Eulerian–Lagrangian Method for Constituent Transport in Water Distribution Networks

The transport and mixing of contaminants in conduits is governed by advection, dispersion, and decay. Several models are available to trace the transport of such constituents and most assume that the principal mechanisms for transport are advection and reaction only. However in pipes where low velocities prevail, longitudinal dispersion is significant and models that neglect the dispersion effects fail to properly simulate the observed concentrations in low velocity pipes. This work presents a method for simulating the advection-dispersion-reaction process of constituent transport in water networks. A Eulerian–Lagrangian method is employed whereby the dispersion term in the governing equation is approximated using finite differences and the resulting first-order partial differential equation is then integrated using the method of characteristics. Analytical solutions of the transport equation are also derived to quantify the effect of neglecting dispersion at pipe junctions and to assess the accuracy of the proposed method. The Eulerian-Lagrangian method is tested on benchmark networks and on the field study at the Cherry Hill/Brushy Plains network. Results show that the model developed is capable of simulating transport with equal accuracy for low and high velocity flows with and without significant dispersion effects. It also performs better than other models because of the nonuniform grid distribution and the interpolation schemes used.