Linear Least-Squares Formulation for Operation of Booster Disinfection Systems

Maintaining a disinfectant residual in drinking water distribution networks is a challenge for water utilities. These challenges arise from the spatial and temporal distribution of water usage, and from chemical reactions that cause disinfectants to decay. A potential solution is booster chlorination, a strategy where disinfectant is reapplied within the network. Here, a linear least-squares problem is formulated to determine the optimal disinfectant injection rates that minimize variation in the system residual space-time distribution. Locations of booster stations are assumed known. The solution is simple and can be analytically derived in some cases. The problem formulation allows an arbitrary weight on the contribution of each consumer node disinfectant residual to the overall objective function; two possible weighting schemes are suggested. In a planning context, the method is shown to apply to network flows whose first and second moments are stationary. In contrast to previous approaches, the number of residual sampling nodes and sampling rate do not affect the size of the optimization problem, nor its computation time. Also, the optimization problem is always feasible, a considerable practical advantage for network models where low chlorine concentrations cannot be avoided (e.g., zones with small or zero water usage). The method is tested on an example network. Results show that booster disinfection can be effective in reducing network-wide variation in disinfectant residual, while reducing the total mass of disinfectant used.