Acta Polytechnica CTU Proceedings https://doi.org/10.14311/APP.2022.37.0054 Acta Polytechnica CTU Proceedings 37:54–57, 2022 © 2022 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague REACTOR CRITICALS AND SPENT FUEL SYSTEMS SIMILARITIES Matěj Šikla,b a Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineerings, Department of Nuclear Reactors, V Holešovičkách 2, 180 00 Prague 8, Czech Republic b NRI Řež, a. s., Department of Reactor Physics, Hlavní 130, 250 68 Husinec – Řež, Czech Republic correspondence: matej.sikl@ujv.cz Abstract. Many conservative assumptions for subcriticality assessment calculations have to be made in current calculations of spent fuel storage systems. This is due to a fact that there is no available database of benchmarks containing spent fuel or materials with isotopic composition like spent fuel. However one potential source of spent fuel system experiments is being omitted – there are hundreds of commercial reactors around the world containing spent fuel on some level of burnup. These reactors have to be tested for safety reasons in the beginning of each cycle and parameters of these test states are well known. In this paper a possibility of using commercial reactor critical states for code validations and for subcriticality assessments of storage systems is discussed and potential approach for criticality safety analysis is given. Keywords: Reactor criticals, spent fuel storage systems, calculation similarity, criticality safety analysis. 1. Introduction Spent fuel storage systems subcriticality limit of keff < 0.95 is set in current Czech [1] and many other countries legislation. This limit is usually ful- filled, even though some adjustments and estimations not reflecting real state have to be used when creating storage models. Firstly, due to a lack of credible benchmarks with spent fuel isotopes, currently there is low knowledge about spent fuel model calculations precision and therefore reliable calculations with fresh fuel are usu- ally performed. This also means that calculated keff s are usually higher than reality, because by using of fresh fuel, falling trend of fuel reactivity with raising level of burnup is omitted. Secondly, some conservative assumptions have to be used about neutron absorbers included in system. But if these would be too conservative, not all systems would fulfil the legislative limit. Because of these adjustments, calculations for prov- ing subcriticality of spent fuel storage system are performed on models, which are not perfectly alike to the reality of storages. Subcriticality calculations of storage systems (and even criticality calculations of systems including spent fuel) would be more reliable, if a calculation code and process could be validated on spent fuel experiments. Luckily one possible source of experiments is available – physical and safety start-up tests from beginning of each cycle of commercial reactors in nuclear power plants. States from these tests has sufficiently known parameters to become benchmark experiments, in- cluding mainly exactly known keff = 1 (that is why these states are being referred as "reactor criticals") and precisely measured core parameters from instru- mentation and control system. As was said, there is potential for development of more trustworthy process for spent fuel systems calculations validation. But the first milestone is to verify that reactor criticals and spent fuel systems are sufficiently similar. This is what will be discussed in this paper. 2. Current approach to subcriticality assessment As was already written in the introduction, spent fuel storage systems subcriticality assessments have to be performed based on calculations using fresh fuel iso- topic composition and conservative assumptions. Brief summary of fresh fuel systems experiments available for code validations and generally used conservative adjustments will be given. 2.1. Generally available benchmarks for code validation In an ideal case calculation codes should be validated using benchmarks of same type of systems calcula- tions like the newly projected system it will be applied to. In reality this is impossible for spent fuel storage systems, because benchmarks with spent fuel compo- sition are usually not described in available databases. Few artificially prepared experiments with spent fuel 54 https://doi.org/10.14311/APP.2022.37.0054 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en vol. 37/2022 Reactor Criticals and Spent Fuel Systems Similarities isotopes were described, but these usually has only units of required isotopes and not in atomic density quantities which are typically present in real spent fuel. Therefore validation of calculation codes for any type of calculation is usually performed using fresh fuel experiments only. This approach is not ideal and in case of using it, calculations of models of different types should be penalized. Main source of benchmarks cases with fresh fuel which can be used for validation of calculation codes is International Handbook of Evaluated Criticality Safety Benchmark Experiments (produced by ICS- BEP) [2]. This database contains sets of various cases of different systems from just uranium sphere in mod- erator to simplified minicores (for example VVER reactors type largest available minicore is with 17 fuel assemblies). Isotopic composition for these bench- marks is fresh fuel and closest to real cores of nuclear reactors are systems with fresh MOX fuel, because of Pu included in it (from comparisons in [3]). Summarized from previous text – benchmarks cur- rently used for code validations are not similar to storage systems on sufficient level and therefore not appropriate for spent fuel systems calculations valida- tion. 2.2. Conservative adjustment of models Fresh fuel isotopic composition is used for currently performed spent fuel storage subcriticality assessment. For that case there are two main generally used ad- justments: • omitting of burnable absorbers, • partial boron credit. In newly produced fuel assemblies burnable ab- sorbers (for VVER it is gadolinium in Gd203 mixed to some pins in fuel assembly) are used for flattening of neutron flux profile in fuel assemblies during reactor operation. These absorbers reduces reactivity and therefore have to be removed from model. Technically after few cycles in reactor, their influence is negligi- ble, but since fresh fuel is used in calculation, these absorbers have to be removed to stay conservative. In spent fuel storage pools a boric acid is dissolved to reduce reactivity. Conservatively the boric acid should be completely removed from model, since it reduces reactivity. On the other side, with zero con- centration of the boric acid and fresh fuel isotopic composition, keff of the pool loaded with currently used fuel assemblies from VVER–440 cycles from last years would not fulfil 0.95 keff limit, because of their initial enrichment. Rule of partial boron credit means utilization of 1/3 of a nominal boron concentration in storage models and was permitted by state supervi- sor. With that amount of boron in the pool system, currently used fuel with original enrichment 4.38 % meets limit requirements [4]. 3. Theory of similarities As was often said in previous text, fresh fuel and spent fuel systems are not similar, but it was not said, how similarity can be measured. This section will quantify similarity. For purposes of this paper when talking about the similarity, the similarity of calculations between mod- elled systems is meant. When a model is prepared and calculations are performed, final keff is based on a geometry of model, an isotopic composition and nuclear data. When nuclear data changes (each time individual value from library), it affects keff – value describing size of this change is called "sensitivity" (of keff to variance of nuclear data). Set of this values describes computational behaving of calculation. For similarity assessment sensitivities for each iso- tope, reaction and energy group are needed. Set of these sensitivity profiles is unique for each calculation and if compared with another systems profiles it gives information about how similar these two systems are. SCALE code system [5] includes module TSUNAMI–IP, which is used for comparison of systems based on sensitivities. There are few simi- larity values produced by TSUNAMI–IP comparison, but only similarity coefficient ck will be used in this paper, because it is most complex coefficient of all coefficients available. ck coefficient describes a total similarity between two systems. This value is normalized, therefore 1 means a total computational similarity, 0 means no similarity. Generally value of 0.95 is considered to be sufficient for similarity , but based on [6] ck > 0.8 will be sufficient, if more than 25 experiments with this level of similarity will be available for a comparison and following (sub)criticality assessment (which will not be described in this paper). Experiments with ck < 0.7 are considered to be "highly dissimilar" based on [7]. Main objective of using a similarity comparison and filtering of experiments dissimilar to newly projected system is that validation of code for final calculations of new system (here for example spent fuel system) should not be performed based on dissimilar experi- ments or benchmarks. 4. Reactor criticals states Start–up tests on commercial reactors have to be performed in the beginning of each cycle after loading of new fuel. Timepoint in the beginning of cycle before powering up means that there is no Xe and other short term decay fission products in core, which would bring in additional uncertainty, because they decay during a shutdown when refuelling. During start–up tests, some of states are so called "hot zero power" (which implies, that power in core is considered to be negligible) and some of these start–up tests are critical (keff = 1, from there comes reactor "criticals") – these states (on Figure 1) can be used as experiments and were used in works described in this paper. 55 Matěj Šikl Acta Polytechnica CTU Proceedings Figure 1. Reactor critical fullcore model For reactor criticals all parameters of core are known from instrumentation and control systems. Therefore reactor criticals are experiments on reliability level of benchmarks, just with no detailed description in generally available database. Data for reactor criticals models used for work de- scribed in this paper were taken from a database of operation histories of Czech commercial reactors in Dukovany and Temelin, which is stored in Depart- ment of Reactor Physics, NRI Rez near Prague. This database contains more than 120 reactor critical states from beginnings of cycles with average core burnups within 16 to 26 GWd/tU. 5. Spent fuel storage systems Typical spent fuel storage systems are of two types – casks and pools. In this paper, a VVER–440 stor- age pool filled with Gd2MP with initial enrichment 4.38 % and a VVER–1000 cask CASTOR filled with TVSA–T c44E12 fuel are used for comparison. For calculations of both models are used states when spent fuel in various levels of burnup is loaded and model is filled with water with no boric acid. These states are used conservatively, because these are potentially most reactive states during lifecycle of storage’s intended usage. Visualisations of spent fuel storage models are showed in Figures 2 and 3. 6. Software used in calculations Comparison calculations were performed in TSUNAMI–IP module of SCALE mentioned above, version used was 6.2.3. Sensitivities were calculated in Serpent 2.1.32, because during works it was found that SCALE code (namely TSUNAMI–3D–K6) was not Figure 2. Spent fuel storage pool Figure 3. Spent fuel storage cask CASTOR able to easily calculate such complex system as a fullcore model of a reactor core. Calculations in Serpent 2 can produce sensitivity data, but they are written in format incompatible to SCALE. Therefore a software for preparation of sensi- tivities, which can read sensitivity data from Serpent 2 outputs and prepare sensitivity inputs for TSUNAMI–IP comparison calculations, had to be created. 7. Results of similarity comparison For this work 19 reactor criticals states from vari- ous cycles of Dukovany and Temelin nuclear power plants start–up tests were taken for sensitivity calcula- tion. Storage systems were prepared artificially, with exactly given burnups on various levels. Similarity coefficients were calculated in TSUNAMI–IP and amounts of reactor criticals which are more similar to individual spent fuel storage systems than various ck values can be seen in Tables 1 and 2. 56 vol. 37/2022 Reactor Criticals and Spent Fuel Systems Similarities Fuel burnup Pool Required ck > [GWd/tU] keff 0.8 0.9 0.95 10 0.890 19 18 16 15 0.862 19 19 16 20 0.836 19 19 19 25 0.814 19 19 19 45 0.720 19 6 0 Table 1. Amounts of reactor criticals with ck sim- ilarity higher than 0.8, 0.9 and 0.95 to pool storage systems in various levels of burnup. From Table 1 can be seen, that for the storage pool there are plenty of sufficiently similar available reactor criticals experiments. In future subcriticality assess- ments of spent fuel storage pool, it will be possible to validate calculation codes based on reactor criticals states. Fuel burnup CASTOR Required ck > [GWd/tU] keff 0.7 0.75 0.8 5 0.801 5 1 0 15 0.796 9 4 0 25 0.744 13 6 0 45 0.649 10 4 2 Table 2. Amounts of reactor criticals with ck sim- ilarity higher than 0.7, 0.75 and 0.8 to storage cask CASTOR systems in various levels of burnup On the other side CASTOR (as can be seen from Table 2) has less sufficiently similar systems. That could be for example due to a pitch between fuel assemblies or support construction itself. Current results for these sets of CASTOR and reactor criticals models are not similar enough for reliable calculations for subcriticality assessment. Anyhow by comparisons presented in this section is shown that calculating states from the reactor criticals database is possible and that they are more similar to spent fuel systems than usually used fresh fuel systems are. 8. Conclusions As was described in the beginning of this paper, cur- rent approach to calculations of spent fuel systems is not considered to be optimal. Conservative assump- tions have to be made, using these it is not automatic to fulfil legislative limits, and credit of burnup lower- ing reactivity is not used. Non-using of burnup credit is mainly due to fact, that there is a lack of spent fuel systems for validation. In this paper the lack is resolved by using reactor critical states from start–up tests of commercial nuclear reactors. Similarities between reactor criticals and spent fuel storage systems were compared using TSUNAMI–IP module from SCALE code system. Based on this comparison it was shown that code validated using reactor criticals would be eligible for calculations of storage pools, but not so adequate for CASTOR cask calculations. Even though similarities were high enough to stor- age pool only, possibility of validation of code for spent fuel systems calculation was proved when reac- tor criticals were used. Generally it was shown and is suggested that codes can and should be validated based not only using fresh fuel benchmarks, but also using reactor criticals states. Acknowledgements Work presented in this report was supported by TAČR grant TK02010136. References [1] Vyhláška č. 329/2017 Sb. O požadavcích na projekt jaderného zařízení, 2017. [2] International Handbook of Evaluated Criciality Safety Benchmark Experiments. NEA/NSC/DOC(95)03, OECD, NEA No. 7382, 2016. [3] M. Šikl. Stanovení neurčitosti ve výpočtech kritičnosti s využitím metodiky TSUNAMI. Master’s Thesis, Department of Nuclear Reactors, FNSPE, CTU in Prague, 2018. http://hdl.handle.net/10467/77139. [4] M. Gren, L. Marková. Průkaz podkritičnosti dolní kompaktní mříže bazénu EDU s implementací PBC při zavezení palivem Gd-2M. UJV Z – 3732, 2013. [5] B. Rearden, M. Jessee, et al. SCALE Code System, ORNL/TM-2005/39, Version 6.2.2. Oak Ridge National Laboratory, Oak Ridge, Tennessee, 2017. [6] B. Broadhead, B. Rearden, C. Hopper, et al. Sensitivity- and Uncertainty-based Criticalitz Safety Validation Techniques. Nuclear Science and Engineering: 146, pp. 340–366, 2004, https://doi.org/10.13182/NSE03-2. [7] B. Rearden, M. Williams, M. Jessee, et al. Sensitivity and Uncertaintz Analysis Capabilities and Data in SCALE. Nuclear Technology, 174:2, pp. 236–288, 2011, https://doi.org/10.13182/NT174-236. 57 http://hdl.handle.net/10467/77139 https://doi.org/10.13182/NSE03-2 https://doi.org/10.13182/NT174-236 Acta Polytechnica CTU Proceedings 37:54–57, 2022 1 Introduction 2 Current approach to subcriticality assessment 2.1 Generally available benchmarks for code validation 2.2 Conservative adjustment of models 3 Theory of similarities 4 Reactor criticals states 5 Spent fuel storage systems 6 Software used in calculations 7 Results of similarity comparison 8 Conclusions Acknowledgements References