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Water consumption is perhaps the main process governing Water Distribution Systems. Due to its uncertain nature, water consumption should be modeled as a stochastic process or characterized using statistical tools. This paper presents a description of water consumption using statistics as mean, variance, and correlation. The analytical equations expressing the dependency of these statistics on the number of served users, the observation time and the sampling rate, namely the scaling laws, are theoretically derived and discussed. Real residential water consumption data are used to assess the validity of these theoretical scaling laws. Results show a good agreement between the scaling laws and the scaling behavior of real data statistics. The scaling laws represent an innovative and powerful tool, allowing to infer the statistical features of overall water

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A numerical approach for generating a limited number of water demand scenarios and estimating their occurrence probabilities in a water distribution network (WDN) is proposed. This approach makes use of the demand scaling laws in order to consider the natural variability and spatial correlation of nodal consumption. The scaling laws are employed to determine the statistics of nodal consumption as a function of the number of users and the main statistical features of the unitary user’s demand. Besides, consumption at each node is considered to follow a Gamma probability distribution. A high number of groups of cross-correlated demands, i.e., scenarios, for the entire network were generated using Latin hypercube sampling (LHS) and the numerical procedure proposed by Iman and Conover. The Kantorovich distance is used to reduce the number of scenarios and estimate their corresponding probabilities, while keeping the statistical information on nodal consumptions. By hydraulic simulation, the whole number of generated demand scenarios was used to obtain a corresponding number of pressure scenarios on which the same reduction procedure was applied. The probabilities of the reduced scenarios of pressure were compared with the corresponding probabilities of demand.

Pressure determination in water distribution systems (WDS) is important because it generally drives the operational actions for leakage and failure management, backwater intrusion and demand control. This determination would ideally be done through pressure monitoring at every junction in the distribution system. However, due to limited resources, it is only possible to monitor at a limited number of nodes. To this end, this work explores the use of an Artificial Neural Network (ANN) to estimate pressure distributions in a WDS using the available data at the monitoring nodes as inputs. The optimal subset of monitoring nodes are chosen through an entropy-based method. Finally, pressure values are compared to synthetic pressure measures estimated through a hydraulic model.