Optimized control rod designs for Generation-IV fast reactors using alternative absorbers and moderators

Annals of Nuclear Energy 132 (2019) 713–722

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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene

Optimized control rod designs for Generation-IV fast reactors using alternative absorbers and moderators H. Guo, L. Buiron, T. Kooyman, P. Sciora Alternative Energies and Atomic Energy Commission, CEA, DEN, SPRC, F-13108 Saint-Paul Les Durance Cedex, France

a r t i c l e

i n f o

Article history: Received 26 April 2019 Accepted 2 July 2019

Keywords: Fast reactor Control rod Design Moderator Absorber

a b s t r a c t The characteristics of Generation-IV fast reactors strongly impact the design of its control rods. The traditional control rod is a cluster of vented pins with boron carbide (B4C) as the absorber. Due to the gas release, the neutron-induced swelling, the melting risk, and the high loss of the reactivity worth, B4C impact the safety performance of control rods and thus limit their operating lifetime. Various alternative absorbers to B4C are assessed in detailed designs according to their neutronic performance, safety performance, and waste management. The hafnium diboride (HfB2) process a high thermal conductivity, a high melting point, and a small neutron-induced swelling, which contributes to an enhanced safety performance. The europium oxide (Eu2O3) process a very small loss of the absorption ability for a long-time utilization. Hafnium hydride (HfH1.62) has a good neutronic performance, but its hydrogen desorption issue should be further investigated. The absorption cross-section decreases generally with the neutron incident energy. Moreover, an important spatial self-shielding effect is found in the control rod, which leads to a peak temperature and peak burnup in the outer zone while a non-optimized utilization of absorber in the inner zone. In this work, the hydrogen-containing moderator is used in independent pins to replace some absorber pins in control rods. The moderator is able to increase significantly the absorption ability of Eu2O3 and of gadolinium oxide (Gd2O3). The moderator optimizes the utilization of absorbers, such as HfB2 and B4C, and save their investment. By homogenizing the absorption distribution, the application of moderators has only a limited influence on safety performance or waste management. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction The characteristics of Generation-IV fast reactors (temperature, flux level, neutron spectrum, cooling medium, etc.) strongly impact the design of their control rods (CRs) (Gosset, 2017). The fast spectrum complicates the choice of absorber materials because the absorption cross-section decreases with the neutron incident energy. Boron carbide (B4C) was widely used in CRs of previous fast reactors (Dünner et al., 1984; International Atomic Energy Agency, 2006). It is possible to tune its reactivity control efficiency by adjusting the enrichment of its effective isotope, i.e. 10 B. However, gas release through (n,a) reactions, the consequent material swelling, and the melting risk impact its safety performance and limit its utilization lifetime (Waltar et al., 2012; Subramanian et al., 2010). Moreover, its simple reaction chain leads to significant degradation of its absorption ability especially for B4C with low 10B enrichment (Blanchet and Fontaine, 2014).

E-mail address: [email protected] (H. Guo) https://doi.org/10.1016/j.anucene.2019.07.007 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.

Important efforts have been invested to evaluate alternative absorbers materials to B4C to improve the safety performance or to extend the lifetime of CRs in sodium fast reactors (SFRs). Gosset (2017) and Donomae and Maeda (2011) have summarized the material properties of various potential absorbers in Generation-IV reactors such as rare earth element oxides and hafnium-based materials. These materials possess better resistance to neutron irradiation, higher thermal transfer ability, and lower gas release rate. Kenji et al. (2006); Iwasaki and Konashi (2009); Ikeda et al. (2014) has investigated in depth the application of hafnium hydride as an absorber SFRs. Their results enable the design of CRs with these alternative absorbers. However, the neutronic performance, safety performance, and the radioactivity hazard of these potential absorbers should be analyzed in more detail. Moreover, the advantages and disadvantages of these materials should be compared to clarify their application range. At the same time, combinations between moderator and absorber were also discussed Gosset (2017); Dujcˇíková and Buiron (2015). It was found in earlier work that the introduction of moderators is able to improve absorption ability and to homogenize the

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absorption distribution in CRs (Guo et al., 2019c; Guo and Buiron, 2018). However, these designs should be evaluated in depth with more accurate calculation schemes. In this paper, alternative absorber materials and moderators will be applied to optimize the control rod designs in a Generation-IV SFR. These designs will be evaluated with respect to their absorption ability, safety performance, waste management, and economic efficiency. The calculation methods used in this work will be presented in Section 2. The requirements on the CRs in Generation-IV fast reactors will be defined in Section 3.1. The characteristics of various materials will be compared in Section 3.2. Finally, the application of moderators will be discussed in Section 3.3.

The key characteristics during cooling i.e. decay heat, activity, and neutron source are one of the key parameters for the choice of absorber materials. However, these parameters were not well evaluated in previous work. In the paper, the DARWIN2.3 code (Tsilanizara et al., 2000) will be used to simulate the evolution of spent absorbers during cooling.

2. Methodologies

3.1.1. Requirement R1: Neutronic performance The CRs are required to absorb neutron efficiently in order to achieve the expected reactivity control functions. That is, CRs should be able to ensure the reactor shutdown with enough margins and the sustained reactor operation. Moreover, it is preferable that absorbers have a small loss of their absorption ability under irradiation so as to increase their lifetime.

An accurate and high-performance neutronic calculation scheme is a key element to design innovative CRs for nextgeneration reactors. The control rod assemblies exhibit usually complex layout and important flux gradient that should be computed accurately (Rowlands, 1985; Tommasi et al., 2004; Andersson et al., 2015). The new deterministic APOLLO3Ò platform (Golfier et al., 2009; Schneider et al., 2016) is chosen for the neutronic simulation in this work because of its good capability to treat unstructured geometries while keeping a high calculation efficiency. The calculation scheme in APOLLO3Ò includes two steps: lattice and core calculation. The lattice calculation is based on the Method of Characteristic (TDT-MOC) (Sciannandrone et al., 2016). Due to the ability of the MOC method to simulate complex geometries, CRs can be precisely described in the lattice calculation. After self-shielding and flux calculation, a homogenized and collapsed cross-section library as a function of burnup is produced for the core calculation. The 3D SN solver MINARET (Moller et al., 2011) is used in the core level calculation. Due to its ability to calculate unstructured geometries, both the traditional homogenous model and the heterogeneous model of CRs in the core level are available in the core level calculation. A heterogeneous model, describing the CRs in a pin by pin way, is shown in Fig. 1. The cornerstone of the depletion calculation of absorbers is to keep track of the evolution of the effective cross-sections with its burnup. Therefore, the update of the cross-sections is adopted in core calculation, which enables to improve the accuracy on the variation of the absorption ability of CRs. The details of the calculation scheme used in this paper are presented in (Guo et al., 2019a,b, 2018). This scheme has been validated against Monte-Carlo code TRIPOLI-4Ò (Brun et al., 2015) and experimental results for various cores, which shows strong robustness of this scheme to conventional and innovative designs of CRs that will be studied in the following parts.

Fig. 1. 1/6th heterogeneous geometry of core geometry.

3. Results and discussions 3.1. Requirements on control rods CRs used in Generation-IV SFR should be designed to satisfy the following requirements.

3.1.2. Requirement R2: Safety and reliability 3.1.2.1. R2.1: Insertion reliability. CRs have to fit in the same assembly hexagonal tube as a fuel assembly. A minimal gap between the control rod body and the hexagonal tube must be kept to avoid mechanical contact and ensure a free movement of the rods in any case. 3.1.2.2. R2.2: Mechanical strength. To keep acceptable mechanical stress of structures, the control rod body and the pin clad should process enough thickness. The mechanical stress induced by the gas release from absorbers should be considered. At the same time, a low chemical reactivity between the absorber and its surrounding materials is required. 3.1.2.3. R2.3: Thermo-hydraulic performance. CRs should be designed to avoid any melting risk of their constituents especially for absorbers that would be a heat source under irradiation. This requires a high thermal conductivity of absorber and an optimized pellet diameter. At the same time, a minimized pressure drop in the control assembly is favorable. 3.1.2.4. R2.4: Compatibility with its surrounding structures. Absorbers are required to have: a high corrosion resistance in the coolant, a low chemical activity with coolant and cladding, and a small neutron induced swelling. The swelling of absorber pellets may trigger Absorber-Clad Contact (ACC) that would induce cladding failure. Therefore, an enough gap between the pellet and the clad is required and the absorber burnup is limited. A thin metal tube (shroud) can be placed around the stack of pellets to slow the material swelling, to prevent the dispersion of fragments, and to reduce the chemical reactions with the cladding. 3.1.3. Requirement R3: Waste management Low induced activity and decay heat are expected for nuclear waste management which includes on-site cooling, sub-assembly transportation, final disposal, etc. The decay heat level should be considered to verify if current devices are able to cool efficiently the sub-assembly in the back-end stages. The activity level of spent control rod assemblies should be classified according to the defined principles for the radioactive waste and thus be managed with related solutions (ASN, 2016).

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3.1.4. Requirement R4: Economic efficiency The cost of CRs should be minimized. The cost is associated with the price of raw materials, the manufacturability, the lifetime, the reprocessing complexity and so on. The economic efficiency is not completely evaluated in this work due to a lack of available data. In a first appreciation, the extension of the lifetime and the savings in absorber investment will improve the economic efficiency of CRs. 3.1.5. Summary To design robust SFR CRs, this section is aimed at defining requirements to be considered at the design stage of CRs. These requirements and their associated parameters are summarized in Table 1. The first requirement is related to the neutronic performance of CRs that expect an efficient absorber with low ability degradation during irradiation. The second requirement considers the safety of CRs during operation, which requires excellent mechanical property, enough margins to the melting and acceptable swelling under irradiation. The third one focuses on the waste management of spent control rod assemblies. The last requirement is about the economic efficiency of CRs. In the following, innovative CRs will be designed and assessed according to the requirements defined in this section. 3.2. Alternative absorbers to boron carbide 3.2.1. Design description Three control rod designs with different pin sizes are presented in Fig. 2 and Table 2. The pellet diameter varies from 9.9 to 18.4 mm, while the pin number varies between 37 and 127 to keep the same absorber fraction i.e. 25.24%. The gap volume is kept at 30% of absorber volume to reserve enough expansion space for absorber swelling under irradiation. These designs should satisfy the requirements for insertion reliability and mechanical strength. The thickness of the cladding and the control rod body is respectively 1 mm and 2 mm. The minimal gap between the control rod body and the assembly hexagonal tube is 12 mm. As shown in Table 3, various absorbers are loaded in these designs. The choice of pin size is associated with the margin to melting of these absorbers that will be discussed in Section 3.2.3.1. The manufacturing of small size oxides, metals, or hydrides is simpler than that of borides. The small B4C pellet is also feasible but its steel shroud would be difficult. There are manufacturing experiences for steel shroud in D4-like design (Kryger et al., 1995). The shroud would be possible for D6 design, but it could require additional R&D. On the other hand, it would be difficult to place the shroud in D7 design. Therefore, two designs for B4C in 90% 10B will be discussed in the following to verify the balance between the

Table 1 Summary of requirements and associated parameters for control rod designs. Requirements

Associated parameters

Requirement R1: Neutronic performance Requirement R2: Safety and reliability R2.1: Insertion reliability R2.2: Mechanical strength R2.3: Thermo-hydraulic performance R2.4: Compatibility with its surrounding structures Requirement R3: Waste management Requirement R4: Economic efficiency

Absorption ability of CRs; Variation of absorption ability

Gap between structures; Materials used Thickness of structures; Gas release Pressure drops; Margin to melting Gap volume; Absorber burnup Activity level; Decay heat level Operating lifetime; Investment of materials; Post-processing of spent CRs; Price of materials

Fig. 2. Layout of control rods.

Table 2 Geometry parameters of control rod layouts. Design name

D4

D6

D7

Absorber ring Absorber pins number Absorber pellet diameter (mm) Clad thickness (mm) Control rod body thickness (mm) Gap between hexagonal tube and control rod body (mm) Absorber fraction (%)

4 37 18.4 1.0 2.0 20.8

6 91 11.7 1.0 2.0 15.4

7 127 9.9 1.0 2.0 12.4

25.24

25.24

25.24

margin to melting and the margin to swelling limitation. There is no need to shroud other materials because of their smaller swelling under irradiation compared to B4C (see Section 3.2.3.2). The helium production from the (n,a) reactions of 10B leads to a significant increase of the mechanical stress on the absorber pin cladding if a closed pin design is used. Therefore, the boronbased materials should adopt the open design with porous ends at both ends of absorber pins. The gap in the open design is filled with sodium, which would increase the thermal transfer but at the same time, the sodium will accelerate the diffusion of carbon to the steel structure i.e. pin clad (Heuvel et al., 1985). Moreover, the open pin would increase contamination risk if the absorber exhibits a significant activity level after irradiation. The rare earth elements and hafnium absorb neutrons principally by (n,c) reactions that release no gas and thus enable closed pin design. For oxide materials, the closed pin design is mandatory because of their strong reactions with sodium. For metals and hydrides forms, both open and closed pin design could be used (Ikeda et al., 2014). The gap is filled with helium in closed pin design that induces a higher temperature drop in this region compared to open pin design. Therefore, the open pin design is considered for HfH1.62 because of its low hydrogen desorption temperature, while the closed pin design is considered for metal Hf. These designs are evaluated as CSD rods in a large SFR reactor (Mignot et al., 2008; Buiron et al., 2010), of which the radial layout is shown in Fig. 1. These rods are inserted 25 cm into the fissile zone which is the critical position for normal operation. The highest flux level in CRs appears in its bottom region that is 1.95  1015 n/cm2/s for natural B4C in D4 design. The peak power and largest irradiation effect appear also in the bottom that will be the concerned region in the following analysis. These CRs use new materials at their Beginning of Life (BOL). Their End of Life (EOL) is 2050 Equivalent Full Power Days (EFPD) i.e. 5 fuel cycles. 3.2.2. Neutronic performance The one group homogenized macroscopic absorption crosssections of the control rod assembly with different absorbers are presented in Fig. 3. In a first approximation, the macroscopic cross-section is a representative indicator for the absorption ability of CRs. Besides the absorbers presented in Table 3, the absorption ability of other absorbers like Er2O3, Sm2O3, DyTi2O5, EuB6, and TiB2 are also evaluated.

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Table 3 Design description of control rods with alternative absorbers. Absorber

Layout

Shroud

Pin

Absorber

Layout

Shroud

Pin

Nat. B4C B4C-90 B4C-90 HfB2

D4 D6 D7 D4

Yes Yes No No

Open Open Open Open

HfH1.62 Hf Gd2O3 Eu2O3

D7 D4 D7 D7

No No No No

Open Closed Closed Closed

Remark: The  in the abbreviations B4C-x and HfB2-x is the enrichment of abbreviation of natural.

10

B in boron. The enrichment of

Fig. 3. Macroscopic absorption cross-sections of different absorbers at the beginning of life.

The black line in Fig. 3 indicates the absorption ability of B4C in different 10B enrichments. The spatial self-shielding effect increases with 10B concentration. Therefore, the concentration of 10 B in B4C-90 is 4.5 times as that in natural B4C, but the absorption ability of B4C-90 is only 2.3 times as that of natural B4C. Other materials are compared to B4C in order to achieve an easy review of innovative designs discussed in the following. For instance, the absorption ability of Eu2O3 is equivalent to B4C-16.5 and HfB2-90 is equivalent to B4C-60.6. The absorption ability of Er2O3, Sm2O3, and DyTi2O5 is smaller than Gd2O3 of which the absorption ability represents only 30 to 40% of natural B4C. The absorption ability of Eu2O3 is close to natural B4C. Among these oxides, Gd2O3 will be investigated in depth because of its relatively low price and Eu2O3 for its high absorption ability. The absorption ability of metallic Hf is close to Gd2O3. The addition of light isotopes largely increases its absorption ability and thus HfH1.62 is equivalent to B4C-59.6. Natural EuB6 has a higher absorption ability compared to other borides studied in this work. However, its thermal conductivity is too small to ensure sufficient heat transfer. Moreover, the high activity level of europium (see Section 3.2.4) in open pin design would complicate the waste management. TiB2 could be less expansive than HfB2, but its high materials swelling will limit its lifetime. The natural HfB2 is close to Eu2O3 and HfB2-90 is close to HfH1.62. The absorber isotopes are consumed under irradiation. The variation of absorption macroscopic cross-sections is defined as the relative difference between EOL and BOL. Variations of various absorber candidates for a 2050 EFPD irradiation are compared in Fig. 4. The black line represents the variation of B4C that decreases with 10B enrichment. B4C-90 loses 10% of its absorption ability at

10

B in natural boron is 19.9%. In the following, Nat. is the

Fig. 4. Variation of macroscopic absorption cross-sections of different absorbers at the end of life.

EOL, while natural B4C loses 35% of its initial absorption ability. The spatial self-shielding effect is important for B4C in high 10B enrichment, but it decreases with irradiation and thus slows down the loss of the absorption ability. The daughter isotopes created from 10B capture have little absorption ability. Other elements like hafnium, europium, and gadolinium have quite long reaction chains and their products under irradiation have considerable absorption ability. Therefore, as shown in Fig. 4, the non-boron-based absorbers have smaller variations with irradiation compared to B4C. The variations of boron-based materials are close to the one of B4C. The hafnium in HfB2 slows down the depletion speed of natural HfB2 whereas it is not the case for HfB2-90 for which the absorption ability is mainly driven by 10B. In summary, the boron-based absorbers have strong absorption ability and high loss under irradiation. The long reaction chains of europium, hafnium, and gadolinium are favorable to the retention of absorption ability. The absorption ability of rare earth element has yet to be increased with application of moderators (see Section 3.3). In view of its neutronic performance, hafnium hydride is a potential absorber for Generation-IV fast reactors. The compliance of these absorbers to other requirements will be discussed in the following.

3.2.3. Safety performance 3.2.3.1. Margin to melting. The margin to melting is related to the linear heat rating of the absorber pins and the associated thermal properties of the absorber, the cladding and the nature of the gap. The foreseen outlet temperature is 545 °C for SFRs that is adopted as the coolant boundary condition temperature for absorber pins design study hereafter. Table 4 compares the maximal

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H. Guo et al. / Annals of Nuclear Energy 132 (2019) 713–722 Table 4 Margin to melting for different control rod designs (Unit: °C). Absorber

Design

Pin

Melting point

BOL temperature

EOL temperature

Minimal margin

Hf Gd2O3 Eu2O3 Nat. B4C HfH1.62 HfB2-90 B4C-90 B4C-90

D4 D7 D7 D4 D7 D4 D6 D7

Closed Closed Closed Open Open Open Open Open

2233 2420 2300 2375 1000 3380 2375 2375

1353 1067 1655 630 614 606 634 615

1251 953 1474 934 602 931 1402 1140

880 1353 645 1442 386 2449 974 1236

temperature at BOL and EOL of these designs as they are parked in the critical position. The maximal temperature increases with time for boron-based material because their thermal conductivity is reduced with irradiation. The B4C designs have sufficient margin to melting. However, the operating temperature of B4C should be less than 1300 °C in the CEA design framework. This value is chosen to reserve a safety margin for accidental situations and to avoid the high carburization rate of its cladding. At EOL (2050 EFPD), B4C-90 in D7 design satisfies the regulation, but the D6 design exceeds this limitation. In the next section, these two designs will be compared in view of irradiation effects to find the optimal design. The high conductivity and high melting point of HfB2 ensure its remarkable margin to melting even in a large pellet size design. The advantage of HfB2 could be greater in high flux level circumstance or in the Very-High-Temperature Reactor (VHTR). The thermal conductivity level of oxide-based absorbers is lower than for carbides or hydrides. The margin to melting for Eu2O3 is 645 °C at EOL and for Gd2O3 is 1353 °C. Due to the high thermal conductivity, the metal Hf has an 880 °C minimal margin in large pin design. For closed pin designs, an important increase occurs in the gap which is filled with helium. For instance, this temperature increase is 500 °C for the Eu2O3 design. As Eu2O3 possess smaller swelling, the gap volume can be reduced in future optimizations (see Section 3.2.3.2). The out-of-pile tests of HfH1.62 showed that hydrogen desorption would occur above 1000 °C (Ikeda et al., 2014), and thus a narrow margin exists even with open pin design with small diameter pellet. In an accidental situation, the outlet sodium temperature would stabilize at 900 °C (Chenaud et al., 2013) compared to 545 °C in normal operations. Hydrogen desorption in case of an accident would be a serious issue. Therefore, important efforts should be addressed to ensure the safety of HfH1.62 in both operation and accidental situations. This table indicates a preliminary result of the margin to melting of various absorbers. The chemical interaction and the material dispersion should be further investigated because these effects will lead to a change in the heat transfer ability in the gap between absorber and cladding. Moreover, the main reaction for Hf, Gd, and Eu is (n, c), while all gamma heating is assumed resting in absorber here, which will lead to an overestimation of the absorber temperature. Therefore, more accurate modeling coupling these effects should be further developed. 3.2.3.2. Margin to limited burnup. As discussed in Section 3.1.2.4, the burnup of absorbers should be limited to avoid the cladding cracking triggered by the mechanical or chemical interaction between absorbers and its cladding. In the following, the burnup of absorbers is defined as the number of accumulated absorption reactions per unit volume. The maximal burnup is 1.5  1022 Abs./cm3 for B4C without the shroud and 2.2  1022 Abs./cm3 for B4C with the shroud according to the experience from PHENIX and SUPERPHENIX (Kryger et al., 1995).

The burnup of different control rod designs is compared in Table 5. The peak burnup of natural B4C is close to the limitation for the pellet without shroud. The B4C-90 is largely over the limitation, which means it could not achieve the target 2050 EFPD lifetime. The lifetime of B4C in high 10B enrichment is limited by both melting and swelling. The D7 design satisfies the temperature requirement, but its non-shroud pellet limits its lifetime at 820 EFPD. The D6 design with steel shroud enables a higher burnup but its lifetime is limited at 1000 EFPD by the temperature requirement. The neutron-induced swelling for Eu2O3 is at least 40% less than B4C (Dünner et al., 1984). Therefore, a conservative burnup limitation for Eu2O3 can be defined as 3.7  1022 Abs./cm3. The neutroninduced swelling would not be a constraint to achieve an enhanced lifetime for oxide absorbers. The gap can be reduced to reduce its temperature drop and to increase absorber volume fraction. The swelling of HfB2 is just one-third of B4C (Hoyt et al., 1962). Therefore, the maximal burnup for HfB2 is defined at 4.5  1022 Abs./cm3. HfB2-90 is able to achieve the target operating life with considerable margin to its limited burnup. Thanks to the good resistance to swelling and heat transfer ability, HfB2-90 can be designed in large pellet size without steel shroud to achieve a long lifetime. After 2050 EFPD irradiation, the peak burnup of HfH1.62 is 2.43  1022 Abs./cm3. The neutron-induced swelling is an important issue for hafnium hydride that requires long-termirradiation tests (Ikeda et al., 2014). The peak burnup occurs in the outer absorber pins, while the inner pins are not efficiently consumed because of the spatial self-shielding effects. The burnup peak factor is important for Eu2O3, HfB2-90, and B4C-90. This clearly leads to a peak temperature and peak burnup in outer pins, while a non-optimum use of absorbers in the inner region. The addition of light isotopes, for instance, the HfH1.62 here, is able to optimize the absorption distribution in CRs. Therefore, the application of moderators will be considered in Section 3.3. As presented in Fig. 5, the spatial distribution is very heterogeneous for the CR with B4C-90. The peak temperature appears in the outermost pins. In the future, the pins with peak temperature could be replaced by HfB2 which has a high melting temperature, a high thermal conductivity, and a small neutron-induced swelling. A large number of pins in the inner zones exhibit a low burnup (<1.5  1022 Abs./cm3). Therefore, the steel shroud in these inner pins can be omitted to simplify manufacture and thus improve economic efficiency. These two options can be summarized as a radially heterogeneous design to optimize the spatial effects in CRs, which will be further investigated. A third option could be the application of moderators to limit the spatial self-shielding effects, which will be presented in Section 3.3. 3.2.4. Waste management The activity level and decay heat of irradiated absorbers are compared to the reference spent MOX fuel (average fuel burnup

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Table 5 Margin to limited burnup at EOL (2050 EFPD) (burnup in unit: Abs./cm3). Absorber Gd2O3 Eu2O3 Nat. B4C HfH1.62 HfB2-90 B4C-90 B4C-90

Design D7 D7 D4 D7 D4 D6 D7

Shroud No No Yes No No Yes No

Limited burnup 22

3.7  10 3.7  1022 2.2  1022 – 4.5  1022 2.2  1022 1.5  1022

Average burnup 22

0.71  10 1.41  1022 1.28  1022 2.32  1022 2.04  1022 2.43  1022 2.47  1022

Peak burnup 22

0.79  10 1.82  1022 1.36E  1022 2.43  1022 2.59  1022 3.44  1022 3.55  1022

Burnup peak factor 1.12 1.20 1.06 1.04 1.26 1.41 1.44

Fig. 5. Distribution of linear heat rating at BOL (left with unit W/cm) and of burnup in control rods (right with unit Abs./cm3) at 1000 EFPD in D6 design with B4C-90.

100 GWd/t). In order to be conservative, we present here the data for an absorber pellet with peak burnup. The depletion calculation is performed by DARWIN2.3 using neutronic input provided by APOLLO3Ò (flux level, self-shielded cross sections, etc.).

According to the radioactive waste classification principals in France (ASN, 2016), HfH1.62 and Gd2O3 could be classified as short-lived intermediate level waste and be ended with surface disposal. B4C, HfB2, and Eu2O3 should be classified as high-level waste with deep geological disposal because their high activity or tritium containing.

3.2.4.1. Activity level. The time evolution of the activity level of different materials is displayed in Fig. 6. At the beginning, the activity of boron (in natural B4C and natural HfB2) is the smallest one among these absorbers. However, it generates tritium, which must be treated in a dedicated way due to its physical properties. At the beginning of cooling, HfH1.62 and Eu2O3 have higher radioactivity than MOX fuel. The activity level of the spent HfH1.62 decreases quickly with time. After 2 cycle cooling (820 EFPD) in the core, the activity level of HfH1.62 is 10% MOX fuel. Eu2O3 has a higher activity level than MOX fuel until the cooling time reaches 82 years.

3.2.4.2. Decay heat. The decay heat of Gd2O3, HfB2, Eu2O3, and HfH1.62 are compared to the reference SFR-V2B fuel in Fig. 7. The decay heat for B4C is much smaller than these absorbers. The decay heat of HfB2 and Gd2O3 is smaller than the reference fuel. These CRs have a limited contribution to the core decay heat at the short timescale. The spent assemblies are firstly moved inside the reactor vessel during the outage. This would be a period from ten days to a hundred days. In view of decay heat per assembly, the device to hand fuel assembly is therefore also able to hand the spent control rod assembly.

Fig. 6. Activity of absorbers compared to reference irradiated SFR MOX fuel.

Fig. 7. Total decay heat of spent absorbers.

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After cooling inside the reactor vessel about 450 days (including one fuel cycle and some operational time), these spent assemblies should be washed and moved to the cooling pool. As HfH1.62 decay very quickly with time, there would be no difficulty to handle this material. After 450 days of cooling, the decay heat intensity of spent Eu2O3 is about 13.5 times as reference fuel. The residual heat (a and b heating) represents only 20% of the total heat for Eu2O3 and its absorber mass per assembly is only 40% as MOX fuel mass. Therefore, in a first approximation, the handing device for the spent fuel assemblies is sufficient for this spent control rod assembly. 3.2.5. Summary Various absorbers are assessed in this work for their absorption ability, safety performance, and waste management. After detailed comparisons in the previous discussions, the relative performance of these absorbers to satisfy the defined requirements is presented in Fig. 8. B4C gives large flexibility in the absorption level thanks to the 10 B enrichment capability. On the other hand, the reactivity worth variation for low 10B enrichment is too penalizing to satisfy requirement on an enhanced lifetime. The swelling and the melting risk limit lifetime for high 10B enrichment. Three hafnium-based materials were investigated: metallic Hf, hafnium hydride, and hafnium diboride. The metallic hafnium itself has poor absorption ability but the in-situ hydrogen can increase it in a significant way. HfH1.62 has excellent neutronic performance, but it should be assessed with more experiments along with the potential hydrogen desorption issue. The 10B enrichment in HfB2 can be adjusted to reach different absorption ability. In a low 10B enrichment configuration, the long reaction chain of hafnium reduces the ‘‘loss” of absorption ability under irradiation. In high 10B enrichment configuration, the limited swelling, high thermal conductivity and high melting point ensure acceptable safety performance with an enhanced lifetime. The activity and decay heat of spent hafnium decrease quickly with time and could be managed by the devices dedicated to spent fuel management. Some oxides with rare earth elements were evaluated. These materials have inherent stability under irradiation without gas release issues. However, their absorption ability is usually not sufficient in fast spectrum reactors. The absorption ability of Eu2O3 is close to natural B4C. In a first approximation, the spent Eu2O3 can be handed with devices dedicated to spent fuel, but further investigation is required. The Gd2O3 has equivalent absorption to the metallic Hf. The hydride compound of rare earth can be considered to increase their absorption ability, but its safety issue would be similar to HfH1.62. In conclusion, the B4C with 10B enrichment lower than 60% can be substituted by alternative absorbers with enhanced safety performance. The economic efficiency in the case of the industrial use

of these materials should be further investigated. The price of final products is dependent on many factors such as the price of raw materials, the manufacture techniques, the quality required, etc. Important spatial self-shielding effects are found, which induce non-optimal use of absorber material. Therefore, the moderator will be used in the next section to homogenize the reaction distribution and save the investment of absorbers. In this section, the various absorbers are compared in the ‘‘traditional” control rod designs. In the future, other solutions need to be investigated beyond simple pin design to adapt the special characteristics of alternative materials. For instance, the radially heterogeneous designs by mixing HfB2 and B4C could be a solution but require further investigations.

3.3. Application of moderators 3.3.1. Design description The absorption cross-sections decrease globally with the incident neutron energy. Moreover, the spatial self-shielding effect in CRs leads to the power peak in outer zones, while a not wellconsumed of inner zones. The moderator materials could be able to increase the absorption rate and to optimize reaction distribution. Hydrogencontaining materials exhibit better moderation ability than other materials such as Be and BeO. HfH1.62 plays both absorber and moderator role. However, the hafnium, an expensive material, is a heat source under irradiation which could challenge its safety performance. In this work, ZrH1.62 is taken as the reference moderator because of its high moderation ability, no heat generation, and low price. Moderator pellets, of the same size of the absorber pellet, will be packed in independent and closed pins, hereafter called as moderator pins. This section uses the same control rod layouts presented in Fig. 2 and Table 2, while some absorber pins will be replaced by moderator pins. The impact of moderator on the insertion reliability and the mechanical performance of CRs are minimized by using the same control rod geometry. The layout and description of CRs with moderators are presented in Table 6 and Fig. 9. Eu2O3, Gd2O3, and HfB2 adopt D7 design while one part of absorber pins is replaced by moderator pins. A small radius pin design is also flexible to introduce moderator in several locations throughout the control rod subassembly. B4C-90 is more suitable for D6 design because it need shroud to extend their limited burnup. The moderator is preferable to be installed in the inner region to homogenize the absorption distribution. The moderator fraction of these designs, i.e. ratio between the surface of the moderator and the surface of the absorber-moderator couple, vary between 0% and 33.9%.

3.3.2. Neutronic performance The absorption ability for CRs with different moderator fractions is presented in Fig. 10. The moderator introduction has two antagonist effects:

Table 6 Description of control rods with moderator.

Fig. 8. Comparison absorber performances.

Design name

D6 + Moderator

D7 + Moderator

Absorber Moderator Absorber/moderator pellet radius Absorber + moderator pin number Moderator fraction (%)

B4C ZrH1.62 11.7 91 0–21%

Eu2O3, Gd2O3, or HfB2 ZrH1.62 9.9 127 0–34%

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Fig. 9. Radial layout of control rods with moderators.

Fig. 10. Macroscopic absorption cross-sections of absorbers with moderators at beginning of life.

 the moderators slow down neutrons and thus enhance the absorption ability;  the reduction of the absorber volume.

The influence of moderator on the absorption ability is the balance between those effects. ZrH1.62 is able to increase the initial absorption level by 91% for the absorption ability of CRs with Gd2O3. The Eu2O3/ZrH1.62 couple is able to achieve a higher absorption level than natural B4C. The couple HfB2-48 is able to achieve equivalent absorption level as B4C-48. The moderators enhance or very slightly reduce the absorption ability of CRs with HfB2-90 and B4C-90. This result indicates that the substitution of expensive absorber material by cheap moderator has a very small impact on the reactivity worth of CRs. The application of moderators increases the absorption rate and thus increases the loss of the absorption ability. This influence is not significant for couples of Eu2O3, HfB2 or B4C-90 with moderators. Although the moderator enlarges the variation for Gd2O3/ ZrH1.62 couple, its loss is still smaller than the natural B4C. 3.3.3. Safety performance The margin to melting of these moderated CRs is presented in Table 7. The moderator increases the average linear heating rate. On the other hand, the moderator reduces the power peak factor. After balancing these two effects, the impact of moderator on the margin to melting is very limited. As shown in Fig. 11, the moderator increases the average burnup by optimizing the utilization of inner zones. It reduces the burnup peak factor from 1.41 to 1.18 for the B4C-90 case. Finally, the peak burnup of the moderated B4C-90 is only increased by 3% and is still under the limitation. The moderator increases significantly the burnup of HfB2-90, Eu2O3, and Gd2O3, but these absorbers keep sufficient margin to limited burnup because of their good resistance to the neutroninduced swelling. 3.3.4. Waste management The decay heat and activity of spent absorbers from moderated CRs are presented respectively in Figs. 12 and 13. The use of mod-

Table 7 Margin to melting for different control rod designs with moderators (Unit: °C). Design

Absorber

Moderator

Melting temperature

BOL Temperature

EOL Temperature

Minimal Margin

D7 D7 D7 D7 D6

Gd2O3 Eu2O3 HfB2-48 HfB2-90 B4C-90

43 43 37 37 19

2420 2300 3380 3380 2375

1461 1729 573 577 637

1214 1775 675 716 1318

959 525 2705 2664 1039

ZrH1.62 ZrH1.62 ZrH1.62 ZrH1.62 ZrH1.62

Remark: The EOL for designs with B4C-90 is 1000 EFPD and for others is 2050 EFPD.

Fig. 11. Distribution of burnup (Abs./cm3) in control rods with B4C-90 (left) and B4C

90 with 19 ZrH1.62 pins (right).

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distribution. With a reduction of the absorption peak, the designs with moderator satisfy the safety requirement on the melting margin and material swelling. In conclusion, the design with independent moderator pins increases and homogenizes the absorption in CRs. It is able to enhance the absorption ability or to improve the economic efficiency of CRs by increasing the utilization of absorbers in the inner zones. 4. Conclusions

Fig. 12. Decay heat of spent absorbers from moderated control rods.

Fig. 13. Activity of spent absorbers from moderated control rods.

erators increases the intensity of decay heat and activity and it also reduces the quantity of spent absorbers. The handling of spent CRs with Eu2O3 with moderator may require further investigation. For others, the handling devices dedicated to spent fuel are sufficient. In the long term view, the moderator does not raise additional issues on waste management. The application of moderators does not change the radioactive waste classification of these absorbers proposed in Section 3.2.4.1. 3.3.5. Summary In this section, we considered the moderator packaged as independent pins to replace absorber ones in CRs. ZH1.62 is investigated as the reference moderator because of its high moderation ability and lack of heat generation under irradiation, which could reduce hydrogen desorption risk. The moderated CRs designs were assessed according to the defined requirements. The substitution of absorbers with moderators increases significantly the absorption ability of CRs with the use of Gd2O3 and Eu2O3. The absorption ability of moderated Eu2O3 does surpass natural B4C and with a very small loss under irradiation. Using small pin designs, the margin to melting is acceptable for these two rare earth oxides. The associated high burnup increases the decay heat and activity of spent absorbers, but the impact of moderator does not raise additional issues on the waste management. The moderators have only a slight influence on the absorption ability of CRs with HfB2-90 and B4C-90, while it could save the investment of expansive absorber and thus improve the economic efficiency CRs. If they are to be used, moderator pins should be located in the inner region of CRs to homogenize the reaction rate

In this paper, traditional and innovative control rods are assessed according to requirements on the absorption ability, safety, reliability, waste management, and economic efficiency. Various potential absorbers and the application of moderator were investigated. The summary of these designs and their respective applications are presented in Fig. 14. The required 10B enrichment in B4C to realize reactivity control function in Gen-IV fast reactor is discussed in previous work (Guo et al., 2019c). The large SFRs, such as commercial reactors, usually exhibits reduced reactivity loss and require long operating life of control rods. In this configuration, the Gd2O3 with moderator and Eu2O3 with/without moderator would be very suitable thanks to their small worth loss under irradiation. The use of moderators increases the absorption ability of these two oxides while keeping a large safety margin. HfH1.62 and the couple between HfB2 and moderator can be applied to small SFRs. For HfH1.62, the margin to melting and hydrogen desorption issue should be assessed with further experiments. HfB2 is an excellent absorber because of its high melting point and limited swelling under irradiation. Its 10B content can be enriched to different concentrations to satisfy various requirements. Plutonium burner cores or some small modular SFRs would require control rods with B4C in high 10B enrichment. An improved design of such control rods is proposed based on the optimal pin size to ensure safety operating time and by introducing moderators to improve economic efficiency, but its operating life is still limited. In the future, the radially heterogeneous control rods by better mixing different absorbers pins to reduce the issues raised by the spatial self-shielding should be investigated. More experimental tests are required to resolve the technical issues of absorbers and

Fig. 14. Summary of innovative control rod designs and their application situations.

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