Introduction to the Numerical Modeling of Groundwater and Geothermal Systems ─ Fundamentals of Mass, Energy and Solute Transport in Poroelastic Rocks

This book provides an introduction to the scientific fundamentals of groundwater and geothermal systems. In a simple and didactic manner the different water and energy problems existing in deformable porous rocks are explained as well as the corresponding theories and the mathematical and numerical tools that lead to modeling and solving them. This approach provides the reader with a thorough understanding of the basic physical laws of thermoporoelastic rocks, the partial differential equations representing these laws and the principal numerical methods, which allow finding approximate solutions of the corresponding mathematical models. The book also presents the form in which specific useful models can be generated and solved. The text is introductory in the sense that it explains basic themes of the systems mentioned in three areas: engineering, physics and mathematics. All the laws and equations introduced in this book are formulated carefully based on fundamental physical principles. This way, the reader will understand the key importance of mathematics applied to all the subjects. Simple models are emphasized and solved with numerous examples. For more sophisticated and advanced models the numerical techniques are described and developed carefully. This book will serve as a synoptic compendium of the fundamentals of fluid, solute and heat transport, applicable to all types of subsurface systems, ranging from shallow aquifers down to deep geothermal reservoirs. The book will prove to be a useful textbook to senior undergraduate and graduate students, postgraduates, professional geologists and geophysicists, engineers, mathematicians and others working in the vital areas of groundwater and geothermal resources.

Prof. Dr. Jochen Bundschuh (1960, Germany), finished his Ph.D. on numerical modeling of heat transport in aquifers in Tübingen in 1990. He is working in international academic and technical co-operation in different fields of geothermics, hydrogeology and integrated water resources management and connected disciplines, including the water-related economic, social, health, and political aspects. He spent many years in various different countries like: Paraguay, Argentina, Brazil, Uruguay, Brazil, Mexico, Bolivia, Costa Rica, Honduras, Guatemala, Panama, Pakistan, India, Bangladesh, Middle East, Tunisia and South Africa.
From 2001 to 2008 he worked within the framework of the German governmental cooperation (Integrated Expert Programme of CIM; GTZ/BA) as advisor in mission to Costa Rica at the ICE Instituto Costarricense de Electricidad). In 2005 he was appointed affiliate professor at the Royal Institute of Technology, Stockhom, Sweden. Since June 2009 he is teaching and researching renewable energies, in particular geothermics, at the University of Applied Sciences in Karlsruhe
Prof. Bundschuh is an editor of the book "Geothermal Energy Resources for Developing Countries" (2002), "Natural Arsenic in Groundwater" (2005), principal editor of the 2-volume work: "Central America: Geology, Resources and Hazards" (2007), "Groundwater for Sustainable Development" (2008), Natural Arsenic in the Groundwater of Latin America" (2008). He is co-author of the book "Low Enthalpy Geothermal Resources for Power Generation" (2008) and Series Editor of the book series: "Multiphysics Modeling" and the book series " Arsenic in the Environment", all published by CRC Press/ Balkema - Taylor & Francis group.
Prof. Ph.D. Mario César Suárez Arriaga (Mexico City, 1950) studied Physics and Mathematics at the National Autonomous University of Mexico (UNAM), and Applied Mathematics and Mechanics at the universities of Toulousem III and Paris VI, France (1981). He obtained his PhD in Petroleum & Geothermal Engineering at the Faculty of Engineering-UNAM (2000).
His main area of scientific research is the mathematical modeling of Complex Natural Systems. He worked several years (1982-2000) as a geothermal reservoir engineer in the Comisión Federal de Electricidad (CFE). Presently he works as Professor and Researcher of Applied Mathematics and Mechanics at the Faculty of Sciences of the Michoacan University (UMSNH) in central Mexico.
He was co-author of the book "Stories from a Heated Earth: Our Geothermal Heritage", published by the Geothermal Resources Council adn IGA (1999). He is editor of the book series "Multiphysics Modeling" and volume 1 in the series: "Numerical Modeling of Coupled Phenomena in Science and Engineering", published by CRC Press/Balkema - Taylor & Francis Group.

Table of ContentsDedications, Foreword and acknowledgements1 Introduction1.1 The water problem—The UN vision1.2 The energy problem—Vision of the Intergovernmental Panel of Climate Change1.3 Multiphysics modeling of isothermal groundwater and geothermal systems1.4 Modeling needs in the context of social and economic development1.5 The need to accelerate the use of numerical modeling of isothermal aquifers and geothermal systems
2 Rock and fluid properties2.1 Mechanical and thermal properties of porous rocks2.2 Linear thermoporoelastic rock deformation2.3 Mechanical and thermodynamical water properties
3 Special properties of heterogeneous aquifers3.1 The problem of heterogeneity in aquifers3.2 The concept of multiple porosity in heterogeneous aquifers3.3 The triple porosity-permeability concept in geothermics3.4 Averages of parameters at different interfaces3.5 Averages for systems with two and three components: General models of mixtures3.6 Some applications to field data3.7 Discontinuities of parameters when crossing heterogeneous interfaces3.8 Examples of heterogeneous non-isothermal aquifers—Petrophysical properties in Mexican geothermal fields
4 Fluid flow, heat and solute transport4.1 The conservation of mass for fluids4.2 General model of fluid flow: The Navier-Stokes equations4.3 Darcy’s law: pressure and head4.4 Flow to wells in homogeneous isotropic aquifers4.5 Pumping test fundamentals4.6 Heat transport equations4.7 Flow of mass and energy in two-phase reservoirs4.8 Solute transport equations
5 Principal numerical methods5.1 The finite difference method5.2 Introduction to the finite element method (FEM)5.3 The finite volume method (FVM)5.4 The boundary element method for elliptic problems
6 Procedure of a numerical model elaboration6.1 Introduction6.2 Defining the objectives of the numerical model6.3 Conceptual model6.4 Types of conceptual models6.5 Field data required for constructing the conceptual model6.6 Numerical formulation of the conceptual model6.7 Parameter estimation6.8 Selection of model type and code6.9 Calibration, verification and sensitivity analysis6.10 Performing numerical simulations6.11 How good is the model? Assessing uncertainties6.12 Model misuse and mistakes6.13 Example of model construction—Assessment of the contamination of an aquifer
7 Parameter identification and inverse problems (by Angel Pérez and Longina Castellanos)7.1 Introduction7.2 Ill-posedness of the inverse problem7.3 Linear least-squares (LLS)7.4 Nonlinear least-squares (NLS)7.5 Application examples
8 Groundwater modeling application examples8.1 Periodical extraction of groundwater8.2 Water exchange between an aquifer and a surface water body by leakage8.3 Scenario modeling of multi-layer aquifers and distribution of groundwater ages caused by exploitation8.4 Point source contamination and aquifer remediation8.5 Boron contamination propagation8.6 Annual temperature oscillations in a shallow stratified aquifer
9 Geothermal systems modeling examples9.1 What is geothermal energy?9.2 Transient radial-vertical heat conduction in wells9.3 The Model of Avdonin9.4 The invasion of geothermal brine in oil reservoirs9.5 Modeling submarine geothermal systems9.6 Modeling processes in fractured geothermal systems
APPENDIXESA: Mathematical appendixA.1 Introduction to interpolation techniquesA.2 Interpolation in two and three dimensionsA.3 Elements of tensor analysisA.4 The integral theorem of stokesB: Tabulated thermal conductivitiesNomenclatureReferencesSubject index