# Thermal Response Testing Results of Different Types of Borehole Heat Exchangers: An Analysis and Comparison of Interpretation Methods

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## Abstract

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## 1. Introduction

^{3}K)]. Preliminary measurements of ground thermal conductivity can be obtained from lithology information available for the installation site and from data reported in the literature. This approach, which may prove quite inaccurate, should be used only when the borehole field simply consists of a few BHEs. When the size of the plant-system increases, knowledge of precise ground thermal properties is important to avoid under- or over-sizing the total borehole length which could cause a fall in energy efficiency over the years in the former case and high installation costs in the latter one.

## 2. Methods

#### 2.1. Test Site

^{2}, the Po Valley is the largest alluvial plain in Western Europe. Alluvial plains are relatively flat areas composed of alluvium sediments; the rivers, which transport water and sediments from higher to lower grounds, eventually reach the sea. During floods coarse-grained sediment is deposited close to streams and fine-grained sediment may be deposited at greater distances. The alternation of coarse (gravel and sand) and fine-grained (silt and clay) sediment materials which form sand dikes or sills with a predominantly horizontal development is characteristic of alluvial deposits. They can thus be described as a dominantly layered structure, and the thermal and hydrogeological properties of these unconsolidated materials show a horizontal versus a vertical anisotropy. The ground heat exchangers that were studied here had been installed in a Late Pleistocenic and Holocenic sandy and clay alluvial sequence. The seven types of BHEs situated in the test area are arranged as illustrated in Figure 1 and they are listed in Table 1.

#### 2.2. The Thermal Response Test

- the outside air temperature;
- the inlet and outlet fluid temperature to the borehole;
- the volumetric fluid flow rate;
- the electric power absorbed by the electrical resistances.

#### 2.3. Thermal Response Test Analysis

- the infinite line source model (ILSM);
- the infinite cylinder source model (ICSM);
- the inverse numerical approach.

^{3}K) considering the lithology data scoring.

#### 2.3.1. The Infinite Line Source Model

_{b}. Finally, the mean fluid temperature T

_{fm}within the BHE can be calculated according to the following relationship:

^{2}):

^{2}) > 5 the error of the approximation of Equation (3) is within 10%. Equation (4) represents the common interpretation of the infinite line source model used by technicians to evaluate the equivalent ground thermal conductivity by means of TRT measurements; here this approach is called the simplified infinite line source model (S-ILSM). In this case, the mean temperature of the inlet and outlet heat-carrier fluid measured at the top of the borehole heat exchanger is plotted against the natural logarithm of time, obtaining a linear relation whose slope k is linked to the equivalent ground thermal conductivity (λ

_{eq}) by means of the following equation:

_{eq}) was also evaluated using the complete infinite line source model (i.e., Equation (2)) (here called ILSM) which was implemented by Matlab [25]; the λ

_{eq}value was calculated minimizing the root mean square error (RMSE) (Equation (6)) between the experimental mean fluid temperature (T

_{m,TRT}) and the corresponding value calculated (T

_{m,calc}) using the analytical model. This approach was also used for the other models presented in the following sections.

#### 2.3.2. The Infinite Cylinder Source Model

_{0}, J

_{1}, Y

_{0}, and Y

_{1}are the Bessel functions of the first and second kind.

_{b}:

_{eq}) was evaluated comparing the analytical result and the measured value of the mean fluid temperature using the same procedure (Equation (6)) described above for the infinite line source model.

#### 2.3.3. The Inverse Numerical Approach

_{g}) was found at the extreme opposite side, at the highest depth, as a boundary condition. CaRM calculates the temperature distribution within the ground, the grouting material and the heat-carrier fluid as a function of position and time; the heat flow can then be computed based on the relationship between the heat flow and the gradient temperature. Details on the model are outlined in [26].

_{g}), the location’s climatic parameters, and the current time. The undisturbed ground temperature (T

_{g}) was set to the result from the TRT measurements conducted on the longest borehole (Borehole A) that was equal to approximately 15 °C and applied 30 m beneath the lower end of the borehole heat exchanger.

_{ppA}and R

_{ppB}) of the double U-tube heat exchanger and between the pipes and the bore wall (R

_{p0}) (Figure 3c) were instead calculated using a commercial software based on the finite element method [19] and then used as input for CaRM. These values are outlined in Table 6.

- The ground zones were divided into vertical sub-regions each of which with a thickness Δz(j) equal to 0.25 m;
- Each vertical sub-region of the borehole zone was divided into 20 annular regions from the borehole axis to the maximum radius (r
_{max}) which was equal to 10 m.

- absorptance (a): 0.7;
- emittance (ε): 0.9;
- specific convection thermal resistance (R
_{ext}): 0.04 (m^{2}K)/W.

## 3. Results and Discussion

_{eq}) which resulted equal to approximately 1.49 W/(m K) at a depth of 96 m. This value was lower than that (i.e., 1.82 W/(m K)) calculated using information obtained from the data sheets of the drilling operations and values outlined by the standard VDI 4640 [23]. The uncertainty analysis of the TRT measurements involved a global error of the equivalent thermal conductivity of approximately ±0.15 W/(m K). The fluid volume within that BHE was approximately 286 L; the effect of the thermal capacity of the heat-carrier fluid can be seen in the first section where the mean fluid temperature profile is plotted (Figure 4b); it initially fell and then started to rise. As can be seen, the greatest difference between the analytical results and the measured values was found during the first six hours of testing; test results were, instead, nearly equivalent over the long-term. The results of CaRM are in agreement also with the short-term experimental values since the model takes into consideration the borehole thermal capacity.

^{−4}m

^{3}/s.

_{b}coefficient was approximately 3.7, 2.4, 2.6 and 3.2 W/(m K) for Borehole C, F, G and H, respectively.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

a | Thermal diffusivity (m^{2}/s), surface absorptance (-) |

C | Volume heat capacity (J/K) |

D | Diameter (m) |

h_{ext} | Convection heat transfer coefficient at ground level (W/(m^{2} K)) |

I | Incident solar radiation (W/(m^{2}) |

i | Ground discretization index in radial direction |

j | Ground discretization index in vertical direction |

k | Slope of the curve |

L | Length (m) |

L_{bore} | Borehole length (m) |

n | Number of the steps (-) |

P | Power (W) |

q′ | Heat rate per unit length (W/m) |

r | Radius (m) |

r_{max} | Radius from axis borehole beyond which the undisturbed ground is considered (m) |

R | Thermal resistance (K/W) |

R_{b} | Borehole thermal resistance ((m K)/W) |

R_{ext} | Convection thermal resistance at ground level per unit area ((m^{2} K)/W) |

R_{p}_{0} | Thermal resistance between the pipe and borehole wall ((m K)/W) |

R_{ppA} | Thermal resistance between adjacent pipes ((m K)/W) |

R_{ppB} | Thermal resistance between the opposite pipes ((m K)/W) |

T | Temperature (K) |

T_{ext} | External air temperature (K) |

T_{g} | Undisturbed ground temperature (K) |

T_{sky} | Sky temperature (K) |

U | Global heat transfer coefficient (W/(m K)) |

## Greek Symbols

β | Integration variable (-) |

ε | Surface emittance (-) |

λ | Thermal conductivity (W/(m K)) |

γ | Euler’s constant |

τ | Time (s) |

∆τ | Discretization time step (s) |

∆z | Length of control volume in vertical direction (m) |

## Subscripts

b | Borehole, borehole zone |

d | Deep zone |

calc | Calculated |

eq | Equivalent |

el | Electrical |

f | Fluid |

g | Ground |

m | Mean |

r | Radial direction |

s | Surface zone |

z | Depth direction |

## Abbreviations

AISI | American Iron and Steel Institute |

HDPE | High density polyethylene |

ICSM | Infinite cylinder source model |

ILSM | Infinite line source model |

PVC | Polyvinyl chloride |

RMSE | Root mean square error |

S-ILSM | Simplified infinite line source model |

TRT | Thermal response test |

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**Figure 3.**The CaRM modelling approach: (

**a**) overview; (

**b**) ground; (

**c**) double U-tube; (

**d**) coaxial pipes; (

**e**) helical shaped pipe.

**Figure 4.**Thermal response test of the Borehole A which was 96 m long: (

**a**) Test measurements; (

**b**) Analysis with analytical and numerical models.

**Figure 5.**Thermal response test of Boreholes C, F, G and H which were all 50 m long: (

**a**,

**c**,

**e**,

**g**) Test measurements of Boreholes C, F, G and H respectively; (

**b**,

**d**,

**f**,

**h**) Analysis with analytical and numerical models of Boreholes C, F, G and H respectively.

**Figure 6.**Thermal response test of the Borehole D which was 15 m long: (

**a**) Test measurements; (

**b**) Analysis with analytical and numerical models.

Borehole | Type | Length [m] | Borehole Diameter [mm] | Notes |
---|---|---|---|---|

A | Coaxial pipes | 96 | 76.1 | Outer pipe in stainless steel. |

C | Double U-tube | 50 | 125 | Pipes in HDPE. |

F | Coaxial pipes | 50 | 101 | Outer pipe in PVC with grouting material. |

G | Coaxial pipes | 50 | 50 | Outer pipe in stainless steel. |

H | Coaxial pipes | 50 | 60.3 | Outer pipe in stainless steel. |

D | Helical shaped pipe | 15 | 400 | Helical pipe in PE-Xa and aluminium with grouting material. |

Borehole | Borehole | Borehole | Borehole | ||
---|---|---|---|---|---|

A | F | G | H | ||

Inner Pipe (Inlet) | |||||

Material | HDPE | HDPE | HDPE | HDPE | |

Thermal conductivity | [W/(m K)] | 0.40 | 0.40 | 0.40 | 0.40 |

Outside diameter | [mm] | 32.0 | 32.0 | 25.0 | 32.0 |

Inside diameter | [mm] | 26.0 | 26.0 | 21.0 | 26.0 |

Insulation foam thickness | [mm] | 4.0 | - | - | 4.0 |

Insulation foam thermal conductivity | [W/(m K)] | 0.09 | - | - | 0.09 |

Outer Pipe (Outlet) | |||||

Material | AISI 304 | PVC | AISI 304 | AISI 304 | |

Thermal conductivity | [W/(m K)] | 16.0 | 0.20 | 16.0 | 16.0 |

Outside diameter | [mm] | 76.1 | 63.0 | 50.0 | 60.3 |

Inside diameter | [mm] | 68.9 | 57.0 | 46.0 | 53.1 |

Borehole diameter | [mm] | 76.1 | 101.0 | 50.0 | 60.3 |

Borehole length | [m] | 96.0 | 50.0 | 50.0 | 50.0 |

Thermal conductivity of the grout | [W/(m K)] | - | 1.6 | - | - |

Thermal diffusivity of the grout | [m^{2}/s] | - | 0.70 × 10^{−6} | - | - |

Pipe | Unit | Description |
---|---|---|

Material | HDPE | |

Thermal conductivity | [W/(m K)] | 0.40 |

Outside diameter | [mm] | 32.0 |

Inside diameter | [mm] | 26.0 |

Spacing between the pipes (centre-to-centre) | [mm] | 90.0 |

Number of pipes | - | 4 |

Connection | - | Parallel |

Borehole diameter | [mm] | 125.0 |

Borehole length | [m] | 50.0 |

Thermal conductivity of the grout | [W/(m K)] | 1.6 |

Thermal diffusivity of the grout | [m^{2}/s] | 0.70 × 10^{−6} |

Pipe | Unit | Description |
---|---|---|

Material | PE-Xa—aluminium—PE co-extruded | |

Thermal conductivity | [W/(m K)] | 0.38 |

Outside diameter | [mm] | 20.0 |

Inside diameter | [mm] | 14.2 |

Length of helical pipe per unit bore length | [m/m] | 1.15 |

Outer diameter of the helix | [mm] | 220.0 |

Borehole diameter | [mm] | 400.0 |

Pitch between the turns | [mm] | 600.0 |

Borehole length | [m] | 15.0 |

Thermal conductivity of the grout | [W/(m K)] | 1.84 |

Thermal diffusivity of the grout | [m^{2}/s] | 0.86 × 10^{−6} |

Layer | Depth [m] | Description | |
---|---|---|---|

From | To | ||

1 | 0 | 0.9 | Topsoil |

2 | 0.9 | 1.5 | Silty clay |

3 | 1.5 | 7 | Silt |

4 | 7 | 9.8 | Silty clay |

5 | 9.8 | 12.3 | Peat |

6 | 12.3 | 12.5 | Sand |

7 | 12.5 | 15.6 | Silty clay |

8 | 15.6 | 21.1 | Clay |

9 | 21.1 | 27 | Silty clay |

10 | 27 | 28.6 | Silt |

11 | 28.6 | 33.5 | Silty clay |

12 | 33.5 | 38.1 | Silt |

13 | 38.1 | 38.6 | Clay |

14 | 38.6 | 42.4 | Silty clay |

15 | 42.4 | 46.8 | Sand |

16 | 46.8 | 55 | Silty clay |

17 | 55 | 56.6 | Clay |

18 | 56.6 | 57.5 | Silty clay |

19 | 57.5 | 57.6 | Peat |

20 | 57.6 | 60 | Clay |

21 | 60 | 64.5 | Silty clay |

22 | 64.5 | 66.4 | Clay |

23 | 66.4 | 70.1 | Silty sand |

24 | 70.1 | 72.2 | Silt |

25 | 72.2 | 72.7 | Clay |

26 | 72.7 | 74.2 | Silty clay |

27 | 74.2 | 76.9 | Sandy silt |

28 | 76.9 | 80.2 | Clay |

29 | 80.2 | 81.3 | Sandy silt |

30 | 81.3 | 82.9 | Sand |

31 | 82.9 | 87.1 | Clay |

32 | 87.1 | 87.7 | Sandy silt |

33 | 87.7 | 88.9 | Sand |

34 | 88.9 | 90.3 | Sandy silt |

35 | 90.3 | 100 | Sand |

Thermal Resistance [(m K)/W] | Borehole | |||||
---|---|---|---|---|---|---|

A | C | F | G | H | D | |

Outer pipe of coaxial BHE | 0.001 | - | 0.080 | 0.001 | 0.001 | - |

Grouting material | - | - | 0.047 | - | - | 0.053 |

Between adjacent pipes in double U-tube (R_{ppA}) | - | 0.613 | - | - | - | - |

Between opposite pipes in double U-tube (R_{ppB}) | - | 0.832 | - | - | - | - |

Between pipe and borehole wall in double U-tube (R_{p}_{0}) | - | 0.160 | - | - | - | - |

Borehole | L_{bore} | q′ | λ_{eq} [W/(m K)] (RMSE, [°C]) | |||
---|---|---|---|---|---|---|

[m] | [W/m] | |||||

S-ILSM | ILSM | ICSM | CaRM | |||

A | 96 | 59 | 1.49 ± 0.15 | 1.32 (0.37) | 1.26 (0.26) | 1.30 (0.10) |

C | 50 | 57 | 1.60 ± 0.13 | 1.58 (0.12) | 1.50 (0.42) | 1.51 (0.05) |

F | 50 | 57 | 1.43± 0.13 | 1.20 (0.45) | 1.20 (0.51) | 1.45 (0.07) |

G | 50 | 57 | 1.35 ± 0.13 | 1.33 (0.31) | 1.24 (0.48) | 1.35 (0.01) |

H | 50 | 57 | 1.59 ± 0.13 | 1.52 (0.46) | 1.40 (0.65) | 1.49 (0.03) |

D | 15 | 87 | 1.39 ± 0.15 | - | - | 1.20 (0.06) |

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## Share and Cite

**MDPI and ACS Style**

Zarrella, A.; Emmi, G.; Graci, S.; De Carli, M.; Cultrera, M.; Santa, G.D.; Galgaro, A.; Bertermann, D.; Müller, J.; Pockelé, L.;
et al. Thermal Response Testing Results of Different Types of Borehole Heat Exchangers: An Analysis and Comparison of Interpretation Methods. *Energies* **2017**, *10*, 801.
https://doi.org/10.3390/en10060801

**AMA Style**

Zarrella A, Emmi G, Graci S, De Carli M, Cultrera M, Santa GD, Galgaro A, Bertermann D, Müller J, Pockelé L,
et al. Thermal Response Testing Results of Different Types of Borehole Heat Exchangers: An Analysis and Comparison of Interpretation Methods. *Energies*. 2017; 10(6):801.
https://doi.org/10.3390/en10060801

**Chicago/Turabian Style**

Zarrella, Angelo, Giuseppe Emmi, Samantha Graci, Michele De Carli, Matteo Cultrera, Giorgia Dalla Santa, Antonio Galgaro, David Bertermann, Johannes Müller, Luc Pockelé,
and et al. 2017. "Thermal Response Testing Results of Different Types of Borehole Heat Exchangers: An Analysis and Comparison of Interpretation Methods" *Energies* 10, no. 6: 801.
https://doi.org/10.3390/en10060801