Mathematical modeling of water pollution in river

Abstract

This project proposed a steady one-dimensional advection-dispersion-reaction equation to calculate the chemical oxygen demand (COD) concentration in a river. (COD) refers to the amount of oxygen required to oxidize the organic compounds in a water sample to carbon dioxide and water[1]. It is used for monitoring and control of discharges, and for assessing water treatment performance[2]. The equation is converted to second order linear ordinary differential equation and solved by using finite difference method (FDM). The method involving finite differences for solving boundary-value problems replace each of the derivatives in the differential equation with an appropriate difference-quotient approximation. The derivatives are approximated by using forward difference, backward difference and central difference. The resulting system of equations is expressed in the tridiagonal N x N matrix form which can be solved by Thomas Algorithm. From the result, a total of 1.0161 mg/L COD concentrations is reduced with the least treatment cost of euro 663. In addition, 1 mg/L of COD concentration is reduced by using 35 pieces of EM mudballs within the 10000m3 of polluted water in two days. The estimated cost is RM 22.75.