Abstract
Leakage in water distribution networks is a main cause of real water loss and plays a significant role in reducing the excellence of water supply services and increasing financial costs. To address this challenge, the study aims to develop the model for leakage flow rates more precisely, with more accurate understanding of leakage behavior. In this context, hydraulic leakage models, including the leakage power and the modified orifice equations, have been creatively applied to identify and analyze leakage at various network nodes. In the second part of the study, controlled pressure reduction using pressure reducing valves is examined as a practical solution for pressure regulation and leakage control. The findings show that this method can reduce leakage flow rates by approximately 14 percent. The study ultimately emphasizes that estimating total network leakage does not require the use of Average Zone Pressure; instead, it can be reasonably estimated using node pressures and leakage coefficients.
Keyword: Water Distribution Network, Leakage, Pressure Management, Field data, Average zone point (AZP)

Introduction

Ensuring a sustainable supply of fresh water has become a critical challenge in many countries. One of the most effective approaches to managing water demand in water distribution systems is reducing water loss. Leakage, which represents a significant portion of real water losses, shows considerable variation across the world. From a managerial perspective, achieving completely leak-free networks is neither technically possible nor economically justified. In many studies, leakage is simplified and its hydraulic basis is often overlooked. The orifice equation, commonly used for leakage analysis, does not accurately reflect real leakage behavior. Experimental and modeling evidence shows that the leakage area is not constant, as assumed in the orifice model, but increases with fluid pressure. This behavior suggests that leakage is pressure-dependent, with the leakage opening expanding linearly as pressure head rises. In contrast, the leakage power law approach is often based on the assumption that leakage occurs only at the average zone pressure. In this study, node-level leakage estimation is carried out using a realistic hydraulic model calibrated with field data. Additionally, pressure management strategies are evaluated to reduce excess pressure in the water network after the leakage modeling process.


Methodology
This study investigates leakage estimation in decentralized water distribution networks, focusing on the precise quantification of leakage at individual nodes using advanced hydraulic modeling. The first section introduces an innovative approach based on field data, integrating pressure and flow rate measurements obtained through pressure step tests. Unlike previous studies, which typically estimated overall network leakage by relying on average zone pressure (AZP), this research independently formulates leakage equations for each node. The second section examines pressure management as a strategy for reducing water losses, emphasizing pressure reducing valves (PRVs) as a key solution for controlling pressure and mitigating leakage. The final section revisits and rejects the conventional assumption of using AZP for total network leakage estimation, demonstrating that accurate leakage calculations can be achieved by considering leakage coefficients (C₁ and C₂) and node-specific pressure values. The findings reveal that even with consumption pattern variations, such as node demand fluctuations or nighttime consumption changes, the overall leakage closely matches the AZP-based calculation. This study bridges the gap between theoretical and practical applications in real water networks, offering improved methods for leak detection and management that could enhance water conservation efforts globally.
Results and Discussion
In this study, the demand for each node in the District Metered Area (DMA), referred to as DMAK, is calculated by considering both leakage (Figure 3-a) and pressure (Figure 3-b). The leakage equation for each node is derived by focusing on two stages of a pressure step test, where pressure changes are similar across the selected time intervals: the first stage from 01:50 to 02:30 AM, and the second from 02:50 to 03:30 AM. During these time periods, the leakage for each node is computed as the difference between node demand and the nighttime consumption (LNC). While the average nighttime consumption (LNC) for the entire DMAKis known, individual node nighttime consumption is not directly measured. However, assuming uniform demand patterns, the nighttime consumption for each node can be calculated relative to its base demand.
In this study, pressure and leakage data from each node were gathered during the two stages of the pressure step test to derive the leakage power equation LP-Eq and the modified orifice equation (LMO-Eq). These models are used to estimate leakage for each node. The leakage profiles for each node using the Eq-LMO model are shown in Figure 4-a. Error distribution for LP-Eq and LMO-Eq models are shown in Figures 4-b and 4-c, respectively. The J3.1 node exhibits the least error, while node J4 shows higher deviations from the LMO-Eq model, indicating the limitations of LP-Eq in predicting leakage at this node.
Using the LMO-Eq model, the total modeled leakage for the DMA was 60.17 m³/day (19.5% of the input flow) on 2022/04/11. The LMO-LN-Eq and LP-Eq models overestimated the leakage by 6% (65.9 m³/day) and 3% (62.5 m³/day), respectively. On 2022/04/12, the measured leakage was 62.2 m³/day (20.2% of input flow), while the models predicted 68.2 m³/day LMO-LN-Eq and 63.34 m³/day LP-Eq, highlighting variable accuracy under different pressure conditions. Reducing leakage by applying pressure management could significantly help conserve water in the region.
Implementing the pressure reduction algorithm (Price et al., 2022) reduced daily leakage from 60.17 m³/day to 51.54 m³/day (14% reduction).
Conclusion
This study developed a nodal leakage model for the decentralized District Metered Area (DMAK) of Mashhad's water distribution network. Unlike previous methods relying on AZP and the power equation, the model uses nodal pressure data and simplified FAVAD coefficients to estimate total network leakage without AZP. Pressure management through PRVs further validated the model’s effectiveness in reducing leakage. The results emphasize the importance of node-specific leakage estimation, improving the accuracy of water loss assessments and supporting sustainable water resource management. This approach offers a more precise method for managing water leakage in decentralized water networks.