Schematic model of the SM-MSR-Pu

The SM-MSR-Pu consists of the active region, fuel chambers, radial reflector, axial reflector, control rod system, heat exchanger system, reactor vessel, and other structural parts. The core structure is shown in Fig. 1. The fuel salts of the primary circuit are mostly distributed in the graphite active region, fuel chambers, heat exchanger systems, and pipelines. The height and diameter of the active region are 3.2 m and 3.0 m, respectively. It is composed of 199 graphite hexagonal prism assemblies whose hexagon pitch size is 20 cm. Graphite subassemblies connect the upper and lower via the card slot, and are finally pressed and fixed by the upper and lower support plate. The supporting plate is a honeycomb structure, composed of hastelloy alloy material, 2.0 cm thick, and embedded in the groove of the graphite assembly. It is located on the core container support, which is used to support all the weight of the reactor core.

Fig. 1Full-screen View

(Color online) Geometrical description of the SM-MSR-Pu core

The graphite reflector is formed by 12 fan-shaped annular graphite tips with an equivalent thickness of 20 cm. A 2.0 cm-thick layer of the B₄C neutron absorber is installed on the outside of the horizontal graphite reflector, primarily to protect the reactor vessel from neutron leakage from the core. Outside the reflector layer, there is a 1.0-cm thick core barrel, which is composed of Hastelloy material to radially fix the graphite tip and form a stable descending ring cavity with the outer container.

Varying from solid fuel assemblies, liquid fuel salts of SM-MSR-Pu also serve as the coolant, circulating in the primary circuit and transferring heat. The designed maximum operating power of the SM-MSR-Pu is 250 MWth, and the average power density of the active zone is 11.0 W/cm³. The electrical power is 100 MW, which is significantly lower than the standard for small reactors (<300 MWe). The designed power and vessel size satisfy the standards of a small modular reactor. The module of the reactor container meets a variety of land transportation standards. Based on the minimum limit of railways and highways, the diameter of the container body was designed according to the limit of less than 3.88 m. Each component of the reactor adopts a modular design, which can be processed and produced in the factory and transported to the destination for installation via railways or highways. The composition and molar ratio of molten salt are as follows: 70%LiF+17.5%BeF₂+12.5%(ThF₄+PuF₃), and the enrichment of Li-7 is 99.995%. The starting fuel, plutonium, is extracted from the spent fuel of a PWR, which consists of approximately 1.8% ²³⁸Pu, 59% ²³⁹Pu, 23% ²⁴⁰Pu, 12.2% ²⁴¹Pu, 4% ²⁴²Pu [12]. The brief physical parameters of the core structure are provided in Table 1.

The off-line batch fuel-processing scheme is adopted in the SM-MSR-Pu. In other MSR designs for fuel breeding, including the molten-salt breeder reactor (MSBR) and molten-salt fast reactor (MSFR), the fuel conversion ability of MSR can be significantly improved by on-line fuel processing technology. Theoretically, MSRs with a closed fuel cycle can be optimized by utilizing thorium resources, and can be considered one of the best models of the thorium uranium cycle [28, 29]. However, on-line fuel processing is restricted by on-line dry-processing technology, which is difficult to achieve in the short term. Therefore, off-line processing is considered to be a preferable transition strategy from the once-through fuel scheme to the on-line processing fuel scheme.

The off-line batch processing scheme of SM-MSR-Pu is mainly based on the helium bubbling system and electrochemical separation system, which can achieve reprocessing of the batch fuel and the on-line continuous removal of insoluble FPs. The reprocessing flowchart of the batch mode is shown in Fig. 2. The helium bubble system is an on-line fuel processing module based on the physical separation method of gas and liquid. A special blowing device is used to blow helium gas into the molten salt fuel in the primary circuit. These helium gases simultaneously flow with the fuel in the primary circuit and are finally separated from the fuel using a gas separation device. Through this process, insoluble gases and heavy metals such as H, He, N, O, Ne, Ar, Kr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Sb, Te, Xe, Rn, and other fission products can be removed from the reactor core; the separation efficiency of this method is significantly high. The extraction time of each bubble-processing cycle was set to 30 s in this study. The electrochemical separation system treats molten salt fuel using electrochemical methods and separates the soluble fission products (such as lanthanides) or secondary actinides that cannot be separated by the bubbling system from the molten salt, and returns the remaining molten salt, including most of the actinides, to the core.

Fig. 2Full-screen View

Flowchart of reprocessing scheme

On-line refueling is another fuel management technology applicable to molten salt reactors. On-line refueling can achieve lower excess reactivity and lower initial fuel loading, while reducing certain requirements for the control rod systems. The critical operating state is easier to maintain by coordinating the operation of the control rods and fuel supply modules. In the fuel scheme of SM-MSR-Pu, dry reprocessing technologies such as fluorination and volatilization, reductive extraction, and reduced pressure distillation are used to separate U, Th, transuranic isotopes(TRUs), and FPs. U, Np, and Pu are first extracted by the fluorination reaction and quickly reinjected into the core, whereas FPs and other discarded salts are further processed, encapsulated, and stored underground.

Calculation tool and methodology

To calculate the burn-up in molten salt reactors with fuel reprocessing, our colleagues developed a customized MSR reprocessing sequence (MSR-RS) [30] that can be applied to the on-line refueling and off-line batch processing for the SM-MSR-Pu. The MSR-RS program is coupled with CSAS6 (criticality analysis module), TRITON (problem-dependent cross section processing module), and ORIGEN-S (depletion and decay calculation module) in the SCALE6.1 program.

The calculation flowchart of the MSR-RS is shown in Fig. 3. After initializing the fuel compositions and core geometry, the TRITON and ORIGEN-S modules are called for neutron transport and depletion calculations, respectively. The specified isotopes set by the user can be reprocessed, and the required fuel will be refueled to maintain the criticality of the reactor. In addition, the CSAS6 module was used to provide a new keff value, a 238-group ENDF/B-VII cross-sectional database was selected, and 388 nuclides were tracked in trace quantities. The nuclide neutron reaction rates were calculated by the KMART6 module in the SCALE6.1 program.

Fig. 3Full-screen View

Flowchart of calculation

Reactor optimization scheme

In our previous study, different fuel salt volume fractions (VF) and hexagon pitch sizes (P) were calculated and compared to evaluate their impact on the neutronics performance [31]. To obtain more specific results, the performance parameters of the ²³³U production, plutonium utilization, MA accumulation, and passive safety for different volume fractions and pitch sizes were calculated to describe the burn-up performance in a small modular MSR.

The moderation ratio can be optimized by changing both the fuel channel radius and hexagon pitch size. The k_inf curve for different fuel volume fractions and pitch sizes is shown in Fig. 4. For larger fuel volume fraction values, the fission cross-sections of ²³⁹Pu and ²⁴¹Pu were smaller owing to significant hardening of the neutron spectrum. Therefore, within the research interval of this study, the value of k_inf was basically inversely proportional to volume fraction. In addition, the influence of the P size on k_inf cannot be underestimated. For larger P sizes, the neutron moderation was more inhomogeneous, thus the distribution of the neutron flux was relatively high in the low and high energy regions, and comparatively lower in the medium energy region. This form of the energy spectrum is more conducive to the fission reaction of plutonium and reduces the neutron resonance absorption, ultimately leading to a larger k_inf.

Fig. 4Full-screen View

(Color online) Time evolution of the initial k_inf and temperature reactivity coefficient for different volume fractions and pitch sizes

The evolution curve of the initial total temperature reactivity coefficient for different volume fractions and pitch sizes is also displayed in Fig. 4. The temperature coefficients dramatically decrease when volume fraction increases from 5% to 25%, from approximately 14 pcm/K to a negative value. The decrease in the temperature coefficient is influenced by the fuel doppler and graphite temperature effects.

The fuel doppler coefficient is negative within volume fraction values ranging from 10% to 25%. For a volume fraction value of less than 10%, the energy spectrum is softer, and broadening of the fission doppler of ²³⁹Pu and ²⁴¹Pu caused by the increase in temperature is more apparent, thus the doppler coefficient becomes a positive value. For larger fuel volume fraction values, the energy spectrum becomes harder, the capture resonance contribution of other actinide nuclides is apparent, and the doppler coefficient becomes negative.

The coefficient of the graphite temperature rapidly decreases as the fuel volume fraction increases, and its variation depends on the competition between the capture reaction of ²³²Th and the fission reaction of ²³⁹Pu and ²⁴¹Pu. For smaller volume fraction values, the proportion of thermal neutrons is higher, and the increase of the graphite temperature causes the neutron energy spectrum to shift to ²³⁹Pu and ²⁴¹Pu fission resonance peaks, resulting in an increased reactivity and positive graphite temperature coefficient. For larger volume fraction values, the neutron spectrum is relatively hard and deviates from the fission resonance peaks of ²³⁹Pu and ²⁴¹Pu. A higher graphite temperature is more favorable to the ²³²Th capture reaction, resulting in a negative graphite reactivity coefficient.

The ²³³U production, amount of TRUs, and MA accumulations for different fuel volume fractions (P=20 cm) during the 50-year operation of the reactor is demonstrated in Fig. 5a, b, c, respectively. The comparative analysis results indicate that a higher thermal neutron flux is conducive to the incineration and utilization of plutonium, whereas a higher resonance neutron flux will deteriorate the neutronics performance. Although a higher fuel volume fraction can achieve a higher ²³³U production, it will result in a higher capture fission ratio, lower neutron economy, and increased plutonium feed rates. Moreover, the accumulation of MAs increases as the fuel volume fraction increases, primarily owing to the higher initial plutonium loading and higher capture cross-section of most of the actinide nuclides.

Fig. 5Full-screen View

(Color online) Time evolution of (a) ²³³U productions, (b)amount of TRUs, and(c) MA accumulations for different volume fractions (when P=20 cm)

In conclusion, within the research interval (VF=10% –40%, P=10 cm – 40 cm), a smaller volume fraction and larger P are preferable for a long-term operation and low radioactive residue, whereas a higher volume fraction and smaller P can contribute to the utilization of plutonium and production of ²³³U. According to the aforementioned results, a smaller fuel volume fraction and higher P size are more favorable for improving the utilization efficiency of plutonium in a small MSR. After comprehensive consideration, a combination of VF=20% and P=20 cm was determined as a relatively excellent design parameter in this study.

Neutron spectrum and flux

The performance of the burn-up process significantly depends on the neutron spectrum, which is largely determined by the core graphite moderation ratio. The normalized neutron energy spectra in various regions for the initial time, 10th year, and 50th year are displayed in Fig. 6, demonstrating that the neutron spectra in molten salt are slightly harder and those in the graphite reflector are the softest. In addition, as the running time increases, the spectra become harder, which occurs owing to the following: 1) increase in the reaction rate of the thermal neutron absorption owing to the accumulation of fission products; 2)buildup of plutonium loading and changes in the composition of the plutonium isotope. The absorption cross-sections of ²⁴⁰Pu and ²⁴²Pu are significantly larger in the thermal neutron area and resonance energy region, and their mass fractions increase as the burnup time increases, which is critical for the hardening of the neutron spectrum.

Fig. 6Full-screen View

(Color online) Normalized neutron energy spectra in different regions and at different operating times

The thermal power distribution is significantly impacted by the spatial distribution of the moderated neutron. The thermal neutron (<0.625 eV) flux density for the entire reactor core decreases from the center to the edges; however, owing to the scattering effect of the graphite reflector, it slightly increases in the reflector. The maximum value of the thermal neutron flux density, with a peak value of approximately 1.128×10¹⁴/cm²/s, was found near the geometric center of the active region, as shown in Fig. 7. The peak of the thermal neutron flux density was dispersed throughout the graphite assembly. The thermal neutron flux of the fuel channel exhibited an apparent declining peak, which was approximately 85% lower than that of the adjacent graphite. The total, axial, and radial peak power factors were 2.78, 1.75, and 1.70, respectively.

Fig. 7Full-screen View

(Color online) Spatial distribution of thermal neutron flux density

The lifespan of the graphite subassembly is significantly impacted by the spatial distribution of fast neutrons (>0.052 MeV); the distribution is complementarily symmetrical to that of the thermal neutron flux, demonstrating an apparent flux peak in the geometric center of the fuel salt channel, as shown in Fig. 8. Moreover, a larger diameter of the channel resulted in a higher flux peak. The geometric center of the active region also demonstrated the highest fast neutron flux density, which was approximately 2.23×10¹⁴/cm²/s. The graphite reflector considerably lowered the fast neutron flux, which effectively reduced the radiation damage to the container vessel and extended its lifespan.

Fig. 8Full-screen View

Spatial distribution of fast neutron flux density

The average fast neutron flux density upon exposure to greater than 52 keV in the graphite assembly for the course of the first ten-year lifespan was determined to be approximately 1.04×10¹⁴/cm²/s. The lifespan of a graphite assembly is expected to be approximately 10 years based on the total fast neutron flux density that it can withstand (3×10²²/cm²) [32, 33]. The graphite irradiation deformation may be significantly influenced by the wide gradient of the fast neutron flux from the channel wall to the center of the graphite assembly. The hexagonal graphite assembly has a large opposite side distance of 20 cm, which is good for fuel utilization and the temperature coefficient. However, further research is needed to determine the effect of the temperature distribution and irradiation stress on the life of the graphite assembly. The lifespan of the core of each generation of reactors may need to be reduced to eight, or shorter, if the graphite life does not satisfy the design criteria.

Amount of actinides and fission contribution

The fluctuations in the amount of primary actinides are complicated as a result of the periodic batch processing and continuous on-line fuel input while the system is in operation. Figure 9(a) presents the temporal evolution of the amount of actinide nuclides throughout the course of a five-generation reactor lifetime. Throughout the burn-up process, plutonium is continuously added to the fuel salts to compensate for the loss of reactivity, increasing the accumulation of plutonium in the core. Additionally, with each off-line fuel process, the accumulated uranium in the fuel salt is separated, and more plutonium is added to the fuel salt for starting the next-generation reactor, causing an increase in the accumulation of plutonium. MAs quickly accumulate to approximately one-tenth the amount of plutonium.

Fig. 9Full-screen View

(Color online) Evolution curves of the (a) amount of actinides and (b) the fission fraction for different fissile isotopes

The total mass of thorium steadily decreases as the burn-up time increases. The loss of thorium is mostly used to absorb neutrons to form ²³³Pa, which subsequently decays into ²³³U. After each start-up, the amount of Pa quickly increases, tends to remain steady, and slightly decreases throughout the burn-up, primarily owing to the hardening of the energy spectrum and decrease in the ²³²Th absorption reaction rate.

The fission cross-section and fission contribution of plutonium decrease despite the amount of plutonium increasing, owing to the hardening of the energy spectrum. The amount of ²³³U continues to increase throughout the course of the 10-year operation cycle, reaching approximately 300 kg before fuel-unloading, and the fission contribution of ²³³U can surpass 10% at the end of each reactor-generation design life, as shown in Fig. 9(b). The by-product content of ²³⁵U is significantly low owing to the high purity of ²³³U production, resulting in a significantly low fission fraction of ²³⁵U, which is limited to 0.3%.

Net production and purity of ²³³U

The production of ²³³U, which is actually the accumulative total mass of ²³³U mixed in the primary fuel salts, is significantly dependent on the neutron absorption of ²³²Th. The reaction chain for the development of ²³²Th into ²³³U is expressed as follows: ${}^{232}\text{Th}{\stackrel{(\text{n,}\gamma )}{\to }}^{233}\text{Th}{\stackrel{\text{β}}{\to }}^{233}\text{Pa}{\stackrel{\text{β}}{\to }}^{233}\text{U}$

The total net ²³³U production for a multi-generation operating cycle can be estimated by adding the amount of ²³³U in the currently operating reactor and the product of (²³³U + ²³³Pa) extracted from the previous replaced core module. The real total production of ²³³U can be calculated as follows: ${}^{\text{233}}\text{U}\left(\text{Prod}\right){\text{=}}^{\text{233}}\text{U}\left(\text{In}{\text{v}}^{\prime }\text{t}\right){\text{+}}^{\text{233}}\text{U}\left(\text{Ext}\right){\text{+}}^{\text{233}}\text{Pa}\left(\text{Ext}\right),$ (1) where ²³³U (Inv’t) represents the residual ²³³U mixed in the fuel currently in operation, ²³³U (Ext) and ²³³Pa (Ext) are the amounts of ²³³U and ²³³Pa extracted from the previously replaced core module.

Uranium is extracted from the fuel salt during each refueling cycle and stored outside the core, where it eventually becomes a high-purity ²³³U product. Approximately 350 kg of uranium is produced and mixed in fuel salt during each 10-year operating cycle, as shown in Fig. 10. During the entire operating period, the increase in the accumulation of TRUs and hardening of the neutron spectrum will lead to a decrease in the ²³²Th neutron absorption rate and ²³³U annual production.

Fig. 10Full-screen View

(Color online)Time evolution of the amount of uranium isotopes

The purity of ²³³U diminishes as the burn-up duration increases during each operating cycle. ²³⁸Pu is continuously accumulated in fuel salts owing to the (n, 2n) reactions of ²³⁹Pu. The decay of ²³⁸Pu produces ²³⁴U, thus the increase in the amount of ²³⁸Pu leads to an accumulation of ²³⁴U, consequently decreasing the purity of ²³³U. After 30 years of operation, the purity of ²³³U can be maintained above 90%, which meets the demand for a pure thorium-uranium fuel cycle in a TMSR.

TRUs mole fraction and amount of MAs

The stability of the physical properties of the SM-MSR-Pu is restricted by the TRU mole fraction in fuel salt. The neutronics performance and physicochemical properties of fuel material are inevitably influenced by the build-up of TRUs. Every 10 days, approximately 5.8 kg of plutonium was loaded on-line into the fuel to compensate for the lost reactivity. Furthermore, approximately 700 kg of additional plutonium was added to the starting fuel for the next-generation reactor, leading to a significant increase in plutonium. The overall amount of plutonium accumulated increased from 821.61 kg to 5536 kg, despite 817.22 kg, 980.72 kg, 1015.83 kg, 1041.85 kg, and 1058.97 kg of plutonium being burned during the five fuel cycles. The time evolution of the amount of plutonium isotopes is shown in Fig. 11.

Fig. 11Full-screen View

(Color online) Amount of plutonium isotopes and MAs

²³⁹Pu and ²⁴¹Pu are the primary fissile materials and have relatively large fission cross-sections. The amounts of ²³⁹Pu and ²⁴¹Pu are typically stable over the period of each operational cycle of the generation-reactor, considering their consumption approximately equates to the amount of on-line feeding. The amount of ²⁴⁰Pu demonstrated the fastest growth and surpassed that of ²³⁹Pu within 50 years, which is mainly owing to the small capture cross-section and long alpha decay period (approximately 6594 y) of ²⁴⁰Pu.

The accumulated masses of MAs (primarily consisting of Np, Am, and Cm) reached 103.57 kg, 251.97 kg, 401.70 kg, 547.48 kg, and 680.92 kg within the five fuel cycles, respectively. The mass growth of Am was the fastest. The accumulation of ²⁴¹Am reached 409 kg, mainly owing to the beta decay of ²⁴¹Pu. The accumulation of ²⁴³Am was also considerable (greater than 135 kg), which was mainly owing to the transformation of ²⁴²Pu. Their nuclear chain reactions can be expressed as follows: $\begin{array}{l}{}^{\text{241}}\text{Pu}{\stackrel{\text{β}\left(\text{14}\text{.35}y\right)}{\to }}^{\text{241}}\text{Am}\\ {}^{\text{242}}\text{Pu}{\stackrel{\text{(n,γ)}}{\to }}^{\text{243}}\text{Pu}{\stackrel{\text{β}\left(\text{4}\text{.956}h\right)}{\to }}^{\text{243}}\text{Am}\end{array}$

The accumulation of Np is notably less than that of Am. The main sources of ²³⁷Np are the decay of ²⁴¹Am and decay of ²³⁷U. Owing to the relatively long half-life period of ²⁴¹Am (approximately 432.2 years) and the four (n,) reactions required to convert ²³³U to ²³⁷U, the production of ²³⁷Np is constrained, and the accumulated mass of Np is the smallest. The chain reactions that produce ²³⁷Np are as follows:

(1): ${}^{\text{241}}\text{Pu}{\stackrel{\text{β(14}\text{.35}y\text{)}}{\to }}^{\text{241}}\text{Am}{\stackrel{\text{(n,}\alpha \text{)}}{\to }}^{\text{237}}\text{Np}$

(2): ${}^{\text{233}}\text{U}{\stackrel{\text{(n,γ)}}{\to }}^{\text{234}}\text{U}{\stackrel{\text{(n,γ)}}{\to }}^{\text{235}}\text{U}{\stackrel{\text{(n,γ)}}{\to }}^{\text{236}}\text{U}{\stackrel{\text{(n,γ)}}{\to }}^{\text{237}}\text{U}{\stackrel{\text{β(6}\text{.75}d\text{)}}{\to }}^{\text{237}}\text{Np}$

To ensure the stability of the physical and chemical properties of fuel salts, the accumulation of TRU cannot exceed its upper solubility limit in molten salt. The mole fraction of the TRUs dramatically increased from the initial moment (7.6 times that of the initial fraction), as shown in Fig. 12. In the LiF-BeF₂ system, the solubility of PuF₃ mainly depends on the temperature of the carrier salt and the molar ratio of LiF and BeF₂, where the molar ratio is generally less than 1 mol% and the temperature ranges between 525-650 ℃. However, adding UF₄ in the carrier salt will increase it by 2-3%. If FLiBe does not meet the requirements, the FLi carrier salt can be considered; the solubility of PuF₃ has been improved, which is near 5 mol% in most temperature ranges. However, for the LiF-BeF₂ salt, the molar ratios of the TRUs increase to approximately 5% after 50 years of operation, exceeding the maximum solubility limit for TRUs. Therefore, a long-term operation of longer than 30 years may cause certain problems in the physical or chemical properties of the SM-MSR-Pu.

Fig. 12Full-screen View

(Color online) Mole fractions of the TRUs and total heavy metal

Temperature feedback coefficient and delayed neutron fraction

The temperature feedback coefficient is a critical factor for evaluating the passive safety performance. During the burn-up phase, the temperature coefficient must have a negative value to guarantee a safe operation of the reactor. The combined effects of the fuel doppler, fuel density, and graphite temperature determines the total temperature coefficient for the graphite-moderated molten salt reactors, as depicted in the following equation: ${\left(\frac{\text{d}\rho }{\text{d}T}\right)}_{\text{total}}={\left(\frac{\text{d}\rho }{\text{d}T}\right)}_{\text{doppler}}+{\left(\frac{\text{d}\rho }{\text{d}T}\right)}_{\text{density}}+{\left(\frac{\text{d}\rho }{\text{d}T}\right)}_{\text{graphite}}$ (2) The over-time variations in the temperature reactivity coefficients are shown in Fig. 13, which clearly demonstrates that the coefficients of the graphite temperature and fuel doppler temperature are both negative and stable. The main contributing factor to the fuel doppler effect is the resonance absorption of actinides, particularly ²⁴⁰Pu and ²⁴²Pu. For fifty years, the temperature feedback coefficient owing to the fuel doppler effect is less than zero. The primary source of the graphite temperature coefficient is the modification of the energy spectrum owing to the increase in temperature. Within 50 years of the burn-up period, the graphite temperature coefficient fluctuates slightly between -2 and -3 pcm/K, which is relatively stable. The changing trend of the total temperature coefficient is highly influenced by the fuel density coefficient, which is primarily determined by the following two antagonistic factors: 1) As the temperature increases, the density of the molten salt decreases, and part of the fuel is forced out of the core, reducing the reactivity. 2) The decreased fuel salt density increases the volume ratio of the moderator, enhances the neutron moderation effect, and shifts the neutron spectrum towards the thermal zone, resulting in an increase in the reactivity. Owing to the latter effect being more pronounced among the two, the density coefficient is positive most of the time, as shown in Fig. 13. During a long-term operation, the increase in plutonium will increase the first effect, which is beneficial for a negative coefficient of the total temperature reaction.

Fig. 13Full-screen View

(Color online) Evolution of the temperature reactivity coefficient

The effective delayed neutron fraction (DNF) is shown in Fig. 14. The initial effective DNF, which is 280 pcm in the absence of a fuel flow, is mostly contributed by ²³⁹Pu. At the end of the initial 10-year operational period, the effective DNF increased to 325 pcm owing to the accumulation of ²⁴¹Pu.

Fig. 14Full-screen View

Evolution of delayed neutron fraction

For the actual operation of the MSR, the fuel salt flow will reduce the DNF in the core. The effective DNF under a stationary flow can be defined by the point kinetics equations as follows [34]: ${\beta }_{\text{i,flow}}={\beta }_{\text{i,static}}\frac{{\lambda }_{\text{i}}}{{\lambda }_{\text{i}}+\frac{1}{{\tau }_{\text{c}}}\left(1-\exp \left(-{\lambda }_{\text{i}}{\tau }_{\text{L}}\right)\right)}$ (3) The residence time inside the reactor core is denoted by τ_c, whereas τ_L is the residence time outside the reactor core. For most operating conditions of the SM-MSR-Pu, the flow effect can reduce the reactivity by more than 100 pcm. The reactivity loss is more sensitive to the residence time inside the active core, and notably increases at the lower residence times. The fuel salt flow velocity and volume distribution determine the residence time; therefore, variations in the flow velocity during the transition process may result in a change in the residence time. A higher flow velocity results in a shorter residence time, thus the loss of reactivity is approximately proportional to the velocity. The instantaneous shutdown of the primary pump may introduce a positive reactivity of approximately 100 pcm, which should be considered particularly for the design and operation of molten salt reactors.

To provide a design margin for the passive safety, thermal disturbance, and reactivity control, the total temperature reactivity coefficient of the SM-MSR-Pu is required to be less than -3.5 pcm/K. For the SM-MSR-Pu, the temperature feedback coefficient is consistently negative and exhibits a downward trend, which ensures a long-term safe operation. Detailed data are shown in Table 2.

Fuel utilization and optimization Schemes

An overview of the consumption and production of certain actinide components is presented in Table 3, in which the initial loading, on-line feeding, quantity, and net production or consumption are counted. For the 50-year operation, 1882.2 kg of thorium and 4890 kg of plutonium was consumed, and 1443.2 kg of ²³³U was newly produced. The mass of uranium quickly reached 350 kg over each 10-year refueling cycle, and the purity of ²³³U was at least 90%. The annual production capacity of ²³³U per the unit thermal power for five generations of reactors was 0.121, 0.120, 0.116, 0.112, and 0.108 kg/y/MWt, respectively. However, after the five generations of the reactor, there was an accumulation of approximately 9.173 kg Np, 544.36 kg Am, and 127.39 kg Cm in the fuel salt.

The stability of the physical and chemical properties of the SM-MSR-Pu may have certain issues with a long-term operation. First, the annual production and purity of ²³³U both decrease during the five-generations of the reactor operation. Second, the rapid accumulation of MAs will increase the difficulty of reprocessing radioactive spent fuel. Lastly, and most importantly, the accumulated mass of TRU may exceed the solubility limit of the FLiBe salt owing to the increasing amount of the plutonium and MAs. Therefore, for a long-term stable functioning of SM-MSR-Pu and for a more effective utilization of the plutonium resource, further research is suggested, for which two feasible optimization schemes are provided herein. Scheme I proposes to extract and separate MAs. The MAs that have accumulated in the core of the 3rd operation cycle will be removed and geologically buried, instead of being transferred back to the core of the 4th operation cycle. The amount of plutonium and the molar fraction of TRUs can both be significantly reduced with this strategy while increasing the accumulation of MAs. Scheme II suggests reducing on-line plutonium feeding as follows: beginning with the 4th operation cycle, no additional plutonium will be supplied to the core to compensate for the reactivity loss. As an alternative, ²³³U produced in the previous generation of reactors will be added on-line to the core as a fissile fuel. This method has the potential to transition to a pure thorium-uranium fuel cycle and minimize the increment of MAs, albeit at the expense of reducing ²³³U production.