Abstract
Groundwater contamination problem is modeled using advection dispersion equation with different phase velocity and dispersion. This type of flow problem can be occurred or visualized depending upon the geometry as the surface of the aquifer is made of various soil materials. We consider different velocity and dispersion for different zones. Initially, the aquifer is contamination free, and advection dispersion equation is used to model the system subject to the condition that the source is acting at origin and contaminant concentration flux is zero at the semi-infinite part of the boundary. Laplace transform technique is used to solve the system analytically, and graphs are plotted to show the effect in the aquifer with multiphase.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aral MM, Liao B (1996) Analytical solutions for two-dimensional transport equation with time-dependent dispersion coefficients. J Hydrol Eng 1:20–32
Arbogast T, Wheeler MF, Zhang NY (1996) A nonlinear mixed finite element method for a degenerate parabolic equation arising in flow in porous media. SIAM J Numer Anal 33:1669–1687
Batu V (1996) A generalized three dimensional analytic solute transport model for multiple rectangular first type sources. J Hydrol 174(1–2):57–82
Diwa EB, Lehmann F, Ackerer Ph (2001) One dimensional simulation of solute transfer in saturated-unsaturated porous media using the discontinuous finite element method. J Contam Hydrol 51(3–4):197–213
Huyakorn PS, Panday S, Wu YS (1994) A three-dimensional multiphase flow model for assesing NAPL contamination in porous and fractured media, 1. Formulation. J Contam Hydrol 16(2):109–130
Kaluarachchi JJ, Parker JC (1989) An efficient finite element method for modeling multiphase flow. Water Resour Res 25(1):43–54
Khoei AR, Mohammadnejad T (2011) Numerical modeling of multiphase fluid flow in deforming porous media: a comparison between two- and three-phase models for seismic analysis of earth and rockfill dams. Comput Geotech 38:142–166
Klubertanz G, Bouchelaghem F, Laloui L, Vulliet L (2003) Miscible and immiscible multiphase flow in deformable porous media. Math Comput Model 37:571–582
Lewis RW, Ghafouri HR (1997) A novel finite element double porosity model for multiphase flow through deformable fractured porous media. Int J Numer Anal Methods Geomech 21:789–816
Lewis RW, Pao WKS (2002) Numerical simulation of three-phase flow in deforming fractured reservoirs. Oil Gas Sci Technol 57:499–514
Logan JD (1996) Solute transport in porous media with scale-dependent dispersion and periodic boundary conditions. J Hydrol 184(3–4):261–276
Moreira DM, Vilhena MT, Tirabassi T, Buske D, Cotta RM (2005) Near-source atmospheric pollutant dispersion using the new GILTT method. Atmos Environ 39:6289–6294
Ngien SK, Rahman NA, Lewis RW, Ahmad K (2011) Numerical modeling of multiphase immiscible flow in double-porosity featured groundwater systems. Int J Numer Anal Methods Geomech
Oliaei MN, Soga K, Pak A (2009) Some numerical issues using element-free Galerkin meshless method for coupled hydro-mechanical problems. Int J Numer Anal Methods Geomech 33:915–938
Rahman NA, Lewis RW (1999) Finite element modeling of multiphase immiscible flow in deforming porous media for subsurface systems. Comput Geotech 24:41–63
Rubin H, Atkinson J (2001) Environmental Fluid Mechanics. Mar-353 cel Dekker New York
Sander GC, Braddock RD (2005) Analytical solutions to the transient, unsaturated transport of water and contaminants through horizontal porous media. Adv Water Resour 28:1102–1111
Singh MK, Kumari P (2014) Contaminant concentration prediction along unsteady groundwater flow, modeling and simulation of diffusive processes. Series: Simulation Foundations, Methods and Applications, Springer, pp. 257–276
Singh MK, Ahamad S, Singh VP (2014) One-dimensional uniform and time varying solute dispersion along transient groundwater flow in a semi-infinite aquifer. Acta Geophys 62(4):872–892. doi:10.2478/s11600-014-0208-7
Wortmann S, Vilhena MT, Moreira DM, Buske D (2005) A new analytical approach to simulate the pollutant dispersion in the PBL. Atmos Environ 39:2171–2178
Yates SR (1992) An analytical solution for one-dimensional transport in porous media with an exponential dispersion function. Water Resour Res 28:49–54
Younes A (2003) On modeling the multidimensional coupled fluid flow and heat or mass transport in porous media. Inter J Heat Mass Transfer 46(2):367–379
Zamani K, Bombardelli FA (2013) Analytical solutions of nonlinear and variable-parameter transport equations for verification of numerical solvers. Fluid Mech, Environ. doi:10.1007/s10652-013-9325-0
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Singh, M.K., Chatterjee, A., Kumari, P. (2018). Mathematical Modeling of One-Dimensional Advection Dispersion Equation in Groundwater Contamination Using Different Velocity and Dispersion for Different Zones. In: Singh, M., Kushvah, B., Seth, G., Prakash, J. (eds) Applications of Fluid Dynamics . Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-10-5329-0_44
Download citation
DOI: https://doi.org/10.1007/978-981-10-5329-0_44
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-5328-3
Online ISBN: 978-981-10-5329-0
eBook Packages: EngineeringEngineering (R0)