Mathematical modelling of salt concentration variations under the influence of groundwater dynamics in a two-layer medium
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Abstract
This study presents a comprehensive analysis of the variation of salt concentration in groundwater within a two-layer geological medium, taking into account both unconfined and confined aquifers. The investigation considers the influence of several significant hydrogeological factors affecting salt migration, including atmospheric precipitation, evaporation processes, infiltration flows, groundwater extraction intensity, interlayer permeability characteristics, filtration coefficients, effective porosity, and aquifer thickness. Under the influence of these factors, convective and diffusive transport mechanisms arise within the groundwater system, leading to the spatial redistribution of dissolved salts and the formation of concentration gradients. In the present research, the dynamics of salt concentration are described mathematically based on the fundamental principles of mass transport in porous media. The proposed model incorporates the processes of mass exchange between the unconfined and confined aquifer layers, as well as solute transport driven by concentration gradients. Such an approach enables a realistic representation of salt migration processes occurring in groundwater systems under natural hydrogeological conditions. The governing processes are formulated in the form of a system of nonlinear differential equations. Due to the complexity of the boundary conditions, obtaining an analytical solution is difficult; therefore, high-accuracy numerical approximation methods are employed to obtain reliable computational solutions for the problem.
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