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(1)Faculty of Physics and Applied Computer Science. Doctoral thesis. Przemysław Stanisz. Lead cooled reactor neutronic study towards verification of nuclear data and modelling methodology for nuclear transmutations. Supervisor: dr hab. Jerzy Cetnar, prof. AGH Department of Nuclear Energy, Faculty of Energy and Fuels AGH University of Science and Technology. Cracov, 2017.

(2) Declaration of the author of this dissertation: Aware of legal responsibility for making untrue statements I hereby declare that I have written this dissertation myself and all the contents of the dissertation have been obtained by legal means. data, podpis autora. Declaration of the thesis Supervisor: This dissertation is ready to be reviewed.. data, podpis promotora rozprawy.

(3) ©Copyright by Przemysław Stanisz 2017 All Rights Reserved. Author: Przemysław Stanisz Department of Nuclear Energy Faculty of Energy and Fuels AGH University of Science and Technology Al. Mickiewicza 30, Cracow 30-059, Poland e-mail: pstanisz@agh.edu.pl. Supervisor: Professor Jerzy Cetnar Department of Nuclear Energy Faculty of Energy and Fuels AGH University of Science and Technology Al. Mickiewicza 30, Cracow 30-059, Poland e-mail: cetnar@ftj.agh.edu.pl. Polish title of the Ph.D. Thesis: Studium fizyki neutronów reaktora chłodzonego ołowiem w celu weryfikacji danych jądrowych, oraz metodologii modelowania dla transmutacji jądrowej.

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(5) Acknowledgments. I am grateful to my supervisor Professor Jerzy Cetnar for his guidance, great scientific support and very valuable suggestions. Author owes a gratitude to many supportive persons from the University of Science and Technology. In particular, author expresses his thanks to Professor Jerzy Janczyszyn for his comments of nuclear reactor physic. Author also thanks Grzegorz Kępisty for his interest and enthusiasm initiating discussion on presented method. Author wishes to thank Marek Biduś for cooperation over the first results. I am obliged to thank the supportive staff of the Department of Nuclear Energy, in particular, to Prof. Stefan Taczanowski, Prof. Ludwik Pieńkowski, Dr Grażyna Domańska, Dr Władysław Pohorecki and Dr Mariusz Kopeć for their guidance during my graduate and PhD studies. My special thanks for friends from my department, Dr Mikołaj Oettingen, Dr Paweł Gajda, Dr Igor Królikowski, Michał Orliński, Mateusz Malicki, Katarzyna Skolik for providing a nice working atmosphere. Considerable personal thanks go to my wife Katarzyna for her substantial support during my studies. Przemysław Stanisz.

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(7) Abstract The highest efficiency in the usage of nuclear energy resources can be implemented in fast breeder reactors of Generation IV. It is achieved thanks to the ability of consuming minor actinides in the production of energy. One of the possibilities of using this benefit is full recycle of minor actinides in order to close the nuclear fuel cycle. The Monte Carlo Burnup (MCB) is an integrated Monte Carlo burnup calculation code which deals with the complexity of the burnup process and which is applied to the European Leadcooled Fast Reactor (ELFR). It copes with continuous energy representation of cross section and spatial effects of full core reactor model, yet it automatically calculates nuclide production in all possible reactions or decay channels. Monte Carlo burnup calculation solves the depletion problem by describing the evolution of the nuclide composition over time. The formation of new isotopes can take place due to natural radioactive decay or due to nuclear reactions induced by neutrons (or other particles). The depletion problem is described by the first-order differential equation, known as the Bateman equation. This problem can be solved by using the linear chain approach, where linear chains represent series of physically occurring nuclide transitions. Transition chains preserve the entire quantitative information about the transmutation process. Consequently, reaction rates in the depletion problem are time-dependent, therefore the procedure is performed in calculation steps. In this way, the properties in which transmutation chains are described by the transition and passage functions after more than one step are lost. The new proposed approach described in the thesis introduces a method which extends the representation of formed trajectory sets described by the transition and passage functions beyond one step. Trajectories prepared for each computational time step are combined in the period folding procedure, enabling the representation of the nuclide field evolution for a broader time interval. This procedure responds to the trajectory period folding methodology. It can be recursively repeated by adding consecutive steps obtained through the standard solution in order to build time-dependent physical evolution of transmutation chains and observe the simulated system with a new specific tool. The novel folding-period method is implemented into the MCB code. In the thesis, aside from the mathematical description, graphical representation of trajectory periodfolding is presented using the parent pointer tree data structure..

(8) As a dedicated task of this study, an extended analysis of nuclear transmutation in the ELFR core designed as a self-breeder was performed. In the so-called adiabatic fuel cycle, the reactor consumes only depleted uranium supplied from the outside and produces fission products. The approach to its equilibrium state is achieved thanks to a specially prepared fuel scheme. The MA multi-recycling can cause an intensified buildup of safety-related isotopes. Some of those isotopes are strong alpha emitter (generating heat) or neutron emitters from spontaneous fission, which hinders the process of reprocessing. The implementation of the novel methodology for trajectory period folding allows us to trace the life cycle of crucial minor actinides from the beginning of reactor life towards the state of adiabatic equilibrium. The results of the performed analysis are presented, showing the sources of strong contribution to the neutron production rate, which helps with verification of nuclear data and modeling methodology for nuclear transmutation. Additionally, parametric sensitivity analysis method for selected reactions is carried out, revealing sensitivity of transmutation chains for production of neutron-emitter isotopes. In order to perform the required calculations, a new computer tool was developed by the author. The algorithm was written using the FORTRAN language. For the needs of fuel cycle calculation, high precision results are required. For that reason, the implementation of the MCB codes is performed on the supercomputer PROMETHEUS cluster at ACK Cyfronet AGH..

(9) Streszczenie Wysoka efektywność w wykorzystaniu zasobów paliw jądrowych może być zaimplementowana za pomocą prędkich reaktorów jądrowych IV generacji. Jest to możliwe do osiągnięcia dzięki wypaleniu wszystkich aktynowców w procesie produkcji energii cieplnej. Jedną z opcją w realizacji tej korzyści jest pełny recykling aktynowców i zamknięcie jądrowego cyklu paliwowego. MCB (Monte Carlo Burnup) jest zintegrowanym kodem obliczeń Monte Carlo i ewolucji paliwa, który został użyty przy symulacji złożonych procesów jądrowych zaaplikowanych w europejskim prędkim reaktorze jądrowym chłodzonym ołowiem (ELFR – the European Lead-cooled Fast Reactor). MCB radzi sobie z ciągłą reprezentacją energetyczną przekrojów czynnych, efektami przestrzenymi całego rdzenia, jak również posiada zautomatyzowany algorytm wyliczający produkcje wszystkich możliwych kanałów reakcji transmutacji jądrowych. Obliczenia Monte Carlo wraz z obliczeniami wypalenia paliwa mają na celu rozwiązanie problemu przewidzenia kompozycji paliwa dla odpowiedniego punktu czasowego. Wytwarzanie nowych nuklidów może odbywać się poprzez naturalne procesy rozpadu promieniotwórczego, jak również w wyniku transmutacji wywołanych przez reakcje z neutronami (i inne cząstki). Rozwiązanie problemu ewolucji paliwa jest opisane równaniami różniczkowymi pierwszego rzędu znanymi jako równania Batemana. Zdefiniowane równania różniczkowe mogą być rozwiązane dzięki użyciu metody liniowych łańcuchów. W metodzie tej otrzymywane łańcuchy transmutacji nuklidów reprezentują bezpośrednio fizycznie zachodzące procesy następujących po sobie reakcji jądrowych. Łańcuchy transmutacyjne zachowują całkowitą ilościową wiedzę na temat ewolującego paliwa jądrowego. W następstwie konsekwencji, że wykorzystywane do tych obliczeń wydajności reakcji są zależne od czasu, procedura obliczająca wypalenie paliwa musi być przeprowadzona w krokach obliczeniowych. Postępując tak, informacje o wydajności reakcji, jak również zestawu trajektorii potrzebnych do opisu łańcuchów transmutacji po jednym kroku obliczeniowych są tracone. W prezentowanej pracy zaproponowano i opisano nowe rozwiązanie, które pozwala na rozszerzenie reprezentacji ewoluowanego paliwa za pomocą zestawu trajektorii poza jeden krok obliczeniowy. Trajektorie przygotowywane dla każdego kroku obliczeniowego są łączone w specjalnej procedurze składania okresów, co pozwala reprezentować ewolujące paliwo przez łańcuchy transmutacyjne w większym przedziale czasowym. Procedura ta może być rekursywnie powtarzana poprzez dodawanie kolejnych kroków obliczeniowych otrzymanych w wyniku standardowego rozwiązania w celu budowy fizycznej ewolucji paliwa. Nowa metoda pozwala na śledzenie zmian nie tylko samych koncentracji nuklidów, które są następstwem fizycznie zachodzących przemian transmutacyjnych, ale również na śledzene ewolucji tychże przemian opisanych poprzez trajektorie, co daje nam nowe narzędzie w analizie cyklu paliwowego. Nowa metoda została zaimplementowana przez autora w kodzie MCB. W tej pracy poza matematycznym opisem pokazany jest graficzny sposób implementacji alogrytmu poprzez reprezentacje struktury danych w formie drzewa..

(10) Projektem dedykowanym nowej metodzie jest model rdzenia ELFR, zaprojektowany jako samo powielający się reaktor. W tak zwanym adiabatycznym cyklu paliwowym rdzeń taki zużywa tylko zubożony uran dostarczany z zewnątrz i produkuje tylko produkty rozszczepienia. Dojście do stanu równowagowego paliwa jest symulowane poprzez specjalnie dobrany schemat tasowania paliwa opisany w pracy. Analizowane w pracy wieloktrotny przerób paliwa może powodować produkcje izotopów wpływających na bezpieczeństwo rozwijanej koncepcji. Niektóre z izotopow są silnymi emiterami netronów otrzymywanych w wyniku reakcji spontanicznego rozszczepiena. Produkcja takich izotopów utrudnia proces przetwarzania paliwa. Implementacja nowej metody analizującej trajektorie dla złożonych przedziałów czasowych pozwala nam na śledzenie cyklu powstawania istotnych aktynowców od uruchomienia aż do osiągnięcia paliwa równowagowego. Wyniki z przeprowadzonej analizy wskazują źródła silnego wkładu do produkowanego źródła neutronów. Nowa metoda jest w stanie pomóc w weryfikacji danych jądrowych i poprawie modelowania transmutacji jądrowych. Dodatkowo praca prezentuje analizę perturbacji dla wybranych reakcji, ukazując wrażliwość istotnych trajektorii na tworzenie źródła nuklidów związanych z bezpieczeństwem. W celu przeprowadzenia koniecznych obliczeń odpowiednie algorytmy numeryczne zostały stworzone i zaimplementowane w programie MCB za pomocą języka FORTRAN. Analizowane cykle paliwowe posiadają duże zapotrzebowanie na zasoby obliczeniowe, co jest związane z potrzebą analizy całego rdzenia z dużą precyzją odzwierciedlenia. Z tego powodu implementacja zmodyfikowanej wersji MCB została dostosowana i uruchomiona na superkomputerze PROMETHEUS znajdującym się w Akademickim Centrum Komputerowym Cyfronet AGH..

(11) Contents 1 Introduction................................................................................................... 17 1.1 Background............................................................................................ 17 1.2 Research & Development....................................................................... 19 2 Fast-neutron Reactors – Design considerations......................................... 23 2.1 The European Lead Fast Reactor........................................................... 23 2.2 Fundamentals of the technology............................................................. 24 2.3 Reactor plant configuration and safety systems..................................... 27 2.4 Core design considerations..................................................................... 29 2.4.1 The ELFR core & barrel................................................................. 31 2.4.2 A fuel bundle................................................................................... 31 2.4.3 Reflector (In-vessel Shielding)....................................................... 32 2.4.4 Control & Shutdown rods............................................................... 33 2.5 Adiabatic equilibrium core concept....................................................... 35 2.5.1 Meaning of fuel cycle strategy........................................................ 35 2.5.2 Adiabatic equilibrium fuel cycle concept....................................... 36 2.5.3 Fuel cycle conditions...................................................................... 37 2.6 ELFR adiabatic cycle modeling method using MCB............................. 39 2.6.1 Introduction..................................................................................... 39 2.6.2 Core configuration.......................................................................... 39 2.6.3 2-batch core & distribution of the fissile material.......................... 40 2.6.4 Adiabatic procedure using MCB.................................................... 42 3 Time evolution of nuclide concentrations................................................... 45 3.1 Description of the nuclide evolution process......................................... 45 3.2 Time treatment of the generalized Bateman equation............................ 49 3.3 Solution of the burnup equation............................................................. 51 3.3.1 Matrix Exponential Method............................................................ 51 3.3.2 Linear chain method....................................................................... 52 3.4 Bateman Equation solution using the linear chain method.................... 53 3.4.1 The transmutation trajectory analysis............................................. 53 3.4.2 Bateman equations for a serial decay chain.................................... 54 3.4.3 Transmutation constants for the linear chain method..................... 55 3.4.4 Bateman equations for transmutation chain.................................... 56 3.4.5 General solution of Bateman equations.......................................... 57 3.4.6 Transmutation trajectory analysis................................................... 58 3.4.7 Numerical generation of transmutation trajectories........................ 59 3.4.8 Fission product & emitted particles................................................ 61 3.5 Case study – TTA................................................................................... 63 3.6 Mathematical formation of the equilibrium state................................... 66 3.7 Summary ............................................................................................... 70 4 The trajectory periods folding method....................................................... 71 4.1 Introduction............................................................................................ 71 4.2 Transition matrix of a folded period....................................................... 72 4.3 Transition trajectories period folding..................................................... 74 4.4 Passage trajectories period folding......................................................... 78 4.5 Other properties...................................................................................... 81 4.6 Case study – period folding.................................................................... 82 4.7 Computer science................................................................................... 87 4.7.1 Trajectory transition data structure................................................. 87 4.7.2 Realization of the trajectory period folding procedure................... 88.

(12) 4.8 Verification of neutron burnup calculations........................................... 90 4.8.1 Introduction.................................................................................. 90 4.8.2 Sensitivity and uncertainty........................................................... 92 4.8.3 Parametric sensitivity analysis methods for option studies......... 94 4.8.4 The replica Monte Carlo simulation............................................ 96 4.8.5 Definition of statistical uncertainties........................................... 97 4.9 Software & Hardware............................................................................ 99 4.10 Summary and discussion......................................................................101 5 Nuclear transmutation for individual MA mass evolution.......................103 5.1 Introduction...........................................................................................103 5.2 Criticality evolution...............................................................................105 5.3 Nuclide mass flow in transmutations....................................................107 5.3.1 Equilibrium compositions...........................................................107 5.3.2 Uranium-234...............................................................................109 5.3.3 Uranium-235...............................................................................111 5.3.4 Uranium-236...............................................................................112 5.3.5 Uranium-238...............................................................................113 5.3.6 Neptunium-237...........................................................................114 5.3.7 Plutonium-238.............................................................................115 5.3.8 Plutonium-239.............................................................................116 5.3.9 Plutonium-240.............................................................................117 5.3.10 Plutonium-241.............................................................................118 5.3.11 Plutonium-242.............................................................................119 5.3.12 Plutonium-243.............................................................................120 5.3.13 Americium-241...........................................................................121 5.3.14 Americium-242m........................................................................122 5.3.15 Americium-243...........................................................................123 5.3.16 Curium-242.................................................................................124 5.3.17 Curium-243.................................................................................125 5.3.18 Curium-244.................................................................................126 5.3.19 Curium-245.................................................................................128 5.3.20 Curium-246, 247, 248.................................................................129 5.4 Higher Curium and Californium Generation.........................................132 5.4.1 Berkelium-249............................................................................133 5.4.2 Californium-249..........................................................................134 5.4.3 Californium-250..........................................................................135 5.4.4 Californium-252..........................................................................136 5.5 Neutron source......................................................................................137 5.6 Summary...............................................................................................140 6 Trajectories evolution..................................................................................143 6.1 Introduction...........................................................................................143 6.2 Transformation chains to 238Pu..............................................................145 6.2.1 Trajectories from 241Am to 238Pu....................................................145 6.2.2 Trajectories from 240Pu to 238Pu......................................................147 6.2.3 Trajectories from 238U to 238Pu........................................................148 6.2.4 238Pu-Total production....................................................................150 6.3 Transformation chain to 244Cm..............................................................151 6.3.1 Trajectories from 240Pu to 244Cm.....................................................152 6.3.2 Trajectories from 238U to 244Cm......................................................155 6.3.3 244Cm-Total production..................................................................158.

(13) 6.4 Transformation chain to 252Cf................................................................160 6.4.1 Trajectories from 242Pu and 243Am to 252Cf.....................................161 6.4.2 Trajectories from 243Am to 252Cf.....................................................163 6.4.3 252Cf-Total production....................................................................164 6.5 Summary...............................................................................................165 7 Parametric sensitivity analysis....................................................................167 7.1 Introduction...........................................................................................167 7.2 Reaction importance in folded trajectories............................................168 7.3 Results for selected trajectories.............................................................171 7.4 Sensitivities coefficients and Conclusions............................................177 8 Conclusions...................................................................................................181 8.1 Summary...............................................................................................181 8.2 Conclusions...........................................................................................182 8.3 Recommendation for future work.........................................................183 References..........................................................................................................185 APPENDIX A.....................................................................................................193 APPENDIX B.....................................................................................................195 APPENDIX C.....................................................................................................198.

(14) Major nomenclature ALFRED ADS BOC BOL DHR EC ELFR ELSY ENDF EOC EOL FP GEN-IV GIF HM IC IAEA JEF JEFF JENDL JRC LBE LEADER LFR LWR MA MCB MCNP MOX MPI NEA OECD PWR UOX SFR SG TPF TRU TTA XS. Advanced Lead Fast Reactor European Demonstrator Accelerator Driven System Beginning of Cycle Beginning of Life Decay Heat Removal European Commission European Lead-Cooled Fast Reactor European Lead Fast Reactor Evaluated Nuclear Data File End of Cycle End of Life Fission Product Generation IV nuclear reactors The Generation IV International Forum Heavy Metal Isolation Condenser International Atomic Energy Agency Joint Evaluated File Joint Evaluated Fission and Fusion Japanese Evaluated Nuclear Data Library Joint Research Center Lead Bismuth Eutectic Lead-cooled European Advanced DEmonstration Reactor Lead Fast Reactor Light Water Reactor Minor Actinides The Monte Carlo Continuous Energy Burnup Code A General Monte Carlo N-Particle Transport Code Mixed Oxide Fuel Message Passing Interface Nuclear Energy Agency Organization for Economic Co-operation and Development Pressurized Water Reactor Uranium Dioxide Fuel Sodium Fast Reactor Steam Generator Trajectory Period Folding TRansUranic element Transmutation Trajectory Analysis Code Cross Section.

(15) Radioactive displacement law of Fajans and Soddy. Kazimierz Fajans (1887–1975). Kazimierz Fajans (1887–1975) was a Polish physicist and chemist, a pioneer in the science of radioactivity. He was researching properties of the radioactive rows. He identified the half-lives of the uranium-actinium row and thorium nuclides. He discovered the phenomenon of the electrochemical branching of the radioactive rows. Independently of other physicist Frederick Soddy in 1912 he discovers and formulated the law of the radioactive shifts which was later named the radioactive displacement law of Fajans and Soddy. Together with Oswald Helmuth Göhring, he discovered in 1913 the radionuclide of a new element named brevium, which was later re-called protactiniumin. This outstanding physical chemist was very close to the Nobel Prize. In 1924 his candidacy – both awards in chemistry and physics – had been offered to the Nobel committee. He was considered as the most serious candidate. He was expected to win in both subjects. The Swedish magazine "Svenska Dagbladet" asked Fajans to send them a photo of his to announce his “victory”. On the day before the date when the Committee was to make the decision, the Swedish magazine had already written that Fajans had won the prize. The next day the Committee announced that no prize in either in chemistry nor physics was to be awarded that year. The Academy wanted to punish the Swedish magazine for the lack of discretion. Fajans’ candidature was later offered twice, but without a result. He was a member of the Polish Institute Of Arts and Sciences in America and of many societies and academies [1]. This thesis refers to a sequential series of transformation which are described by a series of radioactive decay or neutron-induced transmutation. Both type or reaction are described with the law of radioactive displacements, also known as Fajans and Soddy law. In radiochemistry and nuclear physics, it is a rule governing the transmutation of elements during radioactive decay. The law describes which chemical element and isotope is created during the particular type of radioactive decay [2]. At this point I would like to recall the person of Kazimierz Fajans. As one of many Polish contribution to the development of nuclear physics research.. alpha decay: decay decay: neutron abs.:. Displacements resulting from various transmutation of a radionuclide..

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(17) Chapter 1. Introduction 1.1 Background After the COP 21, the global community made a clear message about greenhouse gas reduction. An agreement between 195 countries was signed. The signatories claimed they would do their best to keep global warming below 2 degrees Celsius [3]. The decision was taken under the circumstances in which global power installed capacity is predicted to double by 2050 from 396 GW to 930 GW [4]. It appears likely that in the future, the role of the nuclear power as a low-carbon energy technology for sustainable development will increase. Actually, some people claim that this vision has already become the reality. About sixty reactors in 15 countries were under construction in the first quarter of 2016, which can be seen as the beginning of positive prospects for nuclear energy. From the techno-economic point of view, these numbers will drive the uranium fuel demand. A simple projection of the current rate of uranium consumption by the existing nuclear power plants shows that the discovered conventional resources of uranium will be exhausted in 120 years’ time. Reprocessing of Mixed oxide fuel may increase the uranium resources and extend this period to 300 years [5]. Different scenarios forecast that the exploration of new uranium resources at a higher price will drive the technological demand for wide deployment of advanced reactor technologies, particularly Fast Neutron Reactors, together with new fuel cycles. However, future nuclear capacity is very hard to establish and this is the basis for the global analysis of economy and uranium resources. The global community takes action within the ongoing research and development (R&D) programs sufficient to foster the innovation in nuclear fission technologies which will meet future needs and will be able to utilize even depleted uranium resources, thus increasing total uranium availability for the supply industry by over 8,500 years [6].. Fig. 1.1. Generations of nuclear power: Time ranges correspond to the design and the first deployments of different generations of reactors. 17.

(18) One of the leading initiatives is The Generation IV International Forum (GIF) [7] with the intention to deploy a new type of nuclear system by 2030. The Technology Roadmap [8] established six potential systems including the innovative type of nuclear reactor connected with the necessary fuel cycle technologies. All of the presented concepts should ensure:  sustainability: The designs should provide sustainable energy production providing more efficient use of nuclear fuel and at the same time notably reducing long-term radioactive materials and associated waste;  safety and reliability: The designs will excel in safety and reliability, having a very low likelihood and degree of reactor core damage and no need for off-site emergency response by taking advantage of the use of passive safety systems;  economic competitiveness: The designs should have clear life-cycle cost advantage and low financial risk compared with other energy sources;  proliferation resistance: The design is a very unattractive target for acquisition of weapon-usable materials and it ensures physical protection. According to the GIF 2014 updated Roadmap [9], four technologies are most likely to be demonstrated at the level of constructed prototype. They include Sodium-cooled Fast Reactor (SFR), Lead-cooled Fast Reactor (LFR), SuperCritical Water-cooled Reactor (SCWR) and Very High Temperature Reactor (VHTR). Two of the aforementioned reactor systems are fast reactors in which the fission chain reaction is sustained by fast neutrons, thus no neutron moderator is needed. The main advantages of those fast reactors are better use of fuel and improved waste management, which reduces long-term radiotoxicity. With the same amount of uranium, fast nuclear reactors can produce over 60 times more energy than the reactors of current nuclear generation, which are based on thermal neutrons. Fast systems have a long history of development all over the world, although at the beginning they lost competitiveness against thermal reactors as a result of some technical and material problems, as well as geological exploration showing that uranium shortage would not be an issue for some time. Nowadays, the interest in Fast Nuclear Systems has increased again as they may offer substantial benefits in terms of sustainability, cost-efficiency, safety, reliability and proliferation resistance. A brief overview of the development of those two fast technologies in Europe is presented in order to show the context of the author's work. SFR The technology has been developed in Europe mainly in France, where it was confirmed and established in the projects Phénix and Super-Phénix. Nowadays, new SFR demonstration units are being designed (under the aegis of different EURATOM collaboration programs): for near-term deployment – 600 MWe ASTRID (Advanced Sodium Technological Reactor for Industrial Demonstration) prototype, and in long-. 18.

(19) term (around 2040) – 1500 MWe core for industrial deployment, the ESFR (European Sodium Fast Reactor) technology. LFR The technology is derived from successively operated Pb-Bi cores placed in “Alpha Class” Submarines in the Soviet Union and numerous European experimental test loops using Lead and Pb-Bi. Currently, a demonstrator called ALFRED (the Advanced Lead Fast Reactor European Demonstrator), which Romania wishes to build on its territory by 2025, is being developed under a EU initiative. This project is seen as a prelude to an industrial demonstration unit of about 600 MWe ELFR (European Lead-cooled Fast Reactor). Lead-cooled technology is also designed by SCK-CEN in Belgium where the activities on MYRRHA (Multi-purpose hYbrid Research Reactor for High-tech Applications) are conducted.. 1.2 Research & Development The main objective of the Technology Roadmap Update formulated by the Generation IV (GEN IV) International Forum [9] concerns R&D and prototype/technology demonstration needs in the near term (approximately 10 years). One of the conceptual efforts concerning the implementation of commercial lead and sodium cooled reactor technology will concentrate on closing of the nuclear fuel cycle and actinides management. A fuel cycle based on reprocessing and partitioning of spent nuclear fuel and management of each fraction with the best possible strategy makes it possible to reduce the radiotoxicity for the disposal of ultimate waste. The progress of this kind of analysis depends mainly on the quality of research and design tools used, and on the development of the Transuranium elements separation technologies for Generation IV system. Their improvement is possible through advancement and development of theoretical and computational models, together with subsequent validation of theoretical and experimental benchmarks. This procedure is strongly recommended and supported by working groups such as NEA OECD, IAEA or JRC. Large part of the presented work discusses problems related to efforts undertaken in order to carry on the investigation of fast nuclear core performance. This investigation is conducted on the European Lead-cooled Fast Reactor (ELFR). An example of this particular type of design was carried out by me as a part of research activities of the 7th Framework Program (FP7) LEADER (Lead-cooled European Advanced Demonstration Reactor) project [10]. The definition of the ELFR core is presented with its adiabatic cycle properties that are characterized by fuel zero breeding. The assessment of core physics is performed in order to identify the core features related to the fuel cycle characterization that leads to the refining of the neutronic and fuel cycle modeling methodology. The final configuration is presented with an improved core configuration in terms of burn-up performance. The analysis includes burn-up calculations in fewbatch fuel reloading multi-cycle during its evolution from the Beginning of Life (BOL). 19.

(20) to the equilibrium state. The assessment of core physics is done through the power distribution characterization together with its evolution that influences the burn-up performance. This assessment was possible thanks to the establishment of fuel distribution in the core and modeling of the control rod arrangement, due to its influence on the neutron flux and spectrum during the fuel cycle. Fuel distribution in the core is done by the annular void zoning in the fuel pins proposed by ENEA and JRC. Fuel zoning was designed by using different fuel pellet annular void as an alternative way to the MOX enrichment zoning. The works were performed in a full core calculation model with robust and reliable numerical tools. The Monte Carlo method is the base of the analysis performed in this thesis. Nowadays, this method is widely used in various reactor physics applications. The importance of Monte Carlo calculations is likely to increase in the future, along with the development of computer capacities and parallel calculation. This method can reproduce results traditionally related to criticality safety analyses and it is able to calculate the reaction rates of given nuclear reaction. The main feature of the Monte Carlo method is that the results are provided with the statistical approximation, with the capacity of possible calculation of static or dynamic core behavior. In this thesis I use a special feature of the MCB (Monte Carlo Continuous Energy Burn-up) [11] code, which is the capability to perform burn-up calculation. The MCB code is internally integrated with the wellknown MCNP (Monte Carlo N-Particle Transport Code) code [12]. This software package for nuclear processes has been developed since at least 1960s. MCNP is considered as one of the most advanced and best validated codes for neutron transport available for the variety of neutron, photon and electron transport problems. Hence, including transmutation trajectory analysis, we hold state-of-the-art neutronics software with point depletion module which presents a fully integrated Monte Carlo Burn-up simulation code – MCB. The goal of this doctoral thesis is a detailed analysis of nuclear cross-section impact (which satisfies the adiabatic condition in Lead-cooled Nuclear Fast System) on formation of trajectories and transmutation/decay chains process, having a direct impact on transmutation inside nuclear fuel. This work has been done through Sensitivity Analysis (SA) theory combined with the novel theory based on folding nuclides trajectories formation. The aim of the work is identification of the gateway isotopes in the fuel transmutation process, which are responsible for the creation and build-up of neutron source isotopes in the discharged fuel composition, such as Cm, Bk and Cf. Their detection is possible through establishing joint representation of the set of linear chains of the system. Later, in the second part, the sensitivity analysis of those chains is performed in order to indicate the most sensitive cross-section for the neutron energy spectrum. This is performed through propagation of small changes in the cross-section into the depletion calculation, in order to identify formation of crucial Minor Actinides along with adiabatic multi-cycling towards reaching the fuel equilibrium state. As a result of the calculation performed, the developed methodology may be available for verification and validation of the nuclear libraries with experimental measurements in 20.

(21) order to improve cross-section reliability. The presented work has a potential to improve the future planning of fuel management through reduction of the cross-section uncertainty and subsequent reduction of the neutron source term, which will positively affect the safety of the nuclear fuel cycle facilities. This methodology has not been presented until now. It introduces novel mathematical approach to the transmutation analysis. In addition, the presented methodology may lead to the extension of the engineering tools for industrial and licensing applications.. 21.

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(23) Chapter 2. Fast-neutron Reactor – Design considerations 2.1 The European Lead Fast Reactor The European collaboration of lead-cooled fast reactors started within the Framework Programs (FPs) for research and technological development, created by the European Commission (EC). Initial developments were preceded by the background research on post-irradiation and testing materials experiments. The following line of action is focused on several EC-sponsored projects dedicated to Lead-Bismuth/Lead-cooled subcritical systems called Accelerator Driven Systems (ADS), such as PDS-XADS, EUROTRANS, etc. The studies have provided a lot of experience in the selection of structural materials. The proposed materials have met the demands of high neutron irradiation and temperature. A lot of information was obtained on erosion and corrosion caused by liquid lead. A security and prevention strategy regarding lead chemistry was proposed. The main approach used to reduce the corrosion was the limitation in lead flow velocity and strategy on oxygen control. The conclusions from these studies have shown a new direction for research, dedicated to technical design of a lead-cooled fast critical reactor. Since these initial efforts, an industrial-sized reference plant has been proposed by the ANSALDO and follow-up R&D activities have been concentrated on the lead-cooled fast reactors within the European Lead Fast Reactor (ELSY) 6th FP. The ELSY project tried to design an innovative lead-cooled reactor which would be safe and cost-competitive to the current LWRs. The first reference configuration concerns an industrial size (600 MWe) of pool-type reference plant, the European Lead Fast Reactor (ELFR). The core was characterized by simplicity and compactness, resulting in a capital cost reduction. The ELFR design made progress towards achieving GEN IV goals, such as sustainability, cost-efficiency, safety and reliability, proliferation resistance and physical protection.. Fig. 2.1. Overall of Reactor Vessel and Support assembly 23.

(24) The ELFR design was studied with two different core options: open square and closed hexagonal assembly arrangement. The studies include different fuel cycle strategies. Both options have been studied with the cooperation of the AGH University of Science and Technology in Krakow. The studies have analyzed only single-batch once-through fuel cycle for the understanding of fuel behavior under fast neutron spectrum. The established version of the ELFR plant has been continued within the LEADER (Leadcooled European Advanced Demonstration Reactor) 7th FP project. After an in-depth review of the ELSY results, proven and already available solutions were adopted in order to construct a scaled down ELFR plant, which would be as close to the reference as possible. The demonstrator ALFRED (Advanced Lead Fast Reactor European Demonstrator) was proposed as a 300 MWth pool system, providing a technically feasible product. During the LEADER project kick off meeting it was decided to resign from the open square option and adopt for ALFRED the closed hexagonal assembly arrangement. Although the objectives of the LEADER project activities concern the conceptual design of the demonstrator ALFRED, the thesis develops the study of closed fuel cycle that was established during the LEADER project. The ELFR configuration is demonstrated together with heavy metal-bearing fuel recycling scheme. The presented procedure has a potential to eliminate the bulk of long-lived highly radioactive fuel waste in final geologic disposal. The novel methodology of the trajectory period folding presented in this thesis may help in the assessment of the nuclear reaction on the cycle performances in the multi-recycling strategy.. 2.2 Fundamentals of the technology Unquestionably, the type of coolant mainly determine if designing type of reactor uses fast or thermal neutrons. For fast reactors the choice of the coolant has a primary impact on neutronic properties and a secondary impact on an overall plant layout design [13]. Certain type of coolant determines materials, geometry and later the whole system, i.e. pumps, heat exchangers, number of circuits or safety systems [14]. The primary function of the coolant is to convey the heat from where it is generated towards where it is converted into a more suitable energy form. In general, the coolant fluid for a fast reactor can be characterized by the following features:   . 24. the atomic mass of coolant elements compared to the neutron mass should prevent neutrons from losing energy by collision; small cross section absorption capacity. This criterion is required for an efficient moderator which does not remove free neutrons from the flux; high scattering cross section. It reduces neutron leakage from the system, improving the neutron balance described by neutron transport equation..

(25) From the thermodynamic point of view, the coolant fluid requires high heat transfer rate. These requirements are satisfied by liquid metals such as Na, Hg, Pb or their eutectics, NaK and PbBi. Among the aforementioned metal coolants, Na, Pb, and PbBi have adequate properties to be suitable for a fast reactor. The main thermal properties of Na, Pb, and PbBi are given in Table 2.1. Those coolants are address for public and scientific concerns regarding their future application in nuclear reactors for commercial use. Lead bismuth eutectics has roughly the same thermal properties as pure lead, with the exception of melting temperature. It can be observed that the differences between Na and two remaining coolants are significant. The selection of the best coolant is not obvious. The decision will further determine the properties of the core and will have an impact on the whole power station design. The selection of the coolant influences core features, such as neutron physics or thermodynamics, which has further implications in core safety characteristics. Therefore, the selection of the coolant is a complex decision. Table 2.1. Selected mean thermal properties of lead & sodium [15] Coolant Tmelt [K] Tboil [K] ρ [kg/m3] Cp [J/kg/K] k [W/mK] σc [mb] Na. 371. 1156. 850. 1277. 68. 1.3. Pb. 601. 2016. 10500. 147. 17. 4.4. PbBi. 399. 1943. 10200. 144. 14. 3.6. Lead-cooled fast reactor and sodium-cooled fast reactor are foreseen in three Generation IV plans. In addition, both designs have been supported by the EU research projects. The topic of this thesis is dedicated to the lead coolant technology. However, major physical advantages and disadvantages of the lead technology are identified by comparing liquid lead and liquid sodium properties. Lead and sodium coolants have a different heat removal rate, which determines pin pitch-to-diameter ratio. The sodium heat removal capacity rate is lower for lead. In combination with coolant flow velocity limit, the diameter ratio has to be higher for lead than for sodium coolant in order to stay below cladding temperature limits. Molten lead has a lower heat transfer coefficient and a higher density than sodium, thus it requires using more powerful pumps for the forced convection. The sodium coolant in some parts of the core with high power density bears the risk of gas bubbles creation. This phenomenon has consequences in the reactivity rise. On the other hand, boiling temperature for the lead molten coolant is much above the reactor's operating temperature, also during accident transient scenarios, which minimizes the risk of lead boiling. The possibility of abrupt changes in the void fraction is one of the most dangerous hypothetical accident scenarios. Unfavorable consequences in the thermodynamic behavior lead to the positive reactivity feedback in neutronic core performance. The power rise would lead to serious failures in the core, starting with fuel clad damage. 25.

(26) The reactivity change in the fast reactor can be effected by many physical factors, for example control rod insertion, fuel depletion, temperature, or pressure. Negative reactivity feedback in the fast reactor is guaranteed by natural phenomena, such as partial insertion of control rods, Doppler effect, radial and axial expansion. Those physical phenomena stabilize the reactor and are induced mainly by the temperature change in coolant or fuel. Coolant temperature change is also connected with thermal inertia. High thermal inertia of the lead coolant results in smoother transients. This behavior induces larger time-margin range, dumps coolant response while the temperatures increase, and gives enough time to avoid lead solidification while the temperatures decrease. The aforementioned design, pitch-to-diameter ratio, together with density temperature dependence along the elevation, for the condition of lead coolant, enhance the capability for natural circulation in the fuel assembly lattice. Natural-convection is maintained during reactor outages, which provides desirable and inherent safety criteria protecting the core. As a result, coolant convection can play an important role in maintaining the reactor at acceptable temperature levels, even if a loss of electric power supply of the cooling system occurs. Many other pros and cons of the lead coolant can be identified and compared with the sodium one, such as corrosion resistance of constructed materials installed in the coolant. Lead is highly corrosive above 400 ºC by erosion of iron oxide. That is why the lead coolant flow rate is limited to 2 m/s (under this limit, protective iron film is formed). In such conditions, optimization for new materials or surface treatment, or both, is required. Sodium has high chemical activity with air and water. A small leak can cause fire. This forces the use of additional safety treatment, such as intermediate loop (which increases the cost of the system). Lead has slightly higher cross section for neutron scattering than sodium. In the lead coolant, neutrons will have more acts of scattering and their mean free path is shorter, thus impeding its forward progress. More escaped neutrons will go back to the core and fuel. The results will be similar the use of the reflector. Higher neutron scattering cross section has positive effect on neutron balance in the system. Neutron leakage is smaller and more flat axial power profiles are expected. In the lead coolant system axial peaking factor is expected to be lower than in the sodium coolant. The main advantage of lead-bismuth eutectic is its melting point, which reduces melting freezing risks in the system in comparison with pure lead. High lead freezing temperature level creates problems during long time outages. The solidification of the coolant increases the risk of blockage. The system design has to assert the adequate coolant temperature during long outages above its freezing point.. 26.

(27) Lead-bismuth eutectic has also some disadvantages. World bismuth reserves are too limited to allow the use of PbBi eutectic for the industrial scale. A large fleet of nuclear reactors based on bismuth element would significantly increase the economic costs of the future reactors. Lead-bismuth eutectic is also less attractive due to the formation of Polonium-210 in bismuth (α emitter with short half-life time equal to 138 days) which is 104 order higher than in case of pure lead. Despite some negative properties, the use of PbBi eutectic is not closed for the experimental scale. Projects like those developed in Belgian Nuclear Research Center (SCK-CEN) focus on MYRRHA subcritical core [16]. These projects, among other things, are intend to accelerate the development of fast lead-cooled reactors. Considering the selection of the type of coolant for the fast neutron reactor, lead coolant technology shows to have some advantages in certain areas over the sodium coolant. This is due to better convection properties and higher boiling limit. Non-explosive chemical activity with air and water makes lead a safer material. Lead technology does not require an additional coolant circuit and safety installation, thus more frequent inspection is not required. In addition, the proposed solutions appear to have an impact on the economic competitiveness. Endorsement for the lead coolant nuclear technology can be found in the roadmap proposed by the European Sustainable Nuclear Industrial Initiative GIF, as well as in the responsible design organizations and reactor plant vendors. The database including technical information on the liquid lead-cooled technologies is provided by the Advanced Reactors Information System (ARIS) [17].. 2.3 Reactor plant configuration and safety systems In the previous chapter, the sodium and lead coolant principal objectives were presented and compared. The advantages of the lead coolant over the sodium one were emphasized in order to highlight the role of the lead-cooled fast reactor role as an alternative technology to be developed in parallel with sodium-cooled fast reactors. The present chapter continues the LFR design introduction. In this chapter, the author presents the components that are necessary for the operation of fast reactor systems, particularly the ELFR reference system. It is worth mentioning that the discussed design elements do not appear later in the main analysis of the conducted thesis research. However, they have an important role in the safety of the plant and the core performance. The chapter provides basic answers to the adopted solutions in the ELFR systems. In order to extend the information about fast reactor plant systems, the author refers to the following books [18][19].. 27.

(28) Fig. 2.2. Overall of the European Lead-cooled Fast Reactor plant systems The overriding objective of the ELSY and LEADER projects have been to create a fast system which would be cost-competitive to the current LWRs. Selection of many constructing elements are conducted by those outlines. Presented description bases on the latest configuration of the 1500 MWth pool type reactor with consist of two coolant circuits. The first lead circuit includes all primary elements arranged inside the pool type reactor vessel. The secondary system is based on superheated cycle providing net cycle efficiency greater than 41%. Power conversion is done by eight Steam Generators (SGs), each of 187.5 MWth power capacity. SGs are integrated with mechanical primary pumps, in order to provide circulation. The reactor vessel has a cylindrical shape with height of 12.8 m, inner diameter of 13.77 m, wall thickness of 50 mm and design temperature of 400 ºC, where safety system of primary circuit is placed. The reactor vessel is surrounded by a safety vessel anchored to the reactor pit. This solution protects the surroundings from potential leakage of the coolant from the reactor. It is expected that thanks to high lead density, in the event of accident with core melt, breached fuel may float on the lead surface. For this reason, the use of a “core catcher” at the bottom of the reactor pit would be of no use. The ELFR core, from the conceptual design try impediment robustness with respect to the IV GEN safety criteria. Therefore, safety system elements incorporate a few solutions which exploit full potential of the lead coolant. In normal operation, the transfer of generated heat in primary system relies on eight intermediate Steam Generators converting water into stem circulating inside the secondary system. In the event of unavailability of the secondary system, e.g. due to loss of power supplies or primary pumps, the core is able to sustain lead circulation in the primary circuit solely 28.

(29) by natural circulation cooling. After the reactor is shut down, heat is generated in the core due to radioactive decay of minor actinides and fission products. Enforced natural circulation is regulated by the decay heat and lead coolant properties. Overproduced decay heat needs to be removed so that unacceptable temperature rise could be prevented In order to remove excess decay heat, the ELFR design provides two diverse alternative and fully redundant Decay Heat Removal (DHR) systems:. . . The DHR-1 System – Relies on 4 Isolation Condenser (IC) Systems, equipped with eight dip coolers operating in the water, immersed in the reactor pool. The DHR-2 System – Relies on 4 IC Systems connected to 4 out of 8 SGs. Fig. 2.3. Isolation Condenser – Heat Exchanger. Both DHR systems are ready to operate after the reactor is shut down, providing:    . Independence obtained by means of two different systems, with nothing in common; Diversity obtained by means of two systems based on different physical principles; Redundancy obtained by means of three out of four loops (per system), sufficient to fulfill the DHR safety function in case of failure in one of the loops; Passivity obtained by means of using gravity to operate the system (no need of AC power).. The accident sequence first launches the DHR-2 (connection to SG). The DHR-1 is kept on standby (connected to the coolers in the primary circuit) and eventually starts working if a failure of the DHR-2 occurs.. 2.4 Core design considerations The ELFR core configuration will be presented in the following section. The description presents different types of Fuel Assembly (FA) and fuel pin geometry, along with the description of material composition. The reference reactor core is derived from the ELSY core design [20]. The initial concept investigated two options. The first option is based on square Fuel Assemblies (Fas), without wrapper around the elements. The second option is based on hexagonal close FA. The final decision was taken in order to establish hexagonal arrangement as a reference. The reason is that the established demonstrator ALFRED design favors hexagonal design and the need for coherence of 29.

(30) both designs is required. The starting point for the ELFR specification derived from the ELSY project was numerically reconstructed. Numerous neutronics analyses were carried out on several design options by AGH, ENEA, JRC and KIT (under the LEADER project) with the author’s participation [21]. Identification of several parameters was taken into account in the upcoming design, such as reactivity system margin, maximum discharge burn-up and adoption of number of batches. Finally, the study of the closed fuel-cycle within the reactor itself was applied in order to present the equilibrium approaches. The equilibrium approaches are described in section 2.5. The final optimized core [21] is presented here for the sake of numerical modeling performed in the practical part of the thesis. Table 2.2 shows the primary system components numbers for the final ELFR design. Table 2.2. Specification of ELFR Power [MWth/MWe] 1500/600 Primary coolant Lead Inlet temperature [oC] 400 o Outlet temperature [ C] 480 Coolant velocity [m/s] 1.53 Fuel MOX+MA Pu enrichment [% wt.] 18.15 Fuel irradiation time [days] 2·900 Cooling before recycling [years] 7.5 Barrel diameter [mm] 5600 Barrel thickness [mm] 50 FA geometry Hexagonal Active height [mm] 1400 Number of FA 427 Number of FA per zone 1/2/3 157/270 Number of pins per FA 169 FA pitch [mm] 209 Clearance between FAs [mm] 5 FA apothem [mm] 102 FA wrapper Thickness [mm] 4 Fuel pin pitch [mm] 15 Pellet outer diameter [mm] 9 Pellet inner diameter [mm] 4(2) Fuel pin clad thickness [mm] 0.6 Fuel pin gap thickness [mm] 0.15 Number of CR 12 Number of SR 12 CR(SR) pellet diameter [mm] 14 Number of shield assemblies 132 SA rod diameter [mm] 14 CR(SR, SA) clad diameter [mm] 0.7. 30.

(31) 2.4.1 The ELFR core & barrel The modeling space is represented by the reactor core with surroundings. It is a cylinder with a radius of 3500 mm and height of 6100 mm. The construction consists of the proper core surrounded by the core barrel. The core barrel is a cylindrical tube made of T91 steel at densities of 7.7 g/cm3, with inner radius of 2750 mm, wall thickness of 50 mm, and height equal to that of the reactor core model, that is 6100 mm. Liquid lead is modeled with an assumption that inside the barrel lead enters and effuses the active core and has two different temperatures. Then, application of two independent lead-materials is considered with different densities and nuclear temperature libraries. The bottom active core part has a density of 10.58 g/cm 3 at 400 ºC, while the upper part has a density of 10.48 g/cm3 at the temperature of 480 ºC.. Fig. 2.4. 1/6 ELFR core configuration with INN (yellow) and OUT (red) FA positions surrounded by shield assemblies (white). Blue and green hexagons represent control and shutdown assemblies respectively 2.4.2 A fuel bundle The reactor core consists of 427 fuel hexagonal assemblies, each containing 169 fuel rods (also known as pins) in a triangular lattice. The axial cross section of the pins is presented in Figure 2.5. The pins are represented by a cylinder made of T91 steel with inner radius of 4.65 mm and thickness of 0.6 mm. The space between the inner part of clad and the fuel rods is filled with void and encloses the fuel from the upper to the lower end. Other cylindrical regions are represented by the top spring, top and bottom plugs, as well as the lower gas plenum region. Finally, representation of the spacer grids with inlet and outlet nozzles, placed at the bottom part and top part of the fuel rod, was modeled as a homogeneous material of structure steel T91 and lead.. 31.

(32) Fig. 2.5. ELFR fuel rod longitudinal cross-cut [21] The fuel rod contains nuclear fuel pellets with the same start fuel vector composition. Different scenarios for the initial fuel vector have been studied [21]. Two types of fuel rods are distinguished by two types of annular central void made in the fuel pellet. The original purpose of the central void is to make space for fission-gas-release from fuel. However, the selection of different voiding serves the power profile optimization, as justified in the next section. The rods are immersed in liquid lead and encapsulated in a hexagonal wrapper made of T91 steel. The height of the fuel part is 1400 mm, the pitch for fuel assemblies is 209 mm and the pitch between the fuel rods is 15 mm.. Fig. 2.6. ELFR fuel assembly with annular fuel pins 2.4.3 Reflector (In-vessel Shielding) In fast reactors, just like in thermal reactors, a reflector is required. However, in thermal reactors the basic function of a reflector is to reflect back neutrons into the core by using materials that are characterized by sufficient cross section for scattering. This role in the LFR core is performed by lead coolant, which has adequate cross section for scattering. 32.

(33) In the LFR system the reflector is present but it serves mainly as a shield. Neutron energies and gamma exposition are higher in fast reactors than in thermal reactors. Thus, the role of the reflector, called in-vessel shielding, is to degrade the energy of fast neutrons and effect of irradiation on the core barrel and the core safety systems material. The ELFR project assumes that in-vessel shielding consists of 132 shield assemblies surrounding the active core. The arrangement is presented in Figure 2.4. Each hexagonal assembly contains 127 bundle rods (Figure 2.7.) put inside a wrapper made of Y-stabilized zirconia rods (94.9 wt.% ZrO 2 , 5.1 wt.% Y2O3). The radius of a zirconia rod is 7.18 mm. The thickness of the covering clad is 0.5 mm. The pins are 4900 mm high. The shield wrapper radial configuration is the same as in the fuel assembly wrapper.. Fig. 2.7. The control and Shield assembly cross-sectional view 2.4.4 Control & Shutdown rods Two redundant, independent and diverse shutdown systems, RS1 – the control rod system and RS2 – the safety rod system, are designed for ELFR (derived from the MYRRHA design). Each shutdown system is designed to have reactivity worth margin able to shut down the reactor in case the most reactive rod in the system is postulated to remain stuck. Both systems are made of boron carbide B 4C (90% enriched in 10B) and submerged in the primary coolant. . . RS1: 12 assemblies are used for reactivity control during normal operation and in addition to safety shutdown. 19 rods in each assembly are inserted from the bottom of the core to control the reactivity. Thanks to high lead density compared to the rods material supported by gas plenum collecting the helium, passive safety is guaranteed by buoyancy as the driving force in the event of loss of power (which triggers loss of electromagnet electric supply). RS2: 12 assemblies are used only for scram (controlled shutdown safety procedure). The system consists of 12 rods in each assembly, where each bundle rod has a 19 mm radius and is made of boron carbide. In normal operation the rods are fully extracted from the core. During the shutdown they are fully inserted over the core. During normal operation the rods are withdrawn and 33.

(34) submerged in liquid lead. The Rods bundle is encapsulated by a safety tube. Because of high lead density, safety insertion takes place with a specially designed system based on opposing piston on the same shaft. This solution provides the same pressure when safety rods are released by means of a fail-safe pneumatic system, supplemented by the force of gravity. The solution makes the RS2 system fully passive. Both RS1 and RS2 systems were introduced during the LEADER project [21] as an optimized version of the previous ELSY design. The main changes concern the aforementioned mechanism for insertion and optimization of the fluid dynamics insertion. The rearrangement has changed the number of rods and their diameters. Nevertheless, the simulations performed concern the previous version of safety and control rods based on the original ELSY version. From the neutron physics point of view, both geometrical systems provide comparable reactivity margin of proposed 4500 pcm. Moreover, in the presented examples the evolution is calculated for extreme levels of CR withdrawn. This provides the same initial condition for both versions. In this work exact modeling of the CR rods is not considered. For this purpose reactivity swing is induced only by the fuel burn-up and breeding over the fuel cycle. Like the optimized design, non-optimized design consists of 12 shutdown (RS2) and 12 control (RS1) assemblies located symmetrically in the reactor core (Figure 2.4). The assemblies were modeled as hexagonal wrappers (Figure 2.7), with the same geometrical dimensions as the shield assemblies. 127 absorber rods are filled with B 4C material enriched to 90% 10B. The total length of the absorber pellets is the same as the length of the fuel active part, i.e. 1400 mm. The clearance between the assemblies is 5 mm (2×2.5 mm). Table 2.3. Structural materials and lead coolant T91 Steel. 34. YsZ Density Element. 6.0 g/cm3 wt.%. 88.4. Zr. 70.3. Cr. 9.0. O. 25.7. Mo. 1.0. Y. 4.0. Mn. 0.6. Si. 0.5. V. 0.2. Ni. 0.2. Nb. 0.1. Density Element. 7.7 g/cm wt.%. Fe. 3. Lead Density at 400 ºC. 10.58. Density at 480 ºC. 10.48.

(35) 2.5 Adiabatic equilibrium fuel cycle 2.5.1 Meaning of fuel cycle strategy The fuel cycle strategy applicable to a particular nuclear reactor system impacts the management of nuclear fuel as well as of its waste and plays very important role in many aspects of the nuclear system, such as: • • • • • • •. economy sustainability security of supply radiological hazard public acceptance political acceptance proliferation threats. As some aspects of the fuel cycle strategy may favor one cycle feature, they can be unfavorable regarding the other aspect. For example breeding of plutonium is favorable by the sustainability and supply security aspects, while being unfavorable by the proliferation threat aspect. The trade-offs between the different aspects always exist, which may result in the fuel cycle strategy preferences, yet depending on currently available nuclear technology and the phase of the related nuclear industrial system lifecycle. In this regard the fuel breeding is of the highest priority for times when resources of 235U will become scarce. The fuel breeding needs have been the main incentive to undertake the development of Generation IV reactors, in which the number of fast breeders prevail over the other ones. One may think, the maximization of breeding would be the optimal solution, but the situation is not that simple - the other aspects have to be taken care of. The major concern results form production of MA due to nuclear transmutations that come along with the fuel breeding. The fuel cycle strategy in LFR can serve specific needs of its operator depending on the actual circumstances in nuclear fuel market or regulatory constraints in relation to amount of accumulated plutonium stockpile or even the costs of MA management, including its separation or underground storage. The fuel cycle strategy can also be affected by public factors like their protests against spent fuel transportation to a reprocessing plant. The MA must be properly managed since they increase radiological hazard and can adversely affect the public acceptance for a chosen solution. As transmutation brings MA mass to existence it can also end it, which means that MA can be managed by transmutations within a properly defined fuel cycle strategy. One of the main missions of the LEADER project is the development of a system with fuel self-sufficiency and MA management.. 35.

(36) 2.5.2 Adiabatic equilibrium fuel cycle concept In the adiabatic fuel cycle the reactor consumes only the natural or depleted uranium supplied from the outside and produces fission products, see Figure 2.8. Additionally, to achieve complete adiabatic equilibrium the changes in the isotopic vector of the spent nuclear fuel due to radioactive decay during interim-cooling and losses during fuel reprocessing need to be taken into account. A reactor in adiabatic equilibrium should be characterized by the three main constraints: • • •. Constant cycle-to-cycle fuel composition, Constant cycle-to-cycle core criticality at the reference time, Core breeding over cycle-to-cycle equals zero.. Fig. 2.8. Adiabatic Equilibrium flowchart In addition, the constraints determining the general limitation of core structure, reactor working conditions and material limits must be satisfied. This refers to the dimensions of the reactor vessel and subassemblies; number of specific subassemblies containing fuel and control rods; compositions of structure materials and coolant; fertile feed; material densities and temperature; thermal power; power density and form factors; displacement-per-atom limits and peak burnup limit. Many fuel matrices could be used for the reference fuel vector, e.g. oxide, nitride or advanced inert matrices [22]. However, initially the simple oxide fuel matrix was proposed due to the extensive knowledge of its properties under irradiation. It is worth mentioning that the approach of adiabatic equilibrium can be applied to any system with any option for a closed fuel cycle.. 36.

(37) The claim for the ELFR in the adiabatic equilibrium state imposed a novel procedure for reactor core design, known as the New Paradigm for Nuclear Power [23]. Firstly, the initial geometry of the elementary cell is designed considering the thermal–hydraulic parameters, then the geometry defines the neutron spectrum in a cell and its intrinsic reactivity. Secondly, the equilibrium composition of the nuclear fuel is determined a priori and fixed. Thirdly, the number of elementary cells for criticality, and thus core power and size, is determined. Finally, the desired core power is adjusted iteratively by manipulating the fuel volume fraction in the elementary cell along with the fuel composition. In this way a match is achieved between desired core power and criticality. On the contrary, the old design strategy considered core size and thus power as a fixed parameter and adjusted the fissile fraction in the nuclear fuel to attain criticality. The procedure is a novel, state-of-the art approach and without doubt can be described as an innovation in nuclear reactor core design. 2.5.3 Fuel cycle conditions Since LFR system is flexible in terms of fuel breeding capabilities it can be designed as a breeder, burner or self-breeder. The condition of self-breeder refers to the adiabatic cycle which corresponds to the minimum possible exchange of transuranium elements within the environment of the reactor unit. Therefore, all actinides present in the spent nuclear fuel are reprocessed and reloaded in the reactor core in the following reactor cycles. By using this method it is possible to reach the equilibrium state of the reactor core, which means that the mass and isotopic composition of the transuranium elements in the refueled reactor core or batch are the same as in the discharged fuel after a defined cooling time with refilled deficiencies in the uranium for every reactor cycle. The adiabatic core concept responds to this issue by proposing a solution in which the nuclear system that comprises a fuel factory, reactor park and final waste repository, once it has reached its equilibrium, needs the external supply of fertile material and turns into waste only fission products. Since LFR is designed for the uranium plutonium cycle the fertile material must consists of depleted uranium mostly. However, other HM nuclides that comprise nuclear waste from LWRs may also be included since they are not fuel – at least for LWRs. Once the cycle needs additional fuel loaded in at the fuel cycle front end or must unload surplus fuel at the back end it cannot be considered adiabatic. But still, that kind of cycle can reach its equilibrium as breeder or burner. The adiabatic cycle characterizes self-breeding cores. Summarizing, one can distinguish the following fuel cycles strategy applicable to the uranium-plutonium cycle with the respective equilibrium characterization:. 37.

(38) Cycles without external MA loads I. Adiabatic cycle. The fertile material comprises depleted uranium only, all HM nuclides are recycled, net production of HM nuclides other than fertile is zero, 238 U is reduced. II. Breeding cycle. The fertile material comprises depleted uranium only. The fuel is bred, which then is partially recycled, and partially exported to make the initial load of a new system. 238U is reduced. III. Burning cycle. At the front end a fresh load plutonium or MOX must be added to the fertile material. The fuel is net burned, which serves reduction of the plutonium stockpile from LWRs. Cycles with external MA added at the front end to the recycled fuel IV. Adiabatic cycle. At the front end the fuel is made of the recycled fuel, external MA and depleted uranium. External MA is burned, all remaining HM nuclides are recycled, 238U is reduced. V. Breeding cycle. At the front end the fuel is made of the recycled fuel, external MA and depleted uranium. The fuel is bred but external MA burned. The fuel is partially recycled, and partially exported to a new system. 238U and MA are reduced. VI. Burning cycle. At the front end the fuel is made of the recycled fuel, depleted uranium and a fresh load plutonium or MOX with MA. The fuel is net burned including external MA, which serves reduction of the plutonium and MA stockpile from LWRs or fast neutron systems. Case I is the reference cycle, while cases II and III are a departure from it. This departure may be large on a designer intention or a small one as a result of differences between the calculation model and reality, or due to change in the fuel cycle operational conditions that brake design constrains of the adiabatic cycle. Understanding the way and quantitative consequences of the cycle deviation from its adiabatic state may be important for undertaking required countermeasures in the real operation. Since the thesis deal with estimation LFR back end fuel, the cycles II, III, IV, V and VI would not be discussed here but in the future works.. 38.