Environmental Earth Sciences

, Volume 72, Issue 5, pp 1403–1419 | Cite as

Thermo-optical parameter acquisition and characterization of geologic properties: a 400-m deep BHE in a karstic alpine marble aquifer

  • Clemens LehrEmail author
  • Ingo Sass
Thematic Issue


To dimension a geothermal array, it is necessary to explore the geophysical and geologic qualities of the subsoil. At the following example the project engineering of a prospective geothermal array is shown from the investigation up to the execution planning. For the geothermic investigation a 400 m (1312 ft.) deep drilling was established and equipped with 50 mm (1.97 in.) duplex BHE. With the mounting of the BHE a fiberglass hybrid cable was inserted as a loop parallel to the shanks of the BHE. By means of optical frequency domain reflectometry (OFDR) an enhanced geothermal response test has been executed. Due the high local resolution of the resulting profile of conductivities the geological profile can be differentiated in areas with mainly conductive and areas of convective influenced heat transfer. By knowledge of these both parts and its parameters the incident of groundwater flow on the BHE can be calculated (Peclet number analysis/ Darcy velocity). With the help of the ascertained geophysical and hydraulic rock parameters solid rock, cleavages and karst cavity could be identified. Also the undisturbed ground temperature, the effective thermal conductivity and areas with different geothermal gradients and the groundwater velocity in cleaved and caveated rocks could be determined.


Distributed temperature sensing Inverse modeling Superposition Effective thermal conductivity Groundwater flow 

List of symbols


Thermal diffusivity (m2/s)


Volumetric heat capacity [MJ/(m3 K)]


Gaussian error function


Length of BHE (m)


Exponential integral


Cylinder function after Bessel


Length of pipe (m)


Specific heat input (W/m)


Effective radius of the heat source (m)


Inner radius of pipe (m)


Outer radius of pipe (m)


Radius of cylinder source (m)


Thermal resistivity (K m/W)


Effective thermal resistivity (K m/W)


Mean temperature of the heat exchanger fluid (°C)


Average undisturbed temperature of ground (°C)


Time (s)

x, y, z

Cartesian coordinates


Function of time


Input temperature of heat exchanger fluid (°C)


Output temperature of heat exchanger fluid (°C)


Average undisturbed temperature of ground (°C)


Difference of temperature [K]


Inner temperature of pipe on r 1 (°C)


Outer temperature of pipe on r 2 (°C)


Pi 3.141…


Temperature (°C)


Time-dependent function over radius


Time-dependent functions over x, y, z direction


Euler constant 0.5772…


Thermal Conductivity [W/(mK)]


Effective thermal conductivity [W/(mK)]


Thermal conductivity of a material (i.e., grout, polyethylene) [W/(mK)]


Inclination of temperature curve over logarithmical time scale

\(q_{a }\)

Convective thermal flow (W/m2)


Conductive thermal flow (W/m2)


Density of fluid (kg/m3)


Specific heat capacity of fluid at constant pressure [J/(kg/K)]


Darcy velocity of fluid (m/s)

\(\Delta T\)

Thermal spread (K)

\(\lambda ,\lambda_{\text{cond}}\)

Thermal conductivity of solid [W/(mK)]


Thermal conductivity of fluid [W/(mK)]


Characteristic length (m)


  1. Carslaw HS, Jaeger JC (1959) Conduction of heat in solids, 2nd edn. Oxford University Press, Great BritainGoogle Scholar
  2. Di Sipio E, Galgaro A, Destro E, Teza G, Chies S, Giaretta A, Manzalla A (2014) Subsurface thermal conductivity properties at a regional scale: the Calabria Region case study (southern Italy). Environ Earth Sci (this issue)Google Scholar
  3. Eskilson P (1987) Thermal analysis of heat extraction boreholes. Lund-MPh-87/13. Department of Mathematical Physics, Lund Institute of Technology, SwedenGoogle Scholar
  4. Feldbusch E, Regenspurg S, Banks J, Milsch H, Saadat A (2013) Alteration of fluid properties during the initial operation of a geothermal plant: results from in situ measurements in Gro Schonebeck. Environ Earth Sci 70:3447–3458CrossRefGoogle Scholar
  5. Francke H, Kraume M, Saadat A (2013) Thermal-hydraulic measurements and modelling of the brine circuit in a geothermal well. Environ Earth Sci 70:3481–3495CrossRefGoogle Scholar
  6. Gehlin S (2002) Thermal response test—method development and evaluation. Doctoral Thesis:39. Lund Institute of Technology, SwedenGoogle Scholar
  7. Heidinger G, Dornstädter J, Fabritius A,Welter M, Wahl G, Zurek (2004) EGRT—Enhanced Geothermal Response Test. In: Proceedings 8. Geothermische Fachtagung, 316–323Google Scholar
  8. Hellström G (1991) Ground Heat Storage, Thermal Analysis of Duct Storage Systems, I. Theory. 282 S, Department Mathematical Physics, University of Lund, SwedenGoogle Scholar
  9. Ingersoll LR, Plass HJ (1948) Theory of ground pipe heat source for the heat pump. ASHVE Trans 47:339–348 ChicagoGoogle Scholar
  10. Lord Kelvin (1856) Compendium of the Fourier Mathematics for the conduction of heat in solids, and the mathematically allied physical subjects of diffusion of fluids and transmission of electrical signals through submarine cabels. Q J Math 1Google Scholar
  11. Mogensen P (1983) Fluid to duct wall heat transfer in duct system heat storages. In: Proceedings of the International Conference on Subsurface Heat Storage in Theory and Practice. Swedish Council for Building Research. Stockholm, Sweden, pp 652–657Google Scholar
  12. Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7(1):308–313CrossRefGoogle Scholar
  13. Rogers G, Mayhew Y (1967) Engineering thermodynamics work and heat transfer, 4th edn. Pearson Education Limited, Great BritainGoogle Scholar
  14. Schwartz A, Großwig S, Pfeiffer T (2014) New technologies in hydraulic engineering—the usage of fiber optics. Environ Earth Sci (this issue)Google Scholar
  15. Sanner B et al (2007) Technology, development status, and routine application of Thermal Response Test. In: Proceedings European Geothermal Congress. Unterhaching, GermanyGoogle Scholar
  16. Sass I, Lehr C (2011) Improvements on the Thermal Response Test evaluation applying the cylinder source theory. In: Proceedings Thirty Sixth Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, CaliforniaGoogle Scholar
  17. Signorelli S (2004) Geoscientific Investigations for the use of Shallow Low-Enthalpy Systems. Doctoral Thesis 2004. Swiss Federal Institute of Technology Zurich, SwitzerlandGoogle Scholar
  18. VDI (2001) VDI-Guideline 4640: Thermal use of the underground—ground source heat pump systems. Beuth, BerlinGoogle Scholar
  19. Zschocke A (2005) Correction of non-equilibrated temperature logs and implications for geothermal investigations. J Geophys Eng 2:364–371CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute of Applied GeosciencesTechnische Universität DarmstadtDarmstadtGermany

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