Aperture-matrix parameter estimation method and system considering unbalanced adsorption influence

Abstract

The invention relates to a pore-matrix parameter estimation method and system considering unbalanced adsorption influence, and the method comprises the steps: building a pore-matrix system unbalanced reactive solute transport analytical model, and solving a semi-analytical solution; the method comprises the following steps: acquiring actually-measured soil column experimental data, and monitoring the solute concentration of an organic compound phenol at a fixed observation point within a set time range to obtain a penetration curve; fitting wiring is carried out on the obtained semi-analytical solution and the penetration curve of the actually measured data, a parameter value corresponding to a fitting curve meeting a set condition is selected, and the parameter value is used as an estimated value of a corresponding coefficient; according to the method, the corresponding pore dispersion coefficient, the diffusion coefficient, the first-order adsorption kinetics coefficient in the pores and the first-order adsorption kinetics coefficient in the matrix are determined by using the optimal fitting wiring, the actual measurement result is associated with the theoretical result, and the utilization value of the existing data is fully excavated.

Description

Technical Field

[0001] The present invention relates to the technical field of groundwater pollutant migration prediction, and more particularly to a pore-matrix parameter estimation method and system considering the influence of non-equilibrium adsorption. Background Art

[0002] In groundwater environments, solute transport is significantly influenced by adsorption, with the adsorption mechanism directly determining the migration rate and retention characteristics of pollutants. Traditional solute transport models are generally based on the equilibrium adsorption assumption, which assumes that the adsorption process reaches equilibrium instantaneously and ignores the non-equilibrium characteristics of adsorption dynamics.

[0003] However, in pore-matrix systems composed of porous media such as soil and rock, the mass transfer of solutes between pores (high permeability areas) and matrices (low permeability areas) often exhibits significant non-equilibrium characteristics, making it difficult for traditional models to accurately simulate the actual migration behavior of solutes. A pore-matrix parameter estimation method and system that takes into account the influence of non-equilibrium adsorption and can more realistically reflect the solute migration behavior in complex media is needed. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption, and also provide a pore-matrix parameter estimation system considering the influence of non-equilibrium adsorption, in response to the above-mentioned defects of the prior art.

[0005] The technical solution adopted by the present invention to solve its technical problem is:

[0006] A pore-matrix parameter estimation method considering the effect of non-equilibrium adsorption is constructed, wherein the method comprises the steps of:

[0007] Establish an analytical model of non-equilibrium reactive solute transport in pore-matrix system and obtain a semi-analytical solution of the analytical model in Laplace domain.

[0008] Obtaining the measured soil column experimental data, the concentration of the organic compound phenanthrene solute at a fixed observation point within a set time range is monitored to obtain the breakthrough curve;

[0009] The obtained semi-analytical solution of the analytical model of non-equilibrium reactive solute transport in the pore-matrix system is fitted with the penetration curve of the measured data, and the parameter values ​​corresponding to the fitting curve that meets the set conditions are selected as the estimated values ​​of the corresponding coefficients.

[0010] The pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption of the present invention, wherein the analytical model of non-equilibrium reactive solute transport in the pore-matrix system is established based on the following foundations:

[0011] The pore radius does not change with the pore length;

[0012] The matrix is ​​semi-infinite in length;

[0013] The adsorption processes in the pore and matrix regions are divided into two types: one type assumes that the adsorption is instantaneous, and the other type is dynamic adsorption, which is described by the first-order kinetic coefficients;

[0014] The degradation reaction is first-order in both the pore and matrix regions;

[0015] The model water flow is a steady flow.

[0016] In the pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption of the present invention, the control equation of reactive solute transport in the pore region in the analytical model of non-equilibrium reactive solute transport in the pore-matrix system adopts the formula:

[0017]

[0018] Where: t represents time; r m represents the pore radius; r represents the radial distance; C m represents the pore solute concentration; S m1 It represents the adsorption amount per unit pore cross section due to equilibrium adsorption; S m2 represents the adsorption amount per unit pore cross section due to non-equilibrium adsorption; λ m represents the first-order reaction rate constant in the pore liquid phase; λ m1 represents the first-order reaction rate constant of the adsorption phase point 1 in the pore; λ m2 represents the second-order reaction rate constant of adsorption phase point 2 in the pore; v m represents the pore flow velocity in the pore area; D m represents the longitudinal diffusion coefficient, D m Using the formula:

[0019] D m =α m v m +D m0 (2)

[0020] Where: α m : Pore longitudinal diffusivity D m0 : Pore effective molecular diffusion coefficient

[0021] Porous adsorption uses the formula:

[0022] S m1 =F m K m C m (3)

[0023]

[0024] Where: F m Indicates the proportion of equilibrium adsorption in the pores; K m represents the distribution coefficient in the pores; k m2 : pore first-order adsorption kinetic coefficient;

[0025] The governing equation for solute transport in the matrix region is:

[0026]

[0027] Where: θ a represents the effective porosity in the matrix; D a represents the effective diffusion coefficient within the matrix; C a represents the solute concentration in the matrix; ρ a Indicates density;

[0028] Matrix adsorption uses the formula:

[0029] S a1 =F a K a C a (6)

[0030]

[0031] Where: F a It represents the proportion of equilibrium adsorption in the matrix, with a value between 0 and 1; K a represents the partition coefficient in the matrix; k a2 represents the first-order adsorption kinetic coefficient of the matrix;

[0032] The concentration is continuous at the interface between the pores and the matrix, and the formula used is:

[0033] C a (r m ,z,t)=C m (z,t) ; r m <r≤∞,0≤z<∞ (8)

[0034] The initial and boundary conditions of the analytical model of nonequilibrium reactive solute transport in the pore-matrix system are expressed as follows:

[0035] C m (r,t=0)=0 (9)

[0036] C a (r,z,t=0)=0 (10)

[0037] C m (r=∞,z,t)=Ca (r=∞,z,t)=0 (11)

[0038] The analytical model of nonequilibrium reactive solute transport in the pore-matrix system considering the pulse injection boundary condition is expressed as:

[0039]

[0040] Where: t0 is the pulse injection time;

[0041] Perform Laplace transform on equation (1), where s is the Laplace variable, and we get:

[0042]

[0043] Performing Laplace transform on equation (5) yields:

[0044]

[0045] Performing Laplace transform on equation (3) yields:

[0046]

[0047] Applying Laplace transform to equation (4) yields:

[0048]

[0049] Performing Laplace transform on equation (6) yields:

[0050]

[0051] Performing Laplace transform on equation (7) yields:

[0052]

[0053] Arrange formula (14) as follows:

[0054]

[0055] Substituting equations (17) and (18) into equation (19), we obtain:

[0056] Combining similar terms in formula (20), we get:

[0057]

[0058] Divide θ on both sides of the equation a D a ,get:

[0059]

[0060] Arranging formula (22) yields:

[0061]

[0062] make

[0063] (twenty four)

[0065] The general solution of formula (23) yields:

[0066]

[0067] Performing Laplace transform on the initial condition (11) yields:

[0068]

[0069] From the initial condition (26) and the properties of the first type of void volume function, we can obtain:

[0070] A=0 (27)

[0071] Substituting into formula (25), we get:

[0072]

[0073] Performing Laplace transform on equation (8) yields:

[0074]

[0075] Substituting formula (29) into formula (28), we get:

[0076]

[0077] Substituting formula (3) into formula (28), we get:

[0078]

[0079] Substituting equations (15), (16), and (31) into equation (12), we obtain:

[0080]

[0081] Simplifying formula (32), we get:

[0082]

[0083] make

[0084]

[0085] According to the general solution of the second-order homogeneous linear differential equation, the solution of equation (33) is:

[0086]

[0087] Performing Laplace transform on the pulse injection boundary condition (12) yields:

[0088]

[0089] When the initial and boundary conditions are pulse injection of solute, the solution of equation (36) is:

[0090]

[0091] The pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption described in the present invention has multiple parameter values, and the multiple parameter values ​​are respectively used as estimated values ​​of the pore diffusion coefficient, the diffusion coefficient, the first-order adsorption kinetic coefficient in the pore, and the first-order adsorption kinetic coefficient in the matrix.

[0092] A pore-matrix parameter estimation system considering the influence of non-equilibrium adsorption is used to implement the pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption as described above, wherein the system includes an analytical model construction unit, an analytical model solution unit, a penetration curve generation unit, and a fitting line unit;

[0093] The analytical model building unit is used to establish an analytical model of non-equilibrium reactive solute transport in a pore-matrix system;

[0094] The analytical model solving unit is used to solve the semi-analytical solution of the non-equilibrium reactive solute transport analytical model of the pore-matrix system in the Laplace domain;

[0095] The penetration curve generating unit is used to obtain measured soil column experimental data and monitor the solute concentration of the organic compound phenanthrene at a fixed observation point within a set time range to obtain a penetration curve;

[0096] The fitting and matching unit is used to fit the obtained semi-analytical solution of the analytical model of non-equilibrium reactive solute transport in the pore-matrix system with the penetration curve of the measured data, select the parameter values ​​corresponding to the fitting curve that meets the set conditions, and use the parameter values ​​as the estimated values ​​of the corresponding coefficients.

[0097] The beneficial effects of the present invention are as follows: the present invention obtains a semi-analytical solution of the Laplace domain by establishing a solute transport model of a pore-matrix system affected by non-equilibrium adsorption, monitors the solute concentration at a fixed observation point within a set time range based on indoor measured soil column experimental data, obtains a penetration curve, and matches the penetration curve obtained by the analytical model, and uses the optimal fitting line to determine the corresponding pore diffusion coefficient, diffusion coefficient, first-order adsorption kinetic coefficient in the pore, and first-order adsorption kinetic coefficient in the matrix, and links the measured results with the theoretical results, thereby fully tapping the utilization value of existing data. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the present invention will be further described below with reference to the accompanying drawings and embodiments. The drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive efforts.

[0099] Figure 1 This is a flow chart of a pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption according to a preferred embodiment of the present invention;

[0100] Figure 2 Schematic diagram of the concept of a pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption according to a preferred embodiment of the present invention;

[0101] Figure 3 1 is a fitting diagram of a pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption in a preferred embodiment of the present invention;

[0102] Figure 4 This is a principle block diagram of a pore-matrix parameter estimation system considering the effects of non-equilibrium adsorption according to a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0103] To make the purpose, technical solutions, and advantages of the embodiments of the present invention more clear, the following will be a clear and complete description of the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work shall fall within the scope of protection of the present invention.

[0104] The pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption in a preferred embodiment of the present invention is as follows: Figure 1 See also Figure 2 and Figure 3 , including the steps of:

[0105] S01: Establish an analytical model for non-equilibrium reactive solute transport in pore-matrix systems and obtain a semi-analytical solution of the analytical model for non-equilibrium reactive solute transport in pore-matrix systems in the Laplace domain;

[0106] S02: Obtaining the measured soil column experimental data, monitoring the solute concentration of the organic compound phenanthrene at fixed observation points within a set time range to obtain a breakthrough curve;

[0107] S03: Fit the obtained semi-analytical solution of the analytical model of non-equilibrium reactive solute transport in the pore-matrix system to the penetration curve of the measured data, and select the parameter values ​​corresponding to the fitting curve that meets the set conditions. The parameter values ​​are used as the estimated values ​​of the corresponding coefficients;

[0108] The present invention obtains a semi-analytical solution to the Laplace domain by establishing a solute transport model for a pore-matrix system affected by non-equilibrium adsorption. Based on indoor measured soil column experimental data, the solute concentration at a fixed observation point within a set time range is monitored to obtain a penetration curve, which is then matched with the penetration curve obtained by the analytical model. The corresponding pore diffusion coefficient, diffusion coefficient, first-order adsorption kinetic coefficient in the pores, and first-order adsorption kinetic coefficient in the matrix are determined using the optimal fitting line. The measured results are then linked to the theoretical results, fully tapping the utilization value of the existing data.

[0109] The present method for estimating pore-matrix parameters, which considers the effects of nonequilibrium adsorption, aims to conduct in-depth research on solute transport in pore-matrix systems and characterize solute migration under nonequilibrium adsorption conditions. This approach addresses the insufficient simulation accuracy of traditional equilibrium adsorption models in complex media, accurately characterizing solute migration behavior and improving the reliability of pollutant transport prediction. This method can be widely applied in fields such as groundwater resource protection, pollution plume evolution analysis, and remediation solution optimization, providing core technical support for theoretical research and engineering practice on solute transport in heterogeneous media.

[0110] like Figure 2 As shown, the analytical model of non-equilibrium reactive solute transport in the pore-matrix system of the present invention is established based on the following assumptions:

[0111] The pore radius does not change with the pore length;

[0112] The matrix is ​​semi-infinite in length;

[0113] The adsorption processes in the pore and matrix regions are divided into two types: one type assumes that the adsorption is instantaneous, and the other type is dynamic adsorption, which is described by the first-order kinetic coefficients;

[0114] The degradation reaction is first-order in both the pore and matrix regions;

[0115] The model water flow is a steady flow.

[0116] The governing equation for reactive solute transport in the pore region in the analytical model of nonequilibrium reactive solute transport in the pore-matrix system is:

[0117]

[0118] Where: t represents time [T]; r m represents the pore radius [L]; r represents the radial distance [L]; C m represents the pore solute concentration; S m1 It represents the adsorption amount per unit pore cross section due to equilibrium adsorption [M / L 2 ]; S m2 It represents the adsorption amount per unit pore cross section due to non-equilibrium adsorption [M / L 2 ];λ m represents the first-order reaction rate constant in the pore liquid phase [1 / T]; λ m1 represents the first-order reaction rate constant of the adsorption phase point 1 in the pore [1 / T]; λ m2 represents the second-order reaction rate constant of adsorption phase point 2 in the pore [1 / T]; v m represents the pore flow velocity in the pore area [L / T]; D m represents the longitudinal diffusion coefficient [L 2 / T],D m Using the formula:

[0119] D m =α m v m +D m0 (2)

[0120] Where: α m : Pore longitudinal diffusivity D m0 [L]: Pore effective molecular diffusion coefficient [L 2 / T](usually relative to α m *v m smaller);

[0121] Porous adsorption uses the formula:

[0122] S m1 =F m K m C m (3)

[0123]

[0124] Where: F m Indicates the proportion of equilibrium adsorption in the pores (values ​​between 0 and 1); K mrepresents the distribution coefficient in the pores [L]; k m2 : pore first-order adsorption kinetic coefficient [1 / T];

[0125] The governing equation for solute transport in the matrix region is:

[0126]

[0127] Where: θ a represents the effective porosity in the matrix; D a represents the effective diffusion coefficient in the matrix [L 2 / T]; C a Indicates the solute concentration in the matrix [M / L 3 ];ρ a Indicates density;

[0128] Matrix adsorption uses the formula:

[0129] S a1 =F a K a C a (6)

[0130]

[0131] Where: F a It represents the proportion of equilibrium adsorption in the matrix, with a value between 0 and 1; K a represents the distribution coefficient in the matrix [L]; k a2 represents the first-order adsorption kinetic coefficient of the matrix [1 / T];

[0132] The concentration is continuous at the interface between the pores and the matrix, and the formula used is:

[0133] C a (r m ,z,t)=C m (z,t) ; r m <r≤∞,0≤z<∞ (8)

[0134] The initial and boundary conditions of the analytical model of nonequilibrium reactive solute transport in the pore-matrix system are expressed as follows:

[0135] C m (r,t=0)=0 (9)

[0136] C a (r,z,t=0)=0 (10)

[0137] C m (r=∞,z,t)=C a (r=∞,z,t)=0 (11)

[0138] The analytical model of nonequilibrium reactive solute transport in the pore-matrix system considering the pulse injection boundary condition is expressed as:

[0139]

[0140] Where: t0 is the pulse injection time;

[0141] Perform Laplace transform on equation (1), where s is the Laplace variable, and we get:

[0142]

[0143] Performing Laplace transform on equation (5) yields:

[0144]

[0145] Performing Laplace transform on equation (3) yields:

[0146]

[0147] Applying Laplace transform to equation (4) yields:

[0148]

[0149] Performing Laplace transform on equation (6) yields:

[0150]

[0151] Performing Laplace transform on equation (7) yields:

[0152]

[0153] Arrange formula (14) as follows:

[0154]

[0155] Substituting equations (17) and (18) into equation (19), we obtain:

[0156] Combining similar terms in formula (20), we get:

[0157]

[0158] Divide θ on both sides of the equation a D a ,get:

[0159]

[0160] Arranging formula (22) yields:

[0161]

[0162] make

[0163]

[0164] The general solution of formula (23) yields:

[0165]

[0166] Performing Laplace transform on the initial condition (11) yields:

[0167]

[0168] From the initial condition (26) and the properties of the first type of void volume function, we can obtain:

[0169] A=0 (27)

[0170] Substituting into formula (25), we get:

[0171]

[0172] Performing Laplace transform on equation (8) yields:

[0173]

[0174] Substituting formula (29) into formula (28), we get:

[0175]

[0176] Substituting formula (3) into formula (28), we get:

[0177]

[0178] Substituting equations (15), (16), and (31) into equation (12), we obtain:

[0179]

[0180] Simplifying formula (32), we get:

[0181]

[0182] make

[0183]

[0184] According to the general solution of the second-order homogeneous linear differential equation, the solution of equation (33) is:

[0185]

[0186] Performing Laplace transform on the pulse injection boundary condition (12) yields:

[0187]

[0188] When the initial and boundary conditions are pulse injection of solute, the solution of equation (36) is:

[0189]

[0190] The solutions derived above are all analytical solutions of the pore-matrix nonequilibrium adsorption reactive solute transport model obtained in the Laplace domain.

[0191] There are multiple parameter values, and the multiple parameter values ​​are respectively used as estimated values ​​of the pore diffusion coefficient, the diffusion coefficient, the first-order adsorption kinetic coefficient in the pores and the first-order adsorption kinetic coefficient in the matrix;

[0192] like Figure 3 As shown in the figure, the penetration curve of the analytical model was compared with the penetration curve of the measured data, and then curve fitting was performed to find the optimal parameter combination. The estimated values ​​were determined to be: pore diffusion coefficient Df = 3.1 cm2 / min, diffusion coefficient Dm = 0.0008 cm2 / min, first-order adsorption kinetic coefficient in pores Kf = 0.001 1 / min, and first-order adsorption kinetic coefficient in matrix Km = 0.381 / min.

[0193] Through the above invention content, the method for solving the solute transport model of the pore-matrix system considering the influence of non-equilibrium adsorption is established, which can more accurately describe and predict the migration behavior of solutes in complex geological media, and provide certain technical support for research and practical engineering applications in fields such as environmental science and hydrogeology.

[0194] A pore-matrix parameter estimation system considering the influence of non-equilibrium adsorption is used to implement the pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption as mentioned above, such as Figure 4 As shown, the system includes an analytical model building unit 100, an analytical model solving unit 101, a penetration curve generating unit 102 and a fitting wiring unit 103;

[0195] The analytical model building unit 100 is used to establish an analytical model of non-equilibrium reactive solute transport in a pore-matrix system;

[0196] The analytical model solving unit 101 is used to solve the semi-analytical solution of the non-equilibrium reactive solute transport analytical model of the pore-matrix system in the Laplace domain;

[0197] The penetration curve generating unit 102 is used to obtain the measured soil column experimental data and monitor the concentration of the organic compound phenanthrene solute at a fixed observation point within a set time range to obtain a penetration curve;

[0198] The fitting unit 103 is used to fit the obtained semi-analytical solution of the analytical model of non-equilibrium reactive solute transport in the pore-matrix system to the penetration curve of the measured data, and select the parameter values ​​corresponding to the fitting curve that meets the set conditions, and use the parameter values ​​as the estimated values ​​of the corresponding coefficients;

[0199] By applying the system of this application, a method for solving the solute transport model of the pore-matrix system considering the influence of non-equilibrium adsorption is established, which can more accurately describe and predict the migration behavior of solutes in complex geological media, and provide certain technical support for research and practical engineering applications in fields such as environmental science and hydrogeology.

[0200] It should be understood that those skilled in the art can make improvements or changes based on the above description, and all such improvements and changes should fall within the scope of protection of the appended claims of the present invention.

Claims

1. A pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption, characterized in that: The method comprises the steps of: Establish an analytical model of non-equilibrium reactive solute transport in pore-matrix system and obtain a semi-analytical solution of the analytical model in Laplace domain. Obtaining the measured soil column experimental data, the concentration of the organic compound phenanthrene solute at a fixed observation point within a set time range is monitored to obtain the breakthrough curve; The obtained semi-analytical solution of the analytical model of non-equilibrium reactive solute transport in the pore-matrix system is fitted with the penetration curve of the measured data, and the parameter values ​​corresponding to the fitting curve that meets the set conditions are selected as the estimated values ​​of the corresponding coefficients.

2. The pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption according to claim 1, characterized in that: The analytical model of non-equilibrium reactive solute transport in the pore-matrix system is established based on the following foundations: The pore radius does not change with the pore length; The matrix is ​​semi-infinite in length; The adsorption processes in the pore and matrix regions are divided into two types: one type assumes that the adsorption is instantaneous, and the other type is dynamic adsorption, which is described by the first-order kinetic coefficients; The degradation reaction is first-order in both the pore and matrix regions; The model water flow is a steady flow.

3. The pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption according to claim 2, characterized in that: The governing equation for reactive solute transport in the pore region in the analytical model of nonequilibrium reactive solute transport in the pore-matrix system is: Where: t represents time; r m represents the pore radius; r represents the radial distance; C m represents the pore solute concentration; S m1 It represents the adsorption amount per unit pore cross section due to equilibrium adsorption; S m2 represents the adsorption amount per unit pore cross section due to non-equilibrium adsorption; λ m represents the first-order reaction rate constant in the pore liquid phase; λ m1 represents the first-order reaction rate constant of the adsorption phase point 1 in the pore; λ m2 represents the second-order reaction rate constant of adsorption phase point 2 in the pore; v m represents the pore flow velocity in the pore area; D m represents the longitudinal diffusion coefficient, D m Using the formula: D m =α m v m +D m0 (2) Where: α m : Pore longitudinal diffusivity D m0 : Pore effective molecular diffusion coefficient Porous adsorption uses the formula: S m1 =F m K m C m (3) Where: F m It represents the proportion of equilibrium adsorption in the pores, with a value between 0 and 1; K m represents the distribution coefficient in the pores; k m2 : pore first-order adsorption kinetic coefficient; The governing equation for solute transport in the matrix region is: Where: θ a represents the effective porosity in the matrix; D a represents the effective diffusion coefficient within the matrix; C a represents the solute concentration in the matrix; ρ a Indicates density; Matrix adsorption uses the formula: S a1 =F a K a C a (6) Where: F a It represents the proportion of equilibrium adsorption in the matrix, with a value between 0 and 1; K a represents the partition coefficient in the matrix; k a2 represents the first-order adsorption kinetic coefficient of the matrix; The concentration is continuous at the interface between the pores and the matrix, and the formula used is: C a (r m ,z,t)=C m (z,t) ; r m <r≤∞,0≤z<∞ (8) The initial and boundary conditions of the analytical model of nonequilibrium reactive solute transport in the pore-matrix system are expressed as follows: C m (r,t=0)=0 (9) C a (r,z,t=0)=0 (10) C m (r=∞,z,t)=C a (r=∞,z,t)=0 (11) The analytical model of nonequilibrium reactive solute transport in the pore-matrix system considering the pulse injection boundary condition is expressed as: Where: t0 is the pulse injection time; Perform Laplace transform on equation (1), where s is the Laplace variable, and we get: Performing Laplace transform on equation (5) yields: Performing Laplace transform on equation (3) yields: Applying Laplace transform to equation (4) yields: Performing Laplace transform on equation (6) yields: Performing Laplace transform on equation (7) yields: Arrange formula (14) as follows: Substituting equations (17) and (18) into equation (19), we obtain: Combining similar terms in formula (20), we get: Divide θ on both sides of the equation a D a ,get: Arranging formula (22) yields: make The general solution of formula (23) yields: Performing Laplace transform on the initial condition (11) yields: From the initial condition (26) and the properties of the first type of void volume function, we can obtain: A＝0 (27) Substituting into formula (25), we get: Performing Laplace transform on equation (8) yields: Substituting formula (29) into formula (28), we get: Substituting formula (3) into formula (28), we get: Substituting equations (15), (16), and (31) into equation (12), we obtain: Simplifying formula (32), we get: make According to the general solution of the second-order homogeneous linear differential equation, the solution of equation (33) is: Performing Laplace transform on the pulse injection boundary condition (12) yields: When the initial and boundary conditions are pulse injection of solute, the solution of equation (36) is:

4. The pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption according to claim 1, characterized in that: There are multiple parameter values, and the multiple parameter values ​​are respectively used as estimated values ​​of the pore diffusion coefficient, the diffusion coefficient, the pore first-order adsorption kinetic coefficient and the first-order adsorption kinetic coefficient in the matrix.

5. A pore-matrix parameter estimation system considering the influence of non-equilibrium adsorption, used to implement the pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption as described in any one of claims 1 to 4, characterized in that: The system includes an analytical model building unit, an analytical model solving unit, a penetration curve generating unit and a fitting wiring unit; The analytical model building unit is used to establish an analytical model of non-equilibrium reactive solute transport in a pore-matrix system; The analytical model solving unit is used to solve the semi-analytical solution of the non-equilibrium reactive solute transport analytical model of the pore-matrix system in the Laplace domain; The penetration curve generating unit is used to obtain measured soil column experimental data and monitor the solute concentration of the organic compound phenanthrene at a fixed observation point within a set time range to obtain a penetration curve; The fitting and matching unit is used to fit the obtained semi-analytical solution of the analytical model of non-equilibrium reactive solute transport in the pore-matrix system with the penetration curve of the measured data, select the parameter values ​​corresponding to the fitting curve that meets the set conditions, and use the parameter values ​​as the estimated values ​​of the corresponding coefficients.

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