Definition and application of the Péclet number threshold for water quality analysis in water distribution networks

To assess the water quality within the distribution networks, simplified models are used, which adopt an advective–reactive approach and neglect diffusion–dispersion phenomena. Although such simplifications can be sufficiently accurate in complete turbulent uniform flow regimes, literature works demonstrated that they could produce wrong results in laminar and transitional regimes that are relevant when analysing low flows, dead-end pipes in looped distribution networks or service connections. On the other hand, advective simplification allows for considerable computational savings during the simulation of large networks. Therefore, a criterion is needed for better discriminate pipes in which the advective approach is sufficient or the diffusive approach is required. The present study aims to investigate the use of the Péclet number to discriminate the use of advective simplification both adopting the two-dimensional (2D) advection–dispersion equation and the one-dimensional (1D) cross-section averaged advection–dispersion equation. The numerical analysis was applied to a linear pipeline using the EPANET, 1D advective–dispersive–reactive, and EPANET-DD (Dynamic–Dispersion) models. The results showed the inadequacy of the Péclet number in discriminating the dominance of the advective–dispersive process in real systems, as it is linked to the pipe's length, regardless of the flow regime occurring on the pipeline.