Abstract
Accurate prediction of contaminant transport and self-purification processes in rivers remains challenging because pollutant dispersion, biochemical reactions, and hydrodynamic conditions interact across multiple spatial scales. This study aims to develop and compare mathematical models for soluble contaminant transport and biodegradable organic matter removal in channels and rivers. Unsteady advection–diffusion–reaction equations were formulated for one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) transport scenarios and solved through numerical techniques based on the transformation of partial differential equations into systems of ordinary differential or algebraic equations. In parallel, the classical Streeter–Phelps model and an extended formulation incorporating turbulent diffusion were implemented to evaluate organic load degradation and oxygen deficit dynamics. Simulations were performed using a Matlab R2019a-based computational framework under representative hydraulic and reaction conditions obtained from literature data and empirical correlations. The results showed that, under specific conditions, the 3D model reproduced trends comparable to those predicted by the 2D model, while the latter approached the behavior of the 1D formulation. The Streeter–Phelps model predicted an organic load removal efficiency of 97.74%, a purification index of 1.9564, a critical time of 18.43 h, and a critical distance of 6.93 km. These findings provide a useful framework for river water-quality assessment and support future applications involving complex hydrodynamic and pollutant-loading scenarios.