MATHEMATICAL MODELING TO SIMULATE THE MOVEMENT OF CONTAMINANTS IN GROUNDWATER

Kamel Al-Khaled; Mohamed Ali Hajji

doi:10.11948/2016013

2016 Volume 6 Issue 1

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Kamel Al-Khaled, Mohamed Ali Hajji. MATHEMATICAL MODELING TO SIMULATE THE MOVEMENT OF CONTAMINANTS IN GROUNDWATER[J]. Journal of Applied Analysis & Computation, 2016, 6(1): 156-170. doi: 10.11948/2016013

Citation:

Kamel Al-Khaled, Mohamed Ali Hajji. MATHEMATICAL MODELING TO SIMULATE THE MOVEMENT OF CONTAMINANTS IN GROUNDWATER[J]. Journal of Applied Analysis & Computation, 2016, 6(1): 156-170. doi: 10.11948/2016013

MATHEMATICAL MODELING TO SIMULATE THE MOVEMENT OF CONTAMINANTS IN GROUNDWATER

1 Department of Mathematics & Statistics, Sultan Qaboos University, P. O. Box:36, PC 123, Al-Khod, Muscat, Oman;
2 Department of Mathematics & Statistics, Jordan University of Science & Technology, P. O. Box:3030, Irbid 22110, Jordan;
3 Department of Mathematical Sciences, United Arab Emirates University, P. O. Box:17551, Al-Ain, UAE

Abstract

Abstract

The objectives of this paper are twofold. Firstly, we formulate a system of partial differential equations that models the contamination of groundwater due to migration of dissolved contaminants through unsaturated to saturated zone. A closed form solution using the singular perturbation techniques for the flow and solute transport equations in the unsaturated zone is obtained. Indeed, the solution can be used as a tool to verify the accuracy of numerical models of water flow and solute transport. The second part of this paper, deals with how the water level in a water reserve drops due to pumping water out of a well that is some distance away.
- Approximate solutions /
- singular perturbation method /
- solute transport /
- Talbot's algorithm /
- Bromwich contour /
- Laplace transform /
- Inverse Laplace transform
MSC: 26A33;35F25;35C10

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References

[1]	F. Allan and Emad Elnajjar, The role of mathematical Modeling in understanding the groundwater pollution, Int. J. of Thermal and Enviromental Eng., 4(2012)(2), 171-176. Google Scholar
[2]	Abdon Atangana and P.D. Vermeulen, Analytical solutions of a space-time fractional serivative of groundwater flow equation, Abstract and Applied Analysis, 2014, ID 381753, 11. Google Scholar
[3]	Kamel Al-Khaled and Fathi Allan, Construction of Solutions for the shallow water equations by the decomposition method,Mathematics and Computers in Simulation, 66(2004), 479-486. Google Scholar
[4]	Marwan Alquran, Mohammed Ali and Kamel Al-Khaled, Solitary wave solutions to shallow water waves arising in fluid dynamics, Nonlinear Studies, 19(2012)(4), 555-562. Google Scholar
[5]	J. Bear, Dynamics of Fluids in Porous Media, New York, 1972. Google Scholar
[6]	W.H.J. Beltman, J.I.T.I. Boesten, S.E.A.T.M. Vander Zee and J.J. Quist, Analytical modeling of effects of application frequency on pesticide concentrations in wells, Ground Resource Research, 34(1996)(3), 470-479. Google Scholar
[7]	A.E. Brookfield, D.W. Blowes and K.U. Mayer, Integration of field measurements and reactive transport modelling to evaluate contaminant transport at a sulfide mine tailings impoundment, Journal of Contaminant Hydrology, 88(2006)(1-2), 1-22. Google Scholar
[8]	J.R. Craig and Alan J. Rabideau, Finite difference modeling of contaminant transport using analytic element flow solutions, Advances in Water Resources, 29(2006)(7), 1075-1087. Google Scholar
[9]	F.M. Delay, A numerical method for solving the water flow equation in unsaturated porous media, Ground Water, 34(1996)(4), 666-674. Google Scholar
[10]	Dean and G. Duffy, Transform Methods for Solving Partial Differential Equations, CRC Pres Inc., 1984. Google Scholar
[11]	G.De Marsily, Quantitative Hydrogeology-Groundwater Hydrology for Engineers, Academic Press, Orlando, FL., 1986. Google Scholar
[12]	G.H. de Rooij, Is the groundwater reservoir linear? A mathematical analysis of two limiting cases Hydrol, Earth Syst. Sci. Discuss., 11(2014), 83-108, Google Scholar
[13]	Suresh Kumar, G., Mathematical Modeling of Groundwater Flow and Solute Transport in Saturated Fractured Rock Using a Dual-Porosity Approach, J. Hydrol. Eng., 19(2014)(12), 04014033. Google Scholar
[14]	Shreekant P. Pathak and Twinkle Singh, An Analysis on Groundwater Recharge by Mathematical Model in Inclined Porous Media, International Scholarly Research Notices 2014(2014), ID 189369, 4. Google Scholar
[15]	A.Talbot, The accurate numerical inversion of Laplace transforms, J. Inst. Math. Applic., 23(1970), 97-120. Google Scholar
[16]	Rajen K. Sinha and Jrgen Geiser, Error estimates for finite volume element methods for convection diffusion reaction equations, Applied Numerical Mathematics, 57(2007)(1), 59-72. Google Scholar
[17]	L.D. Connell, Simple models for subsurface solute transport that combine unsaturated and saturated zone pathways, Journal of Hydrology, 332(2007)(3-4), 361-373. Google Scholar
[18]	Cheng-Hung Huang, Jia-Xun Li and Sin Kim, An Inverse Problem in Estimating the Strength of Contaminant Source for Groundwater Systems, Applied Mathematical Modelling, 32(2008)(4), 417-431. Google Scholar
[19]	Fritz Stauffer, Peter Bayer, Philipp Blum, Nelson Molina and G. Kinzelbach, Thermal Use of Shallow Groundwater, CRC Press, Dec. 2013. Google Scholar
[20]	Hai-long YIN, Zu-xin XU, Huai-zheng LI and Song LI, Numerical modeling of wastewater transport and degradation in soil aquifer, Journal of Hydrodynamics, 18(2006)(5), 597-605. Google Scholar
[21]	Hydro-geological Services International (HSI),Hydro-geology of the Disi Sandstone Aquifer, United Nations Development Program, New York, 1990. Google Scholar
[22]	L. Vrankar, G. Turk and F. Runovc, Combining the radial basis function eulerian and Lagrangian schemes with geostatistics for modeling of radionuclide migration through the geosphere, Computers & Mathematics with Applications, 48(2004)(10-11), 1517-1529. Google Scholar
[23]	M. Vurro and L. Castellano, Numerical treatments of the interface discontinuity in solid-water mass transfer problems, Computers & Mathematics with Applications, 45(2003)(4-5), 785-788. Google Scholar
[24]	Gordon H. Huang, Guangming Zeng, Imran Maqsood and Yuefei Huang Jianbing, Li An integrated fuzzy-stochastic modeling approach for risk assessment of groundwater contamination, Journal of Environmental Management, 82(2007)(2), 173-188. Google Scholar