Computational modeling of shallow geothermal systems / Rafid Al-Khoury

"A Balkema book."

Includes bibliographical references (pages 221-224) and indexes

Contents Preface part I Preliminaries 1. Introduction 1.1. Geothermal energy systems 1.1.1. Geothermal electricity 1.1.2. Geothermal direct use 1.1.3. Geothermal heat pumps 1.2. Shallow geothermal systems 1.2.1. Ground-source heat pumps 1.2.2. Underground thermal energy storage 1.3. Book theme and objective 2. Heat transfer 2.1. Introduction 2.2. Heat transfer mechanisms 2.2.1. Heat conduction 2.2.2. Heat convection 2.3. Thermal parameters 2.3.1. Thermal conductivity 2.3.2. Density 2.3.3. Specific heat capacity 2.3.4. Thermal diffusivity 2.3.5. Viscosity 2.3.6. Porosity 2.3.7. Reynolds number 2.3.8. Prandtl number 2.3.9. Peclet number 2.3.10. Nusselt number 3. Heat transfer in porous media 3.1. Introduction 3.2. Energy field equation: Formal representation 3.3. Heat flow in a two-phase soil mass: Engineering representation 3.3.1. Local thermal non-equilibrium 3.3.2. Local thermal equilibrium 4. Heat transfer in borehole heat exchangers 4.1. Introduction 4.2. Heat equation of a multiple component system 4.3. Heat equation of a borehole heat exchanger 4.4. Heat equations of some typical borehole heat exchangers 4.4.1. Heat equations of a single U-tube borehole heat exchanger (1U) 4.4.2. Heat equations of a double U-tube borehole heat exchanger (2U) 4.4.3. Heat equations of a coaxial borehole heat exchanger with annular (CXA) 4.4.4. Heat equations of a coaxial borehole heat exchanger with centered inlet (CXC) 5. Thermal resistance 5.1. Introduction 5.2. Fourier's law vs. Ohm's law 5.2.1. Conductive thermal resistance 5.2.2. Convective thermal resistance 5.3. Series and parallel configurations 5.4. Thermal resistance of a borehole heat exchanger 5.4.1. Experimental methods 5.4.2. Analytical and numerical methods 5.4.3. Thermal circuit methods part II Analytical and semi-analytical modeling 6. Eigenfunction expansions and Fourier transforms 6.1. Introduction 6.2. Initial and boundary value problems 6.3. Sturm-Liouville problem 6.4. Fourier series 6.4.1. Fourier trigonometric series 6.4.2. Complex Fourier series 6.4.3. Fourier-Bessel series 6.5. Fourier integral 6.6. Fourier transform 6.7. Discrete Fourier transform 6.8. Fast Fourier transform 6.8.1. Aliasing 6.8.2. Leakage 6.9. Numerical examples 6.9.1. Example 1: Solution of heat equation in a finite domain 6.9.2. Example 2: Solution of heat equation in an infinite domain 6.9.3. Example 3: Solution of heat equation in a semi-infinite domain 6.9.4. Example 4: Solution of heat equation in an infinite domain using Fourier transform 7. Laplace transforms 7.1. Introduction 7.2. Forward Laplace transform 7.2.1. Properties of Laplace transform 7.2.2. Methods of finding Laplace transform 7.3. Inverse Laplace transform 7.3.1. Direct use of tables 7.3.2. Bromwich integral and the calculus of residues 7.3.3. Numerical inversion 7.4. Numerical examples 7.4.1. Example 1: Solution of heat equation in a finite domain 7.4.2. Example 2: Solution of heat equation in an infinite domain 8. Commonly used analytical models for ground-source heat pumps 8.1. Introduction 8.2. Modeling soil mass 8.2.1. Infinite line source model 8.2.2. Infinite cylindrical source model 8.2.3. Finite line source model 8.2.4. Short-time transient response 8.3. Modeling borehole heat exchanger 9. Spectral analysis of shallow geothermal systems 9.1. Introduction 9.2. Modeling shallow geothermal system 9.2.1. Sub-system 1: Borehole heat exchanger 9.2.2. Sub-system 2: Soil mass 9.3. Verification of the BHE model 9.4. Verification of the soil model 9.5. Computer implementation Appendix 9.1 10. Spectral element model for borehole heat exchangers 10.1. Introduction 10.2. Spectral element formulation 10.3. Spectral element formulation for borehole heat exchangers 10.3.1. Two-node element 10.3.2. One-node element 10.4. Element verification 10.5. Concluding remarks part III Numerical modeling 11. Finite element methods for conduction-convection problems 11.1. Introduction 11.2. Spatial discretization 11.2.1. Galrekin finite element method 11.2.2. Upwind finite element method 11.2.3. Numerical example 11.3. Time discretization 11.3.1. Finite difference time integration schemes 11.3.2. Finite element time integration schemes 11.3.3. Numerical example 12. Finite element modeling of shallow geothermal systems 12.1. Introduction 12.2. Soil finite element 12.2.1. Basic heat equation 12.2.2. Governing equations of heat flow in a fully saturated porous medium 12.2.3. Initial and boundary conditions 12.2.4. Finite element discretization 12.3. Borehole heat exchanger finite element 12.3.1. Governing equations of heat flow in a borehole heat exchanger 12.3.2. Initial and boundary conditions 12.3.3. Steady-state formulation 12.3.4. Transient formulation 12.4. Numerical implementation 12.4.1. Sequential scheme 12.4.2. Static condensation scheme 12.5. Verifications and numerical examples References Author Index Subject Index

"Geothermal heat is a viable source of energy and its environmental impact in terms of CO2 emissions is significantly lower than conventional fossil fuels. Shallow geothermal systems are increasingly utilized for heating and cooling of buildings and greenhouses. However, their utilization is inconsistent with the enormous amount of energy available underneath the surface of the earth. Projects of this nature are not getting the public support they deserve because of the uncertainties associated with them, and this can primarily be attributed to the lack of appropriate computational tools necessary to carry out effective designs and analyses. For this energy field to have a better competitive position in the renewable energy market, it is vital that engineers acquire computational tools, which are accurate, versatile and efficient. This book aims at attaining such tools. This book is the first of its kind. It addresses computational modeling of shallow geothermal systems in considerable details, and provides researchers and developers in computational mechanics, geosciences, geology and geothermal engineering with the means to develop computational tools capable of modeling the complicated nature of heat flow in shallow geothermal systems in rather straightforward methodologies. Coupled conduction-convection models for heat flow in borehole heat exchangers and the surrounding soil mass are formulated and solved using analytical, semi-analytical and numerical methods. Background theories, enhanced by numerical examples, necessary for formulating the models and conducting the solutions are thoroughly addressed.The book concentrates on two main aspects: mathematical modeling and computational procedure. In geothermics, both aspects are considerably challenging because of the involved geometry and physical processes. However, they are highly stimulating and inspiring. A good combination of mathematical modeling and computational procedures can greatly reduce the computational efforts. This book thoroughly treats this issue and introduces step-by-step methodologies for developing innovative computational models, which are both rigorous and computationally efficient. The book is structured in three parts: Part I: preliminaries (chapters 1-5); Part II: analytical and semi-analytical modeling (chapters 6-10); and Part III: numerical modeling (chapters 11-12)"--

"Geothermal heat is a renewable source of energy offering a number of advantages over conventional fossil fuel resources, particularly its environmental impact in terms of CO2 emissions is significantly lower. Shallow geothermal energy is considered as one of the alternative energy resources and has been widely utilized for heating of buildings and greenhouses, using borehole heat exchangers (BHE). This book presents innovative computational modeling of shallow geothermal systems consisting of borehole heat exchangers embedded in a soil mass"--

"Geothermal heat is a viable source of energy and its environmental impact in terms of CO2 emissions is significantly lower than conventional fossil fuels. Shallow geothermal systems are increasingly utilized for heating and cooling of buildings and greenhouses. However, their utilization is inconsistent with the enormous amount of energy available underneath the surface of the earth. Projects of this nature are not getting the public support they deserve because of the uncertainties associated with them, and this can primarily be attributed to the lack of appropriate computational tools necessary to carry out effective designs and analyses. For this energy field to have a better competitive position in the renewable energy market, it is vital that engineers acquire computational tools, which are accurate, versatile and efficient. This book aims at attaining such tools. This book is the first of its kind. It addresses computational modeling of shallow geothermal systems in considerable details, and provides researchers and developers in computational mechanics, geosciences, geology and geothermal engineering with the means to develop computational tools capable of modeling the complicated nature of heat flow in shallow geothermal systems in rather straightforward methodologies. Coupled conduction-convection models for heat flow in borehole heat exchangers and the surrounding soil mass are formulated and solved using analytical, semi-analytical and numerical methods. Background theories, enhanced by numerical examples, necessary for formulating the models and conducting the solutions are thoroughly addressed.The book concentrates on two main aspects: mathematical modeling and computational procedure. In geothermics, both aspects are considerably challenging because of the involved geometry and physical processes. However, they are highly stimulating and inspiring. A good combination of mathematical modeling and computational procedures can greatly reduce the computational efforts. This book thoroughly treats this issue and introduces step-by-step methodologies for developing innovative computational models, which are both rigorous and computationally efficient. The book is structured in three parts: Part I: preliminaries (chapters 1-5); Part II: analytical and semi-analytical modeling (chapters 6-10); and Part III: numerical modeling (chapters 11-12)"--

"Geothermal heat is a renewable source of energy offering a number of advantages over conventional fossil fuel resources, particularly its environmental impact in terms of CO2 emissions is significantly lower. Shallow geothermal energy is considered as one of the alternative energy resources and has been widely utilized for heating of buildings and greenhouses, using borehole heat exchangers (BHE). This book presents innovative computational modeling of shallow geothermal systems consisting of borehole heat exchangers embedded in a soil mass"--