American Society of Civil Engineers

Using Linear Programs to Optimize the Chlorine Concentrations in Water Distribution Networks

by Sophie Constans, (Cemagref Bordeaux, Ouvrages et réseaux hydrauliques, 33612 Gazinet cedex, France; Laboratoire de mathématiques appliquées, Université Bordeaux I, 33405 Talence, France), Bernard Brémond, (Cemagref Bordeaux, Ouvrages et réseaux hydrauliques, 33612 Gazinet cedex, France), and Paul Morel, (Laboratoire de mathématiques appliquées, Université Bordeaux I, 33405 Talence, France)
Section: Water Distribution Systems Analysis: Optimal Water Quality Management, pp. 1-12, (doi:

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Document type: Conference Proceeding Paper
Part of: Building Partnerships
Abstract: Disinfecting the water supplied by a distribution network with chlorine or other disinfectants directly acts on its quality. Good water quality imposes lower and upper bounds on the chlorine concentrations all over the network, at any time. These concentrations may be controlled at the sources and at intermediate points of the network, the booster stations, but determination of the optimal chlorine injection strategy is usually not easy, as the transport and reaction phenomena modifying the chlorine concentrations are complex. We propose linear programming formulations to determine the locations where disinfectant must be added and optimize the injection patterns. The variables we choose are the discretized chlorine concentration values at the nodes of the network and the locations where booster stations are needed. The constraints are linear relations between these variables, obtained thanks to a special code simulating the evolution of the concentrations over the network; they describe the interdependence of the variables over the network and take explicitly the system’s dynamics into account. Besides, lower and upper bounds on the optimum concentrations are also introduced. Finally, the criterion we propose here is the minimization of the maximum difference between optimum and target concentration values. Solving the proposed optimization problem not only gives the best booster stations locations and injection patterns, but also calculates the corresponding chlorine patterns at all the nodes of the network.

ASCE Subject Headings:
Computer programming
Drinking water
Water distribution systems