Mathematical modelling of stream DO-BOD accounting for settleable BOD and periodically varying BOD source

Abstract

The conventional Streeter and Phelps model does not account for the settleable component of BOD. Their model is therefore of little value in the present day context of polluted streams in which part of the BOD removal necessarily takes place through sedimentation, especially when untreated or partially treated wastes are discharged into streams. Several other dispersion models developed to date also do not account for the settleable part of BOD. In the work presented here, an attempt is made to present a mathematical model accounting for dispersion effects, settling of the settleable part of BOD and the periodic variation of the BOD source. The dispersion model takes into account the bioflocculated sedimentation, as well as biochemical decay of nonsettleable BOD. An alternate finite difference scheme is used to solve the model representing the BOD-DO balance under the stated conditions in a stream.The conventional Streeter and Phelps model does not account for the settleable component of BOD. Their model is therefore of little value in the present day context of polluted streams in which part of the BOD removal necessarily takes place through sedimentation, especially when untreated or partially treated wastes are discharged into streams. Several other dispersion models developed to date also do not account for the settleable part of BOD. In the work presented here, an attempt is made to present a mathematical model accounting for dispersion effects, settling of the settleable part of BOD and the periodic variation of the BOD source. The dispersion model takes into account the bioflocculated sedimentation, as well as biochemical decay of nonsettleable BOD. An alternate finite difference scheme is used to solve the model representing the BOD-DO balance under the stated conditions in a stream.