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Research Article

Contaminant transport analysis under non-linear sorption in a heterogeneous groundwater system

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Pages 736-761 | Received 26 May 2022, Accepted 17 Oct 2022, Published online: 31 Oct 2022

References

  • Aral MM, Taylor SW. Groundwater quantity and quality management. Am Soc Civil Eng. 2011. https://doi.org/10.1061/9780784411766.
  • van Genuchten MT. Analytical solutions for chemical transport with simultaneous adsorption, zero-order production and first-order decay. J Hydrol. 1981;49(3-4):213–233. DOI:10.1016/0022-1694(81)90214-6.
  • Yates SR. An analytical solution for one-dimensional transport in porous media with an exponential dispersion function. Water Resour Res. 1992;28(8):2149–2154. DOI:10.1029/92WR01006.
  • Serrano SE. Propagation of non-linear reactive contaminants in porous media. Water Resour Res. 2003;39(8):1288. DOI:10.1029/2002WR001922.
  • Guerrero JP, Skaggs TH. Analytical solution for one-dimensional advection-dispersion transport equation with distance-dependent coefficients. J Hydrol. 2010;390(1-2):57–65. DOI:10.1016/j.jhydrol.2010.06.030.
  • Kumar A, Jaiswal DK, Kumar N. One-dimensional solute dispersion along unsteady flow through a heterogeneous medium, dispersion being proportional to the square of velocity. Hydrol Sci J. 2012;57(6):1223–1230. DOI:10.1080/02626667.2012.695871.
  • van Genuchten MTH, Leij FJ, Skaggs TH, et al. Exact analytical solutions for contaminant transport in rivers 1. The equilibrium advection-dispersion equation. J Hydrol Hydromech. 2013;61(2):146–160. DOI:10.2478/johh-2013-0020.
  • Guerrero JP, Pontedeiro EM, van Genuchten MT, et al. Analytical solutions of the one-dimensional advection-dispersion solute transport equation subject to time-dependent boundary conditions. Chem Eng J. 2013;221:487–491. DOI:10.1016/j.cej.2013.01.095.
  • Wadi AS, Dimian MF, Ibrahim FN. Analytical solutions for one-dimensional advection–dispersion equation of the pollutant concentration. J Earth Syst Sci. 2014;123(6):1317–1324.
  • Hayek M. Analytical model for contaminant migration with time-dependent transport parameters. J Hydrol Eng. 2016;21(5):04016009. DOI:10.1061/(ASCE)HE.1943-5584.0001360.
  • Purkayastha S, Kumar B. Analytical solution of the one-dimensional contaminant transport equation in groundwater with time-varying boundary conditions. Ish J Hydraul Eng. 2018;26(1):78–83. DOI:10.1080/09715010.2018.1453879.
  • Molati M, Murakawa H. Exact solutions of non-linear diffusion-convection-reaction equation: a Lie symmetry analysis approach. Commun Nonlinear Sci Numer Simul. 2019;67:253–263. DOI:10.1016/j.cnsns.2018.06.024.
  • Megahed AM, Reddy MG, Abbas W. Modeling of MHD fluid flow over an unsteady stretching sheet with thermal radiation, variable fluid properties and heat flux. Math Comput Simul. 2021;185:583–593.
  • Megahed AM, Reddy MG. Numerical treatment for MHD viscoelastic fluid flow with variable fluid properties and viscous dissipation. Indian J Phys. 2021;95(4):673–679.
  • Nasr ME, Gnaneswara Reddy M, Abbas W, et al. Analysis of non-linear radiation and activation energy analysis on hydromagnetic Reiner–Philippoff fluid flow with Cattaneo–Christov double diffusions. Mathematics. 2022;10(9):1534.
  • Reddy MG, Kumar KG. Cattaneo-Christov heat flux feature on carbon nanotubes filled with micropolar liquid over a melting surface: a stream line study. Int Commun Heat Mass Transfer. 2021;122:105142.
  • Reddy MG, Shehzad SA. Molybdenum disulfide and magnesium oxide nanoparticle performance on micropolar Cattaneo-Christov heat flux model. Appl Math Mech. 2021;42(4):541–552.
  • Bosma WJP, van Der Zee SE. Transport of reacting solute in a one-dimensional, chemically heterogeneous porous medium. Water Resour Res. 1993a;29:117–131. DOI:10.1029/92WR01859.
  • Dehghan M. Weighted finite difference techniques for the one-dimensional advection-diffusion equation. Appl Math Comput. 2004;147(2):307–319. DOI:10.1016/S0096-3003(02)00667-7.
  • Fares YR, Giacobbe D. Transient transport of reactive and non-reactive solutes in groundwater. Comput Geosci. 2004;30(5):483–492. DOI:10.1016/j.cageo.2004.03.003.
  • Maraqa MA. Retardation of nonlinearly sorbed solutes in porous media. J Environ Eng. 2007;133(6):587–594. DOI:10.1061/(ASCE)0733-9372(2007)133:6(587).
  • Savović S, Djordjevich A. Finite difference solution of the one-dimensional advection-diffusion equation with variable coefficients in semi-infinite media. Int J Heat Mass Transf. 2012;55(15-16):4291–4294. DOI:10.1016/j.ijheatmasstransfer.2012.03.073.
  • Savović S, Djordjevich A. Numerical solution for temporally and spatially dependent solute dispersion of pulse type input concentration in semi-infinite media. Int J Heat Mass Transf. 2013;60:291–295. DOI:10.1016/j.ijheatmasstransfer.2013.01.027.
  • Gharehbaghi A. Explicit and implicit forms of differential quadrature method for advection-diffusion equation with variable coefficients in semi-infinite domain. J Hydrol. 2016;541:935–940. DOI:10.1016/j.jhydrol.2016.08.002.
  • Mojtabi A, Deville MO. One-dimensional linear advection-diffusion equation: analytical and finite element solutions. Comput Fluids. 2015;107:189–195. DOI:10.1016/j.compfluid.2014.11.006.
  • Gorokhovski V, Trofimov V. Advective solute transport through porous media along streamlines. Model Earth Syst Environ. 2017;3(3):839–860. DOI:10.1007/s40808-017-0313-0.
  • Moranda A, Cianci R, Paladino O. Analytical solutions of one-dimensional contaminant transport in soils with source production-decay. Soil Syst. 2018;2(3):40. DOI:10.3390/soilsystems2030040.
  • Li X, Zhan H, Wen Z. Impact of transient flow on subsurface solute transport with exponentially time-dependent flow velocity. J Hydrol Eng. 2018;23(7):04018030. DOI:10.1061/(ASCE)HE.1943-5584.0001679.
  • Yadav RR, Roy J. Solute transport phenomena in a heterogeneous semi-infinite porous media: an analytical solution. Int J Appl Comput Math. 2018;4(6):1–14. DOI:10.1007/s40819-018-0567-x.
  • Das P, Singh MK. One-dimensional solute transport with time-varying dispersion in porous formulation. J Porous Media. 2019;22(10):1207–1227. DOI:10.1615/JPorMedia.2019025964.
  • Singh MK, Singh RK, Pasupuleti S. Study of forward-backward solute dispersion profiles in a semi-infinite groundwater system. Hydrol Sci J. 2020;65(8):1416–1429. DOI:10.1080/02626667.2020.1740706.
  • Banaei SMA, Javid AH, Hassani AH. Numerical simulation of groundwater contaminant transport in porous media. Int J Environ Sci Technol. 2021;18(1):151–162. DOI:10.1007/s13762-020-02825-7.
  • Naveen BP, Sumalatha J, Malik RK. A study on contamination of ground and surface water bodies by leachate leakage from a landfill in Bangalore, India. International J Geo Eng. 2018; 9(1):1–20. DOI:10.1186/s40703-018-0095-x.
  • Andallah LS, Khatun MR. Numerical solution of advection-diffusion equation using finite difference schemes. Bangladesh J Sci Ind Res. 2020;55(1):15–22.
  • Anley EF, Zheng Z. Finite difference approximation method for a space fractional convection–diffusion equation with variable coefficients. Symmetry. 2020;12(3):485.
  • Fadugba SE, Edogbanya OH, Zelibe SC. Crank nicolson method for solving parabolic partial differential equations. IJA2M. 2013;1(3):8–23.
  • Yadav RR, Roy J. Numerical solution for one-dimensional solute transport with variable dispersion. Environ Earth Sci Res J. 2019;6(1):35–42. DOI:10.18280/eesrj.060105.
  • Zhang X, Zhu Y, Wang J, et al. GW-PINN: a deep learning algorithm for solving groundwater flow equations. Adv Water Res. 2022;165:104243.
  • van Genuchten MTH, Alves WJ. Analytical solutions of the one dimensional convective-dispersive solute transport equation. Technical Bulletin No. 1661. United States Department of Agriculture, 151; 1982.
  • Batu V. Applied flow and solute transport modeling in aquifers: fundamental principles and analytical and numerical methods. Boca Raton (FL): CRC Press; 2005.
  • Bosma WJP, van Der Zee SE. Analytical approximation for non-linear adsorbing solute transport and first-order degradation. Transp Porous Media. 1993b;11(1):33–43. DOI:10.1007/BF00614633.
  • Weber WJ, McGinley PM, Katz LE. Sorption phenomena in subsurface systems: concepts, models and effects on contaminant fate and transport. Water Res. 1991;25(5):499–528. DOI:10.1016/0043-1354(91)90125-A.
  • Zheng C, Bennett GD. Applied contaminant transport modeling (Vol. 2). New York: Wiley-Interscience; 2002.
  • Kumar A, Jaiswal DK, Kumar N. Analytical solutions to one-dimensional advection-diffusion equation with variable coefficients in semi-infinite media. J Hydrol. 2010;380(3-4):330–337. DOI:10.1016/j.jhydrol.2009.11.008.
  • Freeze RA, Cherry JA. Groundwater. Englewood Cliffs: Prentice-Hall; 1979.
  • Singh MK, Kumari P. Contaminant concentration prediction along unsteady groundwater flow. In: S Basu, N Kumar, editor. Modelling and simulation of diffusive processes; simulation foundations, methods and applications. Cham: Springer; 2014. p. 257–275. DOI:10.1007/978-3-319-05657-9_12
  • Moriasi DN, Arnold JG, Van Liew MW, et al. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans ASABE. 2007;50(3):885–900.