Computational Modeling of Shallow Geothermal Systems

A Step-by-step Guide to Developing Innovative Computational Tools for Shallow Geothermal SystemsGeothermal 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 addresses computational modeling of shallow geothermal systems in considerable detail, 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 emphasizes two main aspects: mathematical modeling and computational procedures. 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.

Rafid Al-Khoury is a Senior researcher in computational mechanics in the Faculty of Civil Engineering and Geosciences at Delft University of Technology, The Netherlands. His main area of interest is in computational mechanics with emphasis on computational geoenvironment. In particular, he is a developer of analytical, semi-analytical and numerical models for wave propagation in layered systems, multiphase flow and heat and fluid flow in shallow geothermal systems. The main focus of his research work is the development of innovative models and efficient computational procedures capable of simulating physical processes occurring in complicated geometry using minimal computational efforts. Along this line, Dr. Al-Khoury has published several models for different fields of computational mechanics, including wave propagation, parameter identification, fracturing porous media, and geothermics.

Preface
Part I Preliminaries1 Introduction1.1 Geothermal energy systems1.2 Shallow geothermal system1.3 Book theme and objective
2 Heat Transfer2.1 Introduction2.2 Heat transfer mechanisms2.3 Thermal parameters
3 Heat Transfer in Porous Media3.1 Introduction3.2 Energy field equation: formal representation3.3 Heat flow in a two-phase soil mass: engineering representation
4 Heat Transfer in Borehole Heat Exchangers4.1 Introduction4.2 Heat equation of a multiple component system4.3 Heat equation of a borehole heat exchanger4.4 Heat equations of some typical borehole heat exchangers
5 Thermal Resistance5.1 Introduction5.2 Fourier’s law vs. Ohm’s law5.3 Series and parallel configurations5.4 Thermal resistance of a borehole heat exchanger
Part II Analytical and semi-analytical modeling
6 Eigenfunction Expansions and Fourier transforms6.1 Introduction6.2 Initial and boundary value problems6.3 Sturm-Liouville problem6.4 Fourier series6.5 Fourier integral6.6 Fourier transform6.7 Discrete Fourier transform6.8 Fast Fourier transform6.9 Numerical examples
7 Laplace Transforms7.1 Introduction7.2 Forward Laplace transform7.3 Inverse Laplace transform7.4 Numerical examples
8 Commonly used Analytical Models for Ground-Source Heat Pumps8.1 Introduction8.2 Modeling soil mass8.3 Modeling borehole heat exchanger
9 Spectral Analysis of Shallow Geothermal Systems9.1 Introduction9.2 Modeling shallow geothermal system9.3 Verification of the BHE model9.4 Verification of the soil model9.5 Computer implementation
10 Spectral Element Model for Borehole Heat Exchangers10.1 Introduction10.2 Spectral element formulation10.3 Spectral element formulation for borehole heat exchangers10.4 Element verification10.5 Concluding remarks
Part III Numerical Modeling
11 Finite Element Methods of Conduction-Convection Problems11.1 Introduction11.2 Spatial discretization11.3 Time discretization
12 Finite Element Modeling of Shallow Geothermal Systems12.1 Introduction12.2 Soil finite element12.3 Borehole heat exchanger finite element12.4 Numerical implementation12.5 Verifications and numerical examples