Table of content
Nomenclature...ii
Abstract...v
1. Introduction...1
1.1. The open-loop GSHP system...4
1.2. The closed-loop GSHP system...4
1.3. Near-field...6
1.4. Far-field...8
1.5. Contents of the thesis...9
2. General definitions...12
2.1. Thermal transfer...12
2.1.1. Heat flow rate in a BHE...12
2.1.2. Borehole thermal resistance...16
2.2. Thermo-elasticity...16
2.3. Thermo-poroelasticity upon freezing...17
3. Thermo-hydraulic and mechanical characterization of grout materials...19
3.1. Admixtures...21
3.1.1. Commercial grout materials...21
3.1.2. Homemade admixtures...21
3.2. Laboratory characterization of grout materials...22
3.2.1. Permeability...22
3.2.2. Uni-axial compression strength...22
3.2.3. Thermal conductivity...22
3.2.4. Workability...23
3.3. Laboratory test results...24
3.4. Partial conclusion...28
4. Small-scale BHE characterization...30
4.1. The sandbox experiment...30
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4.2. Analytical solution...33
4.2.1. Analytical predictions...33
4.2.2. Experimental evaluations...36
4.3. Sandbox experiment results...37
4.4. Partial conclusion...43
5. Thermal stresses...44
5.1. Analytical model of thermal stress...46
5.1.1. Axisymmetric thermal stresses in a hollow cylinder...47
5.1.2. Continuous constant heat load...49
5.1.3. Discontinuous heat extraction...50
5.2. Numerical model...52
5.3. Thermal loading...52
5.4. Material parameters...53
5.5. Validation...54
5.6. Hollow cylinder approach for a single U-shaped pipe and coaxial pipe BHE...58
5.6.1. Assumptions...58
5.6.2. Results...60
5.7. Thermal stresses compared to grout strength...62
5.7.1. Different scenarios...62
5.7.2. Compressive and tensile strength of grout material...63
5.7.3. Results...65
5.8. Partial conclusion...68
6. Freezing impact...69
6.1. Permeability of grouted BHE...71
6.1.1. Backfilling materials...73
6.1.2. Results...74
6.2. Freezing resistance of grouted BHE...77
6.2.1. Experimental setup...77
6.2.2. Thermo-mechanical model...79
2
6.2.3. Analytical model for thermal stress...84
6.2.4. Results...87
6.3. Partial conclusion...91
7. Analytical solution for discontinuous heat extraction...93
7.1. Introduction...93
7.2. Single BHE...94
7.3. Multi-BHEs...98
7.4. Validation...99
7.4.1. Numerical model setup...100
7.4.2. Single BHE...102
7.4.3. Multi-BHEs...106
7.5. Sustainability and recovery aspects...108
7.5.1. Single BHE...108
7.5.2. Multi-BHEs field...112
7.6. Partial conclusion...116
8. Analytical solution of continuous heat line source for multilayer ground with anisotropic groundwater flow...118
8.1. Introduction...118
8.2. Analytical model for multilayer ground...119
8.2.1. Finite line source model with anisotropic groundwater flow...119
8.2.2. Multilayer method...120
8.3. Numerical Model...123
8.4. Scenarios...124
8.5. Validation results...125
8.6. Heat extraction optimization in multilayer ground...127
8.6.1. Results...128
8.7. Partial conclusion...130
9. Conclusion...131
Bibliography...136 3
Appendix A (Strain in a thermo-elastic hollow cylinder problem)...145
Appendix B (Particular stress solutions for considered thermo-mechanical hollow cylinder problem)...146
Appendix C (Growing ice radius in a spherical cavity)...148
Appendix D (Particular stress and strain solutions for thermo-poroelastic hollow cylinder problem)...150
Appendix E (Integration of the temperature profile in a hollow cylinder problem)...152
Appendix F (Determination of the integral constant in the thermo-poroelastic hollow cylinder problem)...153
Appendix G (MATLAB interface to use the analytical solution)...155
Overview...155
General rules for setting some parameters...156
The components of main menu...156
Single BHE – Time vs. Temperature...156
Single BHE – Contour map...157
Single BHE – Depth profile...158
Multi – BHEs field – Time vs. Temperature...159
Multi – BHEs field – Contour map...160
Appendix H (Ground composite parameters for multilayer model)...162
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