In drinking water networks, hydraulics and water quality stand out as two paramount phenomena, each with its distinct focus and time-scale. Hydraulics is concerned with delivering adequate pressure throughout the network, ensuring that water flows efficiently to meet consumers' needs. On the other hand, water quality focuses on the maintenance of high standards for water safety within the network. These two critical aspects operate on distinct time-scales. Hydraulics undergo changes on a longer time-scale, reflecting the gradual shifts in flow rates and pressure levels across the network. In contrast, water quality dynamics require faster measures, often necessitating the computation of hydraulic profiles in advance. That is, a layer of complexity arises from the interdependency of the water quality dynamics on the system’s hydraulics. This interdependence significantly impacts the performance of the water quality control and regulation algorithm in response to hydraulic adjustments. Prior studies have tended to focus on the two problems separately; Some studies have focused on optimizing the operational hydraulic settings, while others have concentrated on regulating water quality dynamics. Moreover, other studies have coupled these two problems leading to trade-offs between conflicting objectives. In this study, we adopt a control-theoretic perspective to investigate the intricate relationship between optimized hydraulic operation and water quality control. Our proposed framework explores the enhancement of water quality controllability while solving the pump schedule optimization problem. We examine the resultant trade-offs of the operational scheduling problem in comparison to the decoupled approach—and evaluate the impact on the water quality control performance. We assess and validate the proposed approach on various case studies with different scales and hydraulic scenarios. This study offers novel approaches to the integration of hydraulic and water quality control, paving the way for more effective and resource-efficient management of water distribution networks.

Tracing disinfectant (e.g., chlorine) and contaminants evolution in water networks requires the solution of 1-D advection-reaction (AR) partial differential equations (PDEs). While analytical solutions are non-existent in most cases, numerical solutions require high-resolution time- and space-discretizations. This results in large model dimensions even for small networks thereby leading to a physical-driven model that is intractable when considering constrained control and water quality regulation algorithms. In addition, considering multi-species rather than single-species dynamics produces a more accurate description of the reaction dynamics. The multi-species model can be used to model disinfectant interactions with other species (e.g., microbial, chemical) in the bulk flow, attached to the pipe walls, or contamination events. Yet, it adds complexity by introducing nonlinear reaction dynamics to the model. To that end, solving nonlinear 1-D AR PDEs in real time is critical in achieving monitoring and control goals for various scaled networks with a high computational burden. In this work, we propose a comprehensive framework to overcome the large-dimensionality issue by introducing different approaches for applying model order reduction (MOR) algorithms to the nonlinear system followed by applying feedback control to maintain desirable disinfectant levels in water networks. These approaches focus on reducing model dimension by orders of magnitude while preserving important properties of the original system (e.g., controllability). That is, this framework is constructed and tested considering different variables and parameters including hydraulics, network size, events nature, etc. Moreover, it is considered a generalized scalable framework in the sense that simplifications are included to consider single-species water dynamics and differentiations are suggested to consider different chlorine linear/nonlinear decay and reaction models. The performance of this framework is validated using rigorous numerical case studies under a wide range of scenarios demonstrating the challenges associated with controlling chlorine levels under multi-species water quality dynamics.

Water distribution networks (WDN) are considered vulnerable to health violations and contamination events. To better predict such events, a real-time dynamic model—based on PDEs that capture transport and reaction of contamiants and disinfectants—can be instrumented. Such model is essentially a dynamic- and network-theoretic representation of water quality (WQ) states throughout a WDN. Although this model has been thoroughly studied in the recent literature, its control-theoretic properties (stability, controllability, and observability) are neither studied nor understood. Consequently, the objective of this work is to investigate and understand control-theoretic properties of WQ models in drinking WDN. This understanding yields improved placement of decontamination stations, WQ sensors, and ultimately better real-time regulation of water quality.