# Thermo-Economic Analysis of Near-Surface Geothermal Energy Considering Heat and Cold Supply within a Low-Temperature District Heating Network

^{*}

## Abstract

**:**

## 1. Introduction

- Holistic simulation of the heating network, consumers, and geothermal heat sources using resilient user profiles;
- Investigation of geothermal heat sources with respect to the heating and cooling capacity;
- Evaluation of these heat sources for various scenarios in terms of thermodynamic and economic aspects.

## 2. Methodology

- Location and Weather: The weather data used in this model consist of the dry bulb temperature, which is provided by ASHRAE [13] for the investigated region of Stuttgart. In addition, all parameters that characterise the ground of the considered location, such as density, heat capacity, and thermal conductivity are considered;
- Distance: The distance between users is necessary for the calculation of pressure and heat losses or gains within the pipeline;
- Consumers: Each user is described by three thermal demand profiles for heating, cooling, and domestic hot water. Furthermore, the characteristic curves of the heat pump for each load case are implemented.

- Global outputs represent the energy balances that concern the entire network, such as total energy imported or exported from the pipeline and the effect on the geothermal heat source.
- Local outputs show the effects on the consumer, such as electrical power consumption of the heat pump and sufficient supply of the load profiles.

#### 2.1. Distribution System

_{fric}and p

_{geo}being the pressure losses due to friction and geodetic elevation, λ

_{pipe}the friction factor of the pipe, l

_{pipe}the length of the pipe, and d

_{i,pipe}the inner diameter of the pipe. ρ

_{medium}represents the density of the fluid, v

_{pipe}the velocity, z the geodetic elevation, and g the gravitational acceleration. These elements characterise the total pressure drop within the pipeline. The properties of the polyethylene pipes such as length and diameter, as well as the thermal and hydraulic properties of the pipes, can be adjusted in the parameters. The assumptions used are shown in Table 1. Due to the very low mass compared to the ground and the heat transfer fluid, the heat capacity of the pipes was neglected in order to reduce the calculation time [15].

_{soil}is calculated according to Florides et al. [17] and Perpar et al. [18], in accordance with Equation (3)

_{mean}as the mean surface temperature and T

_{amp}as the amplitude of the surface temperature. D describes the depth below the surface and α is the thermal diffusivity of the soil, while t

_{year}and t

_{shift}represent the current time and the day of the year with the minimum surface temperature. For the buried pipe, two heat transfer mechanisms are dominant: heat conduction and heat convection. One-dimensional heat conduction after Fourier is taken into account according to Equation (4)

_{pipe}and λ

_{soil}as the heat conductivity of the pipe and the soil, and r

_{pipe,outer,}r

_{pipe,inner}, and r

_{soil}as the radius of the inner pipe, the outer pipe, and the surrounding cylindrical soil cell.

#### 2.2. Consumer

#### 2.3. Load Profiles

#### 2.4. Geothermal Heat Sources

_{b}(t) as the borehole wall temperature, T

_{g}the undisturbed ground temperature, k

_{s}the ground thermal conductivity, and H as the borehole length. N

_{b}means the number of boreholes in the field and g(t) represents the g-function. The g-function was calculated according to the finite line source solution, using the method by Cimmino and Bernier [33] and Cimmino [34]. Since this g-function is based on line sources of heat rather than cylinders, the g-function was corrected to consider the cylindrical geometry. As correction factor, the difference between the cylindrical heat source solution and the infinite line source solution according to Equation (9) was applied, as proposed by Li et al. [35].

_{FLS}(t) represents the g-function evaluated for the finite line source solution, g

_{CHS}(t) represents the g-function evaluated for the cylindrical geometry, and g

_{ILF}(t) represents the evaluated solution for the infinite line source. According to Equations (7) and (8), the wall temperature of the borehole for every segment and hence, the heat exchange with the surrounding soil, can be calculated. The physical parameters for the GHE simulation are shown in Table 5.

#### 2.5. Economical Assessment

_{i}as the annualised capital cost of investment of the specific component I, and OMi as the sum of annual cost for operation and maintenance. Furthermore, Q

_{i}means the annual amount of energy used and b

_{i}is the cash value factor.

_{0}means the investment amount of the specific component, q the interest factor, and T

_{obs}the observation period in years. Increases in costs for operating and maintenance, as well as energy, are considered via the cash value factor b

_{i}according to Equation (12)

## 3. Results

#### 3.1. Sole Heating Case

_{th}when using horizontal systems and 22.3 ct/kWh

_{th}in the case of a vertical systems. Accordingly, horizontal systems result in significant savings of around 12%.

#### 3.2. Heating and Cooling Scenario

#### 3.3. Variation of the Region

_{H/C}becomes.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Latin Letters | |

b_{i} | Cash value factor |

D | Depth below the surface (surface=0) |

d_{i,pipe} | Inner diameter of the pipe |

g | g-function |

g_{FLS}(t)
| g-function evaluated for the finite line source solution |

g_{CHS}(t)
| g-function evaluated for the cylindrical geometry |

g_{ILF}(t)
| g-function evaluated for the infinite line source solution |

H | Borehole length |

k_{s} | Ground thermal conductivity |

l_{pipe} | Length of the pipe |

N_{b} | Number of boreholes in the field |

O_{Mi} | Sum of annual cost for operation and maintenance |

P_{i} | Annualised capital cost of investment pf the specific component i |

P_{0} | Investment amount of the specific component |

P_{el} | Electrical power |

p_{fric} | Pressure losses due to friction |

p_{geo} | Pressure losses due to geodetic elevation |

Q | Heat flow |

Q_{i} | Annual amount of energy |

q | Interest factor |

R | Annual revenues |

r_{pipe,inner} | Inner radius of the pipe |

r_{pipe,outer} | Outer radius of the pipe |

r_{soil} | Radius of the cylindrical soil cell |

T_{amp} | Amplitude of surface temperature |

T_{b}(t)
| Borehole wall temperature |

T_{g} | Undisturbed ground temperature |

T_{mean} | Mean surface temperature (average air temperature). |

T_{soil} | Soil temperature at depth D and Time of year |

t_{shift} | Day of the year of the minimum surface temperature |

t_{year} | Current time |

v_{pipe} | Velocity within the pipe |

z | Geodetic elevation |

Greek Letters | |

α | Thermal diffusivity of the ground (soil) |

ρ_{medium} | Density of the fluid |

λ_{pipe} | Friction factor |

λ_{pipe} | Heat conductivity of the pipe |

λ_{soil} | Heat conductivity of the soil |

Abbreviations | |

COP | Coefficient of Performance |

GHE | Ground Heat Exchanger |

LCOC | Levelised Cost of Cold |

LCOH | Levelised Cost of Heat |

LTDH | Low-temperature district heating |

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**Figure 1.**Characteristic curves of the used heat pump for heating power (

**a**) and electrical consumption (

**b**) according to flow temperature, own representation according to [20].

**Figure 3.**Schematic illustration of the determination of the load profiles using the Hourly Analysis Program (HAP).

**Figure 5.**Overall COP for the design case (

**a**) and LCOH for various dimensioning of the geothermal heat source (

**b**).

**Figure 6.**Flow temperature profiles for a vertical (

**a**) and a horizontal (

**b**) GHE during the cooling season.

**Figure 9.**LCOH (

**a**) and LCOC (

**b**) for various dimensioning of the geothermal heat source for the region of Oslo.

**Figure 11.**LCOH (

**a**) and LCOC (

**b**) for various dimensioning of the geothermal heat source for the region of Bordeaux.

Parameter | Value | Unit |
---|---|---|

Material | Polyethylene 100 | |

Inner diameter | 25–150 | mm |

Wall thickness | 3–6 | mm |

Thermal conductivity | 0.42 | W/(m·K) |

Pipe roughness | 0.0014 | mm |

**Table 2.**Physical properties of the used water-ethylene glycol mixture at a reference temperature of 10 °C, own representation according to [16].

Parameter | Value | Unit |
---|---|---|

Share of ethylene glycol | 20 | vol% |

Freezing point | −8 | °C |

Density | 1028 | kg/m³ |

Specific heat capacity | 3.97 | kJ/(kg·K) |

Viscosity | 2 × 10^{−3} | Pa·s |

**Table 3.**Physical properties of the soil, own representation according to [19].

Parameter | Value | Unit |
---|---|---|

Ground thermal capacity | 2.6 | MJ/(m³·K) |

Ground thermal conductivity | 1.5–3.5 | W/(m·K) |

Ground thermal diffusivity | 9.77 × 10^{−7} | m/s² |

Depth where the temperature gradient starts | 10 | m |

Vertical temperature gradient | 0.03 | K/m |

**Table 4.**Used building components with corresponding maximum thermal transmittance, own representation according to the KfW-153 standard [21].

Building Component | Thermal Transmittance [W/(m²·K)] |
---|---|

Roof surfaces, top floor ceiling | 0.14 |

Transparent building components | 0.9 |

Opaque components | 0.25 |

Basement | 0.2 |

Exterior walls | 0.2 |

Cellar and exterior doors | 1.2 |

Parameter | Value | Unit |
---|---|---|

Diameter geothermal pipes | 32 | mm |

Wall thickness pipe | 3 | mm |

Heat conductivity pipe | 0.42 | W/(m·K) |

Type of vertical GHE | Double U-pipe | - |

Distance between U-pipes | 5 | m |

Maximum drilling depth | 100 | m |

Borehole radius | 75 | mm |

Density grout | 1600 | kg/m³ |

Heat conductivity grout | 0.81 | W/(m·K) |

Heat capacity grout | 800 | J/(kg·K) |

Depth of the horizontal GHE | 1.5 | m |

Distance between horizontal pipes | 0.7 | m |

Parameter | Value | Unit | Reference |
---|---|---|---|

Installation of LTDH network | 230 | €/m | [28,38] |

Maintenance of LTDH network | 1 | % of total invest/a | [37] |

Installation vertical GHE | 1050 | €/kW | [27] |

Installation horizontal GHE | 450 | €/kW | [38] |

Consumer heat pump | 1000 | €/kW | [27] |

Substation and installation | 4000 | € | - |

Interest factor | 1.05 | - | [37] |

Price change factor | 1.03 | - | [37] |

Observation period | 40 | a | [37] |

Electricity tariff for heat pumps | 22.5 | ct/kWh_{el} | [39] |

Parameter | Value | Unit |
---|---|---|

Number of consumers | 41 | – |

Total length of the grid | 650 | m |

Geothermal extraction power | 200 | kW |

Room heating demand per consumer | 5224 | kWh/a |

Domestic hot water demand per consumer | 3276 | kWh/a |

Calculated cooling demand per consumer | 3938 | kWh/a |

Vertical GHE | Horizontal GHE | |
---|---|---|

Design case | 0% | 0% |

Total invest heat source (€) | 210,000 | 90,000 |

Mean value COP | 4.15 | 3.98 |

Electricity demand (kWh_{el}) | 2048 kWh | 2135 |

LCOH (ct/kWh) | 22.28 | 19.80 |

Optimal case | −15% | +10% |

Invest cost heat source (€) | 178,500 | 99,000 |

Mean value COP | 3.79 | 4.17 |

Electricity demand (kWh_{el}) | 2242 | 2036 |

LCOH (ct/kWh_{th}) | 21.43 | 19.56 |

Savings (%) | 3.8 | 1.5 |

Stuttgart | Oslo | Bordeaux | |
---|---|---|---|

Annual mean ambient temperature (°C) | 10.1 | 7.0 | 13.9 |

Annual amount of heating energy (kWh) | 5224 | 8839 | 1729 |

Annual amount of cooling energy (kWh) | 3938 | 3057 | 6294 |

Annual domestic hot water load (kWh) | 3276 | 3276 | 3276 |

Design installation cost vertical GHE (€) | 210,000 | 296,100 | 123,900 |

Design installation cost horizontal GHE (€) | 90,000 | 126,900 | 53,100 |

Stuttgart | Oslo | Bordeaux | Madrid | |
---|---|---|---|---|

Annual heat demand per consumer [kWh] | 8500 | 12,115 | 5005 | 4321 |

Annual cooling demand per consumer [kWh] | 3938 | 3057 | 6294 | 9677 |

Heating-to-cooling demand ratio | 2.2 | 4.0 | 0.8 | 0.4 |

Most economic GHE system | Horizontal | Horizontal | Vertical | Vertical |

Savings from next most economic GHE [%] | 2.65 | 4.16 | 3.00 | - |

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## Share and Cite

**MDPI and ACS Style**

Kutzner, S.; Heberle, F.; Brüggemann, D. Thermo-Economic Analysis of Near-Surface Geothermal Energy Considering Heat and Cold Supply within a Low-Temperature District Heating Network. *Processes* **2022**, *10*, 421.
https://doi.org/10.3390/pr10020421

**AMA Style**

Kutzner S, Heberle F, Brüggemann D. Thermo-Economic Analysis of Near-Surface Geothermal Energy Considering Heat and Cold Supply within a Low-Temperature District Heating Network. *Processes*. 2022; 10(2):421.
https://doi.org/10.3390/pr10020421

**Chicago/Turabian Style**

Kutzner, Sebastian, Florian Heberle, and Dieter Brüggemann. 2022. "Thermo-Economic Analysis of Near-Surface Geothermal Energy Considering Heat and Cold Supply within a Low-Temperature District Heating Network" *Processes* 10, no. 2: 421.
https://doi.org/10.3390/pr10020421