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<p>The present study is focused on the development of the analytical solution of a one-dimensional advection-dispersion equation (ADE) by using Laplace transform in a semi-infinite multilayer heterogeneous porous medium. Seepage velocity, hydrodynamics dispersion, and retardation factor are considered to decrease exponentially with space. The model is developed with the basic principle of general dispersion theory, where the dispersion parameter is considered to be directly proportional to the flow velocity. The solution is formulated under the assumption that the aquifer is free of pollutants initially. At the input location of the initial boundary of the uppermost layer (UML), a point source is considered, while the concentration at the intermediate inlet layer is directly obtained from the outlet concentration of the preceding layer. The zero gradient condition describes the outlet boundary. The semi-infinite aquifer is divided into discrete sub-layers in a like manner. To demonstrate the validity of the model, the developed analytical solutions are additionally verified by corresponding numerical solutions. Also, the impact of spatially dependent parameters on pollutant migration are graphically depicted. Such a study will be advantageous for the groundwater hydrologist to predict and analyze the flow and transport behavior of the groundwater in various multilayer aquifer systems.</p>

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Analytical study of multi-layer one-dimensional spatially dependent solute transport modeling

  • 期刊论文

  • 发表日期：

    2025年11月5日

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  • Pallawi Bharti,
  • Manish Kumar,
  • Mritunjay Kumar Singh,
  • Manish Chaudhary

摘要

The present study is focused on the development of the analytical solution of a one-dimensional advection-dispersion equation (ADE) by using Laplace transform in a semi-infinite multilayer heterogeneous porous medium. Seepage velocity, hydrodynamics dispersion, and retardation factor are considered to decrease exponentially with space. The model is developed with the basic principle of general dispersion theory, where the dispersion parameter is considered to be directly proportional to the flow velocity. The solution is formulated under the assumption that the aquifer is free of pollutants initially. At the input location of the initial boundary of the uppermost layer (UML), a point source is considered, while the concentration at the intermediate inlet layer is directly obtained from the outlet concentration of the preceding layer. The zero gradient condition describes the outlet boundary. The semi-infinite aquifer is divided into discrete sub-layers in a like manner. To demonstrate the validity of the model, the developed analytical solutions are additionally verified by corresponding numerical solutions. Also, the impact of spatially dependent parameters on pollutant migration are graphically depicted. Such a study will be advantageous for the groundwater hydrologist to predict and analyze the flow and transport behavior of the groundwater in various multilayer aquifer systems.