Booster Disinfection Scheduling under Uncertainty in Water Distribution Systems: Approximate Robust Reformulation Approach

Abstract

One key aspect of ensuring water safety in water distribution systems (WDS) is the controlled use of disinfectants like chlorine within these systems. The number of disinfectant levels in WDS directly impacts the quality and safety of the water supplied to consumers, thus chlorine/disinfectant regulation in WDS is paramount. An upper residual chlorine limit controls the formation of disinfection byproducts, whereas a lower residual chlorine limit guarantees that the water remains free of organic contaminants. However, accurately modeling the chlorine reaction in WDS is a complex task due to various influencing factors, including pipe material, pipe age, water pH, temperature, and more. The variability in the chlorine reaction rate in WDS poses a significant challenge in accurately predicting water quality provided to the consumers and also affects the optimal scheduling of chlorine booster injections. To ensure the water quality remains within the acceptable range, we consider the chlorine reaction rate as an uncertain parameter and propose an approximate robust reformulation approach for the booster chlorination scheduling problem. We utilize two benchmark WDS systems to perform rigorous testing and analysis of our methodology. The proposed approach provides a systematic and robust method to obtain chlorine injection scheduling that adheres to predefined aims to maintain safe water quality levels while considering the uncertain reaction rate coefficients to be within ellipsoidal uncertainty sets. Water utility managers face the critical challenge of maintaining safe and effective disinfection levels across water distribution systems. Variability in chlorine reaction rates—due to factors like temperature, pipe material, and water pH—adds complexity to this task. This study proposes a robust methodology that helps managers optimize the dosage schedule of chlorine injections, ensuring consistent water safety. By using robust optimization approach, the uncertainties in reaction rates are accounted, to ensure the maintenance of chlorine levels within safe thresholds. Balancing the risks of bacterial contamination or harmful disinfection by-products. The methodology’s robust optimization techniques also reduce computational demands compared with the stochastic approach, making it suitable for large urban water networks where real-time decision-making is crucial. In urban areas with aging infrastructure, this methodology enhances public health by ensuring a reliable supply of safe drinking water, meeting water quality standards, and boosting public confidence in the safety of the water supply.