Th-U cycle performance analysis based on molten chloride salt and molten fluoride salt fast reactors

Th-U cycle performance analysis based on molten chloride salt and molten fluoride salt fast reactors 1 2 3 first-author https://orcid.org/0000-0002-8082-5250 1 2 1 2 1 2 3 1 2 3 corresp Corresponding author: liuguimin@sinap.ac.cn; yanrui@sinap.ac.cn Corresponding author: liuguimin@sinap.ac.cn; yanrui@sinap.ac.cn liuguimin@sinap.ac.cn 1 2 3 https://orcid.org/0000-0002-7825-2457 1 2 corresp Corresponding author: liuguimin@sinap.ac.cn; yanrui@sinap.ac.cn Corresponding author: liuguimin@sinap.ac.cn; yanrui@sinap.ac.cn liuguimin@sinap.ac.cn https://orcid.org/0000-0002-5747-2194 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, Chinese Academy of Sciences, Shanghai 201800, China CAS Innovative Academies in TMSR Energy System, Chinese Academy of Sciences, Shanghai 201800, China University of Chinese Academy of Sciences, Beijing 100049, China University of Chinese Academy of Sciences, Beijing 100049, China The recent development of molten salt fast reactors has generated a renewed interest in them. As compared to traditional solid-fueled fast neutron systems, it has many unique advantages, e.g., lower fissile inventory, no initial criticality reserve, waste reduction, and a simplified fuel cycle. It has been recognized as an ideal reactor for achieving a closed Th-U cycle. Based on the carrier-salt, molten salt fast reactors could be divided into either a molten chloride salt fast reactor (MCFR) or a molten fluoride salt fast reactor (MFFR); to compare their Th-U cycle performance, the neutronic parameters in a Breeding and Burning (B&B) transition scenario were studied based on similar core geometry and power. The results demonstrated that the required reprocessing rate for an MCFR to achieve self-breeding was lower than that of an MFFR. Moreover, the breeding capability of an MCFR was better than that of an MFFR; at a reprocessing rate of 40 L/day, using LEU and Pu as start-up fissile materials, the doubling-time (DT) of an MFFR and MCFR were 88.0 years and 48.0 years, and 16.5 years and 16.2 years, respectively. Besides, an MCFR has lower radio-toxicity due to lower buildup of fission products (FPs) and transuranium (TRU), while an MFFR has a larger, delayed neutron fraction with smaller changes during the entire operation. Key words: Th-U cycle Molten salt fast reactor Breeding capability Doubling-time 1. Introduction 1 Molten salt fast reactors have generated a growing interest from both, scientific and industrial perspectives due to their intrinsic characteristics of sustainability, breeding capability, and safety [ 1 1 - 3 3 1-3 ] . Firstly, the closed fuel cycle leads to lower radio-toxicity due to a lower actinide inventory. Moreover, owing to the hard energy spectrum, fast reactors have an outstanding breeding capacity, breeding fissile isotopes from fertile nuclides, significantly extending the fuel-availability. In addition, atmospheric pressure operation and small residual reactivity greatly improves the safety of the system. Finally, the yield and absorption cross-section of fission products are small in the fast spectrum, making online reprocessing less challenging, which is conducive to their deployment. Therefore, molten salt fast reactors have been recognized as ideal reactors for achieving a closed Th-U cycle; they have development potential and research significance. In general, a molten salt fast reactor could use a fluoride or chloride salt as a fuel carrier-salt, corresponding to two reactor types, i.e., a molten fluoride salt fast reactor (MFFR) or a molten chloride salt fast reactor (MCFR). The success of the molten salt reactor experiment (MSRE) led to a development in an understanding of corrosion as well as related reprocessing technologies of fluoride salt; hence, the MFFR was well-developed. For instance, the Molten Salt Actinide Recycler & Transmuter (MOSART) is a typical MFFR [ 4 4 ] , designed for TRU incineration by the Kurchatov Institute of Russia within the International Science and Technology Center project 1606 (ISTC#1606). The feasibility of the Th-U cycle for MOSART was recently evaluated; various fuel cycle programs including the converter, iso-breeder, and breeder were researched. Moreover, under the European Evaluation and Viability of Liquid Fuel Fast Reactor System (EVOL), the Centre National de la Recherche Scientifique (CNRS) proposed the Molten Salt Fast Reactor (MSFR) [ 3 3 , 5 5 ] . The primary difference in the design of an MSFR versus that of other MSRs is the absence of a graphite moderator from the core; hence, it is a breeder reactor with a fast spectrum. Having unique characteristics (lower fissile inventory, excellent safety coefficients, simplified design, and no requirement for criticality reserve ( k eff ≈1.000), it was selected for further research by the Generation IV International Forum in 2008 [ 6 6 ] . Although there is no successful operation experience of MCFR, it has obvious advantages as compared to an MFFR which make it worth researching [ 7 7 , 8 8 ] . First, the atomic mass of Cl is bigger than that of F, making the energy spectrum harder in MCFR than in MFFR; therefore, the extraction period of fission products (FPs) can be prolonged due to their smaller neutron absorption cross-sections and lower content under a faster spectrum. Importantly, the chloride salt has higher solubility among the actinides; hence heavier nuclides could be loaded in the chloride salt, which could further contribute to the breeding capability. Research on MCFR began in the 1950s by Oak Ridge National Laboratory (ORNL), and the design adopted NaCl+MgCl 2 +PuCl 3 +UCl 3 as a fissile fuel-salt and UO 2 +Na as a solid blanket [ 7 7 ] . A breeding ratio (BR) of 1.09 could be achieved, which demonstrated the practicability of using chlorine salt for fuel breeding in a fast reactor. In the 1960s, the British Atomic Energy Authority carried out research on MCFRs [ 9 9 ] , in which NaCl+UCl 3 +PuCl 3 was used as a fuel-salt and NaCl+ 238 UCl 3 as a breeding-salt; a BR of 1.53 was attainable. The chloride salt fast reactor has been receiving increased attention globally. In Britain, Moltex Energy recently proposed a stable salt fast reactor, a pool-type fast reactor, in which the fuel-tube is loaded with chloride fuel; due to good intrinsic safety it has an enormous economic advantage over other fast reactor designs [ 10 10 ] . In addition, the proposed German Dual Fluid Reactor (DFR) [ 11 11 ] combines the advantages of the MSRE, lead-cooled fast reactor (LFR), and very high temperature reactor (VHTR) by using two separate fluids; the molten salt of the DFR is cooled by a separate liquid lead loop, which allows for higher power-density and better breeding capability. However, most of the above research was on the U-Pu cycle performance of MCFRs; in comparison, the Th-U cycle offers unique advantages: the lower mass number of Th fosters a lower endogenous TRU generation, which yields lower radio-toxicity and decay-heat. Hence, it could benefit public acceptance; besides, Th is more abundant than U in nature. Therefore, studying the Th-U cycle performance of an MCFR is of great significance. In previous work, the breeding capability of an MCFR was optimized [ 12 12 ] . Our work aims to identify neutron properties of the Th-U cycle based on an optimized MCFR and compare it with an MFFR under similar conditions. 2. Calculation model and reprocessing schemes 1 2.1 Calculation model 2 Here, the basic core design ( Fig. 1 Fig. 1 ) refers to REBUS-3700 [ 13 13 ] , which is a typical chloride salt fast reactor designed in France. Table 1 Table 1 lists the detailed structural parameters. It is a two-fluid MSR with a thermal power of 2500 MW. The active-zone consists of a compact cylinder (height/diameter ratio = 1) in which liquid fluoride fuel-salt flows from the bottom to the top with no solid moderator. A fertile-zone surrounds the active-core in both, the radial and axial directions (blue-area, Fig. 1 Fig. 1 ). Surrounding the fertile-salt is a graphite reflector (yellow-area, Fig. 1 Fig. 1 ), which is used for saving fertile-fuel [ 14 14 , 15 15 ] . Outside the graphite reflector, B 4 C (green-area, Fig. 1 Fig. 1 ) has been applied to absorb leaking neutrons from the reactor. A Ti-based alloy is used as supporting material on the outermost section. In an MFFR, the composition of the adopted fertile-salt and fuel-salt is 77.5 mol% LiF–22.5 mol% (HM)F 4 in mol%, and the density of both is 4.1 g/cm 3 [ 2 2 , 16 16 ] . In an MCFR, the corresponding composition of both, the fertile-salt and fuel-salt is 55 mol% NaCl–45 mol% (HM)Cl 4 , and their density is 3.6 g/cm 3 [ 17 17 ] . Note that (Th+U)Cl 4 could be soluble to 45 mol% in the chloride salt, and to only 22.5 mol% in LiF, resulting from a higher solubility of actinides in chloride salt. 1 1 Parameters 1 1 MFFR 1 1 MCFR 1 1 Thermal power (MW) 1 1 2500 1 1 2500 1 1 Fuel-salt (%) 1 1 LiF:(HN)F 3 =77.5:22.5 1 1 NaCl:(HN)Cl 3 =55:45 1 1 Fertile-salt (%) 1 1 LiF:ThF 4 =77.5:22.5 1 1 NaCl:ThCl 4 =55:45 1 1 Enrichment of 7 Li (%) 1 1 100 1 1 -- 1 1 Enrichment of 37 Cl (%) 1 1 -- 1 1 100 1 1 Temperature of fuel-salt (K) 1 1 1023 1 1 1023 1 1 Temperature of fertile-salt (K) 1 1 973 1 1 973 1 1 Thermal  expansion  (K) 1 1 -1.78E-04 1 1 -3.00E-04 1 1 Density of graphite (g.cm -3 ) 1 1 2.3 1 1 2.3 1 1 Density of B 4 C (g.cm -3 ) 1 1 2.52 1 1 2.52 1 1 Density of salt (g.cm -3 ) 1 1 4.1 1 1 3.6 1 1 Radius of core (cm) 1 1 158.5 1 1 158.5 1 1 Thickness of blanket (cm) 1 1 60 1 1 60 1 1 Thickness of reflector (cm) 1 1 45 1 1 45 1 1 Thickness of B 4 C (cm) 1 1 35 1 1 35 2.2 Reprocessing schemes 2 Online molten salt reprocessing is one of the most crucial features of an MSR in comparison to a traditional solid-fuel reactor. A diagram of the reprocessing is shown in Fig. 2 Fig. 2 , which refers to an MSFR [ 2 2 , 3 3 ] . Two key systems exist for the online reprocessing: (1) An He gaseous bubbling system, which continuously removes gaseous and non-dissolved FPs (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). The removal time constant is set to 30 s with 100% efficiency; (2) An online chemical reprocessing system which removes soluble FPs from both, fuel-salt and fertile-salt. In online chemical reprocessing, U, Np, and Pu are extracted by fluorination and returned first to the core. Then, most actinides including Th, Pa, and Minor Actinides (MA) are extracted by reductive extraction and stored in a stockpile for several months to let 233 Pa decay into 233 U. Finally, the carrier-salt is recovered through low-pressure distillation, leaving the FPs for disposal. 3. Calculation tools 1 Here, an in-house program (TMCBurnup) which couples a problem-dependent cross-section processing module, a criticality analysis module in the SCALE6.1 program [ 18 18 ] , and a novel depletion code MODEC was used for calculation [ 19 19 ] . SCALE6.1 is a comprehensive code package developed by ORNL, which is used to analyze criticality safety, radiation shielding design, sensitivity etc [ 18 18 ] . In an MSR, due to on-line reprocessing and refueling, the depletion equation can be described as follows: <math display="block" id="M1"><mrow><mrow><mo>{</mo><mtable columnalign="left"><mtr><mtd><mfrac><mrow><mtext>d</mtext><mi>N</mi><mi>i</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mstyle displaystyle="true"><msub><mo>∑</mo><mi>j</mi></msub><mrow><mi>λ</mi><mi>j</mi><mo>,</mo><mi>i</mi><mi>N</mi><mi>j</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>−</mo><mi>λ</mi><mi>i</mi><mi>N</mi><mi>i</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo><mi>C</mi><mi>i</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mi>λ</mi><mi>j</mi><mo>,</mo><mi>i</mi><mo>=</mo><msub><mi>f</mi><mrow><mi>j</mi><mo>→</mo><mi>i</mi></mrow></msub><msubsup><mi>σ</mi><mi>j</mi><mrow/></msubsup><mi>ϕ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo><msub><mi>γ</mi><mrow><mi>j</mi><mo>→</mo><mi>i</mi></mrow></msub><msubsup><mi>λ</mi><mi>j</mi><mrow/></msubsup><mo>,</mo><mtext>   </mtext><msub><mi>λ</mi><mi>i</mi></msub><mo>=</mo><msubsup><mi>σ</mi><mi>i</mi><mrow/></msubsup><mi>ϕ</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo><msubsup><mi>λ</mi><mi>i</mi><mrow/></msubsup><mo>+</mo><msubsup><mi>λ</mi><mi>i</mi><mtext>c</mtext></msubsup></mtd></mtr></mtable></mrow></mrow></math> where N i ( t ) and N j ( t ) refer to the number density of nuclide i and j , respectively; γ j→i indicates the branching-ratio of decay from nuclide j into i ; λ i and λ j refer to the decay constant of nuclide i and j, respectively; f j→i represents the probability of nuclide j to i by neutron absorption; λ i c indicates the fictive decay constant of nuclide i due to chemical reprocessing; σ i and σ j denote the absorption cross-sections of nuclide i and j , respectively ; and C i refers to the feed-rate of nuclide i . To solve this nonhomogeneous equation, an in-house Molten Salt Reactor Specific Depletion Code (MODEC) was developed in our previous work [ 18 18 ] , which implemented two depletion algorithms to solve the depletion equation: the transmutation trajectory analysis (TTA); and the Chebyshev rational approximation method (CRAM). To simulate the on-line reprocessing, the fictive decay constant method was applied. Three methods were implemented in MODEC to solve the nonhomogeneous burnup equation in the continuously refueling problems. On comparison with ORIGEN-S [ 20 20 ] , the validity of MODEC in terms of the burnup calculations with on-line reprocessing and with continuous refueling was proved [ 21 21 , 22 22 ] . A flowchart of TMCBurnup is shown in Fig. 3 Fig. 3 . The test results in MSFR show that the calculations using TMCBurnup agreed well with the reference values and were suitable for analyzing the Th-U cycle performance of MCFR and MFFR [ 21 21 ] . Due to the deep burnup of the molten salt reactor, the transition time from start-up to an equilibrium state is quite long, so the simulation of the entire burn-up process would take longer. For some studies, only the equilibrium state analysis was needed. Therefore, MESA (Molten Salt Reactor Equilibrium-State Analysis Code) [ 22 22 ] , an in-house program was used to quickly obtain the equilibrium state of the molten salt reactor; Table 2 Table 2 shows the test results. The nuclide content, including that of the fission products and MA, could be found to be nearly the same as those calculated by TMCBurnup. 1 1 Nuclides 1 1 TMCBurnup (460 years) 1 1 MESA 1 1 Relative deviation (%) 1 1 238 Pu 1 1 758.1356 1 1 763.8841 1 1 0.75 1 1 239 Pu 1 1 300.7233 1 1 302.7175 1 1 0.66 1 1 240 Pu 1 1 253.5638 1 1 255.2068 1 1 0.65 1 1 241 Pu 1 1 50.1238 1 1 51.2117 1 1 2.09 1 1 242 Pu 1 1 43.1527 1 1 44.1117 1 1 2.18 1 1 233 Pa 1 1 560.0238 1 1 564.0204 1 1 0.71 1 1 232 Th 1 1 223732.3670 1 1 223911.3605 1 1 0.08 1 1 232 U 1 1 52.5322 1 1 54.5737 1 1 3.73 1 1 233 U 1 1 20147.4153 1 1 20253.4150 1 1 0.52 1 1 234 U 1 1 10468.3838 1 1 10668.8636 1 1 1.87 1 1 235 U 1 1 2493.3333 1 1 2520.9230 1 1 1.08 1 1 237 Np 1 1 677.0324 1 1 697.0632 1 1 2.87 1 1 244 Cm 1 1 14.9982 1 1 15.1728 1 1 1.16 1 1 241 Am 1 1 11.9948 1 1 12.3778 1 1 3.09 1 1 243 Am 1 1 12.1382 1 1 12.4944 1 1 2.85 1 1 126 Sn 1 1 1579.7802 1 1 1598.7732 1 1 1.20 1 1 93 Zr 1 1 37728.1378 1 1 37739.5628 1 1 0.04 1 1 79 Se 1 1 589.5328 1 1 592.5327 1 1 0.49 1 1 90 Sr 1 1 21037.1562 1 1 21108.5632 1 1 0.34 1 1 137 Cs 1 1 9300.1377 1 1 9308.6855 1 1 0.09 4. Results and discussion 1 Here, the Th-U cycle performance of an MCFR and MFFR was investigated under a B & B scenario [ 23 23 ] , in which some 233 U produced by the decay of the extracted 233 Pa needed to be refueled to the reactor to maintain criticality. Due to the lack of naturally available 233 U, High Assay Low Enriched Uranium (HALEU) and Pu elements produced by current LWRs were used as start-up fissile materials to achieve a transition to the Th-U cycle [ 24 24 ] . For the HALEU-started mode, the enrichment of 235 U was 19.75%; for Pu-started mode, it appeared more practical as it employed the prevailing PUREX reprocessing technique and facilities to recover Pu from LWRs. Initial nuclei inventories of the MFFR and MCFR with various fuel-types are detailed in Table 3 Table 3 . For comparison, the 233 U-started case is also listed. 1 1 Nuclides 3 1 MFFR 3 1 MCFR 1 1 1 1 HALEU 1 1 Pu 1 1 233 U 1 1 HALEU 1 1 Pu 1 1 233 U 1 1 U-235 1 1 9.20E+06 1 1 1 1 1 1 7.68E+06 1 1 U-238 1 1 3.73E+07 1 1 1 1 1 1 3.11E+07 1 1 Pu-238 1 1 1 1 2.93E+05 1 1 1 1 1 1 1.77E+05 1 1 Pu-239 1 1 1 1 8.51E+06 1 1 1 1 1 1 5.14E+06 1 1 Pu-240 1 1 1 1 4.12E+06 1 1 1 1 1 1 2.49E+06 1 1 Pu-241 1 1 1 1 5.92E+05 1 1 1 1 1 1 3.58E+05 1 1 Pu-242 1 1 1 1 1.19E+06 1 1 1 1 1 1 7.18E+05 1 1 Th-232 1 1 1.36E+07 1 1 4.52E+07 1 1 5.31E+07 1 1 1.18E+07 1 1 4.13E+07 1 1 4.44E+07 1 1 U-233 1 1 1 1 1 1 6.52E+06 1 1 1 1 1 1 5.20E+06 1 1 Total mass 1 1 6.02E+07 1 1 5.99E+07 1 1 5.97E+07 1 1 5.06E+07 1 1 5.02E+07 1 1 4.96E+07 1 1 Fissile isotope fraction 1 1 3.44% 1 1 3.42% 1 1 2.46% 1 1 6.84% 1 1 4.93% 1 1 4.69% Here, the characteristics of the B & B thorium fuel cycle transition scenario in an MCFR and MFFR were studied based on several important parameters including neutron spectra, evolution of main heavy nuclides, breeding capacity, Temperature Coefficient of Reactivity (TCR), delayed neutron fraction ( β eff ), and radiotoxicity. A 238-group ENDF-B/VII.0 cross-section library was used in the calculation. In addition, there were 10000 neutrons per k eff cycle. We skipped the first 15 k eff cycles to allow the spatial fission source to attain equilibrium, before the k eff values were used for averaging for the final k eff estimate. A total of 285 k eff cycles were run in a criticality calculation with an average error of about 25 pcm. 4.1 Comparison of neutron spectra 2 Neutron spectra which could help fundamentally indicate subsequent interpretations of results based on the actinide buildup and TCR were researched here. Fig. 4(a) Fig. 4(a) shows the initial neutron spectra; those of the MCFR were harder than those of the MFFR, using either HALEU or Pu as start-up fissile materials, thanks to the larger relative atomic mass of NaCl as compared to LiF. It resulted in a weaker moderating ability in the MCFR. Moreover, due to the slowing of neutrons on the outer graphite besides the blanket, a peak appeared in the thermal spectrum zone in both, the MFFR and MCFR. In order to quantitatively describe neutron spectra during the entire operation, the energy of the average lethargy causing fission (EALF) was introduced [ 25 25 ] , which was used as a quantization parameter of the average neutron energy in a reactor expressed as: <math display="block" id="M2"><mrow><mi>E</mi><mi>A</mi><mi>L</mi><mi>F</mi><mo>=</mo><mi>exp</mi><mrow><mo>{</mo><mrow><mfrac><mrow><mstyle displaystyle="true"><mrow><mo>∫</mo><mrow><mo stretchy="false">(</mo><mi>ln</mi><mi>E</mi></mrow></mrow></mstyle><mo stretchy="false">)</mo><mi>ϕ</mi><mo stretchy="false">(</mo><mi>E</mi><mo stretchy="false">)</mo><mstyle displaystyle="true"><msub><mo>∑</mo><mtext>f</mtext></msub><mrow><mo stretchy="false">(</mo><mi>E</mi><mo stretchy="false">)</mo><mtext>d</mtext><mi>E</mi></mrow></mstyle></mrow><mrow><mstyle displaystyle="true"><mrow><mo>∫</mo><mrow><mi>ϕ</mi><mo stretchy="false">(</mo><mi>E</mi><mo stretchy="false">)</mo></mrow></mrow></mstyle><mstyle displaystyle="true"><msub><mo>∑</mo><mtext>f</mtext></msub><mrow><mo stretchy="false">(</mo><mi>E</mi><mo stretchy="false">)</mo><mtext>d</mtext><mi>E</mi></mrow></mstyle></mrow></mfrac></mrow><mo>}</mo></mrow><mo>,</mo></mrow></math> where ϕ( E ) and Σ f ( E ) represent the energy-dependent neutron-flux and macroscopic fission cross-section, respectively. Higher the value of EALF, harder the neutron spectrum. Fig. 4(b) Fig. 4(b) shows the evolution of EALF; Neutron spectra of the MCFR were found to be harder than that of MFFR during the entire operation. In addition, neutron spectra of the Pu-started mode were harder than that of the HALEU-started mode, initially. Moreover, due to the accumulation of FPs during the operation, EALF gradually decreased except for that of the HALEU-started mode in the MFFR, resulting from its relatively lighter atomic mass than that of the fissile and fertile nuclides, bringing about a stronger moderating effect on the neutrons. For the HALEU-started mode in the MFFR, EALF of the LEU-started mode increased slightly in the first few years due to a decrease in 238 U; it had a broader resonance peak and a larger resonance capture cross-section than 232 Th, resulting in a more obvious resonance in the neutron spectra. Then, it gradually attained an equilibrium-state on consumption of 238 U and buildup of FPs. 4.2 Breeding capability 2 Here, the breeding performance of an MFFR and MCFR were explored based on the Breeding Ratio (BR), net production of 233 U, and doubling-time (DT), the three important parameters for evaluating fuel breeding performance. BR, which represents the ratio of the capture rates of all fertile isotopes and the absorption rate of all fissile isotopes, is expressed by Eq. (3). During the operation, 233 Pa was extracted from the core and blanket, and stored outside the reactor to let it decay into 233 U. To maintain criticality, some 233 U needed to be fed back into the core; the amount of remaining 233 U outside the reactor is the net 233 U production. When the mass of 233 U outside the reactor equaled that at initial 233 U loading, it indicated that the produced 233 U was sufficient to start a new MCFR/MFFR. DT is the time required to double the amount of 233 U [ 26 26 ] . <math display="block" id="M3"><mrow><mi>B</mi><mi>R</mi><mo>=</mo><mfrac><mrow><mi>R</mi><mtext>c</mtext><mo stretchy="false">(</mo><mmultiscripts><mtext>U</mtext><mprescripts/><mi/><mn>234</mn></mmultiscripts><mo>+</mo><mmultiscripts><mtext>T</mtext><mprescripts/><mi/><mrow><mn>232</mn></mrow></mmultiscripts><mtext>h</mtext><mo>+</mo><mmultiscripts><mtext>P</mtext><mprescripts/><mi/><mrow><mn>240</mn></mrow></mmultiscripts><mtext>u</mtext><mo>+</mo><mmultiscripts><mtext>U</mtext><mprescripts/><mi/><mrow><mn>238</mn></mrow></mmultiscripts><mo stretchy="false">)</mo><mo>−</mo><mi>R</mi><mtext>a</mtext><mo stretchy="false">(</mo><mmultiscripts><mtext>P</mtext><mprescripts/><mi/><mrow><mn>233</mn></mrow></mmultiscripts><mtext>a)</mtext></mrow><mrow><mi>R</mi><mtext>a</mtext><mo stretchy="false">(</mo><mmultiscripts><mtext>U</mtext><mprescripts/><mi/><mrow><mn>233</mn></mrow></mmultiscripts><mo>+</mo><mmultiscripts><mtext>U</mtext><mprescripts/><mi/><mrow><mn>235</mn></mrow></mmultiscripts><mo>+</mo><mmultiscripts><mtext>P</mtext><mprescripts/><mi/><mrow><mn>241</mn></mrow></mmultiscripts><mtext>u</mtext><mo>+</mo><mmultiscripts><mtext>P</mtext><mprescripts/><mi/><mrow><mn>239</mn></mrow></mmultiscripts><mtext>u</mtext><mo stretchy="false">)</mo></mrow></mfrac></mrow></math> where R c indicates the neutron capture reaction rate of fertile isotopes, and R a denotes the neutron absorption reaction rate of fissile nuclides. Firstly, MESA was used to investigate the BR of an MCFR and MFFR in equilibrium state at varying reprocessing rates. The results are shown in Fig. 5 Fig. 5 . At the same reprocessing rate, the BR in an MCFR was higher than that in an MFFR at an equilibrium state. As the reprocessing rate reached 3.25 L/day, the BR of an MCFR equaled 1, suggesting that it could be self-sustaining at that reprocessing rate; while, an MFFR became self-sustaining as the reprocessing rate increased to 9.6 L/day. As the reprocessing rate increased to 200 L/day, the BR of an MFFR and MCFR was 1.12 and 1.31, respectively. As the online reprocessing of fast reactors, especially that of Th-U-Pu mixed fast reactors is challenging, a reprocessing rate of 40 L/day was selected for the subsequent calculation [ 1 1 ] . A 200 year burn-up was simulated here, as it takes longer for some neutron parameters in molten fast reactors to reach an equilibrium state, which include delayed neutron fraction ( β eff ), mass of actinides, as well as the BR [ 5 5 , 24 24 ] . It involves many fertile and fission nuclides in the initial stage when using Pu or LEU as start-up fissile materials, so as to express the relationship between 233 U generation and direct disappearance. Regeneration Ratio (RR) is defined by Eq. (4); an RR greater than 1 suggests that the production of 233 U is greater than its consumption. <math display="block" id="M4"><mrow><mi>R</mi><mi>R</mi><mo>=</mo><mfrac><mrow><mi>R</mi><mtext>c</mtext><mo stretchy="false">(</mo><mmultiscripts><mi mathvariant="normal">T</mi><mprescripts/><mi/><mrow><mn>232</mn></mrow></mmultiscripts><mi>h</mi><mo stretchy="false">)</mo><mo>−</mo><mi>R</mi><mtext>a</mtext><mo stretchy="false">(</mo><mmultiscripts><mtext>P</mtext><mprescripts/><mi/><mrow><mn>233</mn></mrow></mmultiscripts><mtext>a</mtext><mo stretchy="false">)</mo></mrow><mrow><mi>R</mi><mtext>a</mtext><mo stretchy="false">(</mo><mmultiscripts><mtext>U</mtext><mprescripts/><mi/><mrow><mn>233</mn></mrow></mmultiscripts><mo stretchy="false">)</mo></mrow></mfrac></mrow></math> Fig. 6(a) Fig. 6(a) shows the evolution of k eff and RR during the reactor operation. During the entire operation, k eff was maintained between 1.000 and 1.005; while RR decreased in the early years, gradually tending to an equilibrium state. This mainly occurred as the core maintains its criticality by consuming 239 Pu and 235 U in the early stage; the consumption of 233 U is small. As 233 U gradually becomes the dominating fissile isotope, its consumption rate increases, leading to a decrease in the RR. In addition, due to the harder neutron spectra in an MCFR, its capture to fission ratio (α) is smaller, resulting in an obviously larger RR throughout the operation. The evolution of net production of 233 U is shown in Fig. 6(b) Fig. 6(b) ; the dashed-line represents the initial 233 U inventories, using 233 U as the start-up fissile material. A higher RR in an MCFR resulted in a faster net accumulation of 233 U. The DT of HALEU-started and Pu-started modes in an MFFR and MCFR was 88.0 and 48.0 years, and 16.5 years and 16.2 years, respectively. For comparison, the DT of an MSCFR which used NaCl as a carrier-salt was 17 years, while that of an MSFR using LiF as a carrier-salt was 56 years in the TRU-started mode [ 24 24 , 27 27 ] . Besides, at the equilibrium state, the average annual net production of 233 U for an MCFR and MFFR was 243 kg and 86 kg, respectively. 4.3 Evolution of heavy nuclides 2 The evolution of heavy nuclides and U isotopes for an MFFR and MCFR initiated with Pu and HALEU is presented in Figs. 7 (a–b) Figs. 7 (a–b) and 8 (a–b) 8 (a–b) , and provides an important basis for analyzing core critical performance and nuclear waste production. Despite an equilibrium state determined by the feeding fuel composition, some different features in the transition state with the same feeding fuel still exist. Achieving equilibrium of heavy nuclides in an MCFR is more time-consuming due to its harder neutron spectrum. Moreover, for the Pu-started mode, fewer neutrons need to be absorbed to reach equilibrium; hence, the time required to reach equilibrium is shorter than that for the HALEU-started mode. Although the total mass of U isotopes is larger in an MCFR than MFFR, the 232 U content of an MCFR is always higher than that of an MFFR throughout the operation. This is because the generation of 232 U mainly relies on the (n, 2n) reaction of 233 U [ 28 28 ] ; the reaction cross-section increases with the hardening of the neutron spectrum. As is well-known, 232 U decay chains contain a number of highly radioactive decay products, particularly 208 Tl, which emits gamma rays of up to 2.6 MeV, increasing the nonproliferation capacity of an MCFR. The molar ratio of U isotopes in the blanket at equilibrium state is shown in Table 4 Table 4 . It indicates that the purity of 233 U is considerably high with the molar ratio for an MCFR and MFFR being 95.28% and 99.22%, respectively. Importantly, the 232 U content for an MCFR and MFFR is only 6 ppm and 0.03 ppm, respectively. Thus, nuclear proliferation issues could arise, 233 U being easily retrievable through fluorination from the blanket. 1 1 Nuclides 1 1 MCFR 1 1 MFFR 1 1 232 U 1 1 0.13 1 1 3.74E-3 1 1 233 U 1 1 95.28 1 1 99.22 1 1 234 U 1 1 4.24 1 1 0.77 1 1 235 U 1 1 0.35 1 1 0.01 4.4 Safety parameters 2 TCR and β eff are important parameters that could provide insights on the safety and relative potential for various modes. In one-group approximation, k eff can be expressed as: <math display="block" id="M5"><mrow><mi>k</mi><mtext>eff</mtext><mo>=</mo><mfrac><mrow><msub><mi>k</mi><mi>∞</mi></msub></mrow><mrow><mn>1</mn><mo>+</mo><msup><mi>B</mi><mn>2</mn></msup><msup><mi>L</mi><mn>2</mn></msup></mrow></mfrac></mrow></math> where, k ∞ refers to infinite multiplication; B represents buckling; and L stands for diffusion length. TCR is mainly determined by the effect of the fuel density and Doppler coefficient; the Doppler effect which is paramount to TCR, acts on the k eff . For a molten salt fast reactor, an increasing temperature contributes negatively to reactivity due to an increased capture of fertile isotopes in the region of resonance. In general, the impact of the Doppler effect will weaken with local spectrum hardening; hence, the absolute value of the Doppler coefficient in an MFFR is larger. Moreover, a second reactivity feedback depends on fuel expansion, and impacts the term L 2 along with the Doppler effect, simultaneously. In one-group approximation, L 2 is defined as: <math display="block" id="M6"><mrow><msup><mi>L</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><msup><mi>D</mi><mrow/></msup></mrow><mrow><mstyle displaystyle="true"><msub><mo>∑</mo><mtext>a</mtext></msub><mrow/></mstyle></mrow></mfrac><mo>∝</mo><mfrac><mn>1</mn><mrow><msup><mi>d</mi><mn>2</mn></msup></mrow></mfrac><mo>,</mo></mrow></math> where, d represents the density of the fuel-salt; D is the diffusion coefficient; and ∑ a indicates the macroscopic absorption cross-section. Density decreases with an increase in temperature, resulting in a negative feedback coefficient. While B 2 is mainly caused by the expansion of the core structure, and the feedback coefficient is clearly positive, nevertheless, the expansion coefficient of the structure is much lower than that of the salt. Besides, during a transient, the fuel-salt undergoes quick temperature excursions, while a much slower temperature variation is expected from the core structure; thus, this effect can be ignored. Due to the absence of a moderator in an MCFR and MFFR, TCR can be expressed as: <math display="block" id="M7"><mrow><mfrac><mrow><mtext>d</mtext><mi>K</mi></mrow><mrow><mtext>d</mtext><mi>T</mi></mrow></mfrac><mo stretchy="false">)</mo><mtext>total</mtext><mo>=</mo><mfrac><mrow><mtext>d</mtext><mi>K</mi></mrow><mrow><mtext>d</mtext><mi>T</mi></mrow></mfrac><mo stretchy="false">)</mo><mtext>fuel Doppler</mtext><mo>+</mo><mfrac><mrow><mtext>d</mtext><mi>K</mi></mrow><mrow><mtext>d</mtext><mi>T</mi></mrow></mfrac><mo stretchy="false">)</mo><mtext>fuel density</mtext><mo>,</mo></mrow></math> where, K and T indicate the k eff and temperature, respectively. Fig. 9 Fig. 9 shows the evolution of TCR for the four Th-U cycle modes. Initially, the TCR of the four Th-U cycle modes was noticeably different; the absolute TCR value of an MCFR was larger than that of an MFFR due to a considerably higher expansion coefficient in molten chloride salt. Moreover, the Pu-started mode demonstrated a higher absolute TCR value than the HALEU-started mode at initial-time; while, the absolute TCR values of the Pu-started and HALEU-started modes were the same at equilibrium. The Doppler effect is mainly driven by resonance captures in the fertile isotopes. The spectrum shift ensues increased fertile captures affecting fission and capture in other isotopes, while the fuel density effect is mainly driven by leakages, which depend only mildly on the fuel composition; the tendency is similarly to the Doppler coefficient. Due to the lower molar fraction of fertile isotopes in the HALEU start-up mode, the absolute TCR value was initially smaller. With the operation, the nuclide composition in an MCFR/MFFR tends to be the same, which leads to the TCR becoming gradually identical. Moreover, the dominant fissile isotope in the Pu-started mode ( 239 Pu, 235 U), has a flatter fission cross-section than 233 U. Thus, spectral hardening has a less negative impact on 239 Pu and 235 U fission rather than on 233 U. In addition, 239 Pu and 235 U also have a steeper capture cross-section as compared to 233 U, suggesting a higher decrease of captures following spectral hardening, positively affecting TCR [ 2 2 ] . Therefore, a high 233 U content is beneficial for the Doppler coefficient. Although 233 U gradually becomes the dominant fissile isotope under the operation, TCR fluctuates slightly due to the buildup of FPs. The spectrum hardening following a temperature increase leads to a decrease in FP captures; thus, a higher FP content suggests a higher decrease in FP captures with spectrum hardening, which leads to increased reactivity, positively affecting TCR. In addition, β eff is extremely important for reactor operation control, which is primarily determined by the fission rate fraction and the single delayed neutron fraction of fissile isotopes ( Table 5 Table 5 ). It can be expressed as: 1 1  Fissile isotopes 1 1 MFFR (pcm) 1 1 MCFR (pcm) 1 1 233 U 1 1 292 1 1 291 1 1 234 U 1 1 535 1 1 532 1 1 235 U 1 1 662 1 1 668 1 1 239 Pu 1 1 219 1 1 218 1 1 241 Pu 1 1 544 1 1 542 <math display="block" id="M8"><mrow><mi>β</mi><mtext>eff</mtext><mo>=</mo><mfrac><mrow><mstyle displaystyle="true"><msub><mo>∑</mo><mi>i</mi></msub><mrow><mover accent="true"><mrow><mi>v</mi><mi>d</mi></mrow><mo stretchy="true">¯</mo></mover><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo><mo>⋅</mo><mi>R</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></mstyle></mrow><mrow><mstyle displaystyle="true"><msub><mo>∑</mo><mi>i</mi></msub><mrow><mo stretchy="false">(</mo><mover accent="true"><mrow><mi>v</mi><mi>d</mi></mrow><mo stretchy="true">¯</mo></mover><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo><mo>+</mo><mover accent="true"><mrow><mi>v</mi><mi>p</mi></mrow><mo stretchy="true">¯</mo></mover><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>⋅</mo><mi>R</mi><mi>f</mi><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></mstyle></mrow></mfrac></mrow></math> where, vd ( i ) and vp ( i ) represent the delayed neutron number and prompt neutron number per fission for nuclide i ; and Rf ( i ) denotes the neutron fission rate for nuclide i . Table 5 Table 5 shows the single β eff of various fissile isotopes. Due to the non-negligible fission cross-section of 234 U in the fast spectrum, the fission contribution of 234 U was also considered. The evolution of the total β eff of different modes is displayed in Fig. 10 Fig. 10 . In HALEU-started modes, the total β eff dropped rapidly in the first few decades, then it increased slightly and gradually transitioned to an equilibrium state. A rapid decline in β eff is primarily due to a decrease in the fission rate fraction of the dominant fissile isotope 235 U, while that of other fissile isotopes, especially 233 U, increased ( Fig. 11 Fig. 11 ). After the first 20 years, with the depletion of 239 Pu, the total β eff gradually increased and then tended to be constant. As for Pu-started modes, with 239 Pu gradually replaced by 233 U, the total β eff gradually increased and then tended to be constant at 291 pcm and 312 pcm in an MCFR and MFFR, respectively. Moreover, due to the higher fission rate fraction of 234 U in an MFFR ( Fig. 11 Fig. 11 ), the total β eff at equilibrium state was higher than that of an MCFR. Throughout the operation, the changes of total β eff in an MCFR and MFFR for the HALEU-started and Pu-started modes were 369 pcm and 62 pcm; and 335 pcm and 89 pcm, respectively. 4.5 Radioactivity analysis 2 Radioactivity analysis is an important aspect of reactor safety analysis. Here, the radioactivity of the fuel-salt in an MCFR and MFFR was analyzed to provide a reference for the radiation shielding design during online reprocessing. Thereafter, the radioactivity of the nuclear waste was analyzed to provide relevant parameters for the intermediate storage and final repository of nuclear waste. Online reprocessing leads to a good breeding performance and neutron economy of an MSR, but at the cost of facing the highly radioactive fuel-salt throughout the operation. In order to be sure of the radiation shielding design, and fuel-salt cooling time, the radioactivity of the fuel-salt in an MCFR and MFFR was analyzed. Fig. 12 Fig. 12 shows the evolution of the decay heat of fuel-salt during reprocessing. Due to a lower content of the short-lived FPs ( 137 Cs and 90 Sr, about 30-year half-life) at equilibrium state ( Fig. 13 Fig. 13 ), the decay heat in an MCFR is much lower than that in an MFFR; it drops to a negligible level much faster. Fig. 14 Fig. 14 shows the evolution of high-energy gamma radiation; the horizontal dashed-line denotes the high-energy gamma-ray level of the spent fuel in a sodium-cooled fast reactor, which has been cooling for 5 years [ 29 29 ] . The high-energy gamma-ray level of an MCFR was also found to be lower than that of an MFFR, and its value dropped to the reference level within three months; however, it took over 2 years in an MFFR to drop to reference level. Due to the specificity of neutron shielding, it is necessary to calculate neutron emissions in a fuel-salt during reprocessing. Fig. 15 Fig. 15 shows the evolution of neutron emissions. The neutron emission rate of an MCFR was only 1/60 th that of an MFFR, with almost all originating from the spontaneous fission of 252 Cf, resulting from a higher content of heavy nuclides in an MFFR due to its softer neutron spectrum. Radio-toxicity and decay heat derived from nuclear waste has a non-negligible impact on reprocessing, manufacturing, and particularly, on the final repository. For a closed cycle, all actinides need to be disposed only when the reactor is decommissioned. Therefore, the radio-toxicity and decay heat during operation are mainly derived from FPs during online reprocessing. Besides, a loss of nuclides occurs during online reprocessing; here, we assume a loss rate of 10 -5 for TRU and 10 -7 for uranium isotopes [ 30 30 ] ; these nuclides are also the source of radio-toxicity and decay heat. Fig. 16 Fig. 16 shows the evolution of decay heat and radio-toxicity of nuclear waste. It can be seen that the radio-toxicity and decay heat are mainly determined by FPs; while that generated by nuclear waste in an MFFR is slightly higher due to its higher FP content. The radio-toxicity of both, an MCFR and MFFR dropped to the radioactivity level of natural uranium ore in 300 years. In addition, due to the buildup of highly radioactive daughter nuclei of 237 Np ( T 1/2 =2.14×10 6 y) and 233 U ( T 1/2 =1.59×10 5 y) such as 229 Th and 225 Ac, the second peak of the radio-toxicity and decay heat of TRU and U appeared at about 10 5 years. 5. Conclusion 1 In view of their good breeding performance, high inherent safety, and simple reprocessing requirements, molten salt fast reactors could be considered as ideal reactors for a closed Th-U cycle. This work focused on an investigation and comparison of the Th-U cycle performance of two typical types, i.e., MCFR and MFFR, using a computing tool developed in-house. Important parameters, including the evolution of heavy nuclides, breeding capability, safety parameters, and radio-toxicity were investigated and discussed to understand the transition behavior throughout the operation. It can be concluded that: 1) Regardless of HALEU or Pu being used as start-up fuels, the initial loading fissile nuclides of an MFFR are heavier than that of an MCFR. An MCFR could become self-sustaining at a reprocessing rate of 3.25 L/day, and an MSFR at 9.6 L/day. At a reprocessing rate of 40 L/day, the DT of an MCFR and MFFR in HALEU-started mode and Pu-started mode was 16.5 and 16.2 years; and 88.0 and 48.0 years, respectively. Moreover, the average 233 U production at equilibrium state for an MCFR and MFFR was 243 kg and 86 kg, respectively. 2) Throughout the operation, TCR was sufficiently negative in an MCFR and MFFR, and the absolute value of TCR in an MCFR was higher due to its obvious fuel density coefficient. 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Pope , et al ., Sustained Recycle in Light Water and Sodium-Cooled Reactors . United States : N. p. , 2010 . Web. (2010) . Sustained Recycle in Light Water and Sodium-Cooled Reactors Aufiero. M , Mariya Brovchenko , Antonio Cammi , et al . Calculating the effective delayed neutron fraction in the Molten Salt Fast Reactor: Analytical, deterministic and Monte Carlo approaches . Ann. Nucl. Energy 65 , 78 - 90 ( 2014 ). https://doi.org/10.1016/j.anucene.2013.10.015 https://doi.org/10.1016/j.anucene.2013.10.015 . Calculating the effective delayed neutron fraction in the Molten Salt Fast Reactor: Analytical, deterministic and Monte Carlo approaches 10.1007/s41365-020-00790-x This work was supported by the Chinese TMSR Strategic Pioneer Science and Technology Project (No. XDA02010000) and the National Natural Science Foundation of China (No. 91326201). 2020-03-06 2020-05-28 2020-05-29 2020-08-08 2020-08-01 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/s41365-020-00790-x http://dx.doi.org/10.1007/s41365-020-00790-x . 2020 Nuclear Science and Techniques 8 31