A Mathematical Model Development for Simulating Nitrate Pollutant Transport along a River

Abstract

Contamination of surface water bodies by a wide range of organic and inorganic pollutants has been a serious problem in the recent time, these have an effect on human and aquatic animals. The water quality deterioration calls for regular monitoring of the water quality in order to maintain the health and sustainability of the aquatic ecosystems. Accurate monitoring of discharged pollutants into the rivers may be time taking and labour intensive. Water quality models are significant tools for simulating water quality and controlling the surface water pollution. The purpose of this study is to develop a simplified mathematical model which is hybrid cells in series model (HCIS) to simulate the spatial and temporal variation of nitrate concentration in natural rivers. The HCIS model was formulated to serve as an alternative method to the Fickian based models. Analytical solutions for the first order reaction kinetics of nitrate with the advection and dispersion process were derived using Laplace transformation technique. The model considered the effect of nitrate concentration at several points along the river downstream by considering the transformation of nitrite to nitrate through nitrification process. In addition, the uptake of nitrate by algae for its growth and conversion of nitrate to nitrogen gas due to denitrification process were considered. The HCIS-NO3 model was applied to uMgeni River, South Africa to investigate the nitrate concentration along the river. Furthermore, the quantitative measures based on the coefficient of determination (R2) and standard errors (SE) were used to evaluate the performance of the model. The result shows that the simulated values agreed with the measured values of nitrate concentration in the river which resulted in a R2 value of 0.72 and a low standard error. Analytical solutions of HCIS - NO3 model were compared with the numerical solutions of the Fickian based ADE model for hypothetical problems. Comparison of the responses indicates that the HCIS - NO3 and ADE- NO3 models were in good agreement. The study shows that the hybrid model is a simple and effective tool for simulating pollutant transport in natural rivers.