Mathematical modeling and theoretical analysis of pollutant transport in porous media: A review of current approaches

The transport of pollutants in soil is one of the main environmental issues and therefore a good understanding of the ways through which the contaminants can reach the soil is a must. After several dialogues, analyses and mathematical presentations, the paper deals with the various issues that control the movement and fixation of the contaminants in the soils. Initially we present the theoretical underpinning of the following study exposing both the regulation of the groundwater resources and the physical processes of advection, dispersion, and sorption. Moreover, combining Darcy's law with the principle of mass conservation, leads us to the system of fundamental equations that we are investigating here. We focus on how to describe the heterogeneity of the soil mathematically. After assessing several models which are in use, we identify the limitations of the traditional analytical methods if they are deployed to tackle intricate pollution situations. This paper theoretically supports the author's PhD. work, which created numerical methods that can deal with the scientific problems of the real world and amended the main concepts that the next powerful simulations can be based on.