Reactor description and modeling

The SM-MSR-Pu consists of an active zone, a graphite reflective layer, upper and lower fuel salt chambers, a descending ring chamber, a heat exchanger, an internal structural component, a control rod system, and a reactor container. A geometric description of the reactor core is shown in Fig. 1. The molten salt is mainly distributed in three parts: the center channel of each hexagonal graphite cell, the upper and lower chambers, the heat exchanger, and the pipes. The height and diameter of the core active zone are 3.2 m and 3.0 m respectively, and the equivalent thickness of the upper and lower reflective layers is 20 cm. The B₄C layer with a thickness of 2 cm is mainly used to reduce the leakage of neutrons from the active zone, thus protecting the external structures from irradiation. The descending ring chamber, filled with fuel salt, is the downflow channel of the cooled fuel. The reactor container is made of Hastelloy material with a thickness of 3 cm. It wraps the entire structural body and serves as the primary circuit boundary. The fuel salt is heated by fission energy in the active zone, flows out of the core, and flows upward into the heat exchanger, transferring energy to the secondary circuit. Then, the fuel salt that flows out of the heat exchanger is collected into the lower chamber through the descending ring chamber, and finally returns to the active zone. The thermal power of the reactor is 250 MW and the electric power is 100 MW. Both the power and size of the core meet the current requirements for miniaturization and modularity. The composition of the fuel salt is 70%LiF+17.5%BeF₂+12.5%(ThF₄+PuF₃), and the enrichment of Li-7 was 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, and 4% ²⁴²Pu [11]. The main reactor parameters are listed in Table 1.

Fig. 1Full-screen View

(Color online) Geometrical description of the small modular molten-salt reactor (SM-MSR) core.

An important advantage of salt reactors is that they can be coupled with flexible fuel reprocessing methods. During operation, a large amount of neutron poisons, such as fission products and minor actinides (MAs), accumulate in the fuel salt. To improve the neutron economy, neutron poisons must be regularly separated and removed from the fuel salt. The post-processing of the fuel salt is mainly divided into two parts: the bubbling system and the electrochemical separation system. The bubbling system is a processing method based on the physical separation of gases and liquids. Gaseous fission products and noble metals can be quickly removed by an online helium bubbling system with a very efficient separation rate [14]. Here, the separation period of the gaseous and noble metal fission products was set to 30 s, which is the same as that of the MSBR [1]. Electrochemical separation systems can separate soluble fission products (FPs) such as lanthanides or MAs, which cannot be separated by bubbling systems.

Methodology of the analysis

The online refueling scheme can allow for lower excess reactivity, achieve lower initial fissile fuel loadings, and simplify the reactor control requirements. Stabilizing k_eff and maintaining a critical state can easily be achieved through the coordination of the control rods and an online fuel refueling module. After each operation cycle of 10 years, the reactor container is replaced, and all the fuel salt is transported to the fuel-processing module for post-processing. In a modular molten-salt reactor, the fuel-processing module is a separate module. A reprocessing flowchart for the batch mode is shown in Fig. 2. In this scheme, dry reprocessing technologies such as fluorination volatilization, reductive extraction, and reduced pressure distillation are used to separate uranium, thorium, transuranic isotopes (TRUs), and fissile products (FPs) from the fuel salt. Uranium, neptunium, and plutonium are first extracted by fluorination and quickly reinjected into the core, while FPs and other radioactive nuclear wastes are processed and buried. ORNL’s related experimental research shows that under suitable separation conditions using fluorinated extraction technology, the separation efficiency of uranium and neptunium can reach 99%, and that of plutonium can reach 90%. Reductive extraction technology can be used to separate thorium and other transuranic elements, and reduced-pressure distillation technology can be used to recover carrier salts. Coupled with fuel reprocessing and container equipment replacement every ten years, an SM-MSR can achieve continuous operation for multiple generations.

Fig. 2Full-screen View

Flowchart of reprocessing scheme.

The TRITON program module in SCALE6.1 can complete the criticality and burnup calculation of solid-state reactors, but it cannot realize the functions of online fuel addition and on-line fission gas removal in salt reactors. To perform the burnup calculation for a MSR with on-line or off-line fuel reprocessing, a special MSR reprocessing sequence (MSR-RS) [25] has been developed in the previous work of our colleagues, which can simulate on-line refueling and batch processing for the SM-MSR-Pu. The MSR-RS program is coupled with the criticality analysis module (CSAS6) [26], problem-dependent cross-section processing module (TRITON) [27], and depletion and decay calculation module (ORIGEN-S) in the SCALE6.1 program [28]. The TRITON module is used to perform critical calculations and generate the corresponding nuclide cross sections and neutron flux files, which provide the required single-group cross sections and neutron flux densities for the ORIGEN-S program calculations. The ORIGEN-S module is used to carry out the burnup calculation, in which on-line refueling and continuous gas removal are implemented by modifying the corresponding terms of the burnup equation, respectively. The CSAS module is used for critical analysis to judge the rationality of on-line refueling.

Neutron spectrum and cross section

The neutron spectrum, which is mainly determined by the graphite moderation ratio, has a strong impact on the performance of the fissile material inventory, Th–U conversion capacity, and passive safety. For the hexagonal cell geometry, the moderation ratio can be controlled by changing both the fuel channel radius and hexagon pitch size. First, the ratio of the channel radius (R) to the hexagon pitch size determines the fuel salt volume fraction in the active zone. Second, for a certain VF, the hexagon P size determines the size of the graphite subassembly and thus affects the uniformity of the neutron moderation. Figure 3(left) shows the initial neutron spectra of different fuel salt volume fractions. It can be observed that the neutron spectrum hardens significantly with increasing VF owing to the reduction of the graphite moderator. When the fuel salt volume fraction is 5%, the neutron spectrum is mainly concentrated in the thermal spectrum. When the fuel salt volume fraction exceeds 20%, the flux of fast neutrons exceeds that of thermal neutrons. Moreover, ²³⁹Pu and ²⁴⁰Pu have obviously high capture cross sections near energies of 0.1 eV and 1.0 eV, respectively, leading to strong neutron absorption peaks and obvious depressions in the spectra.

Fig. 3Full-screen View

Initial neutron spectra for different fuel volume fractions (VF) (left) and different hexagon pitch (P) sizes (right).

Compared with the fuel volume fraction, the hexagon pitch size has a relatively small effect on the neutron spectrum, as shown in Fig. 3(right). The size of the hexagon P mainly affects the neutron-shielding effect. In the case of a larger P size, the neutron moderation is more inhomogeneous, so the neutron flux is relatively high in both the low- and high-energy regions, and the neutron flux in the middle energy region is low. For a smaller P size, the neutron moderation is more uniform and the neutron flux in the resonance energy region is higher, which will lead to larger resonance absorption near the 0.1 eV and 1.0 eV for ²³⁹Pu and ²⁴⁰Pu.

Plutonium is used as the fissile material, so its fission and capture cross-section have a significant impact on the initial heavy metal (HM) mole fractions for criticality. For the same hexagon pitch size, the capture cross-sections of all plutonium isotopes decrease with increasing fuel volume fraction. The fission cross-sections of ²³⁹Pu, ²⁴¹Pu, and²³⁸Pu decrease with increasing fuel volume fraction, whereas the values of the other plutonium isotopes increase slightly with an increase in fuel volume fraction. The capture-to-fission ratio (α) is the ratio of the capture cross-section to the fission cross-section, and its change trend is the combined effect of the two cross-sectional changes of capture and fission. As shown in Fig. 4 (right), with an increase in fuel volume fraction, the capture-to-fission ratio of ²³⁹Pu increases slightly, and the greater the hexagon pitch size, the smaller the capture-to-fission ratio.

Fig. 4Full-screen View

(Color online) Initial loading mole fraction (left) and capture-to-fission ratio (right) of plutonium for different fuel volume fractions and hexagon pitch sizes.

The capture cross-section of the plutonium isotopes showed an increasing trend with the increase in hexagon pitch size. The fission cross-sections of ²³⁹Pu and ²⁴¹Pu increased significantly, whereas the fission cross-sections of other non-fissile isotopes remained basically unchanged. Therefore, the α of ²³⁹Pu and ²⁴¹Pu remained unchanged, and the α values of the other nuclides increased with an increase in the hexagon pitch size. The influence of the fuel VF and P size on the initial plutonium loading molar fraction is shown in Fig. 4(left), and the evolution trend is similar to that of the α variation curve of plutonium. The main difference is that when P = 5 cm, the assembly size limits the thickness of the graphite moderator; thus, it cannot generate sufficient thermal neutrons. Therefore, its neutron spectrum is the hardest, and requires more plutonium loading. Furthermore, a larger volume fraction will lead to a faster neutron flux density and further harden the neutron spectrum, which will instead increase the fission cross-section of ²³⁹Pu. Therefore, the loading mole of plutonium decreased with an increase in volume fraction when volume fraction was greater than 20%.

Table 2 lists the micro cross-sections and inventories of the main heavy nuclides after a 10-year operation. In this table, σ_f denotes the mean microscopic fission cross-section. σ_c denotes the mean microscopic capture cross-section. α is the ratio of σ_c to σ_f; TRUs with small α values, such as ²³⁹Pu and ²⁴¹Pu, are favorable and can provide surplus neutrons to other TRUs, such as ²³⁷Np, ²³⁸Pu,²⁴¹Am, and ²⁴³Am. These nuclei require at least two radiation capture (n, γ) reactions to be transformed into fissile nuclides. Consider the ²³⁷Npreaction chain as an example. ${}^{237}\text{Np}{\stackrel{(\text{n,}\gamma )}{\to }}^{238}\text{Np}{\stackrel{\beta }{\to }}^{238}\text{Pu}{\stackrel{(\text{n,}\gamma )}{\to }}^{239}\text{Pu}\to \mathrm{...}$

²³³U with a lower α value is more advantageous in fuel utilization than ²³⁹Pu, mainly due to its higher effective fission neutrons (η) and lower neutron radiation capture (n, γ) cross sections. In almost all neutron energy ranges, the η of ²³³U is relatively high (greater than 2.0), and a higher η can provide more neutrons for fission reactions. In addition, the atomic weight of ²³³U is much smaller than that of ²³⁹Pu, and the reaction chain for conversion into MAs is longer. Furthermore, the capture cross section of ²³³U (σ_c = 4.33) is much smaller than that of ²³⁹Pu (σ_c = 17.31). This results in a significantly lower probability of converting ²³³U into MAs and reduces the accumulation of radioactive nuclear waste. Therefore, it can be concluded that the neutronic performance of ²³³U is better than that of ²³⁹Pu.

²³³U production

²³³U production is directly determined by the ²³³U accumulated inventory, which is closely related to the neutron absorption reaction rate of ²³²Th and ²³³U. The reaction chain for the evolution of ²³²Th into ²³³U is expressed as ${}^{232}\text{Th}{\stackrel{(\text{n,}\gamma )}{\to }}^{233}\text{Th}{\stackrel{\beta }{\to }}^{233}\text{Pa}{\stackrel{\beta }{\to }}^{\text{233}}\text{U}$

For each generation of reactors, the net production of ²³³U is the accumulation of ²³³U in the fuel salt. At the end of the design life of each reactor, uranium, protactinium, and other actinides are extracted from the fuel salts and stored outside the core. Among them, almost all ²³³Pa is converted to ²³³U by (n,γ) decay with a half-life of 27 days. Therefore, the extracted ²³³Pa should also be counted in the calculation of the breeding of ²³³U. For multi-generation operating cycles, the total net ²³³U production can be calculated by the addition of the ²³³U inventory in the running reactor and the ²³³U and ²³³Pa extracted from the previous-generation reactor. The actual total ²³³U production can be expressed as follows: $\begin{array}{c}{}^{233}\text{U}\left(\text{production}\right){\text{=}}^{\text{233}}\text{U}\left(\text{inventory}\right){+}^{\text{233}}\text{U}\left(\text{extract}\right)\\ {+}^{\text{233}}\text{Pa}\left(\text{extract}\right),\end{array}$ (1) where ²³³U (inventory) refers to the residual ²³³U inventory in the running reactor salt; ²³³U (extract) and ²³³Pa (extract) refer to the ²³³U and ²³³Pa extracted from the previous-generation reactor.

The ²³³U inventories for different fuel volume fractions(P = 20 cm) during the 50-year reactor operation are shown in Fig. 5(a). With increasing fuel volume fraction, the neutron spectrum evidently hardens, and the difference between the neutron absorption reaction rate of ²³²Th and ²³³U continues to increase, resulting in a corresponding increase in ²³³U production. In addition, ²³³U production decreases slowly with the operating time, which is mainly due to the accumulation of TRUs and the consumption of thorium inventory. Further, ²³³U production is not affected by the hexagon pitch size, which will not be discussed in detail here.

Fig. 5Full-screen View

²³³U production and ²³³U purity for different fuel salt volume fractions (P = 20 cm).

Plutonium and thorium are used as starting fuels and are not doped with uranium isotopes such as ²³⁵U and ²³⁸U; therefore, high-purity ²³³U can be obtained by fluorination extraction. Figure 5(b) shows the evolution of ²³³U purity for different fuel volume fractions. In each refueling cycle of 10 years, the purity of ²³³U decreases with operation time because of the accumulation of ²³⁴U produced by the α decay of ²³⁸Pu. Initially, the ²³³U purity was the highest when the fuel volume fraction was 25%. However, the ²³³U purity with VF = 25% decreased faster and was the lowest after 30 years.

In any case, ²³³U purity can still be maintained above 85% during the 50-year operation, and the extracted ²³³U can be used to start the pure thorium–uranium fuel cycle in future TMSRs.

Transuranic isotope (TRU) mole fraction

The molar fraction of the TRUs has an important impact on the long-term stable operation of the SM-MSR. The neutron energy spectrum, radiation intensity, and physicochemical properties of molten salt can be affected by the accumulation of TRUs.

To compensate for the reactivity loss, plutonium is continuously added to the fuel salt during the operation time, and the TRU molar fraction increases slowly. In addition, the accumulated uranium (mainly ²³³U) is extracted from the fuel after a 10-year operation, and more fissile plutonium material is added to the next-generation core, causing a jump in the TRU molar fraction value. The TRU mole fractions for the different fuel volume fraction are shown in Fig. 6(a). It can be observed that the initial TRU molar fractions increase with the increase in fuel volume fraction owing to the harder neutron spectrum. After 10-year operation, the TRU molar fraction is approximately 4–10 times the initial value. Furthermore, a higher fuel volume fraction leads to a higher capture-to-fission ratio, lower neutron economy, and higher ²³³U production, thereby requiring more plutonium feeding. For FLibe salt, the upper limit of TRU solubility is approximately 4%. After 50 years of operation, the TRU molar fractions for VF = 20% and VF = 25% increase to approximately 5% and 6%, respectively, both exceeding the upper limit solubility.

Fig. 6Full-screen View

Transuranic isotope (TRU) mole fraction for different fuel salt volume fractions (P = 20 cm) and hexagon pitch sizes (VF = 15%).

In theory, exceeding the upper solubility limit does not satisfy the stability of the physicochemical properties of molten salts. However, the MSR has the characteristic of fuel batch processing. In the actual operation process, when the TRU molar ratio reaches the upper limit of solubility, the salt can be post-processed to regenerate fresh fuel to ensure the chemical stability of the fuel salt.

The evolution of TRU molar fraction for different hexagon pitch sizes is shown in Fig. 6(b). As discussed in Sect. 3.1, the size of P mainly affects the neutron shielding effect. For a larger P size, neutron moderation is more inhomogeneous. The neutron flux is relatively high in both the low- and high-energy regions, whereas the neutron flux in the middle-energy region is low. Such a neutron energy distribution favors lower capture–fission ratios and better neutron economic performance, which is beneficial for reducing the accumulation of TRUs.

Therefore, from the perspective of TRU molar fraction, a smaller fuel volume fraction and a larger hexagon pitch size are necessary to achieve long-term operation.

Plutonium incineration and minor actinide (MA) accumulation

Plutonium incineration depends on the fission contribution fraction of ²³³U and the neutron absorption reaction rate of the plutonium isotopes.

The incineration of plutonium is inversely proportional to the fission contribution fraction of ²³³U. ²³³U production is completely separated from the fuel in each batch process, and its inventory is much smaller than that of plutonium, by approximately an order of magnitude. Therefore, the ²³³U fission fraction is lower, and more fission reactions come from plutonium isotopes.

The absorption reaction rates of plutonium isotopes increase with spectrum hardening owing to the larger capture–fission ratios of ²³⁹Pu, ²⁴¹Pu, and ²³³U. Larger capture–fission ratios indicate that more neutron capture is required for the same fission reaction rate. Therefore, the consumption of plutonium is higher under the same fission thermal power. As can be observed in Fig. 7, the annual plutonium incineration for the fuel volume fraction range (10%–25%) was approximately 70–105 kg/y.

Fig. 7Full-screen View

(Color online) Plutonium incineration for different fuel salt volume fractions.

Among all the isotopes of plutonium, the incineration rates of ²³⁹Pu, ²⁴⁰Pu, and ²⁴¹Pu are relatively high because of their higher neutron capture and fission cross sections. The incineration rates of ²³⁸Pu and ²⁴²Pu are relatively low because of their lower neutron absorption cross section and because of some key reaction chains, as follows: $\begin{array}{l}{}^{241}\text{Pu}{\stackrel{\beta }{\to }}^{241}\text{Am}{\stackrel{(\text{n,}\gamma )}{\to }}^{242}\text{Am}{\stackrel{\beta }{\to }}^{242}\text{Cm}{\stackrel{\alpha }{\to }}^{238}\text{Pu}\\ {}^{239}\text{Pu}{\stackrel{(\text{n,}\gamma )}{\to }}^{240}\text{Pu}{\stackrel{(\text{n,}\gamma )}{\to }}^{241}\text{Pu}{\stackrel{(\text{n,}\gamma )}{\to }}^{242}\text{Pu}\end{array}$

MAs are major long-lived high-level radioactive wastes, and their production should be minimized. The accumulation of MAs for different fuel volume fractions and hexagon pitch sizes is shown in Fig. 8. It can be observed that MA accumulation increases with an increase in fuel volume fraction and a decrease in the size of the hexagon P. This is mainly due to the higher initial plutonium mole fraction and higher capture-to-fission of TRUs for the higher fuel volume fraction and lower hexagon pitch size. During a 50-year operating period, the accumulated MA inventory reaches at least 400 kg.

Fig. 8Full-screen View

(Color online) Minor actinide (MA) inventory for different fuel salt volume fractions (P = 20 cm) and hexagon pitch sizes (VF = 15%).

For the P = 20 cm, VF = 20% case, the accumulation of MAs (mainly includes Np, Am, and Cm) increased to 103.57, 251.97, 401.70, 547.48, and 680.92 kg during the five generations of the reactor, respectively. Among all the isotopes of MAs, the mass of ²⁴¹Am is the highest, mainly because of the higher decay rate of ²⁴¹Pu. ²³⁷Np is mainly derived from the decay of ²⁴¹Amand the decay of ²³⁷U, shown as follows: $\begin{array}{l}{}^{241}\text{Pu}{\stackrel{\beta (14.35\text{years})}{\to }}^{241}\text{Am}{\stackrel{(\text{n,}\alpha )}{\to }}^{237}\text{Np}\\ {}^{233}\text{U}{\stackrel{(\text{n,}\gamma )}{\to }}^{234}\text{U}{\stackrel{(\text{n,}\gamma )}{\to }}^{235}\text{U}{\stackrel{(\text{n,}\gamma )}{\to }}^{236}\text{U}\stackrel{(\text{n,}\gamma )}{\to }\\ {}^{237}\text{U}{\stackrel{\beta (6.75d)}{\to }}^{237}\text{Np}\end{array}$ It can be observed that the half-life of ²⁴¹Am (approximately 432.2 years) is relatively long, and the reaction chain for the conversion of ²³³U to ²³⁷Np involves four (n,) reactions; therefore, the production of ²³⁷Np is limited in a certain period of time, and the inventory of neptunium is the lowest among all the main MAs.

Therefore, from the perspective of MA accumulation, a lower fuel volume fraction and larger hexagon pitch size are more beneficial for long-term operation and environmental compatibility, while a higher fuel volume fraction and lower hexagon pitch size are beneficial for plutonium incineration and ²³³U production.

Temperature reactivity coefficient

The temperature reactivity coefficient is an important parameter for evaluating the passive safety features of reactors. To ensure the safe operation of the reactor, the temperature reactivity coefficient must have a negative value during the burnup process. For graphite-moderated salt reactors, the total temperature reactivity coefficient depends on the combined effect of the fuel and graphite. Therefore, the total feedback coefficient can be expressed as follows: ${\left(\frac{\text{d}k}{\text{d}T}\right)}_{\text{total}}={\left(\frac{\text{d}k}{\text{d}T}\right)}_{\text{Doppler}}+{\left(\frac{\text{d}k}{\text{d}T}\right)}_{\text{density}}+{\left(\frac{\text{d}k}{\text{d}T}\right)}_{\text{graphite}}$ (2) where ${(\text{d}k/\text{d}T)}_{\text{Doppler}}$ represents the fuel Doppler effect, ${(\text{d}k/\text{d}T)}_{\text{density}}$ represents the fuel density fluctuation effect, and ${(\text{d}k/\text{d}T)}_{\text{graphite}}$ denotes the graphite effect.

The variation curve of the total temperature reactivity coefficient for different fuel volume fractions and hexagon pitch sizes at the start-up time is shown in Fig. 9. When the fuel volume fraction increases from 5% to 25%, the total temperature reactivity coefficients decrease significantly and can decrease from approximately 14 pcm/k to a negative value. For fuel volume fractions in the range of 10% to 25%, the total temperature reactivity coefficients are more obviously affected by the hexagon pitch size. In summary, a larger fuel volume fraction and smaller hexagon pitch size contribute more to a negative temperature reactivity coefficient.

Fig. 9Full-screen View

Initial temperature reactivity coefficient for fuel salt volume fractions and hexagon pitch sizes.

The evolution trends of the fuel Doppler, fuel density, and graphite temperature coefficients with fuel volume fraction and hexagon pitch size are different.

The fuel Doppler coefficient is negative within the VF range of 10%–25%. For a VF less than 10%, the energy spectrum is softer, and the fission Doppler broadening of ²³⁹Pu and ²⁴¹Pu caused by the temperature rise is more obvious; thus, the Doppler coefficient becomes a positive value. With an increase in fuel volume fraction, the energy spectrum becomes harder, the capture resonance contribution of other nuclides is obvious, and the Doppler coefficient becomes negative.

The fuel density coefficient is always positive for a fuel volume fraction less than 25%. As the temperature of the liquid fuel salt increases, the density drop caused by the expansion effect reduces the inventory of the fissile fuel within the active zone and softens the neutron energy spectrum. While the reduction of fissile nuclides can provide negative reactivity, the softening of the neutron spectrum will change the fission and capture cross-sections of the main nuclides, which may lead to positive reactivity. For a fuel volume fraction less than 25%, the effect caused by the shift of the energy spectrum to the thermal neutron energy region is greater than the effect caused by the reduction in the fissile fuel, resulting in a positive value.

The graphite temperature coefficient decreases rapidly with an increase in the fuel volume fraction. For the range of neutron energy from 0.01 eV to 1 eV, the capture cross section of ²³²Th is approximately inversely proportional to the neutron energy, whereas the fission cross section of ²³⁹Pu and ²⁴¹Pu has a fission resonance peak between 0.02 eV and 0.04 eV. The influence of neutron spectrum hardening on the graphite temperature coefficient depends mainly on the competition between the capture reaction of ²³²Th and the fission reactions of ²³⁹Pu and ²³⁹Pu. For a smaller volume fraction, the proportion of thermal neutrons is higher, and the increase in graphite temperature causes a shift in the neutron energy spectrum to ²³⁹Pu and ²⁴¹Pu fission resonance peaks. This is more favorable for the fission reaction rates of ²³⁹Pu and ²⁴¹Pu, resulting in increased reactivity and a positive graphite temperature coefficient. For a larger volume fraction, the neutron spectrum is relatively hard and deviated from the fission resonance peaks of ²³⁹Pu and ²⁴¹Pu. The increase in the graphite temperature is more favorable for the ²³²Th capture reaction, resulting in a negative graphite reactivity coefficient.

The temperature reactivity coefficients change continuously with the evolution of nuclides during the burnup process. The time evolution curves of the fuel Doppler, fuel density, and graphite temperature coefficients of (P = 20 cm VF = 20%) and (P = 20 cm VF = 15%) are shown in Fig. 10(a) and Fig. 10(b), respectively. For (P = 20 cm VF = 20%), the fuel Doppler temperature coefficient and graphite temperature coefficient are all negative and remain stable. The change in the total temperature reactivity coefficient mainly depends on the decrease in the fuel density coefficient. Different from VF = 20%, the graphite temperature coefficient of VF = 15% fluctuates greatly, it is 3.1 pcm/K at the initial moment, and approximately -4.1 pcm/K after 40 years. The high graphite temperature coefficient value at the start-up time renders the design parameters of P = 20 cm VF = 15% unable to meet the requirements of passive safety.

Fig. 10Full-screen View

Evolution of fuel Doppler, fuel density, and graphite temperature coefficients with burnup.

In this study, the variations in the temperature reactivity coefficient with burnup time for different fuel volume fractions and hexagon pitch sizes were calculated. It was found that the overall trend of the total temperature reactivity coefficient declines throughout the burnup cycle. If the temperature coefficient at the initial moment is negative, then a negative reactivity coefficient can be achieved throughout the lifetime. Considering the requirements of inherent safety, thermal hydraulics, and control rod system design, the total temperature reactivity coefficient of the small modular TMSR must be less than -3.5 pcm/K. From the previous results, it can be observed that increasing the fuel volume fraction and decreasing the hexagon pitch size can reduce the value of the total temperature reactivity coefficient. Therefore, the parameter ranges that satisfy the inherent safety constraints are: P = 10 cm (VF ≥ 15%), P = 20 cm (VF ≥ 20%), and P = 30 cm (VF ≥ 25%), and more detailed data is listed in table 3.

Burnup performance

The inventory curves of the main isotopes are shown in Fig. 11. During the 50-year burn-up process, approximately 380 kg of Th is consumed every 10 years, which is mainly converted into ²³³Pa and further decays into ²³³U. The stock of Pa rises rapidly, reaches an extremely high value in a short period of time, and decreases slightly with long-term burnup. The latter phenomenon is mainly due to the gradual decrease in the absorption reaction rate of ²³²Th caused by hardening of the energy spectrum. The ²³³U production in each refueling cycle also reduces gradually. During each 10-year refueling cycle, the mass of U rapidly accumulates to approximately 350 kg, and the purity of ²³³U is approximately 85% or more. The uranium nuclides are then extracted from the cores using dry post-processing methods. Meanwhile, the extracted ²³³Pa is stored outside the core for several months, decaying to ²³³U. All these ²³³U products can be used as starting fuels for other pure thorium–uranium cycle reactors.

Fig. 11Full-screen View

(Color online) Evolution of actinide nuclides over time.

The Pu inventory continues to increase throughout the operating period and remains the most stocked transuranic element, increasing from 821 to 5536 kg. The inventory of MA nuclides (Np, Am, and Cm) increases gradually, and the total mass is approximately 1/8 that of Pu. Among them, the mass of Am is the largest, mainly owing to the (n,γ) decay of ²⁴¹Pu. The inventory of Np is quite small, mainly because the (n,γ) decay of ²³⁷U is the main method for generating ²³⁷Np, whereas the yield of ²³⁷U is extremely low in the Pu–Th fuel cycle.

The utilization and production of the main actinide nuclides during burnup are summarized in Table 4, in which the initial loading, cumulative feeding, inventory, net production, and net consumption are presented. It can be observed from the table that approximately 1.89 tons of thorium and 4.89 tons of plutonium were consumed, and 1.44 tons of ²³³U was newly produced. During the five generations reactor, 302.8, 299.4, 290.0, 279.9, and 271.1 kg of ²³³U were produced, and 817.22, 980.72, 1015.83, 1041.85, and 1058.97 kg of plutonium were incinerated, respectively. However, approximately 680.92 kg of MAs were accumulated in the fuel salt at the end of the five generations reactor.