Effect of Linear Drift on Radial Transport of Tracer in Homogeneous Porous Media

Abstract

Analytical models can be valuable tools to investigate solute transport in porous media. The application of analytical solutions is limited by the perception that they are too cumbersome to derive while their implementation rests on assumptions that are too restrictive. This research is aimed at understanding the effect of linear drift on radial transport of tracer in porous media. It provides an analytical Solution that expresses the Concentration Distribution around the source of tracer injection as a function of Location in two dimensional Cartesian Coordinates and Time. Linear Drift is considered as a scalar velocity field in the positive horizontal axis direction and the concentration distribution is described using a derived Advection Dispersion Equation (ADE). The derived ADE is a time dependent homogeneous PDE that assumes incompressible flow and consists of dispersion and advection components as well as a first order decay term. The concentration distribution is described for an injection well located at the origin in an infinite plane (one that stretches to infinity along both spatial axis in positive and negative directions) and a positive semi finite time domain.