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An Analytical Approach to Contaminant Transport with Spatially and Temporally Dependent Dispersion in a Heterogeneous Porous Medium

Year 2023, Volume: 44 Issue: 3, 538 - 546, 29.09.2023

Sujata Kushwaha , Raja Ram Yadav , Lav Kush Kumar , Joy Roy

https://doi.org/10.17776/csj.1258286

Abstract

This study presents an analytical solution to the one-dimensional advection-dispersion equation (ADE) for a semi-infinite heterogeneous aquifer system with space and time-dependent groundwater velocity and dispersion coefficient. The dispersion coefficient is assumed to be proportional to the groundwater flow velocity. In addition, retardation factor, first-order decay and zero-order production terms are also considered. Contaminants and porous media are assumed to be chemically inert. Initially, it is assumed that some uniformly distributed solutes are already present in the aquifer domain. The input point source is considered uniformly continuous and increasing nature in a semi-infinite porous medium. The solutions are obtained analytically using the Laplace Integral Transform Technique (LITT). The nature of the concentration profile of the resulting solution for different parameters in different time domains is illustrated graphically.

Keywords

Groundwater Pollutant Advection Dispersion Retardation factor.

Supporting Institution

NA

Project Number

NA

References

  • [1] Shi X., Lei T., Yan Y., Zhang F., Determination and impact factor analysis of hydrodynamic dispersion coefficient within a gravel layer using an electrolyte tracer method, International Soil and Water Conservation Research, 4(2) (2016) 87–92.
  • [2] Guerrero J. S. P., Pontedeiro E. M. Van Genuchten M. T., Skaggs T. H., Analytical solutions of the one-dimensional advection– dispersion solute transport equation subject to time-dependent boundary conditions, Chem. Eng. J., 221(2013) 487–491.
  • [3] Bear J., Dynamics of flow in porous media. New York: American ElsevierPublishing Co, (1972).
  • [4] Mishra S., Brigham W. E., Orr Jr. E. M., Tracer and pressure test analysis for characterization of areally heterogeneous reservoirs, Soc. Pet. Engrs. J., 22(4) (1991) 479-489.
  • [5] Elder J. W., The dispersion of marked fluid in turbulent shear flow, J. Fluid Mech., 5 (1959) 544-560.
  • [6] Fischer H. B., The mechanics of dispersion in natural streams, J. Hydraul. Div. ASCE, 93(6) (1967) 187-216.
  • [7] Gelhar L. W., Gross G. W., Duffy C. J., Stochastic methods of analysing groundwater recharge In: Hydrology of areas of low precipitation, In Proc. of the Camberra Symp., (1979) 313-321.
  • [8] Valocchi A. J., Spatial moment analysis of the transport of kinetically adsorbing solutes through stratified aquifers, Water Resources Research, 25(2) (1989) 273-279.
  • [9] Shan C., Javandle I., Analytical solutions for solute transport in a vertical aquifer section, Journal of Contaminant Hydrology, 27(1-2) (1997) 63-82.
  • [10] Wadi A. S., Dimian M. F., Ibrahim F. N., Analytical solutions for one-dimensional advection–dispersion equation of the pollutant concentration, Journal of Earth System Science, 123(2014) 1317-1324.
  • [11] Kumar A., Yadav R. R., One-dimensional solute transport for uniform and varying pulse type input point source through heterogeneous medium, Environmental Technology, 36(4) (2014) 487-495.
  • [12] Natarajan N., Effect of distance-dependent and time-dependent dispersion on nonlinearly sorbed multispecies contaminants in porous media, ISH Journal of Hydraulic Eng., 22 (2016) 16-29.
  • [13] Rubol S., Battiato I, De Barros F. P., Vertical dispersion in vegetated shear flows, Water Resources Research, 52(10) (2016) 8066-8080.
  • [14] Kumar R., Chatterjee A., Singh M. K., Singh V. P., Study of solute dispersion with source/sink impact in semi-infinite porous medium, Pollution , 6(1) (2019) 87-98.
  • [15] Younes A., Fahs M., Ataie-Ashtiani B., Simmons C. T., Effect of distance-dependent dispersivity on density-driven flow in porous media, Journal of Hydrology., 589 (2020) 125204.
  • [16] Yadav R. R., Kushwaha S., Roy J, Kumar, L.K., Analytical Solutions for Scale and Time Dependent solute transport in heterogeneous sorous medium, Journal of Water Resources and Ocean Science, 12(1) (2023) (1-11).
  • [17] Raafat P.B., Ibrahim F.N., Saleh A., On determining conditions and suitable locations for fish survival by using the solution of the two coupled pollution and aeration equations, Sci. Rep., 13 6560 (2023).
  • [18] Esmail S., Agrawal P., Shaban A., A novel analytical approach for advection diffusion equation for radionuclide release from an area source, Nuclear Engineering and Technology, 52(4) (2020) 819-826
  • [19] Yadav R. R., Kumar L. K., Two-dimensional conservative solute transport with temporal and scale-dependent dispersion: Analytical solution, International Journal of Advance in Mathematics, 2 (2018) 90-111.
  • [20] Crank J., The Mathematics of Diffusion, Oxford Univ. Press, London, 2nd Ed., (1975).
  • [21] Kumar A., Jaiswal D. K., Kumar N., Analytical solutions to one-dimensional advection-diffusion equation with variable coefficients in semi-infinite media, J. Hydrol., 380(3-4) (2010) 330-337.
  • [22] Jaiswal D. K., Kumar A., Analytical solutions of advection-dispersion equation for varying pulse type input point source in one-dimension, International Journal of Engineering, Science and Technology, 3(1) (2011) 22-29.

Year 2023, Volume: 44 Issue: 3, 538 - 546, 29.09.2023

Sujata Kushwaha , Raja Ram Yadav , Lav Kush Kumar , Joy Roy

https://doi.org/10.17776/csj.1258286

Abstract

Project Number

NA

References

  • [1] Shi X., Lei T., Yan Y., Zhang F., Determination and impact factor analysis of hydrodynamic dispersion coefficient within a gravel layer using an electrolyte tracer method, International Soil and Water Conservation Research, 4(2) (2016) 87–92.
  • [2] Guerrero J. S. P., Pontedeiro E. M. Van Genuchten M. T., Skaggs T. H., Analytical solutions of the one-dimensional advection– dispersion solute transport equation subject to time-dependent boundary conditions, Chem. Eng. J., 221(2013) 487–491.
  • [3] Bear J., Dynamics of flow in porous media. New York: American ElsevierPublishing Co, (1972).
  • [4] Mishra S., Brigham W. E., Orr Jr. E. M., Tracer and pressure test analysis for characterization of areally heterogeneous reservoirs, Soc. Pet. Engrs. J., 22(4) (1991) 479-489.
  • [5] Elder J. W., The dispersion of marked fluid in turbulent shear flow, J. Fluid Mech., 5 (1959) 544-560.
  • [6] Fischer H. B., The mechanics of dispersion in natural streams, J. Hydraul. Div. ASCE, 93(6) (1967) 187-216.
  • [7] Gelhar L. W., Gross G. W., Duffy C. J., Stochastic methods of analysing groundwater recharge In: Hydrology of areas of low precipitation, In Proc. of the Camberra Symp., (1979) 313-321.
  • [8] Valocchi A. J., Spatial moment analysis of the transport of kinetically adsorbing solutes through stratified aquifers, Water Resources Research, 25(2) (1989) 273-279.
  • [9] Shan C., Javandle I., Analytical solutions for solute transport in a vertical aquifer section, Journal of Contaminant Hydrology, 27(1-2) (1997) 63-82.
  • [10] Wadi A. S., Dimian M. F., Ibrahim F. N., Analytical solutions for one-dimensional advection–dispersion equation of the pollutant concentration, Journal of Earth System Science, 123(2014) 1317-1324.
  • [11] Kumar A., Yadav R. R., One-dimensional solute transport for uniform and varying pulse type input point source through heterogeneous medium, Environmental Technology, 36(4) (2014) 487-495.
  • [12] Natarajan N., Effect of distance-dependent and time-dependent dispersion on nonlinearly sorbed multispecies contaminants in porous media, ISH Journal of Hydraulic Eng., 22 (2016) 16-29.
  • [13] Rubol S., Battiato I, De Barros F. P., Vertical dispersion in vegetated shear flows, Water Resources Research, 52(10) (2016) 8066-8080.
  • [14] Kumar R., Chatterjee A., Singh M. K., Singh V. P., Study of solute dispersion with source/sink impact in semi-infinite porous medium, Pollution , 6(1) (2019) 87-98.
  • [15] Younes A., Fahs M., Ataie-Ashtiani B., Simmons C. T., Effect of distance-dependent dispersivity on density-driven flow in porous media, Journal of Hydrology., 589 (2020) 125204.
  • [16] Yadav R. R., Kushwaha S., Roy J, Kumar, L.K., Analytical Solutions for Scale and Time Dependent solute transport in heterogeneous sorous medium, Journal of Water Resources and Ocean Science, 12(1) (2023) (1-11).
  • [17] Raafat P.B., Ibrahim F.N., Saleh A., On determining conditions and suitable locations for fish survival by using the solution of the two coupled pollution and aeration equations, Sci. Rep., 13 6560 (2023).
  • [18] Esmail S., Agrawal P., Shaban A., A novel analytical approach for advection diffusion equation for radionuclide release from an area source, Nuclear Engineering and Technology, 52(4) (2020) 819-826
  • [19] Yadav R. R., Kumar L. K., Two-dimensional conservative solute transport with temporal and scale-dependent dispersion: Analytical solution, International Journal of Advance in Mathematics, 2 (2018) 90-111.
  • [20] Crank J., The Mathematics of Diffusion, Oxford Univ. Press, London, 2nd Ed., (1975).
  • [21] Kumar A., Jaiswal D. K., Kumar N., Analytical solutions to one-dimensional advection-diffusion equation with variable coefficients in semi-infinite media, J. Hydrol., 380(3-4) (2010) 330-337.
  • [22] Jaiswal D. K., Kumar A., Analytical solutions of advection-dispersion equation for varying pulse type input point source in one-dimension, International Journal of Engineering, Science and Technology, 3(1) (2011) 22-29.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Sujata Kushwaha 0000-0003-0467-3862

Raja Ram Yadav 0000-0002-1311-5435

Lav Kush Kumar 0000-0001-9039-7205

Joy Roy 0000-0003-0403-3048

Project Number NA
Publication Date September 29, 2023
Submission Date March 1, 2023
Acceptance Date August 30, 2023
Published in Issue Year 2023Volume: 44 Issue: 3

Cite

APA Kushwaha, S., Yadav, R. R., Kumar, L. K., Roy, J. (2023). An Analytical Approach to Contaminant Transport with Spatially and Temporally Dependent Dispersion in a Heterogeneous Porous Medium. Cumhuriyet Science Journal, 44(3), 538-546. https://doi.org/10.17776/csj.1258286
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