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Mathematical models for saltwater intrusion in coastal aquifers
 A. G. Bobba
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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.
 Anand, S. G., Pandit, A., Sill, B. L. (1980) Some considerations in finite elements solutions to coupled groundwater flow and convectivedispersion equations. Proc. 3rd Int. Conf. Finite Elements Water Resour.. Univ. of Mississippi, Oxford, Miss
 Anderson, M. P. (1976) Unsteady groundwater flow beneath strip oceanic islands. Water Resour. Res. 12: pp. 640644
 Ayers, J. F., Vacher, H. L. (1983) A numerical model describing unsteady flow in a fresh water lens. Water Resour. Bull. 19: pp. 785792
 Bear, J. (1979) Hydraulics of Groundwater. McGrawHill, New York
 Bear, J., Dagan, G. (1964) Some exact solutions of interface problems by means of the hodograph method. J. Geophys. Res. 69: pp. 15631572
 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.
 Bear, J., Zaslavsky, D., Irmay, S. (1989) Physical Principles of Water Percolation and Seepage. UNESCO, Paris
 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.
 Bobba, A. G., 1992, Field validation of ‘SUTRA’ groundwater flow model to Lambton County, Ontario, Canada. NWRI contribution 92–141.
 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.
 Carr, P. A. (1969) Saltwater intrusion in Prince Edward Island. Canadian J. Earth Sci. 6: pp. 6374
 Charmonman, S. (1965) A solution of pattern of fresh water flow in an unconfined coastal aquifer. J. Geophys. Res. 70: pp. 28132819
 Cheng, R. T. (1972) Numerical solution of the NavierStokes equations by the finite element method. Phys. Fluids. 15: pp. 20982105
 Collins, M. A., Gelhar, L. W. (1971) Seawater intrusion in layered aquifers. Water Resour. Res. 7: pp. 971979
 Contractor, D. N (1983) Numerical modeling of saltwater intrusion in the Northern Guam lens. Water Resour. Bull. 19: pp. 745751
 Cooper, H. H. (1959) A hypothesis concerning the dynamic balance of freshwater and saltwater in a coastal aquifer. J. Geophys. Res. 64: pp. 461467
 Dagan, G., Bear, J. (1968) Solving the problem of local interface upcoming in a coastal aquifer by the method of small perturbations. J. Hydraul. Res. 6: pp. 1544
 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.
 Fetter, C. W. (1972) Position of the saline water interface beneath oceanic islands. Water Resour. Res. 8: pp. 13071314
 Frind, E. O. (1980) Seawater intrusion in continuous coastal aquiferaquitard system. Proc. 3rd Int. Conf. Finite Elements Water Resour.. Univ. of Mississippi, Oxford, Miss., pp. 177198
 Frind, E. O. (1982) Simulaton of long term transient density dependent transport in groundwater. Adv. Water Resour. 5: pp. 7378
 Frind, E. O. (1982) Seawater intrusion in continuous coastal aquiferaquitard systems. Adv. Water Resour. 5: pp. 8997
 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.
 Glover, R. E. (1959) The pattern of freshwater flow in a coastal aquifer. J. Geophys. Res. 64: pp. 457459
 Hantush, M. S. (1968) Unsteady movement of fresh water in thick unconfined saline aquifers. Bull. Int. Assoc. Sci. Hydrol. 13: pp. 4060
 Henry, H. R. (1959) Saltwater intrusion into freshwater aquifers. J. Geophys. Res. 64: pp. 19111919
 Henry, H. R. (1960) Saltwater intrusion into coastal aquifer. Int. Ass. Sci. Hydrol. Publ. 52: pp. 478487
 Henry, H. R., 1962, Transitory movements of the saltwater front in an extensive artesian aquifer, U.S.G.S. Prof. Paper. 450b: 87–88.
 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.
 Herzberg, B. (1901) Die Wasserversorgung einiger Nordseebader. J. Gasbeleuchtung und Wasserversorgung 44: pp. 815819
 Hubbert, M. K. (1940) The theory of ground water motion. J. Geol. 48: pp. 785944
 Huyakorn, P. S., Anderson, P. F., Mercer, J. W., White, H. O. (1987) Saltwater intrusion in aquifers: Development and testing of a threedimensional finite element model. Water Resour. Res. 23: pp. 293312
 Kashef, A. I. (1968) Freshsaltwater interface in coastal groundwater basins. Proc. Internat. Assoc. Hydrogeologists. 8: pp. 369375
 Kashef, A. I. (1986) Groundwater Engineering. McGrawHill, New York
 Katwatni, T. (1980) Behaviour of saltwater intrusion in layered coastal aquifers. Proc. 3rd Int. Conf. Finite Element Water Resour.. Univ. of Mississippi, Oxford, Miss., pp. 199208
 Kohout, F. A. (1960) Cyclic flow of saltwater in the Biscayne aquifer of southeastern Florida. J. Geophys. Res. 65: pp. 21332141
 Kozeny, J. (1953) Hydraulik. Springer, Vienna
 Lee, C. H., Cheng, R. T. (1974) On seawater encroachment in coastal aquifers. Water Resour. Res. 10: pp. 10391043
 Mercer, J., Larson, S., and Faust, C., 1980, FiniteDiifference model to simulate the areal flow of saltwater and freshwater separated by an interface, U.S. Geol. Surv., OpenFile Rep. 80–407.
 Mualem, Y. (1973) Interface refraction at the boundary between two porous media. Water Resour. Res. 10: pp. 12071215
 Mualem, Y., Bear, J. (1974) The shape of the interface in steady flow in a stratified aquifer. Water Resour. Res. 10: pp. 12071215
 Muskat, M. (1946) The Flow of Homogeneous Fluids Through Porous Media. McGrawHill, New York
 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.
 Pinder, G. F., Cooper, H. H. (1970) A numerical technique for calculating the transient position of the saltwater front. Water Resour. Res. 6: pp. 875882
 Pinder, G. F., Frind, E. O. (1972) Application of Galerkin's procedure to aquifer analysis. Water Resour. Res. 8: pp. 108120
 Pinder, G. F., Gray, W. G. (1977) Finite Element Simulation in Surface and Subsurface Hydrology. Academic Press, New York
 PolubarinovaKochina, P. YA (1962) Theory of Groundwater Movement. Princeton University Press, Princeton
 Reddel, D. I., Sunada, D. K. (1970) Numerical simulation of dispersion in groundwater aquifers. Colorado State University, Fort Collins
 Reilly, T. E., Goodman, A. S. (1985) Quantitative analysis of saltwaterfreshwater relationships in groundwater systems — a historical perspective. J. Hydrol. 80: pp. 125160
 Reilly, T. E., Goodman, A. S. (1986) Analysis of saltwater upconing beneath a pumping well. J. Hydrol. 89: pp. 169204
 Rumer, R. R., Shiau, J. C. (1968) Saltwater interface in layered coastal aquifer. Water Resour. Res. 4: pp. 12351247
 Sa da Costa, A. A. G., Wilson, J. L. (1980) Coastal seawater intrusion: A moving boundary problem. Proc. 3rd Int. Conf. Finite Element Water Resour.. Univ. of Mississippi, Oxford, Miss., pp. 209218
 Sahni, B. M. (1973) Physics of brine coning beneath skimming wells. Ground Water 11: pp. 1924
 Schmorak, S., Mercado, A. (1969) Upconing of fresh watersea water interface below pumping wells, field study. Water Resour. Res. 5: pp. 12901311
 Segol, G., Pinder, G. F., Gray, W. G. (1975) A Galerkin finite element technique for calculating the transition position of saltwater front. Water Resour. Res. 11: pp. 343347
 Segol, G., Pinder, G. F. (1976) Transient simulation of saltwater intrusion in Southeastern Florida. Water Resour. Res. 12: pp. 6570
 Shamit, U., Dagan, G. (1971) Motion of the sea water interface in coastal aquifers: A numerical solution. Water Resour. Res. 7: pp. 644657
 Shamir, U., Harleman, D.R.F. (1967) Numerical solution for dispersion in porous mediums. Water Resour. Res. 3: pp. 557581
 Sherif, M. M., Singh, V.P., Amer, A.M. (1988) A twodimensional finite element model for dispersion (2dFED) in coastal aquifers. J. Hydrol. 103: pp. 1136
 Shima, S. (1969) Transient characteristics of a saltwater wedge. Proc. 13th Congr. IAHR 4: pp. 433440
 Souza, W. R., Voss, C. I. (1987) Analysis of an anisotropic coastal aquifer system using variabledensity flow and solute transport simulation. J. Hydrol. 92: pp. 1741
 Taylor, C. and Huyakorn, P.S., 1978, Finite element analysis of threedimensional groundwater flow with convection dispersion,Proc. 2nd Int. Symp. Finite. Element Methods Flow Problems, Italy.
 Todd, D. K. (1980) Groundwater Hydrology. Wiley, New York
 Vappicha, V. N., Nagaraja, S. H. (1976) An approximate solution for the transient interface in a coastal aquifer. J. Hydrol. 31: pp. 161173
 Voss, C. I., 1984, SUTRA — A finite element simulation model for saturatedunsaturated fluid density dependent groundwater flow with energy transport or chemicallyreactive single species solute transport, U.S. Geol. Surv., Water Resour. Invest. Rep., 84–4269.
 Voss, C. I., Souza, W. R. (1987) Variable density flow and solute transport simulation of regional aquifers containing a narrow freshwatersaltwater transition zone. Water Resour. Res. 23: pp. 18511866
 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.
 Wilson, J., Sa da Costa, A. (1982) Finite element simulation of a saltwater/freshwater interface with indirect toe tracking. Water Resour. Res. 18: pp. 10691080
 Title
 Mathematical models for saltwater intrusion in coastal aquifers
 Journal

Water Resources Management
Volume 7, Issue 1 , pp 337
 Cover Date
 19930301
 DOI
 10.1007/BF00872240
 Print ISSN
 09204741
 Online ISSN
 15731650
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Coastal aquifers
 saltwater intrusion
 groundwater
 mathematical models
 analytical and numerical models
 Industry Sectors
 Authors

 A. G. Bobba ^{(1)}
 Author Affiliations

 1. Rivers Research Branch, National Water Research Institute, L7R 4A6, Burlington, Ontario, Canada