A rapid assessment method for seawater intrusion and sustainable freshwater extraction in confined aquifers considering hydraulic boundary variations

Abstract

The present invention discloses a rapid assessment method for seawater intrusion and sustainable freshwater extraction in a confined aquifer that considers hydraulic boundary variations. The method includes constructing a conceptual model based on specific operating conditions; calculating the potential energy distribution within the confined aquifer; determining the seawater intrusion range by interpolating the potential field to find equipotential lines equal to the potential energy at the salt toe and the height of the freshwater-salt interface; and calculating the sustainable freshwater extraction rate: calculating the stagnation point position, and the pumping rate when the stagnation point coincides with the salt toe position is the sustainable freshwater extraction rate. The present invention significantly improves the accuracy and computational efficiency of the assessment of the seawater intrusion range and sustainable freshwater extraction rate while ensuring the accuracy of the results. By adopting a conceptual model based on operating conditions, the scope of the study area and parameter settings can be flexibly adjusted according to actual needs. By optimizing the computational model, the present invention significantly reduces the demand for computing resources and manpower and material resources without increasing the investment of additional equipment or resources.

Description

Technical Field

[0001] The present invention relates to a rapid assessment method for seawater intrusion and sustainable freshwater exploitation, and in particular to a rapid assessment method for seawater intrusion and sustainable freshwater exploitation in a confined aquifer taking into account hydraulic boundary changes. Background Art

[0002] The problem of seawater intrusion is increasingly exacerbated by the combined effects of climate change-induced sea level rise and human freshwater extraction. This deterioration in groundwater quality threatens coastal ecosystems and human livelihoods. Therefore, scientifically and rationally assessing the extent of seawater intrusion and developing sustainable freshwater extraction strategies have become core issues in coastal water resource management.

[0003] Traditional hydraulic boundary conditions, namely constant flow or constant head, are often used in coastal seawater intrusion research. However, neither of these boundary conditions accurately reflects the dynamic hydraulic characteristics of natural boundaries. Specifically, the variations in head and flow across the boundary lack rationality, limiting the reliability of assessments of the extent of seawater intrusion and sustainable freshwater withdrawal. While groundwater numerical modeling methods using general-head boundaries (GHBs) more closely resemble actual hydraulic boundary conditions, they are computationally intensive and time-consuming, making them difficult to meet the needs of rapid assessments. Summary of the Invention

[0004] Purpose of the invention: The purpose of the present invention is to propose a rapid assessment method for seawater intrusion and sustainable freshwater extraction in confined aquifers taking into account changes in hydraulic boundaries, which solves the limitations of traditional hydraulic boundary condition assessment methods and significantly improves computational efficiency.

[0005] Technical solution: The present invention comprises the following steps:

[0006] Construct a conceptual model based on specific working conditions;

[0007] Calculate the potential energy distribution within a confined aquifer:

[0008]

[0009] Where Φ(x,y) is the potential energy field distribution of groundwater, x and y are the coordinates of any point in the study area; H s is the initial sea level, ΔH s is the height of sea level rise; Q is the groundwater extraction rate, x w is the x-coordinate of the freshwater extraction well; L is the length of the study area, B is the aquifer thickness of the confined aquifer, K is the permeability coefficient; α is the correction coefficient; D is the distance between the external hydraulic boundary and the inland hydraulic boundary, H refis the hydraulic head at the external hydraulic boundary, ω is the Fourier transform parameter;

[0010] The range of seawater intrusion is determined by interpolating the potential energy field Φ(x,y) to find the equipotential lines equal to the potential energy at the salt toe and the height of the fresh-salt water interface;

[0011] Calculate the sustainable freshwater extraction rate: Calculate the stagnation point position. The pumping rate when the stagnation point coincides with the salt toe position is the sustainable freshwater extraction rate.

[0012] The correction coefficient α is calculated by the following formula:

[0013]

[0014] Where, ρ f is the density of groundwater, ρ s is the density of seawater, α T is the lateral dispersivity.

[0015] The aquifer thickness B of the confined aquifer is determined by the elevation difference between the impermeable roof and the impermeable base.

[0016] The potential energy at the salt toe position in the confined aquifer is calculated by the following formula:

[0017]

[0018] Where, Φ t is the potential energy at the salt toe.

[0019] The salt-fresh water interface height is determined by the following formula:

[0020]

[0021] Where Z is the height of the fresh water interface.

[0022] The stagnation point position in the confined aquifer is calculated by the following formula:

[0023]

[0024] Where x s is the x-coordinate of the stationary point.

[0025] The construction of the conceptual model based on specific working conditions specifically includes obtaining geological parameters, hydrological parameters and water resource allocation conditions of the study area.

[0026] The geological parameters include aquifer type, elevation of the impermeable base, elevation of the impermeable roof, and aquifer permeability coefficient.

[0027] The hydrological parameters include sea level elevation, head elevation of the external hydraulic boundary, distance between the external hydraulic boundary and the inland hydraulic boundary, seawater density, freshwater density, and lateral dispersion.

[0028] The water resource allocation situation includes groundwater extraction rate and extraction well location.

[0029] Beneficial effects: The present invention can significantly improve the assessment accuracy and computational efficiency of the scope of seawater intrusion and sustainable freshwater extraction rate while ensuring the accuracy of the results; compared with traditional assessment methods, the present invention can dynamically consider the variability of sea level and inland hydraulic boundary parameters, effectively solving the assessment error problem caused by unreasonable traditional boundary condition settings; by adopting a conceptual model based on working conditions, the present invention can flexibly adjust the scope of the study area and parameter settings according to actual needs, and is particularly suitable for the rapid decision-making needs of seawater intrusion problems with relatively simple geological conditions but significant changes in hydrological conditions; in addition, by optimizing the calculation model, the present invention significantly reduces the demand for computing resources and manpower and material resources without increasing additional equipment or resource investment, and has the technical advantages of high efficiency and economy. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 A top view of a model of a rapid assessment method for seawater intrusion and sustainable freshwater extraction in a confined aquifer taking into account hydraulic boundary changes according to the present invention;

[0031] Figure 2 for Figure 1 sectional view of

[0032] Figure 3 This is the fitting result of the seawater intrusion range verified by the numerical simulation method in the embodiment of the present invention;

[0033] Figure 4 This is the fitting result of the sustainable freshwater extraction rate assessment verified by the numerical simulation method in the embodiment of the present invention;

[0034] Figure 5 The figure compares the effects of the evaluation method proposed in this invention and the traditional hydraulic boundary method in the evaluation of sustainable freshwater exploitation. DETAILED DESCRIPTION

[0035] The present invention will be further described below with reference to the accompanying drawings.

[0036] The rapid assessment method of seawater intrusion and sustainable freshwater extraction in a confined aquifer considering hydraulic boundary changes of the present invention is applicable to confined aquifers 1 in coastal areas, such as Figure 1 and Figure 2As shown, the study area includes a seawall 3 located on the seaward side, freshwater extraction wells 4 within the aquifer, and an external hydraulic boundary 6, such as a river, canal, reservoir, or lake, located at a certain distance from the inland hydraulic boundary. This external hydraulic boundary 6 maintains a constant distance from the inland hydraulic boundary of the study area to ensure that the study area maintains hydraulic connection with the outside world. This method is suitable for coastal study areas where the horizontal length (along the coastline) is greater than the vertical length (perpendicular to the coastline). The vertical length of the study area can be adjusted according to actual research needs to ensure reasonable scoping.

[0037] like Figure 2 As shown, the lowest elevation of the foundation of seawall 3 on the seaward side should be below the initial sea level 101; within the confined aquifer 1, the bottom of the seawall should be above the impermeable roof 115; and the freshwater production well 4 draws water only from the aquifer 114. The seawater intrusion range encompasses the steady-state seawater intrusion location along the impermeable base 108, encompassing the area between the impermeable base 108 and the salt toe 13 after sea level rise and the freshwater-salt interface 112 after sea level rise. The assessment results are quantified using length and height. The intersection of the freshwater-salt interface 110 at the initial sea level and the impermeable base 108 is the salt toe 11 at the initial sea level. The sustainable freshwater production rate refers to the maximum freshwater production rate of the freshwater production well before reaching criticality. If the pumping rate exceeds this rate, the freshwater production well will extract saltwater.

[0038] The specific steps include:

[0039] S1. Collect hydrological and geological parameters and construct a conceptual model based on specific working conditions: obtain the geological parameters of the study area, including the type of aquifer, the elevation of the impermeable base, the elevation of the impermeable roof, and the permeability coefficient of the aquifer; obtain hydrological parameters, including sea level elevation, the head elevation of the external hydraulic boundary, the distance between the external hydraulic boundary and the inland hydraulic boundary, seawater density, freshwater density, and lateral dispersion; obtain water resource allocation, including the groundwater extraction rate and the location of the extraction wells.

[0040] Through elevation benchmark conversion, the absolute elevation of the impermeable base is set as the benchmark elevation (elevation is 0), and the elevation of the impermeable top plate, the sea level elevation and the head elevation of the external hydraulic boundary are converted into relative elevations; the sea level elevation includes the initial sea level 101 elevation and the sea level 102 elevation after rising. The initial sea level elevation is the sea level elevation of the historical period when the hydraulic change characteristics are not obvious or the base year, or the sea level elevation of the base year required for the research is used. The height of the sea level 102 after rising can refer to the change relative to the initial height during the evaluation period, or be calculated based on the predicted values ​​of different carbon emission scenarios.

[0041] The water resource allocation situation in the study area can be determined based on the groundwater demand of established groundwater extraction activities or policy plans, and the extraction rate and well location can be determined. Usually, the well is located on the axis of symmetry along the coastline, that is, the x-axis, and its position is the vertical distance from the coastline, that is, the x-coordinate.

[0042] S2. Calculate the potential energy distribution in the confined aquifer

[0043] The origin position is determined. The origin O is located at the intersection of the aquifer base on the inland side of the seawall and the symmetry axis of the study area along the coastline. The x-axis is perpendicular to the coastline and points inland; the y-axis is set along the coastline; and the z-axis is vertically upward. The potential energy distribution in the confined aquifer is calculated using formula (1):

[0044]

[0045] Where Φ(x,y) is the potential energy field distribution of groundwater, x and y are the coordinates of any point in the study area; H s is the initial sea level, ΔH s is the height of sea level rise; Q is the groundwater extraction rate, x w is the x-coordinate of the freshwater extraction well; L is the length of the study area; B is the aquifer thickness of the confined aquifer, which is determined by the elevation difference between the impermeable roof and the impermeable base; K is the permeability coefficient; α is determined by the density difference between seawater and groundwater, the lateral dispersion α T , and the thickness of the aquifer in the confined aquifer, B, which can be calculated by formula (2); D is the distance between the external hydraulic boundary and the inland hydraulic boundary, H ref is the hydraulic head at the external hydraulic boundary, ω is the Fourier transform parameter;

[0046]

[0047] Where, ρ f is the density of groundwater, ρ s is the density of seawater, α T is the lateral dispersivity.

[0048] S3. Calculate the potential energy at the salt toe

[0049] The potential energy at the salt toe position in the confined aquifer is calculated by formula (3):

[0050]

[0051] Where, Φ t is the potential energy at the salt toe.

[0052] S4. Determine the scope of seawater intrusion: Find equipotential lines through potential field interpolation and calculate the height of the freshwater-saltwater interface to comprehensively determine the scope of seawater intrusion.

[0053] The salt toe position is found by interpolating the potential energy field Φ(x,y) to find the value equal to Φ t The position of the fresh-salt water interface in the confined aquifer can be determined by formula (4):

[0054]

[0055] Where Z is the height of the salt-fresh water interface, and the salt toe and the salt-fresh water interface position are used to comprehensively determine the range of seawater intrusion.

[0056] S5. Calculate the sustainable freshwater extraction rate: Calculate the stagnation point position. The pumping rate when the stagnation point coincides with the salt toe position is the sustainable freshwater extraction rate.

[0057] The stagnation point position in the confined aquifer is calculated by formula (5):

[0058]

[0059] Where x s The sustainable freshwater extraction rate is the pumping rate when the stagnation point coincides with the maximum salt toe (the salt toe at y = 0).

[0060] The following is further explained with the help of numerical simulation.

[0061] like Figure 3 As shown, this example selects a study area with dimensions of 500 meters (vertical length) x 1000 meters (horizontal width), containing a confined aquifer 1, whose permeability is set to 10 meters / day. The impermeable base 108 of the aquifer is set at an elevation of 0 meters, and the thickness of the aquifer 114 is 30 meters. The initial sea level 101 is 30 meters, and the sea level rise is 0 meters.

[0062] A freshwater production well 4 is located on the x-axis, 400 meters from the origin, within the study area. The freshwater production rate is set at 150 cubic meters per day. The distance D between the inland hydraulic boundary of confined aquifer 1 and the external hydraulic boundary 6 is 2655 meters, and the hydraulic head at the external hydraulic boundary 6 is set at 35 meters.

[0063] Applying the above parameter settings to the rapid evaluation method of the present invention, we obtain Figure 3 To verify the accuracy of the assessment method, a numerical simulation model of seawater intrusion was constructed using SEAWAT software. Figure 3 The black dashed lines in the fresh-salt water interface and salt toe result diagrams represent the 10% salinity line and 90% salinity line in the numerical simulation results, respectively. Since the head change in the confined aquifer has almost no effect on the evaluation results, it is not shown in the conceptual model. The confined head can be regarded as the pressure head in fluid mechanics.

[0064] It can be seen from the results that the rapid evaluation method proposed in the present invention is highly consistent with the numerical simulation results, can well fit the numerical simulation results, and has high accuracy.

[0065] To further evaluate the accuracy of the sustainable freshwater extraction rate assessment, this example selected a study area with a vertical length of 2,000 meters and a horizontal width of 2,000 meters, encompassing confined aquifer 1. The aquifer's hydraulic conductivity was set to 10 meters per day, the thickness of aquifer 114 was 30 meters, the initial sea level 101 was set to 30 meters, and the sea level rise was 1 meter. The distance between the inland hydraulic boundary of confined aquifer 1 and the external hydraulic boundary 6 was 3,297 meters, and the hydraulic head at the external hydraulic boundary 6 was set to 40 meters.

[0066] In this area, the sustainable freshwater extraction rate of different freshwater extraction well locations from the origin was tested, and the distances between the test points were 400 meters, 500 meters, 600 meters, 700 meters and 800 meters, respectively. During the test, SEAWAT software was used for numerical simulation. In order to obtain the sustainable freshwater extraction rate, the numerical simulation continuously adjusted the pumping volume until the salinity in the freshwater extraction well dropped to one thousandth of the salinity of seawater. This process is very time-consuming, especially under the calculation settings of this embodiment, using a computer with an i7-10700K processor, it takes an average of about one week to calculate the sustainable freshwater extraction rate of a freshwater extraction well. The method of the present invention significantly improves the calculation efficiency, and the test time is shortened to about twenty minutes.

[0067] according to Figure 4 The results shown in the figure show that the method of the present invention can accurately approximate the sustainable freshwater extraction rate. As the distance from the well to the origin increases, the evaluation method slightly overestimates the maximum pumping rate. This is because the method of the present invention is particularly suitable for study areas where the lateral width is greater than the longitudinal length, while the study area selected in this example has equal length and width. Therefore, the lateral boundary effect caused by pumping is significant, resulting in an increase in the evaluation error. However, this error does not affect the overall effectiveness and application value of the evaluation method of the present invention.

[0068] In order to further highlight the advantages of the method proposed in the present invention, this embodiment selects the following seawater intrusion systems with inland boundary conditions for comparison: constant head inland hydraulic boundary ( Figure 5 Figure 6 shows the inland hydraulic boundary (black line with triangles), the constant flow inland hydraulic boundary (black line with circles), and the universal hydraulic head boundary (colored lines) proposed in this invention that takes into account hydraulic boundary variations. Different colors represent how the external hydraulic boundary 6 changes under different hydraulic head conditions. The equivalent inland hydraulic boundary enables comparability between seawater intrusion systems using different hydraulic boundary conditions.

[0069] from Figure 5 As can be seen in the figure, the sustainable freshwater extraction rate assessment for seawater intrusion systems varies under different boundary conditions. Under most operating conditions, the assessment method proposed in this invention, which considers hydraulic boundary changes, yields a lower sustainable freshwater extraction rate. This is because the sustainable freshwater extraction rate is not only determined by the hydraulic gradient of the inland freshwater but is also closely related to the hydraulic conductivity of the external hydraulic boundary. Therefore, the proposed method can more accurately reflect dynamically changing hydraulic boundary conditions. Ignoring the impact of pumping on changes in the inland hydraulic boundary will lead to unrealistic inland freshwater replenishment assessments and may produce dangerous freshwater extraction rate results.

[0070] Based on potential energy theory and the Fourier transform method, combined with universal hydraulic head boundary conditions, this paper develops a mathematical analytical model for confined aquifers, enabling rapid calculation of the steady-state seawater intrusion range and sustainable freshwater extraction. This method not only overcomes the limitations of traditional hydraulic boundary condition assessment methods but also, by rationally setting the study area and hydraulic boundary conditions and simplifying the calculation model, improves computational efficiency while maintaining assessment accuracy, providing a highly efficient and practical solution for water resource management in coastal areas.

Claims

1. A rapid assessment method for seawater intrusion and sustainable freshwater extraction in a confined aquifer considering hydraulic boundary changes, characterized by: The following steps are involved: Construct a conceptual model based on specific working conditions; Calculate the potential energy distribution within a confined aquifer: Where Φ(x,y) is the potential energy field distribution of groundwater, x and y are the coordinates of any point in the study area; H s is the initial sea level, ΔH s is the height of sea level rise; Q is the groundwater extraction rate, x w is the x-coordinate of the freshwater extraction well; L is the length of the study area, B is the aquifer thickness of the confined aquifer, K is the permeability coefficient; α is the correction coefficient; D is the distance between the external hydraulic boundary and the inland hydraulic boundary, H ref is the hydraulic head at the external hydraulic boundary, ω is the Fourier transform parameter; The range of seawater intrusion is determined by interpolating the potential energy field Φ(x,y) to find the equipotential lines equal to the potential energy at the salt toe and the height of the fresh-salt water interface; Calculate the sustainable freshwater extraction rate: Calculate the stagnation point position. The pumping rate when the stagnation point coincides with the salt toe position is the sustainable freshwater extraction rate.

2. A rapid assessment method for seawater intrusion and sustainable freshwater extraction in a confined aquifer considering hydraulic boundary changes according to claim 1, characterized in that: The correction coefficient α is calculated by the following formula: Where, ρ f is the density of groundwater, ρ s is the density of seawater, α T is the lateral dispersivity.

3. A rapid assessment method for seawater intrusion and sustainable freshwater extraction in a confined aquifer considering hydraulic boundary changes according to claim 1, characterized in that: The aquifer thickness B of the confined aquifer is determined by the elevation difference between the impermeable roof and the impermeable base.

4. A rapid assessment method for seawater intrusion and sustainable freshwater extraction in a confined aquifer considering hydraulic boundary changes according to claim 3, characterized in that: The potential energy at the salt toe position in the confined aquifer is calculated by the following formula: Where, Φ t is the potential energy at the salt toe.

5. The rapid assessment method for seawater intrusion and sustainable freshwater extraction in a confined aquifer considering hydraulic boundary changes according to claim 1, characterized in that: The salt-fresh water interface height is determined by the following formula: Where Z is the height of the freshwater interface; Φ is the potential energy.

6. A rapid assessment method for seawater intrusion and sustainable freshwater extraction in a confined aquifer considering hydraulic boundary changes according to claim 1, characterized in that: The stagnation point position in the confined aquifer is calculated by the following formula: Where x s is the x-coordinate of the stationary point.

7. The rapid assessment method for seawater intrusion and sustainable freshwater extraction in a confined aquifer considering hydraulic boundary changes according to claim 1, characterized in that: The construction of the conceptual model based on specific working conditions specifically includes obtaining geological parameters, hydrological parameters and water resource allocation conditions of the study area.

8. A rapid assessment method for seawater intrusion and sustainable freshwater extraction in a confined aquifer considering hydraulic boundary changes according to claim 7, characterized in that: The geological parameters include aquifer type, elevation of the impermeable base, elevation of the impermeable roof, and aquifer permeability coefficient.

9. A rapid assessment method for seawater intrusion and sustainable freshwater extraction in a confined aquifer considering hydraulic boundary changes according to claim 7, characterized in that: The hydrological parameters include sea level elevation, head elevation of the external hydraulic boundary, distance between the external hydraulic boundary and the inland hydraulic boundary, seawater density, freshwater density, and lateral dispersion.

10. A rapid assessment method for seawater intrusion and sustainable freshwater extraction in a confined aquifer considering hydraulic boundary changes according to claim 7, characterized in that: The water resource allocation situation includes groundwater extraction rate and extraction well location.

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