Unsteady-State Inverse Chlorine Modeling in Pipe Networks

A model that directly determines the required source concentration(s) to meet specified chlorine residuals at selected nodes is developed for unsteady flows. The model considers even, over-, and underdetermined cases in which the number of available equations is equal to, greater than, or less than the number of unknowns, respectively. The model computes the unsteady-state flows and chlorine concentrations in the system first. Then it utilizes the inverse method to determine the required source concentration(s) so that specified residuals at selected nodes match the calculated ones. To verify the model, chlorine concentrations computed by the forward method are input to the inverse model to determine the source concentration(s) in two hypothetical networks. Results show that the model computed accurately the source concentrations for the even and the overdetermined cases, but the results were less than satisfactory for the underdetermined case.