Mathematical Modeling of Pesticide Adsorption In A Porous Medium; Convection-Dispersion Transport with Steady State Water Flow in Three Dimensions

Abstract

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 since it helps in assessing the effect of migrating chemical from their disposal sites on the quality of groundwater. Most studies done on the movement of pesticides in the ground environment in terms of mathematical models have so far been simulated and emphasis given to axial movement and in a few cases both axial and radial movements. Soil processes have a 3D (three dimensional) 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 ID (one dimension) and 2D (two dimension) approaches are limited since they are not capable of giving dependable regional influence of pesticides movement in the porous media and groundwater. They give only theoretical results which are devoid of the reality in the field due to lumping of parameters. In this study, 3D formula is derived so that it can enhance our capacity to analyze the realistic regional impact of adsorption of pesticides in a porous media and groundwater in the field condition since there is no lumping of parameters. In most cases we are supposed to adopt an existing equation and use it to solve the problem of research but given the many equations, it is wise to derive from the first principle in order to be sure of applicability of the equation to the research problem. The objective of this study is to develop a mathematical model which can be used to determine the combined 3D movement of pesticides with steady - state water flow in a porous media. The methodology involves determining the comprehensive dispersion equation accounting for 3D movement of solutes in the porous media and finding the solution of the governing equation using unconditionally stable finite difference 3D equation. The experimental results based on ID are applied to 3D based on the dispersion constant being the same longitudinally and laterally at low flow rate in the porous media as informed by Reynold's number being less than 2300 for laminar flows. The equation is applied on the experiment done on adsorption.of pesticide through a porous media. The results are applied to the equation and solved up to ten stepsin order to test equation's suitability.