Applicability of a sharp-interface model for estimating steady-state salinityat pumping wells—validation against sand tank experiments
Lei Shi a, Lei Cui a, Namsik Park a,⁎, Peter S. Huyakorn b
a Department of Civil Engineering, Dong-A University, Saha-gu Hadan 2-dong 840, Busan 604-714, Koreab HydroGeoLogic, Inc., 11107 Sunset Hills Road, Suite 400, Reston, VA 20190, USA
Article history:Received 6 February 2010Received in revised form 19 January 2011Accepted 19 January 2011Available online 26 January 2011
A numerical sharp-interface model of saltwater and freshwater behavior was validated againstexperiments conducted in two small scale sand tanks. A simple algorithm was proposed todetermine saltwater and freshwater withdrawal rates at a pumping well at which a totalpumping rate was specified. Model estimates were compared with transient salinitybreakthroughs and steady-state salinities of water extracted from pumping wells in the sandtanks. Experimental scenarios included various combinations of freshwater pumping andinjection and saltwater pumping. The corresponding Nash–Sutcliffe model efficiency was 0.95,which showed that the agreement between observations and computed results wassatisfactory.
Keywords:Numerical sharp-interface modelingSalinity estimationSaltwater intrusionPumping wellFreshwater injectionSaltwater pumpingSand tank experiment
1. Introduction
Salinity and saltwater intrusion are challenges for coastalgroundwater protection and management. Although consid-erable attention has been focused on understanding andmodeling freshwater and saltwater flows in aquifers, researchon the salinity of pumped water is limited. Moreover, theidentification of sustainable management schemes for ground-water in coastal areas may require numerical modeling toassess responses of groundwater system to anthropogenic andnatural disturbances. A density-dependent flow and advectiveand dispersive solute transport approach (Diersch, 2002; Guoand Langevin, 2002; Kim, 2005; Kipp, 1987; Sanford andKonikow, 1985; Voss, 1984; Zheng and Wang, 1999) is themost rigorous method for simulating groundwater flowphenomena subject to saltwater intrusion.
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Alternatively, a sharp-interface approach may be used forproblems in which transition zones can be neglected. Bear(1979) reviewed two-dimensional analytical solutions basedon the hodograph method and conformal mapping. Strack(1976) derived an analytical solution for groundwater flowand a freshwater–saltwater sharp interface subject toambient flow and a pumping well. Cheng et al. (2000)extended Strack's solution for multiple wells. Kacimov et al.(2006) developed an analytical solution for arid regionswhere evaporation of freshwater may significantly impactgroundwater flow. Park et al. (2009) developed design curvesfor maximum pumping or minimum injection rates using theanalytical solution derived by Cheng et al. (2000). Numericalsharp-interface models have also been developed. Sa da Costaand Wilson (1979) developed a Galerkin finite-elementmodel for freshwater and saltwater flows in a single-aquiferlayer. Essaid (1990) and Huyakorn et al. (1996) developednumerical models for layered aquifer systems. The sharp-interface approach is especially useful for large-scale pro-blems, but simulating the salinities of pumpedwater with it iscumbersome.
36 L. Shi et al. / Journal of Contaminant Hydrology 124 (2011) 35–42
Most modeling studies have dealt with temporal andspatial distributions of salinity, but only a limited number ofstudies have addressed the salinity of water extracted frompumping wells. For example, Paster and Dagan (2008)derived an approximate analytical solution using theboundary-layer approximation and estimated the salinityof pumped water from a confined aquifer by integrating thesaltwater entrainment in the well capture zone. However,their solution was limited to a fully penetrating well inhomogeneous, constant-thickness confined aquifers of semi-infinite areal extent. Therefore, its application is limited toideal situations. Diersch and Nillert (1990), Merritt (1997),and Reilly and Goodman (1987) simulated the salt concen-trations of pumped water using dispersion models andcompared simulated results with observed data from fieldsites. Merritt (1997) was able to calibrate a few modelparameters, including dispersivities, and closely matchedsimulated results to measured data. Comparisons made byothers resulted in larger errors ranging from a few percentto nearly 20%. In their sharp-interface models, Essaid (1990)and Huyakorn et al. (1996) implemented algorithms toestimate the saltwater content in a pumping well. Huyakornet al. (1996) used a simple analytical solution for well flow,while Essaid (1990) distributed the total pumping rate tofreshwater and saltwater equations based on thicknesses atthe well location. In both models, the interface position andthe screen length were the main variables affecting thesalinity of the pumped water. To date, the accuracy ofsalinity predictions using sharp-interface models has notbeen investigated.
Laboratory experiments have been used extensively toinvestigate saltwater intrusion phenomena in porous media(Boufadel, 2000; Goswami and Clement, 2007; Nakagawa et al.,2005; Simmons et al., 2001; Werner et al., 2009). Manyexperiments have also been conducted to test or to validatedispersion models (Mao et al., 2006; Oswald and Kinzelbach,2004; Thorenz et al., 2002; Watson et al., 2002; Zhang et al.,2001). To the best of our knowledge, Hong et al. (2004) andWerner et al. (2009) presented the only laboratory experimentsin which the salinities of pumped water were measured. In bothworks salinities were measured to determine if the wells hadbeen intruded.
Huyakorn et al. (1996) developed a sharp-interface finite-element model for freshwater and saltwater flows in multi-layer aquifer systems. The numerical model was verifiedagainst test problems for which analytical or numericalsolutions were available, and the comparisons showed goodagreement. The objective of this research was to investigatethe applicability of the sharp-interface model (Huyakornet al., 1996) for estimating the salinity of pumped water.Numerical treatment of a well for a multi-layer systeminvolves the additional complication of assigning fluxesacross aquifer layers when a well screen spans multipleaquifer layers. For simplicity, we focused on a single-layernumerical model. Numerical results were compared againstexperimental results conducted in sand tanks. We conductedexperiments to examine modeling capabilities for complexfield problems that may involve not only excessive pumpingfrom freshwater wells but also saltwater pumping andfreshwater injection, which may be used to mitigate saltwaterintrusion or for artificial recharge.
2. Sharp–interface groundwater flow model
For a single-aquifer layer, the vertically averaged governingequations for freshwater and saltwater flows can be simplified asfollows (Huyakorn et al., 1996):
where subscripts f and s refer to freshwater and saltwater,respectively; ∇ is the two-dimensional gradient operator; h isthe piezometric head [L]; b is the thickness of each fluid [L]; K isthe hydraulic conductivity [LT−1]; Ss [L−1] is the aquifer specificstorage; β is the effective porosity (θ) for an unconfined aquiferand is 0 for a confined aquifer; ξ is the elevation of saltwater-freshwater interface [L]; and Q is the flux [LT−1] per unit areadue to pumping (or injection). The interface elevation is calcu-lated by equating pressures at the interface and assuming thehydrostatic condition as follows (Bear, 1979):
ξ =ρf
ρs−ρf
ρsρf
hs−hf
� �=
ρshs−ρfhfρs−ρf
ð3Þ
where ρ is the fluid density [ML−3].At pumping wells, we assumed that the total extraction
rate was constant regardless of the proportions of saltwaterand freshwater encountered in the well. When both fresh-water and saltwater are extracted from a well, the followingrelationship holds:
Q t = Q f + Qs ð4Þ
where subscript t denotes the total amount. Pumping rates ofextracted freshwater and saltwater are assumed to depend onthe interface position within a well screen and on transmis-sivities. Thus, freshwater and saltwater extraction rates arecalculated as follows:
Q f =Kf lf
Kf lf + KslsQ t ð5Þ
Qs =Ksls
Kf lf + KslsQt ð6Þ
where lf and ls are thicknesses [L] of freshwater and saltwater,respectively, in the well screen (see Fig. 1). Here lf and ls canbe determined as follows:
lf = max min zwt; zatð Þ−max zwb; ξð Þ;0ð Þ ð7Þ
ls = l′−lf ð8Þ
l′ = min zwt; zatð Þ−max zwb; zabð Þ ð9Þ
where zwt and zwb are the elevations [L] of the top and bottomof a well screen, respectively; zat is the elevation [L] of the
Fig. 1. Schematic of a well screen containing an interface in an unconfinedaquifer.
Fig. 2. (a) Plan and (b) side views of reservoir levels and well positions (cm)in Tank A.
37L. Shi et al. / Journal of Contaminant Hydrology 124 (2011) 35–42
upper confining layer for a confined aquifer and is ground-water level (hf) for an unconfined aquifer; zab is the bottomelevation [L] of the aquifer; and l′ is the effective screen length[L]. Note that l′ can be equal to the physical screen length (l),but it also can be less than l, as when the water table fallsbelow the top of the well screen in an unconfined aquifer.Fig. 1 illustrates the relevant variables for an unconfinedaquifer case in which the freshwater–saltwater interfacecrosses the well screen.
The Galerkin finite-elementmethodwas used to discretizethe governing equations detailed above. Details of thenumerical treatment and verification of the model weredescribed by Huyakorn et al. (1996).
3. Sand tank experiments
3.1. Experimental setup
Saltwater intrusion experiments were conducted usingtwo sand tanks of different sizes (Tanks A and B), as shown inFigs. 2 and 3. Both tanks had three connected compartments.The middle compartments were filled with local sea sand,which was evenly compacted, and the two end compartmentswere equipped with water supplies and overflow drains andserved as constant-level reservoirs. Themiddle compartmentofTankA had a length of 1.75 m, awidth of 1.60 m and a height of0.58 m. Tank B had a length of 0.43 m, a width of 0.08 m and aheight 0.25 m. Sieve analysis indicated that D60=0.49 mm,D10=0.28 mm, and the coefficient of uniformity was 1.75. Toprevent evaporation loss during experiments, both sand tankswere covered.
The wells were made of acrylic pipes with inside diametersof 5 mmand external diameters of 8 mm. The screen lengths of
the twowells (Fa and Fb in Fig. 2) installed in TankAwere 2 cm.In TankB,five partially penetrating (F1, F2, F4, S1 and S2 in Fig. 3)and one fully penetrating wells (F3 in Fig. 3) were installed.Wells Fa, Fb, F2 and F3 were designed for freshwater pumping.Wells S1 and S2 were designed for saltwater pumping. Wells F1and F4 were designed for freshwater injection. The screenlength of each partially penetratingwell was 1.5 cm. Tapwaterwas used as freshwater, and sea salt was dissolved in tapwaterto produce saltwater. A hydrometer was used to establish thedesired specific gravity of saltwater, and a dye (rhodamine B)was added to the saltwater as a visual tracer.
Variable-speed peristaltic pumps were used for pumpingor injection. The pumps allowed the operation rate to varyfrom 0.06 ml/min to 130 ml/min. An electrical conductivity(EC) meter was also used.
3.2. Determination of hydraulic conductivity
Hydraulic conductivities of the sand media were deter-mined using freshwater flow experiments. Water levels inreservoirs were maintained at constant values. Once the flowhad reached a steady state, flow rates were measuredrepeatedly to ensure steadiness. The average hydraulicconductivities were determined to be 49.4 m/day for Tank Aand 44.1 m/day for Tank B.
Hydraulic conductivities can also be estimated using em-pirical functions and material properties. We selected theKozeny–Carman equation (Bear, 1979) to estimate the range ofhydraulic conductivities of our sand. Driscoll (1986) reportedthat the minimum and the maximum total porosity values forsandmaterialswere 0.25 and0.4, respectively, and theminimum
Fig. 3. (a) Plan and (b) side views of reservoir levels and well positions (cm) in Tank B.
38 L. Shi et al. / Journal of Contaminant Hydrology 124 (2011) 35–42
and the maximum effective porosity values were 0.1 and 0.3,respectively. The Kozeny–Carman equation required estimationof the total porosity. The corresponding hydraulic conductivitieswere 28.9 and 185 m/day. The values measured in the experi-ments fell within this range, but were closer to the minimumvalue.
4. Saltwater intrusion experiments
For the saltwater intrusion experiments, one reservoirwas filled with freshwater, and the other was filled withsaltwater. Freshwater levels weremaintained slightly higherthan saltwater levels to ensure that saltwater wedgesextended well into the sand media and that the toe wasnot too close to the freshwater reservoirs. In all cases,steady-state flow was established prior to pumping orinjection through any well. It took approximately 480 h inTank A and 19 h in Tank B for the measured toe locations tostabilize. Observations of the toe locations were continuedfor an additional 8 (Tank B) and 72 (Tank A) hours to ensurethat steady state had been established. Once the flowsattained steady state, well pumping or injection wasinitiated, and the EC of water withdrawn from pumpingwells was measured.
Adequate withdrawal rates were applied to pumpingwells to induce saltwater intrusion. Instead of comparingsalinities, we compared saltwater contents that could bedirectly obtained from the numerical model. Assuming alinear variation of EC values, the saltwater content (c) of asample can be estimated from experimental data as follows:
c =Qs
Qt≈ Em−Ef
Es−Efð10Þ
where Ef, Es and Em are the ECs for freshwater (424 μS/cm,post-sand medium), saltwater (82,300 μS/cm) and theextracted mixture, respectively. The corresponding specificgravities at 20 °C were 1.0 and 1.040 for freshwater andsaltwater, respectively.
For experiments in Tank A, the ECs were recordedperiodically from the beginning of the pumping period toobtain transient data. For experiments in Tank B, the ECs wererecorded only when the flows reached steady state. In thefollowing sections, the observed saltwater contents arecompared to the computed values from the sharp-interfacemodel.
4.1. Transient experiments
As shown in Fig. 2, the water levels from the bottom of thehorizontal tank were maintained at 35.8 and 34.0 cm in thefreshwater and saltwater reservoirs, respectively. Then, thesteady-state flow field was established in the absence ofpumping. The saltwater wedge intruded 102 cm from thesaltwater reservoir into the sand medium. Observations weremade through the transparent base of the sand tank, and thetoe was clearly delineated. The sharp-interface modelestimated the length of the saltwater wedge to be 104.5 cm.Note that wells Fa and Fb were installed above the saltwaterwedge. The bases of the wells were estimated to be 3.9 cmabove the simulated saltwater-freshwater interface.
Once the flow field established a steady-state condition,80 ml/min was withdrawn from both wells simultaneously.At this pumping rate, saltwater appeared at both wells almostimmediately after pumping started. The EC values of thesamples of pumped water were measured and converted intosaltwater contents. After approximately 20 h, the saltwater
Fig. 5. Transient saltwater contents for well Fb, near the center of Tank A.
39L. Shi et al. / Journal of Contaminant Hydrology 124 (2011) 35–42
contents reached equilibrium values of approximately 25% forwell Fa and 23% for well Fb (see Figs. 4 and 5).
The sharp-interface model was configured to simulatesaltwater contents for the wells using a non-uniformrectangular mesh (97 by 93 gridlines) with 9021 nodes.Smaller elements of 1 cm by 1 cm were used in the areasenclosing the pumping wells, and larger elements of 2 cm by2 cm were used outside these areas. The effective area of thewell node (1 cm2) was comparable to the cross-sectional areaof the physical wells (0.5 cm2).
Transient modeling requires estimation of the effectiveporosity. Here, we show that the measured breakthroughcurves are bounded between two numerical curves based onthe minimum (0.1) and the maximum (0.3) effectiveporosities (see section 3.2). Figs. 4 and 5 present the observedand two numerical breakthrough curves from wells Fa and Fb,respectively.
Both Figs. 4 and 5 show that the numerical modelsimulated saltwater breakthrough times that were earlierthan those observed in the experiment. The faster initialresponses in the numerical model were attributable to thehydrostatic assumption. After the initial stage, numericalbreakthrough curves for the effective porosity of 0.1 closelyfollowed the observed breakthrough curves. The measuredhydraulic conductivity was also close to the estimatedhydraulic conductivity based on the minimum value of thetotal porosity.
The time to reach quasi-steady state differed significantly(approximately 20 and 40 h for the effective porosities of 0.1and 0.3, respectively), revealing the importance of thisparameter in transient modeling. When equilibrium wasapproached, the maximum saltwater content values pre-dicted by the numerical model were slightly higher than theobserved values. Overall, the numerical model generatedbreakthrough curves that were in reasonable agreement withthe experimental results. The main objective of this researchwas to provide an accurate representation of the salinity ofpumped water under steady-state conditions. This compar-ison of transient predictions to experimental results providesan extended evaluation of the model's capabilities.
Fig. 4. Transient saltwater contents for well Fa, near a side wall of Tank A.
4.2. Steady-state experiments
The previous transient case indicated that the sharp-interfacemodel could reproduce steady-state saltwater contents whentwo freshwater pumping wells were operating in the aquifer. Tofurther investigate the model's capability, predictions werecompared to data obtained under a variety of conditions forsteady-state experiments in Tank B. The ECs were recorded onlywhen the flows reached steady state. Pumping from thefreshwater and saltwater zones and freshwater injection wereapplied to different combinations of one fully and five partiallypenetrating wells (see Fig. 3).
For these experiments, thewater levels in the freshwater andsaltwater reservoirs were maintained at 19.2 and 18.0 cm,respectively, above the bottom of the tank. Under theseconditions, the average freshwater discharge was 8.2 ml/min,and the toe of the saltwaterwedgewas located15.9 cm from thesaltwater reservoir (see Fig. 3). The sharp-interface modelindicated that the toewouldbe15.7 cmaway from the saltwaterreservoir, representing an error of approximately 1.3%.
Two sets (SP and SF) of steady-state experiments wereconducted. Both sets consisted of five scenarios, SP-1 to SP-5and SF-1 to SF-5. Table 1 summarizes the experimentalscenarios. In the SP set, a partially penetrating well F2 wasoperated either alone or in combination with another well. Inscenario SP-1, well F2 was pumped alone at three differentover-exploiting pumping rates. In SP-2, wells F2 and S1 wereoperated; in SP-3, wells F2 and S2 were operated. Note that inFig. 3, screened sections of S1 and S2were open in the saltwaterzone. In SP-4 and SP-5, freshwater was injected through wellsF1 and F4, respectively, while excessive pumping was main-tained at well F2. Equilibrium EC values were measured andequivalent saltwater contents were computed for pumpingwells F2, S1 and S2. A total of 9 EC values were obtained for theSP set. In the second set of experiments (SF), the scenarios SF-1to SF-5 were repeated with a fully penetrating well (F3),resulting in another 9 measurements.
The proposed sharp-interface model was constructed usinga uniform finite-element mesh of 1 cm by 1 cm. Again, the sizeof the finite element was comparable to the size of the wells.Fig. 6 illustrates numerical and observed steady-state saltwatercontents forwells F2 and F3. Fig. 7 depicts saltwater contents for
Freshwater pumping and injection SP-4 F2 −7.0 SF-4 F3 −7.0F1 +3.0 F1 +6.0
SP-5 F2 −7.0 SF-5 F3 −7.0F4 +4.0 F4 +4.5
40 L. Shi et al. / Journal of Contaminant Hydrology 124 (2011) 35–42
wells S1 and S2. Saltwater contents varied from 0 to 12% forwells F2 and F3, and from 40 to 100% for wells S1 and S2.
When either well F2 or F3, with screen openings in thefreshwater zone, was pumping at an excessive rate, saltwaterentered the well. As the pumping rates increased, thesaltwater contents also increased from a few percent toover 10%. Agreements between computed and observedsaltwater contents for four cases were reasonable (SP-1a,SP-1b, SP-1c, and SF-1b in Fig. 6). However, for cases SF-1aand SF-1c the agreements degenerated.
Saltwater may be extracted intentionally to mitigatesaltwater intrusion. When saltwater was pumped from eitherwell S1 or S2, with screen openings in the saltwater zone, inconjunction with excessive pumping at either well F2 or F3,the saltwater contents at well F2 decreased from SP-1b toSP-2 and SP-3; at well F3, they decreased from SF-1b to SF-2and SF-3 (see Fig. 6). It would have been ideal if well S1 orS2 extracted saltwater as shown in Fig. 7 (points SP-2 and
Fig. 6. Steady-state saltwater contents for wells F2 and F3 (screens in thefreshwater zone) in Tank B.
Fig. 7. Steady-state saltwater contents for wells S1 and S2 (screens in thesaltwater zone) in Tank B.
SP-3), but excessive pumping in the saltwater zone hadextracted not only saltwater but also freshwater as shown withpoints SF-2 and SF-3 in Fig. 7. The numerical results for cases SP-2and SF-3 in Fig. 6 and SF-2 in Fig. 7 were largely different frommeasured values, but for cases SP-3 and SF-2 in Fig. 6 and SP-2,SP-3 and SF-3 in Fig. 7, the agreements were reasonable.
Freshwater may also be injected to mitigate saltwaterintrusion. Freshwater was injected at either well F1 or F4 inconjunction with excessive pumping at either well F2 or F3. Theeffects of freshwater injection are clearly shown in Fig. 6 asdecreased saltwater contents atwells F2 (fromSP-1b to SP-4 andSP-5) and F3 (from SF-1b to SF-4 and SF-5). Three cases (SP-4,SF-4 and SF-5) resulted in good agreements, but the agreementin case SP-5 was less desirable.
The average difference (= computed − observed values)for cases in Fig. 6 was less than 1.1%. For the cases in Fig. 7, itwas −6.2%, and the difference for case SF-2 (−31.1%)dominated the average value. The Nash and Sutcliffe (1970)
Fig. 9. Comparison of computed interface (dashed line) and observedsaltwater wedge (darker-shade portion) for scenario SF-2 in Tank B.
41L. Shi et al. / Journal of Contaminant Hydrology 124 (2011) 35–42
model efficiency coefficient is another index frequently usedto quantify comparisons. The coefficient is defined as follows:
E = 1− ∑Ni = 1 coi −cmi
� �2∑N
i = 1 coi −co� �2 ð11Þ
where N is the number of data points; co is observed; cm issimulated; and co is the average saltwater content ofobserved values. A model efficiency of 1 indicates a perfectmatch, and a 0 indicates that the computed values are as goodas the average value. A negative value indicates that thevariance of the computed values is larger than that of theobservations and that the computed values are no better thanthe average value. The model efficiency coefficient for thesteady-state experiments was 0.95. This value indicated thatthe sharp-interface model could simulate saltwater contentswith reasonable accuracy.
Although this research focused on modeling the saltwatercontents of pumped water, photographs of steady-statesaltwater wedges are also presented to further demonstratethe efficacy of the numerical model in simulating saltwaterintrusion phenomena. Two scenarios were selected for thisdemonstration. Scenario SP-4 involved pumping and injectingfreshwater from well F2 and into well F1, respectively. Thisscenario was selected among cases with good agreements onsaltwater contents. Fig. 8 depicts the photograph of thecorresponding saltwater wedge. Despite somedeviation of thesharp-interface (dashed line) from the edge of the observedsaltwater wedge, the overall agreement was reasonable, andthe edge of the saltwater wedge was sharp. However, the colorof the sand prohibited visualization of water with low saltconcentrations.
Scenario SF-2 involved freshwater and saltwater pumpingfrom wells F3 and S1, respectively. This scenario representedthe case for which the difference between the computed andmeasured saltwater contents was largest (SF-2 in Fig. 7).Fig. 9 shows the corresponding photograph. The toe locationswere in reasonable agreement, but the numerical modeloverestimated the thickness of the saltwater zone betweenwells F3 and S1.
The reliability of model predictions varied from scenario toscenario. Sources of error included model or experimental error.Model error might have stemmed from the sharp-interface andthehorizontal-flowassumptions. Theother sourceofmodel error
Fig. 8. Comparison of computed interface (dashed line) and observedsaltwater wedge (darker-shade portion) for scenario SP-4 in Tank B.
might have been the representation of the porous media. The“casing” above a screened section of a physical well isimpervious; therefore, flow is blocked by the casing. Thisblocking, however, was not represented in the verticallyintegrated numerical model. The error might not have beennegligible for Tank B, which had a width of only 8 cm. However,this assumption may not cause problems for field-scale simula-tions in which computational well blocks are generally muchlarger than wells. Potential sources of experimental errorincluded variations in pumping and injection rates, changes insalinity of source saltwater, andfluctuations ofwater levels in thereservoirs.
Overall, the numerical model overestimated salinity bymore than 2% in two cases and underestimated it by less than2% in three cases. The model overestimated salinity by 1% infive cases and underestimated it by 1% in four cases. Becausethe numbers of over- and underestimations were similar,differences were mainly attributed to experimental errorrather than model error, which would cause more consistentdeviation.
5. Conclusions
In this research, the applicability of a numerical sharp-interface model, with a simple pumping well algorithm forestimating steady-state saltwater contents of pumped watersubject to saltwater intrusion was demonstrated. A series ofexperiments were conducted using sand tanks, and numericalresults were compared against laboratory data. Test scenariosincluded various combinations of freshwater pumping, fresh-water injection, and saltwater pumping. The steady-statesaltwater contents ofwater extracted from freshwater pumpingwells ranged from 0 to 25%. The contents from saltwaterpumping wells ranged from 38 to 100%. The Nash–Sutcliffemodel efficiency for the numerical results was 0.95, indicatinggood overall agreement between simulated and observedsaltwater contents.
Sharp-interface models are generally accepted for regionalflow problemswhere transition zones can be neglected. Three-dimensional, density-dependent flow and transport modelsrequire extensive preparation of input data and lengthycomputation time, which may be impracticable for coastalgroundwater planning. Conversely, sharp-interface modelsrequire less input data and computation time. This studydemonstrated that a sharp-interfacemodelmight be applicable
42 L. Shi et al. / Journal of Contaminant Hydrology 124 (2011) 35–42
to well-scale flow problems. The extended applicability of asharp-interface model may also benefit optimization-simula-tion approaches for groundwater management schemes incoastal areas. The ability to model and predict saltwatercontents in pumping wells aids the optimization process todistinguish among poorly performing wells and to indentifydirections in which the objective function values improve.
The results from this study were based on experiments inwhich freshwater–saltwater transition zones were abrupt. Forproblems with dispersed transition zones, the applicability ofthe proposed approach must be investigated. Further, typicalfield problems involve much larger grids than those found inwells. In these cases, both numerical and analytical methodsmay be needed.
Acknowledgments
This research was supported by a grant (Code# 3-3-3)from Sustainable Water Resources Research Center of 21stCentury Frontier Research Program. The authors would like tothank Dr. Weixing Guo, anonymous reviewers and the editorfor their valuable comments.
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