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

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## Abstract

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.

## Keywords

Distributed temperature sensing Inverse modeling Superposition Effective thermal conductivity Groundwater flow## List of symbols

- a
Thermal diffusivity (m

^{2}/s)- \(\rho\)
*c*_{p} Volumetric heat capacity [MJ/(m

^{3}K)]- erf(
*x*) Gaussian error function

*H*Length of BHE (m)

- Ei(
*x*) Exponential integral

*I*_{0}(*x*)Cylinder function after Bessel

*l*Length of pipe (m)

- \({\dot{Q}}_{H}\)
Specific heat input (W/m)

*r*Effective radius of the heat source (m)

*r*_{1}Inner radius of pipe (m)

*r*_{2}Outer radius of pipe (m)

*R*Radius of cylinder source (m)

*R*_{B}Thermal resistivity (K m/W)

*R*_{Beff}Effective thermal resistivity (K m/W)

*T*_{f}Mean temperature of the heat exchanger fluid (°C)

*T*_{0}Average undisturbed temperature of ground (°C)

*t*Time (s)

*x*,*y*,*z*Cartesian coordinates

- \(\tau\)
Function of time

- \({\vartheta}_{in}\)
Input temperature of heat exchanger fluid (°C)

- \({\vartheta}_{out}\)
Output temperature of heat exchanger fluid (°C)

- \({\vartheta}_{0}\)
Average undisturbed temperature of ground (°C)

- \(\Delta\vartheta\)
Difference of temperature [K]

- \({\vartheta}_{1}\)
Inner temperature of pipe on

*r*_{1}(°C)- \({\vartheta}_{2}\)
Outer temperature of pipe on

*r*_{2}(°C)- \(\pi\)
Pi 3.141…

- \(\vartheta\)
Temperature (°C)

- \(\varphi\)
Time-dependent function over radius

- \({\zeta},{\psi},{\xi}\)
Time-dependent functions over

*x*,*y*,*z*direction- \(\gamma\)
Euler constant 0.5772…

- \(\lambda\)
Thermal Conductivity [W/(mK)]

- \({\lambda}_{Eff}\)
Effective thermal conductivity [W/(mK)]

- \({\lambda}_{Mat}\)
Thermal conductivity of a material (i.e., grout, polyethylene) [W/(mK)]

- ϕ
Inclination of temperature curve over logarithmical time scale

- \(q_{a }\)
Convective thermal flow (W/m

^{2})- \(q_{c}\)
Conductive thermal flow (W/m

^{2})- \(\rho\)
Density of fluid (kg/m

^{3})- \(c_{p}\)
Specific heat capacity of fluid at constant pressure [J/(kg/K)]

- \(v_{f}\)
Darcy velocity of fluid (m/s)

- \(\Delta T\)
Thermal spread (K)

- \(\lambda ,\lambda_{\text{cond}}\)
Thermal conductivity of solid [W/(mK)]

- \(\lambda_{\text{conv}}\)
Thermal conductivity of fluid [W/(mK)]

- \(l_c\)
Characteristic length (m)

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