Acta Polytechnica CTU Proceedings doi:10.14311/APP.2018.19.0007 Acta Polytechnica CTU Proceedings 19:7–13, 2018 © Czech Technical University in Prague, 2018 available online at http://ojs.cvut.cz/ojs/index.php/app SCALE AND SERPENT TWO-GROUP CROSS-SECTION DATA GENERATION Ondřej Nováka, ∗, Jan Frýborta, Lubomír Sklenkaa, Jan Rataja, Ondřej Chválab a Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Nuclear Reactors, Prague, Czech Republic b University of Tennessee at Knoxville, Department of Nuclear Engineering, Tennessee, USA ∗ corresponding author: ondrej.novak2@fjfi.cvut.cz Abstract. In this work, VVER fuel assembly is calculated using two different codes - Serpent and SCALE. Multiplication factor and several two-group macroscopic parameters including scattering cross-section, fission cross-section, total cross-section and diffusion coefficient were studied. In addition to this, fuel isotopic composition dependency on burnup was calculated as a part of this study. Obtained data are compared and differences are discussed. Both codes provides similar results for all studied parameters. Keywords: VVER, Serpent, VVANTAGE-6, fuel cycle, burnup, SCALE, Temelin nuclear power plant, depletion calculation, homogenized cross-sections. 1. Introduction The crucial part of nuclear safety is based on results obtained by calculation. To ensure accurate results, codes are compared with experimental data (bench- marking) and also among each other [8], [6]. In this work, VVER fuel assembly depletion is calculated using two different codes - Monte-Carlo code Serpent and deterministic sequence TRITON from SCALE package. Multiplication factor and sev- eral two-group macroscopic parameters including scat- tering cross-section, fission cross-section, total cross- section and diffusion coefficient are calculated and compared. In addition to that, fuel isotopic compo- sition dependency on burnup were calculated. All values are calculated during the fuel depletion in or- der to cover the whole fuel cycle, which means burnup up to 60.5 MWd/kgU. In addition, several Serpent memory optimization settings and their impact on macroscopic data generation were tested. The TRITON calculation sequence from the SCALE package [5] represents the traditional approach to fuel depletion calculations and few-group data generation. It is based on deterministic code NEWT producing data for the well–established ORIGEN depletion code. Serpent code [9] was selected due to the fact that the code is designed directly for reactor core calculations combining Monte-Carlo based transport calculations and advanced CRAM fuel depletion method [10]. Serpent and SCALE codes allow homogenized few- group cross-sections and other nuclear constants de- scribing fuel assembly behavior to be produced. These results can be later used in full-core calculations. Both codes use different approach to obtain homogenized cross-section and other nuclear data. Therefore, com- parison provides valuable information about the meth- ods used. SCALE code has a longer history in this field of application compared to Serpent code, thus SCALE code was selected as the reference code for this study. Firstly, the model and the calculation itself is de- scribed, then results are presented and discussed. 2. Fuel assembly description For this particular study, fuel assembly model was created based on VVANTAGE-6 fuel design [2] (see Figure 1). VVANTAGE-6 fuel was developed by West- inghouse company for VVER-1000 reactors. There- fore, it features hexagonal fuel lattice. This fuel type was used in the Temelin Nuclear Power Plant reactor for the first 10 years of operation. The fuel assembly without IFBA absorber was selected for this study. Assembly parameters are listed in the Table 1. All fuel pins are identical, with flat 3% enrichment. Tem- peratures used in this study are listed in the Table 2. 3. Calculation setup Two dimensional models of the fuel assembly in Ser- pent code (version 2.1.27) and SCALE code (version 6.2.1) were created based on the VVANTAGE-6 design specified in Table 1. Specific power 35.54 W/gHM was used in both calculations. B1-leakage corrected criti- cal spectrum was applied in both calculations as well. In Serpent calculation, B1 correction used 238 group energy structure (scale238 [5]). Fast group (group 1) was above 0.625 eV and thermal group (group 2) below that for both codes. Serpent calculation were conducted with 10000 neu- trons per cycle, 400 active cycles and 50 inactive cycles. Input cross-section data for Serpent calcula- tions were obtained from ENDF/B-VII.1 library [7]. 7 http://dx.doi.org/10.14311/APP.2018.19.0007 http://ojs.cvut.cz/ojs/index.php/app O. Novák, J. Frýbort, L. Sklenka et al. Acta Polytechnica CTU Proceedings Figure 1. VVANTAGE-6 fuel assembly [11]. Parameter VVANTAGE 6 Pin cladding outer diameter [mm] 9.144 Pin cladding inner diameter [mm] 8.001 Pin cladding thickness [mm] 0.5715 Pin cladding material Zr-4 (303) Fuel pellet outer diameter [mm] 7.844 Number of fuel pins in FA 312 Pin pitch [mm] 12.75 Number of instrumentation tubes 1 Tube material Zr-4 (303) Inner tube diameter [mm] 12.6 Outer tube diameter[mm] 11.0 Tube thickness [mm] 0.8 Number of guide tubes 18 Tube material Zr-4 (303) Outer tube diameter over the absorber area [mm] 12.6 Inner tube diameter over the absorber area [mm] 11.0 Tube thickness over the absorber area [mm] 0.8 Outer tube diameter in the absorber area [mm] 10.41 Inner tube diameter in the absorber area [mm] 8.6 Tube thickness in the absorber area [mm] 0.905 Total assembly weight [kg] 766 UO2 density [g/cm3] 10.412 Zr-4 density [g/cm3] 6.53 Table 1. Fuel assembly parameter summary [3]. 8 vol. 19/2018 SCALE and Serpent two-group cross-section data generation Fuel temperature 1005 K Soluble boron concentration 525 ppm (3 g/kg) Coolant density 0.7169 g/cm3 Coolant temperature 578 K Table 2. Calculation parameters. SCALE code used the default detailed ENDF/B-VII.1 252 group library. Reflective boundary conditions resulted in infinite lattice calculation for both codes. Serpent allows automatic division of fuel pins into radial regions for more realistic depletion calculations. All fuel pins were divided into 5 radial regions and each region was burned separately in this study. In addition, there were unique materials for all fuel pins in the fuel assembly, thus their material compositions were treated separately. SCALE calculation used 60◦ symmetry to limit the number of depleted materials. Fuel pins in symmet- rical positions were considered as identical material. No radial regions in fuel pins were defined as there is no burnable absorber. SCALE and Serpent calculation used 51 burn steps with final burnup at 60.5 MWd/kgU1. Seven steps were between 0 MWd/kgU to 1, followed by 44 steps with approximately 1.3 MWd/kgU distance. Additional 231 isotopes were added in SCALE bur- nup calculation using addnux=3 parameter. Serpent used the default isotope inventory setting. 4. Results The following parameters were studied: multiplication factor, scattering cross-section (from first group to the second one). In addition to these, fission cross-section, total cross-section and diffusion coefficient, all for two groups. All these parameters were studied for dif- ferent Serpent memory optimization setup. Nominal optimization (number 4) was used to produce results which are compared with SCALE values. 4.1. Multiplication factor Multiplication factor results are plotted in Figure 2a. In order to better show the differences, absolute dif- ferences between SCALE and Serpent results were calculated and plotted in Figure 2b (SCALE is the ref- erence one). Statistical uncertainty in Serpent results is only 22 pcm. Uncertainty introduced by nuclear data may reach several hundreds of pcm. However, Serpent and SCALE calculation used nuclear data from an identical library (ENDF/B-VII.1). SCALE calculation used preprocessed data in 252 group li- brary, Serpent used continuous version. Serpent values are higher compared to SCALE results for BOC and EOC. Values around 30 MWd/kgU are similar for both codes. Initial multiplication factors differ more than 900 pcm from SCALE results. Difference change to 0 160 MWd/kgU is considered as maximal burnup value for currently fuel used. (a). (b). Figure 2. Multiplication factor from SCALE and Serpent calculation (a) and SCALE difference from Serpent results (b). pcm reached around 30 MWd/kgU. EOC difference reached almost 600 pcm. 4.2. Total cross-section Total cross-sections for both codes are in good agree- ment. Values are plotted in Figure 3a for the fast group and in Figure 3b for the thermal group. The Serpent code initially calculates the total cross-section by about 0.4 % greater than SCALE. The value grad- ually increase during the course of fuel depletion. At burnup level about 20 MWd/kgU the SCALE value gets greater and the final difference is 0.4 %. Results for the thermal group results are almost identical. Ex- cept for the initial limited period, the differences are limited to 0.1 %. Serpent value relative uncertainty is only 0.015% for thermal group and 0.014% for fast group. 4.3. Diffusion coefficient The diffusion coefficient is an important macroscopic parameter. Diffusion coefficient was calculated for both groups. The coefficient values are plotted in 9 O. Novák, J. Frýbort, L. Sklenka et al. Acta Polytechnica CTU Proceedings (a). (b). Figure 3. Total cross-section dependency on burnup for fast group (a) and for thermal group (b). Figures 4a and 4b. Fast group coefficient obtained by SCALE calculation is higher compared to Serpent results. Thermal group results are opposite, Serpent values are higher compared to SCALE results. Dif- ference for fast group starts approximately at 10% at BOC, slowly decreasing and reaching only 3% at EOC. Slow group values differs by −7% at BOC, drop to −8.6% where it remains till the end. The difference observed in both groups is probably rooted in code structure (stochastic vs deterministic) and in nuclear data difference. Serpent value relative uncertainty is only 0.025% for thermal group and 0.021% for fast group. 4.4. Fission cross-section Fission cross-sections for two energy groups are plotted in Figures 5a and 5b. Discrepancies from Serpent results are plotted in Figures 6a (fast group) and 6b (thermal group). Fission cross-section for thermal group behaves similarly to the multiplication factor. SCALE cross-section increases in the first part of fuel cycle, which probably results in decrease of keff difference. Maximum is observed similar to minimum (a). (b). Figure 4. Diffusion coefficient dependency on burnup for fast group (a) and for thermal group (b). of keff difference around 30 MWd/kgU. Serpent value relative uncertainty is only 0.038% for thermal group and 0.053% for fast group. 4.5. Scattering cross-sections Scattering cross-section from fast group to thermal group is plotted in Figure 7. Both results have similar behavior. Serpent values differ from 0.7% to 1% in discrepancy. Serpent value relative uncertainty is only 0.014%. 4.6. Isotope concentrations Number densities of dominant actinides 235U, 238U, and 239Pu during fuel burnup were calculated to sup- port understanding of fuel behavior. Results are printed in figures 8a, 8b and 8c (including difference from SCALE results). The observed isotopic changes are consistent but there are differences that can ex- plain differences in the few-group cross-sections. It can be seen that Serpent calculates faster 235U de- pletion than SCALE and also 239Pu number density is lower for the majority of burnup levels. This con- 10 vol. 19/2018 SCALE and Serpent two-group cross-section data generation (a). (b). Figure 5. Fission cross-section dependency on bur- nup for fast group (a) and for thermal group (b). tributes to different and total cross-sections calculated by these two codes. 4.7. Memory optimization option in Serpent code Serpent 2 allows modify calculation in the RAM re- quirements using memory optimization. Default mode 4 is recommended for cross-section and other nuclear data generation and has the highest memory require- ments. Modes 3, 2 and 1 have lower memory re- quirements and extend calculation duration. More differences are described in Serpent forum [1]. In order to compare memory optimization, multipli- cation factor and other nuclear data were calculated with different optimization. Results obtained are sim- ilar for all cases and the difference is under statistical uncertainty. The difference for multiplication factors are smaller than 70 pcm which within three standard deviations of the calculation. 5. Conclusion Monte Carlo code Serpent and TRITON calculation sequence from the SCALE package were used to solve (a). (b). Figure 6. SCALE fission cross-section discrepancy to Serpent values for fast group (a) and for thermal group (b). the identical task: calculations of multiplication factor and several two-group macroscopic parameters includ- ing scattering cross-section, fission cross-section, total cross-section and diffusion coefficient during depletion of a VVANTAGE-6 fuel assembly. In addition, fuel isotopic composition evolution of selected nuclides was determined. Both codes use different methods for solv- ing this neutron transport and depletion coupled task. The results obtained were compared and differences were discussed for each studied parameter. The multiplication factor obtained by both codes are compared in the Figure 2a and the differences are plotted in 2b. The initial multiplication factors determined by Serpent differs by more than 900 pcm from the SCALE code results, then it decreased to 0 pcm at around 30 MWd/kgU, however the EOC difference reached almost 600 pcm. Total cross-section for both codes is in a good agree- ment. Values are plotted in Figure 3a for the fast group and in Figure 3b for the thermal group. The relative difference is between ±0.4 %. 11 O. Novák, J. Frýbort, L. Sklenka et al. Acta Polytechnica CTU Proceedings Figure 7. Scattering cross-section from fast group to thermal group, dependency on burnup. The next studied parameter was the diffusion coef- ficient. Results for the fast group are shown in Figure 4a and for the thermal group in 4b. Higher differences can be seen for this parameter. They start for the fast group at approximately 10% for BOC, slowly decreas- ing and reaching only 3% at EOC. The thermal group values differs by −7 % at BOC, than dropping to −8.6 % where it remains till the end of fuel depletion. The fission cross-section results are plotted in Figure 5a for the fast group and in in Figure 5b for the thermal group. Differences between codes shown in Figures 6a and 6b have similar trends and Serpent results are consistently lower. The last macroscopic parameter studied was the scattering cross-section. Obtained values are shown in Figure 7. Both codes determined similar burnup dependence with Serpent values being different from the SCALE results by 0.7% to 1%. In addition to macroscopic cross-sections, several isotopic concentration were calculated and studied as well. Number densities of dominant actinides 235U, 238U, and 239Pu during fuel burnup were calcu- lated. Results (including Serpent differences from the SCALE results) can be seen in Figures 8a, 8b and 8c. Isotopic changes are mostly in agreement, however, Serpent calculates faster 235U depletion than SCALE. Moreover, 239Pu number density is lower for majority of burnup levels. This contributes to above observed differences of fission cross-section between these two codes. The memory optimization option in Serpent code was studied as a part of this study. All four memory optimization were tested. Results for all cases were similar and therefore it can be stated that different memory optimization do not affect the results. Only the memory requirements and required computational time is affected. In summary, Serpent and SCALE code were com- pared for burnup calculation and macroscopic cross- section data generation for VVANTAGE-6 fuel assem- bly. Both codes provided mostly similar results. Some (a). (b). (c). Figure 8. Isotope concentration of (a) 235U, (b) 238U and (c) 239Pu for both codes and difference between them. differences were however observed in isotopic compo- sitions. It is also reflected in the relevant macroscopic cross-sections. Acknowledgements The paper was supported by the project “Strengthen- ing and development of research at Czech Technical Uni- 12 vol. 19/2018 SCALE and Serpent two-group cross-section data generation versity in Prague with the use of research infrastruc- ture VR-1 Training Reactor for research activities” (reg. nr. CZ.02.1.010.00.016_0130001790) supported by Opera- tional Programme Research, Development and Education co-financed from European Structural and Investment Funds and from state budget of the Czech Republic. Sup- port from IAEA fellowship number C6/CZR/14007 was used in this work. References [1] Discussion forum for Serpent users [online]. 2007 [Accessed on 2017-04-15]. 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Available at: https://www.academia.edu/32855663/Study_of_VVER_- 1000_Fuel_Cycle_Using_NESTLE_and_ORIGEN_Codes [5] B.T. Rearden and M.A. Jessee. SCALE Code System, ORNL/TM-2005/39, Version 6.2.1, Oak Ridge National Laboratory, Oak Ridge, Tennessee (2016). Available from Radiation Safety Information Computational Center as CCC-834. [6] E. Fridman, J. Leppänen, "On the use of the Serpent Monte Carlo code for few-group cross section generation," Annals of Nuclear Energy, 2011, 38(6), 1399-1405. DOI: 10.1016/j.anucene.2011.01.032. ISSN 0306-4549. [7] M.B. Chadwick, M. Herman, P. Oblozinsky, et al.: "ENDF/B-VII.1 Nuclear Data for Science and Technology: Cross Sections, Covariances, Fission Product Yields and Decay Data." Nuclear Data Sheets, 2011, 112(12). DOI: 10.1016/j.nds.2011.11.002. 2887-2996. [8] T. Lötsch, "Fuel assembly burnup calculations for VVER fuel assemblies with the MONTE CARLO code Serpent." Kerntechnik, 2014, 79(4), 295-302 [cit. 2017-02-16]. DOI: 10.3139/124.110455. ISSN 0932-3902. [9] J. Leppänen, M. Pusa, T. Viitanen, V. Valtavirta, T. Kaltiaisenaho: "The Serpent Monte Carlo code: Status, development and applications in 2013," Ann. Nucl. Energy, 82 (2015) 142-150. [10] J. Leppänen, A. Isotalo: "Burnup calculation methodology in the Serpent 2 Monte Carlo code." In proc. PHYSOR 2012, Knoxville, TN, Apr. 15-20, 2012. [11] Mecir, V. "Temelin NPP fuel experience". 7 International conference on WWER fuel performance, modelling and experimental support, Bulgaria, 2008. 13 Acta Polytechnica CTU Proceedings 19:7–13, 2018 1 Introduction 2 Fuel assembly description 3 Calculation setup 4 Results 4.1 Multiplication factor 4.2 Total cross-section 4.3 Diffusion coefficient 4.4 Fission cross-section 4.5 Scattering cross-sections 4.6 Isotope concentrations 4.7 Memory optimization option in Serpent code 5 Conclusion Acknowledgements References References