Transmutation and Breeding Performance Analysis of Molten Chloride Salt Fast Reactor Using a Fuel Management Code with Nodal Expansion Method

: The transmutation of transuranic (TRU) elements produced by pressurized water reactors (PWRs) can effectively reduce their radioactive hazards. The molten chloride salt fast reactor (MCSFR) is a type of liquid-fueled molten salt reactor (MSR) using fuel in the form of molten chloride salts. The MCSFR utilizing a fast neutron spectrum and high actinide fraction is considered to be a potential reactor type for TRU transmutation. An online refueling and reprocessing scenario is the unique feature of liquid-fueled MSRs. On account of this characteristic, a new fuel management code named ThorNEMFM with a nodal expansion method (NEM) was developed and validated with the molten salt breeder reactor (MSBR) and the molten salt fast reactor (MSFR) benchmarks. Then, the transmutation and breeding performances of the MCSFR were simulated and analyzed with the ThorNEMFM code. The MCSFR adopts TRU elements as initial ﬁssile loads and online feeding ﬁssile materials. The results show that the transmutation ratio of TRU elements in the MCSFR can reach 50%, and the breeding ratio can reach 1.359. Moreover, the MCSFR has low radiotoxicity due to lower buildup of ﬁssion products (FPs).


Introduction
The transuranic (TRU) waste produced by pressurized water reactors (PWRs) is highly radioactive, and can remain radiotoxic for thousands of years [1].The transmutation of TRU elements can effectively reduce their radioactive hazards [2,3].The fast reactor is considered to be an ideal TRU transmutation system because of its hard neutron spectrum [4,5].Several types of fast reactors-such as sodium-cooled fast reactors (SFRs) [6], lead-cooled fast reactors (LFRs) [5], and gas-cooled fast reactors (GFRs) [7]-have been investigated for TRU transmutation.
The molten salt reactor (MSR) is one of the six candidate nuclear systems chosen by the Generation IV International Forum (GIF) [8].In the liquid-fueled MSR concepts, fissile and fertile fuel compounds are dissolved in fluoride or chloride carrier salts.The liquid-fueled MSRs can be operated with widely varying fuel compositions due to their online refueling and reprocessing scenario.The initial fissile load can be 233 U, 235 U, enriched natural uranium, or the TRU elements.Therefore, the fast neutron spectrum liquid-fueled MSRs have been investigated for the TRU transmutation and breeding.The molten salt actinide recycler and transmuter (MOSART) is a liquid-fueled fluoride-based fast-spectrum MSR concept designed for TRU incineration by the Kurchatov Institute of Russia [9].With a pure TRU loading during 100 years of operation, the MOSART can achieve an approximate 83% TRU transmutation ratio [9].The Laboratoire de Physique Subatomique et de Cosmologie (LPSC) proposed a 3000 MWth fluoride-based molten salt fast reactor (MSFR) concept with TRU elements and Th as initial fuel materials [10].The MSFR can burn about 690 kg of Energies 2022, 15, 6299 2 of 15 TRU elements and simultaneously produce 173 kg of 233 U per year.The chloride-based fast spectrum MSRs can provide harder spectra and a higher actinide fraction compared to fluoride-based fast-spectrum MSRs.Although the interests of research on chloride-based fast-spectrum MSRs currently focus on the breed-and-burn fuel cycle capability-such as the molten chloride fast reactor (MCFR) developed by TerraPower, LLC [11] or the breedand-burn molten salt reactor (BBMSR) proposed by the University of Cambridge [12]-the transmutation ability of chloride-based fast-spectrum MSRs is still worth researching.
On account of the special features of liquid fuel in liquid-fueled MSRs, many fuel management codes for liquid-fueled MSRs were developed over the past few years.National Tsing-Hua University developed a special sequence based on SCALE6/TRITON to perform the fuel cycle of MOSART [13].The numerical simulations of MSFRs' evolution performed at the LPSC relied on the coupling of the Monte Carlo code MCNP with a homemade materials evolution code REM [10].The AGH University developed a Monte Carlo Continuous Energy Burnup Code named MCB for numerical modeling of fourth generation reactors [14].The Politecnico di Milano (POLIMI) performed the fuel cycle of the MSFR by extending the Monte Carlo code SERPENT-2 [15].Lots of efforts at fuel management codes based on deterministic methods have also been carried out.A modified ERANOS-based EQL3D procedure has been employed to analyze the fuel cycle performances of the MSFR in POLIMI [16].The HELIOS code system is used in Helmholtz-Zentrum Dresden-Rossendorf (HZDR) to analyze the transmutation performance of an MSFR [17].Xi'an Jiaotong University (XJU) extended the DIF3D code and coupled it with an in-house nuclide depletion solver to model the fuel cycle of molten salt reactors [18].The Delft University of Technology (TU Delft) assessed the burnup performance of MSFRs by coupling the three-dimensional diffusion code DALTON with an in-house developed burnup code called LOWFAT [19].The standard exponential matrix methods are widely used in the burnup calculation of liquid-fueled MSRs, such as fourth order Runge-Kutta variable step method adopted in REM, or the Chebyshev rational approximation method (CRAM) adopted in SERPENT-2.The Transmutation Trajectory Analysis (TTA) method is a high-precision depletion algorithm that is an alternative to the standard exponential matrix methods.The MCB code adopts a novel TTA method for burnup calculations and a linear chain method for numerical modeling of burnup systems.
The Monte Carlo code is time-consuming in the fuel cycle simulation of the MSR.The deterministic code could improve the efficiency of neutronics calculation with high accuracy.In this paper, a new fuel management code named ThorNEMFM is developed for the liquidfueled MSRs.The deterministic code ThorCORE3D based on a nodal expansion method (NEM) was employed and coupled with a cross-section processing module and a depletion module.The validation of ThorNEMFM was performed using the molten salt breeder reactor (MSBR) and the MSFR benchmarks.The evolution of the heavy nuclei inventories and breeding performance were compared with the reference results.Furthermore, the breeding and transmutation capabilities of the molten chloride salt fast reactor (MCSFR) were analyzed in detail.

Neutronics Models
The deterministic code ThorCORE3D was applied to perform the neutronics calculations.The ThorCORE3D code was developed for liquid-fueled MSRs to model and analyze the flow-field effect of the delayed neutron precursor (DNP) more systematically.The multigroup diffusion theory was used to deduce the neutronics model of the liquid-fueled MSR, Energies 2022, 15, 6299 3 of 15 which consists of three-dimensional time-space multigroup neutron diffusion equations and DNP balance equations, given in Equations ( 1) and (2) for node n, respectively ∂C n j (r,t) ∂t where Φ is the scalar flux; υ is the neutron velocity; D g is the neutron diffusion coefficient; Σ t , Σ f , and Σ g →g represent the macroscopic total cross-section, macroscopic fission cross-section and macroscopic scattering cross-section, respectively; k e f f is the effective multiplication factor; χ p and χ d represent the energy spectra of prompt and delayed neutrons, respectively; β is the total fraction of delayed neutrons; β j is the fraction of delayed neutrons in each group; λ is the decay constant; C is the DNP concentration; u is the fuel salt velocity; and D c,i and D t are the DNP molecular diffusion and turbulent diffusion coefficients, respectively.The backward Euler method and exponential transform were applied to the timedependent terms of the neutron multigroup diffusion equations, and the equations were solved using NEM [20,21].

Depletion Models
The Bateman equation for a particular nuclide in a burnup chain can be written as follows: where N i and N j are the concentrations of nuclide i and nuclide j, respectively; f ji is the fraction of neutron reactions from nuclide j into nuclide i; σ tot j and σ tot i are the microscopic one-group total cross-sections of nuclide j and nuclide i, respectively; φ is the space-energyaveraged neutron flux; γ ji is the branching ratio for the decay of nuclide j into nuclide i; and λ j and λ i are the decay constants of nuclide j and nuclide i, respectively.
The burnup equations described by Equation (3) for all nuclides can be written in a matrix form: where → N is the vector of nuclide concentrations and A is the transition matrix containing the rate coefficients for radioactive decay and neutron absorption.
A fictive decay of time constant [22] was introduced to model and simulate the online reprocessing of liquid-fueled MSRs.It is described as follows: where ε e i is the extraction efficiency of element i, while T r is the time for reprocessing the entire fuel salt.The matrix form of burnup equations could be modified as follows: Energies 2022, 15, 6299 4 of 15 where diag λ f i is the diagonal matrix composed of fictive decay constants, while A is the new transition matrix.
The continuous refueling is another unique feature of liquid-fueled MSRs.A nonhomogeneous term is introduced into the burnup equations, as follows: where → F is the vector of the external nuclide feed rate.The Taylor series expansion method was used to solve Equation (7) in the present study [23].

Calculation Scheme
The calculation flow scheme of the ThorNEMFM code is shown in Figure 1.The homogenized few-group parameters are generated before neutronics calculation.Then, the neutronics calculation and depletion calculation are carried out.It should be noted that the criticality in the reactor is achieved by adjusting the feeding rates of fissile and fertile materials.The depletion library is updated regularly based on the fuel salt composition at the user-specified time points.
where ( ) is the diagonal matrix composed of fictive decay constants, while ′ is the new transition matrix.The continuous refueling is another unique feature of liquid-fueled MSRs.A nonhomogeneous term is introduced into the burnup equations, as follows: where  ⃗ is the vector of the external nuclide feed rate.The Taylor series expansion method was used to solve Equation (7) in the present study [23].

Calculation Scheme
The calculation flow scheme of the ThorNEMFM code is shown in Figure 1.The homogenized few-group parameters are generated before neutronics calculation.Then, the neutronics calculation and depletion calculation are carried out.It should be noted that the criticality in the reactor is achieved by adjusting the feeding rates of fissile and fertile materials.The depletion library is updated regularly based on the fuel salt composition at the user-specified time points.The MSBR project was re-evaluated in LPSC for energy production with thorium [22].The geometric modeling of the MSBR is shown in Figure 2. The diameter and the height of the active core were both 4.6 m.The core was composed of hexagonal graphite assembles with a side length of 15 cm.The radius of the fuel channel was 7.5 cm.The core was surrounded by a 50 cm graphite reflector together with a 1.3 m axial graphite reflector.The FLiBe salt LiF-BeF 2 -(Th/U)F 4 at 70-17.5-12.5 mol% was chosen as the fuel salt.The main design parameters are shown in Table 1.

Description of MSBR
The MSBR project was re-evaluated in LPSC for energy production with thorium [22].The geometric modeling of the MSBR is shown in Figure 2. The diameter and the height of the active core were both 4.6 m.The core was composed of hexagonal graphite assembles with a side length of 15 cm.The radius of the fuel channel was 7.5 cm.The core was surrounded by a 50 cm graphite reflector together with a 1.3 m axial graphite reflector.The FLiBe salt LiF-BeF2-(Th/U)F4 at 70-17.5-12.5 mol% was chosen as the fuel salt.The main design parameters are shown in Table 1.The MSBR online pyrochemical reprocessing unit is described in Figure 3.The rare gases and noble metals were extracted with flowing helium in 30 s.The soluble fission products (FPs) were reprocessed in 10 days.The extraction efficiencies of rare-earth metals and halogens were 20%, with 5% for semi-noble metals and 1% for alkaline elements.Protactinium was extracted with 100% efficiency.The reactor was kept critical within an uncertainty margin of 200 pcm.The molar proportion of actinides in the salt was kept constant (12.5%).The MSBR online pyrochemical reprocessing unit is described in Figure 3.The rare gases and noble metals were extracted with flowing helium in 30 s.The soluble fission products (FPs) were reprocessed in 10 days.The extraction efficiencies of rare-earth metals and halogens were 20%, with 5% for semi-noble metals and 1% for alkaline elements.Protactinium was extracted with 100% efficiency.The reactor was kept critical within an uncertainty margin of 200 pcm.The molar proportion of actinides in the salt was kept constant (12.5%).

Evolution of the Actinides in the Fuel Salt
Figure 4a shows the buildup of uranium isotopes, while Figure 4b shows that of the other actinides.The numerical results of the ThorNEMFM code are consistent with the LPSC results [22].The inventories of heavy nuclei at equilibrium state are listed in Table 2.The short-half-life nuclides (below 10 h) are deleted in burnup calculation in LPSC, which makes the difference between the two codes.

Evolution of the Actinides in the Fuel Salt
Figure 4a shows the buildup of uranium isotopes, while Figure 4b shows that of the other actinides.The numerical results of the ThorNEMFM code are consistent with the LPSC results [22].The inventories of heavy nuclei at equilibrium state are listed in Table 2.The short-half-life nuclides (below 10 h) are deleted in burnup calculation in LPSC, which makes the difference between the two codes.should be described in detail while well-established methods can be briefly described and appropriately cited.
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Results
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Figures, Tables and Schemes
All figures and tables should be cited in the main text as Figure ??, Table 1, Table 2, etc.The breeding ratio (BR) represents the ratio of 233 U's buildup rate and 233 U's total absorption rate [22], and is expressed as follows: where R c indicates the neutron capture rate and R a denotes the neutron absorption rate.The breeding ratio is 1.036 at equilibrium, which corresponds to a 233 U production of 35.9 kg/y.The doubling time (DT), which is the time required to breed an initial 233 U inventory, is 31 y.The breeding performance is in good agreement with the results from LPSC, as shown in Table 3.The standard MSFR is a 3000 MWth fast-spectrum MSR based on the thorium fuel cycle.The MSFR was performed using a binary fluoride salt LiF-(heavy nuclei)F 4 at a 77.5-22.5 mol% ratio.The total fuel salt volume was 18 m 3 , and was distributed half in the core and half in the external circuit.The radial reflector included a 50 cm thick fertile blanket and a 20 cm thick B 4 C reflector.Two kinds of starting modes were employed in this simulation: one was an MSFR directly started with 233 U as the initial material, and the other used the TRU elements contained in a UOX (60 GWd/ton) fuel after one use in a PWR and 5 years of storage.The fuel salt completed a full cycle in 3.9 s, with a mean temperature of 750 • C. Figure 5 shows the overall scheme of the fuel salt reprocessing system, including a salt control unit, an online gaseous extraction system, and an offline lanthanide extraction component via pyrochemistry.The rare gases and some noble metals were extracted with a removal period of 30 s.A fraction of salt (40 L per day) was periodically withdrawn and reprocessed offline in order to extract the other FPs.The FPs of the fertile blanket were slowly removed at a rate of 0.4 L per day.During MSFR operation, the HN fraction was kept constant and the produced FPs replaced an equivalent proportion of the lithium.

Evolution of the Heavy Nuclei
The amounts of the heavy nuclei initially loaded in the 233 U-and TRU-started MS-FRs are detailed in Table 4.The evolutions of heavy nuclei inventories calculated by ThorNEMFM are given in Figure 6.As is shown in the figure, the numerical results of the ThorNEMFM code are in good agreement with the results of XJU and LPSC.The differences were mainly caused by the adoption of different nuclide cross-section data libraries.The inventories of heavy nuclei at equilibrium state in the 233 U-started MSFR are listed in Table 5 [19,24].The results of ThorNEMFM are in between the results of LPSC and TU Delft.The FPs' extraction can be verified by calculating the total mass of FPs in the 233 U-started MSFR as a function of time, as shown in Figure 7.The ThorNEMFM results are consistent with the results of other institutes [18].The equilibrium mass of FPs is 620 kg, and it takes about 6 years to reach the equilibrium state.

Evolution of the Heavy Nuclei
The amounts of the heavy nuclei initially loaded in the 233 U-and TRU-started MSFR are detailed in Table 4.The evolutions of heavy nuclei inventories calculated b ThorNEMFM are given in Figure 6.As is shown in the figure, the numerical results of th ThorNEMFM code are in good agreement with the results of XJU and LPSC.The diffe ences were mainly caused by the adoption of different nuclide cross-section data librarie The inventories of heavy nuclei at equilibrium state in the 233 U-started MSFR are listed i Table 5 [19,24].The results of ThorNEMFM are in between the results of LPSC and TU Delft.The FPs' extraction can be verified by calculating the total mass of FPs in th 233 U-started MSFR as a function of time, as shown in Figure 7.The ThorNEMFM result are consistent with the results of other institutes [18].The equilibrium mass of FPs is 62 kg, and it takes about 6 years to reach the equilibrium state.

Description of the MCSFR
The basic core design of the MCSFR refers to MSFR and REBUS-3700 [25], which is a fast-spectrum reactor with molten chloride fuel.The composition of the fuel salt and the fertile salt is 55 mol% NaCl and 45 mol% (heavy nuclei) Cl4.The main parameters of the MCSFR are listed in Table 6.As shown in Figure 8, the MCSFR is a two-fluid MSR without a graphite moderator.The mix of TRU elements produced in PWRs is used as fissile material to start the MCSFR and keep the core critical during operation.The radial reflector includes a 50 cm thick fertile blanket in order to breed 233 U.The online repro-

Description of the MCSFR
The basic core design of the MCSFR refers to MSFR and REBUS-3700 [25], which is a fast-spectrum reactor with molten chloride fuel.The composition of the fuel salt and the fertile salt is 55 mol% NaCl and 45 mol% (heavy nuclei) Cl 4 .The main parameters of the MCSFR are listed in Table 6.As shown in Figure 8, the MCSFR is a two-fluid MSR without a graphite moderator.The mix of TRU elements produced in PWRs is used as fissile material to start the MCSFR and keep the core critical during operation.The radial reflector includes a 50 cm thick fertile blanket in order to breed 233 U.The online reprocessing system contains an online gaseous extraction system and an online chemical reprocessing system.

Transmutation and Breeding Performance
The transmutation ratio is an important factor to evaluate the TRU transmutation capability of the MCSFR.It can be expressed as follows: where () is the initial TRU loaded mass; () represents the online TRU feeding mass during operation; and () denotes the residual TRU mass after discharge [26].
Owing to the fast neutron spectrum of the MCSFR, the FP capture cross-sections are small, so the transmutation ratio and breeding ratio are only sensitive to the FPs' extraction, as illustrated in Figure 9.A simulated reprocessing rate of 40 L/day was selected for

Transmutation and Breeding Performance
The transmutation ratio is an important factor to evaluate the TRU transmutation capability of the MCSFR.It can be expressed as follows: TRU(transmutation ratio) = TRU(initial) + TRU( f eeding) − TRU(residual) TRU(initial) + TRU( f eeding) Energies 2022, 15, 6299 11 of 15 where TRU(initial) is the initial TRU loaded mass; TRU( f eeding) represents the online TRU feeding mass during operation; and TRU(residual) denotes the residual TRU mass after discharge [26].
Owing to the fast neutron spectrum of the MCSFR, the FP capture cross-sections are small, so the transmutation ratio and breeding ratio are only sensitive to the FPs' extraction, as illustrated in Figure 9.A simulated reprocessing rate of 40 L/day was selected for the subsequent calculation.Table 7 lists the transmutation ratios of TRU elements in the MCSFR compared with other fast reactors [5,27,28].The transmutation ability of MCSFRs is better than that of SFRs and LFRs due to their online feeding and online reprocessing scenario.The transmutation ratio of MOSART is higher than that of MCSFR due to its higher reprocessing rate.Figure 10 shows the total loaded and discharged inventories of TRU nuclides.The inventories of 237 Np, 239 Pu, 240 Pu, 241 Pu, and 241 Am significantly reduce after 100 years of operation, and their transmutation mass is about 300 kg, 2800 kg, 400 kg, 500 kg, and 100 kg, respectively.The inventories of 238 Pu, 242 Pu, 243 Am, 244 Cm, and 245 Cm increase by about 18 kg, 12 kg, 26 kg, 89 kg, and 21 kg, respectively.Figure 10 shows the total loaded and discharged inventories of TRU nuclides.The inventories of 237 Np, 239 Pu, 240 Pu, 241 Pu, and 241 Am significantly reduce after 100 years of operation, and their transmutation mass is about 300 kg, 2800 kg, 400 kg, 500 kg, and 100 kg, respectively.The inventories of 238 Pu, 242 Pu, 243 Am, 244 Cm, and 245 Cm increase by about 18 kg, 12 kg, 26 kg, 89 kg, and 21 kg, respectively.
The simplified depletion chains of actinides are shown in Figure 11.The inventories of 239 Pu and 241 Pu as fissile materials are depleted to maintain criticality of the reactor.The inventories 237 Np, 240 Pu, and 241 Am decrease because of their large neutron capture cross-sections.The increase in 238 Pu inventory can be attributed to the 237 Np (n,γ) reaction and the 242 Cm α decay.Similarly, the increased inventory of 242 Pu is caused by the 241 Pu (n,γ) reaction and the 242 Am α decay.The inventory of 243 Am is mainly accumulated by the 242 Am/ 242m Am (n,γ) reaction and the 243 Pu β − decay.The increased inventory of 244 Cm is caused by the 243 Cm (n,γ) reaction and the 244 Am β − decay.Additionally the mass of 245 Cm is accumulated by the 244 Cm (n,γ) reaction.The amount of TRU elements could reduce rapidly in the MSCFR, but some TRU elements (such as 243 Am and 244 Cm) increase after discharge due to their relatively low fission cross-sections.Those leftovers after discharge would be temporarily stored and then reprocessed when feasible transmutation technologies were available.

SFR
38.75 LFR 14 MOSART 63 MCSFR 50 Figure 10 shows the total loaded and discharged inventories of TRU nuclides.The inventories of 237 Np, 239 Pu, 240 Pu, 241 Pu, and 241 Am significantly reduce after 100 years of operation, and their transmutation mass is about 300 kg, 2800 kg, 400 kg, 500 kg, and 100 kg, respectively.The inventories of 238 Pu, 242 Pu, 243 Am, 244 Cm, and 245 Cm increase by about 18 kg, 12 kg, 26 kg, 89 kg, and 21 kg, respectively.(n,) reaction and the 242 Am  decay.The inventory of 243 Am is mainly accumulated by the 242 Am/ 242m Am (n,) reaction and the 243 Pu  decay.The increased inventory of 244 Cm is caused by the 243 Cm (n,) reaction and the 244 Am  decay.Additionally the mass of 245 Cm is accumulated by the 244 Cm (n,) reaction.The amount of TRU elements could reduce rapidly in the MSCFR, but some TRU elements (such as 243 Am and 244 Cm) increase after discharge due to their relatively low fission cross-sections.Those leftovers after discharge would be temporarily stored and then reprocessed when feasible transmutation technologies were available.The hard neutron spectrum and the related high neutron economy of the MCSFR enable strong breeding ability.The BR in the whole system is 1.359.The uranium produced in the blanket is extracted in 183 days.With a 233 U production rate ~260 kg/y, the MCSFR can quite efficiently produce initial loading of uranium in support of other systems.The initial 233 U inventory of an MSBR is about 1100 kg, or 5060 kg for a 233 U-started MSFR.It would take 5 years and 20 years to breed an initial 233 U inventory for MSBRs and MSFRs, respectively.

Radioactivity Analysis
Radioactivity analysis is an important criterion to evaluate the long-term potential radiological harmfulness of FPs and fuel after discharge.The radiotoxicity is defined as follows: where  is the decay constant of nuclide i,  is the inventory of nuclide i; and  (in Sv/Bq) represents the dose coefficients given by the International Commission on Radiological Protection [29].Figure 12 shows the evolution of the radiotoxicity generated per GWth.yproduced by discharged TRU waste of the MCSFR and other systems [13,22].The Pu elements dominant the radiotoxicity of total discharged TRU wastes.The inventories of Pu elements significantly decrease after 100 years operation of an MCSFR, meaning that the TRU wastes of MCSFRs are obviously less radiotoxic than those of The hard neutron spectrum and the related high neutron economy of the MCSFR enable strong breeding ability.The BR in the whole system is 1.359.The uranium produced in the blanket is extracted in 183 days.With a 233 U production rate ~260 kg/y, the MCSFR can quite efficiently produce initial loading of uranium in support of other systems.The initial 233 U inventory of an MSBR is about 1100 kg, or 5060 kg for a 233 U-started MSFR.It would take 5 years and 20 years to breed an initial 233 U inventory for MSBRs and MSFRs, respectively.

Radioactivity Analysis
Radioactivity analysis is an important criterion to evaluate the long-term potential radiological harmfulness of FPs and fuel after discharge.The radiotoxicity is defined as follows: where λ i is the decay constant of nuclide i, N i is the inventory of nuclide i; and r i (in Sv/Bq) represents the dose coefficients given by the International Commission on Radiological Protection [29].Figure 12 shows the evolution of the radiotoxicity generated per GWth.yproduced by discharged TRU waste of the MCSFR and other systems [13,22].The Pu elements dominant the radiotoxicity of total discharged TRU wastes.The inventories of Pu elements significantly decrease after 100 years operation of an MCSFR, meaning that the TRU wastes of MCSFRs are obviously less radiotoxic than those of PWRs.The inventory of Cm is increased during operation, and provides a major contribution to radiotoxicity in the first 20 years after discharge.However, the radiotoxicity of Cm decreases rapidly due to the decay of 244 Cm.The radiotoxicity of FPs during online reprocessing has a non-negligible impact on the final repository.A loss rate of 10 −5 for TRU elements and 10 −7 for uranium isotopes is assumed during reprocessing.Figure 13 shows the evolution of radiotoxicity of nuclear waste.The radiotoxicity drops to the radioactivity level of natural uranium ore within 300 years.

Conclusions
The fast neutron spectrum MSR is considered to be a potential system for the purpose of TRU transmutation and breeding.The hard neutron spectrum and high actinide fraction of the MCSFR enable a good transmutation and breeding capability.Considering the online refueling and processing of liquid-fueled MSRs, a fuel management code named ThorNEMFM was developed based on NEM.A fictive decay constant method was introduced to simulate online reprocessing, and the continuous refueling characteristic introduced an external term into the burnup equations.The verifications of the ThorNEMFM code were performed using the MSBR benchmark and the MSFR bench- The radiotoxicity of FPs during online reprocessing has a non-negligible impact on the final repository.A loss rate of 10 −5 for TRU elements and 10 −7 for uranium isotopes is assumed during reprocessing.Figure 13 shows the evolution of radiotoxicity of nuclear waste.The radiotoxicity drops to the radioactivity level of natural uranium ore within 300 years.The radiotoxicity of FPs during online reprocessing has a non-negligible impact on the final repository.A loss rate of 10 −5 for TRU elements and 10 −7 for uranium isotopes is assumed during reprocessing.Figure 13 shows the evolution of radiotoxicity of nuclear waste.The radiotoxicity drops to the radioactivity level of natural uranium ore within 300 years.

Conclusions
The fast neutron spectrum MSR is considered to be a potential system for the purpose of TRU transmutation and breeding.The hard neutron spectrum and high actinide fraction of the MCSFR enable a good transmutation and breeding capability.Considering the online refueling and processing of liquid-fueled MSRs, a fuel management code named ThorNEMFM was developed based on NEM.A fictive decay constant method was introduced to simulate online reprocessing, and the continuous refueling characteristic introduced an external term into the burnup equations.The verifications of the ThorNEMFM code were performed using the MSBR benchmark and the MSFR bench-

Conclusions
The fast neutron spectrum MSR is considered to be a potential system for the purpose of TRU transmutation and breeding.The hard neutron spectrum and high actinide fraction of the MCSFR enable a good transmutation and breeding capability.Considering the online refueling and processing of liquid-fueled MSRs, a fuel management code Energies 2022, 15, 6299 14 of 15 named ThorNEMFM was developed based on NEM.A fictive decay constant method was introduced to simulate online reprocessing, and the continuous refueling characteristic introduced an external term into the burnup equations.The verifications of the ThorNEMFM code were performed using the MSBR benchmark and the MSFR benchmark.The heavy nuclei evolution results and breeding performance were compared with the results in the benchmarks.It can be concluded that the ThorNEMFM code is capable of simulating the fuel cycle of liquid-fueled MSRs with good accuracy.
Finally, the ThorNEMFM code was applied to the transmutation and breeding performance analysis of the MCSFR.The transmutation ratio of TRU elements was about 50%, and the breeding ratio was 1.359, amounting to a 233 U production of 260 kg/y.Due to the excellent TRU transmutation capability of the MCSFR, the total TRU radiotoxicity after discharge is much smaller than that of spent PWR fuel, and the radiotoxicity of nuclear waste from online reprocessing has drops to the radioactivity levels of natural uranium ore in 300 years.

Figure 4 .
Figure 4. Evolution of the heavy element inventory for the MSBR: (a) U isotopes and (b) TRU + Pa.

Figure 5 .
Figure 5. Overall scheme of the fuel salt management, including the online gaseous extractio system (top) and the offline reprocessing unit (bottom) [10].

Figure 5 .
Figure 5. Overall scheme of the fuel salt management, including the online gaseous extraction system (top) and the offline reprocessing unit (bottom) [10].

Figure 6 .
Figure 6.Time evolution of the heavy element inventory for the MSFR: (a) 233 U-started and (b) TRU-started.

Figure 6 .
Figure 6.Time evolution of the heavy element inventory for the MSFR: (a) 233 U-started and (b) TRU-started.

Figure 7 .
Figure 7.Total mass of FPs in the 233 U-started MSFR as a function of time.

Figure 7 .
Figure 7.Total mass of FPs in the 233 U-started MSFR as a function of time.

Figure 9 .
Figure 9. Influence of the reprocessing rate on the breeding ratio and transmutation ratio.

Figure 9 .
Figure 9. Influence of the reprocessing rate on the breeding ratio and transmutation ratio.

Figure 10 .Figure 10 .
Figure 10.Total TRU-loaded inventory and residual TRU inventory after discharge.The simplified depletion chains of actinides are shown in Figure 11.The inventories of 239 Pu and 241 Pu as fissile materials are depleted to maintain criticality of the reactor.The inventories 237 Np, 240 Pu, and 241 Am decrease because of their large neutron capture cross-sections.The increase in 238 Pu inventory can be attributed to the 237 Np (n,) reaction and the 242 Cm  decay.Similarly, the increased inventory of 242 Pu is caused by the 241 Pu Figure 10.Total TRU-loaded inventory and residual TRU inventory after discharge.

Table 2 .
Inventories of heavy nuclei at equilibrium state in kg.

Table 2 .
Inventories of heavy nuclei at equilibrium state in kg.

Table 3 .
Breeding performance of the MSBR.

Table 4 .
Initial heavy nuclei inventories of different MSFR starting modes.

Table 4 .
Initial heavy nuclei inventories of different MSFR starting modes.

Table 5 .
Inventories of heavy nuclei at equilibrium state in a 233 U-started MSFR in kg.

Table 5 .
Inventories of heavy nuclei at equilibrium state in a 233 U-started MSFR in kg.