Abstract
Saltwater, or brine, underlies freshwater in many aquifers, with a transition zone separating them. Pumping freshwater by a well located above the transition zone produces upconing of the latter, eventually salinizing the pumped water, forcing shut-off. Following the well’s shut-off, the upconed saltwater mound undergoes decay, tending to return to the pre-pumping regime. The FEAS code is used for the simulation of coupled density-dependent flow and salt transport involved in the upconing–decay process. In this code, the flow equation is solved by the Galerkin finite element method (FEM), while the advective–dispersive salt transport equation is solved in the Eulerian–Lagrangian framework. The code does not suffer from the instability constraint on the Peclet number. The code is used to investigate the transient upconing–decay process in an axially symmetric system and to discover how the process is affected by two major factors: the density difference factor (DDF) and the dispersivities. Simulation results show that under certain conditions, pumping essentially freshwater can be maintained for a certain time period, the length of which depends on the dispersivity values used. A recirculating flow cell may occur in the saltwater layer beneath the pumping well, widening the saltwater mound. The decay process is lengthy; it takes a long time for the upconed saltwater to migrate back to its original shape of a horizontal transition zone prior to pumping. However, the wider transition zone caused by hydrodynamic dispersion can never return to the initial one. This indicates that once a pumping well is abandoned because of high salinity, it can be reused for groundwater utilization only after a long time. It is also shown that the upconing–decay process is very sensitive to DDF, which, in our work, ranges from 0 (for an ideal tracer) to 0.2 (for brine). For a DDF of 0.025 (for seawater), local upconing occurs only for low iso-salinity surfaces, while those of high salt concentration remain stable after a short time. For an ideal tracer, all iso-salinity surfaces rise toward the pumping well, whereas for brine only iso-salinity surfaces of very low salinity upcone towards the pumping well. This may imply that the traditional finding that the sharp interface approximation is practically close to the 0.5 iso-salinity surface may not be true for a high DDF solution.
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References
O. Axelsson V.A. Barker (1984) Finite Element Solution of Boundary Value Problem, Theory and Computation Academic Press Orlando
M.A. Ajiz A. Jennings (1984) ArticleTitleA robust incomplete Choleski conjugate gradient algorithm Int. J. Numer. Methods Eng. 20 949–966
R. Barrett M. Berry T.F. Chan J. Demmel J.M. Donato J. Dongarra V. Eijkhout R. Pozo C. Romine H. Vander Vorst (1994) Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods SIAM Philadelphia
J. Bear G. Dagan (1964) ArticleTitleMoving interface in coastal aquifers Proc. ASCE. 99 IssueIDHY4 193–216
J. Bear (1979) Hydraulics of Groundwatet McGraw-Hill New York
J. Bear A. Verruijt (1990) Modeling Groundwater Flow and Pollution Kluwer Academic Publishers Dordrecht
J. Bear Y. Bachmat (1991) Introduction to Modeling of Transport Phenomena in Porous Media Kluwer Academic Publishers Dordrecht
J. Bear A.H-D. Cheng S. Sorek D. Ouazar I. Herrera (Eds) (1999) Seawater Intrusion in Coastal Aquifers – Concepts, Methods and Practices Kluwer Academic Publishers Dordrecht
Bear J., Zhou Q., Bensabat J. (2001). Three dimensional simulation of seawater intrusion in heterogeneous aquifers: application to the coastal aquifer of Israel, in: proceedings of the First International Conference on Saltwater Intrusion and Coastal Aquifers-Monitoring, Modeling, and Management , Essaouira, Morocco, April 23–25
Bennett G.D., Mundorff M.J., Hussain S.A. (1968). Electric-Analog Studies of Brine Coning Beneath Freshwater Wells in the Punjab Region , West Pakistan, U.S. Geological Survey Water-Supply Paper, 1608-J
J. Bensabat Q. Zhou J. Bear (2000) ArticleTitleAn adaptive pathline-based particle tracking algorithm for the Eulerian-Lagrangian method Adv. Water Resour. 23 IssueID4 383–397 Occurrence Handle10.1016/S0309-1708(99)00025-1
J.W. Bower L.H. Motz D.W. Durden (1999) ArticleTitleAnalytical solution for determining the critical condition of saltwater upconing in a leaking artesian aquifer J. Hydrol. 221 43–54 Occurrence Handle10.1016/S0022-1694(99)00078-5 Occurrence Handle1:CAS:528:DyaK1MXlvFCqsro%3D
G. Dagan (1989) Flow and Transport in Porous Formations Springer-Verlag Berlin
G. Dagan D.G. Zeitoun (1998) ArticleTitleFree-surface flow toward a well and interface upconing in stratified aquifers of random conductivity Water Resour. Res. 34 IssueID11 3191–3196 Occurrence Handle10.1029/98WR02039 Occurrence Handle1:CAS:528:DyaK1cXnsFSis7c%3D
H.J. Diersch D. Prochnow M. Thiele (1984) ArticleTitleFinite element analysis of dispersion-affected saltwater upconing below a pumping well Appl. Math. Model. 8 IssueID5 305–312 Occurrence Handle10.1016/0307-904X(84)90143-4
L.W. Gelhar (1993) Stochastic Subsurface Hydrology Prentice Hall Englewood Cliffs
H.M. Haitjema (1991) ArticleTitleAn analytic element model for transient axi-symmetric interface flow J. Hydrol. 129 215–244 Occurrence Handle10.1016/0022-1694(91)90052-J Occurrence Handle1:CAS:528:DyaK38XhtlGrsLc%3D
S.M. Hassanizadeh A. Leijnse (1988) ArticleTitleOn the modeling of brine transport in porous media Water Resour. Res. 24 321–330 Occurrence Handle1:CAS:528:DyaL1cXhslehsrc%3D
R.G. Haubold (1975) ArticleTitleApproximation for steady interface beneath a well pumping freshwater overlying saltwater Ground Water. 13 IssueID3 254–259
A.W. Herbert L.P. Jackson D.A. Lever (1988) ArticleTitleCoupled groundwater flow and solute transport with fluid density strongly dependent upon concentration Water Resour. Res. 24 1781–1795 Occurrence Handle1:CAS:528:DyaL1MXmtlahtQ%3D%3D
M. Kemblowski (1987) ArticleTitleThe impact of the Dupuit–Forchheimer approximation on saltwater intrusion simulation Ground Water. 25 IssueID3 331–336 Occurrence Handle1:CAS:528:DyaL2sXks1CnsL8%3D
K. Johannsen W. Kinzelbach S. Oswald G. Wittum (2002) ArticleTitleThe saltpool benchmark problem – numerical simulation of saltwater upconing in a porous medium Adv. Water Resour. 25 335–348 Occurrence Handle10.1016/S0309-1708(01)00059-8
Lever D.A., Jackson C.P. (1985). On the equations for the flow of a concentrated salt solution through a porous medium, Harwell Rep. AERE-R. 11765, HMSO, London
T-S. Ma M. Sophocleous Y-S. Yu R.W. Buddemeier (1997) ArticleTitleModeling saltwater upconing in a freshwater aquifer in south–central Kansas J. Hydrol. 201 120–137 Occurrence Handle10.1016/S0022-1694(97)00048-6 Occurrence Handle1:CAS:528:DyaK2sXnvVegsbo%3D
M. Muskat R.D. Wyckoff (1935) ArticleTitleAn approximate theory of water-coning in oil production Trans. Am. Inst. Min. Metall. Petrol. Eng. 114 144–163
M. Muskat (1937) The Flow of Homogeneous Fluids Through Porous Media McGraw-Hill New York
S.P. Neuman (1984) ArticleTitleAdaptive Eulerian–Lagrangian finite element method for advection-dispersion Int. J. Numer. Methods Eng. 20 321–337
Oswald S.E. (1998). Density-driven flow in porous media: three-dimensional experiments and modeling, PhD Thesis, Institute of Hydromechanics and Water Resources Management. ETH Zurich, Switzerland.
S.E. Oswald M.B. Scheidegger W. Kinzelbach (2002) ArticleTitleTime-dependent measurement of strongly density-dependent flow in a porous medium via nuclear magnetic resonance imaging Transport Porous Media. 47 IssueID2 169–193 Occurrence Handle10.1023/A:1015508410514 Occurrence Handle1:CAS:528:DC%2BD38Xltleksr4%3D
Pinder G.F., Page R.H. (1977). Finite element simulation of salt water intrusion on the South Fork of Long Island, In: Finite Elements in Water Resources , Proceeding of the 1st international Conference Finite Elements in Water Resources , Pentech, London, pp. 2.51–2.69
T.E. Reilly A.S. Goodman (1987) ArticleTitleAnalysis of saltwater upconing beneath a pumping well J. Hydrol. 89 169–204 Occurrence Handle10.1016/0022-1694(87)90179-X Occurrence Handle1:CAS:528:DyaL2sXhs1aiurk%3D
T.E. Reilly M.H. Frimpter D.R. LeBlanc A.S. Goodman (1987) ArticleTitleAnalysis of steady-state salt-water upconing with application at Truro well field, Cape Code, Massachusetts Ground Water. 25 IssueID2 194–206 Occurrence Handle1:CAS:528:DyaL2sXitVWgtrg%3D
H. Rubin G.F. Pinder (1977) ArticleTitleApproximate analysis of upconing Adv. Water Resour. 1 IssueID2 97–101 Occurrence Handle10.1016/0309-1708(77)90027-6
B.M. Sahni (1973) ArticleTitlePhysics of brine upconing beneath skimming wells Ground Water. 11 IssueID1 19–24
O.D.L. Strack (1972) ArticleTitleSome cases of interface flow towards drains J. Eng. Math. 6 175–191 Occurrence Handle10.1007/BF01535101
G.I. Voss W.R. Souza (1987) ArticleTitleVariable density flow and solute transport simulation of regional aquifers containing a narrow freshwater-saltwater transport zone Water Resour. Res. 23 IssueID10 1851–1866 Occurrence Handle1:CAS:528:DyaL1cXktlCqtQ%3D%3D
R.C. Weast (Eds) (1989) Handbook of Chemistry and Physics EditionNumber70 Chemical Rubber Publishing Company (CRC) Boca Raton
P. Wirojanagud R.J. Charbeneau (1985) ArticleTitleSaltwater upconing in unconfined aquifers J. Hydraul. Eng. ASCE. 111 IssueID3 417–434
Zhou Q. (1999). Modeling seawater intrusion in coastal aquifers , PhD Thesis, Technion-Israel Institute of Technology.
Q. Zhou J. Bensabat J. Bear (2001) ArticleTitleAccurate calculation of specific discharge in heterogeneous porous media Water Resour. Res. 37 IssueID12 3057–3069 Occurrence Handle10.1029/1998WR900105
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Zhou, Q., Bear, J. & Bensabat, J. Saltwater Upconing and Decay Beneath a Well Pumping Above an Interface Zone. Transp Porous Med 61, 337–363 (2005). https://doi.org/10.1007/s11242-005-0261-4
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DOI: https://doi.org/10.1007/s11242-005-0261-4