Generalized resilience and failure indices for use with pressure-driven modeling and leakage

In 2000, the resilience and failure indices were introduced as a convenient and compact tool to express respectively water-distribution network (WDN) surplus and deficit in satisfying users' demand, in terms of delivered power. In their original formulation, the mentioned indices, originally thought as WDN design tools, were developed only considering the demand-driven modeling approach, which would include pumps but not leakage. This paper extends the formulation of both indices and presents a generalized expression, more convenient for use when dealing with pressure-driven modeling and capable of including the effect of leakage. Following the original concept, the generalized indices were developed by calculating the power dissipated in the network as a function of the difference between the total power inserted through source nodes and pumps and the net delivered power, whereas the leakage-related power is considered as a loss similarly to the internally dissipated one. Applications to WDN analysis and design proved that using the new formulation in the presence of leakage and pressure-dependent consumptions yields better description of the delivered power excess, compared to the original demand-driven formulation and to another pressure-driven formulation present in the scientific literature.