भौतिक गणित

Mathematical Modelling to Determine the Velocity of the Contaminant in a Flow through a Porous Medium

Abstract

Sheila Kiprotich

The transport of contaminants emanating from localized sources such as factories and agricultural farms in porous media, is of hydro dispersion phenomena, and has been the major subject for more than four decades. Because of industrial and agricultural activities, inorganic wastes mainly non-biodegradable substances from oil spills, human wastes, fertilizers among others, percolates through porous media and eventually find their way to water bodies and food crops in the farms. Some of these substances are harmful to human health and gets to our bodies through the water we drink or the food we eat. This research study aims to formulate a particle tracking mathematical model of contaminant flow through a porous media. The governing equation of three-dimensional concentration distribution in fluid flow through porous media has been formulated using advection-dispersion equation. This equation has been solved analytically and numerically using three-dimensional finite difference algorithm. Simulation to validate solutions is done using data from agricultural chemicals as the source point. Results confirm that the concentration of one time source of contaminant decreases as it diffuses away from the source point with respect to distance and time. The plume evolved horizontally and vertically, with peak concentration at the source, and decays further and downwards due to degradation, reaction and sorption. Particle concentration tracking shows that concentration of 100 mg/l at a point source decreases to 0 mg/l, after a distance of 300 m. For a toxic chemical like sulphur dioxide, glyphosate, and trinidol, if released from a point near borehole or food crops less than 300 m, the contaminant can be traced to the drinking water and edible parts of the crop and accumulation in the body may be carcinogenic or cause kidney and liver infections. We recommend that for water pollution minimization, and safe food crops, the source of contaminant should be more than 300 m. Additional reaction methods can be used to decompose the contaminant before reaching unwanted places.