# Theoretical and Experimental Cost–Benefit Assessment of Borehole Heat Exchangers (BHEs) According to Working Fluid Flow Rate

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## Abstract

**:**

## 1. Introduction

- (i)
- the thermal conductivity of the ground ($\lambda $),
- (ii)
- the thermal resistance of the borehole heat exchanger (${R}_{b}$),
- (iii)
- the undisturbed ground temperature (${T}_{0}$), and,
- (iv)
- the injection (or extraction) of heat ratio (thermal power input) (q) (that depends on flow rate and temperature gap of working fluid).

- –
- Properties and flow rate of the fluid through the heat exchanger,
- –
- Diameter of the geothermal borehole,
- –
- Geometry and materials of the heat-exchanger pipe, and,
- –
- Grouting material.

## 2. Methodology

#### 2.1. Analytical Tool to Evaluate Thermal Efficiency of BHE According to Hydrogeological Conditions, Geometric Characteristics and Material Properties

#### 2.1.1. Heat Transfer Assessment

#### 2.1.2. Hydraulic Assessment

- ${P}_{h}$ is the hydraulic power per unit of length (W/m),
- ${q}_{f}$ is the volume flow (m${}^{3}$/s), and,
- $\delta p$ is the differential pressure (Pa/m) [from Equation (8)]

#### Friction Coefficient and Pumping Losses Calculation

#### 2.2. Capital and Operating Costs

- ${C}_{1}$ is the total cost of an equipped borehole per drilled meter (€/m),
- n is the number of boreholes,
- L is the borehole depth (m), and,
- N is installation amortization period (years).

- $AO{C}_{HP}$ is the Annual energy Operating Cost of Heat Pump (€/year)
- $AO{C}_{CP}$ is the Annual energy Operating Cost of Circulating Pump (€/year)
- ${C}_{HP}$ is the Heat-Pump electrical hourly consumption (kW),
- ${C}_{CP}$ is the Circulation Pump electrical hourly consumption (kW),
- h is the number of operating hours per year, and,
- ${C}_{e}$ is the electricity cost (€/kWh).

## 3. Experimental Validation

#### 3.1. Experimental Data

#### 3.2. Comparing Results

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## 4. Optimization Assessment

#### 4.1. Thermal Resistance and Pressure Losses Analysis by Means of Analytic Calculations

#### 4.2. Multi-Parameter Analysis

#### 4.3. Scenario Analysis

Borehole field | |||
---|---|---|---|

Borehole type | single U-tube | Borehole parameters | See Table 1 |

Borehole field | 9 × 90 m | Borehole separation | 6 m |

Ground properties | |||

Undisturbed ground temperature ${}^{1}$ | 18 ${}^{\xb0}$C | Ground conductivity | 2.3 W/mK |

Pipe properties${}^{2}$ | |||

Installation properties | |||

Heat Pump | GMSW 28 HK ${}^{3}$ | Pipe distance from borehole to Heat Pump | 2 × 35 m |

Common pressure losses (filter, heat pump heat exchanger, fittings,⋯) | 90 kPa |

#### 4.3.1. Same Borehole Field

- –
- The annual evolution of the inlet and outlet temperatures of the heat transfer fluid, which depend on the thermal performance of the borehole (${R}_{b}$).
- –
- The hourly thermal capacity of the heat pump and the rate of heat injected to the borehole throughout the year.
- –
- The electric consumption of the heat pump and its efficiency (Coefficient of Performance—COP) calculated based on the heat pump rating. The value of the SPF indicated in the analysis is the COP annual average.

#### 4.3.2. Same Heat-Pump Efficiency

## 5. Conclusions

- –
- As expected, the borehole thermal resistance value significantly depends on the flow rate (see Figure 7). Within laminar flow (below 0.04 l/s), borehole thermal resistance is rapidly increasing with small flow rate decreases, whereas in turbulent flow, a further increase in the flow rate produces only a marginal decrease in the borehole thermal resistance.
- –
- Since pressure losses in the borehole heat exchanger are correlated with the value of the thermal resistance (see Figure 8), an optimum value is observed where the pressure losses have already decreased considerably, reducing the electrical pumping costs.
- –
- For the same flow rate value and hydraulic losses, the borehole characteristic that most penalizes borehole thermal efficiency is the low thermal conductivity of the pipe material (Figure 10), with more influence on the borehole thermal efficiency than the value of the grout thermal conductivity.
- –
- The difference obtained in borehole thermal efficiency values between the lowest pipe thermal conductivity and the highest for the same grout conductivity is about 0.2 mK/W for all values of flow rates analyzed. This relevant result, which is not a main objective of this article, opens an interesting field to analyze in future works.

- –
- As shown in Table 5, for the same increase in circulating flow, the improvement in the energy consumption of the heat pump is higher at low flow rates. For example, the running cost of the heat pump is reduced 4% with a flow increase from 0.033 to 0.044 l/s, but the reduction is about 0.4% in the range between 0.2 and 0.25 l/s.
- –
- When the flow rate exceeds a certain value, the penalty in the pumping operating costs are higher than the decrease in electricity consumption due the improved heat-pump performance. An optimum flow rate that optimizes the total costs of a certain BHE can be determined according to the scenario characteristics. In the case studied, this optimum is at a value of 0.1 l/s (Figure 14) representing 70% of nominal design flow rate.
- –
- If the design objective is to set the performance of the heat pump, there is a carrier flow threshold value from which a decrease in the total costs of the installation is not very significant (Figure 15).
- –

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

$\lambda $ | Ground thermal conductivity (W/mK) |

${\lambda}_{f}$ | Fluid thermal conductivity (W/mK) |

$AO{C}_{HP}$ | Annual energy Operating Cost of Heat Pump (€/year) |

$AO{C}_{CP}$ | Annual energy Operating Cost of Circulating Pump (€/year) |

BHE | Borehole Heat Exchanger |

CAPEX | Capital Expenses |

COP | Coefficient of Performance |

GSHP | Ground-Source Heat Pump |

GHE | Ground Heat Exchanger |

H | Borehole deep (m) |

$Nu$ | Nusselt number |

OPEX | Operating Expenses |

$\Delta P$ | Pressure drop (Pa) |

$\delta p$ | Pressure drop per unit length of BHE (Pa/m) |

$Pr$ | Prandtl number |

PID | Proportional Integral Derivative (PID) Control |

q | Thermal power heat ratio (W/m) |

${R}_{b}$ | Borehole thermal resistance (mK/W) |

$Re$ | Reynolds number |

${r}_{po}$ | Outer radius of the pipe (m) |

${r}_{p}$ | Inner radius of the pipe (m) |

${R}_{tot}$ | Total borehole resistance (mK/W)) |

SPF | Seasonal Performance Factor |

${T}_{0}$ | Undisturbed ground temperature [${}^{\xb0}$C] |

${T}_{f}$ | Fluid temperature (${}^{\xb0}$C) |

${T}_{g}$ | Surrounding ground temperature (${}^{\xb0}$C) |

TRT | Thermal Response Test |

## Appendix A. Case 1: Flow 0.033 L/S

**Figure A2.**Thermal power extracted from the borehole field and Thermal power capacity of the heat pump.

## Appendix B. Case 2: Flow 0.044 L/S

**Figure A5.**Thermal power extracted from the borehole field and Thermal power capacity of the heat pump.

## Appendix C. Case 3: Flow 0.064 L/S

**Figure A8.**Thermal power extracted from the borehole field and Thermal power capacity of the heat pump.

## Appendix D. Case 4: Flow 0.083 L/S

**Figure A11.**Thermal power extracted from the borehole field and Thermal power capacity of the heat pump.

## Appendix E. Case 5: Flow 0.1 L/S

**Figure A14.**Thermal power extracted from the borehole field and Thermal power capacity of the heat pump.

## Appendix F. Case 6: Flow 0.15 L/S

**Figure A17.**Thermal power extracted from the borehole field and Thermal power capacity of the heat pump.

## Appendix G. Case 7: Flow 0.2 L/S

**Figure A20.**Thermal power extracted from the borehole field and Thermal power capacity of the heat pump.

## Appendix H. Case 8: Flow 0.25 L/S

**Figure A23.**Thermal power extracted from the borehole field and Thermal power capacity of the heat pump.

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Sample Availability: Raw data of the thermal test is available from the authors under request. |

**Figure 3.**Average Temperature (in black color) and Thermal Power injected (in grey color) (

**a**) Test 1; (

**b**) Test 2; (

**c**) Test 3.

**Figure 10.**${R}_{b}$ Surfaces for different Flow values (in $l/s$): (

**a**) 0.01; (

**b**) 0.02; (

**c**) 0.05 and (

**d**) 0.25.

**Figure 13.**Performance curves of GMSW 28 HK Heat Pump depending on supply temperature of heating system [42].

Borehole | Borehole | Borehole | Outer | Pipe | Pipe Thermal |

Type | Depth | Diameter | Diameter | Thickness | Conductivity |

single U-tube | 15 m | 126 mm | 32 mm | 2.9 mm | 0.41 W/mK |

Borehole | Effective Borehole | Casing | Inner | Distance between | Grout Thermal |

Probe | Depth | Thickness | Diameter | centers | Conductivity |

RAUGEO PE-Xa | 14.6 m | 12.5 mm | 26.2 mm | 75 mm | 1.2 W/mK |

Test # | Flow | Reynolds Number ${}^{1}$ | Thermal Power Injected |
---|---|---|---|

(l s${}^{-1}$) | (W m${}^{-1}$) | ||

1 | 0.022 | 1625 | 40 |

2 | 0.044 | 3249 | 80 |

3 | 0.083 | 5908 | 60 |

Test # | TRT Results | Analytical Tool | ||||
---|---|---|---|---|---|---|

$\mathit{\lambda}$ | ${\mathit{R}}_{\mathit{b}}$ | Ad. R-Squared | Mean Squared Error | ${\mathit{R}}_{\mathit{b}}$ | Error | |

(W/mK) | (mK/W) | (mK/W) | (%) | |||

1 | 2.22 | 0.221 | 0.89 (FLSm) | 1.92 × ${10}^{-2}$ (FLSm) | 0.224 | 1.36 |

2 | 2.23 | 0.167 | 0.99 (FLSm) | 2.21 × ${10}^{-3}$ (FLSm) | 0.166 | −0.60 |

3 | 2.22 | 0.159 | 0.97 (ILSm) | 8.77 × ${10}^{-3}$ (ILSm) | 0.157 | −1.26 |

Case # | Flow | Borehole | CAPEX | OPEX | Total | |||||
---|---|---|---|---|---|---|---|---|---|---|

($\mathit{l}\phantom{\rule{4pt}{0ex}}{\mathit{s}}^{-1}$) | Field | Cost ${}^{1}$ | SPF ${}^{2}$ | h ${}^{3}$ | ${\mathbf{AOC}}_{\mathbf{HP}}$${}^{4}$ | $\mathbf{\Delta}{\mathit{P}}_{\mathit{b}}$${}^{5}$ | CP ${}^{6}$ | ${\mathbf{AOC}}_{\mathbf{CP}}$${}^{7}$ | Costs | |

1 | 0.033 | 9 × 90 m | 2106 €/year | 3.88 | 2980 h | 2429.65 €/year | 0.8 kPa | 64.2 W | 24.88 €/year | 4560.53 €/year |

2 | 0.044 | 9 × 90 m | 2106 €/year | 4.02 | 2882 h | 2337.81 €/year | 1.32 kPa | 86.1 W | 32.26 €/year | 4476.07 €/year |

3 | 0.064 | 9 × 90 m | 2106 €/year | 4.30 | 2701 h | 2183.70 €/year | 2.54 kPa | 126.9 W | 44.56 €/year | 4334.26 €/year |

4 | 0.083 | 9 × 90 m | 2106 €/year | 4.37 | 2660 h | 2148.04 €/year | 4.01 kPa | 167.2 W | 57.82 €/year | 4311.86 €/year |

5 | 0.100 | 9 × 90 m | 2106 €/year | 4.41 | 2637 h | 2128.11 €/year | 5.56 kPa | 204.8 W | 70.20 €/year | 4304.31 €/year |

6 | 0.150 | 9 × 90 m | 2106 €/year | 4.48 | 2600 h | 2096.65 €/year | 11.30 kPa | 325.6 W | 110.06 €/year | 4312.71 €/year |

7 | 0.200 | 9 × 90 m | 2106 €/year | 4.51 | 2582 h | 2081.48 €/year | 18.70 kPa | 465.8 W | 156.37 €/year | 4343.85 €/year |

8 | 0.250 | 9 × 90 m | 2106 €/year | 4.53 | 2571 h | 2072.25 €/year | 27.63 kPa | 630.2 W | 210.62 €/year | 4388.87 €/year |

Case # | Flow | Borehole | CAPEX | OPEX | Total | |||||
---|---|---|---|---|---|---|---|---|---|---|

($\mathit{l}\phantom{\rule{4pt}{0ex}}{\mathit{s}}^{-1}$) | Field | Cost ${}^{1}$ | SPF | h ${}^{2}$ | ${\mathbf{AOC}}_{\mathbf{HP}}$${}^{3}$ | $\mathbf{\Delta}{\mathit{P}}_{\mathit{b}}$${}^{4}$ | CP ${}^{5}$ | ${\mathbf{AOC}}_{\mathbf{CP}}$${}^{6}$ | Costs | |

1 | 0.033 | 1215 m | 3159.00 €/year | 4.30 | 2701 h | 2183.70 €/year | 0.8 kPa | 64.2 W | 24.88 €/year | 5367.58 €/year |

2 | 0.044 | 990 m | 2574.00 €/year | 4.30 | 2701 h | 2183.70 €/year | 1.32 kPa | 86.1 W | 32.26 €/year | 4789.96 €/year |

3 | 0.064 | 810 m | 2106.00 €/year | 4.30 | 2701 h | 2183.70 €/year | 2.54 kPa | 126.9 W | 44.56 €/year | 4334.26 €/year |

4 | 0.083 | 738 m | 1918.80 €/year | 4.30 | 2701 h | 2183.70 €/year | 4.01 kPa | 167.2 W | 57.82 €/year | 4160.32 €/year |

5 | 0.100 | 702 m | 1825.20 €/year | 4.30 | 2701 h | 2183.70 €/year | 5.56 kPa | 204.8 W | 70.20 €/year | 4079.10 €/year |

6 | 0.150 | 657 m | 1708.20 €/year | 4.30 | 2701 h | 2183.70 €/year | 11.30 kPa | 325.6 W | 110.06 €/year | 4001.96 €/year |

7 | 0.200 | 630 m | 1638.00 €/year | 4.30 | 2701 h | 2183.70 €/year | 18.70 kPa | 465.8 W | 156.37 €/year | 3978.07 €/year |

8 | 0.250 | 617 m | 1604.20 €/year | 4.30 | 2701 h | 2183.70 €/year | 27.63 kPa | 630.2 W | 210.62 €/year | 3998.52 €/year |

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## Share and Cite

**MDPI and ACS Style**

Badenes, B.; Mateo Pla, M.Á.; Magraner, T.; Soriano, J.; Urchueguía, J.F.
Theoretical and Experimental Cost–Benefit Assessment of Borehole Heat Exchangers (BHEs) According to Working Fluid Flow Rate. *Energies* **2020**, *13*, 4925.
https://doi.org/10.3390/en13184925

**AMA Style**

Badenes B, Mateo Pla MÁ, Magraner T, Soriano J, Urchueguía JF.
Theoretical and Experimental Cost–Benefit Assessment of Borehole Heat Exchangers (BHEs) According to Working Fluid Flow Rate. *Energies*. 2020; 13(18):4925.
https://doi.org/10.3390/en13184925

**Chicago/Turabian Style**

Badenes, Borja, Miguel Ángel Mateo Pla, Teresa Magraner, Javier Soriano, and Javier F. Urchueguía.
2020. "Theoretical and Experimental Cost–Benefit Assessment of Borehole Heat Exchangers (BHEs) According to Working Fluid Flow Rate" *Energies* 13, no. 18: 4925.
https://doi.org/10.3390/en13184925