Analysis of two-dimensional solute transport through heterogeneous porous medium

Abstract

In this study, an analytical solution is developed for solute transport through heterogeneous porous medium in two-dimensional horizontal Cartesian plane. In the present problem, the domain is considered semi-infinite extent and of heterogeneous nature along the both perpendicular directions of the plane. In surface water body, the aquifer of shallow depths and lateral component of velocity also considered. Due to heterogeneity of the medium, the velocity components of the flow transporting the solute through the medium along both the directions are considered spatially dependent. The velocity along each direction is supposed to increase linearly while passing through a finite region (into which the solute concentration values are evaluated) starting from the origin, by using interpolating formula. Solute dispersion along both the directions is considered proportional to square of the respective velocity component. The present problem is derived for two cases: first one is uniform pulse type input point source and other one is for varying pulse type input point source. The first input condition is considered initially and second is the far end of the domain. It is considered flux type of homogeneous nature. In the both cases, domain is considered initially not solute free. In the process of analytical solutions, a new space or positional variable is introduced. After that, introducing the Laplace transform to get the analytical solutions of our problems. In both the cases, effects of heterogeneity/inhomogeneity of the medium and solute/solute transport behavior have discussed in the presence and absence of the source. All the possible solute/solute transport behaviors are shown graphically interpreted through MatLab 7.0.