  Chlorine is a widely used disinfectant and proxy for water quality (WQ)
monitoring in water distribution networks (WDN). Chlorine-based WQ regulation
and control aims 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, and Crank- Nicolson) and
Lagrangian-based schemes (method of characteristics) in contrast with EPANET
and its EPANET-MSX extension. Numerical case studies reveal that the
Lax-Wendroff scheme and method of characteristics outperform other schemes with
reliable results under reasonable assumptions and limitations.
