# Optimization of Water Network Topology and Pipe Sizing to Aid Water Utilities in Deciding on a Design Philosophy: A Real Case Study in Belgium

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## Abstract

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## 1. Introduction

#### 1.1. Context and Motivation

- Time savings, thanks to partial automation of the design process;
- A more explicit understanding of the hydraulic performance of the current water distribution network (e.g., minimum pressure, velocity in pipes, resilience, continuity and security of supply) under different scenarios (e.g., changes in water demand and pipe breaks);
- Greater confidence in design choices, thanks to the ability to thoroughly explore the various trade-offs and thanks to the possibility of reproducing the design choice in the future in an objective way;
- More efficient investments, thanks to the optimization of cost vs. performance within the design.

#### 1.2. Simultaneous Layout and Pipe-Sizing Optimization in the Scientific Literature

- New network design—determining optimal pipe sizes to minimize the project cost;
- Strengthening/paralleling of an existing network—determining optimal pipe sizes to reinforce an existing network to meet future demands through lying duplicated pipes in parallel with existing pipes, with objective to minimize the project cost;
- Rehabilitation of an existing network—determining optimal rehabilitation alternative between replacement of pipes with the same or larger diameters, cleaning or cleaning and lining existing pipes, with the objective to minimize the project cost;
- Expansion of an existing network—developing or expanding the existing network beyond its current boundaries.

#### 1.3. Aim and Novelties of the Contribution

## 2. Materials and Methods

#### 2.1. Practical Approach

- Discussion of the objective(s), constraints and decision variables of the optimization problem and inventory of the necessary data;
- Evaluation of preliminary results, identification of eventual bottlenecks and (if necessary) fine-tuning of the optimization problem and required data;
- Interpretation and discussion of definitive results, and the added value of applying numerical optimization.

#### 2.2. Case Study Objective

#### 2.3. Optimization Problem Formulation

#### 2.3.1. Decision Variables

#### 2.3.2. Objective Function

- Every time the removal of a pipe leads to part of the network becoming branched, the objective is minimized further, reflecting De Watergroep’s desire to introduce branched sections into the network;
- Every time the diameter of a part of the looped network is reduced, the objective is minimized further, reflecting De Watergroep’s wish to have a network design with as small as possible volume.

#### 2.3.3. Constraints

- At every junction in the looped part of the network (set $\mathit{S}\mathit{J}$) that also connects to a branched section, a pressure (${p}_{i}$) is enforced to be equal to 22.5 m plus the elevation difference ($\mathsf{\Delta}{Z}_{i}$) between that junction and the highest junction in the branched section (solutions that do not satisfy this constraint are discarded);$${P}_{1}={c}_{1}\mathrm{max}\left\{0,\underset{i\in \mathit{S}\mathit{J}}{\mathrm{max}}\left(22.5+\mathsf{\Delta}{Z}_{i}-{p}_{i}\right)\right\},$$
- At every other junction, also in the branched structure, a pressure of >0 is enforced. This is important to reject infeasible topologies.$${P}_{2}={c}_{2}\mathrm{max}\left\{0,\underset{i\in \mathit{J}}{\mathrm{max}}\left(-{p}_{i}\right)\right\},$$
- For every junction in the looped part of the network that also connects to a branched section, the objective is penalized with a value of ${c}_{3}$= 1 × 10
^{5}for every meter the pressure is below 28 m plus the elevation difference between that junction and the highest junction in the branched section;$${P}_{3}={c}_{3}{{\displaystyle \sum}}_{i\in \mathit{S}\mathit{J}}\mathrm{max}\left\{0,28+\mathsf{\Delta}{Z}_{i}-{p}_{i}\right\}.$$ - The objective is penalized for every branched cluster in the network that contains more than 50 equivalent customer connections (${N}_{connections}$). The penalty coefficient is ${c}_{4}$=100.$${P}_{4}={c}_{4}{{\displaystyle \sum}}_{i\in \mathit{S}\mathit{J}}{\left(\mathrm{max}\left\{0,{N}_{connections}-50\right\}\right)}^{2}$$

#### 2.4. Optimization Settings

#### 2.5. Post-Optimization Checks

^{3}h

^{−1}could be supplied at that junction while maintaining at least 5 m of pressure on all other junctions.

## 3. Results

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustration of the structured design of a WDN according to Dutch best practices, i.e., considering primary (blue), secondary (orange) and tertiary pipes (grey) [26].

**Figure 2.**Illustration of the EPANET-model of the drinking water distribution network of City X. Connections to the utility’s transport network (modeled as reservoirs in the hydraulic model) are indicated by a magenta circle.

**Figure 3.**Convergence curve of the optimization of the final design, with the number of generations on the x-axis (log-scale) and the performance on the y-axis.

**Figure 4.**Layout of the secondary (magenta) and tertiary (grey) pipes in the current design (

**a**) and the optimized design (

**b**). Compared to the current design, the optimized design shows a clearer secondary structure and a greater number of branched tertiary pipes.

**Figure 5.**Sections with more than 50 connections in the optimized network design. Sections that do not meet the requirement even in the current design are marked with a color with a corresponding number of connections.

**Table 1.**Summary of the best-practice structured design of a WDN in the Netherlands, considering a primary, secondary and tertiary part in a network.

Description | Guiding Principle | Design | |
---|---|---|---|

Primary | Transport function. Diameters > 300 mm. No direct connections. | Security of supply (according to Dutch drinking water law) | Looped |

Secondary | Distribution function. Diameters ~160–300 mm. Customer connections if needed. | Continuity of supply (i.e., robustness against hydraulic disturbance from incidents) If possible, water quality. | Looped, try to decrease diameters, goal is unidirectional flow as much as possible. |

Tertiary | Connecting function. Diameters ~40–160mm. Preferred location for customer connections. | Fire flow and water quality. | Branched, avoiding sediment with ‘self-cleaning’ velocities. |

**Table 2.**Commercially available pipe diameters and materials, PVC and ductile cast iron (FNG), to be used in the design of the network blueprint for City X.

Name | Material | External Diameter (mm) | Internal Diameter (mm) | Roughness Coefficient (mm) |
---|---|---|---|---|

PVC-100 | PVC_U R10 | 110 | 99.4 | 0.05 |

PVC-150 | PVC_U R10 | 160 | 144.6 | 0.05 |

FNG-200 | FNG K9 | 222 | 209.2 | 0.1 |

FNG-250 | FNG K9 | 274 | 260.4 | 0.1 |

FNG-300 | FNG K9 | 326 | 311.6 | 0.1 |

FNG-400 | FNG K9 | 429 | 412.8 | 0.1 |

Criterion | Current Network | Final Design |
---|---|---|

Pipes removed [-] | 0 | 764 |

Proportion meshed [% length pipes] | 73 | 33 |

Proportion branched [% length pipes] | 27 | 67 |

Estimated pipe costs [EUR M] | 26.9 | 21.9 |

Mean residence time [h] | 7.5 | 3.6 |

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**MDPI and ACS Style**

Vertommen, I.; Mitrović, D.; van Laarhoven, K.; Piens, P.; Torbeyns, M. Optimization of Water Network Topology and Pipe Sizing to Aid Water Utilities in Deciding on a Design Philosophy: A Real Case Study in Belgium. *Water* **2022**, *14*, 3973.
https://doi.org/10.3390/w14233973

**AMA Style**

Vertommen I, Mitrović D, van Laarhoven K, Piens P, Torbeyns M. Optimization of Water Network Topology and Pipe Sizing to Aid Water Utilities in Deciding on a Design Philosophy: A Real Case Study in Belgium. *Water*. 2022; 14(23):3973.
https://doi.org/10.3390/w14233973

**Chicago/Turabian Style**

Vertommen, Ina, Djordje Mitrović, Karel van Laarhoven, Pieter Piens, and Maarten Torbeyns. 2022. "Optimization of Water Network Topology and Pipe Sizing to Aid Water Utilities in Deciding on a Design Philosophy: A Real Case Study in Belgium" *Water* 14, no. 23: 3973.
https://doi.org/10.3390/w14233973