# Exergy Evaluation of a Water Distribution System

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## Abstract

**:**

## 1. Introduction

## 2. Methods of Evaluation

^{3}/kg], p is the water pressure in pipes [Pa], and p

_{0}is the reference pressure [Pa].

_{0}is the reference height [m].

## 3. Exergy Model of a Water Supply System

#### 3.1. Exergy Model for Reservoirs

^{3}/kg], g is the gravity [m/s

^{2}], ${\mathrm{p}}_{\mathrm{r}}$ is the water pressure in the reservoir [Pa], and ${\mathrm{H}}_{\mathrm{r}}$ is the head water in the reservoir [m].

#### 3.2. Exergy Model for Pumps

#### 3.3. Exergy Model for Pipes

#### 3.4. Exergy Model for Nodes

#### 3.5. Exergy Model for Valves

#### 3.6. Exergy Model for Tanks

- $\Delta {\dot{\mathrm{B}}}_{\mathrm{t}}=0$—water levels in the tank at the beginning and end of analysis are equal.
- $\Delta {\dot{\mathrm{B}}}_{\mathrm{t}}>0$—water level in the tank is higher at the end than at the start of analysis.
- $\Delta {\dot{\mathrm{B}}}_{\mathrm{t}}<0$—water level in the tank is lower at the end than at the start of analysis.

#### 3.7. Exergy Model for Devices

## 4. Case Studies

#### 4.1. Water Distribution Network

^{3}/day. The network scheme is presented in Figure 9.

_{2}O (2 bar) and the water loss was 15%. The analyses were conducted for 1 d, with 1-h time steps (24 time steps in total).

^{3}) in pipes, Figures S2 and S3 (Attachment 1) present visualisation of exergy destruction for nodes. For the complex evaluation of the overall system, exergy balance was developed based on Equation (32):

- $\sum}{\mathrm{B}}_{r,\mathrm{use}$—the sum of exergy outflow from reservoir [kWh],
- $\sum}{\mathrm{B}}_{\mathrm{use}$—the sum of usable exergy outflow from the thermodynamical system [kWh],
- $\sum}{\mathsf{\delta}\mathrm{B}}_{\mathrm{exc}$—the sumof internal exergy destructions caused by excess pressure higher than required in the node [kWh],
- $\sum}{\mathsf{\delta}\mathrm{B}}_{\mathrm{loss}$—the sum of exergy destructions, caused by loss of water mass because of leakage [kWh]
- $\sum}{\mathsf{\delta}\mathrm{B}}_{\mathrm{p}$—the sum of internal exergy destruction in the pipes (caused by friction) [kWh].

#### 4.2. Water Treatment Plant

^{3}) in the water treatment plant. For the complex evaluation of the overall system, exergy balance was developed based on Equation (33):

- $\sum}{\mathrm{B}}_{\mathrm{in},\mathrm{pump}$—the sum of exergy inflow to the thermodynamical system (inlet pipse) [kWh]
- $\sum}{\mathrm{B}}_{\mathrm{r},\mathrm{out}$—the sum of exergy outflow from reservoir [kWh], $\sum}{\mathrm{B}}_{\mathrm{use}$—the sum of usable exergy outflow from the thermodynamical system [kWh],
- $\sum}{\mathrm{B}}_{\mathrm{use}$—the sum of usable exergy outflow from the thermodynamical system [kWh],
- $\sum}{\mathsf{\delta}\mathrm{B}}_{\mathrm{p}$—the sum of internal exergy destruction in the pipes (caused by friction) [kWh],
- $\sum}{\mathsf{\delta}\mathrm{B}}_{\mathrm{pump}$—the sum of internal exergy destruction in the pump [kWh].
- $\sum}{\mathsf{\delta}\mathrm{B}}_{\mathrm{fill}$—the sum of internal exergy destruction in the filter [kWh].
- $\sum}{\mathsf{\delta}\mathrm{B}}_{\mathrm{aer}$—the sum of internal exergy destruction in the aerator [kWh].
- $\sum}{\mathsf{\delta}\mathrm{B}}_{\mathrm{v}$—the sum of internal exergy destruction in the valves (minor losses) [kWh].
- $\sum}{\mathsf{\delta}\mathrm{B}}_{\mathrm{well}$—the sum of internal exergy destruction in well [kWh].
- $\sum}{\mathrm{B}}_{\mathrm{t}$—exergy stored in tank at the end simulation [kWh],
- $\sum}{\mathsf{\delta}\mathrm{B}}_{\mathrm{loss}$—the sum of exergy destructions, caused by loss of water mass because of leakage [kWh]

## 5. Discussion

## 6. Conclusions

- Exergy analysis is an effective method of assessing the water supply system. It enables both quantitative and qualitative assessment of energy transformations,
- Analyse of exergy balance allow the determination of the most exergy-consuming elements in the system and assess the possibility of reducing exergy destruction during modernisation,
- The developed tools can be used to support decision making in the design, operation, and maintenance of water-supply systems,
- Using developed open source tool, it is possible to automatically perform an exergy analysis of the system. This approach can be helpful in maintenance processes to determine system insufficiencies.

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Types of Elements | Source of Exergy Destructions |
---|---|

Pumps | Hydraulic friction Electrical energy transformation to the kinetic and potential energy of water |

Pipes | Hydraulic friction External exergy destructions (caused by leakage) |

Nodes | Maintaining pressure higher than required |

Valves | Hydraulic friction |

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**MDPI and ACS Style**

Bylka, J.; Mróz, T.
Exergy Evaluation of a Water Distribution System. *Energies* **2020**, *13*, 6221.
https://doi.org/10.3390/en13236221

**AMA Style**

Bylka J, Mróz T.
Exergy Evaluation of a Water Distribution System. *Energies*. 2020; 13(23):6221.
https://doi.org/10.3390/en13236221

**Chicago/Turabian Style**

Bylka, Jedrzej, and Tomasz Mróz.
2020. "Exergy Evaluation of a Water Distribution System" *Energies* 13, no. 23: 6221.
https://doi.org/10.3390/en13236221