ЗАДАЧІ ДРОБОВО-ДИФЕРЕНЦІЙНОЇ ДИНАМІКИ КОНВЕКТИВНОГО МАСОПЕРЕНОСУ ТА МАСООБМІНУ ПРИ ДВОВИМІРНІЙ ГЕОФІЛЬТРАЦІЇ
The development of scientific methods for studying the processes of pollution and salinization of groundwater is of particular relevance regarding the problems of water resources protection. Problems such as studies of groundwater salt regime in irrigated areas, analyses of groundwater pollution con...
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| Date: | 2020 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine
2020
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| Subjects: | |
| Online Access: | https://jais.net.ua/index.php/files/article/view/480 |
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| Journal Title: | Problems of Control and Informatics |
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Problems of Control and Informatics| Summary: | The development of scientific methods for studying the processes of pollution and salinization of groundwater is of particular relevance regarding the problems of water resources protection. Problems such as studies of groundwater salt regime in irrigated areas, analyses of groundwater pollution conditions in water intake areas, problems of underground disposal of industrial and domestic wastewater, etc., require effective consideration of the phenomena of physicochemical interaction between a liquid and a porous medium. Taking into account the presence of interphase mass exchange is a necessary element of a study, since the nature of interphase interaction significantly influences the change in the concentration of soluble substances in the underground filtration flow. In cases when the migration of water-soluble substances is carried out mainly due to convection, the mathematical model of the migration process is formed by the differential equations of convective mass transfer supplemented with the equation of mass exchange kinetics and the geofiltration equation. In this paper closed solutions are obtained for some boundary-value problems of the dynamics of anomalous convective mass transfer and mass exchange of soluble substances during twodimensional steady-state filtration of groundwater posed within the framework of non-local in time fractional-differential mathematical models. In particular, we consider the problems: of fractional-differential dynamics of the process of convective mass transfer under the conditions of mass exchange in accordance with the generalized equation of non-equilibrium reversible adsorption and desorption as well as under the conditions of mass exchange in accordance with the generalized equation of kinetics of ion-exchange sorption; fractional-differential dynamics of convective mass transfer in the case of nonlinear mass exchange kinetics in the presence of dissolution and precipitation of soluble substances. Also, a simplified mathematical model for studying anomalous dynamics of convective mass transfer during the washing of saline soils under the conditions of mass exchange is proposed in the paper and within the framework of this model a closed solution to the simplest washing problem is obtained. |
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