# Numerical Simulation of Operating Parameters of the Ground Source Heat Pump

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## Abstract

**:**

## 1. Introduction

#### 1.1. Energy Market in Poland and the European Union

#### 1.2. Modern Energy-Efficient Construction Challenges

#### 1.3. nZEB Building Concept

#### 1.4. Primary Enery Usage Reduction in nZEB Buildings

#### 1.5. COP Optimisation Methods

- Suitable for modelling a two-stage heat pump;
- Simplicity in the application of linear modelling;
- High accuracy considering heat source temperature, heat sink temperature and heat pump load;
- Applicable to both heat pumps and chillers.

## 2. Materials and Methods

#### 2.1. Heat Pump Thermodynamics

- Compression (1–2);
- Condensation (2–3);
- Expansion (3–4);
- Evaporation (4–1).

_{H}, Q

_{C}, N).

#### 2.2. COP

_{H}). The main parameter allowing optimisation of the heat pump efficiency is the temperature of the heat source, by increasing it, it is possible to increase the COP indicator of the heat pump and reduce the electricity consumption.

#### 2.3. Carnot COP Coefficient

#### 2.4. Lorenz COP Coefficient

_{Lift}= T

_{H}− T

_{C}. Assuming that the heat sink and heat source have constant heat capacity, the logarithmic mean temperatures were calculated as seen in Equation (3) [20]:

#### 2.5. COP Based on Thermodynamic Properties Obtained in Python’s CoolProp

_{2}point can be calculated with sufficient accuracy using the following equation [22]:

_{2}is a point located on saturation point (x = 1) of condensation temperature. The COP for the system can be defined as:

- H—enthalpy (kJ/kg)
- S—entropy (kJ/kg·K)
- P—pressure (Pa)
- T—temperature (K)

#### 2.6. SOPSAR System

- Use solar heat as the primary energy source;
- Produce heat and electricity using photovoltaic (PV-T) panels;
- Seasonal energy storage in the ground;
- Supply heat and cold to a building through a heat pump;
- Supply electricity to a building through a PV panel system;
- Use of waste heat from intelligent solar collectors or PV-T panels for regeneration of the ground;
- Maintain the heat pump’s high COP for subsequent heating seasons by using regeneration of the ground.

## 3. Results

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

COP | COP for heat pump Carnot cycle, (-) |

T | Temperature, (K) |

$\overline{\mathrm{T}}$ | Logarithmic mean temperature, (K) |

h | Enthalpy, (kJ/kg) |

H | Enthalpy, (kJ) |

Q | Energy flow (kJ) |

s | Entropy, (kJ/kg·K) |

N | Energy input for heat pump, (kJ) |

V | Volumetric flow, (m^{3}/h) |

## Subscripts

C | Source |

H | Sink |

Car | Carnot cycle |

I | Inflow |

O | Outflow |

Lorenz | Lorenz cycle |

## Abbreviations

COP | Coefficient of Performance |

nZEB | Nearly zero-energy building |

PV-T | Photovoltaics thermal panels |

GSHP | Ground source heat pump |

SGSHP | Solar assisted ground source heat pump |

COP(t) | COP function of temperature |

M | Million |

RMSD | Root mean square deviation |

## References

- Eurostat. Gross Production of Electricity and Derived Heat from Non-Combustible Fuels by Type of Plant and Operator. 2021. Available online: https://appsso.eurostat.ec.europa.eu (accessed on 25 September 2021).
- Statista. Annual Amount of Heat Pumps in Operation in the European Union (EU) from 2013 to 2019. 2020. Available online: https://www.statista.com/statistics/739745/heat-pumps-in-operation-eu/ (accessed on 25 September 2021).
- Eurobserv’er. Heat Pumps Barometer. 2020. Available online: https://www.eurobserv-er.org/pdf/eurobserver-heat-pumps-barometer-2020 (accessed on 23 May 2021).
- Nowak, T. Heat Pumps—Integrating Technologies to Decarbonise Heating and Cooling, EHPA. 2018. Available online: www.ehpa.org/fileadmin/red/03._Media/Publications/ehpa-white-paper-111018.pdf (accessed on 30 September 2021).
- Conrad, J.; Greif, S. Modelling Load Profiles of Heat Pumps. Energies
**2019**, 12, 766. [Google Scholar] [CrossRef] [Green Version] - Shimada, Y.; Uchida, Y.; Takashima, I.; Chotpantarat, S.; Widiatmojo, A.; Chokchai, S.; Charusiri, P.; Kurishima, H.; Tokimatsu, K. A Study on the Operational Condition of a Ground Source Heat Pump in Bangkok Based on a Field Experiment and Simulation. Energies
**2020**, 13, 274. [Google Scholar] [CrossRef] [Green Version] - Shin, D.U.; Jeong, C.-H. Energy Savings of Simultaneous Heating and Cooling System According to Indoor Set Temperature Changes in the Comfort Range. Energies
**2021**, 14, 7691. [Google Scholar] [CrossRef] - Anna, B. Architektura Energoaktywna po 2021. T. 1, Zagadnienia Architektoniczno—Budowlane; Oficyna Wydawnicza Politechniki Wrocławskiej: Wrocław, Poland, 2020. [Google Scholar]
- Magrini, A.; Lentini, G.; Cuman, S.; Bodrato, A.; Marenco, L. From nearly zero energy buildings (NZEB) to positive energy buildings (PEB): The next challenge—The most recent European trends with some notes on the energy analysis of a forerunner PEB example. Dev. Built Environ.
**2020**, 3, 100019. [Google Scholar] [CrossRef] - Fadejev, J.; Simson, R.; Kurnitski, J.; Kesti, J.; Mononen, T.; Lautso, P. Geothermal Heat Pump Plant Performance in a Nearly Zero-energy Building. Energy Procedia
**2016**, 96, 489–502. [Google Scholar] [CrossRef] - Gondal, I.A. Prospects of shallow geothermal systems in HVAC for NZEB. Energy Built Environ.
**2021**, 2, 425–435. [Google Scholar] [CrossRef] - Li, H.; Xu, W.; Yu, Z.; Wu, J.; Sun, Z. Application analyze of a ground source heat pump system in a nearly zero energy building in China. Energy
**2017**, 125, 140–151. [Google Scholar] [CrossRef] - Zhou, S.; Cui, W.; Zhao, S.; Zhu, S. Operation analysis and performance prediction for a GSHP system compounded with domestic hot water (DHW) system. Energy Build.
**2016**, 119, 153–163. [Google Scholar] [CrossRef] - Chu, G.; Wang, Y.; Chu, M. Measurement and Analysis of a GSHP System Operation in Winter. Procedia Eng.
**2016**, 146, 573–578. [Google Scholar] [CrossRef] [Green Version] - Pieper, H.; Krupenski, I.; Markussen, W.B.; Ommen, T.; Siirde, A.; Volkova, A. Method of linear approximation of COP for heat pumps and chillers based on thermodynamic modelling and off-design operation. Energy
**2021**, 230, 120743. [Google Scholar] [CrossRef] - Girard, A.; Gago, E.J.; Muneer, T.; Caceres, G. Higher ground source heat pump COP in a residential building through the use of solar thermal collectors. Renew. Energy
**2015**, 80, 26–39. [Google Scholar] [CrossRef] - Chen, J. Optimal Performance Characteristics of a Solar-Driven Heat Pump at Maximum COP. Energy Convers. Manag.
**1994**, 35, 1009–1014. [Google Scholar] [CrossRef] - Dincer, I.; Rosen, M.A. Energy, Environment and Sustainable Development; Elsevier: Oxford, UK, 2020. [Google Scholar]
- Duarte, M.V.; Pires, L.C.; Silva, P.D.; Gaspar, P.D. Experimental comparison between R409A and R437A performance in a heat pump unit. Open Eng.
**2017**, 7, 77–90. [Google Scholar] [CrossRef] - Jensen, J.K.; Ommen, T.; Reinholdt, L.; Markussen, W.B.; Elmegaard, B. Heat pump COP, part 2: Generalised COP estimation of heat pump processes. In Proceedings of the 13th IIR Gustav Lorentzen Conference on Natural Refrigerants (GL 2018), Valencia, Spain, 18–20 June 2018. [Google Scholar]
- Byrne, P.; Miriel, J.; Lénat, Y. Modelling and simulation of a heat pump for simultaneous heating and cooling. Build. Simul.
**2012**, 5, 219–232. [Google Scholar] [CrossRef] [Green Version] - Patwardhan, V.R.; Patwardhan, V.S. A simplified procedure for the estimation of (COP)R for heat pumps. Heat Recovery Syst. CHP
**1987**, 7, 435–440. [Google Scholar] [CrossRef] - Ocłoń, P. Renewable Energy Utilization Using Underground Energy Systems; Springer Nature: Cham, Switzerland, 2021. [Google Scholar]

**Figure 1.**Log T-s diagram of the vapour-compression refrigeration cycle. Reprinted with permission from ref. [19]. 2017 Duarte et al.

**Figure 2.**Log p-h diagram of the vapour-compression refrigeration cycle. Reprinted with permission from ref. [19]. 2017 Duarte et al.

**Figure 3.**Schematics of the vapour-compression device. Reprinted with permission from ref. [19]. 2017 Duarte et al.

**Figure 4.**Schematics of RESHeat system. Reprinted with permission from ref. [23]. 2021 Ocłoń.

**Figure 5.**Characteristic points for R410A refrigerant cycle generated by the Python script for source temperature equal to 5 °C and sink temperature of 45 °C.

**Figure 6.**Elements of existing SOPSAR system, solar tracked collectors manufactured by the Elfran company (

**top left corner**), solar tracked PV-T panels manufactured by the Elfran company (

**top right corner**), underground heat storage tanks (

**bottom left corner**), and heat pump (

**bottom right corner**). Reprinted with permission from ref. [23]. 2021 Ocłoń.

**Table 1.**Wind and photovoltaic energy production (GWh) Reprinted with permission from ref. [1]. 2021 Eurostat.

2011 | 2012 | 2013 | 2014 | 2018 | 2019 | 2020 | ||
---|---|---|---|---|---|---|---|---|

EU-27 | Wind | 165,346.9 | 187,460.6 | 209,474.8 | 222,356.7 | 320,506.5 | 367,115.3 | 397,054.8 |

PV | 45,329.5 | 66,401.5 | 79,334.7 | 88,714.1 | 110,480.5 | 120,034.7 | 140,244.4 | |

Poland | Wind | 3204.5 | 4746.6 | 6003.8 | 7675.6 | 12,798.8 | 15,106.8 | 15,799.7 |

PV | 0.2 | 1.1 | 1.5 | 6.9 | 300.5 | 710.7 | 1990.3 |

T_{sink} (°C) | T_{source} (°C) | ΔT_{Evap} (K) | ΔT_{Cond} (K) | V_{sink} (m ^{3}/h) | V_{source} (m ^{3}/h) | Subcooling (K) | Superheating (K) | Pinch-Point (K) |
---|---|---|---|---|---|---|---|---|

45; 50 | 5–20 | 6.1 | 6.9 | 5.6 | 4.6 | 2 | 5 | 1 |

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**MDPI and ACS Style**

Bartyzel, F.; Wegiel, T.; Kozień-Woźniak, M.; Czamara, M.
Numerical Simulation of Operating Parameters of the Ground Source Heat Pump. *Energies* **2022**, *15*, 383.
https://doi.org/10.3390/en15010383

**AMA Style**

Bartyzel F, Wegiel T, Kozień-Woźniak M, Czamara M.
Numerical Simulation of Operating Parameters of the Ground Source Heat Pump. *Energies*. 2022; 15(1):383.
https://doi.org/10.3390/en15010383

**Chicago/Turabian Style**

Bartyzel, Filip, Tomasz Wegiel, Magdalena Kozień-Woźniak, and Marek Czamara.
2022. "Numerical Simulation of Operating Parameters of the Ground Source Heat Pump" *Energies* 15, no. 1: 383.
https://doi.org/10.3390/en15010383