Article

Mathematical modelling of the pollution processes of the Southern Bug River by nitrogen-containing compounds

Sviatoslav Mandebura, Serhii Kvaterniuk, Vasyl Petruk
Abstract

Critical ecological state of the Southern Bug River, caused by intensive pollution with nitrogen-containing compounds, requires the implementation of reliable mathematical forecasting tools to mitigate the effects of eutrophication and achieve the objectives of national water resources management strategies. The study aimed to mathematically model the processes of transport and transformation of nitrogen-containing compounds in the Southern Bug River system to quantitatively assess the spatio-temporal dynamics of pollution and provide a scientific basis for environmental protection measures. For the mathematical modelling, a system of differential equations based on one- and two-dimensional advection-dispersion-reaction models was applied, the numerical solution of which was conducted using the operator splitting method. Developed a model that integrated the three key nitrogen components and accounted for the mechanisms of advection, dispersion and biochemical transformations. The model described the processes of nitrification and denitrification in detail, incorporating temperature and dissolved oxygen concentration according to the Michaelis-Menten kinetics. Modelling was conducted to assess the impact of ammonium nitrogen pollution, using the example of discharges from municipal wastewater treatment plants in the upper reaches. The verification results demonstrated the model’s ability to reproduce the spatial reduction in pollutant levels due to natural self-purification processes. The model identified the formation of a “nitrite peak”, which is spatially shifted downstream relative to the maximum ammonium concentrations. High levels of toxic nitrites persist at distances of up to 15 km from the source of pollution. A scenario analysis has shown that the immediate implementation of tertiary treatment at the most significant facilities is a priority measure for restoring the river’s oxygen regime. If the river’s water flow decreases by 40% of the normal low-water level, a catastrophic increase in the concentrations of nitrogen-containing compounds and oxygen depletion is expected across significant sections of the river channel, provided that current discharge volumes remain unchanged. The model developed serves as a tool for optimising management decisions within the framework of the Southern Bug River Basin Management Plan and created a comprehensive environmental monitoring system to ensure the region’s sustainable development

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Received 22.12.2025

Revised 30.04.2026

Accepted 12.06.2026

Published 30.06.2026

https://doi.org/10.63341/esbur/1.2026.115
Retrieved from Vol. 17, No. 1, 2026
Pages 115-128

Suggested citation

Mandebura, S., Kvaterniuk, S., & Petruk, V. (2026). Mathematical modelling of the pollution processes of the Southern Bug River by nitrogen-containing compounds. Ecological Safety and Balanced Use of Resources, 17(1), 115-128. https://doi.org/10.63341/esbur/1.2026.115

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