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

Abstract

The present invention discloses a rapid assessment method for seawater intrusion and sustainable freshwater extraction in a phreatic 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 phreatic 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 salt-fresh water interface; and calculating the sustainable freshwater extraction rate by calculating the stagnation point position, and determining the pumping rate when the stagnation point coincides with the salt toe as 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 phreatic 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) can more closely align with 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 a phreatic aquifer 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 unconfined 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 production well; L is the length of the study area, 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, and φ0 is the phreatic level of the phreatic aquifer at the inland boundary;

[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, b' refers to the maximum phreatic level in the phreatic aquifer; α T is the lateral dispersivity.

[0015] The relationship between the phreatic level φ0 and the potential energy of the unconfined aquifer at the inland boundary is as follows:

[0016]

[0017] Where φ0 is obtained by solving Φ(L,y) according to the functional relationship of the above equation, and Φ(L,y) is the potential energy expression of the potential energy field Φ(x,y) at x=L.

[0018] The potential energy at the salt toe position in the unconfined aquifer is calculated as follows:

[0019]

[0020] Where, Φ t is the potential energy at the salt toe.

[0021] The salt-fresh water interface height is determined by the following formula:

[0022]

[0023] Where Z is the height of the fresh water interface.

[0024] The stagnation point position in the unconfined aquifer is calculated by the following formula:

[0025]

[0026] Where x s is the x-coordinate of the stationary point, φ 0,y＝0 is the inland water level when y=0.

[0027] 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.

[0028] The geological parameters include aquifer type, absolute elevation of the impermeable base, and aquifer hydraulic conductivity.

[0029] 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.

[0030] The water resource allocation situation includes groundwater extraction rate and extraction well location.

[0031] 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

[0032] Figure 1 A top view of a model of a rapid assessment method for seawater intrusion and sustainable freshwater extraction in a phreatic aquifer taking into account hydraulic boundary changes according to the present invention;

[0033] Figure 2 for Figure 1 sectional view of

[0034] Figure 3 This is the fitting result of the seawater intrusion range and the phreatic level assessment at the inland boundary verified by the numerical simulation method in the embodiment of the present invention;

[0035] 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;

[0036] 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

[0037] The present invention will be further described below with reference to the accompanying drawings.

[0038] The rapid assessment method of seawater intrusion and sustainable freshwater exploitation in a phreatic aquifer considering hydraulic boundary changes of the present invention is applicable to phreatic aquifers 1 in coastal areas, such as Figure 1 and Figure 2 As 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.

[0039] 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 unconfined aquifer 1, seawall 3 should not vertically penetrate the aquifer to the impermeable base 108. The pumping range of freshwater production well 4 should be below the phreatic level. 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 salt-fresh water interface 112 after sea level rise. The assessment results are quantified using length and height. The intersection of the salt-fresh water 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 a freshwater production well before reaching criticality. If the pumping rate exceeds this rate, the freshwater production well will extract saltwater.

[0040] The specific steps include:

[0041] S1. Collect hydrological and geological parameters and construct a conceptual model based on specific working conditions: obtain geological parameters of the study area, including aquifer type, absolute elevation of impermeable base, and aquifer permeability coefficient; obtain hydrological parameters, including sea level elevation, head elevation of external hydraulic boundary, distance between external hydraulic boundary and inland hydraulic boundary, seawater density, freshwater density, and lateral dispersion; obtain water resource allocation status, including groundwater extraction rate and extraction well location.

[0042] Through elevation benchmark conversion, the absolute elevation of the impermeable base is set as the benchmark elevation (elevation is 0), and 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 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.

[0043] 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.

[0044] S2. Calculate the potential energy distribution in the unconfined aquifer

[0045] 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 phreatic aquifer is calculated using formula (1):

[0046]

[0047] 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, K is the permeability coefficient; α is determined by the density difference between seawater and groundwater, and the lateral diffusion coefficient α T , and the maximum phreatic level b' in the phreatic aquifer, 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 of the external hydraulic boundary, ω is the Fourier transform parameter, φ0 is the phreatic level of the phreatic aquifer at the inland boundary, and its relationship with the potential energy is shown in Equation (3):

[0048]

[0049] Where, ρ f is the density of groundwater, ρ s is the seawater density, b' refers to the maximum phreatic level in the phreatic aquifer; φ0 is the functional relationship of Φ(L,y) obtained by solving Equation (3), and Φ(L,y) is the potential energy expression of the potential energy field Φ(x,y) at x = L.

[0050] S3. Calculate the potential energy at the salt toe

[0051] The potential energy at the salt toe position in the unconfined aquifer is calculated by formula (4):

[0052]

[0053] Where, Φ t is the potential energy at the salt toe.

[0054] 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.

[0055] 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 phreatic aquifer can be determined by formula (5):

[0056]

[0057] 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.

[0058] 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.

[0059] The stagnation point position in the phreatic aquifer is calculated by formula (6):

[0060]

[0061] Where x s is the x-coordinate of the stationary point, φ 0,y＝0 is the inland water table at y = 0, i.e., the value of φ0 at y = 0. The pumping rate at which the stagnation point coincides with the maximum salt toe (the salt toe at y = 0) is the sustainable freshwater extraction rate.

[0062] The following is further explained with the help of numerical simulation.

[0063] like Figure 3 As shown, this example selects a study area with dimensions of 500 meters (vertical length) x 1000 meters (horizontal width), including a phreatic aquifer 1. The permeability of the phreatic aquifer 1 is set to 10 meters / day. The elevation of the impermeable base 108 of the aquifer is set to 0 meters. The initial sea level 101 is 30 meters, and the sea level rise is 0 meters.

[0064] 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 unconfined aquifer 1 and the external hydraulic boundary 6 is 2695 meters, and the hydraulic head at the external hydraulic boundary 6 is set at 35 meters.

[0065] 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 freshwater-salt water interface and salt toe result diagram represent the 10% salinity line and 90% salinity line in the numerical simulation results, respectively; φ0 shows the distribution of the groundwater level at the inland boundary.

[0066] 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.

[0067] To further evaluate the accuracy of the sustainable freshwater extraction rate assessment, this example selected a study area with a vertical length of 2000 meters and a horizontal width of 2000 meters, encompassing unconfined aquifer 1. The aquifer's hydraulic conductivity was set to 10 meters per day, 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 unconfined aquifer 1 and the external hydraulic boundary 6 was 3505 meters, and the hydraulic head at the external hydraulic boundary 6 was set to 40 meters.

[0068] 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.

[0069] according to Figure 4The 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.

[0070] 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.

[0071] from Figure 5 As can be seen in the figure, there are differences in the assessment of the sustainable freshwater extraction rate of the seawater intrusion system under different boundary conditions. Under most operating conditions, the assessment method proposed in this invention, which takes into account the changes in hydraulic boundaries, produces a smaller 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 and the area of ​​the water-passing cross-section. Therefore, the method proposed in this invention can more accurately reflect the dynamically changing hydraulic boundary conditions. Ignoring the impact of pumping on the changes in the inland hydraulic boundary will lead to unrealistic inland freshwater replenishment assessments and may produce dangerous freshwater extraction rate results.

[0072] 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 phreatic 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 phreatic aquifer taking into account 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 unconfined 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 production well; L is the length of the study area, 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, and φ0 is the phreatic level of the phreatic aquifer at the inland boundary; 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 phreatic 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, b' refers to the maximum phreatic level in the phreatic aquifer; α T is the lateral dispersivity.

3. A rapid assessment method for seawater intrusion and sustainable freshwater extraction in a phreatic aquifer considering hydraulic boundary changes according to claim 1 or 2, characterized in that: The relationship between the phreatic level φ0 and the potential energy of the unconfined aquifer at the inland boundary is as follows: Where φ0 is obtained by solving Φ(L,y) according to the functional relationship of the above equation, and Φ(L,y) is the potential energy expression of the potential energy field Φ(x,y) at x=L.

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

5. A rapid assessment method for seawater intrusion and sustainable freshwater extraction in a phreatic 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 phreatic aquifer considering hydraulic boundary changes according to claim 1, characterized in that: The stagnation point position in the unconfined aquifer is calculated by the following formula: Where x s is the x-coordinate of the stationary point, φ 0,y＝0 is the inland water level when y=0.

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

9. A rapid assessment method for seawater intrusion and sustainable freshwater extraction in a phreatic 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 phreatic 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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