1st Edition

Computational Modeling of Shallow Geothermal Systems

By Rafid Al-Khoury Copyright 2012
    254 Pages
    by CRC Press

    254 Pages
    by CRC Press

    A Step-by-step Guide to Developing Innovative Computational Tools for Shallow Geothermal Systems

    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 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.


    Part I Preliminaries

    1 Introduction
    1.1 Geothermal energy systems
    1.2 Shallow geothermal system
    1.3 Book theme and objective

    2 Heat Transfer
    2.1 Introduction
    2.2 Heat transfer mechanisms
    2.3 Thermal parameters

    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

    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

    5 Thermal Resistance
    5.1 Introduction
    5.2 Fourier’s law vs. Ohm’s law
    5.3 Series and parallel configurations
    5.4 Thermal resistance of a borehole heat exchanger

    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
    6.5 Fourier integral
    6.6 Fourier transform
    6.7 Discrete Fourier transform
    6.8 Fast Fourier transform
    6.9 Numerical examples

    7 Laplace Transforms
    7.1 Introduction
    7.2 Forward Laplace transform
    7.3 Inverse Laplace transform
    7.4 Numerical examples

    8 Commonly used Analytical Models for Ground-Source Heat Pumps
    8.1 Introduction
    8.2 Modeling soil mass
    8.3 Modeling borehole heat exchanger

    9 Spectral Analysis of Shallow Geothermal Systems
    9.1 Introduction
    9.2 Modeling shallow geothermal system
    9.3 Verification of the BHE model
    9.4 Verification of the soil model
    9.5 Computer implementation

    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
    10.4 Element verification
    10.5 Concluding remarks

    Part III Numerical Modeling

    11 Finite Element Methods of Conduction-Convection Problems
    11.1 Introduction
    11.2 Spatial discretization
    11.3 Time discretization

    12 Finite Element Modeling of Shallow Geothermal Systems
    12.1 Introduction
    12.2 Soil finite element
    12.3 Borehole heat exchanger finite element
    12.4 Numerical implementation
    12.5 Verifications and numerical examples


    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.