PARTICLE TRACKING MODEL OF CONTAMINANT IN A FLOW THROUGH A POROUS MEDIUM TO DETERMINE CONCENTRATION AND DECAY

Main Article Content

SHEILA KIPROTICH
DAVID ANGWENYI
TITUS ROTICH

Abstract

The transport of contaminants in porous media from localised sources such as factories and agricultural farms is a hydro dispersion phenomenon that has been a major topic for more than four decades. Inorganic wastes, primarily non-biodegradable substances from oil spills, human wastes, fertilisers, and other sources, percolates through porous media and eventually finds its way to water bodies and food crops on farms as a result of industrial and agricultural activities.  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 100mg/l at a point source decreases to 0mg/l, after a distance of 300m. For a toxic chemical like sulphur dioxide, glyphosate, and trinidol, if released from a point near borehole or food crops less than 300m, 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 300m. Additional reaction methods can be used to decompose the contaminant before reaching unwanted places.

Keywords:
Agricultural activities, contaminant, inorganic wastes, porous media

Article Details

How to Cite
KIPROTICH, S., ANGWENYI, D., & ROTICH, T. (2022). PARTICLE TRACKING MODEL OF CONTAMINANT IN A FLOW THROUGH A POROUS MEDIUM TO DETERMINE CONCENTRATION AND DECAY. Journal of Applied Physical Science International, 14(2), 1-17. https://doi.org/10.56557/japsi/2022/v14i27972
Section
Original Research Article

References

Zheng C, Bennett GD. Applied contaminant transport modeling: Theory and practice, Van Nostrand Reinhold: New York. 1995;440.

Jaiswal KD, Kumar A, Yadav RR. Analytical solution to the one-dimensional advection- diffusion equation with temporally dependent coefficient. Luncknow University: Llucknow, India; 2010.

Aminzadeh F, Barhen J, Glover CW, Toomanian NB. Estimation of reservoir parameters using a hybrid neural network. Journal of Science and Sulphur dioxide and agricultural inputs Engineering. 2008;24:49-56.

Kosso C, Scott A. The nature and function of water baths, bathing and hygiene from antiquity through the renaissance. Leiden and Boston Brill; 2009. ISBN 978-90-04-17357-6.

Herlander ML. Reservoir characterization with iterative direct sequential co- simulation, Integrating fluid dynamic data into stochastic model, sulphur dioxide and agricultural inputs science and engineering. ISSN 0920-4105 CODEN JPSEE. 2008;4 (16):263-274.

Anderson MP, Woessner WW. Applied groundwater modeling: simulation of flow and advective transport. Academic Press: San Diego. 2010;13-20.

Beaugendre H, Huberson S, Mortazari A. Numerical simulation of transport and diffusion in porous media using a particle sets of contour method. University Press: Bordeaux; 2015.

Bear J, Bachmat Y. Introduction to modeling phenomena of transport in porous Media. Kluwer Academic Publishers, Dordrecht: Netherlands; 1990.

Berkowitz J, Scher A. Modeling flow and contaminant transport in fractured rocks, in Flow and Contaminant Transport in Fractured Rocks, Academic Press: San Diego. 1998;1–36.

Benson DA, Meerchaert MM. Simulation of chemical reaction via particle tracking; diffusion versus thermodynamics rate limited regimes water resources w. 2008;12201.

DOI:10:1029|2008WR007111

Cosgrove WJ, Rijsberman D. World water vision: Making water Everybody’s’ Business, London: Earth Scan Publication; 2000.

Dean SO, Albert CR, Ning L. Inverse theory for sulphur dioxide and agricultural inputs. Reservoir Characterization and History Matching: Cambridge University Press; 2008.

Sudicky EA. The Laplace transforms Galerkin technique: A time continuous finite element theory and application to mass transport in groundwater, water resource; 1989.

Eckhard CS. Principles of mathematical modeling, (2nd Edition). Academic Press: New York; 2004.

Gevorkian G. Darcy's law and underground water flow. California State, Science Fair Abstract; 2004.

Huang TK. Stability analysis of an earth dam under steady state seepage. Academic Press: New York; 2004.

Kithiia SM. Water quality degradation trends in Kenya over the last decade. University of Nairobi: Kenya; 2010.

Marino MA. Distribution of contaminants in porous media flow. AN AGU Journal. 1974;10(5).

DOI:10.1029/Wr0101005P0103

Kok WW, Yew SO, Tamás DG, Chun CF. Reservoir characterization using support vector machines. The 2005 International Conference on computational Intelligence for Modeling, Control and automation, and International Conference on intelligent agents, Web Technologies and Internet commerce (CIMCA-IAWTIC’05); 2005.

Kamanbedast AB, Norbakhsh A, Aghamajidi G. Seepage analysis of Earth’s dams with using seep/w software case study: Karkhehdam: World Academy of Science, Engineering and Technology. 2010;69:1272-1277.

Anderson RN, Boulanger A, Winston J, Xu L, Mello U, Wiggins W. Sulphur dioxide and agricultural inputs reservoir simulation and characterization system and method; 2004.

Mercer JW, Cohen RM. A review of immiscible fluids in the subsurface: Properties, models, characterization, and remediation. Journal of Contaminant Hydrology. 2006, 2009;6:107-163.

Huyakom PS, Pinder GF. Computational methods in subsurface flow, Academic Press; New York; 1983.

Neuman SP. Adaptive Eulerian- Langarian finite element method for advection- dispersion. Int. J Numerical Method; 1984.

Frind EO. Three dimensional modeling of groundwater flow systems. Water Resources Research. 1987;14(15):844-858.

Amarsinh LB. Groundwater contaminant transport in 1-FDM Approach, Government college of Engineering. Karad, Maharashtra: India-415124; 2014.

Yaniv E, Jaiswal KD, Kumar A, Yadav RR. Analytical solution to the one-dimensional advection- diffusion equation with temporally dependent coefficient. Luncknow University: Llucknow, India; 2010.