# A Quick Survey of the Most Vulnerable Areas of a Water Distribution Network Due to Transients Generated in a Service Line: A Lagrangian Model Based on Laboratory Tests

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Experimental Setup

#### 2.2. Preliminary Tests for the End-User and Service Line Characterization

#### 2.3. Laboratory Transient Tests

#### 2.4. The Lagrangian Model (LM)

## 3. The Effect of the Network Topology

## 4. The Effect of the Transient Generation Point

## 5. Maps of Vulnerability by the Lagrangian Model (LM)

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Martínez García, D.; Lee, J.; Keck, J.; Kooy, J.; Yang, P.; Wilfley, B. Pressure-based analysis of water main failures in California. J. Water Resour. Plan. Manag.
**2020**, 146, 05020016. [Google Scholar] [CrossRef] - Prescott, S.L.; Ulanicki, B. Improved control of pressure reducing valves in water distribution networks. J. Hydraul. Eng.
**2008**, 134, 56–65. [Google Scholar] [CrossRef] - Meniconi, S.; Brunone, B.; Mazzetti, E.; Laucelli, D.B.; Borta, G. Hydraulic characterization and transient response of Pressure Reducing Valves. Laboratory experiments. J. Hydroinform.
**2017**, 19, 798–810. [Google Scholar] [CrossRef] - Gong, J.; Stephens, M.L.; Lambert, M.F.; Zecchin, A.C.; Simpson, A.R. Pressure surge suppression using a metallic-plastic-metallic pipe configuration. J. Hydraul. Eng.
**2018**, 144, 04018025. [Google Scholar] [CrossRef] - Marsili, V.; Meniconi, S.; Alvisi, S.; Brunone, B.; Franchini, M. Experimental analysis of the water consumption effect on the dynamic behaviour of a real pipe network. J. Hydraul. Res.
**2021**, 59, 477–487. [Google Scholar] [CrossRef] - Kwon, H.J.; Lee, C.E. Reliability analysis of pipe network regarding transient flow. KSCE J. Civ. Eng.
**2008**, 12, 409–416. [Google Scholar] [CrossRef] - Rezaei, H.; Ryan, B.; Stoianov, I. Pipe failure analysis and impact of dynamic hydraulic conditions in water supply networks. Procedia Eng.
**2015**, 119, 253–262. [Google Scholar] [CrossRef] - Xing, L.; Sela, L. Transient simulations in water distribution networks: TSNet python package. Adv. Eng. Softw.
**2020**, 149, 102884. [Google Scholar] [CrossRef] - Huang, Y.; Zheng, F.; Duan, H.F.; Zhang, Q. Multi-objective optimal design of water distribution networks accounting for transient impacts. Water Resour. Manag.
**2020**, 34, 1517–1534. [Google Scholar] [CrossRef] - Duan, H.F.; Tung, Y.K.; Ghidaoui, M.S. Probabilistic Analysis of Transient Design for Water Supply Systems. J. Water Resour. Plan. Manag.
**2010**, 136, 678–687. [Google Scholar] [CrossRef] - Meniconi, S.; Capponi, C.; Frisinghelli, M.; Brunone, B. Leak Detection in a Real Transmission Main Through Transient Tests: Deeds and Misdeeds. Water Resour. Res.
**2021**, 57, e2020WR027838. [Google Scholar] [CrossRef] - Duan, H.F. Accuracy and Sensitivity Evaluation of TFR Method for Leak Detection in Multiple-Pipeline Water Supply Systems. Water Resour. Manag.
**2018**, 32, 2147–2164. [Google Scholar] [CrossRef] - Huang, Y.; Duan, H.F.; Zhao, M.; Zhang, Q.; Zhao, H.; Zhang, K. Probabilistic analysis and evaluation of nodal demand effect on transient analysis in urban water distribution systems. J. Water Resour. Plan. Manag.
**2017**, 143, 04017041. [Google Scholar] [CrossRef] - Meniconi, S.; Cifrodelli, M.; Capponi, C.; Duan, H.F.; Brunone, B. Transient response analysis of branched pipe systems toward a reliable skeletonization. J. Water Resour. Plan. Manag.
**2021**, 147, 04020109. [Google Scholar] [CrossRef] - Boulos, P.F.; Karney, B.W.; Wood, D.J.; Lingireddy, S. Hydraulic Transient Guidelines for Protecting Water Distribution Systems. J. Am. Water Work. Assoc.
**2005**, 97, 111–124. [Google Scholar] [CrossRef] - Meniconi, S.; Brunone, B.; Frisinghelli, M. On the role of minor branches, energy dissipation, and small defects in the transient response of transmission mains. Water
**2018**, 10, 187. [Google Scholar] [CrossRef] - McInnis, D.; Karney, B.W. Transients in distribution networks: Field tests and demand models. J. Hydraul. Eng.
**1995**, 121, 218–231. [Google Scholar] [CrossRef] - Creaco, E.; Pezzinga, G.; Savic, D. On the choice of the demand and hydraulic modelling approach to WDN real-time simulation. Water Resour. Res.
**2017**, 53, 6159–6177. [Google Scholar] [CrossRef] - Wylie, E.; Streeter, V. Fluid Transients in Systems; Prentice-Hall Inc.: Hoboken, NJ, USA, 1993; p. 463. [Google Scholar]
- Pezzinga, G. Quasi-2D model for unsteady flow in pipe networks. J. Hydraul. Eng.
**1999**, 125, 676–685. [Google Scholar] [CrossRef] - Duan, H.F.; Meniconi, S.; Lee, P.J.; Brunone, B.; Ghidaoui, M.S. Local and integral energy-based evaluation for the unsteady friction relevance in transient pipe flows. J. Hydraul. Eng.
**2017**, 143, 04017015. [Google Scholar] [CrossRef] [Green Version] - Pezzinga, G.; Brunone, B.; Cannizzaro, D.; Ferrante, M.; Meniconi, S.; Berni, A. Two-dimensional features of viscoelastic models of pipe transients. J. Hydraul. Eng.
**2014**, 140, 0401403. [Google Scholar] [CrossRef] - Creaco, E.; Campisano, A.; Fontana, N.; Marini, G.; Page, P.; Walski, T. Real time control of water distribution networks: A state-of-the-art review. Water Res.
**2019**, 161, 517–530. [Google Scholar] [CrossRef] [PubMed] - Abreu, J.; Cabrera, E.; Izquierdo, J.; Garcia-Serra, J. Flow modeling in pressurized systems revisited. J. Hydraul. Eng.
**1999**, 125, 1154–1169. [Google Scholar] [CrossRef] - Filion, Y.; Karney, B.W. Extended period simulation with a transient model. J. Hydraul. Eng.
**2002**, 128, 616–624. [Google Scholar] [CrossRef] - Nault, J.; Karney, B.W. Improved Rigid Water Column Formulation for Simulating Slow Transients and Controlled Operations. J. Hydraul. Eng.
**2016**, 142, 04016025. [Google Scholar] [CrossRef] - Nault, J.D.; Karney, B.W. Adaptive Hybrid Transient Formulation for Simulating Incompressible Pipe Network Hydraulics. J. Hydraul. Eng.
**2016**, 142, 04016050. [Google Scholar] [CrossRef] - Hampson, W.; Collins, R.; Beck, S.; Boxall, J. Transient source localization methodology and laboratory validation. Procedia Eng.
**2014**, 70, 781–790. [Google Scholar] [CrossRef] - Zeng, W.; Zecchin, A.C.; Cazzolato, B.S.; Simpson, A.R.; Gong, J.; Lambert, M.F. Extremely Sensitive Anomaly Detection in Pipe Networks Using a Higher-Order Paired-Impulse Response Function with a Correlator. J. Water Resour. Plan. Manag.
**2021**, 147, 04021068. [Google Scholar] [CrossRef] - Fathi-Moghadam, M.; Kiani, S. Simulation of transient flow in viscoelastic pipe networks. J. Hydraul. Res.
**2020**, 58, 531–540. [Google Scholar] [CrossRef] - Lee, J.; Lohani, V.K.; Dietrich, A.M.; Loganathan, G. Hydraulic transients in plumbing systems. Water Sci. Technol. Water Supply
**2012**, 12, 619–629. [Google Scholar] [CrossRef] - Lee, J. Hydraulic transients in service lines. Int. J. Hydraul. Eng.
**2015**, 4, 31–36. [Google Scholar] - Stephens, M.L.; Lambert, M.F.; Simpson, A.R.; Vitkovsky, J. Calibrating the water-hammer response of a field pipe network by using a mechanical damping model. J. Hydraul. Eng.
**2011**, 137, 1225–1237. [Google Scholar] [CrossRef] - Starczewska, D.; Collins, R.; Boxall, J. Transient behavior in complex distribution network: A case study. Procedia Eng.
**2014**, 70, 1582–1591. [Google Scholar] [CrossRef] - Meniconi, S.; Brunone, B.; Ferrante, M.; Capponi, C.; Carrettini, C.; Chiesa, C.; Segalini, D.; Lanfranchi, E. Anomaly pre-localization in distribution–transmission mains by pump trip: Preliminary field tests in the Milan pipe system. J. Hydroinform.
**2015**, 17, 377–389. [Google Scholar] [CrossRef] - Starczewska, D.; Boxall, J.; Collins, R. A method to characterise transients from pressure signals recorded in real water distribution networks. In Proceedings of the 12th International Conference on Pressure Surges, Dublin, Ireland, 18–20 November 2015; BHR Group: Cranfield, UK, 2015; pp. 609–623. [Google Scholar]
- Starczewska, D.; Collins, R.; Boxall, J. Occurrence of transients in water distribution networks. Procedia Eng.
**2015**, 119, 1473–1482. [Google Scholar] [CrossRef] - Marsili, V.; Meniconi, S.; Alvisi, S.; Brunone, B.; Franchini, M. Stochastic approach for the analysis of demand induced transients in real water distribution systems. J. Water Resour. Plan. Manag.
**2022**, 141, 04021093. [Google Scholar] [CrossRef] - Blokker, E.; Vreeburg, J.; Dijk, J. Simulating residential water demand with a stochastic end-use model. J. Water Resour. Plan. Manag.
**2010**, 136, 19–26. [Google Scholar] [CrossRef] - Idel’cik, I.E. Handbook of Hydraulic Resistance; Hemisphere Publishing Corp.: New York, NY, USA, 1986. [Google Scholar]
- Keramat, A.; Wang, X.; Louati, M.; Meniconi, S.; Brunone, B.; Ghidaoui, M.S. Objective functions for transient-based pipeline leakage detection in a noisy environment: Least square and matched-filter. J. Water Resour. Plan. Manag.
**2019**, 145, 04019042. [Google Scholar] [CrossRef] - Ferrante, M.; Brunone, B.; Meniconi, S. Leak detection in branched pipe systems coupling wavelet analysis and a Lagrangian model. J. Water Supply Res. Technol.
**2009**, 58, 95–106. [Google Scholar] [CrossRef] - Swaffield, J.; Boldy, A. Pressure Surges in Pipe and Duct Systems; Ashgate Publishing Group: Farnham, UK, 1993; p. 380. [Google Scholar]
- Duan, H.F.; Ghidaoui, M.S.; Lee, P.J.; Tung, Y.K. Unsteady friction and visco-elasticity in pipe fluid transients. J. Hydraul. Res.
**2010**, 48, 354–362. [Google Scholar] [CrossRef] - Brunone, B.; Meniconi, S.; Capponi, C. Numerical analysis of the transient pressure damping in a single polymeric pipe with a leak. Urban Water J.
**2018**, 15, 760–768. [Google Scholar] [CrossRef] - Mitosek, M.; Chorzelski, M. Influence of visco-elasticity on pressure wave velocity in polyethylene MDPE pipe. Archit. Hydrol. Eng. Environ. Mech.
**2003**, 50, 127–140. [Google Scholar] - Pezzinga, G.; Brunone, B.; Meniconi, S. On the relevance of pipe period on Kelvin-Voigt viscoelastic parameters: 1-D and 2-D inverse transient analysis. J. Hydraul. Eng.
**2016**, 142, 04016063. [Google Scholar] [CrossRef]

**Figure 1.**Water Distribution Network (WDN) at the Water Engineering Laboratory of the University of Perugia: (

**a**) general layout with the indication of the pipe length and principal measurement sections and the service line installed at node 5 (test #1 configuration); (

**b**) end-user 5u; (

**c**) location of the measurement sections around junction 5; and (

**d**) junction 5 (as an example of the service line connection to the WDN).

**Figure 2.**(

**a**) Comparison of the geometric characteristics of the ball valve obtained at WEL and by [40]; (

**b**) hydraulic characteristics of the end-user.

**Figure 3.**Test #1—pressure signals acquired at measurement sections: (

**a**) 5u; (

**b**) 5, 5${}_{4}$, 5${}_{6}$, and 5${}_{8}$; (

**c**) 4, 6, and 8; (

**d**) 7, 32, and 1. Note that to highlight the pressure variations into the network, the y-axis of (

**b**–

**d**) is significantly reduced with respect to the one at 5u (

**a**).

**Figure 4.**Test #1—one of the paths of the generated pressure wave of Figure 3 in the network—pressure signals at measurement sections: (

**a**) 5u; (

**b**) 5; (

**c**) 5${}_{4}$; (

**d**) 45; (

**e**) 4; (

**f**) 47; and (

**g**) 7.

**Figure 5.**Test #1—experimental pressure disturbances, $H-{H}_{0}$, vs. the impulse response function, $\Delta {H}_{n}$ (blue stems), and numerical reconstruction, ${H}_{n}-{H}_{n,0}$ (red line), carried out by the Lagrangian model (LM) at measurement sections: (

**a**) 5u; (

**b**) 5; (

**c**) 4; (

**d**) 6; (

**e**) 8; (

**f**) 7; and (

**g**) 32.

**Figure 6.**Pressure signals acquired during tests #1 (blue lines), #2 (black lines), and #3 (red lines) with ${Q}_{0,5u}$ = ${Q}_{0,6u}$ = ${Q}_{0,7u}$ = 0.12 L/s at measurement sections: (

**a**) end-user (5u/6u/7u); (

**b**) 32; (

**c**) 4; (

**d**) 5; (

**e**) 6; (

**f**) 7; and (

**g**) 8.

**Figure 7.**Tests #2, and #3—experimental pressure disturbances, $H-{H}_{0}$, vs. the impulse response function, $\Delta {H}_{n}$, (blue stems) and numerical reconstruction, ${H}_{n}-{H}_{n,0}$, (red line) carried out by the Lagrangian model (LM) at measurement sections: (

**a**) 6u; (

**b**) 6; (

**c**) 5; (

**d**) 4; (

**e**) 7; (

**f**) 8; and (

**g**) 32, for test #2, and (

**h**) 7u; (

**i**) 7; (

**j**) 5; (

**k**) 4; (

**l**) 6; (

**m**) 8; and (

**n**) 32, for test #3.

**Figure 8.**Frequency distribution of the relative amplitude of the pressure waves given by the LM for test #1 at measurement sections: (

**a**) 5u and 5; (

**b**) 32; (

**c**) 4; (

**d**) 6; (

**e**) 7; (

**f**) 8.

**Figure 9.**Map of vulnerability evaluated by the LM for tests: (

**a**) #1; (

**b**) #2; and (

**c**) #3; respectively (numbers at nodes indicate the value of the index of vulnerability, V).

**Figure 10.**Map of vulnerability evaluated by the LM for a numerical test equivalent to test #1, but with a diameter distribution reversed with respect to the laboratory layout (numbers at nodes indicate the value of the index of vulnerability, V).

Test No. (#) | Layout | Maneuver Type | Discharge [L/s] |
---|---|---|---|

1 | service line connected at node 5 | Total closure of 5u | ${Q}_{0,5u}$ = 0.12 |

2 | service line connected at node 6 | Total closure of 6u | ${Q}_{0,6u}$ = 0.12 |

3 | service line connected at node 7 | Total closure of 7u | ${Q}_{0,7u}$ = 0.12 |

**Table 2.**The reflection and transmission coefficients given by the Lagrangian model (LM) for the singularities of the network.

Singularity | Reflection Coefficient, ${\mathit{C}}_{\mathit{R}}$ | Transmission Coefficient, ${\mathit{C}}_{\mathit{T}}$ |
---|---|---|

constant head reservoir | −1 | 0 |

closed valve/dead end | 1 | 0 |

junction | $\frac{{A}_{j}/{a}_{j}-\left({\sum}_{\begin{array}{c}i=1\\ i\ne j\end{array}}^{n}{A}_{i}/{a}_{i}\right)}{{\sum}_{i=1}^{n}{A}_{i}/{a}_{i}}$ | $\frac{2{A}_{j}/{a}_{j}}{{\sum}_{i=1}^{n}{A}_{i}/{a}_{i}}$ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Meniconi, S.; Maietta, F.; Alvisi, S.; Capponi, C.; Marsili, V.; Franchini, M.; Brunone, B.
A Quick Survey of the Most Vulnerable Areas of a Water Distribution Network Due to Transients Generated in a Service Line: A Lagrangian Model Based on Laboratory Tests. *Water* **2022**, *14*, 2741.
https://doi.org/10.3390/w14172741

**AMA Style**

Meniconi S, Maietta F, Alvisi S, Capponi C, Marsili V, Franchini M, Brunone B.
A Quick Survey of the Most Vulnerable Areas of a Water Distribution Network Due to Transients Generated in a Service Line: A Lagrangian Model Based on Laboratory Tests. *Water*. 2022; 14(17):2741.
https://doi.org/10.3390/w14172741

**Chicago/Turabian Style**

Meniconi, Silvia, Filomena Maietta, Stefano Alvisi, Caterina Capponi, Valentina Marsili, Marco Franchini, and Bruno Brunone.
2022. "A Quick Survey of the Most Vulnerable Areas of a Water Distribution Network Due to Transients Generated in a Service Line: A Lagrangian Model Based on Laboratory Tests" *Water* 14, no. 17: 2741.
https://doi.org/10.3390/w14172741