Advection-dispersion-reaction modeling in water distribution networks

An Eulerian-Lagrangian numerical solution for the advection-dispersion equation in water supply networks is presented. Because of the dispersion term, the numerical scheme produces a large linear system of equations. A technique that uses numerically computed Green's functions is proposed to decompose this large system into three tridiagonal systems for each pipe and one (much smaller) system for the concentration at the pipe junctions. The resulting system is thus efficiently solved and the model can be applied to large networks at a reasonable computer cost. The proposed model is applied to simulate fluoride and chlorine propagation in a real network for which published data of field measurements and simulation with the EPANET advection-reaction model are available. Comparisons are presented which show that, while for high and medium pipe-flow velocities the two models give similar results, for low pipe velocities the new advection-dispersion model predicts more closely the concentration evolution, provided an appropriate value for the dispersion coefficient is used.