Environ Earth Sci DOI 10.1007/s12665-014-3996-9

ORIGINAL ARTICLE

Assessment of sharp-interface approach for saltwater intrusion prediction in an unconfined coastal aquifer exposed to pumping S. Sadjad Mehdizadeh • Freydoon Vafaie Hosein Abolghasemi

•

Received: 28 June 2014 / Accepted: 22 December 2014 Ó Springer-Verlag Berlin Heidelberg 2015

Abstract Water over-exploitation becomes a common problem in coastal aquifers as it disarranges the dynamic equilibrium of saltwater and freshwater and causes saltwater intrusion (SWI). Mathematical simulations become a necessary tool nowadays to predict SWI under future pumping scenarios. This study aims to assess the validity of sharp-interface approach for an unconfined coastal aquifer subjected to pumping by comparison with sand-tank observation and dispersive approach results. The comparison was in terms of (1) transient movement of saltwater toward the well screen and (2) prediction of well salinity in times. The sharp-interface approach produced acceptable results, although it over-predicted the toe position of saltwater wedge. Salinity of extracted water was less predicted by sharp-interface modeling. The sharp-interface approach was then applied for a synthetic field-scale unconfined aquifer in steady condition with different pumping rates and well placements to explore the sensitivity of the modeling. The results were compared with salinity contours of dispersive modeling. The sharp-interface approach produced better result for higher pumping rates where the saltwater was reached to the well screen. Additionally, the results of fully penetrating wells (compare to partially penetrating one) and also closer location of well to

S. S. Mehdizadeh (&)  F. Vafaie  H. Abolghasemi Civil Engineering Faculty, K.N. Toosi University of Technology, No. 1346, Vali Asr Street, Mirdamad Intersection, P.O. Box 15875-4416, Tehran, Iran e-mail: [email protected]; [email protected] F. Vafaie e-mail: [email protected] H. Abolghasemi e-mail: [email protected]

shoreline matched better with the dispersive modeling outputs. In real cases, where the saltwater may wend a long distance toward the well screen, the sharp-interface modeling weakly matched with the dispersive modeling specially in terms of well salinities that is attributed to wider mixing zone. Keywords Sharp-interface approach  Dispersive approach  Pumping rate  Saltwater intrusion  Sand-tank experiment

Introduction In many parts of the world, coastal aquifers constitute an important source of water supply. Any changes in coastal hydrology result in movement of saltwater–freshwater interface toward the land (Watson et al. 2010) commonly named as saltwater intrusion (SWI) problem. Pumping from aquifers along with lack of adequate freshwater surface recharge have increased stresses on aquifers, especially in arid areas (Osman and Abdullah 2013). As the small quantity of groundwater salinization makes freshwater unsuitable for use, investigation on SWI problem regarding the effect of water extraction in coastal aquifers has become a common issue in recent years (Werner et al. 2009). Controlling or predicting SWI under future climatic or anthropogenic scenarios requires mathematical tools. The application of these tools initiated by simple Ghyben– Herzberg equation to predict freshwater–saltwater interface (Feseker 2007) and then followed by analytical solutions that were basically associated with simple hypothetical assumptions (e.g., Bear and Dagan 1964; Strack 1976; Motz 1992; Cheng et al. 2000; Mantoglou 2003; Park et al. 2009; Werner et al. 2012). Depending on the representation

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of freshwater–saltwater interface, numerical simulations are based on dispersive or sharp-interface approaches. The dispersive approach accounts for the effects of hydrodynamic dispersion and is more accurate as it provides more details concerning the mixing zone (Abd-Elhamid and Javadi 2011). Alternatively, the sharp-interface approach assumes immiscibility of freshwater and saltwater and separates them by a sharp interface. Although the dispersive modeling has become the most rigorous approach nowadays, but because of the scarcity of available data and lack of reliable estimates of involved parameters (LlopisAlbert and Pulido-Velazquez 2014), sharp-interface approach is more practical for its simplicity. The sharpinterface approach is especially useful for large-scale problems (Shi et al. 2011) and it can successfully be applied for cases where the transition zone is thin relative to the depth of aquifer (Bear 1979). The sharp-interface approach has been applied previously to predict SWI for homogeneous and layered aquifers successfully. Sa da Costa and Wilson (1979) developed a finite element model for single layer, while Essaid (1990) and Huyakorn et al. (1996) used this approach for layered coastal aquifers. Sakr (1999) examined the applicability of sharp-interface approach against dispersive model for confined aquifer in terms of dimensionless parameters including geometry and dispersivity. He concluded that the steady-state sharp-interface prediction is valid only when the system is dominated by advection and the applicability of the sharp-interface approach is sufficiently accurate at early times in transient simulation. Mantoglou et al. (2004) used the steady sharp-interface approach to maximize the pumping rates while protecting the wells from SWI and then Mantoglou and Papantoniou (2008) investigated further about optimum pumping rates by means of both sharpinterface modeling and genetic algorithm. Shi et al. (2011) validated the steady-state salinities of pumped water with the results of sand-tank experiments in a homogeneous aquifer and Llopis-Albert and Pulido-Velazquez (2014) assessed the application of sharp-interface approach compared to dispersive modeling for fully penetrating wells in an unconfined aquifer for large domain of involved parameters. They have found that the applicability of the sharp-interface approach strongly depends on well placement and hydrodynamic coefficient. In term of toe position, they showed that higher values of layer thickness and longitudinal dispersion coefficients led to better approximation compared to dispersive modeling approach. Moreover, lower surface recharge, transmissivity and distance of the wells to shoreline also led to better results in their study. They mostly focused on steady cases and defined a critical pumping rate (i.e., the maximum permissible discharge without salinizing the well) as a threshold, thus salinities of pumped water have not been addressed in their study.

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Recently, the investigation of SWI problem has progressed using physical models. These models help us to observe the intrusion mechanism at controlled laboratory conditions and also provide the reliable data to verify the solutions. Experimental models have been developed previously focusing on other aspect of SWI rather than pumping effect (e.g., Zhang et al. 2002; Simmons et al. 2002; Goswami and Clement 2007; Luyun et al. 2009; Abdollahi-Nasab et al. 2010) and less attention is considered for future over-exploitation effect. Werner et al. (2009) conducted a two-dimensional upcoming experiments with different pumping rates and saltwater salinities and compared the observation data with the analytical equation proposed by Dagan and Bear (1968). Jakovovic et al. (2011) afterward simulated those experiments by dispersive model and showed the reasonable accuracy of SWI prediction by the modeling. Shi et al. (2011) placed multiple pumping/injection wells into two tanks with different sizes and assessed the well salinities predicted by sharp-interface modeling with the measured salinities at the experiments and gained comparable results. Literature studies demonstrate that the unsteady simulation of SWI processes due to pumping by sharp-interface approach has received less attention and the validity of sharp-interface approach has not been examined previously with laboratory results. The application of sharp-interface approach for different pumping scenarios also needs more investigation with regard to salt wedge shape and well salinities. Thus in this study, to complete the previous researches about the applicability of sharp-interface approach, the results of numerical sharp-interface approach are firstly assessed with the laboratory observation and dispersive modeling results in terms of salt wedge shape and well salinities and then the model is applied for a hypothetical field-scale unconfined coastal aquifer to explore the sensitivity of the model to different scenarios including different pumping rates and longitudinal or altitudinal position of well placements.

Materials and methods Experimental setup The experimental setup is adopted from the experiments conducted by Mehdizadeh et al. (2014) who used the same sand tank. The sand-tank internal dimensions were 1170 mm length, 600 mm height and 52 mm width. Twelve plastic inflow and outflow taps have been installed at 50 mm intervals on both lateral sides and a fine metal mesh was inserted in each taps to avoid sand clogging. A PVC tube with internal diameter of 10 mm was selected and was modified to have a short screened section with the length of 25 mm at 20 mm above the bottom of tube. The

Environ Earth Sci Fig. 1 Schematic diagram of the experimental setup, modified from Mehdizadeh et al. (2014)

slotted interval was wrapped with geotextile and the opening at the bottom was plugged to prevent sand clogging. The bottom of the well was then placed at 150 mm above from base of the tank and 300 mm far from saltwater boundary (Fig. 1). Water was supplied from constant head reservoirs (6 9 20 L Mariotte bottles as freshwater reservoirs and 2 9 20 L Mariotte bottle as saltwater reservoirs). A silastic tube with 2.79 mm internal diameter was placed into the well and connected to peristaltic pump (Masterflex, 8 roller, L/S type, 07519-25 pump head with small cartridge, 07519-85 type) to extract water at desired flow rate. The porous media was sand (i.e., ‘16–30’ grade sand, Sloan Sands P/L, Dry Creek, South Australia) that was placed in tank with layer thickness of 530 mm. A wetpacking method similar to that described by Ataie-Ashtiani (1998) was used to obtain uniform sand packing with minimum entrapped air and consolidation. Saltwater solution was produced by dissolving 35 g of calcium chloride dehydrate (CaCl2 2H2O) in 1 L of tap water. Rhodamine WT type (fluorescent FWT Red dye, ENVCO, Australia) with concentration of 500 mg/L was dissolved with salt to trace the saltwater in the tank and monitor the wedge visually. Freshwater entered through the system via L2–L11 taps while saltwater flowed to the tank via R2–R7 taps. Mixed water was discharged from the system via R8–R11 taps. Two manometers were attached to the system in taps L1 and R1 to measure the heads in boundaries. Hydraulic gradient toward saltwater boundary was established by setting constant freshwater and saltwater head, respectively, equaled to 0.513 and 0.495 m in boundaries. The experiments were recorded by an eight mega pixel digital camera every 15 min in steady condition (i.e., before pumping) and every 5 min during transient SWI caused by pumping. The experiment was assumed under steady state after 290 min when the toe position of salt wedge remained constant in two consecutive images. The salinity and discharge of mixing outflow were measured at the end of steady experiment. After that, the peristaltic pump started

to extract water at the rate of 30 ml/min. The pumping experiment was lasted for 310 min until a new steady state was achieved. The porosity (n) was obtained 0.41 from the common water saturation method (Fetter 2001). The hydraulic conductivity (K) was estimated using the Darcy column test. The test was carried out three times and the average value of K was 270 m/d. The saturation and drainage method described by Johnson (1966) was implemented to determine the specific yield (Sy) as 0.33. For the longitudinal dispersivity (aL), the breakthrough curve of dimensionless parameter C/C0 versus time was fitted to the onedimensional analytical solution of Ogata and Banks (1961). The 2 mm value for aL satisfactorily fitted. The transverse dispersivity (aT) is assumed to be 1/20th of longitudinal dispersivity, following Jakovovic et al. (2011). Table 1 summarizes the experimental parameters. Sharp-interface approach development In the sharp-interface approach, freshwater and saltwater are assumed completely immiscible and a sharp interface exists between two regions. Sharp-interface approach Table 1 Parameters of laboratory experiments Parameters

Values a

Freshwater head, hf0 (m) a

0.513

Saltwater head, hs0 (m)

0.495

Freshwater density, qf (kg/m3)

1000.16

Saltwater density, qs (kg/m3)

1024.20

Saltwater concentration, C0 (kg/m3)

33.65

Extracted water, Qw (m3/s)

0.5 9 10-6

Hydraulic conductivity, K (m/d)

270

Porosity, n (-)

0.41

Specific yield, Sy (-)

0.33

Longitudinal dispersivity, aL (m)

0.002

Transverse dispersivity, aT (m)

2.0 9 10-4

a

Aquifer base is considered as datum

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couples freshwater and saltwater flows based on the continuity of flux and pressure on the interface. In this approach, the equation of continuity integrated vertically while the Dupuit approximation and Darcy’s law are valid. Equations for freshwater and saltwater are given, respectively, in the following equations (Gemitzi and Tolikas 2007):     o ohf o ohf ohf bf Kfx bf Kfy þ ¼ bf Ssf ox oy ox oy ot ð1Þ ohf oZ  Qf n þ ng ot ot     o ohs o ohs ohs oZ bs Ksx bs Ksy  Qs þn þ ¼ bs Sss ox oy ot ox oy ot ð2Þ where Kfx and Ksx are, respectively, hydraulic conductivities of freshwater and saltwater in X direction [LT-1]; Kfy and Ksy are, respectively, hydraulic conductivities of freshwater and saltwater in Y direction [LT-1]; (K values assumed to be the same for simplicity); X is direction perpendicular to coastline and Y is along it (Fig. 2); hf and hs are, respectively, the freshwater and saltwater heads and bf and bs refer to their thicknesses [L]; Qf and Qs are, respectively, freshwater and saltwater fluxes as sources or sinks (e.g., surface recharge or pumping) [LT-1]; g is a dimensionless parameter with the value equals to 1 for an unconfined and 0 for a confined aquifer; Ssf and Sss are, respectively, specific storage of the two regions [L-1] (in unconfined condition bf Ssf will be modified by bf Ssf ? Sy in freshwater equation); and Z is the elevation of the interface above the arbitrary datum [L] (see Fig. 2). Z is given by Eq. (3), and the freshwater and saltwater thicknesses can be determined through Eqs. (4, 5). Z ¼ ð1 þ dÞhs  dhf

ð3Þ

bf ¼ ZT  Z

ð4Þ

bs ¼ Z  Z B

ð5Þ

where d = qf/(qs - qf); qf and qs are, respectively, freshwater and saltwater densities [ML-3]; ZB and ZT are, respectively, the elevations of bottom and top of the aquifer [L] (hf replaces ZT in unconfined conditions). Equations (1) and (2) are non-linear partial differential equations that are solved simultaneously for freshwater and saltwater heads. Z must be replaced in terms of hf and hs in Eqs. (1) and (2) according to Eq. (3). Once the first two main equations are solved, the interface elevation can be obtained from Eq. (3). The solution scheme in this study involves a cell-centered finite-volume formulation. A central-difference scheme is used to resolve the spatial gradient of heads with uniform rectangular grid of Dx = 1 cm for the experiment. An explicit scheme is implemented for the discretization of time in transient modeling with Dt = 1 min. An appropriate under-relaxation factor of 0.5 is considered. Head differences between two consecutive iterations are used to assess as a convergence criterion with the value of 0.01 cm. Constant head values of hf0 and hs0 are adopted at the landside and seaside boundaries, respectively. The analytical solution of freshwater discharge derived by Bear and Dagan (1964) is used for the freshwater boundary at seaside. No-flow boundary conditions are assigned to the bottom of the aquifer and the aquifer top boundary condition is the water table elevation. Qw is divided into two separate freshwater and saltwater extracted rates (i.e., Qw = Qfw ? Qsw) in a similar manner described by Shi et al. (2011). They assumed that each extracted water type is determined linearly on the basis of the proportion of screen penetrating the freshwater and saltwater zones relative to the total open interval of the well. To verify the model, it was compared to existing steadystate analytical solutions (e.g., Glover 1959; Strack 1976) and to the experimental data provided by Goswami and Clement (2007) for transient case. In all cases, the interface predictions are in good agreement with both analytical solutions and experimental observations with maximum 28 % over-prediction in the toe position of transient simulation at later times. Density-dependent approach development

Fig. 2 Interface and other related elevation in a specific vertical direction

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In this approach, freshwater and saltwater are assumed to be in a dynamic equilibrium resulting from advection and dispersion of solute within the aquifer. The equation of flow and solute transport is solved simultaneously and the heads and salt concentration distribution in the aquifer derived from the simulation. The present study used the finite-difference model SEAWAT developed by Guo and Langevin (2002) to simulate three-dimensional, variable

Environ Earth Sci Table 2 Additional parameters and settings for SEAWAT simulation of laboratory experiments Parameters

Values

Molecular diffusion coefficient, Dm (m2/d)

8.64 9 10-5

Table 3 Parameters for large-scale aquifer modeling Parameters

Values

Freshwater inflow, Qf0 (m2/d)

0.1

hs0 (m)

30.0 1.0

Cell size, Dx 9 Dz (m)

0.005 9 0.004

K (m/d)

Solver for flow/transport simulation

PCG2/GCGa

n (-)

0.35

Advection solution scheme

Third-order TVD

1.0

Head convergence value (m)

1 910-5

aL (m) aT (m)

0.1

Advection scheme courant number

0.75

0.0

Concentration convergence value (kg/m3)

1 9 10-5

Dm (m2/d)

a

Respectively refers to pre-conditioned conjugate-gradient and generalized conjugate-gradient packages

density, transient groundwater flow in porous media. It combines the modified MODFLOW and MT3DMS into a single program that solves the coupled groundwater flow and solute transport equations. SEAWAT is widely used and is not explained in detail here for brevity (SEAWAT version 4 manual is provided by Langevin et al. 2008). Parameters of laboratory experiments (Table 1) were used in the simulation, with additional parameters listed in Table 2. Simulation in SEAWAT was achieved by setting flow time steps to 30 s and transport step sizes to 3 s. The appropriate grid size is selected by maintaining the Peclet number (Pe) criterion less than 4 (Voss and Souza 1987). The uniform grid size (Table 2) produced Pe = 2.5. Two stress periods were defined in the model. The model was first run for 600 min to reach steady condition in the first stress period by adopting constant heads at the sea and land boundaries, and then the pumping commenced at determined location and the model ran for 400 min to reach to new steady condition. Well screen zone was simulated using high K of 2880 m/d by selecting 1.5 cm (including 3 cells) in length and 2.8 cm (including 7 cells) in height at the well location. Models implementation for field-scale aquifer The hypothetical conceptual unconfined aquifer with the length of 500 m and the height of 30 m was selected with the homogeneous porous media and vertical face at seaside. Reasonable properties are considered and summarized in Table 3. Eleven steady scenarios including different pumping rates and different well screen locations are assumed according to Table 4. For all simulations, the constant freshwater flux at land boundary was considered and the other boundary types remained the same as in the experiment. The screen height is considered 1.0 m in the sharp-interface approach. The screen length in SEAWAT is provided by assigning the pumping rate for two cells. It

qf (kg/m3)

1000.0

qs (kg/m3)

1025.0

C0 (kg/m3)

35.0

SEAWAT mesh size (m) Sharp-interface mesh size (m)

2.0 9 0.5 (Dx 9 Dz) 2.0 (Dx)

Table 4 Different scenarios for sharp-interface evaluation, Xw represents well distance from seaside and Zw shows well bottom elevation from aquifer base Scenario Id

Qw (m3/d)

Xw (m)

Zw (m)

Sc-1

0.1

150

15

Sc-2

0.05

150

15

Sc-3 Sc-4

0.07 0.15

150 150

15 15

Sc-5

0.1

150

0

Sc-6

0.1

150

25

Sc-7

0.1

200

15

Sc-8

0.1

300

15

Sc-9

0.1

100

15

Sc-10

0.07

150

0

Sc-11

0.07

150

25

is important to note that a two-dimensional tank-scale and field-scale aquifer is considered in this study for time efficiency of the simulations. Pumping from aquifer is a radial flow problem and hence a pumping well can only be properly considered in an aerial two-dimensional model or a fully three-dimensional model. The objective of this study is not to predict the position of saltwater wedge for a specific real system; rather it is to develop a conceptual field-scale aquifer to assess the applicability of sharp-interface modeling. Therefore, all the two-dimensional scenarios defined here are not a true scenarios but as both sharp-interface and dispersive approaches used the same geometry and properties, the results are reliable for only comparison. Pumping wells in two-dimension cross section could only be similar to a line of wells running parallel to the coastline and there are not situations involving two-dimensional cross-section problem in real world.

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Results and discussions Evaluation of the experiment Experimental data are first verified by dispersive modeling result in terms of transient salt wedge shape and well salinities. Figure 3 demonstrates the laboratory observation with SEAWAT 5 and 95 % salinity contours. Salt wedge shape was well produced in the laboratory, although a small difference is observed that could be attributed to ideal dispersive simulation such as: (1) the soil texture assumed to be completely homogeneous in the model but a little heterogeneity is unavoidable during packing method, (2) A slight fluctuation has been observed at peristaltic pump extracted rate in the experiment while a constant Qw is applied in the model and (3) Continuous heads had been applied in the dispersive model due to consistent condition with sharp-interface approach, while point inflows occurred in the experiment. The comparison also shows that the mixing zone in dispersive model was thicker at initial times

when the toe position moves slowly toward the land but gradually become narrower as the salt wedge reaches to the well screen and new steady state is going to be established. Well salinity (Cw) in the model and in the experiment is presented in Fig. 4. Extracted water was sampled at specified times and Cw is obtained by the electrical conductivity (EC) conversion relation proposed by Fofonoff and Millard (1983). The dispersive results are reasonable, although the salinities in the experiment are less obtained than the dispersive model prediction. Evaluation of tank-scale sharp-interface modeling The freshwater–saltwater interface in the sharp-interface modeling is shown in Fig. 5. SEAWAT 50 % salinity contour is also provided for comparison. As the figure exhibits, the sharp-interface approach produced logical and comparable predictions, although in terms of toe position, it over-predicted the interface with maximum error of 11.1 % in the new steady-state after pumping (i.e., Fig. 5e

Fig. 3 Images of laboratory observation and salinity contours of dispersive model. a Steady state before pumping, b, c, d and e, respectively, 30, 60, 120 and 270 min after pumping

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Cw (kg/m3)

6.0

distance. This non-overlapping is more apparent as the salt wedge approaches to the well screen. Basically, well salinities cannot be compared with SEAWAT due to sharp-interface incapability to produce Cw. Shi et al. (2011) introduced salt content (c) as the ratio of Qsw and Qw according to Eq. (6):

4.0

SEAWAT Experiment

2.0

c¼ 0.0

0

50

100

150

200

250

300

Fig. 4 Transient salinities in SEAWAT and in the experiment

and regardless of the steady result before pumping). It is also observed that the coning shape of salt wedge close to well screen is not well simulated by the sharp-interface approach. That is because at each distance, the sharp interface can produce only one interface elevation while the aquifer height is discrete at dispersive model by introducing Dz and thus it can readily have ranges of values (including concentrations and hydraulic heads) at any

Sharp-interface SEAWAT Experiment

0.5

0.4

0.3 0.2 0.1 0

Sharp-interface SEAWAT Experiment

0.5

(a) z (m)

z (m)

0.4

ð6Þ

where ECf is the EC of freshwater, EC0 is the EC of sea (i.e., in the reservoirs) and ECm is the EC of extracted water. In the present experiment, ECf measured to be 476 ls/cm and ECm obtained to be 39.9 ms/cm at laboratory temperature of 16 °C (room temperature reached to 17 °C at the end of transient experiment). Salt content derived in the sharp-interface model by the above equation is presented in Fig. 6. Under the condition that has been defined in this study, it is found that the sharp-interface model estimated the salinities of the extracted water less than that in the experiment. Time delay was also observed in the sharp-interface model. The total simulation time showed that it took longer in the sharp-

Time (min)

0.3

0.1 0.0

0.2

0.5

0.4

0.6

0.8

0

1.0

0.0

0.2

0.4

0.4

0.2

0.1

0.1 0.4

0.6

0.8

0

1.0

0.0

0.2

0.4

x (m)

(d)

0.6

0.8

1.0

x (m) 0.5

Sharp-interface SEAWAT Experiment

0.4

z (m)

0.2

1.0

0.3

0.2

0.0

0.8

Sharp-interface SEAWAT Experiment

0.5

(c) z (m)

0.3

0.6

x (m)

Sharp-interface SEAWAT Experiment

0.4

0

(b)

0.2

x (m)

z (m)

Fig. 5 Comparison of salt wedge shape in different times, a steady state before pumping, b, c, d and e transient simulation, respectively, 30, 60, 120 and 270 after pumping

Qsw ECm  ECf  Qw EC0

0.3

(e)

0.2 0.1 0

0.0

0.2

0.4

0.6

0.8

1.0

x (m)

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c (%)

well locations. All the results are compared with the 50 % salinity contour derived from SEAWAT model.

Sharp-interface Experiment SEAWAT

Pumping rates

10 5 0

0

50

100

150

200

250

300

Time (min)

Fig. 6 Comparison of salinities in the experiment with sharpinterface and dispersive model estimation

interface model to reach the new steady state (approximately 70 min after the time that the experiment is reached). In comparison with the experiments conducted by Shi et al. (2011) with multi-extraction/injection wells, it is found that they manipulated the sand tank with the pumping rate noticeably less than that in the present study while injection was also applied in some tests. This slow saltwater motion toward the well screens in their study led to longer time and may cause to better results. Steady SWI prediction for field-scale unconfined aquifer

Well location in height

The assessment of sharp-interface approach is continued for the field-scale aquifer. Field-scale simulations are implemented to first verify that the proximate predictions of SWI which were achieved at the laboratory are not caused by the small scale of the sand tank. Second, we aim to explore the sensitivity of the sharp-interface modeling to different scenarios including different pumping rates and

30

Well screen is placed in top, middle and bottom of the aquifer to analyze the sensitivity of sharp interface for full penetrating or partially penetrating wells. Two different pumping rates are also considered here. As Fig. 8 shows, the sharp-interface approach acts better in fully penetrating wells and when gradually the well screen location moves vertically to the top of the aquifer there will be more differences. It is noteworthy to observe that in case of lower 30

Sharp-interface SEAWAT

20

Sharp-interface SEAWAT

(a) z (m)

10

0

10

0

100

200

300

400

0

500

0

100

200

x (m)

300

400

500

x (m)

30

30

Sharp-interface SEAWAT

(c)

Sharp-interface SEAWAT 20

(d)

z (m)

z (m)

20

10

0

10

0

100

200

300

x (m)

123

(b)

20

z (m)

Fig. 7 Comparison of sharp interface and 50 % salinity contour from dispersive modeling for different pumping rates, a Sc-1, b Sc-2, c Sc-3 and d Sc-4. The dotted lines indicate 5 and 95 % salinity contours from SEAWAT and the solid rectangular shows well screen location

Assessment of sharp-interface modeling for different pumping rates is presented in Fig. 7. As it is seen, the sharp-interface approach generally over-predicts the SWI. The comparisons demonstrate that better agreement is achieved for the higher pumping rates where the saltwater salinized the well screen in dispersive model, although the sharp-interface approach did not well produce the salt wedge shape near the seaside for the maximum considered pumping rate (i.e., for Sc-4 in Fig. 7d). The freshwater boundary at seaside always allows freshwater to be discharged through the fine opening in sharp-interface approach, thus in cases that high pumping rate makes water table salinization the results show more differences with SEAWAT. It is noticed that the low pumping rate led to slower movement of saltwater toward the well and consequently it widened the mixing zone. The wider mixing zone increases the discrepancy between the 50 % salinity contours and the sharp interfaces.

400

500

0

0

100

200

300

x (m)

400

500

Environ Earth Sci 30

Sharp-interface SEAWAT

z (m)

20

(Sc-5)

(Sc-6)

(Sc-1)

10 0 0

200

0

400

200

x (m) 30

400

0

200

(Sc-11)

(Sc-10)

(Sc-3)

400

x (m)

x (m)

z (m)

20 10 0

0

200

400

0

200

x (m)

400

0

200

x (m)

400

x (m)

Fig. 8 Representation of sharp-interface and dispersive modeling results (50 % salinity contour) for different well locations in height, Sc-1, Sc-5 and Sc-6 for Qw = 0.1 m3/d and Sc-3, Sc-10 and Sc-11 for

Qw = 0.07 m3/d. The dotted lines indicate 5 and 95 % salinity contours from SEAWAT and the solid rectangular shows well screen location

pumping rate (i.e., Sc-3 and Sc-11), the results of both dispersive and sharp-interface models do not differ appreciably. That may means both models are not very sensitive to the location of partially penetrating well along the specified vertical direction when the pumping rate is low and hence saltwater does not reach to the well screen. Nevertheless, the mixing zone is wider when the well is moved toward top of the aquifer. This is consistent with previous researches in this regard (e.g., Llopis-Albert and Pulido-Velazquez 2014). When the critical pumping rate is defined (i.e., the maximum permissible discharge without

salinizing the well), the dispersive simulation produces wider mixing zone while narrower mixing zone is produced when well salinization occurs.

30

Four longitudinal places are selected to investigate the applicability of sharp-interface approach. As it is observed in Fig. 9, better result is obtained for the well screen position close to seaside, even though the results of simulation for three other cases (i.e., Sc-1, Sc-7 and Sc-8) are

Sharp-interface SEAWAT

(Sc-7)

z (m)

20

(Sc-1) 10

0 0

200

400

0

200

x (m)

400

x (m)

30

(Sc-9)

(Sc-8) 20

z (m)

Fig. 9 Representation of sharpinterface and dispersive modeling results (50 % salinity contour) for different longitudinal well locations. The dotted lines indicate 5 and 95 % salinity contours from SEAWAT and the solid rectangular shows well screen location

Well location in length

10

0 0

200

x (m)

400

0

200

400

x (m)

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also close to each other, indicating less sensitivity of the sharp-interface model to horizontal direction especially when saltwater reached the well screen. Again, the elongation of mixing zone in Sc-8 which is farther from seaside is observed in dispersive modeling which seems logical when the saltwater has to wend more distances to reach the well screen. The salinity of well estimated by the sharp-interface approach has also been analyzed with dispersive modeling results. Significant mismatch has been observed. Surprisingly, only Sc-4 has produced Qsw which was significantly less than that in the dispersive model. It is understood that in the large-scale aquifers where a wide mixing zone (i.e., wide concentration distribution) may potentially be produced; the estimation of well salinities by the sharp-interface method may not be accurate and reliable as it is weakly matched with the real salinity of the extracted water.

Conclusion In this research, sharp-interface modeling of SWI problem due to pumping in homogeneous unconfined costal aquifer has been evaluated. A transient experiment had been set up for this assessment and the results of modeling and experiments were compared with dispersive prediction of SWI. The experiment was performed in the sand tank with constant heads at boundaries and a desired pumping rate was applied to partially penetrating well. The comparison was in terms of salt wedge shape and well salinity. It is found that the sharp-interface approach produced the transient freshwater–saltwater interface satisfactory but it over-predicted the toe position of salt wedge compared to that in the experiment or in the dispersive model. Salinity estimation in the sharp-interface approach was provided as the ratio of extracted saltwater to total pumped water and has been compared to salinity of the well that was provided by measuring the electrical conductivity at specified times. Under the condition that has been conducted in this research, salinity was less predicted by the sharp-interface modeling and also started with delay. Further investigation may be needed for better estimation of well salinity in the sharp-interface modeling. Simulations representing an unconfined coastal aquifer at idealized real scale were then undertaken to assess the sharp-interface modeling in more details. All the results were compared with 0.5 isochlor dispersive model simulation. The comparisons showed that better agreement is achieved for the cases with the higher pumping rates, where the saltwater was reached to the well screen. Additionally, the result of fully penetrating wells and also

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closer location of wells to sea boundary matched better with the dispersive modeling results. Sharp-interface approach generally can be used as a good alternative of the dispersive modeling but with more attention in cases with a wide mixing zone, where the salt concentration varies in wider domain. Acknowledgments The experiment part of this research was completed at Flinders University, Adelaide, Australia during visiting research period of the first author. We would like to acknowledge the National Center for Groundwater Research and Training (NCGRT) team for their fund and laboratory facilities. The authors also would like to thank greatly Dr. Adrian Werner for his helps and advices.

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