TVE-F 17 009 juni Examensarbete 15 hp Juni 2017 Nuclear reactor core model for the advanced nuclear fuel cycle simulator FANCSEE. Advanced use of Monte Carlo methods in nuclear reactor calculations Alexander Skwarcan-Bidakowski Abstract Nuclear reactor core model for the advanced nuclear fuel cycle simulator FANCSEE. Advanced use of Monte Carlo methods in nuclear reactor calculations Alexander Skwarcan-Bidakowski Teknisk- naturvetenskaplig fakultet UTH-enheten A detailed reactor core modeling of the LOVIISA-2 PWR and FORSMARK-3 BWR was performed in the Serpent 2 Continuous Energy Monte-Carlo Besöksadress: code. Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Both models of the reactors were completed but the approximations of the atomic densities of nuclides present in the core differed Postadress: significantly. Box 536 751 21 Uppsala In the LOVIISA-2 PWR, the predicted atomic density for the nuclides Telefon: approximated by Chebyshev Rational Approximation method (CRAM) 018 – 471 30 03 coincided with the corrected atomic density simulated by the Serpent Telefax: 2 program. In the case of FORSMARK-3 BWR, the atomic density from 018 – 471 30 00 CRAM poorly approximated the data returned by the simulation in Serpent 2. Due to boiling of the moderator in the core of FORSMARK-3, Hemsida: the model seemed to encounter problems of fission density, which http://www.teknat.uu.se/student yielded unusable results. The results based on the models of the reactor cores are significant to the FANCSEE Nuclear fuel cycle simulator, which will be used as a dataset for the nuclear fuel cycle burnup in the reactors. Handledare: prof. Waclaw Gudowski, Blazej Chmielarz Ämnesgranskare: Changqing Ruan Examinator: Martin Sjödin ISSN: 1401-5757, TVE-F 17 009 juni 1 Populärvetenskaplig sammanfattning av projektet Kärnkraftverk kan vara svaret till en hållbar och pålitlig energiutvinning som ersätter förbrännin- gen av fossila bränslen. Idag står kolkraftverk för ca 40% av världens elektricitet men samtidigt har det varit en av anledningarna till de höga koldioxidutsläppen. Ersättning av kolkraftverk med exempelvis kärnkraft skulle kräva en del planering och uppskattning av bland annat, hur mycket kärnbränsle som krävs och hur mycket avfall som måste förvaras eller anrikas för vidare operation. Dagen teknik tillåter användningen av dator-simuleringar för en bra uppskattning av dessa värden. FANCSEE är en sådan kärnbränsle-simulator som nuvarande utvecklas i Institutionen för Reak- torfysik på Kungliga Tekniska Högskolan och ska ha ett grafisk användargränssnitt till skillnad från andra programvaror. Detta gör det enklare för beslutsfattare att göra informativa beslut. Pro- gramvaran använder sig av värden framtagna från simulationer av detaljerade modeller baserade på verkliga reaktorer. I detta projekt har två brett använda reaktormodeller undersökts och modelerats i ett program som simulerar reaktionerna i en reaktorkärna. Resultaten från dessa simuleringar används sedan i FANSCEE för att uppskatta kärnavfall, bränslebehov, energinätkapacitet eller budget för en kärn- reaktor. Har man kunskap av hur mycket kärnavfall som produceras, kan man exempelvis i god tid planera hur mycket som ska förvaras eller berikas för fortsatt användning. Just nu är FANCSEE fortfarande under utveckling. Fler reaktormodeller ska implementeras för bredare data-bibliotek. Med detta verktyg kommer kärnbränsleplaneringen gå fortare, och vara enklare än någonsin tidigare. 1 Contents 1 Populärvetenskaplig sammanfattning av projektet1 2 Introduction 3 2.1 Principles of nuclear reactors..............................3 2.2 Objective.........................................3 2.3 FANCSEE.........................................4 3 Monte Carlo method4 4 Serpent 2 5 5 Theory 6 5.1 Process of radioactive decay and transmutation through neutron induced reactions7 5.2 Bateman Equation....................................8 5.3 Neutron cross-section...................................9 5.4 Burnup calculation.................................... 10 5.5 Chebyshev Rational Approximation method...................... 11 6 Method 12 6.1 LOVIISA-2........................................ 13 6.2 FORSMARK-3...................................... 17 6.3 Implementation of core design to Serpent 2 syntax.................. 21 6.4 Reactor profile...................................... 23 7 Results 24 7.1 LOVIISA-2........................................ 24 7.2 FORSMARK-3...................................... 26 8 Conclusions 28 9 Future work 28 10 Acknowledgements 29 2 2 Introduction Nuclear energy provides about 11% of the electricity of the world, while burning of coal provides a staggering 40% [1]. The need for nuclear energy will likely increase as the burning of coal decreases due to the global problem of climate change. Though renewable energy sources are popular with the public, they are not as reliable or stable as nuclear power, hence nuclear power is likely to carry the burden of increased energy demand. For a number of reasons, including safety, politics and environmental concerns, nuclear power is still a controversial topic to the public, but only through continuous research, development and communication these concerns can be addressed. Working towards sustainable, safe and economically viable nuclear power, simulations are crucial to finding scenarios of reactor cycles. These reactor cycles include, but are not limited to, simulations of neutron reactions, core criticality or the burnup of nuclear fuel and nuclear transmutation, the latter two whom will be the objective of this paper. 2.1 Principles of nuclear reactors The energy generated by nuclear reactors come from the fission of certain heavy metals, ie. elements with proton number between 90 and 100. Nuclear reactors mostly use uranium as nuclear fuel, which is extracted from natural uranium ore. Natural uranium is mostly composed of uranium-238 with low enrichments of the fissile isotope uranium-235 (mass fraction 0.72%), which can be found naturally in the environment. The fuel however, is generally an enriched mixture of 238U and 235U. The measure of how much energy is extracted from the nuclear fuel is called Burnup, also known as fuel utilization and is measured in fissions per initial metal atom, %FIMA or the total energy released per ton of initial mass of uranium [MW d=kgU]. 2.2 Objective The objective of this paper is to simulate neutronics of two detailed nuclear reactor core designs in the Monte-Carlo particle transport code [2]- Serpent 2, and to simulate burnup cycle calculations of them. From these burnup cycles, depletion matrices will be derived and used in future work to model realistic fuel cycle scenarios in a fuel cycle simulator, FANCSEE being developed at KTH. Figure 1 shows the process of transforming the results of the burnup cycles to usable data in the FANCSEE software. The nuclear reactors under consideration will be the Pressurized Water Reactor LOVIISA-2 (VVER- 440/213) in Finland and the Boiling Water Reactor FORSMARK-3 (ABB-III) in Sweden. Both reactor types were some of the first reactors developed in the 1950s and have since been improved on. They are also the most common reactor types which make them important for the FANCSEE project. 3 Figure 1: The Figure shows parts of the process, from simulating the Burnup cycle to the final software. Red - Developers side, green - User side, blue - focus of the project. 2.3 FANCSEE The FANCSEE simulator was initially developed at the Royal Institute of Technology in Stock- holm, KTH, by Torbjörn Bäck and prof. Wacław Gudowski, and during the years progressively developed in cooperation with the University of Tartu. The FANCSEE software is in its final stages of development by Błażej Chmielarz, KTH [3], with a ultimate goal to create a user-friendly, graph- ically controlled software, allowing advanced simulations of a nuclear fuel cycle scenario, even for very complex and diversified scenarios and has the ability of tracking 1307 nuclides at any point in the cycle for up to 1100 years. The target audience would not only include scientists in the field, but also for policymakers as a source of well informed decisions and for educational purposes for students. It could also serve as a way of planning nuclear waste repositories, fuel needs, energy grid capacity or budget in a nuclear park. 3 Monte Carlo method The Monte Carlo method is a stochastic method of approximating solutions to mathematical prob- lems using computational algorithms that rely on repeated statistical sampling from a probability distribution function. It is often used in problems with probabilistic structures where variables follow a pattern. The randomness of the Monte Carlo method is only applied to the degrees of freedom that are defined and limited by the user, and have great advantages over a deterministic method mainly because it does not require new analytical solutions for every change of the system, is a more flexible method and can be applied to a system of any complexity. 4 4 Serpent 2 Serpent 2 is a universe based stochastic Monte-Carlo code [2]. It utilizes a user defined geometry (2-3 dimensional) with materials and their densities to simulate neutron reactions and transmu- tations of isotopes in a reactor core. The components that assemble the reactor are defined in separate universes, ie. a space which is filled with a specific geometrical structure with a defined material. What is returned by the simulation are the reaction rates of the neutrons, containing atomic density vectors of all