Evaluating thermal response tests using parameter estimation for thermal conductivity and thermal capacity

Abstract

Thermal response tests (TRT) record the temperature variation of closed-loop shallow borehole heat exchangers (BHE) due to fluid circulation. The average change of fluid temperature is directly related to the rock thermal conductivity λ around the well. If environmental and experimental conditions satisfy the usual experimental standards, TRT can predict effective ground thermal conductivity within an error of approximately ±10%. This accuracy is generally accepted as sufficient for an appropriate prediction of the geothermal heat yield. However, the line source approach (on which the analysis of the TRT experiment is based) does not allow us to derive thermal capacity independently from thermal conductivity, and the soil thermal capacity ρc is usually assumed constant here. We calculate the response temperature of a synthetic TRT experiment as a reference for a subsequent joint estimation of rock thermal conductivity and thermal capacity. Within a reasonable computing time, a comprehensive parameter estimation is impossible, if coupled fluid flow and heat transport in the BHE tubes are explicitly simulated. Therefore, we substitute the BHE tube by a constant heat source with diffusive heat transport only. Although this simplification limits the application of the method to synthetic TRT data, we perform a systematic study of the method's accuracy to analyse thermal capacity with respect to data noise and test duration. Finding the minimum misfit with respect to the reference experiment, we obtain both thermal conductivity and thermal capacity, i.e. more information on ground thermal properties than the line source theory can provide. The effect of the additional information on the ground thermal capacity is demonstrated by a numerical simulation of a real TRT, where the fluid flow and the heat transport within the BHE tube are explicitly simulated. Nevertheless, thermal capacity is generally variable within ±20% for the same rock type. In our analysis, this uncertainty results in a variation of ±2% of the outlet temperature. © 2005 Nanjing Institute of Geophysical Prospecting.