1 Introduction

Radionuclides are widely used in medical treatment, metallurgy, mineral exploration, industry, and other fields. Among them, ⁹⁰Sr, an artificial radionuclide with a high yield in nuclear reactions, has a high application value. The nuclide can emit beta-rays with an energy of 0.546 MeV, and the penetration depth of the ray in soft tissues is 1.38 mm, which allows it to be used for skin scarring. In addition, the long-term stable power brought by ⁹⁰Sr’s 28-year half-life makes it suitable for manufacturing nuclear batteries for long-term missions such as maritime navigation marks. Finally, the popularity of ⁹⁰Y radiopharmaceuticals makes it a great prospect in the production of ⁹⁰Sr-⁹⁰Y generators. According to the forecast of some institutions, the global market demand for ⁹⁰Sr is over $100 million per year, and ⁹⁰Y Ibritumomab is worth $30 million per year in sales. ¹³¹I is a pure beta radionuclide with a half-life of 8.05 days. It is mainly used in the treatment of thyroid diseases and malignant tumors, as iodine can be enriched in the thyroid. Currently, there are two mature ¹³¹I medical products: Na¹³¹I injection and Na¹³¹I capsules. With an annual sale of $400 million, ¹³¹I is one of the three most sought-after radionuclides in the radiation market [1]. Simultaneously, the domestic production of medical radionuclides in China tends to be stagnant. In 2014, the import quantity of ¹³¹I was as high as 20.5 kCi [2], while ⁹⁰Sr was mostly imported. The common production methods of radionuclides include the accelerator method, post-treatment product extraction method, reactor irradiation method[3], and reactor production method. Among them, the latter two have higher flexibility. Since 2007, the number of existing irradiation and processing facilities for medical isotopes in the world has been limited, and many of them are aging, with problems such as imminent withdrawal from the supply chain, target conversion, decommissioning and maintenance, and some planned and unplanned reactor shutdowns affect market supply [4]. Therefore, many countries have begun to develop research on the production of medical isotopes based on new reactors and processes.

Therefore, research on nuclide production based on a molten salt reactor (MSR) has also attracted people's interest after the aqueous solution reactor [5]. As one of the four generation reactors, the MSR has the advantages of on-line addition of fission fuel and on-line treatment of fission products because of its use of liquid fuel, which can flow in the entire main loop. Thus, the extraction of isotopes from fission products of fluorinated salts in MSRs may be an attractive technique with the feasibility of large-scale on-line mass production of isotopes. Research has indicated that for inert gases and volatile metals produced by fission, an on-line bubbling and purging device can be used to introduce a tail gas treatment system that can then be radionuclide by an electric field or spray. Chuvilin [6] and Kang [7] evaluated the potential of a MSR to produce ⁹⁹Mo, and designed the relevant in-reactor and out-reactor extraction devices, which entered the gas phase through the gas–liquid interface, and has the capacity to produce 1.96×10⁶ Bq of ⁹⁹Mo by-products per 1 MW of electricity produced. Sheu [8] studied the production characteristics of ⁹⁹Mo under different core designs. Result shows that compared with HomoType and RingType, the HeteType core model, which offered superior fuel utilization and radiotoxicity minimization, was considered the most promising design. Yu [9] studied the recovery of ¹³¹I from MSRs by extracting solid Te through a solid separator of a by-pass loop system (BPLS). The result shows that in a 2 MW reactor, about 155000 Ci of ¹³¹I could be produced annually. From the above, it can be concluded that many research institutions are producing radionuclides in MSRs. Additionally, there are other nuclides and methods that have potential research value.

A considerable amount of I and Sr deposits were found in the tail gas system of MSRE [10], which reveals a new method of extracting ⁹⁰Sr and ¹³¹I from a MSR. ¹³¹I exists mainly in the ionic state in the molten salt, and ¹³¹Te, the precursor of ¹³¹I, is a semi-soluble noble metal, half of which is dissolved in salt in the form of tellurium ions such as Te_3-[11] or Te_2-[12]. The other half enters the exhaust gas in the form of gaseous Te [10], and then decays in the trap before being collected. Furthermore, ¹³¹I can be removed from the molten salt by HF-H₂ bubbling [13] and then collected by spray. ⁹⁰Sr and its precursor ⁹⁰Rb are dissolved in the salt in the form of stable fluoride, while ⁹⁰Kr, the precursor of ⁹⁰Rb, is an insoluble rare gas, which will overflow at the gas–liquid interface of the molten salt pump or be carried by helium bubbles out of the molten salt into the off-gas treatment system.

In this study, a fundamental benchmark of a small modular MSR was established. Then, critical calculation and burn-up analysis of the core physical model will be carried out by SCALE6.1. Later, the reaction chain analysis, fission yield, equilibrium concentration, yield, and cooling time of ⁹⁰Sr and ¹³¹I nuclides, and their precursors ⁹⁰Kr and ¹³¹Te, in the core will be launched. This provides key input data for the study of target isotope production, migration rules, and extraction methods.

2 Model and method

In this study, a thorium molten salt reactor (TMSR) with a miniaturized and modular design was studied. The entire reactor block, which contains the reactor container, core, and fuel salt, is designed as a common module which is replaced every 10 years by lifting. The thermal power of the reactor is 30 MW. One of the two molten salt loops is a fuel salt loop loaded with LiF-BeF₂-ZrF₄-UF₄-ThF₄ (compared with the chloride used in MCFR [14], the behavior of fission products in fluoride salt has been studied more maturely, hence, fluoride salt is selected here), and the other is a cooling salt loop loaded with FLiBe or FNaBe.

From inside to outside, the modular reactor core consists of the core active region, the graphite reflector, and the down-comer. A schematic diagram is shown in Fig. 1. The main parameters are listed in Table 1. The active region is composed of 127 hexagonal graphite assemblies with an edge distance of 18 cm and a height of 300 cm, of which 116 are fuel channels with an inner diameter of 6 cm, eight control rod channels, and three molten salt contact irradiation channels. The other four irradiation channels are located in a reflective layer with an equivalent thickness of 35 cm formed by splicing fan-shaped assemblies. The graphite reflective layer can reduce the neutron leakage rate and slow down the fast neutrons to reduce the radiation damage to the alloy material.

Fig. 1.Full-screen View

(Color online) Horizontal(a) and vertical(b) sections of the core model

SCALE [15](Standardized Computer Analyses for Licensing Evaluation), a modular programming system, released in 1980 by Oak Ridge National Laboratory, is widely used in nuclear safety analysis and design, covering reactor criticality safety, reactor physics, radiation shielding, spent fuel and radioactive source term analysis, sensitivity and uncertainty analysis, etc. At present, it is widely used in the optimization design of water reactors and various advanced nuclear energy systems, such as gas-cooled fast reactors and MSRs [16-20]. This study is based on SCALE 6.1 updated in 2008. In the calculation, TRITON, a control module, is used for the coupling calculation of transport and fuel consumption. The functional modules involved include KENO-VI of the Monte Carlo transport program, Origen-S of the burn-up calculation module, and the corresponding coupling program.

The burn-up equation used for calculating the nuclides concentration is as follows:

Among which:

where λ is the decay constant, γ_i,i’ is the yield of nuclide i when nuclear fission reaction occurs on fissile nuclide i’. The first term on the right of Eq.(1) represents the rate of production of the isotope i-1 due to neutron absorption or decay, the second term represents the total loss rate of isotope i due to neutron absorption or decay, and the third term represents the rate of production due to fission reactions.

Figure 2(a) shows the main decay-transmutation chain of ¹³¹I (the path that accounts for less than 5% of the fission yield is omitted in the figure). The fission reaction induced by thermal neutrons produces radionuclide ¹³¹Sb. The vast majority decay products of ¹³¹Sb are ¹³¹Te, and only 6.2% of ¹³¹Sb produces ^131mTe in the excited state when it decays, which accounts for half of all ^131mTe sources. The excited state of ^131mTe has two decay pathways. Approximately 3/4 of the ^131mTe is converted into ¹³¹I through β-decay, and the remaining ^131mTe returns to the ground state ¹³¹Te (T_1/2=25 min) by emitting internal conversion electrons. Finally, the ¹³¹I produced by the two pathways generates stable ¹³¹Xe through β-decay (T_1/2=8 d). Figure 2(b) shows the main decay-transmutation chain of ⁹⁰Sr (the path that accounts for less than 5% of the fission yield is omitted in the figure). The analysis of the decay-transmutation chain starts at ⁹⁰Kr due to the short half-life of ⁹⁰Br (T _1/2 = 1.92 s). When a thermal neutron bombards a ²³⁵U atom to initiate a fission reaction, ⁹⁰Kr and a small amount of ^90mRb is produced, of which 87% of ⁹⁰Kr produces ⁹⁰Rb via β-decay, and the remaining ⁹⁰Kr produces ^90mRb. A small number (< 5%) of ^90mRb produces ⁹⁰Rb by emitting an internal conversion electron, and most of ^90mRb produces ⁹⁰Sr by β-decay. ⁹⁰Sr has a long half-life of 28.79 a, the decay product is ⁹⁰Y, which can be used in radiopharmaceuticals, and the final product of the decay chain is a stable nuclide-⁹⁰Zr.

Fig. 2.Full-screen View

Decay-transmutation chain of ¹³¹I (a) and ⁹⁰Sr (b)

3 Results and Discussion

3.1 Yield analysis of ⁹⁰Sr, ¹³¹I, and their precursors

The reactor block was designed to be replaced once every 10 years. The fuel is not processed on-line during the entire life, but rather processed in batches after being removed as a whole. To maintain the backup reactivity required for long-life full-power operation, a higher initial fuel load is used. The initial concentration of UF₄ was 7.77%, ThF₄ was 1.78%, and the corresponding initial k_eff was 1.2972. As burn-up proceeds, ²³⁵U is consumed, and ²³⁸U and ²³²Th absorb neutrons to produce fissionable nuclides ²³⁹Pu and ²³³U. Since there are three fissionable nuclides, and the yield of different fissionable nuclides to the target nuclides may not be the same, the variation in the total amount and percentage of fissionable nuclides in the reactor is discussed to measure the change in the average fission yield, as shown in Fig. 3. As the burn-up time increases, the fissile nuclides in the reactor are gradually consumed and the total mass continues to decrease. U is dominant in the initial charge and the other two fissionable nuclides need to absorb neutrons before they can be produced, therefore, the proportion of ²³⁵U in the entire lifetime is extremely high. However, even at the end of its life, ²³⁵U accounts for more than 90% of the fissionable nuclides, whereas ²³⁹ Pu and ²³³ U account for only about 5%.

Fig. 3.Full-screen View

Percentage (a) and total (b) change of fissile nuclides

The thermal neutron yield data of isotopes ¹³¹I, ¹³¹Te, and ^131mTe are shown in Table 2 [21]. The independent yield is on the left, which is the yield before the β-decay but after the fission reaction. On the right is the sum of the cumulative yield, which is the independent yield and the yield of nuclides produced by β-decay. From ²³⁵U to ²³³U to ²³⁹Pu, the yield of fission nuclides to the same nuclides increases gradually. Among them, the independent yield of ¹³¹I accounted for 0% of ²³⁵U, 0.7% of ²³³U, and 0.8% of ²³⁹Pu, indicating that ¹³¹I is basically derived from the decay of the precursor rather than the direct fission of the fissile nuclide, such as ²³⁵U. Furthermore, the fission yields of ¹³¹Te accounted for 89.3% of ²³⁵U, 79.0% of ²³³U, and 82.6% of ²³⁹Pu of the cumulative yield of ¹³¹I, therefore, ¹³¹Te of the two precursors contributed most of the fission yields of ¹³¹I.

Table 2.Full-screen View

Fission yield of ¹³¹I and its precursors

Nuclide	131Te		131mTe		131I
	Independent yield	Cumulative yield	Independent yield	Cumulative yield	Independent yield	Cumulative yield
235U	6.79 × 10-4	1.84 × 10-2	1.47 × 10-3	3.02 × 10-3	0	2.06 × 10-2
233U	8.44 × 10-4	1.92 × 10-2	4.95 × 10-3	6.28 × 10-3	1.70 × 10-4	2.43 × 10-2
239Pu	2.70 × 10-3	3.17 × 10-2	5.75 × 10-3	8.13 × 10-3	3.20 × 10-4	3.84 × 10-2

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Since the yields of the three fissionable nuclides to the target nuclides is different, the average cumulative yields of ¹³¹I and ¹³¹Te over the burn-up time of the three fissionable nuclides is studied in combination with the fission yield of the fissionable nuclides to ¹³¹I and ¹³¹Te, as shown in Fig. 4. The yields of ¹³¹I and ¹³¹Te increased continuously during the lifetime, which resulted from the increase in the contents of ²³⁹Pu and ²³³U in the fissile nuclides. The cumulative yield of ¹³¹Te was approximately 3 and 10 times that of ²³⁵U, respectively. Even though the yields of ¹³¹I and ¹³¹Te were 1.84% and 2.06%, respectively, the yields of ¹³¹I and ¹³¹Te reached 1.72 × 10^-4 TBq/MW/s and 0.282 TBq/MW/s, respectively.

Fig. 4.Full-screen View

Fission yield of ¹³¹I and ¹³¹Te varied with burn-up time

In addition, ¹³¹Te has a short half-life of 25 min, therefore, it takes less time to reach equilibrium. From Fig. 5(a), at around 250 min, the production rate and decay rate of ¹³¹Te become balanced, and the saturation activity of ¹³¹Te in molten salt is about 37405 TBq, while the corresponding activity of ^131mTe is about 261 TBq. Consequently, if 50% of Te enters the gas phase, the annual ¹³¹I produced by Te decay in the tail gas can reach 66310 TBq.

Fig. 5.Full-screen View

Activity of ¹³¹Te(a) and ¹³¹I(b) varied with burn-up time

The activity changes of ¹³¹I and its precursors are illustrated in Fig. 6, which shows that ^131mTe has the lowest activity, of only about 1/10 of that for ¹³¹Te. In fact, although the yield of ^131mTe is less than ¹³¹Te (about 20% of ¹³¹Te of the total lifetime), the cumulative concentration of ^131mTe in the reactor is higher than ¹³¹Te due to the long half-life of ^131mTe (about 80 times that of ¹³¹Te). After reaching equilibrium, the concentration of ^131mTe can reach about six times that of ¹³¹Te. The activity of ¹³¹I is the highest because ¹³¹I is the decay product of ¹³¹Te and ^131mTe, and ¹³¹I has a longer half-life.

Fig. 6.Full-screen View

Yields of ¹³¹I and its precursors varied with burn-up time

From Fig. 5(b), the production and disappearance of ¹³¹I reached equilibrium after running for about 40 days, and the equilibrium value was about 40300 TBq. Since then, although the yield of nuclides continued to increase, as shown in Fig. 3, the yield did not change much for the total mass of fissile nuclides is decreasing. Even at the end of its life, the activity is only 1.06 times the equilibrium activity. If the HF-H₂ bubbling method is used to extract ¹³¹I from molten salt, and the recovery rate is 95%[22], the annual ¹³¹I that can be recovered from molten salt is 3.49 × 10⁵ TBq.

Table 3[21] shows the thermal neutron fission yield of ⁹⁰Sr and its precursor. The proportions of the independent ⁹⁰Sr yield of the three fissile nuclides in the cumulative yield were 2.1% (²³⁵U), 6.8% (²³³U), and 5.1% (²³⁹Pu). It can be seen that ⁹⁰Sr mainly originates from the decay of the precursors ⁹⁰Rb and ^90mRb. Figure 7 displays the average cumulative yield of ⁹⁰Kr and ⁹⁰Sr and the ratio of the average cumulative yield of ⁹⁰Kr to ⁹⁰Sr versus time. Fig. 7(b) shows that the average cumulative yield of ⁹⁰Kr in the entire lifetime accounts for more than 80% of the average cumulative yield of ⁹⁰Sr, which indicates that ⁹⁰Kr contributes most of the ⁹⁰Sr yield. Therefore, most of the ⁹⁰Sr in the reactor was produced by the path that ⁹⁰Kr decays to ⁹⁰Rb and ^90mRb, and ultimately, these two nuclides decay into ⁹⁰Sr. This also suggests that blowing ⁹⁰Kr out of the core can greatly reduce the ⁹⁰Sr content of the salt. The upper curve in Fig. 7(a) is the curve of the ⁹⁰Kr fission yield over the burn-up time. As the burn-up increased, the yield gradually decreased. This is mainly due to the decrease in the proportion of ²³⁵U in fissile nuclides, whose contribution to yield is higher than that of the other two nuclides. Even at the end of its life, its yield is about 5.76%, which corresponds to a yield of approximately 53.7 TBq/MW/s.

Table 3.Full-screen View

Fission yield of ⁹⁰Sr and its precursor

Nuclide	90Kr		90Sr
	Independent yield	Cumulative yield	Independent yield	Cumulative yield
235U	4.66 × 10-2	5.09 × 10-2	1.23 × 10-3	5.90 × 10-2
233U	4.47 × 10-2	4.64 × 10-2	4.46 × 10-3	6.61 × 10-2
239Pu	1.64 × 10-2	1.76 × 10-2	1.23 × 10-3	2.40 × 10-2

Show more

Fig. 7.Full-screen View

Average cumulative yield of ⁹⁰Kr and ⁹⁰Sr(a) and the ratio of the average cumulative yield of ⁹⁰Kr to ⁹⁰Sr (b)versus burn-up time

Figure 8 shows the yield variation of ⁹⁰Sr and ⁹⁰Kr. The ⁹⁰Kr nuclide, represented by the upper curve, reaches the highest activity (about 68000 TBq) at the first burn-up step (0.25 d), then the activity decreases gradually. This is mainly due to its short half-life (T_1/2 = 32 s), which is much smaller than the first burn-up step (d) chosen in the calculation. The lower curve represents the activity curve of ⁹⁰Sr. In contrast to the activity change of ⁹⁰Kr, the activity of ⁹⁰Sr increased slowly with the increase in running time, and the activity of ⁹⁰Sr did not reach equilibrium at the end of life, however, the increasing speed was obviously slowed down, and the final activity reached 10⁴ TBq. This is because ⁹⁰Sr has a long half-life (T_1/2 = 28.79 a), which is about three times the lifetime of the reactor, hence, the disappearance rate caused by its decay is relatively small. At the same time, ⁹⁰Rb and ^90mRb were produced and decayed in the reactor, which led to an increase in the ⁹⁰Sr activity. In conventional pressurized water reactors, ⁹⁰Sr is one of the main sources of radioactivity for reprocessing waste. Therefore, removing ⁹⁰Kr on-line by the bubbling method can greatly reduce the workload of post-processing [23]. If the Sr produced by Kr decay is collected directly from the exhaust gas and the time of nuclide generation to exhaust gas is ignored, the Kr overflow rate is 90%[10], and the ⁹⁰Sr entering the exhaust gas every year is approximately 327 TBq, which can reach 20% of ⁹⁰Sr activity in fuel in one year.

Fig. 8Full-screen View

Yields of ⁹⁰Sr and ⁹⁰Kr varied with burn-up time

4 Conclusion

The radionuclides ¹³¹I and ⁹⁰Sr are both widely used in industry and medicine. Traditional production methods, such as target irradiation or radioactive waste extraction, are costly and waste-intensive, and face the problems of reactor-type aging and unscheduled shutdown with uncertain yields. If the production of these two nuclides is considered in a MSR, ¹³¹I can be blown out of the molten salt in the form of HI or Te (g), and ⁹⁰Sr can be blown out of salt in the form of Kr.

In this study, the burn-up chains of ¹³¹I and ⁹⁰Sr nuclides that are suitable for extraction from the reactor are arranged. ¹³¹I mainly originates from the decay of ¹³¹Te and ^131mTe, and ⁹⁰Sr mainly originates from the decay of ⁹⁰Kr, ⁹⁰Rb, and ^90mRb. Subsequently, we analyzed the yield and the proportion of fissionable nuclides in the lifetime of a 30 MW MSR. The results show that the total amount of fissionable nuclides continues to decrease, and the proportion of ²³⁵U becomes smaller, while the proportions of ²³³U and ²³⁹Pu gradually increased, however, the minimum proportion of ²³⁵U was greater than 90%. Consequently, the yield changes of the target nuclides and their precursors were analyzed by combining the yield contribution and the ratio change of fissile nuclides. The results showed that the yields of ¹³¹I and ¹³¹Te increased gradually, while the yields of ⁹⁰Sr and ⁹⁰Kr decreased gradually.

Furthermore, we discussed the time and saturation activity required for the nuclide in the reactor to reach equilibrium activity. The equilibrium time of ¹³¹I is about 40 days, and the saturation activity in salt is approximately 40300 TBq. The equilibrium time of ¹³¹Te with a slightly shorter half-life is approximately 250 min, and the equilibrium activity is 37405 TBq. Subsequently, the number of nuclides that migrate into the exhaust gas is estimated based on the migration probability in the literature. If ¹³¹I is extracted from the molten salt by the HF-H₂ bubbling method, it can be recovered from the molten salt to 3.49 × 10⁵ TBq per year and transported into tail gas to 66310 TBq. Additionally, ⁹⁰Sr can be transported into tail gas to 327 TBq per year by the helium bubbling method, which can reach 20% of ⁹⁰Sr activity in fuel within one year. The results show that the yield of nuclides is doubled when the power is doubled. The yield of ¹³¹I and ⁹⁰Sr nuclides per unit power is approximately 1350 TBq and 530 TBq, respectively. Finally, the minimum cooling time of the isotope corresponding to the medicinal use is discussed, and the results showed that the impurity of I extracted by the electric field was less than 0.1% after cooling for 13 days, which could meet the medicinal requirements. The remaining ¹³¹I is now 32.5% of the original. After 11 days of cooling of the extracted I collected by HF-H₂ bubbling, the remaining ¹³¹I was 38.8% of the initial, and the impurities were less than 0.1%, which meets the requirements for medicinal purposes.