The application of dispersion models in estimating the concentration levels of a solute, or a pollutant constituent, resulting from discharging waste into reservoirs and natural streams is presented. For the reservoir case, the mass balance principle of the aggregated dead zone (ADZ) model is employed, from which a general formulation for the dispersion of a pollutant constituent is derived. A hypothetical case is presented where an accidental spillage of a chemical discharge into a reservoir is considered. The prediction of the transient change in the concentration levels is analytically derived for the general case of reservoirs of arbitrary volumes and of various influx rates and duration. For the case of natural streams, the classic version of the Fickian diffusion model is modified, from which an expression for quantifying the coefficient of dispersion is proposed. The proposed dispersion model has been applied to a case study carried out on Waikato River, in New Zealand, where a dye is released in the river for the purpose of providing information about flushing rates at low steady flows. It has been demonstrated that the proposed dispersion model gives a more realistic estimation of the concentration profiles than those obtained from other existing models. Reasonably good comparisons were obtained with the measured concentration levels in the river at both the near-field and the far-field locations from the injection site.
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