Unsteady Transport of Pollutants in Rivers Due to Pulse Disposal

Mixing of pollutants in rivers is accomplished by the process of mechanical dispersion. Physically, dispersion may be considered as a hydraulic mixing process, by which the waste concentrations are attenuated while the waste pollutants are being transported downstream. Turbulent diffusion and velocity gradients are the two main mechanisms in dispersion. An exact analytical solution is developed for the two-dimensional unsteady convective-dispersion equation. The solution describes the concentration distribution for a conservative pollutant or substance injected as a pulse (not continuous) into a river by a diffuser pipe installed normal to the direction of the river bank. The river has a constant mean velocity and a relatively large discharge in comparison to the pollution discharge.

The solution is developed using Laplace and Finite Fourier Transforms. The distribution of the transporting concentration of the pollutant in the river due to such disposal is developed in terms of error functions, exponential, and trigonometric series. Variations in the location of the diffuser pipe in the river are examined. The concentration distribution is determined across and along the river as a function of time. The effects of variations in river velocity, lateral and longitudinal dispersion coefficients on the mixing patterns are presented. The solution presents variations in concentration distribution in the river with time during and after the pulsing injection period of the pollutant. Sensitivity analysis is carried out to determine significant variations in the solution due to changes in various parameters.