Study of Pollutant Dispersion in Finite Layers of Semi-infinite Geological Formation

Document Type : Original Research Paper


Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad-826004, Jharkhand, India


The present study deals with groundwater pollution in multilayer aquifer. The model is based on decomposition of finite layers in semi-infinite groundwater reservoir. A constant pollutant source is injected at the input boundary of the uppermost layer (UML) of the landfill. At the intermediate inlet boundary, some average value for the longitudinal exchange of the input source concentration in each sub-layer is considered from the previous layer. Initially, the aquifer is not solute free in each sub layer that means some constant background contaminant concentration exists. In each sub layer, concentration gradient is assumed to be zero at the extreme boundary. The linear sorption and first orders decay terms are considered to model the groundwater pollution in multilayer aquifer. The Laplace transform technique is adopted to solve one-dimensional (1D) advection-dispersion equation (ADE). This approach is helpful to understand the solute migration in finite sub layers. The results are elucidated for the different time periods to examine the peak of pollutant concentration level in geological formations.


Al-Niami, A. N. S. and Rushton, K. R. (1979). Dispersion in stratified porous media, Water
Resour. Res., 15(5); 1044-1048.
Chatterjee, A. and Singh, M. K. (2018). Two-dimensional advection-dispersion equation with
depth-dependent variable source concentration. Pollut., 4(1); 1-8.
Pollution 2021, 7(2): 257-274 273
Chen, J. S. and Liu, C. W. (2012). Generalized analytical solution for advection dispersion equation in finite spatial domain with arbitrary time-dependent inlet boundary condition. Hydrol. and Earth Sys. Sci., 15(8); 2471-2479. Chen, J. S., Lai, K. H., Liu, C. W. and Ni, C. F. (2012). A novel method for analytically solving multi-species advective–dispersive transport equations sequentially coupled with first-order decay reactions. J. Hydrol., 420; 191-204.
Corey, J. C., Hawkins, R. H., Overman, R. F. and Green, R. E. (1970). Miscible displacement measurements within laboratory columns using the gamma photo neutron method. Soil Sci. Soc. Am. Proc., 34(6); 854-858.
Crank, J. (1979): The mathematics of diffusion. Oxford University Press.
Ebach, E. H. and White R. (1958). The mixing of fluids flowing through packed solids. J. Am. Inst. Chem. Engg., 4; 161-164. Freeze, R. A. and Cherry, J. A. (1979). Groundwater. Pretice-Hall. Inc., Englewood Cliffs, NJ. Gangopadhyay, S. and Gupta, A. D. (1995). Simulation of salt-water encroachment in a multilayer groundwater system, Bangkok, Thailand. Hydrogeol. J. 3(4); 74-88.
Gelhar, L.W., Welty, C. and Rehfeldt, K. R. (1992). A critical review of data on field-scale dispersion in aquifers. Water Resour. Res., 28(7); 1955-1974.
Gelher, L. W. and Collins, M. A. (1971). General analysis of longitudinal dispersion in non-uniform flow. Water Resour. Res., 7; 1511-1521.
Gershon, N. D. and Nir, A. (1969). Effects of boundary conditions of models on tracer distribution in flow through porous medium. Water Resour. Res., 5(4); 830-839. Ghamariadyan, M., Meraji, S. H. and Ghaheri, A. (2016). Solute Transport In Two Layered Porous Media (Separated Diagonally) Using Suitable DQM Scheme. Guerrero, J. P., Pimentel, L. C. G. and Skaggs, T. H. (2013). Analytical solution for the advection–dispersion transport equation in layered media. Int. J. Heat and Mass Trans., 56(1-2); 274-282. Higashi, K. and Pigford, T. H. (1980). Analytical models for migration of radionuclides in geologic sorbing media. J. Nuclear Sci. and Tech., 17(9); 700-709. Kumar, R., Chatterjee, A., Singh, M. K. and Singh, V. P. (2020). Study of Solute Dispersion with Source/Sink Impact in Semi-Infinite Porous Medium. Pollut., 6(1); 87-98. Leij, F. J. and Van Genuchten, M. T. (1995). Approximate analytical solutions for solute transport in two-layer porous media. Trans. Por. Media., 18(1); 65-85. Li, Y. C. and Cleall, P. J. (2011). Analytical solutions for advective–dispersive solute transport in double‐layered finite porous media. Int. J. Num. & Anal. Methods Geomech., 35(4); 438-460. Liu, C., Ball, W. P. and Ellis, J. H. (1998). An analytical solution to the one-dimensional solute advection-dispersion equation in multilayer porous media. Trans. Por. media, 30(1); 25-43. Manger, G. E. (1963). Porosity and bulk density of sedimentary rocks.
Ogata, A. (1970). Theory of dispersion in a granular medium. US Government Printing Office, Washington. Rowe, R. K. and Booker, J. R. (1985). 1-D pollutant migration in soils of finite depth. J. Geotech. Eng., 111(4); 479-499.
Saied, E. A. and Khalifa, M. E. (2002). Analytical solutions for groundwater flow and transport equation. Transp. Por. Medi., 47; 295-308.
Sim Y. and Chrysikopoulos C. V. (1999). Analytic solution for solute transport in saturated porous media with semi-infinite or finite thickness. Adv. Water Res., 22(5); 507-519. Singh, M. K. and Das, P. (2015). Scale dependent solute dispersion with linear isotherm in heterogeneous medium. J. Hydrol., 520; 289-299.
Singh, M. K. and Kumari, P. (2014). Contaminant concentration prediction along unsteady groundwater flow. In: Basu S., Kumar N. (eds.) Modelling and Simulation of Diffusive Processes. Simulation Foundations, Methods and Applications. Springer Cham, pp. 257-275.
274 Singh & Rajput
Singh, M. K., Ahamad, S. and Singh, V. P. (2014). One-dimensional uniform and time varying solute dispersion along transient groundwater flow in a semi-infinite aquifer. Acta Geophy., 62(4); 872–892. Singh, M. K., Singh, R. K. and Pasupuleti, S. (2020). Study of forward–backward solute dispersion profiles in a semi-infinite groundwater system. Hydrologic. Sci. J., 65(8); 1416-1429.
Singh, M. K., Mahato, N. K. and Kumar, N. (2015). Pollutant’s horizontal dispersion along and against sinusoidally varying velocity from a pulse type point source. Acta Geophysica, 63(1); pp.214-231.
Smedt, F. D. (2006). Analytical solution for transport of decaying solutes in rivers with transient storage. J. Hydrol., 330(3-4); 672–680.
Srinivasan, V. and Clement, T. P. (2008). An analytical solution for sequentially coupled one-dimensional reactive transport problems. Part-I: Mathematical derivations: Water Resour. Res., 31; 203. Székely, F. (1987). Coupled flow and advective transport simulation in multilayer leaky aquifer systems. In Proceedings of International Symposium on Groundwater Monitoring and Management, (pp. 23-28). van Genuchten, M. T. (1985). Convective-dispersive transport of solutes involved in sequential first-order decay reactions. Comp. & Geosci., 11(2); 129-147. Vilhena, M. T., Rizza, U., Degrazia, G. A., Mangia, C., Moreira, D. M. and Tirabassi, T. (1998). An analytical air pollution model: development and evaluation. Contr. Atmos. Phys., 71(3); 315-320. Yoshida, M., Ibrahim, A. N., Tarhouni, J. and Ghrabi, A. (2002). Groundwater pollution and subsurface sediment contamination in closed MSW landfill, Henchir El Yahoudia. INRST-JICA Report Solid Waste Landfill and Soil/Sediment Contamination: Case Studies in Tunisia, 30-43.