Electromagnetic Instability Studies in Fusion Plasmas Edge

Este trabajo esta dedicado al estudio de las estructuras macroscópicas conocidas en la literatura como filamentos o blobs que han sido observadas de manera universal en el borde de todo tipo de dispositivos de fusión por confinamiento magnético. Estos filamentos, celdas convectivas elongadas a lo largo de las líneas de campo que surgen en el plasma fuertemente turbulento que existe en este tipo de dispositivos, parecen dominar el transporte radial de partículas y energía en la región conocida como Scrape-off Layer, en la que las líneas de campo dejan de estar cerradas y el plasma es dirigido hacia la pared sólida que forma la cámara de vacío. Aunque el comportamiento y las leyes de escala de estas estructuras son relativamente bien conocidos, no existe aún una teoría generalmente aceptada acerca del mecanismo físico responsable de su formación, que constituye una de las principales incógnitas de la teoría de transporte del borde en plasmas de fusión y una cuestión de gran importancia práctica en el desarrollo de la siguiente generación de reactores de fusión (incluyendo dispositivos como ITER y DEMO), puesto que la eficiencia del confinamiento y la cantidad de energía depositadas en la pared dependen directamente de las características del transporte en el borde. El trabajo ha sido realizado desde una perspectiva eminentemente experimental, incluyendo la observación y el análisis de este tipo de estructuras en el stellarator tipo heliotrón LHD (un dispositivo de gran tamaño, capaz de generar plasmas de características cercanas a las necesarias en un reactor de fusión) y en el stellarator tipo heliac TJ-II (un dispositivo de medio tamaño, capaz de generar plasmas relativamente más fríos pero con una accesibilidad y disponibilidad de diagnósticos mayor). En particular, en LHD se observó la generación de filamentos durante las descargas realizadas en configuración de alta _ (alta presión cinética frente a magnética) mediante una cámara visible ultrarrápida, se caracterizó su comportamiento y se investigó, mediante el análisis estadístico y la comparación con modelos teóricos, el posible papel de la Criticalidad Autoorganizada en la formación de este tipo de estructuras. En TJ-II se diseñó y construyó una cabeza de sonda capaz de medir simultáneamente las fluctuaciones electrostáticas y electromagnéticas del plasma. Gracias a este nuevo diagnóstico se pudieron realizar experimentos con el fin de determinar la presencia de corriente paralela a través de los filamentos (un parámetro de gran importancia en su modelización) y relacionar los dos tipos de fluctuaciones por primera vez en un stellarator. Así mismo, también por primera vez en este tipo de dispositivo, fue posible realizar mediciones simultáneas de los tensores viscoso y magnético (Reynolds y Maxwell) de transporte de cantidad de movimiento. ABSTRACT This work has been devoted to the study of the macroscopic structures known in the literature as filaments or blobs, which have been observed universally in the edge of all kind of magnetic confinement fusion devices. These filaments, convective cells stretching along the magnetic field lines, arise from the highly turbulent plasma present in this kind of machines and seem to dominate radial transport of particles and energy in the region known as Scrapeoff Layer, in which field lines become open and plasma is directed towards the solid wall of the vacuum vessel. Although the behavior and scale laws of these structures are relatively well known, there is no generally accepted theory about the physical mechanism involved in their formation yet, which remains one of the main unsolved questions in the fusion plasmas edge transport theory and a matter of great practical importance for the development of the next generation of fusion reactors (including ITER and DEMO), since efficiency of confinement and the energy deposition levels on the wall are directly dependent of the characteristics of edge transport. This work has been realized mainly from an experimental perspective, including the observation and analysis of this kind of structures in the heliotron stellarator LHD (a large device capable of generating reactor-relevant plasma conditions) and in the heliac stellarator TJ-II (a medium-sized device, capable of relatively colder plasmas, but with greater ease of access and diagnostics availability). In particular, in LHD, the generation of filaments during high _ discharges (with high kinetic to magnetic pressure ratio) was observed by means of an ultrafast visible camera, and the behavior of this structures was characterized. Finally, the potential role of Self-Organized Criticality in the generation of filaments was investigated. In TJ-II, a probe head capable of measuring simultaneously electrostatic and electromagnetic fluctuations in the plasma was designed and built. Thanks to this new diagnostic, experiments were carried out in order to determine the presence of parallel current through filaments (one of the most important parameters in their modelization) and to related electromagnetic (EM) and electrostatic (ES) fluctuations for the first time in an stellarator. As well, also for the first time in this kind of device, measurements of the viscous and magnetic momentum transfer tensors (Reynolds and Maxwell) were performed.

Propagation of nuclear data uncertainties in fuel cycle calculations using MONTE-CARLO Technique

The uncertainty propagation in fuel cycle calculations due to Nuclear Data (ND) is a important important issue for : issue for : • Present fuel cycles (e.g. high burnup fuel programme) • New fuel cycles designs (e.g. fast breeder reactors and ADS) Different error propagation techniques can be used: • Sensitivity analysis • Response Response Surface Method Surface Method • Monte Carlo technique Then, p p , , in this paper, it is assessed the imp y pact of ND uncertainties on the decay heat and radiotoxicity in two applications: • Fission Pulse Decay ( y Heat calculation (FPDH) • Conceptual design of European Facility for Industrial Transmutation (EFIT)

Interstitial defects stability in FeCr alloys vs Cr concentration

Finding adequate materials to withstand the demanding conditions in the future fusion and fission reactors is a real challenge in the development of these technologies. Structural materials need to sustain high irradiation doses and temperatures that will change the microstructure over time. A better understanding of the changes produced by the irradiation will allow for a better choice of materials, ensuring a safer and reliable future power plants. High-Cr ferritic/martensitic steels head the list of structural materials due to their high resistance to swelling and corrosion. However, it is well known that these alloys present a problem of embrittlement, which could be caused by the presence of defects created by irradiation as these defects act as obstacles for dislocation motion. Therefore, the mechanical response of these materials will depend on the type of defects created during irradiation. In this work, we address a study of the effect Cr concentration has on single interstitial defect formation energies in FeCr alloys.

A proposed parameterization of interface discontinuity factors depending on neighborhood for pin-by-pin diffusion computations for LWR

There exists an interest in performing full core pin-by-pin computations for present nuclear reactors. In such type of problems the use of a transport approximation like the diffusion equation requires the introduction of correction parameters. Interface discontinuity factors can improve the diffusion solution to nearly reproduce a transport solution. Nevertheless, calculating accurate pin-by-pin IDF requires the knowledge of the heterogeneous neutron flux distribution, which depends on the boundary conditions of the pin-cell as well as the local variables along the nuclear reactor operation. As a consequence, it is impractical to compute them for each possible configuration. An alternative to generate accurate pin-by-pin interface discontinuity factors is to calculate reference values using zero-net-current boundary conditions and to synthesize afterwards their dependencies on the main neighborhood variables. In such way the factors can be accurately computed during fine-mesh diffusion calculations by correcting the reference values as a function of the actual environment of the pin-cell in the core. In this paper we propose a parameterization of the pin-by-pin interface discontinuity factors allowing the implementation of a cross sections library able to treat the neighborhood effect. First results are presented for typical PWR configurations.

Thermal diffusion profile by NRA of Deuterium implanted in solid breeder blanket materials

This paper studies the relationship between aging, physical changes and the results of non-destructive testing of plywood. 176 pieces of plywood were tested to analyze their actual and estimated density using non-destructive methods (screw withdrawal force and ultrasound wave velocity) during a laboratory aging test. From the results of statistical analysis it can be concluded that there is a strong relationship between the non-destructive measurements carried out, and the decline in the physical properties of the panels due to aging. The authors propose several models to estimate board density. The best results are obtained with ultrasound. A reliable prediction of the degree of deterioration (aging) of board is presented. Breeder blanket materials have to produce tritium from lithium while fulfilling several strict conditions. In particular, when dealing with materials to be applied in fusion reactors, one of the key questions is the study of light ions retention, which can be produced by transmutation reactions and/or introduced by interaction with the plasma. In ceramic breeders the understanding of the hydrogen isotopes behaviour and specially the diffusion of tritium to the surface is crucial. Moreover the evolution of the microstructure during irradiation with energetic ions, neutrons and electrons is complex because of the interaction of a high number of processes.

Application of gas-cooled Accelerator Driven System (ADS) transmutation devices to sustainable nuclear energy development

The conceptual design of a pebble bed gas-cooled transmutation device is shown with the aim to evaluate its potential for its deployment in the context of the sustainable nuclear energy development, which considers high temperature reactors for their operation in cogeneration mode, producing electricity, heat and Hydrogen. As differential characteristics our device operates in subcritical mode, driven by a neutron source activated by an accelerator that adds clear safety advantages and fuel flexibility opening the possibility to reduce the nuclear stockpile producing energy from actual LWR irradiated fuel with an efficiency of 45?46%, either in the form of Hydrogen, electricity, or both.

Application of Ultraintense Lasers to validate materials for laser fusion: production of ions and other relevant species

Justification of the need and demand of experimental facilities to test and validate materials for first wall in laser fusion reactors - Characteristics of the laser fusion products - Current ?possible? facilities for tests Ultraintense Lasers as ?complete? solution facility - Generation of ion pulses - Generation of X-ray pulses - Generation of other relevant particles (electrons, neutrons..)

Estudio de la digestión anaerobia en dos fases para el tratamiento de las aguas residuales de despulpe del beneficiado húmedo del café

Debido al aumento de los estándares de calidad exigidos internacionalmente, así como por una mayor presión sobre la industria mediante legislaciones ambientales más rigurosas, el sector cafetalero está obligado a buscar, a través de la investigación, un sistema adecuado de tratamiento para las aguas residuales generadas en el beneficiado húmedo del café. En este trabajo se evaluó el funcionamiento de la digestión anaerobia para el tratamiento de las aguas residuales de despulpe. Para ello, se utilizaron dos sistemas anaerobios, uno en una etapa (UASB), y otro con separación de fases (2PUASB). Se investigó el efecto en la digestión anaerobia de tres cargas orgánicas volumétricas (OLR) y de las dos configuraciones de reactor usadas. Los valores de OLR de operación en el sistema UASB variaron en un intervalo de 3.6-4.1 kgCOD m-3 d-1, con una tasa de recirculación del efluente de 1.0. El sistema 2PUASB fue alimentado con OLR similares a las que se emplearon en el sistema en una etapa. El reactor de acidificación fue cargado a 11.0 kgCOD m-3 d-1, mientras que en el reactor metanogénico varió en el intervalo de 2.6-4.67 kgCOD m-3 d-1. El uso de reactores UASB en una etapa y en dos fases, bajo las mismas condiciones de operación ya descritas, propiciaron el logro de una eficiencia de degradación de COD total superior al 75% y al 85% para la COD soluble, respectivamente. Sin embargo, el sistema en dos fases mostró mejores resultados en el tratamiento de este tipo de agua residual, no solo en cuanto a eficiencia de eliminación de la carga orgánica contaminante así como una menor concentración de ácidos grasos volátiles (VFA) en el efluente. Obtenidas las mejores condiciones de trabajo, fue evaluada la separación de fases bajo el efecto de la recirculación. Los grupos de fermentaciones producidos fueron similares a los obtenidos en el experimento sin recirculación, indicando que está última no afectó la composición relativa de los VFA del reactor anaerobio, por lo que no cambió el patrón de degradación del residuo. Una tasa de recirculación de 1.0 del efluente del reactor metanogénico al reactor acidogénico mejoró significativamente el proceso, ya que se incrementó la conversión de los VFA (31%), la eliminación de la fracción total y soluble del residuo tratado (6.5%) y la reducción del consumo de alcalinizante (39%); manteniendo similares producciones de metano. El uso de la digestión anaerobia en dos fases demostró una mejora en la estabilidad del proceso y un incremento de la eficiencia de operación y de la producción de metano, respectivamente.Tesis Doctoral Yans Guardia Puebla Abstract ix ABSTRACT Due to the increase of quality standards internationally demanded, as well as for a greater pressure on the industry by means of more rigorous environmental legislations, the coffee sector is forced to search, through the research, an appropriated treatment system for coffee wet wastewaters generated. In this work the performance of the anaerobic digestion for the coffee wet wastewater treatment was evaluated. For it, two anaerobic systems, one in single-stage (UASB), and another with two-phase (2PUASB) were used. The effect in the anaerobic digestion of three organic loading rates (OLR) and of two reactor configurations used was investigated. OLR operation values in UASB system varied in an interval of 3.6-4.1 kgCOD m-3 d-1, with a recycle rate of the effluent of 1.0. 2PUASB system was fed with OLR similar to those that were used in the reactor in a stage. The acidification reactor was loaded to 11.0 kgCOD m-3 d-1, whereas in the methanogenic reactor varied in the interval of 2.6-4.67 kgCOD m-3 d-1. The use of single-stage and two-phase UASB reactors, under the same operation conditions already before described, a total COD removal efficiency of 75% and 85% for the soluble COD removal efficiency, respectively, was achieved. However, two-phase system showed better results in the treatment of this wastewater type, not only as for removal efficiency of loading organic polluting as well as a smaller volatile fatty acid (VFA) concentration in the effluent. Obtained the best work conditions, the two-phase system under the effect of the recycle was evaluated. Fermentations groups produced were similar to those obtained in the experiment without recycle, indicating that it last one do not affect the relative composition of VFA of the anaerobic reactor, for that reason the degradation pattern of the residue does not change. A recycle rate of 1.0 of the effluent of the methanogenic reactor to the acidogenic reactor improved the process significantly, since it was increased the VFA conversion (31%), the removal of total and soluble fraction of the residue treated (6.5%) and the decrease of the alkalinity consumption (39%); maintaining similar methane productions. The use of the two-phase anaerobic digestion demonstrated to an improvement in the stability of the process and an increase of the operation efficiency and methane production, respectively.

Análisis Integrado de Seguridad de un accidente de SGTR en un reactor nuclear tipo PWR

El accidente de rotura de tubos de un generador de vapor (Steam Generator Tube Rupture, SGTR) en los reactores de agua a presión es uno de los transitorios más exigentes desde el punto de vista de operación. Los transitorios de SGTR son especiales, ya que podría dar lugar a emisiones radiológicas al exterior sin necesidad de daño en el núcleo previo o sin que falle la contención, ya que los SG pueden constituir una vía directa desde el reactor al medio ambiente en este transitorio. En los análisis de seguridad, el SGTR se analiza desde un punto determinista y probabilista, con distintos enfoques con respecto a las acciones del operador y las consecuencias analizadas. Cuando comenzaron los Análisis Deterministas de Seguridad (DSA), la forma de analizar el SGTR fue sin dar crédito a la acción del operador durante los primeros 30 min del transitorio, lo que suponía que el grupo de operación era capaz de detener la fuga por el tubo roto dentro de ese tiempo. Sin embargo, los diferentes casos reales de accidentes de SGTR sucedidos en los EE.UU. y alrededor del mundo demostraron que los operadores pueden emplear más de 30 minutos para detener la fuga en la vida real. Algunas metodologías fueron desarrolladas en los EEUU y en Europa para abordar esa cuestión. En el Análisis Probabilista de Seguridad (PSA), las acciones del operador se tienen en cuenta para diseñar los cabeceros en el árbol de sucesos. Los tiempos disponibles se utilizan para establecer los criterios de éxito para dichos cabeceros. Sin embargo, en una secuencia dinámica como el SGTR, las acciones de un operador son muy dependientes del tiempo disponible por las acciones humanas anteriores. Además, algunas de las secuencias de SGTR puede conducir a la liberación de actividad radiológica al exterior sin daño previo en el núcleo y que no se tienen en cuenta en el APS, ya que desde el punto de vista de la integridad de núcleo son de éxito. Para ello, para analizar todos estos factores, la forma adecuada de analizar este tipo de secuencias pueden ser a través de una metodología que contemple Árboles de Sucesos Dinámicos (Dynamic Event Trees, DET). En esta Tesis Doctoral se compara el impacto en la evolución temporal y la dosis al exterior de la hipótesis más relevantes encontradas en los Análisis Deterministas a nivel mundial. La comparación se realiza con un modelo PWR Westinghouse de tres lazos (CN Almaraz) con el código termohidráulico TRACE, con hipótesis de estimación óptima, pero con hipótesis deterministas como criterio de fallo único o pérdida de energía eléctrica exterior. Las dosis al exterior se calculan con RADTRAD, ya que es uno de los códigos utilizados normalmente para los cálculos de dosis del SGTR. El comportamiento del reactor y las dosis al exterior son muy diversas, según las diferentes hipótesis en cada metodología. Por otra parte, los resultados están bastante lejos de los límites de regulación, pese a los conservadurismos introducidos. En el siguiente paso de la Tesis Doctoral, se ha realizado un análisis de seguridad integrado del SGTR según la metodología ISA, desarrollada por el Consejo de Seguridad Nuclear español (CSN). Para ello, se ha realizado un análisis termo-hidráulico con un modelo de PWR Westinghouse de 3 lazos con el código MAAP. La metodología ISA permite la obtención del árbol de eventos dinámico del SGTR, teniendo en cuenta las incertidumbres en los tiempos de actuación del operador. Las simulaciones se realizaron con SCAIS (sistema de simulación de códigos para la evaluación de la seguridad integrada), que incluye un acoplamiento dinámico con MAAP. Las dosis al exterior se calcularon también con RADTRAD. En los resultados, se han tenido en cuenta, por primera vez en la literatura, las consecuencias de las secuencias en términos no sólo de daños en el núcleo sino de dosis al exterior. Esta tesis doctoral demuestra la necesidad de analizar todas las consecuencias que contribuyen al riesgo en un accidente como el SGTR. Para ello se ha hecho uso de una metodología integrada como ISA-CSN. Con este enfoque, la visión del DSA del SGTR (consecuencias radiológicas) se une con la visión del PSA del SGTR (consecuencias de daño al núcleo) para evaluar el riesgo total del accidente. Abstract Steam Generator Tube Rupture accidents in Pressurized Water Reactors are known to be one of the most demanding transients for the operating crew. SGTR are special transient as they could lead to radiological releases without core damage or containment failure, as they can constitute a direct path to the environment. The SGTR is analyzed from a Deterministic and Probabilistic point of view in the Safety Analysis, although the assumptions of the different approaches regarding the operator actions are quite different. In the beginning of Deterministic Safety Analysis, the way of analyzing the SGTR was not crediting the operator action for the first 30 min of the transient, assuming that the operating crew was able to stop the primary to secondary leakage within that time. However, the different real SGTR accident cases happened in the USA and over the world demonstrated that operators can took more than 30 min to stop the leakage in actual sequences. Some methodologies were raised in the USA and in Europe to cover that issue. In the Probabilistic Safety Analysis, the operator actions are taken into account to set the headers in the event tree. The available times are used to establish the success criteria for the headers. However, in such a dynamic sequence as SGTR, the operator actions are very dependent on the time available left by the other human actions. Moreover, some of the SGTR sequences can lead to offsite doses without previous core damage and they are not taken into account in PSA as from the point of view of core integrity are successful. Therefore, to analyze all this factors, the appropriate way of analyzing that kind of sequences could be through a Dynamic Event Tree methodology. This Thesis compares the impact on transient evolution and the offsite dose of the most relevant hypothesis of the different SGTR analysis included in the Deterministic Safety Analysis. The comparison is done with a PWR Westinghouse three loop model in TRACE code (Almaraz NPP), with best estimate assumptions but including deterministic hypothesis such as single failure criteria or loss of offsite power. The offsite doses are calculated with RADTRAD code, as it is one of the codes normally used for SGTR offsite dose calculations. The behaviour of the reactor and the offsite doses are quite diverse depending on the different assumptions made in each methodology. On the other hand, although the high conservatism, such as the single failure criteria, the results are quite far from the regulatory limits. In the next stage of the Thesis, the Integrated Safety Assessment (ISA) methodology, developed by the Spanish Nuclear Safety Council (CSN), has been applied to a thermohydraulical analysis of a Westinghouse 3-loop PWR plant with the MAAP code. The ISA methodology allows obtaining the SGTR Dynamic Event Tree taking into account the uncertainties on the operator actuation times. Simulations are performed with SCAIS (Simulation Code system for Integrated Safety Assessment), which includes a dynamic coupling with MAAP thermal hydraulic code. The offsite doses are calculated also with RADTRAD. The results shows the consequences of the sequences in terms not only of core damage but of offsite doses. This Thesis shows the need of analyzing all the consequences in an accident such as SGTR. For that, an it has been used an integral methodology like ISA-CSN. With this approach, the DSA vision of the SGTR (radiological consequences) is joined with the PSA vision of the SGTR (core damage consequences) to measure the total risk of the accident.

Neighborhood-corrected interface discontinuity factors for multi-group pin-by-pin diffusion calculations for LWR

Performing three-dimensional pin-by-pin full core calculations based on an improved solution of the multi-group diffusion equation is an affordable option nowadays to compute accurate local safety parameters for light water reactors. Since a transport approximation is solved, appropriate correction factors, such as interface discontinuity factors, are required to nearly reproduce the fully heterogeneous transport solution. Calculating exact pin-by-pin discontinuity factors requires the knowledge of the heterogeneous neutron flux distribution, which depends on the boundary conditions of the pin-cell as well as the local variables along the nuclear reactor operation. As a consequence, it is impractical to compute them for each possible configuration; however, inaccurate correction factors are one major source of error in core analysis when using multi-group diffusion theory. An alternative to generate accurate pin-by-pin interface discontinuity factors is to build a functional-fitting that allows incorporating the environment dependence in the computed values. This paper suggests a methodology to consider the neighborhood effect based on the Analytic Coarse-Mesh Finite Difference method for the multi-group diffusion equation. It has been applied to both definitions of interface discontinuity factors, the one based on the Generalized Equivalence Theory and the one based on Black-Box Homogenization, and for different few energy groups structures. Conclusions are drawn over the optimal functional-fitting and demonstrative results are obtained with the multi-group pin-by-pin diffusion code COBAYA3 for representative PWR configurations.

Experimental results on advanced inertial fusion schemes obtained within the HiPER project

This paper presents de results of experiments conducted within the Work Package 10 (fusion experimental programme) of the HiPER project. The aim of these experiments was to study the physics relevant for advanced ignition schemes for inertial confinement fusion, i.e. the fast ignition and the shock ignition. Such schemes allow to achieve a higher fusion gain compared to the indirect drive approach adopted in the National Ignition Facility in United States, which is important for the future inertial fusion energy reactors and for realising the inertial fusion with smaller facilities

Assessment of Content of Tritium, Other Hydrogen Isotopes and Helium in a W Armor for an Experimental HIPER Chamber

Tritium breeding is an essential component of future fusion nuclear reactors. Nuclear fusion reactors require Kg quantities of tritium per year of operation.

Plasma facing materials for fusion reactor applications

The lack of plasma facing materials (PFM) able to withstand the severe magnetiicffusiion radiation conditions expected in fusion reactors is the actual bottle In both fusions approaches energy is released in the form of kinetic energy of neck for fusion to becomes a reality.

Stability of vacancy clusters in FeCr alloys: A study of the Cr concentration dependence

Fe–Cr based alloys are the leading structural material candidates in the design of next generation reactors due to their high resistance to swelling and corrosion. Despite these good properties there are others, such as embrittlement, which require a higher level of understanding in order to improve aspects such as safety or lifetime of the reactors. The addition of Cr improves the behavior of the steels under irradiation, but not in a monotonic way. Therefore, understanding the changes in the Fe–Cr based alloys microstructure induced by irradiation and the role played by the alloying element (Cr) is needed in order to predict the response of these materials under the extreme conditions they are going to support. In this work we perform a study of the effect of Cr concentration in a bcc Fe–Cr matrix on formation and binding energies of vacancy clusters up to 5 units. The dependence of the calculated formation and binding energy is investigated with two empirical interatomic potentials specially developed to study radiation damage in Fe–Cr alloys. Results are very similar for both potentials showing an increase of the defect stability with the cluster size and no real dependence on Cr concentration for the binding energy.

On track for solar grade silicon through a siemens process-type laboratory reactor: operating conditions and energy savings

Polysilicon cost impacts significantly on the photovoltaics (PV) cost and on the energy payback time. Nowadays, the besetting production process is the so called Siemens process, polysilicon deposition by chemical vapor deposition (CVD) from Trichlorosilane. Polysilicon purification level for PV is to a certain extent less demanding that for microelectronics. At the Instituto de Energía Solar (IES) research on this subject is performed through a Siemens process-type laboratory reactor. Through the laboratory CVD prototype at the IES laboratories, valuable information about the phenomena involved in the polysilicon deposition process and the operating conditions is obtained. Polysilicon deposition by CVD is a complex process due to the big number of parameters involved. A study on the influence of temperature and inlet gas mixture composition on the polysilicon deposition growth rate, based on experimental experience, is shown. Moreover, CVD process accounts for the largest contribution to the energy consumption of the polysilicon production. In addition, radiation phenomenon is the major responsible for low energetic efficiency of the whole process. This work presents a model of radiation heat loss, and the theoretical calculations are confirmed experimentally through a prototype reactor at our disposal, yielding a valuable know-how for energy consumption reduction at industrial Siemens reactors.