# Optimizing the Design of a Vertical Ground Heat Exchanger: Measurement of the Thermal Properties of Bentonite-Based Grout and Numerical Analysis

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{m}(J/(kgK)) is the SHC, c

_{v}(J/(m

^{3}K)) the VHC and $\rho $ (kg/m

^{3}) the bulk density [31].

## 3. Experimental Results and Discussion

## 4. Numerical Analysis

#### 4.1. Numerical Method

- -
- To investigate the effects of the SHC of bentonite-based grouts, HDPE pipe length, and working fluid velocity, the model simulated the cooling mode during intermittent operation (3 h operation time and 3 h off-time) and during continuous 24-h operation.
- -
- To investigate the effects of the operation time and off-time on vertical GHE, the model simulated the cooling mode during intermittent operation (3 h operation time and 3 h off-time) over three days.
- -
- To simulate the intermittent operation mode, user-defined operation times and off-times were modeled.
- -
- When exploring the effects of HDPE pipe length and working fluid velocity, and operation time and off-time, numerical simulations were performed using the thermal properties of the most diverse grout specimens (i.e., BS20-0, which has the lowest TC and the highest SHC, and BS30-30, which has the highest TC and the lowest SHC).

#### 4.2. Validation

#### 4.3. Numerical Results and Discussion

#### 4.3.1. Effects of the Specific Heat Capacity of Bentonite-Based Grouts

#### 4.3.2. Effects of Working Fluid Velocity and HDPE Pipe Length

#### 4.3.3. Effects of Various Operation Times and Off-Times during Intermittent Operation

## 5. Conclusions

- (1)
- Under saturated conditions, the TC and SHC of bentonite-based grouts ranged from 0.728–1.127 W/(mK) and 2519–3743 J/(kgK), respectively. As the proportion of silica sand increased, the TC of the bentonite-based grouts increased, but the SHC decreased. The thermal properties of bentonite-based grouts were affected principally by composition and porosity.
- (2)
- For bentonite-based grouts, the mean HER was 27% higher during intermittent operation than during continuous operation. Also, during intermittent operation, grout with high TC and high SHC improved GHE performance. Because the SHC of bentonite-based grout is higher than that of cement-based grout, the effect of bentonite-based grout was more significant.
- (3)
- During both continuous and intermittent operation, GHE performance improved as the working fluid velocity increased. However, there was a critical working fluid velocity that greatly affected the performance of the vertical GHE, regardless of the operation mode, HDPE pipe length, or grout thermal properties; this value was 0.3 m/s. Therefore, it is recommended to set the velocity for operation of the vertical GHE to 0.3 m/s or higher.
- (4)
- During intermittent operation, depending on the operation time and off-time, we found critical time intervals at which the ground temperature was almost completely restored, or any benefit of intermittent operation almost disappeared. Moreover, the method to estimate the critical time intervals for optimizing intermittent operation was proposed. Our results can be used as input data for analyses of the thermal behavior of vertical GHEs to improve GHE performance and operation.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**(

**a**) Thermal conductivity and (

**b**) specific heat capacity of specimens with various proportions of additives.

**Figure 4.**The relationships between porosity and thermal properties. (

**a**) Thermal conductivity vs. porosity; (

**b**) Specific heat capacity vs. porosity.

**Figure 6.**Numerical simulation of the present study, the in situ thermal response testing (TRT) data, and the numerical simulation of Lee et al. [17].

**Figure 7.**(

**a**) Mean heat exchange rates in different operation modes; (

**b**) Percentage changes in heat exchange rates between different operation modes (${c}_{m}$ (J/(kgK)): the specific heat capacity of each specimen).

**Figure 8.**The effects of working fluid velocity and high-density polyethylene (HDPE) pipe length in different operation modes.

**Figure 10.**(

**a**) Ground temperature distribution 3 h after operation; (

**b**) Ground temperature distribution after 3 h of off-time; (

**c**) Ground temperature distribution after 6 h of off-time; (

**d**) Ground temperature distribution after 9 h of off-time.

Permeability (cm/s) | Swelling Potential | Montmorillonite Content (%) | Thermal Conductivity (W/(mK)) | Specific Gravity |
---|---|---|---|---|

≤1 × 10^{−7} | 25 mL/2.0 g | ≤90 | 0.74 | 2.60 |

Specimen No. | Bentonite (wt %) | Silica Sand (wt %) | Water (wt %) |
---|---|---|---|

BS20-0 | 20 | 0 | 80 |

BS20-10 | 10 | 70 | |

BS20-20 | 20 | 60 | |

BS20-30 | 30 | 50 | |

BS30-0 | 30 | 0 | 70 |

BS30-10 | 10 | 60 | |

BS30-20 | 20 | 50 | |

BS30-30 | 30 | 40 |

Specimen No. | Saturated Bulk Density (kg/m^{3}) | Porosity (%) | Thermal Conductivity (W/(mK)) | Specific Heat Capacity (J/(kgK)) |
---|---|---|---|---|

BS20-0 | 1096 | 91.57 | 0.728 | 3743 |

BS20-10 | 1170 | 86.56 | 0.791 | 3363 |

BS20-20 | 1298 | 80.17 | 0.855 | 2960 |

BS20-30 | 1354 | 74.19 | 0.988 | 2770 |

BS30-0 | 1158 | 86.64 | 0.775 | 3443 |

BS30-10 | 1256 | 80.78 | 0.846 | 3056 |

BS30-20 | 1359 | 74.06 | 0.976 | 2752 |

BS30-30 | 1439 | 67.11 | 1.127 | 2519 |

Item | Description | |||
---|---|---|---|---|

Inlet water velocity | 0.3 m/s | |||

Inlet water temperature | 35 °C (308.15 K) | |||

Turbulence intensity | 5% | |||

Initial ground temperature | 18.2 °C (291.35 K) | |||

Physical Parameters | Density (kg/m^{3}) | Thermal Conductivity (W/(mK)) | Specific Heat Capacity(J/(kgK)) | Viscosity(kg/(ms)) |

Working fluid | 998.2 | 0.6 | 4182 | 0.001003 |

HDPE pipe | 955 | 0.4 | 525 | |

Ground | 2600 | 4.0 | 790 |

**Table 5.**Summary of CFD model equations [34].

Continuity equation | $\frac{\partial \rho}{\partial t}+\nabla \left(\rho \overrightarrow{v}\right)=0$ | |

Momentum equation | $\frac{\partial \rho \overrightarrow{v}}{\partial t}+\nabla \left(\rho \overrightarrow{v}\times \overrightarrow{v}\right)-\nabla \left({\mu}_{eff}\nabla \overrightarrow{v}\right)=-\nabla p+\nabla {\left({\mu}_{eff}\nabla \overrightarrow{v}\right)}^{T}+S$ | |

Energy equation | $\frac{\partial \left(\rho h\right)}{\partial t}-\frac{\partial \left(p\right)}{\partial t}+\nabla \left(\rho \overrightarrow{v}h\right)=\nabla \left[\left(\mathsf{\mu}+\frac{{\mu}_{t}}{{\sigma}_{t}}\right)\nabla h\right]-{S}_{h}$ | |

Turbulence equations | Turbulent energy equation | $\frac{\partial \left(\rho k\right)}{\partial t}+\nabla \left(\rho \overrightarrow{v}k\right)=\nabla \left[\left(\mathsf{\mu}+\frac{{\mu}_{t}}{{\sigma}_{k}}\right)\nabla k\right]+{G}_{k}+{G}_{b}-\rho \epsilon $ |

Turbulence dissipation rate equation | $\frac{\partial \left(\rho \epsilon \right)}{\partial t}+\nabla \left(\rho \overrightarrow{v}\epsilon \right)=\nabla \left[\left(\mathsf{\mu}+\frac{{\mu}_{t}}{{\sigma}_{\epsilon}}\right)\nabla \mathsf{\epsilon}\right]+\frac{\epsilon}{\lambda}\left({c}_{\epsilon 1}{G}_{k}-{c}_{\epsilon 2}\rho \epsilon \right)$ | |

${c}_{\epsilon 1}$: 1.44, ${c}_{\epsilon 2}$: 1.92 | $\epsilon $: turbulent dissipation rate (m^{2}/s^{2}) | |

${G}_{b}$, ${G}_{k}$: turbulence kinetic energies (m^{2}/s^{2}) | $\mu $: viscosity ((Ns)/m^{2}) | |

$h$: enthalpy of the fluid (J) | ${\mu}_{eff}$: effective viscosity ((Ns)/m^{2}) | |

$k$: turbulence kinetic energy (m^{2}/s^{2}) | ${\mu}_{t}$: turbulence viscosity ((Ns)/m^{2}) | |

$p$: pressure (Pa) | $\overrightarrow{v}$: velocity (m/s) | |

$S$: source term | $\rho $: density (kg/m^{3}) | |

${S}_{h}$: volumetric heat source (kJ/(m^{3}s)) | ${\sigma}_{\epsilon}$: 1.2, ${\sigma}_{k}:\text{}1$, ${\sigma}_{t}$: constant | |

$t$: time (h) | ||

$T$: Temperature (°C) |

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**MDPI and ACS Style**

Kim, D.; Oh, S.
Optimizing the Design of a Vertical Ground Heat Exchanger: Measurement of the Thermal Properties of Bentonite-Based Grout and Numerical Analysis. *Sustainability* **2018**, *10*, 2664.
https://doi.org/10.3390/su10082664

**AMA Style**

Kim D, Oh S.
Optimizing the Design of a Vertical Ground Heat Exchanger: Measurement of the Thermal Properties of Bentonite-Based Grout and Numerical Analysis. *Sustainability*. 2018; 10(8):2664.
https://doi.org/10.3390/su10082664

**Chicago/Turabian Style**

Kim, Daehoon, and Seokhoon Oh.
2018. "Optimizing the Design of a Vertical Ground Heat Exchanger: Measurement of the Thermal Properties of Bentonite-Based Grout and Numerical Analysis" *Sustainability* 10, no. 8: 2664.
https://doi.org/10.3390/su10082664