Neutronic investigation of the thorium-based mixed-oxide as an alternative fuel in the TRIGA Mark-II research reactor – Part I: A beginning of life calculations

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Neutronic investigation of the thorium-based mixed-oxide as an alternative fuel in the TRIGA Mark-II research reactor – Part I: A beginning of life calculations Ouadie Kabach a,⇑, Abdelouahed Chetaine a, Abdelfettah Benchrif b, Hamid Amsil b a Mohammed V University, Faculty of Science, Nuclear Reactor and Nuclear Security Group Energy Centre, Physics Department, 4 Avenue Ibn Battouta B.P. 1014 RP, Rabat 10000, Morocco b National Centre for Nuclear Energy, Sciences and Technology (CNESTEN), Morocco

a r t i c l e

i n f o

Article history: Received 29 April 2019 Received in revised form 29 August 2019 Accepted 18 September 2019 Available online xxxx Keywords: Thorium oxide Alternative fuel Seed-blanket Neutronic parameters MCNPX2.6

a b s t r a c t This article presents a neutronic investigation of the effect of replacing some uranium zirconium hydride (U-ZrH1.6) fuels with thorium-based mixed-oxide ((Th,U)O2) fuels in the TRIGA Mark-II research reactor without changing the core geometry, while the only variable is the fuel material. The possibility of utilizing thorium mixed oxide fuel in the TRIGA Mark-II reactor is assessed using the famous seed-blanket configuration or also known as Radkowsky Thorium Fuel (RTF) concept. Using the RTF concept, a long core lifetime can be achieved by enhancing the internal conversion rate of fertile to fissile materials, thanks to the thermal capture cross-section of 232Th that is around three times that of 238 U. Additionally, on the fuel cycle aspect of using the thorium-based fuel is that the thorium cycle produces much less plutonium and other transuranic radioactive elements than uranium fuel cycle. Actually, neutronic and kinetic calculations, at the beginning of life conditions, for nine different seedblanket configurations have been investigated using the MCNPX2.6 code. These calculations for all proposed configurations in comparison with the conventional U-ZrH1.6 fueled core were performed to pick out an optimal core(s) design ensuring the most efficient use of (Th,U)O2 fuel in it and with minimum changes in the main safety parameters. The parameters consist of effective multiplication factor keff , delayed neutron fraction beff , neutron flux distribution, power distribution and radial hot rod power peaking factor (FHR ), and shutdown margin (SDM). The calculation results exhibit that the highest initial criticality achieved is 1.07716. The results of the other neutronic investigations of thorium-based mixed-oxide fuel elements and their positions, including their numbers in the core are summarized and discussed in the following paper. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Uranium-zirconium hydride fuel has been in use in many water-cooled TRIGA research reactors around the world since 1958. The TRIGA fuel elements were manufactured by the General Atomics in the United States and the Company for the Study of Atomic Fuel Creation France (CERCA). The CERCA company is responsible now for delivering fuel elements in the US and internationally for other existing TRIGA reactors worldwide since 1996. However, as a result of the Fukushima accident, the CERCA stopped its fuel production to make safety upgrades mandated by the French Nuclear Safety Authority and the European Commission (Böck et al., 2016). Therefore, many TRIGA reactors around the ⇑ Corresponding author. E-mail address: [email protected] (O. Kabach).

world are now in a difficult fuel situation such as the United States (Office of Nuclear Energy, 2017), Bangladesh and Morocco. This critical situation guided us to search for a serious and effective candidate for the conventional U-ZrH1.6 fuel. Since the beginning of nuclear energy development, thorium was considered as a potential alternative fuel. Its abundance in the earth’s crust is roughly 3 to 4 times greater than uranium mainly as fertile isotope 232Th (IAEA, 2005; Tucker et al., 2015). Unlike natural uranium, which contains fissile isotope 235U, thorium has no fissile isotope. So its utilization in the initial stage requires the aid of fissile material from the uranium cycle (235U, 233U or 239Pu) to ‘‘ignite” the system and to allow the generation of a sufficient amount 01n

b ð21:83 minÞ

b ð26:967 daysÞ

of 233U ( 90232Th ! 90233Th ! 91233Pa ! 92233U), then to achieve desired operating cycles (Todosow et al., 2005). Thorium-based fuels offer quite a lot of potential advantages over

https://doi.org/10.1016/j.anucene.2019.107075 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: O. Kabach, A. Chetaine, A. Benchrif et al., Neutronic investigation of the thorium-based mixed-oxide as an alternative fuel in the TRIGA Mark-II research reactor – Part I: A beginning of life calculations, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107075

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uranium fuels such as: higher fissile conversion rates, higher thermal fission factor (g) (Radkowsky and Galperin, 1998), lower capture-to-fission ratio as shown in Table 1, low production of plutonium and actinides (americium and curium) for better nuclear proliferation resistance (Breza et al., 2010; Tucker et al., 2015) and chemically very stable. In addition, one attraction of using the thorium-based fuel in fissile nuclear reactors is its relatively improved thermo-physical properties, such as higher melting points (340 °C higher than that of UO2), higher thermal conductivity (about 50% higher), lower coefficient of thermal expansion and a negative reactivity feedback (Tucker and Usman, 2018; Boczar et al., 2002; IAEA, 2006; IAEA, 2008; Liu et al., 2018; Insulander Björk and Netterbrant, 2018). Overall, many studies concluded (Csom et al.,

Table 1 Mean fissile and fertile nuclei parameters in a thermal neutron spectrum (Puill, 2002). Mean fissile nuclei parameters in a thermal neutron spectrum 233

r capture ðbarnsÞ r fission ðbarnsÞ a ¼ rc =rf g ¼ mrf =ra Eff:b fact ðpcmÞ

U

46 525 0.088 2.300 270

235

239

U

101 577 0.175 2.077 650

Pu

271 742 0.365 2.109 210

241

Pu

368 1007 0.365 2.151 490

Parameters of fertile nuclei 232

r capture ðbarnsÞ I.R* capture (barns) Fission cutoff (MeV) Eff:b fact ðfast fissionÞ

Th

7.40 85 1.5 2030

* I.R: integral resonance in infinite dilution (0.625 eV at 20 MeV).

238

U

2.73 272 0.8 1480

2012) that the thorium fuel cycle is considered a suitable alternative candidate for the uranium-plutonium fuel cycle option for future core designs. One of the commonly studied configurations for thorium reactors is the seed-blanket configuration as shown in Fig. 1, which is also known as Radkowsky thorium fuel concept (Radkowsky and Galperin, 1998; NEA, 2015). Radkowsky embarked on a completely different core layout utilizing special multiple seed-blanket arrangements. The seed regions are fueled with non-proliferative enriched uranium in zirconium alloy to assure an acceptable power share of the blanket during the preliminary period of 233U build-up. The blanket fuel elements are supposed to be thorium oxide spiked with a few percent’s of non-proliferative uranium oxide (>5 wt% 235 U but less than the limit of 20 wt% 235U) (Todosow et al., 2005). The uranium is added for two reasons: i) Natural thorium has no fissile content, so enriched uranium is required to provide adequate neutron population in the blanket during the period of 233 U accumulation; ii) The 238 U and other non-fissile isotopes denature the discharged blanket residual 233U, thus the respect of the non-proliferation treaty (Radkowsky and Galperin, 1998). In fact, the use of thorium as a fertile absorber was proposed for light water reactors, heavy water, and molten salt ‘‘Gen IV” reactors since the 1960s and is still under investigation. For light water reactors, such as the pressurized water reactors (Radkowsky and Galperin, 1998; Todosow et al., 2005; Lucas et al., 2018; Takei and Yamaji, 2018), the boiling water reactors (Radkowsky and Galperin, 1998; Todosow et al., 2005; Insulander Björk and Netterbrant, 2018), the water-water energetic reactors (Breza et al., 2010) and the supercritical water reactor ‘‘Gen IV” (Csom et al., 2012), the ThO2 fuel was mixed with either enriched uranium (233U/235U) or plutonium. In the heavy water reactors like CANDU’s, three seeds enriched uranium (SEU) techniques were

Fig. 1. Examples of seed-blanket core configuration concepts (NEA, 2015).

Please cite this article as: O. Kabach, A. Chetaine, A. Benchrif et al., Neutronic investigation of the thorium-based mixed-oxide as an alternative fuel in the TRIGA Mark-II research reactor – Part I: A beginning of life calculations, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107075

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used: i) the SEU elements were enriched to 1.3 wt% for all cycles; ii) the SEU elements were enriched to 1.6 wt% for all cycles; iii) the SEU elements were enriched to 1.6 wt% for the first cycle and 1.3 wt% for the rests of the cycles. (Boczar et al., 2002). For molten salt reactors, two configurations were used: i) thorium fuel in a solid form surrounded by molten salt and ii) thorium fuel homogeneously mixed with molten salt in a liquid (Eom et al., 2002). The present work aims at investigating the potentiality that thorium-based fuel can be used as an alternative candidate of the conventional U-ZrH1.6 fuel element in the TRIGA Mark-II research

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reactor using nine selected cores to pick out the best possible configurations to achieve an optimal design(s) of the reactor. The selected cores were based on multiple seed-blanket arrangements. The seed is represented by the U-ZrH1.6 as the main part of the fuel that provides neutron avalanche to a blanket of thorium, whereas the ðTh0:75 ; U0:25 ð20%ÞÞO2 fuel acts as a neutron absorber at the beginning of life (BOL), but 232Th acts as a fertile material during the cycle. Actually, at least 25% of uranium is necessary for normal operating cycle lengths when the thorium is initially primed with denatured 235U in thorium-based fuel cycle (IAEA, 2005). As a part

Fig. 2. Technical characteristics (a) and the present core configuration (b) of the TRIGA Mark-II research reactor (Boulaich et al., 2011).

Please cite this article as: O. Kabach, A. Chetaine, A. Benchrif et al., Neutronic investigation of the thorium-based mixed-oxide as an alternative fuel in the TRIGA Mark-II research reactor – Part I: A beginning of life calculations, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107075

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of the comparison process, we have taken into account the calculation results of the standard U-ZrH1.6 fueled reactor core. 2. Model, materials, and methods 2.1. Brief description of the TRIGA Mark-II reactor The TRIGA Mark-II reactor has been constructed for basic research on the characteristics of materials, education and training, production of radioisotopes, and studies of different fields of nuclear research. It is a pool-type reactor cooled and moderated by light water. The fuels are composed of mixture of uranium (8.5 wt%, enriched at 19.7% with 235U), zirconium hydride UZrH1.6 and encapsulated in a stainless-steel cladding, whereas five control rods contain boron carbide that controls the reactor. The TRIGA core consists of 101 fuel elements and 17 graphite elements (see Fig. 2). Further description of the TRIGA reactor can be found in (IAEA, 2016; Boulaich et al., 2011).

The TRIGA reactor core contains 101 fuel elements (96 standard fuel elements +5 control rods) and 17 graphite elements distributed over 6 rings B, C, D, E, F, and G as shown in Fig. 2. Ring B is the closest ring to the central experiment tube, and ring G is located at the outermost of the core. The number of fuel rods grows up with the increase of ring distance from innermost ring B (6 fuel rods) to outermost ring G (11 fuel rods). The core with seedblanket configurations (from configuration 2 to 10) with various (Th,U(20%))O2 and U-ZrH1.6 compositions are shown in Fig. 4, where configuration 1 is considered as the standard core (without thorium fuel). The material compositions are presented in Table 2. Except for the (SDM) parameter, all calculations were run with withdrawing all the control rods to maximize the neutron population inside the reactor to transmute into (Th,U)O2 fuel elements. Table 2 Material compositions.

Fuel Zirconium rod Cladding Reflector

S¼



MeV fission




m

neutron fission




 P½W

 1:602:1013




J MeV

 keff

ð1Þ

where m is the average number of neutrons released by fission, P the
MeV reactor power and  fission the energy released by fission. Therefore:

2.2. Methodology

Material

The reactor core calculations were performed with MCNPX2.6 Monte Carlo code (Pelowitz, 2008) developed by the Los Alamos National Laboratory. The Monte Carlo code helps to generate the 3D model of either simple or complex geometry in detail. As presented in Figs. 3 and 4, the MCNPX input was prepared in such a way to preserve as far as possible all the characteristics related to the geometry, dimensions, and compositions. Additionally, to achieve a precision of 10 pcm in keff , fifty million neutron histories (1000 active KCODE cycles of 50,000 histories) were used. Since the MCNPX results were given by particle source, for example in tally F4: N. the results should be properly normalized to the steady-state thermal power of the system in order to get the absolute comparison with the measured quantities. The Monte Carlo source normalization factor F4 was estimated as follows (X-5 Monte Carlo Team, 2003):

Composition U-ZrH1.6 (8.5 wt%, enriched at 19.7%) ðTh0:75 ; U0:25 ð20%ÞÞO2 Zirconium Aluminum alloy Graphite

Density (g/cm3) 5.74 10.246 6.49 2.7 1.65

  neutron ¼ S  UF4 cm2 :s

U

 tally

1 cm2

 ð2Þ

In Section 3.4, the radial hot rod power peaking factor (FHR ) is defined as the ratio of the power generated in the hottest fuel rodðProd Þ to the core average power generation ðPcore Þ, and is determined in MCNPX using the following component values (Huda et al., 2004):

FHR ¼

ðProd Þmax

ð3Þ



Pcore

For a partial fuel rod elements type such as (Th,U)O2 or U-ZrH, the hot rod power peaking factor could be determined as the ratio of the power generated in the hottest fuel ((Th,U)O2 or U-ZrH) rod to the average power generated in all the same fuel elements type:

FHR ¼

ðProd Þmax ðin a fuel element 

Pðin the same

typeÞ

ð4Þ

fuel element typeÞ

Finally, the ENDF-VII.1 (Chadwick et al., 2011) cross-section library was used (Kabach et al., 2017) to apply neutron-induced cross-sections at 293 K. The thermal scattering data treatment sða; bÞ was also used for crystalline graphite, zirconium hydride,

Fig. 3. Side (a) and Top (b) view of the MCNPX computational model of the TRIGA Mark II research reactor.

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Fig. 4. Configurations of zone-type cores.

and water. Those thermal scattering treatments are a complete representation of thermal neutron scattering by molecules and crystalline solids (Macfarlane et al., 2017). Furthermore, all calculations were performed on a machine with an Intel Xeon Core 2.40 GHz * 2 CPUs, 16 Threads and 12 GB of RAM under Win 10 operating system and utilizing MPICH2 (Liang et al., 2008). The goal of MPICH is to provide an MPI implementation that efficiently supports multi-core architectures.

The ðTh0:75 ; U0:25 ð20%ÞÞO2 density was calculated using the following formula (Ghosh et al., 2016):

qðTÞ ¼ C1 þ C2 T þ C3 T2 þ C4 T3

ð5Þ

where:

C1 ¼ 10:3102 C2 ¼ 2:1423:104

C3 ¼ 4:9352:108

C4 ¼ 1:4689:1012

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Table 3 Effective multiplication factor and the reactivity changes caused by the substitution of U-ZrH1.6 by (Th0.75,U0.25(20%))O2 for different reactor configurations. Configuration

Position of (Th,U)O2 fuel

Number of (Th,U)O2 fuel rods

Effective multiplication factor keff

Reactivity difference (pcm) for configuration without thorium fuel Dq

1 2 3 4 5 6 7 8 9 10

Standard core Ring B Ring C Ring D Ring E Ring F Ring G Rings FG Rings EFG Rings BDF

– 6 12 18 24 30 11 41 65 54

1.07451 ± 0.00010 1.06412 ± 0.00010 1.04634 ± 0.00010 1.04326 ± 0.00010 1.04380 ± 0.00010 1.06243 ± 0.00010 1.07716 ± 0.00010 1.06095 ± 0.00010 1.01814 ± 0.00011 1.01118 ± 0.00010

– 908.687 ± 9.307 2505.553 ± 9.307 2787.706 ± 9.307 2738.117 ± 9.307 1058.172 ± 9.307 228.958 ± 9.307 1189.472 ± 9.307 5152.643 ± 9.308 5828.685 ± 9.308

which contains more thorium oxide, seems to be smaller than that of the core that holds less thorium oxide. This diminution is principally related to the decrease in mrf =ra factor caused by the higher absorption cross-section of the 232Th. Conversely, the higher capture cross-section of 232Th as compared with 238U leads to high internal conversion rates, which means an increase in the reactivity of the fuel during the cycle due to the formation of 233U (further burn-up analysis is needed in these cases).

Table 4 beff for different reactor configurations. Position of (Th,U)O2 fuels

keff;ðtotalÞ

keff;ðpromptÞ

beff (pcm)

Standard core Ring B Ring C Ring D Ring E Ring F Ring G Rings FG Rings EFG Rings BDF

1.07451 ± 0.00010 1.06412 ± 0.00010 1.04634 ± 0.00010 1.04326 ± 0.00010 1.04380 ± 0.00010 1.06243 ± 0.00010 1.07716 ± 0.00010 1.06095 ± 0.00010 1.01814 ± 0.00011 1.01118 ± 0.00010

1.06684 ± 0.00010 1.05641 ± 0.00010 1.03853 ± 0.00010 1.03561 ± 0.00010 1.03640 ± 0.00011 1.05489 ± 0.00010 1.06941 ± 0.00010 1.05329 ± 0.00010 1.01084 ± 0.00010 1.00358 ± 0.00010

714 ± 19 725 ± 19 746 ± 19 733 ± 19 709 ± 20 710 ± 19 719 ± 19 722 ± 19 717 ± 21 752 ± 20

3.2. Delayed neutron fraction (beff ) Since a small variation in beff might reduce the reactor’s controllability, beff is a vital parameter to investigate (Khan et al., 2013). In addition, the beff of any fuel depends on both the fissile and fertile materials that are used. The beff fraction can be calculated using MCNPX and MCNP codes applying the prompt method which requires two calculations with and without the TOTNU NO card (X-5 Monte Carlo Team, 2003). The TOTNU NO card was also used to calculate the effective multiplication factor taking into account just the prompt neutron contribution. The summary of investigation results of kinetic coefficients calculated into the fuel rods, and the average number of neutrons released per fission (m), prompt neutrons (mp) and delayed neutron yields (md) are provided in Table 4 and 5, respectively.

3. Results and discussion 3.1. Results for keff with various arrangements The keff calculation results for configurations 2 to 10 compared with configuration 1 (standard core) are listed in Table 3. The reactivity difference (Dq) is also shown. It can be seen from Table 3 that a maximum keff of 1.07716 with an overestimated reactivity value of 228.957 was achieved for a critical core configuration consisting of 11 (Th,U)O2 fuels in ‘ring G’. This result seems reasonable since i) configuration 7 has the closest look likes the standard core; ii) the thorium-based fuels were positioned in the outermost ring of the core, which they did not significantly effect on mrf =ra factor; iii) the increase in keff may due to the reduction of neutron leakage. It can also be seen from the table that configurations 2, 6, and 8 give good keff results compared to the core without thorium fuel. Underestimated reactivity values of 908.687, 1058.171 and 1189.472 were assessed for configurations 2, 6, and 8, respectively. However, the smallest value of keff that was estimated is obtained from configuration 10 (1.01118), with reactivity differenceDq = 5828.684. It is clearly observed that the keff for the core,

beff ffi 1 

keff;ðpromptÞ keff;ðtotalÞ

ð6Þ

For configurations 5 and 6, beff is slightly lower than the corresponding value for the configuration without thorium fuel. However, it is rather slightly higher for configurations 2, 7, and 8 and the maximum value of beff was estimated for configurations 3 and 10. Those differences were mainly occurred because of the delayed neutron fraction of the 232Th that is higher than of the 238 U as shown in Table 1. However, in thermal reactor spectra as for the case of the TRIGA reactor, the beff of 232Th has minor effects

Table 5 The comparison of the estimated values of average number of neutrons released per fission (m), prompt neutron (mp) and delayed neutron yields (md). Position of (Th,U)O2 fuels

Standard core Ring B Ring C Ring D Ring E Ring F Ring G Rings FG Rings EFG Rings BDF

m

mp

md

U-ZrH fuels

(Th,U)O2 fuels

U-ZrH fuels

(Th,U)O2 fuels

U-ZrH fuels

(Th,U)O2 fuels

2.4385 2.4385 2.4386 2.4386 2.4386 2.4386 2.4385 2.4386 2.4386 2.4391

– 2.4458 2.4462 2.4460 2.4462 2.4454 2.4436 2.4457 2.4473 2.4458

2.4226 2.4226 2.4226 2.4227 2.4227 2.4227 2.4226 2.4227 2.4227 2.4231

– 2.4295 2.4300 2.4298 2.4299 2.4292 2.4274 2.4295 2.4310 2.4295

0.0159 0.0159 0.0159 0.0159 0.0159 0.0159 0.0159 0.0159 0.0159 0.0160

– 0.0162 0.0162 0.0162 0.0162 0.0162 0.0161 0.0162 0.0163 0.0162

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Fig. 5. Comparison of the neutron flux spectra obtained from different configurations in the fuel volumes.

Fig. 6. Difference in neutron flux spectra between configuration 1 and other configurations.

compared to the fast one. Nonetheless, acceptable kinetic coefficients were obtained during the calculations compared to the standard core configuration. 3.3. Neutron spectrum analysis Using MCNPX, the total neutron flux profiles inside the fuel volumes were calculated and plotted in Fig. 5, whereas Fig. 6 presents

the differences in neutron flux between configuration 1 and other configurations. It is noticeably observed that the neutron spectrum change systematically with varying the number of thorium oxide rods. Except for configuration 7, a general tendency is recognized between the difference in total flux that contains more (Th,U)O2 fuel and the standard core. An increase in the neutron flux between (0  0:625:107 MeV) energy range and a decrease in the neutron flux between (104  8:2:107 MeV) energy range, although the

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Table 6 Comparison radial hot rod power peaking factor of for each configuration.

Configuration 1

Configuration 2

Configuration 3

Configuration 4

Configuration 5

Fuel Type

FHR

Hot Rod Identifier

Whole Core ðTh0:75 ; U0:25 ð20%ÞÞO2 U-ZrH1.6 Whole Core ðTh0:75 ; U0:25 ð20%ÞÞO2 U-ZrH1.6 Whole Core ðTh0:75 ; U0:25 ð20%ÞÞO2 U-ZrH1.6 Whole Core ðTh0:75 ; U0:25 ð20%ÞÞO2 U-ZrH1.6 Whole Core ðTh0:75 ; U0:25 ð20%ÞÞO2 U-ZrH1.6

1.61 – 1.61 1.51 1.01 1.32 1.40 1.02 1.32 1.71 1.09 1.80 1.83 1.09 1.84

B3 – B3 B3 B3 D5 C4 C4 B3 B4 D5 B4 B3 E7 B3

Configuration 6

Configuration 7

Configuration 8

Configuration 9

Configuration 10

Fuel Type

FHR

Hot Rod Identifier

Whole Core ðTh0:75 ; U0:25 ð20%ÞÞO2 U-ZrH1.6 Whole Core ðTh0:75 ; U0:25 ð20%ÞÞO2 U-ZrH1.6 Whole Core ðTh0:75 ; U0:25 ð20%ÞÞO2 U-ZrH1.6 Whole Core ðTh0:75 ; U0:25 ð20%ÞÞO2 U-ZrH1.6 Whole Core ðTh0:75 ; U0:25 ð20%ÞÞO2 U-ZrH1.6

1.73 1.09 1.60 1.59 1.11 1.54 1.76 1.21 1.45 2.10 1.41 1.37 1.74 1.51 1.33

B3 F4 B3 B3 G2 B3 B3 F4 B3 B2 E7 B2 B2 B2 C3

neutron flux is slightly decreased in the fast energy range. This tendency might be explained by the fact that the neutron capture cross-section of 232Th is nearly two and a half times higher than that of 238U in the thermal and the epithermal neutron spectrum, respectively. However, in the fast field, the capture cross-section of both isotopes is similar. On the other hand, the smallest differences in neutron flux spectra were observed for configurations 2, 6, 7, and 8. The Difference in neutron flux was calculated using the following equation:

Difference ¼

ðUðStandard configurationÞ  UðringðsÞ}x}ÞÞ UðStandard configurationÞ

ð7Þ

where: UðStandard configurationÞ : is the neutron flux in the standard configuration. UðringðsÞ}x}Þ: is the neutron flux in the proposed configuration. 3.4. Power distributions and radial hot rod power peaking factor (F HR ) The FHR factor is considered as an important safety parameter and strongly depends on the core configuration. It is used in the thermal-hydraulic studies. In this regard, it is important that replacing a partial U-ZrH with (Th,U)O2 fuel rods does not completely change the core’s power distribution or induce hot channel factors beyond prescribed limits (Tucker et al., 2015). In this context, during the simulations, the F7 tally (track length estimator of fission energy deposition) was used to calculate the radial hot rod power peaking factor and the power distributions (multiplied by normalization Eq. (1)). The outcomes of these calculations are presented in Table 6. As shown in Table 6, the hottest rod, accounting for the maximum power generation among the 101 fuel rods was observed to be the element identified as B3 for configurations (1, 2, 5, 6, 7, and 8), B2 for configurations (9 and 10), C4 for configuration 3 and as B4 for configuration 4. The radial hot rod power peaking factor for the standard configuration (without thorium fuel) is found to be in very good concurrence with the reference value of 1.59 reported by (Chham et al., 2016). In general, the FHR values range between 1.40 and 2.10 for all the configurations. However, for the configurations 2, 6, 7, and 8 (with the smallest reactivities |Dq |), the factor FHR values range from 1.51 to 1.76, that also be found in very good agreement with the values reported by (Huda, 2006; El Bakkari et al., 2010).

Fig. 7. Comparison between the measured radial (a) power distribution and (b) flux with different core configurations loading patterns.

The radial power distribution and the total power distribution produced within the fuel and fuel follower elements with different core configurations loading patterns are plotted in Figs. 7 and 8, respectively. As demonstrated in Table 6 and illustrated in Fig. 7, the maximum power produced in the hottest fuel element in the standard configuration is found to be 31.0 kW in B3 fuel elements

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Fig. 8. Radial power distribution within the fuel and fuel follower elements for different core configurations of the TRIGA reactor. Table 7 Calculated shutdown margin for different configurations.

which it shows fairly good agreement with the value reported by (El Bakkari et al., 2010). Regarding configurations with thorium fuel, the maximum power production of 38.22 kW is observed for configuration 9 in the B2 fuel element. On the other hand, for configurations 2, 6, 7, and 8 the maximum power production is observed to be 30 kW, 33 kW, 31 kW, and 33.4 kW, respectively. These results demonstrate good behavior compared to the standard configuration.

Configuration 1 2 6 7 8 SDM reported by Chham et configuration

Position of (Th,U)O2 fuel Standard core Ring B Ring F Ring G Rings FG al., 2016 for the standard

SDM ($) 2.03 2.12 2.18 1.98 2.09 1.82

Please cite this article as: O. Kabach, A. Chetaine, A. Benchrif et al., Neutronic investigation of the thorium-based mixed-oxide as an alternative fuel in the TRIGA Mark-II research reactor – Part I: A beginning of life calculations, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107075

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O. Kabach et al. / Annals of Nuclear Energy xxx (xxxx) xxx

3.5. Shutdown margins (SDM)

Acknowledgments

A safety analysis of any reactor will invariably include determination of the SDM. In our case, the SDM was evaluated as the difference between the core excess reactivity and the combined reactivity of 4 out of the 5 control rods, and assuming that the highest worth rod is stuck. The calculation was performed only for the configurations 2, 6, 7, and 8 that were selected based on the good neutronics and kinetic results discussed before at (BOL). For that reason, however, it is necessary to determine which control rod is the highest worth rod. Therefore, we made a simple calculation in KCODE with all rods except the highest worth rod

The authors wish to thank Nuclear Reactor and Nuclear Security Group Energy Centre members (Mohamed V University, Morocco) for their support, helpful suggestions and discussions.

Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.anucene.2019.107075.

i

insertedkout . From this, kin (in the case that all control rods fully inserted) is subtracted to find the worth of that rod qirod as in Eq (8) (Tucker and Usman, 2018):

qirod ¼ kiout  kin

ð8Þ

Regarding the definition of SDM, a value of 2.03$ obtained using the standard core configuration, found to be in very good agreement with the reference value of 1.82$ reported by Chham et al., 2016. On the other hand, the SDM results for configurations 2, 6, 7, and 8, are 2.12$, 2.18$, 1.98$ and 2.09$, respectively. They show a very good agreement with the value 2.03$ of the standard configuration (see Table 7).

4. Conclusions and future work Based on this investigation, we might underline the possibility that the TRIGA Mark-II reactor can be operated with ðTh0:75 ; U0:25 ð20%ÞÞO2 fuel instead of the conventional fuel U-ZrH1.6. Neutronic calculation studies at the beginning of the life of the thorium-loaded reactor installation in nine different configurations were performed with the purpose of selecting optimal designs of the reactor and its fuel load ensuring the most efficient use of thorium in it with assuring minimum changes in the main safety parameters. Among several seed-blanket configurations considered in this paper, it was recognized that the most promising configurations to achieve a supercritical condition are; configuration ‘‘200 (thorium in ‘ring B’), configuration ‘‘6” (thorium in ‘ring F’), configuration ‘‘7” (thorium in ‘ring G’), and configuration ‘‘8” (thorium in ‘rings FG’), by comparison to the standard configuration (contains only uranium U-ZrH1.6 fuel rods). Except for configuration ‘‘7”, it can be noticed that keff for the core that contains less thorium is higher than that has more thorium because of the absorption crosssection of neutrons in thorium. However, the thorium can be used as a fertile material during the life cycle to produce 233U. The kinetic and control parameter like beff is a good safety indicator of a reactor’s chronological response. For thorium-based fuel configurations, beff is around 720 ± 20 pcm for the proposed configurations (2, 6, 7, and 8). Those results were found to be acceptable compared to the standard configuration (714 ± 20 pcm). In all the proposed configurations (2, 6, 7, and 8), neutron flux distribution, power distribution and FHR factor show very good agreement with the standard core configuration. The SDM was the final safety parameter used in this investigation. It was found that the SDM for the thorium-based fuel variates from 1.98$ to 2.12$, which was acceptable compared to 100% (UZrH1.6) configuration 2.03$. Finally, it is worth mentioning that all investigations presented in this paper were performed at the beginning of life (BOL), and without either any thermal fluid considerations or burn-up calculation. Hence, the fission products build-up was not included in the neutronic simulations.

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Please cite this article as: O. Kabach, A. Chetaine, A. Benchrif et al., Neutronic investigation of the thorium-based mixed-oxide as an alternative fuel in the TRIGA Mark-II research reactor – Part I: A beginning of life calculations, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107075