Steady-state boundary driven solute transport model solution and parameter calculation method based on Laplacian transformation

Abstract

The invention discloses a Laplace transformation-based steady-state boundary driven solute transport model solution and parameter calculation method, which comprises the following steps of: establishing a one-dimensional finite-scale underground water solute transport mathematical model on the basis of an underground water solute transport system; solving the mathematical model by combining groundwater dynamics, a convection-dispersion equation and a Laplacian transformation method, deducing a convection-dispersion test theoretical model under the condition of different Peclet numbers, and obtaining a standard curve for determining a medium permeability coefficient and a hydrodynamic dispersion parameter under the condition of different Peclet numbers; and carrying out a convection-dispersion test, and determining permeability coefficients and hydrodynamic dispersion parameters of the medium under different Peclet numbers by adopting a wiring method. The method has a rigorous mathematical model and strict mathematical theory derivation, perfects related theories and methods for determining the medium permeability coefficient and the hydrodynamic dispersion parameter in the convection-dispersion test under different Peclet numbers, and solves the technical problems existing in application of the convection-dispersion test in a one-dimensional finite scale model.

Description

Technical Field

[0001] The present invention relates to a method for determining a permeability coefficient and a hydrodynamic dispersion parameter, and in particular to a method for solving a steady-state boundary-driven solute transport model and calculating parameters based on Laplace transform. Background Art

[0002] Permeability and hydrodynamic dispersion parameters are key parameters in groundwater resource assessment and environmental protection and remediation. Existing convection-dispersion experimental methods typically assume that the test medium is approximately a semi-infinite space in the flow direction when deriving analytical expressions for parameter calculations. A constant source term is given at the inlet, while the concentration is often assumed to be zero or to spread undisturbed at the outlet, simplifying the boundary conditions to a semi-infinite domain model. This assumption allows for the development of classical one-dimensional convection-dispersion analytical solutions for continuous injection. However, these solutions rely on the semi-infinite domain assumption and cannot describe the actual behavior of solute convection-dispersion within a finite test section.

[0003] Moreover, in indoor columnar or small-scale experiments, the test section length is limited, and the semi-infinite domain model cannot accurately describe the process after the solute reaches the outlet. In addition, the commonly used "far-field constancy" assumption does not match the actual closed or reflux outlet conditions. If the semi-infinite solution is directly used for finite-scale one-dimensional experiments, deviations will often occur in the later concentration change stage, thereby affecting the fitting accuracy of the hydrodynamic dispersion parameters. At the same time, the semi-infinite domain model cannot effectively calculate the permeability coefficient.

[0004] Therefore, although traditional methods have been maturely applied in large-scale aquifer logging and tracer tests in the field, they lack effective means for the finite-scale model and outlet boundary conditions of real indoor test scenarios. There is an urgent need to construct and solve a finite-scale model to improve the fitting precision and accuracy of the test data. Summary of the Invention

[0005] Purpose of the invention: The present invention aims to address the problem that the one-dimensional convection-diffusion analytical solution under the traditional semi-infinite domain assumption cannot accurately describe the outlet behavior of indoor finite-scale tests. A Laplace transform-based steady-state boundary-driven solute transport model solution and parameter calculation method is creatively proposed, which can quickly and accurately obtain key parameters such as the permeability coefficient and hydrodynamic dispersion parameters of the medium.

[0006] In order to solve the above technical problems, the technical solutions adopted by the present invention are as follows:

[0007] A method for solving a steady-state boundary-driven solute transport model and calculating parameters based on Laplace transform includes the following steps:

[0008] S1: Based on the groundwater solute transport system, a one-dimensional finite-scale mathematical model of groundwater solute transport is established;

[0009] S2: Combining groundwater dynamics, convection-dispersion equations and the Laplace transform method to solve the mathematical model, derive the theoretical model of convection-dispersion experiments under different Peclet numbers, and obtain the standard curves for determining the medium permeability coefficient and hydrodynamic dispersion parameters under different Peclet numbers;

[0010] S3: Conduct convection-diffusion experiments and use the matching method to determine the permeability coefficient and hydrodynamic dispersion parameters of the medium under different Peclet numbers.

[0011] The theoretical model of the convection-diffusion test in step S2 is established based on the following assumptions:

[0012] (1) Assume that the groundwater solute transport system is a one-dimensional soil column model;

[0013] (2) The hydrodynamic field in the model remains stable, and the groundwater velocity at each point in the soil column is the same and remains constant;

[0014] (3) Ignore the mixing of solutes within the water column at the upper boundary of the soil column, that is, the concentration at each point in the upper water column remains stable and equal;

[0015] (4) Ignore the mechanical diffusion effect at the outlet of the lower boundary of the soil column and only consider the convection effect;

[0016] Furthermore, in step S1, a one-dimensional finite-scale mathematical model of groundwater solute transport is established based on the groundwater continuity equation, the convection-diffusion equation, and the solute conservation law;

[0017] One-dimensional steady flow groundwater continuity equation:

[0018]

[0019] Boundary conditions of the hydrodynamic field:

[0020] H(0,t)=H1(2)

[0021] H(L,t)=H2(3)

[0022] One-dimensional convection-diffusion equation:

[0023]

[0024] The convection-diffusion equation includes convection, molecular diffusion, and mechanical diffusion. The parameter relationship between the three is as follows:

[0025] D L =D0+α L u(5)

[0026] Chemical field initial conditions:

[0027] C(z,0)=C0(6)

[0028] Boundary conditions at the chemical field entrance:

[0029] C(0,t)=C w0 +C0(7)

[0030] At the outlet of the chemical field, the convection of water flow is allowed to transfer solutes, and the diffusion effect at the outlet is ignored. This is the biggest difference from the semi-infinite boundary model. Therefore, the boundary conditions at the outlet of the finite scale model are as follows:

[0031]

[0032] Integrate equation (1) twice and substitute it into equations (2) and (3), and we can get the water head distribution in the model:

[0033]

[0034] According to Darcy's law, the permeability coefficient of the aquifer medium and the seepage velocity of the test section can be further calculated:

[0035]

[0036] Where: H is the water head at any point in the test section, L; H1 is the boundary water head at the entrance of the test section, L; H2 is the boundary water head at the exit of the test section, L; C is the concentration of the solute at any point in the test section, ML -3 ;D L is the longitudinal hydrodynamic dispersion coefficient, L 2 T -1 ; u is the average particle seepage velocity, LT -1 ; D0 is the molecular diffusion coefficient, L 2 T -1 ; α L is the longitudinal dispersivity, L; L is the length of the model test section, L; z is the spatial position coordinate, L; C(z,0)=C0 is the initial concentration, ML -3 ; C w0 is the upper boundary concentration increment, ML -3 ; K is the permeability coefficient of the aquifer medium, LT -1 ; Q is the seepage rate per unit time, L 3 T -1 , A is the cross-sectional area of ​​water flow, L 2 ; n is the porosity of the aquifer medium; t is the measurement time, T.

[0037] The units used in this application are expressed in international dimensions.

[0038] Furthermore, in step S2, the one-dimensional finite-scale mathematical model of groundwater solute transport needs to be dimensionless, and the dimensionless factors selected are:

[0039] Dimensionless distance:

[0040]

[0041] Dimensionless concentration:

[0042]

[0043] Dimensionless time:

[0044]

[0045] Peclet number (Peclet number):

[0046]

[0047] By non-dimensionalizing equations (4) to (7), we can obtain the new solution to the problem after non-dimensionalization:

[0048]

[0049] Furthermore, in step S2, the new fixed-solution problem after dimensionless transformation is solved using the Laplace transform method;

[0050] For both sides of equation (16) with respect to t D By Laplace transform, the convection-diffusion equation becomes D The ordinary differential equation for :

[0051]

[0052] The boundary conditions in the pull-type space become:

[0053]

[0054] Solving the ordinary differential equation in the Laplace domain, we can obtain the general solution of Equation (17):

[0055]

[0056] Where: 1,2 is the characteristic equation λ 2 -Peλ-s=two roots of 0, A(s) and B(s) are the parameters to be determined.

[0057] Apply the boundary conditions to obtain A(s) and B(s):

[0058]

[0059] Substituting Equations (21) and (22) into (20) yields the frequency domain solution of the convection-dispersion equation in the Laplace domain:

[0060]

[0061] The Stehfest algorithm can be used to directly perform numerical inverse transformation on Equation (23). The core idea is to approximate the Bromwich integral as a linear combination of a set of discrete points, thereby obtaining a semi-analytical solution to the newly defined problem after dimensionless transformation:

[0062]

[0063] Where: N is an even number, usually ranging from 8 to 16; represents the value point of the Laplace variable s, which is used to approximate the Bromwich integral; Indicates the weight of each value point on the inverse transformation result.

[0064] Furthermore, in step S2, a program code is written in Python to plot different dimensionless positions z D and the dimensionless concentration C under the Peclet number Pe D Standard curve as a function of dimensionless time.

[0065] Furthermore, in step S3, according to the dimensionless concentration change value C at the observation point collected, D ' and time t observation data, plot the concentration change C with the same modulus as the standard curve D ' and time t, the measured time t is taken as logarithm, so that the coordinate origin of the measured curve and the coordinate origin of the standard curve are at the same height of the coordinate layer. The measured curve layer is fitted with the standard curve by translating it, and the optimal fitting position is selected. The dimensionless position z of the fitted standard curve is recorded. D value, Peclet number Pe value, dimensionless time t D value and measured time t value.

[0066] Furthermore, in step S3, the specific process of calculating the permeability coefficient and the hydrodynamic diffusion parameter based on the test data is as follows:

[0067] A1: Carry out the experiment and record all the raw data required during the experiment;

[0068] A2: Calculate the longitudinal hydrodynamic diffusion coefficient D of the aquifer medium according to equations (14) and (15): L1 and particle velocity u1;

[0069] A3: Calculate the permeability coefficient K1 and porosity n1 of the aquifer medium according to equations (10) and (11);

[0070] A4: Change the hydrodynamic field conditions and conduct the test again. Repeat the above A1-A3 process to obtain the permeability coefficient K2, particle flow velocity u2 and longitudinal hydrodynamic diffusion coefficient D L2 ;

[0071] A5: The permeability coefficient and porosity are calculated based on the permeability coefficient values ​​of the two tests. The molecular diffusion coefficient D0 and longitudinal diffusivity α are calculated according to formula (5): L .

[0072] After the above steps, the longitudinal hydrodynamic diffusion coefficient D of the medium can be calculated through a single test. L , particle flow velocity u, permeability coefficient K and porosity n, the molecular diffusion coefficient D0 and longitudinal diffusivity α can be calculated through at least two tests L .

[0073] The entire process of the above method has the significant advantages of rigorous theoretical derivation, convenient operation, efficient calculation and accurate results, and has good engineering application and promotion value.

[0074] This invention, with its rigorous mathematical model and rigorous theoretical derivation, improves the theories and methods for determining the permeability coefficient and hydrodynamic dispersion parameters of media using convection-diffusion experiments at different Peclet numbers, resolving the challenges associated with applying convection-diffusion experiments to one-dimensional finite-scale models. Furthermore, the method employs a wiring method to calculate the permeability and hydrodynamic dispersion parameters of media at different Peclet numbers. This method is simple and efficient, allowing for the acquisition of multiple parameters with high accuracy, and possesses significant application and promotional value.

[0075] For technologies not mentioned in this invention, reference is made to the prior art.

[0076] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0077] 1. A finite-scale convection-diffusion model was constructed, and the boundary condition of zero diffusion flux at the outlet was adopted to eliminate the process error of concentration changes in the late stage of the semi-infinite model in indoor experiments.

[0078] 2. Combine dimensionless transformation, Laplace transform and Stehfest algorithm to quickly generate high-precision standard curve.

[0079] 3. Can simultaneously calculate the permeability coefficient K and longitudinal hydrodynamic diffusion coefficient D L , molecular diffusion coefficient D0 and longitudinal diffusivity α L And other key parameters, high test efficiency.

[0080] 4. The test is simple and convenient, with strong versatility and high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 is an operational flow chart of the method of the present invention;

[0082] Figure 2 Standard curves for convection-dispersion experiments to determine the hydrodynamic dispersion parameters of aquifers;

[0083] Figure 3 This is the measured curve of the first set of convection-diffusion experiments;

[0084] Figure 4 This is the measured curve of the second group of convection-diffusion experiments;

[0085] Figure 5 This is the fitting curve of the first set of convection-diffusion experiments;

[0086] Figure 6 This is the fitting curve diagram of the second group of convection-diffusion experiments; DETAILED DESCRIPTION

[0087] The present invention is further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0088] like Figure 1 As shown, the present invention provides a method for solving a steady-state boundary-driven solute transport model and calculating parameters based on Laplace transform, comprising the following steps:

[0089] 1) A finite-scale one-dimensional convection-dispersion model was constructed, and an appropriate dimensionless factor was selected for normalization. The frequency domain solution was obtained by Laplace transform, and the inverse transform was performed using the Stehfest algorithm to obtain the dimensionless concentration-time standard curves at different dimensionless distances and Peclet numbers.

[0090] A one-dimensional finite-scale mathematical model of groundwater solute transport is established based on the groundwater continuity equation, convection-diffusion equation and solute conservation law.

[0091] One-dimensional steady flow groundwater continuity equation:

[0092]

[0093] Boundary conditions of the hydrodynamic field:

[0094] H(0,t)=H1(2)

[0095] H(L,t)=H2(3)

[0096] One-dimensional convection-diffusion equation:

[0097]

[0098] The convection-diffusion equation includes convection, molecular diffusion, and mechanical diffusion. The parameter relationship between the three is as follows:

[0099] D L =D0+α L u(5)

[0100] Chemical field initial conditions:

[0101] C(z,0)=C0(6)

[0102] Boundary conditions at the chemical field entrance:

[0103] C(0,t)=C w0 +C0(7)

[0104] At the outlet of the chemical field, the convection of water flow is allowed to transfer solutes, and the diffusion effect at the outlet is ignored. This is the biggest difference from the semi-infinite boundary model. Therefore, the boundary conditions at the outlet of the finite scale model are as follows:

[0105]

[0106] Integrate equation (1) twice and substitute it into equations (2) and (3), and we can get the water head distribution in the model:

[0107]

[0108] According to Darcy's law, the permeability coefficient of the aquifer medium and the seepage velocity of the test section can be further calculated:

[0109]

[0110] Where: H is the water head at any point in the test section, L; H1 is the boundary water head at the entrance of the test section, L; H2 is the boundary water head at the exit of the test section, L; C is the concentration of the solute at any point in the test section, ML -3 ;D L is the longitudinal hydrodynamic dispersion coefficient, L 2 T -1 ; u is the average particle seepage velocity, LT -1 ; D0 is the molecular diffusion coefficient, L 2 T -1 ; α L is the longitudinal dispersivity, L; L is the length of the model test section, L; z is the spatial position coordinate, L; C(z,0)=C0 is the initial concentration, ML -3 ; C w0 is the upper boundary concentration increment, ML -3; K is the permeability coefficient of the aquifer medium, LT -1 ; Q is the seepage rate per unit time, L 3 T -1 , A is the cross-sectional area of ​​water flow, L 2 ; n is the porosity of the aquifer medium.

[0111] The mathematical model of one-dimensional finite-scale groundwater solute transport needs to be dimensionless, and the dimensionless factors selected are:

[0112] Dimensionless distance:

[0113]

[0114] Dimensionless concentration:

[0115]

[0116] Dimensionless time:

[0117]

[0118] Peclet number (Peclet number):

[0119]

[0120] By non-dimensionalizing equations (4) to (7), we can obtain the new solution to the problem after non-dimensionalization:

[0121]

[0122] The new solution problem after dimensionless transformation is solved by Laplace transform method; the two sides of equation (16) with respect to t D By Laplace transform, the convection-diffusion equation becomes D The ordinary differential equation for :

[0123]

[0124] The boundary conditions in the pull-type space become:

[0125]

[0126] Solving the ordinary differential equation in the Laplace domain, we can obtain the general solution of Equation (17):

[0127]

[0128] Where: 1,2 is the characteristic equation λ 2 -Peλ-s=two roots of 0, A(s) and B(s) are the parameters to be determined.

[0129] Apply the boundary conditions to obtain A(s) and B(s):

[0130]

[0131] Substituting Equations (21) and (22) into (20) yields the frequency domain solution of the convection-dispersion equation in the Laplace domain:

[0132]

[0133] The Stehfest algorithm can be used to directly perform numerical inverse transformation on Equation (23). The core idea is to approximate the Bromwich integral as a linear combination of a set of discrete points, thereby obtaining a semi-analytical solution to the newly defined problem after dimensionless transformation:

[0134]

[0135] Where: N is an even number, usually ranging from 8 to 16; represents the value point of the Laplace variable s, which is used to approximate the Bromwich integral; Indicates the weight of each value point on the inverse transformation result.

[0136] Use Python to write program code to draw different dimensionless positions z D and the dimensionless concentration C under the Peclet number Pe D Standard curve as a function of dimensionless time;

[0137] 2) Conduct a convection-diffusion test in a one-dimensional soil column indoors, record the solute concentration change data of each observation point over time, and draw the measured curve on a semi-logarithmic coordinate. Align the measured curve with the standard curve of the same modulus on the semi-logarithmic paper, fit the measured curve layer with the standard curve by translating it, and select the optimal fitting position. Note the dimensionless position, Peclet number, dimensionless time and measured time of the fitted standard curve, substitute them into the (semi-) analytical formula, and calculate the permeability coefficient, particle flow rate and longitudinal hydrodynamic diffusion coefficient. If the molecular diffusion coefficient and longitudinal diffusivity need to be further determined, the test can be repeated under the condition of changing the flow rate and combining the two sets of fitting parameters. The key parameters such as permeability coefficient, longitudinal hydrodynamic diffusion coefficient, molecular diffusion coefficient and longitudinal diffusivity can be calculated at one time through the closed-form relationship.

[0138] According to the dimensionless concentration change value C at the observation point collected D ' and time t observation data, plot the concentration change C with the same modulus as the standard curve D' and time t, the measured time t is taken as logarithm. Make the coordinate origin of the measured curve and the coordinate origin of the standard curve at the same height of the coordinate layer, fit the measured curve layer with the standard curve by translating it, select the best fitting position, and record the dimensionless position z of the fitted standard curve D value, Peclet number Pe value, dimensionless time t D value and measured time t value.

[0139] The specific process of calculating the permeability coefficient and hydrodynamic dispersion parameters based on the test data is as follows:

[0140] A1: Carry out the experiment and record all the raw data required during the experiment;

[0141] A2: Calculate the longitudinal hydrodynamic diffusion coefficient D of the aquifer medium according to equations (14) and (15): L1 and particle velocity u1;

[0142] A3: Calculate the permeability coefficient K1 and porosity n1 of the aquifer medium according to equations (10) and (11);

[0143] A4: Change the hydrodynamic field conditions and conduct the test again. Repeat the above A1-A3 process to obtain the permeability coefficient K2, particle flow velocity u2 and longitudinal hydrodynamic diffusion coefficient D L2 ;

[0144] A5: The permeability coefficient and porosity are calculated based on the permeability coefficient values ​​of the two tests. The molecular diffusion coefficient D0 and longitudinal diffusivity α are calculated according to formula (5): L .

[0145] After the above steps, the longitudinal hydrodynamic diffusion coefficient D of the medium can be calculated through a single test. L , particle flow velocity u, permeability coefficient K and porosity n, the molecular diffusion coefficient D0 and longitudinal diffusivity α can be calculated through at least two tests L .

[0146] In order to verify the practical effect of the method of the present invention, the above scheme is applied as an example in this embodiment, and the specific test process is as follows:

[0147] 1. Equipment preparation and test medium selection

[0148] Assemble a one-dimensional finite-scale convection-dispersion test device with an inner diameter of 125 mm (water cross-sectional area A = 0.0123 m 2 ), with a total height of 350 mm. The test medium was selected as a representative aquifer material, silica fine sand with a particle size range of 0.3-0.6 mm. This material is stable and chemically resistant, with a uniform particle size distribution, simulating a homogeneous, isotropic aquifer medium.

[0149] 2. Observation point layout and medium filling

[0150] The upper surface of the sand layer is set as z = 0, and the coordinate axis z is established with the downward direction as the positive direction. Four observation points are arranged along the z axis, at -21.5mm, 27mm, 132mm and 232mm from the upper surface of the sand layer. Among them, the probe at -21.5mm is in the water column area and is used to collect the upper boundary water level and concentration changes. The other three probes are buried inside the sand layer to collect water level, temperature and conductivity data during the solute migration process at different depths. The sand sample is filled and the probe is laid out from bottom to top to ensure that the sample is evenly loaded in the entire device and the probe is accurately laid out. The final uniform filling height of the sand sample in the device is 282mm.

[0151] 3. Sand sample saturation treatment and solution preparation

[0152] To eliminate the effects of gas in the aquifer and ensure consistent test conditions, the filled sand samples were repeatedly oversaturated with water until the aquifer reached full saturation. A 1g / L NaCl solution was prepared with deionized water and placed in the same constant temperature environment as the test apparatus for 24 hours to ensure consistent temperatures.

[0153] 4. Conduct convection-diffusion experiments

[0154] Four LTC high-precision probes were activated at a sampling frequency of 10 seconds. A peristaltic pump was used to continuously inject a 1g / L NaCl solution into the upper portion of the apparatus, maintaining a constant head at the upper and lower boundaries of the test apparatus. The probes automatically collected water level, temperature, and conductivity data at each observation point, capturing the solute concentration profile at each depth. The test duration should cover the entire process from concentration rise to peak concentration, and then to concentration stabilization at all observation points.

[0155] 5. Data Analysis and Parameter Calculation

[0156] The concentration-time data at different observation points are dimensionless and the measured curves are plotted on the semi-logarithmic coordinate graph (e.g. Figure 3-4 As shown), and the corresponding analytical results were deduced to the obtained standard curve (as shown Figure 2 As shown) to perform line fitting (as shown) Figure 5-6 The longitudinal hydrodynamic diffusion coefficient, particle velocity, permeability and porosity of the medium are calculated using the formula.

[0157]

[0158]

[0159] Continuing the experiment and repeating the above steps can obtain the longitudinal hydrodynamic diffusion coefficient, particle flow rate, permeability coefficient and porosity under different flow rate conditions.

[0160]

[0161] According to formula (5), the following relationship can be obtained:

[0162] D L1 =D0+α L u1

[0163] D L2 =D0+α L u2

[0164] The molecular diffusion coefficient and longitudinal diffusivity can be obtained by combining the two equations:

[0165] D0=4.87×10 -7 m 2 / s

[0166] α L =1.03×10 -3 m

[0167] At this point, the longitudinal hydrodynamic diffusion coefficient, particle flow velocity, permeability and porosity of the medium can be calculated through at least one set of convection-diffusion tests, and the molecular diffusion coefficient and longitudinal diffusivity can be calculated through at least two sets of tests.

[0168] In addition, to verify the accuracy of the parameter calculation method proposed in this patent, the basic parameters of the same test medium were tested using a constant head test, a porosity measurement test, and a traditional convection-diffusion test. The parameter values ​​measured by the traditional method were compared with those measured by the new method (Table 1). The comparison results show that the relevant parameters measured by the new method proposed in this patent are consistent with the relevant parameters measured by conventional tests, further verifying the accuracy of the method proposed in this patent.

[0169] Table 1 Comparison of test results between traditional test method and new method

[0170]

Claims

1. A method for solving a steady-state boundary-driven solute transport model and calculating parameters based on Laplace transform, characterized in that: The steps include: S1: Based on the groundwater solute transport system, a one-dimensional finite-scale mathematical model of groundwater solute transport is established; S2: Combine groundwater dynamics, the convection-diffusion equation, and the Laplace transform method to solve the mathematical model of one-dimensional finite-scale groundwater solute transport, derive the theoretical model of convection-diffusion experiments under different Peclet numbers, and obtain the standard curves for determining the medium permeability coefficient and hydrodynamic dispersion parameters under different Peclet numbers; S3: Conduct convection-diffusion experiments and use the matching method to determine the permeability coefficient and hydrodynamic dispersion parameters of the medium under different Peclet numbers.

2. The method for solving the steady-state boundary-driven solute transport model and calculating parameters based on Laplace transform according to claim 1 is characterized in that: In step S1, a one-dimensional finite-scale mathematical model of groundwater solute transport is established based on the groundwater continuity equation, the convection-diffusion equation, and the solute conservation law; One-dimensional steady flow groundwater continuity equation: Boundary conditions of the hydrodynamic field: H(0,t)=H1 (2) H(L,t)=H2 (3) One-dimensional convection-diffusion equation: The convection-diffusion equation includes convection, molecular diffusion, and mechanical diffusion. The parameter relationship between the three is as follows: D L =D0+α L u (5) Chemical field initial conditions: C(z,0)=C0 (6) Boundary conditions at the chemical field entrance: C(0,t)=C w0 +C0 (7) At the outlet of the chemical field, the convection of water flow is allowed to transfer solutes, and the diffusion effect at the outlet is ignored. The boundary conditions at the outlet of the finite-scale model are established as follows: Integrate equation (1) twice and substitute it into equations (2) and (3), and we can get the water head distribution in the model: According to Darcy's law, the permeability coefficient of the aquifer medium and the seepage velocity of the test section can be further calculated: Where: H is the water head at any point in the test section, L; H1 is the boundary water head at the entrance of the test section, L; H2 is the boundary water head at the exit of the test section, L; C is the concentration of the solute at any point in the test section, ML -3 ;D L is the longitudinal hydrodynamic dispersion coefficient, L 2 T -1 ; u is the average particle seepage velocity, LT -1 ; D0 is the molecular diffusion coefficient, L 2 T -1 ; α L is the longitudinal dispersivity, L; L is the length of the model test section, L; z is the spatial position coordinate, L; C(z,0)=C0 is the initial concentration, ML -3 ; C w0 is the upper boundary concentration increment, ML -3 ; K is the permeability coefficient of the aquifer medium, LT -1 ; Q is the seepage rate per unit time, L 3 T -1 , A is the cross-sectional area of ​​water flow, L 2 ; n is the porosity of the aquifer medium; t is the measurement time, T.

3. The method for solving the steady-state boundary-driven solute transport model and calculating parameters based on Laplace transform according to claim 2, characterized in that: The convection-diffusion test theoretical model in step S2 is established based on the following assumptions: (1) Assume that the groundwater solute transport system is a one-dimensional soil column model; (2) The hydrodynamic field in the model remains stable, and the groundwater velocity at each point in the soil column is the same and remains constant; (3) Ignore the mixing of solutes within the water column at the upper boundary of the soil column, that is, the concentration at each point in the upper water column remains stable and equal; (4) Ignore the mechanical diffusion effect at the outlet of the lower boundary of the soil column and only consider the convection effect.

4. A method for solving a steady-state boundary-driven solute transport model and calculating parameters based on Laplace transform according to claim 2 or 3, characterized in that: The step S2 comprises the following steps: S21: Dimensionless processing of the mathematical model of one-dimensional finite-scale groundwater solute transport: the dimensionless factors selected are: Dimensionless distance: Dimensionless concentration: Dimensionless time: Peclet number: By non-dimensionalizing equations (4) to (7), we can obtain the new solution to the problem after non-dimensionalization: S22: The new solution problem after dimensionless is solved using the Laplace transform method: For both sides of equation (16) with respect to t D By Laplace transform, the convection-diffusion equation becomes D The ordinary differential equation for : The boundary conditions in the pull-type space become: Solving the ordinary differential equation in the Laplace domain, we can obtain the general solution of Equation (17): Where: 1,2 is the characteristic equation λ 2 -Peλ-s=two roots of 0, A(s) and B(s) are the parameters to be determined. Apply the boundary conditions to obtain A(s) and B(s): Substituting Equations (21) and (22) into (20) yields the frequency domain solution of the convection-dispersion equation in the Laplace domain: The Stehfest algorithm is used to directly perform numerical inverse transformation on Equation (23). The core idea is to approximate the Bromwich integral as a linear combination of a set of discrete points, thereby obtaining a semi-analytical solution to the newly defined problem after dimensionless transformation: Where: N is an even number, usually ranging from 8 to 16; represents the value point of the Laplace variable s, which is used to approximate the Bromwich integral; Indicates the weight of each value point on the inverse transformation result. S23: Use Python to write program code to plot different dimensionless positions z D and the dimensionless concentration C under the Peclet number Pe D Standard curve as a function of dimensionless time.

5. The method for solving the steady-state boundary-driven solute transport model and calculating parameters based on Laplace transform according to claim 4, characterized in that: In step S3, the dimensionless concentration change value C at the observation point is collected. D ' and time t observation data, plot the concentration change C with the same modulus as the standard curve D ' and time t, the measured time t is taken as logarithm, so that the coordinate origin of the measured curve and the coordinate origin of the standard curve are at the same height of the coordinate layer. The measured curve layer is fitted with the standard curve by translating it, and the optimal fitting position is selected. The dimensionless position z of the fitted standard curve is recorded. D value, Peclet number Pe value, dimensionless time t D value and measured time t value.

6. The method for solving the steady-state boundary-driven solute transport model and calculating parameters based on Laplace transform according to claim 5, characterized in that: In step S3, the specific process of calculating the permeability coefficient and the hydrodynamic diffusion parameter based on the test data is as follows: A1: Carry out the experiment and record all the raw data required during the experiment; A2: Calculate the longitudinal hydrodynamic diffusion coefficient D of the aquifer medium according to equations (14) and (15): L1 and particle velocity u1; A3: Calculate the permeability coefficient K1 and porosity n1 of the aquifer medium according to equations (10) and (11); A4: Change the hydrodynamic field conditions and conduct the test again. Repeat the above A1-A3 process to obtain the permeability coefficient K2, particle flow velocity u2 and longitudinal hydrodynamic diffusion coefficient D L2 ; A5: The permeability coefficient and porosity are calculated based on the permeability coefficient values ​​of the two tests. The molecular diffusion coefficient D0 and longitudinal diffusivity α are calculated according to formula (5): L .

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