Solute Transport in a Semi-Infinite Porous Media with Input through a Curved Line Source
Abstract: Analytical solutions of two-dimensional advection-dispersion equation (ADE) with variable dispersion coefficient and velocity are obtained using Laplace Transformation Technique. This paper describes the solute transport phenomena with non-point source of conservative solute in two-dimensional heterogeneous semi-infinite porous media. A rectangular form of hyperbolic curve is considered as non-point source. Since in real life situations sources may not always be point or straight line sources, analytical solution of present study can be taken as a step toward irregular sources. Groundwater velocity is considered spatially and temporally dependent. It depends linearly to space variable. Curved shape input source injects constant input and medium is assumed uniformly polluted initially. The dispersion is considered linearly and squarely proportional to the velocity in temporal and spatial measurement respectively. New independent variables are introduced through separate transformations to advection-dispersion equation into constant coefficient. The obtained solution has also been developed for curved surface input source in a two-dimensional flow. The derived results are illustrated graphically demonstrating interesting features of the transport phenomena. Retardation factor that occurs in the porous medium due to adsorption is also taken into account.
Keywords: Advection; Dispersion; Retardation Factor; Laplace Transformation Technique; Porous medium.
How to cite this article:
R. R. Yadav and Joy Roy, Solute Transport in a Semi-Infinite Porous Media with Input through a Curved Line Source, International Journal of Advances in Mathematics, Volume 2019, Number 4, Pages 35-52, 2019.