CASMO-5 - Uncertainty quantification of LWR-PROTEUS Phase II experiments using
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Annals of Nuclear Energy 131 (2019) 9–22 Contents lists available at ScienceDirect Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene Uncertainty quantification of LWR-PROTEUS Phase II experiments using CASMO-5 Jinsu Park a, Wonkyeong Kim a, Mathieu Hursin b,⇑, Gregory Perret b, Alexander Vasiliev b, Dimitri Rochman b, Andreas Pautz b, Hakim Ferroukhi b, Deokjung Lee a a Department of Nuclear Engineering, Ulsan National Institute of Science and Technology, UNIST-gil 50, Ulsan 44919, Republic of Korea b Paul Scherrer Institut, Nukleare Energie und Sicherheit, PSI Villigen, 5232, Switzerland a r t i c l e i n f o a b s t r a c t Article history: This paper presents an improved uncertainty quantification technique for the validation of CASMO-5 on Received 4 December 2018 the spent fuel reactivity worth experiments of the LWR-PROTEUS Phase II program. In the program, Received in revised form 14 March 2019 eleven spent fuel samples manufactured from rods irradiated in a Swiss PWR (discharge burnups of Accepted 16 March 2019 20–120 MWd/kg) were measured in the PROTEUS research reactor. In this work, both irradiation and reactivity worth measurement steps were modeled with CASMO-5 and the uncertainty on the code pre- diction were calculated using SHARK-X. For the first time in this work, we propagated the nuclear data Keywords: uncertainties coming from cross-sections and fission yields for all samples in both fuel irradiations and LWR-PROTEUS Phase II experiment Spent fuel the reactivity worth experiment models. We found that the fission yield and cross section uncertainties Uncertainty quantification have similar contributions to the uncertainty of the reactivity worth prediction and that the reactivity SHARK-X worth probability distribution is non-normal because of the non-normal distribution of the perturbed CASMO-5 fission yield data produced by the GEF code. Propagating input uncertainties through fuel irradiation Fission yield perturbation as well as considering fission yield uncertainty led to larger computational uncertainty than previously reported. However, the observed trends with respect to exposure, fuel type, and moderating conditions are similar. In particular, a linear regression analysis showed that the predictions of reactivity with exposure by CASMO-5 are very accurate for various moderating conditions and for very high burnup. Finally, we estimated the effects of the irradiation history specifications on the relative reactivity worth bias and its uncertainty using two independent irradiation histories. While the bias uncertainty coming from uncertain cross sections was similar when considering either irradiation histories, we observed dif- ferences in the bias value. The irradiation history specification is a significant source of modeling bias and should be further investigated. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction plants. By cutting samples from highly burnt fuel rods irradiated in Swiss LWRs and oscillating them in the zero-power research With increasing discharge burnups of commercial Light Water reactor of PSI, PROTEUS, their reactivity worths were measured Reactor (LWR) fuels, reactivity loss during irradiation must be val- to determine accurately the fuel reactivity loss during irradiation. idated to support core design calculations as well as the use of bur- Such reactivity measurements were complemented by the deter- nup credit for the storage and transportation of spent fuel. As mination of the burnt fuel sample isotopic compositions by chem- comprehensive experimental data related to spent fuel is scarce, ical analysis. a high-quality set of measured isotopic compositions and reactivity Those reactivity worth and isotopic concentration data have effects measurements involving spent fuel has been carried out at been used extensively at PSI for validation activities related to the Paul Scherrer Institut (PSI) in the framework of the LWR- the depletion capabilities of the CASMO-4/5 code (Grimm et al., PROTEUS Phase II program (Gunther-Leopold, 2007; Grimm et al., 2014, 2017, 2008). However, only a limited amount of work 2001, 2006). This experimental program aims at investigating the (Grimm et al., 2017; Leray et al., 2016; Rochman et al., 2018) has physics of highly burnt fuel samples from Swiss nuclear power been dedicated to the quantification of computational uncertainties required for meaningful validation. For these activi- ties, the SHARK-X platform (Hursin et al., 2015; Wieselquist, ⇑ Corresponding author. 2012; Leray, 2015) has been used. SHARK-X is a set of Perl based E-mail address: Mathieu.firstname.lastname@example.org (M. Hursin). https://doi.org/10.1016/j.anucene.2019.03.023 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
10 J. Park et al. / Annals of Nuclear Energy 131 (2019) 9–22 scripts developed by PSI for nuclear data uncertainty propagation were irradiated in a Swiss PWR. Table 1 represents the description in CASMO-5. of each fuel sample. The exposure of the fuel samples varies from So far, only a reduced set of nuclear data was considered as 20 to 120 MWd/kg. To reach large burnup, samples went through uncertain input and the propagation of input uncertainty was lim- multiple reactor cycles and were relocated in several fuel assem- ited to the modeling of the oscillation measurements (reactivity blies, as recorded in Table 1. The burnup of a given fuel sample is worth measurements) in PROTEUS (Grimm et al., 2017). The main determined using the concentration of 148Nd measured through objective of the present paper is to summarize recent improve- chemical assay on neighboring pieces of the same fuel rod. ments made to SHARK-X to carry out the Uncertainty Quantifica- The PROTEUS reactor is a zero-power experimental reactor tion (UQ) of the simulation of the LWR-PROTEUS Phase II operated at PSI between 1968 and 2011. The reactivity worth of program with CASMO-5. More specifically, the updated UQ analy- a given burnt fuel sample is measured by inserting and withdraw- sis includes cross section and fission yield data perturbations and ing the sample into a guide tube in the center of the PROTEUS core. concerns both CAMSO-5 calculations required for the fuel sample For each measurement, the absolute reactivity worth of burnt fuel irradiation in the Swiss power plant as well as its oscillations in samples is measured against the one of a fresh 3.5 wt% enriched PROTEUS. Cross sections, averaged number of neutrons produced UO2 sample. This allows measurement of the reactivity loss of fuel per fission (t), and fission spectrum (v) are perturbed for the full caused by exposure in a nuclear power plant. In addition, the abso- set of isotopes considered in CASMO-5 as well as the fission yields lute reactivity worth of naturally enriched sample was measured. of four major fissile isotopes following recent method develop- Both measurements were performed for various moderating condi- ments in this area at PSI (Leray et al., 2017). Their effects on the tions. The ratio of the two reactivity worths is used for comparison UQ results are investigated. Finally, as nuclear data uncertainty with CASMO-5 instead of absolute reactivity worth for two rea- may not be the leading source of uncertainty for such simulations, sons. The first one is to cancel out possible errors in the experimen- the effect of the irradiation history description on the computa- tal design and measurement techniques, and the second is to tional uncertainty is estimated by comparing two independent correct for the 2D, single assembly nature of the CASMO-5 model irradiation histories (one determined internally at PSI and one pro- used for comparison with measurements in the multi-zone driven vided by the fuel vendor). A previous publication (Rochman et al., reactor PROTEUS. Strictly speaking, the relative reactivity worth 2018) summarized a detailed estimation of the effect of the irradi- ratio is not a quantity of interest for burnup credit applications, ation history on the computational uncertainty for the determina- but it is the quantity computed by CASMO-5 that can be compared tion of burnt fuel isotopic composition. As the quantity of interest to the measurements. As a result, it is used for validation purposes considered in the present work is different (reactivity worth as in the present paper. opposed to isotopic composition), using this information imposes establishing a link between isotopic composition and reactivity 2.2. Modeling of the LWR-PROTEUS Phase II experiment worth uncertainties. Such link would require determining sensitiv- ity coefficients of the reactivity worth to each isotope of the burnt The LWR-PROTEUS Phase II experiments are modeled using fuel sample. Due to the number of isotopes considered, it is a fairly CASMO-5. CASMO-5 (Rhodes et al., 2012) is a two-dimensional lat- expensive calculation, which has not been envisioned in this work. tice physics code with depletion capabilities developed by the As such the conclusions of the previous study is not used. Instead Studsvik Scandpower, Inc. In this work, CASMO-5 uses a 586 of performing a similar analysis in this paper, we chose a simpler energy groups neutron cross section library based on ENDF-B/ approach as we are only interested in the magnitude of the compu- VII.1 (Chadwick, 2011). Two separated procedures are required tational uncertainty associated with the irradiation history. In for the modeling of the LWR-PROTEUS Phase II experimental cam- other words, two specific irradiation histories are considered in paign. First, the irradiation of the burnt fuel samples in the nuclear the depletion calculation without random perturbations of the power plant is modeled through a depletion calculation. Next, the irradiation history related parameters such as power density, fuel oscillations of the burnt fuel sample in the PROTEUS reactor are and moderator temperatures, depletion step, etc. modeled. Both calculations are described in detail in the following This paper is organized as follows. Section 2 describes the LWR- sections. PROTEUS Phase II experiments, including details on the CASMO-5 calculations required for the modeling of the fuel sample irradia- 2.2.1. Determination of the fuel samples composition tion and their oscillations in PROTEUS. Section 3 presents the Fig. 1 shows the geometrical configuration of the UO2 and MOX SHARK-X methodology used for the propagation of nuclear data fuel assemblies for the CASMO-5 depletion calculation. The assem- uncertainty in CASMO-5. The list of input parameters perturbed, blies containing the UO2 samples are depleted considering a single including fission yields is reviewed. Section 4 describes the numer- fuel assembly and reflective boundary conditions. In the case of ical results for the reactivity worth UQ for all fuel samples and MOX fuel samples, the depletion calculations are performed using moderating conditions as well as discusses the effects of the irradi- a 2-by-2-assemblies model, a MOX assembly surrounded by UO2 ation history on the UQ results. Special consideration is given to assemblies as shown in Fig. 1 on the right. The locations of each the propagation of fission yields uncertainty. In the light of the fuel sample in the fuel assembly are represented in Fig. 1. uncertainty propagation results, the performance of the CASMO-5 In this work, two irradiated histories are considered for the for the modeling of the LWR-PROTEUS Phase II experiments is dis- depletion calculation of fuel samples. The first irradiation history cussed focusing on the prediction of reactivity loss of the fuel with as well as the burnup of the irradiated fuel samples is provided exposure. Finally, conclusions are presented in Section 5. by the fuel vendor based on the pre-cycle core analysis using a nodal core simulator with pin power reconstruction (not CMSYS). It is referred to as VENDOR history. The second irradiation history 2. LWR-Proteus Phase II experiments was generated using the BOHR methodology of PSI (Herrero, 2017). It is referred to as BOHR history. The BOHR methodology allows re- 2.1. Measurements of the LWR-PROTEUS Phase II running CASMO-5 with operating conditions extracted from refer- ence CASMO5-SIMULATE3 core models developed and validated A total of eleven 40-cm long PWR fuel samples were investi- for all Swiss reactors and operated cycles within the CMSYS plat- gated during the LWR-PROTEUS Phase II experiments. Seven sam- form (Ferroukhi et al., 2008). The BOHR history contains more ples are made of UO2 fuel and four of MOX fuel. Those samples detailed information about the irradiation conditions at each
J. Park et al. / Annals of Nuclear Energy 131 (2019) 9–22 11 Table 1 Description of the fuel samples. Sample Fuel type Initial fissile No. of No. of Burnup DBurnup ID contents cycles relocation (MWd/kg) VENDOR-BOHR (MWd/kg) U1 UO2 4.1% 2 0 40 2.4 U2 3.5% 3 0 50 1.9 U3 3.5% 5 1 70 0.7 U4 3.5% 5 1 80 0.4 U5 3.5% 7 3 90 0.4 U6 3.5% 7 3 90 0.1 U7 3.5% 10 4 120 0.6 M1 MOX 5.5% 1 0 20 0.9 M2 5.5% 2 0 40 0.4 M3 5.5% 3 0 60 0.4 M4 5.5% 4 0 70 0.6 Fig. 1. CASMO-5 models for depletion calculation. burnup step. Fig. 2 illustrates the input parameters such as power power density for all burnup steps during the irradiation. Such density, boron concentration, fuel and moderator temperatures as adjustment resulted in differences of calculated exposure when a function of time for both VENDOR and BOHR irradiation histories considering the VENDOR or the BOHR irradiation history as of the U1 sample. As shown in Fig. 2, the VENDOR irradiation his- reported in Table 1. tory of U1 sample uses a finer burnup grid (30 and 28 burnup The effects of the different irradiation histories in terms of points for first and second cycle, respectively) with only four oper- uncertainty propagation are investigated in Section 4.3. ating conditions per cycle for depletion calculation. In contrast, the BOHR irradiation history uses a smaller number of burnup points 2.2.2. Calculation of relative reactivity worth (22 and 21 burnup points for first and second cycle, respectively) For the modeling of the LWR-PROTEUS Phase II experiments, with different operating conditions for each burnup point. The the PROTEUS test zone, where burnt fuel samples were oscillated, BOHR irradiation history always uses different operating condition is modelled with CASMO-5 through an 11-by-11 array of PWR UO2 for each burnup point. fuel rods. Fig. 3 shows the CASMO-5 model of the LWR-PROTUES A careful reader would have noticed in the BOHR history of Phase II experiments. The simulation of the Phase II experiment Fig. 2, that while the power density increases slowly during the is performed in three different moderating conditions: pure light course of the first cycle, the fuel temperature decreases by about water (H2O), a mixture of light and heavy water (DHO), and 100 K. Such phenomenon is due to the change of heat conduction borated light water (B2023). properties of the fuel under irradiation (both the heat conductivity In the CASMO-5 model, the reference case, which uses the fresh and gap conductance). fuel sample at the center of test zone, is made critical (keff = 1) by The burnt fuel sample exposure value obtained with the BOHR automatically adjusting the axial buckling. The reactivity of the history is adjusted to match the measured 148Nd content within its naturally enriched and the burnt fuel samples are calculated by experimental uncertainty: a constant coefficient is applied to the keeping this axial buckling value constant; the underlying assump-
12 J. Park et al. / Annals of Nuclear Energy 131 (2019) 9–22 Fig. 2. Input parameters as a function of time for the VENDOR and BOHR irradiation histories of the U1 sample. 1 X M X N ðC n;m =En;m 1Þ2 v2 ¼ : ð2Þ M N m¼1 n¼1 r2n;m The averaged chi-squared value for the VENDOR and BOHR irra- diation histories are 0.86 and 1.39, respectively. Consequently, the BOHR irradiation history does not produce more accurate relative reactivity worth results, even though more detailed irradiation conditions are provided during the depletion calculation. As a result, the irradiation history will be considered as an uncertain input parameter for the uncertainty propagation. As it is difficult to formalize such source of uncertainty rigorously, the present work only provides an attempt at estimating such uncertainty in Section 4.3. For the reminder of the paper, the C/E produced with Fig. 3. CASMO-5 model of LWR-PROTEUS Phase II experiments. the VENDOR irradiation history are used. The uncertainty of the calculated results needs to be assessed to draw any conclusion from the C/E distribution. It is the subject of the next sections of the present paper. tion is that the neutron leakage out of the model is not influenced significantly by the presence of the burnt fuel and natural uranium sample. The keff values obtained for each of the burnt, fresh and 3. Uncertainty quantification with SHARK-X natural uranium samples are used to calculate the relative reactiv- ity worth following Eq. (1). SHARK-X (Hursin et al., 2015; Wieselquist, 2012; Leray, 2015) is a set of Perl based scripts developed at PSI for nuclear data uncer- fresh sample 1=keff 1=keff tainty propagation with CASMO-5. SHARK-X provides two major Dqrel ¼ fresh natural : ð1Þ approaches for UQ calculations. The first one relies on the calcula- 1=keff 1=keff tion of sensitivity coefficients using a Direct Perturbation (DP) fresh sample In Eq. (1), keff , keff , and keff natural are the values for the fresh, approach and subsequent use of the Sandwich rule. The second method relies on Stochastic Sampling (SS). Because of the large burnt, and natural uranium fuel samples, respectively. number of uncertain inputs involved in the depletion calculations Fig. 4 shows the calculated over experimental (C/E) relative (16,283 uncertain cross sections with a 19 energy group structure reactivity worth obtained with both irradiation histories. The VEN- and 1304 fission yields for 384 isotopes), the DP approach is not DOR results are the ones reported in a previous publication convenient due to its high computational cost. Consequently, the (Grimm et al., 2017). For a detailed discussion about the C/E distri- SS method is used. bution, the reader is referred to this publication. The C/E values range from 0.88 to 1.07 for both irradiation histories. The averaged chi-square value for relative reactivity worths is calculated using 3.1. Stochastic sampling method Eq. (2) for each irradiation history. In Eq. (2), M is the number of moderating conditions and N is the number of fuel samples. And, The SS method requires the perturbation of input data consid- Cn,m and En,m are the calculated and experimental relative reactivity ered as random variables with presumed probability distribution worth values of fuel sample n in moderating condition m. The bias functions. SS calculations consist in the process of assigning distri- relative uncertainty of relative reactivity worth ratio is expressed butions to inputs, sampling the inputs (accounting for possible cor- as rn;m , which is equal here to the experimental relative relations between the inputs), performing independent uncertainty. calculations with each sample, and statistically analyzing the dis-
J. Park et al. / Annals of Nuclear Energy 131 (2019) 9–22 13 Fig. 4. Calculated over experimental value of relative reactivity worth using nuclear data nominal values. tribution of outputs. The SS approach can produce meaningful and 2017). The SCALE-6.0 VCM library was collaboratively developed reliable UQ results with much fewer runs than the DP methods. For from Brookhaven National Laboratory (BNL), Oak Ridge National relative reactivity worth UQ, each input sample is used in the three Laboratory (ORNL), and Los Alamos National Laboratory (LANL), transport calculations needed to compute the relative reactivity and it contains 402 nuclides with various reaction channels. Table 2 worth as expressed in Eq. (1). represents the list of perturbed nuclides with corresponding The SS method produces an estimate for the variance VR of a nuclear reaction channels considered in this work. For the given given response R, which converges to its true value (r2) as the isotope, only the covariance data between reactions and energy number of samples increases. Because it is not possible to run an groups are available. The covariances between isotopes are infinite number of samples, a confidence interval is a useful quan- neglected. The MT numbers listed in Table 2 are represented as tity for evaluating the reliability of the estimate VR. Assuming the follows. considered response has a normal distribution characterized by its mean and variance (VR), the confidence interval shown in Eq. 1. MT = 2: Elastic scattering, rs,el (3) would contain the true variance (1 a)100% of the time. In 2. MT = 4: Inelastic scattering, rs,in practice, different values can be attributed to a to determine lower 3. MT = 16: (n,2n) neutron production, rn,2n and upper bounds. In the present work, both values for a are set to 4. MT = 18: fission, rf 5% and the interval is referred to as the 95% confidence interval. 5. MT = 101: capture, rc (including MT = 102–107, rn,c, rn,proton, " # rn,deuteron, rn,triton, rn,hydrogen, rn,a) h i ðN 1ÞV R ðN 1ÞV R 6. MT = 452: average number of neutron per fission, m r2lower ; r2upper ¼ ; : ð3Þ v1a=2;N1 2 va=2;N1 2 7. MT = 1018: average fission spectrum, v where v2N1 is the v2 distribution with N 1 degree of freedom. For a desired probability level (1 a), the critical values v2a=2;N1 and 3.3. Fission yields uncertainties v 2 of the v distribution are tabulated and can be looked 1a=2;N1 2 Fission yields are perturbed during the depletion calculations up for a given number of degree of freedom N. In this paper, Eq. involved in the modeling of the nuclear power plant irradiation. (3) is used to calculate the confidence intervals even for non- As the decay constants were shown to have a negligible contribu- normally distributed responses. tion to the overall computational uncertainty (Ferroukhi et al., 2014), they are neglected here. 500 ENDF-formatted files contain- 3.2. Cross sections, t and v uncertainty ing perturbed fission yields are produced by the PSI-GEF method as reported in Leray et al. (2017) using a modified version of the GEF The SCALE-6.0 Variance Covariance Matrix (VCM) library code (Schmidt et al., 2016; Schmidt and Jurado, 2014): the GEF (Williams et al., 2009; Rearden, 2009) is used in this study to code is modified so that 21 model parameters are sampled inde- describe the behavior of uncertain cross sections, averaged number pendently according to normal distributions (for the magnitude of neutrons produced per fission (t), and fission spectrum (v). of their uncertainties, please refer to Table 1 in Leray et al. Even if the more recent sources of nuclear data uncertainties can (2017). Then, for each set of sampled parameters, a corresponding be also utilized in SHARK-X, the SCALE-6.0 VCM library is used in set of perturbed fission yields is calculated with GEF. This process this study to compare consistently the behavior of uncertainty is repeated 500 times. This process gives the advantage of produc- from this study with that from previous work (Grimm et al., ing random fission yields based on a theoretical model, as in the
14 J. Park et al. / Annals of Nuclear Energy 131 (2019) 9–22 Table 2 SHARK-X perturbed nuclides and reaction channels. Isotope (ZA) Perturbed MT number 1 3 186-187 197 253 H, He, Re, Au, Es 2, 101 2 H, 9Be, 59Co, 59Ni 2, 16, 101 3 H 2, 16 4 He, 7Be 2 6-7 Li, 10B 2, 4, 101 11 B, 14-15N, 16-17O, 19F, 23Na, 24-26Mg, 27Al, 28-31Si, 32-34S, 36S, 35Cl, 37Cl, 36Ar, 38Ar, 40Ar, 39-41K, 40Ca, 42-44Ca, 46Ca, 48Ca, 46-47Ti, 49-50Ti, 50Cr, 52-54Cr, 2, 4, 16, 101 55 Mn, 54Fe, 56-58Fe, 58Co, 60mCo, 58Ni, 60-62Ni, 64Ni, 63Cu, 65Cu, 69Ga, 71Ga, 70Ge, 72-74Ge, 76Ge, 74-75As, 74Se, 76-80Se, 82Se, 79Br, 81Br, 78Kr, 80Kr, 82-86 Kr, 85-87Rb, 84Sr, 86-90Sr, 89-91Y, 90-96Zr, 93-95Nb, 92Mo, 94-100Mo, 99Tc, 96Ru, 98-106Ru, 103Rh, 105Rh, 102Pd, 104-108Pd, 110Pd, 107Ag, 109Ag, 111 Ag, 111mAg, 106Cd, 108Cd, 110-114Cd, 116Cd, 117mCd, 113In, 115In, 112-120Sn, 122-126Sn, 121Sb, 123-126Sb, 120Te, 122-126Te, 128Te, 130Te, 132Te, 133mTe, 134m Te, 127I, 129-131I, 135I, 123-124Xe, 126Xe, 128-136Xe, 133-137Cs, 130Ba, 132-138Ba, 140Ba, 138-140La, 136Ce, 138-144Ce, 141-143Pr, 142-148Nd, 150Nd, 147-149 Pm, 151Pm, 152mPm, 144Sm, 147-154Sm, 151-157Eu, 152-158Gd, 160Gd, 159-160Tb, 156Dy, 158Dy, 160-164Dy, 165Ho, 166mHo, 162Er, 164Er, 166-168Er, 170 Er, 175-176Lu, 174Hf, 176-180Hf, 181-182Ta, 182-184W, 186W, 191Ir, 193Ir, 196Hg, 198-202Hg, 204Hg, 204Pb, 206-208Pb, 209Bi, 225-226Ac 45 Sc 101 48 Ti 4, 16, 101 227 Ac, 230Th, 239Np, 237Pu, 243-244Pu, 241Am, 241Cm, 248Cm, 250Cf 2, 4, 16, 18, 101, 452 227-229 Th, 233-234Th, 232Pa, 232U, 234U, 236-237U, 239-241U, 235-238Np, 236Pu, 238Pu, 246Pu, 242-244Am, 242mAm, 244mAm, 242-247Cm, 249-250Cm, 249Bk, 2, 4, 16, 18, 101 249-251 Cf, 254Cf, 254-255Es 232 Th 2, 18, 101, 452, 1018 231 Pa, 233Pa 2, 16, 18, 101 233 U, 235U, 238U, 239-241Pu, 252Cf 2, 4, 16, 18, 101, 452, 1018 242 Pu 2, 4, 16, 18, 101, 1018 253 Cf 2, 18, 101, 452 Total Monte Carlo approach (Rochman and Koning, 2011). This the perturbed CASMO-5 library that was used during the depletion method is different from another attempt at propagating fission calculation. The relative reactivity worth computational uncer- yield uncertainties reported in Leray et al. (2016) where the per- tainty is then determined from the set of 500 LWR-PROTEUS Phase turbed fission yields were sampled from a VCM which was deter- II model outcomes. mined from correlations obtained from the GEF code and variance from evaluated data files. As reported in Leray et al. (2017), the chosen approach overestimates the fission yield uncer- 4. Numerical results tainties and as such, the approach reported in Leray et al. (2016) is probably better. However, it is chosen to allow for future activities In this section, the results of the uncertainty propagation for the where the C/E of the fission products concentrations will be used to modeling of the LWR-PROTEUS Phase II experiments are presented adjust directly the GEF model parameters. and discussed. First, the effect of the cross section and fission yield The ENDF-formatted file contains perturbed fission yield data perturbations on the relative reactivity worth uncertainty is ana- for around 1300 isotopes. Because of the simplified decay chains lyzed. Then, the UQ results are presented for all samples and mod- of CASMO-5, the fission yield data contained in the ENDF file needs to be reduced to the set of isotopes considered in CASMO-5. Conse- quently, an additional treatment is required to convert the per- turbed fission yield data available in the ENDF files into a format usable by CASMO-5. Such process is done at PSI using a set of scripts called ‘‘Efficace”. In the first step of Efficace, a mapping between the independent and cumulated yields of the various iso- topes of the respective chains of the ENDF file and CASMO-5 library is determined. Next, the information in each perturbed ENDF file is processed using the previously determined mapping to generate the perturbed fission yields corresponding to the CASMO-5 decay chains. To preserve the accuracy of the fission yields available in the CASMO-5 library, the perturbed fission yield data are expressed as relative perturbations. Fig. 5 illustrates the algorithm used in Efficace. Only the fission yields of the 235U, 238U, 239Pu, and 241Pu isotopes are currently perturbed in SHARK-X. 3.4. Uncertainty quantification of LWR-PROTEUS Phase II The uncertainty propagation for the simulation of the LWR- PROTEUS Phase II experiment is conducted based on the computa- tional scheme described in Section 2.2. The depletion calculations are repeated 500 times based on the same input model but with 500 perturbed cross sections and fission yields libraries. With respect to the reactivity worth measurements, the isotopic composition of the burnt fuel sample is extracted from each per- turbed depletion output. The calculations required for the determi- nation of the relative reactivity worth are then carried out using Fig. 5. Algorithm of efficace to generate the fission yield data for SHARK-X.
J. Park et al. / Annals of Nuclear Energy 131 (2019) 9–22 15 erating conditions. Next, the effect of the choice of irradiation his- tory option is investigated. The implications in terms of validation of reactivity loss predictions are discussed at the end of the section. 4.1. Effect of fission yield perturbation The fission yield perturbation impacts only the depletion calcu- lation, i.e. the determination of the burnt fuel sample composition. Consequently, its effect is analyzed for the kinf uncertainty during the depletion calculation. The cross sections are not perturbed in this section. The depletion calculation is performed with the U1 sample and the VENDOR irradiation history. The dotted line of Fig. 6 shows the evolution of kinf with burnup using the nominal fission yields, whereas the solid line shows kinf absolute standard deviation when propagating the uncertainty of the fission yields. At the beginning of the shutdown cooling period, the reactivity increases by about 9000 pcm. Because the fuel and moderator tem- perature are set to room temperature at the beginning of shutdown cooling period, the reactivity increases by about 4000 and 2000 pcm due to the moderator and fuel temperature, respectively. Fig. 7. Histogram of kinf at EOC for the U1 fuel sample with the VENDOR irradiation After one cooling step, many of fission products, especially xenon, history due to fission yield variation. have decayed out, so that the reactivity also increases by about 3000 pcm. The absolute kinf uncertainty increases with exposure. It is equal that the distribution of kinf values for a given exposure is not a nor- to 470 pcm at end of cycle (EOC) before shutdown and cooling. As mal distribution. Fig. 7 shows the histogram of kinf samples at EOC reported in previous publications (Leray et al., 2016, 2017), the before shutdown cooling for the U1 fuel sample. The kinf distribu- PSI-GEF method utilized in this paper overestimates the kinf uncer- tion is clearly non-normal as revealed by a Shapiro-Wilk test tainty. Other work in the field (Williams, 2013; Zwermann, 2014; (Yap and Sim, 2011) with 5% significance level. Díez, 2015; Rochman et al., 2018; Gauld, 2011) have produced much The non-normal kinf distribution hints at an input parameter lower estimates for kinf uncertainty (Williams, 2013) or showed that with a non-normal input probability distribution function (PDF) the contribution of fission yield uncertainty to decay heat is small or at non-linearities introduced by CASMO-5 during the depletion (Rochman et al., 2018; Gauld, 2011). It is also visible that the kinf calculation. The bottom panels of Fig. 8 show the distribution and uncertainty increases during the cooling periods. Such behavior is convergence of the 134I cumulative fission yield data due to ther- explained by the buildup of isotopes with large absorption cross sec- mal fissions in 239Pu considering the 500 perturbed ENDF files. tion coming from the decay of daughter nuclides with short half-life The top panels show the resulting perturbation factors for the (149Pm and 143Pr for 149Sm and 143Nd respectively) (Leray, 2017). CASMO-5 library obtained with Efficace. It should be noted that Moreover, the difference of kinf between the mean value of the the 134I fission yield is the largest among the yields for fissions in 239 perturbed samples and the nominal (unperturbed) value is mono- Pu. However other daughter isotopes have non-normal distribu- tonically increasing up to around 200 pcm at 755 days suggesting tions. A detailed sensitivity analysis could be carried out to deter- Fig. 6. Evolution of the nominal kinf and its absolute standard deviation with the VENDOR irradiation history when propagating the fission yield uncertainties.
16 J. Park et al. / Annals of Nuclear Energy 131 (2019) 9–22 Nominal Nominal 134 239 Fig. 8. Convergence and histogram of I cumulative fission yield from thermal fission in Pu. mine the largest contributors to the kinf uncertainty. It will be done moderating conditions. The correlations are shown in Fig. 10. All in a later communication. As shown in the convergence behavior of Pearson coefficients are larger than 0.7 which suggests that even fission yield value, the mean of the perturbed fission yields does though the exposure of the fuel samples and the spectral condi- not converge to the nominal (unperturbed) value. Moreover, the tions considered vary widely, the behavior of the relative reactivity histograms of the ENDF and CASMO fission yields do not have nor- worth with respect to perturbations to cross sections and fission mal distributions. Therefore, this suggests that the non-normal kinf yields is similar. distribution shown in Fig. 7 is due to the non-normal distribution The correlations are generally of lower magnitude when consid- of fission yields obtained from the ENDF files. Of course, non- ering different fuel type (UO2 and MOX) as between the samples of linearities due to the depletion chain itself cannot be excluded. the same fuel type but with different exposure. The moderating However, normal kinf distributions cannot be excluded when per- conditions affect the correlation coefficients the most. Even though turbing individually the fission yields of the other fissile isotopes, the correlation coefficients are fairly large between the UO2 sam- which suggests that the non-linearity due to the depletion chain ples in the light water and the mixture of light and heavy water are small. conditions, their magnitude is reduced in the borated water condi- tions. The MOX samples are affected less by the type of the moderator. 4.2. Relative reactivity worth UQ The uncertainty propagation results for the relative reactivity 4.3. Effect of irradiation history worths are obtained assuming perturbations to the following set of input parameters: cross sections, averaged number of neutrons In this section, the effect of the irradiation history description on produced per fission (t), fission spectrum (v) and fission yields the relative reactivity worth UQ is analyzed by considering the for all isotopes considered in CASMO-5. Fig. 9 shows the conver- VENDOR and BOHR irradiation histories. First, the depletion calcu- gence behavior as well as the output distributions for the relative lations and relative reactivity worth calculations are carried out for reactivity worth of the U1 sample in the H2O moderating condition the U1 sample only considering the uncertainties on the cross sec- with the VENDOR irradiation history. The 95% confidence intervals tions. Fig. 11 shows the evolution of the nominal kinf of the assembly of the mean and the standard deviation of the population of results containing the U1 sample together with its absolute standard devi- are illustrated. Due to the proprietary nature of the data, the rela- ation during irradiation in the nuclear power plant. Although the tive reactivity worth is normalized to one and its distribution mod- nominal kinf values are different with difference up to 1300 pcm ified accordingly. The relative standard deviation is equal to 3.2%. It at EOC for the two irradiation histories, the uncertainties of kinf corresponds to the quadratic sum of the cross section and fission due to cross sections perturbations show a similar trend. (Note that yield uncertainties, respectively 2.2% and 2.1% suggesting that the difference of discharge burnup between the two histories stems cross sections and fission yields can be considered as independent from the adjustment of the burnup in the BOHR methodology to parameters and that no large interactions exist in the model. match the measured 148Nd content (see Section 2.2.1).) A normality test for the relative reactivity worth distribution of Table 3 shows the C/E uncertainty values for the relative reac- each fuel sample in each moderating condition is performed consid- tivity worths obtained assuming the VENDOR and BOHR histories. ering fission yields perturbations separately from the cross sections The magnitudes of the C/E uncertainties are similar for both irradi- perturbations. Considering only the cross sections perturbations, the ation histories. With 500 samples, the observed differences are not null hypothesis that the distribution is normal is not rejected. How- statistically significant. It suggests that uncertainty estimates for ever, the hypothesis is rejected when fission yields are perturbed. the relative reactivity worth are not affected by the modeling of Similarly to the kinf distribution at EOC investigated in Section 4.1, the irradiation history. the relative reactivity worths have non-normal distributions due Second, the comparison of the relative reactivity worths pre- to the non-normal distributions of the fission yields. dicted with CASMO-5 for all burnt fuel samples, all moderating Using the perturbed samples for the relative reactivity worth, it conditions and for both irradiation histories is detailed below. It is possible to compute the correlations (Pearson correlation coeffi- allows estimating the variations of the computational results due cients) between the various fuel samples and for the three to the specification of the irradiation history. Because we are com-
J. Park et al. / Annals of Nuclear Energy 131 (2019) 9–22 17 Fig. 9. Histogram and convergence behavior for the normalized relative reactivity worth of the U1 sample in the H2O moderating condition with the VENDOR irradiation history when considering uncertainties on cross section (left), fission yield (middle) and cross section plus fission yield (right). paring only two irradiation histories (VENDOR and BOHR), we can- ference is in the percent range (0.93–2.20%) and is similar irrespec- not strictly speaking extract an uncertainty on the sample reactiv- tive of the moderating condition. At the same time, the difference ity worth due to this parameter. We can, however, calculate a for the UO2 fuel samples is larger than that for the MOX fuel sam- difference between the results obtained with either irradiation ples. As shown in Table 3, the relative uncertainty of the C/E value modeling and compare its magnitude with that of the uncertainty from cross sections perturbation is around 2.3% regardless of the due to nuclear data. irradiation history. Therefore, the uncertainty propagated from The difference of C/E values due to the irradiation history is cal- cross section is only slightly larger than the difference in reactivity culated by Eq. (4) which represents the mean of the C/E bias worth coming from the irradiation history. This estimation is only obtained for a given group of C/E values. In order to identify poten- preliminary. A more complete analysis would require investigating tial trends, the C/E values are grouped by fuel or moderator type. many more plausible irradiation histories (e.g. different discharge The full set of groups considered here is shown in Table 4. burnup, admissible power, etc.) for a stochastic treatment of the uncertainty such as in Rochman et al. (2018) or defining ‘‘en- VENDOR BOHR 1X N b c;g bc;g velope” irradiation histories to obtain a conservative estimate of dirradiation ¼ ð4Þ g N c¼1 BOHR the impact of this parameter. b c;g VENDOR BOHR where bc;g and bc;g are the respective C/E value for the VENDOR 4.4. Validation of CASMO-5 calculations for the reactivity worth and BOHR histories in a given group g. N is the total number of C/E measurements of LWR-Proteus Phase II values in the group g. The goal of this section is to estimate how dependent are the simulation results to the irradiation history with The relative reactivity worth bias uncertainties obtained with respect to the other source of computational uncertainty considered. SHARK-X are listed in Table 5. Only the uncertainties due to cross Table 4 shows the differences in reactivity worth due to the sections and fission yields are considered and the VENDOR irradi- specifications of the irradiation history. The amplitude of the dif- ation history is considered. The latter choice is made as impact of
18 J. Park et al. / Annals of Nuclear Energy 131 (2019) 9–22 Fig. 10. Pearson coefficients for the relative reactivity worth of the eleven burnt fuel samples and three moderating conditions based on the 500 samples. Fig. 11. Evolution of the nominal kinf and its absolute standard deviation using the VENDOR and BOHR irradiation histories for the U1 sample. the irradiation history modeling on the uncertainty of the relative The bias uncertainties vary from 1.2% to 8.9% as a function of reactivity worth is limited (see previous section). With the esti- the moderating conditions as well as of the fuel type and burnup mates for the calculated and experimental uncertainties of relative of the LWR-PROTEUS Phase II sample. The uncertainty of the rela- reactivity worth, the z-score can be calculated using Eq. (5). tive reactivity worth tends to decrease with burnup. As reported in Grimm et al. (2017), the major contributors to the relative reactiv- jbc 1j ez ¼ : ð5Þ ity worth computational uncertainty for all burnt fuel samples is rbc the average number of neutrons per fission for 239Pu because of
J. Park et al. / Annals of Nuclear Energy 131 (2019) 9–22 19 Table 3 smaller, but increases with exposure in absolute term (the relative Uncertainty of C/E for the U1 relative reactivity worth considering the VENDOR and uncertainty decreases). Also, the bias uncertainty of the UO2 fuel BOHR irradiation histories. samples in the B2023 moderating condition is smaller than that Moderator History C/E Rel. std. Confidence Interval (95%) in the H2O and DHO moderating conditions. In contrast with the H2O VENDOR 2.26% [2.06%, 2.46%] UO2 fuel sample, the bias uncertainty of the MOX fuel samples in BOHR 2.30% [2.10%, 2.51%] B2023 moderating condition is larger than that in the H2O and DHO VENDOR 2.25% [2.05%, 2.44%] DHO moderating conditions. BOHR 2.29% [2.08%, 2.48%] In any case, the z-scores as obtained from these UQ estimates B2023 VENDOR 2.25% [2.05%, 2.45%] are lower than 2 for most of the burnt fuel samples when consid- BOHR 2.30% [2.10%, 2.51%] ering the uncertainties on the cross sections and fission yields. CASMO-5 performs very well at predicting the relative reactivity worth of the LWR-PROTEUS Phase II experiment. For the sake of completeness, Table 5 also shows the bias uncer- the large input uncertainties in the VCM library used. As a result, tainty and z-score for each burnt fuel sample and each moderating the magnitude of the bias uncertainty of the UO2 fuel samples is condition from a previous work (Grimm et al., 2017). In this work, smaller than that of the MOX fuel samples due to larger Pu content cross section data were only perturbed in the simulations of the of the MOX fuel as shown at the bottom of Table 5. The MOX sam- reactivity worth measurements at PROTEUS. The isotopic composi- ples have a larger uncertainty (both relative and absolute), which tion of each burnt fuel sample was assumed to be a normally dis- decreases with exposure, while the UO2 samples uncertainty is tributed random variable with its mean equals to the nominal Table 4 Differences in reactivity worth due to the irradiation history. Case Number of responses dirradiation (%) Mean standard error g (68% confidence) All sample 32 1.73% [1.67%, 1.78%] Fuel type UO2 20 2.20% [2.09%, 2.31%] MOX 12 0.93% [0.86%, 1.01%] Moderating condition H2O 11 1.55% [1.41%, 1.69%] DHO 11 1.52% [1.38%, 1.66%] B2023 10 2.15% [1.93%, 2.36%] Table 5 Bias uncertainty and z-score for each burnt fuel sample and each moderating condition with VENDOR irradiation history. (The approximate Pu content of each sample is also provided.) H2O U1 U2 U3 U4 U5 U6 U7 M1 M2 M3 M4 Previous work (Grimm et al., 2017) Nominal C/E 0.921 0.972 0.937 0.931 0.948 0.950 0.983 0.954 0.940 0.953 0.996 Mean C/E 0.921 0.972 0.937 0.931 0.948 0.950 0.983 0.954 0.940 0.953 0.996 C/E unc. (%) 2.2% 1.7% 1.6% 1.7% 1.6% 1.6% 1.7% 4.9% 3.3% 2.6% 2.4% ez * 3.6 1.6 3.8 4.1 3.2 3.2 1.0 0.9 1.8 1.8 0.2 Present work Nominal C/E 0.921 0.971 0.933 0.927 0.942 0.944 0.971 0.959 0.941 0.949 0.992 Mean C/E 0.930 0.981 0.943 0.936 0.952 0.954 0.981 0.972 0.953 0.961 1.004 C/E unc. (%) 3.4% 2.7% 2.6% 2.6% 2.5% 2.5% 2.5% 5.2% 3.9% 3.3% 3.1% ez 2.1 0.7 2.2 2.4 1.9 1.8 0.8 0.5 1.2 1.2 0.1 DHO U1 U2 U3 U4 U5 U6 U7 M1 M2 M3 M4 Previous work (Grimm et al., 2017) Nominal C/E 0.972 0.999 0.974 0.983 0.987 0.972 0.980 0.983 0.985 0.980 0.995 Mean C/E 0.972 0.999 0.974 0.983 0.987 0.972 0.980 0.983 0.985 0.980 0.995 C/E unc. (%) 2.2% 1.9% 1.8% 1.8% 1.8% 1.8% 1.9% 4.3% 3.1% 2.5% 2.4% ez 1.3 0.0 1.4 1.0 0.7 1.6 1.1 0.4 0.5 0.8 0.2 Present work Nominal C/E 0.972 1.000 0.973 0.979 0.982 0.967 0.970 0.989 0.988 0.977 0.993 Mean C/E 0.980 1.009 0.982 0.989 0.992 0.977 0.979 1.000 0.999 0.988 1.003 C/E unc. (%) 3.2% 2.6% 2.5% 2.5% 2.5% 2.5% 2.4% 4.5% 3.5% 3.1% 2.9% ez 0.6 0.3 0.7 0.4 0.3 1.0 0.9 0.0 0.0 0.4 0.1 B2023 U1 U2 U3 U4 U5 U6 U7 M1 M2 M3 M4 Previous work (Grimm et al., 2017) Nominal C/E 0.950 1.012 0.975 – 0.999 0.986 0.992 1.036 1.051 1.014 1.029 Mean C/E 0.950 1.012 0.975 – 0.999 0.986 0.991 1.035 1.052 1.014 1.029 C/E unc. (%) 2.0% 1.4% 1.3% – 1.2% 1.2% 1.3% 8.8% 4.3% 2.8% 2.4% ez 2.5 0.9 2.0 – 0.1 1.2 0.7 0.4 1.2 0.5 1.2 Present work Nominal C/E 0.951 1.011 0.973 – 0.996 0.983 0.984 1.050 1.056 1.013 1.027 Mean C/E 0.959 1.019 0.981 – 1.004 0.991 0.992 1.075 1.072 1.026 1.039 ** C/E unc. (%) 3.1% 2.2% 2.0% – 1.9% 1.9% 1.9% 8.9% 4.9% 3.6% 3.2% ez 1.3 0.9 1.0 – 0.2 0.5 0.4 0.8 1.5 0.7 1.2 239 Pu content (mg/gU) 6.5 5.6 5.5 5.8 5.5 5.5 6.0 40 26 18 15 * ez: z-score. ** Extreme value of bias uncertainty.
20 J. Park et al. / Annals of Nuclear Energy 131 (2019) 9–22 Table 6 Component of relative reactivity worth uncertainty of the U1 sample in each moderating condition with the VENDOR irradiation history. (XS stands for cross sections and FY for fission yields.) U1 C unc. (%) H2O DHO B2023 Previous work (Grimm et al., 2017) XS 2.07% 2.11% 1.88% Tech. Param. 0.57% 0.58% 0.55% Present work XS 2.20% 2.19% 2.19% FY 2.27% 2.07% 1.87% depletion calculation results and its uncertainty taken as the 1.87% and 2.27%, which is similar to the uncertainties resulting experimental uncertainty of the isotopic composition measured from cross section perturbations. As discussed above, in the previ- through chemical assay. The effects of both source of uncertainties ous work, the isotopic composition of burnt fuel sample is assumed on the relative reactivity worth (combination of three keff calcula- to be a normally distributed random vector. The resulting uncer- tions – see Eq. (1)) were summed quadratically to determine the tainties on the reactivity worth bias (labelled Technological Param- computational uncertainty of relative reactivity worth. eter in Table 5) ranged from 0.55% to 0.58% and impact In the present work, the cross section and fission yield perturba- significantly less the bias uncertainty than the fission yields uncer- tions are considered throughout the modeling of the irradiation of tainty. As the fission yields uncertainties drive the uncertainty of the fuel samples in the nuclear power plant as well as that of the the fission products composition (Aures et al., 2017), their effects oscillation measurements in PROTEUS. The burnt fuel sample com- can be compared to the technological parameter uncertainties position uncertainties are a byproduct of the uncertainty propaga- reported in the previous work, as both represent the effect of the tion during the depletion calculation. Propagating input fuel composition uncertainty on the relative reactivity worth of uncertainty through the irradiation of the fuel samples with the burnt fuel sample. It should be noted however, that the uncer- CASMO-5 as well as considering fission yield uncertainties among tainty on the relative reactivity worth due to the fission yield per- the input uncertainties lead to larger computational uncertainty on turbation should be lower than the technological parameter the relative reactivity worth than previously reported. uncertainty of (Grimm et al., 2017) because the effect of the fission In order to better understand the larger uncertainty estimates yield uncertainty does not affect the actinide concentration uncer- obtained in this work, the breakdown of the contributions of the tainty. As reported in Leray et al. (2017), Rochman (2017), fission various type of input parameters to the computational uncertainty yield input uncertainties vary widely depending on the library of the U1 sample is reported in Table 6. The computational uncer- and method used to determine them. The method used in this tainty coming from cross section perturbations is slightly larger work (PSI-GEF method) appears to overestimate the uncertainty than that reported in the previous work since the cross section (Leray et al., 2017). Finally, the behavior of bias uncertainty with uncertainties have been propagated through the fuel irradiation respect to exposure, fuel type, and moderating condition does and the fuel sample oscillations calculations (while they were not change between the previous and present works. propagated only through the oscillation calculations in the previ- Combining the C/E and its uncertainty, the performance of ous work). Moreover, the uncertainties on the calculated relative CASMO-5 to predict the LWR-PROTEUS Phase II reactivity worth reactivity worth due to fission yield uncertainties range between measurements is assessed. Fig. 12 shows the mean values of the Fig. 12. Mean of the C/E distributions for the relative reactivity worth of all samples with 2-r error bars.
J. Park et al. / Annals of Nuclear Energy 131 (2019) 9–22 21 Table 7 Fitting results of linear regression analysis on the C/E values. Fuel type Moderating condition C/E Confidence interval Slope Confidence interval of C/E (95%) of slope (95%) UO2 H2O 0.954 [0.939, 0.969] 3.53E04 [4.16E04, 1.12E03] DHO 0.987 [0.978, 0.995] 1.86E04 [6.19E04, 2.46E04] B2023 0.991 [0.974, 1.007] 8.07E05 [7.84E04, 9.45E04] MOX H2O 0.972 [0.950, 0.994] 6.72E04 [2.49E03, 3.83E03] DHO 0.997 [0.991, 1.004] 3.29E05 [1.11E03, 1.05E03] B2023 1.053 [1.029, 1.077] 9.82E04 [3.38E03, 1.42E03] C/E distributions for the relative reactivity worth with its uncer- tions. Indeed, at first the authors did not consider any uncertainty tainty for all samples. As mentioned in Section 4.2, nominal and on the code values and in a later stage considered only an approx- mean values are different due to the non-normal distribution of imate uncertainty estimation in which they propagated the cross relative reactivity worth. The differences are small even though section uncertainties in the reactivity measurements at PROTEUS statistically significant (see Table 5). but not in the model for the fuel irradiation. Instead, they assumed, The distributions of the C/E ratios grouped by moderator and as a proxy, that the uncertainty on the burnt fuel sample isotopic fuel type are normal according to a Shapiro-Wilk test (Yap and composition (labelled technological parameters) was that of the Sim, 2011) with a 5% significance level. They can be subjected to burnt fuel isotopic composition measurements. a paired t-test to see if their means are similar or not. Considering In this paper, we proposed an improved treatment of the the UO2 samples, the t-tests show significant differences at the 95% sources of uncertainties for the reactivity worth code predictions, confidence level between the mean values for H2O and B2023 con- which was tested previously on a single spent fuel sample (Leray ditions as well as between the H2O and DHO conditions, but no sig- et al., 2016; Rochman et al., 2018). We propagated the cross section nificant differences between the DHO and B2023 conditions. and fission yield uncertainties in the simulations of the NPP and Considering the MOX samples, the paired t-tests show significant PROTEUS irradiations and quantified the impact of refining the differences at the 95% confidence level between the values for irradiation history. The resulting total relative uncertainties on H2O and B2023 as well as between the DHO and B2023 conditions, the C/E values for the relative reactivity worth varied from 1.2% but no significant difference between the H2O and DHO conditions. to 8.9% for all moderating conditions and fuel types. The uncertain- For the H2O moderating condition and the UO2 samples, all ties on cross sections and fission yields contributed at the same CASMO-5 simulations under-predict the experimental values for level to this uncertainty (2.0%). The cumulative fission yields of 239 relative reactivity worth by an average of 0.046, with a 95% confi- Pu produced by the GEF code had non-normal probability distri- dence interval of ±0.020 around that value. Consequently, on aver- butions and led to non-normal distributions for the relative reac- age simulations and experiments show a significant bias for this tivity worths. The non-normal distributions were coming from moderation condition. The conclusions are the same for the the data produced by the GEF code itself and not by the treatment B2023 moderating conditions, as all CASMO-5 simulations over- to adapt them to the simplified decay chains of CASMO-5. predict the experimental value by an average of 0.053 with a 95% As we observed no linear trend with burnup in the bias between confidence interval for the mean of ±0.024 around that value. the measured relative reactivity worth and that predicted with Finally, a linear regression analysis is performed on the C/E val- CASMO-5, this work confirms that CASMO-5 can predict accurately ues for each population defined by the previous statistical analysis the changes of reactivity with fuel exposure up to large burnup val- with respect to burnup, considering the updated bias uncertainties ues (120 MWd/kg). determined in the present work. The fitting results as well as their Finally, we estimated the effect of the irradiation history uncertainties are shown in Table 7. The zero slope is within the description on the relative reactivity worths by comparing two confidence interval for each fit which suggests that there is no lin- independent irradiation histories (a detailed one determined inter- ear trend with burnup in the accuracy of the prediction of relative nally at PSI and a coarser one provided by the fuel vendor). The dif- reactivity worth. That is, the change of reactivity with increased ference in the C/E values for the relative reactivity worth obtained fuel exposure is captured accurately by CASMO-5, even for the with the two irradiation histories is around 2%, i.e. on par with the cases for which CASMO-5 may have a computational bias (the uncertainty coming from nuclear data. This suggests that we H2O moderating condition). It should be noted here that the fitting should more carefully estimate the role of the irradiation history is done assuming normal distribution for the relative reactivity modelling in the future. worth. As shown in Section 4.2, it is not the case due to the fission yields uncertainties. However, as the difference between the mean and nominal values is small as reported in Table 5, it is expected Acknowledgements that such non-normal distribution may not affect significantly the validation outcomes of this study. The work was partially funded by the Swiss Nuclear Power Plants (swissnuclear) in the framework of the QUASAR project. The LWR-PROTEUS program was conducted jointly by PSI and 5. Conclusion swissnuclear, with specific contributions from Kernkraftwerk Goes- gen (KKG) for Phase II. Many thanks are also due to the PROTEUS This paper summarizes additional work performed towards the experimental team for their precise work and to the operational validation of the CASMO-5 lattice and depletion code against the team for reliable operation and maintenance of the facility. reactivity worth measurements of the 11 PWR spent fuel samples of the LWR-PROTEUS program. In a previous publication (Grimm et al., 2017), the authors determined biases between measured Appendix A. Supplementary data and calculated values for all these burnt fuel samples and dis- cussed trends of the bias with burn-ups, fuel type and moderation Supplementary data to this article can be found online at conditions. However, the bias analysis suffered from several limita- https://doi.org/10.1016/j.anucene.2019.03.023.
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