Acta Polytechnica CTU Proceedings doi:10.14311/APP.2018.14.0014 Acta Polytechnica CTU Proceedings 14:14–20, 2018 © Czech Technical University in Prague, 2018 available online at http://ojs.cvut.cz/ojs/index.php/app CALCULATION UNCERTAINTIES IN SPENT FUEL INVENTORY DETERMINATION Tomas Czakoja, ∗, Jan Fryborta, Martin Loveckyb a Czech Technical University in Prague, FNSPE, DNR, V Holesovickach 2, 18000 Prague, Czech Republic b SKODA JS a.s., Orlik 266/15, 31600 Bolevec, Plzen, Czech Republic ∗ corresponding author: tomas.czakoj@gmail.com Abstract. In the depletion calculation of the nuclear fuel, the uncertainty is of utmost importance, as it affects the uncertainty of the subsequent calculation, when the calculated composition is used. The calculations are even more important when they are safety related, e. g., when determining the reactivity or emissions of radioactivity to the environment. This work covers the depletion model of Gd-2M+ fuel which was developed in ORIGEN-ARP/TRITON calculation sequences, both being parts of a SCALE 6.2.1 package. The uncertainties of the respective calculation model were determined by comparison with experimental data for both calculation sequences. The effects of operational and manufacturing uncertainties on concentration of the most important nuclides using TRITON depletion model of Gd-2M+ fuel were determined. The effect of respective uncertainties manifested in changes of composition on the multiplication factor using Monte-Carlo sequence KENO-VI were also specified. Keywords: Uncertainties, nuclear, fuel, calculation, depletion. 1. Introduction The awareness of the uncertainty of a calculation is very important, especially in nuclear reactor applica- tions. Inaccurate determination of spent fuel inventory can result in higher decay power, higher emissions or by increased reactivity which can be very dangerous. This work estimates the accuracy of the calcula- tion performed by comparison of experimentally de- termined spent nuclear fuel inventory with the cal- culated one. The study of influence of variation in some operational and manufacturing input aspects, such as temperature, power level or enrichment, was conducted. The respective study focuses on the spent fuel inventory determination and calculation of its multiplication factor. 2. Calculation methods All calculations described in this paper were made in SCALE code system version 6.2.1 [1]. The depletion was simulated in TRITON and ORIGEN-ARP se- quence, the determination of the reactivity important nuclides was carried out in TSUNAMI-2D sequence and the determination of the multiplication factor was obtained with the use of the KENO-VI stochastic sequence. Both depletion and sensitivity calculations used a multigroup version of ENDF/B VII.1 nuclear data library, KENO-VI simulation used continuous energy version of the aforementioned library [1, 2]. 2.1. Depletion model Two depletion models of Gd-2M+ fuel were created. The fuel used in the depletion models is currently used in VVER-440 reactors in Dukovany power plant. This fuel assembly contains fuel pins without a burnable Figure 1. Enrichment of each fuel pin in the Gd2M+ fuel assembly. Numbers mean enrichment in weight fractions and the hexagon with brown color shows position of fuel pin with burnable absorber. [3]. absorber which does not have a central hole in the fuel pellets. Only exception is six fuel pins with Gd2O3 which contain a central hole [3]. Figure 1 shows the enrichment of each fuel pin in the respective fuel assembly, as well as the position of central tube (CT) and fuel pin with burnable absorber Gd2O3. The numbers in Figure 1 mean enrichment in weight fractions and the hexagon with brown color shows position of fuel pin with the burnable absorber [3]. The first depletion model was created in TRITON sequence. The detailed model included the description of geometry, composition, power history and several other important parameters affecting the accuracy of 14 http://dx.doi.org/10.14311/APP.2018.14.0014 http://ojs.cvut.cz/ojs/index.php/app vol. 14/2018 Calculation Uncertainties in Spent Fuel Inventory Determination the calculation. This model contained an infinite array of the fuel assemblies with B1 buckling, where the assumed spectrum is identical to the critical one [4]. The depletion model used five cycles with a duration of 330 days with the specific power set to 30.535 W g−1HM and the shutdown between cycles of 35 days. The time step between depletion was 1.2 days for first 6 days of cycle, next 24 days used 6 days long time step and following 300 days used 20 days long time step. The depletion model was originally set to maxi- mum accuracy and after the creation of the model, many optimization calculations were conducted. Each calculation used the basic model with one modified parameter thus quantified the effect of selected reduc- tion. In case the effect was negligible, the reduction was implemented in the final model. The optimized final model was twice faster than the basic one and the accuracy of the results was not affected [1]. The optimized parameters were time steps or Leg- endre order in the transport theory. Next optimized parameter was addnux, which adds trace quantities of certain groups of nuclides to the inventories of deple- tion materials which causes better tracking of these nuclides during the calculation. Last optimized pa- rameter was assign. This parameter groups depletion materials. Each material of the respective group is in- dependently depleted, but the calculation uses average cross section. The second depletion model was made in ORIGEN- ARP sequence. This sequence, together with the model, is very fast and simple, however it requires a data file from the previous TRITON calculation. The results are similar to results from slow detailed TRITON calculation, if an appropriate data file is used. The ORIGEN-ARP model contained only a homo- geneous composition and the power history, no other parameters are required [1]. 2.2. Comparison with experimental data Because there were no avaliable experimental data of the spent Gd-2M+ fuel, it was nessesary to use the data of another fuel type. The data used for the comparison were retrieved from Project ISTC # 3958. The goal of the project was to obtain data from the spent nuclear fuel for description of its composition [5]. The fuel assembly used in the ISTC project differed from the Gd-2M+ fuel assembly in several aspects. The first difference was in enrichment because ISTC fuel assembly contained fuel pins with constant en- richment. Next difference was in the geometry be- cause ISTC fuel contained central hole and also had moderately different dimensions. Because of these dis- tinctions, the ISTC fuel assembly contained smaller amount of uranium than the Gd-2M+ fuel assembly. Another significant difference was the absence of any burnable absorber in ISTC fuel. All these diferences are listed in Table 1 [3, 5, 6]. Gd-2M+ ISTC #3958 Fuel enrichment 3.6/4.0/4.6 % 4.4 % Outer fuel diameter 0.78/0.76 cm 0.757 cm Inner fuel diameter 0/0.12 cm 0.12 cm Inner cladding radius 0.793/0.773 cm 0.772 cm Burnable absorber Gd2O3 - Table 1. Differences between Gd-2M+ and ISTC fuel 157Gd 156Gd 158Gd 159Tb 155Gd 161Dy 154Gd 239Pu 238U 241Pu 240Pu 135Xe 103Rh 143Nd 133Cs 237Np 149Sm 131Xe 242Pu 236U 99Tc 155Eu 153Eu 151Sm 154Eu 152Sm 147Pm 145Nd 243Am 109Ag 101Ru 95Mo 238Pu 148mPm 150Sm 105Pd 147Sm 134Cs 105Rh 141Pr 139La 241Am 235U 234U 16O 242Cm* 244Cm* 108Pd* Table 2. Nuclides with big impact on the reactivity The ISTC project # 3958 published information about 12 samples which came from the above men- tioned fuel assembly. It includes information about burnup, location of samples in the fuel assembly and also the content of certain nuclides in each sample. Based on the published information, two depletion models describing depletion of ISTC fuel were made. One model was made in the TRITON sequence and one was made in the ORIGEN-ARP sequence. The model for comparison was similar to the model de- scribed in previous section, only the geometry and composition were modified for description of the fuel assembly from the project [5, 6]. 2.3. Influence of uncertainties 2.3.1. Effect on the spent fuel inventory Study of the influence of uncertainties was performed on changes in a content of group of nuclides in the spent fuel inventory. These nuclides were determined using the TSUNAMI sensitivity calculation which determined that said nuclides affect reactivity consid- erably. The sensitivity calculation used spent fuel inventory determined by the model described in the section 2.1. The inventory was loaded into the TSUNAMI model, which was obtained from the depletion model by modification of depletion parameters to sensitivity control parameters. Determined nuclides are listed in Table 2. Nuclides listed in this table had the minimal sensitivity of 10−4 in at least one material. Three nuclides marked with the star had smaller sensitivity, however they were accounted for because of their significant inaccuracy determined by the comparison with experimental data. Effect of the uncertainties on the spent fuel in- ventory was studied by comparison of the inventory calculated without any applied uncertainty and the inventory calculated with one arbitrary uncertainty applied. Uncertainties used in this comparison in- clude changes of parameters describing the operation of the reactor, fuel assembly geometry or composition. 15 T. Czakoj, J. Frybort, M. Lovecky Acta Polytechnica CTU Proceedings Quantity Nominal Lower Higher Moderator temperature 555 K 541 K 573 K Fuel temperature 885 K 785 K 985 K Boron content 524 ppm 0 ppm 1049 ppm Power level 30.535 g cm−3 27.4815 g cm−3 33.5885 g cm−3 Table 3. Operational uncertainties Uncertainty Nominal Lower Higher Absorber content (wt) 3.35 % 3.2 % 3.5 % Uranium content 1230/1141 g 1213/1124 g 1247/1158 g Enrichment (wt) 3.6/4/4.6 % 3.55/3.95/4.55 % 3.65/4.05/4.65 % Outer fuel diameter 0.78/0.76 cm 0.777/0.757 cm - Inner fuel diameter 0/0.12 cm 0/0.09 cm - Outer cladding radius 0.91 cm 0.906 cm 0.914 cm Inner cladding radius 0.793/0.773 cm - 0.799/0.779 cm Table 4. Material uncertainties Element Content [%] Element Content [%] N 2,9E-03 Pb 8,0E-04 F 2,2E-02 Zn 1,1E-03 Na 5,2E-03 Cu 1,1E-03 Mg 7,0E-03 Ni 1,4E-02 Si 7,1E-03 Co 2,0E-05 Cr 3,0E-03 Fe 1,6E-02 Mn 2,0E-04 Table 5. Content of impurities [7] Complete list of the used uncertainties is presented in Tables 3, 4 and 5. All the calculated inventories had equal burnup of 50.4 MWd kg−1HM, which corresponds to the burnup of spent fuel after five years depletion in the nuclear reactor. Because of the preservation of the burnup, cases with lower or higher power level were depleted for longer or shorter time, respectively. 2.3.2. Effect on the multiplication factor Effect of the uncertainty on the multiplication factor was evaluated by determination of the multiplication factor of spent fuel. The composition of this fuel was calculated in previous part. The evaluation was made in KENO-VI 3D stochas- tic sequence. The model was created by loading of the composition to the Gd-2M+ depletion model and its modification for KENO-VI sequence. The calculation used 2000 neutron generations with 50000 neutrons per generation and first 50 generations being inac- tive. The calculation was automatically terminated once the stochastic deviation decreased below 0.00020 because of the limited available computation time. 3. Results and discussion 3.1. Comparison with experimental data Calculated content of selected nuclides in each sam- ple was compared to the experimentally determined content. This comparison was created as a fraction of computed and experimental data, marked as C/E. An arithmetic mean of C/E for every nuclide is in Table 6 and in Figure 2. As presented in table 6, the results are relatively accurate for most of the elements, such as uranium, cesium or neodymium, but for some elements the in- accuracies are larger, such as for 108Pd or 151Eu. At the moment, there are no clear reasons for these inac- curacies and more detailed research for clarification of these inaccuracies is needed. 3.2. Influence of uncertainties 3.2.1. Effect on spent fuel inventory Figure 3 depicts changes in the spent fuel inventory after the modification of moderator temperature. Re- sults show that the biggest changes in the content are for the isotopes with high cross section in thermal energies. This phenomenon is caused by the worsened moderation, which leads to the worsened absorption in thermal part of the spectrum. Changes in the spent fuel inventory after modifi- cation of fuel temperature are presented in Figure 4. The effect of change of fuel temperature is smaller in comparison with the effect of change of modera- tor temperature, but is important to take account that change in fuel temperature is usually many times higher than changes in moderator temperature. The change in inventory after the modification of fuel temperature is mainly caused by change of Doppler Effect. Higher temperature decreases the maximum of the resonance, which results in higher resonance absorption. Higher absorption at isotope of 238U then leads to higher production of actinides such as plutonium [8]. Figure 5 shows results for changes of boron content in the moderator. It is obvious that higher concentra- tion of boron leads to higher content of gadolinium in the spent fuel. This is caused by the worsened mod- eration which results in lower absorption in thermal part of the spectrum. 16 vol. 14/2018 Calculation Uncertainties in Spent Fuel Inventory Determination C/E C/E C/E Nuclide TRITON ORIGEN-ARP Nuclide TRITON ORIGEN-ARP Nuclide TRITON ORIGEN-ARP 234U 1.03 ± 0.09 1.03 ± 0.09 242Cm 1.23 ± 0.14 1.24 ± 0.14 149Sm 0.80 ± 0.67 0.80 ± 0.67 235U 0.96 ± 0.00 0.96 ± 0.00 244Cm 1.23 ± 0.05 1.23 ± 0.05 150Sm 1.07 ± 0.43 1.07 ± 0.43 236U 0.95 ± 0.00 0.95 ± 0.00 241Am 1.17 ± 0.01 1.17 ± 0.01 151Sm 1.09 ± 0.45 1.09 ± 0.45 238U 0.99 ± 0.00 0.99 ± 0.00 243Am 0.91 ± 0.03 0.91 ± 0.03 152Sm 1.05 ± 0.37 1.04 ± 0.37 238Pu 1.19 ± 0.01 1.20 ± 0.01 133Cs 0.99 ± 0.01 0.99 ± 0.01 155Gd 1.13 ± 0.15 1.13 ± 0.15 239Pu 1.23 ± 0.00 1.23 ± 0.00 134Cs 0.94 ± 0.01 0.94 ± 0.01 95Mo 0.49 ± 0.15 0.49 ± 0.15 240Pu 1.16 ± 0.00 1.16 ± 0.00 135Cs 1.15 ± 0.01 1.10 ± 0.01 105Pd 1.13 ± 0.62 1.13 ± 0.62 241Pu 1.20 ± 0.00 1.20 ± 0.00 137Cs 0.99 ± 0.00 0.99 ± 0.00 108Pd 2.67 ± 3.73 2.67 ± 3.73 242Pu 1.14 ± 0.01 1.14 ± 0.01 151Eu 0.39 ± 0.09 0.39 ± 0.09 109Ag 0.70 ± 0.11 0.70 ± 0.11 143Nd 1.05 ± 0.00 1.05 ± 0.00 153Eu 1.12 ± 0.73 1.12 ± 0.73 101Ru 1.06 ± 0.40 1.06 ± 0.41 145Nd 1.02 ± 0.00 1.02 ± 0.00 154Eu 1.22 ± 0.94 1.22 ± 0.94 237Np 0.79 ± 0.01 0.79 ± 0.01 146Nd 1.01 ± 0.00 1.01 ± 0.00 155Eu 1.09 ± 0.68 1.09 ± 0.67 144Ce 0.99 ± 0.15 0.99 ± 0.15 148Nd 1.01 ± 0.00 1.01 ± 0.00 147Sm 1.03 ± 0.36 1.03 ± 0.36 Table 6. Comparison of calculated and experimental data Figure 2. Comparison of calculated and experimental data Figure 3. Effect of change in moderator temperature on composition. Similar observation can be seen in the content of samarium. Both its isotopes 149Sm and 151Sm have a high microscopic cross section for absorption in ther- mal energies. Similarly to gadolinium, higher boron Figure 4. Effect of change in fuel temperature on composition. content worsens moderation which causes lower ab- sorption in samarium isotopes [2]. Results for different power levels are shown in Fig- ure 6. The power level change affects only few isotopes, content of most of the isotopes remains almost un- 17 T. Czakoj, J. Frybort, M. Lovecky Acta Polytechnica CTU Proceedings Figure 5. Effect of change in boron content on com- position. Figure 6. Effect of change in power level on compo- sition. changed. These changes are mainly caused by longer depletion time, which allows for a higher accumu- lation of certain isotopes in the spent fuel, caused by the decay of their parent nuclides. Another rea- son for the changes in content is connected to the higher production of short-lived fission products and its daughter isotopes for higher power levels, such as 135Xe or 105Rh [9]. Figure 7 shows results of impact of the variation in the Gd2O3 content in spent fuel. This variation affects mainly the gadolinium content in spent fuel inventory, yet it also leads to increased content of 161Dy and 159Tb isotopes, due to them originating from gadolinium according to Equations (1) - (3) [10]. Effect on content of any other nuclides is negligible. 158Gd + n → 159Gd β − −−−−−→ 18,479h 159Tb (1) 159Tb + n → 160Tb   β−−−−→ 72,3d 160Dy + n → 161Dy +n → 161Tb β − −−−−→ 6,906d 161Dy (2) 160Gd + n → 161Gd β − −−−−−→ 3,66min 161Tb β − −−−−→ 6,906d 161Dy (3) Figure 8 shows results of impact of change in the uranium content. As expected, the higher initial con- tent of uranium leads to higher final content of all Figure 7. Effect of change in Gd2O3 content on composition. Figure 8. Effect of change in uranium content on composition. investigated nuclides, however, the difference between content of various nuclides is visible. The results of variations in the enrichment are de- picted in Figure 9. The changes in uranium isotopes content were expected because their initial content was also modified together with the enrichment [11]. Variations in content of isotopes 242Am, 244Cm or 242Pu are also observed. Their content in spent fuel is higher with lower enrichment. This phenomenon is caused by their production from the 238U because the initial content of this isotope also varies with enrichment. Another effect of change in enrichment is also connected to modification of neutron spectrum because lower content of 238U leads to lower parasitic absorption. Figures 10 and 11 show results for changes in fuel and cladding radii. The impact of fuel radius change is negligible, which is probably caused by modification of fuel density made with the objective of preserva- tion of fuel content. Bigger effects observed for fuel pins without gadolinium are obviously caused by their higher number in the fuel assembly. Effect of modification of outer cladding radius is higher, which is caused by change of the amount of moderator near to the fuel pin. This change leads to better (or worse) moderation and subsequently to a modification of the neutron spectrum. Effect of varia- tion of inner cladding radius is negligible because it only changes the amount of cladding material, which has only small influence on neutrons. 18 vol. 14/2018 Calculation Uncertainties in Spent Fuel Inventory Determination Figure 9. Effect of change in enrichment on compo- sition. Figure 10. Effect of change in fuel radius Figure 12 shows the effect of impurities in fuel. This effect is both positive and negative and for most appli- cations, it can be considered negligible. Nevertheless it is possible to find some cases, in which the impurities can be important. For example, content of nitrogen can lead to production of radioactive 14C, which may have impact on the overall activity [12]. 3.2.2. Effect on multiplication factor Effect of the operational uncertainties was tested only with investigated uncertainty included in the depletion simulation. This means that the determination of multiplication factor is not influenced by presence of the uncertainty, but it is influenced only by change in inventory. Results of this calculation can by seen in Figure 13. The biggest impact definitely comes from the change of boron content in the moderator. Much smaller, but also important is the effect of change in the modera- tor temperature. Other uncertainties are of smaller importance. Both this effects are mainly caused by modification of content of nuclides with high cross section for absorption such as 155Gd, 157Gd, 149Sm and 151Sm which negatively influence neutron balance [2]. Figure 14 shows the influence of the material uncer- tainties on the multiplication factor. This influence has smaller importance than the operational uncer- tainties. The most important uncertainty is initial enrichment of the fuel, which will be mainly caused by change in final content of fissile isotope 235U. Second Figure 11. Effect of change in cladding radius Figure 12. Effect of impurities in the fuel biggest effects comes from different initial uranium content, which can probably mainly assigned to change in boron content together with changed content of fissile isotopes of plutonium and uranium. Figure 15 shows impact of changes in geometry. These uncertainties have only small importance and the most significant is the change in the outer diameter of fuel with gadolinium absorber together with the change in its inner cladding diameter. 4. Conclusions Two depletion models of Gd-2M+ fuel were created and the TRITON model was optimized for faster calcu- lation. This model was used for the study of influence of the operational and manufacturing uncertainties. Comparison of computed and experimental data was conducted for both used depletion sequences. No important difference in results from both sequence was found. Obtained results were relatively accurate, but few nuclides, such as 108Pd or 151Eu, with inaccurate determination were found. The dependence between the inaccuracy of 108Pd or 151Eu and between the group of tested uncertainties was not found. On the contrary, the sensitivity of 242Cm and 244Cm content to the boron content in the moderator and to the moderator temperature was found, which is caused by modification of neutron spectrum. The influence of uncertainties on the spent fuel in- ventory and the multiplication factor was investigated. The determination of the multiplication factors has 19 T. Czakoj, J. Frybort, M. Lovecky Acta Polytechnica CTU Proceedings Figure 13. Effect of operational uncertainties on multiplication factor - only with uncertainty included in fuel depletion Figure 14. Effect of material uncertainties on multi- plication factor allowed for a comparison of importance of each un- certainty. It was found that most important are the operational uncertainties, especially boron content in the moderator and the moderator temperature. Al- though fuel temperature change seems to be much low important than the previously mentioned, it is impor- tant to remember that fuel temperature changes are much high than the moderator temperature changes. Importance of other investigated operational uncer- tainties is much lower than the importance of the previous. Furthermore, it was discovered that in order to apply the conservative approach, it is necessary to set up lower boron content and higher temperature of moderator. This approach leads in faster depletion of gadolinium burnable absorber which leads in lower absorption. On the contrary, higher fuel temperature leads in higher gadolinium content, but this effect is prevailed by higher production of fissile isotopes of plutonium together with lower 235U depletion. Due to this fact, higher fuel temperature is more conservative. Effect of all manufacturing uncertainties is lower than the most important operational uncertainties. The most important is correct set up of the enrichment and the uranium content in fuel. It is conservative to overestimate both values. References [1] B. T. Rearden, M. A. Jessee. SCALE code system 6.2.1. Tech. rep., 2016. doi:10.2172/1326509. Figure 15. Effect of uncertainties of geometry on multiplication factor [2] M. Chadwick, M. Herman, P. Obložinský, et al. ENDF/B-VII.1 nuclear data for science and technology: Cross sections, covariances, fission product yields and decay data. Nuclear Data Sheets 112(12):2887 – 2996, 2011. Special Issue on ENDF/B-VII.1 Library, doi:10.1016/j.nds.2011.11.002. [3] P. Mikolas, Z. Fakezasova, M. Sasek, et al. Zmena casti ppbz pro zavedeni paliva gd-2m+edu: 4.3 jaderne charakteristiky, 2013. [4] J. Leppanen, M. Pusa, E. Fridman. Overview of methodology for spatial homogenization in the serpent 2 monte carlo code. 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Ministerstvo skolstvi, mladeze a telovychovy. [10] Y. Tanoue, T. Yokoyama, M. Ozawa. Resource evaluation of heavy rare earth derived from the spent gd2o3 burnable poison in LWRs. Journal of Energy and Power Engineering 10(4), 2016. doi:10.17265/1934-8975/2016.04.004. [11] S. Cerne, O. Hermann, R. Westfall. Reactivity and isotopic composition of spent PWR (pressurized-water- reactor) fuel as a function of initial enrichment, burnup, and cooling time. Tech. rep., 1987. doi:10.2172/5561567. [12] M.-S. Yim, F. Caron. Life cycle and management of carbon-14 from nuclear power generation. Progress in Nuclear Energy 48(1):2 – 36, 2006. doi:https://doi.org/10.1016/j.pnucene.2005.04.002. 20 http://dx.doi.org/10.2172/1326509 http://dx.doi.org/10.1016/j.nds.2011.11.002 http://dx.doi.org/https://doi.org/10.1016/j.anucene.2016.06.007 http://dx.doi.org/10.17265/1934-8975/2016.04.004 http://dx.doi.org/10.2172/5561567 http://dx.doi.org/https://doi.org/10.1016/j.pnucene.2005.04.002 Acta Polytechnica CTU Proceedings 14:8–14, 2018 1 Introduction 2 Calculation methods 2.1 Depletion model 2.2 Comparison with experimental data 2.3 Influence of uncertainties 2.3.1 Effect on the spent fuel inventory 2.3.2 Effect on the multiplication factor 3 Results and discussion 3.1 Comparison with experimental data 3.2 Influence of uncertainties 3.2.1 Effect on spent fuel inventory 3.2.2 Effect on multiplication factor 4 Conclusions References