Method for determining p-wave velocity of fluid replacement in anisotropic media and related apparatus

Abstract

The application provides a method for determining the longitudinal wave velocity after fluid replacement in an anisotropic medium and a related device. The method comprises determining an average bulk modulus based on a matrix bulk modulus; determining a first bulk modulus when the medium contains fluid based on first property data; determining a second bulk modulus when the medium does not contain fluid based on the first property data, the matrix bulk modulus, the average bulk modulus and the first bulk modulus; determining a second vertical stiffness coefficient when the medium does not contain fluid based on the first property data, the average bulk modulus, the first bulk modulus and the second bulk modulus; obtaining second property data of each predetermined replacement fluid; and determining the longitudinal wave velocity after the fluid in the medium is replaced by the predetermined replacement fluid based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient and the second property data. The technical problem that the longitudinal wave velocity determined after fluid replacement in an anisotropic medium is not accurate in the prior art is solved.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a method and related equipment for determining the longitudinal wave velocity of fluid replacement in anisotropic media. Background Technology

[0002] Fluid substitution plays a crucial role in rock physics analysis, reservoir characteristic analysis, and time-lapse seismic monitoring, and is widely used in geophysical exploration. Current technologies typically determine the P-wave velocity after fluid substitution based on classical fluid substitution theory. This classical fluid substitution theory, proposed by Gassmann (1951), establishes the relationship between the porous medium skeleton, pore fluid, and overall elastic modulus based on the isotropic assumption, serving as a fundamental tool for reservoir fluid identification and velocity prediction. However, this theory has significant limitations when applied to actual VTI (Vertical Transversely Isotropy) media: the classical fluid substitution theory, based on the isotropic assumption, is inconsistent with the characteristic of VTI media, which is only transversely isotropic and anisotropic in other directions, and cannot accurately describe the impact of fluid substitution on the vertical elastic response of VTI media. Consequently, the P-wave velocity fails to reflect the propagation characteristics of seismic waves in real strata. VTI media is a classic type of anisotropic medium. Furthermore, existing techniques typically assume that the average bulk modulus is equal to the matrix bulk modulus, neglecting the influence of formation stress state on the overall compressibility of the medium, thus introducing systematic errors when calculating the P-wave velocity after fluid replacement. All of these factors contribute to the inaccuracy in determining the P-wave velocity after fluid replacement in the medium. Summary of the Invention

[0003] In view of this, the purpose of this application is to propose a method and related equipment for determining the longitudinal wave velocity of fluid replacement in anisotropic media, so as to overcome all or part of the deficiencies in the prior art.

[0004] To achieve the above objectives, this application provides a method for determining the longitudinal wave velocity in an anisotropic medium by fluid replacement, comprising: acquiring first property data and matrix bulk modulus of the medium, wherein the medium contains a fluid; determining an average bulk modulus based on the matrix bulk modulus; determining a first bulk modulus in the medium containing the fluid based on the first property data; and determining a second bulk modulus in the medium without the fluid based on the first property data, the matrix bulk modulus, the average bulk modulus, and the first bulk modulus; determining a second vertical stiffness coefficient in the medium without the fluid based on the first property data, the average bulk modulus, the first bulk modulus, and the second bulk modulus; acquiring second property data for each predetermined replacement fluid; and for each predetermined replacement fluid, determining the longitudinal wave velocity after the fluid in the medium is replaced by the predetermined replacement fluid based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, and the second property data.

[0005] Optionally, determining the average bulk modulus based on the matrix bulk modulus includes: determining the average bulk modulus based on a pre-constructed curve showing the relationship between the ratio of the average bulk modulus to the matrix bulk modulus as a function of effective pressure and the matrix bulk modulus.

[0006] Optionally, determining the second bulk modulus of the medium when it does not contain the fluid, based on the first property data, the matrix bulk modulus, the average bulk modulus, and the first bulk modulus, includes: determining the second bulk modulus using the following formula: ,in, The second bulk modulus, The first bulk modulus, The porosity of the medium. For fluid bulk modulus, The bulk modulus of the matrix is... The average bulk modulus is given.

[0007] Optionally, determining the second vertical stiffness coefficient when the medium does not contain the fluid based on the first property data, the average bulk modulus, the first bulk modulus, and the second bulk modulus includes: determining the first vertical stiffness coefficient when the medium contains the fluid based on the first property data; and determining the second vertical stiffness coefficient based on the first property data, the average bulk modulus, the first bulk modulus, the second bulk modulus, and the first vertical stiffness coefficient.

[0008] Optionally, determining the second vertical stiffness coefficient based on the first property data, the average bulk modulus, the first bulk modulus, the second bulk modulus, and the first vertical stiffness coefficient includes: determining the second vertical stiffness coefficient using the following formula: ,in, This is the second vertical stiffness coefficient. This is the first vertical stiffness coefficient. The first bulk modulus, The second bulk modulus, A parameter describing the degree to which the phase velocity of a longitudinal wave propagating near the axis of symmetry changes with the phase angle. The average bulk modulus is given.

[0009] Optionally, determining the longitudinal wave velocity after replacing the fluid in the medium with the predetermined replacement fluid based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, and the second property data includes: determining a third bulk modulus in the medium containing the predetermined replacement fluid based on the first property data, the average bulk modulus, the second bulk modulus, and the second property data; determining a third vertical stiffness coefficient in the medium containing the predetermined replacement fluid based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, the second property data, and the third bulk modulus; and determining the longitudinal wave velocity based on the second property data and the third vertical stiffness coefficient.

[0010] Optionally, determining the third vertical stiffness coefficient when the medium contains the predetermined replacement fluid, based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, the second property data, and the third bulk modulus, includes: determining the third vertical stiffness coefficient using the following formula: ,in, The third vertical stiffness coefficient, This is the second vertical stiffness coefficient. The third bulk modulus, The second bulk modulus, A parameter describing the degree to which the phase velocity of a longitudinal wave propagating near the axis of symmetry changes with the phase angle. The average bulk modulus is given.

[0011] Based on the same inventive concept, this application also provides a device for determining the longitudinal wave velocity of fluid replacement in an anisotropic medium, comprising: an acquisition module configured to acquire first property data and matrix bulk modulus of the medium, wherein the medium contains a fluid; a first determination module configured to determine an average bulk modulus based on the matrix bulk modulus; a second determination module configured to determine a first bulk modulus when the medium contains the fluid based on the first property data, and to determine a second bulk modulus when the medium does not contain the fluid based on the first property data, the matrix bulk modulus, the average bulk modulus, and the first bulk modulus; a third determination module configured to determine a second vertical stiffness coefficient when the medium does not contain the fluid based on the first property data, the average bulk modulus, the first bulk modulus, and the second bulk modulus; and a fourth determination module configured to acquire second property data for each predetermined replacement fluid, and for each predetermined replacement fluid, to determine the longitudinal wave velocity after the fluid in the medium is replaced by the predetermined replacement fluid based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, and the second property data.

[0012] Based on the same inventive concept, this application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable by the processor, wherein the processor implements the method described above when executing the computer program.

[0013] Based on the same inventive concept, this application also provides a non-transitory computer-readable storage medium that stores computer instructions for causing a computer to perform the method described above.

[0014] As can be seen from the above, the method and related equipment for determining the longitudinal wave velocity of fluid replacement in anisotropic media provided in this application include acquiring first property data and matrix bulk modulus of the medium, wherein the medium contains fluid. Based on the matrix bulk modulus, the average bulk modulus is determined, ensuring the reliability of the calculation basis by using stable physical property parameters as the calculation basis. Based on the first property data, the first bulk modulus when the medium contains the fluid is determined. The first bulk modulus is calculated directly based on the first property data, with clear physical meaning and stable and reliable calculation, accurately determining the true bulk modulus of the medium containing fluid. Furthermore, based on the first property data, the matrix bulk modulus, the average bulk modulus, and the first bulk modulus, a second bulk modulus when the medium does not contain the fluid is determined. By introducing the true difference between the matrix bulk modulus and the average bulk modulus, and combining it with the first bulk modulus under saturated fluid conditions, the influence of fluid can be eliminated, obtaining the second bulk modulus of a pure solid skeleton, thereby avoiding errors caused by neglecting pressure effects and modulus differences in traditional methods. Based on the first property data, the average bulk modulus, the first bulk modulus, and the second bulk modulus, a second vertical stiffness coefficient is determined when the medium does not contain the fluid. By determining the second vertical stiffness coefficient, the systematic error caused by neglecting this difference in the fluid replacement method based on Gassmann theory is theoretically corrected. By fully considering the difference between the average bulk modulus and the matrix bulk modulus, the elastic response of the VTI medium in the direction of the vertical axis of symmetry can be accurately characterized, providing the necessary core parameters for the dry medium for fluid replacement. The second property data of each predetermined replacement fluid is obtained. For each predetermined replacement fluid, based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, and the second property data, the P-wave velocity after the fluid in the medium is replaced with the predetermined replacement fluid is determined. This application uses a stiffness domain calculation method throughout, maintaining the characteristics of simplicity, intuitiveness, and strong engineering feasibility. It continuously considers the difference between the average bulk modulus and the matrix bulk modulus, further consolidating the correction effect on the errors of the classical fluid replacement theory and effectively improving the accuracy of the P-wave velocity after the fluid in the medium is replaced with the predetermined replacement fluid. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in this application or related technologies, the drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are only embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a flowchart illustrating the method for determining the longitudinal wave velocity by fluid replacement in an anisotropic medium according to an embodiment of this application.

[0017] Figure 2 This is a schematic diagram illustrating the fitting relationship between the average bulk modulus and the ratio of the matrix bulk modulus to the effective stress in an embodiment of this application. Figure 3 This is a schematic diagram of the VTI media fluid replacement process according to an embodiment of this application; Figure 4 A schematic diagram showing the result of Backus equivalent averaging of the logging response data in this application embodiment; Figure 5 This is a schematic diagram illustrating the predicted formation pore pressure and effective stress according to an embodiment of this application. Figure 6 This is a schematic diagram illustrating the agreement between the cross-layer predicted vertical P-wave velocity and the actual well logging interpretation results in an embodiment of this application. Figure 7 This is a schematic diagram of the structure of the longitudinal wave velocity determination device for fluid replacement in anisotropic media according to an embodiment of this application. Figure 8 This is a schematic diagram of the hardware structure of an electronic device according to an embodiment of this application. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with specific embodiments and the accompanying drawings.

[0019] It should be noted that, unless otherwise defined, the technical or scientific terms used in the embodiments of this application should have the ordinary meaning understood by one of ordinary skill in the art to which this application pertains. The terms "first," "second," and similar terms used in the embodiments of this application do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are only used to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0020] As described in the background section, fluid substitution plays a crucial role in rock physics analysis, reservoir characteristic analysis, and time-lapse seismic monitoring, and is widely used in geophysical exploration. By using fluid substitution to determine the P-wave velocity parameters of reservoirs saturated with different fluids, the changes in rock elasticity and seismic response caused by differences in fluids such as oil and gas and formation water can be clarified. This clarifies the constraints on seismic inversion, AVO (amplitude versus offset) analysis, and forward modeling, enabling the identification of underground reservoir fluid types, characterization of oil and gas distribution, and dynamic seismic monitoring of reservoirs. In existing technologies, the P-wave velocity after fluid substitution is typically determined based on classical fluid substitution theory (i.e., Gassmann theory). This classical fluid substitution theory, proposed by Gassmann, establishes the relationship between the porous medium skeleton, pore fluid, and overall elastic modulus based on the isotropic assumption, serving as a fundamental tool for reservoir fluid identification and velocity prediction. Isotropicity means that the physical properties, elastic parameters, and mechanical responses of the porous medium are identical in all directions, independent of the measurement direction. However, this theory has significant drawbacks when applied to actual VTI media: the classical fluid substitution theory, based on the assumption of isotropic media, is inconsistent with the characteristic of VTI media in actual formations—transverse isotropy and anisotropy in other directions. It cannot accurately describe the impact of fluid substitution on the vertical elastic response of VTI media, and the determined P-wave velocity is inaccurate, making it difficult to reflect the propagation characteristics of seismic waves in real formations. VTI media is a classical type of anisotropic media.

[0021] Furthermore, the classical fluid substitution theory, based on the assumption of a single-mineral medium framework, uses only the bulk modulus of a single solid particle to describe the characteristics of the medium framework, making it unsuitable for actual formations containing mixtures of multiple minerals such as quartz, feldspar, and clay. Brown and Korringa (1975) extended the classical fluid substitution theory, proposing the Brown theory... Korringa's theory establishes fluid substitution equations applicable to multi-mineral mixed media frameworks. Its core feature lies in its generalization of classical fluid substitution theory in the compliance domain. However, the average bulk modulus of minerals introduced in its equations is difficult to obtain directly from measured data, limiting its practical application. When the media framework consists of a single mineral, the average bulk modulus of the mineral is equal to the bulk modulus of the matrix. In this case, Brown... Korringa's theory can be reduced to a simple and easy-to-apply classical fluid substitution theory.

[0022] Furthermore, Hart and Wang (2010) confirmed through undrained, drained, and unjacketed tests that there is a significant difference between the average bulk modulus and the matrix bulk modulus of Berea sandstone, with the difference reaching up to 40%. Thomsen (2023) pointed out that Gassmann's fluid substitution theory contains logical errors in its derivation, directly applying relationships established under open hydraulic systems to closed systems, which introduces theoretical errors when used for fluid substitution. Existing technologies, regardless of whether they use classical fluid substitution theory or its simplified form, cannot fully explain the differences between the mean and matrix bulk modulus of Berea sandstone. Korringa's theory ignores the influence of formation stress state on the overall equivalent compressibility of the medium, and directly equates the overall equivalent bulk modulus of the medium to the bulk modulus of the matrix. This introduces systematic errors when calculating the P-wave velocity after fluid replacement, ultimately leading to inaccurate determination of the P-wave velocity after fluid replacement.

[0023] In view of this, embodiments of this application propose a method for determining the longitudinal wave velocity of fluid displacement in anisotropic media, referring to... Figure 1 This includes the following steps: Step 101: Obtain first property data of the medium and matrix bulk modulus, wherein the medium contains a fluid.

[0024] In this step, simulating the seismic response characteristics after fluid state changes through fluid replacement is a core component of reservoir rock physics analysis and prediction. Therefore, accurately calculating the P-wave velocity after target fluid replacement based on the known initial fluid state is of great significance for reservoir fluid identification. This application first obtains the initial property data of the medium, wherein the medium is a porous medium with a porous structure, the solid skeleton is composed of a mixture of various minerals, and its pores are filled with a fluid of known type and properties. This fluid has definite fluid properties, such as known bulk modulus, density, and specific fluid saturation.

[0025] For example, consider VTI media, such as silty mudstone commonly found in sedimentary basins. The solid framework is composed of a mixture of minerals including quartz, feldspar, and clay minerals. Pores develop between the grains, and these pores are filled with one or more fluids, such as oil, gas, or water, the specific type and properties of which are known. VTI media are widely present and representative anisotropic media in sedimentary strata, typically formed from layered sedimentary rocks. This medium possesses a vertical axis of symmetry. In all horizontal directions perpendicular to this axis, physical properties such as elastic parameters and seismic wave propagation velocities remain consistent, exhibiting lateral isotropy. However, significant differences exist between the vertical and horizontal directions in elastic parameters, P-wave velocity, and S-wave velocity, resulting in overall macroscopic anisotropy. Therefore, VTI media are a typical type of anisotropic medium.

[0026] The first type of data includes directly acquired logging response data and indirectly determined medium characteristic parameters. The logging response data consists of raw, measured data obtained through logging instruments, and may include P-wave velocity (Vp). P ), transverse wave velocity (V) S The original logging density (ρ) and porosity are considered. Medium characteristic parameters are media property parameters obtained from measured data through equivalent transformation or calculation. They can be processed using Backus equivalent theory to convert logging response data into medium characteristic parameters. For example, medium characteristic parameters include vertical P-wave velocity (ρ). ), vertical transverse wave velocity ( ), equivalent density ( The parameters include fluid bulk modulus and anisotropy parameters (such as Thomsen anisotropy parameters, a set of dimensionless parameters proposed by Thomsen (1986) for weakly anisotropic VTI media). Besides using Backus equivalent theory to obtain media characteristic parameters, other methods can be used, such as indoor rock physics experiments (e.g., ultrasonic experiments), numerical simulations, or combinations with other geophysical inversion methods, to directly obtain or constrain media characteristic parameters. Specifically, vertical P-wave velocity is the P-wave velocity propagating vertically in the medium; vertical S-wave velocity is the S-wave velocity propagating vertically in the medium; equivalent density is the average density of the entire medium; fluid bulk modulus is the compressibility parameter of the fluid in the medium, which can be fitted through a "pressure-volume" experiment; anisotropy parameters are standardized parameters used to quantitatively describe the strength of anisotropy in VTI media, which cannot be directly measured by instruments and must be indirectly calculated based on measured velocity, density, and other data. Anisotropy parameters may include ε, which characterizes the difference between horizontal and vertical P-wave velocities, and δ, which describes the variation of the P-wave phase velocity with phase angle as it propagates near the axis of symmetry.

[0027] It is also necessary to obtain the matrix bulk modulus of the medium. The matrix bulk modulus refers to the bulk modulus of the solid minerals that make up the medium. It only characterizes the compressibility of the solid minerals, does not include pores or pore fluids, and is an inherent physical property of the medium itself. It is not affected by the type of pore fluid, saturation, or formation pressure, and belongs to the basic physical property parameters of the medium.

[0028] Step 102: Determine the average bulk modulus based on the bulk modulus of the matrix.

[0029] In this step, under actual formation conditions, the compressibility of the medium is significantly affected by factors such as formation confining pressure, pore fluid pressure, and effective stress. Classical fluid substitution theory does not consider the influence of these factors on the medium's bulk modulus, directly using the matrix bulk modulus as the true equivalent bulk modulus of the medium, leading to certain errors in subsequent calculation results. This step determines the average bulk modulus based on the matrix bulk modulus and the effective stress fitting relationship. The average bulk modulus is the equivalent bulk modulus reflecting the overall compressibility of the medium under actual formation conditions. Its magnitude is influenced by factors such as formation confining pressure, pore fluid pressure, and effective stress, comprehensively reflecting the macroscopic mechanical response of the medium in a real formation environment. Unlike the matrix bulk modulus, which only characterizes the inherent properties of the solid mineral skeleton, it can more realistically characterize the overall compressibility of the medium under pressure, making it a more accurate equivalent mechanical parameter in VTI medium fluid substitution. Determining the average bulk modulus based on the matrix bulk modulus ensures the reliability of the calculation basis by using stable physical property parameters as the calculation basis. Meanwhile, by introducing the influence of effective stress, the determined parameters not only maintain a high degree of consistency in a physical sense, but also can be accurately adapted to the actual conditions of different strata, thereby effectively improving the overall accuracy and stability of the calculation.

[0030] This application introduces and precisely addresses the difference between the average bulk modulus of the medium and the bulk modulus of the matrix during the fluid replacement process. By determining the average bulk modulus, it fully considers the influence of actual formation conditions such as confining pressure, pore fluid pressure, and effective stress, accurately distinguishing between the matrix bulk modulus and the overall equivalent modulus of the medium. This avoids the systematic errors caused by direct equivalence in traditional methods and overcomes the large theoretical errors caused by existing VTI medium fluid replacement methods based on classical fluid replacement theory neglecting the difference between the average bulk modulus and the matrix bulk modulus. It more realistically reflects the mechanical properties of the medium in the underground environment, thereby improving parameter accuracy and providing reliable support for subsequent high-precision VTI medium fluid replacement.

[0031] Step 103: Based on the first property data, determine the first bulk modulus when the medium contains the fluid, and based on the first property data, the matrix bulk modulus, the average bulk modulus, and the first bulk modulus, determine the second bulk modulus when the medium does not contain the fluid.

[0032] In this step, based on the first property data, the first bulk modulus when the medium contains fluid is determined. Specifically, based on the vertical transverse wave velocity and equivalent density, the shear modulus is determined; based on the vertical longitudinal wave velocity, equivalent density, and shear modulus, the bulk modulus when the medium contains fluid is determined, which is the first bulk modulus. Directly calculating the first bulk modulus based on the first property data has a clear physical meaning, is computationally stable and reliable, and can accurately determine the true bulk modulus when the medium contains fluid.

[0033] For example, the shear modulus is determined by the following formula: (1), where, Shear modulus For equivalent density, The vertical transverse wave velocity.

[0034] The first bulk modulus is determined by the following formula: (2), where, The first bulk modulus, For equivalent density, The vertical longitudinal wave velocity, This is the shear modulus.

[0035] The mechanical properties of the solid skeleton of a medium are inherent and stable, unchanged by variations in pore fluid type and saturation. However, the elastic properties of the medium's fluids vary significantly depending on the fluid type (oil, water, gas). Only by first obtaining the solid skeleton parameters (second bulk modulus) without fluid can we replace it with any target fluid in subsequent steps and accurately predict the medium's elastic response under different fluid filling conditions. Therefore, based on the first property data, matrix bulk modulus, average bulk modulus, and first bulk modulus, the second bulk modulus of the medium without fluid is determined. By introducing the true difference between the matrix bulk modulus and the average bulk modulus, and combining it with the first bulk modulus under saturated fluid conditions, we can eliminate the influence of fluids and obtain the second bulk modulus of a pure solid skeleton. This avoids the errors caused by neglecting pressure effects and modulus differences in traditional methods, providing real, stable, and reliable solid skeleton parameters for subsequent fluid replacement with other types of fluids, ensuring higher accuracy and better alignment with actual formation conditions in the final fluid replacement results.

[0036] Step 104: Based on the first property data, the average bulk modulus, the first bulk modulus and the second bulk modulus, determine the second vertical stiffness coefficient when the medium does not contain the fluid.

[0037] In this step, Brown The generalization of Korringa's theory to classical fluid substitution theory in the compliance domain has the following drawbacks: the compliance domain formulas are complex, parameters are difficult to assign values ​​to, and it cannot be directly applied to VTI media. To address these issues, this application will use Brown... Korringa theory transforms the fluid substitution relationship from the flexibility domain to the stiffness domain, establishing a fluid substitution relationship applicable to VTI media and fully considering the difference between the average bulk modulus and the matrix bulk modulus to correct theoretical errors. Therefore, based on the first property data, the average bulk modulus, the first bulk modulus, and the second bulk modulus, a second vertical stiffness coefficient is determined when the medium is fluid-free. This second vertical stiffness coefficient refers to the fourth-order stiffness coefficient of the VTI medium in the direction perpendicular to the axis of symmetry. It quantitatively describes the elastic deformation characteristics of the VTI medium in the vertical direction and is a core elastic parameter characterizing the vertical P-wave response of anisotropic media, directly determining the magnitude and propagation characteristics of the vertical P-wave velocity. The transformation from the flexibility domain to the stiffness domain creates a more intuitive and engineering-friendly anisotropic fluid substitution calculation method, solving the problems of complex formulas, difficult parameter assignment, and inability to be directly applied to VTI media inherent in the original flexibility domain. By determining the second vertical stiffness coefficient, the systematic error caused by neglecting this difference in the fluid replacement method based on Gassmann theory is theoretically corrected. By fully considering the difference between the average bulk modulus and the matrix bulk modulus, the elastic response of the VTI medium in the direction of the vertical symmetry axis can be accurately characterized, providing the necessary dry medium core parameters for fluid replacement. Here, the dry medium is the remaining part of the medium after removing the pore fluid, consisting of a solid skeleton and pores.

[0038] This application will Brown The formulas in Korringa's theory were transformed from their complex flexibility domain representation to a more physically intuitive stiffness domain form. Based on this, a simplified fluid substitution approximation formula was derived and applied to the porous rock characteristics of VTI. This innovative transformation and simplification solved the Brownian problem. The difficulty in obtaining parameters and the computational complexity of the formulas in Korringa theory make the theoretically rigorous anisotropic fluid replacement formulas efficient and feasible in engineering practice.

[0039] Step 105: Obtain second property data for each predetermined replacement fluid. For each predetermined replacement fluid, based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, and the second property data, determine the longitudinal wave velocity after the fluid in the medium is replaced by the predetermined replacement fluid.

[0040] In this step, second property data for each predetermined replacement fluid is obtained, wherein the predetermined replacement fluid refers to the target fluid pre-set during the fluid replacement process to replace the original pore fluid of the medium. For example, the predetermined fluid is a mixture of multiple fluids in a predetermined proportion, such as 30% oil and 70% water; the second property data includes at least the bulk modulus of the predetermined replacement fluid.

[0041] P-wave velocity is a key parameter for identifying reservoir fluids and evaluating reservoir properties in seismic exploration. Replacing the fluid in the medium with a predetermined fluid and calculating the P-wave velocity can clarify the seismic response patterns corresponding to different fluids, providing a direct basis for identifying underground oil, gas, and water and predicting reservoir properties. Therefore, accurately determining the P-wave velocity after replacing the fluid in the medium with the predetermined replacement fluid is crucial. This application determines the P-wave velocity after replacing the fluid in the medium with the corresponding predetermined replacement fluid based on first property data, average bulk modulus, second bulk modulus, second vertical stiffness coefficient, and second property data of each predetermined replacement fluid. Here, P-wave velocity refers to the propagation speed of seismic P-waves in VTI media, directly reflecting the elastic properties of the medium and the internal fluid filling state, and is a key geophysical parameter for reservoir identification, fluid discrimination, and time-lapse seismic analysis. By determining the P-wave velocity of the replaced medium, the geophysical response under different fluid filling conditions can be quickly output, providing intuitive quantitative results for reservoir fluid identification and reservoir parameter prediction. This application adopts the stiffness domain calculation method throughout, maintaining the characteristics of simplicity, intuitiveness and strong engineering feasibility. It also continuously considers the difference between the average bulk modulus and the matrix bulk modulus, further consolidating the correction effect on the error of the classical fluid replacement theory, and effectively improving the accuracy of the longitudinal wave velocity after the fluid in the medium is replaced with the predetermined replacement fluid.

[0042] High-precision fluid substitution results can provide more reliable parameters for rock physics analysis, optimize reservoir characteristic analysis, thereby improving the success rate of oil and gas reservoir prediction and reducing exploration risks. In fields such as time-lapse seismic monitoring, this application can provide more refined fluid change monitoring capabilities, helping to more accurately assess the dynamic changes and development potential of oil and gas reservoirs.

[0043] The above scheme obtains the first property data and matrix bulk modulus of the medium, wherein the medium contains fluid. Based on the matrix bulk modulus, the average bulk modulus is determined, ensuring the reliability of the calculation basis by using stable physical property parameters as the calculation basis. Based on the first property data, the first bulk modulus when the medium contains the fluid is determined. The first bulk modulus is calculated directly based on the first property data, with clear physical meaning and stable and reliable calculation, accurately determining the true bulk modulus of the medium containing fluid. Furthermore, based on the first property data, the matrix bulk modulus, the average bulk modulus, and the first bulk modulus, the second bulk modulus when the medium does not contain the fluid is determined. By introducing the true difference between the matrix bulk modulus and the average bulk modulus, and combining it with the first bulk modulus under saturated fluid conditions, the influence of fluid can be eliminated, and the second bulk modulus of the pure solid skeleton can be obtained, thereby avoiding the errors caused by neglecting the influence of pressure and modulus differences in traditional methods. Based on the first property data, the average bulk modulus, the first bulk modulus, and the second bulk modulus, the second vertical stiffness coefficient when the medium does not contain the fluid is determined. By determining the second vertical stiffness coefficient, the systematic error caused by neglecting this difference in the fluid replacement method based on Gassmann theory is theoretically corrected. By fully considering the difference between the average bulk modulus and the matrix bulk modulus, the elastic response of the VTI medium in the direction of the vertical symmetry axis can be accurately characterized, providing the necessary core parameters for fluid replacement. Second property data for each predetermined replacement fluid are obtained. For each predetermined replacement fluid, based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, and the second property data, the P-wave velocity after the fluid in the medium is replaced with the predetermined replacement fluid is determined. This application uses a stiffness domain calculation method throughout, maintaining the characteristics of simplicity, intuitiveness, and strong engineering feasibility. It continuously considers the difference between the average bulk modulus and the matrix bulk modulus, further consolidating the correction effect on the errors of the classical fluid replacement theory and effectively improving the accuracy of the P-wave velocity after the fluid in the medium is replaced with the predetermined replacement fluid.

[0044] In some embodiments, determining the average bulk modulus based on the matrix bulk modulus includes: determining the average bulk modulus based on a pre-constructed curve showing the relationship between the ratio of the average bulk modulus to the matrix bulk modulus as a function of effective pressure and the matrix bulk modulus.

[0045] In this embodiment, to overcome the theoretical defects of existing technologies that conflate matrix bulk modulus with average bulk modulus and assume they are equal, this application fully considers the actual influence of formation confining pressure and fluid pressure on average bulk modulus, and establishes a method for determining average bulk modulus with clear physical meaning and conforming to real formation conditions, thereby improving the theoretical rigor and calculation accuracy of fluid replacement. The matrix bulk modulus obtained in this application is the matrix bulk modulus under the effective pressure corresponding to the medium. Specifically, it is found in the pre-constructed curve showing the relationship between the ratio of average bulk modulus to matrix bulk modulus with effective pressure, specifically by searching for the average bulk modulus corresponding to the matrix bulk modulus under effective pressure. The average bulk modulus is an overall elastic parameter of the medium that is affected by the formation stress state, pore structure, and skeleton, and has a clear physical difference from the matrix bulk modulus, which only represents the properties of the solid skeleton. It is a key parameter for improving the accuracy of fluid replacement in anisotropic media. The effective pressure of the medium is obtained by subtracting the formation pore fluid pressure corrected by the effective stress coefficient from the total confining pressure generated by the overlying rock strata. This application pre-constructs a curve showing the relationship between the ratio of average bulk modulus to matrix bulk modulus and effective pressure using experimental data. For example, the experimental data consists of the average bulk modulus and matrix bulk modulus of Berea sandstone measured under different confining and pore pressures. Based on the above experimental data, the influence of formation confining pressure and pore fluid pressure is effectively coupled to fit and obtain the ratio of average bulk modulus to matrix bulk modulus, which is expressed as a formula: (3), among which, The average bulk modulus, The bulk modulus of the matrix. For effective pressure.

[0046] This formula, based on extensive experimental test data under various pressure conditions, is an empirical relationship obtained through regression analysis. It reflects the variation of the overall elastic compressibility and the elastic properties of the matrix skeleton in porous media under different effective stress states. Using this formula, this application can directly calculate the average bulk modulus under the corresponding effective pressure environment, given the matrix bulk modulus and formation pressure. This ensures that the parameter values ​​accurately reflect the elastic response of the medium under the combined action of formation confining pressure and fluid pressure. This approach not only strictly distinguishes the physical connotations of the average bulk modulus and the matrix bulk modulus, avoiding conceptual confusion in existing technologies, but also solves the problem of quantitatively obtaining the average bulk modulus under real formation conditions using traditional methods. It provides a physically meaningful and numerically reliable parameter basis for subsequent VTI medium stiffness coefficient calculations and fluid replacement, effectively improving the theoretical rigor and computational accuracy of the fluid replacement method. This allows the fluid replacement results to better simulate real formation conditions, enhancing the method's universality, physicality, and applicability.

[0047] This application's fluid replacement technique comprehensively considers the influence of rock confining pressure and fluid pressure on the average bulk modulus, thereby improving the accuracy and applicability of the fluid replacement results. By establishing a fitting relationship between the ratio of average bulk modulus and matrix bulk modulus and effective stress, the fluid replacement results comprehensively consider rock confining pressure and fluid pressure, enabling better simulation of fluid replacement behavior under real formation conditions and improving the applicability and reliability of the results. The effective stress can be determined through formation confining pressure and pore fluid pressure. This application simplifies Brown... Korringa's anisotropic fluid replacement formula fully considers the difference between the average bulk modulus and the matrix bulk modulus to achieve high-precision fluid replacement.

[0048] like Figure 2 As shown, Figure 2 This is a schematic diagram illustrating the fitting relationship between the ratio of the average bulk modulus and the matrix bulk modulus of the present application and the effective stress, showing the ratio of the average bulk modulus of the medium to the matrix bulk modulus (K). M / K S ) with the effective stress logarithm (ln(P) d The fitting relationship of the variation reveals the influence of rock confining pressure and fluid pressure on the average bulk modulus, which is crucial for accurately determining K in the method of this application. M The parameters provide the basis.

[0049] In some embodiments, determining the second bulk modulus of the medium when it does not contain the fluid, based on the first property data, the matrix bulk modulus, the average bulk modulus, and the first bulk modulus, includes determining the second bulk modulus using the following formula: ,in, The second bulk modulus, The first bulk modulus, The porosity of the medium. For fluid bulk modulus, The bulk modulus of the matrix is... The average bulk modulus is given.

[0050] In this embodiment, the formula is Brown This paper presents an engineering implementation of Korringa's theory for VTI (Vacuum-Induced Tensor) media fluid replacement scenarios, after the transition from the flexibility domain to the stiffness domain. It retains the physical rigor of the original theory while mathematically transforming it into an explicit calculation formula with the second bulk modulus as the core variable, allowing for direct numerical solutions. This transforms the originally complex flexibility tensor calculations into algebraic operations that can be directly solved using experimental or well-logging data, effectively improving the method's practicality and feasibility. Unlike Gassmann's theory, which assumes that the average bulk modulus and matrix bulk modulus are equal, this formula explicitly introduces the average bulk modulus and matrix bulk modulus, strictly distinguishing them in physical meaning. The average bulk modulus represents the overall compressibility of the medium under pressure influence, while the matrix bulk modulus represents the solid skeleton properties. This eliminates theoretical errors caused by confusing the two, achieving a rigorous transition from the flexibility domain to the stiffness domain.

[0051] First, the formula is expressed directly as a bulk modulus, avoiding the complexity of compliance matrix calculations, effectively reducing the difficulty of engineering calculations and improving the practicality of the method. Second, the formula structure fully couples porosity, fluid bulk modulus, and various key elastic moduli, accurately characterizing the dynamic changes in the medium's bulk modulus before and after fluid replacement. Finally, the second bulk modulus calculated by this formula can truly reflect the elastic skeleton behavior of VTI media in the dry state, providing a solid and reliable mathematical foundation for subsequent high-precision fluid replacement and P-wave velocity prediction, effectively improving the accuracy and robustness of the overall technical solution.

[0052] In some embodiments, determining a second vertical stiffness coefficient when the medium does not contain the fluid, based on the first property data, the average bulk modulus, the first bulk modulus, and the second bulk modulus, includes: determining a first vertical stiffness coefficient when the medium contains the fluid, based on the first property data; and determining a second vertical stiffness coefficient based on the first property data, the average bulk modulus, the first bulk modulus, the second bulk modulus, and the first vertical stiffness coefficient.

[0053] In this embodiment, the first vertical stiffness coefficient is determined based on the first property data when the medium contains fluid. By determining the first vertical stiffness coefficient in the fluid-containing state, a realistic elastic state of the medium that closely matches the actual formation can be constructed based on the first property data, providing a reliable starting point for subsequent inverse solutions of dry medium-related parameters and avoiding a disconnect between theoretical assumptions and actual formation conditions. Then, based on the first property data, average bulk modulus, first bulk modulus, second bulk modulus, and first vertical stiffness coefficient, the second vertical stiffness coefficient is determined. The first vertical stiffness coefficient refers to the fourth-order stiffness coefficient of the fluid-containing VTI medium in the direction perpendicular to the axis of symmetry. It is used to directly characterize the vertical elastic response of the medium in the fluid-containing state and is a key bridge connecting measured data and theoretical models. By determining the first vertical stiffness coefficient in the fluid-containing state, a realistic elastic model of the medium can be constructed based on measured data, providing a reliable starting point for subsequent inverse solutions and avoiding a disconnect between theoretical assumptions and actual formation conditions. Based on the relationship between this parameter and the stiffness domain, by solving the second vertical stiffness coefficient, we can obtain a second vertical stiffness coefficient with clear physical meaning that is not affected by approximation errors. This not only conforms to the physical mechanism of fluid replacement in porous media, but also ensures the accuracy of subsequent parameter calculations, providing reliable support for the calculation of longitudinal wave velocity under different fluid replacement scenarios.

[0054] Based on the primary property data of the medium, a reliable vertical stiffness coefficient containing fluid is determined, namely the first vertical stiffness coefficient. Then, based on strict physical relationships, the vertical stiffness coefficient of the dry medium is obtained, namely the second vertical stiffness coefficient. This ensures the accuracy and rationality of the solution for the second vertical stiffness coefficient, establishes a quantitative correspondence between the fluid-containing state and the dry medium state, and reduces the calculation deviation introduced by approximation.

[0055] In some embodiments, determining the second vertical stiffness coefficient based on the first property data, the average bulk modulus, the first bulk modulus, the second bulk modulus, and the first vertical stiffness coefficient includes: determining the second vertical stiffness coefficient using the following formula: ,in, This is the second vertical stiffness coefficient. This is the first vertical stiffness coefficient. The first bulk modulus, The second bulk modulus, A parameter describing the degree to which the phase velocity of a longitudinal wave propagating near the axis of symmetry changes with the phase angle. The average bulk modulus is given.

[0056] In this embodiment, the formula takes the first vertical stiffness coefficient with fluid as input, combines the first property data, average bulk modulus, first bulk modulus, and second bulk modulus, and inversely solves for the second vertical stiffness coefficient. Calculating the second vertical stiffness coefficient using this formula ensures that, on the one hand, it strictly follows the physical process of fluid replacement, starting from measured data to obtain a physically meaningful second vertical stiffness coefficient, thus ensuring the self-consistency and accuracy of the solution process; on the other hand, by introducing the parameter δ, unique to VTI media, which describes the degree of change of the longitudinal wave phase velocity with phase angle near the axis of symmetry, quantitative correction of anisotropic effects is achieved. This avoids the deficiency of traditional isotropic approximate fluid replacement methods in failing to describe vertical elastic differences, enabling the calculation of the second vertical stiffness coefficient to truly reflect the anisotropic characteristics of the formation framework. Meanwhile, the formula continues to consider the difference between the average bulk modulus and the matrix bulk modulus, further correcting the systematic errors of the classical fluid substitution theory. It provides a parameter basis with both anisotropic correction capability and high accuracy for subsequent fluid substitution and P-wave velocity prediction, effectively improving the applicability and prediction accuracy of the VTI medium fluid substitution method.

[0057] In some embodiments, determining the longitudinal wave velocity after replacing the fluid in the medium with the predetermined replacement fluid based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, and the second property data includes: determining a third bulk modulus in the medium when the predetermined replacement fluid is present, based on the first property data, the average bulk modulus, the second bulk modulus, and the second property data; determining a third vertical stiffness coefficient in the medium when the predetermined replacement fluid is present, based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, the second property data, and the third bulk modulus; and determining the longitudinal wave velocity based on the second property data and the third vertical stiffness coefficient.

[0058] In this embodiment, a third bulk modulus is determined based on the first property data, the average bulk modulus, the second bulk modulus, and the second property data when the medium contains the predetermined replacement fluid. The third bulk modulus is the equivalent bulk modulus after the fluid in the medium is replaced with the predetermined replacement fluid, reflecting the overall compressibility characteristics of the medium under the new fluid filling state. The third bulk modulus is determined using the following formula: (4), where, The third bulk modulus, The second bulk modulus, The average bulk modulus, Porosity of the medium The bulk modulus of the intended replacement fluid is defined. By first determining the third bulk modulus corresponding to the intended replacement fluid, a correspondence between the new fluid properties and the overall elastic compressibility characteristics of the medium can be established based on the stiffness domain, providing reliable intermediate parameters for subsequent stiffness coefficient calculations.

[0059] Based on the first property data, average bulk modulus, second bulk modulus, second vertical stiffness coefficient, second property data, and third bulk modulus, the third vertical stiffness coefficient is determined when the medium contains a predetermined replacement fluid. The third vertical stiffness coefficient is the fourth-order stiffness coefficient in the direction perpendicular to the axis of symmetry of the VTI medium under the predetermined replacement fluid filling state, characterizing the vertical elastic response of the medium under new fluid conditions. This method, with full consideration of anisotropy correction, yields elastic parameters with clear physical meaning and consistent with actual formation pressure conditions when containing the predetermined replacement fluid.

[0060] Based on the second property data and the third vertical stiffness coefficient, the P-wave velocity is determined, realizing a complete chain conversion from fluid properties to elastic response and then to observable seismic velocity. This solution process retains the rigor of stiffness domain theory while reducing the complexity of direct solutions and improving computational stability through step-by-step calculation of intermediate parameters. Simultaneously, it continues to consider the difference between the average bulk modulus and the matrix bulk modulus, and combines VTI medium anisotropy correction to fundamentally correct the systematic errors and isotropic approximation defects of classical fluid substitution theory. This makes the predicted P-wave velocity more closely match the anisotropic response of the actual formation, significantly improving the applicability of the fluid substitution method and the accuracy of reservoir fluid identification.

[0061] In some embodiments, determining the third vertical stiffness coefficient when the medium contains the predetermined replacement fluid, based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, the second property data, and the third bulk modulus, includes: determining the third vertical stiffness coefficient using the following formula: ,in, The third vertical stiffness coefficient, This is the second vertical stiffness coefficient. The third bulk modulus, The second bulk modulus, A parameter describing the degree to which the phase velocity of a longitudinal wave propagating near the axis of symmetry changes with the phase angle. The average bulk modulus is given.

[0062] In this embodiment, the formula, based on the elastic skeleton parameters of the dry medium and combined with the bulk modulus and anisotropic correction parameters of the new fluid, directly establishes the calculation relationship for the vertical stiffness coefficient under the new fluid filling state. Calculating the third vertical stiffness coefficient using this formula enables a direct conversion from the elastic parameters of the dry medium to the elastic response under the new fluid state, maintaining the continuity and physical consistency of the calculation process. Furthermore, the formula continues to incorporate the average bulk modulus, ensuring continuous correction of systematic errors in classical fluid replacement theory. This provides a foundation of elastic parameters with both anisotropic correction capabilities and high accuracy for subsequent P-wave velocity prediction, effectively improving the prediction accuracy and applicability in multi-fluid replacement scenarios.

[0063] In another embodiment, the fluid properties of the known initial fluid within the medium are obtained; based on the fluid properties of the predetermined fluid replacement, the theoretically predicted P-wave velocity after replacing the initial fluid with the predetermined replacement fluid is determined; the observed P-wave velocity of the actual formation is matched with the theoretically predicted P-wave velocity to determine the target fluid properties within the actual formation. Forward fluid replacement based on known initial fluid information can obtain relevant parameters of the medium under the new fluid-filled state (such as the theoretically predicted P-wave velocity). The target fluid properties refer to the physical parameters of the fluid within the reservoir pores, including fluid type, bulk modulus, density, and saturation, which are crucial for evaluating reservoir hydrocarbon potential and formulating development plans. Determining fluid properties based on P-wave velocity allows matching the theoretically predicted velocity under different fluid-filled states with the observed velocity in the actual formation, achieving a quantitative inversion of the true fluid type and state within the reservoir, overcoming the limitation of traditional methods that can only qualitatively determine fluid type and cannot quantitatively characterize fluid physical parameters. Simultaneously, relying on the correspondence constructed by the stiffness domain fluid substitution model, the model's ability to correct for the anisotropy and pressure effects of VTI media can be fully utilized, making the fluid properties obtained by inversion more consistent with real formation conditions. This avoids the risk of misjudgment caused by traditional fluid identification methods ignoring anisotropy or using approximate assumptions. Furthermore, a complete technical closed loop from forward fluid substitution to inverse fluid identification has been formed, significantly improving the accuracy and engineering practicality of reservoir fluid evaluation and providing reliable technical support for oil and gas exploration and development.

[0064] In another embodiment, the fluid replacement theory of VTI porous elastic media is explained in detail through this embodiment.

[0065] Brown and Korringa (1975) extended the classical fluid substitution theory and proposed Brown's theory. Korringa's theory provides compliance coefficients for arbitrarily anisotropic saturated fluid filling conditions. Compliance coefficient with dry rock Relationship: (5) (6) (7) in, This refers to the compliance coefficient under conditions of arbitrary anisotropic saturated fluid filling; for example, it can be the compliance coefficient when the VTI medium contains fluid. This represents the compliance coefficient for dry rock; for example, it could be the compliance coefficient for VTI media when it does not contain fluid. This is a reduced form of the dry rock skeleton compliance tensor, implicitly summing over the subscript q in the range of 1, 2, and 3, characterizing the volumetric strain response of the dry rock skeleton to triaxial stress. To form the compliance tensor components of the rock equivalent matrix, This is a reduced form of the flexibility tensor of the dry rock skeleton, implicitly summing over the subscript r, with physical meaning similar to... resemblance, For the compliance tensor components of the rock equivalent matrix, Porosity of the medium The compliance coefficient of the pore fluid. The porosity coefficient is the pore flexibility coefficient. The scalar parameter is obtained by fully reducing and summing all four subscripts of the dry rock compliance tensor. The average compliance coefficient of the medium is given by the average bulk modulus, but the introduced average bulk modulus is difficult to obtain directly from measured data, which limits the practical application of this theory. The total volume of the fluid. For the macroscopic equivalent tensor components of porous media, the infinitesimal change is denoted as . This represents the infinitesimal change in pore pressure of the fluid. For externally applied stress, For porous rocks, the volume-average effective strain tensor component is... To represent space x j The partial derivative operator, For particles inside the medium along i Displacement vector components in the direction, To represent space x i The partial derivative operator, For particles inside the medium along j The displacement vector component in the direction. It should be added that the aforementioned "dry rock" refers to a medium that does not contain fluid; the aforementioned "fluid-filled" refers to a medium that contains fluid.

[0066] The above content is from Brown. The following is the improvement process of this application, based on the Korringa theory: Assuming the average compliance coefficient of the medium is equivalent to isotropic, then equation (5) simplifies to: (8) in, For the Kronecker function, i = j Its value is 1 when it is active, and 0 otherwise. Also known as the Kronecker function, k = l Its value is 1 when it is active, and 0 otherwise. Using Voigt notation (Voigt notation) , Equation (8) can be rewritten as: (9) in, (10) In the formula: ε1=ε2=ε3=1, ε4=ε5=ε6=0. When represented in matrix form, and Both are 6×6 matrices. It is a 6×1 column vector. It is a 1×6 column vector. For the Voigt notation, the first in the dry rock compliance matrix m The compliance component of the row and column 1. For the Voigt notation, the first in the dry rock compliance matrix m The compliance component in row 2 and column 2. For the Voigt notation, the first in the dry rock compliance matrix m The compliance component in row 3 and column 4. Let be the column vector components of the unit second-order tensor, denoted by Voigt notation. The Sherman-Morrison formula is used to solve for the inverse matrix of a rank-one perturbation. Given the inverse of the original matrix, it can quickly calculate the inverse of the newly modified matrix after a small correction, avoiding repeated large-scale matrix inversion operations. Based on the Sherman-Morrison formula and the inverse relationship between the compliance and stiffness tensors, a replacement formula for anisotropic fluids expressed in terms of second-order stiffness coefficients can be given. (11) (12) in, For stiffness tensor, For the flexibility tensor, For the Voigt notation, the first in the dry rock stiffness matrix m The stiffness components of the row and column 1, The first in the dry rock stiffness matrix m The stiffness components of the second row and second column. The first in the dry rock stiffness matrix m The stiffness components of the row and the third column, The porosity-fluid compressibility intermediate scalar coefficient for fluid substitution. A transition column vector constructed from the combination of dry rock stiffness coefficient and average flexibility coefficient. b m The first element, Transition column vector b m The second element, Transition column vector b m The third element.

[0067] Voigt notation is used again, and the second-order stiffness components are converted back to a fourth-order tensor, namely C. ijkl =c mn , where C ijkl Let c be the fourth-order stiffness tensor component in tensor representation. mn Using the second-order stiffness matrix components after dimensionality reduction using Voigt notation, the relationship between the anisotropic stiffness constants of rocks containing saturated fluid and their dry counterparts can be established: (13) in, Let be the stiffness tensor components under anisotropic saturated fluid filling conditions. For the stiffness tensor components of the dry rock skeleton, For the reduced form of the dry rock stiffness tensor, the last two subscripts are... q Summing in directions 1, 2, and 3. This is a reduced form of the dry rock stiffness coefficient, with the first two subscripts... r Summing in directions 1, 2, and 3. The scalar parameter is obtained by fully reducing and summing all four subscripts of the dry rock stiffness tensor. It is the average bulk modulus of the rock. It is the fluid modulus. It is the bulk modulus of the matrix.

[0068] For VTI media, the vertical stiffness coefficients of saturated fluid rock and dry rock satisfy the following relationship: (14) Based on the relationship between VTI medium parameters, the VTI medium stiffness coefficient (C) can be established. 3333 C 2323 C 1111 C1212 C 1133 ) and vertical longitudinal wave velocity (V P0 ), vertical transverse wave velocity (V S0 The relationship between the original logging density (ρ) and the Thomsen anisotropy parameters (ε, δ, γ) is as follows: (15) (16) (17) (18) , (19) in, is the longitudinal wave stiffness coefficient in the vertical direction of the VTI medium. is the shear stiffness coefficient within the vertical symmetry plane of the VTI medium. The longitudinal wave stiffness coefficient in the isotropic plane of the VTI medium. The shear stiffness coefficient in the isotropic plane of the VTI medium. γ is the cross-coupling stiffness coefficient of the VTI medium in the horizontal and vertical directions, and γ is the Thomsen transverse wave anisotropy parameter.

[0069] Then we have: (20) ,(twenty one), in, This is the equivalent reduction stiffness coefficient of the dry rock skeleton. The vertical longitudinal wave velocity of the dry rock skeleton. The vertical transverse wave velocity of the dry rock skeleton.

[0070] Assuming the existence of an isotropic medium, the P-wave velocity, S-wave velocity, and density in the case of dry rock are respectively... , Let ρ be the bulk modulus. Equations (20) and (21) can be simplified to: ,(twenty two), ,(twenty three), in, This is the bulk modulus of dry rock, i.e., the bulk modulus of the medium when it contains no fluid.

[0071] Substituting equations (22-23) into formula (14) yields: ,(twenty four), When the VTI medium has weak anisotropy and high porosity, there is <<1 and >>(K F / K M )× Then equation (24) can be simplified to: (25) Compared to Brown Korrigna's isotropic fluid substitution formula: ,(26) Then we have: ,(27) Equations (26) and (27) are the fluid substitution formulas for isotropic and VTI media, respectively. They can also be rewritten in the following form: ,(28) , (29) The above is the theoretical basis for fluid replacement of fluid media in VTI.

[0072] In another embodiment, after determining the P-wave velocity after the fluid in the medium is replaced with a predetermined replacement fluid, the P-wave velocity is verified to ensure the reliability and applicability of the calculation results. The method in this application mainly addresses the fluid replacement process in in-situ anisotropic media, enabling a quantitative mapping between fluid changes and seismic response while considering the anisotropic characteristics of the formation. To fully verify the effectiveness and applicability of the proposed method, especially for practical exploration scenarios lacking time-delayed seismic data and insufficient monitoring data, this application also proposes a technical solution for cross-layer fluid identification based on measured well logging data. After determining key parameters such as the bulk modulus and vertical stiffness coefficient of dry rock through rock physical analysis, it is necessary to combine predetermined empirical formulas, such as the Nur empirical formula (Nur, 1991, 1998), to convert the dry rock parameters of the target layer, and then perform cross-layer fluid replacement, providing a reliable basis for fluid identification under conditions without monitoring data.

[0073] In another embodiment, such as Figure 3 As shown, Figure 3This is a schematic diagram of the VTI medium fluid replacement process according to an embodiment of this application. Well logging response data and medium characteristic parameters are acquired. For example, the well logging response data includes P-wave velocity, S-wave velocity, and original well logging density. The medium characteristic parameters include the vertical propagation direction response parameters of the VTI medium. For example, the medium characteristic parameters include vertical P-wave velocity, vertical S-wave velocity, equivalent density, and anisotropy parameters. The anisotropy parameters are determined based on the well logging response data using Backus equivalent theory.

[0074] Based on well logging response data and medium characteristic parameters, determine the saturated isotropic medium bulk modulus, i.e., the bulk modulus when the medium contains fluid. Based on well logging response data, medium characteristic parameters, and the saturated isotropic medium bulk modulus, determine the isotropic fluid-replaced dry rock bulk modulus, i.e., the bulk modulus when the medium does not contain fluid, which can be determined by the aforementioned equation (28). Based on well logging response data and medium characteristic parameters, determine the saturated VTI medium vertical stiffness coefficient, i.e., the vertical stiffness coefficient when the medium contains fluid. Based on well logging response data, medium characteristic parameters, saturated isotropic medium bulk modulus, isotropic fluid-replaced dry rock bulk modulus, and saturated VTI medium vertical stiffness coefficient, determine the dry rock VTI medium vertical stiffness coefficient, i.e., the vertical stiffness coefficient when the medium does not contain fluid, which can be determined by the aforementioned equation (29).

[0075] Based on well logging response data, medium characteristic parameters, isotropic fluid replacement of dry rock bulk modulus, and the property data of the intended replacement fluid, the isotropic fluid replacement of saturated rock bulk modulus, i.e., the bulk modulus when the medium contains the intended replacement fluid, can be determined using the aforementioned equation (26). Based on well logging response data, medium characteristic parameters, isotropic fluid replacement of dry rock bulk modulus, dry rock VTI medium vertical stiffness coefficient, the property data of the intended replacement fluid, and VTI medium fluid replacement of dry rock bulk modulus, the VTI medium fluid replacement of saturated rock vertical stiffness coefficient, i.e., the vertical stiffness coefficient when the medium contains the intended replacement fluid, can be determined using the aforementioned equation (27). Based on the property data of the intended replacement fluid and the VTI medium fluid replacement of saturated rock vertical stiffness coefficient, the P-wave velocity of the intended replacement fluid is determined.

[0076] The Nur empirical formula can also be used to determine the dry rock bulk modulus of the interlayer isotropic medium, thereby realizing interlayer fluid replacement; similarly, the Nur empirical formula can also be used to determine the dry rock vertical stiffness coefficient of the interlayer VTI medium, so as to complete the corresponding interlayer fluid replacement.

[0077] In another embodiment, such as Figure 4 As shown, Figure 4 A schematic diagram showing the result of Backus equivalent averaging of the logging response data in this application embodiment. Figure 4This paper presents the results of Backus equivalent averaging of logging response data from a certain well and its corresponding formation interpretation. Figure 4 (a) in the figure represents the well logging interpretation results, showing the formation lithology and fluid distribution; Figure 4 In the diagram, (b) represents the P-wave velocity (V). P ) curve; Figure 4 In the equation (c), the S-wave velocity (V) is... S ) curve; Figure 4 In the figure, (d) represents the density (ρ) curve; Figure 4 In the figure, (e)~(g) are the Thomsen anisotropy parameters ε, δ, γ curves, respectively. These parameters are used as inputs to the method of this application.

[0078] like Figure 5 As shown, Figure 5 This is a schematic diagram illustrating the predicted formation pore pressure and effective stress according to an embodiment of this application. Wherein, Figure 5 In the figure (a), shale volume fraction (V) is represented. sh )curve; Figure 5 (b) in the figure represents the normal compaction tendency (NCT); Figure 5 (c) in the figure represents the pore pressure (P). f ), hydrostatic pressure (P) hyd ) and overlying formation pressure (P c )curve; Figure 5 In the figure, (d) represents the effective stress (P). d These parameters play an important role in determining the average bulk modulus of rocks.

[0079] like Figure 6 As shown, Figure 6 This diagram illustrates the agreement between the predicted vertical P-wave (longitudinal wave) velocity across layers and the actual well logging interpretation results in an embodiment of this application. Figure 6 The vertical P-wave velocity (Vt) predicted across layers using the method described in this application was compared in the well section at depths of 4120-4170 meters. P0 The agreement between the results and the actual well logging interpretation. Among them, Figure 6 (a) in the diagram represents the well logging interpretation results for that well section; Figure 6 (b) in the figure represents porosity. ) curve; Figure 6 In this context, (c) represents the bulk modulus of the mineral (K). S ) and average bulk modulus (K M ) curve; Figure 6 In the figure, (d) represents the predicted vertical P-wave velocity (V). P0 ) curve. Figure 6 The accuracy of the prediction results of the method in this application is demonstrated intuitively.

[0080] Furthermore, as shown in Table 1, Table 1 is a comparison table of the prediction results of Gassmann theory and the formula of this application: Table 1 Comparison of Prediction Results between Gassmann Theory and the Formula in This Application

[0081] Table 1 quantitatively assesses and compares the differences in prediction results between Gassmann's theory and the formula proposed in this application. The table lists the root mean square error (RMSE), mean absolute error (MAE), maximum absolute percentage error (MaxAPE), and coefficient of determination (R-squared, R0). 2 Four key statistical parameters. Data shows that compared to the predictions of Gassmann theory, the formula proposed in this application achieves significant reductions in all error indicators: the root mean square error (RMSE) decreases from 70.20 m / s to 17.31 m / s, a reduction of 52.89 m / s; the mean absolute error (MAE) decreases from 69.14 m / s to 16.79 m / s, a reduction of 52.35 m / s; and the maximum absolute percentage error (MaxAPE) decreases significantly from 3.44% in Gassmann theory to 0.49% in the formula of this application, demonstrating a significant improvement in accuracy. The coefficient of determination (R-squared, R...) 2 The accuracy of the proposed formula is significantly improved, reaching 0.945, indicating a very high goodness of fit for the vertical P-wave velocity, while the Gassmann theory only achieves 0.097, showing a poor fit. These data fully demonstrate that the proposed method can provide more accurate and reliable fluid substitution results. The proposed formula significantly outperforms the Gassmann theory in all indicators, reflecting the superior performance of the proposed method.

[0082] It should be noted that the method in this embodiment can be executed by a single device, such as a computer or server. The method can also be applied in a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method in this embodiment, and the multiple devices will interact with each other to complete the method described.

[0083] It should be noted that some embodiments of this application have been described above. In some cases, the actions or steps described in the above embodiments can be performed in a different order than that shown in the above embodiments and the desired result can still be achieved. In addition, the processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0084] Based on the same inventive concept, and corresponding to any of the above embodiments, this application also provides a device for determining the longitudinal wave velocity of fluid replacement in anisotropic media.

[0085] refer to Figure 7 The device for determining the longitudinal wave velocity by fluid displacement in the anisotropic medium includes: The acquisition module 10 is configured to acquire first property data of the medium and matrix bulk modulus, wherein the medium comprises a fluid; The first determining module 20 is configured to determine the average bulk modulus based on the matrix bulk modulus; The second determining module 30 is configured to determine, based on the first property data, a first bulk modulus when the medium contains the fluid, and, based on the first property data, the matrix bulk modulus, the average bulk modulus, and the first bulk modulus, a second bulk modulus when the medium does not contain the fluid. The third determining module 40 is configured to determine a second vertical stiffness coefficient when the medium does not contain the fluid, based on the first property data, the average bulk modulus, the first bulk modulus and the second bulk modulus; The fourth determining module 50 is configured to acquire second property data for each predetermined replacement fluid, and for each predetermined replacement fluid, based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, and the second property data, determine the longitudinal wave velocity after the fluid in the medium is replaced by the predetermined replacement fluid.

[0086] The aforementioned apparatus acquires first property data and matrix bulk modulus of a medium, wherein the medium contains a fluid. Based on the matrix bulk modulus, an average bulk modulus is determined, ensuring the reliability of the calculation basis by using stable physical property parameters as the calculation basis. Based on the first property data, a first bulk modulus is determined when the medium contains the fluid. Calculating the first bulk modulus directly based on the first property data provides clear physical meaning, stable and reliable calculation, and accurately determines the true bulk modulus of the medium containing the fluid. Furthermore, based on the first property data, the matrix bulk modulus, the average bulk modulus, and the first bulk modulus, a second bulk modulus is determined when the medium does not contain the fluid. By introducing the true difference between the matrix bulk modulus and the average bulk modulus, and combining it with the first bulk modulus under saturated fluid conditions, the influence of the fluid can be eliminated, yielding a second bulk modulus of a pure solid skeleton, thereby avoiding errors caused by neglecting pressure effects and modulus differences in traditional methods. Based on the first property data, the average bulk modulus, the first bulk modulus, and the second bulk modulus, a second vertical stiffness coefficient is determined when the medium does not contain the fluid. By determining the second vertical stiffness coefficient, the systematic error caused by neglecting this difference in the fluid replacement method based on Gassmann theory is theoretically corrected. By fully considering the difference between the average bulk modulus and the matrix bulk modulus, the elastic response of the VTI medium in the direction of the vertical symmetry axis can be accurately characterized, providing the necessary core parameters for fluid replacement. Second property data for each predetermined replacement fluid are obtained. For each predetermined replacement fluid, based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, and the second property data, the P-wave velocity after the fluid in the medium is replaced with the predetermined replacement fluid is determined. This application uses a stiffness domain calculation method throughout, maintaining the characteristics of simplicity, intuitiveness, and strong engineering feasibility. It continuously considers the difference between the average bulk modulus and the matrix bulk modulus, further consolidating the correction effect on the errors of the classical fluid replacement theory and effectively improving the accuracy of the P-wave velocity after the fluid in the medium is replaced with the predetermined replacement fluid.

[0087] In some embodiments, the first determining module 20 is further configured to determine the average bulk modulus based on a pre-constructed curve showing the relationship between the ratio of average bulk modulus to matrix bulk modulus as a function of effective pressure and the matrix bulk modulus.

[0088] In some embodiments, the second determining module 30 is further configured to determine the second bulk modulus using the following formula: ,in, The second bulk modulus, The first bulk modulus, The porosity of the medium. For fluid bulk modulus, The bulk modulus of the matrix is... The average bulk modulus is given.

[0089] In some embodiments, the third determining module 40 is further configured to determine a first vertical stiffness coefficient when the medium contains the fluid, based on the first property data; and to determine a second vertical stiffness coefficient based on the first property data, the average bulk modulus, the first bulk modulus, the second bulk modulus, and the first vertical stiffness coefficient.

[0090] In some embodiments, the third determining module 40 is further configured to determine the second vertical stiffness coefficient using the following formula: ,in, This is the second vertical stiffness coefficient. This is the first vertical stiffness coefficient. The first bulk modulus, The second bulk modulus, A parameter describing the degree to which the phase velocity of a longitudinal wave propagating near the axis of symmetry changes with the phase angle. The average bulk modulus is given.

[0091] In some embodiments, the fourth determining module 50 is further configured to: determine a third bulk modulus when the predetermined replacement fluid is contained in the medium, based on the first property data, the average bulk modulus, the second bulk modulus, and the second property data; determine a third vertical stiffness coefficient when the predetermined replacement fluid is contained in the medium, based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, the second property data, and the third bulk modulus; and determine the longitudinal wave velocity based on the second property data and the third vertical stiffness coefficient.

[0092] In some embodiments, the fourth determining module 50 is further configured to determine the third vertical stiffness coefficient using the following formula: ,in, The third vertical stiffness coefficient, This is the second vertical stiffness coefficient. The third bulk modulus, The second bulk modulus, A parameter describing the degree to which the phase velocity of a longitudinal wave propagating near the axis of symmetry changes with the phase angle. The average bulk modulus is given.

[0093] For ease of description, the above devices are described in terms of function, divided into various modules. Of course, in implementing this application, the functions of each module can be implemented in one or more software and / or hardware.

[0094] The apparatus of the above embodiments is used to implement the longitudinal wave velocity determination method for fluid replacement in the corresponding anisotropic medium in any of the foregoing embodiments, and has the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0095] Based on the same inventive concept, corresponding to the methods of any of the above embodiments, this application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the method for determining the longitudinal wave velocity of fluid replacement in anisotropic media as described in any of the above embodiments.

[0096] Figure 8 This embodiment illustrates a more specific hardware structure of an electronic device. The device may include a processor 1010, a memory 1020, an input / output interface 1030, a communication interface 1040, and a bus 1050. The processor 1010, memory 1020, input / output interface 1030, and communication interface 1040 are interconnected internally via the bus 1050.

[0097] The processor 1010 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this specification.

[0098] The memory 1020 can be implemented in the form of ROM (Read Only Memory), RAM (Random Access Memory), static storage device, dynamic storage device, etc. The memory 1020 can store the operating system and other applications. When the technical solutions provided in the embodiments of this specification are implemented by software or firmware, the relevant program code is stored in the memory 1020 and is called and executed by the processor 1010.

[0099] The input / output interface 1030 is used to connect input / output modules to realize information input and output. The input / output modules can be configured as components in the device (not shown in the figure) or externally connected to the device to provide corresponding functions. Input devices may include keyboards, mice, touch screens, microphones, various sensors, etc., and output devices may include displays, speakers, vibrators, indicator lights, etc.

[0100] The communication interface 1040 is used to connect a communication module (not shown in the figure) to enable communication between this device and other devices. The communication module can communicate via wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0101] Bus 1050 includes a pathway for transmitting information between various components of the device, such as processor 1010, memory 1020, input / output interface 1030, and communication interface 1040.

[0102] It should be noted that although the above-described device only shows the processor 1010, memory 1020, input / output interface 1030, communication interface 1040, and bus 1050, in specific implementations, the device may also include other components necessary for normal operation. Furthermore, those skilled in the art will understand that the above-described device may only include the components necessary for implementing the embodiments of this specification, and not necessarily all the components shown in the figures.

[0103] The electronic device described in the above embodiments is used to implement the longitudinal wave velocity determination method for fluid replacement in the corresponding anisotropic medium in any of the foregoing embodiments, and has the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0104] Based on the same inventive concept, corresponding to the methods of any of the above embodiments, this application also provides a non-transitory computer-readable storage medium storing computer instructions for causing the computer to execute the longitudinal wave velocity determination method for fluid replacement in anisotropic media as described in any of the above embodiments.

[0105] The computer-readable medium of this embodiment includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. Information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transfer medium that can be used to store information accessible by a computing device.

[0106] The computer instructions stored in the storage medium of the above embodiments are used to cause the computer to execute the longitudinal wave velocity determination method for fluid replacement in anisotropic media as described in any of the above embodiments, and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0107] Based on the same concept, corresponding to the methods of any of the above embodiments, this application also provides a computer program product, including computer program instructions, which, when the computer program instructions are run on a computer, cause the computer to execute the longitudinal wave velocity determination method for fluid replacement in anisotropic media as described in any of the above embodiments, and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0108] It is understood that before using the technical solutions of the various embodiments in this disclosure, users will be informed of the type, scope of use, and usage scenarios of the personal information involved in an appropriate manner, and user authorization will be obtained.

[0109] For example, upon receiving a user's active request, a prompt message is sent to the user to explicitly inform them that the requested operation will require the acquisition and use of the user's personal information. This allows the user to independently choose, based on the prompt message, whether to provide personal information to the software or hardware such as electronic devices, applications, servers, or storage media performing the operations of this disclosed technical solution.

[0110] As an optional but not limited implementation, in response to a user's active request, sending a prompt message to the user can be done via a pop-up window, where the prompt message can be presented in text format. Furthermore, the pop-up window can also include a selection control allowing the user to choose "agree" or "disagree" to provide personal information to the electronic device.

[0111] It is understood that the above notification and user authorization process are merely illustrative and do not constitute a limitation on the implementation of this disclosure. Other methods that comply with relevant laws and regulations may also be applied to the implementation of this disclosure.

[0112] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of this application is limited to these examples; under the concept of this application, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of the embodiments of this application as described above, which are not provided in detail for the sake of brevity.

[0113] Additionally, to simplify the description and discussion, and to avoid obscuring the embodiments of this application, the well-known power / ground connections to integrated circuit (IC) chips and other components may or may not be shown in the provided drawings. Furthermore, the apparatus may be shown in block diagram form to avoid obscuring the embodiments of this application, and this also takes into account the fact that the details of the implementation of these block diagram apparatuses are highly dependent on the platform on which the embodiments of this application will be implemented (i.e., these details should be fully understood by those skilled in the art). While specific details (e.g., circuits) have been set forth to describe exemplary embodiments of this application, it will be apparent to those skilled in the art that the embodiments of this application can be implemented without these specific details or with variations thereof. Therefore, these descriptions should be considered illustrative rather than restrictive.

[0114] Although this application has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed.

[0115] The embodiments of this application are intended to cover all such substitutions, modifications, and variations that fall within the broad scope of this application. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the embodiments of this application should be included within the protection scope of this application.

Claims

1. A method for determining the longitudinal wave velocity of fluid displacement in an anisotropic medium, characterized in that, include: Acquire first property data of the medium and matrix bulk modulus, wherein the medium comprises a fluid; Based on the matrix bulk modulus, the average bulk modulus is determined; wherein, the ratio of the average bulk modulus to the matrix bulk modulus is obtained, expressed in formula form as follows: ,in, The average bulk modulus, The bulk modulus of the matrix is... For effective pressure; Based on the first property data, a first bulk modulus is determined when the medium contains the fluid, and based on the first property data, the matrix bulk modulus, the average bulk modulus, and the first bulk modulus, a second bulk modulus is determined when the medium does not contain the fluid. Based on the first property data, the average bulk modulus, the first bulk modulus and the second bulk modulus, a second vertical stiffness coefficient is determined when the medium does not contain the fluid; Acquire second property data for each predetermined replacement fluid. For each predetermined replacement fluid, based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, and the second property data, determine the longitudinal wave velocity after the fluid in the medium is replaced by the predetermined replacement fluid.

2. The method according to claim 1, characterized in that, Determining the average bulk modulus based on the matrix bulk modulus includes: The average bulk modulus is determined based on the pre-constructed curve showing the relationship between the ratio of average bulk modulus to matrix bulk modulus as a function of effective pressure and the matrix bulk modulus.

3. The method according to claim 1, characterized in that, The step of determining the second bulk modulus of the medium when it does not contain the fluid, based on the first property data, the matrix bulk modulus, the average bulk modulus, and the first bulk modulus, includes: The second bulk modulus is determined by the following formula: ， in, The second bulk modulus, The first bulk modulus, The porosity of the medium. For fluid bulk modulus, The bulk modulus of the matrix is... The average bulk modulus is given.

4. The method according to claim 1, characterized in that, The step of determining the second vertical stiffness coefficient of the medium when it does not contain the fluid, based on the first property data, the average bulk modulus, the first bulk modulus, and the second bulk modulus, includes: Based on the first property data, a first vertical stiffness coefficient is determined when the fluid is contained within the medium. Based on the first property data, the average bulk modulus, the first bulk modulus, the second bulk modulus, and the first vertical stiffness coefficient, the second vertical stiffness coefficient is determined.

5. The method according to claim 4, characterized in that, The step of determining the second vertical stiffness coefficient based on the first property data, the average bulk modulus, the first bulk modulus, the second bulk modulus, and the first vertical stiffness coefficient includes: The second vertical stiffness coefficient is determined by the following formula: ， in, This is the second vertical stiffness coefficient. This is the first vertical stiffness coefficient. The first bulk modulus, The second bulk modulus, A parameter describing the degree to which the phase velocity of a longitudinal wave propagating near the axis of symmetry changes with the phase angle. The average bulk modulus is given.

6. The method according to claim 1, characterized in that, The step of determining the longitudinal wave velocity after replacing the fluid in the medium with the predetermined replacement fluid, based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, and the second property data, includes: Based on the first property data, the average bulk modulus, the second bulk modulus, and the second property data, a third bulk modulus is determined when the medium contains the predetermined replacement fluid; Based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, the second property data, and the third bulk modulus, a third vertical stiffness coefficient is determined when the medium contains the predetermined replacement fluid. Based on the second property data and the third vertical stiffness coefficient, the longitudinal wave velocity is determined.

7. The method according to claim 6, characterized in that, The step of determining the third vertical stiffness coefficient when the medium contains the predetermined replacement fluid, based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, the second property data, and the third bulk modulus, includes: The third vertical stiffness coefficient is determined using the following formula: ， in, The third vertical stiffness coefficient, This is the second vertical stiffness coefficient. The third bulk modulus, The second bulk modulus, A parameter describing the degree to which the phase velocity of a longitudinal wave propagating near the axis of symmetry changes with the phase angle. The average bulk modulus is given.

8. A device for determining the longitudinal wave velocity of fluid displacement in an anisotropic medium, characterized in that, include: The acquisition module is configured to acquire first property data of the medium and matrix bulk modulus, wherein the medium comprises a fluid; The first determining module is configured to determine the average bulk modulus based on the matrix bulk modulus; wherein the ratio of the average bulk modulus to the matrix bulk modulus is expressed in formula form as follows: ,in, The average bulk modulus, The bulk modulus of the matrix is... For effective pressure; The second determining module is configured to determine, based on the first property data, a first bulk modulus when the medium contains the fluid, and, based on the first property data, the matrix bulk modulus, the average bulk modulus, and the first bulk modulus, a second bulk modulus when the medium does not contain the fluid. The third determining module is configured to determine a second vertical stiffness coefficient when the medium does not contain the fluid, based on the first property data, the average bulk modulus, the first bulk modulus, and the second bulk modulus. The fourth determining module is configured to acquire second property data for each predetermined replacement fluid, and for each predetermined replacement fluid, based on the first property data, the average bulk modulus, the second bulk modulus, the second vertical stiffness coefficient, and the second property data, determine the longitudinal wave velocity in the medium after the fluid is replaced by the predetermined replacement fluid.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium storing computer instructions, characterized in that, The computer instructions are used to cause the computer to perform the method described in any one of claims 1 to 7.

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