Effect of ³⁷Cl enrichment on neutrons in a Molten Chloride Salt Fast Reactor

Effect of 37 Cl enrichment on neutrons in a Molten Chloride Salt Fast Reactor 1 2 3 first-author https://orcid.org/0000-0002-8082-5250 4 https://orcid.org/0000-0003-0096-1955 2 3 https://orcid.org/0000-0002-0087-7991 1 2 3 corresp Corresponding author, chenjg@sinap.ac.cn Corresponding author, chenjg@sinap.ac.cn chenjg@sinap.ac.cn https://orcid.org/0000-0001-5677-058X 1 2 3 https://orcid.org/0000-0002-7825-2457 1 2 3 University of Chinese Academy of Sciences, Beijing 100049, China University of Chinese Academy of Sciences, Beijing 100049, China Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China CAS Innovative Academies in TMSR Energy System, Shanghai 201800, China CAS Innovative Academies in TMSR Energy System, Shanghai 201800, China Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China A molten chloride salt fast reactor (MCFR) is well suited to fuel breeding and the transmutation of transuranium (TRU) elements owing to its advantageous features of fast neutron spectrum and high TRU solubility. However, the neutron absorption cross section of 35 Cl is approximately 1000 times greater than for 37 Cl, which has a significant impact on the neutron physical characteristics of a MCFR. Based on an automatic online refueling and reprocessing procedure, the influences of 37 Cl enrichment on neutron economy, breeding performance, and the production of harmful nuclides were analyzed. Results show that 37 Cl enrichment strongly influences the neutron properties of a MCFR. With natural chlorine, 233 U breeding cannot be achieved and the yields of S and 36 Cl are very high. Increasing the 37 Cl enrichment to 97% brings a clear improvement in its neutronics property, making it almost equal to that corresponding to 100% enrichment. Moreover, when 37 Cl is enriched to 99%, its neutronics parameters are almost the same as for 100% enrichment. Considering the enrichment cost and the neutron properties, a 37 Cl enrichment of 97% is recommended. Achieving an optimal neutronics performance requires 99% 37 Cl enrichment. Molten salt reactor Molten chlorine salt fast reactor 37 Cl enrichment Th-U fuel breeding 1 Introduction 1 The molten salt reactor (MSR) was selected as one of the six candidate reactors by the Generation-IV International Forum (GIF) for its outstanding features in terms of inherent safety, economics, reliability, and proliferation-resistance [ 1 1 ]. It is the only liquid fuel reactor where molten salt serves as both the fuel and the coolant, implying that no fuel fabrication is needed and online fuel reprocessing can be implemented without stopping the reactor [ 2 2 ]. Furthermore, based on the thorium-uranium fuel cycle, fuel breeding is achievable in both thermal and fast MSRs, which can improve the utilization of nuclear fuel while lowering the production of long-lived radioactive transuranic elements, compared to the uranium-plutonium fuel cycle [ 3 3 ]. An MSR can use fluoride salt or chloride salt as a fuel carrier, depending on which of two reactor types is considered, i.e., a molten fluoride salt reactor or a molten chloride salt fast reactor (MCFR). Owing to the high corrosiveness of the chloride salt, however, most pioneering studies have focused on molten fluoride salt reactors, such as the advanced high-temperature reactor (AHTR) in the USA [ 4 4 ], the molten salt actinide recycler and the transforming system (MOSART) in Russia [ 5 5 ], the FUJI series reactors in Japan [ 6 6 ], and the molten salt fast reactor (MSFR) in France [ 7 7 ]. However, several advantages are still worthy of consideration in assessing the MCFR concept [ 8 8 ]. First, the slowing down of neutrons in chloride salt is not as severe as in fluoride salt, which makes the energy spectrum much harder in a MCFR than in a fluoride salt reactor. This is significantly advantageous for the breeding performance of fissionable nuclides and the transmutation of transuranium elements in a chloride salt fast reactor. In addition, the extraction period of fission products (FPs) can be prolonged because of the small neutron absorption cross section under the fast spectrum in an MCFR. More importantly, the actinides are highly soluble in chloride salt. A large amount of heavy nuclides can therefore be loaded into the chloride salt, which further contributes to the breeding performance and transmutation capacity of an MCFR. Research into chloride salt reactors began in the 1950s at the Oak Ridge National Laboratory (ORNL). The MCFR concept was then proposed, involving NaCl+MgCl 2 +PuCl 3 +UCl 3 as the fissile fuel salt and UO 2 +Na as the solid breeding layer [ 8 8 ]. The breeding ratio (BR) was evaluated as 1.09, which served as a preliminary proof of the feasibility of fuel breeding using chloride salt in fast reactors. In the 1960s, the British Atomic Energy Authority also carried out research into MCFRs [ 9 9 ], in which NaCl+UCl 3 +PuCl 3 was used as the fuel salt and NaCl+UCl 3 as the breeding salt. The evaluated BR attained 1.53, which further proved the aptitude of MCFR for fuel breeding. Chloride salt fast reactors are presently receiving increasing attention worldwide. The Moltex [ 10 10 ] and DFR [ 11 11 ] conceptual designs have been proposed in Britain and Germany, respectively. TerraPower in the USA is also involved in the design of a simple and safe chloride salt fast reactor [ 12 12 ]. In 2011, the Strategic Project "Future Advanced Nuclear Energy–Thorium-based Molten Salt Reactor System (TMSR)" was launched by the Chinese Academy of Sciences (CAS). Its aim was to address the key technical issues of TMSRs and realize the efficient utilization of thorium [ 13 13 ]. Studies were carried out to assess the approaches to thorium fuel utilization for various MSRs, including fuel breeding in a FLiNaK MSFR [ 14 14 ], in an improved MSFR (IMSFR) [ 15 15 ], in a single-fluid double-zone thorium molten salt reactor (SD-TMSR) [ 16 16 ], and in a MCFR [ 17 17 ]. The MCFR results show that the molten chloride salt contributes to the fuel breeding performance, and that NaCl is a more suitable carrier salt than other chloride salts because of its high TRU solubility. However, some problems remain to be addressed in MCFR design [ 18 18 ]. One of these relates to the high corrosiveness of chloride salt, which implies the need for the development and testing of structural materials suitable for providing reliable MCFR components such as the core vessel, pipes, pumps, and heat exchangers. Another issue concerns the 35 Cl atomic-number ratio in chloride. The neutron capture cross section is much greater for 35 Cl than for 37 Cl, implying a deterioration of the breeding performance and of the neutron economy of the MCFR. Furthermore, 35 Cl reacts by (n, γ ) to form 36 Cl, which has a long half-life of 301000 years and is easily soluble in water. Fuel salt leaking is consequently a significant human-health and environmental hazard. 35 Cl can also absorb a neutron to form sulfur [ 19 19 ], which can penetrate the alloy surface, thereby causing sulfur brittleness and hence affecting the mechanical properties of the structural materials. The influences of 37 Cl enrichment on the operation of MCFR must therefore be investigated. In this study, different levels of 37 Cl enrichments, varying from 24.23% to 100%, were analyzed based on the MCFR. A general description of the MCFR and the calculation tools is provided in Sec. 2. In Sec. 3, the influences of 37 Cl enrichment are discussed from the viewpoint of the breeding performance at startup and of depletion over up to 100 years. The results, including the BR, the net production of 233 U, the doubling time (DT), and the production of 36 Cl and S are exhibited. In addition, two safety parameters for all the cases, i.e., the temperature coefficient of reactivity (TCR) and the decayed neutron fraction ( β eff ) are also discussed. Finally, conclusions are given in Sec. 4. 2 General description of the MCFR and analysis methodology 1 2.1 General Description of the MCFR 2 The MCFR model used in this paper is a non-moderated chloride molten salt reactor, which is obtained by modifying the MSFR conceptual design [ 7 7 , 20 20 ]. As shown in Fig. 1 Fig. 1 , there are two molten salt zones in the MCFR, namely the fuel zone and the fertile zone. The fuel zone (the red area in Fig. 1 Fig. 1 ) consists of the active core, the surrounding primary circuit pipe, the heat exchangers, etc. The active core is a compact cylinder with equal diameter and height. The liquid fuel salt is pumped through the core from the bottom to the top and then to the heat exchangers. During this flow, the nuclear heat is transferred from the active core to the heat exchangers and then to the secondary loop. The fertile zone surrounds the active core in both the radial and axial directions, and has a thickness of 70 cm (the blue area in Fig. 1 Fig. 1 ). The fuel salt and the fertile salt are separated by a Ti-based alloy of thickness 2 cm. The activation products of the alloy in a fluoride-salt-cooled high-temperature reactor (FHR) have been studied [ 21 21 ], but further study is still needed in a MCFR to confirm its stability and safety. The graphite reflector surrounding the fertile salt (the yellow area in Fig. 1 Fig. 1 ) is adopted for fertile fuel saving [ 22 22 ]. Outside the graphite reflector, a 10-cm-thick B 4 C layer (the green area in Fig. 1 Fig. 1 ) is arranged for the purpose of absorbing small amounts of neutrons leaking from the reactor. The outermost layer is also made of Ti-based alloy and serves as a supporting structure. The MCFR operates with a thermal power density of 60 MWth/m -3 and the mean fuel temperature is 923 K. The main parameters are listed in Table 1 Table 1 . The fuel salt is 55NaCl-45(Th+U)Cl 4 in mol%, while the fertile salt is 55NaCl-45ThCl 4 . The Th and U in the fuel salt are 232 Th and 233 U, respectively, and their ratio is adjusted so as to maintain the reactor criticality. Because of the small difference in atomic mass between 232 Th and 233 U, the fuel salt and the fertile salt have the same density 3.6 g/cm -3 . There are two noteworthy and important differences between a MCFR and the MSFR. Firstly, the carrier salt changes from LiF for a MSFR to NaCl for a MCFR. The second difference relates to the proportion of heavy metal in the molten salt. (Th+U)Cl 4 can dissolve to a concentration of 45 mol% in chloride salt, while (Th+U)F 4 attains only 22.5 mol% in LiF, owing to the higher solubility of actinides in the chloride salt than in the fluorine salt. 1 1 Parameter 1 1 Value 1 1 Thermal power density (MWth/m 3 ) 1 1 60 1 1 Fuel salt composition (mol%) 1 1 55NaCl-45(Th+U)Cl 4 1 1 Fertile salt composition (mol%) 1 1 55NaCl-45ThCl 4 1 1 Fuel salt temperature (K) 1 1 923 1 1 Fertile salt temperature (K) 1 1 873 1 1 Molten salt density at 923 K (g ⋅ cm -3 ) 1 1 3.60 1 1 Alloy density (g ⋅ cm -3 ) 1 1 8.86 1 1 B 4 C density (g ⋅ cm -3 ) 1 1 2.52 1 1 10 B enrichment (%) 1 1 18.4 1 1 Core diameter (cm) 1 1 500 1 1 Core height (cm) 1 1 500 1 1 Fuel salt volume (m 3 ) 1 1 98 1 1 Fertile salt volume (m 3 ) 1 1 107 1 1 Initial inventory of 233 U (t) 1 1 22.6 1 1 Initial inventory of 232 Th (t) 1 1 391.3 (fuel: 174.4+fertile: 216.9) 1 1 Reprocessing period of the gas and insoluble heavy metal (s) 1 1 30 1 1 Reprocessing period of the fuel salt (L ⋅ d -1 ) 1 1 100 1 1 Reprocessing period of the fertile salt (L ⋅ d -1 ) 1 1 100 2.2 Reprocessing Scheme 2 Online reprocessing and refueling are two outstanding features for MSRs compared with traditional solid-fuel reactors. FP extraction constitutes a significant advantage to the neutron economy and to Th-U fuel breeding, while 233 U fuel could be added into the core without stopping the reactor, which would be beneficial for decreasing the initial excess reactivity and the initial loading of nuclear fuel. In addition, fertile 232 Th is added online to maintain the heavy metals at a constant level, and 233 Pa is also extracted to reduce its neutron absorption. Both of these actions are beneficial to the Th-U breeding performance. The reprocessing diagram shown in Fig. 2 Fig. 2 refers to a MSFR [ 20 20 , 23 23 ]. There are two key processes in the extracting system. The first is the He gaseous bubbling system, which extracts FPs and non-dissolved metals (H, He, N, O, Ne, Ar, Kr, Xe, Rn, Zr, Ga, Ge, As, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, and Sb) mechanically. The removal period is set to 30 s in the calculation. The second is online pyrochemical reprocessing, which extracts soluble FPs from the bypass circuit. UCl 3 and PuCl 3 are first oxidized to UCl 6 and PuCl 6 , respectively, which can be removed in gas form from the liquid salt by distillation; they are reinjected into the core after distillation. Then, most actinides, including Th, Pa, and minor actinides (MA), are extracted by reductive extraction and stored in the stockpile for several months to allow 233 Pa to decay into 233 U. Finally, the carrier salt is recovered through low-pressure distillation technology, leaving the FPs for disposal. At this stage, some of the 233 U is refueled into the core to maintain criticality and any remainder constitutes the net 233 U production. The chemical reprocessing rate is set to 100 L/day, which is much lower than the processing rate of 4600 L/d in a TMSR with a thermal spectrum [ 23 23 ]. Considering the fuel salt and the fertile salt volumes of 98 m 3 and 107 m 3 , the corresponding reprocessing periods are set to 980 d and 1070 d, respectively. 2.3 Calculation tool 2 SCALE6.1 is a comprehensive code package developed by ORNL, which can be used to analyze criticality safety, burn-up, radiation shielding, radioactive source terms, sensitivity, and uncertainty [ 24 24 ]. In this study, the CSAS module was used for the criticality calculation, while TRITON served for the problem-dependent cross-section processing and the multi-group neutron transport calculation. KENO-VI was suitable for the transport calculation. Other modules, such as CENTRM/PMC and BONAMI, were also invoked as required when used to process the cross sections in the resolved and unresolved resonance energy regions, respectively. The ORIGEN-S module was used for the time-dependent depletion and decay calculations in SCALE 6.1. However, it was replaced with MODEC in this study, which can accurately track the evolution of nuclides inside and outside the core. The MODEC program, which includes a high-precision fuel-consumption solver based on the Chebyshev Rational Approximation Method (CRAM) and the improved Transmutation Trajectory Analysis (TTA), ensures the accuracy of the calculation [ 25 25 ]. It considers the unique fuel-consumption characteristics of a liquid MSR and introduces the pseudo-decay factors for online post-treatment. To deal with the non-homogeneous term for the continuous feeding characteristics of liquid MSR, the program adopted two optional methods of numerical integration and augmented matrix to extend the CRAM solver, and the TTA solver was extended by the pseudo-nuclear method to increase the calculation accuracy. To simulate the special burn-up mode of a MSR (online reprocessing), the in-house program TMCBurnup was developed according to the flowchart in Fig. 3 Fig. 3 . First, the parameters of the molten salts and the core geometry are input for initialization. Second, the neutron transportation and depletion are calculated by the TRITON and MODEC modules, respectively, where Pa and FPs are extracted from both the fuel and fertile salts. Third, the 233 U and Th heavy metals are injected into the molten salt to keep the total inventory of actinides constant to maintain the stability of the molten salt, and the molar fraction ratio of 233 U and Th is adjusted to maintain the reactor’s criticality. In this study, the effective multiplication factor ( k eff ) was set to 1.005±0.005 throughout the operation. The number of neutrons per k eff cycle was 10000. The first 15 k eff cycles were skipped to allow the spatial fission source to settle to an equilibrium before obtaining the final k eff estimate by averaging. In total, 285 k eff cycles were executed in the criticality calculation, with an average error of approximately 25 pcm. To verify the TMCBurnup simulation of a fast MSR, we tested it on the basis of the MSFR concept and compared the neutronics parameters such as the evolution of nuclides and the BR in a MSFR using reference values [ 7 7 ]. The comparisons, displayed in Figs. 4 Figs. 4 and 5 5 , show that the TMCBurnup results agree well with the reference values, which proves the reliability of TMCBurnup for calculations for a MSFR. 3 Results and discussion 1 This section investigates different 37 Cl enrichments, ranging from natural enrichment (24.23%) to 100%, based on the MCFR. The results corresponding to the range 95%-100% (especially 97%-100%) are very similar, as displayed by the near overlap of the data in the figure. For clarity, only seven representative lines are plotted. The calculation results corresponding to different 37 Cl enrichments are listed in Tables 2 Tables 2 and 3 3 . First, the 233 U concentration and the BR at startup are given in subsection 3.1, followed by the excess reactivity and the operation period without processing in subsection 3.2. Then, the breeding performance with online reprocessing and the production of 36 Cl and S are given in subsections 3.3 and 3.4, respectively. Finally, the safety parameters, including TCR and β eff , are presented in subsection 3.5. 1 1 37 Cl enrichment (%) 1 1 annual production of 233 U (kg/a) 1 1 BR 1 1 M 0 (t) 1 1 DT (year) 1 1 Nat 1 1 -237 1 1 0.956 1 1 22.42 1 1 - 1 1 70 1 1 156 1 1 1.169 1 1 19.63 1 1 125.38 1 1 90 1 1 228 1 1 1.146 1 1 18.54 1 1 81.43 1 1 95 1 1 263 1 1 1.285 1 1 18.04 1 1 68.43 1 1 96 1 1 270 1 1 1.292 1 1 17.95 1 1 66.52 1 1 97 1 1 277 1 1 1.299 1 1 17.86 1 1 64.47 1 1 98 1 1 280 1 1 1.303 1 1 17.83 1 1 63.68 1 1 99 1 1 283 1 1 1.306 1 1 17.81 1 1 62.93 1 1 100 1 1 284 1 1 1.307 1 1 17.81 1 1 62.71 1 1 37 Cl enrichment (%) 1 1 36 Cl (ppm) 1 1 S (ppm) 1 1 Nat 1 1 948 1 1 802 1 1 70 1 1 558 1 1 361 1 1 90 1 1 256 1 1 141 1 1 95 1 1 97 1 1 62 1 1 96 1 1 66 1 1 46 1 1 97 1 1 36 1 1 30 1 1 98 1 1 22 1 1 20 1 1 99 1 1 13 1 1 12 1 1 100 1 1 11 1 1 9 3.1 233 U concentration and the BR at startup 2 Online refueling allows the critical state to be maintained by adjusting the molar concentration of 233 U. Therefore, the critical concentration of 233 U at startup was explored first for different core radii and 37 Cl enrichments. For Th-U fuel cycle starting with 233 U and 232 Th, the BR is defined as [ 26 26 ]: <math display="block" id="M1"><mrow><mi>B</mi><mi>R</mi><mo>=</mo><mfrac><mrow><msubsup><mi>R</mi><mtext>c</mtext><mrow><msup><mrow/><mrow><mtext>232</mtext></mrow></msup><mtext>Th</mtext></mrow></msubsup><mo>−</mo><msubsup><mi>R</mi><mtext>c</mtext><mrow><msup><mrow/><mrow><mtext>233</mtext></mrow></msup><mtext>Pa</mtext></mrow></msubsup></mrow><mrow><msubsup><mi>R</mi><mtext>a</mtext><mrow><msup><mrow/><mrow><mtext>233</mtext></mrow></msup><mtext>U</mtext></mrow></msubsup></mrow></mfrac><mn>,</mn></mrow></math> where R a and R c denote the neutron capture and absorption rates, respectively. This equation is applied to the calculation for a total BR in core and blanket. At startup, the BR can be simplified as: <math display="block" id="M2"><mrow><mi>B</mi><mi>R</mi><mo>=</mo><mfrac><mrow><msubsup><mi>R</mi><mtext>c</mtext><mrow><msup><mrow/><mrow><mtext>232</mtext></mrow></msup><mtext>Th</mtext></mrow></msubsup></mrow><mrow><msubsup><mi>R</mi><mtext>a</mtext><mrow><msup><mrow/><mrow><mtext>233</mtext></mrow></msup><mtext>U</mtext></mrow></msubsup></mrow></mfrac><mn>.</mn></mrow></math> It should be noted that the initial BR is oversimplified. However, for an MSR with a given reprocessing rate, a greater initial BR also implies a greater BR at equilibrium. Thus, Eq. (2) is still used in this subsection to predict a suitable geometry with a large BR, and the actual 233 U production is analyzed according to mass evolution in subsection 3.3. The initial 233 U concentration and the BR are plotted as functions of the core radius in Fig. 6(a) Fig. 6(a) and Fig. 6(b) Fig. 6(b) , respectively. For a certain 37 Cl enrichment, the 233 U concentration clearly decreases while BR increases with increasing core radius when the radius is less than 250 cm, resulting from the decrease in neutron leakage when the core increases. In other words, an increase in core radius contributes to a decrease in neutron leakage from the fuel salt, and therefore less 233 U is needed to maintain the reactor in a critical state. Simultaneously, more neutrons are absorbed by 232 Th for fuel breeding, while the neutron absorption of 233 U remains nearly constant because of the adjustments of the 233 U molar fraction to maintain criticality. Thus, according to Eq. (1), the BR increases with increasing core radius. When the radius exceeds 250 cm, both the 233 U concentration and the BR remain nearly constant, signifying that the core is sufficiently large and neutron leakage from the fuel salt is sufficiently low. Furthermore, the dependences of the 233 U concentration and of the BR on the core radius show almost the same trends for other 37 Cl enrichments. Therefore, the following study was performed with a core radius of 250 cm. For a certain core radius, the 233 U concentration is also seen to decrease and the BR to increase with increasing 37 Cl enrichment. The reason is that the neutron absorption rate of 35 Cl decreases with increasing 37 Cl enrichment (as shown in Fig. 7 Fig. 7 ) and more neutrons are absorbed by 232 Th and 233 U. This is helpful for fissile fuel saving with the increase of 37 Cl enrichment in the carrier salt. When the 37 Cl enrichment is greater than 97%, the neutron absorption of 35 Cl is very small, which has little impact on neutron economy and the breeding performance. 3.2 Excess reactivity and operation period without processing 2 As mentioned above, for a given core radius, different 37 Cl enrichments correspond to different 233 U concentrations. To explore the neutron characteristics without post-processing, the 233 U concentration was fixed to 5.0 mol%, the critical value for chloride salt with natural enrichment. Then, the effect of 37 Cl enrichment on the initial reactivity and full-power operation period was analyzed (as reported in this subsection). The result with online processing is given in the next subsections. The initial excess reactivity is plotted as a function of 37 Cl enrichment in Fig. 8 Fig. 8 . When the 37 Cl enrichment is 24.23% (natural chloride), the initial excess reactivity is 122 pcm, and it increases to approximately 15823 pcm when the 37 Cl enrichment is 97%. The reason is that the neutron absorption cross section of 35 Cl is very large. With increasing 37 Cl enrichment, the 35 Cl content and hence its neutron absorption rate decrease. Thus, the neutron utilization efficiency improves, which in turn results in an improvement of the excess reactivity. When the 37 Cl enrichment increases to 100%, the initial excess reactivity equals 15858 pcm. This value is almost equal to that corresponding to 97% enrichment, since the 35 Cl content and its corresponding neutron absorption rate are very low and the excess reactivity is less affected by increasing 37 Cl enrichment. Besides, the k eff evolution under full-power operation without post-processing is shown in Fig. 9 Fig. 9 . The operation period is only 175 days when the 37 Cl enrichment is 24.23%, and it increases to 2245 days when the enrichment is 97%, which is almost the same as for 100% enrichment. The trend followed by the full-power operation period with respect to increasing 37 Cl enrichment is very similar to that of the initial excess reactivity. This is also because a decrease in 35 Cl leads to a decrease in its neutron absorption, which further improves the neutron utilization efficiency in the active core and then extends the full-power operation period. When the 37 Cl enrichment exceeds 97%, the operation period remains almost constant because the neutron absorption of 35 Cl is sufficiently low. 3.3 Breeding performance with online reprocessing 2 This subsection explores depletion with online reprocessing from the perspective of the BR, the net production of 233 U, and the doubling time (DT), three important parameters for evaluating the fuel breeding performance in a MSR. As explained in Sect. 2.2, with online reprocessing, 233 U can be added into the core to maintain criticality without stopping the reactor, such that k eff can be maintained between 1.000 and 1.005 throughout the operating time. The parameters that reflect the breeding capability of a MCFR include M 0 , the DT, and the average annual production of 233 U for different 37 Cl enrichments, and are listed in Table 2 Table 2 . Under this condition, the BR is obtained using Eq. (1), as displayed in Fig. 10 Fig. 10 . 37 Cl enrichment clearly plays an important role in the evolution of the BR. Fig. 10 Fig. 10 shows that, for a given 37 Cl enrichment, the BR increases slightly over time, in contrast to a thermal reactor like a MSBR. This is due to the accumulation of 234 U, which has a large neutron fission cross section under a fast spectrum and provides additional neutrons for nuclear fuel breeding. In addition, the FPs produced during the operation have a much smaller absorption cross section in a MCFR than in a thermal reactor, which implies little impact on the MCFR breeding capability. Besides, when chloride with a natural enrichment level is adopted, the BR is even less than 1.0, meaning that more fissile fuel is consumed than produced, and fuel breeding cannot be realized. Increasing 37 Cl enrichment can improve its BR significantly. When 37 Cl enrichment increases to 97%, the BR can be improved to 1.299, which is only 0.6% lower than for 100% 37 Cl enrichment. The net annual production of 233 U was then explored since it is the dominant fissile material in the Th-U fuel cycle. Because of the on-line reprocessing, 233 Pa could be extracted from the active core and from the fertile salt to decay into 233 U. The 233 U obtained from the decay of 233 Pa in the fertile salt was also extracted. The extracted 233 U was partially refueled into the active core to ensure criticality. Thus, the annual net production of 233 U can be expressed as [ 26 26 ]: <math display="block" id="M3"><mrow><mi>M</mi><mo>=</mo><msubsup><mi>M</mi><mrow><mtext>ex</mtext></mrow><mrow><msup><mrow/><mrow><mtext>233</mtext></mrow></msup><mtext>U</mtext></mrow></msubsup><mo>+</mo><msubsup><mi>M</mi><mrow><mtext>ex</mtext></mrow><mrow><msup><mrow/><mrow><mtext>233</mtext></mrow></msup><mtext>Pa</mtext></mrow></msubsup><mo>−</mo><msubsup><mi>M</mi><mrow><mtext>re</mtext></mrow><mrow><msup><mrow/><mrow><mtext>233</mtext></mrow></msup><mtext>U</mtext></mrow></msubsup><mn>,</mn></mrow></math> where the subscripts ex and re denote extraction and refueling, respectively. The annual net production of 233 U is plotted in Fig. 11 Fig. 11 , and shows that 37 Cl enrichment also has a significant impact. When the chloride at the natural enrichment level is adopted, the net production of 233 U is negative, signifying that fuel breeding cannot be realized without enriching 37 Cl. When 37 Cl enrichment increases from 96% to 97%, the annual net 233 U production increases by 7 kg, the same result as by increasing 37 Cl enrichment from 97% to 100%. In addition, the annual net 233 U production of the 99% 37 Cl enrichment is 283 kg/a, which is almost the same as for 100% enrichment. When the net production of 233 U ( M ) equals the initial inventory of 233 U ( M 0 ), the fissile fuel doubles. This is sufficient for starting a new MCFR, and the corresponding time is the doubling time. Table 2 Table 2 shows that the DT of the MCFR is much longer than that of the MSFR (48 years), owing to its larger core volume and the larger initial inventory of 233 U. When the 37 Cl enrichment increases from 96% to 97%, the DT decreases by 2.05 a, which is slightly greater than the decrease in DT resulting from increased 37 Cl enrichment from 97% to 100%. When the 37 Cl enrichment increases to 99%, the DT is shortened to 62.93 a, which is only 0.3% longer than the DT for 100% 37 Cl enrichment. In summary, the results for the BR, the net production of 233 U, and the DT all display very similar trends. When using natural chloride salt, 233 U breeding cannot be realized owing to the high neutron absorption rate of 35 Cl. When the 37 Cl enrichment is increased, its breeding performance displays a clearer improvement. When the enrichment increases to 97%, its breeding performance is very close to 100%. When it is enriched to 99%, its breeding capability is almost the same as for 100%. 3.4 Production of 36 Cl and S 2 Because of the neutron absorption of 35 Cl, S and 36 Cl are generated through the reactions of (n, γ ), (n,p) and (n, α ) [ 19 19 ], as shown in Fig. 12 Fig. 12 . Element S can cause "sulfur cracks" that corrode the structural material. 36 Cl is a long-lived radionuclide that is easily soluble in water [ 8 8 ] and a leak would be toxic to human health and the environment. Thus, it is necessary to reduce the production of these two elements. The impact of 37 Cl enrichment on the production of S and 36 Cl was determined, giving the results shown in Fig. 13 Fig. 13 . The S and 37 Cl contents after 100 years are listed in Table 3 Table 3 . It appears that the buildup of S and 36 Cl is much faster when natural chloride salt is used. After 100 years, the S and 36 Cl contents reach approximately 802 and 948 ppm, respectively, but only approximately 30 and 36 ppm in the case of 97% 37 Cl enrichment. When the 37 Cl enrichment increases to 99%, the S and 36 Cl contents are 12 and 13 ppm, respectively, nearly equal to the values corresponding to 100% enrichment, namely 9 and 11 ppm. From the perspective of reducing the production of harmful isotopes and ensuring the normal operation of the reactor, 37 Cl also needs to be enriched. When the enrichment of 37 Cl increases from 96% to 97%, the S and 36 Cl contents after 100 years decrease by 30 and 26 ppm, which is sightly more than the decrease caused by an increased 37 Cl enrichment from 97% to 100%. When the 37 Cl enrichment increases to 99%, the production of harmful isotopes is almost the same as for 100% enrichment. The evolution of S isotopes was also explored to obtain a clearer understanding of the production of various nuclides under 90% 37 Cl enrichment. As displayed in Fig. 14 Fig. 14 , S mainly exists as the isotopes 32 S and 34 S, while 35 S increases rapidly during the first 2 years and then remains constant because of the equilibrium reactions <math id="M4"><mrow><msubsup><mrow/><mrow><mn>17</mn></mrow><mrow><mn>35</mn></mrow></msubsup><mtext>Cl</mtext><msubsup><mrow><mover><mo>→</mo><mrow><mo stretchy="false">(</mo><mi>n</mi><mn>,</mn><mi>p</mi><mo stretchy="false">)</mo></mrow></mover></mrow><mrow><mn>16</mn></mrow><mrow><mn>35</mn></mrow></msubsup><mtext>S</mtext><msubsup><mrow><munderover><mo>→</mo><mrow><mn>88</mn><mtext> </mtext><mtext> days</mtext></mrow><mrow><msup><mi>β</mi><mo>−</mo></msup></mrow></munderover></mrow><mrow><mn>17</mn></mrow><mrow><mn>35</mn></mrow></msubsup><mtext>Cl</mtext></mrow></math> . From Fig. 13 Fig. 13 and Fig. 14 Fig. 14 , the S and 36 Cl contents increase almost linearly over 100 years of operation, as a result of the slow depletion rate of 35 Cl, which deceases by only approximately 0.67%. 3.5 Safety parameters 2 This subsection investigates two safety parameters, namely the temperature coefficient of reactivity (TCR) and the delayed neutron fraction ( β eff ). For safety reasons, the TCR must be kept negative during the reactor’s operation. For an MSR, it is a comprehensive effect containing the fuel temperature coefficient (FTC) and the moderator temperature coefficient (MTC), while the FTC consists of the fuel density coefficient and the fuel Doppler coefficient. Given the absence of a moderator in a MCFR, the TCR is defined as: <math display="block" id="M5"><mrow><mfrac><mrow><mtext>d</mtext><mi>K</mi></mrow><mrow><mtext>d</mtext><mi>T</mi></mrow></mfrac><msub><mo stretchy="false">)</mo><mrow><mtext>total</mtext></mrow></msub><mo>=</mo><mfrac><mrow><mtext>d</mtext><mi>K</mi></mrow><mrow><mtext>d</mtext><mi>T</mi></mrow></mfrac><msub><mo stretchy="false">)</mo><mrow><mtext>fuel</mtext></mrow></msub><mo>=</mo><mfrac><mrow><mtext>d</mtext><mi>K</mi></mrow><mrow><mtext>d</mtext><mi>T</mi></mrow></mfrac><msub><mo stretchy="false">)</mo><mrow><mtext>fuel</mtext><mtext> </mtext><mtext> density</mtext></mrow></msub><mo>+</mo><mfrac><mrow><mtext>d</mtext><mi>K</mi></mrow><mrow><mtext>d</mtext><mi>T</mi></mrow></mfrac><msub><mo stretchy="false">)</mo><mrow><mtext>fuel doppler</mtext></mrow></msub><mn>,</mn></mrow></math> where K and T represent the effective multiplication factor and the fuel salt temperature, respectively. The evolution of the TCR over time under different 37 Cl enrichments is plotted in Fig. 15 Fig. 15 . For a given depletion time, the absolute value of the TCR for natural chloride salt is much smaller than that for 100% 37 Cl enrichment owing to the large neutron absorption cross section of 35 Cl. When the 37 Cl enrichment exceeds 70%, the temperature coefficient is negative and varies within a small range. Additionally, Fig. 15 Fig. 15 shows that, for a given 37 Cl enrichment, the TCR increases during the first 20 years as a result of the accumulation of FPs, which causes an adverse effect on the negative feedback of the temperature. Then, the amount of FPs remains constant because of the online reprocessing, so that the TCR also remains nearly unchanged over the subsequent 80 years. However, regardless of the changes in enrichment, the TCR can remain sufficiently negative over 100 years of operation, thereby ensuring the safe operation of the MCFR. Another important parameter for ensuring the reactor’s safety is β eff , which is mainly driven by the delayed neutron fraction of fissile nuclides. It is defined as: <math display="block" id="M6"><mrow><msub><mi>β</mi><mrow><mtext>eff</mtext></mrow></msub><mo>=</mo><mfrac><mrow><msub><mo>∑</mo><mi>i</mi></msub><msub><mrow><mover accent="true"><mi>v</mi><mo stretchy="true">¯</mo></mover></mrow><mi>d</mi></msub><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo><mo>⋅</mo><msub><mi>R</mi><mi>f</mi></msub><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow><mrow><msub><mo>∑</mo><mi>i</mi></msub><mo stretchy="false">(</mo><msub><mi>v</mi><mi>d</mi></msub><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo><mo>+</mo><msub><mi>v</mi><mi>p</mi></msub><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>⋅</mo><msub><mi>R</mi><mi>f</mi></msub><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></mfrac><mn>,</mn></mrow></math> where <math id="M7"><mrow><msub><mrow><mover accent="true"><mi>v</mi><mo stretchy="true">¯</mo></mover></mrow><mi>d</mi></msub></mrow></math> and <math id="M8"><mrow><msub><mrow><mover accent="true"><mi>v</mi><mo stretchy="true">¯</mo></mover></mrow><mi>p</mi></msub></mrow></math> denote the average delayed and prompt neutrons per fission of nuclide i , while R f denotes the fission rate of nuclide i . The evolution of β eff over time, given in Fig. 16 Fig. 16 , shows that, for a given depletion time, β eff for natural chloride salt is less than for 100% 37 Cl enrichment. This phenomenon originates from the differences in the fission fraction of fissile nuclides under different 37 Cl enrichments. This is further studied and exhibited as follows. For simplicity, only two cases are shown. The solid lines in Fig. 17 Fig. 17 represent the fission rate fraction of fissile nuclides for a 24.23% 37 Cl enrichment, while the dashed lines represent that for 97% 37 Cl enrichment. The fissile nuclides, including 233 U, 235 U, 241 Pu, 239 Pu, and 234 U, are all considered for their high content and large fission cross section under the fast spectrum [ 27 27 ]. The single delayed neutron fractions of 233 U, 234 U, 235 U, 241 Pu, and 239 Pu in the MCFR spectrum are 291, 531, 668, 543, and 219 pcm, respectively. The fission rate fraction of 233 U decreases while that of the other fissile nuclides especially 234 U and 235 U increases during operation. Thus, their total β eff increases during operation. For a given time of depletion, β eff is greatest when the 37 Cl enrichment is 100%, owing to the smallest fission rate fraction of 233 U. But β eff for different 37 Cl enrichments increases less than 5 pcm over 100 years of operation, because 233 U has a dominant fission fraction during 100 years of operation. Thus, no significant problem would be posed to the reactor’s safety with regard to the delayed neutron fraction. 4 Summary 1 This study discussed the influences of 37 Cl enrichment in a MCFR from the perspectives of neutron economy, the breeding performance, the production of harmful nuclides, and safety parameters. The results show that 37 Cl enrichment significantly influences the neutronics properties of a MCFR. With natural chloride, 233 U breeding cannot be achieved, and the yields of S and 36 Cl reach 802 and 948 ppm in 100 years of operation. This is clearly unfavorable for the normal operation of a MCFR. Therefore, it is necessary to enrich 37 Cl. Increasing the 37 Cl enrichment to 97% yields a clear improvement in its neutronics properties owing to the large decrease in the absorption rate of 35 Cl, and its neutronics performance is similar to that corresponding to 100% 37 Cl enrichment. Besides, when the 37 Cl enrichment increases to 99%, the values of its neutronics performance are almost identical as for 100% enrichment. Considering the enrichment cost and the neutronics properties, a 37 Cl enrichment of 97% is recommended. However, achieving optimal neutronics performance requires a 37 Cl enrichment of 99%. In addition, during 100 years of operation, the TCR can remain sufficiently negative, and β eff changes only slightly, regardless of the level of 37 Cl enrichment. 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Energy , 68 , 153 - 168 ( 2013 ). https://doi.org/10.1016/j.pnucene.2013.06.006 https://doi.org/10.1016/j.pnucene.2013.06.006 Investigation of the MSFR core physics and fuel cycle characteristics 10.1007/s41365-020-0740-x This work was supported by the Chinese TMSR Strategic Pioneer Science and Technology Project (No. XDA02010000), the Frontier Science Key Program of the Chinese Academy of Sciences (No. QYZDY-SSW-JSC016), and the Nuclear Energy Development Project (No. 20154602098). 2019-10-21 2020-01-06 2020-01-18 2020-02-25 2020-03-01 2021-04-10 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2020 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-020-0740-x http://dx.doi.org/10.1007/s41365-020-0740-x . 2020 Nuclear Science and Techniques 3 31