# Optimal Placement and Operation of Chlorine Booster Stations: A Multi-Level Optimization Approach

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## Abstract

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## 1. Introduction

_{2}[8]. Regulations in the United States of America (USA) established the maximum residual disinfectant level as 4.0 mg/L, above this level exist the potential risk of eyes/nose irritation and possible stomach discomfort, also a minimum of 0.2 mg/L which guarantee disinfection of pathogenic bacteria [9]; while there exists different regulations for each country, the World Health Organization (WHO) recommends a maximum FRC concentration of 0.5 mg/L and minimum of 0.2 mg/L in the WDN to guarantee the disinfection of water on consumer nodes.

## 2. Materials and Methods

#### 2.1. Bioinspired Algorithms

#### 2.1.1. Genetic Algorithms (GA)

#### 2.1.2. Particle Swarm Optimization (PSO)

- $\mathrm{Vi}=\mathrm{Velocity}\mathrm{of}\mathrm{the}\mathrm{particle}$
- ${\mathrm{C}}_{1,2}=\mathrm{leaning}\mathrm{factors}$
- ${\mathrm{g}}_{\mathrm{best}}=\mathrm{Global}\mathrm{best}\mathrm{position}\mathrm{for}\mathrm{the}\mathrm{particle}$
- ${\mathrm{P}}_{\mathrm{best}}=\mathrm{Personal}\mathrm{best}$
- ${\mathrm{r}}_{1,2}=\mathrm{random}\mathrm{values}\mathrm{between}\left[0,1\right)$

#### 2.2. Problem Formulation and Simulation Conditions

- Finding the most important CBS locations for guaranteeing supply safe water in all nodes with at least the minimal FRC of 0.2 mg/L in compliance with regulations.
- To determine the schedule pattern dosing to reduce the amount of chlorine per day, for reducing economic and environmental impact.

#### 2.3. Fitness Function (FF) Formulation

_{(i,t)}= concentration in the node (i) at the time (t) within last 24 h of simulation, Nn = number of nodes, t = simulation time step, T = last hour of simulation established, C

_{min}= minimal concentration by regulation presented in this study (0.2 mg/L), DEL

_{(i,t)}= matrix with the difference of concentration out of the regulation in each node on the last 24 h.

_{max}= maximal concentration by regulation presented in this paper (4.0 mg/L).

_{min}$\le {\mathrm{C}}_{\left(\mathrm{i},\mathrm{t}\right)}\le \mathrm{Cmax}$ then ${\mathrm{DEL}}_{\left(\mathrm{i},\mathrm{t}\right)}=0.$

## 3. Application of the Methodology

#### 3.1. Case Study 1

^{−1}while wall chlorine decay is zero as in previous studies. Additionally, for comparison the values of Minimal Chlorine Concentration of 0.2 mg/L and Maximal Chlorine Concentration of 4 mg/L according to the WDN regulations in the USA are used, the time simulation is 72 h, with 5 min for water quality time step, and 1 h for hydraulic time step [32].

#### 3.2. Case Study 2

^{3}which is continuously filled (Figure 2). The distribution work by gravity flowing out from the DWTP (node RDTOT29) in the north-east of the city and ending at the south-west. The local Water Utility Plant provided the model. The pipelines material is mainly PVC and iron, the main pipeline has diameters between 6 to 24 inches, and the rest of pipes are between ¾ and 4 inches, the Hazen–Williams coefficient roughness is from 110 to 140 and the total length pipes is 30.84 kms. The water is supplied from a dam upstream of the city and the DWTP is located near the city, where the disinfection process uses gas chlorine as pre- and post-treatment.

^{−1}and it has different values of Wall Decay Coefficient with a minimal and maximal of 0.02 and 1.5 m/d, respectively.

## 4. Results

#### 4.1. Statistical Results from GA Location for Case Study 1

#### 4.2. Statistical Results from PSO location for the Case Study 1

#### 4.3. Scheduling in CBS Results from GA and PSO

#### 4.4. CBS Location and Dosage Results for the Case 1

#### 4.5. CBS Location Results for the WDN “SF812” in Case Study 2

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**WDN Net Example 2 by Boccelli and adapted from EPANET. Where arrows represent the water flow direction. Red dashed squares remark the nodes analyzed later.

**Figure 8.**FRC distribution at hour 72. (

**a**) Generated by the GA solution. (

**b**) Generated by the PSO solution.

**Figure 9.**(

**a**) FRC Distribution concentrations on the nodes of the WDN for the solution by GA. (

**b**) FRC Distribution concentrations on the nodes of the WDN for the solution by PSO.

**Figure 11.**(

**a**) FRC concentrations on the farthest modes from the initial distribution (node 30). Last day of simulation obtained for GA and PSO. (

**b**) FRC concentrations on the farthest modes from the initial distribution (N = node 34). Last day of simulation obtained for GA and PSO. (

**c**) FRC concentrations on the farthest modes from the initial distribution (node 36). Last day of simulation obtained for GA and PSO.

**Figure 16.**FRC distribution in Case 2 by scheduling hourly dosage pattern obtained in Figure 15.

**Table 1.**Number of CBS distribution and frequency proposed by GA technique, (Statistical GA Location at Case 1).

CBS | CBS Simulation Reached | CBS ID |
---|---|---|

2 | 56 | Node 1, Tank |

3 | 30 | Node 1, Node 14, Tank |

4 | 13 | Node 1, Node 14, Node 29, Tank |

5 | 1 | Node 1, Node 29, Node E, Node 32 |

Total | 100 ^{1} |

^{1}Simulations by GA.

**Table 2.**Number of CBS distribution and frequency proposed by PSO, (statistical PSO location at Case 1).

CBS | CBS Reached | CBS ID |
---|---|---|

2 | 71 | Node 1, Tank |

3 | 19 | Node 1, Node 14, Tank |

4 | 8 | Node 1, Node 14, Node 29, Tank |

5 | 2 | Node 1, Node 14, Node 29, (Node E or Node 8) |

Total | 100 ^{1} |

^{1}Simulations by PSO.

Metaheuristic Technique | Mean | Standard Deviation Mean | Min | Max |
---|---|---|---|---|

GA | 0.64 | 0.25 | 0.20 | 2.24 |

PSO | 0.53 | 0.43 | 0.20 | 3.87 |

**Table 4.**Comparison of the total mass injected by the CBS obtained with GA and PSO with those described in the literature review for Case 1.

Author and Year | Optimization Technique | Selected Nodes | Mean Dosage (mg/L) | Total Dosage (g/Day) |
---|---|---|---|---|

This paper | GA (Case study 1) | Node 1 Node 25 | 0.79 1.29 | 1762 |

This paper | PSO (Case study 1) | Node 1 Tank | 1.13 0.76 | 1279 |

Boccelli et al., 1998 [32] | ^{1} Linear Programming. Case IV | Link 1 (A) Link 8 (B) Link 9 (C) Link 38 (D) Link 34 (E) Link 29 (F) | 318.8 ^{1}4.65 ^{1}2089.6 ^{1}0.01 ^{1}0.6 ^{1}- | 3475 |

Propato and Uber, 2004 [36] | Linear Least Squares | Link 1 (A) Link 29 (F) | 0.26 0.22 | 1321 |

Ayvaz et al., 2018 [37] | Hybrid optimization with solver Harmony Search | Node 2 Node 25 | 0.517 0.349 | 1213 |

^{1}Mean dosage are in mg/min units.

Nodes ID | Elevation (m) | Node Demand (L/s) | Pressure (m) |
---|---|---|---|

‘DQ512’ | 2071.38 | 0.04 | 31.63 |

‘QD106’ | 2021.63 | 0.02 | 43.11 |

‘DQ938’ | 2059.97 | 0.06 | 17.87 |

‘800’ | 1998.83 | 0.06 | 62.68 |

‘QD238’ | 1966.00 | 0.22 | 94.84 |

‘DQ17’ | 2035.64 | 0.14 | 20.86 |

Metaheuristic Technique | Mean | Std Deviation Mean | Min | Max | Hours Upper 0.2 |
---|---|---|---|---|---|

PSO | 0.71 | 0.25 | 0 | 1.5 | 95.85% |

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**MDPI and ACS Style**

Pineda Sandoval, J.D.; Brentan, B.M.; Lima, G.M.; Cervantes, D.H.; García Cervantes, D.A.; Ramos, H.M.; Delgado Galván, X.; Mora Rodríguez, J.d.J.
Optimal Placement and Operation of Chlorine Booster Stations: A Multi-Level Optimization Approach. *Energies* **2021**, *14*, 5806.
https://doi.org/10.3390/en14185806

**AMA Style**

Pineda Sandoval JD, Brentan BM, Lima GM, Cervantes DH, García Cervantes DA, Ramos HM, Delgado Galván X, Mora Rodríguez JdJ.
Optimal Placement and Operation of Chlorine Booster Stations: A Multi-Level Optimization Approach. *Energies*. 2021; 14(18):5806.
https://doi.org/10.3390/en14185806

**Chicago/Turabian Style**

Pineda Sandoval, Joseph D., Bruno Melo Brentan, Gustavo Meirelles Lima, Daniel Hernández Cervantes, Daniel A. García Cervantes, Helena M. Ramos, Xitlali Delgado Galván, and José de Jesús Mora Rodríguez.
2021. "Optimal Placement and Operation of Chlorine Booster Stations: A Multi-Level Optimization Approach" *Energies* 14, no. 18: 5806.
https://doi.org/10.3390/en14185806