Determination of the activity inventory and associated uncertainty quantification for the CROCUS zero power research reactor

Annals of Nuclear Energy 136 (2020) 107034

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Determination of the activity inventory and associated uncertainty quantification for the CROCUS zero power research reactor Wonkyeong Kim a, Mathieu Hursin b,c,⇑, Andreas Pautz b,c, Lamirand Vincent b,c, Frajtag Pavel c, Deokjung Lee a a b c

Department of Nuclear Engineering, Ulsan National Institute of Science and Technology, UNIST-gil 50, Ulsan 44919, Republic of Korea Nukleare Energie und Sicherheit, Paul Scherrer Institut, PSI Villigen 5232, Switzerland Ecole Polytechnique Fédérale de Lausanne (EPFL), Laboratory for Reactor Physics and Systems Behaviour (LRS), CH-1015 Lausanne, Switzerland

a r t i c l e

i n f o

Article history: Received 7 June 2019 Received in revised form 5 September 2019 Accepted 6 September 2019

Keywords: EPFL CROCUS reactor Radioactivity Uncertainty quantification Source term MCS

a b s t r a c t The paper describes the source term estimation of CROCUS, the zero power research reactor of EPFL, to be used for dispersion analysis under accidental conditions. To fulfil regulatory requirements, the source term of the CROCUS fuel is estimated through Monte Carlo simulations supplemented by uncertainty quantification, both obtained from the Monte Carlo code MCS developed at UNIST. Even though the depletion capabilities of MCS were pre-existing to this work, no verification has been documented so far. A comparison of MCS and SERPENT results for the determination of the activity inventory for the CROCUS fuel is presented; both codes agree within the 1% for the major isotopes contributing to both inhaled and ingested doses. The source term of CROCUS is calculated under a postulated accident. Eight isotopes, 90Sr, 91Y, 131I, 137Cs, 140Ba, 140La, 144Ce, and 239Pu produce the largest contributions to the effective dose to the public. For uncertainty quantification, nuclear data uncertainties, specifically cross sections and fission yields are considered. Three stochastic sampling methods are implemented in the MCS code namely, TMC, fastTMC and fast-GRS methods. The performances of the two fast methods have been analyzed when applied to the CROCUS reactor. All three methods produce consistent uncertainty estimates and the two fast methods showed a reduced computational cost compared to the original TMC method. The fission yield uncertainty is the leading factor for the determination of uncertainty of the activity for 90Sr, 91Y, 131I, 137 Cs, 140Ba, 140La and 144Ce isotopes. On the other hand, the cross section uncertainty is the leading factor for the uncertainty of 239Pu activity. Finally, the modeling of the irradiation history for CROCUS is simplified to reduce the computational cost. It is demonstrated that the activities for the short lived isotopes (131I and 144Ce) are very sensitive to the irradiation history specifications. Nonetheless, the irradiation history used for the determination of the nominal fuel inventory activity is conservative as it overestimates the activity of the short lived isotopes. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction CROCUS is a teaching and research zero power reactor operated by the Laboratory for Reactor Physics and Systems Behaviour (LRS) at the Swiss Federal Institute of Technology (EPFL). CROCUS has been being operated for 35 years, since 1983 (Früh and Réacteur, 1993). Upon request of the Swiss Nuclear Safety Authority (ENSI), the activity inventory of the reactor core was estimated for the determination of the radioactive source term. Such information is ⇑ Corresponding author at: Paul Scherrer Institut, Nukleare Energie und Sicherheit, PSI Villigen 5232, Switzerland. E-mail address: [email protected] (M. Hursin). https://doi.org/10.1016/j.anucene.2019.107034 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.

required for downstream dispersion analysis under accidental conditions. The lack of the experimental data for the current CROCUS activity inventory leads to estimate the source term through simulations supplemented by uncertainty quantification. Radioactive isotopes are created by fission reactions and radioactive decay. These isotopes have different activities depending on their decay constants and isotopic compositions. The concentration of those isotopes can be determined by solving a system of first-order differential equation, called the Bateman equation, which requires careful consideration of the complex transmutation paths resulting from both neutron induced reactions and radioactive decay. It also requires calculating neutron

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induced reaction rates in a region of interest and consequently an accurate solution of the neutron transport equation. Among computational methods, the Monte Carlo approach allows avoiding the computational biases involved in the deterministic solution of the neutron transport equation. However, its large computational cost, even with nowadays’ computers, make it difficult to handle large nuclear power plants. The analysis of a relatively small-scale research reactor like CROCUS is however feasible. Moreover, it allows handling explicitly the unique geometric configuration of CROCUS when deterministic methods have to rely on approximations (Downar, 2010). Consequently, the determination of CROCUS source term is carried out using the Monte Carlo code, MCS. The major contributors to the effective dose to the population during a hypothetical accidental release are identified for the CROCUS fuel, considering a given accident scenario. In the present manuscript, the uncertainty of the activity inventory of CROCUS due to uncertainty in nuclear data is obtained using the MCS code and a stochastic sampling (SS) approach. Numerous studies and efforts have been undertaken to quantify the uncertainty in neutron transport related parameters due to nuclear data uncertainty. They are documented in the review paper (Rochman et al., 2017). The determination of isotopic composition uncertainty through burnup calculations requires large computational resources (Zwermann et al., 2014). Nonetheless, such studies have been carried out for particular applications like spent fuel pools (Leray et al., 2016; Ferroukhi et al., 2014). Moreover, since a Monte Carlo code is involved, it is necessary to carefully consider the statistical uncertainties caused by the Monte Carlo solution itself. These statistical uncertainties are propagated to the output quantity of interest and may affect the output uncertainty estimate (Zwermann and Krzykacz-Hausmann, 2012). Two proven fast methods show improvements compared to the intuitive TMC method (Koning and Rochman, 2008) of computing uncertainty by repeating the Monte Carlo calculation many times for a large number of neutron histories. In contrast, the fast methods use a reduced number of neutron histories and shows similar precision to the TMC method (Rochman et al., 2014; Rochman et al., 2014) in terms of uncertainty estimation at a much lower computational cost. Thus, in this study, these three methods are introduced and a comparative analysis is performed considering the activity of the CROCUS fuel as the quantity of interest. In addition, the effect of the inherent statistical uncertainty of the Monte Carlo method is estimated on the activity inventory uncertainty. Finally, the results of activity inventory calculation and its associated uncertainty are presented. The present paper is structured as follows: Section 2 describes the computational models of the EPFL CROCUS zero power reactor, its irradiation history, and the accident scenario considered. In Section 3, the methods used in MCS for determining the source term of the current CROCUS fuel rods as well as its associated uncertainty are summarized. Section 4 includes the verification of both transport and burnup capability of MCS code used in this study against the results of the well-validated codes, MCNP6 (Pelowitz, 2012) and Serpent2 (Leppänen et al., 2015). Section 4 also includes CROCUS source term estimates and the effect of the irradiation history on the effective doses. Finally, in Section 5, the uncertainty of the activity inventory due to the nuclear data uncertainties is presented considering the three uncertainty quantification methods.

2. EPFL CROCUS model 2.1. CROCUS zero power reactor The CROCUS reactor, operated by the Swiss Federal Institute of Technology, Lausanne (Früh and Réacteur, 1993), is a two-zones

uranium-fueled, H2O-moderated critical research facility. This facility is a zero power reactor with a maximum allowed power of 100 W. The core is approximately cylindrical in shape with a diameter of about 60 cm and a height of 100 cm. The CROCUS core is composed of a central zone of 1.806 wt%-enriched UO2 rods and an outer zone of 0.947 wt%-enriched uranium metal rods. The reactivity in the CROCUS reactor is controlled by variation of the water level, or by movement of two B4C control rods. The maximum water height is 100 cm, while the critical water height for the configuration with 176 metallic uranium rods according to Fig. 1 is above 95 cm. The right part of Fig. 1 depicts axial cross-section of the CROCUS reactor. The core is bound axially by an upper and a lower grid plate. Both grid plates incorporate a cadmium layer with a thickness of 0.50 mm. The active fuel length starts at the top surface of the lower cadmium layer and extends to 100 cm. The left part of Fig. 1 shows the radial cross-section of the CROCUS vessel. Because of the different pitches used, the two fuel zones are separated by a varying water gap, as indicated in Fig. 1. The outer fuel zone is surrounded by a water reflector with an outer radius of 65 cm. The vessel wall consisting of aluminum has a thickness of 1.2 cm. All other parameters and detailed configuration for the two types of fuel rods are given in Table 1 and Fig. 2. All fuel rods have an aluminum cladding and are maintained in a vertical position by the upper grid and lower grid plates (Kasemeyer et al., 2007; Paratte et al., 2006). In this work, two single fuel rod models are also utilized for the verification of isotopic inventory calculation with MCS and for the uncertainty quantification of the fuel isotopic inventory using a stochastic sampling method. We have used ‘‘reflective boundary” condition to the fuel rod model. Therefore, the spectra of the single UO2 rod is probably representative of the inner lattice of the core. However, the spectra of the single Umetal rod will be harder as the reflector effect is not taken into account. Such simpler model is required to reduce the computational cost of such analysis as the stochastic sampling methods considered require many simulations. 2.2. CROCUS irradiation history The irradiation history has been determined based on the CROCUS operational records. The first criticality of the CROCUS reactor was achieved on 13th July 1983 and the reactor has now been operated for 35 years. The operation record includes: 1) the energy released [Wh], 2) start and end time of operation. The energy released [Wh] is divided by operating hours [h] to determine the average power [W] required in the burnup calculations. Considering the detailed representation of irradiation history in hours and even minutes is extremely computationally expensive due to large number of transport calculation required. Consequently, a coarser irradiation history is built: based on the operation records, the irradiation history is grouped on yearly basis, assuming two time steps: one cooling step followed by one irradiation step assuming all the irradiations of the year happened continuously at the end of the year. The resulting irradiation history for CROCUS reactor is represented in Fig. 3. The effects of this approximation to describe the irradiation history are analyzed in Section 4.4. 2.3. Accident scenario The source term calculation is an important step in the estimation of the amount of radioactive substances released based during a given accident scenario. In this study, the postulated accident is the following: a small airplane crashes on the CROCUS facility while the fuel is outside of the containment. Such situation happens during maintenance activities when CROCUS is unloaded, and the fuel is transported to its external storage. It is assumed that

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Fig. 1. Configuration of CROCUS core model (left: mid-height x-y cross-section/right: central y-z cross-section).

Table 1 Main specifications of CROCUS fuel. Description

Inner lattice

Outer lattice

Fuel Enrichment [%] Number of rods Density [g/cm3] Fuel height [cm]

UO2 1.806 336 10.555 100

Umetal 0.947 Up to 176 18.6945 100

all the fuel rods will have their cladding ruptured resulting in the complete release of their activity inventory in the atmosphere. Such scenario of an airplane crash represents the most extreme case in terms of impact to the public health. As the burnup of CROCUS is low, the source term of the fuel lies mostly in the short lived fission products. The postulated accident scenario also assumes that the event happens two weeks after the last irradiation. This is the typical cooling time used before unloading the core to reduce

the dose to the workers. The last irradiation is assumed to be done at 1 W and to last 4 h which represents a typical use of CROCUS for education purposes. To estimate the consequences associated with such a scenario, dose coefficients to convert the activity of the CROCUS fuel in the effective dose by the inhalation or the ingestion have been adopted from directive ENSI-G14 of the Swiss regulator, the Federal Nuclear Safety Inspectorate (ENSI). The dose coefficients given in ENSI-G14 are built in the library of the MCS code. The inhaled and the ingested effective doses produced in this work are calculated by multiplying the activity derived from the irradiation calculation by the dose coefficient. The values of the effective dose by the inhalation or the ingestion presented in this paper are not relevant as they assume that the source term of CROCUS is inhaled or ingested by one person. An additional dispersion analysis taking into consideration the surrounding terrain and environment (beyond the scope of the present paper) is required to estimate the risk to the public.

Fig. 2. Configuration of two fuel rod models for CROCUS reactor.

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applied to produce long-lived metastable isotopes such as Am. The computation of those transmutations requires an effective one-group cross section, which is determined by a reaction rate tally and the flux tally during the transport simulation. Even though the depletion capability of MCS was pre-existing to this work, no real benchmarking analysis has been done with the depletion solver. Conventionally, the depletion calculation is performed with the constant power condition so that continuous power change cannot be explicitly considered. To help the consideration of the continuous power change, full predictor-corrector called as ‘‘CE/BE” and semi predictor-corrector called as ‘‘Ce/BE” algorithms (Isotalo and Sahlberg, 2015) are supported in the MCS code in addition to simple predictor algorithm. Full predictorcorrector algorithm is employed for all depletion calculations in this paper. Consequently, a verification of MCS depletion calculation capability is carried out with Serpent2, an established Monte Carlo depletion code as a reference. A pin cell problem representative of the CROCUS fuel and power history is considered. The results are discussed in Section 4.2. 242m

Fig. 3. Modeled irradiation history of the CROCUS reactor.

Nonetheless, the effective dose calculated by MCS is used as a metric for comparison of toxicity between the various isotopes in the CROCUS fuel. Finally, the directive ENSI-A08 also provides the set of 116 isotopes that must be considered for the source term analysis in the event of fuel cladding failures. The present work focuses on a subset of those isotopes with the largest contribution to the effective dose. 3. Computational methods 3.1. MCS Monte Carlo code A Monte Carlo code called MCS has been developed at Ulsan National Institute of Science and Technology (UNIST) since 2013. The target of MCS is to solve complex whole core problems like BEAVRS (Hyunsuk, et al., 2017). MCS can treat the 3D whole core geometry and the neutron physics with probability-table, freegas treatment, S(a, b) and Doppler Broadening Rejection Correction. MCS uses data libraries in the Evaluated Nuclear Data File (ENDF) format, consisting of continuous energy neutron cross section data, neutron induced fission yields and decay constants. MCS uses ENDF-VII.1 nuclear data library by default but user can use any version of ENDF format library for the continuous neutron cross section, decay and fission yield data. MCS neutron transport kernel has been validated against the 300 benchmarks of the International Criticality Safety Benchmark Experimental Problem (ICSBEP) database (Jang et al., 2018). The MCS code has a built-in depletion module which uses the CRAM method (Pusa, 2011) to solve the Bateman equation. Additional complementary data for the ternary fission is used by extraction from the fission yield library of JEFF-3.1.1 evaluation. Spontaneous fission is explicitly handled with the spontaneous fission yield data if an isotope has the transmutation path by the spontaneous fission. The burnup chain can consider all the 3820 isotopes available in the decay library of ENDF/B-VII.1, but 1640 isotopes are used as default for the burnup calculation in the MCS to reduce its computational cost. However, in this paper, the depletion calculation is performed with all the 3820 isotopes. All transmutation paths by the radioactive decay available in ENDF/ B-VII.1 are explicitly considered, i.e. beta decay, electron capture, alpha decay etc. The neutron induced transmutations are implemented with 6 major types of reaction: (n,c), (n,2n), (n,3n), (n,a), (n,p), 3 energy group fission. Additionally, branching ratios are

3.2. Stochastic sampling methods for uncertainty quantification on isotopic inventory In recent years, the increase in computational power has made it possible to propagate input data uncertainty in a given computational scheme using SS. In this approach, the transport calculations are repeated hundreds or thousands of times with the same code and perturbed nuclear data library sampled according to existing covariance matrices. The distribution of results is analyzed to quantify the uncertainty of output parameters. Several publications reported the development of various methodologies which lead to the estimation of isotopic inventory uncertainties with SS methods: XSUSA (Zwermann et al., 2014), SAMPLER (Williams et al., 2017), Shark-X (Aures et al., 2017), TMC (Rochman et al., 2016; Rochman et al., 2011), NUSS (Zhu et al., 2015). By denoting X i (i = 1. . .n for n data sets) a realization of the random input parameter X or a set of random input parameters, i.e., fission cross section of 235U for single energy point or whole energy grid, we can compute the associated output quantity, Y i . The variance (V Y ) and mean (Y) of the associated random variable Y can be defined from the n simulation runs as follows:

Y¼

n 1X Yi n i¼1

VY ¼

n  2 1 X Yi  Y n  1 i¼1

ð1Þ

ð2Þ

For Monte Carlo simulations, the variance of output quantity implies both the statistical uncertainty that results from the intrinsic nature of the Monte Carlo (MC) solution and the uncertainty arising from input parameter variations. Thus, the variance of the output parameters V Y of interest can be expressed by the following Eq. (3) assuming the two uncertainty sources are not correlated

V Y  V stat þ V X

ð3Þ

where V stat and V X means the statistical variance and the variance due to the nuclear data uncertainty. To obtain the uncertainty due to only nuclear data uncertainty, the statistical uncertainty pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffi ( V stat ) should be negligible compared to the uncertainty ( V X ) resulting from input parameter variations. From this point on, the statistical uncertainty intrinsic to Monte Carlo simulations is called ‘‘aleatoric” uncertainty, and uncertainty due to lack of knowledge, i.e., nuclear data uncertainty, is called ‘‘epistemic” uncertainty (Zwermann and Krzykacz-Hausmann, 2012).

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The propagation of input uncertainty carried out with the MCS code adopts the following steps: - Perturbed pointwise nuclear data is provided to MCS using Nuclear data Uncertainty Stochastic Sampling – Simple Random Sampling (NUSS-SRS) tool (Zhu et al., 2015). Specifically, elastic scattering, inelastic scattering, (n, 2n), fission, capture, average number of neutrons per fission, average fission spectrum (Wieselquist et al., 2013) are perturbed. Only perturbation to the nuclear data of 1H, 16O, 235U and 238U are considered. - Random fission yields are provided for 235U, 238U, 239Pu and 241 Pu. They are coming from TENDL 2015 data library (Koning and Rochman, 2012). The incoming neutron energy is equal to 0.0253 eV except for 238U, for which an incoming neutron energy of 500 keV is assumed. - Beside the original TMC approach, two fast SS methods are adopted for uncertainty analysis, significantly reducing the computational time. One is the fast Total Monte Carlo (TMC) method, the other is the fast-GRS method. Both methods will be briefly explained in this paper, and a detailed description and verification can be found in Ref. (Rochman et al., 2014; Rochman et al., 2014). 4. Determination of the CROCUS source term To obtain a reliable estimate of the CROCUS source term, the following approach is used. First the CROCUS whole core model used in MCS is verified against existing models with MCNP6 and Serpent2. The quantities of interest are the multiplication factor and the fuel pin power. Second, the verification of the MCS burnup solver is performed for the case of a single fuel rod model based on the CROCUS UO2 fuel and the irradiation history given in Fig. 3. The activities of selected isotopes in the fuel are compared to the results of Serpent2. Third, the CROCUS source term is evaluated considered the CROCUS core model. The spatial activity distributions of the major contributors to effective dose by inhalation and ingestion are determined. Finally, the effect of the irradiation history on the fuel composition is evaluated. 4.1. Verification of MCS CROCUS core model The initial steady state of the CROCUS core model is calculated by the MCS code, in which the ENDF/B-VII.0 (Chadwick, 2006) continuous neutron cross section data is used instead of the default data library. 50 inactive cycles, 500 active cycles and 1,000,000 neutrons are used. The MCS keff result is compared to the one of Serpent2 and MCNP6. The results are summarized in Table 2. The reference keff is calculated by MCNP6 with the ENDF/B-VII.0 continuous energy cross section library, and both MCS and Serpent2 results show excellent agreement with the reference result within 2 standard deviations. The Shannon entropy indicator is obtained from the MCS calculation. It is illustrated in Fig. 4. The average entropy is estimated from its mean over all active cycles. Looking at the evolution of the Shannon entropy for a given cycle, the fission source appears converged after 10 cycles. Nonetheless, 50 cycles are discarded as inactive to insure a well converged fission source. The normalized pin power distribution is compared with the results obtained from the MCNP6 code. In whole core configuration

Table 2 Multiplication factor result of CROCUS core model.

keff

MCS

Serpent2

MCNP6

1.00209 ± 0.00003

1.00198 ± 0.00005

1.00204 ± 0.00003

Fig. 4. Shannon entropy for fission source convergence.

shown in Fig. 5, the power distribution comparison is represented by separating the inner lattice consisting of the UO2 fuel rods and the outer lattice of the Umetal fuel rods. Root mean square errors of 0.15% and 0.18% with respect to the MCNP6 solution are obtained with MCS and Serpent2 respectively. The results dividing the difference with the root sum square of the standard deviation estimated by each code also show good agreement with MCNP6, in which the results are less than 3 sigma except for one UO2 rod in each result from MCS and Serpent2. The discrepancy larger than 3 sigma are of statistical nature and are likely to occur as 512 fuel rod powers are considered here.

4.2. Verification of MCS burnup calculation Even though the depletion capabilities of MCS were pre-existing to this work, no real benchmarking analysis has been reported in the literature about its depletion solver. A pin cell problem based on a typical CROCUS UO2 fuel rod as shown in Fig. 2 is used for verification purposes. The irradiation history of Fig. 3 is used. The Serpent code of version 2.1.29 is used as a reference. The comparison of the activity inventory is carried out 2 weeks after the last irradiation on 31th July 2017. For this verification, 35 isotopes contributing more than 99.9% to both inhaled and ingested doses (99.98% for inhaled dose and 99.95% for ingested dose) are selected and their contributions to the respective total dose are shown in Fig. 6. The two codes have used same ENDF/B-VII.0 nuclear data which contains decay and fission yield library, as well as the neutron cross section library. The MCS considered all isotopes of 3820 included in the decay data library, however Serpent2 uses truncated burnup chains including around 1400 isotopes. The results for the isotopic inventory are represented in Fig. 6. Among isotopes contributing more than 1% to both doses, 131I, 143 Pr and 106Ru show the difference of doses close to 1%. Noticeable differences are observed for 129mTe, 125Sb, 127mTe, 127Sb, 111Ag and 125 Sn (87%, 26%, 11%, 11%, 33% and 31% respectively). The aleatoric uncertainty associated with the activity of the UO2 fuel is estimated through 500 MC simulations with different random seeds and unperturbed nuclear data using the fast-TMC method. 10 active and inactive cycles in each are used for 20,000 neutrons per cycle for the calculation. Among the 35 isotopes, the aleatoric uncertainty of 237U is largest, around 1.8%. The others are below the 0.1% range for the considered number of neutron histories except for 239Np, 111Ag and 125Sn where their aleatoric uncertainties are around 0.19%, 0.24% and 0.13% respectively. Therefore,

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Fig. 5. Normalized power distribution in CROCUS reactor model.

energy grids for each fissile nuclide to apply the linear-linear interpolation scheme for all the energy dependent fission yield data. In any case, both inhaled and ingested doses due to isotopes which have noticeable differences are negligible for the accident scenario envisioned in this work: 0.05% and 0.16% of the total amount of each quantity are due to 129mTe, 125Sb, 127mTe, 127Sb, 111 Ag and 125Sn. Such discrepancies will not affect the determination of CROCUS source term. The verification is deemed successful. 4.3. CROCUS source term

Fig. 6. Comparison of activity inventory calculated with the MCS and the Serpent2 codes (contribution to total dose in black for inhaled dose and white ingested dose, and comparison in red). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

for most of isotopes except for 239Pu, 239Np and 237U, the aleatoric uncertainty is lower than the difference respectively, suggesting a statistically significant difference between MCS and Serpent2. A plausible explanation for such differences could be the treatment of the energy dependent fission yield in each code. MCS computes one-group fission yield by group condensation averaging threegroup fission yield with three-group fission reaction rates. MCS has 3 energy grids for tallying fission reaction rates in the thermal, the intermediate and the fast region each. Here, there is no interpolation scheme of the fission yield data depending on the incoming neutron energy. Serpent2, on the other hand, has nuclide-wise

Table 3 represents the source term results for the CROCUS fuel corresponding to the accidental scenario. The calculations are carried out with the whole core model and the activity released under the considered accident scenario is the inventory of the whole core model. The source term calculation is performed with the ENDF/BVII.1 nuclear data library for the decay data, fission yield data, and neutron cross section. 10 inactive cycles, 100 active cycles and 1,000,000 neutrons are used. The eight isotopes contributing most

Table 3 Major contributor to the CROCUS source term. Isotopes

Activity [Bq]

Inhaled dose [mSv]

Ingested dose [mSv]

239

4.12E+05 7,39E+07 6,19E+07 2,41E+07 1,68E+08 1,93E+08 2,55E+07 9,60E+07 1.93E+09

2.06E+04 (68.3%2)) 2.66E+03 (8.8%) 1.24E+03 (4.1%) 8.69E+02 (2.9%) 8.58E+02 (2.8%) 7.03E-01 (0.7%) 6.01E-01 (0.4%) 4.20E-01 (2.3%) 3.01E+04 (90.4%3))

1.03E+02 3.85E+02 1.36E+03 6.76E+02 4.37E+02 3.87E+02 3.31E+02 2.30E+02 5.35E+03

Pu 144 Ce 131 I 90 Sr 140 Ba 140 La 137 Cs 91 Y Total1)

(1.9%) (7.2%) (25.4%) (12.6%) (8.2%) (7.2%) (6.2%) (4.3%) (73.0%)

1) Total dose for selected 116 isotopes, but not for eight isotopes. 2) The ratio of quantity for each isotope to total quantity. 3) The ratio of the sum of quantity for eight isotopes to total quantity.

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the distribution of 235U fission and 238U capture reaction rates considering their amount contained in Umetal and UO2 fuel rods as shown in Fig. 7.

to both inhaled and ingested doses among the 116 isotopes are listed with their activities, inhaled doses and ingested doses in Table 3. Fig. 7 shows the activity distribution for each fuel rod in CROCUS, for the eight isotopes (239Pu, 144Ce, 131I, 90Sr, 140Ba, 140La, 137 Cs and 91Y) contributing most to the inhaled and ingested dose. Most of the activity is found in the Umetal fuel rods located at the interface between outer and inner fuel lattices: they are about twice the average values. The numerical values for the maximum activities for a given fuel rod in the whole core distribution are shown in Table 4. In the case of 239Pu, the difference in activity between the UO2 and the Umetal fuel zones is larger than for 144 Ce, 131I, 90Sr, 140Ba, 140La, 137Cs and, 91Y which are mainly produced through fission of 235U. Even though its enrichment is lower, a fuel rod made of Umetal contains about three times more 235U than a fuel rod made of UO2 due the difference of the density and volume. On the other hand, 239Pu is mainly produced by the capture reaction of 238U. As a Umetal fuel rod contains about five times more 238U than a UO2 fuel rod, it is expected that the amount of 239Pu produced in the Umetal fuel is larger. It is consistent with

4.4. Effect of the irradiation history approximation In this section, the effect of the irradiation history modeling on the activity inventory is investigated. The purpose of this evaluation is to estimate the uncertainty resulting from approximations in the irradiation history description. Its detailed modeling would result in an impracticable computational cost. The calculations are performed with the CROCUS core model. Five different grouping for the irradiation and cooling times are considered and illustrated in Fig. 8: the black block represents the irradiation stage, the white block a cooling stage. As a starting point, it is assumed that the recent fuel history is most important for the determination of the source term. Hence, we focus on the time period from 1 January on 2016 to 15 July on 2017. Case 1 represents the irradiation history shown already in Fig. 3. In Case 2, the cooling stage is eliminated by lowering the power level in the irradiation stage; it

1) Activity of 239Pu (scaled)

2) Activity of 144Ce

3) Activity of 131I

4) Activity of 90Sr

5) Activity of 140Ba

6) Activity of 140La

Fig. 7. Core distribution on activity of most toxic isotopes (239Pu,

144

Ce,

131

I,

90

Sr,

140

Ba,

140

La,

137

Cs and

91

Y) and

235

U fission and

238

U capture reaction rates.

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7) Activity of 137Cs

8) Activity of 91Y

9) 235U fission reaction rate

10) 238U capture reaction rate Fig. 7 (continued)

Table 4 Average, maximum, and minimum activity per fuel rod, for the eight isotopes contributing the most to the CROCUS source term. Activity [Bq]

239

144

131

Average Maximum Minimum

804 1,974 456

144,409 279,631 101,814

120,824 235,524 84,619

Pu

Ce

I

Fig. 8. Various representation of the irradiation history.

corresponds to a constant irradiation with a reduced power level. The Case 3 and 4 irradiation histories contain the full details of the irradiation history for a given period. Case 5 represents grouping irradiation and cooling periods, having the irradiation stage at the start of the period. The activities for major isotopes in terms of toxicity (eight isotopes highlighted in Table 3 of Section 4.3) are evaluated two weeks after the last irradiation. The results are shown in Fig. 9.

90

Sr

140

140

328,508 637,111 231,035

377,669 732,453 265,609

Ba

47,127 90,659 33,414

La

137

Cs

49,706 96,512 34,987

91

Y

187,429 361,827 132,287

When we compare the irradiation histories from Case 1 to Case 5, the activity differences are negligible for the long lived isotopes such as 239Pu, 90Sr, and 137Cs. The remaining five isotopes (144Ce, 131 140 I, Ba, 140La, and 91Y) are affected by the grouping of irradiation and cooling intervals. Due to the large contributions of the short/ medium lived isotopes to the overall dose shown in Table 3, this analysis demonstrates that the description of the irradiation history can lead to large modeling biases. Even though the irradiation histories of Case 4 is the most accurate description of the situation of CROCUS, the consideration of the fine irradiation history in hours or even minutes results in large computational costs even if we only consider the period from January 1 to July 15, 2017. Therefore, we have chosen the worst scenario of Case 1 as a conservative approach as it produces the largest activities. The solution pursued in this work is to estimate the uncertainty in the activity of each isotope introduced by approximating the irradiation history. It is estimated with the small number of samples shown in Fig. 8 and simple statistics of Eq. (4).

    N Ai;c  Ai  1X   DAi ð%Þ ¼   N c¼1 Ai 

ð4Þ

where Ai and DAi are the respective activity and its relative uncertainty for an isotope i in a given irradiation history. A is the mean of the activity for the isotope i.

W. Kim et al. / Annals of Nuclear Energy 136 (2020) 107034

9

Fig. 9. Effect of the irradiation history approximation to the activities (Case 1–Case 5) on selected isotopes.

It is a very crude estimate, but the goal of the present analysis is to estimate the uncertainty magnitude. A more complete estimation would require a large number of samples with various combinations (alternating frequency and different intervals, etc.) which is beyond the scope of this article. Table 5 shows the uncertainty on the activity of each isotope. The activity of 131I shows the largest uncertainty around 120% which represent an uncertainty of 4.8% and 30.0% in terms of total inhaled and ingested doses, respectively. Unless the full detail irradiation history is used, a large uncertainty in the activity due to the

short and medium lived isotopes should be considered. Nonetheless, the use of Case 1 irradiation history allows obtaining conservative results as the activities for the short lived fission products is overestimated while offering a reduced computational cost.

5. Uncertainty quantification of the CROCUS source term In this section, the uncertainty of the activity inventory of the CROCUS fuel is quantified using the three SS methods described

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Table 5 Uncertainty on activity of eight selected isotopes due to the irradiation history approximation. Isotope

DAi ð%Þ

Mean standard error (68% confidence)

Uncertainty in the total dose1) (%) Inhaled dose

Ingested dose

239

0.029 21 120 0.81 110 110 0.77 49

[0.019, 0.038] (Hyunsuk, et al., 2017; Chadwick, 2006) [78,160] [0.62, 0.99] [75,150] [75,150] [0.60, 0.94] [32,67]

0.0 1.8 4.8 0.0 3.2 0.8 0.0 1.1

0.0 1.5 30.0 0.1 9.2 8.2 0.0 2.1

Pu 144 Ce 131 I 90 Sr 140 Ba 140 La 137 Cs 91 Y

1) The ratio of quantity for each isotope to total quantity DAi .

in Section 3.2, considering perturbations in nuclear data (cross sections, fission yields) for the main isotopes found in the CROCUS reactor. The increase in computer performance over the last few decades makes it possible to apply the Monte Carlo (MC) method to large scale nuclear reactor analysis. However, the application of a strict SS method, i.e., the original TMC approach, to the whole core problem requires hundreds or even thousands of repetitive MC depletion calculations with a large number of neutron histories. It is too computationally expensive. Therefore, two fast SS methods (Rochman et al., 2014; Rochman et al., 2014) have been considered for the uncertainty analysis to reduce such computational costs by using fewer number of neutron histories than that of the original TMC. Before applying these methods to the CROCUS reactor, their respective performances and convergence properties are assessed at the fuel rod level. The most efficient method is applied at the core level. Finally, the importance of the various source of input uncertainty (cross sections, fission yields, aleatoric uncertainty and irradiation history) in terms of activity inventory is analyzed. 5.1. Uncertainty quantification of the CROCUS activity inventory at the fuel rod level The uncertainties on the activity of the CROCUS inventory at the fuel rod level due to nuclear data are computed. The nuclear data considered are the neutron cross section data as well as the fission yields. The uncertainty due to the decay constants is assumed negligible (Ferroukhi et al., 2014) so that non-perturbed ENDF/B-VII.1 (Chadwick, 2011) decay data is used. For the neutron cross section data, the microscopic data for 235U, 238U, 1H, and 16O is randomly

perturbed using the covariance information of ENDF/B-VII.1 (Chadwick, 2011). Since the CROCUS zero power reactor has an extremely low burnup (0.3Wd/kgU), it is reasonable to consider only those isotopes as uncertain parameters. Perturbations to the thermal scattering data for 1H in H2O is also not considered. The uncertainty related to the fission products cross sections is neglected in this work. It may be an issue for isotope like (n,c) of 156 Gd for example since the 156Gd capture has an uncertainty of almost 40% in the thermal region. However due to the short irradiation time and to the otherwise very large fission yield uncertainties, it is considered a second order effect. The uncertain inputs are described as multivariate normal distributions. 500 perturbed samples are considered and 500 MCS fuel rod simulations are carried out. In the TMC method, the neutron history used in the activity inventory calculations was 110 cycles using 200,000 neutrons per cycle; 10 cycles were discarded. The activity uncertainty estimates of the isotopes relevant for dose calculation are obtained with the original TMC method and shown in Table 6. The uncertainty of activity inventory of the CROCUS fuel due to cross section uncertainty is found to be negligible except for the 239 Pu activity for which it is around 1.5%. The main reason for the uncertainty of the 239Pu activity is the uncertainty in the 238U capture cross section. With respect to the fission products, their activity uncertainty is driven by the fission yields uncertainty as the assumption of constant power during the depletion calculation imposes the fission rate to be constant, e.g. there is a negligible uncertainty due to cross sections perturbation. Only the fast-GRS method is used for the uncertainty quantification of the inventory of UO2 fuel rod. Due to its similarity to

Table 6 Uncertainty on the activity inventory due to uncertainty of microscopic cross section data and fission yield for CROCUS fuel at the fuel rod level. Uncertainty

Isotopes

Uncertainty [%] Umetal

UO2

TMC

fast-TMC

fast-GRS

fast-GRS

Cross sections

239

Pu 144 Ce 131 I 90 Sr 140 Ba 140 La 137 Cs 91 Y

1.7 ± 0.1 0.13 ± 0.00 0.10 ± 0.00 0.23 ± 0.01 0.082 ± 0.003 0.082 ± 0.003 0.049 ± 0.002 0.18 ± 0.01

1.7 ± 0.1 0.13 ± 0.00 0.10 ± 0.00 0.23 ± 0.01 0.082 ± 0.003 0.082 ± 0.003 0.049 ± 0.002 0.18 ± 0.01

1.7 ± 0.1 0.13 ± 0.00 0.10 ± 0.00 0.23 ± 0.01 0.081 ± 0.003 0.081 ± 0.003 0.049 ± 0.002 0.17 ± 0.01

1.5 ± 0.0 0.036 ± 0.001 0.029 ± 0.001 0.066 ± 0.002 0.023 ± 0.001 0.024 ± 0.001 0.014 ± 0.000 0.050 ± 0.002

Fission yields

239

0.0044 ± 0.0001 1.8 ± 0.1 4.8 ± 0.2 1.8 ± 0.1 1.8 ± 0.1 1.8 ± 0.1 1.8 ± 0.1 1.5 ± 0.0

0.046 ± 0.001 1.8 ± 0.1 4.8 ± 0.2 1.8 ± 0.1 1.8 ± 0.1 1.8 ± 0.1 1.8 ± 0.1 1.5 ± 0.0

0.010 ± 0.000 1.8 ± 0.1 4.8 ± 0.2 1.8 ± 0.1 1.8 ± 0.1 1.8 ± 0.1 1.8 ± 0.1 1.5 ± 0.0

0.018 ± 0.001 1.8 ± 0.1 4.4 ± 0.1 1.6 ± 0.1 1.6 ± 0.1 1.6 ± 0.1 1.7 ± 0.1 1.4 ± 0.0

Pu Ce 131 I 90 Sr 140 Ba 140 La 137 Cs 91 Y 144

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the Umetal fuel rod model, it is assumed that the underlying requirements of the fast methods (low aleatoric uncertainty) are respected. It allows reducing the computational cost of such analysis. The uncertainties for the activity of the UO2 fuel rod are consistent with those of the Umetal fuel within their respective confidence intervals. For the most toxic isotopes, 239Pu and 131I, the evolution of the activity uncertainty with the number of samples is shown in Fig. 10. The standard error of the uncertainty is shown. The uncertainty appears to converge after about 200 samples based on the variance of the variance (VOV) (X-5 Monte Carlo team, 2005). As a results. the 500 samples considered provide reliable uncertainty estimates. The convergence of the uncertainty estimates for other isotopes has a similar trend. 5.2. Comparison of TMC, fast-TMC and fast-GRS uncertainty estimates The comparison of the three SS methods is carried out for the Umetal fuel rod model only. For the two fast methods, the neutron history considered is composed of 20 active and 10 inactive cycles of 20,000 neutrons each. The results are shown in Table 6. Except for 239Pu, the uncertainty estimates due to cross section uncertainty or fission yield uncertainty show excellent agreement for all three SS methods within the confidence interval of the TMC method. The aleatoric uncertainty associated with the activity of the Umetal fuel is estimated through 500 MC simulations with different random seeds and unperturbed nuclear data using the fast-TMC method. 10 active and inactive cycles in each are used for 20,000 neutrons per cycle for the calculation. The aleatoric uncertainty is well below 0.01% for the considered number of neutron histories except for 239Pu where the aleatoric uncertainty is around 0.046%. According to previous publication (Zwermann and KrzykaczHausmann, 2012; Rochman et al., 2014), the three methods should agree provided that the aleatoric uncertainty is at least 50% lower than the epistemic uncertainty. The non-zero uncertainty of 239Pu due to fission yield uncertainty predicted by the fast-TMC method is then clearly a result of the aleatoric uncertainty of the MC solution as the epistemic uncertainty is zero. Compared to the original TMC method, the fast-TMC method showed a 50–60 times reduction in the computational time and the fast-GRS method which requires two separate calculations per input sample, showed a 20–30 times reduction in the computational time. However, if the aleatoric uncertainty is large but below the epistemic uncertainty, the fast GRS method is the best option as it does not require

to determine accurately the aleatoric uncertainty. In this work, we pre-calculated the aleatoric uncertainty for the comparative analysis at the core level before to estimate the epistemic uncertainty as shown in Table 8: the aleatoric uncertainty for the activity of selected isotopes is much lower than major epistemic uncertainty. As a result, the fast-TMC method is used to estimate the uncertainty of the CROCUS activity inventory due to nuclear data because the accuracy is guaranteed by the low aleatoric uncertainty. 5.3. Uncertainty quantification of the CROCUS activity inventory at the core level 500 perturbed samples are prepared for the perturbed cross section data and the perturbed fission yield data respectively. 500 simulations are used for estimating the aleatoric uncertainty by varying the random number seed and leaving the nuclear data at their nominal values, and another 500 simulations by varying the nuclear data for estimating the combined uncertainty of the aleatoric- and the epistemic- uncertainty. For each whole core MC calculation, 110 cycles are used with 100,000 neutrons per

Table 7 Uncertainty on the total activity inventory due to uncertainty of microscopic cross section data and fission yield for CROCUS fuel at the core level. Uncertainty

Isotopes

Uncertainty [%] Umetal

UO2

Total

fast-TMC Cross sections

239

Pu 144 Ce 131 I 90 Sr 140 Ba 140 La 137 Cs 91 Y

1.5 ± 0.0 0.44 ± 0.01 0.52 ± 0.02 0.38 ± 0.01 0.46 ± 0.01 0.46 ± 0.01 0.48 ± 0.02 0.41 ± 0.01

1.7 ± 0.1 0.36 ± 0.01 0.32 ± 0.01 0.38 ± 0.01 0.34 ± 0.01 0.34 ± 0.01 0.34 ± 0.01 0.37 ± 0.01

1.6 ± 0.0 0.066 ± 0.002 0.018 ± 0.001 0.12 ± 0.00 0.042 ± 0.001 0.042 ± 0.001 0.025 ± 0.001 0.091 ± 0.003

Fission yields

239

0.014 ± 0.000 1.8 ± 0.1 4.8 ± 0.2 1.8 ± 0.1 1.8 ± 0.1 1.8 ± 0.1 1.8 ± 0.1 1.5 ± 0.0

0.011 ± 0.000 1.8 ± 0.1 4.5 ± 0.1 1.6 ± 0.1 1.6 ± 0.1 1.6 ± 0.1 1.7 ± 0.1 1.4 ± 0.0

0.0057 ± 0.0002 1.8 ± 0.1 4.6 ± 0.1 1.7 ± 0.1 1.7 ± 0.1 1.7 ± 0.1 1.7 ± 0.1 1.4 ± 0.0

Pu Ce I 90 Sr 140 Ba 140 La 137 Cs 91 Y 144 131

Fig. 10. Evolution of the activity uncertainty of 239Pu (left) and 131I (right) obtained with the TMC method, with the number of samples due to perturbed cross section (239Pu) and perturbed fission yield (131I).

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cycle. 10 cycles are discarded as inactive cycles. The number of neutron histories considered is 10 times lower than for the calculation the source term presented in Section 4.4. The activity uncertainties of the CROCUS fuel inventory predicted by the fast-TMC method are shown in Table 7. The uncertainty estimates are provided for total activity inventory as well as for each fuel type, e.g. UO2 and Umetal fuel rods. In addition, the distribution for 239Pu concentration uncertainty estimates due to perturbing cross sections only and the distribution for 131I concentration uncertainty estimates due to perturbing fission yields only are represented in Fig. 11. The aleatoric uncertainties for all eight isotopes in three categories are below the 0.01% range for the considered number of neutron histories. When comparing the activity uncertainty of CROCUS fuel at the core level with the uncertainties at fuel rod level, the only noticeable difference is the uncertainty on the activity inventory due to the cross section uncertainty. In the case of 239Pu, it is consistent within the confidence interval at the core level and at the fuel rod level. However, for the other isotopes, the difference is significant. This shows that the activity uncertainty for fission products due to the uncertainty of the cross section has relatively larger variation depending on an arrangement of fuel rods or a type of fuel than those due to the uncertainty of the fission yield. For the sake of completeness, the evolution of the activity uncertainty for the most toxic isotopes, e.g. 239Pu and 131I for

Fig. 11. Uncertainty distribution of

Fig. 12. Evolution of the activity uncertainty of (239Pu) and perturbed fission yield (131I).

239

239

Pu (left) and

Pu (left) and

131

131

inhalation and ingestion respectively, with the number of samples is shown in Fig. 12. Like in a single fuel rod model, the uncertainty appears to converge after about 100 samples for the full core model. The 500 samples considered provide reliable uncertainty estimates. 5.4. Comparison between the various sources of uncertainty The effect of the various sources of uncertainty considered (nuclear data, MC aleatoric and irradiation history) on the activity inventory of CRCOCUS are compared. Table 8 summarizes the results. The total uncertainty for the CROCUS fuel inventory is obtained by the summing the contribution of the various source of input uncertainty quadratically, assuming their independence. The specification of the irradiation history is clearly the leading source of computational uncertainty (as compared to the nuclear data or MC intrinsic uncertainty) for the short lived isotopes (144Ce, 131I, 140Ba, 140La and 91Y). The uncertainties for the long lived isotopes such as 90Sr and 137Cs are driven by the fission yields uncertainty. In case of 239Pu, the cross sections are the major source of uncertainty. Finally, the aleatoric uncertainty introduced by stochastic nature of the Monte Carlo transport solution is in general negligible, except when the epistemic uncertainty is small, for example the uncertainty in the 239Pu activity due to fission yields.

I (right) due to perturbed cross section (239Pu) and perturbed fission yield (131I).

I (right) obtained with the fast TMC method, with the number of samples due to perturbed cross section

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W. Kim et al. / Annals of Nuclear Energy 136 (2020) 107034 Table 8 Summary on the uncertainty of the activity inventory due to various sources of uncertainty considered for CROCUS fuel. Isotopes

239

Pu Ce I 90 Sr 140 Ba 140 La 137 Cs 91 Y 144 131

Uncertainty [%] Cross section

Fission yield

Stochastic nature2)

Irradiation history

Total1)

1.6 0.066 0.018 0.12 0.042 0.042 0.025 0.091

0.0057 1.8 4.6 1.7 1.7 1.7 1.7 1.4

0.0061 0.00051 0.00065 0.00054 0.00058 0.00058 0.00013 0.00086

0.029 21 120 0.81 110 110 0.77 49

1.6 21 120 1.9 110 110 1.9 49

1) Quadratic sum of the uncertainty from each source (cross section, fission yield and irradiation history). 2) Statistical uncertainty intrinsic to Monte Carlo simulations.

6. Conclusion The paper described joint activities of the LRS and UNIST research groups towards the determination of the fuel inventory activity for the zero power research reactor CROCUS. It is a critical part for the establishment of a reliable source term for CROCUS; a source term needed for downstream dispersion analysis under accidental conditions. First, the computational scheme relying on the Monte Carlo code, MCS used to determine the fuel inventory of the EPFL CROCUS reactor is presented. The calculation sequence is successfully verified through the comparison of the transport module of MCS in terms of multiplication factor and power distribution against existing MCNP6 and Serpent2 results; the depletion capability of MCS is verified against Serpent2 for a fuel rod model representative of the CROCUS fuel. Statistically significant differences are observed for following isotopes, 129mTe, 125Sb, 127mTe, 127Sb, 111Ag and 125Sn; those isotopes are however not relevant for the CROCUS source term determination. Then, the total activity of the CROCUS fuel inventory is determined for eight isotopes contributing the most to both inhaled and ingestion doses. The contributions of 239Pu, 144Ce, 131I, 90Sr, 140 Ba, 140La, 137Cs and 91Y are estimated to be more than 90% for the total inhalation dose, and more than 73% of the total ingestion dose. The fission products activity distribution follows the 235U fission reaction rates while the 239Pu activity distribution follows the 238 U capture reaction rates. 239Pu is produced mostly in Umetal fuel. Due to its large computational cost, the modeling of the irradiation history for CROCUS is simplified. The bias on the activity inventory resulting from such approximation is investigated. It demonstrated that the doses for the short lived isotopes (131I and 144 Ce) are very sensitive to the irradiation history specification. Considering their contribution to total effective dose, an additional uncertainty of 4.8% for the inhaled dose and 30% for the ingested dose should be taken into account to reflect this approximation. Nonetheless, it is also demonstrated that the irradiation history used for the determination of the nominal fuel inventory activity is conservative as it overestimates the activity of the short lived isotopes. The uncertainty in the activity of the CROCUS fuel inventory due to the nuclear data (cross sections and fission yields) as well as the stochastic nature of the Monte Carlo solution is estimated by using three stochastic sampling (SS) methods. It is first time that MCS has been applied to uncertainty quantification calculations. The approach presented in the paper relies on pre-generated perturbed cross sections and fission yields data sets for a limited number of relevant isotopes. The two fast methods, i.e., fast-TMC and fastGRS reduce the computational time significantly compared to the standard TMC approach. The fast-TMC offers the best combination of accuracy and computational cost. The uncertainty in the CRO-

CUS fuel inventory due to cross sections uncertainty is found to be very small except for 239Pu. The magnitude of the uncertainty is in the 5% range for 131I and around 2% for the other major isotopes responsible for the activity and the doses. Acknowledgements This work was supported by the Young Researchers’ Exchange Programme between Korea and Switzerland, Korea, 2017. (NRF2016K1A3A1A14953265). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.anucene.2019.107034. References Aures, A., Bostelmann, F., Hursin, M., Leray, O., 2017. Benchmarking and application of the state-of-the-art uncertainty analysis methods XSUSA and SHARK-X. Ann. of Nucl. Energy 101, 262–269. Chadwick, M.B. et al., 2006. ENDF/B-VII.0: Next Generation Evaluated Nuclear Data Library for Nuclear Science and Technology. Nucl. Data Sheets 107, 2931–3060. Chadwick, M.B. et al., 2011. ENDF/B-VII.1 nuclear data for science and technology: cross sections, covariances, fission product yields and decay data. Nucl. Data Sheets 112, 2887–2996. Downar, T. J., 2010, PARCS v3.0 U.S NRC Core Neutronics Simulator USER MANUAL. UM-NERS-09-0001. Ferroukhi, H., Leray, O., Hursin, M., Vasiliev, A., Perret, G., Pautz, A., 2014. Study of nuclear decay data contribution to uncertainties in heat load estimations for spent fuel pools. Nucl. Data Sheets 118, 498–501. Ferroukhi, H., Leray, O., Hursin, M., Vasiliev, A., Perret, G., Pautz, A., 2014. Study of nuclear decay data contribution to uncertainties in heat load estimations for spent fuel pools Nucl. Data Sheets 118, 498–501. Früh, R., Réacteur CROCUS, Complément au rapport de sécurité: Réactivité et paramètres cinétiques, LPR 196, EPFL Lausanne, December 1993. Hyunsuk, Lee, et al., 2017, Preliminary Simulation Results of BEAVRS Threedimensional Cycle 1 Wholecore Depletion by UNIST Monte Carlo Code MCS, M&C2017, Jeju, Korea, April 16-20. Isotalo, A., Sahlberg, V., 2015. Comparison of neutronics-depletion coupling schemes for burnup calculations. Nucl. Sci. Eng. 179, 434–459. Jang, Jaerim, Kim, Wonkyeong, Jeong, Sanggeol, Jeong, Eun, Park, Jinsu, Lemaire, Matthieu, Lee, Hyunsuk, Jo, Yongmin, Zhang, Peng, Lee, Deokjung, 2018. Validation of UNIST monte carlo code MCS for criticality safety analysis of PWR spent fuel pool and storage cask. Ann. Nucl. Energy 114, 495–509. https:// doi.org/10.1016/j.anucene.2017.12.054. Kasemeyer, U., Früh, R., Paratte, J. M., Chawla, R., Benchmark on Kinetic Parameters in the CROCUS Reactor, International Reactor Physics Experiments Handbook (IRPhE), no. 4440, OECD, Ed. 2007, 94. Koning, A.J., Rochman, D., 2008. Towards sustainable nuclear energy: Putting nuclear physics to work. Ann. of Nucl. Energy 35, 2024–2030. Koning, A.J., Rochman, D., 2012. Modern Nuclear Data Evaluation With The TALYS Code System. Nucl. Data Sheets 113, 2841. Leppänen, J., Pusa, M., Viitanen, T., Valtavirta, V., Kaltiaisenaho, T., 2015. The Serpent Monte Carlo code: status, development and applications in 2013. Ann. Nucl. Eng. 82, 142–150. Leray, O., Rochman, D., Grimm, P., Ferroukhi, H., Vasiliev, A., Hursin, M., Perret, G., Pautz, A., 2016. Nuclear data uncertainty propagation on spent fuel nuclide compositions. Ann. of Nucl. Energy 94, 603–611.

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