Introduction: The phenomenon of saltwater advance in coastal aquifers is a global problem. Until now, most of the laboratory studies carried out regarding the advance of sea saltwater have considered the beach boundary as vertical, while the penetration and advance of saltwater from non-vertical beaches to coastal aquifers is a common phenomenon. Laboratory models can simulate the phenomenon of saltwater advancing on sloping beaches. This research expands the past research by building a 3D laboratory model and creating sloping beach conditions. The main purpose of this research is to investigate the phenomenon of saltwater advance on a sloping beach in a laboratory and numerical 3D manner in permanent and non-permanent conditions. An image processing technique was used to analyze the images obtained from the progress of salt water in the laboratory model. Validation of laboratory results was done with SEAWAT model.
Methodology: In this research, a laboratory model of a three-dimensional flow tank was built. The flow tank of this model included a central chamber containing the porous medium of the aquifer and two side chambers on the right and left side of the central chamber to adjust the saltwater and freshwater head. According to the purpose of this research, the grid plate on the saltwater side was connected to the bottom of the tank by a hinge to create a sloping beach. To create a porous medium, glass beads with a diameter of 1000 to 1200 microns and a specific weight of 2400 kg/m3 were used (Figure 1). The experiments were conducted in three stages. The permanent condition of the first stage was used as the initial condition for the second stage of the experiment. In the second stage (advance stages), the level of freshwater in the left lateral chamber decreased and in the third stage (recede stages), the level of freshwater was returned to its original state. In this research, an image processing technique was used to identify the behavior of saltwater advance in the porous medium and calculate the characteristics of the saltwater wedge. From all stages of the advance and recede Experiments of the saltwater wedge, images of the flow tank were automatically taken at intervals of 60 seconds. The level curve with saltwater diluted by 50% was considered as the boundary of the mixing zone of salt-freshwater and determined the characteristics of the saltwater wedge. After obtaining the numerical value equivalent to saltwater with a concentration of 50% (Equation 2) and the modified pixel values of each model image (Equation 1), the contour of saltwater with a concentration of 50% was drawn in MATLAB software and the position of the saltwater wedge was determined. SEAWAT finite difference model has been used to simulate the experiments performed in the laboratory model. The conceptual model and boundary conditions used to simulate the numerical model are shown in Figure 3.
Results and Discussion: In this research, three indicators of length, height, and area of the saltwater wedge were considered as parameters representing the progress of the saltwater wedge. Pictures of laboratory observations and numerical model results of saltwater wedge advance and recede are shown in Figures 4, 5, and 6. A good match between the laboratory observations and the simulation results of the numerical model is observed. The reduction of the freshwater level at the beginning of the advanced stage of saltwater decreased the interaction forces exerted by the freshwater on the saltwater wedge. As a result, the wedge advanced into the laboratory model until reaching new equilibrium conditions (Figure 5). On the other hand, in the third stage, with the increase in freshwater level, the interaction forces applied by the freshwater on the wedge increased and the wedge was pushed back towards the sea (Figure 6).
To further investigate the behavior of the saltwater wedge in the advance and recede stages, the relative displacement parameter of each index was used, which is a dimension less parameter and allows comparison independent of the unit and the total size of the change (Equation 3). Figure 8, shows that the toe length of wedge index reaches permanent conditions earlier in the recede phase of the wedge compared to the advancing time. This phenomenon was reported in experimental and numerical studies by Chang and Clement (2012), Lu and Werner (2013), Robinson et al., (2015), and Rezapour et al., (2018). However, the wedge height index reaches permanent conditions in both the advance and recede stages in an almost equal period. The value of each index over time and the relative changes of each index over time are displayed in a single figure (Figure 9). In the advancing stage, due to the decrease in the height of freshwater, the pressure field of freshwater decreases. Therefore, the salty waters are brought together. Due to the difference in density between saltwater and freshwater, as the depth of the interface increases, its advance rate increases in permanent conditions. As the rate of advance increases, the relative rate of advance decreases. Therefore, the height of the wedge, as the highest point of the interface, starts to move with the highest relative rate and reaches permanent conditions sooner. Accordingly, the toe wedge has the lowest relative displacement rate with the greatest advance.
Conclusion: The present study proposes and presents a three-step hybrid method (laboratory model, image processing, and numerical simulation) to analyze flow patterns with variable density in porous media. The height of the wedge reaches permanent conditions in both advance and recede stages in almost equal periods. But the toe length of the wedge reaches permanent conditions much earlier in the recede stages than in the advanced stages. During the intrusion of saltwater, the height of the wedge reaches a permanent condition much earlier than the toe and area of the wedge, but during the recede stages, all three almost stop together. In addition to permanent conditions, the toe length index is also a suitable representative for expressing the amount of saltwater entering the coastal aquifer in transient conditions.
Keywords: Seawater, Physical Model, Image Processing Technique, SEAWAT