The Non-Fickan Effects of the Advective Diffusion on the Contaminants Transport in Porous Medium

Abstract

The transport equation of contaminants in a porous medium is usually described by parabolic convection diffusion differential equations. The implicit infinite velocity of propagation is apparently contrary to the reality of mass transport. In this paper, based on the modified Fick's law of non-equilibrium transmission, a hyperbolic convection diffusion differential equation is established, and the analytical solution of the concentration distribution of the pollutant transport in the half space is given. Numerical results show that the concentration distribution of contaminants from hyperbolic convective diffusion equation is limited in finite time, and the contaminant transport speed is limited. When the convection velocity is lower than the diffusion velocity, the concentration is reduced from the surface to the interior; while the convection velocity is greater than the diffusion velocity, the concentration distribution increases to the interior.