Propagation of Nuclear Data Uncertainties in Transmutation Calculations Using ACAB Code

The assessment of the accuracy of parameters related to the reactor core performance (e.g., ke) and f el cycle (e.g., isotopic evolution/transmutation) due to the uncertainties in the basic nuclear data (ND) is a critical issue. Different error propagation techniques (adjoint/forward sensitivity analysis procedures and/or Monte Carlo technique) can be used to address by computational simulation the systematic propagation of uncertainties on the final parameters. To perform this uncertainty assessment, the ENDF covariance les (variance/correlation in energy and cross- reactions-isotopes correlations) are required. In this paper, we assess the impact of ND uncertainties on the isotopic prediction for a conceptual design of a modular European Facility for Industrial Transmutation (EFIT) for a discharge burnup of 150 GWd/tHM. The complete set of uncertainty data for cross sections (EAF2007/UN, SCALE6.0/COVA-44G), radioactive decay and fission yield data (JEFF-3.1.1) are processed and used in ACAB code.

Development of a methodology for nuclear data uncertainty propagation on isotopic evolution calculations for advanced nuclear systems

Una apropiada evaluación de los márgenes de seguridad de una instalación nuclear, por ejemplo, una central nuclear, tiene en cuenta todas las incertidumbres que afectan a los cálculos de diseño, funcionanmiento y respuesta ante accidentes de dicha instalación. Una fuente de incertidumbre son los datos nucleares, que afectan a los cálculos neutrónicos, de quemado de combustible o activación de materiales. Estos cálculos permiten la evaluación de las funciones respuesta esenciales para el funcionamiento correcto durante operación, y también durante accidente. Ejemplos de esas respuestas son el factor de multiplicación neutrónica o el calor residual después del disparo del reactor. Por tanto, es necesario evaluar el impacto de dichas incertidumbres en estos cálculos. Para poder realizar los cálculos de propagación de incertidumbres, es necesario implementar metodologías que sean capaces de evaluar el impacto de las incertidumbres de estos datos nucleares. Pero también es necesario conocer los datos de incertidumbres disponibles para ser capaces de manejarlos. Actualmente, se están invirtiendo grandes esfuerzos en mejorar la capacidad de analizar, manejar y producir datos de incertidumbres, en especial para isótopos importantes en reactores avanzados. A su vez, nuevos programas/códigos están siendo desarrollados e implementados para poder usar dichos datos y analizar su impacto. Todos estos puntos son parte de los objetivos del proyecto europeo ANDES, el cual ha dado el marco de trabajo para el desarrollo de esta tesis doctoral. Por tanto, primero se ha llevado a cabo una revisión del estado del arte de los datos nucleares y sus incertidumbres, centrándose en los tres tipos de datos: de decaimiento, de rendimientos de fisión y de secciones eficaces. A su vez, se ha realizado una revisión del estado del arte de las metodologías para la propagación de incertidumbre de estos datos nucleares. Dentro del Departamento de Ingeniería Nuclear (DIN) se propuso una metodología para la propagación de incertidumbres en cálculos de evolución isotópica, el Método Híbrido. Esta metodología se ha tomado como punto de partida para esta tesis, implementando y desarrollando dicha metodología, así como extendiendo sus capacidades. Se han analizado sus ventajas, inconvenientes y limitaciones. El Método Híbrido se utiliza en conjunto con el código de evolución isotópica ACAB, y se basa en el muestreo por Monte Carlo de los datos nucleares con incertidumbre. En esta metodología, se presentan diferentes aproximaciones según la estructura de grupos de energía de las secciones eficaces: en un grupo, en un grupo con muestreo correlacionado y en multigrupos. Se han desarrollado diferentes secuencias para usar distintas librerías de datos nucleares almacenadas en diferentes formatos: ENDF-6 (para las librerías evaluadas), COVERX (para las librerías en multigrupos de SCALE) y EAF (para las librerías de activación). Gracias a la revisión del estado del arte de los datos nucleares de los rendimientos de fisión se ha identificado la falta de una información sobre sus incertidumbres, en concreto, de matrices de covarianza completas. Además, visto el renovado interés por parte de la comunidad internacional, a través del grupo de trabajo internacional de cooperación para evaluación de datos nucleares (WPEC) dedicado a la evaluación de las necesidades de mejora de datos nucleares mediante el subgrupo 37 (SG37), se ha llevado a cabo una revisión de las metodologías para generar datos de covarianza. Se ha seleccionando la actualización Bayesiana/GLS para su implementación, y de esta forma, dar una respuesta a dicha falta de matrices completas para rendimientos de fisión. Una vez que el Método Híbrido ha sido implementado, desarrollado y extendido, junto con la capacidad de generar matrices de covarianza completas para los rendimientos de fisión, se han estudiado diferentes aplicaciones nucleares. Primero, se estudia el calor residual tras un pulso de fisión, debido a su importancia para cualquier evento después de la parada/disparo del reactor. Además, se trata de un ejercicio claro para ver la importancia de las incertidumbres de datos de decaimiento y de rendimientos de fisión junto con las nuevas matrices completas de covarianza. Se han estudiado dos ciclos de combustible de reactores avanzados: el de la instalación europea para transmutación industrial (EFIT) y el del reactor rápido de sodio europeo (ESFR), en los cuales se han analizado el impacto de las incertidumbres de los datos nucleares en la composición isotópica, calor residual y radiotoxicidad. Se han utilizado diferentes librerías de datos nucleares en los estudios antreriores, comparando de esta forma el impacto de sus incertidumbres. A su vez, mediante dichos estudios, se han comparando las distintas aproximaciones del Método Híbrido y otras metodologías para la porpagación de incertidumbres de datos nucleares: Total Monte Carlo (TMC), desarrollada en NRG por A.J. Koning y D. Rochman, y NUDUNA, desarrollada en AREVA GmbH por O. Buss y A. Hoefer. Estas comparaciones demostrarán las ventajas del Método Híbrido, además de revelar sus limitaciones y su rango de aplicación. ABSTRACT For an adequate assessment of safety margins of nuclear facilities, e.g. nuclear power plants, it is necessary to consider all possible uncertainties that affect their design, performance and possible accidents. Nuclear data are a source of uncertainty that are involved in neutronics, fuel depletion and activation calculations. These calculations can predict critical response functions during operation and in the event of accident, such as decay heat and neutron multiplication factor. Thus, the impact of nuclear data uncertainties on these response functions needs to be addressed for a proper evaluation of the safety margins. Methodologies for performing uncertainty propagation calculations need to be implemented in order to analyse the impact of nuclear data uncertainties. Nevertheless, it is necessary to understand the current status of nuclear data and their uncertainties, in order to be able to handle this type of data. Great eórts are underway to enhance the European capability to analyse/process/produce covariance data, especially for isotopes which are of importance for advanced reactors. At the same time, new methodologies/codes are being developed and implemented for using and evaluating the impact of uncertainty data. These were the objectives of the European ANDES (Accurate Nuclear Data for nuclear Energy Sustainability) project, which provided a framework for the development of this PhD Thesis. Accordingly, first a review of the state-of-the-art of nuclear data and their uncertainties is conducted, focusing on the three kinds of data: decay, fission yields and cross sections. A review of the current methodologies for propagating nuclear data uncertainties is also performed. The Nuclear Engineering Department of UPM has proposed a methodology for propagating uncertainties in depletion calculations, the Hybrid Method, which has been taken as the starting point of this thesis. This methodology has been implemented, developed and extended, and its advantages, drawbacks and limitations have been analysed. It is used in conjunction with the ACAB depletion code, and is based on Monte Carlo sampling of variables with uncertainties. Different approaches are presented depending on cross section energy-structure: one-group, one-group with correlated sampling and multi-group. Differences and applicability criteria are presented. Sequences have been developed for using different nuclear data libraries in different storing-formats: ENDF-6 (for evaluated libraries) and COVERX (for multi-group libraries of SCALE), as well as EAF format (for activation libraries). A revision of the state-of-the-art of fission yield data shows inconsistencies in uncertainty data, specifically with regard to complete covariance matrices. Furthermore, the international community has expressed a renewed interest in the issue through the Working Party on International Nuclear Data Evaluation Co-operation (WPEC) with the Subgroup (SG37), which is dedicated to assessing the need to have complete nuclear data. This gives rise to this review of the state-of-the-art of methodologies for generating covariance data for fission yields. Bayesian/generalised least square (GLS) updating sequence has been selected and implemented to answer to this need. Once the Hybrid Method has been implemented, developed and extended, along with fission yield covariance generation capability, different applications are studied. The Fission Pulse Decay Heat problem is tackled first because of its importance during events after shutdown and because it is a clean exercise for showing the impact and importance of decay and fission yield data uncertainties in conjunction with the new covariance data. Two fuel cycles of advanced reactors are studied: the European Facility for Industrial Transmutation (EFIT) and the European Sodium Fast Reactor (ESFR), and response function uncertainties such as isotopic composition, decay heat and radiotoxicity are addressed. Different nuclear data libraries are used and compared. These applications serve as frameworks for comparing the different approaches of the Hybrid Method, and also for comparing with other methodologies: Total Monte Carlo (TMC), developed at NRG by A.J. Koning and D. Rochman, and NUDUNA, developed at AREVA GmbH by O. Buss and A. Hoefer. These comparisons reveal the advantages, limitations and the range of application of the Hybrid Method.

Efficient methodologies for system matrix modelling in iterative image reconstruction for rotating high-resolution PET

A fully 3D iterative image reconstruction algorithm has been developed for high-resolution PET cameras composed of pixelated scintillator crystal arrays and rotating planar detectors, based on the ordered subsets approach. The associated system matrix is precalculated with Monte Carlo methods that incorporate physical effects not included in analytical models, such as positron range effects and interaction of the incident gammas with the scintillator material. Custom Monte Carlo methodologies have been developed and optimized for modelling of system matrices for fast iterative image reconstruction adapted to specific scanner geometries, without redundant calculations. According to the methodology proposed here, only one-eighth of the voxels within two central transaxial slices need to be modelled in detail. The rest of the system matrix elements can be obtained with the aid of axial symmetries and redundancies, as well as in-plane symmetries within transaxial slices. Sparse matrix techniques for the non-zero system matrix elements are employed, allowing for fast execution of the image reconstruction process. This 3D image reconstruction scheme has been compared in terms of image quality to a 2D fast implementation of the OSEM algorithm combined with Fourier rebinning approaches. This work confirms the superiority of fully 3D OSEM in terms of spatial resolution, contrast recovery and noise reduction as compared to conventional 2D approaches based on rebinning schemes. At the same time it demonstrates that fully 3D methodologies can be efficiently applied to the image reconstruction problem for high-resolution rotational PET cameras by applying accurate pre-calculated system models and taking advantage of the system's symmetries.

Evaluación y análisis de la trazabilidad metrológica en redes para la verificación y calibración de instrumental GNSS (Global Navigation Satellite System)

Los estudios realizados hasta el momento para la determinación de la calidad de medida del instrumental geodésico han estado dirigidos, fundamentalmente, a las medidas angulares y de distancias. Sin embargo, en los últimos años se ha impuesto la tendencia generalizada de utilizar equipos GNSS (Global Navigation Satellite System) en el campo de las aplicaciones geomáticas sin que se haya establecido una metodología que permita obtener la corrección de calibración y su incertidumbre para estos equipos. La finalidad de esta Tesis es establecer los requisitos que debe satisfacer una red para ser considerada Red Patrón con trazabilidad metrológica, así como la metodología para la verificación y calibración de instrumental GNSS en redes patrón. Para ello, se ha diseñado y elaborado un procedimiento técnico de calibración de equipos GNSS en el que se han definido las contribuciones a la incertidumbre de medida. El procedimiento, que se ha aplicado en diferentes redes para distintos equipos, ha permitido obtener la incertidumbre expandida de dichos equipos siguiendo las recomendaciones de la Guide to the Expression of Uncertainty in Measurement del Joint Committee for Guides in Metrology. Asimismo, se han determinado mediante técnicas de observación por satélite las coordenadas tridimensionales de las bases que conforman las redes consideradas en la investigación, y se han desarrollado simulaciones en función de diversos valores de las desviaciones típicas experimentales de los puntos fijos que se han utilizado en el ajuste mínimo cuadrático de los vectores o líneas base. Los resultados obtenidos han puesto de manifiesto la importancia que tiene el conocimiento de las desviaciones típicas experimentales en el cálculo de incertidumbres de las coordenadas tridimensionales de las bases. Basándose en estudios y observaciones de gran calidad técnica, llevados a cabo en estas redes con anterioridad, se ha realizado un exhaustivo análisis que ha permitido determinar las condiciones que debe satisfacer una red patrón. Además, se han diseñado procedimientos técnicos de calibración que permiten calcular la incertidumbre expandida de medida de los instrumentos geodésicos que proporcionan ángulos y distancias obtenidas por métodos electromagnéticos, ya que dichos instrumentos son los que van a permitir la diseminación de la trazabilidad metrológica a las redes patrón para la verificación y calibración de los equipos GNSS. De este modo, ha sido posible la determinación de las correcciones de calibración local de equipos GNSS de alta exactitud en las redes patrón. En esta Tesis se ha obtenido la incertidumbre de la corrección de calibración mediante dos metodologías diferentes; en la primera se ha aplicado la propagación de incertidumbres, mientras que en la segunda se ha aplicado el método de Monte Carlo de simulación de variables aleatorias. El análisis de los resultados obtenidos confirma la validez de ambas metodologías para la determinación de la incertidumbre de calibración de instrumental GNSS. ABSTRACT The studies carried out so far for the determination of the quality of measurement of geodetic instruments have been aimed, primarily, to measure angles and distances. However, in recent years it has been accepted to use GNSS (Global Navigation Satellite System) equipment in the field of Geomatic applications, for data capture, without establishing a methodology that allows obtaining the calibration correction and its uncertainty. The purpose of this Thesis is to establish the requirements that a network must meet to be considered a StandardNetwork with metrological traceability, as well as the methodology for the verification and calibration of GNSS instrumental in those standard networks. To do this, a technical calibration procedure has been designed, developed and defined for GNSS equipment determining the contributions to the uncertainty of measurement. The procedure, which has been applied in different networks for different equipment, has alloweddetermining the expanded uncertainty of such equipment following the recommendations of the Guide to the Expression of Uncertainty in Measurement of the Joint Committee for Guides in Metrology. In addition, the three-dimensional coordinates of the bases which constitute the networks considered in the investigationhave been determined by satellite-based techniques. There have been several developed simulations based on different values of experimental standard deviations of the fixed points that have been used in the least squares vectors or base lines calculations. The results have shown the importance that the knowledge of experimental standard deviations has in the calculation of uncertainties of the three-dimensional coordinates of the bases. Based on high technical quality studies and observations carried out in these networks previously, it has been possible to make an exhaustive analysis that has allowed determining the requirements that a standard network must meet. In addition, technical calibration procedures have been developed to allow the uncertainty estimation of measurement carried outby geodetic instruments that provide angles and distances obtained by electromagnetic methods. These instruments provide the metrological traceability to standard networks used for verification and calibration of GNSS equipment. As a result, it has been possible the estimation of local calibration corrections for high accuracy GNSS equipment in standardnetworks. In this Thesis, the uncertainty of calibration correction has been calculated using two different methodologies: the first one by applying the law of propagation of uncertainty, while the second has applied the propagation of distributions using the Monte Carlo method. The analysis of the obtained results confirms the validity of both methodologies for estimating the calibration uncertainty of GNSS equipment.

Extreme flood abatement in large dams with fixed-crest spillways

This study characterises the abatement effect of large dams with fixed-crest spillways under extreme design flood conditions. In contrast to previous studies using specific hydrographs for flow into the reservoir and simplifications to obtain analytical solutions, an automated tool was designed for calculations based on a Monte Carlo simulation environment, which integrates models that represent the different physical processes in watersheds with areas of 150?2000 km2. The tool was applied to 21 sites that were uniformly distributed throughout continental Spain, with 105 fixed-crest dam configurations. This tool allowed a set of hydrographs to be obtained as an approximation for the hydrological forcing of a dam and the characterisation of the response of the dam to this forcing. For all cases studied, we obtained a strong linear correlation between the peak flow entering the reservoir and the peak flow discharged by the dam, and a simple general procedure was proposed to characterise the peak-flow attenuation behaviour of the reservoir. Additionally, two dimensionless coefficients were defined to relate the variables governing both the generation of the flood and its abatement in the reservoir. Using these coefficients, a model was defined to allow for the estimation of the flood abatement effect of a reservoir based on the available information. This model should be useful in the hydrological design of spillways and the evaluation of the hydrological safety of dams. Finally, the proposed procedure and model were evaluated and representative applications were presented

Iterative determination of clinical beam phase space from dose measurements

Monte Carlo (MC) method can accurately compute the dose produced by medical linear accelerators. However, these calculations require a reliable description of the electron and/or photon beams delivering the dose, the phase space (PHSP), which is not usually available. A method to derive a phase space model from reference measurements that does not heavily rely on a detailed model of the accelerator head is presented. The iterative optimization process extracts the characteristics of the particle beams which best explains the reference dose measurements in water and air, given a set of constrains

Analysis of a Spanish energy scenario with Generation IV nuclear reactors

The advantages of fast-spectrum reactors consist not only of an efficient use of fuel through the breeding of fissile material and the use of natural or depleted uranium, but also of the potential reduction of the amount of actinides such as americium and neptunium contained in the irradiated fuel. The first aspect means a guaranteed future nuclear fuel supply. The second fact is key for high-level radioactive waste management, because these elements are the main responsible for the radioactivity of the irradiated fuel in the long term. The present study aims to analyze the hypothetical deployment of a Gen-IV Sodium Fast Reactor (SFR) fleet in Spain. A nuclear fleet of fast reactors would enable a fuel cycle strategy different than the open cycle, currently adopted by most of the countries with nuclear power. A transition from the current Gen-II to Gen-IV fleet is envisaged through an intermediate deployment of Gen-III reactors. Fuel reprocessing from the Gen-II and Gen-III Light Water Reactors (LWR) has been considered. In the so-called advanced fuel cycle, the reprocessed fuel used to produce energy will breed new fissile fuel and transmute minor actinides at the same time. A reference case scenario has been postulated and further sensitivity studies have been performed to analyze the impact of the different parameters on the required reactor fleet. The potential capability of Spain to supply the required fleet for the reference scenario using national resources has been verified. Finally, some consequences on irradiated final fuel inventory are assessed. Calculations are performed with the Monte Carlo transport-coupled depletion code SERPENT together with post-processing tools.

Application of a Bayesian/Generalised Least-Squares method to generate correlations between independent neutron fission yield data

Fission product yields are fundamental parameters for several nuclear engineering calculations and in particular for burn-up/activation problems. The impact of their uncertainties was widely studied in the past and valuations were released, although still incomplete. Recently, the nuclear community expressed the need for full fission yield covariance matrices to produce inventory calculation results that take into account the complete uncertainty data. In this work, we studied and applied a Bayesian/generalised least-squares method for covariance generation, and compared the generated uncertainties to the original data stored in the JEFF-3.1.2 library. Then, we focused on the effect of fission yield covariance information on fission pulse decay heat results for thermal fission of 235U. Calculations were carried out using different codes (ACAB and ALEPH-2) after introducing the new covariance values. Results were compared with those obtained with the uncertainty data currently provided by the library. The uncertainty quantification was performed with the Monte Carlo sampling technique. Indeed, correlations between fission yields strongly affect the statistics of decay heat. Introduction Nowadays, any engineering calculation performed in the nuclear field should be accompanied by an uncertainty analysis. In such an analysis, different sources of uncertainties are taken into account. Works such as those performed under the UAM project (Ivanov, et al., 2013) treat nuclear data as a source of uncertainty, in particular cross-section data for which uncertainties given in the form of covariance matrices are already provided in the major nuclear data libraries. Meanwhile, fission yield uncertainties were often neglected or treated shallowly, because their effects were considered of second order compared to cross-sections (Garcia-Herranz, et al., 2010). However, the Working Party on International Nuclear Data Evaluation Co-operation (WPEC)