Round Table

Current Trends in Energy and Sustainability 2017 Edition Invited Editors:

Roberto Gómez-Calvet (Univ. Europea de Valencia) José M. Martínez-Duart (Univ. Autónoma de Madrid)

Symposium on Energy and Sustainability. XXXVI Biennial. Spanish Royal Physics Society Santiago de Compostela (Spain), July 17-21. 2017

Book title: Current Trends in Energy and Sustainability. 2017 Edition Invited Editors: Roberto Gómez-Calvet (Universidad Europea de Valencia) and José M. Martínez-Duart (Universidad Autónoma de Madrid). ([email protected] - [email protected])

Copyright © 2017, Real Sociedad Española de Física ISBN: 978-84-0903541-0 Depósito Legal: M-26519-2018 Dep. Legal: ALL RIGHTS RESERVED. This book contains material protected under International and Federal Copyright Laws and Treaties. Any unauthorized reprint or use of this material is prohibited. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system without express written permission from the author / publisher.

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Current Trends in Energy and Sustainability. 2017 Edition

Current Trends in Energy and Sustainability 2017 Edition

Symposium on Energy and Sustainability. XXXVI Biennial. Spanish Royal Physics Society Santiago de Compostela (Spain), July 17-21. 2017

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CONTENTS PREFACE

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PART I: ROUND TABLE SUMMARY AND VIDEOS Invited Speakers Video

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Round Table Video

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PART II: CONTRIBUTION CHAPTERS I

Energías renovables y generación distribuida. Domínguez, J., Amador, J. and Martín, A.M.

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Optical Characteristics of Smart Windows based on Electrochromic Materials and Low Emittance Coatings. Guillén, Cecilia, Trigo, Juan Francisco and Herrero, José.

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III

Plasterboard thermal characterization in dynamic conditions by using thermography. D. Blasco Avellaneda, I. Naveros and Diego P. Ruiz.

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IV

Hybrid Brayton thermosolar systems: thermodynamic prediction of annual efficiencies and emissions. R.P. Merchán,, M.J. Santos, A. Medina, and A. Calvo Hernández.

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Band alignment of polar and non-polar interfaces between the CuGaS2/CuAlSe2 and CuGaS2/ZnSe. J. E. Castellanos Águila, P. Palacios, J. Arriaga and P. Wahnón.

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VI

Impact of V-implantation and Si-Vacancies on Crystal Structure and Optical Absorption Properties of Silicon. Gregorio García, Marcos Casanova-Páez, Pablo Palacios, Eduardo Menéndez-Proupin and Perla Wahnón.

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VII

Green and Circular Economy: A Case Study in Extremadura (Spain). F. Cuadros Blázquez, C. Sánchez Sánchez, A. González González and F. Cuadros Salcedo.

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PREFACE The volume we are now introducing, “Current Trends in Energy and Sustainability. 2017 Edition” rises as a compilation of the contributions presented at the Biennial Conferences of the Spanish Physical Royal Society (RSEF) within the Energy and Sustainability Symposium organized by the Specialized Energy Group in Santiago de Compostela (Spain), July 17-21, 2017. For the elaboration of the book, the Editors invited some of the participants to submit an expanded contribution of their presentations at the Symposium. The volume is divided into two parts, the first comprising the videos of the Invited Conferences and the Round Table, and the second one some of the regular contributions. As expected from the broad title of the Symposium, there is a large variety of topics presented, but all can be framed under the area of energy and sustainability. Accordingly the topics of this volume deal with renewable energies, CO2 emissions, building conditioning, C-free technologies, energy generation and distribution, bioenergy, etc. In addition to the contributors to this volume, the Editors would like to acknowledge other persons whom without their assistance this publication would have not been possible. Among them Prof. José Adolfo Azcárraga, President of the RSEF, Profs. Dolores Cortina and Elena López, organizers of XXXVI Biennial of the RSEF, Prof. Joaquín Marro, General Editor RSEF, Itziar Serrano of the Editorial Department RSEF, and Concepción Zocar, Manager RSEF. Finally, we are especially indebted to Dr. Silvia Serrano who acted as general coordinator of the Symposium Committee.

THE EDITORS: Roberto Gómez-Calvet José Manuel Martínez-Duart Valencia, December 2017

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Part I Round Table Summary - Videos

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Invited Conferences – Workshop: High Integration of Variable Renewable Energy Sources in the Spanish electricity grid: storage, backup and future scenarios Grupo Especializado en Energía - RSEF

Summary Since Spain is clearly isolated from most of the European Union electric grid, only a small share of energy can be traded with France and Portugal. Therefore, due to its geographic location, electricity self-sufficiency is a major policy consideration. Some rough figures for 2015 generation show a total yearly consumption of 280 TWh total, of which 57 TWh come from nuclear, 55 TWh coal, 51 TWh gas, 15 TWh oil, 31 TWh hydro, 49 TWh wind, and 14 TWh solar. The lack of fossil fuels resources has traditionally led to a high dependence from third countries. So as to minimize this problem, during the last two decades Spain has carried out a massive promotion of renewable sources. This development has not been entirely free of controversy. The present energy situation at the country level is analyzed in this workshop as well as the impact that the promotion of renewable energy has on the environment and climate. In the following document the reader can watch the video of the invited conferences, that took place previous to the round table. These contributions belong to Francisco Javier Domínguez (CIEMAT), Jose Ignacio Cruz Cruz (CIEMAT) and Roberto Gómez-Calvet (Universidad Europea de Valencia). The videos of these contributions can be found at the following link.

Link to Invited Speakers Videos

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Round Table – Workshop: High Integration of Variable Renewable Energy Sources in the Spanish electricity grid: storage, backup and future scenarios Grupo Especializado en Energía - RSEF

ABSTRACT In the following document we present the round table that took place on the 20th of July, 2017 during the workshop organized by the Grupo Especializado en Energía (GEES) of the Real Sociedad Española de Física (RSEF). In this Round Table, keynote speaker from the academia, as well as from the Spanish grid operator (Red Eléctríca Española) and research institutes (CIEMAT -Spain- and Ecole Royale Militaire -Belgium-), presented the latest research, news and conclusion that will surely impact on the nearly future Spanish renewable scenario. The round table panel was composed by Silvia Serrano Calle -Universidad Politécnica de Madrid-, Jef Ongena -Ecole Royale Militaire-, Francisco Javier Domínguez Bravo -CIEMAT-, María Luisa Castaño -CIEMAT-, Jose Manuel Martínez-Duart Universidad Autónoma de Madrid- and Concepción Sánchez -Jefa del Departamento de Planificación Energética de Red Eléctrica Española-.

A full video of the Round Table can be accessed in the following link:

Link to Round Table Video

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Activities of the Energy Group-European Physical Society Jef Ongena, President EG-EPS

ABSTRACT In this presentation, the objectives and activities of the Energy Group of the European Physical Society (EG-EPS) are described. The EG-EPS was founded about six years ago and the first chairman was Fritz Wagner. At present all the countries of the European Union are represented in the EG-EPS. The Group meets regularly at least once a year: Budapest (2013), Lisbon (2014) and Rome (2015). In addition, the Group has organized three editions of the Energy Summer School in Varenna (Italy). One of the major aims of the EG-EPS is to provide information on sustainable energy technologies to scientists, students and policy-makers. As an example, it has recently drawn up a document called EPS Energy Group Position Letter on the current EU Energy Policies. The document deals with the present role of the EU curbing CO2 emissions, implementation of Low-C technologies, the reconsideration of the 2050 European Energy Roadmap and the fostering of educational programs for students and policy-makers.

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Part II Contribution Chapters

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XXXVI Biennial Meeting of the Real Sociedad Española de Física Energy and Sustainability Simposiumon Energy and Sustainability

Energías renovables y generación distribuida J. Domínguez1,*, J. Amador2, A.M. Martín3 1 Grupo

de Tecnologías de Información Geográfica y Energías Renovables (CIEMAT) Técnica Superior de Ingeniería y Diseño Industrial (Universidad Politécnica de Madrid) 3 Facultad de Geografía e Historia (Universidad Complutense de Madrid) 2 Escuela

* [email protected]

El autoconsumo y la generación distribuida con energías renovables están llamados a convertirse en uno de los motores de la alta penetración renovable en el nuevo modelo energético. La ponencia que presentamos aborda esta problemática desde la perspectiva del apoyo a la toma de decisiones por parte de los ciudadanos y las autoridades municipales convirtiéndoles en agentes claves de este nuevo paradigma. Introducción Las energías renovables y el autoconsumo desarrollan un papel fundamental no solo en el cambio de modelo energético, sino en la democratización y descentralización del sistema. De esta manera los ciudadanos se hacen partícipes de la transformación energética, pudiendo decidir la fuente de energía que desean utilizar para abastecerse y producir y volcar energía a la red, lo cual les beneficiará económicamente, al tiempo que servirá para aliviar los peores efectos del cambio climático. Desde la perspectiva de su disposición física podemos clasificar los sistemas tecnológicos de energías renovables como generación aislada de la red, generación centralizada conectada a la red y generación distribuida conectada a la red. [1] En el primer caso, aislada, tendremos sistemas térmicos y eléctricos de baja potencia situados próximos al punto de consumo (zonas rurales, montañosas, islas, etc). Estos sistemas deben de ser analizados desde una óptica social, no económica. En el segundo caso, Generación Centralizada conectada a la Red, se distribuyen formando un gran bloque de potencia, distantes del consumo. Si bien contribuye a disminuir la emisión de CO2, mantiene la misma lógica de mercado que la generación centralizada. Finalmente, la Generación Distribuida (GD) conectada a la Red, está formada fundamentalmente por sistemas de baja potencia, distribuidos y situados próximos al punto de consumo. Este nuevo paradigma crea nuevos derechos y obligaciones al Prosumidor. Podemos definir entonces a la GD como la generación de energía eléctrica por medio de muchas y pequeñas fuentes de energía, distribuidas espacialmente, conectadas a la red de baja y media tensión e instaladas en puntos cercanos al consumo. En este sistema, el consumidor deja de ser un sujeto pasivo de la red pasando a convertirse en productor-consumidor (prosumer en su acepción anglosajona) y poniendo al ciudadano como partícipe fundamental en la Transición Energética. En este modelo, los sistemas generadores pueden ser: Sistemas FV, Minihidros, Aerogeneradores, Motores alternativos, Microturbinas de gas, etc., muchas veces colocados sobre los tejados de las propias viviendas, e incorporando elementos comunes como pueden ser un inversor, equipos de medida, almacenamiento, etc. Las formas de conexión y facturación de la GD pueden implementarse por medio de diferentes tipos de metodologías de tarifación (balance neto de energía, balance neto de cuentas, tarifa diferencial) y de subsidios ofrecidos (según paridad de red del lugar). En el caso del Balance Neto de Energía o Net Metering, tendríamos que: Energía entregada por el SFV - Energía entregada por la Red = ΔE Si ΔE >0 el G acumula a favor excedentes

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Si ΔE< 0 el G paga la diferencia a la red

En el caso del Balance Neto de Cuentas o Net Billing, tendríamos que: Energía entregada por el SFV  Se paga según precio acordado Energía entregada por la Red  Se paga a la tarifa de la red

El Modelo Futuro del Sistema de Energía se puede definir por las 3D: Descarbonizar; Distribuir y Digitalizar. Los aspectos que incorporará serán entre otros:  Matriz de Energía diversificada (Fósiles y EERR) con Almacenamiento de energía  Generación Centralizada y Distribuida  Sentido bidireccional de la energía  Presencia de Redes Inteligentes que optimizan el uso de la energía generada  Transporte eléctrico Como propuestas para este cambio de modelo energético, dentro del ámbito de la generación distribuida con energía solar fotovoltaica, vamos a desarrollar a continuación los trabajos del grupo de Tecnologías de la Información Geográfica del CIEMAT, quien en colaboración con la UPM, han implementado un modelo de evaluación del potencial solar a escala municipal (gSolarRoof).

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Modelo geográfico gSolarRoof A medida que la demanda de energías renovables ha ido creciendo, también lo ha hecho la necesidad de cuantificar el potencial de sus recursos. La estimación de los recursos energéticos requiere de un detallado análisis de la información espacial disponible [1]. En la actualidad, el desarrollo que han alcanzado las tecnologías de detección de sensores remotos como el LIDAR (Light Detection and Ranging), junto con la capacidad de análisis de los Sistemas de Información Geográfica (SIG), ofrecen herramientas que facilitan el levantamiento de modelos urbanos y el estudio del planeamiento territorial y sectorial. Los datos LIDAR permiten una adecuada descripción del entorno urbano, determinando la posición y dimensiones de los edificios y la presencia de obstáculos ocasionados por la forma del terreno, otros elementos urbanos e infraestructuras circundantes y formaciones arbóreas. Los tejados de los edificios representan zonas de los entornos urbanos donde siempre se pueden localizar áreas sin un uso concreto que pueden ser aprovechadas para la instalación de módulos solares. Con el modelo geográfico gSolarRoof se desarrolla un sistema de análisis del potencial solar (térmico y fotovoltaico) de las cubiertas de los edificios para la generación de energía. El modelo establece las variables y reglas que determinarán el potencial solar y, considerando la estructura de la zona urbana y la tipología de los edificios, determina la energía potencial generable con las principales tecnologías solares, así como delimita aquellas zonas de los tejados que reúnen las mejores condiciones para instalar estos sistemas. Además, el estudio asigna un papel importante a la representación y la difusión de la información. Utilizando como soporte el geoportal web de ArcGIS Online se crean los mapas con los resultados obtenidos para ayudar a los usuarios a visualizar los datos, realizar consultas y compartir la información de una forma sencilla. Este modelo ha sido diseñado por el grupo de Tecnologías de la Información Geográfica y Energías Renovables del CIEMAT que, en colaboración con Escuela Técnica Superior de Ingeniería y Diseño Industrial (Universidad Politécnica de Madrid), han desarrollado una línea de investigación dirigida a evaluar la capacidad de los diferentes entornos urbanos para incorporar la energía solar como parte de la planificación urbana cuyo objetivo es el ahorro y la eficiencia energética. Metodología El estudio del potencial solar se basa en el levantamiento de un modelo tridimensional para el área urbana a analizar, generado a partir de una nube de puntos LIDAR y complementado con la información de la zona obtenida de diferentes bases de datos geográficas de acceso libre [3]]. Para el desarrollo del análisis es necesario utilizar las siguientes fuentes de información: Nube de puntos LIDAR del Plan Nacional de Ortofotografía Aérea (PNOA) [3] del año 2010 del Instituto Geográfico Nacional (IGN). Los ficheros, en formato ‘.las’, están formados por hojas de 2x2 km con una densidad media de 0,5 puntos/m2. Catastro urbano de la Dirección General de Catastro [6], en formato ‘shapefile’. Proporciona información de ámbito municipal como el parcelario catastral (referencia catastral) y la delimitación de edificios (elementos constructivos y número de plantas). Localización de monumentos y edificios protegidos elaborada a partir de la Infraestructura de Datos Espaciales Comunidad de Madrid (IDEM) [7], mapas turísticos y planes de ordenación urbana de los municipios. Datos de radiación solar de la base de datos Photovoltaic Geographical Information System (PVGIS) [8] que permite consultar diferentes parámetros climáticos. Datos de la posición del Sol disponibles en la web SoDa (Solar Energy Services for Professionals) [9]. Proporciona enlaces a diferentes recursos relacionados con la radiación solar, como el servicio Solar Geometry 2 (SG-2) que permite determinar la situación del Sol para un periodo de tiempo determinado. Datos de temperaturas de la Agencia Estatal de Meteorología (AEMET) [10] que facilita 19


series de datos e información climatológica general de sus estaciones meteorológicas.

Figura 1. Muestra de la nube de puntos LIDAR del municipio de Miraflores de la Sierra (Madrid). Previamente a realizar el estudio es necesario un tratamiento adecuado de la información para dotarla del formato y la estructura necesarios para realizar el análisis. Es importante depurar y clasificar la nube de puntos LIDAR, extrayendo todos aquellos elementos necesarios para el estudio (edificios, masas de vegetación y superficie del terreno). El conjunto de datos obtenido se integra en un modelo geográfico, implementado con el software ArcGIS, en el que se establecen las variables que influirán en el emplazamiento de los módulos solares y la energía generada, considerando la estructura de la zona urbana, la radiación solar recibida en los tejados y la tipología de los edificios.

Figura 2. Esquema de las fases de la metodología. El modelo realiza los cálculos globales para toda la zona urbana y para cada uno de los edificios que la componen. Es de destacar que el modelo es personalizable según las necesidades del proyecto, pudiéndose aplicar para usos eléctricos y/o térmicos, diferentes entornos urbanos (zonas residenciales, industriales o de servicios), diferentes fuentes de datos y resoluciones. La implementación actual del modelo consta de las siguientes fases: 1. Levantamiento de un Modelo Digital de Superficies (MDS) de todo el entorno urbano donde se representa la distribución de los edificios con un tamaño de celda de 1 m². 2. Análisis de la radiación solar [11] recibida anualmente en cada punto del tejado teniendo en cuenta la variación en la posición del Sol, la disposición de los edificios y la diversidad de

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4.

5.

6. 7. 8.

formas que pueden presentar los tejados. La radiación calculada para un área determinada se da como radiación global (directa + difusa) en Wh/m². Determinar la orientación e inclinación de los tejados para establecer las pérdidas en la generación de energía ocasionadas por la situación de los mismos conforme a las directrices establecidas por el ‘Código Técnico de la Edificación’ de España [12]. Análisis de la superficie de los tejados afectada por sombras a lo largo del año, teniendo en cuenta el efecto de los edificios adyacentes, zonas arboladas, o cualquier otro elemento presente en el entorno. Cálculo de la superficie disponible en los tejados para la instalación de sistemas solares y selección de los emplazamientos más adecuados, diferenciando entre los tejados inclinados y planos. Estimación de la potencia disponible y la producción de energía eléctrica anual [13] con diferentes tipos de módulos fotovoltaicos para todos los edificios del área de estudio. Estimación de la producción de energía anual para agua caliente sanitaria (ACS) con colectores solares términos de ‘Placa Plana’ [14] para los edificios de viviendas. Cálculo de las emisiones a la atmósfera de CO2 evitables [15] con la energía solar generada.

Figura 3. Principales factores analizados en el estudio del potencial solar. Presentación de los resultados de los casos de estudio realizados con el modelo gSolarRoof Los lugares seleccionados para el diagnóstico del modelo son los municipios de Miraflores de la Sierra [16] y Alpedrete, además del polígono industrial de Leganés Tecnológico, todos situados en la provincia de Madrid. La estructura urbana de estos municipios se caracteriza por la presencia de numerosas viviendas unifamiliares, en ocasiones rodeadas de vegetación que constituyen un tejido urbano discontinuo con una densidad construida mayoritariamente media y baja. En estos municipios, aunque en su conjunto pueden proporcionar de un potencial considerable, resulta escasa la disponibilidad de grandes edificios (industriales y comerciales), que aporten mayores superficies de tejado libre para las instalaciones solares. 21


Los resultados obtenidos en los diferentes casos de estudio realizados hasta el momento con la aplicación del modelo se resumen en las siguientes tablas: Tabla 1. Síntesis de resultados del núcleo urbano de Miraflores de la Sierra (Madrid). Edificios Número de edificios analizados

2.849 382.683 m2

Superficie total construida Número edificios con superficie disponible

2.611 111.770 m2

Superficie de tejados disponible Módulos Fotovoltaicos Silicio Monocristalino Silicio Multicristalino CIS CdTe Silicio amorfo

Potencia instalada

18 MWp

Energía anual generada

17 GWh

Potencia instalada

17 MWp


16 GWh

Potencia instalada

12 MWp


11 GWh

Potencia instalada

12 MWp


11 GWh

Potencia instalada

7 MWp


6 GWh

Tabla 2. Síntesis de resultados del término municipal de Alpedrete (Madrid). Módulos Fotovoltaicos (Silicio Multicristalino) Número de edificios analizados

4.053

Superficie total construida

698.677 m²

Número edificios con superficie disponible Superficie de tejados disponible

3.656 186.903 m²

Potencia instalada

23 MWp


33 GWh

Emisiones evitadas de CO2

21.417 T

Colectores Solares Térmicos (Placa Plana) Número de edificios de viviendas analizados Superficie total construida

3.746 573.895 m²


3.412 135.214 m²


100 GWh

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Emisiones evitadas de CO2

20.400 T

Tabla 3. Síntesis de resultados del Polígono Industrial Leganés Tecnológico (Madrid). Edificios Número de edificios analizados

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Superficie total construida

62.622 m²


19 42.591 m²

Módulos Fotovoltaicos (Silicio Multicristalino) Potencia instalada

7 MWp


10 GWh

Si comparamos estos datos con los ofrecidos sobre demanda eléctrica por la Comunidad de Madrid podemos observar que el grado de potencial cobertura está entre el 80 y el 100% de las necesidades eléctricas anuales de ambos municipios. [17] Una vez realizado el análisis, es imprescindible servir los resultados obtenidos para que los diferentes usuarios puedan acceder a los datos, realizar consultas y compartir la información de una forma sencilla. Indudablemente, las tecnologías de la información facilitan esta labor con la creación de geoportales en internet, que pone a disposición de los ciudadanos y las instituciones la información geográfica, representando un apoyo fundamental en la toma de decisiones. En este tipo de plataformas se pueden incluir presentaciones cartográficas de los resultados obtenidos en el análisis y además, ofrecer la posibilidad de completar esta información con tablas, gráficos y la generación de informesresumen. Entre las diferentes plataformas donde alojar los datos geográficos en internet, hemos seleccionado ArcGIS Online de ESRI para la publicación de los resultados en los diferentes geoportales gSolarRoof para cada zona analizada. En el desarrollo del visor se ha tratado de diseñar una interfaz sencilla que dispone de una serie de botones, desplegables y ventanas que permiten de forma cómoda y rápida visualizar la información y realizar consultas [17] [19] [20]. Las capas de información incluidas, se han representado mediante unos rangos de valores mostrados por su correspondiente escala de color que sirven para conocer las características más importantes de cada edificio, considerando como unidad de representación la parcela catastral.

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Figura 4. Energía anual generada con módulos fotovoltaicos (Silicio Monocristalino). Municipio de Miraflores de la Sierra (Madrid) [16].

Figura 5. Superficie disponible de tejados para instalar módulos fotovoltaicos. Polígono Industrial Leganés Tecnológico (Madrid) [18].

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Figura 6. Energía anual generada con colectores solares térmicos (Placa Plana) para agua caliente sanitaria en viviendas. Municipio de Alpedrete (Madrid) [19]. Conclusiones

El modelo gSolarRoof está dirigido a proporcionar una visión precisa de la disponibilidad de energía solar en los edificios, siendo un excelente soporte con el que mostrar las posibilidades que ofrecen nuestras ciudades para la generación de energía. Los resultados arrojan un altísimo potencial, cuyo desarrollo dependerá, en gran medida, de las posibilidades que ofrezca el marco político, energético y económico a sus ciudadanos.

References [1] J.A. Gonzalez, Generación Distribuida mediante el uso de Energías Renovables, VII SEMANA IBEROAMERICANA DE LA JUSTICIA INTERNACIONAL. Universidad de La Haya para las Ciencias Aplicadas (2017). [2] A.M. Martín, J. Domínguez, J. Amador, Applying LIDAR datasets and GIS based model to evaluate solar potential over roofs: a review, AIMS Energy 3 (2015) 326-343. [3] A.M. Martín, J. Domínguez, J. Amador, Desarrollo de un modelo geográfico para la evaluación del potencial fotovoltaico en entornos urbanos, GeoFocus 18 (2016) 147-167. [4] A.M. Martín, J. Domínguez, J. Amador, Estudio del potencial solar del municipio de Alpedrete (Comunidad de Madrid, España), Informes Técnicos Ciemat (2018). [5] Ministerio de Fomento, Instituto Geográfico Nacional (IGN), Centro de descargas del Centro Nacional de Información Geográfica, (2010). Disponible en: http:// centrodedescargas.cnig.es/CentroDescargas/index.jsp [Consulta: 6 de febrero de 2018]. [6] Ministerio de Hacienda y Función Pública, Secretaría de Estado de Hacienda. Dirección General del Catastro, Portal de la Dirección General del Catastro, (2017). Disponible en: http://www.catastro.meh.es/ [Consulta: 6 de febrero de 2018].

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[7] Comunidad de Madrid, Geoportal de la Infraestructura de Datos Espaciales de la Comunidad de Madrid (IDEM), (2017). Disponible en: http://www.madrid.org/cartografia /idem/html/index.htm [Consulta: 6 de febrero de 2018]. [8] Comisión Europea, Centro Común de Investigación, Instituto de Energía y Transporte, Sistema de Información Geográfica Fotovoltaica - Mapa Interactivo (PVGIS), (2012). Disponible en: http://re.jrc.ec.europa.eu/pvgis/apps4/pvest.php?lang=es&map= europe [Consulta: 6 de febrero de 2018]. [9] MINES ParisTech, SoDa: Solar radiation data, Solar Geometry 2 (SG2), (2017). Disponible en: http://www.soda-pro.com/web-services/astronomy/solar-geometry-2 [Consulta: 6 de febrero de 2018]. [10] Ministerio de Agricultura y Pesca, Alimentación y Medio Ambiente, Agencia Estatal de Meteorología (AEMET), AEMET OpenData, (2017). Disponible en: http://www.aemet.es /es/datos_abiertos/AEMET_OpenData [Consulta: 6 de febrero de 2018]. [11] A. Verso, A.M. Martín, J. Amador, J. Domínguez, GIS-based method to evaluate the photovoltaic potential in the urban environments: The particular case of Miraflores de la Sierra, Solar Energy 117 (2015) 236-245. [12] Ministerio de Fomento, Código Técnico de la Edificación. Documento Básico HE: Ahorro de energía, (2009, 2017), Madrid: Ministerio de Fomento. [13] L.K. Wiginton, H.T. Nguyen, J.M. Pearce, Quantifying rooftop solar photovoltaic potential for regional renewable energy policy, Computers, Environment and Urban Systems 34 (2010) 345357. [14] Instituto para la Diversificación y Ahorro de la Energía (IDAE), Instalaciones de Energía Solar Térmica. Pliego de Condiciones Técnicas de Instalaciones de Baja Temperatura, (2009), Madrid: IDAE. [15] Instituto para la Diversificación y Ahorro de la Energía (IDAE), Ministerio de Industria, Energía y Turismo y Ministerio de Fomento, Factores de emisiones de CO2 y coeficientes de paso a energía primaria de diferentes fuentes de energía final consumidas en el sector de edificios en España, (2014), Madrid: IDAE. [16] A.M. Martín, A. Berdugo, J. Domínguez, J. Amador, Estudio del potencial fotovoltaico sobre los tejados de núcleo urbano de Miraflores de la Sierra (Madrid), Informes Técnicos Ciemat 1367 (2015) 80. [17] Comunidad de Madrid. Instituto de Estadística, 2017. ALMUDENA, Banco de Datos Municipal y Zonal. Disponible en: http://www.madrid.org/desvan/Inicio.icm?enlace=almudena [Consulta: 19 de febrero de 2018]. [18] Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Visor gSolarRoof Miraflores de la Sierra, Ciemat (2015). Disponible en: http://ciemat.maps.arcgis.com/apps/webappviewer/index.html?id=75bd823d86a84e38a280dd1 ca44d76e8 [Consulta: 6 de febrero de 2018]. [19] Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Visor gSolarRoof Leganés Tecnológico, Ciemat (2016). Disponible en: http://ciemat.maps.arcgis.com/apps/webappviewer/index.html?id=b8cc20032b53416caff0c74e 0fc63383 [Consulta: 6 de febrero de 2018]. [20] Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Visor gSolarRoof Alpedrete, Ciemat (2017). Disponible en: http://ciemat.maps.arcgis.com/apps/webappviewer/index.html?id=676dc33b47f24c4da3493bed 36107e52 [Consulta: 6 de febrero de 2018].

26

Optical Characteristics of Smart Windows based on Electrochromic Materials and Low Emittance Coatings

Optical Characteristics of Smart Windows based on Electrochromic Materials and Low Emittance Coatings Guillén, Cecilia1, Trigo, Juan Francisco2, Herrero, José3 Departamento de Energía Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT) Avda. Complutense 40, Madrid 28040 1

2

e-mail: [email protected] e-mail: [email protected] 3 e-mail: [email protected]

Abstract. Smart windows based on electrochromic materials and low emittance coatings have been analyzed under laboratory conditions, by measuring the spectral optical characteristics according to the European standards on building glazings. The visible light transmittance depends on the electrochromic materials state and it can be varied from 58% to 18% by applying a switching voltage ~ 2 V, whereas the solar transmittance and the solar gain coefficient are also changed accordingly. The inclusion of a low emittance coating with high infrared reflectance increases the thermal resistance of the glazing and contributes to decrease the solar gain, without a significant effect on the visible transmittance. Keywords: Smart windows, Visible transmittance, Solar gain. 1. INTRODUCTION The search for high energy performance in buildings has generated a major debate about the role of the windows and/or the area they must occupy, since windows are considered a weak link in the energy chain of the building, due to their lower insulation capacity and higher solar heat gain compared to a solid wall. Therefore, the discussion on the proportion of glazing to be used leads to a dilemma between providing acceptable window areas for natural lighting and achieving energy efficiency goals, all while ensuring the visual and thermal comfort of the occupants. In this sense, green building codes (such as the International Green Construction Code and other related documents [1, 2]) have sections requiring daylight and outdoor views, taking into account the importance of the environmental light in the human health and recognizing that a sustainable design cannot be based solely on energy efficiency. New windows are being developed to solve the dilemma discussed above [3-5]. The named Low Emittance Glass uses an ultra-thin metal or metal oxide coating with high infrared reflectance, which limits solar heat gain while transmits visible light [6]. This technology provides a good and reliable means for improving insulating glass performance; it generally cost 10 to 15 percent more than regular windows but can reduce energy loss by as much as 30 to 50 percent [7]. A newer option is known as Electrochromic Glazing, which changes color to control the amount of sunlight that enters a space, through the application of a low voltage. Electrochromic devices are constituted by stacked nanometer-thick films, with transparent conductors forming the outer layers of the stack, electrochromic electrodes in the middle layers, and an ion-conducting electrolyte layer in the center portion [2]. These glazings are considered

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XXXVI Biennial Meeting of the Real Sociedad Española de Física Energy and Sustainability Symposium

Smart Windows because they can change both visible light transmission and solar heat gain over a wide range, manually or through an automation system [8]. They allow energy savings in all climate zones by providing passive solar gains during cold seasons, minimizing cooling loads during hot seasons and decreasing the use of artificial light at all stations, providing maximum utilization of the daylight [7, 8]. Optical characterization of the smart windows is essential for their evaluation in terms of comfort and energetic efficiency [9]. It should be made according to a number of specific parameters that are determined by the European standard on building glazings [10]. The most important is the transmittance modulation range in the visible and global solar spectrum. Furthermore, the solar reflectance and absorptance should be determined in order to calculate the solar factor and the shading coefficient. Other parameter to take into account is the general color rendering index, which stand for the accuracy in the colors reproduction through the glazing. In the present work, optical characterization has been performed on a type of smart windows that combines electrochromic materials and low emittance coatings [11], analyzing its properties under laboratory conditions and exploring its potential for daylight and solar energy control in buildings. 2. WINDOWS DESCRIPTION AND METHODOLOGY A schematic representation of the type of smart window selected is shown in Figure 1. The glazing has 40 x 55 cm2 area and 29 mm thickness, consisting of a 9 mm electrochromic pane (electrochromic device supported by two 4 mm glasses), 16 mm cavity filled with argon and 4 mm inner pane with low emittance coating. This glazing system combines the high thermal resistance of a low emittance window with the variable transmittance of an electrochromic pane, allowing control of the solar gain. The combination proposed may enable optimal visual and thermal comfort to be provided with limited use of auxiliary heating and artificial light in the inner building space.

Visible Light Infrared Light

Glass

Low-e coating

Glass

Glass

EC materials

Internal Heat

Figure 1. Light and heat management by the smart window including electrochromic materials and a low emittance coating.

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The electrochromic pane is detailed in Figure 2. It consists of five different layers inserted between two conventional glasses. The two outer layers are formed by transparent conductive oxides (TCO) which are connected to the electric font. Among them are three central layers where the chemical reaction that darkens the window occurs. One of the layers is the named working electrode (WO3 the best known and used), another is the counter electrode capable of storing cations (like NiO) and between them is a high transparency ionic conductor. When a low voltage (< 2 V) is applied between the TCO layers, electrochromism is produced by the ionic intercalation reaction between the counter electrode containing the cations and the working electrode, changing its color during the process from transparent to dark blue (in the case of WO3). In fact, the oxides based on Ni and W exhibit anodic and cathodic electrochromism (they are represented as E1 and E2 in Figure 2), according to the schematic reactions for the case of proton extraction/insertion [2]: [𝑁𝑖(𝑂𝐻)2 ]𝑏𝑙𝑒𝑎𝑐ℎ𝑒𝑑 ↔ [𝑁𝑖𝑂𝑂𝐻 + 𝐻 + + 𝑒 − ]𝑐𝑜𝑙𝑜𝑟𝑒𝑑

(1)

[𝑊𝑂3 + 𝐻 + + 𝑒 − ]𝑏𝑙𝑒𝑎𝑐ℎ𝑒𝑑 ↔ [𝐻𝑊𝑂3 ]𝑐𝑜𝑙𝑜𝑟𝑒𝑑

(2)

Once the desired coloring level has been reached, the electric current can be stopped. The material remains tinted until a new current is aimed in the reverse direction, which causes the positive ions to return to the counter electrode and the working electrode to recover its transparency. In the present work, five different states or charge levels have been established in order to analyse the evolution of the optical properties from the bleached state (named as n1) to the darkest one (n5), passing through intermediate levels (n2, n3 and n4).

Glass

Glass

E2 (reduced) TCO

TCO E1 (oxidized)

E2 (oxidized) TCO

Ion conductor

TCO E1 (reduced) Glass

Ion conductor

+ V -

- V +

Glass

Figure 2. Schematic representation of the electrochromic pane in the bleached and colored states.

For the smart window fixed at different electrochromic states, the transmittance (T) and reflectance (R) have been measured in the wavelength () range from 300 to 2500 nm with a Perkin Elmer Lambda 900 spectrophotometer. Subsequently, several calculations have been performed with the measured transmittance and reflectance spectra, by applying the European Norm EN410:2011 about glass in building [10]. First, the visible light transmittance and reflectance (v, v), which represent the fraction of the incident light coming from a D65 standard illuminant (𝐷𝜆𝐷65 spectrum comprised between 380 and 780 nm wavelengths) that is transmitted or reflected by the glazing and is viewed by a standard photopic observer (the standard V()):

29


𝜏𝑉 = 𝜌𝑉 =

𝐷65 ∑780𝑛𝑚 𝑉(𝜆)Δ𝜆 𝜆=380𝑛𝑚 𝑇(𝜆)𝐷𝜆 𝐷65 ∑780𝑛𝑚 𝑉(𝜆)Δ𝜆 𝜆=380𝑛𝑚 𝐷𝜆

𝐷65 ∑780𝑛𝑚 𝑉(𝜆)Δ𝜆 𝜆=380𝑛𝑚 𝑅(𝜆)𝐷𝜆 𝐷65 ∑780𝑛𝑚 𝑉(𝜆)Δ𝜆 𝜆=380𝑛𝑚 𝐷𝜆

(3) (4)

Analogously, the solar direct transmittance and reflectance (s, s), which represents the fraction of the incident solar radiation (𝑆𝜆 spectrum from 300 to 2500 nm) that is transmitted or reflected by the glazing: 𝜏𝑆 = 𝜌𝑆 =

∑2.5𝜇𝑚 𝜆=0.3𝜇𝑚 𝑇(𝜆)𝑆𝜆 Δ𝜆 ∑2.5𝜇𝑚 𝑆 Δ𝜆 𝜆=0.3𝜇𝑚 𝜆

∑2.5𝜇𝑚 𝜆=0.3𝜇𝑚 𝑅(𝜆)𝑆𝜆 Δ𝜆 ∑2.5𝜇𝑚 𝜆=0.3𝜇𝑚 𝑆𝜆 Δ𝜆

(5)

(6)

Besides, the solar direct absorptance is calculated as: 𝛼𝑆 = 1 − 𝜏𝑆 − 𝜌𝑆

(7)

Followed by the solar factor (solar gain or g-value) that represents the total solar energy transmitted indoors through the glazing, both by direct transmission and by the indoor emission of part of the absorbed energy: 𝑈

𝑔 = 𝜏𝑆 + 𝛼𝑆 ℎ𝐿 𝑒

(8)

, where UL and he are the overall heat loss and the external heat transfer coefficients, respectively. Other parameters of interest included in the European norm EN 410:2011 and considered in this work are the shading coefficient (SC) that compares the g-value of the tested sample with that of a standard 3-4 mm thick float glass: 𝑔

𝑆𝐶 = 87(%)

(9)

and the general color rendering index (Ra), which stands for the accuracy in the colors reproduction through the glazing: 2 1/2

1

∗ ∗ 𝑅𝑎 = 8 ∑8𝑖=1 {100 − 4.6 [∑𝑋=𝑈,𝑉,𝑊(𝑋𝑡,𝑖 − 𝑋𝑟,𝑖 ) ]

}

(10)

∗ ∗ ∗ ∗ ∗ ∗ , where (𝑈𝑡,𝑖 , 𝑉𝑡,𝑖 , 𝑊𝑡,𝑖 ) and (𝑈𝑟,𝑖 , 𝑉𝑟,𝑖 , 𝑊𝑟,𝑖 ) are the CIE 1964 color space coordinates for the eight test colors illuminated with and without interposed glazing, respectively.

30


3. RESULTS AND DISCUSSION Initially, the visible light transmittance has been calculated for the glazing fixed at the various electrochromic states using the respective transmittance spectra weighted by the D65 standard illuminant and the V standard photopic, as it is illustrated in Figure 3. In general, the optical measurements are made by facing the electrochromic pane to the light source, although the transmittance is the same when the low emittance pane of the window is faced. Otherwise, it should be noted that the European norm EN 410:2011 gives the values D*V* for wavelength intervals of 10 nm [10], being elaborated in such a way that (D*V*= 1 (or 100 % for the notation used in Figure 3). The visible transmittance value ranges from v,n1 = 58% for the window in the bleached state to v,n5 = 18% in the darkest level. At intermediate charge levels (especially for the named n2) the transmittance maximum is located near  = 550 nm, where the human eye has the highest sensitivity. At the bleached and the darkest states the transmittance maximum is more pronounced and it is located at different wavelengths, around 630 nm and 490 nm, respectively. The visible reflectance coefficient has been calculated in the same way from the corresponding reflectance spectrum, which has been taken by facing the electrochromic pane to the light source. The values obtained for the glazing in the various electrochromic states are summarized in Table 1, where it can be seen that the variation in reflectance is smaller than in transmittance, changing from v,n1 = 11% to v,n5 = 8%.

Figure 3. Transmittance spectra (T) and visible transmittance coefficient (V) obtained for the smart window in the bleached state (n1) and after different darkening levels (n2 to n5).

Figure 4 shows the transmittance and reflectance spectra for the bleached and the darkest states in the whole wavelength range from 300 to 2500 nm. These spectra have been used to calculate the solar transmittance and solar reflectance values after weighted by the fraction of the incident solar radiation S. It is noted that the European norm EN 410:2011 gives the values S* for wavelength intervals 20 nm from 300 to 800 nm, 50 nm from 800 to 2100 nm and 100 nm from 2100 to 2500 nm, being (S*= 1 (or 100 % for the notation used in Figure 4).

31


The solar transmittance coefficient changes from S,n1 = 39% for the window in the bleached state to S,n5 = 9% in the darkest level. These values for the overall solar transmittance are lower than those obtained for the visible transmittance, owing to the transmittance decreases sharply out of the visible spectral range. The opposite behaviour has been observed for the solar reflectance, which is higher in the near infrared region and varies from S,n1 = 15% to S,n5 = 11%. Such relatively high infrared reflectance is attributed to the TCO layers constituting the electrochromic device (as shown in Figure 2) because of their plasmonic characteristics that depend mainly on the charge carrier concentration [12]. As expected, an increment in the solar reflectance has been obtained by facing the low emittance pane to the light source. This is illustrated in Figure 5, which shows the values Se,n1 = 27% and Se,n5 = 25% calculated for the other face of the window, that should be placed toward the inner of building. The solar transmittance is the same for both faces, as it has been mentioned above.

Figure 4. Spectral transmittance (T), reflectance (R) and respective solar coefficients (S, S) obtained for the window in the bleached (n1) and darkest (n5) states, with the electrochromic pane facing to the light source.

Figure 5. Spectral reflectance (Re) and solar reflectance coefficient (Se) obtained for the smart window in the bleached (n1) and the darkest (n5) states, with the low emittance pane facing to the light source.

32


The solar absorptance value, calculated from the respective solar transmittance and reflectance following equation (7), is included in Table 1. It increases from S = 46% for the bleached state to S = 80% for the most colored. In order to obtain the solar gain factor by applying equation (8), the overall heat loss and the external heat transfer coefficients should also be known. The overall heat loss coefficient for the smart window schematized in Figure 1 is given by UL= (he-1 + L1*k1-1 + L2*k2-1 + L3*k3-1 + hi-1)-1, being he and hi the heat transfer coefficients at the external and internal interfaces, whereas Li and ki are the thicknesses and thermal conductivities of the outer pane (i = 1), the intermediate gap (i = 2) and the inner pane (i = 3) respectively [13]. According to the composition and dimensions of the smart window, the values are k1 = k3 = 1.0 Wm-1K-1 for float glasses constituting the external and internal panes with L1 = 9 mm and L3 = 4 mm thicknesses, being L2 = 16 mm and k2 = 0.02 Wm-1K-1 for the argon filled gap. At the external interface, the standard value he = 25 Wm-2K-1 should be applied, which corresponds to a wind velocity of 3.7 m/s [9]. For the internal interface, the expression hi = (3.6 + 5.3) Wm-2K-1 has been used, being  the emissivity of the inner pane that can be estimated from the infrared reflectance as  = 1 – R [6, 9]. Following this approach,  = 0.25 for the inner low emittance pane (below  = 0.55 for the outer electrochromic pane and  = 0.84 for float glass) and hi = 4.9 Wm-2K-1. After the above considerations, the value obtained is UL/he = 0.04, which has been used together with the solar transmittance and absorptance data to calculate the solar gain factor. The gain ranges from g = 41% for the window in the bleached state to g = 12% for the darkest one, as it can be seen in Table 1, below the respective values (g = 59-28%) attained by analogous electrochromic panes without the additional low emittance coating [14]. It is important to note the ability of such smart windows to modulate the amount of light and heat coming into the building depending on the exterior environmental conditions. This allows energy savings in all climate zones by providing passive solar gains or minimizing cooling loads according to the different regions or seasons, and providing maximum daylight collection to replace the use of electric lights with natural light in all cases.

State

n1

n2

n3

n4

n5

𝜏𝑉 (%)

58

45

36

27

18

𝜌𝑉 (%)

11

9

8

8

8

𝜏𝑆 (%)

39

27

20

14

9

𝜌𝑆 (%)

15

12

11

11

11

𝜌𝑆𝑒 (%)

27

26

25

25

25

𝛼𝑆 (%)

46

61

69

75

80

g (%)

41

29

23

17

12

SC (%)

47

33

26

19

14

𝑅𝑎 (%)

94

95

88

80

73

Coeff.

Table 1: Optical coefficients obtained for the smart window in the various electrochromic states.

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The color of the light in a room is very important for occupant acceptance. The color rendering index is a measure of how close the color of light is to the reference “daylight” spectrum; but it should be noted that the spectrum of sunlight changes through the day, starting bluer in the morning and ending more red at the sunset, so even the spectrum of daylight is not static. The color of light coming through the smart window in the darkest states is markedly blue, as shown by the transmittance maximum at 490 nm wavelength in Figure 3, and this fact makes to decrease the color rendition index at the highest charged or tinted levels. Figure 6 shows the evolution of the particular color indexes (calculated for each of the eight test color samples) corresponding to the smart window at the different electrochromic states. The general color 1 rendering index gives an average for the test samples, 𝑅𝑎 = 8 ∑8𝑖=1 𝑅𝑖 , being considered acceptable when 40% ≤ Ra ≤ 59%, good for 60% ≤ Ra ≤ 79% and excellent for Ra ≥ 80%, according to the normative DIN-5035. For the glazing analysed here, excellent color rendering values have been obtained in all cases except at the darkest level (n5). Nonetheless, it has been confirmed [15, 16] that the light in spaces glazed with analogous electrochromic panes is essentially the same as in spaces glazed with clear glass as long as a small proportion of the windows is kept in the highest transmittance states.

Figure 6. Representation of the particular color indexes (corresponding to the eight test color samples) for the smart window in different electrochromic states (from the clearest n1 to the darkest n5).

4. CONCLUSIONS The optical characteristics of smart windows based on electrochromic materials and low emittance coatings have been obtained following the European standards on building glazings. These data show the ability of the windows to modulate their optical performance by applying a small switching voltage to the electrochromic materials. Besides, the low emittance coating decreases the overall solar gain at the various electrochromic states. Both visible light transmission and solar factor can be changed over a wide range, stopping at selected points at the touch of a button or command from an automation system. Such dynamic behavior makes possible to increase daylight and views without energy penalty or visual discomfort.

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ACKNOWLEDGEMENTS This work has been carried out within the framework of the OMEGA-CM program, Ref. S2013/MAE-2835 ("Technologies 2013"), which is a multidisciplinary R&D program financed by the Autonomous Community of Madrid and co-financed by Structural Funds of the European Union. REFERENCES [1] International Green Construction Code, ISBN: 978-1-60983-488-3, International Code Council, 2015. [2] Granqvist, C.G. (2014). Electrochromics for smart windows: Oxide-based thin films and devices. Thin Solid Films, 564: 1–38. [3] Baetens, R., Jelle, B.P. and Gustavsen, A. (2010). Properties, requirements and possibilities of smart windows for dynamic daylight and solar energy control in buildings: A state-of-theart review. Sol Energy Mater Sol Cells, 94: 87–105. [4] Jelle, B.P., Hynd, A., Gustavsen, A., Arasteh, D., Goudey, H. and Hart, R. (2012). Fenestration of today and tomorrow: A state-of-the-art review and future research opportunities. Sol Energy Mater Sol Cells, 96: 1–28. [5] Wong, K.V. and Chan, R. (2014). Smart glass and its potential in energy savings. J Energy Resour Technol, 136: 012002. [6] Granqvist, C.G. (2007). Transparent conductors as solar energy materials: A panoramic review. Sol Energy Mater Sol Cells, 91: 1529–1598. [7] Piccolo, A. (2010). Thermal performance of an electrochromic smart window tested in an environmental test cell. Energy and Buildings, 42: 1409–1417. [8] Sbar, N.L., Podbelski, L., Yang, H.M. and Pease, B. (2012). Electrochromic dynamic windows for office buildings. Intern J Sustainable Built Environment, 1: 125–139. [9] Jelle, B.P. (2013). Solar radiation glazing factors for window panes, glass structures and electrochromic windows in buildings—Measurement and calculation. Sol Energy Mater Sol Cells, 116: 291–323. [10] Glass in building. Determination of luminous and solar characteristics of glazing, EN 410:2011, EN, 2011. [11] Fang, Y., Hyde, T., Hewitt, N., Eames, P.C. and Norton, B. (2010). Thermal performance analysis of an electrochromic vacuum glazing with low emittance coatings. Solar Energy, 84: 516–525. [12] Guillén, C. and Herrero, J. (2016). Comparing the plasmonic characteristics of sputtered ZnO:Al and In2O3:Sn thin films as a function of the heating temperature and atmosphere. Thin Solid Films, 605: 136–142. [13] Bansal, N.K., Shail and Gaur, R.C. (1996). Application of U and g values for sizing passive heating concepts. Solar Energy, 57: 361–373. [14] Martín-Chivelet, N., Guillén, C., Trigo, J.F., Herrero, J., Pérez, J.J and Moralejo, F.J. (2017). Characterization of semitransparent PV modules and Smart Windows as advanced constructive elements for energy saving in buildings. Internat. Research Conf. on Sustainable Energy, Engineering, Materials and Environment, Newcastle, England, 26-28 July 2017. [15] Mardaljevic, J., Waskett, R.K. and Painter, B. (2014). Electrochromic glazing: avoiding the blues, CIBSE ASHRAE Technical Symposium, Dublin, Ireland, 3-4 April 2014. [16] Sanders, H. and Podbelsk, L. (2015). Dynamic façades: solving the high performance building challenge without design compromise, fourth Conference on Building Enclosure Science & Technology (BEST4), Kansas, 13-15 April 2015.

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XXXVI Biennial Meeting of the Real Sociedad Española de Física Energy and Sustainability Simposium

Plasterboard thermal characterization in dynamic conditions by using thermography D. Blasco Avellaneda, I. Naveros and Diego P. Ruiz Departamento de Física Aplicada, Universidad de Granada, Av. Severo Ochoa s/n 18071 Granada, España Abstract Thermal characterization of wall materials is needed to improve energy efficiency of buildings. This requires the study of heat flux throughout such materials for estimating their thermal properties, as thermal resistance and thermal capacity. Experiment in-situ need to be carried out besides experiments at laboratory level. This work aims to show guidance for thermally characterizing different wall materials by using thermal images, i.e. thermography as an alternative to the use of heat-flux meters. The main idea is to isolate all material borders less two faces where heat will mainly flow as it is expected to occur in-situ. For this purpose, a methodology, which considers surface temperatures as dependents on air ambient temperatures and infrared irradiance, is presented to be used in a laboratory experience. The experience consists in a box where the material to characterize is placed. The only important face is the one where the material is placed, since heat flux through the material may be assumed independent on the other box faces. In this work, plasterboard has been tested. Preliminary results, which should be replicated in future improved experiences, are presented.

Introduction Energy efficiency is one of the two pillars to decrease the use of non-renewable energy besides the use of renewables energies. In this sense, buildings are central to energy efficiency policies since an important percentage of the final energy consumption and greenhouse gas emissions take place in them, including commercial and institutional buildings. Energy-savings in buildings require to improve their energy performance and this first needs to state a verifiable and reproducible methodology to estimate energy efficiency of buildings. This methodology should consider the intrinsic performance of buildings as well as weather conditions and user behavior, since it has been observed that the energy consumption of similar buildings may vary from 30% to 300%, and about 70% of this variability may be explained by user behavior [1]. On site data acquisition about systems and equipment of buildings is required for dealing with energy performance of buildings, as well as using mathematical models to develop automated tools [2]. In the long term, thermal energy performance of walls tested under dynamic outdoor weather conditions may be inferred by using regression methods based on average data. This method has different capabilities and limitations related to: 1) the physical variables to be measured for correctly representing the energy balance, 2) the total length of the time series of measurements and 3) the minimum average time used for obtaining a physical variable value to be used in the regression. Different kinds of walls may have different specifications regarding to the length of the time series and the minimum average time, this is a limitation to be solved by standard tests considering the wall kinds that are mostly employed in the building sector. In addition, the main physical variables considered in the literature to be taken into account are temperatures (air ambient and surface), solar irradiance, wind speed and long wave radiation. Results obtained in different works show that temperatures are crucial in average methods and the relevance of other physical variables, e.g. solar irradiance [3], depend on the characteristics of the wall and its orientation. Regarding to steady state methods, dynamic methods have proved an advantage for reducing the total length of measurements used for energy performance characterization of building components. Furthermore, building energy performance estimation requires using dynamic methods if we seek to control building energy consumption in real time. For this reason, dynamic methods are widely studied

37

Plasterboard thermal characterization in dynamic conditions by using thermography

in the literature [4-5]. Dynamic models characterizing energy performance of buildings seek to facilitate the optimal control of building energy consumption [6, 7]. This may be persuasive information for improving user behaviour still keeping user liberty of choice. Physical variables of dynamic models used for energy performance characterization of whole buildings need to be measured on site. In general, air ambient temperatures and energy consumption, besides solar gains are considered [1]. Heat flux through different components is usually required too [8-9], this implies a problem since heat flux-meters are usually employed and they have theoretical and experimental limitations, e.g. high frequency noise amplification and almost punctual measurements on surfaces [10, 11]. A solution proposed in the literature is to consider surface temperatures instead of heat flux by using infrared cameras [12]. In this way, we can obtain long wave radiation from building surfaces to be transformed into surface temperatures by considering relations between both physical variables. The use of thermal cameras solves the two limitations drawn above. This paper aims to use a methodology using surface temperatures, at laboratory level instead on insitu, for characterizing a plasterboard wall and comparing the results of thermal resistances and capacities obtained with those known a priori from independent sources. Firstly, we briefly detail the experiment set-up; next the methodology is outlined before results and discussion are presented. Finally, we draw the main conclusions. Experiment set-up The measurement variables taken into account are illustrated in Table 1. The following list summarizes the sensors that were used in the experiment:   

Air temperature: 7 TFA 30.3039.IT KlimaLogg professional thermo-hygrometer with data logger. Inside surface temperature: FLIR E-60 thermographic camera. Outside surface temperature: PCE-TC 3 thermographic camera.

Table 1. Measured variables and sensor characteristics. Measured Variable Inputs Outdoor temperature Indoor temperature Outside surface temperature Inside surface temperature

Symbol

Units

Accuracy

Range of device

Range of measurements

𝑇𝑜 𝑇𝑖 𝑇𝑠𝑜

°C °C °C

0.1℃ 0.1℃ 0.15℃

[-20÷60] [-20÷60] [-10÷250]

[20÷30] [20÷30] [20÷30]

𝑇𝑠𝑖

°C

0.07℃

[-20÷650]

[20÷30]

Data were collected different day, between13th September 2016 and 20th September 2016. Data are sampled every minute and split into 3 sets of 4-5 hours. The total length of the experiment seeks to provide statistically significant results. The sampling time and the length of series are chosen to have the minimum volume of data allowing to identify the parameters according to the materials used and the procedure of analysis. Figure 1 shows the temperature data collected on 13th September 2016 from 19:20.

38


303.5

Temperature / K

303

302

301

300

299

0

50

100

150

200

250

300

Time / min

Figure 1. Temperature data. 13th September 2016 from 19:20. 𝑻𝒐 (red), 𝑻𝒔𝒐 (purple), 𝑻𝒔𝒊 (yellow), 𝑻𝒊 (blue).

Methodology The plasterboard wall can be represented using a first order lumped model, N=3, represented by one differential and two algebraic equations, is used and detailed as an example, Figure 2.

Figure 2. Thermal network using Ghiaus notation (Ghiaus, 2013): wall represented by 3 nodes. Let us note 𝐞 = [𝑒1 𝑒2 𝑒3 𝑒4 ]𝑇 𝐛 = [𝑏1 𝑏2 𝑏3 𝑏4 ]𝑇 ≡ [𝑇𝑜 0 0 −𝑇𝑖 ]𝑇 𝛉 = [𝜃1 𝜃2 𝜃3 ]𝑇 ≡ [𝜃𝑠𝑜 𝜃 𝜃𝑠𝑖 ]𝑇 For the thermal network, Figure 2, which represents the wall, the temperature differences for each thermal resistance are:

39


𝑒1 = 𝑏1 − 𝜃1 𝑒 = 𝜃1 − 𝜃2 { 2 𝑒3 = 𝜃2 − 𝜃3 𝑒4 = 𝜃3 + 𝑏4

(1)

The incidence matrix can be obtained from Figure 2, as: 1 0 0 −1 1 0] 𝐀 =. [ 0 −1 1 0 0 −1

(2)

Then, the system of Eq. (1) can be written in matrix form as: 𝑒1 𝑏1 1 0 0 𝜃 1 𝑒2 1 0 ] [𝜃 ] + [ 0 ] [𝑒 ] = − [−1 2 0 0 −1 3 1 𝜃 3 𝑒4 𝑏4 0 0 −1

(3)

The heat transfer rates in the network branches can be expressed as: 𝑞1 𝑞2 𝑞3 {𝑞4

= 𝑅1−1 𝑒1 = 𝑅2−1 𝑒2 = 𝑅3−1 𝑒3 = 𝑅4−1 𝑒4

(4)

By putting 𝐪 = [𝑞1 𝑞2 𝑞3 𝑞4 ]𝑇 ≡ [𝑞𝑐𝑜 𝑞𝑤1 𝑞𝑤2 𝑞𝑐𝑖 ]𝑇 −1 0 0 0 𝑅𝑐𝑜 𝑅1−1 0 0 0 −1 0 −1 0 0 0 𝑅 𝑅 𝐆 = [ 0 2 −1 0 ] ≡ [ 0 𝑤1 −1 0 ] 𝑅 𝑅 0 0 𝑤2 −1 0 0 3 −1 0 0 0 𝑅𝑐𝑖 0 0 0 𝑅4

the system of Eq. (4) can be written in matrix form as: 𝑞1 𝑒1 𝑅1−1 0 0 0 −1 0 𝑞2 𝑒 0 𝑅 [𝑞 ] = [ 0 2 −1 0 ] [𝑒2 ] 3 0 0 𝑅3 −1 3 𝑞4 𝑒4 0 0 0 𝑅4

(5)

The heat balance in each temperature node 𝛉 = [𝜃𝑠𝑜 𝜃 𝜃𝑠𝑖 ]𝑇 gives: 0 = 𝑞1 − 𝑞2 + 𝑓1 { 𝐶2 𝜃̇2 = 𝑞2 − 𝑞3 + 𝑓2 0 = 𝑞3 − 𝑞4 + 𝑓3 Noting 𝐶1 𝐂= [0 0

0 𝐶2 0

0 0 0 0 ] ≡ [0 𝐶 𝐶3 0 0

0 0] 0

𝐟 = [𝑓1 𝑓2 𝑓3 ]𝑇 ≡ [0 0 𝐼]𝑇

40

(6)


1 −1 0 0 𝐀𝑇 = [0 1 −1 0 ] 0 0 1 −1 we obtain in matrix form: 𝐶1 [0 0

0 𝐶2 0

𝑞1 0 𝜃̇1 0 1 −1 0 0 𝑞 0 ] [𝜃̇2 ] = [0 1 −1 0 ] [𝑞2 ] + [0] 3 0 0 1 −1 𝑞 𝐶3 𝜃̇ 𝐼 3 4

(7)

Taking into account Eq. (3) and (5) we could write Eq. (7) as: 𝐶1 [0 0

0 𝐶2 0

0 𝜃̇1 0 ] [𝜃̇2 ] 𝐶3 𝜃̇ 3

𝑅1−1 + 𝑅2−1 = − [ −𝑅2−1 0

−𝑅2−1 𝑅2−1 + 𝑅3−1 −𝑅3−1

0 𝜃1 −𝑅3−1 ] [𝜃2 ] 𝑅3−1 + 𝑅4−1 𝜃3

(8)

𝑏1 0 𝑅1−1 −𝑅2−1 0−1 0 0 ] [ 0 ] + [ 0] + [ 0 𝑅2−1 −𝑅3 0 −1 𝑅3−1 −𝑅4 𝐼 0 0 𝑏4

To obtain a matrix relation where nodes with non-negligible heat capacities are separated, as it was seen in previous section, the system given in Eq. (8) is rearranged. First, interchanging rows 2 and 3 in matrix 𝐂 implies interchanging rows 2 and 3 in −𝐀𝑇 𝐆𝐀, 𝐀𝑇 𝐆, and 𝐟: 𝐶1 [0 0

0 0 𝐶2

0 𝜃̇1 𝐶3 ] [𝜃̇2 ] 0 𝜃̇ 3

𝑅1−1 + 𝑅2−1 = −[ 0 −𝑅2−1

−𝑅2−1 −𝑅3−1 −1 𝑅2 + 𝑅3−1

0 𝜃1 −1 𝜃 + 𝑅4 ] [ 2 ] 𝜃3 −𝑅3−1

𝑅3−1

(9)

𝑏1 0 0 𝑅1−1 −𝑅2−1 0−1 0 −1 𝑅 +[ 0 + ] [ ] [ −𝑅 0 3 0] 4 0 −1 −1 𝐼 0 0 𝑅2 −𝑅3 𝑏 4

Second, interchanging columns 2 and 3 in matrix 𝐂 implies interchanging rows 2 and 3 in vector 𝛉̇ and requires interchanging column 2 and 3 in matrix −𝐀𝑇 𝐆𝐀 and rows 2 and 3 in vector 𝛉 to conserve relations between 𝛉̇ and 𝛉:

41


𝐶1 [0 0

0 𝜃̇1 0 ] [𝜃̇3 ] 𝐶2 𝜃̇ 2

0 𝐶3 0

𝑅1−1 + 𝑅2−1 = −[ 0 −𝑅2−1

−𝑅2−1 𝜃1 −𝑅3−1 ] [𝜃3 ] 𝑅2−1 + 𝑅3−1 𝜃2

0 −1 𝑅3 + 𝑅4−1 −𝑅3−1

(10)

𝑏1 0 0 𝑅1−1 −𝑅2−1 0−1 𝑅3 −𝑅4−1 ] [ 0 ] + [ 𝐼 ] +[ 0 0 0 0 0 𝑅2−1 −𝑅3−1 0 𝑏 4

Since for nodes 1 and 3 the heat capacity is considered negligible, Eq. (10) can be written as 0 0 [0 0 0 0

0 𝜃̇1 0 ] [𝜃̇3 ] 𝐶2 𝜃̇ 2

𝑅1−1 + 𝑅2−1 = −[ 0 −𝑅2−1

−𝑅2−1 𝜃1 −1 𝜃 ] [ 3] −𝑅3 𝑅2−1 + 𝑅3−1 𝜃2

0 −1 𝑅3 + 𝑅4−1 −𝑅3−1

(11)

𝑏1 0 0 𝑅1−1 −𝑅2−1 0 −1 −1 𝑅3 −𝑅4 ] [ 0 ] + [ 𝐼 ] +[ 0 0 0 0 0 𝑅2−1 −𝑅3−1 0 𝑏 4

Once the heat balance matrix expression is rearranged, the partition matrix, 𝐊, is:  R11  R21  0 R21   1 1 1  R3  R4 K 0 R3  1 1 1 1   R R  R  R 2 3 2 3  

(12)

where the blocks are: −𝑅−1 − 𝑅2−1 𝐊11 = [ 1 0 𝐊 21 = [𝑅2−1

𝑅2−1 0 ] ] ; 𝐊 = [ 12 𝑅3−1 −𝑅3−1 − 𝑅4−1

𝑅3−1 ]; 𝐊 22 = [−𝑅2−1 − 𝑅3−1 ]

and to partition matrix 𝐊 𝑏 :  R11  Kb   0  0 

 R21 0 1 2

R

0 1 3 1 3

R

R

0    R41  0 

where the blocks are: −1

𝐊 𝑏1 = [𝑅1 0 𝐊 𝑏2 = [0

−𝑅2−1 0

𝑅2−1

0 𝑅3−1

−𝑅3−1

0 ] −𝑅4−1

0]

Other relations to consider when the number of nodes is 𝑁 = 3 are:

42

(13)


𝐂𝐶 = [𝐶2 ]; 𝐈22 = [1]; 𝐟 = [𝐟0

𝒇𝑪 ]𝑻 ; 𝐟0 = [0 𝐼 ]; 𝐟𝐶 = [0]

State-space and measurement equations can be deduced by introducing the block matrices given by Eq. (12), 𝑁 = 3): (14)

−1 𝐀𝑆 = 𝐂𝐶−1 (−𝐊 21 𝐊11 𝐊12 + 𝐊 22 ) −1 𝐁𝑆 = 𝐂𝐶−1 [−𝐊 21 𝐊11 𝐊 𝑏1 + 𝐊 𝑏2

−1 −𝐊 21 𝐊11

(15)

𝐈22 ]

the next state space matrices are obtained: 𝑅−1 𝑅−1

1

𝑅−1 𝑅−1

1 2 3 4 𝐀𝑆 = 𝐶 (− 𝑅−1 − 𝑅−1 ) the state matrix, +𝑅−1 +𝑅 −1 2

𝐁𝑆 =

1

2

1 𝑅1−1 𝑅2−1 [ 𝐶2 𝑅1−1 +𝑅2−1

4

3

−𝑅2−2 −1 𝑅1 +𝑅2−1

𝑅3−2 −1 𝑅3 +𝑅4−1

+ 𝑅2−1

− 𝑅3−1

𝑅 −1 𝑅−1

4 3 − 𝑅−1 +𝑅−1 4

3

𝑅2−1 −1 𝑅1 +𝑅2−1

𝑅3−1 −1 𝑅3 +𝑅4−1

1] the input

matrix and, 𝐮 = [𝑇𝑜 0 0 −𝑇𝑖 0 𝐼 0]𝑇 the input vector. Then, since the state vector is 𝛉𝐶 = 𝜃, the next relation can be obtained from Eq. (11): 𝜃̇ =

1 𝑅1−1 𝑅2−1 𝑅3−1 𝑅4−1 𝑅3−1 (𝑇 (𝑇 − 𝜃) + − 𝜃) + 𝐼) ( −1 𝑖 𝐶2 𝑅1 + 𝑅2−1 𝑜 𝑅3−1 + 𝑅4−1 𝑅3−1 + 𝑅4−1

(16)

On the other hand, by introducing the block matrices given by Eq. (13), for 𝑁 = 3, into: (17)

−1 𝐂𝑆 = −𝐊11 𝐊12 −1 [𝐊 𝐃𝑆 = −𝐊11 𝑏1

𝐈11

(18)

𝟎]

it is obtained: 𝑅2−1 −1 𝑅1 +𝑅2−1 𝑅3−1 −1 𝑅3 +𝑅4−1

𝐂𝑆 = [

] the output matrix, and

𝑅1−1 −1 𝑅1 +𝑅2−1

𝐃𝑆 = [

0

𝑅2−1 −1 𝑅1 +𝑅2−1

0

0

𝑅3−1 −1 𝑅3 +𝑅4−1

0

−𝑅4−1 −1 𝑅3 +𝑅4−1

1 𝑅1−1 +𝑅2−1

0

0 1

𝑅3−1 +𝑅4−1

0 ] the feed through matrix. 0

Furthermore, from Eq. (11) the next two measurement equations can be obtained: 𝑅2−1 𝑅1−1 𝜃 + 𝑇 𝑅1−1 + 𝑅2−1 𝑅1−1 + 𝑅2−1 𝑜

(19)

𝑅3−1 𝑅4−1 1 𝜃 + 𝐼 −1 −1 −1 −1 𝑇𝑖 + −1 𝑅3 + 𝑅4 𝑅3 + 𝑅4 𝑅3 + 𝑅4−1

(20)

𝜃𝑠𝑜 =

𝜃𝑠𝑖 =

43


Results and discussion By representing the phsyical system composed by the box and the plasterboard wall using a thermal network of first order, Equations deduced above may be used for identifying thermal resistances and thermal capacity by using the measurement data presented in the previous section. Next, we present the results obtained in Table 2. Different time series, as previously detailed, were used and the different values and their uncertainties estimated are presented. Table 2. Estimated values of thermal resistance and capacity of a plasterboard wall. Serie 1 Serie 2 Serie 3 Thermal resistance R (m2K/W) Heat capacity C (J/m2K)

Mean value

Design value

0.050

0.051

0.060

0.054 ± 0.001

0.052 ± 0.06

8250

9500

11000

9580 ± 250

11000 ± 2100

Conclusions The heat capacity and thermal resistance of a plasterboard wall have been identified using an ARX model deduced from a thermal network, which is the graphical representation of the thermal system (a simple and homogeneous plasterboard wall) from where heat exchange equations are obtained. Thermal cameras have been used for measuring surface temperatures of the simple and homogeneous plasterboard wall. Surface temperatures have been the outputs of the heat exchange model, a thermal network, which made no necessary the use of heat flux-meters. Future studies needs to test the methodology with a different materials as well as with heterogeneous walls. The comparison with the use of heat flux-meters also needs to be checked. Acknowledgments This work was supported by the “Ministerio de Economía y Competitividad” of Spain under Project TIN2015-64776-C3-1-R References [1] P. de Wilde, “The gap between predicted and measured energy performance of buildings: A framework for investigation,” Automation in Construction, vol. 41, no. 0, pp. 40-49, 2014. [2] A. Foucquier, S. Robert, F. Suard, L. Stéphan and A. Jay, "State of the art in building modelling and energy performances prediction: A review," Renewable and Sustainable Energy Reviews, vol. 23, pp. 272-288, 2013. [3] I. Naveros, M. J. Jiménez and M. R. Heras, "Analysis of capabilities and limitations of the regression method based in averages, applied to the estimation of the U value of building component tested in Mediterranean weather," Energy and Buildings, vol. 55, pp. 854-872, 2012. [4] I. Naveros, P. Bacher, D. Ruiz, M. Jiménez and H. Madsen, "Setting up and validating a complex model for a simple homogeneous wall," Energy and Buildings, vol. 70, pp. 303-317, 2014. [5] I. Naveros, C. Ghiaus, D. Ruíz and S. Castaño, “Physical parameters identification of walls using ARX models obtained by deduction,” Energy and Buildings, vol. 108, pp. 317-329, 2015. [6] I. Naveros and C. Ghiaus, “Order selection of thermal models by frequency analysis of measurements for building energy efficiency estimation,” Applied Energy, vol. 139, no. 0, pp. 230-244, 2015. [7] T. Roubicek and M. Valasek, “Optimal control of causal differential-algebraic systems,” Journal of Mathematical Analysis and Applications, vol. 269, no. 2, pp. 616-641, 2002.

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[8] P. Biddulph, V. Gori, C. A. Elwell, C. Scott, C. Rye, R. Lowe and T. Oreszczyn, “Inferring the thermal resistance and effective thermal mass of a wall using frequent temperature and heat flux measurements,” Energy and Buildings, vol. 78, no. 0, pp. 10-16, 2014. [9] D. Kim, J. Cai, K. B. Ariyur and J. E. Braun, "System identification for building thermal systems under the presence of unmeasured disturbances in closed loop operation: Lumped disturbance modeling approach," Building and Environment, vol. 107, pp. 169-180, 2016. [10] I. Naveros, C. Ghiaus, D.P. Ruíz, “Frequency response limitation of heat flux meters”, Building and Environment, Volume 114, 2017, Pages 233-245. [11] X. Meng, B. Yan, Y. Gao, J. Wang, W. Zhang and E. Long, “Factors affecting the in situ measurement accuracy of the wall heat transfer coefficient using the heat flow meter method,” Energy and Buildings, vol. 86, pp. 754-765, 2015. [12] R. Albatici, A.M. Tonelli A.M. Infrared thermovision technique for the assessment of thermal transmittance of opaque buildings elements on site Energy and Buildings 42, pp. 2177-2183, 2010.

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46

XXXVI Biennial Meeting of the Real Sociedad Española de Física Symposium on Energy and Sustainability

Hybrid Brayton thermosolar systems: thermodynamic prediction of annual efficiencies and emissions R.P. Merchán1,*, M.J. Santos1, A. Medina1, A. Calvo Hernández1 1 Department

of Applied Physics, University of Salamanca, Plaza de la Merced s/n, 37008, Salamanca, Spain

* [email protected]

1. Introduction The necessity to diversify the energy sources in power generation and to look for renewable ones is undoubted. Thermosolar power plants, which constitute one of the main ways of solar energy exploitation, are competing with other renewable energy sources for generating clean electrical energy, reducing fuel consumption. Hybrid thermosolar plants combine two great advantages on electricity generation: the emissions reduction of thermosolar energy, as well as the stable supply of power output to the grid of conventional power plants, avoiding the use of storage systems. For those reasons in the last years a big effort has been done in the development of prototypes and experimental plants in order to investigate the viability of thermosolar hybrid Brayton cycle plants. A working fluid, usually air, is preheated by concentration solar energy, before entering a combustion chamber. Then, the fluid performs a thermodynamic cycle (in this case, a Brayton cycle), generating electrical energy indirectly. In this way fossil fuel and the associated emissions are reduced. It is important to note that apart from being easily scalable, gas-turbines can be combined with other cycles like bottoming Rankine. Also they do not require too much water for operation, which makes them suitable for electrical generation in arid regions, and are extremely versatile [1]. Experimental projects and prototypes developed up to date show that this technology is viable, but they also reveal that it is necessary to improve their efficiency, in order to generate electricity at competitive prices. Apart from R+D projects, prototypes, and experimental installations, several research works have been published in the last times. Some of them make use of commercial simulation environments, which allow a detailed description of all plant components and specific calculations on the solar subsystem. However, it is not easy to extract direct physical information about the main losses sources in the plant and to perform a global optimization of the plant design. Because of this reason, in this paper the next modus operandi is followed instead of this one. A second type of strategy is to build a theoretical model of the plant, in terms of a reduced number of parameters, allowing a simple but realistic picture of plant operation and to estimate its performance records. Thermodynamic analyses can provide an integrated point of view of all subsystems and their importance in the overall efficiency. Moreover, they help to predesign future generations of plants based in this concept because of their flexibility to survey the adequate intervals of key parameters for optimal plant operation. There are several theoretical works that start from the ideal Brayton cycle and thereafter refinements are included in the analysis of the thermodynamics of the cycle in order to recover realistic output records. Usually, in these works, the model for the concentrated solar subsystem, although including the main heat transfer losses, is simple. This allows to obtain closed analytical expressions for thermal efficiencies and power output, and then check the model predictions for particular design point conditions, with fixed values of direct solar irradiance and ambient temperature. But also by means of this thermodynamic model, a dynamic analysis that varies solar irradiance and external temperature conditions with time can be carried out. And in a possible step forward to suggest and guide optimization strategies.

47


2. Plant thermodynamics A thermodynamic model for hybrid Brayton thermosolar plants, which has been proposed recently by the same authors, is going to be presented [2-5]. These plants have three main elements: the heliostat field, the receiver, and the power conversion system. The model, in which refers to the thermodynamic cycle, starts from a closed Brayton cycle however incorporating the main losses and irreversibility sources: pressure decays, non-ideal compressor and turbine, heat transfer losses in the solar collector, combustion inefficiencies, heat exchangers, etc.

Figure 1. Scheme of the hybrid solar Brayton plant considered. The main heat transfers and temperatures are shown. Also the key losses sources considered in the model are depicted.

A central tower hybrid solar thermal installation, as depicted in Fig. 1, is considered. The whole system receives two energy inputs. On one hand, a heat input, 𝐺𝐴𝑎 , coming from the sun, where 𝐺 is the direct solar irradiance and 𝐴𝑎 , the aperture area of the solar field. For the solar subsystem, a simple model, which accounts for heat losses in the solar collector due to radiation and conduction/convection terms, was supposed. 1 4 [𝛼𝜎(𝑇𝐻𝑆 − 𝑇𝐿4 ) + 𝑈𝐿 (𝑇𝐻𝑆 − 𝑇𝐿 )] (1) 𝐺𝐶 In this equation 𝜂𝑆 is the solar collector efficiency, 𝜂0 the optical efficiency, 𝐶 the concentration ratio, 𝛼 the effective emissivity of the collector, 𝜎 the Stefan-Boltzmann constant, 𝑇𝐻𝑆 the collector working temperature, 𝑇𝐿 the ambient temperature and 𝑈𝐿 the conduction/convection heat loss coefficient. On the other hand, the energy input at the combustion chamber is 𝑚̇𝑓 𝑄𝐿𝐻𝑉 , being 𝑚̇𝑓 the fuel mass flow rate and 𝑄𝐿𝐻𝑉 , its corresponding lower heating value. Finally, the heat engine generates a mechanical power output, 𝑃, and releases a heat flux to the ambient, 𝑄̇𝐿 . The overall thermal efficiency (𝜂) was found as a function of the efficiency of the plant subsystems (solar 𝜂𝑆 , combustion 𝜂𝐶 , and gas turbine 𝜂𝐻 ), the effectivenesses of the heat exchangers linking subsystems (𝜀𝐻𝑆 for solar subsystem and 𝜀𝐻𝐶 for combustion subsystem) and the solar share fraction (𝑓). 𝜂𝑆 = 𝜂0 −

48


𝜂 = 𝜂𝑆 𝜂𝐶 𝜂𝐻 [

𝜀𝐻𝑆 𝜀𝐻𝐶 ] 𝜂𝐶 𝜀𝐻𝐶 𝑓 + 𝜂𝑆 𝜀𝐻𝑆 (1 − 𝑓)

(2)

There is another interesting performance, denominated fuel conversion rate, that relates power output to the required heat with an associated economical cost (fuel burned). It does not represent a thermodynamic efficiency because it is defined in the range [0, ∞]: 𝜂𝑒 =

𝑃 𝜂𝜂𝑆 𝜂𝐻 𝜀𝐻𝑆 = 𝑚̇𝑓 𝑄𝐿𝐻𝑉 𝜂𝑆 𝜂𝐻 𝜀𝐻𝑆 − 𝜂𝑓

(3)

A mass rate of an ideal gas (pressurized air) undergoes an irreversible recuperative closed Brayton cycle, in which the recuperator can be removed. The working gas is first compressed in a non-ideal compressor; and then it is heated up by the recuperator, the solar collector, and the combustion chamber. After the heating stage, the air is expanded and cooled irreversibly through a non-ideal turbine. And finally, the working gas recovers its initial conditions releasing heat with the recuperator and with another heat exchanger that connects the cycle to the surroundings. Turbine model includes these existing losses and irreversibilities. On the one hand, the geometric parameters related to the size of the cycle are taken into account. And, on the other hand, the heat losses irreversibilities in the compressor and turbine, in the recuperator and in all the heat exchangers and the pressure drop irreversibilities in the heat absorption and extraction processes are included. The key of the model resides in the fact that all the involved temperatures can be expressed in terms of the whole set of geometric and irreversibility parameters, so the performance of the plant is a function of these parameters [2]. 3. Numerical implementation and validation Once the thermodynamic model has been proposed, a numerical implementation is performed. This validation has been widely addressed by the same authors in [2]. Table 1. Top: output records from the manufacturer and from our model for the pure combustion mode. Bottom: estimated parameters and efficiencies from our model for the hybrid thermosolar mode.

GAS TURBINE: PURE COMBUSTION MODE Mercury 50 turbine: manufacturer’s output records (Caterpillar) 𝑇3 = 1423 𝐾

𝑇𝑦 = 647 𝐾

𝜂ℎ = 0.385

|𝑊̇ | = 4.6 𝑀𝑊

Model: estimated output records 𝑇3 = 1418 𝐾

𝑇𝑦 = 650 𝐾

𝜂ℎ = 0.387

|𝑊̇ | = 4.5 𝑀𝑊

Relative deviations 0.4 %

0.4 %

0.6 %

1.4 %

GAS TURBINE: HYBRID THERMOSOLAR MODE (at design point) Estimated output parameters 𝑇3 = 1423 𝐾

𝑓 = 0.42

𝑚̇𝑓 = 0.151 𝑘𝑔/𝑠

|𝑊̇ | = 4.2 𝑀𝑊

Estimated efficiencies 𝜂𝐻 = 0.393

𝜂𝑆 = 0.697

𝜂 = 0.317

49

𝜂𝑒 = 0.647


In order to introduce the solar heat, researchers from SOLUGAS Project [6] have modified Mercury 50 turbine (manufactured by Caterpillar). Output values of our model can be obtained and compared to the ones of manufacturer for the pure combustion mode (see Table 1). In accordance with this, relative deviations are very small, hence the turbine model agrees very well with real turbine data. However, it is not possible to validate the thermosolar plant itself because the owner company has not published all the results, but a stationary estimation at the design point can be done. In this way, output parameters and efficiencies are estimated and all the results are perfectly reasonable, so it is concluded that the thermosolar plant model works fairly properly. 4. Results 4. 1. Temperature dependent specific heat (𝒄𝒑 ) Needed meteorological data (solar direct irradiance and ambient temperature) have been obtained from Meteosevilla database [7]. As probably Solugas design point conditions are too optimistic, average conditions are taken into account. So, an average calculation process is followed for obtaining annual mean values of these meteorological data [4]. In this way, the surrounding averaged temperature is 𝑇𝐿 = 291.575 𝐾, while annual mean solar irradiance is 𝐺 = 457.874 𝑊/ 𝑚2 . This last one value can be considered a realistic value since it constitutes about half of the design point irradiance considered in Solugas project, 𝐺 = 860 𝑊/𝑚2 [6]. As the temperature changes in this Brayton cycle are high (from about 300𝐾 to approximately 1400𝐾), the influence of the temperature on the specific heat, 𝑐𝑝 (𝑇), may be important. The polynomial fit for this constant pressure specific heat has been determined by taking into account NIST data through RefProp software [8]. In order to analyze this influence, a comparison between the case when specific heat is supposed constant and the case when specific heat depends on the temperature has been carried out. Table 2 shows these results together with relative deviations between the two alternatives, related to the temperature dependent case: 𝑥𝑐 𝑝(𝑇) − 𝑥𝑐̅𝑝 ∆𝑥 (%) = ∗ 100 (4) 𝑥𝑐 𝑝(𝑇) Table 2. Comparison of output values for temperature independent (𝑐̅𝑝 ) and dependent specific heat (𝑐𝑝 (𝑇)), with relative deviations (∆𝑥 (%)).

AVERAGE CONDITIONS

WITH RECUPERATION

𝑐̅𝑝

𝑐𝑝 (𝑇)

∆𝑥 (%)

𝜂

0.323

0.324

0.475

𝜂𝑒

0.449

0.450

0.267

𝜂𝑆

0.610

0.609

−0.472

𝜂𝐻

0.392

0.393

0.463

𝑓

0.163

0.161

−1.023

𝑇𝐻𝑆 (𝐾)

948.886

971.150

2.293

𝑃 (𝑀𝑊)

4.621

4.677

1.207

𝑚𝑓,𝑠𝑝𝑒𝑐 (𝑘𝑔/𝑀𝑊ℎ)

170.037

169.582

−0.268

50


In view of the results the differences between output variables with 𝑐̅𝑝 and 𝑐𝑝 (𝑇) are very small. For instance, overall thermal efficiency, solar collector efficiency, and solar share change only in the third decimal place. At the other extreme, temperatures present larger changes, although they are still small. The main conclusion obtained from this study is that both models can be applied because results are very similar. So henceforth the model with constant specific heat will be used, since it is simpler and allows a completely analytical description. But the opposite approach, the cycle with temperature dependent specific heat, has been followed in [5]. It should be highlighted that our result contradicts conclusions from [9]. 4. 2. Theoretical limits of the plant Starting from real conditions (also called operating point), other four hypothetical configurations can be investigated with the goal of examining possible plant improvements over the real conditions of the plant: first the heat exchangers are considered as ideal, then the solar subsystem, after it is the Brayton cycle which is supposed ideal, and finally a completely ideal system is assumed. (see Fig. 2).

Figure 2. Scheme of the analyzed cases.

Apart from those five configurations, four operating modes are analyzed according to the existence or not existence of solar input and recuperator. At real conditions (Table 3), a power output of 4.5 𝑀𝑊 can be achieved, very close to that of the design point. It should be highlighted that exhaust temperature presents a high value in all cases, which is important to take advantage of residual heat with cogeneration or bottoming cycles. Overall thermal efficiency of the recuperative plant is larger if there is no solar input: a 6.9 % higher than for hybrid operation, due to energy losses in solar subsystem associated with high temperatures. On the other hand, fuel conversion rate takes its larger value when there is solar input and recuperation. It can be confirmed that, in combustion mode, the fuel conversion rate is the overall thermal efficiency. In addition, solar collector efficiency is relatively good; however, solar share is still small.

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XXXVI Biennial Meeting of the Real Sociedad Española de Física Symposium on Energy and Sustainability Table 3. Annual means of most important plant performance records: (A) operating point. Relative differences are calculated with respect to the layout with no solar input.

Operating point

Without recuperation

With recuperation

(A)

Without solar input

With solar input

Without solar input

With solar input

𝑃 (𝑀𝑊)

4.370

4.377 (+0.16%)

4.469

4.476 (+0.16%)

𝜂

0.262

0.250 (−4.75%)

0.367

0.342 (−6.94%)

𝜂𝑒

0.263

0.283 (+7.39%)

0.367

0.406 (+9.54%)

𝜂𝐻

0.274

0.274 (+0.04%)

0.383

0.383 (+0.08%)

𝑇𝐻𝑆 (𝐾)

−

730.1

−

946.6

𝜂𝑆

−

0.620

−

0.586

𝑓

−

0.123

−

0.164

Table 4 is obtained when a completely ideal system is assumed. So, these are the maximum achievable values that mark the plant performance limits. A great power output can be reached: almost 8 𝑀𝑊. Also, an overall efficiency of 0.6, a fuel conversion rate of about 0.8, and a solar share of 0.3 (double that for the real conditions) are predicted. Table 4. Annual means of most important plant performance records: (E) completely ideal system. Relative differences are calculated with respect to the layout with no solar input.

Completely ideal

Without recuperation

With recuperation

Without solar input

With solar input

Without solar input

With solar input

𝑃 (𝑀𝑊)

7.988

7.988 (+0. %)

7.988

7.988 (+0. %)

𝜂

0.452

0.452 (+0. %)

0.628

0.628 (+0. %)

𝜂𝑒

0.452

0.522 (+15.68%)

0.628

0.792 (+26.0%)

𝜂𝐻

0.452

0.452 (+0. %)

0.628

0.628 (+0. %)

𝑇𝐻𝑆 (𝐾)

−

722.1

−

971.0

𝜂𝑆

−

1.

−

1.

𝑓

−

0.218

−

0.301

system (E)

The intermediate configurations have been also analyzed [4], but for the sake of brevity their tables results are not exposed here. As a summary, Fig. 3 is presented, where some output records are shown for the five configurations. It is clear that configurations (D) and (E), that is to say, assuming the Brayton cycle and the whole system as ideal, is which affects more to overall efficiency, to fuel conversion rate and to power output. When the solar subsystem is supposed ideal, the solar collector efficiency raises fairly significantly. However, these increments are not reflected on the overall thermal efficiency.

52


Figure 3. Some output records for the five layouts. Top left: overall thermal efficiency, 𝜂; up right: fuel conversion rate, 𝜂𝑒 ; bottom left: power output, 𝑃. The lines between dots are just a guide for the eyes. Legend: YSYR= With solar input and with recuperation, NSYR=Without solar input and with recuperation, YSNR=With solar input and without recuperation, NSNR=Without solar input and without recuperation.

In Figs. 4 and 5 two Sankey diagrams representing the main plant losses can be seen for the real conditions configuration as well as for the layout when the completely system is assumed as ideal. Looking at the solar part, 𝑄̇𝑙 and 𝑄̇𝑖𝐻𝑆 are the losses associated to the heat transfers on the solar receiver and 𝑄̇𝐻𝑆 denotes the heat rate input from the solar collector. And regarding at combustion part, 𝑄̇𝐶 is related to the heat losses in combustion subsystem, 𝑄̇𝑖𝐻𝐶 refers to the heat losses at its heat exchanger and 𝑄̇𝐻𝐶 is the heat rate input from combustion chamber. These energy fluxes are normalised to unity and so, in the first case, the solar input is 26 % of the total and the combustion input constitutes the rest, 74 %. It is quite visible that the first diagram presents small energy losses both in combustion and solar subsystems; while the other does not have any heat loss. Moreover, it must be stressed that, at real conditions, the wasted heat flux, which is released to the ambient, is higher than the one of power output; however, in the completely ideal system configuration, the power output flux is quite higher than the wasted heat, due to the high increment of heat engine efficiency. Despite Brayton cycle subsystem can achieve the highest improvements for the performance of the hybrid plant, technical feasibility and room for improvement have to be considered, since it may be easier to improve solar subsystem performance, due to the fact that thermosolar technology is considerably less mature than gas-turbine equipment. On the other hand, the solar flux is always smaller than the combustion one, since the solar share does not exceed 30 % in any case. This fact means that the solar collector field is very small for the desired power output, and so the turbine inlet temperature required for obtaining this power is not reached only with solar subsystem. Therefore it is always necessary to burn quite fuel. This is a plant sizing problem, which is solved by reducing the power output supplied to the grid or by increasing the heliostat field size.

53


Figure 4. Sankey diagram for the real conditions configuration (A), for the hybrid recuperative case. Energy fluxes are normalised to unity.

Figure 5. Sankey diagram for the completely ideal system (E), for the hybrid recuperative case. Energy fluxes are normalised to unity.

Finally, the specific natural gas consumption and the pollutant emissions can be analyzed. They are directly estimated through the natural gas emission factors. However, the calculated predictions on emissions should only be taken as a guide, because each plant could have particular technologies to reduce emissions or CO2 capture mechanisms.

54


In Table 5 both specific fuel consumption and emissions are collected for the operating point case (A). In the case of recuperation and solar input, the fuel consumption is about 187 𝑘𝑔/𝑀𝑊ℎ, value that rises until 284 𝑘𝑔/𝑀𝑊ℎ when no recuperation and no solar input are taken. Comparing pure combustion and hybrid modes, fuel savings of 8.3 % and 6.2 % can be achieved for recuperative and non-recuperative cases, respectively. These percentages can seem relatively small, but this consumption saving can supposed important advantages for companies in annual terms. Table 5. Annual means of fuel specific consumption and of specific emissions: (A) real conditions.

Without recuperation Operating point (A)

Without solar input

With recuperation

With solar input

Without solar input

With solar input

𝑚𝑓 (𝑘𝑔/𝑀𝑊ℎ)

283.995

266.463

203.485

186.569

𝐶𝑂2 (𝑘𝑔/𝑀𝑊ℎ)

702.758

659.374

503.534

461.674

𝐶𝐻4 (𝑔/𝑀𝑊ℎ)

13.296

12.475

9.527

8.735

𝑁2 𝑂 (𝑔/𝑀𝑊ℎ)

1.291

1.211

0.925

0.848

−6.173%

Relative differences

−8.313%

Also, it is important to note that, comparing recuperative and non-recuperative modes, a 30 % of fuel reduction can be reached for solar input and a 28 % for no solar input. In addition, the pollutant gases emission associated with the natural gas burning are estimated, namely, the methane, the nitrous oxide, and the carbon dioxide generation. Specific emissions of carbon dioxide at normal performance (operating point, recuperation, and solar input) are 𝐶𝑂2 = 461.674 𝑘𝑔/𝑀𝑊ℎ, whereas those of CH4 and N2O are 𝐶𝐻4 = 8.735 𝑔/𝑀𝑊ℎ and 𝑁2 𝑂 = 0.848 𝑔/𝑀𝑊ℎ, respectively. Table 6. Annual means of fuel specific consumption and of specific emissions in the five configurations, for the hybrid recuperative case. The increments are relative differences of the particular configuration with respect to configuration (A).

With recuperation and solar input

Operating point (A)

Ideal heat exchangers (B)

Ideal solar

Ideal Brayton

part (C)

cycle (D)

Completely ideal system (E)

𝑚𝑓 (𝑘𝑔/𝑀𝑊ℎ)

186.569

173.516

169.781

112.204

101.019

𝐶𝑂2 (𝑘𝑔/𝑀𝑊ℎ)

461.674

429.374

420.13

277.654

249.977

𝐶𝐻4 (𝑔/𝑀𝑊ℎ)

8.735

8.124

7.949

5.253

4.730

𝑁2 𝑂 (𝑔/𝑀𝑊ℎ)

0.848

0.789

0.772

0.510

0.459

−

−6.996%

−8.998%

−39.859%

−45.854

Relative differences

The same variables but for the five before mentioned configurations are displayed in Table 6, where also relative differences are shown with respect to operating point. Also here it is observed that the leap occurs when approaching the ideal Brayton power unit, with almost a 40 % of decrease in fuel consumption and pollutant emissions. Ideal heat exchangers and ideal solar part models give a smaller reduction on consumption: approximately 7 % and 9 %, respectively. Of

55


course, the completely ideal system configuration presents the higher decrease, around 46 %. Those percentages correspond with theoretical limits for greenhouse emissions reduction. Therefore, the room for improvement is wide. If the complete system was ideal, specific carbon dioxide emission would be 𝐶𝑂2 = 249.977 𝑘𝑔/𝑀𝑊ℎ, which is a very promising result. In doing the same as before, comparing the carbon dioxide production for the five configurations, Fig. 6 can be obtained, where it is clearly visible that considering the Brayton cycle or the complete system as ideal have a great effect on emissions reduction, reaching the same values of before, 40 % and 46 %, respectively.

Figure 6. Relative differences of specific emissions of 𝐶𝑂2 between configurations (B)-(E) and configuration (A) quantified as relative increments in percentages with respect to the real conditions configuration (A). Hybrid and combustion modes and recuperative and nonrecuperative configurations are considered. Legend: YSYR= With solar input and with recuperation, NSYR=Without solar input and with recuperation, YSNR=With solar input and without recuperation, NSNR=Without solar input and without recuperation.

4. 3. Sensitivity analysis A sensitivity analysis is performed in order to study the influence of the main subsystems irreversibilities on the overall plant performance records. Heat engine losses parameters will be varied, starting from design point conditions. But also the influence of solar subsystem losses parameters and that of pressure losses in the heat absorption process, ∆𝑝𝐻 /𝑝𝐻 , can be analysed [4]. Changes on the losses parameters associated to the heat engine will greatly affect plant performance, as it is surveyed in Fig. 7. The evolution of all variables is also almost linear, however the scales of the vertical axes indicate much more important variations on the performance records. For example, an increment of 10 % on compressor isentropic efficiency, 𝜀𝑐 , will lead to 10 % rise on power output and the same increment on turbine isentropic efficiency, 𝜀𝑡 , to more than 20 % on 𝑃. Great improvements are achieved when both the compressor and turbine efficiency are incremented simultaneously, almost 40 % on power output can be reached if 𝜀𝑐 + 𝜀𝑡 rises up to 10 %. As recuperation is an internal process of the heat engine, recuperator effectiveness changes would not have any influence on power output, nevertheless other output records would be affected. The other analyzed output records (overall efficiency, 𝜂, Brayton subsystem efficiency, 𝜂𝐻 , and fuel conversion rate would, 𝜂𝑒 ) change in the interval [−30 %, +30 %] for variations in the losses coefficients of the power unit in the interval [−10 %, +10 %]. In short, reductions on Brayton losses would be increased by a factor 3 on the plant records.

56


Figure 7. Sensitivity of different output records, power output (P), overall thermal efficiency (η), Brayton cycle efficiency (η H), and fuel conversion efficiency (ηe), to several irreversibility parameters of the heat engine: isentropic efficiency of the turbine (ε t), isentropic efficiency of the compressor (εc), recuperator effectiveness (εr), and effectiveness of the heat exchanger associated to the combustion chamber (ε HC). Another case is also considered: when εc and εt are simultaneously changed in the same way. Both axis are represented in relative terms as percentages. The central point is related to the yearly averages of the recuperative plant at real operating conditions.

5. Future work

Figure 8: Scheme of a thermodynamic plant with Nc compressors and Nt turbines.

57


Currently this project continues with other lines of research, among them: multistage plants, different working fluids, parabolic dishes, and combined cycles. The inclusion of several turbines and compressors in the thermodynamic plant’s scheme (Fig. 8) results in an increase of the overall efficiency and of the net power, although the economic investment also rises. Changing the working fluid from dry air to other less usual gases as nitrogen, helium or carbon dioxide can be beneficial from the viewpoint of the reduction of temperatures (CO2) or the pressure losses (He), but it can also lead to some disadvantages like the lower experience (see Table 7) [10]. Table 7. Comparative table of some working fluids.

Working fluid

Advantages

Disadvantages

Dry air

Experience, abundant, free

High pressure losses, high temp.

N2

Similar to air

High pressure losses, high temp.

Low pressure losses, inert,

More stages, high temp., few

non-toxic

experience, leaks

Moderate temp., good critical

Fast variations of critical point,

point, inert, non-toxic

scarce experience

He

CO2

Another possibility for future work is to change the tower Central Receiver System by parabolic dishes, which allow an electric generation in a smaller scale, with only a few kW, thanks to the microturbines set up in their receivers. Therefore, parabolic dishes can be employed for distributed generation in isolated places without access to the electric gird or also, when lot of them are placed in fields, for releasing energy to the grid.

Figure 9: Scheme of a combined thermodynamic plant (Brayton cycle + Rankine bottoming cycle).

58


On the other hand, setting up a Rankine cycle bottoming the Brayton one (combined cycle) can lead to the use of the excess of heat after the turbine (Fig. 9) and can improve the overall efficiency and increase the power output. 6. Conclusions Finally, the most important conclusions obtained from this study are summed up here:  A thermodynamic model for a hybrid system composed of a solar central receiver heliostat field and a Brayton gas turbine was developed.  Additionally, the system is described in terms of a reduced number of parameters, with clear physical meaning each.  Furthermore, the model was validated by the consideration of the SOLUGAS Project, developed by the company Abengoa Solar, near Seville.  Likewise, the model incorporates the main losses and irreversibility sources: nonideality turbine and compressor, pressure decays, real heat exchangers, heat transfer losses in the solar collector, combustion inefficiencies, etc.  It was shown that since the model is flexible, it allows to check the performance of several plant configurations.  As summary, it can be said that the most important improvements are related to the Brayton cycle, since higher increments can be observed in all the variables.  Also, it is interesting to stress that high increments on solar collector efficiency do not raise significantly overall thermal efficiency. Nevertheless, they can increase fuel conversion rate.  As mentioned before, numerically, the most influential factor corresponds to improvements on Brayton cycle. On the other side, the technical possibilities have to be taken into account. This issue is outside the range of this study. However, we are aware that it has to be accounted, since Brayton cycle improvements may not be feasible nowadays, although they are the most effective ones, and perhaps the solar efficiency improvements are easier achievable.  In conclusion, this kind of plants are especially interesting for regions with good insolation ratios and scarce hydric resources, because allow an appreciable reduction of fossil fuel consumption. There is still room for improvement in the economic issues, so further research and development are needed; but these facilities are worth the effort from the ecological point of view, since they reduce significantly pollutant emissions related to greenhouse effect, so they can help to mitigate the anthropogenic intensification of climate change. Acknowledgments The authors acknowledge financial support from MINECO of Spain, Grant ENE2013-40644-R and University of Salamanca. References [1] O. Behar, A. Khellaf, K. Mohammedi, Rene. Sust. Energ. 23 (2013) 12-39. [2] D. Olivenza-León, A. Medina, A. Calvo Hernández, Energ. Conv. Manage. 93 (2015) 435-447. [3] M.J. Santos, R.P. Merchán, A. Medina, A. Calvo Hernández, Energ. Convers. Manage. 115 (2016) 89-102. [4] R.P. Merchán, M.J. Santos, I. Reyes-Ramírez, A. Medina, A. Calvo Hernández, Energ. Convers. Manage. 134 (2017) 314-326. [5] R.P. Merchán, M.J. Santos, A. Medina, A. Calvo Hernández, Renew. Energ. xxx (2017) 1-11. https://doi.org/10.1016/j.renene.2017.05.081

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[6] R. Korzynietz, J.A. Brioso, A. del Río, M. Quero, M. Gallas, R. Uhlig, M. Ebert, R. Buck, D. Teraji, Sol. Energy 135 (2016) 578-589. [7] Meteosevilla. http://www.meteosevilla.com. [8] E. W. Lemmon, M. L. Huber, M. O. McLinden. NIST Standard Reference Database 23: Reference fluid thermodynamic and transport properties-REFPROP, version 9.1. National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg (2013). [9] L. Wu, G. Lin, J. Chen, Renew. Energ. 35 (2010) 95-100. [10] O. Olumayegun, M. Wang, G. Kelsall, Fuel 180 (2016) 694-717.

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XXXVI Biennial Meeting of the Real Sociedad Española de Física Simposium on Enegy and Sustainability

Band alignment of polar and non-polar interfaces between the CuGaS2/CuAlSe2 and CuGaS2/ZnSe J. E. Castellanos Águila1, P. Palacios2,3*, J. Arriaga1, P. Wahnón,3,4 1Instituto

de Física, Benemérita Universidad Autónoma de Puebla, Av. San Claudio y 18 Sur. C.U. 72570. Puebla, México. Dpt. de Física Aplicada a las Ingenierías Aeronáutica y Naval, ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, 28040, Madrid, Spain. 3Instituto de Energía Solar, ETSI Telecomunicación, Universidad Politécnica de Madrid, 28040, Madrid, Spain. 4Dpt. de Tecnología Fotónica y Bioingeniería, ETSI Telecomunicación, Universidad Politécnica de Madrid, 28040 Madrid, Spain. 2

Abstract Band alignment is key to enhance the performance of heterojunction for chalcopyrite thin film solar cells. In this work, we report theoretical calculations of the valence and conduction band offset for the polar and non-polar interfaces.The systems under consideration are CuGaS2, CuAlSe2 and CuGaS2 doped with Cr. The doped chalcopyrite contains an intermediate band which is a very promise concept to be used in photovoltaic solar energy production. The calculations are carried out using the density functional theory and the more accurate self-consistent GW scheme to obtain improved bulk band-gaps and band offsets; additionally, we use the semi-empirical Tight-Binding formalism to calculate the electronic band structure of the CuGaS2:Cr. The difference of valence and conduction band offsets of them is primarily attributed to the variations in dipole contributions due to the polar or non-polar character of the interface. We show that the CuGaS2/CuAlSe2 and CuGaS2/ZnSe heterostructures, in both polar and non-polar interfaces, forms a characteristic staggered band alignment for the design of heterojunction devices in photovoltaic applications. Introduction Current Cu(In,Ga)Se2 photovoltaics devices, on a laboratory scale, reach conversion efficiencies about 22.3% [1]. This improvement on the efficiency is mainly due to the improvement to the CIGS absorber layer and the junction formation process. One of the most important aspect of CuChalcopyrite solar cells is the interface between the Chalcopyrite and the buffer layer, where the essential physics of photovoltaics takes place. However, the efficiency is still lower than the single gap Shockley–Queisser limit[2]. In a previous report[3], we study the band alignment of the interfaces between CuGaS2 and several contact materials and we have found that the CuAlSe2/CuGaS2 and CuGaS2/ZnSe interfaces show the characteristics for the design and development of thin film solar cells. The results suggest that the interfaces between them would affect the conversion eficiency in solar cells [4]. However, theoretical complications arising from complex interfacial bonding interactions and the lattice mismatch between the compounds, have hindered the development of general, analytic models capable of accurately predicting fundamental interfacial quantities [5]. The large lattice mismatch between the CuGaS2 and the contact material (CuAlSe2 ~ 6% and ZnSe ~ 5%) and the staggered (type-II) band alignment of the two interfaces, have motivated intensive studies on CuGaS2 heterostructures, because the type of alignments is always accompanied by natural charge separation, which is advantageous for promising solar cells. On the other hand, due to the growing interest of increase the efficiency of a solar cell by considering CuGaS2 semiconductor as the active material hosting an intermediate-band (IB), it becomes necessary a detailed study of the electronic properties of such system [6–11]. If we consider Chromium transition atom replacing Gallium atom in a CuGaS2 semiconductor, additional states within the band-gap are observed due to the Cr, as described in Ref. [6-8, 12, 13]. However, up to date it is not known which will be the behaviour of the intermediate band material taking into account the rest of materials which are in contact in the complete solar cell. For this reason, a precise knowledge of the band structure of these heterojunctions becomes necessary.

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Band alignment of polar and non-polar interfaces between the CuGaS2/CuAlSe2 and CuGaS2/ZnSe

Unfortunately, due to the large unit cells necessary to manage small doping levels, first principles calculations requires very large time consuming computer calculations, which makes this methodology unfeasible. For systems of such complexity, it is very convenient to have simpler methods available as an alternative tool. The Tight-Binding (TB) method is one such possibility, since it gives solutions showing all the correct symmetry properties of the energy bands, and it is rather easy to get solutions for energy bands at an arbitrary point in the Brillouin zone. The time required by this semi-empirical method depends only on the size of the matrix to diagonalize, which in the worst case is very small compared to the time required for a first principles calculation. In this work we use calculations based on density functional theory to study interfaces between the CuGaS2 and the CuAlSe2 and ZnSe having the polar directions (001) and (1̅1̅2̅), and the nonpolar direction (110) and (102). For the energy band alignment between the IB materialsemiconductor heterojunction [14, 15], we considered for the interface the (110) plane. All distinct interfaces are treated individually with respect the both valence band offsets (∆𝐸𝑉𝐵 ) and the electrostatic potential-based reference levels. The dependence of interface properties on signed orientation and chemical termination plays a central role in our results. Finally, we present a TB study of the electronic band structure of the CuGaS2 doped with Cr in order to obtain an intermediate band. Theoretical Model and Computational Details We perform first-principles calculations based on the GGA approximation [16], the HeydScuseria-Ernzerhof (HSE06) hybrid functional [17-19] and many body perturbation theory (quasiparticle energy calculations) [20, 21] as implemented in the Vienna ab-initio simulation package (VASP) [22-24]. The interactions between the ionic cores and the valence electrons were introduced using the projector-augmented wave method (PAW) [25]. The valence configurations used in the PAW pseudopotentials were: 3𝑑10 4𝑠1 for Cu; 4𝑠 2 4𝑝1 for Ga; 3𝑠 2 3𝑝4 for S, 3𝑑 5 4𝑠1 for Cr, 4𝑠 2 4𝑝4 for S, 3𝑠 2 3𝑝1 for Al and 4𝑠 2 3𝑑10 for Zn. Ga potential without semi-core d states reproduces quite well the experimental valence band levels in CuGaS2 semiconductor so they have not been included. The Perdew–Burke–Ernzerhof (PBE) [16] functionals are employed for the GGA exchangecorrelation potential. The valence electronic wave-functions are expanded in a plane wave basis set up to a kinetic energy cut-off of 450 eV. For CuGaS2:Cr, quasi-particle energy calculations are based on a restricted self-consistent scGW scheme, where, the wave-functions and energies of the PBE calculations were used as the starting point to compute the quasiparticle band structure, subsequently, we update the quasi-particle wave-function four times in both Green’s function G and screened potential W [26]. The total number of valence and conduction band states in the scGW procedure was set to 320 for all materials. To calculate the valence and conduction band offset, we used an electrostatic potential-based alignment method [18, 27]. The goal of the method is to model a real epitaxial interface and according this model, the band gap of the materials forming the interface can be different from that in the bulk due to the deformed lattice. The electrostatic potential is necessary to connect the macroscopic band energy levels for the bulk systems and the interfaces [28, 29]. We averaged the electrostatic potential within the xy plane parallel to the interface between the two semi-infinite semiconductors. The valence band offset can be determinate from the energy difference between the valence band maximum (VBM) and the reference level of the distorted bulk obtained for the two semiconductors, and by the difference of the reference level of the two semiconductors in the interface. The supercell slab model are employed to calculate the interface between the CuGaS2 and/or CuAlSe2 and ZnSe phases. For suficiently thick layers the electrostatic potentials in the center of each layer become bulk-like, and allow extraction of band alignment representative of an infinite interface. Four interfaces are considered in this study, two polar interfaces (001) and (1̅1̅2̅), and two non-polar interfaces (110) and (102) (Figure 1(a-d)). We typically take the z coordinate to be in a direction normal to the interfaces under consideration. For polar surface calculations, slabs of up to eight CuGaS2 atomic layers are used. For non-polar surfaces, the slab model contain eight CuGaS2 atomic layers. The heterointerfaces between the IB material and CuAlSe2 or ZnSe phases are studied using 62


a supercell with eight atomic layers for each of the two materials stacked in the [110] direction (Figure 1(e)). Here, Г-centred k-point Monkhorst–Pack [30] mesh of 6 × 6 × 1 was used, due to the relatively large supercell size. For the bulk calculations we use a 6 × 6 × 2 k-point mesh.

Figure 1. Structures of selected CuGaS2 surfaces. (a) ideal (001)surface; (b) ideal (1̅1̅2̅) surface; (c) ideal (110) surface; (d) ideal (102) surface. In all cases the structures are shown from the side view. (e) Structure of the supercell for the CuGaS2:Cr/CuAlSe2 (110) interface. For the CuGaS2:Cr/ZnSe interface, the supercell is constructed similarly.

The calculation for CuGaS2:Cr was carried out using the TB formalism. A monoclinic unit cell in which one of the Ga atoms was replaced by a Cr atom (at tetrahedral sites), which corresponds to the 25% dopant concentration. The electronic wave function is written as a linear combination of atomic orbitals as, 𝛹𝑘 (𝑟) = ∑ 𝐶𝜈 𝜙𝜈 (𝑟 + 𝑅𝑗 )𝑒 𝑖𝑘∙𝑅𝑗 𝜈,𝑗

where ν is the atomic orbital, and the sum over j consider all the atoms in the crystal. We have used a 𝑠𝑝3 orbital basis for the Ga, Al, Se, and S atoms, and a 𝑠𝑝3 𝑑 5 basis for the Cu atom. When the previous equation is inserted in the Schrödinger equation, the matrix elements of the Hamiltonian, for first neighbor interactions, can be written as, ′

𝜇 ̂ 𝛹 𝜇′ (𝑘 ′ , 𝑟)𝑑 3 𝑟 = 𝛿𝑘𝑘 ′ ∑ 〈𝜙𝜈 |𝐻 ̂ |𝜙𝜈′ 〉 𝑑𝜇𝜇′ 𝑒 𝑖𝑘∙𝑑𝜇𝜇′ 𝐻𝜈𝜈′ = ∫ 𝛹𝜈 (𝑘, 𝑟)𝐻 𝜈 𝑑𝜇𝜇′

where ∗

′

̂ |𝜙𝜈′ 〉𝑑𝜇𝜇′ = ∫ 𝜙𝜈𝜇 (𝑟) 𝐻 ̂ 𝜙 𝜇′ (𝑟 + 𝑑𝜇𝜇′ )𝑑 3 𝑟 〈𝜙𝜈 |𝐻 𝜈 are the matrix elements between different atomic orbitals, and 𝑑𝜇𝜇′ is the vector connecting first neighbors only. The form of these matrix elements are written as 𝐸𝛼𝛽 , and the states are represented by their angular form and written as subscripts, 𝛼 for the left, and 𝛽 for the right state, and they were given by Slater and Koster since 1954 [31]. These matrix elements depend on the vector 𝑑𝜇𝜇′ which is written in terms of direction cosines along the 𝑥̂, 𝑦̂, and 𝑧̂ directions as, 𝑑̂𝜇𝜇′ = 𝑙𝑥̂ + 𝑚𝑦̂ + 𝑛𝑧̂ . The expressions of these parameters appear explicitly in [32].

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Results As in previous work [3], the lattice mismatch determines the magnitude of the structural variation displayed by the different types of interfaces and this can generates band gap fluctuations in the CuGaS2 than those of contact material. According to the strain perpendicular to the interface, the polar interfaces have a similar effect on lattice mismatch than the non-polar interfaces, nevertheless, the size of the area perpendicular in the non-polar interfaces is large than the polar interfaces and this makes the slab size computationally very demanding. Also according to experimental reports [33], epilayers of ternary chalcopyrite semiconductors grown on GaAs(111) or GaAs (110), exhibits several epitaxial orientations. For this reason is important study how the polarity of the interfaces affect in the band alignment. An orientationally depend change in the interface dipole magnitude may shift the relative positions of the valence band in the two semiconductors. The ∆𝐸𝑉𝐵 of the interfaces with different orientations for the CuGaS2/CuAlSe2 interface can be calculated from the following equation: 𝐶𝑢𝐺𝑎𝑆2

∆𝐸𝑉𝐵 = ∆𝐸𝑃 𝑆𝑙𝑎𝑏 + (∆𝐸𝑃𝐵𝑢𝑙𝑘 𝐶𝑢𝐺𝑎𝑆

𝐶𝑢𝐺𝑎𝑆2

− ∆𝐸𝑉𝐵𝑀

𝐶𝑢𝐴𝑙𝑆𝑒

𝐶𝑢𝐴𝑙𝑆𝑒2

) + (∆𝐸𝑃𝐵𝑢𝑙𝑘

𝐶𝑢𝐴𝑙𝑆𝑒2

− ∆𝐸𝑉𝐵𝑀

)

where ∆𝐸𝑃 𝑆𝑙𝑎𝑏 = 𝐸𝑃𝑆𝑙𝑎𝑏 2 − 𝐸𝑃𝑆𝑙𝑎𝑏 2 is the average electrostatic potential difference between the 𝐶𝑢𝐺𝑎𝑆 𝐶𝑢𝐺𝑎𝑆 CuGaS2 and the CuAlSe2, 𝐸𝑃𝐵𝑢𝑙𝑘 2 − 𝐸𝑉𝐵𝑀 2 is the energy difference between the average 𝐶𝑢𝐴𝑙𝑆𝑒 𝐶𝑢𝐴𝑙𝑆𝑒 electrostatic potential and VBM in the polar and non-polar CuGaS2 bulks, and 𝐸𝑃𝐵𝑢𝑙𝑘 2 − 𝐸𝑉𝐵𝑀 2 is the energy difference between the average electrostatic potential and VBM in the polar and nonpolar CuAlSe2. Knowing the relative position of the valence bands, we simply add the theoretical band gaps for each semiconductor forming each slab to obtain the conduction band offsets (∆𝐸𝐶𝐵 ). For the CuGaS2/ZnSe interface, the ∆𝐸𝑉𝐵 and ∆𝐸𝐶𝐵 is calculated similarly. However, the ∆𝐸𝐶𝐵 values given by standard DFT calculations are incorrect because the GGA functionals underestimate the band gap of CuGaS2, CuAlSe2 and ZnSe. Unfortunately, experimentally measured values also have very large uncertainties [34, 35]. Therefore, the DFT calculations under the precision of HSE06 are needed not only for evaluating the band gaps but also for determining the band alignments. We then calculated the band gap of the CuGaS2, CuAlSe2 and ZnSe from the adjustment of the HF mixing in the hybrid functional. Increasing the mixing from the standard value of 0.25 in the HSE06 functional gives the band gap of 2.43 eV for the CuGaS2, 2.65 for the CuAlSe2 and 2.82 eV for the ZnSe [3], which agrees pretty well to the experimental values [15, 36, 37]. As we mentioned early, the distortion induced for the interface generates band gap fluctuations in the CuGaS2 and the contact material. In Table 1 we can observe how these values change respect to the strain. Particularly, the CuGaS2 band gap decreases (respect to the bulk materials without distortion) by a significant amount (0.06-0.28 eV) depending on the interface orientation and the contact material. Inversely, for the CuAlSe2 and ZnSe the internal compression produced an opening of the band gap. In the case of the CuAlSe2 increases to 0.19 eV as lattice mismatch increases. For the ZnSe, the band gap increases by a negligible amount (~ 0.085 eV) as the internal stress increase. In Figure 2 we shows the position of the VBM and CBM of the CuGaS2 and CuAlSe2 with or without the effect of the distortion (generated for the different polar and non-polar orientations). The results corroborate the band gap shift of the CuGaS2 (Fig. 2(a)). According to our results, the band gap decreases more through an upward shift of the VBM than an downward shift of the CBM. This would imply a ± 0.2 eV deviation of the ∆𝐸𝑉𝐵 and not cause a substantial error in the ∆𝐸𝐶𝐵 . For the CuGaS2, the top of the valence band is weighted more heavily by Cu 𝑑 and S 𝑝 contributions [38]. We see that the lattice parameters parallel to the interface of the CuGaS 2 and the Cu-𝑆 bond length increases. The Cu 𝑑 orbitals are more diffuse, overlapping more effectively with the S orbitals. This leads to a substantial upward repulsion of the anion 𝑝 states and a reduction in the band gap. The conduction band minimum also contributes in the reduction in the band gap. This could be attributed to the fact that the conduction band minimum has strong Ga 𝑠 states whereas the other states in the conduction band are more heavily mixed with other atomic orbitals such as S 𝑝 states [39, 40]. 64


Table 1. Theoretical band-gap (in eV) obtained for the semiconductors forming the interfaces at the different orientation, modified from the experimental one due to the strain.

(001) (1̅1̅2̅) (110) (102)

CuGaS2/CuAlSe2 2.37 2.67 2.17 2.78 2.19 2.84 2.25 2.70

CuGaS2/ZnSe 2.26 2.85 2.31 2.91 2.17 2.87 2.16 2.87

For the CuAlSe2 (Figure 2(b)), the structurally responds in an opposite way to the CuGaS2 and the band gap expansion occurs through an upward shift of the conduction band minimum. The CBM consists mostly of the anti-bonding states of Al 𝑠 and Se 𝑠 orbitals. Since the selenium atom is closer to aluminum atom the anti-bonding state resulting from Se 4𝑝 - Al 3𝑠 hybridization is pushed to higher energies and the band gap is increased [39, 40]. The general trend that we find for the CuGaS2/CuAlSe2 interface is similar for the CuGaS2/ZnSe interface.

Figure 2. Energy levels of the gap edges obtained for the CuGaS2 and CuAlSe2 in the polar and non-polar surfaces. (a) CuGaS2 single phases distorted due to the epitaxial strain (red lines) and bulk material without distortion (black lines). (b) Valence and Conduction bands edges for the CuAlSe2 with (red lines) and without (black lines) distortion. The Valence Band Maximum and the Conduction Band Minimum are referred to the Fermi Level.

In Figure 3, we present the average of the electrostatic potential computed in planes parallel to the interface between the two semiconductors, for the CuGaS2/CuAlSe2 slab model, at a polar and non-polar surfaces. At the middle layer of each material, uniquely defined between maximum of EP, was further averaged and compared to the EP from bulk calculations to deduce the shift in the reference level. In all cases the potential electrostatic for the bulks change respect to the electrostatic potential of the interface. Particularly, we can observe that the EP for the bulk CuGaS 2 decreases in the energy when conform the CuGaS2/CuAlSe2 interface, meanwhile the bulk CuAlSe2 tends to increase the EP value. In the polar CuGaS2/CuAlSe2 interfaces, the average EP in the CuGaS2 sides bend upward, which is caused for some negative charges fixed at the interface. The charges negatives are probably attributed to Cu-S and Al-S bonds at the polar interface. For the non-polar interfaces, where each atomic plane parallel to the interface is stoichiometrically neutral, is expected avoiding any charge accumulation and dipole moment in the interface. Table 2 shows theoretical band offsets for the polar and non-polar CuGaS2/CuAlSe2 and CuGaS2/ZnSe interfaces. We have used a sign convention such that a positive value of the band offset for the discontinuity at the junction CuGaS2/CuAlSe2 corresponds to an upward step in going from CuGaS2 to CuAlSe2 as employed in Ref. [41]. From the calculated ∆𝐸𝑉𝐵 and calculated ∆𝐸𝐶𝐵 for both CuGaS2/CuAlSe2 and CuGaS2/ZnSe interfaces, we find a band alignment of type II. In this type of band alignment, the two bands are shifted in the same direction, leading to a band structure in which the lowest CBM occurs on one of the sides, the highest VBM on the other, with an energy separation between the two less than the lower of the two bulk band gaps [42].

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Figure 3. Representation of the electrostatic potential averaged over the 𝑥𝑦 plane plotted along the 𝑧 direction, for the CuGaS2/CuAlSe2 at a polar and non-polar interface. At the middle of the each side, we include the electrostatic potential calculated for the corresponding bulk materials forming the interface (red and blue lines).

According to Figure 3 and Table 2, the band alignment of the CuGaS 2/CuAlSe2 (1̅1̅2̅) polar surface agree with those for the non-polar surfaces to within 0.1 eV, which is consistent with experimental observation [33]. However, we find that the band alignment in the (001) surface orientation leads a dramatic decrease in the ∆𝐸𝐶𝐵 to 0.3 eV with those for the (1̅1̅2̅), (110) and (102) surfaces. This could be attributed to the surface atomic arrangements of the different surfaces and the distance between atomic planes in the unit cell, which could affect the surface chemistry. The (001) polar surfaces of CuGaS2 can be terminated by cationic layers that consist either of 50 % of Cu and 50 % of Ga atoms (see Figure 1), meanwhile the anionic layers consist of the 100 % of S atoms, so they can generate an interface dipole that can shift the band alignment. For the CuGaS 2/ZnSe polar interfaces, the ∆𝐸𝑉𝐵 was estimated to be 0.74-1.27 eV, meanwhile the ∆𝐸𝑉𝐵 of non-polar surfaces gave a value of 0.87-1.03 eV, these results are consistent with the empirical work of Chen et al. [38]. Table 2: Calculated valence ∆𝐸𝑉𝐵 and conduction ∆𝐸𝐶𝐵 band offsets (in eV) for the different interfaces referred to the valence and conduction bands of the CuGaS2.

(001) (1̅1̅2̅) (110) (102)

CuGaS2/CuAlSe2 ∆𝐸𝑉𝐵 ∆𝐸𝐶𝐵 0.03 0.32 0.18 0.79 0.21 0.86 0.16 0.62

CuGaS2/ZnSe ∆𝐸𝑉𝐵 ∆𝐸𝐶𝐵 -0.74 -0.15 -1.27 -0.67 -1.03 -0.34 -0.87 -0.15

For the CuGaS2:Cr/CuAlSe2 and CuGaS2:Cr/ZnSe heterojunctions, we consider the interface in the (110) plane, which is formed by an atomic layer having the stoichiometric Cu–S–Ga–S composition. In this case we use slabs which stack eight such monolayers. From this, the created supercell contains sixteen atomic layers for both the CuGaS2:Cr/CuAlSe2 and CuGaS2:Cr/ZnSe interfaces, as it is shown in Fig. 1(e) for the interface to CuAlSe2 case. Fig. 4 shows the PDOS (from the GGA calculation) for the interface and the first three sub-interface layers (one of them containing the transition metal).

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Figure 4. Projected density of states as a function of the distance for the CuGaS 2:Cr/CuAlSe2(110) interface.

We observe that the electronic properties of each material are maintained in the heterojunction. In the interface layers, the effect of the lattice mismatch is observed in the edge of the valence and conduction band, where the band-gap is almost equal and the bulk features converges very quickly as one moves away from the interface. For the CuGaS2:Cr interfacial layer, the hybridization from the Cu 3𝑑𝑧 2 states with the Se 4𝑝𝑦,𝑧 orbitals of the ZnSe slab, expands the valence band and the band gap decreases. The minimum of the conduction band in the CuGaS2:Cr interfacial layer, comes from the 4𝑝𝑥,𝑧 of the Gallium and the 4𝑠 orbital of the Selenium, and pushes down into the upper part of the band gap. The opposite effect is observed for the interfacial layer of CuAlSe2. However, the band alignment between two materials cannot be achieved from a direct comparison of the corresponding band edge son both sides of the interfaces [43]. The reason for that is due to: (i) the lack of a common reference energy between the energy levels of the materials which comprise the heterojunction, in this case, the average electrostatic potential, and (ii) the underestimation of the band-gaps, as this affects mainly the conduction band offset. Therefore, to calculate the band alignment between two materials, we follow the procedure introduced before. However, the conventional DFT approaches have deficiencies in describing the band gap due to the self-interaction. Besides this approach is totally inadequate to study the electronic structure of materials where the band gap is influenced by the hybridization of the 𝑑 orbitals of a transition metal with 𝑝 orbitals of other atom [44]. So we have used a self-consistent GW procedure which has been extremely successful in describing quasi-particles energies for transition metal compounds, where perturbative GW fails [45, 46]. Under the scheme of the scGW calculations, the band gaps of pure CuGaS2, CuAlSe2 and ZnSe were of 2.24 eV, 2.41 eV and2.69 eV respectively. These results show that the standard DFT approach underestimate the band gap (0.65 eV for CuGaS2, 0.87 eV for CuAlSe2 and 1.18 eV for ZnSe), and the self-consistent quasi-particle GW calculations agrees pretty well with the experimental values (2.43 eV [47], 2.49 eV [36] and 2.82 eV [37] for CuGaS2, CuAlSe2 and ZnSe respectively). Fig. 5 shows the densities of states of CuGaS2:Cr calculated within GGA and the scGW approach. In both cases, the IB is located in the band gap formed by spin up states from Cr dopant and is partially occupied with the Fermi level crossing it. At the 25% dopant concentration, the IB is located at the energy region from −0.35 eV to 0.73 eV, which is very wide, generating a slight overlap with the valence band, because of the weak hybridization of the 𝑡2 states of the Cr with the 3𝑝 states

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of the neighbouring S atoms. The IB is composed of three states and according to the tetrahedral crystal field, is mainly contributed from the 𝑡2 states, since the Cr 3𝑑 states are split into the lower energy e (𝑑𝑧 2 , 𝑑𝑥 2 −𝑦 2 states, which will contain two of the three electrons in the 3𝑑 band of the (formally) Cr(3+) ion, and higher energy 𝑡2 states (𝑑𝑥𝑦 , 𝑑𝑦𝑧 , 𝑑𝑧𝑥 ) which will contain the third electron. This splitting shows how in the CuGaS2:Cr material the main band gap is divided into two sub-bands, which is an important feature to consider when carrying out the band alignment with CuAlSe2 and ZnSe. For the spin down states, it can be seen that chromium does not changes the host electronic structure significantly, however, under the scGW scheme, the 𝑒 and 𝑡2 states break the hybridization with the conduction band and are localized at lower energies.

Figure 5. Spin polarized total DOS curves obtained within GGA and scGW for theCuGaS 2:Cr. The dotted line indicates the Fermi level.

In order to have a better understanding of the position of the IB, we study at the GGA level the effect of the dopant concentration at 25%, 12.5%, 6.25%, 4.16% and 3.125%. The use of large supercells shows only a slightly change in the position of the IB. Besides, as the size of the supercell is increased, the width of the intermediate band decreases. In Table 3, we present the energetic difference between the Fermi level and the valence band maximum at different concentrations. It is shown that this difference is similar for different concentrations. Therefore, the use of a 16 atom supercell is reasonable, since scGW is an expensive technique and scales as 𝑛3 with the number of atoms in the unit cell, so up to date is unpractical for the study of large systems. These results suggest that the use of large supercells (less dopant concentration) isolates the IB from the valence band and the conduction band and will allow us the absorption of two photons (𝐸𝐼𝐵 – 𝐸𝑉𝐵 and 𝐸𝐶𝐵 – 𝐸𝐼𝐵 ) in addition to the photon absorbed in the host semiconductor band gap (𝐸𝐶𝐵 – 𝐸𝑉𝐵 ) without facilitating transfer of photogenerated carriers between the IB and the VB or CB via thermalization. Table 3. 𝐸𝐹 − 𝐸𝑉𝐵 (in eV) calculated at GGA level for different concentrations of Cr.

𝐸𝐹 − 𝐸𝑉𝐵 0.368 0.383 0.350 0.377 0.372

Concentration 25 % 12.5 % 6.25 % 4.166 % 3.125 %

𝐶𝑢𝐺𝑎𝑆

Therefore, for the CuGaS2:Cr/CuAlSe2 heterojunction, ∆𝐸𝑃 𝑆𝑙𝑎𝑏 =0.503 eV, and the 𝐸𝑃𝐵𝑢𝑙𝑘 2 𝐶𝑢𝐺𝑎𝑆 and 𝐸𝑉𝐵𝑀 2 are 0.786 eV and -0.0069 eV respectively. From these values the ∆𝐸𝑉𝐵 for the CuGaS2:Cr/CuAlSe2 interface has a value of -0.29 eV, where the valence band of the CuGaS2:Cr lying in energy below the corresponding one of the CuAlSe2. Results for the CuGaS2:Cr/ZnSe

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interface were also obtained in a similar way, nevertheless, the valence band offset gives ∆𝐸𝑉𝐵 equal to 0.92 eV, with CuGaS2:Cr valence band above the ZnSe valence band. Finally, from the correct description of the band gaps and the position of the IB in the CuGaS2:Cr in conjunction with the relative position of the valence bands for each interface, the resulting band alignments are shown in Fig. 6. From the figure, the CuGaS2:Cr/CuAlSe2 interface shows a type II (staggered) alignment, with both the valence and conduction band of CuGaS2:Cr lying in energy below the corresponding ones of the CuAlSe2, ∆𝐸𝐶𝐵 = 0.66 eV. This facilitates that electrons and holes to be locate on different sides of the interface, thus avoiding direct recombination. The CuGaS2:Cr/ZnSe interface also exhibits a staggered band lineup, where the ∆𝐸𝐶𝐵 of CuGaS2:Cr is 0.27 eV higher than ZnSe. Therefore a ZnSe/CuGaS2:Cr/CuAlSe2 setup would be ideal to efficiently separate electrons and holes generated with the help of the intermediate band. Is important to note that the position of the Fermi level in these alignments are not overlapping the valence or conduction band in the heterojunction.

Figure 6. Band alignment for the CuGaS2:Cr/CuAlSe2 and CuGaS2:Cr/ZnSe heterojunctions.

As has been established before, doping this semiconductor could modify the electronic structure of the semiconductor giving rise to an intermediate band [56]. This band appears located in the band gap of the host semiconductor. As we pointed out in the introduction, semiconductors with an intermediate band are very promise materials in solar cells technology due to the ability of increase the efficiency of solar cells. There have been published many results of chalcopyrite semiconductors doped with metallic elements with the purpose to obtain an intermediate band [6-8, 49-51]. Unfortunately, first principles calculations are very expensive from the computational point of view, because of the large number of atoms in the unitary cell needed to manage realistic levels of doping. Due to this tough task, first-principles calculations are carried out considering large fractions of doping only. Even in this case, first-principles studies are mainly concentrated in calculate the band gap, or the density of states. On the other hand, semi-empirical TB approach allow us to consider levels of doping as small as a few percent. The only prize to pay for this approach is the cumbersome work in writing the matrix, and the time needed to diagonalize the TB matrix, which in the worse case, cannot be compared with first-principles calculations. If we doped the CuGaS2 chalcopyrite with Cr atoms, the size of the TB matrix increases due to the presence of the metallic atom in the unitary cell. For a 25% of Cr concentration the size of the TB matrix goes from 42×42 to 178×178. For this percentage of Cr atoms, the unitary cell contains 16 atoms: 4 Cu atoms (9 atomic orbitals per atom), 3 and 8 atoms of Ga and S, respectively (4 atomic orbitals per atom), and 1 Cr atom with a 𝑠𝑝3 𝑑5 orbital basis. In addition to the above, for this doped chalcopyrite, spin-orbit effect must be taken into account to obtain a correct description of the band structure. This is because, for the doped chalcopyrites, previous first-principles calculations have demonstrated that the spin with a very definite component contributes to the density of states of the intermediate band [7].

69


Figure 7: Local density of states as a function of energy at k = (0; 0; 0) for the CuGaS2:Cr. The upper (lower) part corresponds to the component of the LDOS with spin up (down), and the vertical dotted line corresponds to the Fermi level.

We have adjusted the ”on site” parameters for the Cr atom. The parameters that take into account the spin-orbit effect λa have been adjusted to reproduce first-principles calculations recently reported [61]. The values of these parameters used in the present work, for the 𝑑 orbitals of the Cu and Cr atoms were 0.012 and 0.2 respectively; meanwhile for the 𝑝 orbitals on the Ga and S atoms were, 0.007 and 0.004 respectively. In Figure 7 we show the local density of states (LDOS) for the CuGaS2:Cr chalcopyrite as a function of energy at k=(0,0,0). We can observe the appearance of the intermediate band located slightly down the center of the band gap. The upper part of Figure 7 corresponds to the component of the LDOS with spin up, whereas the low part corresponds to the component of the LDOS with spin down. The general characteristic of the LDOS corresponds very well with those obtained from first principles [48]. We can observe that there is a splitting of degeneration locating the component of spin up of the intermediate band within the band gap. The component of spin down appears located at higher energies as it can be clearly observed. This effect is attributed to the crystal field effect due to the tetrahedral environment on the orbitals 𝑑 of the Cr atoms. In Figure 8 we show the band structure for the CuGaS2:Cr chalcopyrite doped with 25 % of Cr atoms, obtained using the TB parameters adjusted to reproduce the DOS of reference [48]. For the doped CuGaS2 chalcopyrite, the symmetry of the unitary cell is tetragonal. The Fig. 8 shows the band structure along the principal directions of the Brillouin zone. We clearly observe the intermediate band located nearly in the center of the band gap. Both, the states of the intermediate band, and those at the bottom of the conduction band, correspond to the Cr atom. We observe that the Fermi level appears inside the intermediate band, guaranteeing that the band is partially full. The dispersion of this intermediate band is very small along the directions of symmetry displayed in the Figure. The presence of this intermediate band is very important to ensure the existence of two absorption channels compared with the absorption of only one photon present in conventional solar cells.

70


Figure 8: Electronic band structure for the CuGaS2:Cr along the principal directions of the Brillouin zone. The intermediate band appears at the center of the band gap.

Conclusions In summary, we have presented results of first-principles calculations which properly include strain and relaxation effects at the polar and non-polar interface between CuGaS2 and the CuAlSe2 and ZnSe semiconductors. Based on above analysis, the distortions of the lattice at the interface induced shifts in ∆𝐸𝑉𝐵 meanwhile the band gap variation shifts in ∆𝐸𝐶𝐵 , and with these in the band alignment. Our studies show that the band offsets depend weakly on the surface orientations. The structurally induced changes in the atomic character of various band states. The potential shift of each semiconductor side in the interface is insensitive to the detailed local structure or dipole of the interface, whether it is non-polar or polar. Rather it is determined by the intrinsic nature of the atoms at both sides. Additionally, we present the band alignment of CuAlSe2/CuGaS2:Cr and CuGaS2:Cr/ZnSe heterojunctions. The used scGW calculations reproduce accurately experimental band-gaps and hence correct band offsets can be obtained. The alignment, using as reference the average electrostatic potential, predicts that CuGaS2:Cr/CuAlSe2 and CuGaS2:Cr/ZnSe interfaces are from type II and possess a staggered alignment. These are the appropriate conditions to match two interfaces into a heterojunctions with three semiconductors (CuAlSe2/CuGaS2:Cr/ZnSe) so that electrons and holes photo-generated in the CuGaS2:Cr absorber layer, can be extracted selectively as desired, at both sides of the device. It is expected, that these theoretical values of ∆𝐸𝑉𝐵 and ∆𝐸𝐶𝐵 will provide further understanding of the fundamental properties of CuGaS2:Cr/CuAlSe2 and CuGaS2:Cr/ZnSe heterojunctions, which will be very useful in the design, modelling and analysis of the optoelectronic devices. Finally, we have calculated the electronic properties for the doped CuGaS2:Cr chalcopyrite using the TB methodology. The electronic structure exhibits an intermediate band located inside the band gap, in accordance with previous first-principles calculations. Using this methodology is possible to calculate the dispersion relation for these kind of semiconductors along the whole Brillouin zone without the expensive computational resources required by first principles.

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Acknowledgments This work was partially supported by CONACyT under doctoral scholarship No. 271481 and by the Comunidad de Madrid project MADRID-PV (S2013/MAE/2780) and by the Ministerio de Economía y Competitividad through the project SEHTOP-QC (ENE2016-77798-C4-4-R). The authors thankfully acknowledge the computer resources, technical expertise and assistance provided by the Red Española de Supercomputación, the Centro de Supercomputación y Visualización de Madrid (CeSViMa) and the Laboratorio Nacional de Supercómputo del Sureste de México (LNS1). References [1] Solar Frontier Achieves World Record Thin-Film Solar Cell Efficiency: 22.3%, Solar Frontier K.K. Press Release (2015). [2] W. Shockley, H. J. Queisser, J. Appl. Phys. 32 (1961) 510. [3] J. E. Castellanos Águila, P. Palacios, J. C. Conesa, J. Arriaga, P. Wahnón, Comp. Mat. Sci. 121 (2016) 79. [4] R. Herberholz, V. Nadenau, U. Rhle, C. Köble, H. W. Schock, B. Dimmler, Sol. Energy Mater. Sol. Cells 49 (1997) 227. [5] Z. Wang, M. Zhao, X. Wang, Y. Xi, X. He, X. Liu, S. Yan Shishen, Phys. Chem. Chem. Phys. 14 (2012) 15693. [6] P. Palacios, K. Sánchez, J. C. Conesa, P. Wahnón, Phys. Status Solidi (a) 203 (2006) 1395. [7] P. Palacios, K. Sánchez, J. C. Conesa, J. J. Fernández, P. Wahnón, Thin Solid Films 515 (2007) 6280. [8] I. Aguilera, P. Palacios, P. Wahnón, Sol. Energy Sol. Cells 94 (2010) 1903. [9] C. Yang, M. Qin, Y. Wang, D. Wan, F. Huang, J. Lin, Scientific Reports 3 (2013) 1286. [10] L. Mohammed, M. A. Saeed, and A. Musa, Solar Energy 137 (2016) 621. [11] S. Andalibi, A. Rostami, G. Darvish, M. Kazem, M. Farshi, Opt. Quant. Electron 48 (2016) 258. [12] P. Chen, M. Qin, H. Chen, Ch. Yang, Y. Wang, F. Huang, Phys. Status Solidi (a) 210 (2013) 1098. [13] I. Aguilera, J. Vidal, P. Wahnón, L. Reining, S. Botti, Phys. Rev. B 84 (2011) 085145. [14] F. T. Vasko, A. V. Kuznetsov, Electronic States and Optical Transitions in Semiconductor Heterostructures, Springer, New York, (1999). [15] C. G. Van de Walle, R. M. Martin, Phys. Rev. B 35 (1987) 8154. [16] J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1986) 3865. [17] A. V. Krukau, O. A. Vydrov, A. F. Izmaylov, G. E. Scuseria, J. Chem. Phys. 125 (2006) 224106. [18] J. Heyd, G. Scuseria, M. Ernzerhof, J. Chem. Phys. 118 (2003) 8207. [19] J. Heyd, G. Scuseria, J. Chem. Phys. 120 (2004) 7274. [20] M. Shishkin, G. Kresse, Phys. Rev. B 75 (2007) 235102. [21] G. Kresse, J. Hafner, Phys. Rev. Lett. 99 (2007) 246403. [22] G. Kresse, J. Hafner, Phys. Rev. B 48 (1993) 13115. [23] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169. [24] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [25] P. E. Blöchl, Phys. Rev. B 50 (1994)17953. [26] J. E. Coulter, E. Manousakis, A. Gali, Phys. Rev. B 88 (2013) 041107. [27] J. C. Conesa, J. Phys. Chem. C 116 (2012) 18884. [28] G. Paasch, E. von Faber, Prog. Surf. Sci. 35 (1990) 19. [29] H. Xiao, W. A. Goddard III, The Journal of Chemical Physics 141 (2016) 094701. [30] H. J. Monkhorst, J. D. Pack, Phys. Rev. B 13 (1976) 5188. [31] J. C. Slater, G. F. Koster, Phys. Rev., 94, 1498 (1954). [32] W. A. Harrison, Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond, Dover Pubications (1989). [33] S. Chichibu, Y. Harada, M. Sugiyama, H. Nakanish, J. Phys. Chem. Solids 64 (2003) 1481. [34] Y. Zhang, X. Yuan, X. Sun, B. Shih, P. Zhang, W. Zhang, Phys. Rev. B 84 (2011) 075127. [35] Inorganic Crystal Structure Database (ICSD) [http://www._zkarlsruhe.de/icsd.html]. [36] Y. Shim, K. Hasegawa, K. Wakita, N. Mamedov, Thin Solid Films 517 (2008) 1442. [37] K. K. Ng, S. M. Sze, Physics of Semiconductor Devices, third ed., WILEY-VCH Verlag, Berlin GmbH (2007). [38] S. Chen, X. G. Gong, S. Wei, Phys. Rev. B 75 (2007) 205209. [39] Ph. Sainctavit, J. Petiau, A. M. Flank, J. Ringeissen, S. Lewonczuk, Physica B: Condensed Matter 158 (1989) 623. [40] J. E. Jaffe, A. Zunger, Phys. Rev. B 29 (1984) 1882. [41] C. G. Van de Walle, R. M. Martin, Phys. Rev. B 34 (1986) 5621. [42] H. Kroemer, Rev. Mod. Phys. 73 (2011) 783. [43] J. Junquera, M. Zimmer, P. Ordejón, P. Ghosez, Phys. Rev. B 67 (2003) 155327. [44] F. Bruneval, N. Vast, L. Reining, Phys. Rev. B 74 (2006) 045102. [45] S. V. Faleev, M. van Schilfgaarde, T. Kotani, Phys. Rev. Lett. 93 (2004) 126406. [46] M. van Schilfgaarde, T. Kotani, S. V. Faleev, Phys. Rev. Lett. 96 (2006) 226402.

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[47] B. Tell, J. L. Shay, H. M. Kasper, Phys. Rev. B 4 (1971) 2463. [48] J. E. Castellanos Águila, P. Palacios, J. C. Conesa, J. Arriaga, P. Wahnón, Appl. Surf. Sci., 424 (2017) 132. [49] A. Martí, E. Antolín, C. R. Stanley, C. D. Farmer, N. López, P. Díaz, E. Cánovas, P. G. Linares, A. Luque, Phys. Rev. Lett. 97 (2006) 247701. [50] A. Martí, M. D. Fuertes, A. Luque, J. Appl. Phys. 103 (2008) 073706. [51] R. Lucena, I. Aguilera, P. Palacios, P. Wahnón, J. C. Conesa, Chem. Mater. 20 (2008) 5125.

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74

XXXVI Biennial Meeting of the Real Sociedad Española de Física Simposium on Energy and Sustainability

Impact of V-implantation and Si-Vacancies on Crystal Structure and Optical Absorption Properties of Silicon Gregorio García,1,2 Marcos Casanova-Páez,3 Pablo Palacios,1,4 Eduardo Menéndez-Proupin3& Perla Wahnón1,2 1 Instituto

de Energía Solar, ETSI Telecomunicación, Universidad Politécnica de Madrid, 28040, Madrid, Spain. de Tecnología Fotónica y Bioingeniería, ETSI Telecomunicación, Universidad Politécnica de Madrid, 28040 Madrid,

2Departamento

Spain. 3Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile. 4Departamento de Física aplicada a las Ingenierías Aeronáutica y Naval. ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, 28040 Madrid, Spain. * corresponding author e-mail: [email protected]

Introduction Infrared photodetectors have applications in areas such as civil security and surveillance, environmental monitoring and telecommunications.1,2 Nowadays, commonly used infrared photodetection devices are based in mercury cadmium telluride3 or quantum-dot infrared photodetectors.4 However, while these materials allow high performances, they suffer some drawbacks, e.g.: high production costs and hardly integration in CMOS (chip complementary metaloxide semiconductor) technology. Silicon based devices guarantee the low cost and CMOS compatibility criteria. The band gap of silicon is 1.12 eV (1,100 nm), which hiders its applications in the infrared region.5 Hence, the extent of absorption properties of silicon up to the infrared region would be a promising approach to design new Si-based infrared photodetectors. It has been proven that the incorporation of a dopant element creates a partially filled level that allows sub-bandgap absorption.5,6,7,8,9 In this sense, photodiodes based on S-hyperdoped5,9 and Se-hyperdoped6,10,11 silicon yield improved spectral response up to the infrared region. In addition to an extended absorption up to the infrared, a good detectivity of extrinsic photoconductive response under infrared light is also need. Optoelectronic devices based on chalcogen hyperdoped silicon have only demonstrated IR photoresponse at low temperature.12 Chalcogen hyperdopoing mainly introduces filled (donor) states in the bandgap leading to a high carrier concentration at room-temperature,7,8 which overcomes the sub-bandgap photoconductivity signal at room temperature.12 Other commonly used dopants such as elements of groups III (B, Al and Ga) and V (As and Sb) are also limited to low temperatures because of dopant states are thermally ionized at room-temperature.3 The operation temperature may be also increased by doping with deep level impurities that require higher temperatures for thermal ionization.3 Silicon highly doped with transition elements such as Ti,13,14,15,16,17 V,18,19,20 Ni21 or Au22,23 have demonstrated strong sub-bandgap optical absorption as well as an increase in the high infrared absorption features at room temperature. Transition metals introduce deep levels in the bandgap of the host silicon,24 which allow an extended sub-bandgap response up to the infrared region due to the ability of studied dopant elements to introduce new level states in the gap of bulk Si. These dopant level states obtained at high concentration (high enough to avoid non-radiative recombination, commonly known as Mottlimit) results in the formation of a continuous energy band inside the bandgap of the host semiconductor known as intermediate band (IB). The so called intermediate band (IB) consists in a partially filled electronic band, placed into the host semiconductor gap and isolated from the valence band (VB) and the conduction band (CB). Intermediate band has to have a small dispersion and must not be a discrete level, whereas it has to be narrow enough to be well isolated from both VB and CB. Thereby, in addition to prompting electrons from VB to CB (VB-CB), transitions from the VB to IB (VB-IB) and from IB to CB (IB-CB) by absorbing photons with lower energy than the bandgap are also allowed. As a result, IB materials are attracting increasing interest towards

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Impact of V-implantation and Si-Vacancies on Crystal Structure and Optical Absorption Properties of Silicon

developing new photovoltaic materials with an improved efficiency.17,25,26 These same features also make intermediate band materials suitable for their use in infrared photodetectors.5,6,7,8,9,10,11,22 Previous works shown that materials based on doped-Si with transition metals such as Ti,13,14,15,16,17 Ni,21 Au22,23 or Co27 would lead to the formation of an new band within the gap of Si host semiconductor. Recently, an extended photoresponse up to the infrared region for vanadium hyperdoped silicon obtained by ion implantation has been reported.18,20 Our work explores the effect of introducing vanadium to explain the formation of an intermediate band with the desired properties by using first principle calculations. For that, structural, energetic and electronic properties of different V-implanted Si are studied in detail through quantum calculations. On the other hand, defects comprising vacancies and interstices are common in natural materials. Such defects can be innate or created during the material manufacturing process. In semiconductors the presence of (undesired) defects can modify their electrical and optical properties.28,29 Hence, models of V-implanted silicon compounds with Si vacancies were also studied. Theoretical Details Density Functional Theory (DFT) calculations were carried out using the generalized gradient approximation of Perdew, Burke and Ernzerhof (PBE)30 as implemented in the VASP code,31,32 along to projector augmented wave (PAW) potentials to represent the inert core electrons.33,34 Structural relaxations were done by conjugate gradients, with a convergence criteria that forces acting on all atoms do not exceed 0.01 eV Å-1, with a k-point mesh of 6×6×6 in the MonkhorstPack scheme.35 The unit cell of silicon model system was described as a supercell 2x2x2 of Si8 cubic unit cell (i.e., 64 atoms, labeled as Si64). Structures obtained from Si64 due to the addition of V atoms and / or Si vacancies were relaxed to study the effects of introducing V atoms and Si vacancies on structural and electronic properties. In this way, one V atom leads to a concentration [V] >>1020cm-3. Nevertheless, it is expected that the electronic structure for such dilution would elucidate whether an isolated IB can be obtained or if the energy levels from 3d electrons overlap with VB and/or CB of bulk Si, although that the bandwidth of the IB would be slightly increased.17,36 Optical properties were assessed by means of the absorption coefficient derived from the dielectric functions as implemented in VASP code. Thus, the imaginary part was obtained as the sum of independent transitions between Kohn-Sham states, without local field effects, while the real part was obtained from the imaginary part by the Kramers-Krönig relations. To get converged frequency-dependent dielectric properties, approximately 250 bands and an 8x8x8 sampling of the Brillouin zone were needed. The imaginary part of the dielectric function has been analyzed as a simple sum over independent transitions, which would allow separating it into the contributions from different transitions. Most of the calculations available in the literature for this kind of materials are based on DFT in the Kohn-Sham implementation with LDA (Local Density Approximation) or GGA (Generalized Gradient approximation) schemes for the exchange-correlation functional, due to their efficiency to deduce structural, electronic and other properties of a multitude of condensed matter systems. Unfortunately, commonly GGA and LDA functionals fail to correctly predict the bandgap.37 To overcome the “bandgap problem”, we employ many-body perturbation theory in GW approximation to calculate quasiparticle self-energy corrections for the electronic states, which yields results that are in very good agreement with experiments for a wide range of materials.38 The GW approach is based on a dynamic dielectric screening of the Coulomb potential, while the electronic self energy is approximated by a convolution in terms of the Green’s function G and the screened interaction W. In this paper, GW calculations were carried out to correct DFT eigenvalues without further interactions, i.e., G0W0 approach,38 wherein the calculations start from DFT eigenvalues and eigenfunctions to obtain many-body GW self energy. This method yields successfully agreement with experiment results for intermediate band materials, within the limits of the approach.39,40 Unfortunately, GW approximation is very time consuming. Thus, quasi particle energies were only

76


computed for Si64 and Vi-implanted compound without vacancies just at the Γ-point through the G0W0 approach. Results Main structural parameters. This work includes the study for bulk-Si (based on Si64 model) and V-implanted compounds in substitutional (VSi) and interstitial (Vi) cases. Figure 1 displays the applied procedure to built unit cells for V-implanted compounds here studied, while the most important parameters of Si64 and V-implanted compounds are collected in Table 1. The optimized structure for Bulk-Si (described as a supercell 2×2×2 of Si8 cubic unit cell with 64 atoms, Si64) yields a lattice parameter a = 5.465 Å, while the interatomic distances between Si atoms are 2.366 Å. The departure of the lattice cell a and Si-Si bond length (d[Si– Si]) from the experimental values (a = 5.431 Å, d[Si-Si] = 2.352 Å)41 turn out to be ≈ 0.6%. This slight overestimation of the lattice cell agrees with the expected behavior of GGA functionals.

Figure 1. Applied protocol to build different structures studied in this work. Table 1. Main structural parameters obtained for the optimized structures of selected compounds. Compound a (Å) d[V-Si] a (Å) d[Si-Si] b (Å) Si64 5.465 2.366 VSiSi63 5.471 2.431 2.368 ViSi64 5.465 2.440 / 2.746 2.367 ViSi63 5.437 2.483 / 2.769 2.356 a The shortest distance between V and Si atoms. b Distance between Si atoms located as far as possible of V atom.

The lattice parameter of VSiSi63 is increased up to a = 5.471 Å. The presence of V atom also causes an increment of 0.065 Å in the distance to the four nearest Si atoms (d[V-Si] = 2.431 Å), while the distance for the farthest pair of Si atoms from VSi is 2.368 Å. The four nearest Si atoms are tetrahedrally coordinated to the V atom. The increment of both lattice cell parameter and d[VSi] with regard to d[Si-Si] for Si64 could be related to the fact that V atom owns a larger atomic radii than Si one (1.740 Å and 1.110 Å for V and Si, respectively). Hence, V Si-implantation does not considerable modify the bulk-Si structure. The relaxed unit cell for Vi-Si compound (ViSi64) in absence of Si vacancies leads to a disposition wherein V atom is tetrahedrally coordinated to the four nearest neighbors Si atoms with a distance ≈ 2.440 Å, while the six second nearest atoms are placed of around 2.746 Å in an octahedrical configuration (see Figure 2). Note that the void of the tetrahedron defined by four Si atoms as well as the void of the octahedral defined by the six second nearest Si atoms are enough to allocate V atom without steric hindrance with Si atoms. Although, at short range (i.e. in the vicinity of vanadium atom) Si-Si bond-lengths are slightly modified respect to bulk Si (studied as Si64), this effect decreases with the distance respect to vanadium atom. Hence, at long range d[Si-Si] and lattice parameter tend to be similar than those obtained for bulk Si. As concerns as the effect of Vi-implantation on the main unit cell parameters of the host Si64, both lattice parameter a and d[Si-Si] (measured between two Si atoms located in the available farthest positions) keep constant or vaguely affected.

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Figure 2. Optimized geometry of V atom at interstitial position in ViSi64 compound. Green, blue and red colors stand for the V atom, the four nearest neighbors in tetrahedral coordination and the six second-nearest neighbors in octahedral configuration (red). Purple balls stand for Si atoms not coordinated with vanadium one.

As shown in Figure 1, Vi-implanted compounds with one Si vacancy were obtained i) from bulk Si (Si64) by the simultaneous addition and removal of one V and Si atom, respectively; ii) from optimized structure of ViSi64 removing one Si atom; iii) from optimized structure of bulk Si with defects (Si63) by adding one Vi atom. Among them, results here presented are referred to those optimized structure with the lowest energy. As concerns as the relative position between V implanted atom and Si vacancy, the minimal energy is obtained for the structure that allows the farthest position between V implanted atom and Si vacancy. For this compound, the lattice cell parameter a = 5.437 Å, while the first four closest Si atoms and the second nearest Si atoms are located at 2.483 Å and 2.769 Å from V atom. Instead of the relative disposition between V atom and Si vacancy, optimized structures of ViSi63 lead to the shortest distances between Si atoms (d[Si– Si] = 2.360 Å). Since similar effects are also found for Si63, this distortion would be mainly due to the Si vacancy. Based on unit cell parameter a, it can be also concluded that the presence of both V atom and Si vacancy leads to the largest cell distortion. Again two sets of Si atoms are also found around V as a function of the V-Si distance for Vi-implanted Si with one Si vacancy, the presence of a Si vacancy distorts the tetrahedrical and octahedrical coordination of V atom above described for Vi-implanted Si without vacancies. DFT calculated formation energies (Ef) V-implanted Si would provide some information about their. Formation energies (Ef) were defined as: 1

63

𝐸 𝑓 [𝑉𝑆𝑖 𝑆𝑖63 ] = 𝐸[𝑉𝑆𝑖 𝑆𝑖63 ] − ( 𝐸[𝑆𝑖64 ] + 𝐸[𝑉2 ]) = 3.06𝑒𝑉 64

𝐸 𝑓 [𝑉𝑖 𝑆𝑖64 ]

2

1

= 𝐸[𝑉𝑖 𝑆𝑖64 ] − (𝐸[𝑆𝑖64 ] + 𝐸[𝑉2 ]) = 0.97𝑒𝑉 63

2

(2)

1

𝐸 𝑓 [𝑉𝑖 𝑆𝑖63 ] = 𝐸[𝑉𝑖 𝑆𝑖63 ] − ( 𝐸[𝑆𝑖64 ] + 𝐸[𝑉2 ]) = 2.25𝑒𝑉 64

(1)

2

(3)

where E[Si64], E[VSiSi63], E[ViSi64], E[ViSi63] and E[V2] stand for the total energies of Si64, VSiimplanted Si (VSiSi63), Vi-implanted Si without vacancies (ViSi64), Vi-implanted Si with one vacancy (ViSi63) and BCC crystalline structure of Vanadium (made up of two atoms per formula). Although both implantation processes bring out high energy penalization per vanadium inserted, this energy change is considerable lower (2.09 eV) for Vi-implanted compound. In the case of Viimplanted compound with one silicon vacancy, Ef[ViSi63 ] = 2.25 eV (for the largest V-vacancy distance). Even in presence of one Si vacancy, interstitial implantation of V atom is more favorable than substitutional positioning. The formation energy of one silicon vacancy also implies a high formation energy value (Ef[Si63] = 3.55eV), which is the same order than the formation energies of V-implanted compounds in presence of Si vacancies. Thus, formation energies corresponding to VSiSi63 and ViSi63 compounds would be mainly due to the formation energy of one silicon vacancy. Thus, formation energies of VSi implanted compound (VSiSi63) and Vi-implanted silicon (ViSi63) with one vacancy were also obtained considering the presence of one Si vacancy before V implantation: 1

𝐸 𝑓 [𝑉𝑆𝑖 𝑆𝑖63 ] = 𝐸[𝑉𝑆𝑖 𝑆𝑖63 ] − (𝐸[𝑆𝑖63 ] + 𝐸[𝑉2 ]) = −0.49𝑒𝑉 𝐸 𝑓 [𝑉𝑖 𝑆𝑖63 ]

1

2

= 𝐸[𝑉𝑖 𝑆𝑖63 ] − (𝐸[𝑆𝑖63 ] + 𝐸[𝑉2 ]) − 1.30𝑒𝑉

(4) (5)

2

78


Again, V implantation at interstitial positions would be the most favorable process. Note that V i implantation in the remotest position respect to one Si vacancy entails formation energies much lower than zero, i.e., such process would be energetically more favored. Electronic Structure. For simplicity, discussions on the bulk-Si electronic structure were not deeply done herein as they have been extensively studied in the literature.17,42,43 Figures 2-4 plots density of states and band structure of studied V-implanted compounds. For VSi-implanted compound (VSiSi63, Figure 2) the presence of vanadium atom introduces new impurity bands, which overlaps with the valence band (VB) and conduction band (CB) of the host semiconductor. Due to the tetrahedrical coordination between V atom and the four nearest Si, the band structure shows that d levels for the transition metals split into a low energy eg doublet and a high energy t2g triplet. For spin up channel, this eg doublet is mainly filled (i.e., appears above the Fermi level), just slightly overlapping with the rest of the valence band (VB). Note that at X-point, the eg doublet is partially filled, with a bandwidth of 0.18 eV. The high energy t2g triplet is empty and is overlapping with the conduction band (CB) of bulk Si. At Γ-point, the splitting energy between low energy eg doublet and high energy t2g triplet is equal to 0.98 eV (1.28 eV after applying the rigid shift), which is the same than VB and CB difference between for VSiSi63 compound. This energy difference is somewhat slower than the value measured between VB and CB coming from host Si 64, 1.07 eV (1.37 eV). Regarding to spin down component, both eg doublet and t2g triplet are above the Fermi level. The latter is highly overlapped with empty levels of host Si64. At Γ-point, the bandgap of the host semiconductor becomes 1.61 eV (1.91 eV), while other important transitions between the CB and impurity bands of the V atoms should be also mentioned, whose energies are ranged between 0.70 eV (1.00 eV) and 1.29 eV (1.59 eV). Note that bandgap for bulk Si is considerably opened due to V impurity bands.

Figure 2. Left: Total Density of States of VSiSi63 (blue line) and projected Density of States of vanadium atom (green line); Right: Band structure for VSiSi63 compound along to main energy differences between VB-CB (black) measured at Γ point and bandwidth for IB (green). Results after applying a rigid shift are in brackets. Energy values are plotted with respect to the Fermi level (E Fermi) of VSiSi63, while solid / dotted lines stands for spin up / spin down channels.

For interstitial configuration in absence of Si vacancies (ViSi64, Figure 3), the effect of the octahedral crystal field originated by the six second nearest Si atoms splitting 3d levels into a low energy t2g triplet and a high-energy eg doublet. The most obvious change is the appearance of an additional intermediate band (IB) within the bandgap of the host semiconductor (due to the low energy t2g triplet for spin down) with a bandwidth equal to 0.24 eV, while the high-energy eg doublet appears above the Fermi level. At Γ-point, the low energy doublet yields a difference of 0.35 eV, while the largest energy difference, 1.74 eV (1.82 eV), is measured at X-point. Such transitions are labeled as CB-IB. The splitting energy between high energy eg doublet and low energy t2g triplet (IB-CB energy difference) is equal to 0.47eV (0.69 eV). The eg doublet appears at 0.82 eV (1.12 eV) over the CB of the host Si. The energy difference between the VB and the CB is 0.87 eV (1.17 eV), which is less important than that found for VSiSi63 compound. As concerns as spin up component, the triplet is located below the Fermi energy, while the doublet has larger energy than the Fermi level. The energy difference, measured at Γ-point, between the VB and CB is 0.98eV (1.28 eV), which is also lower than that found VSi-implanted compound. In addition, filled 79


t2g levels could allow new transitions energies up to empty eg levels and CB of bulk-Si, with energies equal to 0.45 eV (0.67 eV) and 0.53 eV (0.75 eV), respectively. For clarity, these transitions are labeled as IB-CB, which easily allow to identity that they start from donor levels due to V atom (i.e., t2g). Finally, since eg doublet is very close to the CB, new transitions (also labeled as VB-CB) with somewhat lower energy, 0.92 eV (1.32 eV), would be also possible.

Figure 3. Left:Total Density of States of ViSi64 (blue) and projected Density of States of vanadium atom (gren line); Right: Band structure for ViSi64 compound along to main energy differences between VB-CB (black), VB-IB (blue) and IB-CB (pink) measured at Γ point and bandwidth for IB (gren). Results after applying a rigid shift are in brackets. Energy values are plotted with respect to the Fermi level (EFermi) of ViSi64, while solid / dotted lines stands for spin up / spin down channels.

For ViSi63 (ViSi63, Figure 4), two sets of vanadium bands are located into the bandgap of the host. For spin up channel, there is a doublet located over the Fermi energy, which fulfills the requirements to play as IB, i.e., this is partially filled and isolated from both conduction and valence bands. This IB owns a bandwidth = 0.21 eV. Main energy differences related with this IB are those labeled as VB-IB and IB-CB, with values equal to 0.50eV (0.58eV) and 0.47 eV (0.69 eV), respectively, at Γ-point. There is also an empty band, located with an energy of 0.89 eV (1.19 eV) over the VB and 0.38 eV (0.60 eV) over the IB. Both levels forming the IB and this empty level would be related with the low energy t2g triplet originated by the (distorted) octahedrical coordination of V atom along to the vacancy, while high energy eg doublet is highly hybridized with unoccupied levels of bulk-Si. For spin down component, similar results are displayed in Figure 4. Nonetheless, the t2g triplet is empty, while the eg doublet appears again hybridized with the conduction bands coming from silicon. Hence, only energy differences taking into account VB as reference are displayed in Figure 4, which lie between 0.43 eV (0.73 eV) and 0.82 eV (1.12 eV). It should be noted that the bandgap for host Si is opened up to 0.97 eV (1.27 eV) / 0.82 eV (1.12 eV) for spin up / down component, which is similar than that obtained in absence of Si vacancy.

Figure 4. Left:Total Density of States of ViSi64 (blue) and projected Density of States of vanadium atom (gren line); Right: Band structure for ViSi64 compound along to main energy differences between VB-CB (black), VB-IB (blue) and IB-CB (pink) measured at Γ point and bandwidth for IB (gren). Results after applying a rigid shift are in brackets. Energy values are plotted with respect to the Fermi level (E Fermi) of ViSi64, while solid / dotted lines stands for spin up / spin down channels.

80


G0W0 results and bandgap correction. In this work quasiparticle energies through G0W0 approach have been applied to obtained accurate bandgap values. Due to the high computational requirements, quasiparticle energies were only calculated for Si64 and ViSi64 at Γ-point. We are aware that these G0W0 results should be treated with caution. In the case of Si64 (not shown), G0W0 yields a bandgap equal to 1.03 eV, which clearly improves DFT underestimation (theoretical bandgap = 0.63 eV). Thus, results for Si64 will undergo a bandgap correction based on a rigid shift of 0.40 eV applied over empty bands. Figure 5 plots computed energies for ViSi64 at Γ-point by using GGA (GGA (Γ-point)) and G0W0 (G0W0 (Γ-point)) approaches along to GGA energies obtained also at Γ-point with an 8×8×8 sampling of the Brillouin zone (GGA (8×8×8)) and obtained energies after applying the rigid shift (GGA (shifted)). As concerns as Vi-implanted compound, although the position of those bands in the vicinity of the Fermi level is affected by sampling of the Brillouin zone, similar energies are obtained for the key transitions, i.e., VB-CB, VB-IB and IB-CB. Based on G0W0 results, a rigid shift of 0.30 eV should be applied to CB-VB transitions. The energy difference between VB and partially filled is also opened (0.08 eV). Hence, a rigid shift of 0.08 eV and 0.22 eV will be applied to VB-IB and IB-CB transitions, respectively. These same rigid shifts will be also applied for the remaining V-implanted compounds.

Figure 5. Eigenvalues calculated for ViSi64 at Γ-point and those obtained after applying rigid shift.

Optical Properties. Optoelectronic properties of V-implanted compounds have been studied through the imaginary component of the dielectric function (see Figure 6-8). For Si64, our results agree with experimental absorption spectrum (except for those features related to indirect transitions and exciton effects).44 In general, the absorption features of V-implanted compounds would be enhanced in the energy range below 2.8 eV. For VSi-implanted Si (VSiSi63, Figure 6) yields a notable diminution of the dielectric constant below 2.0 eV. The broad peak centered at 2.0 eV is mainly due to CB-VB transitions. It can be seen that the contribution from VB-CB transitions start to appear at ≈ 1.0 eV with very low intensity, which increases as a function of the energy reaching the largest intensity at ≈ 2.0 eV. These results correspond to the bands structure shown in Figure 1S. Thus, at energies larger than 2.0 eV the main contributions come from CB-VB transitions of bulk Si, while CB-VB transitions located between 1.0 eV and 2.0 eV are due to the presence of new donor and acceptor levels from V atom, which overlaps with the valence and conduction bands, respectively, allowing a narrowing of the energy difference between the highest occupied band and the lowest unoccupied band. In fact, as seen in Figure 1S, the lowest energy difference is measured for spin down channel for the transitions between the conduction band and the valence band due to eg empty states of V atom, with energy of 1.0 eV.

81


Figure 6. Imaginary part of the dielectric function for VSiSi63 compound. Partial contributions due to VB-CB, IB-CB, VB-IB and IB-IB electronic transitions multiplied by the frequency as well as the results for Si 64 have been also included.

For compounds with interstitial implantation (Vi, Figures 7 and 8), the absorption enhancement is extended up to 0.25 eV and 0.18 eV for ViSi64 (Vi-implanted without vacancy) and ViSi63 (Vi-implanted with a Si vacancy), respectively. These peaks are due to IB-IB transitions. For Vi-implanted compound in absence of silicon vacancies, the dielectric function gradually decreases between 2.8 eV and 0.25 eV. VB-CB contributions gradually increase their intensity up to 2.8 eV, from where the largest contribution is due to VB-CB of the host. Note that VB-CB transitions start to appear at 1.10 eV, which is related to energy differences of ≈ 1.15 eV shown in Figure 2 for spin down component, measured between the VB and the CB as well as between the VB and empty eg states of V atom. Contributions from IB-CB transitions for spin up become visible at ≈ 0.65 eV (in agreement with those energy differences labeled as IB-CB corresponding to energy differences between t2g and eg states in Figure 2 for spin up). This contribution yields two main peaks. The first one located at 0.75 eV is assigned to IB-CB transitions due to the energy difference between filled t2g states of V atom and CB of bulk-Si). The broad peak lying between 1.40 eV and 2.50 eV is due to electronic transition between occupied t2g donor levels of V atom and high energy empty bands. The peaks appearing at ≈ 0.70eV, 1.10eV and 1.80 eV are assigned to IB-CB transitions for spin down. The former can be related to the energy difference of 0.69 eV measured between the intermediate band (due to partially filled t2g triplet) and high energy (empty) eg doublet in Figure 2for spin down, while the remaining two peaks are due to electronic transitions between partially filed t2g levels of V atom and high energy empty bands.

Figure 7. Imaginary part of the dielectric function for ViSi64 compound. Partial contributions due to VB-CB, IBCB, VB-IB and IB-IB electronic transitions multiplied by the frequency as well as the results for Si 64 have been also included.

82


In presence of both Vi-implanted and Si vacancy (ViSi63, see Figure 8), the main enhancement of the absorption coefficient is due to two transitions involving contributions across the IB. As said, the main difference with the absorption features of Vi-implanted compound in absence of a Si vacancy is the presence of differentiated peaks at 0.20 eV, 0.80 eV and 1.80 eV, wherein the first one is due to IB-IB transitions. It should be noted that ViSi63 yields IB-IB transitions with the largest dielectric constant. The peak at 1.20 eV is associated with vanadium-assisted VB-CB electronic transitions, which yields a very similar profile for both spin up and spin down components. VB-CB transitions emerge at ≈ 1.10 eV, in concordance with energy differences measured in Figure 3 between VB and CB or empty states or V atoms. The peak at 0.80 eV should be described as the sum of two contributions at roughly 0.84 eV and 0.67 eV due to IB-CB and VBIB transitions, respectively. Results here exposed for Vi-implanted compounds are in agreement with results of GarcíaHemme et al., who found an important increase of the photoresponse with respect to a Si reference, which extends into the infrared regions, at room temperature. 20 The peak estimated at 0.80 eV could be associated with the photoresponse measured at ≈ 0.60 eV. Though, this value would be slightly overestimated respect to experimental measurements. IB-IB transitions cannot be measured in photoconductance experiments because they are internal transitions that do not generate free electron-hole pairs. Thus, the abrupt photoresponse edge at ≈ 0.25 eV experimentally measured could be due to indirect IB-CB transitions that provide the lowest IB-CB energy differences. These observations support our main conclusion, that the infrared photoresponse is directly related with optical transitions including the IB.

Figure 8. Imaginary part of the dielectric function for ViSi63 compound. Partial contributions due to VB-CB, IB-CB, VB-IB and IB-IB electronic transitions multiplied by the frequency as well as the results for Si 64 have been also included. The inset shows experimental data extracted from reference 20.

Conclusions This works reports a detailed first principle study based on Density Functional Theory simulations on V-implanted Si compounds. The full relaxation of atomic structures yield high formation energy values for all implantation process, being Vi in absence of Si vacancy the most favorable one. Regarding to electronic structures of V-implanted compounds, for Vi-implanted compound in absence of Si vacancies (ViSi64), the octahedral crystal field due the six second nearest Si atoms leads to splitting 3d levels into low energy t2g triplet and a high-energy eg doublet, where the low energy t2g triplet for spin down channel would fulfill the requirements to be defined as an intermediate band (IB). Vi-implanted in presence of a Si vacancy also displays an IB due to t2g 83


levels for spin up channel. Nonetheless, the Si vacancy leads to only two t2g level are occupied, while the other one is empty and highly in energy. As concerns as the optical absorption features, our results point out that there is a considerable improvement in the absorption coefficient below 2.8 eV. In addition, Vi-implanted compounds also exhibit adequate absorption features below 1.0 eV due to different transitions across the intermediate band. Note that the formation of this intermediate band with the adequate properties is only possible for interstitial vanadium in presence of silicon vacancies. Our first principles calculations allow to explain experimental measured photoresponse in V-implanted compounds, which is due to new sub-bandgap transitions across the intermediate band coming from V-implantation. Acknowledgments This work was partially supported by the Comunidad de Madrid project MADRID-PV (S2013/MAE/2780) and by the Ministerio de Economía y Competitividad through the project SEHTOP-QC (ENE2016-77798-C4-4-R). The author acknowledges the computer resources and technical assistance provided by the Centro de Supercomputación and Visualización de Madrid (CeSViMa). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]

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Green and Circular Economy: A Case Study in Extremadura (Spain). F. Cuadros Blázquez1, C. Sánchez Sánchez1,*, A. González González2, F. Cuadros Salcedo2 1Departamento 2Metanogenia

de Física Aplicada. Universidad de Extremadura. Avda. de la Física s/n. 06006. Badajoz. Spain. S.L. Campus Universitario. Avda. de la Innovación s/n. 06006. Badajoz. Spain.

* [email protected]

1.

INTRODUCCIÓN

En la UE, la industria alimentaria es la principal actividad de la industria manufacturera, representando el 14.6% de las ventas y un valor superior a los 1 244 000 millones de euros, con un incremento del 17.1% respecto al año anterior [1a]. Cuenta con unas 289 000 empresas que dan empleo a 4.22 millones de personas, representan el 49.6% del total de las ventas del sector alimentario y el 63.3% del conjunto de los puestos de trabajo que genera. En España, la Industria de productos de alimentación y bebidas es la primera rama industrial, según la última Encuesta Industrial de Empresas del INE (Instituto Nacional de Estadística), a 31 de diciembre de 2014, representando el 20.5% de las ventas netas de producto, el 18.3% de las personas ocupadas, el 17.8% de las inversiones en activos materiales y el 15.5% del valor añadido. El sector de mayor tamaño económico dentro de la industria agroalimentaria es el cárnico, con un total de ventas de 20 079 millones de euros (21.5%) en 2014. Le siguen las grasas y aceites, y los productos de alimentación animal (9.4%) e Industrias Lácteas con un 9.2 % [1a]. Dentro de la industria agroalimentaria en Extremadura destacan los mataderos de cerdo, vacuno y aves. Estas instalaciones generan gran cantidad de residuos líquidos (aguas residuales, sangre, fangos, etc.) y sólidos (huesos, entrañas, patas, cabezas, piel, contenido de panzas, etc.), y son muy contaminantes. Tienen la ventaja de que en su mayoría son biodegradables, si se aplican las técnicas adecuadas para su eliminación. Desgraciadamente, estos desechos no son utilizados por las empresas y a menudo son enviados a vertederos [2], y lo que es peor, en algunos casos son vertidos directamente al ambiente. Algunas empresas generadoras destinan estos residuos para la producción de compost, pero, en el caso de residuos avícolas, éstos poseen un alto contenido en nitrógeno que se une orgánicamente al compost, teniendo así un impacto negativo en el medio ambiente. Por otra parte, Extremadura es una región que está considerada como una reserva natural de Europa. Su actividad económica principal está basada en tres sectores fundamentales: el agroindustrial, el cultural y el turismo ecológico. El Gobierno Regional ha implementado políticas con el fin de conservar su patrimonio natural y proteger su medio ambiente [3]. En este contexto se establece la Red Natura 2000, que es una red de lugares de alto valor ecológico que constituye el principal instrumento para desarrollar las políticas de la UE orientadas a garantizar la conservación de la biodiversidad, prestando especial atención a los hábitats y a las especies de flora y fauna más amenazadas. Hay, pues, dos sectores importantes de la economía extremeña “enfrentados” entre sí, uno, el de la industria cárnica (en particular, la producción de carne de ave para consumo humano), y otro, el de preservar el medio ambiente, haciendo cumplir la normativa de la Red Natura 2000. Creemos que la Digestión Anaerobia (DA) es una buena alternativa para resolver este problema. El emblema “Una Europa que utilice eficazmente los recursos” es una de las principales estrategias de Europa 2020 para generar un crecimiento inteligente, sostenible e integrador. Esta iniciativa emblemática pretende crear un marco político destinado a apoyar el cambio a una economía eficiente en el uso de los recursos y de baja emisión de carbono que nos ayude a: -Mejorar los resultados económicos al tiempo que se reduce el uso de los recursos; -Identificar y crear nuevas oportunidades de crecimiento económico e impulsar la innovación y la competitividad de la UE; -Garantizar la seguridad del suministro de recursos esenciales;

87

Green and Circular Economy: A Case Study in Extremadura (Spain).

-Luchar contra el cambio climático y limitar los impactos medioambientales del uso de los recursos. La mencionada iniciativa ofrece un marco de medidas a largo plazo y, de manera coherente, otras a medio plazo entre las cuales ya está identificada una estrategia destinada a convertir a la UE en una «economía circular (EC)» basada en una sociedad del reciclado, a fin de reducir la producción de residuos y utilizarlos como recursos. La Economía Circular se describe como “una economía industrial que es restaurativa o regenerativa por intención y diseño” [4]. En este enfoque desaparece el concepto de residuos, ya que los componentes de los mismos vuelven a formar parte de los ciclos naturales o industriales con un consumo mínimo de energía. Los componentes de los residuos de origen orgánico serán biodegradados, mientras que los componentes de origen tecnológico o industrial serán reutilizados de manera sencilla y con bajo coste energético. Se trata de cerrar el ciclo de vida de los productos; o sea, de pasar de un modelo de economía lineal (producir, usar y tirar) a otro circular, tal como ocurre en la naturaleza. El actual modelo lineal basado en el incremento de la producción, consumición, and crecimiento económico parece que está llegando a su fin [5,6]. En este trabajo se aplica el concepto de economía circular a la descontaminación y valorización energética de los residuos de un matadero de aves ubicado en Extremadura , mediante la técnica de DA. No se entra a analizar en detalle el ciclo de vida completo de la producción de carne de ave, sino que nos centraremos en cuantificar la disminución de los consumos de energía fósil en la etapa de elaboración de los productos cárnicos; es decir, en la etapa en la que entran los animales vivos y salen convertidos en productos aptos para el consumo humano, ya que una de las principales características de la EC se centra en el uso de la energía. Por ello, se propone la construcción de una planta de DA (biometanización) en una industria avícola ubicada en la Región de Extremadura, con el fin de garantizar, por un lado, su autoconsumo de energía térmica mediante la combustión del biogás generado, y por otro, ofrecer una alternativa al del tratamiento tradicional (compostaje) de los residuos cárnicos avícolas (sólidos y líquidos). El análisis de sensibilidad económica dentro de una planta de biogás es de gran importancia ya que manifiesta el hecho de que los valores de las variables que se han utilizado para llevar a cabo la evaluación del proyecto pueden tener desviaciones con efectos de consideración en los resultados. La evaluación del proyecto será sensible a las variaciones de uno o más parámetros si, al incluir estas variaciones en el criterio de evaluación empleado, la decisión inicial cambia. El análisis de sensibilidad, a través de los diferentes modelos, revela el efecto que tienen las variaciones sobre la rentabilidad en los pronósticos de las variables relevantes. Es importante visualizar qué variables tienen mayor efecto en el resultado frente a distintos grados de error, en su estimación permite decidir acerca de la necesidad de realizar estudios más profundos de esas variables, para mejorar las estimaciones y reducir el grado de riesgo. Por último, en las últimas décadas los fenómenos meteorológicos extremos han aumentado y es que el efecto invernadero es un problema muy grave en el mundo de hoy. El problema se puede definir como un aumento de la temperatura en la atmósfera, causado principalmente por los gases como el vapor de agua, el dióxido de carbono, el metano, el óxido de nitrógeno... Estos no permiten que el calor de la Tierra se reirradie y salga al espacio, siendo atrapado por la atmósfera. El metano es considerado un gas de efecto invernadero relativamente potente que contribuye al Calentamiento Global del planeta, ya que tiene un potencial de calentamiento superior al del dióxido de carbono. En las últimas décadas, la concentración de metano en la atmósfera se ha incrementado de manera importante, hasta un 1% por año, siendo su principal origen las actividades humanas. Además se espera que a finales del siglo XXI el efecto de este gas supere al del dióxido de carbono [7]. En este sentido, la construcción de una planta de DA en la industria avícola ayudará a disminuir la emisión de metano, cuantificando el efecto ambiental positivo debido a dicha reducción.

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Los objetivos específicos que se plantean a través de este trabajo son: i) Mostrar el cambio de paradigma desde una economía lineal tradicional a otra circular, en el que el uso de la energía y la preservación del medio ambiente están interrelacionados y juegan un papel principal; ii) Formación de una conciencia social y política de la nueva economía; iii) Ayudar a la penetración del principio de EC en el sector agroindustrial de Extremadura, que genera gran cantidad de residuos biomásicos húmedos altamente contaminantes; iv) Servir de modelo prioritario en regiones con grandes extensiones de terreno en forma de reserva natural; v) Incentivar la I+D+i en este sector, así como su enseñanza y divulgación a todas las escalas; vi) Mostrar la viabilidad económica y medioambiental de la tecnología de DA; vii) Analizar la sensibilidad económica de la planta; viii) Realizar una estimación de las emisiones de dióxido de carbono al utilizar el metano generado como combustible. 2.

MATERIALES Y MÉTODOS

2.1

Experiencias de digestión anaerobia

Los ensayos de digestión anaerobia con residuos de matadero de aves se realizaron en un reactor anaerobio semicontinuo; es decir, diariamente se extrae del reactor un determinado volumen de lodo digerido y se introduce el mismo volumen de residuo alimento, con el objetivo de mantener constante el volumen del reactor [8]. La Figura 1 muestra una fotografía del dispositivo experimental en los que se desarrollaron las experiencias de digestión anaerobia en modo semicontinuo. El reactor semicontinuo está constituido por un tarro de vidrio de 2 litros de capacidad, unido a una tapadera móvil que presenta un orificio al cual se acopla una pieza que dispone de dos salidas. Una de ellas está unida a un tubo central que se sumerge en el medio de reacción, a través de esta se extrae el lodo digerido y se introduce el sustrato (residuo alimento) en el interior del reactor. La otra salida se utiliza para evacuar el biogás producido. Éste es conducido mediante tubos de silicona hasta una campana gasométrica construida con tubos de PVC. El medio de reacción se mantiene a 38 ºC sumergiendo el reactor en un baño de agua calentada mediante una resistencia eléctrica. El contenido del reactor se homogeneiza utilizando un agitador magnético y un diablillo (Fig. 1).

Figura 1: Dispositivo experimental utilizado durante Los ensayos de digestión anaerobia en modo semicontinuo.

2.2

Preparación del sustrato y puesta en marcha del proceso de digestión anaerobia

El sustrato a tratar está compuesto por sangre, aguas residuales (que llevan en suspensión algunos restos sólidos) y fangos, procedentes de un matadero de aves situado en el Norte de Extremadura, sin ningún tipo de pretratamiento. Para iniciar el proceso de biometanización se

89


utiliza un inóculo aclimatado al residuo a tratar, que proviene de ensayos previos realizados en el laboratorio. 2.3

Métodos Analíticos

Se tomaron muestras de sustrato para cuantificar los Sólidos Totales (ST), pH, Demanda Química de Oxígeno (DQO), según el método estándar [9a]. Por otra parte, se tomaron muestras del digestor anaerobio dos veces por semana para controlar los siguientes parámetros: DQO total (utilizando kits Nanocolor® Macherey-Nagel), Ácidos Grasos Volátiles (AGV), Alcalinidad, pH, Sólidos Volátiles en Suspensión (SVS) y Sólidos Volátiles Disueltos (SVD) [9a]. El procedimiento descrito ha sido seguido con éxito en varios trabajos publicados por nuestro Grupo de Investigación [10;11]. 2.4

Estimación del potencial energético

Las cantidades medias de residuos que se generan en la mencionada industria cárnica son: 2 340 m3/año de sangre y 156 000 m3/año de agua residual (aguas de lavado y fangos); o sea, un total de 158 340 m3/año. La Potencia térmica, Pt, generada por la combustión del biogás obtenido en la planta de biometanización que se pretende construir, viene dado por la siguiente expresión: Pt(kW) = ((Psustrato x PCH4 x CVCH4) / n) x η

(1)

Siendo, Psustrato, la cantidad total de sustrato (residuo) a tratar, que es igual a 158 340 m3/año, PCH4, la producción de metano obtenida en las experiencias (ensayos) de AD en el laboratorio, medida en Nm3 CH4 / m3 de sustrato, (N significa Condiciones Normales de presión y temperatura). CVCH4 = 10 kWh / Nm3 CH4 es el valor calorífico del metano, n = 8 000, el número de horas anuales de funcionamiento de la planta, equivalente a 333 días / año, y η = 0,85, el rendimiento térmico de la caldera donde se quemará el biogás. La energía térmica total, Et, que se obtendría al quemar el biogás generado durante un año sería, Et (kWh) = Psustrato x PCH4 x CVCH4 x η

(2)

Parte de esta energía se invierte en mantener el digestor a la temperatura óptima de reacción, que se estimó en Td = 38 ºC. La temperatura ambiente media anual de la región está en torno a Ta = 15 ºC. La energía consumida en este proceso sería: Econsumida (kWh) = Psustrato x Cp x (Td – Ta) x 1,60 (3) Siendo Cp el calor específico del sustrato, que al estar compuesto principalmente por agua, lo tomaremos como Cp = 1.163 kWh / m3K. El factor 1,60 se debe a que hemos considerado unas pérdidas caloríficas a través de la superficie, suelo y cubierta del digestor del 60%. Así pues, la energía disponible, Ed, para autoconsumo en el matadero será: Ed = Et - Econsumida 2.5

(4)

Dimensionamiento de la planta de DA

2.5.1 Dimensionamiento del tanque de mezcla y alimentación En el tanque de mezcla se lleva a cabo la homogenización del sustrato y su volumen deberá ser suficiente para tratar la cantidad de sustrato equivalente a 3 días. Se aumentará este volumen en un 25% por razones de seguridad en agitación y aireación. Vtanque (m3) = (Psustrato /333) x 3 x 1,25

90

(5)


2.5.2 Dimensionamiento del digestor anaerobio y de su aislamiento El volumen útil del digestor anaerobio debe ser tal que permita la biometanización de los residuos durante el Tiempo de Retención Hidráulico (TRH) con el que se han obtenido los mejores resultados en los ensayos de laboratorio. El volumen del reactor será entonces, Vreactor (m3) = (Psustrato / 333) x HRT x 1,25,

(6),

donde se ha añadido otro 25% de seguridad. Para calcular la superficie de aislante necesario para cubrir tanto las paredes como el fondo del digestor e incluso la parte superior, si el gasómetro es externo, hay que partir de las dimensiones del reactor. Como norma general los digestores anaerobios suelen ser más anchos que altos para favorecer la mezcla perfecta. Aislamiento de la pared (m2) = h x D x π,

(7),

donde, h (m) y D (m) son la altura y el diámetro del digestor, respectivamente. Aislamiento del fondo (m2) = π × r2,

(8)

donde, r (m) es el radio del digestor. 2.5.3 Dimensionamiento del tanque de almacenamiento del efluente digerido Por razones de seguridad, se diseña el tanque con un volumen suficiente para que pueda almacenar durante dos días el efluente generado en la planta de DA. Vtanque efluente digerido (m3)= 2 x (Psustrato / 333)

(9)

2.5.4 Dimensionamiento del separador sólido-líquido Posteriormente, el efluente digerido (digestato) se separa en dos fracciones: líquida y sólida. El separador se ha dimensionado con una capacidad para tratar el efluente generado de 1 día cada 8 horas, Vseparador = (Psustrato / 333) / 3

(10)

2.5.5. Dimensionamiento del gasómetro La planta de DA se ha diseñado para que el biogás producido sea quemado en una caldera y proporcionar el agua caliente necesaria para las operaciones que se desarrollan en el propio matadero. Puesto que no todo el biogás producido se consume instantáneamente, éste se debe almacenar en un gasómetro, que en nuestro caso, se ha diseñado para almacenar el 35% de la producción diaria de biogás. El volumen del gasómetro será entonces, Vgasometro = Pbiogas x 0,35,

(11),

siendo Pbiogas la producción de biogás, en Nm3biogás / día. 2.6 Análisis de viabilidad económica de la planta de DA 2.6.1 Costes de instalación Que incluyen los costes de construcción, costes de los materiales y equipos de la planta de DA, gastos administrativos (autorizaciones y licencia de obras), y otros costes, como son los correspondientes a los elementos de seguridad, análisis de viabilidad económica y asesoramiento industrial y los relativos a la puesta en marcha. 2.6.2 Inversión total

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Para evaluar la inversión económica total en la planta de DA, se ha tenido en cuenta el Decreto 169/2016, de 18 de octubre, del Gobierno Autónomo de Extremadura, por el que se establece una subvención máxima a este tipo de proyectos de 300 000 € [12]. Además, se considera que el promotor va a solicitar un préstamo bancario igual al 75% del coste total de la planta de DA, siendo la aportación propia del promotor del 25%. 2.6.3 Gastos anuales Costes anuales de operación y mantenimiento (recepción, manejo y control de los residuos, reparación y sustitución de equipos, gestión administrativa, mantenimiento preventivo de la planta, etc.), que asumiremos que son iguales al 1 % del coste total de la planta. Amortizaciones del préstamo bancario. Supondremos que el préstamo solicitado es a 15 años, con un interés medio del 2,5%. Se estima que la vida útil de la planta está entre 25-30 años. 2.6.4 Ingresos anuales Que provienen de los ahorros anuales en combustible fósil de la industria cárnica. Actualmente, esta industria consume gasóleo, con un precio medio en España, el día 21/03/2017, de 0,810 €/L[13]. 2.6.5 Parámetros económicos Para determinar el análisis de sensibilidad de una planta de DA se han calculado el Periodo de Retorno de la Inversión (PRI), Valor Actualizado Neto (VAN) y la Tasa Interna de Retorno (TIR) ya que gracias a ellos se permite conocer preliminarmente la rentabilidad de este tipo de proyecto. 2.6.5.1 Periodo de Retorno de la Inversión (PRI) Este indicador calcula el tiempo en que el periodo tarda en recuperar la inversión según la fórmula: 0 = −𝐼𝑜 + ∑𝑇𝑖=1 𝐹𝑖 (12), donde, Io, corresponde a la inversión inicial del proyecto, Fi, al flujo de efectivo en el período i y T al periodo de retorno de la inversión, donde la ecuación se cumple. 2.6.5.2 Valor actual neto (VAN) El VAN es la métrica principal para determinar si una inversión debe ser aceptada o rechazada. Este indicador corresponde a la suma de los flujos de efectivo del proyecto para un tiempo cero (actual). Para un proyecto en el que se están evaluando N periodos el VAN se calcula según: 𝐹

𝑖 𝑉𝐴𝑁 = −𝐼𝑜 + ∑𝑁 𝑖=0 (1+𝑟)𝑖

(13),

donde r representa la tasa de descuento del proyecto, que aumenta para sistemas de mayor riesgo y representa el valor del dinero en el tiempo. Un proyecto que retorne flujos de efectivo posee un VAN mayor a cero. 2.6.5.3 Tasa interna de retorno (TIR) Este indicador se define como la tasa de descuento a la que el proyecto posee VAN igual a cero. Luego la TIR se puede calcular igualando a cero la Ecuación (13): 𝐹

𝑖 0 = −𝐼0 + ∑𝑁 𝑖=0 (1+𝑇𝐼𝑅)𝑖

(14).

La TIR es la tasa de interés o rentabilidad que ofrece una inversión. Es decir, es el porcentaje de beneficio o pérdida que tendrá una inversión para las cantidades que no se han retirado del proyecto.

92


La TIR nos da una medida relativa de la rentabilidad, es decir, va a venir expresada en tanto por ciento. El principal problema radica en su cálculo, ya que el número de periodos dará el orden de la ecuación a resolver. El período de amortización se alcanza cuando una inversión ha tenido suficiente flujo efectivo neto positivo hasta el punto de equilibrio de la inversión. Un período de recuperación aceptable para esta inversión probablemente oscilará entre 1 y 15 años. Cuanto más rápidamente se alcance el período de recuperación, mejor será la inversión. 3.

RESULTADOS Y DISCUSIÓN

3.1. Ensayos de digestión anaerobia Se realizaron diversas experiencias de digestión anaerobia con los residuos generados por un matadero de aves para determinar las condiciones de operación que permitieran alcanzar las mayores producciones de metano y la mayor degradación de la carga contaminante del sustrato. El sustrato a tratar en este trabajo está compuesto por el 1.5% de sangre, el 86.2% de agua residual y el 12.3% de fango procedentes del precitado matadero. Con un tiempo de residencia hidráulico (TRH) de 13 días, lo que supone una carga orgánica de aproximadamente 1,68 kg DQO/m3 reactor y día, es posible generar 11.89 Nm3 de biogás por cada m3 de residuo tratado. Como la cantidad de residuos a tratar diariamente es de 475,5 m3 / día, se obtiene una producción de biogás de 5 653.7 Nm3 biogás / día. El porcentaje de metano del biogás obtenido es del 58.37%, y la producción neta de metano, PCH4 = 6.94 Nm3 CH4 / m3 de sustrato. La misma Tabla 1 muestra que la reducción de la DQO debido a la biodigestión de estos residuos es del 24.76 ± 21.01 %. Tabla 1: Resultados experimentales de la biometanización.

Parámetros

Sustrato 2

pH

7,63± 0,10

Ácidos Grasos Volátiles (g CH3COOH/L)

0,49± 5,21

Alcalinidad (g CaCO3/L)

3,68± 0,39

Sólidos Disueltos Volátiles (g/L)

1,50± 0,48

Sólidos en Suspensión Volátiles (g/L)

7,03± 2,31

DQO total (g O2/L)

17,29± 4,72

Reducción DQO (%)

24,76± 21,01

CH4 (%)

58,37± 14,10

CO2 (%)

19,77± 5,21

O2 (%)

4,10± 3,44

H2S (ppm) 3

122,67± 63,13 3

Nm biogás/m sustrato 3

11,89± 4,53

3

Nm metano/m sustrato

6,94 ± 2,64

3.2. Usos potenciales del efluente digerido (digestato) El efluente digerido, tras ser sometido a un proceso de centrifugación, permite recuperar un 70% de agua (fase líquida) y un 30% de fango (fase sólida). El Real Decreto 1620/2007 de 7 de diciembre establece el régimen jurídico de reutilización de aguas depuradas [14]. Así, teniendo en cuenta la caracterización físico-química del agua recuperada

93


tras el tratamiento anaerobio de los residuos de matadero, se puede afirmar que, después de someterla a un proceso de eliminación de sólidos en suspensión y a una desinfección, podría aplicarse a cualquier uso natural, industrial y agrícola, siempre que este agua no esté en contacto con productos destinados para el consumo humano sin ningún tipo de transformación industrial. Además, el fango recuperado del lodo digerido (fase sólida) puede ser utilizado como enmendante agrícola en cualquier tipo de terreno y sin pretratamiento previo, según lo dictado por el Real Decreto 1310/1990 de 29 de Octubre, que regula la utilización de los lodos de depuración en el sector agrario[15]. A pesar de que el compost es un material con buen mercado, en el estudio económico que se realizará posteriormente no se han tenido en cuenta los posibles ingresos obtenidos por su venta. 3.3. Presupuesto económico de la planta de biogás En la Tabla 2 se muestran las dimensiones de los elementos y equipos que constituyen la planta de DA que se ha diseñado para tratar un caudal anual de 158 340 m3 de residuos procedentes de un matadero de aves (475.5 m3 de residuos / día), con un TRH = 13 días, y con un caudal de producción de biogás igual a 235.6 Nm3 biogás / h. En la Tabla 3 se muestra el coste estimado de los equipos y de los estudios de ingeniería necesarios para la construcción de la proyectada planta de DA, así como el coste total de la misma, que alcanza la cifra de 1 154 941 € (IVA no incluido). En esta estimación de costes se han tenido en cuenta los siguientes supuestos: i) Se ha considerado un margen de seguridad en los cálculos de un 5%; ii) Se ha tenido en cuenta un TRH ligeramente superior al calculado; iii) Se han incluido los costes de ingeniería y desarrollo, de puesta en marcha y de post-tratamiento del digestato, que normalmente no se incluyen en el coste de la obra civil; iv) No se sustituye la caldera que actualmente tiene la industria avícola, alimentada por gasóleo, sino solo el quemador. Si restamos estos sobrecostes, la construcción de la planta de DA para tratar los residuos del matadero de aves bajo estudio sería de 1 013 244 €. Para este caudal de biogás, Bauer et al. [16] estiman que el costes de inversión específicos de una planta de DA está entre 3 000 y 4 600 € / Nm3 biogás / h. Según esta referencia la planta proyectada tendría un coste de entre 706 800 € y 1 083 760 €. Así pues, hay concordancia entre nuestras estimaciones y las de Bauer et al. acerca del coste de una planta de DA, cuyas características se han mencionado anteriormente. La tabla 4 lista los parámetros relativos a la viabilidad económica de la planta de DA. En ella podemos comprobar que PRI = 7 años, VAN = 2 894 685 € y TIR = 14%, lo cual es indicativo de que la planta proyectada es viable económicamente. Tabla 2: Dimensionado de la planta de digestión anaerobia para tratar los residuos generados por el matadero en estudio.

Componentes

Características

Pasteurizador de sangre

20 m3

Almacenamiento de lodos

1200 m3

Tanque de alimentación

1800 m3

Reactor anaerobio

8000 m3

Almacenamiento del efluente

1200 m3

Separador sólido-líquido

60 m3

Gasómetro

1800 m3

94


Tabla 3.- Coste estimado de los equipos y de las actuaciones a desarrollar para la construcción y puesta en marcha de la planta de DA.

Descripción

Total

1

Ingeniería y Desarrollo

23 000 €

2

Almacenamiento de sustrato

164 850 €

3

Digestor Primario

630 800 €

4

Sistema de bombeo del sustrato

30 135 €

5

Canalización y condicionamiento del biogás

34 597 €

6

Cambiar el quemador de la caldera

11 109 €

7

Almacenamiento de efluentes

122 600 €

8

Sistema de distribución de calor

13 375 €

9

Caja de control y automatización / instalación eléctrica

40 425 €

10

Construcción e Ingeniería

10 500 €

11

Puesta en marcha

24 150 €

12

Elementos de seguridad y salud

12 600 €

13

Separador de las fases sólida y líquida del efluente

36 800 €

Coste total de la planta de biogás (Sin IVA)

1 154 941 €

Tabla 4.- Viabilidad económica de la planta de DA.

PRODUCCIÓN COSTE TOTAL PLANTA

DE

LA

GASTOS ANUALES

INGRESOS ANUALES

Energía térmica producida (kWht/ año)

9 153 922

Potencia térmica anual (kWt)

1 144

Calor consumido por la planta (kWht / año)

6 817 487

Energía Disponible (kWht / año)

2 336 435

TOTAL (€)

1 154 941

Mantenimiento de la planta (€ / año)

11 078

Amortización (€ / año)

13 518

TOTAL (€ / año)

24 596

Ahorro en energía térmica (€ / año)

202 481

TOTAL (€ / año)

202 481

BENEFICIOS ANUALES (€)

177 885 PRI (años)

7

RATIOS

VAN (€)

2 894 685

ECONÓMICOS

TIR (%)

14

95


3.4. Análisis de sensibilidad económica El análisis de sensibilidad económica proporciona resultados flexibles que pueden usarse para ayudar a analizar los efectos producidos por el aumento o la disminución de alguna/s variable/s. En este caso, consideraremos como variable más influyente el precio del gasóleo. Para calcular la incertidumbre del precio del gasóleo se ha tenido en cuenta la variación que se puede producir, que se ha considerado entre 0,6 €/L gasóleo C y 1,2 €/L gasóleo C. Los resultados, mostrados en la Tabla 5, corresponden a los valores obtenidos tras 20 años de operación de la planta. Tabla 5: Análisis de sensibilidad económica de una planta de DA que trate los residuos de un matadero de aves debido a la variación en el precio del gasóleo C.

GASTOS (€) INGRESOS Precio gasóleo C (€/L gasoleo C)

(€)

TOTAL Mantenimiento

Préstamo

GASTOS (€)

BENEFICIOS (€) VAN (€)

PRI

TIR

(años)

(%)

1,2

286 094

11 078

0

11.078

275 016

4075028

5

21

1,15

274 173

11 078

0

11.078

263 096

3836616

5

20

1,1

262 253

11 078

0

11.078

251 175

3598205

6

19

1,05

250 332

11 078

0

11.078

239 254

3359793

6

18

1

238 412

11 078

0

11.078

227 334

3121381

6

17

0,95

226 491

11 078

0

11.078

215 413

2882970

6

16

0,9

214 571

11 078

0

11.078

203 493

2644558

7

15

0,85

202 650

11 078

0

11.078

191 572

2406146

7

14

0,8

190 729

11 078

0

11.078

179 651

2167734

8

13

0,75

178 809

11 078

0

11.078

167 731

1929323

8

11

0,7

166 888

11 078

0

11.078

155 810

1690911

9

10

0,65

154 968

11 078

0

11.078

143 890

1452499

10

9

0,6

143 047

11 078

0

11.078

131 969

1214088

11

8

96

23

14

21

13

19

12

17

11

15

10

13

9

11

8

9

7

7

6

5

PRI (Años)

TIR (%)


5 0,5 0,55 0,6 0,65 0,7 0,75 0,8 0,85 0,9 0,95 1 1,05 1,1 1,15 1,2 Precio gasóleo C (€/L gasóleo C)

Figura 2: Gráfico de sensibilidad obtenido tras representar, pasados 20 años, el TIR y PRI vs precio del gasóleo.

Por tanto, y gracias al análisis de sensibilidad podemos decir que la máxima rentabilidad de la planta de biometanización para el matadero de aves en estudio se obtendrá cuando el precio del gasóleo sea igual o superior a 0,75 €/L gasóleo C. El TIR 11 % y el periodo de recuperación PRI  8 años. Por debajo de estos valores no es aconsejable realizar una inversión económica ya que el inversor tendrá un mayor nivel de riesgo. En cambio, si se añade al sustrato en estudio una cantidad determinada de material poroso con el objetivo de aumentar la superficie de adhesión bacteriana, y, por tanto, aumentar la población microbiana en el medio de reacción, se espera obtener un aumento en la producción de biogás, consiguiendo de este modo maximizar los rendimientos energéticos de la co-digestión de esta mezcla de residuos (sustrato). Se ha realizado un ensayo introduciendo en el biodigestor 1 g /L de carbón vegetal previamente tratado, observando un incremento de la producción de metano del 27,82%. En este caso, como se muestra en la tabla 6, se mejora la viabilidad económica. Tabla 6: Análisis de sensibilidad obtenido tras la variación en el precio del gasóleo C con un incremento en la producción de metano del 27,82% obtenido tras añadir carbón vegetal como material poroso.

Precio gasoil C INGRESOS

GASTOS (€)

TOTAL

BENEFICIOS

(€/L gasoleo C)

(€)

Mantenimiento

GASTOS (€)

(€)

1,2

597 925

11 078

11 078

586 847

1,15

573 012

11 078

11 078

1,1

548 098

11 078

1,05

523 185

1

PRI

TIR

(años)

(%)

10 311 651

3

48

561 934

9 813 380

3

46

11 078

537 020

9 315 109

3

44

11 078

11 078

512 107

8 816 838

3

42

498 271

11 078

11 078

487 193

8 318 567

3

40

0,95

473 357

11 078

11 078

462 280

7 820 296

3

38

0,9

448 444

11 078

11 078

437 366

7 322 025

3

36

0,85

423 530

11 078

11 078

412 452

6 823 754

4

33

0,8

398 617

11 078

11 078

387 539

6 325 483

4

31

0,75

373 703

11 078

11 078

362 625

5 827 212

4

29

97

VAN (€)


0,7

348 790

11 078

11 078

337 712

5 328 941

4

27

0,65

323 876

11 078

11 078

312 798

4 830 670

5

25

0,6

298 963

11 078

11 078

287 885

4 332 399

5

23

6 48 5,5

43

TIR (%)

4,5

33 28

4

23

3,5

18

PRI (Años)

5

38

3 0,5 0,55 0,6 0,65 0,7 0,75 0,8 0,85 0,9 0,95 1 1,05 1,1 1,15 1,2 Precio gasóleo C (€/L gasóleo C)

Figura 3: Gráfico de sensibilidad obtenido tras representar pasados 20 años el TIR y PRI vs precio del gasóleo una vez añadido carbón vegetal como material poroso en el medio de digestión.

En este segundo caso, el análisis de sensibilidad permite determinar qué tan sensible es un aumento en la producción de biogás con respecto al precio del combustible fósil. Esta sensibilidad se determina gracias a la TIR o el VAN obtenido (Tabla 6). Como puede observarse en la Fig. 3, se sigue obteniendo una rentabilidad positiva de la planta en estudio cuando el precio del combustible fósil es igual o superior a 0,75 €/L gasóleo C. Sin embargo, los parámetros económicos son mucho más favorables en este segundo caso, ya que el PRI disminuye a la mitad con respecto al primer caso (Fig. 2), por lo que los beneficios obtenidos, al cabo de 20 años de operación de la planta, serán mayores que en el caso anterior (Tabla 5). Esto también lo confirma el valor del TIR que será igual o superior al 29%, el doble del obtenido sin añadir el carbón vegetal como material poroso. 3.5. Estimación de la reducción de las emisiones de dióxido de carbono al utilizar el metano generado como combustible Dada la naturaleza orgánica de los residuos de matadero de aves (sangre, fangos, huesos, entrañas, patas, cabezas, piel, estómagos, intestinos, etc.), su depósito en vertedero y posterior descomposición natural conllevaría la emisión de gases de efecto invernadero, principalmente dióxido de carbono y metano. Si admitimos que las proporciones de CH4 y de CO2 obtenidas en la DA de este sustrato son las mismas que se producirían a partir de su degradación natural (teniendo en cuenta que la duración del proceso es de varios años para la descomposición natural, mientras que en la DA es de varios días), y despreciando el efecto de los demás gases traza que se obtienen en la DA, es posible cuantificar el efecto medioambiental positivo, debido a la reducción de gases de efecto invernadero, que aportaría la construcción de una planta de este tipo [17], [18]. Como se puede deducir de la Tabla 1, la DA de 158 340 m3 de sustrato /año generaría 1 098 879 Nm3 de CH4 /año y 525 689 Nm3 de CO2 /año. Si tenemos en cuenta las densidades normales del CH4 (0.680 kg /m3 ) y del CO2 (1.870 kg /m3 ) y las masas moleculares del CH4 (16 kg /kmol) y 98


del CO2 (44 kg/kmol), es posible obtener las toneladas totales de ambas sustancias así como el número de moles totales de las mismas que se obtienen en dicha DA. El resultado es: 747,24 t de CH4 (correspondiente a 46 577 kmoles de CH4) y 967,27 t de CO2 (correspondientes a 21 978 kmoles de CO2). Esas mismas cantidades se habrían liberado a la atmósfera si la degradación se realizase de forma natural. Como se informó en el IPCC (2014), el CH4 puede considerarse aproximadamente 28 veces más efectivo en producir el efecto invernadero que el CO2, de modo que si se tiene en cuenta esta equivalencia relativa entre estos dos gases de efecto invernadero, si sumamos las dos contribuciones obtendríamos un total de 21 890 t equivalentes de CO2 las que serían emitidas en el proceso de descomposición natural de este sustrato (residuo). Si quemamos este biogás en una caldera, tal como se propone en el presente trabajo, la combustión del contenido de metano daría: CH4 + 2 O2 CO2 + 2 H2O + 9.8 kWh /m3 de CH4

(15)

Por supuesto, el contenido (%) de CO2 del biogás no se tiene en cuenta en la reacción de combustión, ya que este gas es un producto de la misma sin valor calorífico alguno. Según la Ec. (15), en la combustión de 46 577 kmoles de CH4 se generan 46 577 kmoles de CO2; o sea, 2 050 t de CO2. Si a esta cantidad sumamos el contenido en CO2 del biogás (967,27 t de CO2), obtendríamos, en este caso, un total de 3 017 t equivalentes de CO2. Si comparamos ambos resultados; esto es, la emisión de las toneladas equivalentes de CO2 debido a la descomposición natural de los residuos de este matadero (21 890 t) y la correspondiente a la combustión del biogás generado en la DA de dichos residuos (3 017 t), se tendría que esta segunda opción reduciría las emisiones de CO2 equivalentes en un factor igual a 7,25 veces. 4.

CONCLUSIONES

Se ha llevado a cabo un extenso número de ensayos de DA, a escala laboratorio, que nos han permitido determinar el TRH óptimo del tratamiento de los residuos de una industria cárnica ubicada en la Comunidad Autónoma de Extremadura. Teniendo en cuenta los resultados obtenidos en el presente trabajo, se pueden extraer las siguientes conclusiones: 1.- El TRH óptimo para el tratamiento anaerobio (biodigestión) de los 158 340 m3 de residuos anuales procedentes de dicho matadero de aves (475,5 m3 de residuos / día) es de 13 días. 2.- Las producciones de biogás obtenidas han sido de 11,89 Nm3 biogás / m3 de residuo de matadero, siendo el porcentaje de metano igual al 58.37%. De modo que la producción neta de metano es de 6,94 Nm3 CH4 / m3 de sustrato. El caudal medio de biogás es de 235,6 Nm3 biogás / h. 3.- Estas producciones de biogás permiten disponer de una energía térmica útil anual de 2 336 435 kWh, lo que equivale a sustituir 233 643,5 L de gasóleo. Esta energía es suficiente para cubrir las necesidades anuales de calor de dicha industria, y genera un ahorro de unos 202 481 € / año, suponiendo un coste del gasóleo de 0,810 € / L y un aumento anual medio de su precio del 2 %. 4.- El coste total de la planta se eleva a 1 154 941 € (IVA no incluido). A pesar de este alto coste, el análisis económico realizado muestra que la construcción de una planta de DA para la biodegradación de estos residuos es rentable económicamente. Los parámetros económicos del proyecto así lo indican: PRI = 7 años, VAN = 2 894 685 € y TIR = 14%. 5.- El análisis de sensibilidad económica respecto al precio del gasóleo indica que por debajo de 0,75 €/L gasóleo C no es aconsejable realizar una inversión económica ya que los parámetros económicos que se obtienen no son tan favorables y el inversor tendrá un mayor nivel de riesgo. 6.- Si en la operación de la planta añadimos carbón vegetal como material poroso, el correspondiente análisis de sensibilidad económica respecto al precio del gasóleo sale aún más favorable, ya que aunque al igual que en el caso anterior, el precio del gasóleo tenga que ser igual o superior a 0,75 €/L gasóleo C, los parámetros de rentabilidad obtenidos son mucho más positivos, el 99


PRI se reduce a la mitad y el TIR aumenta el doble con respecto el apartado anterior ( siendo PRI4 años y TIR29 %). 7.- El proyecto que se presenta es también medioambientalmente viable. En efecto, la reducción de la DQO debido a la biodigestión de estos residuos es del 24.76 ± 21.01 %. La posterior separación de las fracciones líquida y sólida del digestato, permite reducir los valores de la DQO hasta límites compatibles con la legalidad medioambiental vigente. Por otra parte, los materiales de construcción empleados en esta planta de DA son fácilmente reutilizables o reciclables, demostrando que este caso de estudio es un buen ejemplo de EC. 8.- El biogás generado en la planta DA y quemado en una caldera aporta una reducción significativa de los gases de efecto invernadero estimada de 18 872,8 toneladas equivalentes de CO2, respecto a la que se liberaría si este sustrato se descompone de forma natural. Ello representa un factor de reducción de CO2 igual a 7,25 veces. 9.- Este tipo de proyectos son fundamentales para un desarrollo sostenible, tanto económico como medioambiental, y pueden servir de modelo para regiones con una fuerte influencia del sector agroindustial y con alto valor ecológico. AGRADECIMIENTOS Los autores agradecen a la Junta de Extremadura y a la Unión Europea (Fondos FEDER) por la ayuda económica para la realización de este trabajo, a través del Proyecto GR15146 REFERENCIAS [1] Ministerio de Agricultura y Pesca, Alimentación y Medio Ambiente, 2014-2015 http://www.mapama.gob.es/es/alimentacion/temas/industria-agroalimentaria/_informeanualindustriaalimentaria20142015_tcm7-421229.pdf [2] P F. Almeida, J A A.Salles, T M B. Farias, J C. Curvelo S, Aprovechamiento de patas de pollo como alternativa para disminuir residuos generados en los mataderos. Inf. tecnol. 23 (2012) 4. [3] Consejería de Agricultura; desarrollo Rural, Medio Ambiente y Energía, 2015. Decreto 110/2015, de 19 de mayo, por el que se regula la red ecológica europea Natura 2000 en Extremadura. DOE nº 105, pp. 19598-21816. http://doe.gobex.es/pdfs/doe/2015/1050o/15040122.pdf [4] P. Potocnik, Towards the Circular Economy - Economic and Business Rationale for an Accelerated Transition. Ellen MacArthur Foundation (2013). [5] P. Ghisellini, C. Cialani, S. Ulgiati, A review on circular economy: the expected transition to a balanced interplay of environmental and economic systems. J. Clean Prod. 114 (2016) 11–32. [6] Fundación Vida Sostenible http://www.vidasostenible.org/informes/metano-vacas-y-cambio-climatico/ [7] A.Fischer, S. Pascucci, Institutional incentives in circular economy transition: The case of material use in the Dutch textile industry. Journal of Cleaner Production. (2016). [8] A.González-González, F. Cuadros, A.Ruiz Celma, F, López Rodríguez. “Energy-environmental benefits and economic feasibility of anaerobic codigestion of Iberian pig slaughterhouse and tomato industry wastes in Extremadura (Spain)”. Bioresource Technology. 136 (2013) 109-116. [9] APHA, AWWA, WPCF. Métodos Normalizados para el Análisis de Aguas Potables y Residuales,Díaz de Santos S.A. Madrid, 1992. [10] A. González, F. Cuadros, Optimal and cost-effective industrial biomethanation of tobacco.Renew. Energy. 63 (2014) 280–285. [11] L. Moreno, A. González, F. Cuadros-Salcedo, F. Cuadros-Blazquez, Feasibility of a novel use for agroindustrial biogas. Journal of Cleaner Production. 144 (2017) 48-56.

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[12] Consejería de Economía e Infraestructuras, 2016. Decreto 169/2016, de 18 de octubre por el que se modifica el Decreto 115/2015, de 19 de mayo, por el que se establecen las bases reguladoras para el régimen de concesión de subvenciones para actuaciones en energías renovables en Extremadura y se aprueba la primera convocatoria. http://doe.gobex.es/pdfs/doe/2016/2040o/16040194.pdf

[13] Precio del Gasoil de Calefacción http://www.dieselogasolina.com/precio-del-gasoil-o-gasoleo-de-calefaccion.html [14] Real Decreto 1620/2007 de 7 de diciembre establece el régimen jurídico de reutilización de aguas depuradas https://www.boe.es/boe/dias/2007/12/08/pdfs/A50639-50661.pdf [15] Real Decreto 1310/1990, de 29 de octubre por el que se regula la utilización de los lodos de depuración en el sector agrario. http://www.boe.es/boe/dias/1990/11/01/pdfs/A32339-32340.pdf [16] F. Bauer, C. Hulteberg, T. Persson, D. Tamm, Biogas upgrading- Review of commercial Technologies.(2013) http://www.sgc.se/ckfinder/userfiles/files/SGC270.pdf [17] A. González-González, Viabilidad medioambiental, energética y económica de la biometanización de residuos provenientes de la industria agroalimentaria de Extremadura. (2014) Tesis Doctoral. Universidad de Extremadura. [18] A. González González, F. Cuadros, Continuous biomethanization of agrifood industry waste: A case study in Spain. Process Biochemistry. 48 (2013) 920-925.

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