Advection-Dispersion Equation For Pollutant Concentration

Abstract

The advection-dispersion-reaction equation is used to describe the dispersion process. Here, we solve one-dimensional steady advection-dispersion equation numerically by using nite di erence method. Also, we formulate the model to minimize the cost of wastewater treatment. Analytical solution to unsteady advection-dispersion equation using Laplace transformation technique is derived to describe the pollutant concentration C(x; t). We have obtained analytic unsteady solution by taking the water velocity u in the x-direction as a linear function of x and dispersion coe cient D as zero in case of concentration of pollutant in one region. Numerical studies show variation of C with time t. If the added pollutant rate along the river q is very small amount, the variation of C along the river at di erent times coincide to each other. In case of concentration of pollutant in two regions, analytical solutions are determined by taking dispersion coe cient D as non-zero. A coupled system of advection-dispersion equations based water pollution model is presented that incorporates di erent parameters. We have proposed analytical solution for mathematical model. One dimensional model is used to observe the concentrations by taking dimension along the length of river. By considering the removal of pollutant by aeration, event of steady states is investigated. In this model, coupled advection-dispersion equations are solved by taking dispersion coe cient as zero and non-zero, respectively. Keywords: Pollutant, Concentration, Laplace transformation, Dispersion, Analytical solution, Dissolved oxygen.