Rapid assessment method for seawater intrusion and sustainable freshwater exploitation in phreatic aquifer considering hydraulic boundary change

Abstract

The invention discloses a rapid assessment method for seawater intrusion and sustainable freshwater exploitation in an phreatic aquifer considering hydraulic boundary changes. The method comprises the following steps: constructing a conceptual model based on specific working conditions; potential energy distribution in the phreatic aquifer is calculated; the seawater intrusion range is determined by searching an equipotential line equal to potential energy at a salt toe position in a potential energy field through interpolation and the height of a salt-fresh water interface; and calculating the sustainable fresh water exploitation rate: calculating the stagnation point position, wherein the water pumping rate when the stagnation point coincides with the salt toe position is the sustainable fresh water exploitation rate. According to the method, the evaluation precision and calculation efficiency of the seawater invasion range and the sustainable fresh water exploitation rate can be remarkably improved while the result accuracy is ensured; by adopting the conceptual model based on the working condition, the research area range and parameter setting can be flexibly adjusted according to actual requirements, and by optimizing the calculation model, the requirements of calculation resources and manpower and material resources are remarkably reduced under the condition that additional equipment or resource investment is not increased.

Description

Technical Field

[0001] The 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 becoming increasingly serious due to the combined effects of sea level rise caused by climate change and human freshwater exploitation. Seawater intrusion can lead to deterioration of groundwater quality, threatening the ecosystem and human production and life in coastal areas. Therefore, scientifically and rationally assessing the scope of seawater intrusion and formulating sustainable freshwater exploitation strategies have become one of the core issues in water resource management in coastal areas.

[0003] In the study of seawater intrusion in coastal areas, traditional hydraulic boundary conditions, i.e., constant flow or constant head, are usually used. However, both types of boundaries are difficult to accurately reflect the hydraulic dynamic characteristics of natural boundaries, i.e., the changes in head and flow on the boundary lack rationality, which limits the reliability of the assessment results of the scope of seawater intrusion and sustainable freshwater extraction. Although the groundwater numerical modeling method using the general-head boundary (GHB) can be closer to the actual hydraulic boundary conditions, it is computationally intensive and time-consuming, and it is difficult to meet the needs of rapid assessment. 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 exploitation 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 conceptual models 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 height, 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, φ0 is the phreatic level of the unconfined aquifer at the inland boundary;

[0010] The range of seawater intrusion is determined by interpolating the potential field Φ(x,y) to find the equipotential lines equal to the potential 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, and 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] In the formula, 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 dispersion.

[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 formula, 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 by the following formula:

[0019]

[0020] In the formula, 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] In the formula, 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 impermeable substrate, and aquifer permeability coefficient.

[0029] The hydrological parameters include 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.

[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 calculation efficiency of the seawater intrusion range 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, and effectively solve 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, the present invention significantly reduces the demand for computing resources and manpower and material resources by optimizing the calculation model 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 exploitation in a phreatic aquifer taking into account hydraulic boundary changes according to the present invention;

[0033] Figure 2 for Figure 1 A cross-sectional view of

[0034] Figure 3 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 sustainable freshwater extraction rate assessment verified by numerical simulation method in the embodiment of the present invention;

[0036] Figure 5 The figure compares the effects of the assessment method proposed in the present invention and the traditional hydraulic boundary method in the assessment of sustainable freshwater exploitation. DETAILED DESCRIPTION

[0037] The present invention will be further described below in conjunction with 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 set on the sea side, a freshwater extraction well 4 in the aquifer, and an external hydraulic boundary 6 at a certain distance from the inland hydraulic boundary, such as a river, canal, reservoir or lake, etc. The external hydraulic boundary 6 maintains a constant distance from the hydraulic boundary of the study area on the inland side to ensure that the study area maintains hydraulic connection with the outside world. This method is suitable for coastal study areas where the lateral length (along the coastline direction) is greater than the longitudinal length (perpendicular to the coastline direction), and the longitudinal length of the study area can be adjusted according to actual research needs to ensure that the scope is reasonably delineated.

[0039] like Figure 2 As shown, the lowest elevation of the foundation of the seawall 3 on the sea side should be lower than the initial sea level 101; in the phreatic aquifer 1, the seawall 3 should not penetrate the aquifer to the impermeable base 108 in the vertical direction; the pumping range of the freshwater production well 4 should be below the phreatic level. The seawater intrusion range includes the steady-state seawater intrusion position along the impermeable base 108, that is, the area between the impermeable base 108 to the salt toe position 13 after the sea level rises and the salt-fresh water interface position 112 after the sea level rises, and its evaluation results are quantitatively measured in length and height. The intersection of the salt-fresh water interface position 110 at the initial sea level height and the impermeable base 108 is the salt toe position 11 at the initial sea level height. The sustainable freshwater production rate refers to the maximum freshwater production rate of the freshwater production well before reaching the critical state. When the pumping rate exceeds this rate, the freshwater production well will extract salt water.

[0040] The specific steps include:

[0041] 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 absolute elevation of the impermeable base, and the permeability coefficient of the aquifer; obtain hydrological parameters, including sea level elevation, 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 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 the research is used. The height of the sea level 102 after rising can refer to the change in the evaluation period relative to the initial height, 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 planning, 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. Calculation of 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 by 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 height, 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 the density difference between seawater and groundwater, and the lateral dispersion 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 formula (3):

[0048]

[0049] In the formula, 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 function 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 position

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

[0052]

[0053] In the formula, 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 fresh-salt water interface to comprehensively determine the scope of seawater intrusion.

[0055] The salt toe position is obtained by interpolating the potential energy field Φ(x,y) to find a 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 fresh-salt water interface, and the salt toe and the fresh-salt water interface position are used to comprehensively determine the scope 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 unconfined aquifer is calculated by formula (6):

[0060]

[0061] In the formula, x s is the x coordinate of the stationary point, φ 0,y＝0 is the inland water level at y = 0, that is, the value of φ0 at y = 0. The pumping rate when the stagnation point coincides with the maximum salt toe position (the salt toe position at y = 0) is the sustainable freshwater extraction rate.

[0062] The following is further explained in combination with numerical simulation.

[0063] like Figure 3 As shown, in this embodiment, a research area is selected, the area size is 500 meters (longitudinal length) × 1000 meters (lateral width), including a phreatic aquifer 1, and the permeability coefficient 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 height is 30 meters, and the sea level rise height is 0 meters.

[0064] A freshwater production well 4 is set in the study area, located on the x-axis 400 meters from the origin, and the freshwater production rate is set to 150 cubic meters per day. The distance D between the inland hydraulic boundary of the unconfined aquifer 1 and the external hydraulic boundary 6 is 2695 meters, and the hydraulic head of the external hydraulic boundary 6 is set to 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 fresh-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 fit the numerical simulation results well, and has high accuracy.

[0067] To further evaluate the accuracy of the sustainable freshwater extraction rate assessment, this embodiment selects a study area with a longitudinal length of 2000 meters and a lateral width of 2000 meters, covering the unconfined aquifer 1. The permeability of the aquifer is set to 10 meters / day, the height of the initial sea level 101 is set to 30 meters, and the sea level rise is 1 meter. The distance between the inland hydraulic boundary of the unconfined aquifer 1 and the external hydraulic boundary 6 is 3505 meters, and the head of the external hydraulic boundary 6 is 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 of 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 seawater salinity. 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 Figure 2 show that the method of the present invention can fit the sustainable freshwater extraction rate more accurately. As the distance from the well to the origin increases, the evaluation method will slightly overestimate the maximum pumping volume. This is because the method of the present invention is particularly suitable for research areas where the lateral width is greater than the longitudinal length, while the research area selected in this embodiment is equal in length and width. Therefore, the lateral boundary effect caused by pumping is relatively large, resulting in an increase in the evaluation error. However, this error does not affect the overall effect 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 The figure shows the inland hydraulic boundary with a constant flow rate (indicated by the black line marked with a triangle in the figure), the inland hydraulic boundary with a constant flow rate (indicated by the black line marked with a circle), and the universal hydraulic boundary with a constant flow rate (indicated by the colored straight line) proposed in the present invention. Different colors represent the changes of the external hydraulic boundary 6 under different hydraulic head conditions. The equivalent inland hydraulic boundary makes the seawater intrusion systems with different hydraulic boundary conditions comparable.

[0071] from Figure 5 It can be seen that there are differences in the evaluation of sustainable freshwater extraction rate of seawater intrusion systems under different boundary conditions. Under most working conditions, the evaluation method proposed in the present invention that considers the change of hydraulic boundaries obtains a smaller sustainable freshwater extraction rate. This is because the sustainable freshwater extraction rate is not only determined by the hydraulic gradient of inland freshwater, but also closely related to the hydraulic conductivity of the external hydraulic boundary and the area of ​​the water-passing section. Therefore, the method proposed in the present invention can more accurately reflect the dynamically changing hydraulic boundary conditions. Ignoring the impact of pumping on the change of inland hydraulic boundaries will lead to unrealistic inland freshwater replenishment assessments and may produce dangerous freshwater extraction rate results.

[0072] Based on potential energy theory and Fourier transform method, combined with universal head boundary conditions, this paper develops a mathematical analytical model suitable for phreatic aquifers, which can quickly calculate the range of steady-state seawater intrusion and sustainable freshwater extraction. This paper not only solves the limitations of traditional hydraulic boundary condition assessment methods, but also simplifies the calculation model by reasonably setting the research area and hydraulic boundary conditions, improves the calculation efficiency while maintaining the assessment accuracy, and provides an 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 in that: The following steps are involved: Construct conceptual models 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 height, 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, φ0 is the phreatic level of the unconfined aquifer at the inland boundary; The range of seawater intrusion is determined by interpolating the potential field Φ(x,y) to find the equipotential lines equal to the potential at the salt toe and the height of the fresh-salt water interface; Calculate the sustainable freshwater extraction rate: Calculate the stagnation point position, and 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 exploitation in a phreatic aquifer taking into account hydraulic boundary changes according to claim 1, characterized in that: The correction coefficient α is calculated by the following formula: In the formula, 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 dispersion.

3. A rapid assessment method for seawater intrusion and sustainable freshwater exploitation in a phreatic aquifer taking into account 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 formula, 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 exploitation in a phreatic aquifer taking into account hydraulic boundary changes according to claim 3, characterized in that: The potential energy at the salt toe position in the unconfined aquifer is calculated by the following formula: In the formula, Φ t is the potential energy at the salt toe.

5. A rapid assessment method for seawater intrusion and sustainable freshwater exploitation 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 fresh water / salt water interface; Φ is the potential energy.

6. A rapid assessment method for seawater intrusion and sustainable freshwater exploitation 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: In the formula, 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 exploitation 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 exploitation in a phreatic aquifer taking into account hydraulic boundary changes according to claim 7, characterized in that: The geological parameters include aquifer type, absolute elevation of impermeable substrate, and aquifer permeability coefficient.

9. A rapid assessment method for seawater intrusion and sustainable freshwater exploitation in a phreatic aquifer taking into account hydraulic boundary changes according to claim 7, characterized in that: The hydrological parameters include 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.

10. A rapid assessment method for seawater intrusion and sustainable freshwater exploitation in a phreatic aquifer taking into account 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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