**5. Results and Discussion**

The thermal response test is the most favored way of determining the basic BHE parameters. The effective thermal conductivity *λeff* is the most important value for characterizing a BHE, and it is used for determining its energy efficiency. The effective thermal conductivity is mainly dependent on the thermal conductivity of rocks *λ*, especially when the BHE has been correctly performed. In reality, *λeff* is also dependent on the heat transfer resistivity between the heating agent circulating in the BHE and the rock mass. This heat transfer resistivity accounts for:


An analysis of the experimental and analytical results reveals that, despite a correctly performed TRT, the values of *λeff* are not constant with the time of test. This is caused by the assumed duration of the test. Such differences with respect to the value that was obtained for the full time of the test (100 h) may as great as 16.50%, relative to the traditional method (Table 5), and 9.69% for the new method (Table 7). The greatest percentage difference between the values of *λeff* and *Rb* are underlined in bold in Tables 4–7. The relative change of *Rb* or *λeff* with respect to the full measurement range is calculated in %, relative to the values in the first time interval (*t*<sup>0</sup> to *t*5). Accordingly, the percentage difference for this interval (i.e., the full range of data, *t*<sup>0</sup> to *t*5) is always zero.

The new method is observed to be more accurate and stable in time for calculating the effective thermal conductivity *λeff* in BHEs. However, when analyzing the BHE thermal resistivity *Rb*, larger discrepancies can be observed for relative deviations from the basic value (for the full test duration). A maximum deviation of 1.80% for the traditional method (Table 5) and 9.70% for the new method is observed (Table 7). The greatest differences are observed for the TRT performed at the Laboratory of Geoenergetics, Faculty of Drilling, Oil, and Gas, AGH University of Science and Technology. For TRTs

performed in Zar ˙ ów, the corresponding deviations are much smaller. Therefore, more analyses of TRT data are needed while using the new methodology to assess these discrepancies, and that is the topic of ongoing research by the authors.

Many more analyses of TRT results are needed, along with the corresponding statistical analyses, to choose a better method for the interpretation of TRT results. In practice, there is no ideal TRT. The functional variation of temperature with time has many distortions. Simultaneously with improving TRT interpretations, the TRT measuring procedure also needs improvement. The inflow of material at the outside temperature should be reduced/eliminated, and a reliable automatic system is needed for maintaining a constant heating power when the variable voltages are present in the electrical network. Both of these requirements are being addressed at the Laboratory of Geoenergetics.

The accuracy of the calculation of the effective thermal conductivity coefficient and the thermal resistance has not been extensively examined in this article. That is because the target of this article is to describe the new methodology. Research by the present authors is ongoing to assess the precision of the results that were obtained with the new method, and it is expected to be reported soon.

#### **6. Conclusions**

The thermal response test is the most accurate way of determining parameter values of borehole heat exchangers. The effective thermal conductivity *λeff* and thermal resistivity of borehole *Rb* can be used in the design of an appropriate number of borehole exchangers for a given heating power demand and for a given time duration.

However, when interpreting the thermal response test, there are sometimes problems with the resulting values. That is, the values of thermal conductivity *λeff* and thermal resistivity *Rb* can differ depending on the assumed range of data, especially the time data. Various values of basic parameters are seen to be obtained, even for correctly performed tests, when analyzing various TRT time intervals.

The proposed method of determining basic TRT parameters is based on the BHE thermal resistivity *Rb* equation. This dependence (Equation (9)) is also observed to be a function of effective thermal conductivity *λeff* of the borehole heat exchanger. It is suggested that, a pair of the test results, i.e., effective thermal conductivity *λeff* and BHE thermal resistivity *Rb*, can predict the dependence of resistivity as a function of time, such that the slope coefficient of the regression line that is based on this approach is zero.

It is concluded from the analyses that the proposed new method of determining the values of the basic parameters of a BHE is more accurate and independent of thermal response test duration. The differences that were obtained for various TRT times with the proposed method for *λeff* are lower than with the traditional method. However, larger differences are obtained for *Rb*. Further work to assess the usefulness of this method in the interpretation of TRT data appears to be merited.

**Author Contributions:** Conceptualization, A.S.-S., A.G. and M.A.R.; methodology, A.S.-S.; software, T.S.; validation, A.S.-S. and T.S.; formal analysis, J.K.; investigation, T.S.; resources, A.S.-S. and A.G.; data curation, T.S.; writing, reviewing and editing of manuscript, A.S.-S., T.S. and M.A.R.; visualization, T.S.; supervision, A.S.-S.; project administration, A.S.-S.; funding acquisition, A.S.-S. and T.S.

**Funding:** This research was funded by statutory research programme at the Faculty of Drilling, Oil and Gas, AGH University of Science and Technology in Krakow, Poland, grant number 11.11.190.555.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Nomenclature/Glossary**

