Minor Actinides Transmutation and ²³³U Breeding in a Closed Th-U Cycle Based on Molten Chloride Salt Fast Reactor

Abstract

Long-lived minor actinides (MAs) are one of the primary contributors to the long-term radiological hazards of nuclear waste, and the buildup of MAs is hampering the development of nuclear power. The transmutation of MAs in reactors is regarded as a potential way to replace direct disposal to reduce the impact of MA on the environment and improve the utilization of fuel. Due to its superior features, such as outstanding neutron economy, no fuel assembly fabrication, high neutron flux, and especially online refueling and reprocessing, the molten chloride salt fast reactor (MCFR) is regarded as one of the potential reactors for MA incineration. In this work, MA transmutation capability and ²³³U breeding performance for an optimized MCFR have been evaluated in different scenarios. The results show that the MA transmutation capability and ²³³U breeding performance with online transuranic elements (TRU) and ²³²Th feeding scenario are improved significantly compared with the case in online ²³³U and ²³²Th feeding, when the initial MA loading is 5 mol%, the total mass of MA transmutation and MA incineration is 7160 kg and 1759 kg during the whole 100 years operation under online TRU and ²³²Th feeding scenario, and the corresponding average annual net production of ²³³U is 450 kg, however, the MA transmutation amount, MA incineration amount and average annual net production of ²³³U for online ²³³U and ²³²Th feeding scenario is 5298 kg, 1315 kg, and 249 kg, respectively. In addition, the research also shows that the increase in initial loading of MA has no obvious effect on the improvement of the ²³³U breeding performance but can improve the transmutation efficiency of MA under online TRU and ²³²Th feeding scenarios. Furthermore, if ²³³U is continuously extracted online from the core during the operation, the ²³³U breeding performance will be significantly improved, but it will deteriorate the safety performance, such as the fuel temperature coefficient of reactivity (TCR) and the effective delayed neutron fraction (EDNF), more importantly, it will also put forward higher requirements for the immature online reprocessing technology.

1. Introduction

With the rapid development of nuclear energy, the inventory of long-lived high-level wastes (MAs and LLFPs) produced by the reactors will increase correspondingly, thus, how to deal with the accumulated MAs and LLFPs has become a more and more serious problem. The partition and transmutation (P and T) method is regarded as an effective way for managing MAs and LLFPs. Partition is to separate MA and LLFPs from highly radioactive waste liquid based on existing reprocessing technology. Transmutation means transforming them into short-lived, stable, or valuable nuclides through reactor transmutation [1]. Since the partition involves a complicated chemical process that is beyond the scope of this work, this work mainly focuses on transmutation. Transmutation of MA in reactors cannot only reduce heat generation and radiotoxicity of the high-level, long-lived waste but also generate more power with the energy released from the transmutation of Mas. This is of great significance to alleviate the challenges encountered in the development of nuclear energy. Therefore, it is of great significance to research the effectiveness of MAs transmutation in different types of reactors.

Various research has been carried out to explore the transmutation of MAs in different types of reactors, including both thermal and fast reactors. For example, in PWR [2], boiling water reactor (BWR) [3], lead-cooled fast reactor (LFR) [4], and sodium-cooled fast reactor (SFR) [5], new approaches for MA transmutation, are under research. Among them, MA transmutation in PWR was studied most extensively due to its mature operation technology, and various useful conclusions were proposed [6]. Although the cross-sections of the long-lived MAs in the fast neutron region are lower than those in the thermal neutron region, the fast reactor has a higher neutron flux, and a larger fission-to-capture cross-section ratio [7], which are beneficial to MA transmutation. Thus, the fast reactor is recognized as an alternative and promising system for the transmutation of MA. However, there are also many technical challenges for the transmutation of MA in fast reactors. For example, in liquid-metal fast reactors, such as LFR, the highly corrosive environment caused by using liquid-metal coolant presents a severe challenge [8]. For gas-cooled fast reactors, the material lifespan will be shortened due to the high temperature [9]. For subcritical fast reactors, such as the accelerator driven subcritical system (ADS), the spallation target design, the requirement of reliable accelerator technology, and the high produced MA content’s effect on the safety coefficients result in a non-negligible technical challenge [10].

The molten salt reactor (MSR), as the only liquid fuel reactor selected for the next-generation reactors in the generation IV international forum (GEN-IV), has many remarkable merits, for example, inherent safety, excellent neutron economy, no fuel assembly fabrication, and especially online reprocessing and refueling, which make the closed fuel cycle possible [11]. Considering its features above, especially the online reprocessing and refueling that will greatly improve the transmutation efficiency, MSR is suitable for MA transmutation. Due to the merits of MSR in MA transmutation, a series of studies on MA transmutation in MSR have been carried out. For instance, O. Ashraf et al. compared the MA transmutation capability in the thermal MSR and fast MSR [12], it shows that fast MSR has a higher transmutation ratio (TR). Yu et al. researched the MA transmutation capability in SMSFR for different MA loadings [13], it found that when MA = 18.17 mol%, the TR can achieve to approximately 95% on iso-breeding. In addition, The MOlten Salt Actinide Recycler and Transmuter proposed by the Kurchatov Institute of Russia aims to effectively transmute transuranium (TRU) [14]. Although, the Molten Salt Fast Reactor (MSFR) aims at breeding ²³³U in a closed Th-U cycle, some research about the transmutation of TRU elements has also been carried out in the MSFR [15]. Since the requirements for online reprocessing in molten salt fast reactors are lower than those in molten salt thermal reactors, it reduces the challenge brought by the immature online reprocessing technology, and the larger fission-capture cross-section ratio for MA in the fast spectrum can make the transmutation more efficient [16,17]. Therefore, MA transmutation in a molten salt fast reactor is very attractive and valuable for research.

For the molten salt fast reactors, it can use fluoride salt or chloride salt as carrier salt, the former is called molten fluoride salt fast reactor (MFFR), and the latter is called molten chloride salt fast reactor (MCFR). Compared with MFFR (LiCl is usually used as carrier salt), MCFR usually has a harder neutron spectrum due to the slighter slowing down of neutrons [18], which is helpful for improving the breeding performance and MA transmutation capability. In addition, due to the harder neutron spectrum in a MCFR, the effect of neutron absorption of fission products (FPs) on the neutron performance is significantly smaller, and the reprocessing cycle can be prolonged to lower the difficulty of reprocessing. Furthermore, the solubility of HM (heavy metal nuclides) in MCFR is much higher, thus, more HM can be loaded in MCFR during the operation, which is beneficial to further improve breeding and MA transmutation performance [19]. Thus, MCFR has great potential for transmuting MA and breeding fissile nuclides and is worth studying.

Research on MCFR can date back to the 1950s, Oak Ridge National Laboratory (ORNL) mainly studied the breeding performance of MCFR in a closed U-Pu cycle, and the breeding ratio (BR) can be achieved at 1.09 when using NaCl + MgCl₂ + PuCl₃ + UCl₃ as fissile fuel salts and UO₂ + Na as a solid blanket [18]. Then, Atomic Energy Authority in the UK carried out a series of research on MCFR in 1960s, NaCl + ²³⁸UCl₃ + PuCl₃ was applied as the driving fuel salt and NaCl + ²³⁸UCl₃ was employed as the breeding fuel salt and found that the BR can obtain a significant improvement [20]. Later, in Britain, Moltex Energy proposed a pool-type fast reactor [21], in which the fuel tube is loaded with chloride fuel, it has an enormous economic advantage and inherent safety. At the same time, Merk team of the University of Liverpool in the UK also carried out some important research on the key performance of MCFR [22]. In addition, France proposed REBUS design, it is designed to be operated in the power of 3700 MWth [23], it combines a positive breeding gain and a strong negative temperature coefficient of reactivity (TCR), and based on the closed U-Pu cycle, many simulations have been carried out to prove its excellent thermo-hydraulics and neutrons performance. Terrapower also announced its research and development plan for the MCFR at the ORNL’s 50th Anniversary Conference. In August 2019, the MCFR project achieved an important breakthrough, with its completed carrier salt loop (non-nuclear device) successfully operating continuously for more than 1000 h [24]. It can be found that almost all the above studies about MCFR were focused on breeding performance and were based on the U-Pu cycle. However, MCFR also has great advantages and potential in MA transmutation, which is worth studying. Furthermore, compared with the closed U-Pu cycle, the closed Th-U cycle has unique advantages. The lower mass number of Th fosters a lower trans uranium (TRU), which leads to a fuel inventory with lower radiotoxicity and less MA production, it is helpful to reduce the difficulty of fuel waste treatment and improve the transmutation efficiency of MA [25]. In addition, Th-U cycle is known to improve the safety parameters [26]. Thus, in this work, MA transmutation and ²³³U breeding capability will be evaluated in different cycle scenarios based on the optimized MCFR in closed Th-U cycle.

2. General Description of MCFR and Analysis Methodology

2.1. Description of the Optimized MCFR and Online Reprocessing

In our previous work, a series of basic research on MCFR was carried out [27,28,29], including the effect of enrichment with ³⁷Cl, the reprocessing method suitable for MCFR, the carrier salt selection, as well as the evaluation of different designs, then, referred to the configuration of REBUS-3700 [23]. The preconcept design scheme of MCFR was finished, and the basic cross and vertical sections of MCFR are shown in Figure 1. The whole reactor is mainly composed of two parts, namely the active zone and the fertile zone. In the active zone, the fuel salt flows from the bottom to the top, then, it flows out of the core through pipes to exchange heat with heat exchangers, and finally returns to the core from the bottom. The blanket surrounds the active core (blue area in Figure 1) for breeding ²³³U, and the two main zones are separated by a Ti-based alloy. In addition, for fertile fuel savings, graphite reflector (yellow area in Figure 1) is applied beside the blanket. Near the graphite reflector, B₄C (green area) is employed for absorbing the leaking neutrons. In order to reduce the influence of neutron irradiation, a Ti-based alloy acts as the structural material surrounding the whole core. The total power of the optimized MCFR is 2500 MWth, and the composition of carrier salt is 55 mol% NaCl and 45 mol% (²³³U + ²³²Th)Cl₄-MACl₃.

Furthermore, to improve the neutronics performance of MCFR in the equilibrium state (EQL), the multi-objective optimization of MCFR was carried out using a script that couples the molten salt reactor equilibrium-state analysis code (MESA) with a novel intelligent optimization algorithm [29], and the final optimized design parameters are listed in

Table 1. Parameters of the optimized MCFR.

Parameters	MCFR
Thermal power density (MWth/m3)	100
Composition of fuel salt (mol%)	NaCl:(HM) Clx = 55:45
Enrichment of 37Cl (%)	97
Temperature of fuel salt (K)	923
Density of molten salt (g·cm3)	3.60
Density of alloy (g·cm3)	8.86
Density of B4C (g·cm3)	2.52
Volume (m3)	25
Thickness of graphite (cm)	40
Thickness of B4C (cm)	35
Thickness of blanket (cm)	60
Thermal expansion (K−1)	−3.00 × 10−4

.

Compared with other types of reactors, the most important characteristic of MSR is that it can be continuously refueled and reprocessed online without shutting down, which also allows it to operate in a closed fuel cycle. For online reprocessing, two special reprocessing systems are employed for both the fuel salt and fertile salt: a helium-bubble reprocessing system is applied for removing non-soluble gases and metal FPs, and pyrochemical reprocessing system is used for removing soluble FPs and extracting heavy nuclides on-line [30]. The nuclides involved in reprocessing systems are listed in

Table 2. Reprocessing system of MSR.

Reprocessing System	Nuclides
Chemical reprocessing	Zn, Ga, Ge, As, Se, Br, Rb, Sr, Y, Zr, Cd, In, Sn, I, Cs, Ba, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb
Gaseous bubbling	H, He, N, O, Ne, Ar, Kr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Sb, Te, Xe, Rn

, and the detailed reprocessing flowchart that has been discussed in our previous work is shown in Figure 2 [31].

In general, in pyrochemical reprocessing, U, Np, and Pa is extracted by fluorination reaction from the reactor core, and the blanket, ²³³Pa is stored in a stockpile to let it decay into ²³³U first. Then, actinide nuclides like Np, Am, and Pu are recovered using reductive extraction technology, and the carrier salts are recovered by the reduced pressure distillation method to remove FPs.

2.2. Simulation Tool

Unlike the traditional reactors, the continuous on-line refueling and removal of FPs in MSR make the depletion calculation more difficult. To simulate the depletion of MSR with continuous online refueling and reprocessing, an in-house program called TMCBurnup was developed in our previous work [32]. It couples the cross-section processing and multigroup neutron transport calculation module (TRITON) and a novel depletion code MOlten salt reactor specific DEpletion Code (MODEC) [33,34]. The flowchart of TMCBurnup is shown in Figure 3. First, the parameters of core and blanket are initialized by the user. Then, the neutron transportation and depletion calculations are performed by the TRITON module and MODEC, respectively. Next, fissile nuclides and ²³²Th need to be refueled into the core, the total mass and the ratio of fueled ²³²Th and fissile nuclides are determined by ensuring the total heavy metal inventory is constant and keeping the reactor critical. The calculation is performed iteratively until the pre-set burn up period is reached.

To demonstrate the accuracy of TMCBurnup in the depletion calculations of a molten salt fast reactor, the depletion calculations using TMCBurnup based on MSFR were performed with different startup fuel and compared with the reference [15], the evolution of heavy nuclides calculated by TMCBurnup and the reference are shown in Figure 4, and it can be noticed that the evolution of heavy nuclides calculated by TMCBurnup is in good agreement with the reference regardless of which fuel is used to start the reactor, which proves the suitable for TMCBurnup in depletion calculation of molten salt fast reactor. Thus, TMCBurnup is applied for the depletion calculation of MCFR.

3. Results and Discussion

The primary objective of this research is to evaluate and compare the MA transmutation performance as well as the ²³³U breeding capability of the optimized MCFR under different scenarios, the five different scenarios are listed in

Table 3. MA incineration scenarios.

Scenario	1	2	3	4	5
Fuel composition	NaCl-MACl3-ThCl4-UCl4	NaCl-MACl3-ThCl4-UCl4	NaCl-MACl3-ThCl4-UCl4	NaCl-MACl3-ThCl4-UCl4	NaCl-ThCl4-UCl4
Mole ratio	55%-5%-35.0%-5.0%	55%-5%-35.0%-5.0%	55%-7%-33.3%-4.7%	55%-7%-33.3%-4.7%	55%-5.2%-39.8%
Nuclides feeding in core	232Th-233U	232Th-TRU	232Th-TRU	232Th-TRU	232Th-TRU
Nuclides extraction from core	233Pa	233Pa	233Pa	233Pa-233U	233Pa

. Scenario 1 is researched by considering on-line ²³³U and/or Th feeding, ²³³Pa is extracted from both the core and blanket, and ²³³U is only extracted from blanket. In order to investigate the effect of on-line TRU feeding, we proposed scenario 2, in which TRU and/or ²³²Th is injected on-line into the core to keep critical and ensure the total inventory of heavy nuclides constant during the whole operation. In addition, ²³³Pa is extracted on-line from both the core and blanket, and ²³³U is extracted from blanket. Considering the complexity of separating MA from TRU and the drastic oscillation of reactivity caused by continuous online MA feeding, a five-year-cooled TRUs from LWR instead of MA is fed into the core online together with ²³²Th [35], the total mass and the ratio of fueled TRU and ²³²Th is determined by ensuring the total heavy metal inventory constant and keeping the reactor critical. Based on scenario 2, the effect caused by initial MA loading was researched, scenario 3 and scenario 2 have the same cycle schemes except for the initial MA loading is different. In our previous studies, it was found that when the initial loading of MA exceeds 7 mol% in the optimized MCFR, even if only Th is fed during the operation, the corresponding k_eff will exceed 1.1 for up to several decades due to the delayed reaction released by the accumulated Pu, which will make reactivity control difficult and will affect neutron economy. Therefore, the maximum initial loading of MA is limited to 7 mol% here.

In order to study the influence of online extraction of the ²³³U from core on MA transmutation capability, ²³³U breeding performance, and safety performance, scenario 4 was introduced. It has the same MA loading as scenario 3, but scenario 4 extracts ²³³U from both the core and blanket. In addition, in order to verify the impact of the initial loading of MA more clearly, scenario 5 was designed, the initial loading of MA is 0 mol%, and other operating conditions are the same as those of scenario 2 and scenario 3.

A 238-group ENDF-B/VII.0 cross-section library was applied in the calculation. In addition, there were 10,000 neutrons per k_eff cycle and a total of 285 cycles were run for a calculation. In order to keep safety and neutron economy of MCFR, the k_eff is between 1.000 and 1.005 during the whole operation by continuous online feeding and reprocessing.

3.1. Evolution of Neutron Spectrum

In this subsection, neutron spectrum at the initial of different scenarios is investigated first, and the results are shown in Figure 5a, since the initial fuel composition of scenario 2, scenario 3 and scenario 4 is the same, only the neutron spectrum of scenario 1, scenario 2 and scenario 5 are shown. It can be found that the corresponding neutron spectrum of the three scenarios is roughly the same, the neutron spectrum of scenario 1 and scenario 2 is a little harder due to the MA loading at the initial.

In order to give a quantitative description for neutron spectrum, the energy of the average lethargy-causing fission (EALF) is introduced [36], which is defined as follows:

$$EALF=\exp \left\{\frac{{\displaystyle \int \ln E\varphi (E){\displaystyle {\sum }_f(E)dE}}}{{\displaystyle \int \varphi (E){\displaystyle {\sum }_f(E)dE}}}\right\}$$

(1)

where ϕ(E) and ∑_f(E) refer to the energy-dependent neutron-flux and macroscopic fission cross-sections, respectively.

The evolution of EALF and k_eff are shown in Figure 5b, and we can find that the k_eff of those five scenarios are all within our preset range (1.000–1.005). Furthermore, when the loading of MA increases, its corresponding EALF value also increases at the initial stage, which is due to the fact that the fission cross-section of MA in the high-energy region increases rapidly with the increase in neutron energy, leading to a harder neutron spectrum. With the deepening of burnup, due to the accumulation of FPs and the transmutation of MA, the EALF of scenario 1–4 gradually decreases. As for scenario 5, the EALF first decreases due to the accumulation of FPs, and then it gradually increases to EQL due to the increase in MA content in the core, and this effect is more obvious than the accumulation of FPs. Since the same feeding and refueling modes are used in scenario 2, scenario 3, and scenario 5, the composition of these scenarios is the same in EQL, thus, the corresponding EALF in EQL is the same. Due to the continuous extraction of ²³³U from the core and the continuous feeding of TRU, the content of Pu and MA in scenario 4 is the highest, however, the continuous feeding of ²³³U online results in the main fissile nuclides of scenario 1 is ²³³U. Therefore, scenario 4 and scenario 1 correspond to the highest and lowest EALF values, respectively.

3.2. Evolution of Heavy Nuclides Inventories and Mass Flow

The evolution of primary heavy nuclides under different scenarios was investigated, and the calculation results are shown in Figure 6a–c. For a clear comparison, only the evolutions of heavy nuclides in the core for scenario 1 and scenario 2 are shown, the masses of the main heavy nuclides at the initial stage and in EQL are listed in

Table 4. Mass flow and MA incineration performances for different scenarios.

Scenario	1	2	3	4	5
MA loading (kg)	5308	5308	7494	7494	0
MA feeding (kg)	0	2420	2265	9237	2869
MA residue at EQL (kg)	83	612	610	1880	620
MA transmutation mass (kg)	5222	7116	9145	14,851	2255
MA incineration mass (kg)	1316	1759	2251	3608	540
MA transmutation ratio	98.38%	92.08%	93.74%	88.76%	78.45%
MA incineration ratio	24.79%	22.61%	23.07%	21.56%	18.78%
Pu residue at EQL (kg)	59	2787	2799	9076	2818
Pu feeding (kg)	0	16,944	15,855	64,506	20,081
233U loading (kg)	5220	5220	4926	4926	5323
233U feeding (kg)	17,872	0	0	0	0
233U produced from core (kg)	1032	4015	3985	54,659	4112
233U produced from blanket (kg)	41,312	41,881	41,711	43,667	42,351
233U residue in core (kg)	4834	3575	3583	834	3562
233U residue in blanket (kg)	685	697	697	728	699
233U net production (kg)	24,901	45,079	45,176	95,190	45,528
232Th loading (kg)	137,054	137,054	135,276	135,276	142,148
232Th feeding (kg)	124,328	122,924	124,012	122,966	119,437
232Th residue at EQL (kg)	139,412	137,863	137,919	134,842	137,706
232Th consumption (kg)	121,970	123,733	121,369	123,400	123,879
232Th conversion ratio	20.42%	36.42%	37.23%	37.14%	36.75%

. It can be found that, for scenario 1, the mass of MA decreases monotonically due to the fission and capture reactions. The mass of Pu increases rapidly at the beginning to reach its maximum value at 12 years due to the competition between the generation from MA and the fission reaction of Pu itself, and then declines due to their fission consumption. Furthermore, the mass of ²³⁸Pu is the largest of the Pu isotopes, which can be 992 kg at 10 years. The evolution tendency of Pa is almost the same as that of Th, the mass of them increases gradually until EQL is reached, but the amount of ²³³Pa is much smaller than Th since it is the direct neutron capture production of the ²³²Th. Different from the evolution of other nuclides, the mass of U declines during the first 10 years due to the fission depletions and then increases to the EQL due to the delayed reactivity of Pu and the capture reaction of ²³²Th.

As for scenario 2, the mass of MA decreases rapidly during the first 39 years and then tends to be constant due to the online feeding of TRU. On the contrary, the mass of Pu increases during the first 23 years and then is almost constant during the last 77 years. Along with the evolution of Pu, the required mass of ²³³U to maintain criticality decreases at first and then becomes constant due to the delayed reactivity results caused by the accumulated Pu. Since TRU contains a large amount of ²³⁹Pu, its fission reaction capacity is greater than that of ²³³U and MA, with the feeding of TRU, the content of fissile nuclides needed to maintain criticality decreases, the total mass of heavy nuclides is kept constant during operation to ensure the stability of fuel, thus, the mass of Th inventories increases in the first years and then tends to be gradual. In addition, since TRU is continuously fed online in scenario 2, the content of MA and TRU in the core is greater than that in scenario 1 in EQL, so less content of ²³³U is needed to maintain the criticality.

In addition, as can be seen from Table 4, since the extraction of ²³³U from the core occurs in scenario 4, the content of Pu and MA in EQL corresponding to scenario 4 is the most, while the content of U is the least. Furthermore, although the initial MA loading in scenario 2, scenario 3, and scenario 5 is different, the final contents of heavy nuclides tend to be the same due to the same online feeding and online extraction method.

3.3. ²³³U Breeding Performance

The ²³³U’s breeding performance may be significantly different under different feeding and cycling scenarios. Therefore, the ²³³U’s breeding capability under the above five scenarios is evaluated here. Generally, the breeding ratio (BR), net ²³³U yield, and doubling time (DT) are used as the main indicators to evaluate the breeding capability. The BR indicates the ratio of the generation to the consumption of fissile nuclides, which can be expressed in Equation (2):

$$BR=\frac{Rc({}^{234}U+{}^{232}Th+{}^{240}Pu+{}^{238}U-{}^{233}Pa)}{Ra({}^{235}U+{}^{241}Pu+{}^{233}U+{}^{239}Pu)}$$

(2)

where R_c and R_a stand for the neutron capture rate and absorption rate, respectively. Since the focus of this work is to study the breeding capability of ²³³U, the definition of regeneration ratio (RR), which is expressed in Equation (3), is introduced. It refers to the relationship between the generation rate and the disappearance rate of ²³³U directly.

$$RR=\frac{Rc({}^{232}Th-{}^{233}Pa)}{Ra({}^{233}U)}$$

(3)

The net production of ²³³U is expressed as the difference between the bred and consumption of ²³³U. The actual net production of ²³³U can be defined as:

$$M=M_{in}^{{}^{233}U}(t)+M_{ex}^{{}^{233}Pa}(t)+M_{ex}^{{}^{233}U}(t)-M_{re}^{{}^{233}U}-M_{Bol}^{{}^{233}U}$$

(4)

where ex and re stand for extracting and refueling, respectively, in refers to the remaining nuclides in the core and blanket, and Bol indicates initial loading at the beginning of the lifetime.

When the net production of ²³³U is the same as the initial loading of ²³³U, it means that the net produced ²³³U can be used as new fuel to start another MCFR, and the corresponding time is called DT.

The evolution of RR and the net production of ²³³U are shown in Figure 7. It can be noticed that online feeding of TRU is beneficial to the improvement of the RR and net yield of ²³³U. Compared with scenario 1, the average annual net production of ²³³U in scenario 2 is 200 kg higher, mainly because the online feeding of TRU reduced the fission consumption of ²³³U. As can be seen from Table 4, the mass of ²³³U fed online in scenario 1 is as high as 17,872 kg during the whole operation, and the continuous feeding of ²³³U also reduced the conversion utilization of ²³²Th to a certain extent. In addition, the net production of ²³³U corresponding to scenario 2, scenario 3, and scenario 5 is almost the same during the 100-year operation, indicating that the initial loading of MA has a limited impact on the net production of ²³³U with online feeding of TRU when the burnup is deep enough. Furthermore, for scenario 4, the continuous online feeding of TRU and extraction of ²³³U results in a decrease in the consumption of ²³³U in the core and, consequently, an increase in the net production of ²³³U. The DT corresponding to scenario 4 is approximately 9.7 years; it is almost 17 years for scenario 2, scenario 3, and scenario 5. Due to the slightly poor breeding performance of scenario 1, its corresponding DT is approximately 20.3 years.

In order to research the evolution law of RR, the fission fraction of each fission nuclide and the (n, γ) reaction rate of ²³²Th and ²³³Pa is shown in Figure 8. It can be noticed that the (n, γ) reaction rate of ²³³Pa is much lower than ²³²Th, and in the initial stage, the increasing (n, γ) reaction rate of ²³²Th caused by the softening of neutron spectrum leads to the increase in the corresponding RR under different scenarios. In scenario 1, with the deepening of burnup, the fission fraction of MA decreases, and the fission fraction of ²³³U increases, which results in a gradual decline of RR. However, in scenario 2 (scenario 3, scenario 5), due to the delayed reactive release of accumulated Pu, the fission fraction related to ²³³U decreases, so the corresponding RR gradually increases to EQL. As for scenario 4, due to the continuous online feeding of TRU and the extraction of ²³³U from the core, the fission fraction of ²³³U decreases, resulting in a rapid increase in RR in the first 10 years. Then, the fission fraction of ²³³U increases with burn-up, and the corresponding RR gradually decreases to EQL. The continuous extraction of ²³³U from the reactor core has an obvious effect on the RR. In the whole 100-year operation, the RR of scenario 4 reaches 5.7 at its highest, and in the EQL, the corresponding RR is approximately 5.25, which is much higher than in other scenarios.

Furthermore, the plot in Figure 9 shows the separate contributions to the ²³³U production for scenario 3 and scenario 4. It can be seen that the net production of ²³³U mainly comes from the blanket for scenario 3, while the ²³³U produced from the core and the blanket is comparable in scenario 4. In scenario 3 and scenario 4, the production of ²³³U from the blanket is almost the same, while much more ²³³U is produced from the core in scenario 4, resulting in a significantly larger net ²³³U production. As seen from Table 3, it can be found that in scenario 4, the ²³³U produced from the core up to 54,659 kg during the whole operation is approximately 50,000 kg more than scenario 3, and its corresponding feeding amount of TRU is also almost 50,000 kg more than that of scenario 3, which leads to a significant increase in the ²³³U net production. However, the online reprocessing technology is not yet mature. It is undoubtedly more difficult to continuously extract ²³³U from the core online.

3.4. MA Transmutation Capability

In this subsection, the transmutation performance of MA in the different scenarios is analyzed. In general, the transmutation of MA is evaluated by the transmutation mass (TM) and transmutation ratio (TR) of MA, TM stands for the difference between the sum of the initial loading and feeding of MA and the remaining MA after burnup, TR stands for the ratio of MA disappeared to the sum of MA loading and feeding. The TM and TR is defined as Equations (5) and (6).

$$TM(t)=M(B)+M_{feed}(t)-M(t)$$

(5)

$$TR(t)=1-\frac{M(t)}{M(B)+Mfeed(t)}$$

(6)

where M(t) refers to the MA inventory at operating time t, M(B) and M_feed(t) stand for the total mass of the initial loading MA and the total mass of MA fed on-line at time t.

In general, MA transmutation can be achieved with neutron capture and neutron fission. However, MA can only be completely converted into short-lived nuclides by fission reactions to effectively eliminate its long-lived radioactive hazards [25]. Thus, some views even suggest that the fission reaction is the only effective way for MA transmutation. In order to truly reflect the relationship between the fission MA and the total loading of MA, the incineration mass (IM) and incineration ratio (IR) of MA must be defined in Equations (7) and (8).

$$IM(t)={\displaystyle {\sum }_i(M_i}(B)+M_i^{feed}(t)-M_i(t))\times \frac{R_{f(i)}(t)}{R_{a(i)}(t)}$$

(7)

$$IR(t)=1-\frac{{\displaystyle {\sum }_i(M_i(B)+M_i^{feed}(t)-M_i(t)})\times \frac{R_{f(i)}(t)}{R_{a(i)}(t)}}{{\displaystyle {\sum }_i{M}_i(B)+M_i^{feed}(t)}}$$

(8)

where R_f(i)(t) and R_a(i)(t) refer to the neutron fission rate and the neutron absorption rate for nuclide i at operating time t.

The evolution of TM, IM, TR, and IR is shown in Figure 10a,b, more details about MA transmutation and incineration performance after 100 years of depletion are listed in Table 4 above. It can be found that TM and IM increase gradually with the depletion, while IM and TM increase rapidly in the first few years and then gradually slow down with the depletion for scenarios 1–4, however, for scenario 5, the increase rate of TM and IM does not change much with the burnup because there is no MA loading at the initial stage. Therefore, from scenario 1 to scenario 4, TR and IR gradually increase at first and then almost remain unchanged, while in scenario 5, TR and IR gradually increase with burnup. From scenario 1 to scenario 4, although scenario 1 has the smallest TM and IM, its IR and TR are the largest results because no TRU is fed online, which leads to more efficient MA transmutation. The TR and IR are the smallest for scenario 4 due to the TRU fed in scenario 4 (approximately 74,000 kg). The IR for scenario 1 and scenario 4 is 24.79% and 21.56%, and the corresponding TR is 98.38% and 88.76%, respectively. For scenario 5, the corresponding TM, IM, TR, and IR are all smaller than other scenarios; since there is no MA loaded in the beginning, it can be predicted that if the burn-up time is extended, the value of TM and TR in scenario 5 will exceed that of scenario 1 and be almost equal to scenario 2 and scenario 3.

Then, the transmutation performance of separate nuclides in different scenarios was researched. The plot in Figure 11a,b show the evolution of TR and IR related to Np, Am, and Cm for scenario 1 and scenario 2. We can notice that except for ²⁴⁵Cm, the TR and IR of other MAs increase monotonically to EQL. Since ²⁴⁵Cm is at the bottom end of the depletion chains of actinides, its generation from other actinides is greater than its consumption in the early stage, thus, the TR and IR of ²⁴⁵Cm are negative during the first 40 years for scenario 1, then, as the burn-up deepens, the consumption of ²⁴⁵Cm increases, ²⁴⁵Cm begins to be truly transmuted and eventually achieve positive IR and TR. For scenario 2, the TR and IR of ²⁴⁵Cm are negative during the first 52 years and eventually reach approximately 0.29 after 100 years of depletion. Furthermore, although the TR of ²⁴⁴Cm and ²⁴⁵Cm is smaller than that of Np and Am, their corresponding IR is the highest due to the high fission-capture ratio.

3.5. Radiotoxicity and Safety Performance

In this subsection, radiotoxicity as well as two important parameters, the temperature coefficient of reactivity (TCR) and the effective delayed neutron fraction (ENDF), are researched for different scenarios.

The evolution of radiotoxicity for the five scenarios above is shown in Figure 12. It can be noticed that due to the continuous online feeding of TRU and extraction of ²³³U, the content of Pu and MA in the core of scenario 4 is the highest, and the radiotoxicity is the lowest in scenario 1 due to the lowest Pu and MA content. In addition, scenario 2, scenario 3, and scenario 5 are almost the same in terms of radiotoxicity because of the same feeding and nuclide extraction method during the whole operation. The high radiotoxicity of scenario 4 during operation will present a greater challenge for immature online reprocessing and spent fuel disposal.

TCR, as one of the most important safety parameters, must be negative enough during the whole operation to ensure the safety of the reactor [37]. For the MCFR, the TCR is mainly affected by the changes in fuel salt because there is no moderator in MCFR and the temperature change in the core structure is small and slow, thus, the effect of structure expansion can be ignored [38,39]. Therefore, the TCR in MCFR is defined as follows:

$$\frac{dK}{dT}total=(\frac{dK}{dT})fuel density+(\frac{dK}{dT})fuel doppler$$

(9)

where K and T refer to the k_eff and the temperature, respectively. The evolution of TCR for 5 scenarios is shown in Figure 13. It can be noticed that due to the large fuel salt expansion feedback coefficient of the MCFR, the TCR is negative enough for all scenarios. Furthermore, the constant value of the TCR for scenario 5 is the largest at BOL since no MA is loaded in the core at the beginning. Due to the same online reprocessing and extraction methods, the TCR is nearly the same for scenario 2, scenario 3, and scenario 5 in EQL, while the TCR for scenario 1 is the largest due to the lowest MA and Pu contents and the highest ²³²Th content in EQL.

Due to the same expansion coefficient and density of fuel salt for different scenarios, the fuel density effect is nearly the same for five scenarios, thus, the Doppler effect is predominant for the evolution rule of TCR. MA has a flatter fission cross-section and a steeper capture cross-section than ²³³U; from Figure 3, it can be noticed that the increasing MA hardens the neutron spectrum, having a smaller negative effect on MA fission than on ²³³U fission. Additionally, the steeper capture cross-section for MA suggests a higher decrement of captures with the hardening of the neutron spectrum. Both effects result in an absolute value decrease in TCR with the increasing MA loading. Furthermore, the absolute value of TCR decreases with the deepening of burnup, which is mainly due to the accumulation of FPs during the operation. The FPs have a decreased cross-section with neutron spectra hardening, which leads to increased reactivity, and positively affects the TCR. The MA transmutation can increase the absolute value of the TRC during operation, but this effect is not as obvious as that caused by FP accumulation in all scenarios. Thus, the TCR increases gradually for all scenarios until the primary nuclides in the core are in EQL.

In addition, the ENDF (β_eff) is another safety parameter that plays an important role in reactor operation control, too small or too severe a fluctuation of β_eff during operation is detrimental to safety. It can be expressed as follows:

$${\beta }_{\mathrm{eff}}=\frac{{\displaystyle {\sum }_i\overline{v_d(i)}\cdot R_f(i)}}{{\displaystyle {\sum }_i(\overline{v_d(i)}+\overline{v_p(i)})\cdot R_f(i)}}$$

(10)

where v_d(i) and v_p(i) refer to the average delayed neutrons and the prompt neutrons per fission, and R_f(i) indicates the fission rate of nuclide i.

The evolution of total β_eff is shown in Figure 14, it can be found that the higher the initial loading of MA, the smaller the initial value of β_eff. In addition, the value of β_eff declines monotonically to a minimum value first and then rebounds except for scenario 4. To explore the source of the changes in β_eff, the β_eff for the main single nuclides (β_I) and the actual contribution of single nuclides to β_eff (β_s) are introduced and defined in Equations (11) and (12), respectively.

$${\beta }_I(i)=\frac{\overline{v_d(i)}}{(\overline{v_d(i)}+\overline{v_p(i)})}$$

(11)

$${\beta }_s(i)=\frac{\overline{v_d(i)}\cdot R_f(i)}{{\displaystyle {\sum }_i(\overline{v_d(i)}+\overline{v_p(i)})\cdot R_f(i)}}$$

(12)

Although β_I is slightly different under different neutron spectrums, calculation results show the difference between β_I in different scenarios and burn-up depths is less than 2 pcm. The β_I of ²³³U, ²³⁷Np, ²⁴¹Am, ²⁴³Am, ²³⁹Pu, ²⁴¹Pu, and ²³⁵U are calculated to be 291 pcm, 398 pcm, 136 pcm, 239 pcm, 218 pcm, 542 pcm, and 668 pcm, respectively. Since the value of β_I for ²³³U is larger than that of MA mixture, the larger the initial loading of MA, the smaller its initial β_eff.

The β_s of different scenarios with different depletion times are shown in

Table 5. The β_s of main nuclides for different scenarios with different depletion time (unit: years, pcm).

Scenario	Time	233U	237Np	241Am	243Am	239Pu	241Pu	235U
1	0	134	110	20	17	0	0	0
	10	174	65	11	12	5	0	5
	50	266	3	0	1	2	1	31
	100	271	4	0	0	0	0	37
4	0	107	130	24	20	0	0	0
	10	28	93	18	20	66	34	0
	50	42	26	11	20	89	68	0
	100	42	24	11	23	86	69	0
5	0	291	0	0	0	0	0	0
	10	212	9	3	3	35	20	6
	50	188	11	4	8	35	25	24
	100	187	12	4	9	31	25	27

. Since the evolution of β_eff is almost the same for scenario 2, scenario 3, and scenario 5, thus, only three different scenarios are shown in. For scenario 4, due to the continuous online feeding of TRU and extraction of ²³³U, ²³⁹Pu rapidly becomes the major fission nuclide instead of ²³³U (see Figure 8a); however, since the β_I of ²³⁹Pu is smaller than that of ²³³U, the β_s decreases rapidly during the first 20 years, and almost tends to be stable during the remaining 80 years. As for scenario 1, the effect resulting from the MA transmutation (especially ²³⁷Np) leads to a decrease in the total β_eff. Then, with the incineration of MA, the content of ²³³U gradually increases, and the positive effect of increasing ²³³U content on β_eff is greater than the negative effect caused by MA transmutation. In addition, the accumulated ²³⁵U during the operation also improves the total β_eff due to its large value of β_I. Thus, the total β_eff increases gradually over the last 90 years. The evolution of the total β_eff for scenario 5 is almost the same as that of scenario 1, but the final β_eff of scenario 5 is 14 pcm smaller than scenario 1 due to its higher MA and ²³⁹Pu content in the EQL.

The initial value, maximum value, minimum value, and other information of β_eff under different scenarios are listed in

Table 6. The β_eff for different scenarios.

Scenarios	βeff (pcm)
	BOL	Minimum	Maximum	Fluctuation	EQL
1	288	285	313	28	313
2	288	284	299	15	299
3	287	283	299	16	299
4	287	268	287	19	268
5	291	289	299	10	299

. It can be noticed that the fluctuation of β_eff for scenario 1 is the most severe, and the β_eff for scenario 4 is the smallest in EQL, it is 45 pcm smaller than scenario 1 and 31 pcm smaller than scenario 2. The difference will be even larger when the flow of molten salt is taken into account, the fuel salt flow will cause the flow of delayed neutron precursor and lead to the reduction in β_eff, which will weaken the reactivity control of the core.

4. Conclusions

In order to alleviate the problem of long-lived, high-level waste disposal faced by the development of nuclear energy, the MAs transmutation in different scenarios has been evaluated based on an optimized MCFR. The neutron spectrum, ²³³U breeding capability, MA transmutation performance, radiotoxicity, and the safety of MCFR are analyzed and compared for different scenarios. In general, the MCFR has obviously better MA transmutation performance due to superior merits. In addition, the results of this work also provide a reference for the Th-U fuel cycle strategy of the MCFR.

Compared with online feeding of ²³³U/²³²Th, online feeding of TRU/²³²Th can significantly improve ²³³U breeding performance and MA transmutation capability, when the initial loading of MA is 5 mol%, the latter scenario will increase the net production of ²³³U by 20,178 kg and the transmutation of MA by 1894 kg during the whole 100-year operation. In addition, the DT with online feeding of TRU/²³²Th is approximately 17.3 years, which is 3.3 years less than online feeding of ²³³U/²³²Th.

Furthermore, the calculation results of feeding TRU/²³²Th online and only extracting ²³³Pa from the core and blanket show that the initial loading of MA has almost no effect on the breeding performance of ²³³U and safety parameters, increasing the initial loading of MA is beneficial to improve the MA transmutation performance. Compared with the initial loading MA = 0 mol% scenario, the mass of transmuted and incinerated MA for the initial loading MA = 7 mol% during the whole operation increased by 6890 kg and 1711 kg, respectively, and the corresponding TR and IR increased by approximately 15% and 4.4%, respectively.

In addition, the extraction of ²³³U from the core with online feeding of TRU will greatly improve ²³³U breeding and MA transmutation performance, which is mainly due to the significant increase in the net production of ²³³U from the core. However, extracting ²³³U from the core will deteriorate the safety performance and significantly increase the radiotoxicity level during the operation. For example, the β_eff for this scenario is 268 pcm. If the motion of fuel salt is considered, there will be approximately a 50% loss for the β_eff when the volume fractions of the core and out-core are the same, which will further weaken the reactivity control of the core. Most importantly, the continuous online extraction of ²³³U from the core will pose a greater challenge to immature reprocessing technologies.

In the closed Th-U cycle of MCFR, it is recommended to load an appropriate amount of MA at the initial and feed TRU/²³²Th online to improve the ²³³U breeding capability and MA transmutation performance. In addition, when the online reprocessing technology is mature, it can be considered to extract ²³³U from the core online under the premise of ensuring safety to further improve the capability of breeding and transmuting more MA.