2.1 Calculation model

Here, the basic core design (Fig. 1) refers to REBUS-3700^[13], which is a typical chloride salt fast reactor designed in France. 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). Surrounding the fertile-salt is a graphite reflector (yellow-area, Fig. 1), which is used for saving fertile-fuel ^[14,15]. Outside the graphite reflector, B₄C (green-area, 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)F₄ in mol%, and the density of both is 4.1 g/cm^{3 [2,16]}. In an MCFR, the corresponding composition of both, the fertile-salt and fuel-salt is 55 mol% NaCl–45 mol% (HM)Cl₄, and their density is 3.6 g/cm^3[17]. Note that (Th+U)Cl₄ 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.

Fig. 1.Full-screen View

(Color online) Cross and vertical sections of the calculation model

2.2 Reprocessing schemes

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, which refers to an MSFR^[2,3]. 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 ²³³Pa decay into ²³³U. Finally, the carrier-salt is recovered through low-pressure distillation, leaving the FPs for disposal.

Fig. 2.Full-screen View

Reprocessing of the core

4.1 Comparison of neutron spectra

Neutron spectra which could help fundamentally indicate subsequent interpretations of results based on the actinide buildup and TCR were researched here. 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.

Fig. 4.Full-screen View

(Color online) Neutron spectra at initial-time (a) and the evolution of EALF (b)

In order to quantitatively describe neutron spectra during the entire operation, the energy of the average lethargy causing fission (EALF) was introduced^[25], which was used as a quantization parameter of the average neutron energy in a reactor expressed as:

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) 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 ²³⁸U; it had a broader resonance peak and a larger resonance capture cross-section than ²³²Th, resulting in a more obvious resonance in the neutron spectra. Then, it gradually attained an equilibrium-state on consumption of ²³⁸U and buildup of FPs.

4.2 Breeding capability

Here, the breeding performance of an MFFR and MCFR were explored based on the Breeding Ratio (BR), net production of ²³³U, 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, ²³³Pa was extracted from the core and blanket, and stored outside the reactor to let it decay into ²³³U. To maintain criticality, some ²³³U needed to be fed back into the core; the amount of remaining ²³³U outside the reactor is the net ²³³U production. When the mass of ²³³U outside the reactor equaled that at initial ²³³U loading, it indicated that the produced ²³³U was sufficient to start a new MCFR/MFFR. DT is the time required to double the amount of ²³³U^[26].

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. 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.

Fig. 5.Full-screen View

(Color online) The BR of an MCFR and MFFR in an equilibrium state versus reprocessing rate

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]. 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^[5,24]. 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 ²³³U generation and direct disappearance. Regeneration Ratio (RR) is defined by Eq. (4); an RR greater than 1 suggests that the production of ²³³U is greater than its consumption.

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 ²³⁹Pu and ²³⁵U in the early stage; the consumption of ²³³U is small. As ²³³U 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 ²³³U is shown in Fig. 6(b); the dashed-line represents the initial ²³³U inventories, using ²³³U as the start-up fissile material. A higher RR in an MCFR resulted in a faster net accumulation of ²³³U. 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^[24,27]. Besides, at the equilibrium state, the average annual net production of ²³³U for an MCFR and MFFR was 243 kg and 86 kg, respectively.

Fig. 6.Full-screen View

Evolution of the RR (a) and net production of ²³³U (b)

4.3 Evolution of heavy nuclides

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) and 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 ²³²U content of an MCFR is always higher than that of an MFFR throughout the operation. This is because the generation of ²³²U mainly relies on the (n, 2n) reaction of ²³³U ^[28]; the reaction cross-section increases with the hardening of the neutron spectrum. As is well-known, ²³²U decay chains contain a number of highly radioactive decay products, particularly ²⁰⁸Tl, which emits gamma rays of up to 2.6 MeV, increasing the nonproliferation capacity of an MCFR.

Fig. 7.Full-screen View

(Color online) Evolution of heavy nuclides (a) and U isotopes (b) for an MFFR and MCFR started with Pu

Fig. 8.Full-screen View

(Color online) Evolution of heavy nuclides (a) and U (b) isotopes started with HALEU

The molar ratio of U isotopes in the blanket at equilibrium state is shown in Table 4. It indicates that the purity of ²³³U is considerably high with the molar ratio for an MCFR and MFFR being 95.28% and 99.22%, respectively. Importantly, the ²³²U content for an MCFR and MFFR is only 6 ppm and 0.03 ppm, respectively. Thus, nuclear proliferation issues could arise, ²³³U being easily retrievable through fluorination from the blanket.

4.4 Safety parameters

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:

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 L² along with the Doppler effect, simultaneously. In one-group approximation, L² is defined as:

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 B² 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:

where, K and T indicate the k_eff and temperature, respectively. 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.

Fig. 9.Full-screen View

(Color online) Evolution of TCR for different modes

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 (²³⁹Pu, ²³⁵U), has a flatter fission cross-section than ²³³U. Thus, spectral hardening has a less negative impact on ²³⁹Pu and ²³⁵U fission rather than on ²³³U. In addition, ²³⁹Pu and ²³⁵U also have a steeper capture cross-section as compared to ²³³U, suggesting a higher decrease of captures following spectral hardening, positively affecting TCR^[2]. Therefore, a high ²³³U content is beneficial for the Doppler coefficient.

Although ²³³U 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). It can be expressed as:

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 shows the single β_eff of various fissile isotopes. Due to the non-negligible fission cross-section of ²³⁴U in the fast spectrum, the fission contribution of ²³⁴U was also considered. The evolution of the total β_eff of different modes is displayed in Fig. 10.

Fig. 10.Full-screen View

(Color online) Evolution of total β_eff of different modes

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 ²³⁵U, while that of other fissile isotopes, especially ²³³U, increased (Fig. 11). After the first 20 years, with the depletion of ²³⁹Pu, the total β_eff gradually increased and then tended to be constant. As for Pu-started modes, with ²³⁹Pu gradually replaced by ²³³U, 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 ²³⁴U in an MFFR (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.

Fig. 11.Full-screen View

(Color online) Evolution of fission rate fraction with (a) HALEU, and (b) Pu as start-up materials

4.5 Radioactivity analysis

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 shows the evolution of the decay heat of fuel-salt during reprocessing. Due to a lower content of the short-lived FPs (¹³⁷Cs and ⁹⁰Sr, about 30-year half-life) at equilibrium state (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 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]. 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.

Fig. 12.Full-screen View

Evolution of decay heat of fuel-salt for an MCFR (solid-line) and MFFR (dashed-line)

Fig. 13.Full-screen View

(Color online) Mass of heavy nuclides (a) and FPs (b) at equilibrium state

Fig. 14.Full-screen View

(Color online) Evolution of high-energy gamma radiation for an MCFR (solid-line) and MFFR (dashed-line)

Due to the specificity of neutron shielding, it is necessary to calculate neutron emissions in a fuel-salt during reprocessing. 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 ²⁵²Cf, resulting from a higher content of heavy nuclides in an MFFR due to its softer neutron spectrum.

Fig. 15.Full-screen View

(Color online) Evolution of neutron emissions for an MCFR and MFFR

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]; these nuclides are also the source of radio-toxicity and decay heat. Fig. 16 shows the evolution of decay heat and radio-toxicity of nuclear waste.

Fig. 16.Full-screen View

Evolution of (a) Decay heat, and (b) 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 ²³⁷Np (T_1/2=2.14×10⁶ y) and ²³³U (T_1/2=1.59×10⁵ y) such as ²²⁹Th and ²²⁵Ac, the second peak of the radio-toxicity and decay heat of TRU and U appeared at about 10⁵ years.