2.1 General Description of the MCFR

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, 20]. As shown in 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) 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). 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], 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) is adopted for fertile fuel saving [22]. Outside the graphite reflector, a 10-cm-thick B₄C layer (the green area in 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.

Fig. 1.Full-screen View

(Color online) Axial and vertical cross sections of a MCFR

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. The fuel salt is 55NaCl-45(Th+U)Cl₄ in mol%, while the fertile salt is 55NaCl-45ThCl₄. The Th and U in the fuel salt are ²³²Th and ²³³U, respectively, and their ratio is adjusted so as to maintain the reactor criticality. Because of the small difference in atomic mass between ²³²Th and ²³³U, 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)Cl₄ can dissolve to a concentration of 45 mol% in chloride salt, while (Th+U)F₄ attains only 22.5 mol% in LiF, owing to the higher solubility of actinides in the chloride salt than in the fluorine salt.

2.2 Reprocessing Scheme

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 ²³³U 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 ²³²Th is added online to maintain the heavy metals at a constant level, and ²³³Pa 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 refers to a MSFR [20, 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. UCl₃ and PuCl₃ are first oxidized to UCl₆ and PuCl₆, 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 ²³³Pa to decay into ²³³U. Finally, the carrier salt is recovered through low-pressure distillation technology, leaving the FPs for disposal. At this stage, some of the ²³³U is refueled into the core to maintain criticality and any remainder constitutes the net ²³³U 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]. Considering the fuel salt and the fertile salt volumes of 98 m³ and 107 m³, the corresponding reprocessing periods are set to 980 d and 1070 d, respectively.

Fig. 2.Full-screen View

Reprocessing diagram for a MCFR

2.3 Calculation tool

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]. 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]. 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. 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 ²³³U 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 ²³³U 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]. The comparisons, displayed in Figs. 4 and 5, show that the TMCBurnup results agree well with the reference values, which proves the reliability of TMCBurnup for calculations for a MSFR.

Fig. 3.Full-screen View

TMCBurnup flowchart

Fig. 4.Full-screen View

Evolution of heavy nuclides with respect to time

Fig. 5.Full-screen View

Evolution of the breeding ratio with respect to the reprocessing time

3.1 ²³³U concentration and the BR at startup

Online refueling allows the critical state to be maintained by adjusting the molar concentration of ²³³U. Therefore, the critical concentration of ²³³U at startup was explored first for different core radii and ³⁷Cl enrichments. For Th-U fuel cycle starting with ²³³U and ²³²Th, the BR is defined as [26]:

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:

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 ²³³U production is analyzed according to mass evolution in subsection 3.3.

The initial ²³³U concentration and the BR are plotted as functions of the core radius in Fig. 6(a) and Fig. 6(b), respectively. For a certain ³⁷Cl enrichment, the ²³³U 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 ²³³U is needed to maintain the reactor in a critical state. Simultaneously, more neutrons are absorbed by ²³²Th for fuel breeding, while the neutron absorption of ²³³U remains nearly constant because of the adjustments of the ²³³U 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 ²³³U 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 ²³³U concentration and of the BR on the core radius show almost the same trends for other ³⁷Cl enrichments. Therefore, the following study was performed with a core radius of 250 cm.

Fig. 6.Full-screen View

²³³U concentration and the BR at startup as functions of the MCFR core radius.

For a certain core radius, the ²³³U concentration is also seen to decrease and the BR to increase with increasing ³⁷Cl enrichment. The reason is that the neutron absorption rate of ³⁵Cl decreases with increasing ³⁷Cl enrichment (as shown in Fig. 7) and more neutrons are absorbed by ²³²Th and ²³³U. This is helpful for fissile fuel saving with the increase of ³⁷Cl enrichment in the carrier salt. When the ³⁷Cl enrichment is greater than 97%, the neutron absorption of ³⁵Cl is very small, which has little impact on neutron economy and the breeding performance.

Fig. 7.Full-screen View

Relative absorption of nuclides as a function of ³⁷Cl enrichment.

3.2 Excess reactivity and operation period without processing

As mentioned above, for a given core radius, different ³⁷Cl enrichments correspond to different ²³³U concentrations. To explore the neutron characteristics without post-processing, the ²³³U concentration was fixed to 5.0 mol%, the critical value for chloride salt with natural enrichment. Then, the effect of ³⁷Cl 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 ³⁷Cl enrichment in Fig. 8. When the ³⁷Cl enrichment is 24.23% (natural chloride), the initial excess reactivity is 122 pcm, and it increases to approximately 15823 pcm when the ³⁷Cl enrichment is 97%. The reason is that the neutron absorption cross section of ³⁵Cl is very large. With increasing ³⁷Cl enrichment, the ³⁵Cl 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 ³⁷Cl enrichment increases to 100%, the initial excess reactivity equals 15858 pcm. This value is almost equal to that corresponding to 97% enrichment, since the ³⁵Cl content and its corresponding neutron absorption rate are very low and the excess reactivity is less affected by increasing ³⁷Cl enrichment. Besides, the k_eff evolution under full-power operation without post-processing is shown in Fig. 9. The operation period is only 175 days when the ³⁷Cl 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 ³⁷Cl enrichment is very similar to that of the initial excess reactivity. This is also because a decrease in ³⁵Cl 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 ³⁷Cl enrichment exceeds 97%, the operation period remains almost constant because the neutron absorption of ³⁵Cl is sufficiently low.

Fig. 8.Full-screen View

Initial excess reactivity as a function of ³⁷Cl enrichment.

Fig. 9.Full-screen View

Evolution of K_eff without online reprocessing.

3.3 Breeding performance with online reprocessing

This subsection explores depletion with online reprocessing from the perspective of the BR, the net production of ²³³U, 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, ²³³U 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 M₀, the DT, and the average annual production of ²³³U for different ³⁷Cl enrichments, and are listed in Table 2.

Under this condition, the BR is obtained using Eq. (1), as displayed in Fig. 10. ³⁷Cl enrichment clearly plays an important role in the evolution of the BR. Fig. 10 shows that, for a given ³⁷Cl enrichment, the BR increases slightly over time, in contrast to a thermal reactor like a MSBR. This is due to the accumulation of ²³⁴U, 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 ³⁷Cl enrichment can improve its BR significantly. When ³⁷Cl enrichment increases to 97%, the BR can be improved to 1.299, which is only 0.6% lower than for 100% ³⁷Cl enrichment.

Fig. 10.Full-screen View

Evolution of the BR as a function of time

The net annual production of ²³³U was then explored since it is the dominant fissile material in the Th-U fuel cycle. Because of the on-line reprocessing, ²³³Pa could be extracted from the active core and from the fertile salt to decay into ²³³U. The ²³³U obtained from the decay of ²³³Pa in the fertile salt was also extracted. The extracted ²³³U was partially refueled into the active core to ensure criticality. Thus, the annual net production of ²³³U can be expressed as [26]:

where the subscripts ex and re denote extraction and refueling, respectively.

The annual net production of ²³³U is plotted in Fig. 11, and shows that ³⁷Cl enrichment also has a significant impact. When the chloride at the natural enrichment level is adopted, the net production of ²³³U is negative, signifying that fuel breeding cannot be realized without enriching ³⁷Cl. When ³⁷Cl enrichment increases from 96% to 97%, the annual net ²³³U production increases by 7 kg, the same result as by increasing ³⁷Cl enrichment from 97% to 100%. In addition, the annual net ²³³U production of the 99% ³⁷Cl enrichment is 283 kg/a, which is almost the same as for 100% enrichment.

Fig. 11.Full-screen View

Net ²³³U production over time

When the net production of ²³³U (M) equals the initial inventory of ²³³U (M₀), the fissile fuel doubles. This is sufficient for starting a new MCFR, and the corresponding time is the doubling time. 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 ²³³U. When the ³⁷Cl 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 ³⁷Cl enrichment from 97% to 100%. When the ³⁷Cl enrichment increases to 99%, the DT is shortened to 62.93 a, which is only 0.3% longer than the DT for 100% ³⁷Cl enrichment.

In summary, the results for the BR, the net production of ²³³U, and the DT all display very similar trends. When using natural chloride salt, ²³³U breeding cannot be realized owing to the high neutron absorption rate of ³⁵Cl. When the ³⁷Cl 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 ³⁶Cl and S

Because of the neutron absorption of ³⁵Cl, S and ³⁶Cl are generated through the reactions of (n,γ), (n,p) and (n,α) [19], as shown in Fig. 12. Element S can cause "sulfur cracks" that corrode the structural material. ³⁶Cl is a long-lived radionuclide that is easily soluble in water [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.

Fig. 12.Full-screen View

Reaction chain of ³⁵Cl to produce S and ³⁶Cl.

The impact of ³⁷Cl enrichment on the production of S and ³⁶Cl was determined, giving the results shown in Fig. 13. The S and ³⁷Cl contents after 100 years are listed in Table 3. It appears that the buildup of S and ³⁶Cl is much faster when natural chloride salt is used. After 100 years, the S and ³⁶Cl contents reach approximately 802 and 948 ppm, respectively, but only approximately 30 and 36 ppm in the case of 97% ³⁷Cl enrichment. When the ³⁷Cl enrichment increases to 99%, the S and ³⁶Cl 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, ³⁷Cl also needs to be enriched. When the enrichment of ³⁷Cl increases from 96% to 97%, the S and ³⁶Cl contents after 100 years decrease by 30 and 26 ppm, which is sightly more than the decrease caused by an increased ³⁷Cl enrichment from 97% to 100%. When the ³⁷Cl enrichment increases to 99%, the production of harmful isotopes is almost the same as for 100% enrichment.

Fig. 13.Full-screen View

Contents of S (solid lines) and ³⁶Cl (dotted lines) over time.

The evolution of S isotopes was also explored to obtain a clearer understanding of the production of various nuclides under 90% ³⁷Cl enrichment. As displayed in Fig. 14, S mainly exists as the isotopes ³²S and ³⁴S, while ³⁵S increases rapidly during the first 2 years and then remains constant because of the equilibrium reactions ${}_{17}^{35}\text{Cl}{\stackrel{(n\mathrm{,}p)}{\to }}_{16}^{35}\text{S}{\underset{88\text{ days}}{\overset{{\beta }^{-}}{\to }}}_{17}^{35}\text{Cl}$. From Fig. 13 and Fig. 14, the S and ³⁶Cl contents increase almost linearly over 100 years of operation, as a result of the slow depletion rate of ³⁵Cl, which deceases by only approximately 0.67%.

Fig. 14.Full-screen View

Mass of S as a function of time, for a ³⁷Cl enrichment of 90%

3.5 Safety parameters

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:

where K and T represent the effective multiplication factor and the fuel salt temperature, respectively.

The evolution of the TCR over time under different ³⁷Cl enrichments is plotted in Fig. 15. For a given depletion time, the absolute value of the TCR for natural chloride salt is much smaller than that for 100% ³⁷Cl enrichment owing to the large neutron absorption cross section of ³⁵Cl. When the ³⁷Cl enrichment exceeds 70%, the temperature coefficient is negative and varies within a small range.

Fig. 15.Full-screen View

Temperature coefficient of reactivity as a function of time

Additionally, Fig. 15 shows that, for a given ³⁷Cl 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:

where ${\overline{v}}_d$ and ${\overline{v}}_p$ denote the average delayed and prompt neutrons per fission of nuclide i, while Rf denotes the fission rate of nuclide i.

The evolution of β_eff over time, given in Fig. 16, shows that, for a given depletion time, β_eff for natural chloride salt is less than for 100% ³⁷Cl enrichment. This phenomenon originates from the differences in the fission fraction of fissile nuclides under different ³⁷Cl enrichments. This is further studied and exhibited as follows.

Fig. 16.Full-screen View

Total delayed neutron fraction as a function of time

For simplicity, only two cases are shown. The solid lines in Fig. 17 represent the fission rate fraction of fissile nuclides for a 24.23% ³⁷Cl enrichment, while the dashed lines represent that for 97% ³⁷Cl enrichment. The fissile nuclides, including ²³³U, ²³⁵U, ²⁴¹Pu, ²³⁹Pu, and ²³⁴U, are all considered for their high content and large fission cross section under the fast spectrum [27]. The single delayed neutron fractions of ²³³U, ²³⁴U,²³⁵U, ²⁴¹Pu, and ²³⁹Pu in the MCFR spectrum are 291, 531, 668, 543, and 219 pcm, respectively. The fission rate fraction of ²³³U decreases while that of the other fissile nuclides especially ²³⁴U and ²³⁵U increases during operation. Thus, their total β_eff increases during operation.

Fig. 17.Full-screen View

Fission rate fraction of fissile nuclides under ³⁷Cl enrichments of 24.23% (solid lines) and 97% (dashed lines)

For a given time of depletion, β_eff is greatest when the ³⁷Cl enrichment is 100%, owing to the smallest fission rate fraction of ²³³U. But β_eff for different ³⁷Cl enrichments increases less than 5 pcm over 100 years of operation, because ²³³U 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.