# On the Influence of Operational and Control Parameters in Thermal Response Testing of Borehole Heat Exchangers

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## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Description of Borehole Heat Exchanger

#### 2.1.1. Hydraulic Components and Sensors

#### 2.1.2. System Control and Data Acquisition

- (i)
- the state of the pump (on or off)
- (ii)
- the type of control for the electric immersion heater: PID or a manual
- (iii)
- the reference for internal PID heating control (heat injection rate in kW) or manual setting (fixed rate of use of the electric immersion heater in percentage)
- (iv)
- the sample period for data acquisition in milliseconds

#### 2.1.3. Setting of a TRT Experiment

#### 2.2. Experiments Description

#### 2.2.1. Raw Data Description

- ${T}_{in}$: temperature at the inlet of the borehole
- ${T}_{out}$: temperature at the outlet of the borehole
- G: water flow
- ${T}_{amb}$: ambient temperature

#### 2.3. Data Processing

#### 2.4. Application of Different Analytic Models to TRT Data

#### 2.4.1. Infinite Line Source Theory

#### 2.4.2. Least Square Approach with FLS and ILS

#### 2.5. Model Adequacy and Long Term Effects

## 3. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

Abbreviations | |

UPV | Universitat Politècnica de València |

HVAC | Heating, ventilation and air conditioning |

TRT | Thermal Response Test |

BHE | Borehole Heat Exchanger |

PID | Proportional, Integral and Derivative |

PWM | Pulse Width Modulation |

ILS | Infinite Line Source Model |

FLS | Finite Line Source Model |

LSQ | Lest squares fitting algorithm |

MSE | Mean Squared Error |

Cheap-GSHPs | Cheap and Efficient Application of reliable Ground Source Heat Exchangers and Pumps |

GEOCOND | Advanced materials and processes to improve performance and cost-efficiency of Shallow Geothermal systems and Underground Thermal Storage |

Nomenclature | |

H | BHE depth (m) |

${r}_{0}$ | temperature observation point distance to the line source (m) |

${r}_{b}$ | BHE radius (m) |

${T}_{amb}$ | Ambient temperature (${}^{\circ}$C) |

${T}_{in}$ | Inlet temperature at te BHE (${}^{\circ}$C) |

${T}_{out}$ | Outlet temperature at te BHE (${}^{\circ}$C) |

${T}_{f,ILS}$ | Mean temperature at the BHE (${}^{\circ}$C) calculated by means of the ILS model |

${T}_{f,FLS}$ | Mean temperature at the BHE (${}^{\circ}$C) calculated by means of the FLS model |

${T}_{0}$ | Undisturbed ground temperature (${}^{\circ}$C) |

G | Water flow (m${}^{3}$ s${}^{-1}$) |

${q}_{z}$ | Injected heat flow per unit length (W m${}^{-1}$) |

${C}_{f}$ | Water volumetric heat capacity (J m${}^{-3}$ k${}^{-1}$) |

$\alpha $ | Ground thermal diffusivity (m${}^{2}$ s${}^{-1}$) |

$\lambda $ | Ground thermal conductivity (W K${}^{-1}$ m${}^{-1}$) |

${R}_{b}$ | Borehole thermal resistance (K m W${}^{-1}$) |

$\gamma $ | Euler’s constant |

$\beta $ | ratio between ${r}_{b}$ and H |

${\overline{\u03f5}}^{2}$ | mean of squared residuals |

## References

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**Figure 1.**Diagram showing: (

**a**) the vertical layout of the borehole, indicating the underground stratigraphy and (

**b**) the top layout with the position and diameter of installed pipes.

**Figure 3.**Time plot of heat injection flow rates obtained in the different TRT experiments: (

**a**) using a fixed amount of energy on the heating element and (

**b**) using a PID to control the injected heat flow rate.

**Figure 4.**Comparing ambient temperature effect: (

**a**) when there are no automatic control on injected power and (

**b**) using a PID to maintain stable the amount of injected heat rate.

**Figure 9.**Graphical representation of measured data once it is transformed using Equation (5).

**Figure 10.**Experimental data against ILS and FLS model prediction for experiments with (

**a**) 3 kW fixed heat rate and (

**b**) 2.5 kW controlled heat rate.

**Figure 12.**Temperatute residuals (in ${}^{\circ}$C) versus time (in days) for: (

**a**) tests with traditional setup and (

**b**) tests with controlled heat injection rate.

**Figure 13.**Experimental data against ILS and FLS model prediction for experiment test_2_25. Using the same three days obtained model for (

**a**) comparing only the first 3 days and (

**b**) comparing 15 days.

Sensor Name | Units | Description | Specification |
---|---|---|---|

${T}_{i{n}_{1}}$ | ${}^{\circ}$C | Temperature at borehole inlet | IFM TA3130 [16] |

${T}_{i{n}_{2}}$ | PT100 Class A | ||

${T}_{ou{t}_{1}}$ | ${}^{\circ}$C | Temperature at borehole outlet | Range: 0–140 ${}^{\circ}$C |

${T}_{ou{t}_{2}}$ | Output: 4–20 mA | ||

${T}_{amb}$ | ${}^{\circ}$C | Ambient temperature | Res < 0.02 ${}^{\circ}$C |

Pressure | Pa | System pressure | OSAKA PP10 [17] |

Range: 0–1000 kPa | |||

Output: 4–20 mA | |||

Linearity: 0.3% | |||

Stability: 0.2% | |||

Flow | m${}^{3}$ h${}^{-1}$ | Water Flow | IFM SM8000 [18] |

Range: 0.01–6.00 m${}^{3}$ h${}^{-1}$ | |||

Output: 4–20 mA | |||

Res < 0.005 m${}^{3}$ h${}^{-1}$ |

**Table 2.**Brief description of included experiments. Column Control indicates what system has been used to control the injected heat rate as described in the above section. Column Reference indicates the power used to operate the electric immersion heater when no control is used or the set-point for PID controller.

Experiment | Start Date | Duration | Control | Heat Injection Rate (W) | ||
---|---|---|---|---|---|---|

(yyyy-mm-dd) | (Days) | Reference | Mean | Standard Deviation | ||

test_0_1 | 2011-09-25 | 10 | None | 1000 | 795 | 39 |

test_0_2 | 2012-02-10 | 3.5 | None | 2000 | 1626 | 51 |

test_0_3 | 2012-03-10 | 7 | None | 3000 | 2405 | 66 |

test_1_1 | 2015-10-21 | 12 | PID | 1000 | 954 | 17 |

test_1_2 | 2016-03-07 | 11 | PID | 2000 | 1982 | 26 |

test_2_15 | 2017-03-07 | 9 | PID | 1500 | 1497 | 24 |

test_2_25 | 2017-04-10 | 31 | PID | 2500 | 2428 | 22 |

**Table 3.**Values of coefficients of Equation (4), thermal parameters and confidence intervals as inferred with the Infinite Line Source Model (ILS) method.

Experiment | a | $\mathbf{\Delta}\mathit{a}$ | $\mathit{\lambda}$ | $\mathbf{\Delta}\mathit{\lambda}$ | b (=R${}_{\mathit{b}}$) | $\mathbf{\Delta}\mathit{b}$ (=$\mathbf{\Delta}{\mathit{R}}_{\mathit{b}})$ |
---|---|---|---|---|---|---|

test_0_1 | 0.0394 | 0.0003 | 2.02 | 0.02 | 0.179 | 0.0012 |

test_0_2 | 0.0422 | 0.0008 | 1.89 | 0.04 | 0.195 | 0.0027 |

test_0_3 | 0.0403 | 0.0005 | 1.97 | 0.02 | 0.187 | 0.0016 |

test_1_1 | 0.0365 | 0.0002 | 2.18 | 0.01 | 0.233 | 0.0007 |

test_1_2 | 0.0397 | 0.0002 | 2.01 | 0.01 | 0.198 | 0.0007 |

test_2_15 | 0.0387 | 0.0002 | 2.06 | 0.01 | 0.193 | 0.0007 |

test_2_25 | 0.0379 | 0.0002 | 2.10 | 0.01 | 0.191 | 0.0007 |

**Table 4.**Thermal parameters inferred with ILS line method and the Lest squares fitting algorithm (LSQ) method for ILS and FLS models.

Experiment | ILS Line | ILS | FLS | |||
---|---|---|---|---|---|---|

$\mathbf{\lambda}$ | ${\mathit{R}}_{\mathit{b}}$ | $\mathbf{\lambda}$ | ${\mathit{R}}_{\mathit{b}}$ | $\mathbf{\lambda}$ | ${\mathit{R}}_{\mathit{b}}$ | |

test_0_1 | 2.02 | 0.179 | 1.93 | 0.173 | 1.95 | 0.173 |

test_0_2 | 1.89 | 0.195 | 1.80 | 0.188 | 1.82 | 0.189 |

test_0_3 | 1.97 | 0.187 | 1.88 | 0.180 | 1.91 | 0.181 |

test_1_1 | 2.18 | 0.233 | 2.08 | 0.227 | 2.11 | 0.227 |

test_1_2 | 2.01 | 0.198 | 1.91 | 0.191 | 1.94 | 0.192 |

test_2_15 | 2.06 | 0.193 | 1.96 | 0.186 | 1.99 | 0.187 |

test_2_25 | 2.10 | 0.191 | 2.00 | 0.185 | 2.03 | 0.186 |

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**MDPI and ACS Style**

Badenes, B.; Mateo Pla, M.Á.; Lemus-Zúñiga, L.G.; Sáiz Mauleón, B.; Urchueguía, J.F.
On the Influence of Operational and Control Parameters in Thermal Response Testing of Borehole Heat Exchangers. *Energies* **2017**, *10*, 1328.
https://doi.org/10.3390/en10091328

**AMA Style**

Badenes B, Mateo Pla MÁ, Lemus-Zúñiga LG, Sáiz Mauleón B, Urchueguía JF.
On the Influence of Operational and Control Parameters in Thermal Response Testing of Borehole Heat Exchangers. *Energies*. 2017; 10(9):1328.
https://doi.org/10.3390/en10091328

**Chicago/Turabian Style**

Badenes, Borja, Miguel Ángel Mateo Pla, Lenin G. Lemus-Zúñiga, Begoña Sáiz Mauleón, and Javier F. Urchueguía.
2017. "On the Influence of Operational and Control Parameters in Thermal Response Testing of Borehole Heat Exchangers" *Energies* 10, no. 9: 1328.
https://doi.org/10.3390/en10091328