Leakage Modeling

The largest component of non-revenue water in utilities around the world is leakage. Leakage increases due to asset aging, high operating pressures, surge events, corrosion, external pressures, etc. In the worst cases, it can account for more than half of the produced water. Leaks are classified based on their size, either as detectable or as background (undetectable using current techniques).

As opposed to regular demands, leakage flow has a much closer relationship with pressure. During periods of peak consumption with lower pressures, leaks are at their minimum. Conversely, during the early morning, when the consumption is minimal and pressures are highest, leakage is at its maximum. For this reason, models should incorporate the pressure dependence of leakage to produce accurate estimates. When modeling leakage as standard demands, even if the associated patterns follow the typical daily pressure dynamics, the model will fail to accurately mimic the real behavior of leaks—especially as a response to anomalous pressure conditions.

Enabling pressure-dependent leakage in water distribution modeling contributes towards important goals, such as:

• Quantifying more accurately the amount of leakage throughout the network and throughout time
• Assessing the impact on leakage reduction when implementing pressure control programs (like lowering valve settings at night), or other interventions
• Narrowing down the estimated location of potential detectable leaks to be addressed by surveying and maintenance crews
• Narrowing down the list of potential assets to be replaced due to high background leakage

Assigning emitters to junctions is one way in which pressure-dependent leakage can be modeled. However, introduced in version 2025.4, the Leakage module further facilitates pressure-dependent leakage modeling, with several advantages over emitters:

• Can be assigned to pipes directly and not only to junctions
• Input values are expressed in terms of leakage area (of cracks, fissures, openings, punctures, etc.), which eases comprehension by representing a straightforward physical property
• Input area values at pipes are normalized by length, so that the numbers are more indicative of the relative condition of the assets
• Much higher accuracy when simulating flexible pipes, such as those made of PVC, through the adoption of the fixed and variable area discharge (FAVAD) paradigm

Fixed and variable area discharge (FAVAD) paradigm

The leak flow (Q) using the established emitter paradigm is computed with this equation: Q = Ch^N1.

C is the emitter coefficient, N1 is the global emitter exponent (defined in Simulation Options Demand and usually set to 0.5), and h is the pressure. However, it has been shown that the exponent is larger when leaks behave elastically, and that it changes with pressure. This is because flexible leaks do not behave like a rigid orifice, as their area also increases with pressure. Totally rigid leaks have an N1 value of 0.5, while totally flexible ones with an initial area of zero have a value of 1.5.

To overcome this limitation, the FAVAD paradigm utilizes this extended equation for Q:

C_d is the known discharge coefficient and g is the acceleration due to gravity. A₀ is the area of the leak when the pressure is zero. M is the expansion rate of the leak area as pressure increases. Under this paradigm, and following EPANET's 2.3 current unreleased implementation, the values for A₀ and M need to be assigned to each pipe. More specifically, the user needs to input unit values a₀ and m that are normalized by pipe length (l): A₀ = a₀l; M = ml.

In some cases, leaks can be assumed to be fully rigid. This is typically the case for pipes with thick walls made of rigid materials such as cast iron or steel, and where water leaks from breached joints. Rigid leaks have a very small unit expansion rate m, which can be assumed to be negligible (m = 0.0) for practical purposes.

In other cases, leaks can be assumed to be fully flexible. This can typically be assumed for pipes with thin plastic walls. In this case, the initial leakage area is assumed to be negligible (a₀ = 0.0). Most leakage is semi-rigid, though, with both fixed and variable area components. While the pipe material's elasticity plays an important role, the degradation mechanism of pipes may shift initial classification. For example, circumferential cracks, which can be caused by soil movements due to seasonal temperature and moisture variations, have a more rigid behavior. Longitudinal cracks, usually resulting from high pressures and pressure variations, have a more flexible behavior. Even leaks in highly rigid metal pipes might eventually behave elastically due to corrosion.

Ideally, leakage parameters, including the level of rigidity of leakage, would be estimated by simultaneously considering the following sources of information:

• Mass balance and derived total leakage (e.g., by contrasting produced measured volumes with totalized measured consumption values)
• Asset information for pipes: age, material, structural vulnerability, chemical vulnerability, maintenance history, etc.
• Hydraulic conditions: historic operating pressure, current average pressure ranges, pressure surge events, etc.
• Additional SCADA measurements (e.g., pressure sensors)

The following paper describes an example that uses field test data analysis and model calibration: Deyi, M., van Zyl, J., & Shepherd, M. (2014). Applying the FAVAD concept and leakage number to real networks: A case study in Kwadabeka, South Africa. Procedia Engineering, 89, 1537-1544.

The sections below can be used to first estimate the initial leakage area for pipes assuming full rigidity (next section: Background parameters for rigid leakage) and then, depending on the selected level of flexibility, redistribute that estimate between the fixed and variable area components (last section: Background parameters for semi-rigid and flexible leakage).

Reference papers:

• van Zyl, J. E., & Cassa, A. M. (2014). Modeling Elastically Deforming Leaks in Water Distribution Pipes. Journal of Hydraulic Engineering, 140, 182-189.
• López, L. L., van Zyl, J. E., & Harkness, B. (2024). Analysis and Modeling of Pressure Pipe Failures in Auckland, New Zealand. Journal of Water Resources Planning and Management, 150(4), 04024007.
• Cassa, A. M., & van Zyl, J. E. (2013). Predicting the head-leakage slope of cracks in pipes subject to elastic deformations. Journal of Water Supply: Research and Technology-Aqua, 62(4), 214-223.

Background parameters for rigid leakage

For pipes with rigid leakage, the initial leakage area a₀ typically ranges between 0.1 mm²/1000ft (ideal conditions) to values of around 5.0 mm²/1000ft. Values can be much larger if there are leaks that become detectable through acoustic or other means (and thus cannot be said to be background leaks anymore).

As an initial approximation to the parameterization of leakage in pipes, we include here estimates derived from the AWWA's M36 Manual "Water Audits and Loss Control Programs". The initial unit background leakage area a₀ for rigid pipes can be estimated as:

Symbols:

• ICF: The Infrastructure Condition Factor. 1.0 under ideal conditions (new pipe, high-quality installation, proper surge protections, intensive active leakage control). Usually, no higher than 3.0. Please refer to the M36 manual for methods on computing the ICF.
• p_av : Average pressure at the pipe in psi
• N_c : Number of service connections per 1000 feet
• L_c : Average length of service connections, from the curb stop to the customer meter, in feet

This equation is derived mainly from equation 7-5 for the Target Background Leakage (TBL). Please note that the AWWA's method is intended for background, undetectable leakage only. Detectable leakage is assumed to be considered separately in their methodology. Here are some examples of a₀ (in mm²/1000ft):

• 0.14 - A newly installed transmission line with no service connections, ideal operation and maintenance, and an average operating pressure of 60 psi
• 0.30 - A middle-aged transmission line with no service connections, and an average operating pressure of 80 psi
• 0.47 - A newly installed main with 10 service connections every 1000 feet (18 feet each), ideal operation and maintenance, and an average operating pressure of 60 psi
• 0.61 - A sub-urban middle-aged main with 4 service connections every 1000 feet (48 feet each), and an average operating pressure of 95 psi
• 0.84 - An old, low pressure main with 8 service connections every 1000 feet (18 feet each), and an average operating pressure of 50 psi
• 1.12 - A 20-year-old high-pressure main with 10 connections every 1000 feet (18 feet each), and an average operating pressure of 110 psi
• 1.25 - A high-density urban main with 20 service connections every 1000 feet (12 feet each), and an average operating pressure of 70 psi
• 2.11 - An old main in poor condition with 10 connections every 1000 feet (18 feet each), and an average operating pressure of 90 psi

Background parameters for semi-rigid and flexible leakage

The rigidity of leakage depends mostly on the rigidity of the pipe material and on the geometry of defects. The material can be characterized by the Elasticity modulus (E) and the thickness. Cast iron pipes have very large values of E (>1.5x10⁷ psi or 100 GPa) and relatively thick walls. PVC pipes are usually thinner and have a much smaller value of E (~4.4x10⁵ psi or 3 GPa). Pipes of other materials will sit somewhere in the middle. For example, asbestos cement pipes have a thick wall and an intermediate value of E (~1.7x10⁶ psi or 12 GPa).

On the other hand, defects that cause leaks are usually longitudinal (more sensitive to pressure), circumferential (less sensitive to pressure), or other shapes. The defects themselves are shaped by different phenomena, as mentioned above.

To create an initial estimate of the leakage parameters for flexible or semi-rigid pipes, follow these steps:

1. Compute the initial rigid leakage area a_0r with the equation above (derived from the AWWA M36 manual).
2. Estimate the elastic modulus E and wall thickness of the pipe.
3. Determine potential historical deterioration mechanisms that may have been present.
4. Estimate a degree of rigidity for the pipe based on those attributes:
   1. If rigid, keep the rigid value of a₀ = a_0r and assign m = 0.0; finish.
   2. If flexible, make the variable area leakage contribution v = 100%
   3. If semi-rigid, assign a variable area leakage contribution 0% < v < 100%
5. Compute a₀ and m by distributing the initial rigid area a_0r at the average pressure p_av according to the ratio v:
   1. 
   2.