TR(BR)-128 : Prediction of longitudinal dispersion coefficient for natural stream

Abstract

One of the most common means for disposal of liquid effluents from municipal, industrial, agricultural and blowdown discharges from fossils or nuclear power plants is to discharge them into the nearest perennial stream. Besides such pollutants, incidental spills from treatment plants and pollution originates from natural hazards are other sources concern to river pollution. Rising demand , on the other hand, increasing pressure of pollution, in recent year, has given rise to the more concern of conservation of water pollution and the study of water pollution. Unless the mixing and transport pattern of pollutants in a river system is understood properly and studied thoroughly, it would be difficult to take any preventive measure to control pollution of river waters.

The movement and mixing of pollutants in a river system is basically governed by the advection-dispersion, growth and decay of pollutants. The combined action of advection and dispersion is important to study the movement of pollutants for conservative materials while for non-conservative matters, growth and decay is more predominant. Advection being the movement of pollutants, therefore, govern by the velocity of flow, while dispersion is mainly governed by the molecular diffusion of particles in the three coordinate systems. For one dimensional river system, it is the longitudinal dispersion co-efficient which characterizes the mixing and spreading of pollutants. To study the phenomelogical behaviour of pollutants in a river system, the study of prediction of dispersion co-efficient is necessary.

There are many approaches available to compute the longitudinal dispersion co-efficient for well mixed stream and they have their own limitations that have been critically reviewed in this report.

The study attempted in this report addresses an approach to compute the longitudinal dispersion co-efficient for a completely mixed river system from a given input time-concentration data and known time-concentration data measured at any location downstream of point of release. Laplace transformation which is a very powerful technique to solve any linear differential equations, in combination with Discrete Kernels approach have been used to compute the longitudinal dispersion co-efficient. It has been observed that upon a good approximation of Laplace transform co-efficient,'S' and time step of computations, the dispersion co-efficient with an accuracy above 95% of the actual value of dispersion co-efficient can be obtained by this method. A procedure for selection of laplace transform co-efficient and time step has been given in the report.