A method and system for inverting parameters of a fractured aquifer in response to a groundwater solid tide

Abstract

This invention relates to a method and system for inverting parameters of fractured aquifers in response to groundwater solid tides, comprising the following steps: establishing a mathematical model of the groundwater solid tide response of a fractured aquifer considering both pore and fractured media, and solving the mathematical model to obtain an analytical solution; acquiring hydrological borehole water level data of the fractured aquifer to be estimated, and obtaining the amplitude ratio and phase difference characteristic parameters of the water level response to solid tide stress changes; fitting the analytical solution with the amplitude ratio and phase difference characteristic parameters, and selecting the coefficient of determination R. 2 The parameter value corresponding to the largest fitted curve is used as the inversion result of the fractured aquifer parameters. The dual-medium model can realistically depict the groundwater movement law in the pore-fracture system of the fractured aquifer under solid tide response, and can intuitively understand the influence of the hydrogeological parameters of the dual media in the fractured aquifer on the groundwater solid tide response, providing a more reliable theoretical basis and method for accurate inversion of fractured aquifer parameters.

Description

Technical Field

[0001] This invention relates to the field of groundwater parameter inversion technology, and more specifically, to a method and system for inverting groundwater solid tide response fracture aquifer parameters. Background Technology

[0002] Groundwater plays a crucial role as a key freshwater resource in global water supply and ecosystem maintenance. However, with climate change leading to increasingly uneven precipitation distribution and escalating water scarcity, the rational development and sustainable utilization of groundwater resources has become a critical issue for all countries. Against this backdrop, determining aquifer parameters has become a core factor in addressing these challenges. Solid tides, as a natural hydraulic phenomenon, provide important data for aquifer parameter inversion. Accurate aquifer parameter inversion results not only provide reliable foundational data for aquifer numerical simulation and flow prediction but are also key to achieving effective water resource management and protection.

[0003] As geological media for groundwater storage and movement, fractured aquifers exhibit a complex internal structure and properties that significantly influence groundwater flow patterns. In real geological environments, they exhibit a distinct dual-medium characteristic, consisting of both porous and fractured media. Traditional equivalent porous media models are insufficient in describing this heterogeneity, typically assuming the aquifer as a homogeneous, isotropic continuous medium, neglecting the coupling effect between the porous and fractured media, leading to low accuracy in inversion results. Constructing a groundwater solid tide response parameter inversion method and corresponding system based on a dual-medium model is an economical and effective approach. Combining this with long-term water level observation data allows for a more accurate inversion of the aquifer's true physical characteristics, providing more precise and efficient data support for related work. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for inverting parameters of groundwater solid tide response fractured aquifers, and to provide a system for inverting parameters of groundwater solid tide response fractured aquifers, in view of the above-mentioned defects of the prior art.

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

[0006] A method for inverting parameters of fractured aquifers in response to groundwater solid tides is constructed, wherein the method includes the following steps:

[0007] A dual-medium mathematical model considering the groundwater response to solid tides in the pore-fracture system of a fractured aquifer is established. The mathematical model based on the dual-medium theory is solved to obtain analytical solutions for the amplitude ratio and phase difference of the hydraulic head in the fractured aquifer under tidal stress.

[0008] Obtain hydrological borehole water level data of the aquifer to be estimated, and obtain the amplitude ratio and phase difference characteristic parameters of the water level response to solid tidal stress changes;

[0009] The analytical solution was fitted with the amplitude ratio and phase difference characteristic parameters of the solid tidal stress change in the water level response, and the determination coefficient R was selected. 2 The parameter values ​​corresponding to the largest fitted curve are used as the inversion results of the fractured aquifer parameters.

[0010] The groundwater solid tide response fractured aquifer parameter inversion method of the present invention, wherein the establishment of a dual-medium mathematical model considering the groundwater response to solid tide in the fractured aquifer pore-fracture system is based on the following conditions:

[0011] Confined aquifers are assumed to extend horizontally indefinitely with uniform thickness, and vertical overflow recharge is ignored;

[0012] The pores and fractures in the aquifer are evenly distributed in space;

[0013] Each fracture and matrix continuum is assumed to be homogeneous and isotropic;

[0014] At any point, there exists a dual head of water in pores and fissures, and there is a water exchange between the two. The amount of exchange depends on the head difference between the media and obeys Darcy's law.

[0015] The pumping well is located in a fractured medium, with water entering the well wall evenly, and it is a complete well for pumping.

[0016] The groundwater solid tide response fractured aquifer parameter inversion method of this invention, wherein the establishment of a dual-medium mathematical model considering the groundwater response to solid tide in the pore-fracture system of the fractured aquifer, and the solution of the mathematical model based on the dual-medium theory to obtain the analytical solution of the hydraulic head amplitude ratio and phase difference of the fractured aquifer under tidal stress includes:

[0017] The governing equations for water flow in the two-medium model can be described by the following equations:

[0018]

[0019] In the formula, T is the hydraulic conductivity of the aquifer; h f h m These represent the water head in the fissures and the matrix, respectively; s f s m These represent the water storage capacity in the fractures and matrix, respectively; B is the Skempton coefficient of the aquifer; K u ρ is the non-drained bulk modulus of the aquifer; g is the gravitational acceleration; ε is the pore elastic volumetric strain caused by Earth's tides; and r is the radial distance from the wellbore.

[0020] Fluid exchange between pores and fissures is represented by the following equation:

[0021]

[0022] Where μ is the water exchange parameter between pores and fissures;

[0023] Set boundary conditions:

[0024] h f (r,t)=h ∞ (t), r=∞ (3)

[0025] h m (r,t)=h ∞ (t), r=∞ (4)

[0026] h f (r,t)=h w (t),r=r w (5)

[0027] h m (r,t)=h w (t),r=r w (6)

[0028]

[0029] In the formula, r w r c These are the outer diameter and inner diameter of the well shaft, respectively.

[0030] The continuity equations for seepage at infinity for equations (1) and (2) are:

[0031]

[0032] Because of infinity h ∞ (m)=h ∞,0 e iωt h ∞ (m)=h ∞,0 e iωt Let ε0 be the amplitude of ε. Substituting this into the above equation, we get:

[0033]

[0034] In the formula, h w (m)=h w,0 e iωt The water level in the well is a periodic level with a complex amplitude h. w,0 ω = 2π / τ is the angular frequency, and τ is the tidal oscillation period. Assume:

[0035] h f (r,t)=Δhf (r,t)+h ∞ (t) (11)

[0036] h m (r,t)=Δh m (r,t)+h ∞ (t) (12)

[0037] Substituting equation (11) into equation (1) yields:

[0038]

[0039] According to equation (8), we can obtain:

[0040]

[0041] Substituting equation (12) into equation (2), we get:

[0042]

[0043] According to equation (9), we can obtain:

[0044]

[0045] Let Δh f =Δh f,0 (r)e iωt ,Δh m =Δh m,0 (r)e iωt Equations (15) and (17) are expressed as:

[0046]

[0047] iωs m Δh m,0 =μ(Δh) f,0 -Δh m,0 (19)

[0048] but,

[0049]

[0050] Substituting equation (20) into equation (18), we get:

[0051]

[0052] The boundary conditions are now:

[0053] Δh f,0 (r→∞)=0 (22)

[0054]

[0055] The general solution of equation (21) is:

[0056] Δh f,0 =C I I0(βr)+C K K0(βr) (25)

[0057] In the formula, I0 and K0 are the first and second kind zero-order modified Bessel functions, respectively;

[0058] but,

[0059]

[0060] As r→∞, the first-order zero-order modified Bessel function I0 grows exponentially. From the boundary condition (18), we know that C I =0, then:

[0061] Δh f,0 =C K K0(βr) (27)

[0062] According to equation (24), C K expression:

[0063]

[0064] Substitute equation (29) into equation (23):

[0065]

[0066] in,

[0067]

[0068] Define amplitude ratio:

[0069]

[0070] The phase difference is:

[0071]

[0072] The present invention discloses a method for inverting parameters of fractured aquifers in response to groundwater solid tides, wherein the method involves acquiring hydrological borehole water level data of the fractured aquifer to be estimated. The amplitude ratio and phase difference of the water head in the fractured aquifer under solid tidal stress are obtained using the Baytap solid tide analysis program.

[0073] A groundwater solid tide response fractured aquifer parameter inversion system is applied to the groundwater solid tide response fractured aquifer parameter inversion method as described above. The system includes: a model building unit, a data acquisition and processing unit, and a fitting wiring unit.

[0074] The model building unit is used to establish a dual-medium mathematical model considering the groundwater response to solid tides in the pore-fracture system of the fractured aquifer, solve the mathematical model based on the dual-medium theory, and obtain analytical solutions for the amplitude ratio and phase difference of the hydraulic head in the fractured aquifer under tidal stress.

[0075] The data acquisition and processing unit is used to acquire hydrological borehole water level data of the fractured aquifer to be estimated, and to obtain the amplitude ratio and phase difference characteristic parameters of the water level response to the change in solid tidal stress.

[0076] The fitting wiring unit is used to fit the analytical solution with the amplitude ratio and phase difference characteristic parameters of the water level response solid tidal stress change, and select the determination coefficient R. 2 The parameter values ​​corresponding to the largest fitted curve are used as the inversion results of the fractured aquifer parameters.

[0077] The beneficial effects of this invention are as follows: by employing the method of this application and using a dual-medium model, the groundwater movement law in the pore-fracture system of fractured aquifers under solid tide response can be more realistically depicted. The influence of hydrogeological parameters of the dual media in fractured aquifers on the solid tide response of groundwater can be intuitively understood, providing a more reliable theoretical basis and method for the accurate inversion of fractured aquifer parameters. Attached Figure Description

[0078] 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:

[0079] Figure 1 This is a flowchart of the groundwater solid tide response fracture aquifer parameter inversion method according to a preferred embodiment of the present invention;

[0080] Figure 2 This is a schematic diagram of the groundwater solid tide response fracture aquifer parameter inversion method according to a preferred embodiment of the present invention.

[0081] Figure 3 This is a phase difference fitting diagram of the groundwater solid tide response fracture aquifer parameter inversion method according to a preferred embodiment of the present invention;

[0082] Figure 4 This is a schematic diagram of the groundwater solid tide response fracture aquifer parameter inversion system according to a preferred embodiment of the present invention. Detailed Implementation

[0083] 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.

[0084] The preferred embodiment of the present invention is a method for inverting groundwater solid tide response fractured aquifer parameters, such as... Figure 1 As shown, see also Figure 2 and Figure 3 The steps include:

[0085] S01: Establish a dual-medium mathematical model considering the groundwater response to solid tides in the pore-fracture system of the fractured aquifer, solve the mathematical model based on the dual-medium theory, and obtain analytical solutions for the amplitude ratio and phase difference of the water head in the fractured aquifer under tidal stress; S02: Obtain hydrological borehole water level data of the fractured aquifer to be estimated, and obtain the characteristic parameters of the amplitude ratio and phase difference of the water level response to the change of solid tidal stress.

[0086] S03: Fit the analytical solution to the amplitude ratio and phase difference characteristic parameters of the solid tidal stress change in the water level response, and select the coefficient of determination R. 2 The parameter value corresponding to the largest fitted curve is used as the inversion result of the aquifer parameters;

[0087] By employing the methods and approaches of this application and using a dual-medium model, the movement of groundwater in the pore-fracture system of a fractured aquifer under solid tide response can be realistically depicted. Furthermore, the influence of hydrogeological parameters of the dual media in a fractured aquifer on the solid tide response of groundwater can be intuitively understood, providing a more reliable theoretical basis and method for the accurate inversion of fractured aquifer parameters.

[0088] In terms of applications, the inversion method based on the dual-medium model can significantly improve the accuracy of parameter inversion. By combining it with solid tide signals, more effective information can be extracted from hydrological monitoring data. After processing with optimized algorithms, aquifer parameter estimates that are closer to reality can be obtained. This is of great practical significance for realizing refined numerical simulation and prediction of aquifers, optimizing groundwater resource development and utilization schemes, strengthening groundwater pollution prevention and control, and ensuring the sustainable use of groundwater resources.

[0089] A dual-medium mathematical model considering the groundwater response to solid tides in a fractured aquifer pore-fracture system is established based on the following conditions:

[0090] Confined aquifers are assumed to extend horizontally indefinitely with uniform thickness, and vertical overflow recharge is ignored;

[0091] The pores and fractures in the aquifer are evenly distributed in space;

[0092] Each fracture and matrix continuum is assumed to be homogeneous and isotropic;

[0093] At any point, there exists a dual head of water in pores and fissures, and there is a water exchange between the two. The amount of exchange depends on the head difference between the media and obeys Darcy's law.

[0094] The pumping well is located in a fractured medium, with water entering the well wall uniformly, and it is a complete well pumping operation. (Combined with...) Figure 2 A dual-medium mathematical model considering the groundwater response to solid tides in the pore-fracture system of a fractured aquifer is established. The mathematical model based on dual-medium theory is solved to obtain analytical solutions for the amplitude ratio and phase difference of the hydraulic head in the fractured aquifer under tidal stress. More specific calculations include:

[0095]

[0096] In the formula, T is the hydraulic conductivity of the aquifer; h f h m These represent the water head in the fissures and the matrix, respectively; s f s m These represent the water storage capacity in the fractures and matrix, respectively; B is the Skempton coefficient of the aquifer; K u ρ is the non-drained bulk modulus of the aquifer; g is the gravitational acceleration; ε is the pore elastic volumetric strain caused by Earth's tides; and r is the radial distance from the wellbore.

[0097] Fluid exchange between pores and fissures is represented by the following equation:

[0098]

[0099] Where μ is the water exchange parameter between pores and fissures;

[0100] Set boundary conditions:

[0101] h f (r,t)=h ∞ (t), r=∞ (3)

[0102] h m (r,t)=h ∞ (t), r=∞ (4)

[0103] h f (r,t)=h w (t),r=r w (5)

[0104] h m (r,t)=hw (t),r=r w (6)

[0105]

[0106] In the formula, r w r c These refer to the outer diameter and inner diameter of the well shaft, respectively.

[0107] The continuity equations for seepage at infinity for equations (1) and (2) are:

[0108]

[0109] Because of infinity h ∞ (m)=h ∞,0 e iωt h ∞ (m)=h ∞,0 e iωt Let ε0 be the amplitude of ε. Substituting this into the above equation, we get:

[0110]

[0111] In the formula, h w (m)=h w,0 e iωt The water level in the well is a periodic level with a complex amplitude h. w,0 ω = 2π / τ is the angular frequency, and τ is the tidal oscillation period. Assume:

[0112] h f (r,t)=Δh f (r,t)+h ∞ (t) (11)

[0113] h m (r,t)=Δh m (r,t)+h ∞ (t) (12)

[0114] Substituting equation (11) into equation (1) yields:

[0115]

[0116] According to equation (8), we can obtain:

[0117]

[0118] Substituting equation (12) into equation (2), we get:

[0119]

[0120] According to equation (9), we can obtain:

[0121]

[0122] Let Δh f =Δh f,0 (r)e iωt ,Δh m =Δh m,0 (r)e iωt Equations (15) and (17) are expressed as:

[0123]

[0124] iωs m Δh m,0 =μ(Δh) f,0 -Δh m,0 (19)

[0125] but

[0126]

[0127] Substituting equation (20) into equation (18), we get:

[0128]

[0129] The boundary conditions are now:

[0130] Δh f,0 (r→∞)=0 (22)

[0131]

[0132] The general solution of equation (21) is:

[0133] Δh f,0 =C I I0(βr)+C K K0(βr) (25)

[0134] In the formula, I0 and K0 are the first and second kind zero-order modified Bessel functions, respectively;

[0135] but,

[0136] As r→∞, the first-order zero-order modified Bessel function I0 grows exponentially. From the boundary condition (18), we know that C I =0, then:

[0137] Δh f,0 =C K K0(βr) (27)

[0138] According to equation (24), C K expression:

[0139]

[0140]

[0141] Substitute equation (29) into equation (23):

[0142]

[0143] in,

[0144]

[0145] Define amplitude ratio:

[0146]

[0147] The phase difference is:

[0148]

[0149] Adjust the upper and lower limits of the parameters, compare the amplitude ratio and phase difference expressions of the analytical model with the monitoring data, and perform fitting. Figure 3 Find the optimal parameter combination and determine the estimated values ​​of each permeability coefficient: T = 1 × 10 -8 m 2 / d, S m =0.016,S f =0.023, μ=0.1.

[0150] Solid tides, as a natural and stable periodic stress load acting on the shallow crust over a long period, cause corresponding periodic micro-dynamic changes in well water levels. For example... Figure 2 As shown, the combined force of the gravitational pull of the sun and moon and the inertial centrifugal force generated by the Earth's rotation and revolution, along with tidal stress, causes periodic elastic deformation of the aquifer's solid framework. This results in groundwater flowing into and out of the wellbore as the solid framework is compressed and expanded, causing periodic micro-dynamic changes in the wellbore water level.

[0151] After obtaining periodically changing water level data, the micro-dynamic components affected by the solid tide can be extracted from the macro-level water level dynamics by using a filtering method according to the known frequency range of the solid tide. After removing the other components, the corresponding amplitude ratio and phase difference data can be obtained by using the solid tide analysis program - Baytap to perform harmonic analysis on the micro-dynamic components.

[0152] After writing the analytical solution code for amplitude ratio and phase difference in MATLAB, the obtained data is fitted and compared, and finally plotted. Figure 3 The fitting results are shown in the figure.

[0153] Preferably, hydrological borehole water level data of the aquifer to be estimated is obtained. The amplitude ratio and phase difference of the water head in the fractured aquifer under solid tidal stress are obtained using the Baytap solid tidal analysis program.

[0154] A groundwater solid tide response fractured aquifer parameter inversion system is applied to the groundwater solid tide response fractured aquifer parameter inversion method described above, such as... Figure 4 As shown, the system includes: a model building unit 10, a data acquisition and processing unit 11, and a fitting wiring unit 12;

[0155] Model building unit 10 is used to establish a dual-medium mathematical model considering the groundwater response to solid tides in the pore-fracture system of the fractured aquifer, solve the mathematical model based on the dual-medium theory, and obtain analytical solutions for the amplitude ratio and phase difference of the hydraulic head in the fractured aquifer under tidal stress.

[0156] Data acquisition and processing unit 11 is used to acquire hydrological borehole water level data of the fractured aquifer to be estimated, and obtain the amplitude ratio and phase difference characteristic parameters of the water level response to the change of solid tidal stress.

[0157] Fitting unit 12 is used to fit the analytical solution with the amplitude ratio and phase difference characteristic parameters of the change in solid tidal stress in the water level response, and selects the determination coefficient R. 2 The parameter values ​​corresponding to the largest fitted curve are used as the inversion results of the fractured aquifer parameters.

[0158] By employing the system of this application and utilizing a dual-medium model, the movement of groundwater in the pore-fracture system of fractured aquifers under solid tide response can be realistically depicted. Furthermore, the influence of hydrogeological parameters of the dual-medium system on the solid tide response of groundwater can be intuitively understood, providing a more reliable theoretical basis and method for the accurate inversion of fractured aquifer parameters. 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 inverting parameters of a fractured aquifer in response to groundwater solid tides, characterized in that, The method includes the following steps: A dual-medium mathematical model considering the groundwater response to solid tides in the pore-fracture system of a fractured aquifer is established. The dual-medium mathematical model is solved to obtain analytical solutions for the amplitude ratio and phase difference of the hydraulic head in the fractured aquifer under tidal stress. Obtain hydrological borehole water level data of the fractured aquifer to be estimated, and obtain the amplitude ratio and phase difference characteristic parameters of the water level response to the change in solid tidal stress; The analytical solution was fitted with the amplitude ratio and phase difference characteristic parameters of the solid tidal stress change in the water level response, and the coefficient of determination was selected. R 2 The parameter value corresponding to the largest fitted curve is used as the inversion result of the fractured aquifer parameters; The establishment of the dual-medium mathematical model considering the groundwater response to solid tides in the pore-fracture system of fractured aquifers is based on the following conditions: Confined aquifers are assumed to extend horizontally indefinitely with uniform thickness, and vertical overflow recharge is ignored; The pores and fractures in the aquifer are evenly distributed in space; Each fracture and matrix continuum is assumed to be homogeneous and isotropic; At any point, there exists a dual head of water in pores and fissures, and there is a water exchange between the two. The amount of exchange depends on the head difference between the media and obeys Darcy's law. The pumping well is located in a fractured medium, with water entering the well wall uniformly, and it is a complete well for pumping. The establishment of a dual-medium mathematical model considering the groundwater response to solid tides in the pore-fracture system of a fractured aquifer, and the solution of the dual-medium mathematical model to obtain the analytical solutions for the amplitude ratio and phase difference of the hydraulic head in the fractured aquifer under tidal stress include: The governing equations for water flow in the two-medium model can be described by the following equations: (1) In the formula, T The aquifer's hydraulic conductivity; h f , h m These are the water head in the fissures and the matrix, respectively. s f , s m These represent the water storage capacity in the fissures and the matrix, respectively. B Skempton coefficient of the aquifer; K u The non-drained bulk modulus of the aquifer; ρ The density of water; g It is the acceleration due to gravity; ε The elastic volumetric strain of the well is caused by Earth's tides; r is the radial distance from the wellbore. Fluid exchange between pores and fissures is represented by the following equation: (2) in, μ This refers to the water exchange parameters between pores and fissures. Set boundary conditions: (3) (4) (5) (6) (7) In the formula, r w , r c These are the outer diameter and inner diameter of the well shaft, respectively. The continuity equations for seepage at infinity for equations (1) and (2) are: (8) (9) Due to infinity , , yes Substituting the amplitude of the wave into the above equation, we get: (10) In the formula, The water level in the well is a periodic level with complex amplitude. ; Angular frequency, It is the tidal oscillation period, assuming: (11) (12) Substituting equation (11) into equation (1) yields: (13) (14) According to equation (8), we can obtain: (15) Substituting equation (12) into equation (2), we get: (16) According to equation (9), we can obtain: (17) make , Equations (15) and (17) are expressed as: (18) (19) but, (20) Substituting equation (20) into equation (18), we get: (21) The boundary conditions are now: (22) (23) (24) The general solution of equation (21) is: (25) In the formula, I 0、 K 0 represents the zeroth-order modified Bessel functions of the first and second kind, respectively; but, (26) when At that time, the zeroth-order modified Bessel function of the first kind I 0 grows exponentially, as can be seen from boundary condition (18). ,but: (27) According to equation (24), we know C K expression: (28) (29) Substitute equation (29) into equation (23): (30) in, (31) Define amplitude ratio: (32) The phase difference is: (33)。 2. The method for inverting groundwater solid tide response fractured aquifer parameters according to claim 1, characterized in that, The process involves obtaining hydrological borehole water level data for the fractured aquifer to be estimated, and then using the Baytap solid tidal analysis program to obtain the amplitude ratio and phase difference of the water head in the fractured aquifer under solid tidal stress.

3. A groundwater solid tide response fractured aquifer parameter inversion system, applied to the groundwater solid tide response fractured aquifer parameter inversion method as described in any one of claims 1-2, characterized in that, The system includes: a model building unit, a data acquisition and processing unit, and a fitting wiring unit; The model building unit is used to establish a dual-medium mathematical model considering the groundwater response to solid tides in the pore-fracture system of the fractured aquifer, solve the dual-medium mathematical model, and obtain analytical solutions for the amplitude ratio and phase difference of the hydraulic head in the fractured aquifer under tidal stress. The data acquisition and processing unit is used to acquire hydrological borehole water level data of the fractured aquifer to be estimated, and to obtain the amplitude ratio and phase difference characteristic parameters of the water level response to the change in solid tidal stress. The fitting and wiring unit is used to fit and wire the analytical solution with the amplitude ratio and phase difference characteristic parameters of the water level response solid tidal stress change, and select the coefficient of determination. R 2 The parameter values ​​corresponding to the largest fitted curve are used as the inversion results of the fractured aquifer parameters.

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