Analysis of minor actinides transmutation for a Molten Salt Fast Reactor

Annals of Nuclear Energy xxx (2015) xxx–xxx

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Analysis of minor actinides transmutation for a Molten Salt Fast Reactor Chenggang Yu, Xiaoxiao Li, Xiangzhou Cai, Chunyan Zou, Yuwen Ma, Jianlong Han, Jingen Chen ⇑ Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China CAS Center for Excellence in TMSR Energy System, Chinese Academy of Sciences, Shanghai 201800, China Key Laboratory of Nuclear Radiation and Nuclear Energy Technology, Chinese Academy of Sciences, Shanghai 201800, China

a r t i c l e

i n f o

Article history: Received 30 September 2014 Received in revised form 8 June 2015 Accepted 10 June 2015 Available online xxxx Keywords: Minor actinides Transmutation Molten Salt Fast Reactor Th–U iso-breeding

a b s t r a c t As one of the six candidate reactors chosen by the Generation IV International Forum (GIF), Molten Salt Fast Reactor (MSFR) has many outstanding advantages and features for advanced nuclear fuel utilization. Effective transmutation of minor actinides (MA) could be attained in this kind of fast reactor, which is of importance in the future closed nuclear fuel cycle scenario. In this work, we attempt to study the MA transmutation capability in a MSFR with power of 500 MWth by analyzing the neutronics characteristics for different MA loadings. The calculated results show that MA loading plays an important role in the reactivity evolution of the MSFR. A larger MA loading is favorable to improving the MA transmutation performance and simultaneously to reducing the fissile consumption. When MA = 18.17 mol%, the transmutation fraction can achieve to about 95% on iso-breeding. We also find that although the fuel temperature coefficient (FTC) decreases with the increasing MA loading, it is still negative enough to keep the safety of the MSFR during the whole operation time. The MA contribution to the effective delayed neutron fraction (EDNF) and the intensity of spontaneous fission neutron (ISFN) are also analyzed. Also MA loading can affect the EDNF during the operation and the ISFN of the MSFR is dominated by 244Cm. Finally, we analyze the effect of the core power on MA transmutation capability. The result shows that for all the operating powers the depletion ratio of MA to HN increases with time and reaches a maximum value. And additional MA should be fed into the fuel salt before the MA depletion ratio reaches the peak value to improve its transmutation capability. The net mass of the transmuted MA during the 50 years operation for 500 MWth is 5620 kg which is very close to that of 1000 MWth. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Most current commercial reactors operate with once-through fuel cycle. At the end of burnup (EOB), the accumulated actinide isotopes during operation are unloaded with fission products (FP) as nuclear waste for temporary storage or permanent geological disposal. This is a disadvantage to improve the utilization of nuclear fuels and to reduce the inventory of radioactive nuclear wastes. To solve the problems, there is growing emphasis on the study of transuranic (TRU) transmutation (Ignatiev et al., 2007; Fiorina et al., 2013). The Pu contained in the mixed-oxide (MOX) fuel can be reused in an appropriate thermal reactor. Therefore, it is important to consider the effective transmutation on spent nuclear fuel with only minor actinides (MA) in various kinds of reactors.

⇑ Corresponding author at: Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China. Tel.: +86 21 39194027. E-mail address: [email protected] (J. Chen).

MA transmutation has been studied in different types of reactors including thermal and fast reactors (Takeda et al., 2002; Liu et al., 2013; Liu et al., 2014; Hu et al., 2015; Tucˇek et al., 2008; Perkó et al., 2012). Recently, Liu et al. studied the MA transmutation performances in Pressurized Water Reactor (PWR) by considering the MA adding in uniform distribution with fuel, in the transmutation rods form and in burnable poison rods form, respectively (Liu et al., 2014; Hu et al., 2015). The simulated results indicate that the heterogeneous distributions of MA nuclide can effectively avoid the initial keff reducing drastically. Because MA adding in burnable poison rod just slightly changes the burnable poison rods structure and needs not to change the fuel composition and the core configuration, it is more technically feasible for MA transmutation (Hu et al., 2015). Besides thermal reactors, fast reactors such as Sodium-cooled Fast Reactor (SFR), Lead-cooled Fast Reactor (LFR) and Gas-cooled Fast Reactor (GFR) are also under development to explore new approaches for transmuting MA (Tucˇek et al., 2008; Perkó et al., 2012). Therefore, a fast reactor is recognized as an alternative system to burn MA since it has a larger ratio of fission-capture cross

http://dx.doi.org/10.1016/j.anucene.2015.06.014 0306-4549/Ó 2015 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Yu, C., et al. Analysis of minor actinides transmutation for a Molten Salt Fast Reactor. Ann. Nucl. Energy (2015), http:// dx.doi.org/10.1016/j.anucene.2015.06.014

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C. Yu et al. / Annals of Nuclear Energy xxx (2015) xxx–xxx

section and a negative neutron consumption (Salvatores et al., 1994). The Generation IV International Forum (GIF) selected six advanced nuclear energy systems to develop. It aims to realize enhanced safety and reliability, reduced radioactive waste generation, effective utilization of U and/or Th resources, substantial resistance to proliferation and improved economic competitiveness (U.S. DOE, 2002). Molten Salt Reactor (MSR) is the only liquid-fuel reactor in the GIF reactor systems, which operates with nuclear fuel dissolved in fluoride salt (U.S. DOE, 2002). It has many remarkable characteristics: inherent safety, excellent neutron economy, no fuel fabrication, on-line refueling and reprocessing, etc. (Krˇepel et al., 2014). A closed nuclear fuel cycle is expected to be implemented in MSR considering the unique advantage of on-line reprocessing. Therefore, utilization of nuclear fuel can be significantly improved due to the effective burning of MA in a MSR especially in a fast neutron spectrum MSR. MOlten Salt Actinide Recycler & Transmuter (MOSART) is one of fast MSRs, which was designed for TRU incineration by the Kurchatov Institute of Russia within the International Science and Technology Center project 1606 (ISTC#1606) (Ignatiev et al., 2007). A series of studies have been conducted to demonstrate the feasibility of MOSART for reducing TRU radio-toxicity. Recently, the Th-U fuel cycle feasibility for MOSART was also evaluated. Various fuel cycle programs including the converter, the iso-breeder and the breeder were analyzed (Ignatiev et al., 2014). Under the European Evaluation and Viability of Liquid Fuel Fast Reactor System (EVOL) project, the Centre National de la Recherche Scientifique (CNRS) proposed another fast MSR concept, the Molten Salt Fast Reactor (MSFR) (Merle-Lucotte et al., 2011). It aims at thorium fuel breeding by improving the characteristics of the thermal Molten Salt Breeding Reactor (MSBR) designed by the Oak Ridge National Laboratory (ORNL) in 1970s (ORNL, 1971). Compared to a thermal MSR, MSFR has several potential unique merits such as large negative temperature feedback coefficient, simple fuel reprocessing and low TRU wastes production. The Th breeding characteristics for MSFR with different starter fuels (233U, Pu, TRU, Pu + MOX and enrU + TRU) were investigated based on various reprocessing schemes (Fiorina et al., 2013; Heuer et al., 2014). In addition to the excellent fuel breeding potential, MSFR could also be applicable for MA transmutation due to its fast neutron spectrum. At present, most of the commercial reactors in operation are PWR in the world. As a new concept of fast reactor, a small power MSFR for MA transmutation should be evaluated before it can become a feasible nuclear power plant operating with MA fuel. Considering the technology and operation difficulties of high power fast reactor, a small power MSFR is somewhat suitable to be built before commercial reactor behemoths are deployed (Liu and Fan, 2014; LaMonica, 2015). In addition, building a power plant in smaller chunks, about one third or less the size of today’s plants, should lead to lower up-front costs, site flexibility, and the ability to add more units as needed (LaMonica, 2015). Therefore, in this work we select a 500 MWth MSFR (named SMSFR hereinafter) to evaluate the MA transmutation performance by analyzing its reactivity, actinides loading, fissile fuel depletion, transmutation capability and safety parameters. Besides 500 MWth, we will also present the MA transmutation capability at different thermal powers for comparison. Here we focus ourselves on the neutronics aspect of the core performance without considering any engineering and fuel performance limits. In the calculations, a similar core structure to MSFR (Fiorina et al., 2013; Heuer et al., 2014) but with a much smaller core volume is adopted. The starter fissile fuel is assumed to be 233 U. The Th fertile blanket surrounding the fuel salt is used for breeding 233U to compensate for the fissile depletion during

transmutation. Section 2 describes the SMSFR geometry, the calculation tool and the parameter analysis for criticality safety and transmutation; the results and discussions are presented in Section 3; and the conclusion is given in Section 4. 2. SMSFR description and its physical parameters 2.1. SMSFR core description The quarter vertical section schematic core of the SMSFR is shown in Fig. 1. The total fuel salt volume is 3 m3, in which one half accounts for the inside fuel salt in a cylinder and the other half for the outside of the cylinder. The height and diameter of the cylinder both equal 124 cm. The outside fuel salt volume consists of a top plenum, a bottom plenum and a heat exchanger. A radial fertile blanket with thickness of 50 cm is adopted to achieve to the saturation of neutron capture reaction rate of 232Th. The thickness of the B4C neutron protection layer is 10 cm. The reflector, the vessel and the wall (used for isolating the fuel salt from the fertile salt) are composed of hastelloy. Their thicknesses are 60 cm, 10 cm and 2 cm, respectively. The main parameters of the molten salts are summarized in Table 1. The heavy nuclides (HN) comprise 232 Th, 233U and MA in the fuel salt, while only 232Th is loaded in the fertile salt. For the condition of 22.5 mol% HNF4 in the LiF salt, we assumed that the compositions of actinide nuclide isotopes do not seriously affect the solubility. The MA was partitioned from the spent nuclear fuel (SNF) of a PWR with burnup of 33 GWd/t after 3-year cooling (Mukaiyama et al., 1993). The actinide weight ratios are 56.2% for 237Np, 26.4% for 241Am, 12.0% for 243Am, 0.03% for 243 Cm, 5.11% for 244Cm and 0.26% for 245Cm (Mukaiyama et al., 1993). 2.2. Calculation tool All the results in this work are obtained from the calculations with SCALE6 which was developed at ORNL for reactor criticality and safety analyses (ORNL, 2009). To perform the burnup calculation for a two-flow MSR with on-line fuel reprocessing, a special MSR reprocessing sequence (MSR-RS) is developed in our previous work (Zou et al., 2015) by coupling with the CSAS6, TRITON and ORIGEN-S modules in the SCALE6 program. The CSAS6 module is responsible for criticality analysis. The TRITON module performs the problem-dependent cross-section processing followed by a multi-group neutron transport calculation. The ORIGEN-S module is for depletion and decay calculations.

Fig. 1. Geometrical description for the quarter core of the SMSFR (units: cm).

Please cite this article in press as: Yu, C., et al. Analysis of minor actinides transmutation for a Molten Salt Fast Reactor. Ann. Nucl. Energy (2015), http:// dx.doi.org/10.1016/j.anucene.2015.06.014

C. Yu et al. / Annals of Nuclear Energy xxx (2015) xxx–xxx Table 1 Parameters of the molten salts for the SMSFR. Compositions (mol%) Li enrichment (mol%) Melting point (°C) (Heuer et al., 2014) Dilatation coefficient (g/cm3/°C) (Ignatiev et al., 2012) Fuel salt density at 750 °C (g/cm3) (Heuer et al., 2014) Fuel salt mean temperature (°C) Fuel salt volume (m3) Fertile salt mean temperature (°C) Fertile salt volume (m3)

7

77.5 LiF–22.5 HNF4 99.995 565 8.82  104 4.1 750 3.0 700 2.9

Fig. 2 displays the flowchart of the MSR-RS. First, the molten salts and the core geometry is initialized. Second, the neutron transportation and depletion are calculated by the TRITON and ORIGEN-S modules, respectively, where Pa is extracted and FPs is removed from both the fuel and fertile salts. Third, the 233U and 232 Th fuels are injected into the fuel salt to maintain the reactor critical and to keep the total heavy metal inventory constant for the stability of the molten salt. The cycle calculation is performed iteratively until the cycle time reaches the value set by user. In the calculations, a 238-group ENDF/B-VII cross-section database is selected and various neutron reaction rates of each nuclide are calculated by the KMART6 module. 2.3. Neutronics parameter analysis The effective multiplication factor (keff ), the fuel temperature feedback coefficient (FTC), the effective delayed neutron fraction (bT ), the intensity of spontaneous fission neutron (ISFN), the fractional transmutation (FT) and the net mass of MA transmutation consumption are analyzed to evaluate the MA transmutation of the SMSFR. keff can be defined as the neutron productive-to-disappear ratio in a reactor (Krˇepel et al., 2014):

keff ¼

P ðiÞ Rp Rf ðiÞ  m ¼ Pi ; Rd R ðjÞ þ L a j

ð1Þ

where Rp and Rd refer to the neutron productive rate and the neutron disappear rate, respectively; Rf ðiÞ is the neutron fission rate; mðiÞ represents the average neutron number per fission for actinide isotope i; Ra ðjÞ indicates the neutron absorption rate for nuclide j; L denotes the neutron leakage rate. Therefore, the contribution of actinide i to the total keff can be written as:

ðiÞ Rf ðiÞ  m keff ðiÞ ¼ P : R ðjÞ þL j a

Fig. 2. Flowchart of the MSR-RS.

ð2Þ

3

The total effective delayed neutron fraction (TEDNF) is an important parameter for reactor controlling safety. It can be defined as the ratio of the average delayed neutron number and the total average fission neutron number (Perkó et al., 2012):

bT ¼ P

P

 i mD ðiÞRf ðiÞ ;   ð m ð i i D Þ þ mP ðiÞÞRf ðiÞ

ð3Þ

D ðiÞ and m P ðiÞ denote the average delayed neutron number where m and the average prompt neutron number per fission for actinide i, respectively. As for a single nuclide, the effective delayed neutron fraction (SEDNF) can be simplified as:

bS ðiÞ ¼

mD ðiÞ : mD ðiÞ þ mP ðiÞ

ð4Þ

While regarding to a reactor involved with various actinides, the actual contribution of actinide i to bT should separate Eq. (3) as:

bC ðiÞ ¼ P

m

mD ðiÞRf ðiÞ : P ðiÞÞRf ðiÞ þm

 i ð D ðiÞ

ð5Þ

In general, MA transmutation can be realized with either neutron capture or neutron fission. Nevertheless, only the latter (incineration) can reduce the MA radio-toxicity significantly. Therefore, in this work, the MA transmutation capability for the SMSFR can be evaluated by the time-dependent fractional transmutation (FT) (Becker et al., 2008) and the net mass of the transmuted MA. The FT is defined as:

FTðtÞ ¼ 1 

M ðt Þ ; MBOB

ð6Þ

where MðtÞ and MBOB refer to the MA inventory at operating time t and at the beginning of burnup (BOB), respectively. 3. Results and discussions To evaluate the MA transmutation capability of the SMSFR, the reactivity varying with different MA loadings is analyzed first at the no-refueling condition. Then the fractional transmutation and the related safety parameters for different actinide inventories with on-line refueling will be discussed. 3.1. Reactivity As shown in Table 1, the initial HN molar fraction in the fuel salt is 22.5%. 233U accounts for 5.2% to ensure a sufficient excess reactivity for different MA loadings. The rest 17.3% is composed by 232 Th and MA. As seen from Eq. (1), keff depends on HN fraction, HN fission cross sections and neutron spectrum. Fig. 3 gives the initial keff and the separate contributions of primary actinides (includes 233U, MA and 232Th) calculated by Eq. (2) for different MA loadings (from MA = 0% to MA = 17.3%). To verify the reliability of the SCALE for the SMSFR, the MCNP critical results are calculated and shown in Fig. 3 for comparison. The maximum deviation of keff between SCALE and MCNP is less than 0.4%, which indicates that SCALE is suitable for the SMSFR neutronics description. It can be seen from Fig. 3 that the keff (233U) declines slowly from 1.23 to 0.61 merely due to the reduction of the mean microscopic fission cross section of 233U. The reduction of 233U fission cross section is caused by the spectrum hardening as shown in Fig. 4. The spectrum hardens with the increasing MA loading, thereby changing the mean microscopic fission cross sections of HN. In contrast, the keff (MA) in Fig. 3 rises almost linearly with the increasing MA loading. It indicates that the increase of the keff (MA) is predominantly caused by the increasing MA loading (leads to a direct increase of mean macroscopic fission cross

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Fig. 3. Initial keff and separate contributions of HN for different MA loadings at BOB.

Fig. 5. Time evolutions of the keff for different MA loadings at no-refueling condition.

section of MA) instead of the spectrum hardening. The contribution of 232Th to the keff is slight in all cases for its extremely small mean fission cross section. The total keff declines first with the increasing MA loading to a minimum value at about MA = 10%. Afterwards, it increases slightly since the growth speed of the keff from MA exceeds the loss speed of the keff from 233U. Considering the relatively large fractions of 237Np and 241Am in the MA, a considerable amount of Pu can be produced from the following approaches:

from the produced Pu is much greater than the depletion of the initial reactivity, therefore deepening the burnup significantly. Both a small initial keff and a slow reactivity loss during the operation are desirable for an operating reactor. The former is favorable to the reactor controlling safety and the latter is helpful to improve the fuel burnup and MA transmutation capability. As shown in Fig. 5, a larger MA fraction in the fuel salt can meet the two requirements above.

Np þ n ! 238 Np ! b þ 238 Pu ( b þ 242 Cm ! a þ 238 Pu 241 242 Am þ n ! Am ! bþ þ 242 Pu: 237

As will be seen later, such Pu production results in a delayed contribution to keff during operation. The time evolutions of keff for different MA loadings are shown in Fig. 5. It can be seen that as MA loading increases, the reactivity loss decreases with time because of the prompt reactivity provided by the MA itself and the delayed reactivity by the produced Pu isotopes. One can find from Fig. 5 that for MA < 10%, the initial reactivity decreases with the increasing MA loading. Nevertheless, the produced Pu from MA can compensate nearly for the loss of the initial reactivity during the operation. Thus, the effective-full-power-year (EFPY) almost keeps constant. As MA > 10%, the delayed reactivity

Fig. 4. Normalized neutron spectra for different MA loadings at BOB.

3.2. Actinides inventory for the on-line refueling The low excess reactivity resulting from on-line refueling is an important superiority for MSR, which can not only decrease the required initial fissile fuel inventory but also simplify the reactor control requirements. It is therefore interesting to analyze the MA transmutation under the small excess reactivity condition (keff  1). Considering the relative small neutron absorption cross sections of FPs in the SMSFR, only non-soluble gaseous and metal FPs (Xe, Kr, Tc, etc.) (ORNL, 1971) are continuously removed in the calculations. The removing period is assumed to be 30 s with 100% efficiency (Nuttin et al., 2005). 233Pa is also extracted from both the fuel and fertile salts to breed 233U. The extraction period is set to 180 days considering the feasible on-line fuel reprocessing rate.

Fig. 6. Required initial condition.

233

U loading as function of MA fraction at the critical

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C. Yu et al. / Annals of Nuclear Energy xxx (2015) xxx–xxx

Fig. 6 shows the required initial 233U inventories in the fuel salt at the critical condition (keff  1) for different MA loadings. The 233 U inventory increases with the increasing MA loading to a maximum value at about MA = 10% and then decreases. It is consistent with the situation without refueling (see Fig. 3). Under the critical condition (keff  1), the maximum initial MA loading for the SMSFR is determined to be 18.17% (a bit greater than 17.3% in Fig. 5) and hence the initial 233U loading is 4.33%. The burnup calculation for different initial MA loadings is carried out by on-line refueling 233U and 232Th up to 50 EFPY. For comparison, we present in Fig. 7 the evolutions of actinide inventories in the fuel salt for MA = 0% (solid lines) and MA = 18.17% (dashed lines), corresponding to the smallest and the greatest initial MA loadings, respectively. For the MA = 0% case, only small amounts of Np and Pu are produced from U and Th over the 50-year operation (5.7 kg for Np and 5.2 kg for Pu at EOB). The productions of heavier nuclides Am and Cm are even fewer (<10 g) and not presented in Fig. 7. The inventories of Th, U and Pa display a stable change due to the on-line refueling (233U and/or 232Th) and extracting (233Pa). Regarding to the MA = 18.17% case, the inventories of Np and Am decline monotonically due to their fission and capture depletions. The Pu (mainly 238 Pu and 239Pu) inventory increases rapidly because of the neutron captures of Np and Am and then decreases by their fission depletions. The Th inventory increases from zero at BOB to 4700 kg at EOB to keep the HN inventory constant, which is close to that of the MA = 0% case at EOB. The Pa inventory evolution shows a similar trend to that of Th but with a much smaller amount, since the former is the direct neutron capture production of the latter. Unlike the cases of Th and Pa, the U (mainly 233U) inventory decreases during the first 15 years and then increases during the remaining 35 years. The influences on the 233U inventory evolution for different MA loading are discussed in detail in the next subsection. 3.3.

233

5

where 233U(injected) refers to the initial and the on-line refueled U inventory; 233U(fuel) and 233U(blanket) refer to the residual 233 U inventory in the fuel and fertile salts, respectively; 233 Pa(fuel) and 233Pa(blanket) refer to the extracting 233Pa inventory from the fuel and fertile salts, respectively. Fig. 8(a) shows the 233U depletions during the whole operation time for different MA loadings from MA = 0% to MA = 18.17%. One can see that different MA loadings have significantly different evolution trends. As MA = 0.94%, the 233U depletion increases gradually with the operation time over the whole 50 years. When the MA loading reaches about 8.83%, the 233U depletion increases during the first 10 years, then keeps nearly constant during the next 20 years, and again increases gradually during the final 20 years. When MA = 18.17%, the 233U depletion exhibits a similar evolution with the MA = 8.83% case during the first 10 years, while gradually reduces during the next 30 years and then increases slightly during the rest operation time. The 233U depletion is also associated strongly with the reactivity from MA and the produced Pu. The separate contributions to the 233 U depletion calculated by Eq. (7) for MA = 0% and MA = 18.17% are presented for comparison in Fig. 8(a) and Fig. 8(c), respectively. When MA = 0%, the total reactivity is almost provided by the 233U fission, and simultaneously the bred 233U from 232Th is much smaller than the consumed 233U. Therefore, it needs to feed more 233U to keep the SMSFR critical, which leads to the gradual increase of 233 U depletion with the operation time from BOB to EOB. 233

U depletion for the on-line refueling

The fissile consumption can be calculated by the difference of the initial fissile at BOB and the residual fissile at EOB. For the SMSFR with on-line refueling and extracting of 233U, the fed fissile and extracted bred fissile should also be included in the calculation of the consumption of 233U. So the actual 233U consumption can be expressed as: 233

UðdepletionÞ ¼ 233 UðinjectedÞ  ½233 UðfuelÞ þ 233 PaðfuelÞ þ 233 UðblanketÞ þ 233 PaðblanketÞ:

ð7Þ

Fig. 7. Time evolutions of actinides inventories for MA = 0% (solid lines) and MA = 18.17% (dashed lines).

Fig. 8. Depletive inventories of 233U for different MA loadings (a), and separate contributions to the 233U depletion calculated by Eq. (7) for MA = 0% (b) and MA = 18.17% (c). The quantities in Eq. (7) with minus are presented with negative values in (b) and (c).

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The contributions of important actinides in the fuel salt to the keff for MA = 18.17% during the 50-year operation are calculated by Eq. (2) and listed in Table 2. The substantial reactivity from MA and its generating Pu can last to about 25 years. Therefore it requires only a small amount of feeding 233U during the first 25 years. The 233U feeding increases significantly during the rest 25 years because of the Pu exhaust. Owing to the relative slow on-line 233Pa extraction, the 233U inventory in the reactor rises gradually with the operation time. From all the above contributions, the 233U depletion exhibits a reversal variant during from BOB to 35 years. Then it keeps almost constant during the final 15 years for the notable contribution of the extracted 233Pa from both the fuel and fertile salts. The 233U depletion is smaller than zero at about 32 years, which indicates that the effective transmutation of MA can operate on iso-breeding in the SMSFR.

3.4. Transmutation capability of MA for the on-line refueling

Fig. 9. Time evolutions of FT for different MA loadings.

Fig. 9 shows the fractional transmutations of MA calculated by Eq. (6) for different MA loadings from MA = 0% to MA = 18.17%. When MA < 0.19%, the MA consumption is greater first and smaller then than the MA production. For a very small MA loading (see MA = 0.002% for example), the FT of MA decreases even less than zero implying more MA is produced compared to the initial MA loading. When MA = 0.19%, the FT of MA increases with the operation time until about 30 years and then keeps almost constant during the rest operation time. When MA > 0.94%, the FT of MA can achieve to about 0.95 at EOB. Nevertheless, FT is not enough to draw a definite conclusion when it has close values at EOB for MA loading ranging from 0.94% to 18.17%. Therefore, additional MA mass consumption should be introduced to evaluate the transmutation capability. For example, the MA inventory decreases from 308 kg at BOB to 16 kg at EOB for MA = 0.94%, while it decreases from 5900 kg at BOB to 280 kg at EOB for MA = 18.17%. The net mass of the transmuted MA of the latter is about 5620 kg, which improves by about 19 times than that of the former despite their almost similar FT values (about 0.95) at EOB.

Fig. 10. Time evolutions of FTC for different MA loadings.

detailed analysis on this topic is under progress and not discussed here. The TEDNF (bT ) calculated by Eq. (3) is shown in Fig. 11 for different MA loadings during the whole operation time. The bT decreases with the increasing MA loading at BOB, which is similar to the variation of the initial FTC. During the operation, however, the bT values decrease to a minimum value first and then rebound except for the MA = 0% case. To explore the source of the variation of the bT , the SENDF (bS ) and the separate contributions of actinides (bC ) are extracted from Eq. (4) and Eq. (5), respectively. Fig. 12(a) shows the bS of several

3.5. Safety parameters The fuel temperature coefficient (FTC) is an important parameter for the safety issues, which must be negative during the whole transmuting lifetime of the SMSFR. The evolutions of the FTC for different MA loadings are calculated and shown in Fig. 10. It can be seen that at BOB, the FTC decreases with the increasing MA loading. During the operation, all the FTC values trend to be about 4.3 pcm/K at EOB, which is negative enough for safe operating. For a SMSFR without moderator, FTC is only determined by the fuel type and its compositions including HN, LiF salt and even FPs. A

Table 2 Contributions to the keff of important actinides in the fuel salt for MA = 18.17% during 50 operating years. Time (years)

232

0 5 10 15 20 25 30 35 40 45 50

0.0000 0.0020 0.0038 0.0052 0.0063 0.0070 0.0075 0.0078 0.0079 0.0080 0.0081

Th

233

U

0.5149 0.3867 0.2865 0.2283 0.2175 0.2301 0.2763 0.3397 0.3921 0.4321 0.4915

235

U

0.0000 0.0003 0.0014 0.0032 0.0054 0.0077 0.0098 0.0115 0.0128 0.0139 0.0151

237

Np

0.2606 0.1881 0.1298 0.0855 0.0544 0.0336 0.0208 0.0129 0.0080 0.0050 0.0033

238

Pu

0.0000 0.1685 0.2696 0.3073 0.2983 0.2618 0.2151 0.1692 0.1278 0.0954 0.0716

239

241

0.0000 0.0124 0.0433 0.0799 0.1101 0.1264 0.1286 0.1202 0.1050 0.0887 0.0736

0.1287 0.0892 0.0590 0.0374 0.0230 0.0139 0.0086 0.0056 0.0038 0.0027 0.0022

Pu

Am

244

Cm

0.0359 0.0380 0.0369 0.0335 0.0290 0.0239 0.0193 0.0154 0.0121 0.0095 0.0077

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C. Yu et al. / Annals of Nuclear Energy xxx (2015) xxx–xxx

Fig. 11. Time evolutions of bT for different MA loadings.

important nuclides. Fig. 12(b) presents the bC for different MA loadings (MA = 0%, 8.83% and 18.17%) at BOB. Although 232Th has the greatest bS , actually 233U and 237Np offer the greatest and the second greatest contributions to the bT at BOB, respectively. It attributes to the much smaller fission reaction rate of 232Th than those of 233U and 237Np. Despite the reversal variant of the 233U loading (see Fig. 6), the bC from 233U decreases monotonically (see Fig. 12(b)) due to the decrease of the mean fission cross section of 233U from the spectrum hardening. The increase of bC (MA) results from the double effects of the increasing MA loading and the hardening spectrum. Because the increment of the bC (MA) is smaller than the decrement of the sum of bC (233U) and bC (232Th), the bT decreases with the increasing MA loading at BOB.

Fig. 12. bS (a) and bC for different MA loadings at BOB (b) and for different operating time for MA = 18.17% (c).

7

The variation of the bT broken up into the bC for MA = 18.17% during the whole operation is shown in Fig. 12(c). Obviously, the bC evolution is also dominated by the 233U and MA inventory variations as discussed in detail in SubSections 3.2 and 3.3. An advanced reactor system will utilize remotely-handled facilities for fuel fabrication and reprocessing system (Borrelli, 2013). And the intensity of spontaneous fission neutron (ISFN) plays an important role for evaluating the high reliability safeguards of remotely-handled nuclear facilities (Borrelli, 2013). Therefore, the ISFN is calculated and shown in Fig. 13 with different MA loadings. Compared with other HN, the Cm isotopes provide the majority of contribution to the total ISFN due to their short halftime and large spontaneous fission branches. Meanwhile, 242Cm, 244Cm and 246Cm are the most three important nuclides for the Cm ISFN. Fig. 13(b) gives the total ISFN with different MA loadings. The total ISFN for MA = 0% increases significantly during the whole operation time due to the production of TRU nuclides. It also explains that the total ISFN increases significantly when MA loading varies from 0 to 18.17%. Moreover, there is a small peak in the ISFN evolution at about 5 years. It is caused by 242Cm as shown in Fig. 13(a), which is further determined by the competition between the production from the b decay of 242Am and the consumption of 242Cm itself by neutron absorption and decay. 3.6. Influence of MA transmutation for core power Finally, we should consider the influence of core power on MA transmutation capability. Fig. 14 gives the depletion ratio of MA to HN at 167 MWth, 333 MWth, 500 MWth, 667 MWth, 833 MWth and 1000 MWth. The depletion ratio has a peak value before the 50-year operation except the case of 167 MWth. The higher the core power is, the earlier the peak becomes. In the case

Fig. 13. Intensity of spontaneous fission neutron for the major actinides with MA = 18.17% (a) and for total HN with different MA loadings (b).

Please cite this article in press as: Yu, C., et al. Analysis of minor actinides transmutation for a Molten Salt Fast Reactor. Ann. Nucl. Energy (2015), http:// dx.doi.org/10.1016/j.anucene.2015.06.014

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C. Yu et al. / Annals of Nuclear Energy xxx (2015) xxx–xxx

We also analyze the transmutation capability of MA at 167 MWth, 333 MWth, 500 MWth, 667 MWth, 833 MWth and 1000 MWth for comparison. The depletion ratio of MA to HN has a peak during the 50-year operation except the case of 167 MWth. The decrease of the depletion ratio indicates that the inventory of MA in the fuel salt becomes insufficient; therefore on-line MA adding is needed to improve its transmutation capability. The net mass of transmuted MA increases from 3930 kg to 5876 kg for core power varying from 167 MWth to 1000 MWth during the 50-year operation time. And the net mass of the transmuted MA of 500 MWth is very close to that of 1000 MWth. Acknowledgments

Fig. 14. Depletion ratio of MA to HN with different core power during 50 years operating.

This work is supported by the Chinese TMSR Strategic Pioneer Science and Technology Project under Grant No. XDA02010000 and the National Natural Science Foundation of China under Grant No. 91326201. References

of P = 500 MWth, the MA depletion ratio increases gradually with the operation time during the first 22 years since a lot of Pu isotopes are produced from MA and then burned. After that, because there is no enough MA in the fuel salt, the MA depletion ratio decreases during the final 28 years. The decrease indicates that a large number of 233U from 232Th are consumed rather than the consumption of MA. Therefore, additional MA should be fed into the fuel salt to improve its transmutation inventory before 22 years. The net mass of the transmuted MA increases from 3930 kg to 5876 kg for core power varying from 167 MWth to 1000 MWth during the 50-year operation. As mentioned in SubSection 3.4, the net mass of the transmuted MA during the 50 years operation for 500 MWth is 5620 kg which is very close to that of 1000 MWth. 4. Conclusion The MA transmutation of a 500 MWth MSFR is evaluated. The reactivity, the fuel temperature coefficient, the effective delayed neutron fraction, the 233U depletion and the MA transmutation capability are analyzed for different MA loadings. It is found that if the 233U loading is kept constant, the initial keff decreases with the increasing MA loading to a minimum value at about MA = 10% and then increases. The reactivity loss during the operation, however, decreases with the increasing MA loading, which significantly deepens the burnup and subsequently improves the MA transmutation capability at the no-refueling condition. Furthermore, the transmutation for different MA loadings is analyzed by the on-line refueling 233U and 232Th to keep exact critical and the HN inventory constant in the fuel salt. Because the MA and its produced Pu can compensate for certain reactivity loss, a larger MA loading is favorable to improving the transmutation capability and to decreasing the fissile depletion during the operation. When MA = 18.17%, the fractional transmutation can reach about 0.95 at EOB with iso-breeding and the net mass of the transmuted MA is 5620 kg. Nevertheless, there is still a potential approach for further improving the transmutation capability and saving 233U by considering the on-line MA feeding to the fuel salt. Both FTC and bT decrease with the increasing MA loading at BOB. During the operation, the FTC trends to be a constant of about 4.3 pcm/K which is negative enough for the safe operation of the SMSFR. Also, the MA loading plays an important role in the bT evolution during the operation. The ISFN of the SMSFR is dominated by 244 Cm during the operation.

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Please cite this article in press as: Yu, C., et al. Analysis of minor actinides transmutation for a Molten Salt Fast Reactor. Ann. Nucl. Energy (2015), http:// dx.doi.org/10.1016/j.anucene.2015.06.014