analysis
3.1. Origen 2.1 Software and Computational Methodology
ORIGEN 2.1 is a specialized software for nuclear fuel cycle calculations, developed by the Oak Ridge National Laboratory (ORNL) during the 1970s and 1980s. This code is recognized as a powerful tool for nuclear reactor analysis and radioactive waste management. Among its key capabilities are the accurate data of isotope half-lives, neutron absorption cross-sections, and fission yields, enabled by its extensive nuclear data library.49
The code can predict the composition of radioactive materials in nuclear waste, including fission products, actinides, and activated materials. A prominent feature of ORIGEN 2.1 is its ability to simulate the nuclear fuel cycle, which allows for precise determination of the radiological characteristics of nuclear fuels over extended time periods.
In practical applications, this code plays a critical role in reactor safety assessments, radioactive waste management, and radiation shielding system design. Other significant features include isotopic composition analysis of SNF and radiation source term calculations at various stages of the fuel cycle. These capabilities have established ORIGEN 2.1 as a standard tool in numerous studies related to nuclear technology.
ORIGEN 2.1 solves a coupled system of linear differential equations describing the time-dependent evolution of nuclide concentrations. The general form of the equations is given in a matrix representation:
where:
N(t)
Vector of nuclide concentrations (atoms per cm³)
A: Transition matrix containing decay constants and reaction cross-sections (units: per second)
S(t)
Source/sink terms for generation/disappearing (atoms per cm³ per second)
For decay-only systems, the equation simplifies to:
where:
Ni(t)
Concentration of nuclide i (atoms per cm³)
λi: Decay constant of nuclide i (units: per second)
b(j→i)
Branching ratio for decay of parent nuclide j to daughter nuclide i (dimensionless)
λj·Nj(t)
Decay rate of parent nuclide j (atoms per cm³ per second)
3.2. Technical specification
This section presents the specifications of DPCs designed for the storage and transport of spent fuel assemblies, along with their contents and computational assumptions. The DPC system in this study, is a specialized containment device with a total weight of 115 metric tons (excluding the weight of spent fuel assemblies), an external height of 5,860 mm, and an outer diameter of 2,295 mm, engineered for safe loading, transportation, and long-term storage of SNF assemblies. The general technical parameters of these loaded DPCs are summarized in Table 1.
No. | Parameter(Unit) | Value |
|---|---|---|
1 | Capacity (number of spent fuel assemblies) | 12 |
2 | External cask height (with lid) (mm) | 5,860 |
3 | Internal cask height (without lid) (mm) | 4,890 |
4 | Outer diameter(mm) | 2,295 |
5 | Inner diameter(mm) | 1,490 |
6 | Unloaded cask weight(kg) | 115,000 |
7 | Loaded cask weight (without impact absorber) (kg) | 124,000 |
8 | Loaded cask weight (with shock absorber) (kg) | 133,400 |
9 | Permissible dose rate on cask surfaces(mSv/h) | 2 |
In accordance with Paragraphs 527 and 573 of IAEA Safety Standard SSR-6, the regulatory dose limits on the cask surface must not exceed 2 mSv/h. The elemental composition of the cask body material for these DPCs is provided in the Table 2.
No. | Element | Atomic Number(Z) | Element Wt% |
|---|---|---|---|
1 | C | 6 | 0.2 |
2 | Si | 14 | 0.25 |
3 | P | 15 | 0.035 |
4 | S | 16 | 0.04 |
5 | Cu | 29 | 0.4 |
6 | Cr | 24 | 0.25 |
7 | Mn | 25 | 0.9 |
8 | Fe | 26 | 94.305 |
9 | Ni | 28 | 3.5 |
10 | Mo | 42 | 0.07 |
11 | V | 23 | 0.03 |
12 | Nb | 41 | 0.02 |
Total | 1 | ||
3.3. Nuclear Fuel Assemblies
The reactor core of the WWER-1000 (V-446) reactors contains 163 fuel assemblies (FAs) of the UTVS type. Each FA consists of 311 fuel rods, 15 spacer grids, 18 guide tubes, one channel for the in-core instrumentation (ICID), and a lower protective grid. The fuel rod itself comprises an upper end cap, a lower end cap, a cladding tube, fuel pellets, and a spring. The fuel rod is a tube with an outer diameter of 9.1 × 10⁻³ m, filled with grooved UO₂ pellets. The fuel rod cladding is made of a zirconium alloy (Zr + 1% Nb). To prevent cladding collapse, the internal volume of the fuel rod is pressurized with helium gas at 2 ± 0.25 MPa. Additionally, a plenum is incorporated at the top of the fuel rod to accommodate fission gases released during operation.
The key geometric and operational specifications of the FAs are summarized in the Table 3.
No. | Properties, Unit | Value |
|---|---|---|
1 | Material of fuel pellet | Uranium oxide (UO2) |
2 | Weight of FA, kg | 705 |
3 | Uranium Oxide in Fuel, Wt% | 87.8 |
4 | Weight of Fuel in FA, kg | 489.8 |
5 | Height of FA, mm | 4570 |
6 | Maximum Power for each FA, MW | 27 |
7 | Height of FA Cap, mm | 436 |
8 | Height of FA Tail Piece, mm | 258 |
9 | Maximum Burn-up for each FA, MWd/KgU | 49 |
10 | Fuel Rods location in FA | According to triangular lattice |
11 | Number of fuel rods per FA, pcs | 311 |
12 | Distance between fuel rods, m | 12.75⋅10− 3 |
13 | Cladding material | E110 |
14 | Cladding outside diameter, m | 9,1*10− 3 |
15 | Cladding inside diameter, m | 7,73*10− 3 |
16 | Fuel column height (in cold state), m | 3,53 |
17 | Initial helium pressure within cladding, MPa | 2,0 |
18 | Fuel pellet density, kg/m3 | (10,4–10,7) *103 |
19 | The number of guide channels, pcs | 18 |
20 | Material of guide tube | Alloy Zr + 1% Nb |
21 | Number of spacing grids in FA, pcs | 15 |
22 | Material of spacing grid | Alloy Zr + 1% Nb |
23 | Weight of spacing grid, kg | 0.55 |
24 | Number of instrumentation tubes, pcs | 1 |
25 | Material of ICID and central tube | Alloy Zr + 1% Nb |
26 | Material of FA Cap and Tail | 12X18H10T |
In the analysis of FAs radioactivity, determining the density of various components within the FAs is essential. Accordingly, the densities of key sections of the FAs are provided in the Table 4.
No. | FA parts | Value(g/Cm3) |
|---|---|---|
1 | Fuel pellet | 10.55 |
2 | Clad, Spacing grid, Guide channel, Central tube, Tube for ICID | 6.55 |
3 | FA Cap, FA Tail, Lower Spacing grid | 7.92 |
The chemical composition of the fuel pellets and fuel rod cladding material in the nuclear FA have been characterized in Table 5 and Table 6, respectively.
No. | Element/Isotope | Weight (%) | No. | Element/Isotope | Weight (%) |
|---|---|---|---|---|---|
1 | Uranium-235 | 87.90 | 13 | Tungsten (W) | 1.00E-02 |
2 | Uranium-236 | 1.00E-01 | 14 | Nitrogen (N) | 7.00E-03 |
3 | Iron (Fe) | 3.00E-02 | 15 | Magnesium (Mg) | 5.00E-03 |
4 | Aluminum (Al) | 2.00E-02 | 16 | Copper (Cu) | 4.00E-03 |
5 | Carbon (C) | 1.00E-02 | 17 | Zinc (Zn) | 3.00E-03 |
6 | Vanadium (V) | 1.00E-02 | 18 | Oxygen (O) | 3.00E-03 |
7 | Phosphorus (P) | 2.00E-02 | 19 | Manganese (Mn) | 2.00E-03 |
8 | Calcium (Ca) | 1.50E-02 | 20 | Fluorine (F) | 1.50E-03 |
9 | Chromium (Cr) | 1.00E-02 | 21 | Chlorine (Cl) | 1.50E-03 |
10 | Molybdenum (Mo) | 1.00E-02 | 22 | Cadmium (Cd) | 6.00E-05 |
11 | Silicon (Si) | 1.00E-02 | 23 | Boron (B) | 4.00E-05 |
12 | Nickel (Ni) | 1.00E-02 | 24 | Gadolinium (Gd) | 1.50E-04 |
Total | 100.00 | ||||
No. | Element/Isotope | Weight (%) | No. | Element/Isotope | Weight (%) |
|---|---|---|---|---|---|
1 | Zirconium (Zr) | 98.50 | 13 | Nitrogen (N) | 6.00E-03 |
2 | Niobium (Nb) | 0.9–1.1 | 14 | Molybdenum (Mo) | 5.00E-03 |
3 | Oxygen (O) | 9.90E-02 | 15 | Copper (Cu) | 5.00E-03 |
4 | Iron (Fe) | 5.00E-02 | 16 | Titanium (Ti) | 5.00E-03 |
5 | Tin (Sn) | 5.00E-02 | 17 | Chlorine (Cl) | 3.00E-03 |
6 | Hafnium (Hf) | 5.00E-02 | 18 | Fluorine (F) | 3.00E-03 |
7 | Calcium (Ca) | 3.00E-02 | 19 | Manganese (Mn) | 2.00E-03 |
8 | Nickel (Ni) | 2.00E-02 | 20 | Hydrogen (H) | 1.50E-03 |
9 | Silicon (Si) | 2.00E-02 | 21 | Boron (B) | 5.00E-05 |
10 | Chromium (Cr) | 2.00E-02 | 22 | Cadmium (Cd) | 3.00E-05 |
11 | Carbon (C) | 2.00E-02 | 23 | Lithium (Li) | 2.00E-04 |
12 | Aluminum (Al) | 8.00E-03 | 24 | Potassium (K) | 4.00E-03 |
Total | 100.00 | ||||
3.4. Input Parameters for Source Term Calculations
To ensure conservative radioactivity calculations despite no FAs reaching maximum burnup, a peak burnup value of 49 MWd/KgU was universally applied in ORIGEN simulations. Key methodological assumptions include are summarized in Table 7.
No. | Parameter(Unit) | Value |
|---|---|---|
1 | Maximum initial enrichment (Wt.% ²³⁵U) | 4.1 |
2 | Number of cycles | 4 |
3 | Cycles Irradiation time (days) | 300 |
4 | Cooling periods between cycles(days) | 90 |
5 | Fuel assembly uranium mass (kg) | 430.5 |
6 | Assembly thermal power (MW) | 43.55 |
The PWRU50 cross-section library in ORIGEN-2 was employed for all computations. Conservative temporal resolution was enforced through 60-day time steps until peak burnup attainment, as finer intervals yield more precautionary results. Material compositions of fuel assembly components (Fuel, clad, spacer, etc.) and the DPC structure (detailed in Tables 2–6) were rigorously incorporated.
Radiological characteristics were evaluated at 1, 3, 5, and 10 years post discharge cooling intervals from the reactor core.
3.5. Source Term Calculation Results
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The results of total activity calculations for SNF assemblies, with the temporal evolution of isotopic group activities during cooling periods (from reactor discharge to 10 years post-discharge) are illustrated in Fig. 1 and quantified in Table 8. The results demonstrate that the total radioactivity of SNF primarily consists of three distinct components: fission products (FPs, 76% at discharge), actinides and their decay daughters (ACT + D, 23.5%), and activation products (APs, < 0.5%).Figure 1. Total activity results for SFAs at different cooling time
Isotope Groups | Discharge | 1 year | 3 year | 5 year | 10 year |
|---|---|---|---|---|---|
AP | 6.44E + 06 | 3.61E + 05 | 1.89E + 05 | 1.40E + 05 | 8.57E + 04 |
ACT + Dughters | 3.69E + 08 | 1.25E + 06 | 1.03E + 06 | 9.43E + 05 | 7.61E + 05 |
FP | 1.20E + 09 | 1.76E + 07 | 6.59E + 06 | 4.05E + 06 | 2.71E + 06 |
AP + ACT + FP | 1.57E + 09 | 1.92E + 07 | 7.81E + 06 | 5.14E + 06 | 3.55E + 06 |
Fission products dominate the initial activity profile due to the abundance of short-lived radionuclides generated during nuclear fission. In contrast, the actinide contribution originates principally from long-lived transuranic elements, which exhibit lower specific activity but maintain radiological significance over extended timescales. Activation products constitute only a minor fraction of the total activity.
The analysis reveals a characteristic exponential decay pattern in total activity over time. Fission products show a particularly rapid 99.8% reduction within the first decade after discharge, attributable to the decay of short-lived isotopes. Conversely, actinide activity decreases much more gradually, reflecting their substantially longer half-lives. Of particular importance is the persistence of long-lived isotopes such as ²³⁹Pu, which continue to pose a radiological hazard for millennia despite the initial rapid decline in total activity.
3.6. Photon Source Calculation Results
Photon radiation has been identified as the most significant contributor to the total dose rate in DPCs. Therefore, precise characterization of photon sources across various energy ranges is considered essential for optimization of gamma shielding thickness and material composition.
The photon production rates have been calculated for SNF at reactor discharge and during subsequent cooling periods extending to 10 years post-discharge. The results are categorized into 18 distinct energy groups, and presented in Table 9.
As can be observed from the obtained results, after 10 years of cooling following removal of SFAs from the reactor core, the photon spectrum is dominated by specific energy groups corresponding to rows number 1 and number 9 in the aforementioned table.
No. | Gamma Energy Group(Mev) | Total Photon(#/Sec) | |||||||
|---|---|---|---|---|---|---|---|---|---|
Discharge | 1 | 3 | 5 | 7 | 8 | 9 | 10 | ||
1 | 1.00E-02 | 2.41E + 19 | 1.98E + 17 | 5.77E + 16 | 2.79E + 16 | 2.02E + 16 | 1.87E + 16 | 1.76E + 16 | 1.69E + 16 |
2 | 2.50E-02 | 4.35E + 18 | 4.68E + 16 | 1.43E + 16 | 6.90E + 15 | 4.77E + 15 | 4.26E + 15 | 3.92E + 15 | 3.66E + 15 |
3 | 3.75E-02 | 3.78E + 18 | 4.49E + 16 | 1.40E + 16 | 7.42E + 15 | 5.62E + 15 | 5.19E + 15 | 4.88E + 15 | 4.63E + 15 |
4 | 5.75E-02 | 3.76E + 18 | 4.11E + 16 | 1.18E + 16 | 5.50E + 15 | 3.96E + 15 | 3.65E + 15 | 3.46E + 15 | 3.32E + 15 |
5 | 8.50E-02 | 6.44E + 18 | 2.89E + 16 | 8.12E + 15 | 3.68E + 15 | 2.54E + 15 | 2.30E + 15 | 2.14E + 15 | 2.02E + 15 |
6 | 1.25E-01 | 5.74E + 18 | 3.28E + 16 | 8.82E + 15 | 3.99E + 15 | 2.78E + 15 | 2.50E + 15 | 2.31E + 15 | 2.15E + 15 |
7 | 2.25E-01 | 7.63E + 18 | 2.55E + 16 | 7.05E + 15 | 3.07E + 15 | 2.07E + 15 | 1.87E + 15 | 1.74E + 15 | 1.65E + 15 |
8 | 3.75E-01 | 4.40E + 18 | 1.45E + 16 | 4.43E + 15 | 1.98E + 15 | 1.23E + 15 | 1.05E + 15 | 9.29E + 14 | 8.38E + 14 |
9 | 5.75E-01 | 6.86E + 18 | 1.47E + 17 | 7.95E + 16 | 5.28E + 16 | 4.03E + 16 | 3.66E + 16 | 3.37E + 16 | 3.16E + 16 |
10 | 8.50E-01 | 7.04E + 18 | 7.75E + 16 | 2.80E + 16 | 1.47E + 16 | 8.03E + 15 | 6.03E + 15 | 4.59E + 15 | 3.54E + 15 |
11 | 1.25E + 00 | 3.81E + 18 | 9.46E + 15 | 4.62E + 15 | 2.86E + 15 | 2.03E + 15 | 1.76E + 15 | 1.55E + 15 | 1.38E + 15 |
12 | 1.75E + 00 | 1.44E + 18 | 7.51E + 14 | 2.11E + 14 | 8.86E + 13 | 5.50E + 13 | 4.74E + 13 | 4.22E + 13 | 3.82E + 13 |
13 | 2.25E + 00 | 7.01E + 17 | 1.01E + 15 | 1.81E + 14 | 3.35E + 13 | 6.40E + 12 | 2.83E + 12 | 1.27E + 12 | 5.74E + 11 |
14 | 2.75E + 00 | 2.95E + 17 | 2.11E + 13 | 5.26E + 12 | 1.32E + 12 | 3.37E + 11 | 1.73E + 11 | 9.04E + 10 | 4.91E + 10 |
15 | 3.50E + 00 | 1.38E + 17 | 2.65E + 12 | 6.71E + 11 | 1.70E + 11 | 4.37E + 10 | 2.24E + 10 | 1.17E + 10 | 6.27E + 09 |
16 | 5.00E + 00 | 5.47E + 16 | 5.38E + 08 | 4.64E + 08 | 4.29E + 08 | 3.97E + 08 | 3.82E + 08 | 3.68E + 08 | 3.55E + 08 |
17 | 7.00E + 00 | 9.09E + 14 | 6.21E + 07 | 5.35E + 07 | 4.94E + 07 | 4.58E + 07 | 4.41E + 07 | 4.25E + 07 | 4.09E + 07 |
18 | 9.50E + 00 | 5.62E + 11 | 7.14E + 06 | 6.15E + 06 | 5.68E + 06 | 5.26E + 06 | 5.07E + 06 | 4.88E + 06 | 4.70E + 06 |
TOTAL | 8.05E + 19 | 6.67E + 17 | 2.39E + 17 | 1.31E + 17 | 9.36E + 16 | 8.39E + 16 | 7.69E + 16 | 7.17E + 16 | |
Isotope Groups | Cooling Time (Year) | |||||||
|---|---|---|---|---|---|---|---|---|
Discharge | 1 | 3 | 5 | 7 | 8 | 9 | 10 | |
FP | 5.93638E + 19 | 6.59E + 17 | 2.35E + 17 | 1.29E + 17 | 9.19E + 16 | 8.23E + 16 | 7.54E + 16 | 7.03E + 16 |
ACT | 2.08772E + 19 | 1.67E + 15 | 9.66E + 14 | 9.57E + 14 | 9.77E + 14 | 9.86E + 14 | 9.94E + 14 | 1E + 15 |
AP | 2.69312E + 17 | 6.17E + 15 | 2.35E + 15 | 1.33E + 15 | 8.05E + 14 | 6.31E + 14 | 4.95E + 14 | 3.9E + 14 |
Total | 8.05103E + 19 | 6.67E + 17 | 2.39E + 17 | 1.31E + 17 | 9.36E + 16 | 8.39E + 16 | 7.69E + 16 | 7.17E + 16 |
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Figure 2. Results of total gamma production rates of SFAs at different cooling timeThe results show that fission products (FP) are the dominant source of gamma radiation, with a contribution of 73.8% at discharge and increasing to 98% after 10 years of cooling. In contrast, energy spectrum analysis reveals that at the time of fuel discharge from the reactor core, approximately 29.9% of the total gamma production rate for spent fuel assemblies belongs to low-energy gamma flux in the 0.01 MeV range. Over time, the contribution of 0.575 MeV gamma rays increases from an initial 8% at fuel discharge to 44% of the total after 10 years of cooling.
3.7. Neutron Source Calculation Results
This section presents the results of calculations regarding neutron source generation in SNFs. The neutron source strengths were determined for spent fuel with an initial enrichment of 4.1% and a burn-up of 49 MWd/KgU, considering various cooling times ranging from zero to 10 years in the spent fuel pool.
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The computational results for neutron production in spent fuel indicate two primary neutron sources: spontaneous fission (SF) and (α,n) reactions. Results of neutron source calculation from spontaneous fission have been presented in Table.11 and Fig. 3.Among the isotopes contributing to neutron emission, Cm-244(half-life: 18.1 years) dominates spontaneous fission, accounting for approximately 74% of the total neutron yield at discharge. Due to its relatively long half-life, its contribution decreases only slightly over time, remaining at approximately 68% after 10 years. In contrast, Cm-242 (half-life: 162.8 days) decays rapidly, diminishing to < 0.1% of the total neutron production within a decade.
Element List | Spontaneous fission neutron source (neutrons/sec) | |||||||
|---|---|---|---|---|---|---|---|---|
Cooling Time (Year) | ||||||||
Dischrge | 1 | 3 | 5 | 7 | 8 | 9 | 10 | |
PU240 | 1.40E + 07 | 1.40E + 07 | 1.41E + 07 | 1.41E + 07 | 1.42E + 07 | 1.42E + 07 | 1.42E + 07 | 1.43E + 07 |
PU242 | 1.04E + 07 | 1.04E + 07 | 1.04E + 07 | 1.04E + 07 | 1.04E + 07 | 1.04E + 07 | 1.04E + 07 | 1.04E + 07 |
CM242 | 3.89E + 09 | 8.28E + 08 | 3.75E + 07 | 2.00E + 06 | 4.02E + 05 | 3.41E + 05 | 3.27E + 05 | 3.23E + 05 |
CM244 | 1.16E + 10 | 1.12E + 10 | 1.04E + 10 | 9.60E + 09 | 8.90E + 09 | 8.56E + 09 | 8.24E + 09 | 7.93E + 09 |
CM246 | 1.11E + 08 | 1.10E + 08 | 1.10E + 08 | 1.10E + 08 | 1.10E + 08 | 1.10E + 08 | 1.10E + 08 | 1.10E + 08 |
CF252 | 6.85E + 07 | 5.26E + 07 | 3.11E + 07 | 1.84E + 07 | 1.09E + 07 | 8.36E + 06 | 6.43E + 06 | 4.95E + 06 |
TOTALS | 1.57E + 10 | 1.22E + 10 | 1.06E + 10 | 9.77E + 09 | 9.05E + 09 | 8.72E + 09 | 8.39E + 09 | 8.08E + 09 |
Figure 3. Results of Spontaneous fission for SFAs at different cooling time
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Regarding the (α,n) reaction mechanism, as detailed in Table.12 and Fig. 4., Cm-244 again shows a predominant role in neutron production. Furthermore, Americium-241 plays a key role in this mechanism. As Am-241 is produced from the decay of Plutonium-241, which has a half-life of 14.4 years, its neutron production rate through (α,n) reactions increases during the initial years of cooling. While the contribution of Am-241 to neutron production from this mechanism is negligible at the time of discharge, it rises to approximately 10.5% of the total (α,n) neutrons after 10 years.Element List | (Alpha, N) neutron source (neutrons/sec) | |||||||
|---|---|---|---|---|---|---|---|---|
Cooling Time(Year) | ||||||||
Dischrge | 1 | 3 | 5 | 7 | 8 | 9 | 10 | |
PU238 | 42871214 | 45198744 | 45069437 | 44393513 | 43699956 | 43353178 | 43012277 | 42677254 |
PU239 | 1353611 | 1387114 | 1387114 | 1387114 | 1386526 | 1386526 | 1386526 | 1386526 |
PU240 | 2652561 | 2658438 | 2670781 | 2681949 | 2691941 | 2696643 | 2701345 | 2706047 |
AM241 | 926309.8 | 2472119 | 5342738 | 7940638 | 10285800 | 11379034 | 12413491 | 13395050 |
AM243 | 319212.5 | 319623.9 | 319565.1 | 319506.3 | 319447.6 | 319388.8 | 319388.8 | 319330 |
CM242 | 8.01E + 08 | 1.71E + 08 | 7734922 | 412548.7 | 82815.38 | 70354.87 | 67474.85 | 66593.21 |
CM243 | 592462.1 | 578473.4 | 551025 | 524869.7 | 499948.7 | 487899.6 | 476203.2 | 464741.8 |
CM244 | 96568968 | 92983632 | 86106840 | 79759032 | 73881432 | 71118960 | 68474040 | 65887896 |
TOTALS | 9.46E + 08 | 3.16E + 08 | 1.49E + 08 | 1.37E + 08 | 1.33E + 08 | 1.31E + 08 | 1.29E + 08 | 1.27E + 08 |
Figure 4. Results of (α,n) reaction mechanism for SFAs at different cooling time
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Nevertheless, as shown in Fig. 5, spontaneous fission remains the dominant neutron production source across the entire 10-year cooling period. This is attributed to the fact that heavy isotopes such as Cm-244, even after significant decay, maintain higher neutron production rates via spontaneous fission compared to the (α,n) mechanism.Figure 5. Results of Total neutron sources of SFAs at different cooling time
4. Shielding Calculations
4.1. Assumptions and Methodology
Prior to commencing the fabrication of the radiation shield, the simulation procedures and necessary calculations for selecting the optimal shield were carried out using the Validated software, as detailed below.
This study employs Top-Mc simulations to evaluate neutron shielding effectiveness, conducted under authorized licenses. The calculations model a cask containing 12 SFAs with 4.1% enrichment.
Top-Mc is a Monte Carlo algorithm based (Same as MCNP Code) developed by the FDS team affiliated with the University of Science and Technology of China (USTC).
The latest version of this software, Top-Mc, offers full nuclear reactor design capabilities as well as computational functions such as fuel burn-up analysis, neutron and gamma flux calculations, various neutron transport and shielding analyses, and core activation due to radiation exposure. It also provides dosimetric evaluations using ICRP and NCRU libraries, among other advanced features.
The visualization module of the software supports the display of computational results in both 2D and 3D formats, including contour plots that provide detailed insights into simulation outcomes.
In general, Top-Mc is a multifunctional computational tool designed for large-scale nuclear safety design and evaluation.
Top-Mc supports various particle transport phenomena. For neutrons, it covers elastic and inelastic scattering, as well as multiple nuclear reactions within the energy range of 10⁻¹¹ MeV to 150 MeV. For photons, it simulates Compton and coherent scattering, fluorescence emission after photoelectric absorption, electron-positron pair production, and photonuclear reactions across an energy spectrum ranging from 1 MeV to 100 GeV.
This software has been used in over 70 countries and more than 40 major projects. It has been designated as the reference code by ITER and passed the Generic Design Assessment (GDA) with the HPR1000 in the UK. It is also widely employed by the OECD/NEA database and RIST-NUCIS in Japan.
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The structural diagram of the Top-Mc software is illustrated in Fig. 6.Figure 6. Functional architecture of Top-MC
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The input geometry in software includes the fuel support structure, spent fuel assemblies, cask body, and neutron shielding components, with upper and lower neutron shields of 5 cm and 10 cm thickness, respectively (see Fig. 7). The main steel body thickness for this 12-assembly configuration is 29.5 cm. Due to dimensional constraints, the maximum allowable thickness for lateral neutron shielding - including a 5 mm stainless steel shell for structural integrity and secondary gamma shielding - is 40 cm, resulting in a maximum lateral neutron shield thickness of 10 cm. To determine the optimal lateral shielding thickness, which critically influences total dose reduction, shielding calculations were performed using four 2.5 cm incremental segments.In this study, spent fuel is homogeneously modeled inside a stainless-steel cladding. To accurately assess the particle flux inside the cask and calculate the surface dose, the F5 tally was employed to compute neutron absorbed dose, secondary gamma (neutron-induced gamma), and primary gamma radiation radially and symmetrically from the center of the cask, where the neutron and gamma fluxes are at their peak.
For simplification in modeling the code's input geometry, the various components of the spent fuel assembly were treated as a homogenized mixture.
To enhance the accuracy of the computational results, variance reduction techniques such as Russian roulette combined with particle splitting and importance biasing were employed. Specifically, cells in close proximity to the source and within the shield regions were assigned higher importance values (e.g., 1000), while more distant regions were assigned lower importance values (e.g., 1 or 0). Additionally, cutoff cards were applied for low-energy particles, and weight window cards were implemented to further improve simulation efficiency.
The neutron source was defined as a volumetricsource centrally located within the fuel region. Its energy spectrum spans from 2.5×10⁻⁸ MeV to 12 MeV. This spectrum was adjusted according to the results obtained from ORIGEN code simulations. The source parameters include its position, emission direction along the z-axis, and a uniform radial distribution extending up to a radius of 74 cm.
The tallies employed in these calculations include neutron flux tallies (F5 and F4) and dose equivalent tallies (DE/DF). These tallies were calibrated using ICRP conversion factors to output effective dose in units of sieverts per hour. A mesh tally (RMESH) was also used for spatial analysis of the dose distribution around the system.
The virtual detector array comprised ten spherical neutron detectors (0.5 cm radius) positioned laterally along the z-axis (0-586 cm) and at both ends, enabling precise monitoring of axial and radial neutron flux variations. The modeled cask geometry containing spent fuel assemblies is shown in Fig. 7. Correspondingly, the photon detection system incorporated ten cylindrical detectors (with 1 cm-diameter) positioned at 90° angles to the central axis at varying distances from the source, accurately recording radial and axial photon field distributions based on the data of 18 -group gamma sources derived from ORIGEN calculations.
Figure 7. View of the simulated cask geometry using Top-Mc
4.2. Shielding Simulation Results
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According to the simulated geometry of DPC in Fig. 7 and using Top-Mc software, the flux of primary gamma, neutron and secondary gamma radiation emitted from the cask was calculated. The results are presented as contour plots in Fig. 8–10.Figure 8 - Contour plot of primary gamma flux emitted from DPC, LHS: Y-axis, RHS: Z-axis
Figure 9 - Contour plot of neutron flux emitted from DPC LHS: Y-axis, RHS: Z-axis
Figure 10 - Contour plot of secondary gamma flux emitted from DPC, LHS: Y-axis, RHS: Z-axis
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Additionally, the primary and secondary gamma dose as well as the neutron dose—calculated using the F5 tally across radial direction of DPC are illustrated in Figs. 11–13.Figure 11- simulated primary gamma dose of DPC
Figure 12- simulated neutron dose of DPC
Figure 13- simulated secondary gamma dose of DPC
The attenuation of the primary gamma dose, which originates directly from the decay of radionuclides within the spent fuel assemblies is illustrated in Fig. 11. The high dose magnitude at the innermost regions near the fuel is expected due to the intense gamma emission from fission and activation products. The subsequent exponential decrease in dose with increasing radial distance is characteristic of gamma ray attenuation, primarily governed by the photoelectric effect, Compton scattering and pair production interactions within the dense structural materials of the cask body, such as the steel walls, which effectively absorb and scatter these high-energy photons.
The initial high neutron dose (Fig. 12) is moderated and absorbed as neutrons traverse the shielding materials. The composition of the cask and the hydrogenous materials within the shield facilitate neutron moderation through elastic scattering, effectively reducing neutron energy. Subsequently, neutron-absorbing elements, such as boron in the composite shield, capture these thermalized neutrons via the (n, α) reaction. This two-step process of moderation and absorption is responsible for the significant reduction in neutron dose observed across the radial shield thickness.
The secondary gamma dose profile, shown in Fig. 13, is a direct consequence of the neutron interactions within the shielding structure. This radiation is not emitted from the fuel itself but is produced ex situ by neutron capture reactions (e.g., (n, γ)) and inelastic scattering events with nuclei in the cask materials and shielding.
The dose pattern typically shows an initial rise just inside the shield, corresponding to the region of peak neutron capture, followed by a gradual attenuation as the generated gamma rays themselves are absorbed within the outer layers of the shield.
These simulation results demonstrate that the total dose rate on the external surface of the DPC is calculated to be 1.98 mSv/h. This value represents full compliance with the stringent regulatory limits established by the IAEA, specifically adhering to the requirements outlined in Paragraphs 527 and 573 of the SSR-6 regulations.
4.3. Specifications of the Fabricated Neutron Shield
To evaluate and benchmark the experimental results against simulations, a multifunctional nanocomposite sample was fabricated and tested at the Tehran Research Reactor (TRR) for its thermal neutron attenuation capability. The developed material is a polymer nanocomposite (PNC) with an epoxy matrix and boron carbide (B₄C) as the thermal neutron absorber. The PNC was synthesized via direct mixing, followed by ultrasonic dispersion and degassing processes.
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As illustrated in the SEM images (Fig. 14) the particle size of the boron carbide used in this composite ranges between 5–20 µm. Additionally, montmorillonite and graphite particles were incorporated to enhance and optimize the mechanical and thermal properties of the nanocomposite, respectively.Figure 14. SEM images of the a) B4C, b) PNC nanocomposites
The resin-to-hardener ratio in the composite was set at 100:30. According to the EDX analysis, the material composition of this polymer-based shield, which contains 20 wt% boron carbide, is detailed in Table 13.
No. | Element | Wt.% |
|---|---|---|
1 | C | 67.98 |
2 | O | 8.49 |
3 | B | 15.66 |
4 | Si | 1.77 |
5 | H | 6.03 |
6 | Mg | 0.07 |
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The elemental mapping results (Fig. 15) demonstrate a relatively uniform distribution of boron carbide (B₄C) particles within the polymer matrix. This homogeneous dispersion suggests a strong correlation between the experimental data and simulation results, supporting the validity of the computational model.A
Figure 15. elemental maps of the PNC specimen4.4. TRR test results of PNC and Validation
Upon completion of the simulation phase for shield fabrication and the required testing (both simulation-based and experimental), the following steps were undertaken.
The neutron attenuation performance of synthesized PNCs was investigated using the monochromatic beam Tube (D-channel) of the TRR. The experimental configuration employed a Highly Oriented Pyrolytic Graphite (HOPG) crystal monochromator to produce a collimated thermal neutron beam (λ = 1.18 Å, flux ~ 10⁵ n·cm⁻²·s⁻¹) with minimal fast neutron and gamma contamination (< 3% total flux). Neutron transmission measurements were conducted using a ³He proportional counter system, achieving < 1% measurement uncertainty across sample thicknesses. Data analysis was performed using ORIGIN software.
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As the generated geometry in Fig. 16 illustrates, validation studies employing Monte Carlo simulations via the MCNP code successfully and accurately replicated the experimental setup implemented at the TRR. Table 14 summarizes the results obtained from the empirical tests and the corresponding MCNP simulations.Figure 16. Geometric output of MCNP Code for neutron shielding Set-up test in TRR
The shielding evaluation revealed exceptional performance, with the PNC demonstrating 99.69% thermal neutron absorption at 0.99 cm thickness - a significant improvement over conventional gadolinium oxide-based shield. These results highlight the PNC as a lightweight, high-performance shielding material with minimal secondary radiation production.
No. | Thickness (cm) | Experiment (ΔI/I0 *100) | MCNP (ΔI/I0 *100) | Deviation(%) |
|---|---|---|---|---|
1 | 0.33 | 94.56 | 88.23476 | 6.69 |
2 | 0.66 | 99.25 | 95.64561 | 3.63 |
3 | 0.99 | 99.69 | 95.89014 | 3.81 |
4 | 1.32 | 99.70 | 96.04272 | 3.67 |
5 | 1.65 | 99.71 | 96.14637 | 3.57 |
Comparative analysis showed excellent agreement (< 7% deviation) between simulated and experimental attenuation data, validates the material's uniform microstructure and the accuracy of the characterization methodology. This combined experimental-computational approach provides a robust framework for developing advanced radiation shielding materials with optimized performance characteristics.51,52
5. Conclusion
This research focused on the design, development, and evaluation of an innovative polymer-based composite for radiation shielding in DPCs for spent nuclear fuel. The integrated approach adopted in this study, which combined advanced computational modeling with empirical validation, provides a robust and reliable framework for optimizing radiation shielding systems. Source term calculations using the ORIGEN2.1 code revealed that after 5 years from discharge, the Curium-244 (Cm-244) isotope is the dominant neutron source, contributing over 97.6% of the total neutron emitted from spontaneous fission and (α,n) reaction mechanisms. Radiation transport simulations using the Top-Mc code, directly coupled with ORIGEN2.1 output data, evaluated the effectiveness of a composite shield containing 20% boron carbide (B₄C) at a 10 cm thickness. The results demonstrated that this design successfully reduces the cask surface dose rate to 1.98 mSv/h, clearly complying with the 2 mSv/h limit stipulated by the IAEA SSR-6 safety standard and confirming its suitability for both transport and dry storage.
To validate the simulation results, a sample of the polymer nanocomposite was fabricated and tested under a thermal neutron beam at the TRR. SEM images and elemental mapping analysis confirmed the uniform dispersion of boron carbide particles within the PNC. The shield's remarkable performance in thermal neutron absorption, achieving 94.56% attenuation at a minimal thickness of just 0.33 cm, confirms the high potential of PNC as lightweight and highly efficient neutron shielding materials.
The final comparison between experimental data and MCNP simulation results, which meticulously incorporated the real geometric specifications and EDX data from the fabricated samples, showed a maximum deviation of less than 7%. This strong agreement validates the accuracy of the two-stage simulation methodology (ORIGEN2.1/ Top-Mc) and the homogeneous microstructure of the fabricated composite material.
Electronic Supplementary Material
Below is the link to the electronic supplementary material
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Funding
Declaration
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
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Data Availability
The corresponding author holds the experimental datasets, which can be provided upon reasonable request.
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Author Contribution
M.A.K. conducted the simulations and experiments, and drafted the manuscript. B.K. and M.R. contributed to and reviewed the simulations. M.O., S.J.A., and M.R. supervised the study and reviewed the manuscript. All authors discussed the results and approved the final version.
