Monte Carlo Neutronics and Thermal-hydraulics coupling applied to Fast Reactors

Un escenario habitualmente considerado para el uso sostenible y prolongado de la energía nuclear contempla un parque de reactores rápidos refrigerados por metales líquidos (LMFR) dedicados al reciclado de Pu y la transmutación de actínidos minoritarios (MA). Otra opción es combinar dichos reactores con algunos sistemas subcríticos asistidos por acelerador (ADS), exclusivamente destinados a la eliminación de MA. El diseño y licenciamiento de estos reactores innovadores requiere herramientas computacionales prácticas y precisas, que incorporen el conocimiento obtenido en la investigación experimental de nuevas configuraciones de reactores, materiales y sistemas. A pesar de que se han construido y operado un cierto número de reactores rápidos a nivel mundial, la experiencia operacional es todavía reducida y no todos los transitorios se han podido entender completamente. Por tanto, los análisis de seguridad de nuevos LMFR están basados fundamentalmente en métodos deterministas, al contrario que las aproximaciones modernas para reactores de agua ligera (LWR), que se benefician también de los métodos probabilistas. La aproximación más usada en los estudios de seguridad de LMFR es utilizar una variedad de códigos, desarrollados a base de distintas teorías, en busca de soluciones integrales para los transitorios e incluyendo incertidumbres. En este marco, los nuevos códigos para cálculos de mejor estimación ("best estimate") que no incluyen aproximaciones conservadoras, son de una importancia primordial para analizar estacionarios y transitorios en reactores rápidos. Esta tesis se centra en el desarrollo de un código acoplado para realizar análisis realistas en reactores rápidos críticos aplicando el método de Monte Carlo. Hoy en día, dado el mayor potencial de recursos computacionales, los códigos de transporte neutrónico por Monte Carlo se pueden usar de manera práctica para realizar cálculos detallados de núcleos completos, incluso de elevada heterogeneidad material. Además, los códigos de Monte Carlo se toman normalmente como referencia para los códigos deterministas de difusión en multigrupos en aplicaciones con reactores rápidos, porque usan secciones eficaces punto a punto, un modelo geométrico exacto y tienen en cuenta intrínsecamente la dependencia angular de flujo. En esta tesis se presenta una metodología de acoplamiento entre el conocido código MCNP, que calcula la generación de potencia en el reactor, y el código de termohidráulica de subcanal COBRA-IV, que obtiene las distribuciones de temperatura y densidad en el sistema. COBRA-IV es un código apropiado para aplicaciones en reactores rápidos ya que ha sido validado con resultados experimentales en haces de barras con sodio, incluyendo las correlaciones más apropiadas para metales líquidos. En una primera fase de la tesis, ambos códigos se han acoplado en estado estacionario utilizando un método iterativo con intercambio de archivos externos. El principal problema en el acoplamiento neutrónico y termohidráulico en estacionario con códigos de Monte Carlo es la manipulación de las secciones eficaces para tener en cuenta el ensanchamiento Doppler cuando la temperatura del combustible aumenta. Entre todas las opciones disponibles, en esta tesis se ha escogido la aproximación de pseudo materiales, y se ha comprobado que proporciona resultados aceptables en su aplicación con reactores rápidos. Por otro lado, los cambios geométricos originados por grandes gradientes de temperatura en el núcleo de reactores rápidos resultan importantes para la neutrónica como consecuencia del elevado recorrido libre medio del neutrón en estos sistemas. Por tanto, se ha desarrollado un módulo adicional que simula la geometría del reactor en caliente y permite estimar la reactividad debido a la expansión del núcleo en un transitorio. éste módulo calcula automáticamente la longitud del combustible, el radio de la vaina, la separación de los elementos de combustible y el radio de la placa soporte en función de la temperatura. éste efecto es muy relevante en transitorios sin inserción de bancos de parada. También relacionado con los cambios geométricos, se ha implementado una herramienta que, automatiza el movimiento de las barras de control en busca d la criticidad del reactor, o bien calcula el valor de inserción axial las barras de control. Una segunda fase en la plataforma de cálculo que se ha desarrollado es la simulació dinámica. Puesto que MCNP sólo realiza cálculos estacionarios para sistemas críticos o supercríticos, la solución más directa que se propone sin modificar el código fuente de MCNP es usar la aproximación de factorización de flujo, que resuelve por separado la forma del flujo y la amplitud. En este caso se han estudiado en profundidad dos aproximaciones: adiabática y quasiestática. El método adiabático usa un esquema de acoplamiento que alterna en el tiempo los cálculos neutrónicos y termohidráulicos. MCNP calcula el modo fundamental de la distribución de neutrones y la reactividad al final de cada paso de tiempo, y COBRA-IV calcula las propiedades térmicas en el punto intermedio de los pasos de tiempo. La evolución de la amplitud de flujo se calcula resolviendo las ecuaciones de cinética puntual. Este método calcula la reactividad estática en cada paso de tiempo que, en general, difiere de la reactividad dinámica que se obtendría con la distribución de flujo exacta y dependiente de tiempo. No obstante, para entornos no excesivamente alejados de la criticidad ambas reactividades son similares y el método conduce a resultados prácticos aceptables. Siguiendo esta línea, se ha desarrollado después un método mejorado para intentar tener en cuenta el efecto de la fuente de neutrones retardados en la evolución de la forma del flujo durante el transitorio. El esquema consiste en realizar un cálculo cuasiestacionario por cada paso de tiempo con MCNP. La simulación cuasiestacionaria se basa EN la aproximación de fuente constante de neutrones retardados, y consiste en dar un determinado peso o importancia a cada ciclo computacial del cálculo de criticidad con MCNP para la estimación del flujo final. Ambos métodos se han verificado tomando como referencia los resultados del código de difusión COBAYA3 frente a un ejercicio común y suficientemente significativo. Finalmente, con objeto de demostrar la posibilidad de uso práctico del código, se ha simulado un transitorio en el concepto de reactor crítico en fase de diseño MYRRHA/FASTEF, de 100 MW de potencia térmica y refrigerado por plomo-bismuto. ABSTRACT Long term sustainable nuclear energy scenarios envisage a fleet of Liquid Metal Fast Reactors (LMFR) for the Pu recycling and minor actinides (MAs) transmutation or combined with some accelerator driven systems (ADS) just for MAs elimination. Design and licensing of these innovative reactor concepts require accurate computational tools, implementing the knowledge obtained in experimental research for new reactor configurations, materials and associated systems. Although a number of fast reactor systems have already been built, the operational experience is still reduced, especially for lead reactors, and not all the transients are fully understood. The safety analysis approach for LMFR is therefore based only on deterministic methods, different from modern approach for Light Water Reactors (LWR) which also benefit from probabilistic methods. Usually, the approach adopted in LMFR safety assessments is to employ a variety of codes, somewhat different for the each other, to analyze transients looking for a comprehensive solution and including uncertainties. In this frame, new best estimate simulation codes are of prime importance in order to analyze fast reactors steady state and transients. This thesis is focused on the development of a coupled code system for best estimate analysis in fast critical reactor. Currently due to the increase in the computational resources, Monte Carlo methods for neutrons transport can be used for detailed full core calculations. Furthermore, Monte Carlo codes are usually taken as reference for deterministic diffusion multigroups codes in fast reactors applications because they employ point-wise cross sections in an exact geometry model and intrinsically account for directional dependence of the ux. The coupling methodology presented here uses MCNP to calculate the power deposition within the reactor. The subchannel code COBRA-IV calculates the temperature and density distribution within the reactor. COBRA-IV is suitable for fast reactors applications because it has been validated against experimental results in sodium rod bundles. The proper correlations for liquid metal applications have been added to the thermal-hydraulics program. Both codes are coupled at steady state using an iterative method and external files exchange. The main issue in the Monte Carlo/thermal-hydraulics steady state coupling is the cross section handling to take into account Doppler broadening when temperature rises. Among every available options, the pseudo materials approach has been chosen in this thesis. This approach obtains reasonable results in fast reactor applications. Furthermore, geometrical changes caused by large temperature gradients in the core, are of major importance in fast reactor due to the large neutron mean free path. An additional module has therefore been included in order to simulate the reactor geometry in hot state or to estimate the reactivity due to core expansion in a transient. The module automatically calculates the fuel length, cladding radius, fuel assembly pitch and diagrid radius with the temperature. This effect will be crucial in some unprotected transients. Also related to geometrical changes, an automatic control rod movement feature has been implemented in order to achieve a just critical reactor or to calculate control rod worth. A step forward in the coupling platform is the dynamic simulation. Since MCNP performs only steady state calculations for critical systems, the more straight forward option without modifying MCNP source code, is to use the flux factorization approach solving separately the flux shape and amplitude. In this thesis two options have been studied to tackle time dependent neutronic simulations using a Monte Carlo code: adiabatic and quasistatic methods. The adiabatic methods uses a staggered time coupling scheme for the time advance of neutronics and the thermal-hydraulics calculations. MCNP computes the fundamental mode of the neutron flux distribution and the reactivity at the end of each time step and COBRA-IV the thermal properties at half of the the time steps. To calculate the flux amplitude evolution a solver of the point kinetics equations is used. This method calculates the static reactivity in each time step that in general is different from the dynamic reactivity calculated with the exact flux distribution. Nevertheless, for close to critical situations, both reactivities are similar and the method leads to acceptable practical results. In this line, an improved method as an attempt to take into account the effect of delayed neutron source in the transient flux shape evolutions is developed. The scheme performs a quasistationary calculation per time step with MCNP. This quasistationary simulations is based con the constant delayed source approach, taking into account the importance of each criticality cycle in the final flux estimation. Both adiabatic and quasistatic methods have been verified against the diffusion code COBAYA3, using a theoretical kinetic exercise. Finally, a transient in a critical 100 MWth lead-bismuth-eutectic reactor concept is analyzed using the adiabatic method as an application example in a real system.

Feasibility assessment of the interactive use of a Monte Carlo algorithm in treatment planning for intraoperative electron radiation therapy

This work analysed the feasibility of using a fast, customized Monte Carlo (MC) method to perform accurate computation of dose distributions during pre- and intraplanning of intraoperative electron radiation therapy (IOERT) procedures. The MC method that was implemented, which has been integrated into a specific innovative simulation and planning tool, is able to simulate the fate of thousands of particles per second, and it was the aim of this work to determine the level of interactivity that could be achieved. The planning workflow enabled calibration of the imaging and treatment equipment, as well as manipulation of the surgical frame and insertion of the protection shields around the organs at risk and other beam modifiers. In this way, the multidisciplinary team involved in IOERT has all the tools necessary to perform complex MC dosage simulations adapted to their equipment in an efficient and transparent way. To assess the accuracy and reliability of this MC technique, dose distributions for a monoenergetic source were compared with those obtained using a general-purpose software package used widely in medical physics applications. Once accuracy of the underlying simulator was confirmed, a clinical accelerator was modelled and experimental measurements in water were conducted. A comparison was made with the output from the simulator to identify the conditions under which accurate dose estimations could be obtained in less than 3 min, which is the threshold imposed to allow for interactive use of the tool in treatment planning. Finally, a clinically relevant scenario, namely early-stage breast cancer treatment, was simulated with pre- and intraoperative volumes to verify that it was feasible to use the MC tool intraoperatively and to adjust dose delivery based on the simulation output, without compromising accuracy. The workflow provided a satisfactory model of the treatment head and the imaging system, enabling proper configuration of the treatment planning system and providing good accuracy in the dosage simulation.

Monte Carlo limit cycle characterization

The fixed point implementation of IIR digital filters usually leads to the appearance of zero-input limit cycles, which degrade the performance of the system. In this paper, we develop an efficient Monte Carlo algorithm to detect and characterize limit cycles in fixed-point IIR digital filters. The proposed approach considers filters formulated in the state space and is valid for any fixed point representation and quantization function. Numerical simulations on several high-order filters, where an exhaustive search is unfeasible, show the effectiveness of the proposed approach.

Estudo dos parâmetros dosimétricos de sementes de Iodo-125 desenvolvidas pelo IPEN-CNEN/SP utilizadas em braquiterapia por simulação computacional pelo método de Monte Carlo

As expectativas da Organização Mundial de Saúde para o ano de 2030 são que o número de mortes por câncer seja de aproximadamente 13,2 milhões, evidenciando a elevada parcela desta doença no problema de saúde mundial. Com relação ao câncer de próstata, de acordo com o Instituto Nacional do Câncer, o número de casos diagnosticados no mundo em 2012 foi de aproximadamente 1,1 milhão, enquanto que no Brasil os dados indicam a incidência de 68 mil novos casos. O tratamento deste tipo de neoplasia pode ser realizado com cirurgia (prostatectomia) ou radioterapia. Dentre a radioterapia, podemos destacar a técnica de braquiterapia, a qual consiste na introdução (implante) de pequenas fontes radioativas (sementes) no interior da próstata, onde será entregue um valor elevado de dose no volume de tratamento e baixa dose nos tecidos ao redor. No Brasil, a classe médica estima uma demanda de aproximadamente 8000 sementes/mês, sendo o custo unitário de cada semente de pelo menos U$ 26,00. A Associação Americana de Físicos na Medicina publicou alguns documentos descrevendo quais parâmetros e análises devem ser realizadas para avaliações da distribuição de dose, como por exemplo, os parâmetros Constante de taxa de dose, Função radial e Função de anisotropia. Estes parâmetros podem ser obtidos através de medidas experimentais da distribuição de dose ou por simulações computacionais. Neste trabalho foram determinados os parâmetros dosimétricos da semente OncoSeed-6711 da empresa Oncura-GEHealthcare e da semente desenvolvida pelo Grupo de Dosimetria de Fontes de Braquiterapia do Centro de Tecnologia das Radiações (CTR IPEN-CNEN/SP) por simulação computacional da distribuição de dose utilizando o código MCNP5, baseado no Método de Monte Carlo. A semente 6711 foi modelada, assim como um sistema dosimétrico constituído por um objeto simulador cúbico de 30x30x30 cm3 preenchido com água. Os valores obtidos da semente 6711 foram comparados com alguns apresentados na literatura, onde o parâmetro Constante de taxa de dose apresentou erro relativo em relação ao valor publicado no TG- 43 de 0,1%, sendo que os outros parâmetros analisados também apresentaram boa concordância com os valores publicados na literatura. Deste modo, pode-se considerar que os parâmetros utilizados nas simulações (espectro, modelagem geométrica e avaliação de resultados) estão compatíveis com outros estudos, sendo estes parâmetros também utilizados nas simulações da semente do IPEN. Considerando as análises de incerteza estatística, os valores obtidos da semente do IPEN são semelhantes aos valores da semente 6711.

Tethered Monte Carlo: computing the effective potential without critical slowing down

We present Tethered Monte Carlo, a simple, general purpose method of computing the effective potential of the order parameter (Helmholtz free energy). This formalism is based on a new statistical ensemble, closely related to the micromagnetic one, but with an extended configuration space (through Creutz-like demons). Canonical averages for arbitrary values of the external magnetic field are computed without additional simulations. The method is put to work in the two-dimensional Ising model, where the existence of exact results enables us to perform high precision checks. A rather peculiar feature of our implementation, which employs a local Metropolis algorithm, is the total absence, within errors, of critical slowing down for magnetic observables. Indeed, high accuracy results are presented for lattices as large as L = 1024.

Tethered Monte Carlo: computing the effective potential without critical slowing down

We present Tethered Monte Carlo, a simple, general purpose method of computing the effective potential of the order parameter (Helmholtz free energy). This formalism is based on a new statistical ensemble, closely related to the micromagnetic one, but with an extended configuration space (through Creutz-like demons). Canonical averages for arbitrary values of the external magnetic field are computed without additional simulations. The method is put to work in the two-dimensional Ising model, where the existence of exact results enables us to perform high precision checks. A rather peculiar feature of our implementation, which employs a local Metropolis algorithm, is the total absence, within errors, of critical slowing down for magnetic observables. Indeed, high accuracy results are presented for lattices as large as L = 1024.

Adsorption of Supercritical fluids on graphitised thermal carbon black: Molecular layer structure theory versus grand canonical Monte Carlo simulation

This paper presents a detailed analysis of adsorption of supercritical fluids on nonporous graphitized thermal carbon black. Two methods are employed in the analysis. One is the molecular layer structure theory (MLST), proposed recently by our group, and the other is the grand canonical Monte Carlo (GCMC) simulation. They were applied to describe the adsorption of argon, krypton, methane, ethylene, and sulfur hexafluoride on graphitized thermal carbon black. It was found that the MLST describes all the experimental data at various temperatures well. Results from GCMC simulations describe well the data at low pressure but show some deviations at higher pressures for all the adsorbates tested. The question of negative surface excess is also discussed in this paper.

Gaussian quantum Monte Carlo methods for fermions and bosons

We introduce a new class of quantum Monte Carlo methods, based on a Gaussian quantum operator representation of fermionic states. The methods enable first-principles dynamical or equilibrium calculations in many-body Fermi systems, and, combined with the existing Gaussian representation for bosons, provide a unified method of simulating Bose-Fermi systems. As an application relevant to the Fermi sign problem, we calculate finite-temperature properties of the two dimensional Hubbard model and the dynamics in a simple model of coherent molecular dissociation.

Análise da formulação em Monte Carlo dos pacotes de energia multiespectrais aplicada a meios constituídos por vapor d'água

The Monte Carlo method is accurate and is relatively simple to implement for the solution of problems involving complex geometries and anisotropic scattering of radiation as compared with other numerical techniques. In addition, differently of what happens for most of numerical techniques, for which the associated simulations computational time tends to increase exponentially with the complexity of the problems, in the Monte Carlo the increase of the computational time tends to be linear. Nevertheless, the Monte Carlo solution is highly computer time consuming for most of the interest problems. The Multispectral Energy Bundle model allows the reduction of the computational time associated to the Monte Carlo solution. The referred model is here analyzed for applications in media constituted for nonparticipating species and water vapor, which is an important emitting species formed during the combustion of hydrocarbon fuels. Aspects related to computer time optimization are investigated the model solutions are compared with benchmark line-by-line solutions

Comparing gold nano-particle enhanced radiotherapy with protons, megavoltage photons and kilovoltage photons: a Monte Carlo simulation

Gold nanoparticles (GNPs) have shown potential to be used as a radiosensitizer for radiation therapy. Despite extensive research activity to study GNP radiosensitization using photon beams, only a few studies have been carried out using proton beams. In this work Monte Carlo simulations were used to assess the dose enhancement of GNPs for proton therapy. The enhancement effect was compared between a clinical proton spectrum, a clinical 6 MV photon spectrum, and a kilovoltage photon source similar to those used in many radiobiology lab settings. We showed that the mechanism by which GNPs can lead to dose enhancements in radiation therapy differs when comparing photon and proton radiation. The GNP dose enhancement using protons can be up to 14 and is independent of proton energy, while the dose enhancement is highly dependent on the photon energy used. For the same amount of energy absorbed in the GNP, interactions with protons, kVp photons and MV photons produce similar doses within several nanometers of the GNP surface, and differences are below 15% for the first 10 nm. However, secondary electrons produced by kilovoltage photons have the longest range in water as compared to protons and MV photons, e.g. they cause a dose enhancement 20 times higher than the one caused by protons 10 μm away from the GNP surface. We conclude that GNPs have the potential to enhance radiation therapy depending on the type of radiation source. Proton therapy can be enhanced significantly only if the GNPs are in close proximity to the biological target.

Zastosowanie modelu hantli w badaniach właściwości fizykochemicznych i strukturalnych układów homo- i heterogenicznych metodą Monte Carlo

Wydział Chemii

Identifying stationary series in panels: A Monte Carlo evaluation of sequential panel selection methods

Sequential panel selection methods (spsms — procedures that sequentially use conventional panel unit root tests to identify I(0)I(0) time series in panels) are increasingly used in the empirical literature. We check the reliability of spsms by using Monte Carlo simulations based on generating directly the individual asymptotic pp values to be combined into the panel unit root tests, in this way isolating the classification abilities of the procedures from the small sample properties of the underlying univariate unit root tests. The simulations consider both independent and cross-dependent individual test statistics. Results suggest that spsms may offer advantages over time series tests only under special conditions.