Development of constant and variable density models to study

European Water 55: 53-66, 2016. © 2016 E.W. Publications

Development of constant and variable density models to study groundwater flow and seawater intrusion in the aquifer of Nea Moudania, Greece I. Siarkos* and P. Latinopoulos School of Civil Engineering, Aristotle University of Thessaloniki, GR-541 24, Thessaloniki, Greece * e-mail: [email protected]

Abstract:

Seawater intrusion threatens the groundwater resources of many coastal areas in various parts of the world leading to the limitation of their use. Moreover, it is considered as a complex phenomenon, whose full and proper study requires the implementation of sophisticated methods, such as the application of numerical modeling. In the present study, two different 3-D model categories are developed in order to study both groundwater flow and seawater intrusion in the coastal aquifer of Nea Moudania. The first category includes the development of constant density models (a single fluid of constant density is considered) by applying the MODFLOW and MT3DMS codes, while the second one consists of a variable density model (two miscible fluids of different density are considered) formed by using the SEAWAT code. The results of the two approaches (in the form of both hydraulic head and solute concentrations distributions) are presented, evaluated and compared indicating clearly the specific differences existing between them.

Key words:

Coastal aquifers, groundwater flow, seawater intrusion, numerical modeling, Greece

1. INTRODUCTION Nowadays, seawater intrusion has evolved into a major environmental problem of many coastal areas throughout the world, since it constitutes one of the main factors leading to the qualitative and hence quantitative degradation of the groundwater resources of these regions (Pool and Carrera, 2010; Siarkos et al., 2017; Todd and Mays, 2005; Werner et al., 2013). Seawater intrusion occurs when the natural balance between seawater and freshwater is disturbed and it is mainly caused due to the substantial decline of groundwater levels resulting from the intensive exploitation of groundwater resources to meet various water needs (Kopsiaftis et al., 2009; Todd and Mays, 2005; Werner et al., 2013). Seawater intrusion constitutes the subject of thorough research due to its serious consequences on the environment, ecology and economy of coastal areas and due to the fact that the groundwater resources management of these regions is inextricably linked to this problem (Datta et al., 2009; Papadopoulou, 2011; Siarkos and Latinopoulos, 2015; Werner et al., 2013). Nevertheless, it is a multifunctional phenomenon characterized by complex physical processes which render its study a complex procedure (Bear, 1999; Siarkos and Latinopoulos, 2016; Werner et al., 2013). Numerical modeling is considered to be nowadays one of the most reliable and efficient methods for studying seawater intrusion and, therefore, it is often implemented, contributing significantly to the rational management of coastal aquifer systems (Cobaner et al., 2012; Siarkos and Latinopoulos, 2016; Werner et al., 2013). To study the temporal and spatial evolution of seawater encroachment, both constant (e.g., Kasapaki et al., 2015; Rahmawati et al., 2013) and variable (e.g., Cobaner et al., 2012; Mulligan et al., 2007; Siarkos and Latinopoulos, 2016) density models have been used. Of these two approaches, variable density modeling better reflects reality, since, as it is well-known, variable density induced by salinity changes modifies velocity field and, therefore, affects the dynamics of the flow system. Nevertheless, variable density modeling is a complex procedure, introducing a

54

I. Siarkos & P. Latinopoulos

significant computational burden, particularly, in the case of large-scale heterogeneous aquifer systems (Rao et al., 2004; Sanz-Garrido and Capilla, 2015; Siarkos and Latinopoulos, 2016). To avoid these drawbacks, constant density modeling is used. However, this may affect the simulation results (i.e., hydraulic head distribution and saline plume migration) which may differ from the ones deriving from the application of variable density models. Various studies have been conducted (e.g., Al-Taliby et al., 2016; Arlai, 2007; Payne et al., 2003; Sanz-Garrido and Capilla, 2015) in order to examine these differences, as well as to investigate if and to what extent density effects play a significant role in seawater intrusion modeling. According to these studies, the differences between the results of constant and variable density models are not always quite obvious, while they significantly depend on the existing flow and transport conditions. In this perspective, the present study investigates both groundwater flow and seawater intrusion in the aquifer of Nea Moudania through the development and comparison of two different types of 3D-models in order to shed more light on differentiation between constant and variable density modeling. In the first case, the existence of a single fluid (i.e., freshwater) of constant density, not dependent on the concentration of dissolved mass, is considered. In this approach, two different simulations were conducted: a) a steady-state 3D-simulation of groundwater flow by applying the MODFLOW (Harbaugh et al., 2000; McDonald and Harbaugh, 1988) code; and b) a false transient 3D-simulation of both groundwater flow and solute transport by applying the MODFLOW and MT3DMS (Zheng and Wang, 1999) codes. In the second approach, the simulation of both groundwater flow and solute transport is performed by considering the existence of two fluids (i.e., freshwater and seawater) of different density, which are mixed together forming a transition zone. Within this zone, density values vary from the ones of freshwater to the ones of seawater, based on the concentration of the dissolved mass. In this case, a false transient 3D-model is developed by applying the SEAWAT (Guo and Langevin, 2002; Langevin et al., 2003) code. At this point, it should be noted that a false transient simulation is a transient simulation, since temporal discretization takes place, which reaches equilibrium (i.e., steady-state conditions) under specific simulation conditions (i.e., average aquifer stresses, constant boundary conditions, negligible storativity) (Ganesan and Thayumanavan, 2009; Rao et al., 2004; Zimmermann et al., 2006). As already mentioned, the main scope of the present study is the comparison of the results of the two aforementioned approaches in order to further investigate the differences between constant and variable density models. To this task, the same type of models is used for comparison, i.e., the false transient models, while the simulation conditions (i.e., initial and boundary conditions, hydraulic parameters, recharge and discharge components) remain intact during the development of the models. The only difference is that in the second approach (i.e., variable density model) the effect of solute concentrations in the fluid density is taken into consideration. The necessary input data for the aforementioned models (i.e., hydraulic parameters, recharge and discharge conditions) derive from the steady-state model through its calibration procedure. Finally, the implementation of the two different approaches is performed in the aquifer of Nea Moudania in northern Greece.

2. STUDY AREA The hydrological basin of Nea Moudania extends in the south-western part of the Halkidiki Peninsula (south-east of the city of Thessaloniki) and it is part of a wide region called “Kalamaria Plain”, which constitutes the prime agricultural area of Halkidiki. The basin occupies an area of about 127 km2, with a mean soil elevation of 211 m above mean sea level and a mean soil slope of 1.8%. It is a coastal basin, since it is bordered to the south by Thermaikos Gulf (Latinopoulos, 2003; Siarkos and Latinopoulos, 2012, 2016). Figure 1 depicts both the location and the boundaries of the Nea Moudania basin, which is divided into two sub-regions: the hilly area in the north and the flat area in the south. The climate of the study area is semi-arid to humid, typically Mediterranean, and the average annual precipitation is 417 mm for the flat area and 504 mm for the hilly one. Almost 76% of the

European Water 55 (2016)

55

study area is used as agricultural land, 20% is woodland (mostly the northern part) and the remaining 4% accounts for urban and touristic development. As it is obvious, the whole basin is a typical rural area, where agriculture dominates both the local economy and land use (Latinopoulos and Siarkos, 2014; Latinopoulos, 2003; Siarkos and Latinopoulos, 2016).

Figure 1. Map and location of Nea Moudania basin

With regard to the geology and hydrogeology of the study area, the larger part of the region is located within the Peonia geologic zone (except for the north-eastern part) and more specifically within the Moudania geologic formation. This formation is part of the Neogene sediments which are located in Western Halkidiki and consist mainly of alternated beds of sandstones, conglomerates, sands, silts, and red to brick red clays. These sediments compose the main aquifer system of the study area in the form of successive water-bearing layers without regular geometric growth, separated by lenses of semi-permeable or impermeable materials. The aforementioned aquifer system, which is considered to be a semi-confined/phreatic aquifer, is exclusively used and therefore intensively exploited. Due to this fact, both decline of groundwater levels and seawater intrusion are observed in the study area (Latinopoulos, 2003; Siarkos and Latinopoulos, 2016).

3. MODEL DEVELOPMENT PROCEDURE 3.1 Conceptual model development In the following sub-sections, a brief, yet all-inclusive description of the main components of the conceptual model of Nea Moudania aquifer (i.e., aquifer geometry and boundary conditions, hydraulic-hydrodynamic parameters, recharge and discharge conditions) is provided. An in-depth description is presented in Siarkos and Latinopoulos (2016). All required data are derived from previous research conducted in the study area (Latinopoulos, 2003).

56

I. Siarkos & P. Latinopoulos

3.1.1 Aquifer geometry Τhe outer boundaries of the aquifer system match the boundaries of the Nea Moudania basin, apart from the north-eastern part, where rock formations are located. In order to define the aquifer’s boundary in this part (i.e., the northern boundary) the hydraulic conditions existing in the study area were taken into consideration. More specifically, the piezometric contour of 150 m was used, which refers to the year 2001 and was obtained by applying the Kriging method (Figure 2) (Latinopoulos, 2003). With regard to the aquifer thickness, it is assumed that the various successive permeable layers form a single, unified system with a uniform thickness of 250 m, based on the information derived from various well logs and cross sections.

Figure 2. Flow boundary conditions (CHB – Constant Head Boundary, GHB – General Head Boundary, No flow – No flow boundaries), the six distinct zones of the study area, and the distribution of pumping wells

3.1.2 Boundary conditions As far as the flow problem is concerned, no-flow boundaries were assigned at the eastern and western sides of the model, since no hydraulic connection is observed between the aquifer and the neighboring regions and the flow lines are parallel to these boundaries according to the regional flow regime in the study area (Latinopoulos, 2003). The southern boundary was simulated as a constant head boundary (CHB, h=0 m), since in this section there is a direct hydraulic connection between groundwater and seawater. Finally, the northern boundary was simulated as a general head boundary (GHB, h=150 m) (Figure 2). Regarding this type of boundary (GHB), the determination

European Water 55 (2016)

57

of conductance is required, which was accomplished during the calibration process of the steadystate model. As far as the transport problem is concerned, the southern boundary is the most important since it is in hydraulic connection with the sea. This boundary was simulated as a constant concentration boundary (CCB), where concentration was set equal to 19,000 mg/L, since chloride ions are used as a tracer for the characterization of groundwater salinization. With regard to the remaining boundaries either no water inflow is observed and no dissolved mass as well (eastern and western boundaries) or the chloride concentrations are particularly low (northern boundary). 3.1.3 Hydraulic-hydrodynamic parameters Regarding the wider research area, hydraulic conductivity values along the horizontal directions (Kx, Ky) range between 0.086 and 1.730 m/d (Latinopoulos, 2003). Data deriving from six pumping tests in individual wells allow the division of the study area into six distinct zones (Figure 2); each of them was assigned a different value according to the pumping tests results (0.125 – 0.240 m/d). These values were then properly adjusted through the calibration procedure of the steady-state model. In the Z direction, the conductivity values were assumed to be one-tenth of the aforementioned values (Kz = 1/10Kx) (Mulligan et al., 2007; Rao et al., 2007). For the transport parameters, i.e., effective porosity, dispersivity and molecular diffusion, there are no available data, and therefore, their quantification was based on the results of Kasapaki et al. (2014), who investigated seawater intrusion in the study area by developing constant density models. Thus, effective porosity was assigned a value of 0.14, while longitudinal dispersivity was set equal to 100 m. These values refer to the whole region. Moreover, the ratio of transversal to longitudinal dispersivity was considered equal to 0.1, while the ratio of vertical to longitudinal dispersivity was taken equal to 0.01 (αT = αL/10, αz = αL/100) (Cobaner et al., 2012; Giambastiani et al., 2007; Mahmoodzadeh et al., 2014). Commonly, transverse dispersivity is 1/5-1/10th of horizontal longitudinal dispersivity and vertical transverse dispersivity is 1/50-1/100th of horizontal longitudinal dispersivity (Marsily, 1986). Finally, molecular diffusion was considered to be negligible. 3.1.4 Recharge conditions The aquifer of Nea Moudania is mainly recharged by rainwater and, to a lesser degree, by irrigation return flows and losses from both water supply and wastewater networks. In the first case, the estimation of the amount of water that infiltrates into the ground was accomplished by subtracting from rainfall the surface runoff and evapotranspiration losses, while taking into consideration the division of the basin into two sub-regions (the hilly and the flat one), as well as the distinction between different types of land use (the agricultural and the urban ones). With regard to the other two parameters (i.e., irrigation return flows and water supply/wastewater network leakage), it was assumed that 15% of irrigation water and approximately 50% of the water consumed for domestic use returns to the aquifer (Latinopoulos, 2003). Furthermore, water entering the system from both the northern and southern boundaries contributes to the aquifer recharge, whose exact amount is estimated through the simulation of groundwater flow, and more specifically, through the calculation of the aquifer's flow budget (see section “Comparison of model results”). 3.1.5 Discharge conditions The groundwater resources of the study area are exploited in order to meet irrigation, domestic and livestock needs. For this reason, a large number of private and municipal wells operate in the

58

I. Siarkos & P. Latinopoulos

study area. More specifically, there are 518 wells in total (referring to the year 2001), 479 of which are private irrigation wells, while the remaining 39 wells are water supply wells which are also used for livestock services. The pumping rates of the aforementioned wells were defined based on the amount of water abstracted for each use, taking also into account the division of the study area into various districts with different annual water consumption and different number of operating wells. In this way, the average pumping rate per well was determined for each district and for each water use. 3.2 Constant density model development In this first approach, two different simulations were conducted: a) a steady-state simulation of groundwater flow by applying the MODFLOW code; and b) a false transient simulation of both groundwater flow and solute transport (i.e., chloride ions) by applying the MODFLOW and MT3DMS codes. The main purpose of the steady-state simulation is to form a generic image about aquifer’s behavior, as well as to properly adjust specific aquifer parameters (i.e., hydraulic conductivity, conductance) through the model calibration procedure. The values of the adjusted parameters are used in other simulations as well. The false transient simulation is considered essential due to the fact that the SEAWAT code, which is used for the development of the densitydependent model (see section ‘Variable density model development’), cannot be applied under steady-state flow conditions. Therefore, in order to compare the results between constant and variable density models, a transient simulation had to be carried out. False transient simulation was selected due to the lack of data and in order to simplify the problem. In order to solve the aforementioned mathematical problems the same spatial discretization was used. More specifically, a regularly spaced, two-layer model grid was formed with equal-sized cells in order to minimize the effects of numerical problems observed in solute transport models (Langevin, 2003). Its construction was based entirely on the transport problem, thus considering the Peclet number (Pe) as the main criterion in order to avoid numerical dispersion and oscillation errors (Oude Essink, 2003; Voss and Souza, 1987; Werner and Gallagher, 2006). As a result, and in order to meet the prerequisite condition regarding the finite-difference method, i.e., Pe ≤ 2 (Oude Essink, 2003; Rao et al., 2004), each grid cell was formed with a 100-m side in the horizontal plane, resulting in a Peclet number equal to 1. In the Z-direction, as it was previously mentioned, the grid consisted of two layers of equal thickness, thus resulting in cells with 125-m side in the vertical direction. Building a two-layer model grid was based on the fact that problems arising due to the substantial decline of hydraulic head in the study area (i.e., appearance of “dry” cells) have to be avoided (Werner and Gallagher, 2006). As far as the steady-state model is concerned, all the necessary aquifer parameters (i.e., hydraulic parameters, boundary conditions, recharge and discharge components) were introduced into the model in order to meet the prerequisite conditions (i.e., steady-state conditions). Namely, boundary conditions remained constant, while recharge and discharge components were calculated at an annual base. The model calibration was performed in two steps. At first, an initial estimation regarding the adjusted parameters (i.e., hydraulic conductivity, conductance) was achieved by applying the trial-and-error methodology. The values resulting from the aforementioned procedure were then optimized through the application of the automated inverse model calibration tool PEST (Doherty, 2002). To this task, 17 observation wells, monitored during November 2001, were used (Latinopoulos, 2003). The accuracy of the simulation was tested by calculating the mean error (ME), the mean absolute error (MAE) and the root mean square error (RMSE). The ME was found equal to 0.088 m, indicating that, on average, the simulated groundwater levels were slightly higher than the observed groundwater levels. The MAE and RMSE estimates were found equal to 1.193 m and 1.418 m respectively, signifying a rather successful calibration, and therefore, a satisfactory simulation. Figure 3 shows the results of the steady-state model calibration in a scattergram of observed versus

European Water 55 (2016)

59

simulated groundwater levels. Through the calibration of the steady-state model, both hydraulic conductivity and conductance were adjusted and determined. More specifically, hydraulic conductivity in the six distinct zones of the study area (Figure 2) ranged between 0.116 and 0.669 m/day (maximum values are observed in coastal zones), while conductance was found equal to 65 m2/day.

Figure 3. Scattergram of observed versus simulated groundwater levels for the steady-state simulation

With respect to the false transient model, the flow model was initially developed maintaining exactly the same conditions as the previous steady-state model (i.e., boundary conditions, recharge and discharge components), taking into account the adjusted values of hydraulic conductivity and conductance and, finally, defining the time step of the simulation. In order to avoid long computational times, yet trying not to reduce the accuracy of the model results, a time step of 50 days was selected. Then, the solute transport model was formed on the basis of the information provided in the section “Conceptual model development” and the aforementioned temporal discretization. Furthermore, it was considered that the intrusion of seawater wedge commences at the beginning of the simulation, and, therefore, freshwater conditions were assumed everywhere as initial conditions for the transport problem. The false transient model was run for 50 years, a time period sufficient enough to study the evolution of seawater encroachment. The results of this model are compared with the ones deriving from the variable density model described in the following. 3.3 Variable density model development In this second approach, a false transient simulation of both groundwater flow and solute transport was performed by applying the SEAWAT code. The simulation conditions referring to the initial and boundary conditions, the spatial and temporal discretization, and the values of the individual aquifer parameters (i.e., hydraulic conductivity, conductance, recharge and discharge components) were kept identical to those in the first approach. The only difference is that in this approach the effect of density variations due to the solute concentrations variation is taken into consideration. A linear equation of state is used by the SEAWAT code to convert concentration (C) to fluid density (ρ): ρ=ρf+aC (Cobaner et al., 2012; Li et al., 2009; Mulligan et al., 2007), where ρf is the density of the base fluid, i.e., the freshwater (1,000 kg/m3), and a is the slope of density over concentration. The value of coefficient a is user defined depending on the type of solute mass and the units used for the simulation (Cobaner et al., 2012). In the case of using chloride concentrations as a proxy for salinity, and if liters and milligrams are used, a is set to a value of 1.315x10-3 (Siarkos and Latinopoulos, 2015).

60

I. Siarkos & P. Latinopoulos

4. COMPARISON OF MODEL RESULTS As already mentioned, the two different approaches are compared by observing the results of the two false transient models. This comparison refers both to hydraulic head and chloride concentrations distributions in the horizontal and vertical direction (since 3-D models were developed) at the end of the simulation period (50 years). Furthermore, comparison of the following is performed: a) the flow budget of the aquifer system; and b) the chloride concentrations in five typical aquifer cells located in the semi-confined portion of the aquifer system. With regard to the flow problem, Figure 4 shows the horizontal distribution of the hydraulic head resulting from the application of the two different models. As it is obvious, in the case of the constant density model (MODFLOW) the hydraulic head values are lower than the ones resulting from the application of variable density model (SEAWAT), especially in the central and southern portion of the aquifer system where the influence of seawater intrusion is strong. This is due to the fact that hydraulic head varies not only as do pressure and elevation, but also as water density (Guo and Langevin, 2002), which is taken into consideration in the case of density dependent model. In the northern part of the aquifer, where the influence of mass concentrations in fluid density is negligible, the isopiezometric contours deriving from the two approaches coincide.

Figure 4. Comparison of the horizontal distribution of the predicted hydraulic heads by MODFLOW and SEAWAT

Figure 5 illustrates the vertical distribution of the hydraulic head resulting from the two different models along a typical aquifer cross section (A’-A, Figure 4). Figure 5a refers to the constant density model (MODFLOW), while Figure 5b refers to the variable density one (SEAWAT). As it is apparent, in the first case the isopiezometric contours are vertical indicating that hydraulic head remains constant in the vertical direction. On the contrary, in the second case the isopiezometric contours incline slightly, indicating that hydraulic head varies in the vertical direction. This is caused due to the fact that density variations produce significant changes in the flow field in all directions, even in the vertical one (Todd and Mays, 2005; Werner et al., 2013). In Figure 6, the semi-confined portion of the aquifer system, as it results by applying the MODFLOW (Figure 6a) and SEAWAT (Figure 6b) codes, is illustrated. It is obvious that in the second case more areas characterized by semi-confined conditions (blue cells) are observed than in

European Water 55 (2016)

61

the first case. This is directly related to the hydraulic head distribution and the fact that, in the case of variable density model (SEAWAT), the hydraulic head is higher (Figure 4) resulting in the occurrence of more “wet” cells (i.e., cells where the water level is higher than the aquifer upper boundary).

(a)

(b)

Figure 5. Vertical distribution of hydraulic heads along a typical aquifer cross section (A-A’) resulting from a) MODFLOW and b) SEAWAT

In Table 1, the flow budget of the aquifer system resulting from both models is presented. In both cases, groundwater inflow to the system occurs mostly from recharge, which is due to rainfall and irrigation return flows, while the main source of groundwater outflow is by far water extraction. Moreover, in both approaches the total water budget over the entire aquifer system shows a perfect balance (especially in the case of constant density model) between inflows and outflows, which is consistent with the false transient modeling conditions. Nevertheless, there is one main difference between the two approaches and is related to the amount of water entering the aquifer system both from its northern (GHB) and southern (CHB) boundaries. Of these two boundaries, the southern one is considered more important since in this section the aquifer is in hydraulic connection with the sea, and therefore, the water entering the system through this boundary is actually seawater. So, with regard to this boundary, in the case of variable density model (SEAWAT) the volume of water entering the system is higher than the one estimated in the case of constant density model (MODFLOW). This is consistent with the hydraulic head distribution in the study area (Figure 4) and more specifically with the fact that groundwater levels are higher in the case of variable density model (SEAWAT), since greater volumes of water are introduced to the system. With respect to the transport problem, the horizontal distribution of the chloride concentrations resulting from the application of the two different models is depicted in Figure 7. Figure 7a refers to the first aquifer layer (layer 1), while Figure 7b to the second one (layer 2). The main conclusion stemming from these figures is that the application of the constant density model (MT3DMS) results in higher chloride concentrations in the case of layer 1, while the opposite happens in the case of layer 2, where higher chloride concentrations result from the application of variable density model (SEAWAT). The same conclusion as above derives from Figure 8, in which the vertical distribution of chloride concentrations along a typical aquifer cross section (A-A’, Figure 7) is shown. Namely, the difference between the two approaches regarding the chloride concentrations, and therefore, the seawater wedge advancement in the two aquifer layers is far from obvious. More specifically, the variable density model (SEAWAT) results in higher chloride concentrations in layer 2, providing a better representation of the physical problem, as well as a better depiction of the transition zone caused by the two miscible fluids (i.e., freshwater and seawater). Finally, in Table 2, the chloride concentrations resulting from the application of MT3DMS and SEAWAT in five typical aquifer cells located in the semi-confined portion of the aquifer system (Figure 6a) are presented. In this table, “layer 1” refers to the top aquifer layer, “layer 2” to the bottom aquifer layer, while “total” expresses the chloride concentrations of mixed water abstracted

62

I. Siarkos & P. Latinopoulos

from the whole thickness of the aquifer (i.e., both aquifer layers). In order to determine the chloride concentrations of mixed water and since two layers were considered, the following equation was used: CmixVmix = C1V1 + C2V2

(1)

where: Cmix is the chloride concentrations in mixed water deriving from both aquifer layers Vmix is the volume of mixed water deriving from both aquifer layers C1 is the chloride concentrations in water deriving from the top aquifer layer (layer 1) V1 is the volume of water deriving from the top aquifer layer (layer 1) C2 is the chloride concentrations in water deriving from the bottom aquifer layer (layer 2) V2 is the volume of water deriving from the bottom aquifer layer (layer 2)

(b)

(a)

Figure 6. Depiction of the semi-confined portion of the aquifer (blue cells) resulting from a) MODFLOW and b) SEAWAT Table 1. Flow budget of the aquifer system applying MODFLOW and SEAWAT

Constant Head (CHB) General Head (GHB) Recharge Wells Total sources/sinks

Input (m3/d) MODFLOW SEAWAT 12,180 12,326 8,447 8,358 26,050 26,050 0.0 0.0 46,677 46,734

Output (m3/d) MODFLOW SEAWAT 0.0 50.0 80.0 81.0 0.0 0.0 46,596 46,596 46,676 46,727

Since the selected cells belong to the semi-confined portion of the aquifer (i.e., the water occupies the whole layer volume) and are of equal volume (V1=V2=Vmix/2, based on the spatial discretization of the models), Eq. (1) receives the following form, which was used for the calculation of the chloride concentrations in mixed water:

European Water 55 (2016)

63

Cmix = (C1 + C2 ) / 2

(2)

where Cmix is the chloride concentrations in mixed water deriving from both aquifer layers, and C1 and C2 the chloride concentrations in water deriving from the top aquifer layer (layer 1) and the bottom aquifer layer (layer 2), respectively.

(a)

(b)

Figure 7. Comparison of the horizontal distribution of chloride concentrations for a) layer 1 and b) layer 2

(a)

(b)

Figure 8. Vertical distribution of chloride concentrations along a typical aquifer cross section (A-A’) resulting from a) MT3DMS and b) SEAWAT

The main conclusion arising from Table 2 is, as before, that the constant density model (MT3DMS) results in higher chloride concentrations in the top aquifer layer, in contrast to variable density model (SEAWAT) which results in higher chloride concentrations in the bottom aquifer layer. Besides this, what is worth noting is the conclusion referring to the estimation of the chloride concentrations in mixed water abstracted from both aquifer layers. In this case, the constant density model (MT3DMS) results in higher chloride concentrations in those cells that are located close to the coastline (i.e., cells C1 and C2, Figure 6a) and are characterized by high chloride concentrations (i.e., Ccl>10.000 mg/L). When moving away from the coast (i.e., cells C3, C4 and C5), the variable density model (SEAWAT) provides higher chloride concentrations results in mixed water. At this point, it is worth mentioning that these results could significantly change in the case of considering the phreatic portion of the aquifer, where the volume of water in the bottom layer is greater than in the top layer. In this case, the variable density model (SEAWAT) could result in higher chloride concentrations in mixed water even in those cells located close to the coastline (if

64

I. Siarkos & P. Latinopoulos

phreatic conditions occur). This depends on the difference in the water volume of the two aquifer layers and the form that Eq. (1) receives due to this difference. Table 2. Chloride concentrations resulting from MT3DMS and SEAWAT in five typical aquifer cells (layer 1: the top aquifer layer, layer 2: the bottom aquifer layer, total: mixed water from both layers) Cells C1 C2 C3 C4 C5

layer 1 14,212 10,431 6,120 2,237 140

MT3DMS layer 2 16,679 13,026 8,156 3,211 230

Total 15,446 11,729 7,138 2,724 185

layer 1 13,262 8,707 4,355 1,261 61

SEAWAT layer 2 17,189 14,385 10,226 5,047 616

Total 15,226 11,546 7,291 3,154 339

5. CONCLUSIONS In the present study, the simulation of both groundwater flow and seawater intrusion in the aquifer of Nea Moudania is attempted through the implementation of two different 3D-model approaches, and the comparison of the results of these approaches is presented. The first approach involves the development of constant density models by applying the MODFLOW and MT3DMS codes, while the second one includes the development of a variable density model by applying the SEAWAT code. The comparison of the results of the two different approaches shows clearly the differences existing between them, since constant density models adopt a more simplified representation of the physical phenomenon (i.e., not taking into consideration the density variations due to the variations in solute concentrations). These differences refer both to hydraulic head and chloride concentrations distributions in the horizontal and vertical plane. More specifically, the variable density model results in higher hydraulic head values in the study area which vary in the vertical direction (in the portion of the aquifer where seawater intrusion occurs), as well as in higher chloride concentrations in the bottom layer of the aquifer. According to these results, despite the fact that the variable density model is more computationally intensive, it provides a more realistic representation of the physical problem than the constant density one. Therefore, taking into consideration the specific characteristics of the aquifer under study, it is concluded that in similar aquifer systems density variations due to the variations in solute concentrations considerably affect both the flow and mass transport conditions, rendering the application of variable density models absolutely necessary.

ACKNOWLEDGEMENTS An initial shorter version of the paper has been presented in Greek at the 3rd Common Conference (13th of Hellenic Hydrotechnical Association, 9th of Hellenic Committee on Water Resources Management and 1st of the Hellenic Water Association) “Integrated Water Resources Management in the New Era”, Athens, Greece, December 10-12, 2015.

REFERENCES Al-Taliby W., A. Pandit, H.H. Heck and N. Ali (2016) ‘Numerical modeling of groundwater flow below an estuary using MODFLOW and SEAWAT – Comparison of results’, Proc. World Environmental and Water Resources Congress, 22-26 May, West Palm Beach, U.S.A. Arlai P. (2007) ‘Numerical modeling of possible saltwater intrusion mechanisms in the multiple-layer coastal aquifer system of the Gulf of Thailand’, Ph.D. Thesis, Faculty of Civil Engineering, University of Kassel, Kassel, Germany. Bear J. (1999) ‘Conceptual and mathematical modeling’, In: Bear J., A.H.-D. Cheng, S. Sorek, D. Ouazar, I. Herrera (Eds), Seawater intrusion in coastal aquifers, Dordrecht: Kluwer, 127-161. Cobaner M., R. Yurtal, A. Dogan and L.H. Motz (2012) ‘Three dimensional simulation of seawater intrusion in coastal aquifers: A

European Water 55 (2016)

65

case study in the Goksu Deltaic Plain’, Journal of Hydrology, 464-465, 262-280. Datta B, H. Vennalakanti and A. Dhar (2009) ‘Modeling and control of saltwater intrusion in a coastal aquifer of Andhra Pradesh, India’, Journal of Hydro-environment Research, 3, 148-159. Doherty J. (2002) ‘Manual for PEST’, 5th Edition, Watermark, Brisbane, Australia. Ganesan M. and S. Thayumanavan (2009) ‘Management strategies for a seawater intruded aquifer system’, Journal of Sustainable Development, 2(1), 94-106. Giambastiani B.M.S., M. Antonellini, G.H.P. Oude Essink and R.J. Stuurman (2007) ‘Saltwater intrusion in the unconfined coastal aquifer of Ravenna (Italy): a numerical model’, Journal of Hydrology, 340, 91-104. Guo W. and C.D. Langevin (2002) ‘User’s guide to SEAWAT: a computer program for simulation of three-dimensional variabledensity groundwater flow’, US Geol Surv Tech Water-Resour Invest 6-A7. Harbaugh A.W., E.R. Banta, M.C. Hill and M.G. McDonald (2000) ‘MODFLOW-2000, The U.S. Geological Survey modular ground-water model: user guide to modularization concepts and the ground-water flow process’, US Geol Surv Open-File Rep 0092. Kasapaki M., D. Latinopoulos, I. Siarkos and P. Latinopoulos (2015) ‘A methodological framework to explore the long-term effects of seawater intrusion on groundwater quality and agricultural productivity’, Proc. 14th Int. Conf. on Environmental Science and Technology, 3-5 September, Rhodes, Greece. Kopsiaftis G., A. Mantoglou and P. Giannopoulos (2009) ‘Variable density coastal aquifer models with application to an aquifer on Thira Island’, Desalination, 237, 65-80. Langevin C.D. (2003) ‘Simulation of submarine ground water discharge to a marine estuary: Biscayne Bay, Florida’, Ground Water, 41(6), 58-771. Langevin C.D., W.B. Shoemaker and W. Guo (2003) ‘MODFLOW-2000, the U.S. Geological Survey modular ground-water model: documentation of the SEAWAT-2000 version with variable density flow process (VDF) and the integrated MT3DMS transport process (IMT)’, US Geol Surv Open-File Rep 03-426. Latinopoulos D. and I. Siarkos (2014) ‘Modelling the groundwater flow to assess the long-term economic cost of irrigation water: Application in the Moudania Basin, Greece’, In: Giannino M. (Ed), Drinking water and water management: New research, New York: Nova Publishers, 249-274. Latinopoulos P. (2003) ‘Development of water resources management plan for water supply and irrigation (in Greek)’, Research Project, Final report prepared for the Municipality of Moudania, Aristotle University of Thessaloniki, Greece. Li X., B.X. Hu, X.C. Burnett, I.R. Santos and J.P. Chanton (2009) ‘Submarine groundwater discharge driven by tidal pumping in a heterogeneous aquifer’, Ground Water, 47(4), 558-568. Mahmoodzadeh D., H. Ketabchi, B. Ataie-Ashtiani and C.T. Simmons (2014) ‘Conceptualization of a fresh groundwater lens influenced by climate change: A modeling study of an arid-region island in the Persian Gulf, Iran’, Journal of Hydrology, 519, 399-413. Marsily G. (1986) ‘Quantitative hydrogeology: Groundwater hydrology for engineers’, Academic Press, San Diego, U.S.A. McDonald M.G. and A.W. Harbaugh (1988) ‘A modular three-dimensional finite difference ground-water flow model’, Techniques of Water Resources Investigations, Book 6, USGS, Reston, VA, 586 pp. Mulligan A.E., R.L. Evans and D. Lizarralde (2007) ‘The role of paleochannels in groundwater/seawater exchange’, Journal of Hydrology, 335, 313-329. Oude Essink G.H.P. (2003) ‘Mathematical models and their application to salt water intrusion problems’, In: Proceedings of TIAC’03 Coastal aquifers intrusion technology: Mediterranean countries, Alicante, Spain. Papadopoulou M. (2011) ‘Optimization approaches for the control of seawater intrusion and its environmental impacts in coastal environment’, Pacific Journal of Optimization, 7(3), 479-502. Payne D.F., A.M. Provost and C.I. Voss (2003) ‘Parallel development of MODFLOW and SUTRA models in coastal Georgia, south Carolina, and Florida: an approach to study regional ground-water flow and local saltwater intrusion’, Proc. Georgia Water Resources Conf., 23-24 April, Athens, U.S.A. Pool M. and J. Carrera (2010) ‘Dynamics of negative hydraulic barriers to prevent seawater intrusion’, Hydrogeology Journal, 18(1), 95-105. Rahmawati N., J.-F. Vuillaume and I.L.S. Purnama (2013) ‘Salt intrusion in coastal and lowland areas of Semarang City’, Journal of Hydrology, 494, 146-159. Rao S.V.N., S. Kumar, S. Shekhar, S.K. Sinha and S. Manju (2007) ‘Optimal pumping from skimming wells from the Yamuna River flood plain in north India’, Hydrogeology Journal, 15, 1157-1167. Rao S.V.N., V. Sreenivasulu, S.M. Bhallamudi, B.S. Thandaveswara and K.P. Sudheer (2004) ‘Planning groundwater development in coastal aquifers’, Hydrological Sciences Journal, 49(1), 155-170. Sanz-Garrido I. and J.E. Capilla (2015) ‘Assessment of saltwater intrusion and discharges to a wetland with a 3D transient variable density flow model: The coastal plane Oropesa-Torreblanca aquifer, Spain’, Journal of Water Resource and Protection, 7, 749768. Siarkos I., D. Latinopoulos, Z. Mallios and P. Latinopoulos (2017) 'A methodological framework to assess the environmental and economic effects of injection barriers against seawater intrusion', Journal of Environmental Management, doi: 10.1016/j.jenvman.2017.02.051. Siarkos I. and P. Latinopoulos (2012) ‘Delineation of wellhead protection zones for the control of point pollution sources in the aquifer of N. Moudania, Greece’, European Water, 40, 3-17. Siarkos I. and P. Latinopoulos (2015) ‘Simulation of seawater intrusion through constant and variable density models’, Proc. 3rd Common Conf. of HHA-GCWRM-HWA, 10-12 December, Athens, Greece. Siarkos I. and P. Latinopoulos (2016) ‘Modeling seawater intrusion in overexploited aquifers in the absence of sufficient data: application to the aquifer of Nea Moudania, northern Greece’. Hydrogeology Journal, 24(8), 2123-2141. Todd D.K. and L.W. Mays (2005) ‘Groundwater hydrology’, 3rd Edition, John Wiley & Sons, Inc, New Jersey, U.S.A.

66

I. Siarkos & P. Latinopoulos

Voss C.I. and W.R. Souza (1987) ‘Variable density flow and solute transport simulation of regional aquifers containing a narrow freshwater–saltwater transition zone’, Water Resources Research, 23(10), 1851-1866. Werner A.D., M. Bakker, V.A.E. Post, A. Vandenbohede, C. Lu, B. Ataie-Ashtiani, C.T. Simmons and D.A. Barry (2013) ‘Seawater intrusion processes, investigation and management: Recent advances and future challenges’, Advances in Water Resources, 51, 326. Werner A.D. and M.R. Gallagher (2006) ‘Characterisation of sea-water intrusion in the Pioneer Valley, Australia using hydrochemistry and three-dimensional numerical modelling’, Hydrogeology Journal, 14, 1452-1469. Zheng C. and P.P. Wang (1999) ‘MT3DMS: a modular three-dimensional multispecies transport model for simulation of advection, dispersion, and chemical reactions of contaminants in groundwater systems-documentation and user’s guide’, Contract report SERD-99-1, US Army Corps of Engineers, Washington, DC. Zimmermann S., P. Bauer, R. Held, W. Kinzelbach and J.H. Walther (2006) ‘Salt transport on islands in the Okavango Delta: numerical investigations’, Advances in Water Resources, 29, 11-29.