# Rehabilitation in Intermittent Water Distribution Networks for Optimal Operation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Pump Selection

#### 2.2. Leakage Modeling

#### 2.3. Main Network Modeling

_{.}The $ASPV$ is calculated for each pair of the $n$ nodes of the network (${N}_{I}$ and ${N}_{F}$) and compiled in an $n\times n$ matrix, as in Equation (8), where the rows represent the initial nodes (${N}_{I}$) and the columns the final nodes (${N}_{F}$). After calculating the $ASPV$ for each pair of nodes, each element of $ASPV$ matrix is weighted by the flow of the element linking both nodes, resulting in a new matrix ($ASP{V}^{*}$). In this way, pipes with small diameters and flow rates, which have small relevance to the hydraulic behavior of the system, are disregarded from the main network. Finally, it is possible to visualize the number of nodes/pipes that can be reached from each node, as well as sort them out by importance, where the pipes with higher $ASP{V}^{*}$ values are more relevant for the system.

#### 2.4. Cost Modeling

#### 2.5. Optimization Procedure

^{8}, a value tested and verified to quickly disregard solutions that violate the restriction. Equation (13) mathematically demonstrates the penalty due to violation of the adopted minimum pressure constraint, where ${p}_{j,i}$ is the pressure at node $j$ at time $i$ and ${n}_{pen}$ represents the number of nodes with pressures lower than the minimum pressure ${p}_{min}$.

^{®}software. The stopping criteria, with a number of particles adopted equal to 100, tested and proven to obtain optimized solutions, were: (i) a maximum number of 1000 iterations; or (ii) variation of the objective function equal to or less than 10

^{−10}for 20 consecutive times.

## 3. Case Studies

#### 3.1. Case Study 1: ZJ Network

#### 3.2. Case Study 2: OBCL-1 Network

## 4. Results

#### 4.1. ZJ Network Results

#### 4.2. OBCL-1 Network Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Relation between pump flow and its efficiency at BEP (Source: [23]).

**Figure 7.**Velocity in the main network pressure for the ZJ network: (

**a**) 24 h; (

**b**) 12 h; (

**c**) 12 h optimized.

**Figure 8.**Velocity in the main network from the OBCL-1 network: (

**a**) 24 h; (

**b**) 12 h; (

**c**) 12 h optimized.

Description | Tariff |
---|---|

Energy—non-peak hour (NPH) (R$/kWh) | 0.3567 |

Energy—peak hour (PH) (R$/kWh) | 0.5342 |

Power—non-peak hour (NPH) (R$/kW) | 13.950 |

Power—peak hour (PH) (R$/kW) | 43.950 |

Description | Range of Average Total Expenditure Amounts (IN003) (R$/m³) | Average Total Expenditure Amounts (IN003) (R$/m³) |
---|---|---|

Regional | 1.87 to 7.61 | 3.96 |

Micro-regional | 1.05 to 5.53 | 3.48 |

Local | 0.30 to 7.82 | 2.68 |

Brazil | 0.30 to 7.82 | 3.57 |

**Table 3.**Comparison of hydraulic and economic parameters for the different scenarios studied in the ZJ network.

$tw$ = 0.30 R$/m³ | $tw$ = 7.82 R$/m³ | $tw$ = 3.50 R$/m³ | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Description | 24 h ^{1} | 15 h ^{1} | 12 h ^{1} | 12 h * | 24 h ^{1} | 15 h ^{1} | 12 h ^{1} | 12 h * | 24 h ^{1} | 15 h ^{1} | 12 h ^{1} | 12 h * |

Mean pressure (m) | 55 | 22 | 4 | 33 | 55 | 22 | 4 | 33 | 55 | 22 | 4 | 33 |

Daily distribution (10^{3} m³) | 158.1 | 129.6 | - | 129.1 | 158.1 | 129.6 | - | 129.1 | 158.1 | 129.6 | - | 129.1 |

Daily consumption (10^{3} m³) | 110.9 | 110.9 | - | 110.9 | 110.9 | 110.9 | - | 110.9 | 110.9 | 110.9 | - | 110.9 |

Daily leakage (10^{3} m³) | 47.2 | 18.7 | - | 18.2 | 47.2 | 18.7 | - | 18.2 | 47.206 | 18.7 | - | 18.2 |

Daily leakage (%) | 29.9 | 14.5 | - | 14.1 | 29.9 | 14.5 | - | 14.1 | 29.9 | 14.5 | - | 14.1 |

Daily energy cost (10^{3} R$) | - | - | - | - | - | - | - | - | - | - | - | - |

Daily leakage cost (10^{3} R$) | 14.2 | 5.6 | - | 5.5 | 369.1 | 146.5 | - | 142.6 | 168.5 | 66.9 | - | 65.1 |

Implantation cost (10^{6} R$) | - | - | - | 4.9 | - | - | - | 4.9 | - | - | - | 4.9 |

Project horizon cost (10^{6} R$) | 41.6 | 16.5 | - | 21.0 | 1085.3 | 430.8 | - | 424.1 | 495.5 | 196.7 | - | 196.3 |

Economic efficiency (%) | - | 60.3 | - | 49.6 | - | 60.3 | - | 60.9 | - | 60.3 | - | 60.4 |

^{1}Source: [20]. * Optimized scenarios.

$tw$ = 0.30 R$/m³ | $tw$ = 7.82 R$/m³ | $tw$ = 3.50 R$/m³ | ||||
---|---|---|---|---|---|---|

Description | 15 h * | 12 h * | 15 h * | 12 h * | 15 h * | 12 h * |

Resized extensions (m) | 10,626 | 9513 | 9727 | 10,671 | 11,741 | 12,057 |

**Table 5.**Comparison of hydraulic, energy and economic parameters for the different scenarios studied in the OBCL-1 network.

$tw$ = 0.30 R$/m³ | $tw$ = 7.82 R$/m³ | $tw$ = 3.50 R$/m³ | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Description | 24 h ^{1} | 15 h ^{1} | 15 h * | 12 h ^{1} | 12 h * | 24 h ^{1} | 15 h ^{1} | 15 h * | 12 h ^{1} | 12 h * | 24 h ^{1} | 15 h ^{1} | 15 h * | 12 h ^{1} | 12 h * |

Power-PH (kW) | 35 | 67 | 10 | 211 | 14 | 41 | 71 | 18 | 199 | 14 | 36 | 70 | 17 | 211 | 9 |

Energy-PH (kWh) | 92 | 180 | 29 | 416 | 41 | 97 | 181 | 33 | 417 | 34 | 94 | 173 | 43 | 416 | 19 |

Power-NPH (kW) | 54 | 182 | 41 | 261 | 22 | 33 | 180 | 33 | 258 | 22 | 66 | 180 | 32 | 262 | 19 |

Energy-NPH (kWh) | 489 | 1063 | 253 | 1272 | 148 | 512 | 1046 | 117 | 1250 | 99 | 463 | 1080 | 224 | 1410 | 100 |

Total Energy (kWh/day) | 581 | 1243 | 282 | 1689 | 189 | 608 | 1227 | 150 | 1668 | 134 | 556 | 1253 | 267 | 1825 | 120 |

Mean pressure (m) | 82 | 84 | 74 | 85 | 79 | 80 | 82 | 73 | 84 | 68 | 81 | 81 | 77 | 81 | 67 |

Daily distribution (10^{3} m³) | 20.2 | 18.1 | 17.8 | 17.3 | 17.2 | 20.1 | 18.0 | 17.7 | 17.3 | 17.0 | 20.1 | 18.0 | 17.8 | 17.2 | 16.9 |

Daily consumption (10^{3} m³) | 14.3 | 14.3 | 14.3 | 14.3 | 14.3 | 14.3 | 14.3 | 14.3 | 14.3 | 14.3 | 14.3 | 14.3 | 14.3 | 14.3 | 14.3 |

Daily leakage (10^{3} m³) | 5.9 | 3.8 | 3.5 | 3.1 | 2.9 | 5.8 | 3.7 | 3.5 | 3.1 | 2.7 | 5.8 | 3.7 | 3.6 | 2.9 | 2.7 |

Daily leakage (%) | 29.3 | 21.0 | 19.8 | 17.7 | 16.9 | 28.9 | 20.7 | 19.5 | 17.7 | 15.8 | 29.0 | 20.7 | 20.0 | 17.1 | 15.8 |

Daily energy cost (10^{3} R$) | 2.5 | 5.9 | 1.1 | 13.6 | 1.0 | 2.5 | 6.1 | 1.3 | 13.0 | 1.0 | 2.7 | 6.1 | 1.3 | 13.6 | 0.7 |

Daily leakage cost (10^{3} R$) | 1.8 | 1.1 | 1.1 | 0.9 | 0.9 | 45.6 | 29.2 | 27.0 | 24.0 | 21.0 | 20.8 | 13.3 | 12.8 | 10.5 | 9.5 |

Implantation cost (10^{6} R$) | - | - | 5.0 | - | 5.4 | - | - | 7.2 | - | 9.6 | - | - | 7.8 | - | 8.4 |

Project horizon cost (10^{6} R$) | 12.7 | 21.0 | 11.4 | 43.0 | 10.9 | 141.3 | 103.9 | 90.5 | 109.3 | 74.3 | 69.3 | 57.2 | 49.0 | 71.4 | 38.5 |

Efficiency (%) | - | −65.8 | 10.0 | −239.5 | 14.0 | - | 26.4 | 36.0 | 22.7 | 47.4 | - | 17.5 | 29.2 | −3.1 | 44.5 |

^{1}Source: [20]. * Optimized scenarios.

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**MDPI and ACS Style**

Souza, R.G.; Meirelles, G.; Brentan, B.; Izquierdo, J.
Rehabilitation in Intermittent Water Distribution Networks for Optimal Operation. *Water* **2022**, *14*, 88.
https://doi.org/10.3390/w14010088

**AMA Style**

Souza RG, Meirelles G, Brentan B, Izquierdo J.
Rehabilitation in Intermittent Water Distribution Networks for Optimal Operation. *Water*. 2022; 14(1):88.
https://doi.org/10.3390/w14010088

**Chicago/Turabian Style**

Souza, Rui Gabriel, Gustavo Meirelles, Bruno Brentan, and Joaquín Izquierdo.
2022. "Rehabilitation in Intermittent Water Distribution Networks for Optimal Operation" *Water* 14, no. 1: 88.
https://doi.org/10.3390/w14010088