Comprehensive Framework for Controlling Nonlinear Multi-Species Water Quality Dynamics

TL;DR

This paper presents a comprehensive framework combining model order reduction and real-time control algorithms to manage nonlinear multi-species water quality dynamics efficiently in water networks.

Contribution

It introduces a novel approach for applying model order reduction to nonlinear PDEs and implements a real-time regulation algorithm for multi-species water quality control.

Findings

Framework effectively reduces computational complexity.

Successfully maintains disinfectant levels in simulations.

Handles complex multi-species nonlinear dynamics.

Abstract

Tracing disinfectant (e.g., chlorine) and contaminants evolution in water networks requires the solution of 1- D advection-reaction (AR) partial differential equations (PDEs). With the absence of analytical solutions in many scenarios, numerical solutions require high-resolution time- and spacediscretizations resulting in large model dimensions. This adds complexity to the water quality control problem. In addition, considering multi-species water quality dynamics rather than the single-species dynamics produces a more accurate description of the reaction dynamics under abnormal hazardous conditions (e.g., contamination events). Yet, these dynamics introduces nonlinear reaction formulation 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 novel 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 real-time water quality regulation algorithm that is based on an advanced model to maintain desirable disinfectant levels in water networks under multi-species dynamics. The performance of this framework is validated using rigorous numerical case studies under a wide range of scenarios demonstrating the challenges associated with regulating water quality under such conditions.