Method of Averaging the Effective Thermal Conductivity Based on Thermal Response Tests of Borehole Heat Exchangers

Abstract

This work concerns borehole heat exchangers and their testing using apparatus for thermal response tests. In the theoretical part of the article, an equation was derived from the known equation of heat flow, on which the interpretation of the thermal response test was based. The practical part presents the results of several measurements taken in the AGH Laboratory of Geoenergetics. They were aimed at examining the potential heat exchange capacity between the heat carrier and rock mass. Measurement results in the form of graphs are shown in relation to the examined, briefly described wells. Result analysis made it possible to draw conclusions regarding the interpretation of the thermal response test. The method of averaging the measurement results was subjected to further study. The measuring apparatus recorded data at a frequency of one second, however such accuracy was too large to be analyzed efficiently. Therefore, an average of every 1 min, every 10 min, and every 60 min was proposed. The conclusions stemming from the differences in the values of effective thermal conductivity in the borehole heat exchanger, resulting from different data averaging, were described. In the case of three borehole heat exchangers, ground properties were identical. The effective thermal conductivity λeff was shown to depend on various borehole heat exchanger (BHE) designs, heat carrier flow geometry, and grout parameters. It is important to consider the position of the pipes relative to each other. As shown in the charts, the best (the highest) effective thermal conductivity λeff occurred in BHE-1 with a coaxial construction. At the same time, this value was closest to the theoretical value of thermal conductivity of rocks λ, determined on the basis of literature. The standard deviation and the coefficient of variation confirmed that the effective thermal conductivity λeff, calculated for different time intervals, showed little variation in value. The values of effective thermal conductivity λeff for each time interval for the same borehole exchanger were similar in value. The lowest values of effective thermal conductivity λeff most often appeared for analysis with averaging every 60 min, and the highest—for analysis with averaging every 1 min. For safety reasons, when designing (number of BHEs), safer values should be taken for analysis, i.e., lower, averaging every 60 min.

Estimation of Ground Thermal Properties of Shallow Coaxial Borehole Heat Exchanger Using an Improved Parameter Estimation Method

“…Parameter identification method includes two methods, i.e., direct method and parameter estimation method (PEM). The theory of direct method is infinite line source (ILS) model which solves the heat transfer problem of an infinite line source in the ground, and the result of ILS model shows that ground thermal conductivity tends to be proportional to the slope of the linear equation about the mean fluid temperature (normally assumed as the average of inlet and outlet fluid temperatures) and logarithm of time [10]. Therefore, ground thermal conductivity can be calculated by linear fitting of TRT data, besides, the borehole resistance can also be calculated simultaneously [6].…”

Numerical Study on the Thermal Performance of a Single U-Tube Borehole Heat Exchanger Using Nano-Enhanced Phase Change Materials

“…It was concluded that a BHE with oval cross-section pipes has the potential to decrease the installation costs and increase the thermal performance of the BHE. In a thermal response test (TRT) conducted by Sapinska-Sliwa et al [7] for three types of BHEs, for instance, single U-tube, double U-tube, and coaxial BHE, the last configuration was found to be the best one in achieving the effective thermal conductivity of the ground. In another study, carried out experimentally and numerically by Janiszewski et al [8], a single U-tube BHE was used to inject thermal energy into the surroundings.…”