Two-Dimensional Solute Transport with Exponential Initial Concentration Distribution and Varying Flow Velocity

Document Type : Original Research Paper


1 Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad-826004, Jharkhand, India

2 Ecohydrology, Soil Physics and Land Management, Wageningen University, P.O. Box 47, 6700 AA Wageningen, The Netherlands School of Chemistry, Monash University, Melbourne, 3800 VIC, Australia


The transport mechanism of contaminated groundwater has been a problematic issue for many decades, mainly due to the bad impact of the contaminants on the quality of the groundwater system. In this paper, the exact solution of two-dimensional advection-dispersion equation (ADE) is derived for a semi-infinite porous media with spatially dependent initial and uniform/flux boundary conditions. The flow velocity is considered temporally dependent in homogeneous media however, both spatially and temporally dependent is considered in heterogeneous porous media. First-order degradation term is taken into account to obtain a solution using Laplace Transformation Technique (LTT) for both the medium. The solute concentration distribution and breakthrough are depicted graphically. The effect of different transport parameters is studied through proposed analytical investigation. Advection-dispersion theory of contaminant mass transport in porous media is employed. Numerical solution is also obtained using Crank Nicholson method and compared with analytical result. Furthermore, accuracy of the result is discussed with root mean square error (RMSE) for both the medium. This study has developed a transport and prediction 2-D model that allows the early remediation and removal of possible pollutant in both the porous structures. The result may also be used as a preliminary predictive tool for groundwater resource and management.


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Pollution, 5(4): 721-737, Autumn 2019
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