# Performance Assessment of Horizontal Ground Heat Exchangers under a Greenhouse in Quebec, Canada

^{1}

^{2}

^{3}

^{4}

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## Abstract

**:**

^{2}area) can be covered by HGHEs installed at a 1.5 m depth when there is no greenhouse above. When installed under a greenhouse with a constant inside temperature of 21 °C, the coverage for heating loads increases to 22.8%, while cooling loads decrease to 24.2%. Sensitivity analysis demonstrates that the constant temperature in the greenhouse reduces the system’s reliance on surface temperature fluctuations for both heating and cooling, albeit with reduced efficiency for cooling.

## 1. Introduction

_{2}emissions must be reduced [10]. Hence, the transition toward sustainable renewable energies is important for decarbonising the energy sector. It is therefore critical to provide energy to urban greenhouses according to (1) renewable energy sources, which have a lower carbon footprint compared to traditional fossil fuels; (2) lower energy dependence, where operators will reduce their vulnerability to cost fluctuations and energy supplies disruptions [11]; and (3) social acceptance, where using renewable energies can enhance the public image and reputation of environmentally responsible food producers.

^{−1}K

^{−1}to 0.045 W m

^{−1}K

^{−1}, respectively, tends to reproduce TRT data and the in-situin-situ operation conditions. This present study used the same approach as that developed by Fujii et al. [13,14] since slinky-coil HGHEs are difficult to model. The heat exchange rate per unit length of the straight horizontal heat exchange pipes is significantly lower than that obtained with a vertical ground heat exchanger because shallow ground temperature is affected by seasonal air temperature variations, and dry soils near the ground surface have relatively low thermal conductivity. Using slinky-coil heat exchange pipes instead of straight pipes is, therefore, a good alternative to optimize the HGHEs’ design and reduce trench length, which can facilitate the development of such a system, even in cases of limited land availability [14].

## 2. Background Information

#### 2.1. Previous Site Studies

^{2}with a height of 6.1 m. Work was conducted to evaluate the energy consumption of the greenhouse, and an in-situ subsurface characterisation was achieved to evaluate the pre-feasibility of a shallow geothermal system based on the land area available.

_{2}injection and optimize energy use. The study resulted in an energy consumption profile for heating and cooling, considering dehumidification for the open and closed greenhouse. The consumption profile provides the average and maximum monthly energy to heat and cool the building. The energy profile displays both heating and cooling demand; therefore, the higher consumption is only considered to determine whether each month belongs to a heating or cooling period. Heating-dominated periods are associated with the months of October to February, while cooling-dominated periods are associated with the months of March to September. The energy profile simulating a closed greenhouse was chosen for this study (Figure 2).

#### 2.2. Ground Temperature

## 3. Materials and Methods

#### 3.1. FEFLOW Model for HGHE

#### 3.1.1. Conceptual Model

^{−3}), α is the ground thermal diffusivity (m

^{2}s

^{−1}), ${v}_{\mathrm{i}}$ is the vector of pore velocity (m s

^{1}), Q

_{ρ}is the fluid mass sink/source (s

^{−1}), Q

_{T}is the source of heat (kg m

^{−1}s

^{−3}), ${\mathrm{k}}_{\mathrm{ij}}$ is the permeability tensor (m

^{2}), $\mu $ is the dynamic viscosity of gas (kg m

^{−1}s

^{−1}), $p$ is the gas pressure (Pa), ${j}_{\mathrm{i}T}^{\mathsf{\alpha}}$ is Fourier’s heat flux vector (kg s

^{−3}), ${g}_{\mathrm{j}}$ is the gravitational vector (m s

^{−2}), ${x}_{\mathrm{i}}$ are the Cartesian coordinates (m), and $E$ is the internal (thermal) energy density (m

^{2}s

^{−2}).

#### 3.1.2. Model Geometry

_{inner}, L, X and W are the total thickness of the grid corresponding to the flow path (m), inner diameter of the polyethylene pipe (m), total length of the buried slinky-coil HGHE (m), length of the trench in which the slinky-coil HGHE is buried (m) and the width of the trench where the slinky-coil HGHE is buried (m).

#### 3.1.3. Domain Discretization

^{−5}, respectively. The outer bottom and lateral boundaries of the model are located at a 10 m distance from the HGHE to prevent any influence from the conditions imposed at these boundaries. The size of the model is 34.8 m on the y-axis, 29 m on the x-axis and −20 m on the z-axis. The size of the HGHE is 14.6 m by 9.1 m and comprises 8 trenches of slinky coils. There is a 0.2 m distance between every trench, which is composed of a fluid path (0.8 m) and pipes (2 × 0.05 m).

#### 3.1.4. HGHE Operating Parameters and Model Properties

^{−1}K

^{−1}. The HGHE inner and outer pipe diameters are 0.024 m and 0.034 m, respectively. There is fluid injection at the inlet and pumping at the outlet. The flow rate is set at 0.0002 m

^{3}s

^{−1}. To make sure that the flow is turbulent (Re > 2300), the flow rate chosen for the fluid inside the pipe was the same as the one used by Fujii et al. [13,14] since their model was validated using the results of a TRT on a horizontal HGH and a long-term air-conditioning (A/C) test. The percentage of propylene glycol was set at 20%, with a freezing point of −7.1 °C and a heat capacity of 4.02 MJ m

^{−3}K

^{−1}.

^{−1}and a porosity of 1 [14]. The pipes and the ground have a hydraulic conductivity value of 1 × 10

^{–15}m s

^{−1}and a porosity of 0.0001. These values are set to prevent water flow from leaking outside the flow path. According to Fujii et al. [13,14], the heat transfer medium (flow path) has a heat capacity of 3.800 MJ m

^{−1}K

^{−1}. Both the flow path and the pipes have a thermal conductivity of 0.027 W m

^{−1}K

^{−1}. This last value was determined by calibration to reproduce TRTs made on HGHEs. The ground thermal properties were set according to Géotherma Solutions’ study results [23], with a ground thermal conductivity of 1.414 W m

^{−1}K

^{−1}and a ground heat capacity of 2.86 MJ m

^{−3}K

^{−1}. This last value was also applied for the pipes (layers 10 and 14, Figure 5) since the soil element accounts for a large proportion of the polyethylene pipe element (Table 4).

#### 3.1.5. Model Boundary Conditions

#### 3.1.6. Initial Conditions and Simulation Time

#### 3.2. Coefficient of Performance and Load Coverage Calculations

^{−1}), ${C}_{p}$ is the heat capacity (J Kg

^{−1}°C

^{−1}) and T is the temperature (°C). The thermal power is averaged monthly for the simulation results. The covered building loads were then calculated by the sum of $Q\mathrm{s}$ and $Q\mathrm{c}$ in the heating mode and the subtraction of the last two parameters in the cooling mode. The building loads covered by the HGHE were then compared with the total building load profile (Figure 2).

#### 3.3. Simulation Scenarios

#### 3.4. Sensitivity Analysis

^{−1}K

^{−1}and ±1.086 MJ m

^{−3}K

^{−1}, which represents the maximum and minimum values of the thermal conductivity and heat capacity evaluated for the samples and TRTs made by Géotherma Solutions Inc. [23]. The greenhouse air temperature (21 °C in Scenario 1) always stays the same. Varying input parameters are shown in Table 6.

## 4. Results

## 5. Sensitivity Analysis

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Monthly heating and cooling load profile evaluated for the greenhouse in La Pocatière [22].

**Figure 5.**Excerpt from Figure 4 representing a cross-section of the thin plate model. Blue: flow path. Gray: pipe walls.

**Figure 6.**Model heat transfer boundary conditions for simulations at different depths. A cross-section is shown in Figure 7.

**Figure 7.**The middle slice of the HGHE model (Figure 5) and the key internal conditions used to simulate HGHEs. The Well BC injection and pumping refer to fluid injection and extraction at the beginning and the end of the HGHE, respectively.

**Figure 8.**Cross-section of the numerical model’s temperature in January. (

**Left**), Base case. (

**Right**), Scenario 1.

Samples | OTRT | Chosen Value | |
---|---|---|---|

(Géotherma Solutions Inc.) | (Géotherma Solutions Inc.) | ||

Ground heat capacity (MJ m^{−3} K^{−1}) | 2.85–4.05 | 1.78–2.62 | 2.86 |

Ground thermal conductivity (W m^{−1} K^{−1}) | 1.45–1.50 | 1.07–1.60 | 1.41 |

Months | Ambient Temperature T_{amb} (°C) | Calculated Ground Surface Temperature T_{gs} (°C) | Ground Surface Temperature T_{gs} Considering Snow Isolation (°C) |
---|---|---|---|

January | −11.6 | −6.5 | −1.0 |

February | −9.4 | −4.4 | −1.0 |

March | −4.0 | 0.7 | 0.7 |

April | 3.7 | 8.0 | 8.0 |

May | 11.2 | 15.2 | 15.2 |

June | 15.9 | 19.6 | 19.6 |

July | 18.8 | 22.4 | 22.4 |

August | 18.5 | 22.1 | 22.1 |

September | 13.9 | 17.7 | 17.7 |

October | 6.9 | 11.1 | 11.1 |

November | 0.5 | 5.0 | 5.0 |

December | −7.2 | −2.3 | −1.0 |

HGHE Parameters | |
---|---|

HGHE pitch (m) | 0.6 |

HGHE slinky-coil diameter (m) | 0.8 |

HGHE pipe thermal conductivity (W m^{−1} K^{−1}) | 0.34 |

Inner pipe diameter (m) | 0.024 |

Outer pipe diameter (m) | 0.034 |

Flow rate (m d^{−1}) | 17 |

Fluid composition (% of propylene glycol) | 20 |

Fluid freezing point (°C) | −7.1 |

Fluid heat capacity (MJ m^{−3} K^{−1}) | 4.02 |

Flow Path | Pipes | Ground | ||
---|---|---|---|---|

Hydraulic properties | Hydraulic conductivity (m s^{−1}) | 0.001 | 1.00 × 10^{−15} | 1.00 × 10^{−15} |

Porosity | 1 | 0.0001 | 0.0001 | |

Thermal properties | Heat capacity (MJ m^{−1} K^{−1}) | 3.800 | 2.86 | 2.86 |

Thermal conductivity (W m^{−3} K^{−1}) | 0.027 | 0.027 | 1.414 |

Depth of the HGHE (m) | Presence of Greenhouse Above the System | Surface Ground Temperature Above the System | Number of HGHE Layers | |
---|---|---|---|---|

Base Case | 1.5 | No | Ground surface temperature profile | 1 |

Scenario 1 | 1.5 | Yes | 21 °C | 1 |

Scenario 2 | 1 | Yes | 21 °C | 1 |

Scenario 3 | 2 | Yes | 21 °C | 1 |

Scenario 4 | 1 and 2 | Yes | 21 °C | 2 |

Ground Surface Temperature for Every Month (°C) | Ground Thermal Conductivity (W m ^{−1} K^{−1}) | Ground Heat Capacity (MJ m ^{−3} K ^{−1}) | |
---|---|---|---|

Base case | 0 | 1.414 | 2.860 |

Surface ground temperature increased | +3 | 1.414 | 2.860 |

Surface ground temperature reduced | −3 | 1.414 | 2.860 |

Deteriorated ground thermal properties | 0 | 1.069 | 3.946 |

Improved ground thermal properties | 0 | 1.758 | 1.774 |

Base Case | Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | |
---|---|---|---|---|---|

February (1st year) | 3.78 | 3.88 | 3.96 | 3.84 | 3.80 |

February (5th year) | 3.80 | 3.90 | 3.98 | 3.87 | 3.80 |

July (1st year) | 6.90 | 6.79 | 6.85 | 6.77 | 6.63 |

July (5th year) | 6.84 | 6.74 | 6.58 | 8.65 | 6.60 |

Base Case | Surface Ground Temperature Increased | Surface Ground Temperature Reduced | Deteriorated Ground Thermal Properties | Improved Ground Thermal Properties | |
---|---|---|---|---|---|

February (first year) | 3.62 | 3.64 | 3.63 | 3.63 | 3.64 |

February (fifth year) | 3.69 | 3.70 | 3.68 | 3.68 | 3.69 |

July (first year) | 6.79 | 6.75 | 6.84 | 6.73 | 6.82 |

July (fifth year) | 5.19 | 5.63 | 5.20 | 4.57 | 5.35 |

Scenario 1 | Surface Ground Temperature Increased | Surface Ground Temperature Reduced | Deteriorated Ground Thermal Properties | Improved Ground Thermal Properties | |
---|---|---|---|---|---|

February (first year) | 3.78 | 3.78 | 3.78 | 3.73 | 3.84 |

February (fifth year) | 3.85 | 3.85 | 3.84 | 3.80 | 3.88 |

July (first year) | 6.75 | 6.72 | 6.75 | 6.69 | 6.78 |

July (fifth year) | 5.46 | 6.12 | 5.47 | 4.60 | 6.11 |

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## Share and Cite

**MDPI and ACS Style**

Léveillée-Dallaire, X.; Raymond, J.; Snæbjörnsson, J.Þ.; Fujii, H.; Langevin, H.
Performance Assessment of Horizontal Ground Heat Exchangers under a Greenhouse in Quebec, Canada. *Energies* **2023**, *16*, 5596.
https://doi.org/10.3390/en16155596

**AMA Style**

Léveillée-Dallaire X, Raymond J, Snæbjörnsson JÞ, Fujii H, Langevin H.
Performance Assessment of Horizontal Ground Heat Exchangers under a Greenhouse in Quebec, Canada. *Energies*. 2023; 16(15):5596.
https://doi.org/10.3390/en16155596

**Chicago/Turabian Style**

Léveillée-Dallaire, Xavier, Jasmin Raymond, Jónas Þór Snæbjörnsson, Hikari Fujii, and Hubert Langevin.
2023. "Performance Assessment of Horizontal Ground Heat Exchangers under a Greenhouse in Quebec, Canada" *Energies* 16, no. 15: 5596.
https://doi.org/10.3390/en16155596