Three Dimensional Mathematical Models for ConvectiveDispersive Flow of Pesticides in Porous Media

Abstract

The transport of solutes through porous media where chemicals undergo adsorption or change process on the surface of the porous materials has been a subject of research over years. Usage of pesticides has resulted in production of diverse quantity and quality for the market and disposal of excess material has also become an acute problem. The concept of adsorption is essential in determining the movement pattern of pesticides in soil in order to assess the effect of migrating chemical, from their disposal sites, on the quality of ground water. Most studies made of movement of pesticides in the ground environment, the mathematical models so far developed emphasis axial movement and in a few cases both axial and radial movements. Soil processes have a 3D character; modeling therefore in principle, should employ three dimensions. It should also be noted that the appropriate number of dimensions is closely related to the required accuracy of the research question. The 1D and 2D approaches are limited since they are not capable of giving dependable regional influence of pesticides movement in the porous media and ground water. They give us only theoretical results which are devoid of the reality in the field due to lumping of parameters. In this publication, three dimensional formulas are developed so that it can enhance our capacity to analyze the realistic regional impact of adsorption of pesticides in a porous media and the ground water in the field condition. The methodology will involve determining the comprehensive dispersion equation accounting for 3D movement of solutes in the porous media and finding the solution of the governing equation using Alternate Direction Implicit method (ADI) which is unconditionally stable for 3D equations of Douglas and Gunn approach