Control-theoretic modeling of multi-species water quality dynamics in drinking water networks: Survey, methods, and test cases

Chlorine is a widely used disinfectant and proxy for water quality (WQ) monitoring in water distribution networks (WDN). Chlorine-based WQ regulation and control aim to maintain pathogen-free water. Chlorine residual evolution within WDN is commonly modeled using the typical single-species decay and reaction dynamics that account for network-wide, spatiotemporal chlorine concentrations only. Prior studies have proposed more advanced and accurate descriptions via multi-species dynamics. This paper presents a host of novel state-space, control-theoretic representations of multi-species water quality dynamics. These representations describe decay, reaction, and transport of chlorine and a fictitious reactive substance to reflect realistic complex scenarios in WDN. Such dynamics are simulated over space- and time-discretized grids of the transport partial differential equation and the nonlinear reaction ordinary differential equation. To that end, this paper (i) provides a full description on how to formulate a high fidelity model-driven state-space representation of the multi-species water quality dynamics and (ii) investigates the applicability and performance of different Eulerian-based schemes (Lax–Wendroff, backward Euler, Crank–Nicolson, and Implicit Upwind) and Lagrangian-based schemes (Method of Characteristics) in contrast with EPANET and its EPANET-MSX extension. Numerical case studies reveal that the Implicit Upwind scheme, Method of Characteristics, and Lax–Wendroff scheme outperform other schemes with reliable results under reasonable assumptions and limitations.