Abstract
This work dealt with advection–dispersion problem in heterogeneous medium while the medium is initially considered to be polluted as a functional combination of source term and zero-order production term with distance. Further, Dirichlet-type boundary condition is employed to get insight to the realistic situation for achieving practical solution to the problem. Duhamel’s integration technique has been applied to solve the system. Non-dimensional numbers responsible for the domination of advection and dispersion in the transport of solute have been explored through appropriate graphs. Variability of velocity field and dispersion of the solute due to heterogeneity of the medium has also been taken into consideration while solving the system. The comparison has been made between the different outcomes significantly using graphical approach.
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References
Al-Niami ANS, Rushton KR (1977) Analysis of flow against dispersion in porous media. J Hydrol 33:87–97
Barry DA, Sposito G (1989) Analytical solution of a convection—dispersion model with time dependent transport coefficients. Water Resour Res 25(12):2407–2416
Batu V, van Genuchten MT (1993) A comprehensive set of analytics solutions for non-equilibrium solute transport with first-order decay and zero-order production. Water Resour Res 29:2167–2182
Fry VA, Istok JD, Guenther RB (1993) Analytical solutions to the solute transport equation with rate-limited desorption and decay. Water Resour Res 29(9):3201–3208
Guerrero JSP, Skaggs TH (2010) Analytical solution for one-dimensional advection-dispersion transport equation with space-dependent coefficients. J Hydrol 390:57–65
Harleman DRF, Rumer RR (1963) Longitudinal and lateral dispersion in an isotropic porous medium. J Fluid Mech 385–394
Huang K, van Genuchten MT, Zhang R (1996) Exact solutions for one dimensional transport with asymptotic scale dependent dispersion. Appl Math Model 20:297–308
Kumar N (1983) Unsteady flow against dispersion in finite porous media. J Hydrol 63:345–358
Kumar A, Jaiswal DK, Kumar N (2009) Analytical solutions of one-dimensional advection-diffusion equation with variable coefficients in a finite domain. J Earth Syst Sc 118:539–549
Leij FJ, Skaggs TH, van Genuchten MT (1991) Analytical solutions for solute transport in three-dimensional semi-infinite porous medium. Water Resour Res 27:2719–2733
Marino MA (1974) Distribution of contaminants in porous media flow. Water Resour Res 10:1013–1018
Ogata A, Banks RB (1961) A solution of the differential equation of longitudinal dispersion in porous media. United States Government Printing Office, Washington
Singh MK, Kumari P (2014) Contaminant concentration prediction along unsteady groundwater flow. Modelling and Simulation of Diffusive Processes vol XII‚ pp 257–276
Singh MK, Mahto NK, Singh P (2008) Longitudinal dispersion with time dependent source concentration in semi infinite aquifer. J Earth Syst Sci 117(6):945–949
Singh MK, Singh VP, Singh P, Shukla D (2009) Analytical solution for conservative solute transport in one dimensional homogeneous porous formations with time dependent velocity. J Eng Mech 135(9):1015–1021
Singh MK, Singh P, Singh VP (2010) Analytical solution for two dimensional solute transport in finite aquifer with time dependent source concentration. J Eng Mech 136(1):1309–1315
Fred T (1995) 1-D, 2-D, 3-D analytical solutions of unsaturated flow in groundwater. J Hydrol 170:199–214
van Genuchten MT, Parker JC (1984) Boundry conditions for displacement experiments through short laboratory soil columns. Soil Sci Soc Am J 48:703–708
Yates SR (1990) An analytical solution for one-dimensional transport in heterogeneous porous media. Water Resour Res 26:2331–2338
Yates SR (1992) An analytical solution for one-dimensional transport in porous media with an exponential dispersion function. Water Resour Res 28:2149–2154
Zoppou C, Knight JH (1997) Analytical solutions for advection and advection diffusion equation with spatially variable coefficients. J Hydraul Eng 123:144–148
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Pandey, A.K., Kumar, R., Singh, M.K. (2018). Solution to Advection–Dispersion Equation for the Heterogeneous Medium Using Duhamel’s Principle. 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_42
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DOI: https://doi.org/10.1007/978-981-10-5329-0_42
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