Numerical Modelling and Field Validation of Heavy Metal Transport in Rupingazi River Water Using the Advection –Diffusion Equation

The most important resource of life in this planet is water. With the rapid economic growth, heavy metal pollution has become a key issue in rivers as it is the most common source of drinking water in the world. Heavy metals contamination in river waters poses significant risks to both ecosystems and human health. Accurate prediction of heavy metals concentration is essential for effective water quality management and environmental protection. The objective of this study was to develop and solve a numerical model to predict the spatial and temporal distribution of heavy metal concentration in river water under varying flow conditions. The model incorporates the advection –dispersion equation. The advection diffusion equation was solved numerically to predict the spatial and temporal distribution of heavy metal concentration in a rivers system under varying environmental conditions. The equation was discretized using finite difference method (central differences). The numerical solution was obtained using python programming language and validated using the data collected from Rupingazi river. There was a high correlation between the simulated and field data values of concentration of iron in river water. The correlation coefficient was 0.899 . Sensitivity analysis was done on the model to assess how it was influenced by factors such as velocity, dispersion, sources and sinks. The model was applied to predict the spatial and temporal variations of heavy metals in Rupingazi river. The model provides variable insights for managing pollution and can inform regulatory decisions on water quality control particularly in areas with industrial and agricultural runoff.