# Experimental Hydration Temperature Increase in Borehole Heat Exchangers during Thermal Response Tests for Geothermal Heat Pump Design

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{gr}) and effective borehole thermal resistance (R

_{bhe}) to be estimated from temperature measurements at the BHE top inlet and outlet ports.

_{bhe}, as discussed in several studies [13,14,15,19,20,21]. Zeng et al. [15] in particular obtained a complete set of equations for R

_{bhe}calculation and demonstrated that the U-tube shank spacing and grout thermal conductivity are the prevailing factors in determining the R

_{bhe}.

## 2. Thermal Response Test Theory

_{bhe}).

_{gr}is the ground thermal conductivity and Fo

_{r}is the Fourier number based on the radial distance from the line source, r. In the above expression, the complex Exponential Integral E

_{1}can be accurately approximated by simple series expansions, as discussed, for example, by Fossa [39]. Back to the Mogensen intuition, once the interest is on the fluid temperature and the fluid is circulating inside a BHE pipe which locates some r

_{b}(borehole radius) from the ground medium (where ILS is expected to apply), additional thermal resistance must be added to the ground thermal resistance R

_{gr}:

_{bhe}(after Eskilson definition, [40]). Moreover, one can adopt the second term truncated version of the E

_{1}expansion series, provided that the Fo

_{rb}range of interest is higher than about 10 [38]:

_{gr}estimation:

_{bhe}:

_{gr,∞}is required, and it is usually inferred during the first part of the TRT experiment, when the carrier fluid is circulated without any heat injection or extraction (adiabatic part of the test).

_{bhe}is itself chained with k

_{gr}, and its estimation is possible for any instantaneous fluid temperature value, such as:

_{gr}and R

_{bhe}is strictly related to the knowledge of the undisturbed ground temperature, which in turn is measured though the fluid temperature during the initial adiabatic part of the TRT run, hence provided that any heat source is present at this stage of the experiment.

## 3. Grouting and Hydration Reaction

_{bhe}with respect to the design values, thus worsening the long-term performance of the whole system.

## 4. Experimental Apparatus and Test Sites

^{3}). The sampling frequency has been set to 1 Hz in order to obtain one measurement every 0.1 m approximately.

_{g}

_{r}and the borehole effective resistance R

_{bhe}layer by layer along the BHE depth for proper Fo

_{rb}windows.

#### Test Sites

## 5. Results and Discussion

_{gr}and R

_{bhe}provide estimates of the corresponding quantities at the given depth. Finally, the last row of Table 1 shows the averages of each column.

_{gr}and R

_{bhe}values as estimated with both methods are very similar, and their agreement is within 1%, thus providing a cross validation of the whole experimental procedure.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Symbol | Variable | Unit |

BHE | Borehole Heat Exchanger | - |

TRT | Thermal Response Test | - |

k_{gr} | the effective ground thermal conductivity | W/(m K) |

R_{bhe} | effective borehole thermal resistance | (m K)/W |

Q’ | heat transfer rate per unit length | W/m |

r | radial distance from the line source | M |

r_{b} | borehole radius | M |

Fo | Fourier number | - |

τ | time | S |

T | Temperature | °C |

T_{f,ave} | average fluid temperature | °C |

T_{gr,∞} | undisturbed ground temperature | °C |

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**Figure 3.**Schematics of the test system, including the heating cable and the submersible sensor moving along one leg of the U-pipe.

**Figure 4.**Vertical ground temperature profiles at the FAE-1 pilot borehole heat exchangers (BHE) during the grout hydration period (24 January profile) as compared to one at the end of the chemical reaction, 15 days later.

**Figure 5.**Vertical ground temperature profiles at the FAE-2 pilot BHE during the grout hydration period (24 January profile) as compared to the one at the end of the chemical reaction, 15 days later.

**Figure 6.**Vertical ground temperature profiles at the PIS pilot BHE during the grout hydration period (18 September profile) as compared to the one at the end of the chemical reaction. A “cold zone” appears at both periods.

**Figure 7.**Vertical ground temperature profiles at the TAS-1 pilot BHE during the grout hydration period (5 February profile) as compared to the one at the end of the chemical reaction. A “cold zone” appears at the top BHE.

**Figure 8.**Vertical ground temperature profiles at the ASC-2 BHE during the grout hydration period. A “cold zone” appears in the last 40 m.

**Figure 9.**Vertical ground temperature profiles at the TAS-2 BHE during the grout hydration period. A “cold zone” appears in between 13 and 35 m.

**Figure 10.**Vertical ground temperature profiles at the ASC-1 pilot BHE during the grout hydration period (19 September profile) as compared to the one at the end of the chemical reaction.

**Figure 11.**Distributed Thermal Response Test (TRT) experiment at the ASC site after the complete decay of any hydration effect. Vertical temperature profiles along the BHE depth during a 50 h experiment at a constant heat transfer rate.

**Figure 12.**(

**a**) Estimated conductivity k

_{gr}and (

**b**) thermal resistance R

_{bhe}along the BHE depth as inferred from the ASC-1 measurements. The presence of peak values at the BHE mid depth (circles in figures) can be associated to the presence of groundwater circulation.

**Figure 13.**Depth-averaged temperatures as the function of the logarithm of time. The fitting line is employed for a depth-averaged conductivity estimation.

**Table 1.**A selection of the dataset containing all the measured temperatures in time and space. Column A and B are the Infinite Line Source (ILS) model estimations for the slope and intercept, respectively (Equation 5), as obtained by log-linear regression for each row. Columns k

_{gr}and R

_{bhe}are the estimates for the ground and BHE properties as solutions of Equation (7) applied to each row.

Depth | T at 0 h | T at 3 h | T at 8 h | T at 23 h | T at 50 h | A | B | k_{gr} | R_{bhe} | |
---|---|---|---|---|---|---|---|---|---|---|

1.4 | 14.54 | 14.85 | 15.94 | 16.21 | 16.91 | 0.682 | 8.676 | 2.335 | 0.150 | |

1.5 | 14.54 | 14.85 | 15.94 | 16.21 | 16.91 | 0.722 | 8.194 | 2.206 | 0.169 | |

1.6 | 14.54 | 14.85 | 15.94 | 16.21 | 16.91 | 0.725 | 8.098 | 2.196 | 0.175 | |

1.7 | 14.54 | 14.85 | 15.94 | 16.21 | 16.91 | 0.726 | 8.049 | 2.193 | 0.178 | |

[---] | [---] | [---] | [---] | [---] | [---] | [---] | [---] | [---] | [---] | |

118.7 | 14.47 | 15.45 | 16.17 | 16.81 | 17.06 | 0.587 | 10.089 | 2.713 | 0.096 | |

118.8 | 14.47 | 15.41 | 16.12 | 16.75 | 16.96 | 0.567 | 10.234 | 2.806 | 0.093 | |

118.9 | 14.48 | 15.33 | 16.06 | 16.59 | 16.85 | 0.547 | 10.345 | 2.909 | 0.092 | |

119.0 | 14.47 | 15.28 | 15.93 | 16.51 | 16.56 | 0.480 | 10.926 | 3.316 | 0.076 | |

Average | 16.01 | 16.91 | 17.70 | 18.23 | 16.08 | 0.772 | 8.965 | 2.064 | 0.119 |

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**MDPI and ACS Style**

Minchio, F.; Cesari, G.; Pastore, C.; Fossa, M.
Experimental Hydration Temperature Increase in Borehole Heat Exchangers during Thermal Response Tests for Geothermal Heat Pump Design. *Energies* **2020**, *13*, 3461.
https://doi.org/10.3390/en13133461

**AMA Style**

Minchio F, Cesari G, Pastore C, Fossa M.
Experimental Hydration Temperature Increase in Borehole Heat Exchangers during Thermal Response Tests for Geothermal Heat Pump Design. *Energies*. 2020; 13(13):3461.
https://doi.org/10.3390/en13133461

**Chicago/Turabian Style**

Minchio, Fabio, Gabriele Cesari, Claudio Pastore, and Marco Fossa.
2020. "Experimental Hydration Temperature Increase in Borehole Heat Exchangers during Thermal Response Tests for Geothermal Heat Pump Design" *Energies* 13, no. 13: 3461.
https://doi.org/10.3390/en13133461