TR(BR)-9/99-2000 : Development of reaeration coefficient for Indian conditions using mathematical approach in field studies

Abstract

The river pollution is one of the serious concerns in the present scenario of water resources development. Rivers are one of the most potent sources of water. However, it is being observed that the river quality has been deteriorating for long due to steady growth Lit industries, urbanization, increasing population and use of chemicals and fertilizers for agriculture. There are number of constituents which determine the quality of water, however, dissolved oxygen (DO) is the most important parameter indicating the health of a stream. There is a continual replenishment (reaeration) or utilization (deoxygenation) of dissolved oxygen due to inflow of waste load at different points in a stream. When a waste load is discharged into a flowing stream, it is mainly subjected to advection, dispersion and reaction kinetics. Waste Load Allocation (WLA) studies provide information to assist in making affective decisions on levels of treatment required for a source or sources of pollutant loads.

To model and allocate waste loads in a stream, it is necessary to estimate the deoxygenation rate coefficient (K1) and reaeration coefficient (K2). Rate coefficients, in contrast to loads, sources and sinks generally cannot be directly measured under natural conditions. Indirect measurements, supplemented by calculations provide one of the most reliable techniques for estimating rate coefficients. In addition, laboratory and field experiments can provide information on relative ranges of reaeration and deoxygenation rates. Numerous equations employing depth, velocity and slope have been developed to estimate the stream reaeration and deoxygenation rate coefficient. This leads to uncertainties in modelling analysis because these equations are empirical in nature and may yield very different K1 & K2 values for the same stream. Realizing the uncertainties involved in determining K1 & K2, many modellers have resorted to model calibrations as a way of adjusting values. In fact, in the pioneer work of stream analysis by Streeter and Phelps (1925), K2 was evaluated indirectly by using DO budget and the K1 was evaluated by carrying out laboratory and field experiments.

In the present study, the concept of Streeter and Phelps (1925) with exponential law of non-settleable BOD has been applied to determine the reaeration coefficients and deoxygenation rate coefficients for different reaches of river Kali, a highly polluted river of western Uttar Pradesh (India). The most commonly used predictive equations developed earlier for small streams having flow less than 10 m3/s and depth below 2 m were also tested. The predictive equations have been evaluated using statistics including normal mean error (NME), standard error (SE) and mean multi-plicative errors (MME). The results obtained from these equations have been compared with the field observations carried out at frequent intervals and from Streeter & Phelps technique and a correlation between the two has been obtained. A new predictive equation has been developed for Kali River under different flow conditions and evaluated for errors and correlation with the mass balance approach of Streeter and Phelps.