2.1 Reactor description and modeling

A schematic of the core of the ADS-MSR is shown in Fig. 1. The core was composed of a subcritical cladding and a liquid lead-bismuth alloy spallation target. The subcritical reactor core was cylindrical and no graphite moderator was used in order to improve the neutron economy. A unique characteristic of the ADS-MSR is that, compared to sodium/lead cooled fast reactors, there is no traditional fuel subassembly in the reactor. The fuel was liquid fluoride salt, which was also used as primary circuit coolant. The heavy nuclides (HN) in the fuel salt comprised of ²³³U and ²³²Th, while only ²³²Th was loaded in the fertile salt. The total fuel salt volume was 12 m³, of which approximately one half was inside the active zone and the other half was outside the core. A radial reflector with a thickness of 50 cm was employed to decrease the leakage of the neutrons. A 10 cm thick B₄ C neutron protection layer was placed outside the reflector. The main parameters of the subcritical reactor are summarized in Table 1. The lead-bismuth alloy spallation target was placed at the center of the core. In most the cases, a proton accelerator power was required to achieve an intensity of several tens of milliamperes, depending on the thermal power and the energy amplification coefficient of the reactor. The proton energy was set to 1 GeV, which was proven to be sufficient to obtain a high spallation neutron production. A high-energy proton beam, generated in the accelerator, was shot into the spallation target from the upper pipe, resulting in a spallation reaction with the target, which generated a mass of spallation neutrons to maintain the operation of the subcritical system.

Figure 1:Full-screen View

Geometrical description of the symmetrical half core of the reactor.

An important advantage of the molten salt reactor is that it is relatively easy for liquid salt to implement the online processing. During the operation of the reactor, the reactor core inevitably accumulates large amounts of neutron poisons, which reach an equilibrium mass value over time. The regular separating and removing of these neutron poisons can reduce the invalid neutron absorption and improve core neutron economy, allowing more surplus neutrons for waste transmutation or fuel breeding. The primary aim of online fuel processing is to extract the fission products, while the actinides nuclide can be returned to the core at the same time. The processing units can mainly be divided into two different parts: the bubbling system and the pyro-chemical system. The bubbling system is used to separate the non-soluble gaseous and metal FPs. The electrochemical unit is used to separate and extract actinides nuclide, lanthanide nuclide, and other fission products. The removal period of non-soluble gaseous and metal FPs was set to 30 s, while the period of other FPs were assumed to be 180 days.

2.2 Calculation tool

In this work, the geometrical and particle transport characteristics of the lead-bismuth target were simulated by the Monte Carlo N-Particle eXtended transport code-MCNPX 2.6.0 [15], which is able to trace several particles, including neutrons and protons. Then, the MCNP5 code was used for the neutron transportation calculation of the subcritical core, with the spallation neutrons calculated from MCNPX as the input source, simulating the neutron reaction process after the spallation neutrons entering the fuel salt. Finally, the burnup calculation was completed by combining MCNP5 and ORIGEN2.0 codes with the ENDF/B-VII library [16].

3.1 Conversion ratio and ²³³U production for subcriticality

In this work, to assess the breeding capability of the subcritical Th-²³³U molten salt reactor, the conversion ratios (CRs) for different subcriticalities (k_eff= 0.99/ 0.97/ 0.95 /0.93) were calculated. The CR reflects the breeding capability of fissile materials in the reactor, which can be expressed as

where the number R_c represents the capture reaction rates of fertile nuclides while R_a denotes the absorption reaction rates of the fissile nuclides.

At the beginning of the burnup, only ²³³U and ²³²Th were loaded in the reactor. The variation of CR mainly depends on the initial mass ratio of ²³³U/²³²Th. In this work, the initial ²³³U loadings were 3.53 t, 3.41 t, 3.27 t and 3.16 t with the corresponding initial CRs of 1.076, 1.113, 1.163, and 1.203, respectively, for different subcriticalities ( k_eff= 0.99/ 0.97/ 0.95/ 0.93). The reactor with a deeper subcriticality requires a lower mass ratio of ²³³U/²³²Th, resulting in a higher R_c (²³²Th) / R_a (²³³U) and a higher CR.

Equation (1) defines CR based on the fission and absorption rates of fissile and fertile fuel without considering the effect of the separation of spallation neutrons on the CR. In order to further understand the CR from a different perspective, it was analyzed with respect to the neutron balance. For fissile fuel, the number of absorbed neutrons per fission is 1+α, where α is the capture-to-fission ratio. In addition to the neutron losses and captures in the structural material ( ν_m), the number of available neutrons for regeneration and breeding of nuclear fuel is ν_c=ν -(1+α)-ν_m. For a subcritical reactor, the number of additional spallation neutrons can be expressed as ν_s=((1-k)/k)ν. Then, the CR for a subcritical reactor can be defined as:

Equation (2) above describes the effect of various parameters on the CR more directly. In a critical reactor, the main approaches to improve the CR are design optimizations based on ν_m, ν and α, which depend on the reactor size, structure material, and nuclear fuel, while the design margin is very small for a reactor with a specific neutron spectra and fuel cycle. For a subcritical reactor, it is relatively more flexible to improve CR by regulating the subcriticality. The spallation neutron numbers ν_s is 0.025, 0.077, 0.132, 0.188 for different subcriticalities (k_eff= 0.99/ 0.97/ 0.95/ 0.93) and the CR increase nearly linearly with the increasing ν_s. However, a trade-off needs to be made between the higher conversion ratio and the increasing need to apply an accelerator proton beam.

The nuclear fuel breeding capacity is considered excellent especially in a subcritical reactor using the molten salt fuel, which has the important advantage of online refueling. During the operation of the reactor, ²³³U and ²³²Th can be fed into the core to ensure the reactor steady-state operation, avoiding reactivity fluctuation resulting from the breeding/depletion of the initial nuclear fuel and the accumulation of FPs. The online refueling strategy not only simplifies the reactor control requirements but also suppresses the excess reactivity, which decreases the required initial fissile fuel inventory. In addition, ²³³Pa can also be extracted from the fuel salt to decay into ²³³U to decrease the absorption of ²³³Pa and increase ²³³U production. Variations of k_eff with the burnup for different subcriticalities are shown in Fig. 2. It can be seen, that with online fuel processing and refueling, the k_eff stability at the different subcritical conditions can be maintained during the entire cycle.

Figure 2:Full-screen View

(Color online) Time evolution of k_eff (solid lines) and CR (open lines).

Figure 2 shows the time evolution of CR with the burnup for different subcriticalities. The CR slightly declines in the evolution period of 50 years, which mainly results from the accumulation of actinides, such as plutonium and other uranium isotopes, as shown in Fig. 3. The capture-to-fission ratios ( α) of ²³⁵U, ²³⁹Pu and ²⁴¹Pu under this neutron spectra are about 0.36, 0.50, and 0.22, respectively, while the α of ²³³U is about 0.149. This indicates that ²³³U has a better neutronic performance for breeding. The inventories of these generated ²³⁵U and ²³⁹Pu increase with the time of the burnup, leading to a decline of the fissile fraction of ²³³U from 100% to about 92% and resulting in the decrease of the CR.

Figure 3:Full-screen View

(Color online) Time evolution of actinides inventories for k_eff=0.99 (solid lines) and k_eff=0.93 (dashed lines).

The net ²³³U production can be calculated by the difference of the initial ²³³U loading at the beginning of burnup and the ²³³U inventories at the end of burnup. For a subcritical molten salt reactor with online fuel processing and refueling, most of the regenerative ²³³U originates from ²³³Pa decays outside the core. Some of the ²³³U were fed back into the core to control the reactivity, and the excess ²³³U as a net production can be stored outside the core or used for other reactors. The amount fed ²³³U and the extracted ²³³Pa needs to be included in the calculation of the breeding of ²³³U as well. The actual ²³³U production can be expressed as

where ²³³U (residual) refers to the residual ²³³U inventory in the fuel and fertile salt, ²³³Pa (extract) refers to the ²³³Pa extracted from the fuel and fertile salt, ²³³U (injected) refers to the initial and online ²³³U feeding to the fuel salt.

Figure 4 shows the net ²³³U production during the time of operation for different subcriticalities. It can be seen, that a high subcriticality has a considerable effect on the ²³³U production. The doubling time for k_eff of 0.99 is larger than 80 years, while the counterpart for k_eff of 0.93 is only about 22 years. The ²³³U breeding is closely related to CR, which mainly depends on the inventory mass ratio of ²³²Th /²³³U in the reactor. From the view of fuel processing and refueling, ²³³Pa extraction and ²³³U feeding are factors directly affecting the net ²³³U production. When k_eff=0.93, more ²³³Pa is extracted continuously and placed outside the core to decay into ²³³U due to the higher absorption reaction rate of ²³²Th. Meanwhile, fewer ²³³U needs to be fed back into the core due to the higher subcriticality. Therefore, the accumulation of excess ²³³U outside the core as a net production is higher than that in the reactor of k_eff =0.99.

Figure 4:Full-screen View

(Color online) Time evolution of net ²³³U production as a function of subcriticality.

3.2 Reactivity for MA Loading

In a subcritical system, the higher safety performance allows higher MA loading; thus, it is very flexible for MA transmutation. Meanwhile, MA are expected to show better neutronic performance in reactors with a fast neutron spectrum. When proportional MA are loaded into the fuel salt, it is necessary to analyze the ²³³U breeding capability in the subcritical molten salt reactor. In this work, MA were recovered from the spent nuclear fuel of a pressurized water reactor (PWR) with a burnup of 33 GWd/t following a 3-year cooling period [17], with the weight ratios for ²³⁷Np, ²⁴¹Am, ²⁴³Am, ²⁴³Cm, ²⁴⁴Cm, and ²⁴⁵Cm of 56.2%, 26.4%, 12.0%, 0.03%, 5.11%, and 0.26%, respectively. For the fuel salt 77.5LiF-22.5HNF₄, we assumed that the compositions of actinides were not affecting the solubility strongly. For the selection of k_eff both the safety margin and energy gain were considered. For the low subcriticality case (k_eff >0.98), the introduction of a small amount of positive reactivity results in a significant increase of neutron flux and thermal power, and an additional shutdown protection system is required. Nevertheless, k_eff <0.95 can eliminate the need for shutdown protection systems and has a greater safety margin with respect to the insertion of reactivity; however it reduces the system energy gain and increases the demand for accelerator power. Thus, in this section, k_eff= 0.97 is supposed to better for research purposes.

Figure 5(a) shows the required initial actinides loading as a function of MA fraction for k_eff=0.97. It can be seen, that the ²³²Th inventory decreases nearly linearly with the increasing MA fraction, an the ²³²Th inventory is not required as the MA fraction reaches 19.1%. In addition, the ²³³U loading mass increases with the increasing MA fraction, reaches a peak value at about MA = 9% and then decreases. This results from the change of the cross-section of the actinides fission/capture for different MA loadings. Fig. 5(b) shows the various fission rate fractions of the main heavy nuclides (²³³U, MA and ²³²Th) for different MA loadings at the beginning of the burnup. It can be seen, that when the MA loading varies in the range of 0-19.1%, the fission rate fraction of ²³³U decreases from 98.35% to 50.21% and the contribution of the MAs to the fission reaction is nearly equal to the value of that of ²³³U when the MA = 19.1%,resulting from the variation of the inventory of the actinides, as shown in Fig. 5(a) while the spectrum hardening is shown in Fig. 6. The increasing MA inventory results in a harder spectrum, which can significantly reduce the mean cross-section of the microscopic fission of ²³³U; however, it has a smaller effect on the fission cross-section of MA. The contribution of MA rises nearly linearly with the increasing MA fraction. Compared with ²³²Th which has a low fission rate fraction in all cases for its extremely small fission cross-section, the MA have a non-negligible capability of neutron production with a higher instant reactivity.

Figure 5:Full-screen View

(Color online) Required initial actinides loadings and separate fission rate fractions of heavy nuclides as a function of MA fraction for k_eff=0.97.

Figure 6:Full-screen View

(Color onine) Normalized neutron spectra for different MA loadings at the beginning of the burnup.

The spectrum hardening resulting from the increasing MA loading can further affect the actinide neutronic performance, which can be assessed by using the concept of neutron depletion (ND). ND is defined as the neutron number required to transform a specific actinide nucleus including its capture and decay products into a final state (FPs). Its value indicates the neutron production or consumption of an actinide nucleus during an infinite operation cycle. For most MAs, at least two (n,γ) reactions are needed to be transformed into fissile fuel while for a fertile fuel a single is needed, for example:

$\begin{array}{l}{}^{232}\text{Th}{\stackrel{(\text{n,}\gamma )}{\to }}^{233}\text{Th}{\stackrel{\beta }{\to }}^{233}\text{Pa}{\stackrel{\beta }{\to }}^{233}\text{U}\to \mathrm{...}\\ {}^{237}\text{Np}{\stackrel{(\text{n,}\gamma )}{\to }}^{238}\text{Np}{\stackrel{\beta }{\to }}^{238}\text{Pu}{\stackrel{(\text{n,}\gamma )}{\to }}^{239}\text{Pu}\to \mathrm{...}\end{array}$

In a thermal reactor, for example in a PWR, the ND for most MAs is greater than zero. The MA transmutation in a thermal reactor can result in a remarkable neutron depletion. In contrast, a hard neutron spectrum can decrease α, shorten the reaction chain to fission, and reduce the neutron depletion for actinides incineration. Table 2 shows the ND values of main actinides used in this study, and it can be seen that NDs of main actinides are less than zero, which indicates that these nuclei produce extra neutron as opposed to consume neutron during the total lifetime. In addition, the neutron production capacity of MAs, such as ²³⁷Np and ²⁴¹Am can exceed that of ²³²Th with the increasing MA fraction.

3.3 ²³³U production and conversion ratio for MA loading

To assess the breeding capability of the ADS-MSR for different MA loadings with online fuel processing and refueling, burnup calculations were performed while the net ²³³U productions were calculated and extracted by using Eq. (3).

Figure 7(a) shows the net ²³³U productions during the operation period for different MA loadings in the range of MA = 0-14%. It can be seen that MA loading has a significant effect on the evolution trends of the ²³³U production. For MA = 1%, nearly no ²³³U is produced or depleted in the first 5 years, then the ²³³U production gradually increases similarly to the trend for MA = 0%. When the MA loading fraction reaches 4%, at the early stage of the operation (about the first 10 years), the reactor consumes a certain amount of ²³³U and the ²³³U depletion increases with the increasing MA loading fraction. Afterwards, the reactor stops consuming ²³³U and begins to breed additional ²³³U with a production rate, which increases faster than that of MA<1%. In summary, during the 50 years of operation, the increasing MA loadings (MA>1%) in the ADS-MSR can lead to a higher net ²³³U production, while a certain amount of ²³³U is consumed in the first two decades, compared to the operation with MA<1%.

Figure 7:Full-screen View

(Color online) Time evolution of (a) ²³³U production, (b) CR, and (c) CRCR₂₃₃ for different MA loadings (k_eff=0.97).

Figure 7(b) shows the time evolution of the CR during the operation period. The evolution trends of the CR for different MA loadings are significantly different. The CR for a higher MA loading has an extremely low value at the beginning of the burnup and reaches the peak at the 20th year of the operation period. During the final 30 years, the CR gradually reduces until it became close to the value of MA = 0%. However, the CR defined above, indicating the conversion performance of the whole fissile nuclides (²³³U,²³⁵U, ²³⁹Pu, and ²⁴¹Pu) in the core, is not unambiguous for the breeding analysis of ²³³U. In order to describe the evolution trend of the ²³³U breeding more accurately, a simplified CR can be defined as

where the R_c represents the capture reaction rate of ²³²Th and ²³³Pa while R_a denotes the absorption reaction rate of ²³³U, while the other nuclides involved in Eq. (1) are not considered. Thus CRCR₂₃₃ is informative to show the evolution of ²³³U in the reactor. The time evolution of CRCR₂₃₃ is shown in Fig. 7(c). It can be seen that CRCR₂₃₃ is in good agreement with the trends of the ²³³U net production shown in Fig. 7(a). When MA = 14%, in the 9th year, the reactor stops consuming ²³³U, and the corresponding CRCR₂₃₃ achieves one, while the CR is still less than one.

The variation of CR and CRCR₂₃₃ depends on the evolutions of the inventory of the MAs and their daughter nuclides. In the first 9 years, CRCR₂₃₃ is less than one resulting from the neutron capture of MA. As can be seen in Fig. 8,the Pu inventory increases rapidly and reaches a very high value during the earlier period. These generated Pu isotopes are primarily produced from neutron capture reactions from ²³⁷Np and ²⁴¹Am, which are given by

Figure 8:Full-screen View

(Color online) Time evolution of actinides inventories for MA = 14%.

$\begin{array}{l}{}^{237}\text{Np}{\stackrel{(\text{n,}\gamma )}{\to }}^{238}\text{Np}{\stackrel{\beta }{\to }}^{238}\text{Pu}{\stackrel{(\text{n,}\gamma )}{\to }}^{239}\text{Pu}\\ {}^{241}\text{Am}{\stackrel{(\text{n,}\gamma )}{\to }}^{242}\text{Am}(83.1\%){\stackrel{\beta }{\to }}^{242}\text{Cm}{\stackrel{(\alpha )}{\to }}^{238}\text{Pu}\end{array}$

These reactions consume a certain amount of neutrons, and as a result, the amount of neutrons is not sufficient for the ²³²Th capture to breed ²³³U. However, such Pu production results in a delayed contribution to fission reactions. During the final 40 years, most of the loading MA have been transformed into fissile nuclides and these fissile nuclides begin to provide surplus neutrons for more ²³³U production than depletion. Thus, CRCR₂₃₃ becomes much bigger than CR and then reaches a peak value. After 50 years of operation, nearly all the loading MA are burned with a higher net ²³³U production and then the reactor returns to the operation mode of thorium-uranium fuel cycle.

The time evolution of ²³³U fission fraction can also directly indicate the variation of reactivity during the entire operation cycle, as shown in Fig. 9. It can be seen, that for the high MA loading, ²³³U is not the only contributor to the fission reaction. Especially when most of the MA were transmuted into fissile nuclides during approximately 10-20 years of operation, the ²³³U fission fraction declines to a minimum value. The MA loading, together with its feature of spectrum hardening, improve the immediate reactivity contribution to the core. Online refueling, which is important for a closed fuel cycle, provides a sufficiently long time of operation for the function of delayed reactivity from MA.

Figure 9:Full-screen View

(Color online) Time evolution of ²³³U fission fraction for different MA loadings.

The calculation results above show the ²³³U breeding capability in the subcritical molten salt reactor, when MA are loaded proportionally into the fuel salt. Meanwhile, the reactor has the additional ability of higher amount of MA transmutation than ²³³U production. Fig. 10 shows the MA fractional transmutations (FT) for different MA loadings calculated by

Figure 10:Full-screen View

(Color online) Time evolution of MA fractional transmutation for different MA loadings.

where M(t) denotes the MA inventory at burnup time t and M BOB is the MA inventory at the beginning of the burnup. When the MA fraction is very small (MA = 0.1%), the FT of MA increases first and then declines, because the MA consumption is lower than the MA production during the final runtime. When MA > 1, the FT of MA can achieve 0.93–0.97 indicating that nearly all of the loading MA has been transmuted. It can also be seen, that there is a correlation between the evolution trends of the MA fractional transmutations and the ²³³U fission fraction trends shown in Fig. 9. In approximately 15 years, most of the MA has been burned or transformed into Pu and the ²³³U fission fraction declines to its lowest value. In order to assess the transmutation capability more directly, the net mass of the MA transmutation needs to be calculated. The net MA transmutation mainly depends on the initial MA loading mass. For the different MA fractions of 1%, 4%, 9%, and 14%, the net MA transmutation is approximately 1250 kg, 5180 kg, 11570 kg and 18020 kg, respectively.