A method and system for determining the hydraulic parameters of an aquifer based on pumping tests.

Abstract

This invention discloses a method and system for determining the hydraulic parameters of an aquifer based on pumping tests, relating to the field of formation detection technology. The method includes: conducting pumping tests based on pumping wells in a target area, recording test parameters at various time points during the pumping test, including the static water level of the pumping well, pumping flow rate, wellbore water level changes, and pumping time; the pumping well penetrating the aquifer; constructing a mathematical model for the pumping test considering the decrease in aquifer permeability coefficient with depth based on the test parameters at each time point; deriving an analytical solution to the mathematical model of the pumping test using the Green's function method, obtaining an analytical formula; constructing an optimization model based on pressure data collected by sensors at different depths of the pumping well during the pumping test; and inverting the hydraulic parameters of the aquifer based on the analytical formula and the optimization model to obtain the hydraulic parameters of the aquifer. This invention improves the accuracy of monitoring data.

Description

Technical Field

[0001] This invention relates to the field of formation detection technology, and in particular to a method and system for determining the hydraulic parameters of aquifers based on pumping tests. Background Technology

[0002] Existing pumping test standards for industries other than highway engineering have numerous limitations, often failing to meet the requirements of highway engineering, especially deep-buried tunnels. For example, in terms of data acquisition, the models in existing pumping test procedures for other industries are quite common and cannot meet current technical needs. Moreover, many data acquisition devices have low precision, resulting in poor experimental results and low practicality, making it difficult to achieve efficient data acquisition and analysis. Therefore, existing pumping test procedures for other industries are only applicable to shallow-hole pumping tests and are not suitable for deep-hole pumping tests.

[0003] In existing pumping test procedures in other industries, the models assume that the formation is homogeneous. However, in deep-hole pumping tests, due to the large burial depth of the target aquifer, the formation is often heterogeneous under stress and geological structure conditions. The permeability coefficient of the aquifer decreases rapidly with depth, and there are many unknown underground aquifer problems. As a result, the models in traditional pumping test procedures cannot characterize these problems, which may cause non-negligible errors in the pumping test estimation results. In addition, since the current procedures use steady-flow pumping tests, it is difficult to calculate the important parameter of the aquifer permeability coefficient. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for determining the hydraulic parameters of an aquifer based on pumping tests, thereby improving the accuracy of monitoring data.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A method for determining the hydraulic parameters of an aquifer based on pumping tests, comprising:

[0007] Pumping tests were conducted based on pumping wells in the target area, and test parameters were recorded at various time points during the pumping test. The test parameters included the static water level of the pumping well, the pumping flow rate, the change in water level in the well shaft, and the pumping time; the pumping wells penetrated the aquifer.

[0008] Based on the test parameters at each time point, a mathematical model for pumping tests was constructed that considers the decrease in aquifer permeability coefficient with depth.

[0009] The analytical solution of the mathematical model for the pumping test was derived using the Green's function method, and the analytical formula was obtained.

[0010] An optimization model was constructed based on pressure data collected by sensors at different depths of the pumping well during the pumping test.

[0011] Based on the analytical formula and the optimization model, the hydraulic parameters of the aquifer are inverted to obtain the hydraulic parameters of the aquifer.

[0012] Optionally, based on the experimental parameters at each time point, a mathematical model for the pumping test considering the decrease in aquifer permeability with depth is constructed, specifically including:

[0013] Based on the test parameters at each time point, a mathematical model for pumping tests considering the decrease in aquifer permeability coefficient with depth was constructed using the inverse Laplace transform method.

[0014] Optionally, the hydraulic parameters include the permeability coefficient, storage coefficient, and attenuation coefficient at the top of the aquifer.

[0015] Optionally, first sampling points are set at different depths of the pumping well, and pressure data are collected at each first sampling point through the data monitoring sensor; the test parameters also include each pressure data.

[0016] Optionally, the mathematical model for the pumping test is expressed as:

[0017]

[0018] s(r,z,t)|t ＝0 =0, r≥r w ,0 <z<B;

[0019] s(r,z,t)|r →∞ =0,0 <z<B;

[0020]

[0021]

[0022] K = K0exp(-Az);

[0023] Where r is the radial distance to the well center, K(z) is the permeability coefficient at a vertical distance of z, s is the drawdown, and r w Let B be the wellbore radius, B be the bedrock thickness, s(r,z,t) be the drawdown equation, t be time, K0 be the permeability coefficient at the top of the aquifer, Q be the flow rate, A be the attenuation coefficient, HV(.) be the Heaviside function, and S be the flow rate. s denoted by , l represents the distance from the top of the filter pipe, d represents the distance from the bottom of the filter pipe, and K represents the aquifer permeability coefficient.

[0024] This invention discloses a system for determining the hydraulic parameters of an aquifer based on pumping tests, comprising:

[0025] The test parameter acquisition module is used to conduct pumping tests based on pumping wells in the target area and record the test parameters at each time point during the pumping test. The test parameters include the static water level of the pumping well, the pumping flow rate, the change in water level in the well shaft, and the pumping time.

[0026] The pumping test mathematical model construction module is used to construct a pumping test mathematical model that considers the decrease of aquifer permeability coefficient with depth based on the test parameters at each time point.

[0027] The analytical formula determination module is used to derive the analytical solution of the pumping test mathematical model using the Green's function method, and obtain the analytical formula.

[0028] The optimization model building module is used to build an optimization model based on the pressure data collected by sensors at different depths of the pumping well during the pumping test.

[0029] The hydraulic parameter determination module is used to invert the hydraulic parameters of the aquifer based on the analytical formula and the optimization model to obtain the hydraulic parameters of the aquifer.

[0030] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0031] This invention constructs a mathematical model for pumping tests that considers the decrease in aquifer permeability coefficient with depth based on the test parameters at various time points during the pumping test, and derives analytical formulas. Based on the analytical formulas and the optimized model, the hydraulic parameters of the aquifer are inverted to obtain the hydraulic parameters of the aquifer, thereby improving the accuracy of monitoring data. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 A schematic flowchart of a method for determining the hydraulic parameters of an aquifer based on a pumping test, provided in an embodiment of the present invention;

[0034] Figure 2 This is a schematic diagram of a deep-hole pumping test model provided in an embodiment of the present invention;

[0035] Figure 3 This is a schematic diagram illustrating the inversion relationship of water level recovery parameters provided in an embodiment of the present invention.

[0036] Symbol explanation:

[0037] 1-Thickness of bedrock; 2-Hydraulic conductivity of aquifer; 3-Distance from the top elevation of the closed aquifer to the top of the well network; 4-Distance from the top elevation of the closed aquifer to the bottom of the well network; 5-Flow rate; 6-Well radius; 7-Vertical distance; 8-Horizontal axis; 9-Origin of coordinate system. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] The purpose of this invention is to provide a method and system for determining the hydraulic parameters of an aquifer based on pumping tests, thereby improving the accuracy of monitoring data.

[0040] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0041] like Figure 1 As shown in the figure, this embodiment provides a method for determining the hydraulic parameters of an aquifer based on a pumping test, which includes the following steps.

[0042] Step 101: Conduct a pumping test based on the pumping well in the target area, and record the test parameters at each time point during the pumping test. The test parameters include the static water level of the pumping well, the pumping flow rate, the change in water level in the well shaft, and the pumping time; the pumping well penetrates the aquifer.

[0043] As a specific implementation method: a pumping test is conducted based on the pumping wells and monitoring wells in the target area, and the test parameters at each time point during the pumping test are recorded. The test parameters include the static water level of the pumping well, the pumping flow rate, the change in the water level in the well shaft, and the pumping time; both the pumping well and the monitoring well penetrate the aquifer.

[0044] Step 101 specifically includes: using borehole data and hydrogeological data of the target area to identify the main strata in the target area and their spatial distribution. For each stratum, aquifers with small thickness variations, intact caprock, and complete well penetration through fractures are selected. In this pumping test section, the underlying strata are Devonian granodiorite and diorite, ranging from 8.5 to 700 meters. Suitable wells are selected as pumping wells and monitoring wells, and the well water level and radius are measured, i.e., the well water level and radius of the pumping well, and the well water level and radius of the monitoring well.

[0045] For each formation, based on the hydraulic characteristics of the target fractured aquifer, the range of hydraulic parameters of the aquifer is determined by consulting literature or conducting laboratory tests. These parameters include: pumping flow rate, aquifer thickness, well radius, storage coefficient, permeability coefficient at the top of the aquifer, permeability coefficient attenuation coefficient, and filter pipe length.

[0046] Before conducting the experiment, data monitoring sensors were installed at different depths in the pumping well and the monitoring well. The sensors monitored the pressure data within the well. More specifically, a first sampling point was set at different depths in the pumping well, and a second sampling point was set at different depths in the monitoring well. Pressure data was collected at each of the first and second sampling points through the data monitoring sensors. The experimental parameters also included the pressure data.

[0047] The pumping test specifically included: determining the depth of the test section in the selected pumping well; conducting two drawdown and one water level recovery tests using the unsteady flow single-fall test method; employing a deep well submersible pump; and controlling the flow rate using valves. Throughout the process, it was necessary to record the static water level, pumping flow rate, wellbore water level changes, and pumping time.

[0048] Step 102: Based on the test parameters at each time point, construct a mathematical model for the pumping test that considers the decrease in aquifer permeability coefficient with depth.

[0049] Step 102 specifically includes:

[0050] Based on the test parameters at each time point, a mathematical model for pumping tests considering the decrease in aquifer permeability coefficient with depth was constructed using the inverse Laplace transform method.

[0051] Step 103: Use the Green's function method to derive the analytical solution of the mathematical model of the pumping test and obtain the analytical formula.

[0052] Step 104: Construct an optimization model based on the pressure data collected by sensors at different depths of the pumping well during the pumping test.

[0053] As a specific implementation method: an optimization model is constructed based on the pressure data collected by sensors at different depths in the pumping well and the monitoring well during the pumping test.

[0054] The sensor used is the Solinst three-parameter sensor.

[0055] Step 105: Based on the analytical formula and the optimization model, the hydraulic parameters of the aquifer are inverted to obtain the hydraulic parameters of the aquifer.

[0056] The hydraulic parameters include the permeability coefficient, storage coefficient, and attenuation coefficient at the top of the aquifer.

[0057] The mathematical model for the pumping test is expressed as follows:

[0058]

[0059] s(r,z,t)| t＝0 =0, r≥r w ,0 <z<B (2);

[0060] s(r,z,t)| r→∞ =0,0 <z<B (3);

[0061]

[0062]

[0063] K = K0exp(-Az);

[0064] In the mathematical model of the pumping test, all wells involved are pumping wells, r is the radial distance to the axis of the well, K(z) is the permeability coefficient at a vertical distance of z, s is the drawdown, and r w Let B be the well radius, B be the bedrock thickness, s(r,z,t) be the drawdown equation, t be time, K0 be the permeability coefficient at the top of the aquifer, Q be the flow rate, A be the attenuation coefficient, and H be the well radius. V (.) represents the Heaviside function, K represents the aquifer permeability coefficient, and S s denoted by , l represents the distance from the top elevation of the closed aquifer to the top of the well network, d represents the distance from the top elevation of the closed aquifer to the bottom of the well network, and z represents the vertical distance from the top of the confined aquifer downwards.

[0065] H V (z)=H(zd)-H(zl).

[0066] Where H represents the water level.

[0067] Formula (5) represents the boundary conditions within the wellbore.

[0068] In this embodiment, by combining constant flow pumping, the drawdown curves over time at any location in the aquifer, whether in the pumping well or observation well, can be obtained. Due to the complexity of the mathematical model, this embodiment derives the drawdown formula in Laplace space, and the inverse Laplace transform is performed using the De Hoog numerical inverse transform method. In step 103, the drawdown formula in Laplace space is expressed as follows:

[0069]

[0070]

[0071] in,

[0072] N1 represents the first undetermined coefficient, N2 represents the second undetermined coefficient, N3 represents the third undetermined coefficient, and N4 represents the fourth undetermined coefficient. Let represent a term in the Laplace domain, p and α represent the parameters of the Laplace transform and Goldstein-Weiber transform, λ represent a positive value between 0 and B, J0(·) and J1(·) represent the zeroth and first orders of the first-order Bessel function, Y1(·) and Y0(·) represent the zeroth and first orders of the second-order Bessel function, and g(z,p,α,λ) represent the Green's function. I v(·) Let v(z) represent the first type. th The modified Bessel function of order 1.

[0073] Where Gamma() represents the gamma function, v represents velocity, and i represents the imaginary unit.

[0074] N1 = WN2;

[0075]

[0076]

[0077]

[0078] Where H1 represents the first intermediate parameter, H2 represents the second intermediate parameter, H3 represents the third intermediate parameter, H4 represents the fourth intermediate parameter, H5 represents the fifth intermediate parameter, H6 represents the sixth intermediate parameter, H7 represents the seventh intermediate parameter, and H8 represents the eighth intermediate parameter.

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] in, F2(0), δ, F1(0) and W are all intermediate variables without any special physical meaning. They are intermediate variables defined to simplify the solution process. In log(i), i represents the sequence number of the observation point.

[0089]

[0090] The optimization model in step 104 is represented as follows:

[0091]

[0092]

[0093] Where F represents the objective function of the optimization model, p1~p L Let L be the number of parameters to be determined, j represent the number of sampling points in the iteration process, and i represent the number of stages. For monitoring the observed value or reference benchmark value (i.e., pressure data) at the j-th sampling point of the well, Let μ be the simulated value of the j-th sampling point obtained based on COMSOL numerical simulation software. i f is the weighting coefficient for the i-th stage. i Let Δf be the variance of the i-th stage. i Let be the mean square error value of the i-th stage.

[0094] The analytical formula was combined with the optimization model: Two deep-hole pumping tests were used as the simulation period. The permeability coefficient and specific yield of the aquifer were numerically calculated using MATLAB or Mathematica platforms, categorizing the aquifer into relatively intact, intact, and fractured zones. Model calibration was achieved by finding the best fit between observation data from different locations in the deep well and the model's calculated drawdown, minimizing the objective function and ensuring that the inversely derived hydraulic parameters were within a given range. The inversely derived values ​​then represent the parameters of the target aquifer.

[0095] The beneficial effects of this invention are as follows:

[0096] 1. In terms of data monitoring, this invention will break with traditional data monitoring methods and introduce existing high-precision, large-range, automatic data acquisition sensors into pumping tests to obtain high-precision, high-frequency, multi-level pressure data from observation wells, identify water level information near fracture zones or preferential flow channels, and provide high-quality monitoring data for the parameter inversion model proposed in the regulations.

[0097] 2. Regarding parameter calculation, soil mechanics theory and groundwater seepage theory are combined, taking into account the heterogeneity of the strata. This breaks through the limitations of traditional pumping test methods in calculating the permeability coefficient, constructs a mathematical model for deep-hole pumping tests, derives the corresponding analytical solution, and develops a corresponding computer program to obtain the storage coefficient S. s The permeability coefficient K0 provides a basis for tunnel construction.

[0098] To verify the accuracy of the method of this invention, it is assumed that the aquifer permeability coefficient is known. Then, a numerical simulation software is used to construct a numerical model to replace the actual observation data for illustration. The method of this invention is as follows: Figure 2 A numerical model of the underground aquifer structure is constructed, and deep hole pumping test data are calculated using the constructed numerical model. These calculated data serve as reference benchmarks, and the key parameters of the permeability coefficient are inverted using the method of this invention based on the reference benchmarks.

[0099] Build as Figure 2 The aquifer structure shown is modeled numerically: In this embodiment, COMSOL numerical simulation software is used to construct the model as follows. Figure 2 The aquifer structure shown is used to simulate a deep-hole pumping test, involving the following factors: 1. bedrock thickness; 2. hydraulic conductivity of the aquifer; 3. distance from the top elevation of the closed aquifer to the top of the well network; 4. distance from the top elevation of the closed aquifer to the bottom of the well network; 5. flow rate; 6. well radius; 7. vertical distance; 8. horizontal axis; and 9. coordinate origin. The test depth is determined to be 0-700m, and an unsteady flow single-fall test method is adopted. A 10m submersible pump is used. 3 A deep well submersible pump with a head of 359m and a flow rate of / h was used. The water level was monitored at four locations (242, 300, 319, and 339 meters) using a three-parameter Solinst sensor. Two drawdown experiments and one water level monitoring experiment were conducted.

[0100] Based on the results of deep-hole pumping tests simulated using a numerical model, the specific implementation steps of the technical solution of this invention are as follows:

[0101] Based on the constructed numerical model, the basic parameters of the pumping well can be determined: the well radius r at different depths. wThe wellbore radii are 444.5 mm and 339.7 mm at 280 m to 68.8 m, respectively; and 311.0 mm and 244.5 mm at 700 m to 280 m, respectively, with a water level of 88.38 m.

[0102] The hydraulic parameters of the aquifer can be determined based on the constructed numerical model.

[0103] The sensor required for this experiment is the Solinst three-parameter sensor, which was installed at four locations at 242, 300, 319 and 339 meters to monitor the pressure inside the well.

[0104] A mathematical model for pumping tests was constructed that considers the decrease in aquifer permeability coefficient with depth.

[0105] The calculation formula in step 104 was written using MATLAB. By fitting the experimental data from the pumping test (the benchmark reference value calculated by the numerical model), the key parameters K0 and S of the target aquifer were inverted. S And A, based on the results of parameter inversion, such as Figure 3 As shown, the permeability coefficient exhibits a decreasing trend with depth.

[0106] In this embodiment, through optimized fitting between the method of the present invention and the benchmark reference value calculated by the numerical model, the result of the aquifer permeability coefficient parameter inversion is obtained as follows: K0 = 0.0022 (m / d), S s =3.49×10 -4 (m) and A = 0.00503(1 / m), the fitting results are as follows Figure 3 As shown.

[0107] Figure 3 The results show that the parameter inversion method of the present invention can well interpret the benchmark reference values / observed values, proving that the method of the present invention can effectively invert the key parameters of the pumping test, and indicating that the method of the present invention can solve the problem of parameter identification in the numerical simulation of the pumping test.

[0108] This invention identifies the target aquifer, pumping well, and observation well based on borehole data; determines the range of aquifer hydraulic parameters based on the hydraulic characteristics of the target aquifer; installs data monitoring sensors at different depths in the pumping and observation wells; conducts pumping tests; constructs a mathematical model for the pumping test considering the decrease in aquifer permeability with depth; derives an analytical solution to the mathematical model; and combines the derived analytical solution with an optimization algorithm to obtain the aquifer hydraulic parameters by best fitting the pumping test data. This invention constructs a pumping test mathematical model and simultaneously uses a combination of analytical methods and optimization algorithms to achieve the inversion of aquifer hydraulic parameters, improving the accuracy of aquifer hydraulic parameter inversion. The method proposed in this invention can directly provide a basis for groundwater resource assessment, and the proposed model and parameter inversion method can also provide a reference for foundation pit excavation, underground engineering construction, etc., and has certain demonstrative significance.

[0109] Example 2

[0110] This embodiment provides a system for determining the hydraulic parameters of an aquifer based on pumping tests, including:

[0111] The test parameter acquisition module is used to conduct pumping tests based on pumping wells in the target area and record the test parameters at each time point during the pumping test. The test parameters include the static water level of the pumping well, the pumping flow rate, the change in water level in the well shaft, and the pumping time.

[0112] The pumping test mathematical model construction module is used to construct a pumping test mathematical model that considers the decrease of aquifer permeability coefficient with depth based on the test parameters at each time point.

[0113] The analytical formula determination module is used to derive the analytical solution of the mathematical model of the pumping test using the Green's function method, and obtain the analytical formula.

[0114] The optimization model building module is used to build an optimization model based on the pressure data collected by sensors at different depths of the pumping well during the pumping test.

[0115] The hydraulic parameter determination module is used to invert the hydraulic parameters of the aquifer based on the analytical formula and the optimization model to obtain the hydraulic parameters of the aquifer.

[0116] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0117] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for determining the hydraulic parameters of an aquifer based on pumping tests, characterized in that, include: Pumping tests were conducted based on pumping wells in the target area, and test parameters were recorded at various time points during the pumping test. The test parameters included the static water level of the pumping well, the pumping flow rate, the change in water level in the well shaft, and the pumping time; the pumping wells penetrated the aquifer. Based on the test parameters at each time point, a mathematical model for pumping tests was constructed that considers the decrease in aquifer permeability coefficient with depth. The analytical solution of the mathematical model for the pumping test was derived using the Green's function method, and the analytical formula was obtained. An optimization model was constructed based on pressure data collected by sensors at different depths of the pumping well during the pumping test. Based on the analytical formula and the optimization model, the hydraulic parameters of the aquifer are inverted to obtain the hydraulic parameters of the aquifer. The mathematical model for the pumping test is expressed as follows: , , ； , , ； , ； , ； , ； ； in, The radial distance to the center of the well. The vertical distance is The permeability coefficient at time , where s is the drawdown. The radius of the wellbore. Indicates the thickness of the bedrock. Represent the descent equation, t Indicates time, The permeability coefficient at the top of the aquifer. Q For traffic, A The attenuation coefficient is... For the Heaviside function, Indicates the water storage coefficient. This indicates the distance from the top of the filter pipe. This indicates the distance from the bottom of the filter pipe. This represents the permeability coefficient of the aquifer.

2. The method for determining the hydraulic parameters of an aquifer based on pumping tests according to claim 1, characterized in that, Based on the experimental parameters at each time point, a mathematical model for pumping tests considering the decrease in aquifer permeability with depth is constructed, specifically including: Based on the test parameters at each time point, a mathematical model for pumping tests considering the decrease in aquifer permeability coefficient with depth was constructed using the inverse Laplace transform method.

3. The method for determining the hydraulic parameters of an aquifer based on pumping tests according to claim 1, characterized in that, The hydraulic parameters include the permeability coefficient, storage coefficient, and attenuation coefficient at the top of the aquifer.

4. The method for determining the hydraulic parameters of an aquifer based on pumping tests according to claim 1, characterized in that, First sampling points are set at different depths of the pumping well, and pressure data are collected at each first sampling point through the data monitoring sensor; the test parameters also include each pressure data.

5. A system for determining the hydraulic parameters of an aquifer based on pumping tests, characterized in that, include: The test parameter acquisition module is used to conduct pumping tests based on pumping wells in the target area and record the test parameters at each time point during the pumping test. The test parameters include the static water level of the pumping well, the pumping flow rate, the change in water level in the well shaft, and the pumping time. The pumping test mathematical model construction module is used to construct a pumping test mathematical model that considers the decrease of aquifer permeability coefficient with depth based on the test parameters at each time point. The analytical formula determination module is used to derive the analytical solution of the pumping test mathematical model using the Green's function method, and obtain the analytical formula. The optimization model building module is used to build an optimization model based on the pressure data collected by sensors at different depths of the pumping well during the pumping test. The hydraulic parameter determination module is used to invert the hydraulic parameters of the aquifer according to the analytical formula and the optimization model to obtain the hydraulic parameters of the aquifer. The mathematical model for the pumping test is expressed as follows: , , ； , , ； , ； , ； , ； ； in, The radial distance to the center of the well. The vertical distance is The permeability coefficient at time , where s is the drawdown. The radius of the wellbore. Indicates the thickness of the bedrock. Represent the descent equation, t Indicates time, The permeability coefficient at the top of the aquifer. Q For traffic, A The attenuation coefficient is... For the Heaviside function, Indicates the water storage coefficient. This indicates the distance from the top of the filter pipe. This indicates the distance from the bottom of the filter pipe. This represents the permeability coefficient of the aquifer.

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