Model Description

The model domain is discretized into uniform finite-difference grid composed of 60 rows and 60 columns, so that each model cell has the size of 100 m by 100 m in horizontal plane. Due to the fact that higher vertical resolution is required for the accurate simulation of variable density flow systems, the model domain is dis-cretized into 16 layers. Each of these layers has a thickness of 5 m except the uppermost layer having top elevation equal to the topography, ranges between 5 m asl (above sea level) in the middle of the circular island and 0 m along the coast and the sea, and bottom elevation is fixed at 5 m bsl (below sea level). Finally, a grid of cells having uniform volume, except the top layer, is achieved (Fig. 6.1).

The aquifer parameters and boundary conditions were modified after Masterson and Garabedian [7] who simulated a similar island aquifer (Fig. 6.1). The upper boundary of the model is represented by the water table and the lower boundary of the freshwater aquifer is the calculated boundary between the freshwater and the saltwater. Bottom of the model is simulated as a no flow boundary at a depth sufficient not to affect the flow and transport system. Sea surface at the uppermost model layer and the outermost extent of the model corresponding to all vertical cells are simulated by constant head (0 m) and constant concentration (35,000 mg/L) boundaries. A recharge rate of 700 mm/year is applied to the uppermost active cells of the model.

Fig. 6.1 Model extent and boundary conditions in plan view and cross-section

The system is assumed to be isotropic in lateral direction with a hydraulic conductivity of 90 m/day, while an anisotropy ratio of 1:10 is used to determine the vertical conductivity (9 m/day). Flow parameters such as specific storage, specific yield, total porosity and effective porosity are assumed to be uniform throughout the model domain, having the numerical values of 10-5 m-1, 0.25, 0.3 and 0.25, respectively. Longitudinal, transverse and vertical dispersivity values are also assumed to be uniform and equal to 10, 1 and 0.1 m, respectively.

To assess responses of the system to the imposed change of recharge, initial conditions of hydraulic head and concentration distribution at the virgin state should be known. Consequently, modeling is performed at two stages: setting up the virgin conditions and imposing different pressures to the system. First stage of the modeling is the development of the freshwater lens and freshwater-saltwater interface at virgin conditions. In this stage, initial concentration is assumed to be equal to that of saltwater and initial head is assigned to be zero throughout the model domain. Then a transient simulation of 100 years is performed and due to the recharge having the concentration of freshwater, a freshwater lens floating above the saltwater has emerged. During this simulation, it is observed that system reached steady state conditions in terms of both hydraulic heads and concentrations after 75 years; hence the hydraulic head and concentration distribution at the end of 100 years can be regarded as virgin conditions (Fig. 6.2).

Fig. 6.2 Freshwater lens and concentration (mg/L) distribution in plan view and cross-section

The freshwater lens is bounded above by the water table and below by the freshwater-saltwater interface. However, rather than a sharp interface, there is a transition zone between the freshwater and saltwater. For this reason, the concentration limit of 5,000 mg/L is determined as the lower bound of the freshwater lens. This boundary is calculated to be at an elevation of -41.5 m at virgin conditions, and the volume of water contained within the lens between the interface and the water table is 68 hm3.

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