Water Quality Analysis for the Depletion of Dissolved Oxygen due to Exponentially Increasing Form of Pollution Sources

Abstract

Analyzing and improving mathematical models for water quality investigation are imperative for water quality issues around the world. This study is aimed at presenting the 1D unsteady state regarding analytical and numerical solutions of dissolved oxygen (DO) concentration in a river, in which the increase of pollution from a source is considered as an exponential term. Laplace transformation was utilized to obtain analytical solutions, while the finite difference technique was selected for numerical solutions. The results show that the rate of pollutant addition along the river (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>q</mml:mi></mml:math>) and the arbitrary constants of an exponentially increasing pollution source term (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>λ</mml:mi></mml:math>) affected inversely, while the initial concentration <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:msub><mml:mrow><mml:mi>X</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math> affected directly, DO in the river. These solutions and simulations can be enabled for testing in various scenarios in terms of the behavior of oxygen depletion in polluted rivers.