Introduction

Nuclear energy provides almost 10% of electricity production in the world1. The use of nuclear energy reduces environmental pollution that can be caused by the use of fossil energy but can lead to another issue, i.e., the management of spent nuclear fuels (SNFs). The latter is becoming a major concern because the minor actinides (MAs: 237Np, 241Am, 243Am, 244Cm and 245Cm) and the long-lived fission products (LLFPs: 79Se, 93Zr, 99Tc, 107Pd, 129I and 135Cs) will leave behind in the wastes after extraction of U and Pu by PUREX process2,3,4. These LLFPs are considered important in terms of the radiation safety performance of the disposal sites (future exposure dose to the public)5.

In addition, MAs are the major toxicity source of the SNFs6. It was shown that the potential toxicity can be reduced to 1/100 after 1000 years if effective recovery and transmutation of the MAs can be achieved7. Consequently, worldwide researchers are taking action on exploring novel approaches to manage the SNFs.

There have been many studies on the transmutation of MAs and LLFPs in pressurized water reactors8, fast reactors9,10,11,12,13, accelerator-driven sub-critical systems (ADS)14,15 and other systems16,17. Particularly, the lead-cooled fast reactor (LFR) produces a fast neutron spectrum which is suitable for transmuting both the LLFPs and MAs. Moreover, LFR has a unique safety advantage over other fast reactors and a lot of attention has been paid to the R&D of LFR18.

The feasibility of using reactors or other systems to transmute MAs and LLFPs depends on sufficient neutron excess per fission19,20,21,22. If an average of approximately 1 wt% MAs is loaded to the LFR core, a transmutation rate of 10% per year or more was foreseen without deterioration of the core characteristics6. For LLFPs, an advanced nuclear energy system driven by an intense photoneutron source has been proposed to transmute efficiently the LLFPs assembly composed of 79Se, 93Zr, 99Tc, 107Pd, 129I, 135Cs and 137Cs23. It is shown that the 79Se, 99Tc, 107Pd, 129I and 137Cs could be transmuted by more than 30% within 20 years and their effective half-lives can decrease drastically from ~ 106 to less than 102 years.

In this study, we propose an LFR core arrangement (see Fig. 1) to transmute simultaneously the MAs and LLFPs. The five MAs nuclides (237Np, 241Am, 243Am, 244Cm and 245Cm) are loaded in the fuel assembly region with mixed fuel pins, and the six LLFPs nuclides (79Se, 93Zr, 99Tc, 107Pd, 129I and 135Cs) are loaded in the LLFPs assembly region. The loaded mass of MAs and the composition of LLFPs are optimized to balance the LFR characteristics against their support ratio (SR). Then the effect of MAs loaded on the reactor operation is further investigated in the context of keff and neutron flux distribution. The relationship between the transmutation efficiency and the reactor operation time is also discussed. The result shows that the proposed scheme could effectively transmute MAs and LLFPs.

Figure 1
figure 1

Schematic diagram of the LFR core.

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Methods

Simulation algorithm

OpenMC code24 is an open-source platform for the Monte Carlo simulation of particle transportation, which is spearheaded by the Computational Reactor Physics Group of the Massachusetts Institute of Technology. It uses the continuous-energy cross-section and a constructive solid geometry representation to realize high-fidelity modeling. In our case, we used the ENDF-VIII cross-section library to model the physical processes that occurred in the operation of typical LFRs. The number of total batches is 1200 with each batch taking 10,000 neutron histories. The initial 200 batches were skipped in order to reduce the error caused by source distribution. In the simulations, the neutron energy spectra and the reaction rates are obtained, and the reaction rate has a statistical error of less than 0.05%.

Core configuration

The layout of the LFR core is shown in Fig. 1. The thermal power of the LFR is designed to be 750 MWt, and the electric power is 300 MWe considering thermal to electric energy conversion of 40%. The LFR core has a height of 1200 mm and a diameter of 3200 mm, which includes 205 Fuel (MAs) assemblies, 114 LLFPs assemblies, 12 control rods, and 138 blanket assemblies. Each fuel assembly consists of 91 pins, which are composed of uranium–plutonium MOX fuel pellets covered by stainless steel cladding. The isotope abundances used for Uranium and Plutonium are listed in Table 125. The LLFPs assembly is comprised of 91 pins, each of which contains one LLFP element; the number of pins containing each LLFP element is balanced to optimize their transmutation. By analogy, each MAs assembly have 91 pins and consisted of MAs pins and fuel pin. The blanket assembly is made of uranium dioxide pellets with a 235U enrichment of 0.72%. Note that in the transmutation of LLFPs simulation, we use the “energy-deposition” mode to keep a constant neutron flux over 20 years of operation. The design parameters for the LFR core are detailed in Table 2.

Table 1 The isotopic of LFR fuel used in the simulation.
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Table 2 The main parameters of the LFR used in the simulation.
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Selection of LLFPs and Mas

The isotopic composition of LLFPs and MAs used in the simulation is obtained from the depleted fuel of the LFR with a burnup of 30 GWd/t. For the loading MAs, we mainly consider the isotopes 237Np, 241Am, 243Am, 244Cm and 245Cm. The abundance of loading MAs is listed in Table 3, and all these nuclides are mixed together in a fixed nuclide ratio. Note that 241Am and 243Am account for more than 85 wt% of the total MAs nuclides, whereas the amount of 244Cm and 245Cm is only less than 5 wt%. Thus, an efficient transmutation of 241Am and 243Am is the priority in order to reduce the inventory of MAs. Note that considering that excessive loading of the MAs materials may lead to affect the reactor characteristics26, we should optimize the loading amounts of MAs material to enhance the transmutation efficiency while ensuring the smooth operation of core.

Table 3 Isotope abundance and half-life of loaded MAs nuclides.
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As mentioned above, six radionuclides 79Se, 93Zr, 99Tc, 107Pd, 129I and 135Cs are selected as transmutation candidates. These LLFPs nuclides were mixed with the neutron moderator (70 at% LLFPs + 30 at% YD2) and were loaded into the LLFPs assemblies to improve the transmutation performance since the feasibility of this moderator has been proven9,11,29. The moderator could soften the neutron at the LLFPs assembly region while having little effect on the neutron energy spectrum of the entire core, as it is loaded in the radial blanket region with a small loading mass. The isotope abundances of these LLFPs nuclides are shown in Table 4, and their chemical forms for assembly loading are explained in detail in our previous work23.

Table 4 Isotope abundance and half-life of loaded LLFPs nuclides.
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Transmutation rate and support ratio

The transmutation rate (TR) is defined as the ratio of the transmuted amount to the initially loaded one for a specific nuclide in the LFR system, which can be expressed as

$$TR=\frac{N\left(0\right)-N(T)}{N(0)T},$$
(1)

where N(0) and the T are the initial atomic number of the nuclide and the irradiation time, respectively. The support ratio (SR) is defined as the ratio of the amount of the transmuted to that of the produced one for a specific nuclide over the same time. Here SR is expressed as

$$SR=\frac{N\left(0\right)-N(T)}{YMT},$$
(2)

where the Y and M are the nuclide yield per fission of fuel materials and the total fission rate in the LFR core, respectively. In our study, increasing the mass of initially loaded LLFPs improves SR, and the TR will deteriorate due to neutron self-shielding effects in the loading region. Therefore, comprehensive consideration needs to be taken when evaluating the transmutation efficiency of LLFPs.

Results and discussions

Optimization of loaded mass of the Mas

We start with the optimization of the loaded mass of MAs since they could affect the production of delayed neutrons, which play an important role in reactor control. For instance, excessive loading of MAs will deteriorate the LFR operational performance and the neutronic characteristics of the LFR core since the fraction of delayed neutrons produced by MAs nuclides is less than uranium21,26. Meanwhile, the LFR core must maintain criticality during the operation, which limits the total loading of MAs nuclides in the core. We select 4 different loading amounts that account for 0.5 wt%, 1.0 wt%, 1.5 wt%, and 2.0 wt% of the total fuel to achieve a high transmutation efficiency. Note that different loading amounts are considered for MAs in our study while their isotopic ratios are fixed (See Table 3).

The distribution of the MAs pins and assemblies is shown in Fig. 2. The loading mass and the corresponding transmutation for MAs are presented in Table 5. For 244Cm and 245Cm, their transmutation rate (TR) and SR are negative, which indicates that these MAs cannot be transmuted in this core. However, the impact of 244Cm and 245Cm on the LFR core is insignificant since their relative fractions in MAs are rather small (< 5.0 wt%). For 237Np, 241Am, and 243Am, these three nuclides are the major transmutation objects since their relative fractions are more than 95 wt%. They can be transmuted by the excess neutron per fission since the TR and SR are positive. In addition, Table 5 indicates that the SR of these nuclides increases with the MAs loaded amount. The SR values are higher than 1.0 when the loaded amount reaches 1.5 wt%. It indicates that a self-sustained transmutation can be achieved, i.e., the transmutation of a long-lived radionuclide exceeds its production during the core operation. The operational performance of the core can be affected by the MAs loading. Therefore, the optimization criterion for the loading of MAs is to achieve self-sustained transmutation of the major MAs with as little loading amount as possible. In the following simulations, the MAs loading amount is set to 1.5 wt%, which can minimize the impact of loading on core performance, as discussed later.

Figure 2
figure 2

The distribution of MAs assembly in LFR with different loading amounts. In pads (a) and (b), the loading amounts are 0.5 wt% and 1.0 wt%, respectively and each MAs assembly contains four MAs pins, as shown in pad (d). In pads (b) and (c), the loading amounts are enhanced to 1.5 wt% and 2.0 wt%, respectively, and each MAs assembly contains six MAs pins, as shown in pad (e).

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Table 5 The transmutation rate and support of MAs considering different loading amounts.
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Effects of MAs on the operational performance of LFR

In order to obtain a good transmutation performance, the loaded mass of MAs can be arbitrarily increased. However, the balance between transmutation and operational performance is also required21. Generally, the operational performance is sensitive to neutronic characteristics, such as neutron flux and spectral distributions.

The neutron flux distribution is an important performance characteristic since it could impact lots of many physical parameters including the power peaking factor, which would directly affect the operation of the core. Figure 3 shows the comparison between the neutron flux distributions with and without the 1.5 wt% MAs loaded in the core at the beginning of the fuel cycle. It can be seen that without loading MAs, the neutron flux is peaked at the center of the core and then decreases with the increase of the core radius. With the loading of MAs, the neutron flux also drops with the increase of radius, although it diminishes as seen in the central region compared to the case without loading MAs. We compared the peak fluxes of the two to clarify the differences, and the result shows that the peak flux of the core with 1.5 wt% MAs loaded is 3.98% lower than the case without MAs. Such difference would not significantly deteriorate the physical properties of the core and then affect its operation.

Figure 3
figure 3

The distribution of neutron flux with MAs (a), and without MAs (b) at the beginning of the core cycle.

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The neutron spectrum is another important parameter of the LFR, which is related to the Doppler coefficient and power peaking factor26. More importantly, the neutron spectrum would significantly affect the fission rate and the transmutation rate. The spectral distributions of neutrons inside the whole core with and without the loaded MAs are shown in Fig. 4a. One can see that the neutron spectrum remains almost unchanged with the 1.5 wt% MAs loaded. It indicates that the loading of MAs would not affect the core operation and nuclear transmutation.

Figure 4
figure 4

The neutron energy spectrum (a) and the evaluation of keff with time (b) at the different loading designs (with and without loading MAs).

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On the other hand, during the operation of LFR, the full power operation time would also influence the transmutation of MAs and LLFPs6. Hence, we calculate the time evolution of keff by using the depleted module of OpenMC to investigate the effect of the full power (750 MWth) fuel cycle as adding MAs nuclides to LFR. The corresponding results are shown in Fig. 4b. The keff decreases with operation time no matter whether MAs nuclides are loaded or not. However, the loaded MAs diminish the initial keff and then delays its rate of decline. When irradiation time reaches ~ 1300 days, the keff in the case with MAs loaded is equivalent to that in the case without MAs. As the irradiation time continues to increase, the former one will eventually exceed the latter. This is because the 237Np, 241Am and 243Am will be transmuted to 238Pu, 242Am and 244Am by capturing fast neutrons. These products carrying large fission cross sections could compensate for the reactivity loss27,28. The above result shows that the 1.5 wt% MAs loading has an insignificant impact on the operation of the core, and it would not reduce the fuel cycle length.

Optimization of the LLFPs composition

The transmutation efficiency of LLFPs depends on the neutron capture cross-section and their loading amount. Here we fix the total number of LLFPs pins and adjust the LLFPs composition to investigate the effect of LLFPs loading on the transmutation efficiency. Figure 5a shows an exemplary LLFPs composition in which a maximum loading of 79Se is achieved by giving only one pin for each other LLFPs nuclides. Similarly, a maximum loading of 93Zr, 99Tc, 107Pd, 129I and 135Cs can be realized, respectively. As a result, we obtained six kinds of LLFPs composition schemes. The resulting SR and TR values are shown in Table 6. Here the SR and TR values for the maximum loading are directly obtained, while those for the minimum ones are calculated by averaging the values obtained from the other five LLFPs composition schemes. For 79Se and 93Zr, the TR values obtained at the minimum loading amount are almost two times smaller than those at the maximum loading amount. However, the opposite results are obtained for the 99Tc and 107Pd. For 129I and 135Cs, the TR values obtained at the minimum loading amount are comparable to those at the maximum loading amount. The SR value increases with the loading of all the six LLFPs, which is in agreement with the prediction of Eq. (2). For a minimum loading of 79Se, the SR is obtained to be 1.337, indicating that it is easy to achieve self-sustained transmutation. For 79Se, 99Tc, 107Pd, and 129I, although their SR values are less than 1.0 in the cases of minimum loading, their SR values are more than 1.0 in the cases of maximum loading. It suggests that the above 4 LLFPs nuclides can realize SR > 1.0 by controlling their loading amount. For 135Cs, achieving their self-sustained transmutation is very difficult, because of its neutron capture cross-section.

Figure 5
figure 5

The distribution pattern of pins in LLFPs assembly for the maximum loading of 79Se (a) and the optimal LLFPs scheme used to balance the transmutation efficiencies of all the LLFPs (b).

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Table 6 The TR and SR values were obtained from different LLFPs composition schemes. The minimum load results are obtained by averaging the TR (or SR) values obtained from the other five LLFPs composition schemes.
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In order to achieve the self-sustained transmutation of as many nuclides as possible, a feasible LLFPs scheme is given and is shown in Fig. 5b. In such a scheme, the relative volume ratio of Se, Zr, Tc, Pd, I, and Cs nuclides is set to 2:30:10:10:9:30. Accordingly, the transmutation result is given in Table 7. The SR values of 79Se and 99Tc exceed 1.0 with a factor of more than 0.3. It indicates that some neutrons might be "wasted" for transmuting only 79Se and 99Tc, however, they do not act on other nuclides whose SR < 1.0. Note that the transmutation of as many LLFPs nuclides as possible should be achieved in a self-sustained transmutation. Although, both 93Zr and 135Cs have 30 pins loaded, their SR values are still much less than 1.0. As a result, it is difficult to realize a self-sustained transmutation for these two nuclides by regulating their loaded mass. Other approaches, such as changing neutron moderator and loading method, and employing isotope separation may be useful for enhancing the SR values of the whole system.

Table 7 The TR and SR of LLFPs in the LFR (with MAs) using the optimal scheme used to balance the transmutation efficiencies.
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Transmutation analysis

This section investigates the effects of transmutation on MA inventories as a function of irradiation time. Figure 6 shows the variation of the transmuted MAs within one cycle. During the 600 days of irradiation, a positive transmutation of 237Np, 241Am and 243Am can be achieved with a transmutation percentage higher than 20%. Among these MAs, 241Am has the highest transmutation rate and the transmutation capability of 237Np is very close to that of 243Am. This is because 241Am has the largest fast neutron capture cross-section, whereas those for 237Np and 243Am are visibly lower. Since the fraction of the above three nuclides accounts for more than 95% of the total MAs nuclides in LFR spent fuel, the present scheme could be utilized to reduce the total inventory of MAs. Different to 237Np, 241Am and 243Am, the mass of 244Cm and 245Cm increase with time, which means that they cannot be efficiently transmuted by the LFR.

Figure 6
figure 6

Percentage of MAs remaining in the core over one 600-day cycle. The transmutation percentages for 237Np, 241Am and 243Am are positive (a), and the values for 244Cm and 245Cm are negative (b).

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The LLFPs transmuted in the blanket regions as a function of irradiation time is shown in Fig. 7. It is found that the transmuted LLFPs increases approximately linearly with the irradiation time. After 20-year irradiation, the percentage of transmuted 107Pd and 99Tc are higher than 15%, whereas the other nuclides are less than 10%. The transmutation percentage of LLFPs after 20 years are in the order of 107Pd > 99Tc > 79Se ≈ 129I ≈ 137Cs > 93Zr.

Figure 7
figure 7

Percentage of LLFPs remaining in the core over a 20-year irradiation time.

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Conclusions

We have presented an LFR-based transmutation of MAs and LLFPs through OpenMC simulations. The loading amounts of MAs are optimized to be 1.5 wt%. The neutron flux distribution and spectrum are chosen as representatives to study the effect of MAs loading on the core operating performance. It indicates that loading an appropriate number of MAs (≤ 1.5 wt%) to the LFR core does not significantly disturb its operation. Moreover, the result of keff shows that the refueling cycle is not shortened by the loading of MAs. The transmutation capabilities of MAs and LLFPs are further analyzed by 600 days and 20 years of burnup, receptively. For MAs nuclides, the TR is positive and the SR is more than 1.0 for 237Np, 241Am, and 243Am. Since these MAs account for more than 95 wt% of the total MAs nuclides, the usage of LFR core is expected to reduce the total inventory of MAs. For LLFPs nuclides, The TR is positive for selected six LLFPs nuclides, the SR is more than 1.0 for 107Pd, 79Se, 99Tc and 129I. It indicates that all the LLFPs could be transmuted effectively in the blanket assembly, and 107Pd, 79Se, 99Tc and 129I could realize self-sustained transmutation. We conclude that the proposed LFR core is helpful to handling long-lived nuclear wastes with high radioactivity. It is worth noting that the loading of MAs has the potential to affect the safety of the core, i. e. the reactivity factor, the value of the control rods, the margin for shutdown, etc., and these works may be the subject of future research.