Mathematical Modeling of Filtration and Geomigration Under Conditions of Anthropogenic Load

O. A. Bubnova; V. A. Miroshnyk; R. V. Markul; P. B. Mashykhina; L. H. Tatarko

doi:10.15802/stp2025/330858

Authors

O. A. Bubnova M. S. Poliakov Institute of Geotechnical Mechanics of the National Academy of Sciences of Ukraine, Ukraine https://orcid.org/0000-0001-6064-5204
V. A. Miroshnyk Ukrainian State University of Science and Technologies, SEI DIIT, Ukraine https://orcid.org/0000-0002-8115-0128
R. V. Markul Ukrainian State University of Science and Technologies, SEI DIIT, Ukraine https://orcid.org/0000-0002-7630-8963
P. B. Mashykhina Ukrainian State University of Science and Technologies, SEI DIIT, Ukraine https://orcid.org/0000-0003-3057-9204
L. H. Tatarko Ukrainian State University of Science and Technologies, SEI USUCT, Ukraine https://orcid.org/0000-0002-2080-6090

DOI:

https://doi.org/10.15802/stp2025/330858

Keywords:

mass transfer equation, filtration equation, mathematical model, groundwater pollution, pollution of the aeration zone, solid waste landfill

Abstract

Purpose. The aim of this study is to develop mathematical models for predicting the processes of contamination of the aeration zone and groundwater in the event of leachate leakage from a solid waste landfill. The mathematical models take into account typical hydrological parameters: porosity of the aeration zone, aquifer, filtration coefficient of the aeration zone, filtration coefficient of the underground aquifer, intensity of leachate infiltration into the aeration zone and underground aquifer. Methodology. A one-dimensional filtration equation and a one-dimensional mass transfer equation were used to model the process of infiltrate migration in the aeration zone. The modeling of the process of contamination of the underground aquifer, which receives infiltrate from the landfill, was carried out on the basis of a two-dimensional equation (planned model) of geomigration. For the numerical integration of the model equations, a variable-triangular finite-difference splitting scheme was used. The numerical integration of the two-dimensional geomigration equation is performed using the splitting scheme. The peculiarity of the proposed numerical models is that the value of the unknown function can be determined by an explicit formula. Findings. Numerical models have been developed to solve the complex problem of predicting the contamination of the aeration zone and underground flow in the case of infiltration of an impurity from a solid waste landfill. Originality. Numerical models of filtration and mass transfer of impurities in the case of migration of infiltrate from a municipal solid waste landfill through the aeration zone and into groundwater are proposed. To apply these mathematical models, standard hydrological information is required. The models are aimed at solving complex problems in the field of environmental safety and protection. They make it possible to determine the negative impact of landfills on the environment at the stage of justifying the location of future landfills and their size. Practical value. The proposed mathematical models use standard hydrological information, which is important for serial calculations in design organizations, and can be useful for assessing the impact of landfills on environmental pollution.

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