# Exergy Analysis for Utilizing Latent Energy of Thermal Energy Storage System in District Heating

^{1}

^{2}

^{*}

## Abstract

**:**

^{3}/h. In this case, each power generation facility was 50% of the thermal storage capacity, which was attributed to the variation of actual heat storage from the annual operating pattern analysis. Therefore, it was possible to produce 1200 kW of power by recovering the exergy losses. The payback period of the ORC and the hydraulic turbine will be 3.5 and 7.13 years, respectively.

## 1. Introduction

_{2}emissions avoided, in buildings and in industrial sectors, by more extensive use of heat and cold storage [4].

## 2. Research Methods

#### 2.1. Methods of Exergy Analysis

_{ph}+ E

_{kn}+ E

_{pt}+ E

_{ch},

_{kn}is exergy by velocity or kinetic energy, E

_{pt}is exergy by the potential energy, E

_{ph}is the physical exergy, which is the difference of temperature and pressure between actual state and reference state, and E

_{ch}is chemical exergy, resulting from the reaction. Physical exergy is expressed as follows:

_{ph}= (U − U

_{0}) + p

_{0}(V − V

_{0}) − T

_{0}(S − S

_{0}) = (h − h

_{0}) − T

_{0}(S − S

_{0}) = W

_{c,max},

_{i}), which is the total exergy in the system, is expressed by the sum of exergy loss (E

_{L}), the exergy destruction (E

_{D}), and the outlet of exergy (E

_{e}). Exergy loss (E

_{L}) means loss of exergy, which does not contribute to work or heat transfer (Q). Exergy destruction (E

_{D}) is exergy destroyed by friction within the control volume. They all have the same meaning in that they do not contribute to work or heat transfer in the process of changing the system [22].

_{i}= E

_{e}+ E

_{L}+ E

_{D},

_{0}is the reference temperature for calculating the exergy value of each stream. As shown in Equation (2), the exergy value depends on the reference temperature and the result is the different exergy value. As a result, different exergy analysis results can be derived for the exergy value of each stream. Therefore, selection of the reference temperature in the exergy calculation is very important and should be done depending on the characteristics of the system to be analyzed. In this study, the temperature (T

_{0}) and pressure (P

_{0}) of the reference state for calculating the exergy value were set to the thermodynamic standard temperature of 25 °C.

^{2}g) of each stream and e is the exergy per unit mass (kJ/kg). Therefore, the exergy flow (kJ/s) per unit time of the n

_{th}stream in the target process can be obtained from the following equation:

_{n}(kW) = ṁ

_{n}(kg/s) × e

_{n}(kJ/kg).

_{1}·e

_{1}) + Ẇ

_{DHS}= (ṁ

_{2}·e

_{2}) − E

_{L,①}or E

_{1}+ Ẇ

_{DHS}= E

_{2}− E

_{L,①}.

_{3}− ṁ

_{2})·e

_{2}= (ṁ

_{3}·e

_{3}) − E

_{L,②}or E

_{2}= E

_{3}− E

_{L,②}.

_{3}·e

_{3}) + Ẇ

_{RP}= (ṁ

_{4}·e

_{4}) − E

_{L,③}or E

_{3}+ Ẇ

_{RP}= E

_{4}− E

_{L,③}.

#### 2.2. Analysis of Supply and Return Temperature of District Heating Water

#### 2.3. Analysis of Supply Pressure During Storing Heat in TES

^{2}g, the lowest was 4.3 kg/cm

^{2}g, and the average was 11.6 kg/cm

^{2}g.

#### 2.4. Analysis of Heat Storage Capacity

^{3}. It can pump a volume of 100 Gcal/h (volume of 3000 m

^{3}/h) of DH water. Accordingly, when the heat storage tank capacity is known, the flow rate of the heating water from the amount of storing heat can be calculated. Table 4 presents the heat storage capacity designed with the operational data from the heat management system for TES system and a heat storage capacity of 1000 Gcal.

## 3. Results and Discussion

#### 3.1. Exergy Analysis of the Previous System

#### 3.2. Reduction of Exergy Losses from Thermal Loss

- -
- Amount of heat source water (primary heating water): 1500 m
^{3}; - -
- Temperature of heat source water: 110 °C;
- -
- Temperature of condensing water (return DH water): 45 °C;
- -
- Working fluid: R245fa (environment-friendly refrigerant).

#### 3.3. Reduction of Exergy Loss by Pressure Loss

- -
- Flow rate of turbine inlet: 1500 m
^{3}; - -
- Pressure of turbine inlet: 11.6 kg/cm
^{2}g; - -
- Temperature of turbine inlet: 100 °C;
- -
- Pressure of turbine outlet: 4.5 kg/cm
^{2}g.

#### 3.4. Economic Evaluation

_{0}denotes the initial investment cost and i denotes the discount rate [24,25]. In this study, C

_{0}was obtained from the manufacturer’s proposal and i was assumed to be 5%.

_{el}− C

_{OM}= (PW × PR) − C

_{OM},

_{OM}($) denotes the relative operation and maintenance cost.

## 4. Conclusions

^{3}/h. In this case, each power generation facility is 50% of the thermal storage capacity, which is attributed to the variation of heat storage from the annual operating pattern analysis. Therefore, it is possible to produce 1200 kW of power by recovering 4533.3 kW exergy losses. In addition, economic analysis established that both facilities can reduce exergy losses in the TES system and be practically applicable.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Nomenclature

C_{OM} | Operation and maintenance cost, $ |

DH | District heating |

DHS | District heating supply |

e | Exergy per unit mass, kJ/kg |

E_{ch} | Chemical exergy resulting from the reaction, kJ/kg |

E_{D} | Exergy destruction, kJ/kg |

E_{e} | Outlet of exergy, kJ/kg |

E_{i} | Inlet of exergy, total exergy in the system, kJ/kg |

E_{kn} | Exergy by velocity or kinetic energy, kJ/kg |

E_{L} | Exergy loss, kJ/kg |

E_{ph} | Physical exergy, difference between actual state and reference state, kJ/kg |

E_{pt} | Exergy by the potential energy, kJ/kg |

GM | Gross margin, $/yr |

HT | Hydraulic turbine |

i | Additional ratio, % |

ṁ | Flow rate, kg/s |

P | Pressure, kg/cm^{2}g |

PB | Payback period, $/kWh |

PW | Magnitude of electricity, kWh |

RP | Release pump |

Q | Heat transfer, kJ |

T | Temperature, °C |

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Division | Jan. | Feb. | Mar. | Apr. | May | Jun. | Jul. | Aug. | Sep. | Oct. | Nov. | Dec. |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Highest | 119 | 118 | 117 | 117 | 110 | 110 | 109 | 109 | 112 | 110 | 114 | 116 |

Average | 112 | 112 | 112 | 110 | 96 | 99 | 99 | 99 | 99 | 101 | 107 | 109 |

Lowest | 105 | 104 | 104 | 92 | 87 | 89 | 92 | 89 | 88 | 94 | 97 | 100 |

Division | Jan. | Feb. | Mar. | Apr. | May | Jun. | Jul. | Aug. | Sep. | Oct. | Nov. | Dec. |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Highest | 50 | 49 | 51 | 54 | 96 | 91 | 91 | 65 | 61 | 62 | 67 | 51 |

Average | 43 | 43 | 44 | 44 | 70 | 53 | 57 | 57 | 51 | 50 | 44 | 44 |

Lowest | 37 | 38 | 36 | 35 | 33 | 38 | 48 | 45 | 22 | 39 | 38 | 39 |

Division | Jan. | Feb. | Mar. | Apr. | May | Jun. | Jul. | Aug. | Sep. | Oct. | Nov. | Dec. |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Highest | 14.7 | 14.7 | 14.6 | 12.5 | 9.4 | 9.2 | 8.0 | 9.2 | 9.3 | 12.0 | 15.5 | 14.6 |

Average | 11.4 | 11.7 | 11.9 | 8.2 | 5.4 | 6.0 | 5.9 | 6.6 | 6.4 | 7.5 | 11.0 | 12.2 |

Lowest | 7.2 | 6.8 | 7.7 | 5.1 | 4.5 | 4.3 | 4.9 | 5.1 | 5.1 | 5.3 | 6.2 | 9.2 |

Division | Jan. | Feb. | Mar. | Apr. | May | Jun. | Jul. | Aug. | Sep. | Oct. | Nov. | Dec. |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Highest | 135 | 153 | 120 | 165 | 156 | 138 | 145 | 172 | 169 | 158 | 198 | 145 |

Average | 43 | 55 | 42 | 34 | 20 | 43 | 47 | 74 | 67 | 62 | 50 | 40 |

Lowest | 14 | 16 | 14 | 12 | 6 | 15 | 14 | 20 | 20 | 19 | 17 | 14 |

Time | 331 | 287 | 336 | 360 | 275 | 345 | 300 | 265 | 290 | 313 | 346 | 357 |

No | $\dot{\mathbf{m}}$ (kg/s) | T (°C) | P (kg/cm^{2}g) | e (kJ/kg) | E (kW) | Remarks |
---|---|---|---|---|---|---|

1 | 833.3 | 110 | 4.0 | 42.912 | 35,758.57 | Ẇ_{DHS} |

2 | 833.3 | 110 | 11.6 | 42.912 | 35,758.57 | =910.8 kW |

3 | 416.7 | 110 | 11.6 | 42.912 | 17,881.43 | =455.5 kW |

4 | 416.7 | 98 | 4.5 | 32.295 | 13,457.33 | Ẇ_{RP} |

5 | 416.7 | 98 | 11.6 | 32.295 | 13,457.33 | =425.5 kW |

6 | 833.3 | 44 | 4.0 | 2.427 | 2022.42 | |

7 | 833.3 | 44 | 4.0 | 2.427 | 2022.42 |

Process | Exergy Inlet (kW) | Exergy Outlet (kW) | Exergy Loss (kW) |
---|---|---|---|

① DH Pump | 36,669.37 | 35,758.57 | E_{L,①} = 910.8 |

② Control Valve | 18,336.93 | 13,457.33 | E_{L,②} = 4879.6 |

③ Release Pump | 13,882.83 | 13,457.33 | E_{L,③} = 425.5 |

Location | Heat Source | Working Fluid | Cooling Water | |||
---|---|---|---|---|---|---|

Item | Value | Item | Value | Item | Value | |

Inlet | Temperature | 110 °C | Temperature | 69.01 °C | Temperature | 45 °C |

Flowrate | 1500 t/h | Pressure | 9.257 ata | Flowrate | 2755 t/h | |

Outlet | Temperature | 100 °C | Temperature | 100 °C | Temperature | 50 °C |

Flowrate | 1500 t/h | Pressure | 9.076 ata | Flowrate | 2755 t/h |

Item | Value |
---|---|

Combined heat and power (CHP) Plant Capacity factor | 0.8 |

Discount rate (%) | 5 |

Unit Price of Electricity ($/kWh) | 0.1 |

Operating and Maintenance Cost | 3% of each facility |

Item | ORC | Hydraulic Turbine |
---|---|---|

Investment Cost ($) | 1,870,000 | 945,000 |

Income of Electricity sales ($/yr) | 651,744 | 189,216 |

Operating and Maintenance Cost ($/yr) | 56,100 | 28,350 |

Gross Margin ($/yr) | 595,644 | 160,866 |

Payback Period (yr) | 3.50 | 7.13 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yi, J.Y.; Kim, K.M.; Lee, J.; Oh, M.S.
Exergy Analysis for Utilizing Latent Energy of Thermal Energy Storage System in District Heating. *Energies* **2019**, *12*, 1391.
https://doi.org/10.3390/en12071391

**AMA Style**

Yi JY, Kim KM, Lee J, Oh MS.
Exergy Analysis for Utilizing Latent Energy of Thermal Energy Storage System in District Heating. *Energies*. 2019; 12(7):1391.
https://doi.org/10.3390/en12071391

**Chicago/Turabian Style**

Yi, Joong Yong, Kyung Min Kim, Jongjun Lee, and Mun Sei Oh.
2019. "Exergy Analysis for Utilizing Latent Energy of Thermal Energy Storage System in District Heating" *Energies* 12, no. 7: 1391.
https://doi.org/10.3390/en12071391