1. Applied Geothermics Aachen 0ct 4 2004 Numerical Simulation of a Thermal Response Test (TRT) Experiment R. Wagner Applied Geophysics, Aachen University

2. The thermal power P of borehole Heat Exchangers (BHE) depends on Why run a Thermal Response Test? Circulation Rate [m 3 h -1 ]Thermal Conductivity [W m -1 K -1 ] Thermal Power P [kW] Production Temperature [°C] Circulation rate of BHE fluid Fluid thermal properties Injection and production temperature Rock thermal properties Rock hydraulic properties

3. TRT: Experimental Setup & Theory [Gehlin, 2002]

4. Constraints of The Line Source Approximation Rock thermal capacity can not be calculated independently from data The accuracy significantly depends critically on the length of the test interval No lateral and vertical variation of physical parameters allowed Experimental conditions (in particular Q) must remain constant S. Signorelli, Geoscientific Investigations For The Use of Shallow Low-Enthalpy Systems, Dissertation, Swiss Federal Institute of Switzerland; Zürch, 2004

5. Groenholland BV Test Facility HDPE Concentric Heat Exchanger Length heat exchanger40 m Outer pipe diameter40 mm Wall thickness3.7 mm Inner pipe diameter25 mm Wall thickness2.3 mm HDPE thermal conduct.0.42 W m -1 K -1 Operation Time106.67 h [Witte et al., 2002]

6. TRT Data from Heat Extraction Ground temperature13.75 °C Flow0.73 m 3 h -1 Fluid heat capacity3876 J kg -1 K -1 Fluid thermal conducivity0.502 W m -1 K -1 Fluid Density1026 kg m -3 Power-959.6 W

7. C Brute Force: Numerical Simulation Simulation of BHE Experiment using highly resolved cylindrical FD grid 4940 nodes Cell size 0.75mm … 2.5 m 1.000.000 timesteps  t=0.38 s Courant criterion  t=0.5 ms CPU time  30 h (SUN Enterprise 450) Seeking minimum misfit by variation of  c and

8. R = (0.0028  0.0002) K 2 Data evaluation: temperature residuals Groenholland test facility accuracy Temperature Residual R [K 2 ] Thermal conductivity [W m -1 K -1 ] Thermal capacity  c [MJ m -3 K -1 ]

9. Synthetic Data 2D FD Grid Constant heat extraction  Q = -959,6 W at center node Heat Conduction only Simulation Time 106.67 d Temperature Residual R [K 2 ] Thermal conductivity [W m -1 K -1 ] Thermal capacity  c [MJ m -3 K -1 ]

10. Temperature Residual R [K 2 ] Thermal conductivity [W m -1 K -1 ] Thermal capacity  c [MJ m -3 K -1 ] Synthetic Data 2D FD Grid Varying heat extraction  Q = -959.6 W... +959.6 W at center node Heat Conduction only Simulation Time 106.67 d

11. Conclusion The evaluation of TRT experiments by means of numerical simulation of flow and heat transport yield no unique thermal rock properties Varying heat extraction/injection with time allows to calculate thermal rock properties - Problem: conventional evaluation (line source approximation) can not be applied any more Better forecast: Measurement of thermal rock properties and numerical simulation of BHE Acknowledgments Henk Witte, Groenholland BV Amsterdam