Two-Dimensional Heavy Metal Migration in Soil with Adsorption and Instantaneous Injection
DOI:
https://doi.org/10.11113/mjfas.v19n6.3090Keywords:
Advection diffusion equation, Instantaneous injection, Laplace transform, Two-dimensional, Heavy metalAbstract
This paper studies a two-dimensional transport model to investigate the behavior of heavy metal migration in porous media, specifically considering their transport in soil. The model takes into consideration the combination of adsorption term as well as instantaneous injection at the boundary. Also, the model accounts for both longitudinal and transverse movements, providing a comprehensive understanding of heavy metal transport phenomena. In order to obtain the analytical solution Laplace transform has been implemented. It is found that the peak concentration of heavy metals is found to be greatly affected by the changes in the instantaneous injection value. Additionally, a correlation is observed between retardation factors and heavy metal concentrations, with a decrease in retardation factors resulting in an increase in heavy metal concentration.
References
. Arora, R. (2019). Adsorption of heavy metals–a review. Materials Today: Proceedings. 18, 4745-4750.
. Lakherwal, D. (2014). Adsorption of heavy metals: a review. International Journal of Environmental Research and Development, 4(1), 41-48.
. Sharma,S. K., Sehkon, N. S., Deswal, S., & John, S. (2009). Transport and fate of copper in soils. International Journal of Civil and Environmental Engineering, 3(3), 145-150.
. Guerrero, J. P., Pontedeiro, E. M., Van Genuchten, M. Th., Skaggs, T. H. (2013). Analytical solutions of the one-dimensional advection–dispersion solute transport equation subject to time-dependent boundary conditions. Chemical Engineering Journal, 221, 487-491.
. Kumar, A., D. K. Jaiswal, and N. Kumar. (2009). Analytical solutions of one-dimensional advection-diffusion equation with variable coefficients in a finite domain. Journal of Earth System Science, 118, 539-549.
. Kundu, S. (2019). Analytical solutions of one-dimensional space-fractional advection–diffusion equation for sediment suspension using homotopy analysis method. Journal of Engineering Mechanics, 145(7), 04019048.
. Mojtabi, A. and M. O. Deville. (2015). One-dimensional linear advection–diffusion equation: Analytical and finite element solutions. Computers & Fluids, 107, 189-195.
. Singh, M. K., A. Chatterjee, and V. P. Singh. (2017). Solution of one-dimensional time fractional advection dispersion equation by homotopy analysis method. Journal of Engineering Mechanics, 143(9), 04017103.
. Kumar, A., D.K. Jaiswal, and N. Kumar. (2010). Analytical solutions to one-dimensional advection–diffusion equation with variable coefficients in semi-infinite media. Journal of Hydrology, 380(3-4), 330-337.
. Kumar, A., D. K. Jaiswal, and N. Kumar. (2012). One-dimensional solute dispersion along unsteady flow through a heterogeneous medium, dispersion being proportional to the square of velocity. Hydrological Sciences Journal. 57(6), 1223-1230.
. Yadav, R. and L. K. Kumar. (2017). One-dimensional spatially dependent solute transport in semi-infinite porous media: an analytical solution. International Journal of Engineering, Science and Technology. 9(4), 20-27.
. Yadav, R. and J. Roy. (2018). Solute transport with periodic input point source in one-dimensional heterogeneous porous media. International Journal of Engineering, Science and Technology, 10(2), 50-63.
. Fedi, A., Massabo, M., Paladino, O., Cianci, R. (2010). A new analytical solution for the 2D advection-dispersion equation in semi-infinite and laterally bounded domain. Applied Mathematical Sciences, 4(75), 3733-3747.
. Chen, J.-S., Chen, J.-S., Liu, C.-W., Liang, C.-P., Lin, C.-W. (2011). Analytical solutions to two-dimensional advection–dispersion equation in cylindrical coordinates in finite domain subject to first-and third-type inlet boundary conditions. Journal of Hydrology, 405(3-4), 522-531.
. Chen, Jui-Sheng, Liu, Yiu-Hsuan, Liang, Ching-Ping, Liu, Chen-Wuing, Lin, Chien-Wen. (2011). Exact analytical solutions for two-dimensional advection–dispersion equation in cylindrical coordinates subject to third-type inlet boundary condition. Advances in Water Resources. 34(3), 365-374.
. Derya, A. and A. Yetim. (2018). Analytical solutions to the advection-diffusion equation with the Atangana-Baleanu derivative over a finite domain. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 20(2). 382-395.
. Yadav, R. and L. K. Kumar. (2021). Analytical solution of two-dimensional conservative solute transport in a heterogeneous porous medium for varying input point source. Environmental Earth Sciences. 80, 1-10.
. Wang, H. Q., Crampon, N., Huberson, S., Garnier, J M. (1987). A linear graphical method for determining hydrodispersive characteristics in tracer experiments with instantaneous injection. Journal of Hydrology, 95(1-2), 143-154.
. Aral, M. M. and B. Liao. (1996). Analytical solutions for two-dimensional transport equation with time-dependent dispersion coefficients. Journal of Hydrologic Engineering. 1(1), 20-32.
. De Smedt, F., W. Brevis, and P. Debels. (2005). Analytical solution for solute transport resulting from instantaneous injection in streams with transient storage. Journal of Hydrology, 315(1-4), 25-39.
. Singh, S. K. (2006). Estimating dispersivity and injected mass from breakthrough curve due to instantaneous source. Journal of Hydrology. 329(3-4), 685-691.
. Zhenyu, H., Liangduo, S., Haomin, C., Zhenlei, H. (2020). Instantaneous point sources and continuous sources are diffused with the flow transport. Chinese Navigation. 43(3), 97-100.
. Grolimund, D., Elimelech, M. Borkovec, M. Barmettler, K. Kretzschmar, R. Sticher, Hans. (1998). Transport of in situ mobilized colloidal particles in packed soil columns. Environmental Science & Technology. 32(22), 3562-3569.
. Bedrikovetsky, P., Siqueira, A. G., de Souza, A. L. S., Shecaira, F. S. (2006). Correction of basic equations for deep bed filtration with dispersion. Journal of Petroleum Science and Engineering, 51(1-2), 68-84.
. Soni, P., Kumar, A., Rani, A. (2021). Two-Dimensional Mathematical Model for Fluoride Ion Transport in Soil under Steady Flow Conditions. Advances and Applications in Mathematical Sciences. 20(10), 2113-2126.
. Batu, V. (1983). Two-dimensional dispersion from strip sources. Journal of Hydraulic Engineering, 109(6), 827-841.
. Massei, N., Lacroix, M., Wang, H. Q. Dupont, Jean-Paul. (2002). Transport of particulate material and dissolved tracer in a highly permeable porous medium: comparison of the transfer parameters. Journal of Contaminant Hydrology, 57(1-2), 21-39.
. Wang, H. Q., Lacroix, M., Massei, N., Dupont, J. P. (2000). Particle transport in a porous medium: determination of hydrodispersive characteristics and deposition rates. Comptes rendus de l academie des sciences serie ii fascicule a-sciences de la terre et des planetes, 331(2), 97-104.
. Yadav, R., D. Jaiswal, and H. Yadav. (2011). Temporally dependent dispersion through semi-infinite homogeneous porous media: an analytical solution. International Journal of Research and Reviews in Applied Sciences, 6(2), 158-164.
. Xingxin, C., Bing, B., and Qipeng, C. (2014). Theoretical solution of the particle release-migration problem in saturated porous media. Chinese science: Technical science, 44(6), 610-618.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Liang Ruishi, Zaiton Mat Isa
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
