Universidad Politécnica de Cartagena UPCT
Doctoral Thesis
Numerical solution of type problems in two and three dimensional anisotropic
geothermal domains with sources and sinks of fluid flow. Application to
Flegrea Area reservoir
Author:
Gennaro Sepede Supervisors:
Dr. Salvador A. Gómez-Lopera Dr. Claudio Alimonti
A thesis submitted in fulfillment of the requirements for the PhD degree of Doctor of Philosophy in Renewable Energies and Energy Efficiency in the
Department of Applied Physics and Naval Technology October 6, 2020
DT-17
CONFORMIDAD DE DEPÓSITO DE TESIS DOCTORAL POR LA COMISIÓN ACADÉMICA DEL PROGRAMA
D. DR. ÁNGEL MOLINA GARCÍA, Presidente/a de la Comisión Académica del Programa de DOCTORADO EN ENERGÍAS RENOVABLES Y EFICIENCIA ENERGÉTICA.
INFORMA:
Que la Tesis Doctoral titulada, “Solución numérica de problemas tipo en dominios geotérmicos anisótropos bi y tridimensionales con fuentes y sumideros de flujo de fluido.
Aplicación al reservorio del área Flegrea ha sido realizada, dentro del mencionado Programa de Doctorado, por D. Gennaro Sepede, bajo la dirección y supervisión del Dr.
Salvador Ángel Gómez Lopera, y Dr. Claudio Alimonti.
En reunión de la Comisión Académica, visto que en la misma se acreditan los indicios de calidad correspondientes y la autorización del Director de la misma, se acordó dar la conformidad, con la finalidad de que sea autorizado su depósito por el Comité de Dirección de la Escuela Internacional de Doctorado.
x Evaluación positiva del plan de investigación y documento de actividades por el Presidente de la Comisión Académica del programa (RAPI).
La Rama de conocimiento por la que esta tesis ha sido desarrollada es:
Ciencias
Ciencias Sociales y Jurídicas x Ingeniería y Arquitectura
En Cartagena, a 7 de Julio de 2020
EL PRESIDENTE DE LA COMISIÓN ACADÉMICA
Fdo: ____________________________
ANGEL|
MOLINA|
GARCIA
Firmado digitalmente por ANGEL|MOLINA|GARCIA Fecha: 2020.07.13 10:02:53 +02'00'
Versión de Adobe Acrobat:
2020.009.20074
DT-17 COMITÉ DE DIRECCIÓN ESCUELA INTERNACIONAL DE DOCTORADO
vii
Aim of the thesis (english)
The main aim of this doctoral thesis is to study and characterize the medium and high enthalpy geothermal reservoirs consisting of porous media. The use of new techniques for the eco-sustainable and renewable exploitation of geothermal energy via heat extraction system is proposed, using a wellbore heat exchanger (WBHX).
Among the particular objectives we find:
• The study and definition of the main features that influence the choice of a geothermal site, the type of installations and new techniques for the use of the geothermal resource.
• The study of the physical equations that governing the phenomenon and the pro- posal of a suitable mathematical systems to represent the response of the variables temperature, stream function and components of the fluid velocity vector.
• The implementation of a mathematical numerical method capable of approximat- ing the response of the system composed of highly nonlinear differential equations.
To do this a new powerful numerical software based on the Discontinuous Galerkin Method and implemented in the Matlab environment has been developed.
• The study of theoretical problems whose solution is known in scientific literature for a comparison and validation of the results obtained. This part allows to prove the power of the implemented software.
• The study of real geothermal reservoirs. The response of geothermal reser- voirs is defined by implementing and simulating, bi-dimensionally and three- dimensionally, one of most know geothermal areas in the world, the Phlegraean Fields, Naples, Italy. The study of the results obtained with the developed soft- ware are compared with those deriving from numerical simulations carrie out by well-known numerical commercial software.
• As last objective, the possible effects of alteration of the temperature field and of the flow of groundwater when a heat exchanger (for example a WBHX) is in service in the domain are studied, verifying the eco-sustainability of the proposed calorific energy extraction system studied.
Objetivos de la tesis (spanish)
La tesis doctoral tiene como objetivo principal estudiar y caracterizar las reservas geotérmicas de media-alta entalpía en medios porosos. Se propone el uso de nuevas técnicas para la utilización del recurso de manera eco-sostenible y renovable utilizando un sistema de extracción de calor (wellbore heat exchanger -WBHX-).
Como objetivos particulares podemos destacar:
• El estudio y la definición de las características principales que influyen en la elección de un sitio geotérmico, el tipo de instalaciones y las nuevas técnicas para el uso del recurso geotérmico.
• El estudio de las ecuaciones físicas que rigen el fenómeno y la propuesta de sistemas matemáticos adecuados para representar la respuesta de las variables temperatura, función de corriente y componentes del vector de velocidad del fluido.
• La implementación de un método numérico matemático capaz de aproximar la respuesta del sistema compuesto por ecuaciones diferenciales en derivadas par- ciales altamente no lineales. Para hacer esto, se ha desarrollado un poderoso programa de cálculo basado en el método Matemático Galerkin Discontinuo que se ha implementado en Matlab.
• El estudio de problemas teóricos cuya solución es conocida en la literatura cientí- fica para contrastar y validar los resultados obtenidos. Esta parte permite probar la potencia real del código de cálculo implementado.
• El estudio de yacimientos geotérmicos reales. La respuesta de los reservorios geotérmicos se define implementando y simulando, en 2D y 3D, una de las áreas geotérmicas más conocidas en el mundo, la de los Campos Flegreos, de Nápoles, Italia. El estudio de los resultados obtenidos con el software desarrollado son com- parados con los que derivan de simulaciones numéricas realizadas con conocidos programas de cálculo numerico comerciales.
• Como ultimo objetivo se estudian los posibles efectos de la alteración del campo de temperatura y flujo de agua subterránea cuando un intercambiador de calor (por ejemplo, un WBHX) está presente en el dominio, para verificar la sostteniblidad del sistema de energía calorífica estudiado.
ix
Obiettivi della tesi (italian)
La tesi dottorale ha come obiettivo principale lo studio e la caratterizzazione di ris- erve geotermiche di medio-alta entalpia costituite da mezzi porosi. Si propone l’utilizzo di nuove tecniche per l’approvvigionamento eco-sostenibile e rinnovabile dell’ ener- gia geotermica utilizzando un sistema di sola estrazione del calore, un wellbore heat exchanger (WBHX).
Tra gli obiettivi particolari possiamo evidenziare:
• Lo studio e la definizione delle principali caratteristiche che influiscono sulla scelta di un sito geotermico, sulla tipologia di istallazioni e nuove tecniche per l’utilizzazione della risorsa geotermica.
• Lo studio delle equazioni fisiche di governo del fenomeno e la proposta di sistemi matematici idonei a rappresentare la risposta delle variabili temperatura, funzione di corrente e componenti del vettore velocità del fluido.
• L’implementazione di un metodo numerico matematico capace di approssimare la risposta del sistema composto da equazioni differenziali alle derivate parziali alta- mente non lineari. Per fare questo è stato sviluppato un nuovo potente programma di calcolo basato sul Metodo matematico Galerkin Discontinuo e implementato in ambiente Matlab.
• Lo studio di problemi teorici la cui soluzione sia nota in letteratura scientifica per il confronto e la validazione dei risultati ottenuti. Questa parte permette comprovare l’effettiva potenza del codice di calcolo implementato.
• Lo studio di riserve geotermiche reali. La definizione della risposta delle riserve geotermiche avviene implementando e simulando, bidimensionalmente e tridimen- sionalmente, una delle più note aree geotermiche mondiali quella dei Campi Fle- grei, Napoli, Italia. Lo studio dei risultati ottenuti con il codice di calcolo imple- mentato sono comparati con quelli derivanti da simulazioni numeriche realizzate con noti programmi di calcolo numerici commerciali.
• Come ultimo obiettivo sono studiati i possibili effetti di alterazione del campo della temperatura e del flusso di acque sotterranee quando uno scambiatore di calore (ad esempio un WBHX) è presente nel dominio, per verificare l’eco- sostenibilità del sistema di estrazione di energia calorifica studiato.
xi
“...”
UNIVERSIDAD POLITÉCNICA DE CARTAGENA UPCT
DOCTORAL THESIS
Numerical solution of type problems in two and three dimensional anisotropic geothermal domains with sources and sinks of fluid flow.
Application to Flegrea Area reservoir by Gennaro Sepede
Abstract
This Dissertation presents the most advanced numerical analysis methods used for the sustainable use of geothermal energy in high enthalpy domains. The research work introduces and develops the techniques for a correct assessment of geothermal poten- tial through the development and implementation of an advanced software. The thesis includes 5 chapters. In the first chapter, the methods of exploitation of geothermal energy for the different types of domains are introduced based on geothermal potential and enthalpy. For the high enthalpy domains, the characteristic physical parameters used to estimate the the exploitation potential of the geothermal domain and the pro- ductivity of the plants are described, such as the characteristics of the soil, the flow of fluid and the thermal source. At the end, the main types of plant and the methods of exploitation of the domain are introduced, these are the heat extraction wells and the extraction or re-injection of the fluid wells. The second chapter presents the theoretical foundations of the physical problem studied. The physical governing equations of the problem are based on the laws of conservation of mass, energy and momentum applied to porous media. Depending on the characteristics of the porous medium, composed of a solid matrix and the fluid, the system can be studied as incompressible or com- pressible and saturated or not. Well-known approaches such as Oberberk-Buossinesq are applied in the work. The solution of the physical model, composed of a system of partial differential equations, is solved and discretized using the discontinuous Galerkin method (DGM). Chapter 3 introduces the various resolution techniques for this type of highly non-linear systems based on differential operators. Finally, the various types of elements implemented through the weight functions (shape functions) are presented for the 2D and 3D systems. In the chapter 4 the structure and the implementation meth- ods of the developed software, ”Geothermal Software”, are presented, which allows the numerical study of two-dimensional geothermal domains. In the chapter 5, using the developed software, complex theoretical and real problems are studied. Among the theoretical problems studied there are the Bénard, Elder and Yusa problems. For these the temperature field, stream function and components of the velocity vector results are presented.
xiii
Finally, the study of the Phlegrean Fields area is presented. After a detailed descrip- tion, the results are analyzed and an innovative methodology for the implementation of closed wells for heat extraction is presented. The results of the two-dimensional field of temperature, stream function and fluid velocity components are compared with those obtained using SHEMAT commercial research software. The thesis demonstrates the power of the DGM calculation method, ”Geothermal Software” allows solve precisely and efficiently the heat transfer and fluid flow problems. The study of the Campi Flegrei area, with a closed well and without a fluid extractor, shows that there is the possi- bility of a non-invasive use of geothermal renewable energy. Also, the results obtained demonstrate that heat extraction with closed systems does not significantly alter the range of variables involved, the temperature, stream function and fluid velocity vector in the porous media.
UNIVERSIDAD POLITÉCNICA DE CARTAGENA UPCT
TESIS DOCTORAL
Solución numérica de problemas tipo en dominios geotérmicos anisótropos bi y tridimensionales con fuentes y sumideros de flujo de
fluido. Aplicación al reservorio del Área Flegrea Gennaro Sepede
Resumen
Esta tesis doctoral presenta los métodos de análisis numérico más avanzados utilizados para el uso sostenible de la energía geotérmica en dominios de alta entalpía. El trabajo introduce y desarrolla técnicas para una evaluación correcta del potencial geotérmico a través del desarrollo e implementación de un software numérico. La tesis se divide en 5 capítulos. En el primer capítulo se introducen los métodos de uso de la energía geotérmica para los diferentes tipos de dominios en función del potencial geotérmico y de la entalpía. Para los dominios de alta entalpía se describen los parámetros físicos característicos utilizados para estimar el potencial de explotación del dominio geoter- mico y la productividad de las plantas geotérmicas, tales como las características del suelo, el flujo de fluido y la fuente térmica. Al final se introducen los principales tipos de plantas y los métodos de utilización del dominio, que son los pozos de extracción de calor y extracción o reinyección del fluido. En el segundo capítulo se presentan los fundamentos teóricos del problema físico estudiado. Las ecuaciones físicas que rigen el problema se basan en las leyes de conservación de masa, energía y momento aplicadas a los medios porosos. Dependiendo de las características del medio poroso, compuesto por una matriz sólida porosa y el fluido, el sistema puede estudiarse como incompresible o compresible y saturado o no. En el trabajo se aplican conocidas aproximaciones como la de Oberberk-Buossinesq. La solución del modelo físico, compuesto por un sistema de ecuaciones diferenciales en derivadas parciales, se resuelve y se discretiza utilizando el método discontinuo de Galerkin (DGM). El capítulo 3 presenta las diversas técnicas de resolución para este tipo de sistemas altamente no lineales basados en operadores diferenciales. Finalmente, se presentan los diversos tipos de elementos implementados a través de las funciones peso (funciones de forma) para los sistemas 2D y 3D. En el capítulo 4 se presentan la estructura y los métodos de implementación del software que se ha desarrollado, ”Geothermal Software”, para el estudio numérico de dominios geotérmicos bidimensionales. En el quinto capitulo, utilizando este complejo programa, se estudian diversos problemas teóricos y reales.
xv
Entre los problemas teóricos estudiados están el de Bénard, el de Elder y el de Yusa, de los cuales se presentan los resultados correspondientes al campo de temperatura, la función de corriente y las componentes del vector velocidad del fluido. Finalmente, se presenta el estudio del área dei Campi Flegrei. Después de una descripción detallada, se analizan los resultados de los análisis y se presenta una metodología innovadora para la implementación de pozos cerrados para extracción de calor. Los resultados del campo bidimensional de temperatura, función de corriente y componentes de la velocidad del fluido se contrastan con los obtenidos con el software commercial de in- vestigación SHEMAT. La tesis demuestra la potencia del método de cálculo DGM, ya que el programma ”Geothermal Software” permite resolver de manera precisa y ef- ficiente problemas bidimensionales complejo de trasferencia de calor y movimiento de fluido en medios porosos. El estudio de explotación del área Campi Flegrei, con un pozo cerrado sin extración y reinjeción de fluido al medio, demuestra que es posible el uso no invasivo y sostenible de la energía renovable geotérmica. Además, los resulta- dos obtenidos demuestran que la extracción de calor con sistemas cerrados no altera significativamente los valores de las variables involucradas, temperatura, función de corriente y componentes de la velocidad del fluido en el medio poroso.
UNIVERSIDAD POLITÉCNICA DE CARTAGENA UPCT
Soluzione numerica di distinti problemi in domini geotermici anisotropi bi e tri-dimensionali con immissione e uscita di flusso di
fluido. Applicazione al reservoir dell’ Area Flegrea Gennaro Sepede
TESI DOTTORALE
Abstract
In questa tesi dottorale sono presentati i più avanzati metodi di analisi numerica utilizzati per un uso sostenibile dell’energia geotermica in domini di alta entalpia. Nel lavoro di ricerca sono introdotte e sviluppate le tecniche per una corretta valutazione del potenziale geotermico attraverso lo sviluppo e l’implementazione di un software avanzato. La tesi è divisa in 5 capitoli. Nel primo capitolo sono introdotti i metodi di utilizzo dell’energia geotermica per le differenti tipologie di domini in base al potenziale geotermico e all’entalpia. Per le riserve ad alta entalpia si descrivono i parametri fisici caratteristici utilizzati per stimare il potenziale di sfruttamento del dominio geotermico e la produttività degli impianti, come le caratteristiche del terreno, il flusso di fluido e la sorgente termica. A conclusione sono introdotte le principali tipologie di impianto e le metodologie di utilizzo del dominio che sono i pozzi di estrazione del calore o di estrazione o re-iniezione del fluido. Nella secondo capitolo sono presentati i fondamenti teorici del problema fisico studiato. Le equazioni fisiche che governano il problema si basano sulle leggi di conservazione della massa, dell’energia ed del momento applicate a mezzi porosi. A seconda delle caratteristiche del mezzo poroso, composto da una matrice solida porosa e dal fluido, il sistema può essere studiato come incompressibile o compressibile e saturo o non. Note approssimazioni come quella di Oberberk-Buossinesq sono utilizzate in questo lavoro. La soluzione del modello fisico, composto da un sistema di equazioni differenziali alle derivate parziali, è risolto e discretizzato usando il Metodo discontinuo di Galerkin (DGM). Nel capitolo tre sono introdotte le varie tecniche di risoluzione per questa tipologia di sistemi, altamente non lineari, basati su operatori differenziali. In fine sono presentate, per i sistemi 2D e 3D, le diverse tipologie di el- ementi implementati attraverso le funzioni di peso (funzioni di forma). Nel capitolo 4 è presentata la struttura e il metodo di implementazione del software sviluppato, il
”Geothermal Software”, che permette lo studio numerico di domini geotermici bidi- mensionale. Nel capitolo 5, utilizzando il software sviluppato, sono studiati complessi problemi teorici e reali.
xvii
Tra i problemi teorici troviamo i problemi di Bénard, Elder e Yusa di cui si presen- tano i risultati del campo delle temperature, funzione di corrente e componenti del vet- tore velocità del fluido. Infine è presentato lo studio dell’area dei Campi Flegrei. Dopo una descrizione dettagliata si analizzano i risultati delle analisi si presenta un’innovativa metodologia per l’implementazione dei pozzi chiusi per estrazione di calore. I risultati del campo bidimensionale della temperatura, funzione di corrente e componenti della velocità del fluido sono confrontati con quelli ottenuti utilizzando il software commer- ciale di ricerca SHEMAT. La tesi dimostra la potenza del noto metodo di calcolo DGM, infatti il programma ”Geothermal Software” è stato capace di risolvere in modo ef- ficiente e flessibile i problemi inerenti la trasmissione di calore e movimento di fluido.
Lo studio dell’area di Campi Flegrei, con un pozzo chiuso e senza estrazione di flu- ido, dimostra che esiste la possibilità di un uso non invasivo dell’energia rinnovabile geotermica. I risultati ottenuti dimostrano che l’estrazione di calore con sistemi chiusi non altera notevolmente il campo della temperatura, della funzione di corrente e delle componenti delle velocità del fluido.
xix
Acknowledgements
Special thanks to my dear thesis supervisors, Dr. Salvador A. Gómez-Lopera and Dr. Claudio Alimonti.
I would like to thank Salvador not only for his scientific notations and teachings he has transmitted over the years but also for having inculcated the spirit of hard work and sacrifice and seeking improvement, in both personal life and research.
I would like to thank Claudio for welcoming me and sharing his cultural and personal background with me. Collaborating with you has been a pleasure and a unique oppor- tunity. I hope I have employed your teachings properly.
I would like to thank Professor Dr. Francisco Alhama for his valuable advice, sci- entific indications, and the lessons he has given me during my study. Your preparation and positive spirit have been of great teaching for me.
I appreciate Professor Dr. Mara Lombardi. One of the wonderful people I met on my academic path. Your preparation and dedication to scientific research are exemplary.
Finally my colleagues, Juan Manuel Mariñoso and Alejandro Albero. Thank you for your presence and the beautiful moments spent together. I know that your sacrifices will give you a valuable reward.
My special thanks to Dr. Atousa Ataieyan and Dr. Elena Soldo. Collaborating with you on common research topics has been useful and a pleasure to my scientific education.
Special thanks to those who supported my research. A great thanks to Edison multinational company and the Fondazione Alessandro Volta for having financially supported one part of my research. Thanks to INAIL institute, for supplying the re- search grant at the institute and in particular, thanks to Dr. Eng. Corrado Delle Site for having improved my scientific training.
Finally a special thanks to my second family in Cartagena. Encarna, Ricardo, and all my kind friends. I humbly thank you for welcoming me to your home as a son, a brother, and a friend.
. . .
xxi
Contents
Aim of the thesis (english) vii
Objetivos de la tesis (spanish) viii
Obiettivi della tesi (italian) ix
Abstract (english) xii
Abstract (spanish) xiv
Abstract (italian) xvi
Acknowledgements xix
List of Figures xxv
List of Tables xxxi
List of Abbreviations xxxiii
Physical Constants xxxv
List of Symbols xxxvii
1 METHODS FOR A CORRECT USE OF THE GEOTHERMAL RE-
SOURCES 1
1.1 Introduction . . . 1 1.2 Geothermal energy . . . 2 1.3 Classification of geothermal reservoirs: low, medium and high enthalpy . 4 1.4 Site characteristics . . . 10 1.5 Geothermal systems and power generation . . . 14 1.6 Geothermal wells . . . 17
2 THEORETICAL FOUNDATIONS 19
2.1 Introduction . . . 19 2.2 Mass consevation and momentum equation . . . 20 2.3 Darcy law . . . 26 2.4 Energy equation . . . 26 2.5 Heat and mass transfer in porous media . . . 31
2.6 Oberbeck-Boussinesq approximation . . . 32 2.7 Streamfunction formulation . . . 33 2.8 Mathematical models . . . 34 3 MATHEMATICAL METHODS FOR THE NUMERICAL RESOLU-
TION OF PARTIAL DIFFERENTIAL EQUATIONS SYSTEMS 41 3.1 Introduction . . . 41 3.2 Simulation methods. Analytical and numerical solutions . . . 42 3.3 Numerical solutions . . . 44 3.3.1 Finite Difference Method . . . 44 3.3.2 Integral Formulation Methods. Stationary functional and weighted
residual methods . . . 45 3.4 GDM applied to heat and mass transfer problems . . . 48 3.4.1 Mathematical discretized model . . . 48 3.4.2 Shape functions implementation . . . 53 3.4.3 Discretization and assembly process . . . 59 3.5 Boundary conditions implementation . . . 67 3.6 Methods for the algebraic systems resolution . . . 69 4 GEOTHERMAL SOFTWARE. STRUCTURE AND FEATURES 91 4.1 Introduction . . . 91 4.2 General structure of GS software . . . 92 4.3 Matlab code C structure . . . 97 4.4 Tutorial and research application . . . 102
5 SOLVED PROBLEMS 109
5.1 Introduction . . . 109 5.2 Type problems solved . . . 110 5.3 Numerical simulation of Bénard problem . . . 111 5.4 Numerical simulation of Elder problem . . . 130 5.5 Yusa problem . . . 142 5.6 The case of Naples geothermal reservoir . . . 152 5.6.1 Introduction to the problem . . . 152 5.6.2 Introduction to the Campi Flegrei reservoir . . . 153 5.6.3 3D physical model and discretization of the Naples’ geothermal
reservoir . . . 155 5.6.4 2D and 3D spatial discretization . . . 156 5.6.5 Results of Analysis . . . 159 5.6.6 Sustainable use of Campi Flegrei geothermal field via WBHX . 169 5.6.7 WBHX implementation . . . 170 5.6.8 Results of WBHX implementation analysis . . . 171
xxiii
6 CONCLUSIONS 179
6.1 Conclusions (english) . . . 179 6.2 Conclusiones (spanish) . . . 182 6.3 Conclusioni (italian) . . . 185
A GLOBAL REFERENCES 189
Bibliography . . . 189
xxv
List of Figures
1.1 The demonstration opening of a well (A), Central of “Valle Secolo” (B), Larderello . . . 3 1.2 View of a cooling tower, Larderello (A) and drilling tower of the Euro-
pean project "DESCAMBLE" (B), Larderello . . . 3 1.3 Electrical geothermal installed capacity for the first 11 nations in the
world . . . 4 1.4 Example of a very low enthalpy geothermal system . . . 6 1.5 Graph of seasonal temperature variation versus depth in the soil . . . . 7 1.6 Example of groundwater flow in thermal area (stream function field) and
related velocity vector . . . 8 1.7 Schematic of a high enthalpy geothermal reserve for electricity produc-
tion . . . 9 1.8 Collocation of earthquakes, tectonic plate boundaries and geothermal
regions, NOAA map [22] . . . 10 1.9 3D model of Naples, Area Flegrea, Ischia and mount Vesuvius area . . . 11 1.10 Re-view of [24] geophysical, geological and geothermal functioning scheme
of the Flegrea Area . . . 11 1.11 Single Flash Steam Power Plants, where: PW (extraction or produc-
tion well), IW (injection well), CS (cyclone separetor), BCV Ball check valve, MR (Moisture remover), SP (Steam piping), CSV (Control stop valves), SE/C(Steam ejector/condenser), T/G(Turbine/generator), CP (Condensate pump), CWP (Cooling water pump) [21] . . . 15 1.12 Double Flash Steam Power Plants, where: PW (extraction or production
well), IW (injection well), PH (Powerhouse) [21] . . . 15 1.13 Dry Steam Power Plants, where: PW (extraction or production well),
IW (injection well), WV(Water (brine) piping), MR (Moisture remover), SP (Steam piping), SE/C(Steam ejector/condenser), T/G(Turbine/generator), CP (Condensate pump), CWP (Cooling water pump), C(Condenser) [21-ref. 18] . . . 16 1.14 Binary Cycle Power Plants, where: PW (extraction or production well),
IW (injection well), P(pump), SR(steam receiver), E(evaporator), PH(preheater), T/G(turbine/generator), CP(condensate pump), CWP (cooling water
pump), C(condenser), FF(Final filter), M(make-up water), CSV(control stop valves), CT(cooling tower) [21-ref. 4] . . . 17 1.15 Exemple of geothermal well [34-ref. 4] (A) and wellbore heat exchanger
[35-ref. 37] and [37] (B) . . . 18
2.1 Mass balance in 3D (A) and 2D (B) CV representation . . . 20 2.2 Components of momentum flow in x-direction . . . 22 2.3 Flow model for porous media. Porosity in x-direction . . . 25 2.4 Flow model for porous media. Porosity in x-z directions . . . 25 2.5 Scheme of energy variation (A) and internal heat generation (B) in a
C.V. 1st Law of Thermodynamics . . . 28 2.6 Representation of the implemented water thermal expansion coefficient . 38 2.7 Representation of the implemented viscosity of water . . . 38 2.8 Representation of the implemented fluid density function . . . 39 3.1 Block diagram of different solution methods of engineering ploblems.
Review of [56] . . . 42 3.2 Scheme of resolution for analytical and numerical methods . . . 43 3.3 Example of discretization using FDM. Review of [57] . . . 44 3.4 Linear, quadratical and cubic shape functions trends for a 1D element . 54 3.5 Linear shape functions trends for a 2D rectangular element . . . 55 3.6 Quadratic shape functions trends for a 2D rectangular element . . . 56 3.7 Cubic shape functions trends for a 2D rectangular element . . . 56 3.8 Linear shape functions trends for a 3D cubic element . . . 57 3.9 Quadratic shape functions trends for a 3D cubic element . . . 58 3.10 Cubic shape functions trends for a 3D cubic element . . . 58 3.11 Example of regular grid used in assembly process . . . 59 3.12 Numbering used in the computational integral phase. Example for generic
element of [P 2] matrix . . . 60 3.13 Example of regular grid used in the assembly process . . . 60 3.14 Part of [P 2] assembled Matrix for en≠1(red), en(green) and en+1 (blue)
elements . . . 61 3.15 Network model of a spatial element for solute concentration; (a) in the
stream, c,(b) in the storage zone, cS, and (c) in the streambed sediments, cSed . . . 70 3.16 Newton-Raphson method. Review of [82] . . . 71 4.1 Window for input data in Geothermal Software . . . 92 4.2 A.1 bar. Main menu composition . . . 93 4.3 B.1 bar. Coupling variables process and discretization menu . . . 93 4.4 Table for the implementation of the physical parameters . . . 94 4.5 E.1 bar. Implementation of boundary and initial conditions and Layers 94 4.6 Parameters analysis and problem resolution windows . . . 95 4.7 G.1 bar. Bar for the implementation of the numerical analysis parameters 96 4.8 D.1 bar. Bar for setting the results to be displayed . . . 96 4.9 G.1 bar. Window for saving the results . . . 97 4.10 Geothermal Software main function.m . . . 97 4.11 Implementation steps (1), (2), (3) and (6) . . . 99 4.12 Example of algebraic system generated by Geothermal Software . . . 100 4.13 Implementation steps (4) and data generated during the solve process (6) 101
xxvii
4.14 Step for viewing the results (5) and for the generation of the final results (6) . . . 101 4.15 Step 1. Set working directory . . . 103 4.16 Step 2. Bénard problem implementation. Set geometry of the problem . 103 4.17 Step 3.Implementation soil parameters for Bénard problem . . . 104 4.18 Step 4. Implementation of BCs and IC for Bénard problem . . . 105 4.19 Step 5. Assembly process and final algebraic system generation . . . 106 4.20 Step 6. Setting of the analysis parameters for the solution of the Bénard
problem . . . 106 4.21 Resolution phase for Bénard problem . . . 107 4.22 Step 6. Results obtained . . . 107 5.1 Geometry and boundary conditions for Bénard domain . . . 112 5.2 Temperature field for Ra=40 . . . 115 5.3 Temperature field for Ra=50 . . . 115 5.4 Temperature field for Ra=80 . . . 115 5.5 Temperature field for Ra=100 . . . 115 5.6 Temperature field for Ra=120 . . . 115 5.7 Stream-function field for Ra=40 . . . 116 5.8 Stream-function field for Ra=50 . . . 116 5.9 Stream-function field for Ra=80 . . . 116 5.10 Stream-function field for Ra=100 . . . 116 5.11 Stream-function field for Ra=120 . . . 116 5.12 Horizontal velocity field for Ra=40 . . . 117 5.13 Horizontal velocity field for Ra=50 . . . 117 5.14 Horizontal velocity field for Ra=80 . . . 117 5.15 Horizontal velocity field for Ra=100 . . . 117 5.16 Horizontal velocity field for Ra=120 . . . 117 5.17 Vertical velocity field for Ra=40 . . . 118 5.18 Vertical velocity field for Ra=50 . . . 118 5.19 Vertical velocity field for Ra=80 . . . 118 5.20 Vertical velocity field for Ra=100 . . . 118 5.21 Vertical velocity field for Ra=120 . . . 118 5.22 Temperature (A) and stream function (B) trend in four control nodes,
Ra=40 . . . 119 5.23 Temperature (A) and stream function (B) trend in four control nodes,
Ra=50 . . . 120 5.24 Temperature (A) and stream function (B) trend in four control nodes,
Ra=80 . . . 121 5.25 Temperature (A) and stream function (B) trends in four control nodes,
Ra=100 . . . 121 5.26 Temperature (A) and stream function (B) trend in four control nodes,
Ra=120 . . . 122 5.27 Temperature field for Ra=140, t=2.00e+8 s . . . 122 5.28 Temperature field for Ra=140, t=4.00e+8 s . . . 123
5.29 Temperature field for Ra=140, t=8.00e+8 s . . . 123 5.30 Temperature field for Ra=140, t=1.40e+9 s . . . 123 5.31 Temperature field for Ra=140, t=2.00e+9 s . . . 124 5.32 Stream-function field for Ra=140, t=2.00e+8 s . . . 124 5.33 Stream-function field for Ra=140, t=4.00e+8 s . . . 124 5.34 Stream-function field for Ra=140, t=8.00e+8 s . . . 125 5.35 Stream-function field for Ra=140, t=1.40e+9 s . . . 125 5.36 Stream-function field for Ra=140, t=2.00e+9 s . . . 125 5.37 Horizontal velocity field for Ra=140, t=2.00e+8 s . . . 126 5.38 Horizontal velocity field for Ra=140, t=4.00e+8 s . . . 126 5.39 Horizontal velocity field for Ra=140, t=8.00e+8 s . . . 126 5.40 Horizontal velocity field for Ra=140, t=1.40e+9 s . . . 127 5.41 Horizontal velocity field for Ra=140, t=2.00e+9 s . . . 127 5.42 Vertical velocity field for Ra=140, t=2.00e+8 s . . . 127 5.43 Vertical velocity field for Ra=140, t=4.00e+8 s . . . 128 5.44 Vertical velocity field for Ra=140, t=8.00e+8 s . . . 128 5.45 Vertical velocity field for Ra=140, t=1.40e+9 s . . . 128 5.46 Vertical velocity field for Ra=140, t=2.00e+9 s . . . 129 5.47 Temperature (A) and stream function (B) trends in four control nodes
with Ra=140 . . . 129 5.48 Geometry and boundary conditions for Elder domain . . . 130 5.49 Temperature field after 1 year . . . 131 5.50 Stream-function field after 1 year . . . 131 5.51 Velocity horizontal field after 1 year . . . 132 5.52 Velocity vertical field after 1 year . . . 132 5.53 Temperature field after 4 years . . . 133 5.54 Stream-function field after 4 years . . . 133 5.55 Velocity horizontal field after 4 years . . . 133 5.56 Velocity vertical field after 4 years . . . 134 5.57 Temperature field after 10 years . . . 134 5.58 Stream-function field after 10 years . . . 135 5.59 Horizontal velocity field after 10 years . . . 135 5.60 Vertical velocity field after 10 years . . . 135 5.61 Temperature field after 15 years . . . 136 5.62 Stream-function field after 15 years . . . 136 5.63 Horizontal velocity field after 15 years . . . 137 5.64 Vertical velocity field after 15 years . . . 137 5.65 Temperature field after 20 years . . . 137 5.66 Stream-function field after 20 years . . . 138 5.67 Horizontal velocity field after 20 years . . . 138 5.68 Vertical velocity field after 20 years . . . 138 5.69 Temperature field after 50 years . . . 139 5.70 Stream-function field after 50 years . . . 139 5.71 Horizontal velocity field after 50 years . . . 139
xxix
5.72 Vertical velocity field after 50 years . . . 140 5.73 Temperature (A) and stream function (B) trends in four control nodes . 140 5.74 Horizontal (A) and vertical (B) velocity components trend in four control
nodes . . . 141 5.75 Geometry and boundary condition for Yusa domain . . . 142 5.76 Temperature field for t=5.00e+9 s . . . 143 5.77 Stream function field for t=5.00e+9 s . . . 143 5.78 Horizontal velocity component field for t= 5.00e+9 s . . . 144 5.79 Vertical velocity component field for t= 5.00e+9 s . . . 145 5.80 Temperature field for t=1.00e+10 s . . . 145 5.81 Stream Function field for t=1.00e+10 s . . . 146 5.82 Horizontal velocity component field for t=1.00e+10 s . . . 146 5.83 Vertical velocity component field for t=1.00e+10 s . . . 146 5.84 Temperature field for t= 5.00e+10 s . . . 147 5.85 Stream Function field for t=5.00e+10 s . . . 147 5.86 Horizontal velocity component field for t=5.00e+10 s . . . 148 5.87 Vertical velocity component field for t=5.00e+10 s . . . 148 5.88 Temperature field for t= 5.00e+11 s . . . 149 5.89 Stream-Function field for t= 5.00e+11 s . . . 149 5.90 Horizontal velocity component field for t= 5.00e+11 s . . . 150 5.91 Vertical velocity component field for t=5.00e11 s . . . 150 5.92 Temperature and Stream-function temporal evolution in four control nodes151 5.93 Horizontal and vertical velocity components temporal evolution in four
control nodes . . . 152 5.94 3D rappresentation of Campi Flegrei reservoir with individuation of ex-
isting geothermal extraction wells . . . 154 5.95 3D view of analyzed area . . . 154 5.96 Geometry and B.Cs. used in SHEMAT for the modeling of Campi Flegrei
reservoir. Case (1) and (2) . . . 157 5.97 Geometry and B.Cs. for Campi Flegrei domain. Case (3) . . . 158 5.98 Temperature field at 5 and 10 steep periods . . . 159 5.99 Temperature field at 15 and 20 steep periods . . . 159 5.100 Temperature field at 35 and 40 steep periods . . . 160 5.101 Vertical velocity vector field at 5 and 10 steep periods . . . 160 5.102 Vertical velocity vector field at 15 and 20 steep periods . . . 161 5.103 Vertical velocity vector field at 35 and 40 steep periods . . . 161 5.104 Temperature field obtained by SHEMAT detailed analysis. Period of
analysis 20. Image reprocessed. . . 162 5.105 Temperature field obtained by SHEMAT detailed analysis. Period of
analysis 40. Image reprocessed. . . 162 5.106 Vertical velocity obtained by SHEMAT detailed analysis. Period of
analysis 20. Image reprocessed. . . 163 5.107 Vertical velocity field obtained by SHEMAT detailed analysis. Period
of analysis 40. Image reprocessed. . . 163
5.108 Temperature versus time at nodal points obtained using Geothermal Software . . . 164 5.109 Stream function versus time at nodal points obtained using Geothermal
Software . . . 165 5.110 Vertical component of velocity versus time at nodal points obtained
using Geothermal Software . . . 165 5.111 Horizontal component of velocity versus time at nodal points obtained
using Geothermal Software . . . 166 5.112 Temperature versus time at nodal points obtained using Geothermal
Software . . . 167 5.113 Stream function versus time at nodal points obtained using Geothermal
Software . . . 167 5.114 Horizontal velocity component versus time at nodal points obtained
using Geothermal Software . . . 168 5.115 Vertical velocity versus time at nodal points obtained using Geothermal
Software . . . 168 5.116 Identification of the positioning and type of DBHE used [35] . . . 170 5.117 Thermal disturbance of the WBHX after 1 month. SHEMAT-GEOPIPE 172 5.118 Thermal disturbance of the WBHX after 6 months. SHEMAT-GEOPIPE172 5.119 Thermal disturbance of the WBHX after 1 year. SHEMAT-GEOPIPE 172 5.120 Thermal disturbance of the WBHX after 3 years. SHEMAT-GEOPIPE 173 5.121 Temperature distribution in the reservoir for x = 2300 to 3700 m with ex-
traction well at the initial. Results obtained using Geothermal Software173 5.122 Temperature distribution in the reservoir for x = 2300 to 3700 m with ex-
traction well after 5 years. Results obtained using Geothermal Software174 5.123 Temperature distribution in the reservoir for x = 2300 to 3700 m with
extraction well (a) at the 11 years. Results obtained using Geothermal Sof tware . . . 174 5.124 Temperature distribution in the reservoir for x = 2300 to 3700 m
with extraction well at the last analysis step. Results obtained using Geothermal Sof tware . . . 174 5.125 Temperature field in the reservoir with extraction well. Results obtained
using Geothermal Software . . . 175 5.126 Temporal trend in four control nodes (vertical of the wall well) at the
final time step. Results obtained using Geothermal Software . . . 175 5.127 Stream function field in Phlegrean Field. Results of the analysis with
heat extraction well at the final simulation time. Results obtained using Geothermal Software . . . 176 5.128 Horizontal component of velocity in Phlegrean Field. Results of the
analysis with heat extraction well at the final simulation time. Results obtained using Geothermal Software . . . 176 5.129 Vertical component of velocity in Phlegrean Field. Results of the anal-
ysis with heat extraction well at the final simulation time. Results ob- tained using Geothermal Softwar . . . 177
xxxi
List of Tables
1.1 Classification of geothermal resources. The enthalpy . . . 6 1.2 Thermal and Hydraulic characteristic for different types of soils . . . 13 3.1 Table Analogy of Mustak (1937) [4.1] . . . 70 4.1 Soil properties for Bénard problem discretization . . . 104 5.1 Values used for the Bénard problem discretization . . . 112 5.2 Values used for the Elder problem discretization . . . 131 5.3 Values used for the Yusa problem discretization . . . 142 5.4 Values of the constants used for the Campi Flegrei implementation for
the case (1) and (2) implemented in SHEMAT . . . 157 5.5 Geometry and B.Cs. used in GS for the modeling of Campi Flegrei
reservoir. Case (3) . . . 158
xxxiii
List of Abbreviations
GS Geothermal Software
SHEMAT Simulator for HEeat and MAss Transport DGM Discontinuoust Galerkin Method
FEM Finite Elements Method FEA Finite Elements Analysis FDM Finite Difference Method FVM Finite Volume Method NSM Network Simulation Method PDS Partial Derivatives System PDE Partial Derivatives Equation BC Boundary Condition
IC Initial Condition CV Control Volume
DBHE Deep WellBore Heat Exchanger WBHX WellBore Heat Exchanger
xxxv
Physical Constants
General Constants
g Gravitational acceleration [m s≠2]
Ra Rayleigh number [1]
Thermal constants
D˜ Thermal diffusivity tensor in x,y,z direction [m2 s≠1]
c Specific heat capacity [J kg≠1 K≠1]
Q Total thermal power [W]
Qs Heat source/sink [W m≠3]
q Heat flux [Wm≠2]
˜k Thermal conductivity tensor in x,y,z direction [W m≠1K≠1]
k Convective heat transfer [W m≠2K≠1]
R Thermal resistance [m K m≠2]
T Temperature gradient [¶C m≠1]
“ Ratio of solid-fluid specific heat [ad]
— Thermal expansion coefficient [¶C≠1]
Soil constants
µ Dynamic viscosity [kg2 s≠1m≠1]
K˜ Permeability tensor in x,y,z direction [m2] K˜c Hydraulic conductivity tensor in x,y,z direction [m2]
mf Mass flow rate [kg m≠3]
flf Fluid density [kg m≠3]
flf Change of water density [kg m≠3]
W Fluid source/skin [m3 s≠1]
„ Porosity [1]
m Mass [kg m≠3]
–c Soil compressibility [Pa≠1]
—c Fluid compressibility [Pa≠1]
Ss Specific storage coefficient [m≠1]
xxxvii
List of Symbols
Time analysis
t Time [s]
t Computational time step [s]
tf in Final time for analysis [s]
Variables
T Temperature [¶C]
 Stream function [m2 s≠1]
hp Piezometric head [m]
˛v Velocity vector [m s≠1]
u, v, w Velocity component in x,y,z direction [m s≠1]
e Energy [J]
s Entropy [J K≠1]
h Enthalpy [J]
Spatial variables
x Horizontal first direction [m]
y Horizontal second direction [m]
z Vertical direction [m]
x Vertical distance between nodes in x direction [m]
y Vertical distance between nodes in y direction [m]
z Horizontal distance between nodes in z direction [m]
L Total length [m]
H Total height [m]
r Radius [m]
Mathematical operators and matrices
Ò=
3 ˆ
ˆx,ˆyˆ ,ˆzˆ 4
Ni Generic shape function in the node i
[Nj]=[N1, N2, ....Ni] Matrix of the shape functions for all the (i) nodes of element
[Nl]=[N1, N2, ....Ni]T Transposed of matrix of the shape functions for all the (i) nodes of element
[P ]=[Nj] ◊ [Nl] Square matrix product of the shape functions for all the (i) nodes of element
[B]d=Ò[Nj] ◊ Ò[Nl] Square matrix product of the shape functions for all the (i) nodes of the element, with (d) that denote the direction of derivate (x,y,z),
[K]d=[Nj] ◊ Ò[Nl] Square matrix product of the shape functions for all the (i) nodes of the element, with (d) that denote the direction of derivate (x,y,z),
˜n=[nx, ny, nz] Normal value applied to the line(2D) or the faces (3D) of the elements in x,y,z direction
xxxix
Subscript and superscript
f, Fluid part s, Solid part e, (e) Element w, Well
i, (i) Single element of a matrix
j, (j) Complete elements of a column matrix l, (l) Complete elements of a row matrix T, Transpose matrix
0, For initial time or for reference condition f in, For final time
xli
I dedicate this work to my family, my father Cristofano, my mother Concetta and my brother Salvatore, who have always believed in
me, in my potential and given the right and useful values to
achieve this goal. In the same way to my uncles and cousins.. . .
1
Chapter 1
METHODS FOR A CORRECT USE OF THE GEOTHERMAL RESOURCES
This Chapter contains
1.1 Introduction . . . 1 1.2 Geothermal energy . . . 2 1.3 Classification of geothermal reservoirs: low, medium and high enthalpy . 4 1.4 Site characteristics . . . 10 1.5 Geothermal systems and power generation . . . 14 1.6 Geothermal wells . . . 17
1.1 Introduction
In this chapter the main techniques for the evaluation of the potential of the geothermal areas and its use as renewable resource are introduced. In the first part, a review will be made on the history and evolution of this energy source which can be classified according to the thermal capacity of the reservoir heat source in terms of enthalpy. Thermo and fluid dynamic characteristics of the soils and the groundwater for shallow, medium and high enthalpy domains will be introduced. Thank to this, the potential of a high enthalpy geothermal domain, typically distributed in certain sites of the world, will be introduced defining the geophysical structure and the ground-water field. These aspects plays an important role in the appearance and characteristics determining the feasibility of the different types of installations. Afterwards, the attention will be focused on the different types of plants and the main control variables. The productivity of the installation, its elements and the different types of systems are studied, in particular, the extraction and injection wells of fluid and the closed systems with only extraction of thermal energy. For closed systems, the main characteristics of the exchange system and operating characteristics will be introduced.
1.2 Geothermal energy
The production of clean energy using the geothermal resource is undoubtedly one of the oldest systems for generating of heat and electricity exploiting the thermal po- tential of the subsoil. The geothermal topics are located in a branch of geophysics that studies the thermal and chemical characteristics of the Earth and its thermal potential with the aim of extracting energy in the form of heat using it for multiple purposes, among which we find, conditioning and heating of buildings and neighborhoods, elec- tricity production and use of heat extracted for agri-food purposes. Geothermal energy and heat extraction techniques have undergone considerable development in the last 200 years, even though the exploitation of the reservoirs present in these areas, which possess specific chemical-physical properties of water and minerals, are known by the VI century BC [1] mainly in Italy, in the area known today as "Larderello District".
In fact, the Etruscans already exploited geothermal sources with a high content of boric salts due to their purifying properties mainly in the manufacture of ceramic artifacts.
In the following centuries the importance of the area grew, an example is the construc- tion of the 12th century Rocca Sillana, built in the territory of Pomarance, Tuscany, Pisa, in a strategic position to defend the territories, which were considered fundamen- tal for the extraction of KAl3 (SO4)2 (OH)6, the green vitriol or ferrous sulfate FeSO4
and the sulfur S.
The attention increased in the 16th and 17th centuries, with the discovery of the pres- ence of boric acid in Tuscan geothermal waters by the director of pharmacies of the great duchy of Tuscany Francesco Ugo Hoefer [2] and with Paolo Mascagni who pro- posed the extraction techniques.
François Jacques, later called "de Larderel", started the production in 1818 and in- creased it between 1835 and 1842 with the creation of slate wells and the introduction of steam boilers in the production cycle.
The separation point between the extractive use of chemical compounds and the use of the resource for geothermal purposes started in 1904. Piero Ginori Conti started to use the geothermal energy for the generation of electricity turning on the first 5 lights. In the following year the installation of the first “Cail”, an engine, it marks the foundation of the first geothermal installation in the world.
Today the "Larderello geothermal district" is the largest in Europe for extension and production, starting from the 126,800 KW in the 1944 arriving to 34 power stations with an approximate extension of 500 km2, 500 wells (300 of extraction, 100 of re- injection and 100 of control).
In this district is possible to find the single electricity production plant of ”V alle Secolo”, Figure 1.1 (B), able to produce 120 MW, from the hot fluid that coming out of the extraction well, thanks to two Ansaldo turbines. Another characteristic of the geother- mal district is the research area dedicate to the study of the supercritical fluids with the European project called DESCRAMBLE, [3], Figure 1.2 (B), (“Drilling in dEep, Super-Critical AMBient of continentaL Europe”) managed by S.p.a. Enel Green Power.
1.2. Geothermal energy 3
(a) (b)
Figure 1.1: The demonstration opening of a well (A), Central of “Valle Secolo” (B), Larderello
(a) (b)
Figure 1.2: View of a cooling tower, Larderello (A) and drilling tower of the European project "DESCAMBLE" (B), Larderello
From the end of the 90’s geothermal energy has evolved both in extraction tech- niques and in the size of the plants. Certainly we can no longer conceive these at the same mode only as a tool for the production of large quantities of energy or for the ex- traction of heat. The evolution, goes towards the small plants used for semi-industrial, agricultural, public or domestic uses. The difference between these is that if the first two are localized in specific areas of the world, the second type of installations are free to exploit the geothermal resource or gradient (ÒT) in almost all of the world.
In fact, the operation of these plants is based on the insulating thermo-physical properties of the soil, with constant temperatures or with small seasonal variations during the year. In this case the renewable source finds application for the conditioning
1.3. Classification of geothermal reservoirs: low, medium and high enthalpy 5
to the relationship in [9]:
H= E + P V (1.1)
As in the case of thermodynamic systems even for geothermal ones it is not possible to know the absolute value of the internal energy of the system but the variation of enthalpy H is measurable. Normalizing (1.1) with respect to the mass of the system (1.2) and expressing the differential form of internal energy based on the first principle of thermodynamics (1.3), the enthalpy per unit mass is obtained in partial derivatives form (1.4) using [10]:
h= e + P
fl (1.2)
dh(s, P ) = T ds +dP
fl (1.3)
ˆh ˆP -- --
T
= T ˆs ˆP -- --
T
+1
fl (1.4)
Introducing the definition of volumetric thermal expansion coefficient at constant pressure (1.5) and from the Maxwell relation (1.6) it can be written as (1.7):
— © ≠1 fl
ˆfl ˆT -- --
P
(1.5) ˆs
ˆP -- --
T
= ˆ(1/fl) T
-- --
P
= ˆ(1) fl2
ˆ(fl) ˆT
-- --
P
= —
fl (1.6)
ˆh ˆP -- --
T
= ≠—T fl +1
fl (1.7)
Knowing that the enthalpy can be written in therms of temperature rather (1.8) and replacing (1.7) in the first part of the equation (1.8)
dh= ˆh ˆT -- --
T
dT ≠ ˆh ˆP -- --
P
dP = cpdT + ˆh ˆP -- --
T
dP = cpdT + (1 ≠ —T)dP
fl (1.8)
Considering (1.8) we can reach an equation form expressed in terms of two inde- pendent variables, the temperature (T) and the pressure (P), to describe a typical geothermal problem. How will be explained in the next chapter, referring to an unit mass in Lagrangian mode can get:
dh= dh dt = flcp
dT
dt + (1 ≠ —T)dP
dt (1.9)
For geothermal domains the gradient of the temperature between the bottom and the top of the domain marks the different systems into geothermal energy of low, medium, and high enthalpy and defines the choice of the correct type of system that will interact with this for a correct exploitation of the resource.
An example is reported in the Table 1.1. that relates the enthalpy of the domain with the resources temperature [11] and for the different typology of soils and temper- ature of the geothermal source proposing various types of application.
Geothermal Classification in function of enthalpy
Enthalpy of Reservoir Soil status Temperature of source Possible uses of the resource Min. and Max.
Temperature source
Very Low Soil with or without water 5¶CÆ T Æ 25¶C Space Heating [12]
Soil with water 10¶CÆ T Æ 25¶C Agriculture [13]
Low [11] 90÷150¶C Thermal water 22¶CÆ T Æ 50¶C Aquaculture [14]
Soil with water TØ 100¶C District heating [15]
Medium [11]90÷225¶C - 150¶CÆ T Æ 150¶C Industrial or Electricity Production [16]
Hight [11] 150÷225¶C - TØ 150¶C Production of Electricity [17]
Table 1.1: Classification of geothermal resources. The enthalpy
Another type of distinction can be used for geothermal systems based on the wells extraction depth. These are the shallow (height of wells < 400 m) [18] and the deep geothermal systems. In shallow geothermal systems different technologies of heat ex- changer are used depending on the typology of the well. These can have a horizontal or vertical design and can be with or without mass extraction, open or closed.
For the shallow types, [19] introduces the double well system, the production well with surface water discharge, the lake system (without well), the horizontal loop, the slinky heat exchanger, the coil heat exchanger, the pound heat exchanger, the anergy pile and the borehole heat exchanger. These systems use the thermal insulation proper- ties of the soils or of water. Figure 1.4 depicts an example of a borehole heat exchange.
The soil, surrounding the pipelines which contains the fluid coming to the heat pump, in the winter works as a heat source and in the as a heat sink thank to its seasonal temperature variation.
Figure 1.4: Example of a very low enthalpy geothermal system
may be saturated or not and ÒT (top-botton) in the order of 100¶C due to thermal magmatic sources.
Of course, the types and the geometries of the domains are innumerable due to the different spatial distribution of the stratigraphy and the geophysical structures that in- fluence its thermo-hydraulic response. The most important characteristics include the permeability of the domain and theirs groundwater flow distribution, the intensity and the type of the heat sources (the boundary conditions). In these, due to the character- istics of the soil (permeability and porosity), the steam pressure succeeds in reaching the surface creating real cavities in the ground, gayser effect. Through the Archimedes principle and due to the difference in density, the water changes its directionality mov- ing from points at higher temperatures to those at lower temperatures. Usually, for the first case (low enthalpy), the exploitation of the resource occurs in the surface of the domain, instead in the second case it is necessary to install extraction wells to capture the warm water. If the fluid has not the sufficient thermal energy for the operation of steam turbines (for electricity production) it is used to air-condition houses or entire parts of the city (district heating). An example of thermal area and its ground water flow (stream function field) is presented in Figure 1.6.
Figure 1.6: Example of groundwater flow in thermal area (stream function field) and related velocity vector
The high enthalpy systems are characterized by a high geothermal gradient that can reach and exceed of 200¶C km≠1. These systems are located in specifics areas of the world, typically near volcanic areas characterized by a high seismic-activity (movement of plates) and they are exploited for the production of electricity by means of steam turbines. A study of the characterization and explotation of the Campi Flegrei area in Naples, Italy, using a wellbore heat extractor is presented in Chapter 5.
1.3. Classification of geothermal reservoirs: low, medium and high enthalpy 9
The typical exploitation of the high enthalpy geothermal domain (an example is presented in Figure 1.7) is carried out using specific wells (extraction wells) that can reach depths of the order of 2-5 km. The extracted hot fluid and steam is processed in the steam turbines to generate electricity and after re-injected in the specific re-injection wells.The exploited area is monitored using control well placed in specific areas of the geothermal district. This type of wells allow the control of the characteristics of the domain such as temperature, fluid pressure, percentage of vapor in the fluid and level of the groundwater. Most geothermal plants, after the generation of electricity, do not re-inject the fluid in the aquifer but use it for heating buildings, public works and industrial productions.
Figure 1.7: Schematic of a high enthalpy geothermal reservoir for elec- tricity production
In recent years, the correct sustainable use of geothermal domains and the reduction of plant construction costs has become essential for developing that renewable energy with almost zero cost. The technological development in the sector, both for high and very low enthalpy, allowed to obtain an increase in the plant yields and the number of installations (as seen in the Figure 1.3). At the same time, the attention of the scientific community and also of the communities that live near the large geothermal installations have expressed concerns about the interaction of mining activities with geophysical and volcanic phenomena of the areas adjacent to the installations. In the final part of this thesis, through complex numerical simulations on geothermal domains of high enthalpy, are studied the effects due to the extraction of heat and how these affect the fields of temperatures and fluid flow.
1.4 Site characteristics
The characterization of a geothermal site is a complex phase in which multi- disciplinary area converge among which (geology, seismic, geophysics, engineering and other) for the individuation of a possible area for the exploitation. The first is the localization of an area with a high geothermal potential. Di Pippo, in his book [21], introduces the correlation that exist into the relative motion of plates, the stress and the high-temperature geothermal regions. When the plates are subjected to tension, it can generate cracking areas and rifting, by cracking in several places leading to down- dropping, and by thinning and trenching or subdution. All these are responsible to tension lead and anomalous geothermal regions that may be conducive to exploitation.
At the same time this can generate numerous earthquakes. For this reasons, usually is possible locate the geothermal phenomena using a seismic map. An example is a NOAA map [22].
Figure 1.8: Collocation of earthquakes, tectonic plate boundaries and geothermal regions, NOAA map [22]
Looking this it is clear how the most important geothermal exploitation occur along the edges of the gigantic Pacific plate, eastern plates, the Cocos and the Nazca plates, the Philippine plate, affecting the countries United States, the central and south Amer- ica Pacific coast area, the south Pacific coast area between New Zealand to Japan and Russia, that have exploitable geothermal resources and 13 of them have geothermal power plants in operation as of mid-2007 [21]. Among the other geothermal sites rel- evant in the world, looking the map are identified, the Alaskan Aleutian Islands and Hawaii (Pacific plate), for the mid-Atlantic ridge, the Iceland and the Azores. Other regions such as the Mediterranean and Himalayan belts and the East African Rift zone also are being exploited for geothermal power. In chapter 5, Solved Problems, the Campana geothermal area, in Italy is studied relating to the Flegrea Area, and which
1.4. Site characteristics 11
includes among the most important, the area of Mount Vesuvius, the famous area of Pompeii and the Island of Ischia. A 3D view is presented in the Figure 1.9.
Figure 1.9: 3D model of Naples, Area Flegrea, Ischia and mount Vesu- vius area
Different scientific research studies have been carried out for this area over the years evaluating the geothermal properties, a detailed work is [23] that describes the geother- mal model of the area. In this the geophysical structure limited by Pliocene-Pleistocene tensional faults is described. The area present a complex volcanic system built up by monogenic volcanoes with explosive activity can be considered as due to shallow depth interaction between water and magmatic masses producing breccias, basesurge and ash flow deposits, tuffs and hydromagmatic tuffs (yellow tuffs). The cross-section with the related geophysical, geological and geothermal functioning scheme of the Flegrea Area is presented in Figure 1.10.
Figure 1.10: Re-view of [24] geophysical, geological and geothermal functioning scheme of the Flegrea Area