A two-zone island underground water exploitable quantity rapid evaluation and optimal exploitation position determination method

Abstract

This invention discloses a method for rapidly assessing the exploitable groundwater volume and determining the optimal extraction location in a dual-zone island system. The method includes: constructing a conceptual model of the aquifer in the dual-zone island after reclamation; classifying the study conditions based on the relative positions of the pumping well and the reclamation area: in condition one, the pumping well is located in the original aquifer, and in condition two, the pumping well is located in the aquifer of the newly reclaimed area, and deriving the head expressions after pumping for conditions one and two respectively; calculating the brackish water interface based on the Ghyben-Herzberg relationship; calculating the exploitable volume: the pumping rate corresponding to the point where the height of the brackish water interface after pumping reaches the bottom of the pumping well is the exploitable volume; and calculating the optimal extraction location: the pumping well position corresponding to the derivative of the exploitable volume with respect to the horizontal position of the pumping well is the optimal extraction location. This invention is based on analytical derivation, allowing adjustment of key hydrogeological parameters and reclamation engineering parameters of the study area according to the actual study area, ensuring the accuracy of the results, and improving computational efficiency.

Description

Technical Field

[0001] This invention relates to the study of groundwater resources on islands, and more particularly to a method for rapid assessment of exploitable groundwater volume and determination of optimal extraction location on dual-zone islands. Background Technology

[0002] Compared to mainland areas, islands have smaller land areas, poorer water catchment conditions, and limited recharge sources, making it difficult to form substantial surface water bodies. Therefore, many small and medium-sized islands face severe freshwater scarcity. Groundwater is the only stable and reliable source of freshwater for these islands. Groundwater originates from rainfall on the island. Rainwater, due to its lower density, floats on top of the denser seawater, forming a lens-like structure known as a "freshwater lens." The interface between freshwater and seawater is called the brackish water interface. When this groundwater is extracted using wells, the brackish water interface rises. If the extraction volume is too large, brackish water will enter the wells, affecting freshwater access on the island. Therefore, assessing the exploitable amount of groundwater on islands and planning extraction locations is of significant practical value.

[0003] To fully develop their island economies, coastal countries have undertaken large-scale land reclamation and island expansion projects. Since implementing its maritime power strategy, my country has also carried out a series of land reclamation projects in the South China Sea islands. Because the permeability of reclamation materials typically differs from that of natural island aquifers, land reclamation projects cause aquifers on islands to exhibit vertical zonation due to differences in permeability, forming "dual-zone island aquifers." Currently, the impact of land reclamation projects on groundwater extraction on islands remains unclear.

[0004] Therefore, there is an urgent need to propose a method for rapid assessment of the exploitable amount of water within the aquifer of a two-zone island after land reclamation and for determining the optimal mining location. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to propose a method for rapid assessment of the exploitable amount of groundwater in a dual-zone island and determination of the optimal extraction location, so as to maximize the extraction amount while achieving sustainable utilization of groundwater in the island.

[0006] Technical solution: This invention includes the following steps:

[0007] S1. Construct a conceptual model of the aquifer of the island in the two zones after land reclamation;

[0008] S2. Based on the relative position of the pumping well and the reclamation area, the research conditions are classified: in condition one, the pumping well is located in the original aquifer, and in condition two, the pumping well is located in the aquifer of the newly reclaimed area. The expressions for the water head after pumping in condition one and condition two are derived respectively.

[0009] S3. Calculate the brackish water interface based on the Ghyben-Herzberg relation;

[0010] S4. Calculate the recoverable amount: The pumping rate at which the height of the brackish water interface just reaches the bottom of the pumping well after pumping is the recoverable amount.

[0011] S5. Calculate the optimal mining location: Take the derivative of the exploitable quantity with respect to the horizontal position of the pumping well. The pumping well position corresponding to the derivative being 0 is the optimal mining location.

[0012] The expression for the head after pumping in the first operating condition is:

[0013] ;

[0014] In the formula, x W ≤ D0; h [L] is the groundwater level; w [L / T] is the freshwater recharge intensity received by the island; ε is the Ghyben-Herzberg coefficient, defined as the ratio of the density difference between freshwater and brackish water; the width of the entire island is D[L], the width of the original island aquifer is D0 [L], and the width of the newly reclaimed area is D b [L],D = D0 + D b The permeability coefficient of the aquifer in the original island area is K0 [L / T], and the permeability coefficient of the medium used for reclamation is K. b [L]; The pumping well is located on the right side of the sea boundary x W [L] and below sea level H W At [L], the origin of the coordinate system is established at the intersection of the right sea boundary and the sea level, with horizontal leftward and vertical upward as positive. Therefore, the coordinates of the pumping well are (x... W , -H W ); q l and q r [L 2 [ / T] represents the pumping rates on the left and right sides of the pumping well, respectively, and is related to the total pumping rate q [L]. 2 The / T] relationship is as follows:

[0015] .

[0016] The expression for the head after pumping in the second operating condition is:

[0017] ;

[0018] In the formula, x W ≥ D0, q l and q r The relationship with the total pumping rate q is as follows:

[0019] .

[0020] The brackish water interface is:

[0021] ;

[0022] In the formula, h f [L] represents the depth of the brackish water interface below sea level, and h[L] represents the groundwater level.

[0023] The formula for calculating the recoverable amount under the first working condition is as follows:

[0024] ;

[0025] In the formula, q cr [L 2 [ / T] represents the amount of material that can be extracted per unit length.

[0026] The formula for calculating the recoverable amount under the second working condition is as follows:

[0027] .

[0028] The optimal mining location is the location of the pumping well that yields the maximum extraction volume.

[0029] The formula for calculating the optimal mining location for the first working condition is as follows:

[0030] .

[0031] The formula for calculating the optimal mining location in working condition two is as follows:

[0032] .

[0033] The conceptual model of the aquifer of the dual-zone island after reclamation includes: hydrogeological parameters of the study area, reclamation project details, and the location of groundwater wells. The hydrogeological parameters of the study area include aquifer permeability coefficient, seawater density, freshwater density, and rainfall infiltration recharge. The reclamation project details include the original island width, the width of the reclamation area, and the permeability coefficient of the reclamation materials.

[0034] Beneficial effects: Based on analytical derivation, this invention can adjust key hydrogeological parameters and land reclamation engineering parameters of the research area according to the actual research area, and can be flexibly applied to the formulation of groundwater extraction strategies for islands in two zones after land reclamation; in addition, this invention significantly reduces the demand for computing resources and manpower and materials while ensuring the accuracy of the results, and improves computing efficiency, thus having the technical advantages of high efficiency and economy. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the conceptual model of the aquifer in a dual-zone island after land reclamation according to the present invention (Condition 1).

[0036] Figure 2 This is a schematic diagram of working condition two in an embodiment of the present invention;

[0037] Figure 3 This is a comparison chart of the calculation results and numerical simulation results of this invention. Detailed Implementation

[0038] The invention will now be further described with reference to the accompanying drawings.

[0039] The method for rapid assessment of exploitable groundwater volume and determination of optimal extraction location in a dual-zone island aquifer system of reclaimed land is applicable to a dual-zone strip-shaped island aquifer system, where the length is much greater than the width. Therefore, the groundwater flow per unit length of the aquifer is sufficient to characterize the groundwater flow of the entire island. The method includes the following steps:

[0040] S1. Collect and analyze hydrogeological parameters, land reclamation project details, and groundwater well locations in the study area to construct a conceptual model of the aquifer of the two islands after land reclamation. Land reclamation project data includes the scale of reclamation, source and permeability of reclamation materials; hydrogeological parameters include the width of the natural island, the permeability coefficient of the natural island aquifer, the permeability coefficient of the reclamation area, rainfall infiltration recharge, seawater density, and freshwater density. Establish a rectangular coordinate system based on the conceptual model, with the origin at the intersection of sea level and the right boundary of the island. The x-axis is positive horizontally to the right, and the y-axis is positive vertically upwards.

[0041] like Figure 1 As shown, the study area consists of two parts: a natural island area and a reclaimed area. The two sides are seawater boundaries with constant head and concentration, and the area above is replenished by rainfall. The groundwater of the island is located between the groundwater level 1 and the brackish water interface 2. A pumping well 4 is installed inside the aquifer. The pumping well 4 is located below the mean sea level 3 and above the brackish water interface 2 to avoid pumping out brackish water.

[0042] Based on the relative positions of the reclaimed area and pumping well 4, two research scenarios can be defined: in scenario one, pumping well 4 is located in a natural island area, such as... Figure 1 As shown, in working condition two, pumping well 4 is located in the reclaimed area, as... Figure 2 As shown.

[0043] S2. Considering two operating conditions: the pumping well is located in a natural island area (condition 1) and the pumping well is located in a newly reclaimed area (condition 2), using the Dupuit assumption, the Ghyben-Herzberg relation, and based on Darcy's law and the law of continuous flow, derive the expressions for the head after pumping in conditions 1 and 2 respectively:

[0044] Operating Condition 1 (x) W ≤ D0):

[0045] (1)

[0046] in,

[0047] .

[0048] Operating Condition 2 (x) W ≥ D0):

[0049] ; (2)

[0050] in,

[0051] ;

[0052] In the formula, h[L] is the groundwater level; w[L / T] is the freshwater recharge intensity received by the island; ε is the Ghyben-Herzberg coefficient, defined as the ratio of the density difference between freshwater and brackish water; the width of the entire island is D[L], the width of the original island aquifer is D0[L], and the width of the newly reclaimed area is D b [L], that is, D = D0 + D b The permeability coefficient of the aquifer in the original island area is K0 [L / T], and the permeability coefficient of the medium used for reclamation is K. b [L]; The pumping well is located on the right side of the sea boundary x W [L] and below sea level H W At [L], the origin of the coordinate system is established at the intersection of the right sea boundary and the sea level, with horizontal leftward and vertical upward as positive. Therefore, the coordinates of the pumping well are (x... W , -H W ); q l and q r [L 2 / T] represents the pumping rates on the left and right sides of the pumping well, respectively.

[0053] S3. The expression for the brackish water interface can be obtained from the Ghyben-Herzberg relation:

[0054] (3)

[0055] In the formula, h f [L] is the depth of the brackish water interface below sea level, and h[L] is the groundwater level obtained by equation (1) or equation (2).

[0056] S4. Calculate the recoverable amount: The pumping rate at which the height of the brackish water interface just reaches the bottom of the pumping well after pumping is the recoverable amount.

[0057] Operating Condition 1 (x) W ≤ D0):

[0058] (4)

[0059] Operating Condition 2 (x) W ≥ D0):

[0060] (5)

[0061] In the formula, q cr [L 2 / T] represents the exploitable amount, corresponding to the situation where the brackish water interface obtained from equation (3) reaches the bottom of the pumping well.

[0062] S5. Calculate the optimal mining position: Take the derivative of the exploitable amount with respect to the horizontal position of the pumping well. The pumping well position corresponding to the derivative of 0 is the optimal mining position, that is, the pumping well position that yields the maximum exploitable amount.

[0063] Operating Condition 1 (x) W ≤ D0):

[0064] (6)

[0065] Operating Condition 2 (x) W ≥ D0):

[0066] (7)

[0067] The x obtained from equations (6) and (7) W The value represents the optimal extraction location, i.e., the horizontal position of the pumping well that yields the maximum extraction volume.

[0068] The following section will further elaborate on this point using numerical simulations.

[0069] As shown in Table 1, the study area selected in this embodiment considers an island with a total width of 600 m, a natural island area with a width of 500 m and a permeability coefficient of 10 m / d, and a reclaimed area with a width of 200 m and a permeability coefficient of 10 m / d. The rainfall replenishment is 0.01 m / d, and the freshwater density is 1000 kg / m³. 3 Seawater density is 1025 kg / m³ 3 .

[0070] Table 1. Parameters used in numerical simulation

[0071] parameter Value Island width (D) 600 m <![CDATA[Coefficient of permeability (K0)]]> 100 m / d <![CDATA[Density of salt water (ρ s )]]> <![CDATA[1025 kg / m 3 ]]> <![CDATA[Freshwater density (ρ f )]]> <![CDATA[1000 kg / m 3 ]]> Supply intensity (w) 0.01 m / d <![CDATA[Osmotic coefficient (K in the hypotonic region b )]]> 10 m / d <![CDATA[Width of the low osmotic region (D b )]]> 200 m <![CDATA[Well depth (H W )]]> 0 m, 5 m, 10 m <![CDATA[Horizontal position of the well (x W )]]> 100m, 200m, 300m, 400m, 500m

[0072] Applying the above parameters to this embodiment, and considering pumping wells at arbitrary horizontal positions and three different depths (0 m, 5 m, and 10 m), we obtain... Figure 3The black curve is shown. To verify the accuracy of this evaluation method, a post-reclamation dual-zone island aquifer groundwater flow model was constructed using Flopy and SEAWAT2000. Simulations were performed at horizontal depths of 100m, 200m, 300m, 400m, and 500m, and vertical depths of sea level, 5m below sea level, and 10m below sea level. The specific parameters used in the numerical simulation are shown in Table 1. Figure 3 The rhombus represents the result of the numerical simulation. As can be seen from the results, the recoverable quantity obtained by this invention is highly consistent with the result obtained from the numerical simulation, demonstrating high accuracy.

[0073] When obtaining recoverable quantities through numerical simulation, the pumping rate needs to be continuously adjusted until the average concentration in the pumping well does not exceed 1 g / L at steady state. The process of finding recoverable quantities through numerical simulation is extremely time-consuming; on a computer equipped with an AMD R7 5800H processor, calculating the recoverable quantity of a pumping well at a specific location takes an average of one week. The method of this invention only takes a few seconds, significantly improving computational efficiency while maintaining accuracy.

[0074] In addition, such as Figure 3 As shown, numerical simulation methods provide the recoverable quantities at certain specific locations, but obtaining the optimal mining location through numerical simulation requires a significant amount of work. However, the method proposed in this invention can provide the recoverable quantities corresponding to pumping water at any location in the implementation case within tens of seconds, thus indirectly obtaining the optimal mining location with the maximum recoverable quantity.

[0075] This invention develops a mathematical analytical model applicable to aquifers in dual-zone islands, capable of rapidly estimating exploitable quantities under given pumping well locations, and also used to determine the optimal extraction location when pumping well locations are not fixed. Compared to traditional numerical simulation methods, this invention significantly improves computational efficiency while ensuring accuracy, providing an efficient and practical management solution for the sustainable development and utilization of freshwater resources in island regions.

Claims

1. A method for rapid assessment of exploitable groundwater volume and determination of optimal extraction location in a dual-zone island system, characterized in that, Includes the following steps: S1. Construct a conceptual model of the aquifer of the island in the two zones after land reclamation; S2. Based on the relative position of the pumping well and the reclamation area, the research conditions are classified: in condition one, the pumping well is located in the original aquifer, and in condition two, the pumping well is located in the aquifer of the newly reclaimed area. The expressions for the water head after pumping in condition one and condition two are derived respectively. S3. Calculate the brackish water interface; S4. Calculate the recoverable amount: The recoverable amount is the pumping rate at which the height of the brackish water interface just reaches the bottom of the pumping well after pumping. S5. Calculate the optimal mining location: Take the derivative of the exploitable quantity with respect to the horizontal position of the pumping well. The pumping well position corresponding to the derivative being 0 is the optimal mining location.

2. The method for rapid assessment of exploitable groundwater volume and determination of optimal extraction location in a dual-zone island system according to claim 1, characterized in that, The expression for the head after pumping in the first operating condition is: In the formula, x W ≤ D0; h [L] is the groundwater level; w [L / T] is the freshwater recharge intensity received by the island; ε is the Ghyben-Herzberg coefficient, defined as the ratio of the density difference between freshwater and brackish water; the width of the entire island is D [L], the width of the original island aquifer is D0 [L], and the width of the newly reclaimed area is D b [L],D = D0 + D b The permeability coefficient of the aquifer in the original island area is K0 [L / T], and the permeability coefficient of the medium used for reclamation is K. b [L]; The pumping well is located on the right side of the sea boundary x W [L] and below sea level H W At [L], the origin of the coordinate system is established at the intersection of the right sea boundary and the sea level, with horizontal leftward and vertical upward as positive. Therefore, the coordinates of the pumping well are (x... W , -H W ); q l and q r [L 2 [ / T] represents the pumping rates on the left and right sides of the pumping well, respectively, and is related to the total pumping rate q [L]. 2 The / T] relationship is as follows: 。 3. The method for rapid assessment of exploitable groundwater volume and determination of optimal extraction location in a dual-zone island system according to claim 1, characterized in that, The expression for the head after pumping in the second operating condition is: In the formula, x W ≥ D0, q l and q r With the total pumping rate q [L 2 The / T] relationship is as follows: 。 4. The method for rapid assessment of exploitable groundwater volume and determination of optimal extraction location in a dual-zone island system according to claim 2 or 3, characterized in that, The formula for calculating the brackish water interface is as follows: In the formula, h f [L] represents the depth of the brackish water interface below sea level, and h[L] represents the groundwater level.

5. The method for rapid assessment of exploitable groundwater volume and determination of optimal extraction location in a dual-zone island system according to claim 2, characterized in that, The formula for calculating the recoverable amount under the first working condition is as follows: In the formula, q cr [L 2 [ / T] represents the amount of material that can be extracted per unit length.

6. The method for rapid assessment of exploitable groundwater volume and determination of optimal extraction location in a dual-zone island system according to claim 3, characterized in that, The formula for calculating the recoverable amount under the second working condition is as follows: 。 7. The method for rapid assessment of exploitable groundwater volume and determination of optimal extraction location in a dual-zone island system according to claim 1, characterized in that, The optimal mining location is the location of the pumping well that yields the maximum extraction volume.

8. The method for rapid assessment of exploitable groundwater volume and determination of optimal extraction location in a dual-zone island system according to claim 5, characterized in that, The formula for calculating the optimal mining location for the first working condition is as follows: 。 9. The method for rapid assessment of exploitable groundwater volume and determination of optimal extraction location in a dual-zone island system according to claim 6, characterized in that, The formula for calculating the optimal mining location in working condition two is as follows: 。 10. The method for rapid assessment of exploitable groundwater volume and determination of optimal extraction location in a dual-zone island system according to claim 1, characterized in that, The conceptual model of the aquifer of the dual-zone island after reclamation includes: hydrogeological parameters of the study area, reclamation project details, and the location of groundwater wells. The hydrogeological parameters of the study area include aquifer permeability coefficient, seawater density, freshwater density, and rainfall infiltration recharge. The reclamation project details include the original island width, the width of the reclamation area, and the permeability coefficient of the reclamation materials.

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