ABSTRACT 1 INTRODUCTION

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1 Participation in OECD/NEA Oskarshamn-2 (O-2) BWR Stability Benchmark for Uncertainty Analysis in Modelling Using TRITON for Transport Calculations and SAMPLER for Cross-Sections Error Propagation A. Labarile, R. Miró, C. Mesado, T. Barrachina, G. Verdú Institute for Industrial, Radiophysical and Environmental Safety (ISIRYM) Universitat Politècnica de València, Camí de Vera, s/n, Valencia, Spain ABSTRACT With a large number of light water reactors (LWRs) around the world, there is an increasing interest in improving safety analysis research with best-estimate computer codes, to model the complex system of nuclear power plants and for making predictions that include quantitative uncertainty analysis. This work is related with OECD/NEA coupled code benchmarks based on operating reactor data, which objective is to establish confidence bound calculation as usual practice in extending code applications, from its original intended use to more challenging events, like unstable power oscillations without SCRAM. O-2 Benchmark references are based on measured plant data of boiling water reactor (BWR) Oskarshamn-2 nuclear power plant that experienced a stability event on February 25, However, a steady-state calculation at this operating condition has been performed in this work with the aim of obtaining the keff and cross-sections values as well as sensitivity analysis and uncertainties results. Calculations were carried out for a BWR fuel element, in two different configurations (with and without control rod), at Hot Zero Power (HZP) state. Neutronics calculations were accomplished with the computation of energy collapsed and homogenized macroscopic cross-sections through SCALE-6.2 code (actually in version beta 4). The deterministic lattice modelling is carried out using TRITON/NEWT module for transport calculations, while the uncertainties and sensitivity analysis of cross-sections calculation has been performed using the SAMPLER module, which uses stochastic sampling techniques of cross-sections perturbations. Perturbed values for flux in each energy group are applied many times to the input samples, and the resulting distribution of output responses was analysed to obtain the standard deviations and correlation coefficients for all responses. The results of the keff and cross-sections with its uncertainty will be part of the OECD Benchmark to perform uncertainty analysis of the BWR stability prediction. 1 INTRODUCTION The primary objective of the Oskarshamn-2 BWR stability benchmark is to establish confidence in extending code applications where non-linear models are necessary [1]. The 421.1

2 421.2 Osharshamn-2 BWR fuel assembly is made up of several axial lattice segments (or zones) with different enrichments and burnable poisons. For each fuel segment, two-group cross-sections were generated by the O-2 licensee (OKG), using a lattice physics code CASMO, and were provided to the benchmark participants for the neutron kinetic model development [2]. In this study, for the two-group cross-sections calculation, it was used the SCALE code, an open source validated code developed by Oak Ridge National Laboratory that is currently in version 6.2 beta 4 [3]. The modules of SCALE that have been employed are TRITON [4] coupled with NEWT [5]. This methodology allows carrying out a 2D deterministic transport calculation, based on the Extended Step Characteristic (ESC) approach, with the computation of energy collapsed and homogenized macroscopic cross-sections [6]. One of the fuel assemblies of Oskarshamn-2 BWR was selected, as it is shown in Figure 1, and the O-2 CASMO cross-sections dataset has been compared with the obtained crosssections in TRITON/NEWT with the aim to follow up how sensitive are BWR analysis results to cross-sections generated with different lattice codes. Figure 1: Fuel models used in the lattice code for cross-sections calculation Moreover, the SAMPLER module in SCALE was employed to the collapsed and homogenized libraries for cross-sections uncertainty propagation [7]. The obtained result of SAMPLER can be very useful in Sensitivity and Uncertainty (S&U) Analysis in Best-estimate codes. This paper is organized as follows: in section 1 the introduction is presented; section 2 is devoted to the description of the methodology. In section 3 the results of this work are presented and finally, the conclusions reached are explained in section 4. 2 METHODOLOGY 2.1 Transport Calculation The SCALE input files created in this work is based on the equivalent CASMO input files. Some important aspects to be considered in translating the CASMO model to SCALE for

3 421.3 obtaining more reliable results are TRITON parameters, assembly composition and NEWT parameters [8]. The fuel pin-cell geometry and lattice configuration, taken out from CASMO and used in TRITON/NEWT model, are schematized in Table 1: Table 1: Parameters/Reactor condition Parameter Value Parameter Value Reactor type BWR Array size 9 x 9 Fuel rods 72 Pin pitch [cm] Pellet radius [mm] Clad radius [mm] 5.5 Heat perimeter [mm] Gap radius [mm] Water rod inner diameter [m] m Moderator Temperature [K] 559 Water rod wall thickness [m] 7.05e-4 Clad temperature [K] Fuel radius [mm] 4.75 Clad material Zircaloy-4 Fuel temperature [K] Clad density [g/cm 3 ] Sensitivity and Uncertainty Calculation The multiplicative perturbation factors Qx,g that are applied to the reference data to obtain the altered values are calculated as,,, (1) where, 1,, (2) x represent a reaction in a certain nuclide and g is the energy group. While Δσx,g( )/σx,g( ) is obtained from SCALE covariance matrix [9]. To obtain the uncertainty and the correlation due to all uncertain parameters, all parameters are randomly perturbed for each calculation. Mathematically, the uncertainty in an individual output parameter k is determined as Δ, (3) where Δk exp (i) is the uncertainty in system i due to uncertainties in the input parameters. is the a th Monte Carlo (MC) sample of system i, where all uncertain input parameters have been randomly varied within the specified distribution. The covariance between two systems, i and j, is determined as shown in Eq. (4). Σ, (4) The correlation coefficient between systems i and j can be determined as

4 421.4, 3 (5) RESULTS The fuel assembly of Oskarshamn-2 BWR used in this work is a 9x9 fuel lattice element. The output layout of the fuel assemblies defined in TRITON/NEWT code for transport calculation are shown in Figure 2 and 3: Figure 2: BWR without control rod 2-D assembly 3.1 Figure 3: BWR with control rod 2-D assembly CASMO vs TRITON/NEWT The output values compared in this paper are listed in Table 2. Comparison of CASMO and TRITON/NEWT is carried out for the multiplication factor (keff), the absorption crosssection, the fission cross-section, the transport cross-section, the diffusion coefficients and the neutron flux. All values are presented for both groups, fast and thermal. Output k_assembly fuel_maca_1/2 fuel_macf_1/2 fuel_mactr_1/2 diff_1/2 flux_1/2 Table 2: List of parameters compared Description Eigenvalue/multiplication factor for two-group assembly Macroscopic absorption cross-section for both groups Macroscopic fission cross-section for both groups Macroscopic transport cross-section for both groups Diffusion coefficient for both groups Neutron flux for both groups Units 1/cm 1/cm 1/cm cm 1/cm2s The two tables below summarize the obtained results with the aim of comparing CASMO with TRITON/NEWT simulation using the 238-group nuclear data library collapsed, with the ENDF/B-VII library in SCALE.

5 421.5 Table 3: Comparison of cross-sections values of O-2 HZP_unrodded configuration Table 4: Comparison of cross-sections values of O-2 HZP_rodded configuration Tables 3 and 4 represent unrodded and rodded configuration respectively. The first column shows the output values compared in this paper; the second one are the O-2 CASMO cross-sections dataset values provided by the OKG. The third and fourth columns represent TRITON/NEWT calculations and its error with respect to CASMO values. As it is shown in Tables 3 and 4, there is a good agreement between CASMO values and TRITON/NEWT results for the majority of values. In general, the unrodded configuration gives better results compared to the rodded configuration. Furthermore, some differences in fission cross-section for both groups were found, and probably it is due to little differences in the model definition and fission condition considered in the two codes. More effort is needed to investigate this question. 3.2 SAMPLER Results Sampler calculation provides the expected values of the data and covariance information describing the correlated uncertainty. SAMPLER repeats the perturbation for a specified number of samples (set by the user) to obtain the results distribution with its standard deviation and its correlation coefficients [10]. The SAMPLER module has been used coupled with TRITON/NEWT in this work.

6 421.6 Based on the Wilks approach, the sample size for double tolerance limits with a 95% of uncertainty and with 95% of statistical confidence for the output variables is equal to 146 samples [11, 12], which is the number of runs performed in this work. An interesting result of perturbed variables in SAMPLER layout is the running average, which represent average values and standard deviation for samples of the population during simulation. These results are listed below, for the O-2 reactor, at hot zero power state (HZP) without control rod. a) b) c) Figure 4: Samples values with averaged values and standard deviation for a) keff, b) absorption cross-section and c) diffusion coefficients calculation for O-2 HZP unrodded case for the fast group

7 421.7 a) b) Figure 5: Samples values with averaged values and standard deviation for a) absorption crosssection and b) diffusion coefficients calculation for O-2 HZP unrodded case for the thermal group Figures 4 and 5 show the output of keff, absorption cross-section and diffusion coefficients for fast and thermal group respectively. It is possible to see that the sample values are closer to the average value and almost entirely within its standard deviation. According to Wilks theory, more of 95% of reliability is reached. Moreover, we performed additional correlation analysis for SAMPLER results to identify the relationship between keff, flux and the most important cross-sections. A Circos diagram [13], capturing the significant correlations among all parameters analysed, is shown in figure 6. The external frames in the circle represent the compared output values: the multiplication factor (in light green), the absorption cross-section for group 1 and 2 (in orange), the fission cross-section for both groups (in light blue), the diffusion coefficient for group 1 and 2 (in pink), and the neutron flux for both groups (in violet). The links between variables indicate their correlation: positive values of correlation are shown in blue/violet colour and express direct correlation between two parameters, correlation close to zero, in light yellow, mean that there is low correlation, and variables with many strong inverse correlations are shown in red.

8 421.8 Figure 6: Circos diagram showing the correlation of selected parameters in SAMPLER simulation 4 CONCLUSIONS This work has been carried out in the framework of OECD/NEA Oskarshamn-2 (O-2) BWR Stability Benchmark for Uncertainty Analysis in Modelling which objectives are to establish the confidence bound calculation as a usual practice in extending code applications and quantify the uncertainty in all steps of simulation. Transport calculations have been analysed with the deterministic code SCALE, implementing TRITON/NEWT module with the aim of comparing keff and cross-sections results between CASMO reference values. S&U calculations have been performed with SAMPLER module, for perturbed crosssections with stochastic sampling techniques. The following significant conclusions can be highlighted: - TRITON/NEWT is a solid validated code that has performed well the CASMO even though slight differences in fission cross-section have been found especially for the rodded configuration. - SAMPLER module has been selected to estimate sensitivity and uncertainty analysis. Its results agree very well with reference values and give important information about standard deviation of multiplication factor, flux and the most important cross-sections values.

9 421.9 ACKNOWLEDGMENTS This work contains findings produced within the OECD/NEA UAM Benchmark and has been supported by the Generalitat Valenciana under GRISOLIA/2013/A/006 (037) subvention. REFERENCES [1] M. Avramova, et al., Multi-physics and Multi-scale Benchmarking and Uncertainty Quantification within OECD/NEA Framework, Annals of Nuclear Energy, [2] Tomasz Kozlowski, et al., Analysis of the OECD/NRC Oskarshamn-2 BWR Stability Benchmark, Annals of Nuclear Energy, Volume 67, May 2014, Pages [3] Germina Ilas, Ian C. Gauld, Georgeta Radulescu. Validation of New Depletion Capabilities and ENDF/B-VII Data Libraries in SCALE. Annals of Nuclear Energy 46 (2012) [4] M. A. Jessee, M. D. DeHart, TRITON: A Multipurpose Transport, Depletion, and Sensitivity and Uncertainty Analysis Module, Oak Ridge National Laboratory, version 6.1, Sect T1, June [5] M. A. Jessee, M. D. DeHart, NEWT: A New Transport Algorithm for Two-dimensional Discrete-ordinate Analysis in non-orthogonal Geometries, Oak Ridge National Laboratory, version 6.1, Sect F21, June [6] B. J. Ade, SCALE/TRITON Primer: A primer for Light Water Reactor Lattice Physics Calculations, NUREG/CR-7041, ORNL/TM-2011/21, Oak Ridge National Laboratory, November [7] M. L. Williams, et al., SAMPLER: A Module for Statistical Uncertainty Analysis with SCALE Sequences, SCALE 6.2 beta 1. [8] C. Mesado, R. Miró, T. Barrachina, G. Verdú, Comparación de los resultados de quemado para reactores BWR con CASMO y SCALE 6.2 (TRITON/NEWT), 40º Reunión Anual Sociedad Nuclear Española (SNE), Valencia España, 2014, ISSN [9] M.L. Williams, et al., A Statistical Sampling Method for Uncertainty Analysis with SCALE and XSUSA, Oak Ridge National Laboratory, June [10] C. Mesado, R. Miró, T. Barrachina, G. Verdú, Principales Características y Posibilidades del Nuevo Módulo de SCALE 6.2 para Cálculo de Sensibilidad e Incertidumbre por Muestreo: SAMPLER, 40º Reunión Anual Sociedad Nuclear Española (SNE), Valencia España, 2014, ISSN [11] S. S. Wilks, Mathematical Statistics, John Wiley & Sons, [12] In Seob Hong, Oh and Kim, Generic Application of Wilk s Tolerance Limits Evaluation Approach to Nuclear Safety, OECD/CSNI Workshop on Best Estimate Methods and Uncertainty Evaluations, [13] Krzywinski M, Schein J, Birol I, Connors J, Gascoyne R, Horsman D, Jones SJ, Marra MA: Circos: an information aesthetic for comparative genomics. Genome Res 2009, 19: