Lagrangian Method to Model Advection-Dispersion-Reaction Transport in Drinking Water Pipe Networks

Area of Science:

• Environmental Engineering
• Computational Fluid Dynamics
• Water Quality Modeling

Background:

• Traditional Eulerian and Eulerian-Lagrangian methods for water quality simulation in pipe networks rely on fixed computational grids.
• These fixed grids can be limiting for complex network geometries and nonuniform flow conditions.
• Accurate simulation of constituent transport, including advection, dispersion, and reaction, is crucial for managing drinking water quality.

Purpose of the Study:

• To present a novel Lagrangian method for simulating advection, dispersion, and reaction of constituents in drinking water pipe networks.
• To demonstrate the method's compatibility with existing water quality engines like EPANET.
• To improve the accuracy of water quality simulations, particularly in scenarios dominated by dispersion.

Main Methods:

• Employs a Lagrangian approach, eliminating the need for fixed computational grids and allowing for nonuniform segments.
• Utilizes an operator splitting technique, modeling advection-reaction before dispersion in each water quality step.
• Discretizes the dispersion equation using a segment-centered finite-difference scheme with flux continuity at junctions.
• Implements a staged approach to solve the dispersion equation for interconnected networks, establishing boundary-internal concentration relationships and solving a linear system for junction concentrations.

Main Results:

• The Lagrangian method is fully compatible with the EPANET advection-reaction water quality engine.
• The method produces exact results when analytical solutions are available.
• Simulations show improved accuracy compared to advection-reaction-only models, especially in dispersion-dominated regions.

Conclusions:

• The presented Lagrangian method offers a flexible and accurate alternative for simulating water quality in drinking water pipe networks.
• Its ability to handle nonuniform segments and its compatibility with existing tools make it a valuable advancement.
• The enhanced accuracy, particularly in dispersion-heavy environments, provides more reliable water quality predictions.