The paper deals with the modeling of the transport and mixing of pollutants in any continuum (fluid, gas, electrolyte, solid body). Any chemical substance which mix readily with fluid medium as well as heat, mass or electrical current can be treated as pollutants. All these pollutants mix with medium in very similar way. The concentration field is described by the identical conservation equation. It is shown how to receive this equation and how to use it for the description of the con-centration field in the water reservoir.
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Mathematical description of the concentration field of pollutants in different aquatic systems par-ticularly in rivers, open channel flows and reservoirs is presented. Pollutants are defined here as all kinds of chemical substance that mix readily with water but do not react with it. It is assumed that the pollutants are passive but do not have to be conservative. The heat is also treated as a pollutant and it is shown how to describe the temperature field in the considered aquatic environment. Water flows in rivers, open channels and reservoirs are usually turbulent and the concentration calcula-tions need special treatment. It is shown how to describe mathematically the concentration distribu-tion in turbulent flows and also in shallow rivers and very long rivers. The pollutant transport in shallow rivers is treated as two-dimensional case and in very long rivers as one-dimensional case. The processes of dispersion in two-dimensional and one-dimensional cases are discussed.
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Równania transportu stabilnych i pasywnych zanieczyszczeń w strumieniu wody z uwzględnieniem źródła sorpcji. Analiza procesu sorpcji lokalnej równowagi stężeń w fazie ciekłej i stałej.
EN
Transport equations for conservative and passive contaminant in groundwater stream including adsorption source. Analysis of sorption process for local equilibrium of concentration in liquid and solid phases.
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The need to simulate the conditions of transport of the pollutants and the dissolved oxygen in the flux of sewage arises in the modelling of sewage biode´gradation process in gravitational sewer system. In the properly kept sewers, sewage flow velocity is generally uniform, which allows the model describing the pollutant transport to be simplified. The application of further simplifying assumptions, justified by the conditions inside the modelled object, allows us to get the credible results with the acceptable efforts. These simplifications can be considered, depending on the costs of data for model calibration measurement and the numerical calculation costs. The present work is focused on finding the most convenient description of transport and transformation of dissolved and suspended substances by the advection-dispersion formulas, being one-dimensional description of sewage flow. The literature review concerning various treatment of longitudinal dispersion coefficient was presented. The influence of flow conditions in the modelled system on the dispersion coefficient was also shown. Finally, the matrix description of pollutant fraction transport and biodegradation in gravitational sanitation conduit based on advection-dispersion equation, along with the example of numerical procedure, was described.
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Effective action intended to counter deterioration of ground water resources quality makes it necessary to identify the processes which have a bearing on contaminant infiltration into subterranean waters and design appropriate tools with a view to quantifying the processes in question. In view of the complexity of these issues, the most suitable method for resolving them is by mathematical modelling The present paper discusses two related mathematical models designed to model flow and transport in a three dimensional porous variably saturated medium in unsteady conditions.
PL
Efektywne przeciwdziałanie postępującemu pogarszaniu się jakości wód podziemnych wymaga rozpoznania procesów wpływających na przedostawanie się zanieczyszczeń do tych wód oraz opracowaniu narzędzi umożliwiających ich kwantyfikację. Ponieważ zagadnienia te są złożone, więc aby je rozwiązać najlepiej jest zastosować metody modelowania matematycznego. Przedstawiono dwa powiązane ze sobą modele matematyczne przeznaczone do modelowania przepływu i transportu w trój wymiarowym ośrodku porowatym o zmiennym nasycaniu, w warunkach nieustalonych.
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