A method for calculating the size and location of freshwater lenses in riparian zones

Abstract

The application discloses a kind of river bank zone freshwater lens size and position calculation method, comprising the following steps: establishing two-dimensional river bank zone aquifer groundwater seepage model;Establish groundwater seepage control equation;Suppose the occurrence condition of freshwater lens;Deduce the maximum thickness of freshwater lens;Deduce groundwater seepage flow using control equation;Test whether the occurrence condition of freshwater lens assumed in step 3 is accurate;Calculate the size and position of freshwater lens.The application can calculate the size and position of freshwater lens in layered river bank zone aquifer, can estimate the distribution of freshwater area on both sides of river suffering from underground salt water intrusion, and provide guidance for health assessment and ecological environment protection of river bank vegetation in arid area.

Description

Technical Field

[0001] This invention relates to the field of riparian groundwater environment and ecological protection technology, and in particular to a method for calculating the size and location of freshwater lenses in riparian zones. Background Technology

[0002] Due to intense evaporation in arid and semi-arid regions (hereinafter referred to as "arid areas"), large amounts of salt accumulate in the topsoil of cultivated areas. This salt is leached into groundwater through agricultural irrigation and rainfall, continuously accumulating to form saline groundwater. Driven by hydraulic gradients, this saline groundwater migrates towards the aquifers in low-lying riverbanks. Because of its higher density, the saline groundwater intrudes from the bottom of the aquifers and eventually drains into rivers. Above the aquifers, less dense freshwater floats above the intruding saline water, maintaining its shape through lateral seepage from rivers. This lenticular freshwater body is figuratively called a "freshwater lens." The existence of freshwater lenses directly provides an important freshwater source for the growth of riparian vegetation in arid areas and is a crucial carrier for maintaining the riparian ecosystem. Accurately characterizing this unique freshwater accumulation pattern in arid riparian zones has significant theoretical and scientific implications.

[0003] Currently, most methods for estimating the size and location of freshwater lenses in riparian aquifers, both domestically and internationally, are limited to homogeneous aquifers. However, in reality, riparian aquifers are often heterogeneous. For example, riparian floodplains typically accumulate a certain thickness of low-permeability clay, usually characterized as a stratified aquifer (i.e., an upper layer of low-permeability medium and a lower layer of high-permeability sand). This stratification significantly influences the morphology of freshwater lenses within riparian aquifers. However, analytical solutions for the size and location of freshwater lenses in stratified riparian aquifers are currently lacking, making it impossible to accurately estimate the occurrence of freshwater lenses in actual stratified riparian aquifers. Furthermore, the impact of changes in hydrogeological parameters (such as permeability coefficient and river level) on freshwater lenses in stratified riparian aquifers remains unknown. Summary of the Invention

[0004] The purpose of this invention is to consider the stratification of the aquifer in the riparian zone and to calculate the size and location of the freshwater lens in the riparian zone.

[0005] The technical solution of the present invention is as follows:

[0006] A method for calculating the size and location of a freshwater lens in a riverbank zone includes the following steps:

[0007] Step 1: Establish a two-dimensional groundwater seepage model for the aquifer in the riverbank zone: the groundwater is in a saturated steady-state flow, the seepage medium is isotropic and homogeneous, and the unsteady recharge and evaporation processes are ignored; the left and right boundaries of the seepage model are set as vertical constant head boundaries, the upper and lower boundaries are set as no-flow boundaries, the size and volume of the freshwater lens are stable and unchanged, the mixing of fresh and brackish groundwater is ignored, the river runs through the entire aquifer, and the riverbed is a vertical, uniformly thick, low-permeability layer.

[0008] Step 2, Introduce Darcy's Law and establish the governing equation for groundwater seepage: Using Darcy's Law and the Dubouy assumption, the governing equation for groundwater seepage is established as follows:

[0009]

[0010]

[0011] Where: q s η is the unit width flow rate of groundwater seepage. s h represents the thickness of the underground saline water. s The groundwater head is saline, and the river water level is η. r Inland boundary (x distance from the riverbed) b The groundwater level at the distance is η. B K1 and K2 are the permeability coefficients of the upper and lower layers of sand in the riverbank zone, respectively, with corresponding thicknesses of H1 and H2, ρ f ρ is the density of fresh water. s Let x be the density of the saline water, and x be the distance from the riverbed. L The size of the freshwater lens, x b This represents the total width of the aquifer.

[0012] Step 3, assuming the occurrence conditions of the freshwater lens: The freshwater lens has different positional relationships with the aquifer in the riverbank zone, including the following conditions:

[0013] Operating Condition 1: The freshwater lens is completely located in the upper low-permeability layer;

[0014] Operating Condition 2: The freshwater lens spans the upper low-permeability layer and the lower high-permeability layer;

[0015] Condition 3: The freshwater lens is completely located in the high-permeability layer below.

[0016] Since the specific working conditions are unknown, this step can arbitrarily assume one working condition.

[0017] Step 4, Derive the maximum thickness of the freshwater lens: Derive the maximum thickness of the freshwater lens, which is also derive the height η of the groundwater at the riverbed. sr Specifically, based on the difference in water head caused by the density difference between fresh and salt water on both sides of the riverbed, Darcy's law is used to establish a seepage equation for the riverbed, resulting in the following formula:

[0018]

[0019] In the formula, K r is the permeability coefficient of the riverbed, B r is the thickness of the riverbed.

[0020] Step 5, deriving groundwater seepage discharge by using a governing equation: according to the working condition assumed in step (3), the calculation formula of groundwater seepage discharge under the corresponding working condition can be derived from the governing equation in step (2):

[0021] a. Working condition 1:

[0022]

[0023] b. Working condition 2:

[0024]

[0025] c. Working condition 3:

[0026]

[0027] In the formula, H b is the thickness at the salt groundwater boundary, H r is the river water surface elevation,

[0028] Step 6, checking whether the occurrence working condition of the freshwater lens assumed in step 3 is accurate: according to η obtained in step (4) sr make the following judgment:

[0029] ① If working condition 1 is assumed in step (3), then η sr >H2; if the condition is not satisfied, return to step (4) and re-assume another working condition;

[0030] ② If working condition 2 is assumed in step (3), then η sr <H2 and H r >H2; if the condition is not satisfied, return to step (4) and re-assume another working condition;

[0031] ③ If working condition 3 is assumed in step (3), then η sr <H2 and H r <H2; if the condition is not satisfied, return to step (4) and re-assume another working condition.

[0032] Step 7, calculating the size and position of the freshwater lens: for the working condition that passes the check in step (6), the calculation formulas for the size x of the corresponding freshwater lens L and the position η s are:

[0033] a. Working condition 1:

[0034]

[0035]

[0036] b. Operating Condition Two:

[0037]

[0038]

[0039]

[0040] c. Operating Condition 3:

[0041]

[0042]

[0043]

[0044] In the formula, A1 = K1, B1 = 2H2(K2 - K1),

[0045] x i The x-coordinate of the intersection of the brackish water interface and the aquifer boundary.

[0046] Compared with the prior art, the present invention has the following advantages:

[0047] This invention can estimate the size and location of freshwater lenses in stratified riparian aquifers. The analytical formula can be solved directly using software such as MATLAB, and the estimation result can be obtained within one second. Compared with traditional numerical simulation methods (which usually take several hours), it significantly improves computational efficiency while ensuring a certain level of accuracy. It can provide guidance for vegetation health assessment and ecological environmental protection in arid riparian zones. Attached Figure Description

[0048] Figure 1 This is a flowchart of the method.

[0049] Figure 2 This is a model diagram for working condition one;

[0050] Figure 3 This is a model diagram for working condition two;

[0051] Figure 4 This is a model diagram for working condition three;

[0052] In the diagram: 1: Upper layer of low-permeability clay; 2: Lower layer of high-permeability sand; 3: Boundary between upper and lower aquifers; 4: Freshwater river; 5: Inland saline water level; 6: Groundwater seepage (dark gray); 7: Freshwater lens (light gray); 8: Riverbed; 9: Freshwater-saline water interface.

[0053] Figure 5 The graph shows a comparison between the experimental results, analytical solutions, and numerical simulation results.

[0054] Figure (a): River water level η r A comparison of experimental results, analytical solution calculation results, and numerical simulation results for a homogeneous aquifer at a depth of 0.27m.

[0055] Figure (b): River water level η r A comparison of experimental results, analytical solution calculation results, and numerical simulation results for a stratified aquifer with a depth of 0.27m.

[0056] Figure (c): River water level η r A comparison of experimental results, analytical solution calculation results, and numerical simulation results for a homogeneous aquifer at a depth of 0.28m.

[0057] Figure (d): River water level η r A comparison of experimental results, analytical solution calculation results, and numerical simulation results for a stratified aquifer with a depth of 0.28m.

[0058] Figure (e): River water level η r A comparison of experimental results, analytical solution calculation results, and numerical simulation results for a homogeneous aquifer with a depth of 0.29m.

[0059] Figure (f): River water level η r A comparison of experimental results, analytical solution calculation results, and numerical simulation results for a stratified aquifer with a depth of 0.29m. Detailed Implementation

[0060] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0061] like Figure 2-4 The diagram illustrates the occurrence of a freshwater lens in a stratified aquifer along a riverbank. Driven by the saline water level 5 at the inland boundary, saline water seepage 6 occurs in the stratified aquifer, which consists of an upper layer of low-permeability clay 1 and a lower layer of high-permeability sand 2 (separated by a boundary line 3). After passing through the riverbed 8, it intrudes into the freshwater river 4. Under the influence of buoyancy, the freshwater river 4 laterally seeps into the aquifer via the riverbed 8, forming a stable brackish water interface 9. The freshwater body above the brackish water interface is the freshwater lens 7.

[0062] like Figure 1 A method for calculating the size and location of freshwater lenses in riverbank zones includes the following steps:

[0063] Step 1: Establish a two-dimensional groundwater seepage model for the aquifer in the riverbank zone: the groundwater is in a saturated steady-state flow, the seepage medium is isotropic and homogeneous, and the unsteady recharge and evaporation processes are ignored; the left and right boundaries of the seepage model are set as vertical constant head boundaries, the upper and lower boundaries are set as no-flow boundaries, the size and volume of the freshwater lens are stable and unchanged, the mixing of fresh and brackish groundwater is ignored, the river runs through the entire aquifer, and the riverbed is a vertical, uniformly thick, low-permeability layer.

[0064] Step 2, Introduce Darcy's Law and establish the governing equation for groundwater seepage: Using Darcy's Law and the Dubouy assumption, the governing equation for groundwater seepage is established as follows:

[0065]

[0066]

[0067] Where: q s η is the unit width flow rate of groundwater seepage. s h represents the thickness of the underground saline water. s The groundwater head is saline, and the river water level is η. r The groundwater level at the inland boundary (distance from the riverbed) is η. B K1 and K2 are the permeability coefficients of the upper and lower layers of sand in the riverbank zone, respectively, with corresponding thicknesses of H1 and H2, ρ f ρ is the density of fresh water. s Let x be the density of the saline water, and x be the distance from the riverbed. L The size of the freshwater lens, x b This represents the total width of the aquifer.

[0068] Step 3, assuming the occurrence conditions of the freshwater lens: The freshwater lens has different positional relationships with the aquifer in the riverbank zone, and the conditions include (condition classification as follows) Figure 1-3 ):

[0069] ①Condition 1: The freshwater lens is completely located in the upper layer of low-permeability clay 1;

[0070] ②Condition 2: The freshwater lens spans the upper layer of low-permeability clay 1 and the lower layer of high-permeability sand 2;

[0071] ③ Condition 3: The freshwater lens is completely located in the underlying highly permeable sand.

[0072] Since the specific working conditions are unknown, this step can arbitrarily assume one working condition.

[0073] Step 4, Deriving the maximum thickness of the freshwater lens: deriving the maximum thickness of the freshwater lens, that is, deriving the height η of saline groundwater at the riverbed sr , specifically, according to the water head difference caused by the density difference of salt and fresh water on both sides of the riverbed, Darcy's law is used to establish a seepage equation for the riverbed, and the following formula can be obtained:

[0074]

[0075] wherein K r is the permeability coefficient of the riverbed, and B r is the thickness of the riverbed.

[0076] Step 5, Deriving groundwater seepage discharge using the governing equation: according to the working conditions assumed in Step 3, the calculation formula of groundwater seepage discharge under corresponding working conditions can be derived from the governing equation in Step 2 as follows:

[0077] Working condition 1:

[0078]

[0079] Working condition 2:

[0080]

[0081] Working condition 3:

[0082]

[0083] wherein,

[0084] H b is the thickness at the saline groundwater boundary, H r is the river water surface height,

[0085] Step 6, Checking whether the assumed occurrence working condition of the freshwater lens in Step 3 is correct: according to η obtained in Step 4 sr , the following judgment is made:

[0086] If Step 3 assumes working condition 1, then η sr >H2; if the condition is not satisfied, return to Step 4 and re-assume another working condition;

[0087] If Step 3 assumes working condition 2, then η sr <H2 and H r >H2; if the condition is not satisfied, return to Step 4 and re-assume another working condition;

[0088] If Step 3 assumes working condition 3, then η sr <H2 and H r <H2; if the condition is not satisfied, return to Step 4 and re-assume another working condition.

[0089] Step 7, Calculate the size and position of the freshwater lens: For the condition that passed the inspection in Step 6, the corresponding freshwater lens size x L and position η s The calculation formula is:

[0090] Operating Condition 1:

[0091]

[0092]

[0093] b. Operating Condition Two:

[0094]

[0095]

[0096]

[0097] c. Operating Condition 3:

[0098]

[0099]

[0100]

[0101] In the formula, A1 = K1, B1 = 2H2(K2 - K1),

[0102]

[0103]

[0104]

[0105]

[0106]

[0107] x i The x-coordinate of the intersection of the brackish water interface and the aquifer boundary.

[0108] To verify the accuracy of the analytical solution, indoor experiments and numerical simulations were conducted, and the analytical calculation results were compared with the experimental and numerical simulation results. The indoor experiments divided the river water level into three conditions, with the river water level η... r The groundwater levels at the inland boundary (distance from the riverbed) are η, which are 0.27m, 0.28m, and 0.29m respectively. B =0.30m, total width of aquifer x b=1.2m, permeability coefficient K of the riverbed r =178.6m, riverbed thickness B r =0.005m, the densities of fresh water and salt water are ρ and ρ, respectively. f =1000kg / m 3 and ρ s =1037kg / m 3 .

[0109] For the three working conditions, two types of riverbank aquifer conditions were simulated: stratified and homogeneous. In the homogeneous riverbank aquifer, the sand permeability coefficient K = 1880 m / d and the sand thickness H2 = 0.31 m. In the stratified riverbank aquifer, the upper sand permeability coefficient K1 = 450 m / d, the lower sand permeability coefficient K2 = 1880 m / d, the upper sand thickness H1 = 0.16 m, and the lower sand thickness H2 = 0.15 m.

[0110] In the experiment, saline water turned red upon the addition of a conservative staining agent (Allura Red), while freshwater remained colorless. After the three operating conditions were run to steady state, the experimental results were recorded using a high-definition digital camera. Numerical simulations were performed using the variable density groundwater simulation program SEAWAT 2000. A numerical model was constructed using data measured in the laboratory to simulate the three operating conditions in the experiment.

[0111] The experiment observed the size of the freshwater lens near the riverbank and the location of the brackish water interface, as follows: Figure 5 As shown (dark areas represent brackish water, light areas represent fresh water). Furthermore, the dashed lines in the figure represent the brackish water interface obtained from numerical simulation calculations, while the solid lines represent the brackish water interface and groundwater level calculated using analytical solutions. For example... Figure 5 As shown in Figure AF, the analytical calculation results fit the experimental and numerical simulation results quite well, demonstrating the accuracy of the analytical solution.

[0112] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A method for calculating the size and location of a freshwater lens in a riverbank zone, characterized in that, Includes the following steps: Step 1: Establish a two-dimensional groundwater seepage model of the aquifer in the riverbank zone; Step 2: Establish the groundwater seepage control equation; Step 3, assuming the occurrence conditions of a freshwater lens, the freshwater lens and the aquifer in the riverbank zone have different positional relationships, including: Operating Condition 1: The freshwater lens is completely located in the upper low-permeability layer; Operating Condition 2: The freshwater lens spans the upper low-permeability layer and the lower high-permeability layer; Condition 3: The freshwater lens is completely located in the high-permeability layer below; Step 4: Derive the maximum thickness of the freshwater lens body; Step 5, derive the groundwater seepage flow rate using the governing equations: Based on the assumed working conditions in step (3), the calculation formula for the groundwater seepage flow rate under the corresponding working conditions is derived from the governing equations in step (2): Operating Condition 1: Operating Condition 2: Operating Condition 3: In the formula, Where, x b K represents the total width of the aquifer, K1 and K2 are the permeability coefficients of the upper and lower sandy soil layers of the riverbank, respectively, with corresponding thicknesses of H1 and H2; K r B is the permeability coefficient of the riverbed. r H represents the thickness of the riverbed. b H represents the thickness at the boundary of underground saline water. r The height of the river water level. ρ f ρ is the density of fresh water. s The density is that of saltwater; Step 6: Verify whether the assumed freshwater lens body storage conditions in Step 3 are accurate. Step 7, calculate the size and position of the freshwater lens; for the condition that passes the inspection in step (6), the corresponding freshwater lens size x L and position η s The calculation formula is: Operating Condition 1: Operating Condition 2: Operating Condition 3: In the formula: x L For the size of the freshwater lens, η s This refers to the thickness of the underground saline water. x b q is the total width of the aquifer. s Let A1 = K1 and B1 = 2H2(K2 - K1) be the unit flow rate of groundwater seepage. Among the parameters mentioned above, x i η is the x-coordinate of the intersection of the brackish water interface and the aquifer boundary. sr This represents the maximum thickness of the freshwater lens.

2. The method for calculating the size and location of freshwater lenses in the riverbank zone according to claim 1, characterized in that, In step 1, the groundwater is in a saturated steady-state flow, and the permeable media are all isotropic and homogeneous. Unsteady recharge and evaporation processes are ignored. The left and right boundaries of the seepage model are set as vertical constant head boundaries, and the upper and lower boundaries are set as no-flow boundaries. The size and volume of the freshwater lens are stable and unchanged. The mixing of groundwater and freshwater is ignored. The river runs through the entire aquifer, and the riverbed is a vertical, uniform, low-permeability layer.

3. The method for calculating the size and location of freshwater lenses in the riverbank zone according to claim 2, characterized in that, In step 2, using Darcy's law and the Dubouy assumption, the governing equation for groundwater seepage is established as follows: Where: q s η is the unit width flow rate of groundwater seepage. s h represents the thickness of the underground saline water. s The groundwater head is saline, and the river water level is η. r The groundwater level at the inland boundary is η. B K1 and K2 are the permeability coefficients of the upper and lower layers of sand in the riverbank zone, respectively, with corresponding thicknesses H1 and H2, ρ f ρ is the density of fresh water. s Let x be the density of salt water. L The size of the freshwater lens, x b This represents the total width of the aquifer.

4. The method for calculating the size and location of freshwater lenses in the riverbank zone according to claim 3, characterized in that, In step 4, the maximum thickness of the freshwater lens is derived, which is also the height of the groundwater η at the riverbed. sr : In the formula, K r B is the permeability coefficient of the riverbed. r q represents the thickness of the riverbed. s ρ is the unit width flow rate of groundwater seepage. f ρ is the density of fresh water. s The density is that of saline water.

5. The method for calculating the size and location of the freshwater lens in the riverbank zone according to claim 4, characterized in that, In step 6, based on η obtained in step 4 sr Make the following judgment: If step 3 is assumed to be operating condition one, then η sr >H2; If not satisfied, return to step 4 and re-assume other operating conditions; If step 3 assumes working condition II, then η sr <H2 and H r >H2; if the condition is not satisfied, return to step 4 and re-assume another working condition; If step 3 is assumed to be working condition 3, then η sr <H2 and H r <H2; if the condition is not satisfied, return to step 4 to re-assume another working condition.

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