# Investigating the Influence of Groundwater Flow and Charge Cycle Duration on Deep Borehole Heat Exchangers for Heat Extraction and Borehole Thermal Energy Storage

^{*}

## Abstract

**:**

## 1. Introduction

^{−10}m s

^{−1}) was inferred from the lack of appreciable fluid yield from the borehole [19]. Nevertheless, groundwater was identified during well drilling at higher stratigraphic levels in the well [19]. Therefore, the influence of groundwater movement on extraction and BTES was tested in this study using a modelling approach. OGS software uses the finite-element method for spatial discretisation and has been verified/validated against a series of solutions for shallow and DBHE examples (e.g., [10,12,22,23,24,25]). Further benchmarking was also undertaken in this study in comparison to T2Well-EOS1/TOUGH2. The ‘Dual Continuum’ method is used to model the wellbore, with components of the DBHE (grout, fluid, casing) treated as a 1D line source, integrated within a 3D medium for the subsurface rocks.

## 2. Methods

#### 2.1. Governing Equations

#### 2.2. Model Set Up, Initial Conditions and Parameterisation

#### 2.3. Evaluation Metrics

^{12}joules). The storage efficiency or recovery of heat is essential to understanding the performance of BTES. While different methods are used for calculating this value, in this study the method by Brown et al. [11] was used. Storage efficiency ($S{E}_{new})$ was defined as the difference in energy extracted with and without charge with respect to the total energy injected:

#### 2.4. Benchmarking

## 3. Results

#### 3.1. Extraction Only

#### 3.2. Borehole Thermal Energy Storage

#### 3.2.1. Influence of Inlet Temperature during Charge

#### 3.2.2. Influence of Inlet Temperature during Extraction

#### 3.2.3. Influence of the Deep Borehole Heat Exchanger Internal Flow Rate

#### 3.2.4. Influence of Varying Charge Periods

#### 3.2.5. Long Term Simulations

## 4. Discussion

#### 4.1. Implications of an Active Groundwater Flow on Heat Extraction Only

#### 4.2. Implications of an Active Groundwater Flow on Borehole Thermal Energy Storage

#### 4.3. Implications to Prospective Areas within the UK

#### 4.4. Comparison with Previous Studies for Shallow BTES

## 5. Conclusions

- Groundwater flow from thick aquifers with a Darcy velocity around or greater than 1e-6 m/s has a positive impact on heat extraction using DBHEs and will likely increase the longevity of such systems. The impact of this reduces with increased extraction inlet temperature whilst it significantly improves the achievable thermal power with increased flow rates.
- In contrast, increasing groundwater flow (approaching or above 1e-6 m/s) for BTES in single well DBHEs negatively impacts the storage efficiency (<5%).
- Increasing the internal DBHE fluid flow rate in lower Darcy velocity conditions did improve the performance for BTES by over 5%.
- Reducing the charge period significantly increases the recovery of heat, with charge periods of 1 and 3 months (followed by 11 months and 9 months discharge) resulting in storage efficiencies of up to 34 and 23%, respectively. Therefore, it may be more beneficial for DBHEs used for thermal energy storage to apply short, intense charge periods, followed by longer discharge periods.
- Simulation over a longer (5 year) series of charge-discharge cycles only has a minor impact on the recovery of heat, at least in the “fixed inlet temperature” mode of simulation that has been adopted in this paper.
- To maximize the storage efficiencies in single well BTES systems, specific to the modelled parameters in this paper at 920 m depth, it appears that it is best to have lower charge temperatures (of 65 °C), higher circulation flow rates (of 7 L/s), lower charge periods (of 1 month of less) and target subsurface systems with aquifer Darcy velocity of 1e-7 m/s or less.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**DBHE schematic with cold plume created during extraction (modified from [1]).

**Figure 2.**Map of the UK and approximate location of the study area (from [11]).

**Figure 4.**Comparison between OpenGeoSys (OGS) and T2Well-EOS1/TOUGH2 for the initial charge scenario. (

**a**) Inlet and outlet temperatures for the different software, (

**b**) comparison of the vertical profile with depth at the end of charge and (

**c**) comparison of the vertical profile at the end of the extraction period. Note that the dashed line in (

**b**,

**c**) is the central pipe, whilst the dotted line is for the annular space. For the first 6 months of charge a constant inlet temperature of 95 °C was applied and for the subsequent 6 months of discharge an inlet temperature of 5 °C was used.

**Figure 5.**Varying groundwater flows plotted for extraction operation only for 6 months. (

**a**) is the evolution of outlet temperature with time (note inlet is set equal to 5 °C), (

**b**) is the change in the temperature within the central pipe (solid line) and annulus (dashed line) at the end of the simulation (note that when groundwater flow is set to zero the red line is directly underneath that for the velocity set at 1e-8 m/s), (

**c**) is the thermal propagation around the BHE at 500 m depth (BHE is at point zero) and (

**d**) is the thermal plume at 500 m depth for a flow velocity of 1e-6 m/s.

**Figure 6.**Six-month simulation of heat extraction only from DBHE, with constant inlet temperature and internal fluid flow rate of 5 L/s. (

**a**) shows the impact of varying DBHE constant inlet temperature and groundwater Darcy velocity on DBHE outlet temperature; (

**b**) shows the impact on final thermal output from DBHE after 6 months. Groundwater Darcy velocity is varied between 0 m/s (conduction only) and 1e-6 m/s. Outlet temperatures and thermal powers were recorded at the end of the simulation.

**Figure 7.**Six-month simulation of heat extraction only from DBHE, with constant inlet temperature of 5 °C and varying the constant heat transfer fluid flow rate. (

**a**) shows the impact of varying DBHE internal fluid flow rate and groundwater Darcy velocity on DBHE outlet temperature; (

**b**) shows the impact on final thermal output from DBHE after 6 months. Groundwater Darcy velocity is varied between 0 (conduction only) and 1e-6 m/s. Outlet temperatures and thermal powers were recorded at the end of the simulation.

**Figure 8.**The impact of varying the constant DBHE input temperature during a 6 month heat charge cycle, followed by a 6 month discharge cycle. DBHE internal flow rate = 5 L/s and discharge inlet temperature was maintained constant at 5 °C. (

**a**) energy injected during charge, (

**b**) energy extracted during discharge cycle following charge, (

**c**) energy extracted during a 6 month discharge period without preceding charge and (

**d**) storage efficiency calculated according to Equation (10).

**Figure 9.**Impact of groundwater Darcy velocity on DBHE outlet temperature for a 6 month charge followed by 6 month discharge period. DBHE internal flow rate = 5 L/s and constant inlet temperature during discharge is 5 °C. (

**a**) is for constant 95 °C inlet temperature, (

**b**) is for 85 °C inlet temperature, (

**c**) is for 75 °C inlet temperature and (

**d**) is for 65 °C inlet temperature.

**Figure 10.**The impact of varying the constant DBHE input temperature during a 6 month heat discharge cycle, following a 6 month charge cycle. DBHE internal flow rate = 5 L/s and inlet temperature during charge was maintained constant at 95 °C. (

**a**) energy injected during charge, (

**b**) energy extracted during discharge cycle following charge, (

**c**) energy extracted during 6 month discharge period without preceding charge and (

**d**) storage efficiency calculated according to Equation (10).

**Figure 11.**The impact of varying the DBHE internal fluid circulation rate during a 6 month heat charge cycle, followed by a 6 month discharge cycle. Inlet temperature during charge was maintained constant at 95 °C during charge and 5 °C during discharge. (

**a**) energy injected during charge, (

**b**) energy extracted during discharge cycle following charge, (

**c**) energy extracted during 6 month discharge period without preceding charge and (

**d**) storage efficiency calculated according to Equation (10).

**Figure 12.**The impact of varying the DBHE charge-discharge cycle duration. Inlet temperature during charge was maintained constant at 95 °C during charge and 5 °C during discharge, with an internal DBHE fluid flow rate of 5 L/s. (

**a**) energy injected during charge, (

**b**) energy extracted during discharge cycle following charge (respectively 11, 9 and 6 months for 1, 3 and 6 months charge), (

**c**) energy extracted without preceding charge during 11, 9 and 6 month periods and (

**d**) storage efficiency calculated according to Equation (10).

**Figure 13.**Simulated outlet fluid temperature over multiple charge-extraction cycles. Inlet is fixed at 95 °C during charge and 5 °C during extraction.

**Figure 14.**Cross sections in plan view at 500 m depth at the end of the charge period after 5 annual cycles of 6 months charge and discharge. Image shows conductive heat transfer only in the subsurface and with the influence of groundwater flow (Darcy velocity of 1e-6 m/s).

**Table 1.**Thermo-physical parameters of the model. Model parameters are either taken from the literature, assumed unpublished values (compiled by [42,43]), calculated values or given as the most likely value. Note the inner pipe is the coaxial pipe and the outer pipe is the casing. The real nature of the casing situation is notably more complex than that modelled. The thermal properties of the rock in the subsurface are taken as the weighted average from Kolo et al. [10].

Parameter | Value | Units | Symbol |
---|---|---|---|

Borehole Depth [19] | 920 | m | $L$ |

Borehole Diameter [19] | 0.216 | m | ${D}_{b}$ |

Outer Diameter of Inner Pipe | 0.1005 | m | - |

Thickness of Inner Pipe | 0.00688 | m | - |

Thickness of Outer Pipe | 0.0081 | m | - |

Thickness of Grout | 0.01905 | m | - |

Thermal Conductivity of Polyethylene Inner Pipe | 0.45 | W/(m·K) | - |

Thermal Conductivity of Steel Outer Pipe | 52.7 | W/(m·K) | - |

Density of Rock [10,44] | 2480 | kg/m^{3} | ${\rho}_{r}$ |

Thermal Conductivity of Rock [10,19,45,46,47] | 2.55 | W/(mK) | ${\lambda}_{r}$ |

Specific Heat Capacity of Rock [10,48,49] | 950 | J/(kg·K) | ${C}_{r}$ |

Volumetric heat capacity of rock | 2.356 | MJ/(m^{3}·K) | - |

Density of Grout | 995 | kg/m^{3} | ${\rho}_{g}$ |

Thermal Conductivity of Grout | 1.05 | W/(m·K) | ${\lambda}_{g}$ |

Specific Heat Capacity of Grout | 1200 | J/kgK | ${C}_{g}$ |

Density of Fluid [1] | 998 | kg/m^{3} | ${\rho}_{f}$ |

Thermal Conductivity of Fluid | 0.59 | W/(m·K) | ${\lambda}_{f}$ |

Specific Heat Capacity of Fluid | 4179 | J/kg·K | ${C}_{f}$ |

Surface Temperature [45] | 9 | °C | - |

Geothermal Gradient [19,45] | 33.4 | °C/km | - |

Porosity | 20 | % | $\varphi $ |

Volumetric Flow Rate | 0.005 | m^{3}/s | $Q$ |

Parameter | Minimum | Maximum | Units |
---|---|---|---|

Groundwater Velocity (Darcy velocity) | None (conduction only) | 1e-6 | m/s |

Inlet Temperature (charge) | 65 | 95 | °C |

Inlet Temperature (extraction) | 5 | 20 | °C |

Internal Fluid Flow Rate | 1 | 7 | L/s |

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## Share and Cite

**MDPI and ACS Style**

Brown, C.S.; Doran, H.; Kolo, I.; Banks, D.; Falcone, G.
Investigating the Influence of Groundwater Flow and Charge Cycle Duration on Deep Borehole Heat Exchangers for Heat Extraction and Borehole Thermal Energy Storage. *Energies* **2023**, *16*, 2677.
https://doi.org/10.3390/en16062677

**AMA Style**

Brown CS, Doran H, Kolo I, Banks D, Falcone G.
Investigating the Influence of Groundwater Flow and Charge Cycle Duration on Deep Borehole Heat Exchangers for Heat Extraction and Borehole Thermal Energy Storage. *Energies*. 2023; 16(6):2677.
https://doi.org/10.3390/en16062677

**Chicago/Turabian Style**

Brown, Christopher S., Hannah Doran, Isa Kolo, David Banks, and Gioia Falcone.
2023. "Investigating the Influence of Groundwater Flow and Charge Cycle Duration on Deep Borehole Heat Exchangers for Heat Extraction and Borehole Thermal Energy Storage" *Energies* 16, no. 6: 2677.
https://doi.org/10.3390/en16062677