Definition of a numerical prior indicator to identify the relevance of diffusion and dispersion processes in water distribution networks

The present study aims to provide a quick decision-making tool, to identify the most effective analysis model to be applied to water distribution networks (WDNs) (standard advective model or advective - diffusive models), if one wants to simulate the fate of dissolved contaminants. State-of-the-art applications in water distribution modelling are based on advective approaches in which contaminants are supposed to follow water flows and diffusion can be neglected. One of the most used advective models is EPANET that adopts a simplified advective approach in modelling the water quality, considering simplified reaction kinetics. These simplifications have an enormous advantage, i.e. to reduce the computational load, not producing particularly significant errors in purely turbulent flow regimes. On the other hand, it is not always possible to adopt these simplifications since dispersion-diffusion phenomena are inherent in the transport processes. These processes become relevant in the presence of low speeds and a Reynolds number lower than 50,000, as often happens in urban WDNs at night. The use of diffusive-dispersive models allows obtaining enormous advantages as regards the modelling of the behaviour of solutes, as it improves the prediction of the pulse shape, considerably increasing the computational load. Previous studies, conducted on the real network of Zandvoort (The Netherlands), have shown that, despite mainly turbulent flows, due to the topological complexity of the network, the flows tapped at the nodes, the size of the pipeline, the diffusive - dispersive processes were found to be relevant due to the presence of laminar and transition flow in some of the pipes for some hours during the night. Therefore, the purpose of this study is to determine an indicator that can establish a priori the behaviour of the water network, in such a way as to define a threshold, beyond which the simple advective model is not efficient for modelling water quality and a more complete diffusive - dispersive approach is needed.