Mathematical Modeling of the Self-Purification of Rivers

Abstract

The self-purification process in rivers is described qualitatively. Different ways of representing this process by systems of differential equations are discussed. The parameters of the differential equations cannot be measured directly. but must be estimated from experimental values of the dependent variables. For this problem, called model identification, the quasilinearization technique is recommended and explained. The technique is applied to self-purification models of some simple laboratory studies. A model is given of rivers whose benthos may be neglected. Its dependent variables are: concentration of easily degradable wastes, concentration of slowly degradable wastes, bacterial mass concentration, protozoan mass concentration, and oxygen concentration. Keeping the measurement efforts within reasonable limits, the conditions under which this model can be identified are investigated. Finally, a self-purification model of the Rhine river between Mannheim/Ludwigshafen and the Dutch-German-border is proposed. It is shown that the model is consistent with the measured data. The model is used to estimate the consequences of activities such as waste heat disposal or sewage treatment.