A Two-Dimensional Mathematical Model of Chlorine Residual Transport in a Water Distribution Pipe

This study introduces a two-dimensional (2D) axisymmetric mathematical model for simulating chlorine residual transport in pressurized water distribution pipes. Unlike existing one-dimensional or simplified decay models, the proposed model integrates laminar flow dynamics, advection-diffusion processes, and first-order reaction kinetics with temperature-dependent decay, based on the Navier–Stokes framework. The governing equations are solved using the Finite Element Method (FEM) in COMSOL Multiphysics (6.2), allowing for a more realistic and spatially resolved analysis of chlorine concentration profiles. The model also advances understanding of how Peclet and Reynolds numbers affect chlorine decay and distribution. Results reveal that chlorine concentration decreases progressively along the pipe, with decay rates significantly influenced by the Peclet and Reynolds numbers. Higher Peclet numbers result in advection-dominated transport with steeper concentration gradients, while higher Reynolds numbers enhance mixing and promote more uniform chlorine distribution. The velocity profile exhibits a parabolic shape characteristic of laminar flow, and pressure consistently declines along the pipe due to frictional resistance. Additionally, higher temperatures accelerate chlorine decay, underscoring the importance of thermal effects in disinfection dynamics. These insights enable water utility operators to optimize disinfection processes, ensure compliance with safety standards, and enhance the efficiency of water treatment systems.