Optimal scheduling of booster disinfection in water distribution systems

Booster disinfection is the addition of disinfectant at locations distributed throughout a water distribution system. Such a strategy can reduce the mass of disinfectant required to maintain a detectable residual at points of consumption in the distribution system, which may lead to reduced formation of disinfectant byproducts in particular trihalomethanes. Here an optimization model is formulated for the dynamic schedule of disinfectant injections; this schedule minimizes the total dose required to satisfy residual constraints over an infinite-time horizon. This infinite-time problem is reduced to a solvable finite-time optimal scheduling model by assuming periodicity of mass injections and network hydraulics. Furthermore, this model is linear since the principle of linear superposition is shown to apply to disinfectant concentrations resulting from multiple disinfectant injections over time. A matrix generator code was developed to interface with the EPANET network water quality model. This code automatically generates the Linear programming formulation of the optimal scheduling model, which is then solved using the simplex algorithm. Results from application of the model suggest that booster disinfection can reduce the amount of disinfectant required to satisfy concentration constraints, when compared to conventional disinfection only at the source. The optimal booster schedule reduced the average disinfectant concentration within the distribution system and, in some cases, the variability of these concentrations. The number of booster stations, booster location, and distribution system hydraulics were shown to affect the optimal schedule.