Mathematical Solution for Dispersion of Pollutants in Porous Media

The groundwater is also an important source in the agriculture and industrial sector. In many parts of the world, groundwater resources are under increasing threat from growing demands, wasteful use and contamination. A good planning and management practices are needed to face this challenge. A key to the management of groundwater is the ability to model the movement of fluids and contaminants in the subsurface environment. It is obvious that the contaminant source activities cannot be completely eliminated and perhaps our water bodies will continue to serve as receptors of vast quantities of waste. Water resource remediation has become a serious environmental concern, since it has a direct impact on many aspects of people’s lives. For decades, the pump-and-treat method has been considered the predominant treatment process for the remediation of contaminated groundwater with organic and inorganic contaminants. On the other side, this technique missed sustainability and the new concept of using renewable energy. Permeable reactive barriers (PRBs) have been implemented as an alternative to conventional pump-and-treat systems for remediating polluted groundwater because of their effectiveness and ease of implementation. In this paper, a review of the importance of groundwater, contamination and biological, physical as well as chemical remediation techniques have been discussed. In this review, the principles of the permeable reactive barrier’s use as a remediation technique have been introduced along with commonly used reactive materials and the recent applications of the permeable reactive barrier in the remediation of different contaminants, such as heavy metals, chlorinated solvents and pesticides. The solution is obtained for the given mathematical model in a finite length initially solute free domain. The input condition is considered continuous of uniform and of increasing nature both. The solution has been obtained using Laplace transform, moving coordinates and Duhamel’s theorem is used to get the solution in terms of complementary error function.