Quality Modeling of Water Distribution Systems Using Sensitivity Equations

In this paper, unsteady water quality modeling and the associated sensitivity equations are solved for water distribution systems. A new solution algorithm is proposed, designed for slow varying velocity and based on a time splitting method to separate and solve efficiently each phenomenon such as advection and chemical reaction. This numerical approach allows simultaneous solution of both the direct problem and the sensitivity equations. Special attention is given to the treatment of advection, which is handled with a total variation diminishing scheme. The general model presented in this study permits global sensitivity analysis of the system to be performed and its efficiency is illustrated on two pipe networks. The importance of the sensitivity analysis is shown as part of the calibration process on a real network.