INVERSE MODELING OF CHLORINE CONCENTRATION IN PIPE NETWORKS UNDER DYNAMIC CONDITION

The Surface Water Treatment Rule under the Safe Drinking Water Act and its amendments require that the water utilities maintain a detectable disinfectant residual throughout the distribution system at all times . A new computer model is presented to directly calculate the chlorine concentrations needed at the source(s) to have specified residuals at given locations in a pipe network in unsteady flow conditions by usin g an inverse method. Unlike the forward solution method, which calcula tes the source chlorine concentration by a trial-and-error procedure, the inverse solution technique presented in this paper directly calcul ates the source concentration required to meet a specified value at a particular point in the network. The dynamic flows and pressures are f irst calculated by solving the governing equations by an implicit fini te-difference scheme subject to appropriate boundary conditions. For c hlorine concentrations at various pipe sections and at each node, the one-dimensional transport equation is modified for the advection domin ated how. This modified transport equation is then discretized by usin g the four-point implicit finite-difference scheme and solved simultan eously together with the junction mass balance equations. A first-orde r reaction rate for chlorine decay is assumed and a flow-weighted aver aging procedure is used to calculate the complete mixing of chlorine a t the junctions. For the verification of the inverse method, the compu ted results are compared with those determined by direct simulations. An excellent agreement is observed between the inverse method and dire ct simulation technique.