Water Resources Management

, Volume 7, Issue 1, pp 3–37 | Cite as

Mathematical models for saltwater intrusion in coastal aquifers

  • A. G. Bobba
Review Article

Abstract

Flow of freshwater and saltwater intrusion in coastal aquifers has drawn the attention of many investigators. Several laboratory, as well as mathematical models have been developed to study the pattern of flow of groundwater in coastal aquifers. Mathematical models have wider range of application and are the concern of this paper. Due to the complex nature of the problem, each of these mathematical models are based on certain simplifying assumptions and approximations. This paper presents a critical review of various methods of solution which have been proposed. The validity of the results abtained and the limitations of these models are also discussed.

Key words

Coastal aquifers saltwater intrusion groundwater mathematical models analytical and numerical models 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anand, S. G., Pandit, A., and Sill, B. L., 1980, Some considerations in finite elements solutions to coupled groundwater flow and convective-dispersion equations,Proc. 3rd Int. Conf. Finite Elements Water Resour., Univ. of Mississippi, Oxford, Miss.Google Scholar
  2. Anderson, M. P., 1976, Unsteady groundwater flow beneath strip oceanic islands,Water Resour. Res. 12, 640–644.Google Scholar
  3. Ayers, J. F., and Vacher, H. L., 1983, A numerical model describing unsteady flow in a fresh water lens,Water Resour. Bull. 19, 785–792.Google Scholar
  4. Bear, J., 1979,Hydraulics of Groundwater, McGraw-Hill, New York.Google Scholar
  5. Bear, J. and Dagan, G., 1964, Some exact solutions of interface problems by means of the hodograph method,J. Geophys. Res. 69, 1563–1572.Google Scholar
  6. Bear, J. and Dagan, G., 1968, Solving the problem of local interface upcoming in a coastal aquifer by the method of small perturbations,J. Hydraul. Res. 1.Google Scholar
  7. Bear, J., Zaslavsky, D., and Irmay, S., 1989,Physical Principles of Water Percolation and Seepage, UNESCO, Paris.Google Scholar
  8. Bobba, A. G., 1991, Application of digital simulation model to freshwater aquifer of Lambton County, Ontario, Canada. Paper presented at International Conference on Hydrology and Hydrogeology in the '90s; Orlando, Florida, U.S.A., 3–7 Nov., 1991.Google Scholar
  9. Bobba, A. G., 1992, Field validation of ‘SUTRA’ groundwater flow model to Lambton County, Ontario, Canada. NWRI contribution 92–141.Google Scholar
  10. Bush, W. P., 1988, Simulation of saltwater movement in the Floridan aquifer system, Hilton Head Island, South Caroline., U.S.G.S Water Supply paper 2331.Google Scholar
  11. Carr, P. A., 1969, Salt-water intrusion in Prince Edward Island,Canadian J. Earth Sci. 6, 63–74.Google Scholar
  12. Charmonman, S., 1965, A solution of pattern of fresh water flow in an unconfined coastal aquifer,J. Geophys. Res. 70, 2813–2819.Google Scholar
  13. Cheng, R. T., 1972, Numerical solution of the Navier-Stokes equations by the finite element method,Phys. Fluids. 15, 2098–2105.Google Scholar
  14. Collins, M. A. and Gelhar, L. W., 1971, Seawater intrusion in layered aquifers,Water Resour. Res. 7, 971–979.Google Scholar
  15. Contractor, D. N, 1983, Numerical modeling of saltwater intrusion in the Northern Guam lens,Water Resour. Bull. 19, 745–751.Google Scholar
  16. Cooper, H. H. Jr., 1959, A hypothesis concerning the dynamic balance of freshwater and saltwater in a coastal aquifer,J. Geophys. Res. 64, 461–467.Google Scholar
  17. Dagan, G. and Bear, J. 1968, Solving the problem of local interface upcoming in a coastal aquifer by the method of small perturbations,J. Hydraul. Res. 6, 15–44.Google Scholar
  18. Drabbe, J. and Baden Ghyben, W., 1888–1889, Nota in verband met de voorgenomen putboring nabij Amsterdam,Tijdschrift van het Koninklijk Instituut van Ingenieurs, The Hague, Netherlands, 8–22.Google Scholar
  19. Fetter Jr. C. W., 1972, Position of the saline water interface beneath oceanic islands,Water Resour. Res. 8, 1307–1314.Google Scholar
  20. Frind, E. O., 1980. Seawater intrusion in continuous coastal aquifer-aquitard system.,Proc. 3rd Int. Conf. Finite Elements Water Resour., Univ. of Mississippi, Oxford, Miss. Vol. 2, pp. 177–198.Google Scholar
  21. Frind, E. O., 1982, Simulaton of long term transient density dependent transport in groundwater,Adv. Water Resour. 5, 73–78.Google Scholar
  22. Frind, E. O., 1982, Seawater intrusion in continuous coastal aquifer-aquitard systems,Adv. Water Resour. 5, 89–97.Google Scholar
  23. Ghyben, W. B., 1889, Notes on the probable results of well drilling near Amsterdam (in Dutch).Tijdschrift van het Koninklijk Inst. van Ingenieur., The Hague21.Google Scholar
  24. Glover, R. E., 1959, The pattern of fresh-water flow in a coastal aquifer,J. Geophys. Res. 64, 457–459.Google Scholar
  25. Hantush, M. S., 1968, Unsteady movement of fresh water in thick unconfined saline aquifers,Bull. Int. Assoc. Sci. Hydrol. 13, 40–60.Google Scholar
  26. Henry, H. R., 1959, Saltwater intrusion into freshwater aquifers,J. Geophys. Res. 64, 1911–1919.Google Scholar
  27. Henry, H. R., 1960, Saltwater intrusion into coastal aquifer,Int. Ass. Sci. Hydrol. Publ. 52, 478–487.Google Scholar
  28. Henry, H. R., 1962, Transitory movements of the saltwater front in an extensive artesian aquifer, U.S.G.S. Prof. Paper. 450-b: 87–88.Google Scholar
  29. Henry, H. R., 1964, Interface between salt water and fresh water in coastal aquifers, sea water coastal aquifers. U.S.G.S. Water Supply Paper, 1613 C.Google Scholar
  30. Herzberg, B., 1901, Die Wasserversorgung einiger Nordseebader,J. Gasbeleuchtung und Wasserversorgung.44, 815–819, 842–844.Google Scholar
  31. Hubbert, M. K., 1940, The theory of ground water motion,J. Geol. 48, 785–944.Google Scholar
  32. Huyakorn, P. S., Anderson, P. F., Mercer, J. W., and White, H. O., 1987, Saltwater intrusion in aquifers: Development and testing of a three-dimensional finite element model,Water Resour. Res. 23, 293–312.Google Scholar
  33. Kashef, A. I. 1968, Fresh-salt-water interface in coastal groundwater basins,Proc. Internat. Assoc. Hydrogeologists. 8, 369–375.Google Scholar
  34. Kashef, A. I. 1986,Groundwater Engineering, McGraw-Hill, New York.Google Scholar
  35. Katwatni, T., 1980, Behaviour of saltwater intrusion in layered coastal aquifers,Proc. 3rd Int. Conf. Finite Element Water Resour., Univ. of Mississippi, Oxford, Miss. Vol 2, pp. 199–208.Google Scholar
  36. Kohout, F. A., 1960, Cyclic flow of saltwater in the Biscayne aquifer of southeastern Florida,J. Geophys. Res. 65, 2133–2141.Google Scholar
  37. Kozeny, J., 1953,Hydraulik, Springer, Vienna.Google Scholar
  38. Lee, C. H., and Cheng, R. T., 1974, On seawater encroachment in coastal aquifers,Water Resour. Res. 10, 1039–1043.Google Scholar
  39. Mercer, J., Larson, S., and Faust, C., 1980, Finite-Diifference model to simulate the areal flow of saltwater and freshwater separated by an interface, U.S. Geol. Surv., Open-File Rep. 80–407.Google Scholar
  40. Mualem, Y., 1973, Interface refraction at the boundary between two porous media,Water Resour. Res. 10, 1207–1215.Google Scholar
  41. Mualem, Y. and Bear, J. 1974, The shape of the interface in steady flow in a stratified aquifer,Water Resour. Res. 10, 1207–1215.Google Scholar
  42. Muskat, M., 1946,The Flow of Homogeneous Fluids Through Porous Media, McGraw-Hill, New York.Google Scholar
  43. Pandit, A. and Anand, S. C., 1984, Groundwater flow and mass transport by finite elements — A parametric study,Proc. 5th Int. Conf. Finite Elements Water Resour., Univ. of Vermont.Google Scholar
  44. Pinder, G. F. and Cooper, H. H. Jr., 1970, A numerical technique for calculating the transient position of the saltwater front.,Water Resour. Res. 6, 875–882.Google Scholar
  45. Pinder, G. F. and Frind, E. O., 1972, Application of Galerkin's procedure to aquifer analysis,Water Resour. Res. 8, 108–120.Google Scholar
  46. Pinder, G. F. and Gray, W. G., 1977,Finite Element Simulation in Surface and Subsurface Hydrology, Academic Press, New York.Google Scholar
  47. Polubarinova-Kochina, P. YA, 1962.,Theory of Groundwater Movement (trans. J. M. R. De Wiest), Princeton University Press, Princeton.Google Scholar
  48. Reddel, D. I. and Sunada, D. K., 1970, Numerical simulation of dispersion in groundwater aquifers, Hydrol. Paper 41, Colorado State University, Fort Collins.Google Scholar
  49. Reilly, T. E. and Goodman, A. S., 1985, Quantitative analysis of saltwater-freshwater relationships in groundwater systems — a historical perspective,J. Hydrol. 80, 125–160.Google Scholar
  50. Reilly, T. E. and Goodman, A. S., 1986, Analysis of saltwater upconing beneath a pumping well,J. Hydrol. 89, 169–204.Google Scholar
  51. Rumer, R. R. and Shiau, J. C., 1968, Saltwater interface in layered coastal aquifer,Water Resour. Res. 4, 1235–1247.Google Scholar
  52. Sa da Costa, A. A. G. and Wilson, J. L., 1980, Coastal seawater intrusion: A moving boundary problem,Proc. 3rd Int. Conf. Finite Element Water Resour., Univ. of Mississippi, Oxford, Miss., Vol.2, pp. 209–218.Google Scholar
  53. Sahni, B. M., 1973, Physics of brine coning beneath skimming wells,Ground Water 11, 19–24.Google Scholar
  54. Schmorak, S. and Mercado, A., 1969, Upconing of fresh water-sea water interface below pumping wells, field study,Water Resour. Res. 5, 1290–1311.Google Scholar
  55. Segol, G., Pinder, G. F., and Gray, W. G., 1975, A Galerkin finite element technique for calculating the transition position of saltwater front,Water Resour. Res. 11, 343–347.Google Scholar
  56. Segol, G. and Pinder, G. F., 1976, Transient simulation of saltwater intrusion in Southeastern Florida,Water Resour. Res. 12, 65–70.Google Scholar
  57. Shamit, U. and Dagan, G., 1971, Motion of the sea water interface in coastal aquifers: A numerical solution,Water Resour. Res. 7, 644–657.Google Scholar
  58. Shamir, U. and Harleman, D.R.F., 1967, Numerical solution for dispersion in porous mediums,Water Resour. Res. 3, 557–581.Google Scholar
  59. Sherif, M. M., Singh, V.P., and Amer, A.M., 1988, A two-dimensional finite element model for dispersion (2d-FED) in coastal aquifers,J. Hydrol. 103, 11–36.Google Scholar
  60. Shima, S., 1969, Transient characteristics of a saltwater wedge,Proc. 13th Congr. IAHR, Vol. 4, pp. 433–440.Google Scholar
  61. Souza, W. R. and Voss, C. I., 1987, Analysis of an anisotropic coastal aquifer system using variable-density flow and solute transport simulation.J. Hydrol. 92, 17–41.Google Scholar
  62. Taylor, C. and Huyakorn, P.S., 1978, Finite element analysis of three-dimensional groundwater flow with convection dispersion,Proc. 2nd Int. Symp. Finite. Element Methods Flow Problems, Italy.Google Scholar
  63. Todd, D. K., 1980.,Groundwater Hydrology, Wiley, New York.Google Scholar
  64. Vappicha, V. N. and Nagaraja, S. H., 1976, An approximate solution for the transient interface in a coastal aquifer,J. Hydrol. 31, 161–173.Google Scholar
  65. Voss, C. I., 1984, SUTRA — A finite element simulation model for saturated-unsaturated fluid density dependent groundwater flow with energy transport or chemically-reactive single species solute transport, U.S. Geol. Surv., Water Resour. Invest. Rep., 84–4269.Google Scholar
  66. Voss, C. I. and Souza, W. R., 1987, Variable density flow and solute transport simulation of regional aquifers containing a narrow freshwater-saltwater transition zone,Water Resour. Res. 23, 1851–1866.Google Scholar
  67. Wikramaratna, R. S. and Wood, W. L., 1982, On the coupled equations of the groundwater quality problem,Proc. 4th. Conf. Finite Elements Water Resour., Hannover.Google Scholar
  68. Wilson, J. and Sa da Costa, A., 1982, Finite element simulation of a saltwater/freshwater interface with indirect toe tracking,Water Resour. Res. 18, 1069–1080.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • A. G. Bobba
    • 1
  1. 1.Rivers Research BranchNational Water Research InstituteBurlingtonCanada

Personalised recommendations