Two-step numerical method for improved calculation of water leakage by water distribution network solvers

Rigorous calculations of leakage in water distribution networks (WDNs) requires the adoption of a leakage-pressure relationship and the numerical solution of a set of differential (flow continuity and head loss) equations for each pipe of the network. In order to limit the computational effort necessary to solve differential equations, existing hydraulic solvers commonly make use of simplified methods to estimate pipe leakage and convert it into lumped demands at pipe end nodes. In this paper, three well consolidated literature methods for water leakage calculation and allocation to pipe end nodes are compared against the numerical solution of the differential equation, used as a benchmark. A novel method, based on a two-step estimation of pipe nodal piezometric levels was also proposed in this study. Methods were compared considering a single pipe system and using a dimensionless approach for generalisation of results. An application to a water distribution network case study was carried out to show differences in the results obtained with the various methods for a complex system under extended period simulation (EPS) approach. Calculations carried out using the methods described in prior literature had significant prediction errors basically depending on the chosen value for the leakage exponent of the leakage-pressure relationship. In contrast, the proposed two-step method was determined to provide more accurate predictions of pipe leakage and leakage distribution between ending nodes with evident increased potential for implementation in hydraulic solvers.