Acta Polytechnica CTU Proceedings https://doi.org/10.14311/APP.2022.37.0048 Acta Polytechnica CTU Proceedings 37:48–53, 2022 © 2022 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague ON THE ONGOING COMPUTATION OF THE LVR-15 REACTOR FUEL BURNUP Jan Pintaa, b a Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Nuclear Reactors, V Holešovičkách 2, 180 00 Prague 8, Czech Republic b Research Centre Řež, Department of Neutron Physics, Hlavní 130, 250 68 Husinec-Řež, Czech Republic correspondence: pintajan@fjfi.cvut.cz Abstract. Isotopic composition of the LVR-15 reactor fuel changes significantly during the operation time. In order to enable Monte Carlo calculations of the LVR-15 core throughout any reasonable time period, the isotopic compositions of partially depleted fuel assemblies have to be known at the start of the simulation. Even though the infinite lattice calculation can represent useful initial approximation, the non-leakage assumption is not necessarily valid for compact and highly heterogenous cores like in case of the LVR-15. Therefore, a more advanced calculation process have to be implemented towards appropriate determination of fuel assembly burnup. The main aim of this paper is to describe the current state of the ongoing computation as well as provide an explanation of the chosen calculation scheme of the LVR-15 operation history. Currently available results that are affected by profound inaccuracy are discussed in the final part alongside with planned future improvements. Keywords: Burnup calculation, Serpent, LVR-15 reactor. 1. Introduction The LVR-15 reactor [1] is a tank-type light water research reactor with 10 MW thermal power output. The reactor utilizes the IRT-4M 19.7 % enriched fuel and its main applications are material testing, silicon doping and production of radioisotopes. Currently, the Serpent [2] computational model of the reactor is being developed with aim to perform its experimental qualification in the near future. One of the most crucial challenges concerning the develop- ment is a coverage of fuel burnup. There is an essential question of how to create proper representations of partially depleted fuel assemblies that are present at the start of an operation cycle. In fact, there is a majority of fuel assemblies with nonzero burnup contained inside the LVR-15 reac- tor core at the beginning of each cycle. Therefore, determination of isotopic composition of partially de- pleted fuel have to be implemented in order to obtain convincing initial conditions that are needed for the Serpent calculation of any time step of any LVR-15 reactor cycle. The first obvious possibility is to cal- culate burnup-wise fuel isotopic concentrations in the infinite lattice approximation. However, it will be shown later that such approach does not have to be necessarily valid for compact and highly heterogenous cores with considerable neutron leakage. For this reason, a more advanced fuel burnup computation procedure has been applied. The idea of this procedure is to take into account two important characteristics of the LVR-15 reactor. The first one is the above mentioned compactness and high heterogeneity of the core. The second one is the complicated operation scheme of the reactor, which involves short-term shutdowns in the run of a cycle operation. By adopting these two features, a more ex- act approximation in the fuel burnup implementation should be obtained. This work is particularly focused on the introduc- tion and description of the advanced LVR-15 reactor fuel burnup computation. The results presented in this paper are considered rather preliminary due to the fact that the computational process is still in the on- going state. Nevertheless, the profound improvements will be realized on the basis of these first results in the following iteration of the fuel burnup calculation. 2. Serpent model The current version of the 3D Serpent model of the LVR-15 reactor allows to build the reactor model with any desired core configuration that contains the most frequently used components, i.e. fuel assemblies, beryl- lium blocks, water displacers and irradiation channels. All components in the core are surrounded with wa- ter and placed inside the reactor vessel. An instance of a core configuration geometry plot of the Serpent model is provided in Figure 1. As for fuel components, both standard 8-tube and control 6-tube IRT-4M fuel assemblies can be cho- sen. Control rod positions are adjustable according to the demanded pattern. In addition, both fuel assem- blies can be defined with a variety of possible burnup distribution structures. Different fuel material com- positions can be assigned to corresponding regions of a particular fuel component using these distribution structures. 48 https://doi.org/10.14311/APP.2022.37.0048 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en vol. 37/2022 On the Ongoing Computation of the LVR-15 reactor fuel burnup Figure 1. Serpent geometry plot of the opening LVR-15 core configuration of the K216 cycle; two fuel assemblies with initial zero burnup are highlighted (standard 85A710 – red, control 65C666 – black). The initial fuel burnup implementation is based on burnup-wise isotopic compositions of standard fuel as- sembly calculated with Serpent in axially and radially infinite lattice. The Serpent model utilizes predefined burnup library with atomic densities of considered nuclides as functions of burnup (see Table 1). 3. Computational process The chosen process of the burnup computation is based on the real operation scheme of the LVR-15 research reactor. The complexity of the reactor schedule is emphasized in Figure 2 and Figure 3, where powers and keff from Serpent are visualized, respectively. More than a 2.5 year latest time period of the reactor operation has been considered for the purpose of the computation. This time interval was determined according to the moment when a fuel assembly with the largest burnup in the currently running cycle has been introduced into the reactor core for the first time as a fresh fuel component. This condition is fulfilled by the K216 cycle, where two new fuel assemblies have been added into the operation procedure – one standard (85A710) and one control (65C666). The position of the former is marked with red colour, while the latter is highlighted with black colour in terms of the K216 core layout visualization in Figure 1. The whole computational process consists a total of 14 operation cycles starting from the K216 up to the K229. Two fresh fuel assemblies in average are introduced into the reactor core at the start of each of the examined cycles. Since that point, burnup de- velopment of these fuel assemblies can be calculated without the uncertainty in the fuel material composi- tion. This presumption is supported by the fact that the fresh fuel assemblies have known initial isotopic concentrations. Overview of fuel assemblies with this attribute is listed in Table 2 alongside with the in- formation whether any particular fuel assembly was present in the corresponding operation cycle. The computational process of the latest operation history of the LVR-15 reactor has been designed on the basis of data from the nodal code that is used for cycle designing at the LVR-15 [3]. These data come from nodal calculation of given cycle that has been carried out with genuine operational power data of the reactor. A typical calculation schedule of the LVR-15 reactor cycle contains over a hundred partial critical calculation steps. That reflects the complexity of the reactor operation. The same approach has been adopted in the Serpent based computational process in order to achieve au- thentic operational conditions of the LVR-15 reactor as closely as possible. As for initial step of the entire computation, referred as the step 0 of the K216 cy- cle, the material compositions of fuel assemblies with nonzero burnup have been obtained from the above mentioned infinite lattice burnup library implemented in the Serpent computational model. Axial-wise bur- nup data divided into 5 regions of these fuel assemblies have been taken from the calculation of the previous K215 cycle from the operational nodal code. The scheme of the computational process is ex- pressed in Figure 4. A single step of the computation other than the initial step 0 of the K216 cycle can be described with a sequence of the same partial proce- dures. First, the appropriate operational data of the LVR-15 are loaded and transformed into the input file that is needed for the building of the corresponding LVR-15 reactor Serpent model. These data include: • the name of the current cycle, • the calculation step number in the cycle, • time interval length of the step, • reactor power during the calculation step, • identifiers of present fuel assemblies, • core configuration layout within the step, • control rod insertions in the step core layout, • specifics of uranium targets in the core centre. In addition to the input file, the second set of data has to be provided. The second set contains calcu- lated isotopic compositions of fuel assemblies from the previous step. This data stream is referred as the oldDepFile and it is sent to the slvr15 together with the input file. The slvr15 procedure represents a soft- ware tool designed for creation of the Serpent input file of demanded configuration of the LVR-15 reactor 49 Jan Pinta Acta Polytechnica CTU Proceedings 80160 130270 420950 430990 441010 451030 471090 481130 531350 541350 551330 551340 551350 601430 601450 611470 611490 611510 621470 621490 621500 621510 621520 631530 631550 641550 641570 922340 922350 922360 922380 932370 942380 942390 942400 942410 942420 952410 952430 962430 962440 962450 Table 1. List of 42 considered nuclides that are passed on between subsequent computation steps (ZAI numbers [4]). K216 K217 K218 K219 K220 K221 K222 K223 K224 K225 K226 K227 K228 K229 85A710 × × × × × × × × – × × × × × 65C666 × × × × × × × × × × × × × × 85A711 – × × × × × × × × × × × × × 85A712 – × × × × × × × – × × × × × 65C667 – × × × × × × × × × × × × × 65C668 – – × × × × × × × × × × × × 85A713 – – – × × × × × × × × × × × 85A714 – – – × × × × × × × × × × × 65C669 – – – – × × × × × × × × × × 85A715 – – – – – × × × × × × × × × 65C670 – – – – – × × × × × × × × × 65C671 – – – – – – × × × × × × × × 65C672 – – – – – – × × × × × × × × 85A716 – – – – – – – × × × × × × × 65C673 – – – – – – – × × × × × × × 85A717 – – – – – – – – × × × × × × 85A718 – – – – – – – – × × × × × × 65C674 – – – – – – – – × × × × × × 65C675 – – – – – – – – – × × × × × 85A719 – – – – – – – – – – × × × × 85A720 – – – – – – – – – – × × × × 85A721 – – – – – – – – – – – × × × 65C676 – – – – – – – – – – – × × × 60C834 – – – – – – – – – – – – × × 60C835 – – – – – – – – – – – – × × 85A722 – – – – – – – – – – – – – × 85A723 – – – – – – – – – – – – – × Table 2. The presence of initially fresh fuel assemblies throughout considered cycles K216–K229 (× in the cycle, – not in the cycle). 0 5 10 K216 K217 K218 K219 K220 K221 K222 0 14 28 0 5 10 K223 14 28 K224 14 28 K225 14 28 K226 14 28 K227 14 28 K228 14 28 K229 Time (days) Po w er (M W th ) Figure 2. Power sequence of the LVR-15 reactor operation including cycles K216–K229. 50 vol. 37/2022 On the Ongoing Computation of the LVR-15 reactor fuel burnup 0.9 1.0 K216 K217 K218 K219 K220 K221 K222 0 14 28 0.9 1.0 K223 14 28 K224 14 28 K225 14 28 K226 14 28 K227 14 28 K228 14 28 K229 Time (days) k e ff Figure 3. Development of keff calculated with Serpent throughout cycles K216–K229. LV R -1 5 op er at io n da ta input slvr15 oldDepFile mainSerpent newDepFile step n step n+1 Figure 4. Scheme of the computational process. computational model. The main input file is prepared for the Serpent calculation of particular step of the computational process after the slvr15 execution. One of the step calculation outputs is the Serpent deple- tion file indicated as the NewDepFile. This output file alongside with appropriate operational data is used as the input for the calculation of the following step. The introduced process is repeated n times according to the number of steps in the whole computation. The isotopic composition of fuel assemblies between subsequent steps is passed on for 42 selected nuclides. The list of considered nuclides is written in Table 1. The decision of the usage of the 42 nuclide approxi- mation was made based on the burnup credit isotopes [5] with consideration of 135Xe. The simulation of the xenon poisoning problematics was achieved by the elimination of 135I and 135Xe nuclei before the beginning of each cycle, i.e. K216, K217, K218, etc. This behaviour was assumed to be sufficient enough to simulate actual operational conditions in the LVR-15 reactor core. Parameters for neutron population in criticality source mode of each individual Serpent calculation were set to 100 000 neutrons per generation, 200 active and 40 inactive generation cycles. Standard deviation of keff did not exceed 27 pcm for each calculation step. All Serpent calculations were carried out using the ENDF/B-VIII.0 [6] based cross section library. 4. Results The collection of three entangled types of results is presented in this paper. The first type of results covers calculated atomic densities of chosen nuclide compared to the infinite lattice approximation. Second type of results represents verification of the calculated atomic densities with aim to determine whether the results are credible or not. The final part of the collection supports the statement that has been gained from the previous type of the results. 4.1. Calculated burnup qualification Visualization of 239Pu atomic density burnup depen- dence has been chosen for the purpose of the calcu- lated fuel burnup qualification. The axially averaged 239Pu concentrations in the fuel as functions of bur- nup are provided in Figure 5. These results are taken from the advanced computational process described in Section 3. The visualization of the data is shown for all fuel assemblies with initial zero burnup at the moment of their first introduction into the LVR-15 reactor core during studied cycles K216–K229. The comparison with the infinite lattice calculated 239Pu atomic densities is also included in Figure 5. 51 Jan Pinta Acta Polytechnica CTU Proceedings 0 20 40 60 80 100 Burnup (MWd/kgU) 0.0e+00 1.1e-06 2.3e-06 3.4e-06 4.5e-06 At om ic d en si ty (1 e2 4/ cm 3) 0.0e+00 1.1e-05 2.3e-05 3.4e-05 4.5e-05 In fin ite la tt ic e At om ic d en si ty (1 e2 4/ cm 3) infinite lattice 85A711 65C666 85A710 65C667 85A712 85A713 85A714 65C668 85A715 65C669 65C672 65C671 65C670 85A716 85A717 65C673 65C675 65C674 85A718 85A719 85A720 65C676 85A721 60C835 60C834 Figure 5. Axially averaged atomic densities of 239Pu calculated for all fuel assemblies with initial zero bur- nup (left axis). The calculated values are compared with atomic densities from the infinite lattice approxi- mation (right axis). 0 50 100 150 1.1e-04 7.5e-04 1.4e-03 U-235 0 50 100 150 5.3e-03 5.4e-03 5.5e-03 U-238 0 50 100 150 0.0e+00 2.3e-05 4.5e-05 Pu-239 0 50 100 150 0.0e+00 3.8e-06 7.6e-06 Pu-241 Burnup (MWd/kgU) At om ic d en si ty (1 e2 4/ cm 3) infinite lattice 85A710 65C666 Figure 6. Comparison of assembly-wise atomic den- sities between the infinite lattice approximation and the unbroken burnup simulation of the opening step of the K216 cycle. Two fuel assemblies, standard 85A710 and control 65C666, has been taken into the account in the latter type of the calculation. Values for 235U, 238U, 239Pu and 241Pu are included. A considerably profound discrepancies between the calculated results and the infinite lattice approxima- tion can be observed in Figure 5. It is apparent that the amount of 239Pu in case of the infinite lattice is one order of magnitude higher than in the results from the LVR-15 reactor operation history computation. The result of such kind raises the immediate demand for a validation of the entire computational process and for a verification of the data as well. The attempt to clarify these incompatibilities is the point of interest of the following type of the results collection. 4.2. Computational process validation The validation of the actual computational process has been carried out based on the previous results. Therefore, two kinds of problems have been compared. First, the burnup calculation of the infinite lattice approximation that was used as a prerequisite for the considered burnup library mentioned in Section 2. Second, an uninterrupted burnup calculation of the LVR-15 reactor core in the initial point of the whole computational process, i.e. the step 0 of the K216 cycle configuration. This comparison also represents the difference in the non-leakage approach against the genuine core configuration calculation with emphasis on high het- erogeneity and compactness of the LVR-15 core. The data from the unbroken calculation of the open- ing step of the K216 cycle involves axially averaged atomic densities of the fresh standard and control fuel assemblies with identifiers 85A710 and 65C666, respectively. Altogether, atomic density plots of 4 nuclides, 235U, 238U, 239Pu and 241Pu, are illustrated in Figure 6. The greatest similarity of the atomic density data is observable in case of 235U. Still, Figure 6 shows that the depletion of 235U is slightly more significant in case of both fuel assemblies from the unbroken cycle simulation. However, the differences for 238U and for both pictured isotopes of plutonium are more exten- sive. The production of plutonium is directly linked to the neutron capture on 238U nuclei. The Figure 6 indicates that there is a noticeably higher amount of 238U capture in the infinite lattice approximation and therefore a lesser concentration of the plutonium isotopes in the fuel assemblies of the comparison K216 cycle calculation. To proceed to the main point of this validation analysis, there is a fundamental assumption that the 239Pu atomic densities should be in the same order of magnitude as the atomic densities determined from the unbroken real core burnup calculation. Such accor- dance, however, has not been achieved. This outcome gives an evidence that some presumption in the de- signed computational process has been applied inaccu- rately. The investigation of the cause of the expressed discrepancies in the computational process is carried out in the following type of the results collection. 4.3. The cause of discrepancies The transfer of fuel composition data between par- ticular steps of the computational process has been investigated as a potentially problematic part in the process design. More accurately, in the determination of which nuclides should be chosen for the conservation of atomic densities from one step to another. Originally, there were 42 chosen nuclides as stated in Table 1. A new calculation concerning a first few steps of the carried out computational process was executed with the change in the number of chosen nuclides. This time, atomic densities of all nuclides in the Serpent cross section library from the end of a particular calculation step have been written into the input data of the following step. Due to this deci- sion, the expected results have changed significantly 52 vol. 37/2022 On the Ongoing Computation of the LVR-15 reactor fuel burnup 0.0 0.2 0.4 0.6 0.8 1.0 Burnup (MWd/kgU) 0.0e+00 6.5e-08 1.3e-07 2.0e-07 2.6e-07 3.3e-07 3.9e-07 At om ic d en si ty (1 e2 4/ cm 3) infinite lattice K216 unbroken 42 nuclides all nuclides Figure 7. Short-term development of 239Pu atomic densities for various calculation types. towards the results that were observed in Figure 6. This behaviour for the case of 239Pu atomic densities is shown in Figure 7. 5. Discussion According to the presented results, a misleading as- sumption in the design of the advanced computational process has been made. It has been investigated that the 42 nuclide representation does not reflect realis- tic conditions in the core during the LVR-15 reactor operation and thus a more comprehensive attitude has to be implemented. Clearly, the consideration of all nuclides available in the Serpent cross section library should be involved in the next generation of the LVR-15 reactor burnup computation. Even though such upgrade of the computational process will require a larger amount of space for the output data storage, running time of the Serpent calculation of a single step will not be affected. This indicates the feasibility of the improvement. On the other hand, the obtained results in Figure 5 shows the differences in the fuel composition based on the individual operation scheme of each fuel assembly. Therefore, the data can be used for analysis of the influence of the various schemes on the final form of the atomic density that will be represented in the burnup library of the LVR-15 reactor Serpent model. 6. Conclusions The Serpent computational model of the LVR-15 re- actor has been introduced in this work with focus on the problematics of fuel burnup implementation. The advanced burnup computational process has been described using the most important aspects and oper- ational characteristics of the LVR-15 reactor. Currently available results have been presented and analyzed according to the additional calculations. The analysis has shown that the number of nuclides con- sidered in the transfers between calculation steps have been chosen inaccurately. This misleading nuclide interpretation has caused significant discrepancies in the atomic density values between the computation and the fundamentally anticipated results from the infinite lattice approximation and from the unbroken burnup calculation of the realistic LVR-15 core. The outcome of this paper will be used in the next generation of the advanced burnup computational process in order to determine a more realistic burnup- wise fuel composition of the LVR-15 reactor. List of symbols keff Effective multiplication factor ENDF Evaluated Nuclear Data File References [1] M. Koleška, Z. Lahodová, J. Šoltés, et al. Capabilities of the LVR-15 research reactor for production of medical and industrial radioisotopes. Journal of Radioanalytical and Nuclear Chemistry 305:51–59, 2015. https://doi.org/10.1007/s10967-015-4025-5. [2] J. Leppänen, M. Pusa, T. Viitanen, et al. The Serpent Monte Carlo code: Status, development and applications in 2013. Annals of Nuclear Energy 82:142–150, 2015. https://doi.org/10.1016/j.anucene.2014.08.024. [3] J. Ernest. Abstract of computational program NODER 2006. [4] J. Leppänen, et al. Serpent – a continuous-energy Monte Carlo reactor physics burnup calculation code. VTT Technical Research Centre of Finland 4, 2013. [5] NEA, OECD. Spent Nuclear Fuel Assay Data for Isotopic Validation 2011. State-of-the-art Report, https://www.oecd-nea.org/science/wpncs/ADSNF/ SOAR_final.pdf. [6] D. Brown, M. Chadwick, R. Capote, et al. ENDF/B-VIII.0: The 8th Major Release of the Nuclear Reaction Data Library with CIELO-project Cross Sections, New Standards and Thermal Scattering Data. Nuclear Data Sheets 148:1–142, 2018. https://doi.org/10.1016/j.nds.2018.02.001. 53 https://doi.org/10.1007/s10967-015-4025-5 https://doi.org/10.1016/j.anucene.2014.08.024 https://www.oecd-nea.org/science/wpncs/ADSNF/SOAR_final.pdf https://www.oecd-nea.org/science/wpncs/ADSNF/SOAR_final.pdf https://doi.org/10.1016/j.nds.2018.02.001 Acta Polytechnica CTU Proceedings 37:48–53, 2022 1 Introduction 2 Serpent model 3 Computational process 4 Results 4.1 Calculated burnup qualification 4.2 Computational process validation 4.3 The cause of discrepancies 5 Discussion 6 Conclusions List of symbols References