Modeling of constituent transport in unsteady flows in pipe networks

A new computer model is presented to predict the spatial and temporal distribution of residual constituent in a pipe network under slowly varying unsteady flow conditions. Unlike the other available models, which use steady-state or extended-period simulation of steady flow conditions, thus neglecting inertial effects, the presented model is truly dynamic, using a lumped-system approach to compute unsteady flow conditions. This model also includes dispersion and constituent decay in pipes. Slowly varying flow conditions are computed by numerically integrating the governing equations by an implicit finite-difference scheme subject to the appropriate boundary conditions. The transport equation is solved to compute the propagation of a constituent with a first-order decay rate. To avoid numerical diffusion, the advection and dispersion are solved in two steps: The Warming-Kutler-Lomax explicit scheme is used to solve pure advection while an explicit scheme is used to calculate dispersion and decay. Complete mixing is assumed at the pipe junctions. The model is applied to two typical pipe networks to simulate the transport and decay of chlorine, and the results are compared with another model which uses the standard extended-period simulation technique. The results are found to be in good agreement at the beginning of the simulation. However, the chlorine concentrations at different nodes in the network differ when the flow becomes more unsteady and when reverse flows occur. The model may be used to analyze the propagation and decay of any substance with a first-order reaction rate.