Pore-matrix parameter estimation method and system considering non-equilibrium adsorption effects

Abstract

The present application relates to the pore-matrix parameter estimation method and system considering the non-equilibrium adsorption influence, including the steps: the pore-matrix system non-equilibrium reactive solute transport analytical model is established, and the semi-analytical solution is solved;Obtain the measured soil column experiment data, monitor the organic compound phenanthrene solute concentration of fixed observation point in the set time range to obtain the breakthrough curve;The semi-analytical solution obtained is fitted with the breakthrough curve of the measured data, the parameter value corresponding to the fitting curve meeting the set condition is selected, and the parameter value is used as the estimation value of the corresponding coefficient;The present application utilizes the optimal fitting wiring to determine the corresponding pore dispersion coefficient, diffusion coefficient, first-order adsorption kinetic coefficient in the pore and first-order adsorption kinetic coefficient in the matrix, links the measured results with the theoretical results, and fully excavates the utilization value of the existing data.

Description

TECHNICAL FIELD

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

[0002] In the groundwater environment, the solute transport process is significantly affected by adsorption, and the adsorption mechanism directly determines the migration rate and retention characteristics of pollutants. Traditional solute transport models are generally based on the assumption of equilibrium adsorption, that is, the adsorption process is considered to reach equilibrium instantaneously, and the non-equilibrium characteristics of adsorption kinetics are ignored.

[0003] However, in the pore-matrix system composed of soil, rock and other porous media, the mass transfer between the pores (high permeability region) and the matrix (low permeability region) of the solute often exhibits significant non-equilibrium characteristics, making it difficult for traditional models to accurately simulate the real transport behavior of the solute. A pore-matrix parameter estimation method and system considering non-equilibrium adsorption influence is needed to more truly reflect the solute transport behavior in complex media. SUMMARY

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

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

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

[0007] An analytical model of non-equilibrium reactive solute transport in a pore-matrix system is established, and a semi-analytical solution of the analytical model of non-equilibrium reactive solute transport in the Laplace domain is solved;

[0008] Obtain the measured soil column experiment data, monitor the solute concentration of organic compound phenanthrene at fixed observation points within a set time range to obtain the breakthrough curve;

[0009] The semi-analytical solution of the analytical model of non-equilibrium reactive solute transport in the pore-matrix system is fitted and wired with the breakthrough 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 non-equilibrium adsorption influence, wherein the analytical model of non-equilibrium reactive solute transport in the pore-matrix system is established based on the following basis:

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

[0012] The matrix is ​​semi-infinite;

[0013] The adsorption process in the pore and matrix regions is divided into two types: one is the assumption that adsorption is instantaneous, and the other is dynamic adsorption, which is described by first-order kinetic coefficients.

[0014] Both the pore and matrix regions exhibit primary degradation reactions;

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

[0016] The pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption described in this invention, wherein the governing equation for reactive solute transport in the pore region of the non-equilibrium reactive solute transport analytical model of the pore-matrix system adopts the following formula:

[0017] (1)

[0018] In the formula: t represents time; r m Represents the pore radius; r represents the radial distance; C m S represents the pore solute concentration. m1 S represents the amount of adsorption per unit pore cross-section due to equilibrium adsorption; m2 λ represents the amount of adsorption per unit pore cross-section due to non-equilibrium adsorption; m λ represents the first-order reaction rate constant in the porous liquid phase; m1 λ represents the first-order rate constant of the first kind of reaction at adsorption phase point 1 in the pore; m2 The rate constant of the second kind, representing the first-order reaction of adsorption phase point 2 in the pores; v m D represents the pore flow velocity in the pore region. m D represents the longitudinal dispersion coefficient. m Formula used:

[0019] (2)

[0020] In the formula: α m Longitudinal dispersion of pores; D m0 : Effective molecular diffusion coefficient of pores;

[0021] Pore ​​adsorption uses the following formula:

[0022] (3)

[0023] (4)

[0024] In the formula: F m K represents the proportion of equilibrium adsorption in the pores.m k represents the distribution coefficient in the pores. m2 First-order adsorption kinetic coefficient of pores;

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

[0026] (5)

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

[0028] The matrix adsorption is performed using the following formula:

[0029] (6)

[0030] (7)

[0031] In the formula: F a K represents the proportion of equilibrium adsorption in the matrix, with values ​​between 0 and 1; a k represents the partition coefficient in the matrix. a2 Indicates the first-order adsorption kinetic coefficient of the matrix;

[0032] The concentration remains continuous at the interface between the pore and matrix regions, as shown by the formula:

[0033] (8)

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

[0035] (9)

[0036] (10)

[0037] (11)

[0038] The analytical model of non-equilibrium reactive solute transport in a pore-matrix system, considering pulse injection boundary conditions, is expressed as follows:

[0039] (12)

[0040] In the formula: t0 is the pulse injection time;

[0041] Performing a Laplace transformation on equation (1), with s as the Laplace variable, we obtain:

[0042] (13)

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

[0044] (14)

[0045] Performing a Laplace transform on equation (3), we obtain:

[0046] (15)

[0047] Performing a Laplace transform on equation (4), we obtain:

[0048] (16)

[0049] Performing a Laplace transform on equation (6), we obtain:

[0050] (17)

[0051] Performing a Laplace transform on equation (7), we obtain:

[0052] (18)

[0053] Equation (14) can be rearranged as follows:

[0054] (19)

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

[0056] (20)

[0058] Combining like terms in equation (20), we get:

[0059] (twenty one)

[0060] Divide both sides of the equation by θ a D a ,get:

[0061] (twenty two)

[0062] Rearranging equation (22) yields:

[0063] (twenty three)

[0064] make

[0065] (twenty four)

[0067] The general solution of equation (23) is:

[0068] (25)

[0069] Applying the Laplace transform to the initial condition (11), we obtain:

[0070] (26)

[0071] From the initial condition (26) and the properties of the first kind of imaginary argument function, we can obtain:

[0072] A=0(27)

[0073] Substituting into equation (25), we get:

[0074] (28)

[0075] Performing a Laplace transform on equation (8), we obtain:

[0076] (29)

[0077] Substituting equation (29) into equation (28), we get:

[0078] (30)

[0079] Substituting equation (30) into equation (28), we get:

[0080] (31)

[0081] Substituting equations (15), (16), and (31) into equation (13), we get:

[0082] (32)

[0083] Simplify expression (32) to get:

[0084] (33)

[0085] make

[0086] (34)

[0087] (35)

[0088] The solution to equation (34) can be obtained from the general solution of the second-order homogeneous linear differential equation:

[0089] (36)

[0090] Applying the Laplace transform to the pulse injection boundary condition (12), we obtain:

[0091] (37)

[0092] When the initial and boundary conditions are pulsed solute injection, the solution to equation (36) is:

[0093] (38)

[0094] (39)

[0095] The pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption described in this invention has multiple parameter values, and these multiple parameter values ​​are respectively used as estimated values ​​of pore dispersion coefficient, diffusion coefficient, first-order adsorption kinetic coefficient in pores, and first-order adsorption kinetic coefficient in matrix.

[0096] A pore-matrix parameter estimation system considering the influence of non-equilibrium adsorption is provided to implement the pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption as described above. The system includes an analytical model construction unit, an analytical model solving unit, a breakthrough curve generation unit, and a fitting wiring unit.

[0097] The analytical model building unit is used to establish an analytical model for non-equilibrium reactive solute transport in a pore-matrix system.

[0098] The analytical model solving unit is used to solve the semi-analytical solution of the analytical model of non-equilibrium reactive solute transport in the pore-matrix system in the Laplace domain;

[0099] The penetration curve generation unit is used to obtain experimental data of measured soil columns and monitor the concentration of phenanthrene solute at fixed observation points within a set time range to obtain the penetration curve.

[0100] The fitting wiring unit is used to fit the semi-analytical solution of the obtained analytical model of non-equilibrium reactive solute transport in the pore-matrix system with the breakthrough curve of the measured data, and select the parameter values ​​corresponding to the fitting curve that meet the set conditions. The parameter values ​​are used as the estimated values ​​of the corresponding coefficients.

[0101] The beneficial effects of this invention are as follows: This invention obtains a semi-analytical solution for the Laplace domain by establishing a solute transport model of a pore-matrix system under the influence of non-equilibrium adsorption. Based on indoor measured soil column experimental data, the solute concentration at fixed observation points within a set time range is monitored to obtain the breakthrough curve, which is then matched with the breakthrough curve obtained from the analytical model. The corresponding pore dispersion 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 matching. The measured results are linked with the theoretical results, fully exploring the utilization value of existing data. Attached Figure Description

[0102] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the present invention will be further described below in conjunction with the accompanying drawings and embodiments. 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:

[0103] Figure 1 This is a flowchart of a preferred embodiment of the pore-matrix parameter estimation method considering the effects of non-equilibrium adsorption.

[0104] Figure 2 This is a schematic diagram of the concept of a pore-matrix parameter estimation method considering the effects of non-equilibrium adsorption, according to a preferred embodiment of the present invention.

[0105] Figure 3 This is a fitting wiring diagram of the pore-matrix parameter estimation method considering the effects of non-equilibrium adsorption according to a preferred embodiment of the present invention.

[0106] Figure 4 This is a block diagram of the pore-matrix parameter estimation system considering the effects of non-equilibrium adsorption, which is a preferred embodiment of the present invention. Detailed Implementation

[0107] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, a clear and complete description will be provided below in conjunction with the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0108] A preferred embodiment of the present invention provides a pore-matrix parameter estimation method that considers the effects of non-equilibrium adsorption, such as... Figure 1 As shown, see also Figure 2 and Figure 3 The steps include:

[0109] S01: Establish an analytical model of non-equilibrium reactive solute transport in a pore-matrix system and solve for the semi-analytical solution of the analytical model of non-equilibrium reactive solute transport in a pore-matrix system in the Laplace domain;

[0110] S02: Obtain experimental data of the measured soil column, monitor the concentration of the organic compound phenanthrene solute at fixed observation points within a set time range, and obtain the breakthrough curve;

[0111] S03: Fit the semi-analytical solution of the obtained analytical model of non-equilibrium reactive solute transport in the pore-matrix system with the breakthrough curve of the measured data, select the parameter values ​​corresponding to the fitting curve that meet the set conditions, and use the parameter values ​​as the estimated values ​​of the corresponding coefficients.

[0112] This invention obtains a semi-analytical solution for the Laplace domain by establishing a solute transport model of a pore-matrix system under the influence of non-equilibrium adsorption. Based on indoor measured soil column experimental data, the solute concentration at fixed observation points within a set time range is monitored to obtain the breakthrough curve. The breakthrough curve is then matched with the breakthrough curve obtained from the analytical model. The corresponding pore dispersion coefficient, diffusion coefficient, first-order adsorption kinetic coefficient in the pores, and first-order adsorption kinetic coefficient in the matrix are determined by using the optimal fitting matching. The measured results are linked with the theoretical results, fully exploring the utilization value of existing data.

[0113] This invention presents a pore-matrix parameter estimation method considering the effects of non-equilibrium adsorption. The aim is to conduct in-depth research on solute transport processes in pore-matrix systems, characterize solute migration under non-equilibrium adsorption conditions, and address the insufficient simulation accuracy of traditional equilibrium adsorption models in complex media. This method aims to accurately characterize solute migration behavior and improve the reliability of pollutant transport prediction. It can be widely applied in fields such as groundwater resource protection, pollution plume evolution analysis, and remediation scheme optimization, providing core technical support for theoretical research and engineering practice of solute transport in heterogeneous media.

[0114] like Figure 2 As shown, the analytical model for non-equilibrium reactive solute transport in the pore-matrix system of this invention is established based on the following assumptions:

[0115] The pore radius does not change with the pore length;

[0116] The matrix is ​​semi-infinite;

[0117] The adsorption process in the pore and matrix regions is divided into two types: one is the assumption that adsorption is instantaneous, and the other is dynamic adsorption, which is described by first-order kinetic coefficients.

[0118] Both the pore and matrix regions exhibit primary degradation reactions;

[0119] The water flow in the model is a steady flow.

[0120] The governing equation for reactive solute transport in the pore region in the analytical model of nonequilibrium reactive solute transport in a pore-matrix system is as follows:

[0121] (1)

[0122] In the formula: t represents time [T]; r m The pore radius is represented by [L]; r represents the radial distance [L]; C m S represents the pore solute concentration. m1 S represents the amount of adsorption per unit pore cross-section due to equilibrium adsorption [M / L²]. m2 λ represents the amount of adsorption per unit pore cross-section due to non-equilibrium adsorption [M / L²]; m λ represents the first-order reaction rate constant [1 / T] in the porous liquid phase; m1 λ represents the first-order reaction rate constant of the first kind [1 / T] at adsorption phase point 1 in the pore; m2 The rate constant of the second kind [1 / T] represents the first-order reaction rate at adsorption phase point 2 in the pores; v m D represents the pore flow velocity in the pore region [L / T]; m D represents the longitudinal dispersion coefficient [L² / T]. m Formula used:

[0123] (2)

[0124] In the formula: α m Longitudinal dispersion of pores; D m0 [L]: Effective molecular diffusion coefficient in pores [L² / T] (usually relative to α) m *v m (smaller)

[0125] Pore ​​adsorption uses the following formula:

[0126] (3)

[0127] (4)

[0128] In the formula: F m K represents the proportion of equilibrium adsorption in the pores (value between 0 and 1); m k represents the distribution coefficient in the pores [L]; m2 : First-order adsorption kinetic coefficient of pores [1 / T];

[0129] The governing equation for solute transport in the matrix region is as follows:

[0130] (5)

[0131] In the formula: θ a Indicates the effective porosity in the matrix; D a The effective diffusion coefficient within the matrix is ​​represented by [L² / T]; C a ρ represents the solute concentration in the matrix [M / L³]. a Indicates density;

[0132] The matrix adsorption is performed using the following formula:

[0133] (6)

[0134] (7)

[0135] In the formula: F a K represents the proportion of equilibrium adsorption in the matrix, with values ​​between 0 and 1; a k represents the partition coefficient [L] in the matrix. a2 This represents the first-order adsorption kinetic coefficient of the matrix [1 / T].

[0136] The concentration remains continuous at the interface between the pore and matrix regions, as shown by the formula:

[0137] (8)

[0138] The initial and boundary conditions of the analytical model for nonequilibrium reactive solute transport in a pore-matrix system are expressed as follows:

[0139] (9)

[0140] (10)

[0141] (11)

[0142] The analytical model of non-equilibrium reactive solute transport in a pore-matrix system, considering pulse injection boundary conditions, is expressed as follows:

[0143] (12)

[0144] In the formula: t0 is the pulse injection time;

[0145] Performing a Laplace transformation on equation (1), with s as the Laplace variable, we obtain:

[0146] (13)

[0147] Performing a Laplace transform on equation (5) yields:

[0148] (14)

[0149] Performing a Laplace transform on equation (3), we obtain:

[0150] (15)

[0151] Performing a Laplace transform on equation (4), we obtain:

[0152] (16)

[0153] Performing a Laplace transform on equation (6), we obtain:

[0154] (17)

[0155] Performing a Laplace transform on equation (7), we obtain:

[0156] (18)

[0157] Equation (14) can be rearranged as follows:

[0158] (19)

[0159] Substituting equations (17) and (18) into equation (19), we get:

[0160] (20)

[0162] Combining like terms in equation (20), we get:

[0163] (twenty one)

[0164] Divide both sides of the equation by θ a D a ,get:

[0165] (twenty two)

[0166] Rearranging equation (22) yields:

[0167] (twenty three)

[0168] make

[0169] (twenty four)

[0171] The general solution of equation (23) is:

[0172] (25)

[0173] Applying the Laplace transform to the initial condition (11), we obtain:

[0174] (26)

[0175] From the initial condition (26) and the properties of the first kind of imaginary argument function, we can obtain:

[0176] A=0(27)

[0177] Substituting into equation (25), we get:

[0178] (28)

[0179] Performing a Laplace transform on equation (8), we obtain:

[0180] (29)

[0181] Substituting equation (29) into equation (28), we get:

[0182] (30)

[0183] Substituting equation (30) into equation (28), we get:

[0184] (31)

[0185] Substituting equations (15), (16), and (31) into equation (13), we get:

[0186] (32)

[0187] Simplify expression (32) to get:

[0188] (33)

[0189] make

[0190] (34)

[0191] (35)

[0192] The solution to equation (34) can be obtained from the general solution of the second-order homogeneous linear differential equation:

[0193] (36)

[0194] Applying the Laplace transform to the pulse injection boundary condition (12), we obtain:

[0195] (37)

[0196] When the initial and boundary conditions are pulsed solute injection, the solution to equation (36) is:

[0197] (38)

[0198] (39)

[0199] The solutions obtained above are all analytical solutions obtained in the Laplace domain from the pore-matrix non-equilibrium adsorption reactive solute transport model.

[0200] There are multiple parameter values, and these multiple parameter values ​​are respectively used as estimates of the pore dispersion coefficient, diffusion coefficient, first-order adsorption kinetic coefficient in the pores, and first-order adsorption kinetic coefficient in the matrix.

[0201] like Figure 3 As shown, the breakthrough curve of the analytical model is compared with the breakthrough curve of the measured data, and then curve fitting is performed to find the optimal parameter combination. The estimated values ​​are: pore dispersion 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.

[0202] The invention provides a solution method for the solute transport model of the pore-matrix system that considers the influence of non-equilibrium adsorption. This method can more accurately describe and predict the transport behavior of solutes in complex geological media, providing technical support for research and practical engineering applications in fields such as environmental science and hydrogeology.

[0203] A pore-matrix parameter estimation system considering the effects of non-equilibrium adsorption is provided to implement the pore-matrix parameter estimation method considering the effects of non-equilibrium adsorption as described above. Figure 4 As shown, the system includes an analytical model building unit 100, an analytical model solving unit 101, a penetration curve generation unit 102, and a fitting wiring unit 103;

[0204] Analytical model building unit 100 is used to establish an analytical model of non-equilibrium reactive solute transport in a pore-matrix system;

[0205] Analytical model solving unit 101 is used to solve the semi-analytical solution of the analytical model of non-equilibrium reactive solute transport in the pore-matrix system in the Laplace domain;

[0206] The penetration curve generation unit 102 is used to acquire experimental data of measured soil columns and to monitor the concentration of phenanthrene solute at fixed observation points within a set time range to obtain the penetration curve.

[0207] Fitting wiring unit 103 is used to fit the semi-analytical solution of the obtained analytical model of non-equilibrium reactive solute transport in the pore-matrix system with the breakthrough curve of the measured data, and select the parameter values ​​corresponding to the fitting curve that meet the set conditions, and the parameter values ​​are used as the estimated values ​​of the corresponding coefficients.

[0208] The solute transport model solution method for the pore-matrix system considering the influence of non-equilibrium adsorption, established by applying the system of this application, can more accurately describe and predict the transport behavior of solutes in complex geological media, and provide certain technical support for research and practical engineering applications in environmental science, hydrogeology and other fields.

[0209] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A method for estimating pore-matrix parameters considering the effects of non-equilibrium adsorption, characterized in that, The method includes the following steps: An analytical model of nonequilibrium reactive solute transport in a pore-matrix system was established, and a semi-analytical solution of the analytical model of nonequilibrium reactive solute transport in the pore-matrix system in the Laplace domain was obtained. Obtain experimental data of the measured soil column, and monitor the concentration of the organic compound phenanthrene solute at fixed observation points within a set time range to obtain the breakthrough curve; The semi-analytical solution of the obtained analytical model of non-equilibrium reactive solute transport in the pore-matrix system was fitted with the breakthrough curve of the measured data. The parameter values ​​corresponding to the fitted curve that meet the set conditions were selected and used as the estimated values ​​of the corresponding coefficients. The analytical model for non-equilibrium reactive solute transport in the pore-matrix system is based on the following: The pore radius does not change with the pore length; The matrix is ​​semi-infinite; The adsorption process in the pore and matrix regions is divided into two types: one is the assumption that adsorption is instantaneous, and the other is dynamic adsorption, which is described by first-order kinetic coefficients. Both the pore and matrix regions exhibit primary degradation reactions; The water flow in the model is a steady flow; The governing equation for reactive solute transport in the pore region in the analytical model of non-equilibrium reactive solute transport in the pore-matrix system is as follows: (1) In the formula: t represents time; r m Represents the pore radius; r represents the radial distance; C m S represents the pore solute concentration. m1 S represents the amount of adsorption per unit pore cross-section due to equilibrium adsorption; m2 λ represents the amount of adsorption per unit pore cross-section due to non-equilibrium adsorption; m λ represents the first-order reaction rate constant in the porous liquid phase; m1 λ represents the first-order rate constant of the first kind of reaction at adsorption phase point 1 in the pore; m2 The rate constant of the second kind, representing the first-order reaction of adsorption phase point 2 in the pores; v m D represents the pore flow velocity in the pore region. m D represents the longitudinal dispersion coefficient. m Formula used: (2) In the formula: α m Longitudinal dispersion of pores; D m0 : Effective molecular diffusion coefficient of pores; Pore ​​adsorption uses the following formula: (3) (4) In the formula: F m K represents the proportion of equilibrium adsorption in the pores, with a value between 0 and 1. m k represents the distribution coefficient in the pores. m2 First-order adsorption kinetic coefficient of pores; The governing equation for solute transport in the matrix region is as follows: (5) In the formula: θ a Indicates the effective porosity in the matrix; D a C represents the effective diffusion coefficient within the matrix. a ρ represents the solute concentration in the matrix. a Indicates density; The matrix adsorption is performed using the following formula: (6) (7) In the formula: F a K represents the proportion of equilibrium adsorption in the matrix, with values ​​between 0 and 1; a k represents the partition coefficient in the matrix. a2 Indicates the first-order adsorption kinetic coefficient of the matrix; The concentration remains continuous at the interface between the pore and matrix regions, as shown by the formula: (8) The initial and boundary conditions of the analytical model for nonequilibrium reactive solute transport in a pore-matrix system are expressed as follows: (9) (10) (11) The analytical model of non-equilibrium reactive solute transport in a pore-matrix system, considering pulse injection boundary conditions, is expressed as follows: (12) In the formula: t0 is the pulse injection time; Performing a Laplace transformation on equation (1), with s as the Laplace variable, we obtain: (13) Performing a Laplace transform on equation (5) yields: (14) Performing a Laplace transform on equation (3), we obtain: (15) Performing a Laplace transform on equation (4), we obtain: (16) Performing a Laplace transform on equation (6), we obtain: (17) Performing a Laplace transform on equation (7), we obtain: (18) Equation (14) can be rearranged as follows: (19) Substituting equations (17) and (18) into equation (19), we get: (20) Combining like terms in equation (20), we get: (21) Divide both sides of the equation by θ a D a ,get: (22) Rearranging equation (22) yields: (23) make (24) The general solution of equation (23) is: (25) Applying the Laplace transform to the initial condition (11), we obtain: (26) From the initial condition (26) and the properties of the first kind of imaginary argument function, we can obtain: A=0(27) Substituting into equation (25), we get: (28) Performing a Laplace transform on equation (8), we obtain: (29) Substituting equation (29) into equation (28), we get: (30) Substituting equation (30) into equation (28), we get: (31) Substituting equations (15), (16), and (31) into equation (13), we get: (32) Simplify expression (32) to get: (33) make (34) (35) The solution to equation (34) can be obtained from the general solution of the second-order homogeneous linear differential equation: (36) Applying the Laplace transform to the pulse injection boundary condition (12), we obtain: (37) When the initial and boundary conditions are pulsed solute injection, the solution to equation (36) is: (38) (39) 2. The pore-matrix parameter estimation method considering the influence of non-equilibrium adsorption according to claim 1, characterized in that, The parameter can take multiple values, and each of these multiple parameter values ​​is used as an estimate of the pore dispersion coefficient, diffusion coefficient, pore first-order adsorption kinetic coefficient, and matrix first-order adsorption kinetic coefficient, respectively.

3. 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 1-2, characterized in that, The system includes an analytical model construction unit, an analytical model solving unit, a penetration curve generation unit, and a fitting wiring unit; The analytical model building unit is used to establish an analytical model for 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 analytical model of non-equilibrium reactive solute transport in the pore-matrix system in the Laplace domain; The penetration curve generation unit is used to obtain experimental data of measured soil columns and monitor the concentration of phenanthrene solute at fixed observation points within a set time range to obtain the penetration curve. The fitting wiring unit is used to fit the semi-analytical solution of the obtained analytical model of non-equilibrium reactive solute transport in the pore-matrix system with the breakthrough curve of the measured data, and select the parameter values ​​corresponding to the fitting curve that meet the set conditions. The parameter values ​​are used as the estimated values ​​of the corresponding coefficients.

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