Scholarly record

MATHEMATICAL AND COMPUTER MODELING OF CONTAMINANT MIGRATION TO FILTER TRAP IN TWO-DIMENSIONAL NONLINEAR CASE

Anatoliy Vlasyuk

Abstract

The amelioration fund of Ukraine is 5.4 million hectares. Significant areas of these lands are used by special drainage-modular systems with vertical and horizontal drainage. Such drainage is a system of vertical or horizontal fluid drain storage, located in a parallel way. These systems can be used to inject micro- and nanoparticles of sorbent or as filter-traps for already used sorbent particles. Therefore, a fundamental understanding of the processes of mass transfer in a saturated porous medium in the presence of a filter-trap requires a detailed study of the new mathematical models. In this work, an appropriate mathematical model for the migration of contaminants in a saturated catalytic porous medium in a two-dimensional case is presented. Under the influence of the gradient pressure, there is a transfer of substances dissolved in water by a filtration flow. The filtration of the saline solution is carried out in accordance with the generalized Darcy law. Due to the transfer of substances at a certain speed under the influence of convective diffusion in a catalytic environment in the presence of trap filters the localization of the contaminant happens. Sorption nanoparticles that influence to the dynamics of the filtration process represents the catalytic medium. Finite-difference analogs of differential equations of a corresponding two-dimensional nonlinear boundary value problem are constructed and its numerical solution is obtained by finite difference method. A software package with the use of Orleans parallel calculations has been developed for performing numerical experiments. The interface of the software package is presented as a web application and end-user may use an only web browser for numerical experiments because all calculations are carried out in the Azure cloud service. The web application interface allows to manage the source data (diffusion coefficients, porosity, dispersion, boundary conditions, adsorption isotherms, etc.) that determine the hydrogeological conditions and possible effects of man-made factors; perform the necessary calculations, build comparative 2D/3D graphs and tables of values of concentrations, heads, filtration rates and diffusion coefficients. The influence of the catalytic medium on the process of soil layer refinement was established and various scenarios of vertical migration of contaminants were modeled due to the computer simulation and conducted numerical experiments. These results can be used to predict the refinement of soils from contaminant and predict their possible future use.

Publication Impact Profile

• Citations
• CrossRef - Citation Indexes: 5
• Scopus - Citation Indexes: 8

• Captures
• Mendeley - Readers: 5

PLUMX see details

DOI resolver: doi.org/10.5593/sgem2018/2.2/s08.037

Publication details

Back to publication list