Edited by
Deutsche Gesellschaft für Geotechnik e.V. vertr. durch den Vorsitzenden Herrn Dr.-Ing. Wolfgang Sondermann Gutenbergstr. 43 45128 Essen Germany |
Deutsche Geologische Gesellschaft – Geologische Vereinigung e.V. vertr. durch den Vorsitzenden Herrn Professor Dr. Jan Behrmann Buchholzer Str. 98 30655 Hannover Germany |
Authors: Sass, I., Brehm, D., Coldewey, W. G., Dietrich, J., Klein, R., Kellner, T., Kirschbaum, B., Lehr, C., Marek, A., Mielke, P., Müller, L., Panteleit, B., Pohl, S., Porada, J., Schiessl, S., Wedewardt, M., Wesche, D.
Translated by Philipp Thrift, Hannover
Cover: Schematic drawings showing the arrangements of the different systems, Graphic: Sass & Mielke 2012
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The use of shallow geothermal energy has increased enormously over the past ten years. As the number of geothermal energy installations has risen, so has the number of technical developments in the field. There have been cases of damage in connection with the construction and operation of geothermal energy systems which have attracted much attention in the media. In particular, the cases of damage that have become public show that drilling to depths of several hundred metres is a technical activity that calls for responsible procedures in the sense of quality-assured design, construction and operation of the systems. Avoiding damage caused by shallow geothermal energy installations is a top priority for sustainable geothermal energy uses, especially when bodies of groundwater have to be protected against adverse effects. The recommendations in this book should be regarded as contributions to the quality-assured realisation of such systems. One of the aims of the Geothermal Energy Study Group at the specialist Hydrogeology Section of the German Geological Society (DGGV) and the Engineering Geology Section of both the German Geotechnical Society (DGGT) and the DGGV is to promote the widespread use of geothermal energy as an environment-friendly energy source while prioritising the protection of bodies of water. The authors as well as the DGGV and the DGGT have conceived these recommendations as advice and not as a set of technical regulations in the sense of a standard. Therefore, the recommendations of the Geothermal Energy Study Group include a number of textbook-like passages and much information on the legislation that affects approvals and permits. At the time of going to print, the preparation of a standard for shallow geothermal energy was not in sight; such a standard is, however, still regarded as essential.
The authors and their assistants in the study group are hydrogeologists, engineering geologists and engineers from design consultants, the construction industry, the building materials industry, authorities and universities. They drew up the recommendations over a number of years and all were well aware of the fact that some of the content could certainly trigger controversy in technical circles.
In order to guarantee the technical quality of the recommendations of the Geothermal Energy Study Group, the content was subjected to a peer review process. Prof. Dr. Ingrid Stober (Freiburg Regional Authority), Prof. Dr. Rolf Bracke (International Geothermal Center, Bochum) and Prof. Dr. Dmitry V. Rudakov (National Mining University, Dnipropetrovsk) undertook this important and demanding task, approaching it from different perspectives. Their remarks and comments were carefully considered in the preparation of this current edition of the recommendations.
Besides the peer review process, the publishers made the recommendations publicly available on the Internet for three months. Anybody who was interested was invited to submit their remarks, comments and suggestions for improvements within those three months. The authors read and evaluated every single contribution received, which resulted in many improvements being made to the text and illustrations. We are very grateful to all who made contributions to the work of the study group in this way.
The authors of the recommendations are as follows:
Spokesman for the study group
Deputy spokesman
Permanent members of the study group
Prof. Dr. Ingo Sass
March 2016
Darmstadt
On behalf of the associations responsible for publishing the recommendations and the members of the DGGV/DGGT Geothermal Energy Study Group, we would like to thank all those dedicated people who contributed to and supported the preparation of this book. We are grateful to the following temporary members of the study group:
The tight schedule of working sessions and voting would not have been possible without the relentless organisation and support of Ms. Simone Ross-Krichbaum at TU Darmstadt. Dipl.-Ing. Sebastian Homuth, MSc, TU Darmstadt, took on the task of proofreading the manuscript, for which we are very thankful. Andreas Hofheinz, assistant at TU Darmstadt, proved to be especially dependable when it came to assembling texts, dealing with layout issues, integrating illustrations and typesetting equations for the study group.
We are also grateful to the boards and managers of the DGGV and DGGT and the members of their specialist sections for actively supporting the work of the Geothermal Energy Study Group.
On behalf of all the members of the study group and the DGGV and DGGT, the associations responsible for publishing the recommendations, we would like to thank Prof. Dr. Ingrid Stober, Freiburg, and Prof. Dr. Rolf Bracke, Bochum, for carrying out the highly demanding and very time-consuming peer review.
Fig. 1.0.1 Geothermal energy production forecast for Germany up to 2020; position as of October 2009
Fig. 2.2.1 Principle of heat conduction in a body of rock
Fig. 2.2.2 Effective thermal conductivity of quartz and water depending on the total porosity
Fig. 2.2.3 Effective thermal conductivity of quartz and air depending on the total porosity
Fig. 2.2.4 Effective thermal conductivity of quartz and ice depending on the total porosity
Fig. 2.2.5 Models for determining the effective thermal conductivity
Fig. 2.2.6 Types of underground water
Fig. 2.2.7 Relationship between thermal conductivity of water and temperature
Fig. 2.2.8 Relationship between specific heat capacity csp of water and temperature at standard pressure
Fig. 2.2.9 Relationship between kinematic viscosity of water and temperature
Fig. 2.2.10 Relationship between relative density of water and temperature
Fig. 2.3.1 Schematic diagram showing how solar and terrestrial heat flows create the solar energy zone, geosolar transition zone and terrestrial zone
Fig. 2.3.2 Annual course of temperature in solar energy and geosolar transition zones using the example of Berlin; city outskirts, 20–30% ground sealing
Fig. 2.3.3 Annual course of temperature in solar energy and geosolar transition zones using the example of Berlin; city centre, >60% ground sealing
Fig. 2.4.1 Climate zones to DIN 4710
Fig. 2.4.2 Heat extraction potential depending on climate zone
Fig. 2.6.1 Scheme of a BHE and the heat-affected area without groundwater flow (a) and with a predominant groundwater flow direction (b)
Fig. 3.0.1 How a heat pump works
Fig. 3.1.1 Schematic drawings showing the arrangements of the different systems
Fig. 3.1.2 Schematic drawing of a typical U-pipe BHE system with connection to horizontal pipework laid in the ground, as is frequently the case – also below buildings
Fig. 3.1.3 Schematic drawing of a U-pipe BHE with connection to horizontal pipework laid in a manhole
Fig. 3.1.4 Schematic drawing of a coaxial BHE with connection to horizontal pipework laid in the ground
Fig. 3.1.5 Schematic drawing of a coaxial BHE with connection to horizontal pipework laid in a manhole
Fig. 3.1.6 Sketch showing the principle of a BHE system for a detached house
Fig. 3.1.7 Sketch showing the principle of a horizontal collector for a detached house
Fig. 3.1.8 Sketch showing the principle of a well system for a detached house
Fig. 3.1.9 Sketch showing the principle of the heat pipe
Fig. 3.1.10 Installing a horizontal collector
Fig. 3.1.11 Installing a Slinky-type trench collector
Fig. 3.1.12 The design principle of the geothermal energy basket
Fig. 3.1.13 Installing a geothermal energy basket
Fig. 3.1.14 Thermal piles beneath a high-rise building
Fig. 3.1.15 Site photograph of and a schematic section through a thermal pile installation integrated into an interlocking bored cast-in-place pile wall
Fig. 3.1.16 Sketch showing the principle of a thermal pile installation
Fig. 3.1.17 Heat exchanger pipes threaded through pile reinforcement
Fig. 3.1.18 Routing the pipes from thermal piles in a ground slab for a high-rise building
Fig. 3.1.19 Horizontal connections between thermal piles and manifold
Fig. 3.2.1 Schematic drawing of a production well with submersible pump in the form of a gravel filter well
Fig. 3.2.2 The principle of a geothermal well installation in unconfined groundwater, shown for heat extraction
Fig. 3.2.3 The principle of a geothermal production and injection well installation in confined groundwater, shown for heat extraction
Fig. 3.2.4 Steam escaping from the ‘New Hope’ gallery in Bad Ems, Germany
Fig. 3.2.5 Water-bearing old mine working
Fig. 3.2.6 Iron precipitation at the point where mine water discharges into this channel
Fig. 3.2.7 Sketch showing the principle behind using geothermal energy in flooded mines when the mine water can escape freely
Fig. 3.2.8 Sketch showing the principle behind using geothermal energy in flooded mines in the case of a deep piezometric surface
Fig. 3.3.1 Numerical simulation of a BTES
Fig. 3.3.2 Situation during construction of the BTES system at Crailsheim, Germany, prior to completing the reinstatement works
Fig. 6.1.1 Drilling rig for pneumatic DTH hammer method
Fig. 6.2.1 Reel carriage with built-in drive and loaded with 400 m of pipe for double U-pipe BHE
Fig. 6.3.1 Geometrical borehole deviation for a drilling rig inclined at 1°, 2° and 3°
Fig. 6.3.2 Checking the verticality of a borehole for a BHE produced using the DTH hammer drilling method
Fig. 6.3.3 Schematic view of drilling without a drill stabiliser
Fig. 6.3.4 Properly selected drill string, wellhead and type of driving for controlled vertical drilling with a small drill string bending radius
Fig. 6.3.5 Schematic view of a drill string with a stabiliser
Fig. 6.3.6 Borehole deviation due to change of rock formation: Owing to the steep angle of the change of competence, the drill bit follows the incompetent stratum
Fig. 6.3.7 Borehole widening and initial wandering of a drilling tool at a change of competence at a shallow angle in the rock formation
Fig. 6.3.8 (a) How a change of competence in the rock formation leads to the creation of a dog-leg in the borehole. (b) Deviation of a borehole due to the drilling tool passing through several competent/incompetent transitions
Fig. 6.5.1 Schematic view of a GRT
Fig. 6.5.2 Compact, mobile GRT unit
Fig. 6.5.3 Chronological evolution of flow and return temperatures plus the mean temperature in the thermal transfer fluid during a GRT
Fig. 6.5.4 Example of the regression for evaluating a GRT result
Fig. 6.5.5 Schematic section through a double U-pipe BHE with associated partial thermal resistances (without dynamic resistances)
Fig. 6.5.6 Diagram of a typical GRT measuring curve and its first-order derivative
Fig. 6.5.7 Example of different conductivities for the rocks surrounding a BHE
Fig. 6.5.8 Comparison of the temperatures based on line and cylinder source theories; calculated with Numericallnt GeoLogik software
Fig. 6.5.9 Measurements taken on a double U-pipe BHE and a cylindrical geothermal energy basket
Fig. 6.5.10 Evaluation of measurements taken on a double U-pipe BHE
Fig. 6.5.11 Evaluation of measurements taken on a double U-pipe BHE
Fig. 6.5.12 Evaluation of measurements taken on a cylindrical geothermal energy basket
Fig. 6.5.13 Evaluation by means of time-based superposition with fluctuating electricity supply during the GRT; calculated with TRT 1.1 GeoLogik Software
Fig. 6.5.14 Sensitivity analysis for the thermal conductivity parameter in a GRT; calculated with TRT 1.1 GeoLogik Software
Fig. 6.5.15 Sensitivity analysis for the volumetric heat capacity parameter in a GRT; calculated with TRT 1.1 GeoLogik Software
Fig. 6.5.16 Sensitivity analysis for the heating output parameter in a GRT; calculated with TRT 1.1 GeoLogik Software
Fig. 6.5.17 Sensitivity analysis for the thermal conductivity parameter in a GRT; calculated with TRT 1.1 GeoLogik Software
Fig. 6.5.18 Resistances for a BHE
Fig. 6.5.19 Installing a coaxial BHE based on glass-fibre/copper cables supplied on a reel
Fig. 6.5.20 EGRT measuring results for a 150 m deep BHE
Fig. 6.5.21 Evaluated EGRT measuring results with well log
Fig. 6.5.22 EGRT measuring results for a project near Hamburg
Fig. 6.5.23 Thermal conductivity—depth profiles of two EGRTs with a local, limited groundwater influence
Fig. 7.1.1 Pressure losses depending on the flow rate for double U-pipe BHEs with 32 × 2.9 mm2 and 40 × 3.7 mm2 pipes. thermal transfer fluid = water @ 4 °C, BHE length = 120 m
Fig. 7.1.2 Pressure losses depending on the BHE length for typical double U-pipe BHEs with thermal transfer fluid = water @ 4 °C, flow rate = 2 m3 h–1 (turbulent flow) and associated power consumption of recirculating pump (assumed degree of efficiency: 25%)
Fig. 7.1.3 Guideline figures for embedding the heat exchanger pipework with examples of grouting pipes (grey) and common borehole diameters
Fig. 7.1.4 Examples of BHE bottom end caps
Fig. 7.1.5 Weight of water-filled BHE pipes depending on length of heat exchanger and PE pipe material
Fig. 7.1.6 Uplift force acting on the BHE pipes depending on suspension density and borehole depth
Fig. 7.1.7 Residual uplift depending on length of water-filled BHE pipes for various suspension densities
Fig. 7.1.8 Additional weight necessary depending on length of water-filled PE-100 double U-pipe (32 × 2.9 mm2) BHE for various suspension densities
Fig. 7.1.9 Development of shear strength for a standard backfill material at 10 °C ground temperature
Fig. 7.1.10 Carrying out a laboratory vane shear test on a backfill material that has not yet reached a firm consistency
Fig. 7.1.11 Development of uniaxial cylinder compressive strength for a standard backfill material at 10 °C ground temperature
Fig. 7.1.12 Mud balance
Fig. 7.1.13 Marsh cone
Fig. 7.1.14 Field hydrometer for determining density
Fig. 7.1.15 Imperfections due to areas with different densities
Fig. 7.1.16 Gaps around the pipes
Fig. 7.1.17 Gaps at the side of the borehole
Fig. 7.1.18 Borehole thermal resistance depending on thermal conductivity of backfill material
Fig. 7.1.19 Schematic view of cracking due to alternating freeze-thaw cycles
Fig. 7.1.20 Loss of mass of backfill materials after 10 freeze-thaw cycles
Fig. 7.1.21 Backfill materials with inadequate freeze-thaw resistance after 2–5 freeze-thaw cycles
Fig. 7.1.22 Backfill materials with high freeze-thaw resistance after 10 or more freeze-thaw cycles
Fig. 7.1.23 Course of temperature during a freeze-thaw cycle
Fig. 7.1.24 Water permeability cell for freeze-thaw tests
Fig. 7.1.25 Schematic view of test setup for freeze-thaw cycles
Fig. 7.1.26 Cracks in a test specimen with low freeze-thaw resistance after one freeze-thaw cycle
Fig. 7.1.27 Test specimen made from a material with high freeze-thaw resistance after six freeze-thaw cycles
Fig. 7.1.28 Example of a BHE installed in confined groundwater
Fig. 7.1.29 Example of a BHE installed beyond multi-layer groundwater system
Fig. 7.1.30 Example of a BHE installed in an aquifer in consolidated rock, where the entire weathered zone and the groundwater fluctuation zone must be sealed off
Fig. 7.1.31 Example of a BHE installed in a karst aquifer
Fig. 7.1.32 Example of a BHE installed in a perched body of groundwater in the strata above an aquifer
Fig. 7.1.33 Example of a BHE installed in contaminated ground
Fig. 7.1.34 Successful flow test on a >350 m deep BHE
Fig. 7.1.35 Proof of entrapped air in a 400 m deep BHE by means of a flow test
Fig. 7.1.36 Diagram comparing calculated and measured pressure losses in a BHE array
Fig. 7.1.37 Flow diagram for one BHE with d = 25 mm per circuit for various lengths and water (15 °C)
Fig. 7.1.38 Flow diagram for one BHE with d = 32 mm per circuit for various lengths and water (15 °C)
Fig. 7.1.39 Flow diagram for one BHE with d = 40 mm per circuit for various lengths and water (15 °C)
Fig. 7.1.40 Pressure test; diagram to SIA 384/6
Fig. 7.1.41 Manifold for six BHEs with microbubble air separator
Fig. 7.1.42 Pipes laid separately on a bed of sand for protection
Fig. 7.1.43 Checking the density of a thermal transfer fluid with an areometer and refractometer
Fig. 7.2.1 Influence of pipe spacing on energy efficiency
Fig. 7.2.2 Collector-based annual costs for optimised flow/return temperature difference and optimised pipe run length and 100 m pipe run length
Fig. 8.1.1 Drilling into an artesian well
Fig. 8.1.2 Definition of boundary flow line
Fig. 8.1.3 Determining the minimum distance between two wells
Fig. 8.1.4 Graphic determination of the critical spacing between a pair of production and injection wells for different inflow angles
Fig. 8.1.5 Net thermal capacity depending on circulation flow rate and flow/return temperature difference
Fig. 8.1.6 Simulated hydrothermal interference between three competing geothermal well installations
Fig. 8.1.7 Iron hydroxide deposition
Fig. 8.1.8 Incrustation
Fig. 8.1.9 Scaling
Fig. 8.1.10 Three-dimensional FEM of case study: groundwater flow situation during heating
Fig. 8.1.11 Three-dimensional FEM of case study: groundwater flow situation during cooling
Fig. 8.1.12 Hydro-isohypse and isotherm map following the eighth heating season of the case study
Fig. 8.1.13 Hydro-isohypse and isotherm map following the ninth cooling season of the case study
Fig. 9.1.1 The 5-M risks and the principles regarding accountability based on the 5-M method developed by Prof. Englert
Fig. 9.1.2 Methods (abridged) for influencing the drilling procedure
Fig. 9.3.1 A connection between aquifers caused by a BHE and the ensuing potential hazards: (a) leakage between covered aquifer and aquifer near the surface, (b) uncontrolled flow from a confined aquifer due to perforation of the covering strata, (c) creation of a path for contamination due to a defective annular seal
Fig. 9.5.1 BHE pipes becoming wedged in an oversized borehole
Fig. 9.5.2 Installation difficulties due to the use of unsuitable spacers
Fig. 9.5.3 Installation risks in brittle rock formations
Table 2.1 Heat capacity Ca (Ws · K−1) of non-frozen soils.
Table 2.2 Thermal conductivity (W · m−1 · K−1) of non-frozen soils.
Table 2.3 Heat capacity Ca (Ws · K−1) of frozen soils.
Table 2.4 Thermal conductivity λ (W · m−1 · K−1) of frozen soils.
Table 2.5 Typical thermal conductivity values for various rocks.
Table 2.6 The 15 climate zones in Germany.
Table 5.1 Planning tools and numerical simulation models for designing geothermal energy systems.
Table 6.1 Overview of drilling methods.
Table 6.2 Installation aids for continuous pipes for BHEs.
Table 6.3 Simplified geological conditions and the associated design valuesa for the sample calculation.
Table 6.4 Variation in BHE depth with BHEs in an open rectangle.
Table 6.5 Geological risk features and preparatory measures with technical countermeasures to be carried out during the construction phase (drilling, installation of special pipework, backfilling).
Table 7.1 Backfill materials for BHEs: material parameters and requirements.
Table 7.2 Limit values for exposure classes for water aggressive to concrete according to DIN EN 206.
Table 7.3 Examples of pipes and their volumes.
Table 7.4 Permissible amounts of drained water per metre of BHE according to SN EN 805, which may not be exceeded for the pressure drop.
Table 7.5 Comparison of a number of physico-chemical parameters of monoethylene glycol and monopropylene glycol.
Table 8.1 Chronological workflow for iterative well design.
Table 8.2 Hydrochemistry and well capacity limitations.
Table 8.3 Typical inorganic compounds involved in fouling and scaling phenomena in wells.
Table 8.4 Analytics for investigating a body of groundwater.
Table 8.5 Free analytical and numerical calculation software for hydrochemical issues.
Table 9.1 The occupational hazards faced by a drilling contractor and the associated safeguards.
The members of the Geothermal Energy Study Group, organised under the auspices of the specialist Hydrogeology (FH-DGGV) and Engineering Geology (FI-DGGV/DGGT) sections of the German Geological Society (DGGV) and the German Geotechnical Society (DGGT), are pleased that you are interested in the recommendations contained in Shallow Geothermal Systems – Recommendations on Design, Construction, Operation and Monitoring. These recommendations represent the results of the ongoing work of the Geothermal Energy Study Group (DGGT Working Group 4.11). The members of the study group are experts drawn from all areas involved with geothermal energy: industry, authorities, consulting, polytechnics and universities.
The publication of this book of recommendations is one of the main tasks of the study group. The recommendations are initially limited to shallow geothermal energy, but the intention is to consider aspects of deep geothermal energy as well. Furthermore, the recommendations are intended to form the technical foundation for basic and further training events aimed at the personnel of drilling contractors and based on standard DIN EN ISO 22475-1: ‘Qualification in drilling boreholes for geothermal purposes and installing closed heat transfer systems (borehole heat exchangers)’ (DGGT/DGGV, 2010).
The study group holds regular working sessions – about four to six times a year. One of the main tasks of the study group is the publication of advice and recommendations for the members of the specialist sections at the DGGV/DGGT and DGGV as well as others who are concerned with geothermal energy issues. The recommendations consider, in particular, the underground parts of the different geothermal energy systems. The most important aspects of the geothermal use of the ground are touched upon, although the focus is clearly on the most frequent types of application – borehole heat exchangers and well systems. Many special methods, techniques or combinations of methods are available on the market. The fact that those are not yet discussed in detail in these recommendations in no way implies that, for example, the various specialities represent ineffective or less suitable systems; it was merely decided to limit the recommendations to the most common systems in order not to exceed the scope of this book.
One specific aim of the recommendations is the quality-assured design, construction, operation and monitoring of shallow geothermal energy installations. The recommendations are intended to help guarantee the protection of bodies of groundwater without obstructing the further spread of heating and cooling systems based on geothermal energy. Avoiding damage to geothermal energy installations and damage caused by the construction and operation of such systems is central to the issues discussed. In the light of current projects, the book also includes a chapter on dealing with potential risks.
The use of shallow geothermal energy represents a significant, environment-friendly and also safe way of reducing the primary energy consumption of our society. Some 50–60% of the total energy consumption of the industrialised nations of Central Europe can be attributed to the operation of buildings. With virtually no restrictions on location, no direct emissions, the ability to cover the base load and economical operation, this is where geothermal energy can play a role.
Symbol | Definition | Common unit |
A | Area | m2 |
Af | net filter area | m2 |
ac | dimensionless critical well spacing | 1 |
bwi | capture zone width | m |
Ca | heat capacity of an area | W·s·K−1 |
Cp | heat capacity at constant pressure (isobar) | W·s·K−1 |
CV | heat capacity at constant volume (isochor) | W·s·K−1 |
cmp | molar heat capacity at constant pressure (isobar) | W·s·mol−1·K−1 |
cmv | molar heat capacity at constant volume (isochor) | W·s·mol−1·K−1 |
csp | specific heat capacity | W·s·kg−1·K−1 |
cspp | specific heat capacity at constant pressure (= Cp/m) | W·s·kg−1·K−1 |
cspv | specific heat capacity at constant volume (= CV/m) | W·s·kg−1·K−1 |
d | diameter | m |
das | diameter of annular space | m |
db | borehole diameter | m |
dfa | filter mesh aperture | m |
di | inside diameter (i.d.) | m |
do | outside diameter (o.d.) | m |
dpa | particle size | m |
dpu | pump diameter | m |
dspa | diameter of BHE pipework with spacers | m |
dw | well pipe diameter | m |
Ei | exponential integral | 1 |
F | force | N |
g | local gravitational acceleration | m·s−2 |
haq | thickness of aquifera) | m |
haqo | aquifer overburden | m |
hgws | thickness of groundwater-bearing stratum | m |
I | hydraulic gradient (potential gradient) | 1 |
iz | depth increment | m |
K | intrinsic permeability | m2 |
kf | hydraulic conductivity | m·s−1 |
kfr | hydraulic conductivity of rock formation | m·s−1 |
l | characteristic length, travel distance | m |
lb | borehole depth | m |
lbf | characteristic length of body in flow | m |
lf | filter length | m |
lhe | length of productive heat exchanger | m |
lz | vertical depth below ground level | m |
m | mass | kg |
neff | voids ratio effective for flow | 100% = 1 |
nfl | proportion of voids filled with fluid | 100% = 1 |
ntot | total porosity | 100% = 1 |
p | pressure | Pa = N·m−2 |
p | density | kg·m−3 |
Q | quantity of heat | W·s |
heat flow | W | |
annual heating energy requirement | kWh·a−1 | |
qsp | specific heat flux | W·m−2 |
qv | volumetric heat flux | W·m−3 |
r | measuring distance | m |
r | distance of observation point from line source as mid-point | m |
Rb | borehole thermal resistance | k·W−1 |
Rbeff | effective borehole thermal resistance | k·W−1 |
Rc | thermal resistance of individual compartments | k·W−1 |
rdd | radius of influence of groundwater drawdown | m |
Rs | thermal resistance of skin zone | k·W−1 |
Rth | thermal resistance | k·W−1 |
Rtr | thermal transfer resistance | k·W−1 |
Rλ | thermal resistance | k·W−1 |
RaD | Darcy-modified Rayleigh number | 1 |
RaDcrit | critical Darcy-modified Rayleigh number | 1 |
rb | borehole radius | m |
rs | radius of skin zone | m |
Sed | extent of damage | currency |
Spd | probability of damage occurring | 100% = 1 |
Srd | risk of damage | currency |
Tstd | standardized time | s |
t | time | s |
tmin | minimum time | s |
T0 | critical soil temperature unaffected by air temperature | K |
Tabs | absolute temperature | K |
Tbo | temperature of a body | K |
Tcu | temperature in area unaffected by convection | K |
Tf | temperature of the fluid | K |
Tfin | final temperature (equilibrium temperature) | K |
Tm | mean fluid temperature | K, °C |
Tr | temperature of rock formation | K |
U | integration variable | 1 |
V | volume | m3 |
flow rate | m3·s−1 | |
capacity of one well | m3·s−1 | |
flow rate towards a well | m3·s−1 | |
vav | average linear groundwater velocity | m·s−1 |
v | kinematic viscosity | m2·s−1 |
vcrit | critical flow velocity | m·s−1 |
vD | Darcy velocity | m·s−1 |
vDu | Darcy velocity of unaffected groundwater | m·s−1 |
vfl | flow velocity | m·s−1 |
W | work, energy | W·s |
w | degree of water saturation | 100% = 1 |
xfl | flow distance (leakage flow) | m |
x, y, z | position coordinates | m |
α | thermal diffusivity | m2·s−1 |
αbv | angle of borehole deviation from vertical | ° |
αeff | effective thermal diffusivity | m2·s−1 |
αfl | angle of flow | ° |
βa | seasonal performance factor (SPF) | 1 |
γ | Euler–Mascheroni constant (0.57722) | 1 |
γlin | coefficient of linear thermal expansion | K−1 |
γth | coefficient of volumetric thermal expansion | K−1 |
ΔQ | change in quantity of heat | W·s |
ΔT | temperature difference (absolute temperature) | K |
ΔTi | temperature difference between inflow water and natural groundwater (absolute temperature) | K |
ΔTr | temperature gradient in undisturbed rock formation | K |
ΔTz | vertical temperature gradient | K·m−1 |
Δz | deviation from vertical borehole axis | m−1 |
change in kinematic viscosity, position- and time-dependent temperature change | 1 | |
δ | standard deviation | 1 |
ɛ | coefficient of performance (COP) | 1 |
ζ | primary energy ratio (PER) | 1 |
ζa | annual heating energy ratio | 1 |
η | dynamic viscosity | Pa·s |
θ | temperature gradient | K·m−1 |
ϑ | Celsius temperature | °C |
κ | thermal transmittance (U-value) | W·m−2·K−1 |
λ | thermal conductivity | W·m−1·K−1 |
λdr | thermal conductivity of a dry soil | W·m−1·K−1 |
λeff | effective thermal conductivity | W·m−1·K−1 |
λmax | maximum effective thermal conductivity | W·m−1·K−1 |
λmin | minimum effective thermal conductivity | W·m−1·K−1 |
λsat | thermal conductivity of a saturated soil | W·m−1·K−1 |
λsbo | thermal conductivity of a solid body | W·m−1·K−1 |
λvo | thermal conductivity of the voids | W·m−1·K−1 |
vcrit | critical viscosity | m2·s−1 |
vfl | kinematic viscosity of a fluid | m2·s−1 |
slope of regression line for GRT measurements | 1 | |
ϕ | slope of regression line for straight line method for GRT assessment | 1 |
ξ, ζ, Ψ | direction-dependent temperature function | 1 |
a) see Glossary. |