Comprehensive Framework for Controlling Nonlinear Multispecies Water Quality Dynamics

Abstract

Tracing disinfectant (e.g., chlorine) and contaminants evolution in water networks requires the solution of one-dimensional (1D) advection-reaction (AR) partial differential equations (PDEs). With the absence of analytical solutions in many scenarios, numerical solutions require high-resolution time and space discretizations, resulting in large model dimensions. This adds complexity to the water quality control problem. In addition, considering multispecies 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 introduce a nonlinear reaction formulation to the model. To that end, solving nonlinear 1D AR PDEs in real time is critical to 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 a real-time water quality regulation algorithm that is based on an advanced model to maintain desirable disinfectant levels in water networks under multispecies 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.