A comprehensive work, which compiles and synthesizes the state of the art of the principal fields of numerical modeling of subsurface systems as of fluid flow in saturated groundwater-flow and geothermal systems, including the related solute and heat transport in an authoritative one volume book. Presenting many new and stimulating ideas of possible applications. The book, which covers numerical modeling in an integrated approach, will help to overcome barriers -which yet hinder applications- by presentation of possible applications in theoretical examples and real case studies.

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.

Table of Contents

Dedications, Foreword and acknowledgements

1 Introduction

1.1 The water problem—The UN vision

1.2 The energy problem—Vision of the Intergovernmental Panel of Climate Change

1.3 Multiphysics modeling of isothermal groundwater and geothermal systems

1.4 Modeling needs in the context of social and economic development

1.5 The need to accelerate the use of numerical modeling of isothermal aquifers and geothermal systems

2 Rock and fluid properties

2.1 Mechanical and thermal properties of porous rocks

2.2 Linear thermoporoelastic rock deformation

2.3 Mechanical and thermodynamical water properties

3 Special properties of heterogeneous aquifers

3.1 The problem of heterogeneity in aquifers

3.2 The concept of multiple porosity in heterogeneous aquifers

3.3 The triple porosity-permeability concept in geothermics

3.4 Averages of parameters at different interfaces

3.5 Averages for systems with two and three components: General models of mixtures

3.6 Some applications to field data

3.7 Discontinuities of parameters when crossing heterogeneous interfaces

3.8 Examples of heterogeneous non-isothermal aquifers—Petrophysical properties in Mexican geothermal fields

4 Fluid flow, heat and solute transport

4.1 The conservation of mass for fluids

4.2 General model of fluid flow: The Navier-Stokes equations

4.3 Darcy’s law: pressure and head

4.4 Flow to wells in homogeneous isotropic aquifers

4.5 Pumping test fundamentals

4.6 Heat transport equations

4.7 Flow of mass and energy in two-phase reservoirs

4.8 Solute transport equations

5 Principal numerical methods

5.1 The finite difference method

5.2 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 elaboration

6.1 Introduction

6.2 Defining the objectives of the numerical model

6.3 Conceptual model

6.4 Types of conceptual models

6.5 Field data required for constructing the conceptual model

6.6 Numerical formulation of the conceptual model

6.7 Parameter estimation

6.8 Selection of model type and code

6.9 Calibration, verification and sensitivity analysis

6.10 Performing numerical simulations

6.11 How good is the model? Assessing uncertainties

6.12 Model misuse and mistakes

6.13 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 Introduction

7.2 Ill-posedness of the inverse problem

7.3 Linear least-squares (LLS)

7.4 Nonlinear least-squares (NLS)

7.5 Application examples

8 Groundwater modeling application examples

8.1 Periodical extraction of groundwater

8.2 Water exchange between an aquifer and a surface water body by leakage

8.3 Scenario modeling of multi-layer aquifers and distribution of groundwater ages caused by exploitation

8.4 Point source contamination and aquifer remediation

8.5 Boron contamination propagation

8.6 Annual temperature oscillations in a shallow stratified aquifer

9 Geothermal systems modeling examples

9.1 What is geothermal energy?

9.2 Transient radial-vertical heat conduction in wells

9.3 The Model of Avdonin

9.4 The invasion of geothermal brine in oil reservoirs

9.5 Modeling submarine geothermal systems

9.6 Modeling processes in fractured geothermal systems

APPENDIXES

A: Mathematical appendix

A.1 Introduction to interpolation techniques

A.2 Interpolation in two and three dimensions

A.3 Elements of tensor analysis

A.4 The integral theorem of stokes

B: Tabulated thermal conductivities

Nomenclature

References

Subject index

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.