Forward modeling method for point source excitation wellhole sound field in double-pore medium

Abstract

The invention discloses a forward modeling method for a point source excitation well hole sound field in a dual-pore medium, which belongs to the technical field of geophysics, and comprises the following steps: carrying out Helmholtz decomposition on a displacement vector, and converting a dual-pore medium elastodynamic equation taking displacement as a basic quantity into two groups: a scalar potential function wave equation and a vector potential function wave equation. The vector potential function gives a non-divergence displacement component propagated at a shear wave velocity. Under the axial symmetry condition, a scalar potential function and a vector potential function related to a longitudinal field and a transverse field are solved through a variable separation method, and therefore expressions of basic field quantities such as solid phase displacement and seepage displacement and exported field quantities such as pore pressure and stress in the double-pore medium are obtained. The sound fields inside and outside the well are solved through continuous conditions of field quantities on an axial symmetry problem cylindrical surface with fluid on one side and the double-pore medium on the other side, the calculation efficiency is very high, a basis is provided for researching the characteristics of the well hole sound fields in the double-pore medium, and a positive operator is provided for well hole sound field inversion.

Description

Technical Field

[0001] This invention belongs to the field of geophysics, specifically relating to a forward modeling method for point source-excited borehole acoustic field in a dual-porosity medium. Background Technology

[0002] Sonic logging is a crucial topic in geophysical exploration, widely applied in reservoir property parameter estimation, lithological identification and stratigraphic division, reservoir calculation and monitoring, playing a vital role in mineral resource exploration and development. Furthermore, logging technology is not only a core tool in traditional reservoir evaluation but also indispensable in engineering safety monitoring and unconventional resource development, such as monitoring wellbore and wellbore stability, inspecting cementing quality, and evaluating the effectiveness of tight reservoirs. Currently, oil and gas exploration and development are increasingly focusing on unconventional oil and gas reservoirs, such as tight formations and oil-bearing shale formations. These complex lithological formations are characterized by low porosity and low permeability, but with well-developed fractures or fissures, and often contain strong structural heterogeneity within the rock. Therefore, adapting to the exploration needs of unconventional oil and gas reservoirs, studying the acoustic propagation mechanism and its characteristics in wellbores of complex-porosity and fractured formations is of great significance.

[0003] Traditional elastic wave theory is based on the premise that the medium is a single-phase elastic solid. However, in natural seismology and exploration seismology, the object of study is seismic waves propagating in underground rocks. Underground rocks are mostly porous media, containing fluids within their pores. These fluids are mobile relative to the solid framework and are not considered single-phase elastic solids, but rather multiphase media. The presence of pore fluids affects the velocity and attenuation of seismic waves. Therefore, it is necessary to consider the existence of rock pores.

[0004] The single-pore medium theory, by neglecting the mesoscale inhomogeneity of rocks, often predicts lower P-wave attenuation than actual observations. In contrast, the dual-pore medium theory, by considering the energy attenuation caused by mesoscale local flows between high-pressure and low-pressure zones in the rock due to mesoscale inhomogeneity during seismic wave propagation, predicts P-wave attenuation more closely to observational results.

[0005] Currently, most studies on borehole acoustic fields are based on the theory of single-pore media, neglecting the potential discrepancies between calculated results and observational data caused by the inhomogeneity of formation pore structure. Therefore, inventing a forward modeling method for point-source-excited borehole acoustic fields in dual-pore media can help study the impact of external pore formation inhomogeneity on the borehole acoustic field. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the present invention aims to provide a forward modeling method for point-source-excited wellbore acoustic fields in dual-porous media, in order to simulate wellbore acoustic fields in dual-porous media formations.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] A forward modeling method for point-source-excited wellbore acoustic fields in a dual-porosity medium, the specific process of which includes:

[0009] S1. The time-domain seismic wave propagation equation in a doubly porous medium is transformed to the frequency domain by Fourier transform, and dynamic permeability is introduced.

[0010] S2. By performing Helmholtz decomposition on the displacement vector, the elastic dynamics equations of a doubly porous medium, with displacement as the fundamental quantity, can be reduced to two sets: wave equations with scalar potential functions and wave equations with vector potential functions. In the frequency domain, these two equations are the Helmholtz equations with scalar potential functions and the Helmholtz equations with vector potential functions. The scalar potential function gives the irrotational displacement component propagating at the longitudinal wave velocity, reflecting the magnitude of the volumetric strain; the vector potential function gives the divergence-free displacement component propagating at the transverse wave velocity, reflecting the magnitude of the shear strain.

[0011] S3. Under axisymmetric conditions, the scalar potential function and vector potential function related to the longitudinal field and transverse field are solved by the method of separation of variables, thereby obtaining the expressions of the basic field quantities such as solid phase displacement and seepage displacement, as well as the derived field quantities such as pore pressure and stress in the dual-porosity medium.

[0012] S4. Solve for the acoustic field inside and outside the well by taking advantage of the continuity condition of the field quantity on the cylindrical surface of an axisymmetric problem with fluid on one side and a doubly porous medium on the other side.

[0013] Furthermore, the step of using Fourier transform to convert the time-domain dual-porosity medium control equations to the frequency domain includes:

[0014] Introducing Fourier transform pairs, , The time-domain governing equations are transformed to the frequency domain using a forward transform.

[0015] Representing time-domain variables such as solid displacement , , ; This represents the corresponding frequency domain variable.

[0016] Furthermore, the introduction of dynamic penetration rate includes:

[0017] Dynamic permeability is introduced into the background medium and the embedded medium, respectively:

[0018]

[0019]

[0020] In the above formula and These represent the dynamic permeability in the background medium and the embedded medium, respectively. and These represent the static permeability in the background medium and the embedded medium, respectively. For pore fluid density, The viscosity coefficient of the pore fluid. and These represent the local porosity of the background medium and the embedded material, respectively. This is called the mass coupling coefficient. and It is a characteristic dimension of pores that reflects the (weighted) volumetric surface area ratio and has the dimension of length:

[0021]

[0022] .

[0023] Furthermore, the displacement vector is decomposed using Helmholtz decomposition:

[0024]

[0025] The elastic dynamics equations of a doubly porous medium with displacement as the fundamental quantity are transformed into scalar potential function wave equations:

[0026]

[0027]

[0028]

[0029] Sum of vector potential function wave equations:

[0030]

[0031]

[0032] .

[0033] Furthermore, in the axisymmetric case, the scalar potential function and vector potential function related to the longitudinal and transverse fields are solved separately using the method of separation of variables, thereby obtaining the expressions for the basic field quantities such as solid phase displacement and seepage displacement, as well as the derived field quantities such as pore pressure and stress in the dual-porosity medium:

[0034] The expression for the scalar potential function is:

[0035] ,

[0036] The expression for well pressure is:

[0037] ,

[0038] The radial and axial displacements of the fluid inside the well are as follows:

[0039] ,

[0040] ,

[0041] The solid phase and seepage displacement in porous formations are expressed as follows:

[0042] ,

[0043] ,

[0044] ,

[0045] ,

[0046] ,

[0047] ,

[0048] The expressions for normal stress, shear stress, and pore pressure in the background medium and the embedded body are as follows:

[0049] ,

[0050] ,

[0051] ,

[0052] .

[0053] Furthermore, consider a fully permeable boundary condition on an axisymmetric cylindrical surface where one side is fluid and the other side is a doubly porous medium:

[0054] ,

[0055] ,

[0056] ,

[0057] ,

[0058] ,

[0059] Solve for the linear matrix:

[0060] .

[0061] in A m A pf A ps1 A ps2 A s These represent the amplitude coefficients of the acoustic field inside the well, the fast P-wave, the first type of slow P-wave, the second type of slow P-wave, and the shear wave, respectively. The expressions for all field quantities inside and outside the well are then determined using these amplitude coefficients.

[0062] The beneficial effects of this invention are:

[0063] 1. The point source-excited wellbore acoustic field forward modeling method proposed in this invention is based on the consideration of the sensitivity of wellbore Stoneley waves to formation permeability. It introduces dynamic permeability on the basis of Biot-Rayleigh theory and considers the influence of dynamic permeability in both the background medium and the embedded body. It can simulate the full waveform response of acoustic logging in dual-porosity formations and study the influence of formation pore structure inhomogeneity on wellbore acoustic field.

[0064] 2. The forward modeling method for point source-excited wellbore acoustic field in dual-porous media proposed in this invention obtains the wellbore acoustic field in dual-porous media through analytical algorithms, which has high computational efficiency and provides forward modeling operators for seismic wave inversion. Attached Figure Description

[0065] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0066] Figure 1 This is a flowchart of the forward modeling method according to an embodiment of the present invention;

[0067] Figure 2 This is a schematic diagram of a wellbore model according to an embodiment of the present invention;

[0068] Figure 3 This is a comparison diagram of the calculated wellbore acoustic field results between the single-pore model and the dual-pore medium model according to an embodiment of the present invention;

[0069] Figure 4 This is a comparison diagram of the acoustic field of a wellbore in a single-hole medium and a double-hole medium according to an embodiment of the present invention. Detailed Implementation

[0070] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] This application is preferably applicable to underground exploration using borehole acoustic fields, and is characterized by its ability to efficiently realize numerical simulation of borehole acoustic fields in dual-porosity media.

[0072] like Figure 1 As shown, the specific process of the forward modeling method for point source-excited wellbore acoustic field in a dual-porosity medium includes:

[0073] S1. The time-domain seismic wave propagation equation in a doubly porous medium is transformed to the frequency domain by Fourier transform, and dynamic permeability is introduced.

[0074] S2. By performing Helmholtz decomposition on the displacement vector, the elastic dynamics equations of a doubly porous medium, with displacement as the fundamental quantity, can be reduced to two sets: wave equations with scalar potential functions and wave equations with vector potential functions. In the frequency domain, these two equations are the Helmholtz equations with scalar potential functions and the Helmholtz equations with vector potential functions. The scalar potential function gives the irrotational displacement component propagating at the longitudinal wave velocity, reflecting the magnitude of the volumetric strain; the vector potential function gives the divergence-free displacement component propagating at the transverse wave velocity, reflecting the magnitude of the shear strain.

[0075] S3. Under axisymmetric conditions, the scalar potential function and vector potential function related to the longitudinal field and transverse field are solved by the method of separation of variables, thereby obtaining the expressions of the basic field quantities such as solid phase displacement and seepage displacement, as well as the derived field quantities such as pore pressure and stress in the dual-porosity medium.

[0076] S4. Solve for the acoustic field inside and outside the well by taking advantage of the continuity condition of the field quantity on the cylindrical surface of an axisymmetric problem with fluid on one side and a doubly porous medium on the other side.

[0077] Specifically, the Biot-Rayleigh theoretical governing equations incorporating dynamic permeability can be expressed as:

[0078] ;

[0079] ;

[0080] ;

[0081] in For solid-state displacement, For the background medium seepage displacement, For the seepage displacement of the embedded body, For Biot-Rayleigh variables. For the overall density, For fluid density, The shear modulus of the solid skeleton. Angular frequency, For Hamiltonian operators, For the Laplace operator, For solid-state strain, , , , Let be the bulk modulus of the solid particles. The bulk modulus of the pore fluid. , , , Porosity , , For the local porosity of the background medium, For the local porosity of the embedding, , The bulk modulus of the overall skeleton. , For total porosity, , , Let be the bulk modulus of the solid particles. The background coherent skeleton bulk modulus, , The consolidation coefficient of the background phase skeleton. The bulk modulus of the inlay skeleton. , The consolidation coefficient of the inlay skeleton. The volume strain of the fluid in the pores of the background medium. , The volumetric strain of the fluid embedded in the pores of the body. , , , Background phase permeability, For the permeability of the embedded phase, is the viscosity coefficient of the porous fluid; Represents the imaginary unit. The constant of the wet skeleton. , The shear modulus of the solid skeleton. , Shear modulus of solid particles is the shear consolidation coefficient of the skeleton.

[0082] And the governing equations of local fluid dynamics:

[0083] ,in The radius of the inlay is given.

[0084] Introducing dynamic permeability into the background medium Introducing dynamic permeability into the embedding :

[0085] ,

[0086] ,

[0087] b1 and b2 are represented as follows:

[0088] ,

[0089] .

[0090] Here, The mass coupling coefficient is actually the apparent mass coefficient of an ideal fluid accelerating relative to a solid skeleton, also known as curvature. In the calculations of this paper, we take... . and These are the pore characteristic dimensions that reflect the weighted volumetric surface ratio of the pores in the background medium and the embedded body, respectively, and have the dimension of length. and It can be represented as:

[0091] ,

[0092] .

[0093] in, and These represent the Darcy permeability in the background medium and the embedded medium, respectively.

[0094] The expressions for stress and pressure are:

[0095] ,

[0096] ,

[0097] ,

[0098] .

[0099] in, The background medium pore pressure, The pore pressure of the embedded body. It is radial normal stress. For shear stress, For the radial displacement of the solid phase, This represents the axial displacement of the solid phase.

[0100] Consider as Figure 2 As shown, an axisymmetric model consists of the fluid inside the well and an infinitely extending outer layer of doubly porous media. Helmholtz decomposition of the displacement vector transforms the elastic dynamics equations with displacement as the fundamental quantity into two sets: scalar potential function wave equations and vector potential function wave equations. In the frequency domain, these two sets of equations are respectively the Helmholtz equations for scalar potential functions and the Helmholtz equations for vector potential functions. The scalar potential function gives the irrotational displacement component propagating at the P-wave velocity; the vector potential function gives the divergence-free displacement component propagating at the S-wave velocity, reflecting the magnitude of shear strain. The mathematical expression of the wave equations for the potential function is easy to solve. In the study of the elastic wave field of doubly porous media, the solid phase displacement field and the seepage displacement field in the background medium and embedded body can be represented by the solutions of the wave equations for the potential function through Helmholtz decomposition. First, the fundamental vector... , and Decompose:

[0101]

[0102] in, , and It is a scalar potential function related to the longitudinal field. , and It is a vector potential function related to the transverse field, resulting in the following governing equations:

[0103]

[0104]

[0105]

[0106] Here, - The expression is:

[0107] ,

[0108] ,

[0109] ,

[0110] ,

[0111] ,

[0112] ,

[0113] ,

[0114] ,

[0115] ,

[0116] in, .

[0117] In the three-dimensional case, only two of the three components of the vector potential function are independent. Assume:

[0118]

[0119] Performing divergence and curl operations on the governing equations yields a set of equations related to the longitudinal field:

[0120] ,

[0121] ,

[0122] .

[0123] And a set of equations related to the transverse field:

[0124] ,

[0125] ,

[0126] .

[0127] First, let's study the longitudinal field. Assume... Satisfying the Helmholtz equation with wavenumber l:

[0128] .

[0129] scalar potential function , and Available Represented as:

[0130] .

[0131] Where the superscript "l" represents the coefficient related to the longitudinal field, substituting the above equation into the equation related to the longitudinal field, we obtain the following Christofel equation:

[0132] .

[0133] The condition for this equation to have a nontrivial coupled field solution is that the determinant of the matrix on the left-hand side is equal to zero. This characteristic equation has three roots, namely... , and , which represent the wave numbers of fast longitudinal waves and the two types of slow longitudinal waves, respectively.

[0134] use , and They represent wave numbers respectively. , and The solution to the time-scalar Helmholtz equation, and thus the scalar potential function can be expressed as , and Linear combination:

[0135]

[0136] Here, This represents the ratio of the fast longitudinal wave component of the background medium seepage displacement to the fast longitudinal wave component of the solid phase displacement in the Biot-Rayleigh theory. It is equal to the ratio of the P2 wave component of the background medium seepage displacement to the P2 wave component of the solid phase displacement. This represents the ratio of the P3 wave component of the background medium seepage displacement to the P3 wave component of the solid phase displacement. Correspondingly, This represents the ratio of the fast longitudinal wave component of the seepage displacement in the embedded body to the fast longitudinal wave component of the solid phase displacement. It is equal to the ratio of the P2 wave component of the seepage displacement of the embedded body to the P2 wave component of the solid phase displacement. It is the ratio of the P3 wave component of the seepage displacement in the embedded body to the P3 wave component of the solid phase displacement.

[0137] For the transverse field, assume a vector Satisfying the vector Helmholtz equation for wavenumber m:

[0138]

[0139] Vector potential function , and Available Represented as:

[0140] .

[0141] The superscript "h" indicates the coefficient related to the transverse field. Substituting the above equation into the equation related to the transverse field, we obtain the following Christofel equation:

[0142] .

[0143] The condition for this equation to have a nontrivial coupled field solution is that the determinant of the matrix on the left side is equal to zero, and the root of this characteristic equation is the transverse wave number. .

[0144] use Indicates wave number When, the solution to the vector Helmholtz equation, and thus the vector potential function. , and It can be represented as:

[0145] .

[0146] Here, This represents the ratio of the shear wave component of the background medium seepage displacement to the shear wave component of the solid phase displacement. This represents the ratio of the shear wave component of the seepage displacement in the embedded body to the shear wave component of the solid phase displacement.

[0147] In cylindrical coordinate system (r, , In the case of axisymmetric conditions, the fundamental field quantities can be solved using the method of separation of variables. , , Frequency-wavenumber domain expression:

[0148] ,

[0149] ,

[0150] ,

[0151] ,

[0152] ,

[0153] ,

[0154] Where k is the axial wave number. Indicates radial wavenumber, , . and Let represent the nth-order modified Bessel function, respectively. The frequency-wavenumber domain expressions for stress and pressure can be further derived:

[0155]

[0156] ,

[0157] ,

[0158] .

[0159] Displacement and sound pressure in an ideal fluid can be expressed by the potential function. Represented as:

[0160] ,

[0161] .

[0162] in, Let be the fluid density in the well. A point sound pressure source model is used in the calculation, considering the radiation field of a point sound source located on the well axis. The particular solution is:

[0163] .

[0164] Here, , This is the wavenumber of the sound waves in the fluid. Therefore, the total sound field inside the well is derived:

[0165] ,

[0166] ,

[0167] .

[0168] At this point, there are a total of 5 unknown coefficients in the sound field expressions inside and outside the well, namely... , , , and These unknown coefficients need to be determined through five boundary conditions. Once these five unknown coefficients are obtained, the sound field inside and outside the well can be completely determined.

[0169] Assuming a wellbore with fluid on one side and a dual-porosity medium on the other. For a substance to be completely permeable, the following boundary conditions must be met:

[0170] ,

[0171] ,

[0172] ,

[0173] ,

[0174] .

[0175] These represent the continuity of fluid flow, the continuity of fluid pressure, the continuity of normal stress, and the continuity of axial shear stress, respectively.

[0176] Substituting the field quantity expression into the above boundary conditions, the resulting system of linear equations can be expressed in matrix form as follows:

[0177] .

[0178] in,

[0179] ,

[0180] .

[0181] It is a matrix with 5 rows and 5 columns. Solving the equation determines the amplitude coefficient vector A. At this point, the sound field inside and outside the well can be determined based on the amplitude coefficient A. m A pf A ps1 A ps2 and A s It's completely confirmed.

[0182] The time-domain expressions for each field quantity can be obtained through Fourier transform, taking the sound pressure inside the well as an example:

[0183] .

[0184] Here, Represents fluid pressure in the time domain. Let be the spectrum of the sound source as a time function. The center frequency of the sound source is . The pulse length is cosine envelope pulse Used as a sound source time function:

[0185] .

[0186] To verify the correctness of the method in this invention, the dual-porosity medium was degenerated into a single-porosity medium and compared with existing calculation methods. The model parameters are as follows: , , , , , , , , , , , , , , , At this point, the volume ratio of the embedded material is 0, and the dual-pore medium is degenerated into a single-pore medium.

[0187] Take the center frequency of the sound source time function as The pulse duration is The well radius is a = 0.1 m, and the fluid density inside the well is... Five receivers were installed at equal intervals on the shaft, with the source distance increasing from 3 meters to 5 meters. Figure 3 The red dotted line shows the sound pressure level calculated using the method proposed in this chapter. The P-wave arrives first, followed by the S-wave, pseudo-Rayleigh wave group (pR), and Stoneley wave (ST). The theoretical arrival times for the P-wave and S-wave at a receiver 3 m from the source are 0.95 ms and 1.4 ms, respectively. Figure 3 The results shown are consistent. The waveform calculated using the single-pore medium theory is as follows: Figure 3 As shown by the solid black line, the calculation results of the two methods are in excellent agreement, verifying the effectiveness of the method described in this invention.

[0188] To further verify the effectiveness of the method described in this invention, the acoustic field of the wellbore in the dual-well model and the single-well model are compared. The model parameters are as follows: , , , , , , , , , , , , , , , The center frequency of the sound source's time function is... The pulse duration is The calculated sound pressure Each as Figure 4 As shown by the solid red and blue lines. For easier observation, [the text is incomplete]. Figure 4 The P-wave signal was amplified and displayed. We found that the difference between the S-wave and pseudo-Rayleigh wave in the two models was not significant. The P-wave amplitude in the dual-porosity medium model was lower than that in the single-porosity medium model, while the amplitude of the wellbore Stoneley wave in the dual-porosity medium formation was higher than that in the single-porosity medium formation. This indicates that the heterogeneity of the pore structure in the formation has a non-negligible influence on the wellbore acoustic field. Ignoring the heterogeneity of the pore structure in well logging problems and treating the formation pore parameters as uniform will affect the results. This result is consistent with physical laws, proving the correctness of the method described in this invention.

[0189] This application utilizes the theory of dual-porosity media to calculate the borehole acoustic field excited by a point source, achieving high computational efficiency. The propagation of the borehole acoustic field in dual-porosity media formations differs significantly from that in single-porosity media formations; the heterogeneity of the formation pore structure has a substantial impact on the borehole acoustic field. This provides a foundation for studying the influencing factors of the borehole acoustic field in complex porous formations and offers a forward modeling operator for seismic wave inversion.

[0190] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0191] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A forward method for calculating acoustic field of a point source in a dual-porosity medium, characterized in that, The method comprises the following steps: S1, converting the seismic wave propagation equation in the time domain double-porosity medium into the frequency domain by Fourier transform and introducing dynamic permeability; S2, performing Helmholtz decomposition on the displacement vector, and converting the double-porosity medium elastic dynamics equation taking displacement as a basic quantity into two groups: a scalar potential function wave equation and a vector potential function wave equation; In the frequency domain, the two equations are a Helmholtz equation about the scalar potential function and a Helmholtz equation about the vector potential function; the scalar potential function gives a non-rotational displacement component propagating at a longitudinal wave velocity; and the vector potential function gives a non-divergent displacement component propagating at a transverse wave velocity; S3, in the case of axial symmetry, the scalar potential function and the vector potential function related to the longitudinal field and the transverse field are solved by the separation of variables method, so as to obtain expressions of the solid displacement, the seepage displacement basic field quantity, and the pore pressure and stress derived field quantity in the double-porosity medium; S4, solving the acoustic field inside and outside the well by the continuous condition of the field quantity on the axisymmetric problem cylinder with one side being fluid and the other side being double-porosity medium.

2. The forward method of exciting acoustic field in a wellbore by a point source in a dual-porosity medium according to claim 1, characterized in that, The Fourier transform is used to convert the double-porosity medium control equation group in the time domain into the frequency domain, and specifically includes: introducing a Fourier transform pair, , , converting the time-domain control equations to the frequency domain by a forward transform, denotes a time-domain variable, including solid phase shift 、 、 ; denotes the corresponding frequency-domain variable; Dynamic permeability is introduced in the background medium and the inclusions: ； ； where and denote the dynamic permeability in the background medium and the inlaid body, respectively, and denote the static permeability in the background medium and the inlaid body, respectively, is the pore fluid density, is the pore fluid viscosity coefficient, and denote the local porosity of the background medium and the inlaid body, respectively, is called the mass coupling coefficient, and is the pore characteristic size reflecting the pore channel surface ratio.

3. The forward method of claim 1, wherein, Helmholtz decomposition is performed on the displacement vector, including: The double-porosity medium elastic dynamics equation taking displacement as a basic quantity is converted into: A scalar potential function wave equation: ； ； ； A vector potential function wave equation: ； ； 。 4. The forward method of claim 1, wherein, The expression of the scalar potential function is: ； The expression of the wellbore pressure is: ； The wellbore fluid radial displacement and axial displacement are respectively: ； ； The solid phase and seepage displacement in the porous formation are respectively represented as: ； ； ； ； ； ； The expressions of the normal stress, shear stress, and pore pressure in the background medium and the inclusions are respectively: ； ； ； 。 5. The forward method of exciting acoustic field in a wellbore by a point source in a dual-porosity medium according to claim 1, characterized in that, The fully permeable boundary condition on the axisymmetric cylinder with one side being fluid and the other side being double-porosity medium includes: ； ； ； ； ； Solving a linear matrix: ； wherein , A m , A pf , A ps1 , A ps2 , A s respectively represent the amplitude coefficients of the borehole acoustic field, the fast P-wave, the first type of slow P-wave, the second type of slow P-wave and the S-wave in the porous formation. Once the amplitude coefficients are determined, the expressions of all field quantities in the borehole and outside can be solved.

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