Simulation of Water Quality in Pipeline Networks: A Graph Theory Approach

Water quality analysis in pipe distribution systems utilizes both Eulerian and Lagrangian methodologies to assess zero-, first-, and second-order reactions, with Lagrangian methods widely used in EPANET software. This study introduces steady-state Eulerian formulations based on graph theory, using initial topological matrices derived from pipe and node connections to analyze steady flow conditions. These matrices enable the sequential resolution of linear equations to map water quality distribution. This approach effectively handles both linear and nonlinear scenarios, including first-order decay and growth, as well as second-order decay in various network sizes.