Comparative Study on the Neutronic Performance of Thermal and Fast Molten Salt Reactors under Once-Through Fuel Cycle

Yu, Changqing; Zhu, Guifeng; Liu, Yafen; Yan, Rui; Zou, Yang

doi:https://doi.org/10.1155/2023/8875215

International Journal of Energy Research

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Abstract Introduction Methods Results and Discussion Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 8875215 | https://doi.org/10.1155/2023/8875215

Comparative Study on the Neutronic Performance of Thermal and Fast Molten Salt Reactors under Once-Through Fuel Cycle

Changqing Yu,¹Guifeng Zhu,^1,2Yafen Liu,¹Rui Yan,^1,2and Yang Zou^1,2

Academic Editor: Tholkappiyan Ramachandran

Received28 Nov 2022

Revised18 Jan 2023

Accepted03 Feb 2023

Published22 Mar 2023

Abstract

Once-through molten salt reactors have the advantages of easy availability of fuel, nuclear nonproliferation, and low technical difficulty. It is expected to be the earliest commercial molten salt reactor fuel cycle mode. The current research on the neutronic performance of the once-through fuel cycle mainly focuses on the thermal spectrum range, and broader spectrum research needs to be carried out further. In particular, the fuel utilization characteristics of molten salt fast reactors in once-through fuel cycle are not yet clear. In addition, small modular design is one of the trends of molten salt reactor development, and small modular design under thermal and fast spectrum has different advantages and needs further comparative analysis. In this paper, the single lattice, bare reactor, and core with reflector models are used to compare the neutronic performance in once-through fuel cycle from thermal to fast spectrum, which includes burnup, variation of fuel salt composition and volume with burnup, temperature reactivity coefficient, neutron irradiation lifetime, and small modular size. The results show that the burnup increases first, then decreases, and then increases again with the increase of the average lethargy causing fission (EALF). For small-scale molten salt reactors, the difference in fuel utilization under thermal and fast spectra is small. However, for large-scale reactors, the burnup under fast spectrum is significantly higher than that under thermal spectrum. When the EALF is large enough, and the neutron loss ratio is small enough, the breed-and-burn (BNB) fuel cycle mode can be realized, and then, the fuel utilization will be significantly improved. In the fast spectrum reactors, the HN and volume of molten salt change violently because of the longer burnup period. Based on the infinite single lattice model, the temperature reactivity coefficient increases first, then decreases, and increases again with EALF. It is negative over the entire energy spectrum. In addition, the small modular designs are discussed by the bare reactor model, and the neutron irradiation lifetime of the materials is analyzed by the core model with a reflector.

1. Introduction

Molten salt reactors (MSRs) are one of the six candidate reactors of the generation IV advanced nuclear power systems. Molten salt can be used as a coolant or as a fuel carrier. In the core, fission occurs in the fuel salt, and the heat is transferred to the secondary circuit cooling salt through a heat exchanger [1]. Compared with traditional solid-fuel reactors, MSRs have the advantages of high inherent safety, online feeding and reprocessing, simple structure, etc. and have been widely researched in recent years [2].

Due to the characteristics of liquid fuel, MSRs fuel cycle modes can be divided into three types according to the reprocessing methods: online reprocessing, offline batch processing, and once-through fuel cycle. Online reprocessing refers to treating fuel salts during the reactor operation to improve neutron economy and maintain the stability of the physical and chemical properties of the fuel salt. The processed fuel salt is returned to the core online [3]. Online reprocessing is performed at high radioactivity and high decay heat, which is extremely demanding on the equipment and is still in the experimental stage. Offline batch processing means that the fuel salt is processed centrally after a period of reactor operation and the processed salt does not require to be returned to the core in real-time; the process is similar to online reprocessing [4]. Moreover, to reduce reprocessing difficulties, it is generally necessary to decay the fuel salt to a lower level of radioactivity. Once-through fuel cycle means that the fuel salt is no longer subjected to chemical reprocessing during the reactor operation, and only simple reprocessing or no treatment is performed. Simple reprocessing refers to removing gases and insoluble fission products by bubbling and filtering during reactor operation. It avoids the technically complex chemical reprocessing during reactor operation, thus significantly reducing the risk of nuclear proliferation. Therefore, the once-through fuel cycle can reduce capital investment, R&D, and operating costs and is expected to achieve commercial deployment as soon as possible. Oak Ridge National Laboratory (ORNL) first proposed the once-through fuel cycle mode in the 1970s and designed the denatured molten salt reactor (DMSR) [5].

The earliest built molten salt reactor was the Aircraft Reactor Experiment [6] (ARE) and Molten Salt Reactor Experiment [7] (MSRE) operated by the Oak Ridge National Laboratory in the United States. They preliminarily verified the molten salt reactor’s reliability and left many design concepts and experimental data. Various reactor designs have been proposed in the ensuing decades. For thermal spectrum reactors, there are DMSR [5], Molten Salt Breeder Reactor (MSBR) [8], FUJI [4] series reactors, etc. The fuel salts of thermal spectrum molten salt reactors are mainly fluorine salts. The fast spectrum molten salt reactors include Molten Salt Fast Reactor (MSFR) [9] and Molten Salt Actinide Recycler and Transmuter (MOSART) [10] based on fluorine salts, Molten Chloride Fast Reactor (MCFR) [11] and Dual Fluid Reactor (DFR) [12] based on chloride salts, etc. Thermal spectrum molten salt reactor is more mature than fast spectrum reactor technology. MSRE is also a thermal spectrum reactor based on graphite moderation. However, the advantages of the fast spectrum reactor are also evident. For the fast spectrum reactor, a higher conversion ratio can be achieved, the absorption cross-section of neutron poisons is smaller, and the solubility of actinides in chloride salts is higher. Currently, the representative molten salt reactors in the project construction plan are the Thorium-based Molten Salt Reactor (TMSR) of the Chinese Academy of Sciences [13] and the Molten Chloride Reactor Experiment (MCRE) of Terra Energy Company [14]. They belong to thermal spectrum and fast spectrum reactors, respectively. TMSR is designed to realize the effective utilization of thorium and uranium resources in the molten salt reactor through a small and modular design. The task of MCRE is to verify the reliability of MCFR. The further goal is to utilize the advantages of uranium-plutonium conversion under the fast spectrum to achieve efficient utilization of uranium resources.

Molten salt reactors have different fuel utilization characteristics under different neutron spectra, and each has its advantages. Before this, fuel utilization studies for small modular molten salt reactors have been performed [15]. The fuel utilization of molten salt reactors is optimized and analyzed according to different molten salt components and volume fractions [16, 17], but only in the case of thermal spectrum under the once-through fuel cycle mode. Furthermore, Small Modular Molten Salt Reactor design is one of the key directions in the development of molten salt reactors. This design has the advantages of high outlet temperature, flexible deployment areas, and economic advantages. Currently, research on molten salt fast reactors is mainly focused on high power and large core sizes to emphasize their breeder capabilities, comparison between the neutronic performance of small molten salt reactors under the thermal and fast spectrums is not involved. In order to study the neutronic performance in different energy spectra, more work needs to be done.

The neutronic performance of molten salt reactors under different energy spectrums in once-through fuel cycle, including fuel utilization characteristics, heavy metal mole fraction, and volume of fuel salt, is deeply studied in this paper. To study these issues, a single lattice, bare reactor structure, and core with reflector models are used, and three fuel salts are selected, which are LiF-BeF₂-UF₄, LiF-UF₄, and NaCl-UCl₃. The molten salt volume fraction (VF) is changed by increasing the size of the molten salt channel of the single lattice until VF to 100% for a broader energy spectrum range as soon as possible. When VF is less than 100%, LiF-BeF₂-UF₄ salt is used, and when it is equal to 100%, three fuel salts are used simultaneously. In order to further subdivide the energy spectrum in the fast spectrum, different initial heavy metal mole fractions (HN₀) were set for the LiF-UF₄ and NaCl-UCl₃ fuel salts. For a more general conclusion, a neutron loss ratio (NLR) of 0%-23.1% is considered in the burnup analysis. Therefore, even though single lattice models are used, the effect of neutron loss from the core is also taken into account using the neutron loss ratio. On the whole, the fuel utilization characteristics of molten salt reactors under different energy spectra and different neutron loss ratios are analyzed by the single lattice models. The volume and HN of fuel salts change with burnup, temperature reactivity coefficients, etc. under different energy spectra are also analyzed by the single lattice model. In addition, the small modular molten salt reactor design under different energy spectra is discussed by the bare reactor model, and the neutron irradiation lifetime of the materials is analyzed by the core model with a reflector. These analyses can show the variation laws of neutronic performance under different energy spectra, in particular the difference between the thermal and fast spectra.

2. Models and Methods

The single hexagon lattice model can be used to study the fuel utilization characteristics of molten salt reactors without considering the complex core design. In our previous work, the single lattice model was adopted for burnup analysis and compared it with the core model, which proves that the single lattice model is effective for burnup analysis to explore the fuel utilization rule [18]. Figure 1 is a schematic diagram of the model. Adjust the molten salt channel size to change VF until VF equals 100%. The lattice will have a different spectrum with different VF or channel sizes. And the larger the VF is, the harder the spectrum will be. The lattice pitch is chosen as 20 cm, and the reactor will have a well-negative temperature reactivity coefficient and well space self-shielding effect [18]. The whole reflection boundary condition is used in the neutron transport calculation, and there is no neutron loss. However, different degrees of neutron loss will exist in the actual reactor due to the leakage and absorption of various structural materials. The neutron loss ratio (NLR) is related to core size and structural design. In order to simulate the conditions of different neutron loss ratios, the effective multiplication factor () equivalent method is adopted. For example, when is equal to 1.1, it means that there is a 9.1% neutron loss. This paper will consider 0%-23.1% NLR. More analysis using a bare reactor and a core with a reflector will be described in the later sections.

The fuel salts used in molten salt reactors are mainly divided into fluorine salts and chlorine salts. Fluoride salts can be used for thermal and fast spectra. In contrast, chlorine salts are primarily used for fast spectra, and generally, chlorine salt reactors have a harder energy spectrum than fluorine salt reactors. The study on fuel utilization in this paper involves the full energy spectrum range, so not only single lattice models with different VF are used, but also different molten salts are selected. LiF-BeF₂-UF₄ salt is used in the graphite moderation model (), and the initial heavy metal mole fraction (HN₀) is 10%. While LiF-UF₄ is used in the model without graphite moderation (), and the HN₀ range is 15% to 25%. The reactor will have different spectra under different HN₀ because the neutron moderating abilities of molten salts are different. The larger the HN₀, the weaker the moderation ability of molten salt and the harder the energy spectrum. In both fluoride salts, is maintained constant by the online feeding of 72LiF-28UF₄ salt. Similarly, NaCl-UCl₃ is also used in the model without graphite moderation (), and the HN₀ range is 25% to 40%. is maintained constant by the online feeding of 50NaCl-50UCl₃ salt. This study adjusts the uranium enrichment of the initial fuel salt according to the set value of or NLR, and the uranium enrichment of makeup salt is 20 wt%. According to the characteristics of molten salts, different molten salt temperatures are set, and the temperatures of the three molten salts are 900 K [16], 1023 K [18], and 960 K [19] in turn. Because of the limited solubility of FLiBe carrier salt for heavy metal nuclides, the upper limit of HN in the burnup process is set to 12% [15]. However, for LiF and NaCl carrier salts, HN of the initially molten salts and the makeup salts are both less than the solubility limit at the corresponding temperature, so this limit is not set. The density of molten salts are calculated from the densities of unit salts [20] by volume-weighted average [21]. The density of graphite is 1.86 g/cm³. Molten salt has a power density of 40 MW/m³. The enrichment of ³⁷Li and ³⁷Cl are 99.995 at% and 95 at% [19], respectively. In addition to feeding makeup salt online to maintain reactor criticality during burnup, gas and insoluble fission products can be removed by bubbling and filtration, such as Kr, Xe, and Mo, assuming that the removal period is 30 s [3]. The detailed parameters of the lattice and molten salts are shown in Table 1.

The research range of once-through fuel utilization can be extended from the thermal spectrum to the fast spectrum by the change of molten salt volume fraction (VF) in the graphite moderation model and initial heavy metal mole fraction (HN₀) in the pure molten salt model, VF and HN₀ are defined as follows: where and are the volumes of molten salt and graphite, N_H(0) and N(0) are the initial mole of heavy metal and carrier salt, respectively. Correspondingly, the mole fraction of heavy metals during burnup is: where N_H() and N() are the heavy metal and carrier salt mole at , respectively. HN can reflect the solubility limit of molten salt and is one of the significant variables in the burnup process.

The energy of the average lethargy causing fission (EALF) can be used to characterize the softness and hardness of the reactor’s neutron energy spectrum, the larger the EALF, the harder the energy spectrum [22]. EALF is defined as follows: where and are the energy-dependent neutron flux and macroscopic fission cross-section, respectively.

Due to online refueling, the burnup is the total fission energy per cumulative loaded uranium mass. In order to compare the fuel utilization among different uranium enrichments, the burnup can be converted to the natural uranium burnup, expressed as follows: where , , and are the power (MW), initial uranium mass (kg), and uranium feeding rate (kg/d), respectively. is the mass ratio between natural uranium and enrichment uranium, assuming that the depleted uranium enrichment is 0.2%. Another expression for burnup is FIMA (Fissiong per Initial heavy Metal Atom); FIMA represents the consumption ratio of heavy metal nuclides, expressed as follows: where HM₀ and HM are the number of heavy metal atoms at the initial and time , respectively. HM_feed is the fed number. Heavy metal elements with atomic numbers greater than 89 in this study are included in the calculation of FIMA.

For molten salt fast reactors, fuel self-sustaining can be achieved in once-through fuel cycle due to the better fuel breeder. The neutron balance method can analyze whether the reactor fuel is self-sustaining or not, which can be expressed as neutron surplus [23]: where is the number of excess neutrons. and are the neutron generation and absorption ratio, respectively. N_HM is the atomic density of the initial heavy metal. (BU), (BU), and NLR are the average number of fission neutrons, the infinite multiplication factor, and the neutron loss ratio, respectively. The neutron loss includes leakage and absorption of structural materials, and BU is the FIMA burnup.

The temperature reactivity coefficient must be negative to ensure the inherent safety of the reactor. The temperature reactivity coefficient of MSRs can be divided into two parts: molten salt and moderator (graphite). The molten salt effect is primarily caused by the density and the Doppler effect. There ignore the graphite density effect and only consider the effect of temperature on neutron diffusion. Therefore, the temperature reactivity coefficient of the molten salt reactor can be expressed as: where and are the reactivity and temperature, respectively, and there is no graphite part in the molten salt fast reactor.

Most of the neutrons produced from fission are absorbed by molten salt and structural materials, and some leak out of the core. The neutron leakage ratio of the reactor can be obtained through the neutron balance theory. When the reactor is critical, the neutron leakage ratio is approximately equal to the following: where and are the diffusion length and geometric buckling, respectively. is related to the diffusion coefficient () and macroscopic absorption cross-section (). is related to the radius () and height () of the reactor. The total absorption reactivity includes the absorption of molten salt, graphite, and other structural materials. Neutron leakage is present in the bare reactor and core with reflector models. However, in the single lattice model, due to the total reflection boundary condition, is used to represent the neutron loss ratio (or neutron leakage ratio).

The burnup calculation in this paper adopts the Molten Salt Reactor Refueling and Reprocessing System analysis code (MSR-RRS) [24] developed based on SCALE6.1 [25]. MSR-RRS has been validated in detail and widely used since its development, proving that the MSR-RRS is reliable for molten salt reactor burnup calculation [26, 27]. In the burnup calculation, is maintained constant by online feeding makeup salt. When the is less than the set value, the makeup salt containing 20 wt% enriched uranium is fed. When the exceeds the set value, the makeup salt containing only ²³⁸U is fed. The set value of is related to the neutron loss ratio. For example, if is set to 1.1, it means that NLR is 9.1%. Figure 2 is the flowchart of MSR-RRS. The uranium enrichment of the initial fuel salt is related to the set value of , that is, to the neutron loss ratio. The ENDF/B-VII database with 238 groups is selected in this paper.

3. Results and Discussion

3.1. Neutron Spectrum

The neutron energy spectrum directly determines the reaction cross-section of each nuclide, which has a pivotal influence on the fuel utilization of the reactor. From the graphite-moderated fluoride salt reactor to the unmoderated chloride salt reactor, the neutron energy spectrum spans a great deal. In order to have a more intuitive understanding, the neutron energy spectrum under some VF and HN₀ is shown in Figure 3, where NLR is 0%. For LiF-BeF₂-UF₄ salt, the VF range is 5%-100%, and the neutron energy spectrum spans the widest range from thermal to epithermal and then to fast spectrum. Compared with LiF-BeF₂-UF₄ salt, LiF-UF₄ has no BeF₂ and has a higher mole fraction of heavy metals, so the energy spectrum is also harder. Compared with fluorine salt, NaCl-UCl₃ has a weaker neutron moderating ability, and HN₀ is significantly higher than that of fluorine salt, so the energy spectrum is harder. In addition, compared with chloride salts, ¹⁹F has strong neutron absorption peaks at 0.027 MeV, 0.049 MeV, 0.272 MeV, and 0.421 MeV, so the neutron spectrum of fluoride salts has several concave regions accordingly, as shown in Figure 3.

The energy of the average lethargy causing fission (EALF) can numerically characterize the energy spectrum’s degree of softness and hardness. The larger the EALF, the harder the energy spectrum. Figure 4 shows the EALF of FLiBe salt at different VF and LiF/NaCl salts at different HN₀, where the NLR is 0%. It can be seen from Figure 4 that with the increase of VF and HN₀, the EALF gradually increases. That is, the energy spectrum gradually becomes harder. Among them, under the FLiBe carrier salt, the VF increases from 5% to 100%, and the EALF increases by about four orders of magnitude correspondingly. The EALF under the LiF carrier salt is about one order of magnitude higher than that under the FLiBe carrier salt. The EALF under NaCl carrier salt is about one order of magnitude higher than that under LiF carrier salt. Therefore, EALF spans about six orders of magnitude in the study of fuel utilization, covering a relatively wide energy spectrum.

3.2. Burnup

One of the main contents analyzed in this paper is the fuel utilization of molten salt reactors under different energy spectrums based on the once-through fuel cycle. Figure 5 shows the natural uranium burnup curves of three molten salts under different VF, HN₀, and NLR conditions. Since the 12% solubility upper limit of the heavy metal in FLiBe carrier salt is set, the natural uranium burnup is the value when HN reaches the solubility limit. For LiF and NaCl carrier salts, no solubility limit is set, and the natural uranium burnup is the maximum value during burnup. First of all, it can be seen that with the increase of EALF (or the increase of VF and HN₀), the natural uranium burnup first increases, then decreases, and then increases again. There is a local maximum value in the thermal spectrum region when . The main reason is that when VF is small (about less than 10%), the lattice is in an excessively slowed state, and the graphite absorption accounts for a large proportion, which is not conducive to fuel utilization. When VF is large (about more than 20%), the neutron absorption reactivity of ²³⁸U increases significantly caused by the hardening of the energy spectrum, which is not conducive to the fission absorption reaction, and the burnup begins to decrease [16]. As the EALF gradually increased to the fast spectrum region, the breeder of uranium and plutonium showed a clear advantage, and the burnup starts to increase. On the whole, the burnup in the thermal spectrum region has a local maximum value in the range of , the local maximum is approximately 8 MW·d/kgU_nat, similar to the finding of Tan et al. [16]. The burnup has a local minimum value of burnup in the epithermal spectrum region, which is not conducive to the utilization of fuel. In the fast spectrum region, the burnup increases gradually with the increase of the EALF, and the burnup of chloride salt is larger than the maximum value in the thermal spectrum region with the same NLR.

Burnup decreases with the increase of NLR. For fluoride carrier salt, the natural uranium burnup is less than 0.1 MW·d/kgU_nat when the NLR is equal to 23.1%, and the VF exceeds 30%. It is because that feeding makeup salt with 20 wt% enriched uranium online cannot maintain the criticality of the lattice (actually , we use to simulate neutron loss as described in Section 2). Figure 6 shows the of the makeup salts (72LiF-28UF₄ and 50NaCl-50UCl₃), and the uranium enrichment of the initial fuel salts under different EALF. It can be seen that decreases and then increases with the increase of EALF. The of makeup salt begins to be less than 1.3 when the VF is greater than 30% (EALF is approximately equal to 1 eV), and begins to exceed 1.3 again until the EALF is greater than 20 keV (transition to chloride fuel salt). Hence, in the energy region where the of makeup salt is less than 1.3, feeding makeup salt cannot maintain greater than 1.3. At the same time, the uranium enrichment of the initial fuel salt in this energy region is greater than 20 wt%, which further proves that feeding the makeup salt with uranium enrichment less than 20 wt% cannot maintain the greater than 1.3. Therefore, when the NLR is greater than 23.1%, this energy region cannot realize the effective utilization of low-enriched uranium fuel. The local minimum value of the of makeup salt is about 1.15. Correspondingly, VF is about 50% (EALF is about 100 eV), and the fuel utilization effect is the worst. It can also be seen that the natural uranium burnup is the smallest from Figure 5.

When the neutron loss ratio of the chloride salt reactor is relatively small, the criticality of the lattice can be maintained by only supplementing ²³⁸U because of the higher breeding ratio. It is the main reason why the burnup of the chloride salt reactor is significantly higher than that of the fluorine salt reactor under a low neutron loss ratio, as shown in Figure 5. Figure 7(a) is the curve of as a function of burnup (FIMA, uranium consumption percentage) under the infinite single lattice model, and Figure 7(b) is the neutron balance curve. The uranium of several fuel salts contains only ²³⁸U without ²³⁵U, and is not fed online. It can be seen from Figure 7 that the of the chloride salt reactor can be greater than 1. In addition, there is a surplus of neutrons, that is, the chloride salt reactor can realize the breed and burn fuel cycle mode (Breed and Burn, BNB) [28]. The BNB fuel cycle differs from the once-through fuel cycle of fluorine salt. The BNB can realize the long-term self-sustaining burn of the fuel without using online chemical reprocessing and supply of enriched fuel [29]. Therefore, since a long-term self-sustaining burn can be achieved by adding only ²³⁸U for chlorine salt reactors when the neutron loss ratio is low, the natural uranium burnup difference is orders of magnitude higher than that of the fluorine reactor or the chlorine reactor with a high neutron loss ratio, so it is not shown in Figure 5. As can be seen in Figure 7(b), for the chlorine makeup salt, a theoretical uranium utilization of about 92%FIMA can be achieved at a zero neutron loss ratio, which is much higher than that for the FLiBe salt at (about 14% FIMA). Therefore, chlorine salts have different fuel utilization characteristics under different neutron loss ratios due to their hard enough energy spectrum and good uranium-plutonium breeder effect. The BNB mode can be achieved at a low neutron loss ratio. This is related to the molar ratio of heavy metals, for example, if HN is equal to 50%, the BNB mode can be achieved when the NLR is less than 14%. At a higher neutron loss ratio, supplemental enriched uranium is required to maintain criticality, and the natural uranium burnup is much lower than the BNB mode. In addition, BNB fuel cycle mode is not possible for fluorine salts in both thermal and fast spectra. It is worth noting that in solid fuel fast reactors, the fuels at different burnup moments can be combined and split arbitrarily, so it is theoretically possible to establish the neutron generation and absorption equilibrium at any moment, but in molten salt reactors it is difficult to split the molten salt once it is combined, so it is difficult to separate the fuels under deep burnup, which makes the neutron equilibrium too ideal and the actually obtained burnup will be much lower than the theoretical analysis, as studied in more detail by Hombourger et al. [29].

(a)

(b)

Although long-term fuel self-sustaining can be achieved in the BNB mode, the neutron utilization ratio gradually decreases due to the continuous accumulation of fission products, and supplementary enriched uranium is required to maintain criticality when fuel self-sustaining cannot be achieved. Figure 8 shows the curve of natural uranium burnup with time for a neutron loss ratio of 9.1% () and different heavy metal mole fractions for the fast spectra lattices. As can be seen from Figure 8, for the chloride fuel salt, the natural uranium burnup increases linearly with time at the beginning of the period, which is in the BNB mode, and the criticality is maintained by online replenishment of the makeup fuel containing only ²³⁸U. As neutron poisons accumulate in the fuel salt, the BNB mode is broken, requiring supplementation with 20 wt% enriched uranium makeup salt to maintain criticality, and subsequently, the natural uranium burnup begins to decrease with time. It can also be seen that the larger the initial heavy metal mole fraction is, the longer the BNB mode is maintained. This is because the larger the mole fraction of heavy metals, the harder the energy spectrum and the better the uranium-plutonium breeder effect. At the same time, due to the larger initial heavy metal mole fraction, the rate of burn is slower. In contrast, the BNB mode does not exist for fluorine salts at 20% initial heavy metal mole fraction, and the natural uranium burnup reaches a maximum in a relatively short time and is much lower than for chlorine-salt fast reactors. Therefore, the BNB fuel cycle mode exists at a low neutron loss ratio for chlorine salt fast reactors. Moreover, the lower the neutron loss ratio and the higher the mole fraction of heavy metals, the longer the duration of this mode and the higher the natural uranium burnup.

3.3. Heavy Metal Mole Fraction and Molten Salt Volume Change

A prominent feature of molten salt reactors is that their reactivity can be controlled by real-time replenishment of fuel salt during reactor operation. Therefore, the heavy metal mole fraction and volume of molten salt in the reactor are in a state of change due to fuel consumption and molten salt replenishment during operation. Figure 9 shows the evolution of heavy metal mole fraction and relative volume (ratio of real-time volume to initial volume) with time for the three fuel salts, where the FLiBe salt has a molten salt volume fraction of 15% and the LiF and NaCl salts have an initial heavy metal mole fraction of 20% and 35%, respectively. Since the BNB mode exists in the chlorine salt reactor at a low neutron loss ratio, the heavy metal mole fraction and molten salt volume in this mode have different patterns with time. Therefore, only the variations of HN and with time at zero neutron loss ratio are discussed for fluorine salt, while three cases of 0%, 9.1%, and 23.1% neutron loss ratios are discussed for chlorine salt.

(a)

(b)

As can be seen from Figure 9(a), the HN of FLiBe salt gradually increases with time, and the HN exceeds 12 mol% from about the 21st year. The HN of LiF salt changes slowly with time, because the difference between the HN of the makeup salt (72LiF-28UF₄) and the LiF fuel salt (80LiF-20UF₄) is smaller than that of the FLiBe fuel salt (90FLiBe-10UF₄). For NaCl salt, when the neutron loss ratio is 0%, the increase of HN over time is more obvious, because the reactor has a high breeding ratio at a low neutron loss ratio, and more makeup salt (50NaCl-50²³⁸UCl₃) needs to be fed to inhibit the excess reactivity. When the neutron loss ratio is 9.1%, the HN decreases slightly with time, this is because the reactor breeding ratio is slightly greater than 1 at this time, and only a small amount of makeup salt (50NaCl-50²³⁸UCl₃) is required for the reactor to maintain criticality, even at 225 years after that, the BNB mode ends, and only a small amount of makeup salt containing enriched uranium needs to be fed to maintain criticality for a long time, and the consumed heavy metals are larger than the supplemented heavy metals, resulting in a decrease in HN. When the neutron loss ratio is 23.1%, the breeding ratio is less than 1, and an amount of makeup salt containing enriched uranium needs to be supplemented to maintain the criticality of the reactor, and the HN gradually increases.

The burnup process assumes that the total volume of molten salt is equal to the initial volume in the reactor plus the volume of makeup salt. It can be seen from Figure 9(b) that the molten salt volume gradually increases due to the continuous replenishment of the makeup salt. For FLiBe salt, when the HN reaches 12 mol%, i.e., about 21 years, the molten salt volume is about 1.3 times the initial volume, an increase of 30% (when the neutron loss ratio increases, more makeup salt needs to be fed per unit time, the time to reach 12 mol% is shorter, and the volume of the molten salt is also smaller. For example, when the neutron loss ratio is 9.1%, the time is about 10 years to reach 12 mol%, at which time the molten salt volume is about 1.2 times the initial volume, an increase of 20%). For the LiF salt, the molten salt volume increases to about 2.7 times the initial volume in 100 years, which is slightly faster than the FLiBe salt. For NaCl salt, with a neutron loss ratio of 0%, the volume of molten salt increases to about 5.3 times the initial volume in 100 years due to the need to replenish a large amount of makeup salt (50NaCl-50²³⁸UCl₃) per unit time to maintain the criticality; with a neutron loss ratio of 9.1%, the volume of molten salt increases to about 2.2 times the initial volume in 100 years, with a lower growth rate than FLiBe salt, because the reactor breeding ratio is close to 1, requiring less supplemental makeup salt per unit time; with a neutron loss ratio of 23.1%, the molten salt volume increases to about 3.4 times the initial volume in 100 years.

The method used in this paper to perform the burnup calculations is to maintain the reactor criticality by feeding the makeup salt online. For FLiBe salt, due to the 12 mol% dissolution limit, the volume increase of the molten salt is small, only 30% even at a 0% neutron loss ratio, and it is not necessary to consider discharging the increased molten salt out of the reactor during reactor operation. However, for fast-spectrum reactors, since there is no solubility limit or the solubility range is large, the prolonged supplemental addition of salt causes the volume of molten salt to increase to several times the initial volume, and the excess volume needs to be considered for discharge from the reactor for temporary storage or reuse in a new reactor. It should also be noted that for the BNB fuel cycle mode under NaCl molten salt, the volume of the molten salt increases significantly when supplemented with makeup salt (50NaCl-50²³⁸UCl₃) to maintain the reactor criticality due to the relatively large breeding ratio at low neutron loss ratio, and a combination of control rod control methods can be considered to reduce the amount of molten salt supplementation.

3.4. Temperature Reactivity Coefficient

The temperature reactivity coefficient is one of the key parameters in the physical design of the reactor and must be negative to ensure the inherent safety of the reactor. Figure 10 shows the initial temperature reactivity coefficients for different spectrums, including density, Doppler effect, graphite, and total values, where the neutron loss ratio is 0%. From Figure 10, it can be seen that the total temperature reactivity coefficient tends to increase, then decrease and then increase again with the increase of EALF, and is negative throughout the energy spectrum. Among them, in the graphite moderation model, the graphite temperature reactivity coefficient increases with the EALF until it approaches zero. This is due to the weakening of the graphite moderation effect as the volume fraction of molten salt increases. When the molten salt volume fraction is small, the lattice is in the over-moderated state and the density reactivity coefficient is negative. When the molten salt volume fraction is large, the lattice is in the under-moderated state and the density reactivity coefficient is positive. The density reactivity coefficient has a maximum value at EALF approximatively equal to 1 eV, mainly because the resonance absorption of ²³⁸U is obvious in this energy region. In the fast spectral region, both graphite and density reactivity coefficients are approximately equal to zero due to the absence of graphite. The Doppler effect is mainly related to the resonance absorption cross-section of ²³⁵U and ²³⁸U, and the resonance absorption is obvious in the super thermal spectrum, so the Doppler reactivity coefficient tends to decrease first and then increase with EALF. Overall, the total temperature reactivity coefficients are relatively close at less than -3 pcm/K for the FLiBe thermal and LiF fast reactors, and slightly worse at about -2 pcm/K for the NaCl fast reactors. Moreover, the calculations of temperature coefficients in this paper do not take into account the effect of neutron leakage because of the density change for actual reactors, which have a significant effect on the temperature reactivity coefficients. The influence is greater in the fast reactors and smaller in the thermal reactors [18, 27]. For example, the theoretical temperature reactivity coefficients of the 2500 MWe chlorine-salt fast reactor in the UK [11] and the REBUS-3700 reactor in France [19] are both -6 pcm/K, indicating that the chlorine-salt fast reactor has a high negative temperature reactivity coefficient. Therefore, both thermal and fast molten salt reactors can have a large negative temperature reactivity coefficient, which is one of the advantages of molten salt reactors.

3.5. Neutronic Performance under Small Modular Size

The small modular design has been one of the trends in the development of molten salt reactors. Due to its liquid fuel, high temperature, and lack of need for water as a coolant, SM-MSR is more suitable for commercial applications. “Small” refers to a reactor with electrical power in the range of 10 MWe-300 MWe. Compared to GWe commercial reactors, low power can be applied to scenarios where large reactors cannot be applied, and the deployment areas are much broader. “Modular” means that multiple identical modules can be manufactured and the design simplified, making the SM-MSR (Small Modular Molten Salt Reactor) economically comparable to large commercial reactors [30]. Generally, “Small Modular” prefers a small core size design [31]. Therefore, the small modular design imposes requirements on both core size and power [32]. This section will focus on this issue to analyze the physical parameters of the core in once-through fuel cycle, including the neutron leakage ratio versus core size, the burnup at different core sizes, and the initial fuel loading and burnup time for thermal and fast reactors at low power.

As studied in Section 3.2, the neutron loss ratio plays a very critical role in the utilization of fuel under different energy spectrums, and the higher the neutron loss ratio, the lower the utilization of fuel. Neutron losses are mainly due to absorption by structural materials and leakage, and are related to the structural design of the reactor and the size of the core [33, 34]. In order to investigate the neutron loss ratio of the reactor at different energy spectra with the core size, the bare reactor model is chosen as the object of study, i.e., a model containing only the active zone of the core without the reflector, BC₄ absorber layer, and metallic structural materials. The height of the core is the same as the diameter size, as shown in Figure 11. This way the neutron losses come mainly from leakage in the core, making the calculations simplified. According to the analysis of burnup in Figure 5 at different energy spectra, a molten salt volume fraction of 15% and a heavy metal mole fraction of 10% are chosen for the thermal spectrum. For the fast spectrum, a heavy metal mole fractions of 20% and 35% are chosen for two different fuel salts, fluorine and chlorine salts, respectively. To obtain the neutron loss ratio (or leakage ratio) of the core, the core is made critical by adjusting the ²³⁵U enrichment for different core sizes and the neutron leakage ratio is given by the SCALE calculation.

(a)

(b)

As shown in Figure 12, the neutron leakage ratios for different core sizes, as well as the absorption activity, are given separately for the different fuel salt. Firstly, it is clear from Figure 12(a) that the neutron loss ratio decreases with increasing core size. The neutron leakage ratio of the chlorine-salt fast reactor is much higher than that of the LiF fast reactor and FLiBe thermal reactor, while the neutron leakage ratio of the FLiBe thermal reactor is higher than that of the LiF fast reactor. As explained by Equation (8), the neutron leakage ratio is inversely proportional to the total neutron absorption activity (or macroscopic cross-section) of the core. In the thermal spectrum, the total absorption activity consists of graphite and molten salt. In the fast spectrum, the absorption activity originates only from the molten salt. Although the NaCl fast reactor has a higher heavy metal mole fraction than the LiF fast reactor, the former has a smaller total absorption activity and a higher neutron leakage ratio because the EALF of the former is about 23 times that of the latter, and a harder energy spectrum means a smaller neutron absorption cross-section. Moreover, the average neutron diffusion lengths of the cores with NaCl, FliBe, and LiF carrier salts are 0.33, 0.21, and 0.13 m. The geometric buckling is the same for the same core size, so the corresponding neutron leakage ratio can be deduced.

(a)

(b)

As shown in Figure 12(a), when the radius of the bare reactor is 150 cm, the neutron leakage ratios are approximately 29%, 14%, and 6% for NaCl, FLiBe and LiF carrier salts, respectively, combined with Figure 5, corresponding to natural uranium burnup are approximately 1.7, 3.8, and 3.9 MW·d/kgU_nat, respectively (obtained by linear interpolation). 150 cm is close to the size of a small modular reactor, so it can be tentatively concluded that the burnup of small modular fast reactors with chlorine salt is worse than that of thermal reactors. Moreover, the molten salt volume of the chlorine-salt fast reactor is about 21.2 m³ and that of the thermal reactor is only 15% of its volume (only the core active zone is considered), and the initial ²³⁵U enrichment of both is 16.0 wt% and 1.47 wt%, respectively. Converted to natural uranium, both with an initial uranium loading of 1408 t and 14 t, respectively. So, for small modular chlorine salt fast reactors, the initial uranium fuel investment cost is two orders of magnitude higher than for small modular fluorine salt thermal reactors, which is a challenge for commercial deployment. For fluorine salt thermal reactors, it takes only a few years to reach 3.8 MW·d/kgU_nat, while it takes hundreds of years to reach 1.7 MW·d/kgU_nat for chlorine salt fast reactors. According to the analysis in Section 3.3, the volume of molten salt increases several times for a long burn time, which requires consideration of how the fuel is managed. However, if the effect of the reflector is considered, the corresponding natural uranium burnup is 8.2, 5.9, and 4.2 MW·d/kgU_nat for NaCl, FLiBe and LiF carrier salts, respectively. The reflector has a very significant impact on fuel utilization, especially for chlorine-salt fast reactors. As a comparison, when the radius of the bare reactor is 300 cm, the corresponding natural uranium burnup is approximately 76.5, 6.2, and 5.7 MW·d/kgU_nat for the three carrier salts, respectively.

Therefore, combining Figure 12(a) and Figure 5, it can be seen that for the bare reactor model, when the core size is small, there is not much difference in the burnup under the three carrier salts of NaCl, FLiBe and LiF, and the latter two are more close, larger than the first. When the core size is large, i.e., the neutron leakage ratio is small, the burnup is much higher than the other two carrier salts due to the presence of the BNB mode under the NaCl carrier salt. It is important to note that the actual reactor design includes reflectors, absorbers, and other structural materials and that most of the neutrons are reflected into the core by the reflectors, so the neutron utilization is higher than in the bare reactor model [35]. However, the results in this section are of more general interest and can be used as a reference for more detailed reactor designs.

3.6. Neutron Irradiation Lifetime Challenge

According to the energy spectrum, molten salt reactors can be divided into molten salt thermal reactor and molten salt fast reactors. The main difference between the two is that molten salt thermal reactors use graphite, ZrH [36], water [37], or other moderator materials to moderate neutrons, and MSRE is a molten salt reactor that uses graphite to moderate. The active zone of a molten salt fast reactor core does not contain moderators, but similar to molten salt thermal reactors, there are structures such as reflectors, shields, and metal containers at the periphery of the core, with the usual reflector structures being graphite, carbonized materials, and alloys. Moderators and structural materials around the core have limited lifetimes due to neutron irradiation, high temperature, and corrosion [29, 38]. The neutron irradiation lifetime of both the graphite moderator and the reflector is correlated with the fast neutron flux. The lifetime of graphite moderators ranges from about 2.5 to 30 years depending on the maximum fast neutron flux [39], Terrestrial Energy designed 400-MWth Integrated Molten Salt Reactor (IMSR) with a graphite moderator life of 7 years, where the fuel power density is 86.7 MW/m³ [40], Japanese FUJI-U3 reactor has a graphite moderator life of 30 years through a three-zone core design, where the fuel power density is 23.5 MW/m³ [41]. Although molten salt fast reactors do not have graphite moderators, the reflector material lifetime is also limited by neutron irradiation, which can be estimated by displacement-per-atom (DPA) [42].

In this section, the core model including the reflector is used to simulate the fast neutron flux changes in the graphite moderator or reflector under different energy spectra. The core model is shown in Figure 13. To ensure the consistency of the model, the radial and axial dimensions of the core remain the same, with a diameter and height of 388 cm, where the thickness of the reflector is 30 cm. It is close to the size of small modular reactors. The neutron energy spectrum is altered only by changing the size of the graphite slowing channel or the mole fraction of the molten salt heavy metal. Regardless of the spectrum, the reactor’s total power remains constant at 400 MWth.

(a)

(b)

Figure 14 shows the distribution of fast neutron flux () in the radial direction under the three molten salts, with the axial direction in the middle. The VF under FLiBe carrier salt is 15%, and the HN under LiF and NaCl carrier salts is 20% and 35%, respectively. The three curves represent the radial fast neutron flux distribution in the thermal and two fast spectrum models, respectively. The figure shows that firstly the fast neutron flux decreases from inside to outside along the radial direction. The fast neutron flux distribution is most uniform under the LiF carrier salt. The central fast neutron flux under the thermal spectrum is similar to that at the inner boundary of the reflector under the NaCl carrier salt, i.e., the irradiation of the moderator and reflector by the fast neutron flux is similar for both, and this value is much higher than that at the inner boundary of the reflector under the LiF carrier salt. However, it should be noted that the fast neutron flux under the graphite moderation model can be flattened by optimizing the design. After flattening, the central fast neutron flux can be greatly reduced [4].

The distribution of fast neutron fluxes along the radial direction differs at different energy spectra. In the graphite moderation model, the neutron irradiation lifetime is mainly determined by the central maximum fast neutron flux, whereas in the fast spectrum model with pure molten salt, the neutron irradiation lifetime is mainly determined by the fast neutron flux at the inner boundary of the reflector. Figure 15 shows the fast neutron flux distribution at different energy spectra, where the fast neutron flux for the graphite moderation model (FLiBe carrier salt) is at the central graphite and the values for the fast spectrum of the pure molten salt model (FLiBe/LiF/NaCl three carrier salts) are at the inner boundary of the reflector. According to Figure 15, the fast neutron flux decreases and then increases across the full energy spectrum (a decreasing trend with the same carrier salt). For the same carrier salt, the fast neutron flux decreases as the VF or HN increases. This is due to the reduction in neutron flux caused by an increase in fuel charge with the same total volume and power of the core [43]. Therefore, under the same core volume and power, the material neutron irradiation lifetimes for the FLiBe carrier salt in the thermal spectrum and NaCl are comparable and smaller than those of LiF carrier salts. Although the core volumes in the thermal and fast spectra are the same, the fuel salt volumes differ significantly. However, material lifetimes in contact with molten salts are not only affected by neutron irradiation but also by high temperatures, corrosion, and helium embrittlement [44, 45]. Therefore, the development of novel high-temperature-resistant, corrosion-resistant, and radiation-resistant materials are crucial for the development of molten salt reactors.

4. Conclusions

Molten salt reactors with different energy spectra have different fuel utilization characteristics and utilization efficiencies based on once-through fuel cycle with low-enriched uranium. The fuel utilization, heavy metal mole fraction (HN), molten salt volume, and temperature reactivity coefficients of three fuel salts at different molten salt volume fractions (VF) and different initial heavy metal mole fractions (i.e., at different energy spectra), as well as at different neutron loss ratios, are investigated using single lattice models, and further investigated the small modular and neutron irradiation lifetime using bare reactors and core with reflector models. The following conclusions are drawn: (1)For the same neutron loss ratio, the burnup tends to increase, then decrease, and then increase again as the energy of the average lethargy causing fission (EALF) increases. Specifically, in the thermal spectrum region, there are local maximum values of natural uranium burnup when VF is in the 10%-15% range, the natural uranium burnup can be greater than 8 MW·d/kgU_nat, which is favorable for fuel utilization. In the epithermal spectrum region, the burnup is extremely low, and the natural uranium burnup is less than 1 MW·d/kgU_nat, which is not conducive to fuel utilization. In the fast spectrum region, for the same neutron loss ratio, the burnup is higher than in the thermal spectrum region when the EALF increases in the chlorine salt fast spectra region, while the burnup in the fluorine salt fast spectra region is lower than in the hot spectrum region(2)For chlorine salt fast reactors, fuel utilization has different characteristics because the energy spectrum is sufficiently hard and the uranium-plutonium breeder is more effective. When the neutron loss ratio is low, the BNB fuel cycle mode can be realized, and the burnup is much higher than that of the fluorine salt reactor. As the neutron loss ratio increases and the HN₀ decreases, the duration of the BNB mode will decrease until the BNB fuel cycle mode cannot be achieved(3)In the thermal spectrum region, the burnup time is short, and the heavy metal mole fraction and volume of the fuel salt vary less. In the fast spectra region, the burnup time is long, and the heavy metal mole fraction and volume of the fuel salt vary considerably. The exponential increase in volume requires consideration of the operating mode of the reactor, such as discharge salt to enable a new reactor or to refuel another reactor(4)The temperature reactivity coefficient tends to increase, then decrease, and then increase again with EALF, and is negative over the entire energy spectrum(5)For small modular reactors, there is not much difference in the burnup between fluoride salt thermal reactor and chlorine salt fast reactor, the former is smaller than the latter. The higher burnup of small modular chlorine salt fast reactors comes at the cost of higher initial fuel investment costs and longer-term fuel management planning requirements. For large core sizes, the burnup is much larger than the fluoride carrier salts due to the presence of the BNB mode under the NaCl carrier salt, but this requires a very large volume of fuel salt(6)With the same core and power, the maximum fast neutron flux of the thermal spectrum core is similar to the maximum fast neutron flux of the inner boundary of the reflector in the NaCl fast reactor and higher than that of the LiF fast reactor

Overall, for the once-through fuel cycle mode, the fuel utilization of chlorine-salt fast reactors is higher than that of fluoride salt reactors. And BNB fuel cycle mode exists for chlorine-salt fast reactors at a low neutron loss ratio, the fuel utilization is much higher than that in the non-BNB mode. But, for molten salt fast reactors, the volume and heavy metal mole fraction of fuel salt varies greatly with burnup. In addition to this, the large molten salt volume under the fast spectrum is also a challenge for large-scale commercial deployment. Temperature reactivity coefficients do not seem to be a problem for molten salt reactors, either in the fast or thermal spectra. The maximum fast neutron flux at the inner boundary of the reflector in the fast reactor is comparable to the maximum fast neutron flux at the center of the thermal reactor, but the material is simultaneously subject to corrosion, helium embrittlement, and other factors that require to be further studied.

Data Availability

The data used to support the findings of this study have been deposited in (https://osf.io/5u278/).

Conflicts of Interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Acknowledgments

This study is supported by the National Natural Science Foundation of China (No. 12005290), the Youth Innovation Promotion Association of the Chinese Academy of Sciences (No. 2020261), and the Shanghai Pilot Program for Basic Research–Chinese Academy of Sciences, Shanghai Branch (JCYJ-SHFY-2021-003).

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