A method for inverting rock thermal fracture evolution parameters and constructing anisotropic velocities

Abstract

This invention belongs to the field of rock physics and geophysical exploration, specifically relating to a method for inverting rock thermal fracture evolution parameters and constructing anisotropic velocities. The method includes: obtaining the thermal fracture porosity caused by temperature rise within a preset temperature range and the P-wave and S-wave velocities of the medium before and after thermal fracture formation using a THM model; based on a DEM model, equating the wave velocity response of the thermal fracture medium to the wave velocity response of oriented fractures in a background isotropic environment, constructing an inversion process with minimizing velocity error as the objective function, and solving for the equivalent fracture parameters; establishing a functional mapping relationship between thermal fracture porosity and equivalent fracture parameters, constructing a transversely anisotropic equivalent medium, and obtaining independent anisotropic velocities; further, introducing the directional characterization of the background pore structure into the base medium to form an equivalent medium model of background TI and directional superposition of fractures, and then calculating the anisotropic velocities and their evolution with temperature.

Description

Technical Field

[0001] This invention belongs to the field of rock physics and geophysical exploration, and specifically relates to a method for inverting thermal fracture evolution parameters and constructing anisotropic velocities. Background Technology

[0002] In applications such as geothermal energy development, deep underground engineering, and high-temperature geological environment monitoring, the elastic parameters and seismic wave propagation characteristics of the medium change with temperature under the combined influence of temperature field, pore fluid action, and stress state. Increased temperature often induces thermal damage, accompanied by the generation and evolution of microcracks or thermal cracks, thereby causing changes in P-wave and S-wave velocities and alterations in wave velocity anisotropy. Therefore, it is necessary to propose a method that can invert equivalent crack parameters and construct anisotropic velocities under temperature conditions to more accurately characterize the impact of thermal damage on wave velocity response.

[0003] Numerous studies have shown that the elastic properties and wave velocity response of rocks undergo systematic changes under increasing temperature conditions. The overall trend is as follows: with increasing temperature, both P-wave and S-wave velocities typically show a significant decreasing trend, and the magnitude of these changes may vary across different temperature ranges. When temperature induces thermal damage and generates microcracks or thermal cracks, the medium stiffness decreases, accompanied by pore structure reconstruction, leading to further changes in the wave velocity response. Related research generally considers that temperature-induced crack generation and propagation are one of the important factors controlling changes in medium velocity, and their impact is not only reflected in changes in isotropic velocities but may also be reflected in anisotropic wave velocity responses. To describe the above processes, the thermo-hydraulic-mechanical coupling model (THM) is widely used to characterize the coupling mechanism between the temperature field, pore fluid action, and mechanical response, and can be used to obtain the P-wave and S-wave velocity responses under different temperature conditions, thus providing a basis for understanding the influence of thermal cracks on the acoustic response of the medium.

[0004] However, relying solely on temperature-dependent P-wave and S-wave velocity outputs is often insufficient to directly characterize the geometric and structural information of thermal cracks and the impact of their variations (crack number, geometry) on the acoustic response of rocks. Furthermore, in engineering interpretation and monitoring applications, it is typically necessary to construct a multi-directional wave velocity set under transversely isotropic media to quantitatively characterize crack orientation effects and anisotropic responses. Against this backdrop, the differential equivalent medium model (DEM) provides an effective approach for constructing multi-directional wave velocities. Given parameters such as background medium stiffness, crack inclusion phase stiffness, crack volume fraction, shape, and orientation, this method can calculate the equivalent stiffness of the cracked medium and further obtain multi-directional P-wave and S-wave velocities, thus yielding a complete velocity set of the equivalent medium.

[0005] Although the THM model and the anisotropic DEM method have clear advantages in describing multi-field coupled processes and constructing anisotropic velocities, respectively, existing results still have shortcomings in the quantitative inversion of hot crack evolution parameters and the construction of anisotropic velocities, as follows:

[0006] On the one hand, the THM model focuses on the thermo-fluid-solid coupling process and its macroscopic velocity response output. It usually lacks a general channel to further parameterize the temperature-induced crack effect into equivalent parameters of directional cracks (such as crack porosity and aspect ratio), making it difficult to directly support subsequent anisotropic equivalent medium modeling.

[0007] On the other hand, anisotropic DEMs require parameters such as crack volume fraction, shape and orientation as inputs when constructing transversely isotropic medium wave velocity sets. These parameters are difficult to obtain directly from finite velocity information in temperature-induced thermal crack scenarios.

[0008] Overall, there is currently a lack of a method that can establish a mapping relationship between the temperature-related velocity response obtained by THM and the crack equivalent parameters required by DEM within a unified framework, so that the thermal crack pore information can be transformed into directional crack parameters that can be used to construct anisotropic equivalent media, and further extended to the case of TI background and directional crack superposition considering the influence of background pore structure, thereby realizing the synchronous construction of crack evolution parameter inversion and anisotropic velocity. Summary of the Invention

[0009] This invention overcomes the above-mentioned defects and provides a method for inverting thermal crack evolution parameters and constructing anisotropic velocities, which solves the problem that it is difficult to simultaneously construct crack evolution parameter inversion and anisotropic velocities in the prior art.

[0010] To achieve the above objectives, the present invention provides a method for inverting hot crack evolution parameters and constructing anisotropic velocities, comprising the following steps:

[0011] S1. In an isotropic background, the porosity of the thermal crack and the longitudinal and transverse wave velocities of the thermal crack medium caused by temperature rise within a preset temperature range are obtained by the THM model.

[0012] S2. Based on the isotropic DEM model, the P-wave and S-wave velocities of the thermal fracture medium are equivalent to the P-wave and S-wave velocities of the equivalent medium with directional fractures in an isotropic background. Combined with the P-wave and S-wave velocities of the thermal fracture medium, an inversion process with the minimization of velocity error as the objective function is constructed to solve for the equivalent directional fracture porosity and fracture aspect ratio.

[0013] S3. Establish the functional mapping relationship between the thermal crack porosity and the equivalent directional crack porosity and crack aspect ratio;

[0014] S4. Based on the function mapping relationship and the equivalent directional fracture porosity and fracture aspect ratio, construct a transversely anisotropic equivalent medium and calculate the independent anisotropic velocity.

[0015] Furthermore, the implementation process of step S1 is as follows:

[0016] Under S11 standard conditions, the initial porosity of the hot crack is estimated from two-dimensional measurement data, using the following formula:

[0017] ,

[0018] in, Indicates the average width of the pores. Indicates the length of the pore. Indicates the areal density of pores;

[0019] S12 is obtained through normalization coefficients. By fitting the measured data of rock thermal fractures, an empirical relationship between thermal fracture porosity and temperature was obtained:

[0020] ,

[0021] in, Where T represents the porosity of the thermal crack, and T is the temperature.

[0022] S13 constructs the THM coupling equations and uses the plane wave analysis method to solve for the complex phase velocities corresponding to different wave modes, thereby obtaining the P-wave and S-wave velocities of the hot crack medium:

[0023] ,

[0024] in, For the longitudinal wave velocity, The root of the complex phase velocity corresponding to the longitudinal wave mode. For transverse wave velocity, This is the root of the complex phase velocity corresponding to the transverse wave mode.

[0025] Furthermore, the equivalent medium longitudinal and transverse wave velocities are obtained based on the DEM model by adding ellipsoidal crack inclusions to an isotropic background medium.

[0026] Furthermore, in step S2, the inversion process formula is as follows:

[0027] ,

[0028] in, The aspect ratio of the equivalent directional crack is... For equivalent directional crack porosity, These represent the longitudinal and transverse wave velocities of the hot fracture medium, respectively. These are the longitudinal and transverse wave velocities of the equivalent medium, respectively.

[0029] Furthermore, the function mapping relationship reflects the variation of equivalent directional crack porosity and equivalent directional crack aspect ratio with thermal crack porosity at different temperatures, and establishes a calculable function mapping between thermal crack porosity and equivalent directional crack porosity and equivalent directional crack aspect ratio.

[0030] Furthermore, step S4 is implemented as follows:

[0031] S401 determines the stiffness tensor of the background medium without cracks. ,

[0032] ,

[0033] in, For the longitudinal wave velocity, For transverse wave velocity, Indicates the density of the background medium. is the first Lamé constant, a constant describing the stress-strain relationship of a material under volumetric deformation. Let be the second Lamé constant, describing the material's resistance to shear deformation, then the stiffness tensor of the background medium is... Represented as:

[0034] ;

[0035] After S402 develops cracks due to temperature increase, the Lamé constant is expressed using the bulk modulus and shear modulus of the inclusions in the cracks, as shown in the following formula:

[0036] ,

[0037] in, Indicates bulk modulus, Indicates shear modulus;

[0038] Then the stiffness tensor of the fracture inclusion phase as follows:

[0039] ;

[0040] S403 uses an anisotropic DEM model to construct the coupling effect equation between the background medium and the crack inclusions, and obtains the equivalent stiffness of the crack-introduced medium. , means as follows:

[0041] ,

[0042] in, The aspect ratio of the equivalent crack is given. For equivalent crack porosity, This represents the iterative function for an anisotropic DEM model;

[0043] S404, and utilizes equivalent medium stiffness Calculate independent anisotropic velocities in an isotropic background:

[0044] ,

[0045] in, For quasi-longitudinal wave velocity, For horizontal shear wave velocity, This represents the angle between the propagation direction and the axis of symmetry of the medium. It is equivalent stiffness The component represents the elastic constant of the medium. Represents the equivalent medium density. Indicating quasi-longitudinal waves in The intrinsic stiffness term corresponding to the direction.

[0046] Furthermore, another implementation of step S4 is as follows:

[0047] S411 characterizes the stiffness of the matrix phase in the background medium at standard temperature, denoted as... ,

[0048] ,

[0049] in, Indicates the bulk modulus of the matrix phase. The shear modulus of the matrix phase;

[0050] S412 orients the rigid porous inclusion phases in the background medium and uses an anisotropic DEM model to construct the equivalent stiffness of the medium when the background is anisotropic. , means as follows:

[0051] ,

[0052] in, Indicates the stiffness of the rigid porous inclusion phase. Background porosity, The aspect ratio of the rigid porous inclusion phase in the background medium is given. This represents the iterative function for an anisotropic DEM model;

[0053] S413 Equivalent stiffness of the medium when the background is anisotropic. As the substrate medium stiffness, an anisotropic DEM model is used, with the equivalent directional crack porosity and crack aspect ratio obtained from the inversion in step S3 as crack inclusion phases to calculate the equivalent medium stiffness under anisotropic background and directional crack arrangement. , means as follows:

[0054] ,

[0055] in, The aspect ratio of the equivalent crack is given. For equivalent crack porosity, This represents the iterative function for an anisotropic DEM model;

[0056] S414 utilizes equivalent medium stiffness Calculate independent anisotropic velocities in anisotropic backgrounds:

[0057] ,

[0058] in, For quasi-longitudinal wave velocity, For horizontal shear wave velocity, This represents the angle between the propagation direction and the axis of symmetry of the medium. For equivalent stiffness The component represents the elastic constant of the medium. Represents the equivalent medium density. Indicating quasi-longitudinal waves in The intrinsic stiffness term corresponding to the direction.

[0059] Furthermore, the independent anisotropic velocities at least include , , , , Five independent anisotropic velocities.

[0060] Compared with the prior art, the advantages of the present invention are as follows:

[0061] This application realizes the quantitative inversion of thermal crack evolution parameters and the construction of anisotropic velocity sets under temperature effects, and improves the computational technology route from thermally induced damage response to crack equivalent parameter characterization and TI medium velocity construction, providing a reliable methodological basis for the quantitative interpretation of thermal damage and crack anisotropic response.

[0062] This application enables extended calculations from equivalent isotropic velocities to anisotropic velocities in TI media under finite velocity information constraints, establishing a functional mapping relationship between thermal crack porosity and equivalent crack parameters. The resulting velocity set can be verified for consistency with existing numerical calculations or experimental results, and the calculation path is clear with strong parameter interpretability.

[0063] The modeling method presented in this application has clear physical meaning of parameters, strong scalability, and is easy to compare and verify with experimental or numerical results. It can construct five anisotropic velocities under background isotropic and directional fracture systems, and can also be extended to the more general case of "background TI medium + directional fracture superposition" by directionalizing the background pore structure. This provides a theoretical basis for the characterization of fracture structure and anisotropic interpretation of high-temperature rock masses, and is of great significance for improving geophysical monitoring and engineering evaluation under temperature-induced scenarios. Attached Figure Description

[0064] Figure 1 The diagram shows the equivalent crack parameter inversion fitting and the comparison of P-wave and S-wave velocities. (a) shows the equivalent crack parameters obtained after random thermal crack orientation, and (b) shows the comparison between the equivalent P-wave and S-wave velocities calculated based on the DEM model using the equivalent crack parameters and the P-wave and S-wave velocities obtained by the THM model.

[0065] Figure 2 Five independent velocities of a transversely isotropic medium formed after random thermal cracks are oriented. (a) represents the anisotropic longitudinal wave velocity of the transversely isotropic medium, and (b) represents the anisotropic transverse wave velocity of the transversely isotropic medium. The solid line represents the velocity response of the isotropic background medium superimposed with oriented cracks, and the dashed line represents the velocity response of the TI background medium superimposed with oriented cracks. Detailed Implementation

[0066] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0067] Example 1:

[0068] like Figures 1 to 2 As shown in the figure, this invention proposes a method for inverting rock thermal fracture evolution parameters and constructing anisotropic velocities, specifically including:

[0069] Assuming the granite medium develops thermal cracks when heated, with a temperature range of 20℃-200℃, what is the background porosity of the granite at 20℃? (This can be directly measured in the laboratory using a porosity-permeability measuring instrument.) As temperature increases, the porosity of thermal cracks generated inside the granite becomes... To achieve a quantitative characterization of the relationship between the evolution of thermal cracks and wave velocity anisotropy, and to complete the anisotropic velocity set including five independent velocities under the constraint of limited velocity information, so as to more accurately characterize the influence of thermal damage on wave velocity response.

[0070] Step 1: In an isotropic background, the porosity of thermal cracks caused by temperature rise within a preset temperature range and the longitudinal and transverse wave velocities of the medium before and after the generation of thermal cracks are obtained by the THM model.

[0071] Based on the isotropic assumption, the initial porosity of hot cracks under standard conditions (20 °C) can be estimated from two-dimensional measurement data, using the following formula.

[0072] ,

[0073] in, , and These represent the average width, length, and areal density of the pores contained within the medium under standard conditions, respectively. In this embodiment... .

[0074] Based on Homand-Etienne F., Houpert R., 1989. Thermally induced microcracking in granites: Characterization and analysis [J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 26: 125–134., the proposed granite normalization coefficient... By fitting the measured data of thermal cracks generated in granite under heat, an empirical relationship between thermal crack porosity and temperature was obtained. The calculation formula is as follows:

[0075] ,

[0076] in, The porosity of the thermal cracks generated during the heating process is represented by T, where T is the temperature. The initial porosity of thermal cracks in granite under standard conditions.

[0077] Meanwhile, based on the THM model proposed by Li N., Fu L.-Y., Deng W., José M. Carcione, Yang J., 2023. A thermo-hydro-mechanical model to evaluate the seismic properties of geothermal reservoirs[J]. Geophysics, 88(5): WB23–WB35. (Li Nianqi, Fu Liyun, Deng Wubing, José M. Carcione, Yang Jian, 2023. A thermo-hydro-mechanical model to evaluate the seismic properties of geothermal reservoirs[J]. Geophysics, 88(5): WB23–WB35.), under the given temperature conditions, pore fluid properties, and rock skeleton parameters, the plane wave analysis method is used to solve the wave response of the medium. Specifically, a plane wave form solution is introduced into the THM coupled control equations, and variables such as the displacement field, pore fluid response, and temperature perturbation are expressed in the form of harmonics with the same propagation direction and frequency, so as to transform the control equations into algebraic equations or characteristic equations about the complex phase velocity. By solving, the complex phase velocity corresponding to different wave modes is obtained, and the phase velocity is determined according to the real part of the complex slowness, and the longitudinal wave velocity and transverse wave velocity of randomly distributed thermal fractures under the said temperature conditions (20 °C - 200 °C) are obtained:

[0078]

[0079] Among them, is the longitudinal wave velocity, is the root of the complex phase velocity corresponding to the longitudinal wave mode, is the transverse wave velocity, is the root of the complex phase velocity corresponding to the transverse wave mode.

[0080] Step 2: Based on the isotropic DEM model, the longitudinal and transverse wave velocities of the randomly distributed thermal fracture medium are equivalent to the longitudinal and transverse wave velocities of the equivalent medium with oriented fractures in the isotropic background, and an inversion process with the goal of minimizing the velocity error is constructed by combining the longitudinal and transverse wave velocities of the thermal fracture medium, so as to equivalent the thermal fracture effect into the effect of oriented fractures, and solve the equivalent oriented fracture porosity and fracture aspect ratio.

[0081] Specifically, the embodiment of the present invention is based on an isotropic background medium, and an ellipsoidal crack inclusion corresponding to the geometric shape of the thermal crack is introduced therein , and based on the isotropic DEM model, the longitudinal wave velocity and transverse wave velocity Based on the P- and S-wave velocities of hot cracks and the equivalent medium, an inversion process is constructed using an isotropic DEM model with the objective function of minimizing velocity error. The hot crack effect is equivalent to a directionally aligned crack effect, as shown in the following formula:

[0082] ,

[0083] in, The aspect ratio of the equivalent crack is given. These are equivalent crack porosity, and The equivalent longitudinal wave velocity and transverse wave velocity were obtained by adding ellipsoidal crack inclusions to an isotropic background medium based on an isotropic DEM model.

[0084] Step 3: Establish the functional mapping relationship between thermal crack porosity, equivalent crack porosity, and equivalent crack aspect ratio.

[0085] Specifically, within a preset temperature range, firstly, based on the empirical formula relating thermal crack porosity to temperature, the thermal crack porosity values ​​at different temperatures are calculated. Simultaneously, the equivalent crack porosity and equivalent crack aspect ratio at different temperatures are obtained through DEM model inversion. The thermal crack porosity values ​​at the same temperature correspond one-to-one with the equivalent crack porosity and equivalent crack aspect ratio, thus generating curves showing the changes in equivalent crack porosity and equivalent crack aspect ratio with the thermal crack porosity value. Temperature, as an implicit function, participates in the construction of the function mapping relationship. The function characteristics used are determined based on the curves, thereby establishing the function mapping relationship between thermal crack porosity and equivalent crack porosity and equivalent crack aspect ratio.

[0086] In this embodiment of the invention, within a temperature range of 20-200℃, with temperature intervals of 10℃, the thermal crack porosity, equivalent directional crack porosity, and crack aspect ratio were calculated at 19 temperature points. Analysis of the data patterns shows that the relationship between thermal crack porosity, equivalent directional crack porosity, and crack aspect ratio more closely conforms to an exponential function. Therefore, in this embodiment, the thermal crack porosity... and the equivalent fracture porosity obtained by inversion and equivalent crack aspect ratio The established mapping expressions are as follows:

[0087] ,

[0088] ,

[0089] in, This indicates the goodness of fit; T represents the temperature.

[0090] like Figure 1As shown in (b), by directional equivalence processing of randomly distributed thermally induced cracks, corresponding equivalent crack parameters were obtained, namely equivalent crack aspect ratio and equivalent crack porosity. Based on the equivalent crack parameters, the equivalent P-wave and S-wave velocities calculated using the DEM model are in good agreement with the results obtained from the THM model. This consistency verifies the reliability and accuracy of the inverted crack parameters, indicating that the inverted parameters can effectively characterize the influence of the directional arrangement of thermally induced cracks on the wave velocity. During the heating process, as... Figure 1 As shown in (a), with the increase of thermally induced crack porosity, the equivalent crack porosity also shows an upward trend; while the equivalent crack aspect ratio first increases and then decreases. This result indicates that when the thermal crack effect is equivalent to the oriented crack parameters, the oriented crack porosity increases with the increase of temperature; the evolution law of the crack aspect ratio first increasing and then decreasing reflects that the crack aperture first increases, and then as the temperature continues to rise, the radial propagation effect of the crack gradually strengthens, thus leading to a decrease in the crack aspect ratio.

[0091] The function mapping relationship constructed in this invention plays a key "bridge" role between the THM model and the DEM model. After measuring the porosity of the thermal crack, the equivalent crack porosity and the equivalent crack aspect ratio can be calculated through this function mapping relationship. Then, the equivalent crack porosity and the equivalent crack aspect ratio are substituted into the DEM model to transfer the anisotropic velocity that cannot be calculated using the THM model to the DEM for calculation. Moreover, the influence of the equivalent crack porosity and the equivalent crack aspect ratio on the anisotropic velocity is consistent with the influence of the thermal crack on the anisotropic velocity. Therefore, the anisotropic velocity calculated in the DEM is essentially the change in the anisotropic velocity of the medium caused by the thermal crack.

[0092] Step 4: Based on the above function mapping relationship and the inverted directional fracture porosity and fracture aspect ratio, construct the equation of the coupling effect between the background medium and the fracture inclusion phase through an anisotropic DEM model.

[0093] Specifically, based on the equivalent crack parameters obtained by inversion Using the anisotropic DEM model proposed by Nishizawa O., 1982. Seismic velocity anisotropy in a medium containing oriented cracks transversely isotropic case[J]. Journal of Physics of the Earth, 30(4): 331–347. (Nishizawa O., 1982. Seismic velocity anisotropy in a medium containing oriented cracks transversely isotropic case[J]. Journal of Geophysics, 30(4): 331–347.), the equivalent stiffness of the overall medium introduced by the cracks is obtained by constructing the equation of the coupling effect between the background medium and the crack inclusion. The details are as follows:

[0094] (1) Determine the stiffness tensor of the intact medium (background medium) without cracks. Among them, the longitudinal and transverse wave velocities and medium density of the medium before crack formation. The calculation formula between them is as follows:

[0095] ,

[0096] in, For the longitudinal wave velocity, For transverse wave velocity, Indicates the density of the medium. is the first Lamé constant, a constant describing the stress-strain relationship of a material under volumetric deformation. This is the second Lamé constant, which describes the material's ability to resist shear deformation.

[0097] Therefore, the stiffness tensor of the background medium It can be represented as:

[0098] ;

[0099] (2) Crack inclusions are introduced into the isotropic background medium. The bulk modulus and shear model of the introduced crack inclusion phases are respectively... , (Both are inherent properties of the introduced crack inclusions, used to characterize the volumetric compressibility and shear deformation capacity of the crack inclusions), then the Lamé constant is expressed as:

[0100] , ,

[0101] Then, the stiffness tensor of the introduced crack inclusion phase The formula is as follows:

[0102] ,

[0103] In actual reservoirs, fracture cavities are typically filled with fluids such as oil or water. However, assuming fractures are cavities in research scenarios deviates significantly from engineering realities. In this embodiment of the invention, water is used as the saturated fluid to fill the fracture cavities, thus increasing the bulk modulus. shear modulus At this point, the P-wave and S-wave velocities of the isotropic granite medium containing random thermal cracks have been calculated using the THM model:

[0104] ,

[0105] Rock skeleton density Then the bulk modulus The Batzle-Wang formula, proposed by Batzle M., Wang ZJ, 1992. Seismic properties of pore fluids[J]. Geophysics, 57(11): 1396–1408. (Batzle M., Wang ZJ, 1992. Seismic properties of porosity fluids[J]. Geophysics, 57(11):1396–1408.), is given as follows:

[0106] ,

[0107] in, This indicates the velocity (km / s) of the saturated fluid. The density of a saturated fluid (g / cm³) 3 The calculations for both are as follows:

[0108] ,

[0109] ,

[0110] in, S represents the velocity of sound waves in water, S represents the mineralization, T represents the ambient temperature of the saturated fluid, and P represents the pore pressure. Indicates the density of water;

[0111] ,

[0112] in, for The coefficient matrix of the bivariate polynomial expansion is used to characterize the effects of temperature and pressure on the acoustic velocity of pure water, and its specific values ​​are shown below.

[0113] ,

[0114] Based on the bulk modulus of water and shear modulus Lamé constant can then be obtained, thereby yielding the stiffness tensor of the fracture inclusion phase when water is the saturated fluid. .

[0115] (3) Obtain the stiffness tensor of the background medium. and the stiffness of the crack inclusion phase Then, the equivalent stiffness of the medium was obtained iteratively using the anisotropic DEM model proposed by Nishizawa. The iterative formula is as follows:

[0116] ,

[0117] in, Represents the equivalent crack aspect ratio. F represents the equivalent crack porosity, and F(·) represents the iterative function of the anisotropic DEM model, which describes the evolution of the equivalent stiffness after gradually introducing crack inclusions into the background medium. It decomposes the equivalent crack porosity into small step sizes, iteratively updates the equivalent stiffness of the medium, and continues until the results converge, thus obtaining the final equivalent stiffness. .

[0118] equivalent stiffness The different components represent the elastic properties of the background and fractured medium, utilizing... The independent anisotropic velocities are calculated by inputting different components into the Christoffel equation, and the calculation formula is as follows:

[0119] ,

[0120] in, For quasi-longitudinal wave velocity, For horizontal shear wave velocity, This represents the angle between the propagation direction and the axis of symmetry of the medium. It is equivalent stiffness The component represents the elastic constant of the medium. Represents the equivalent medium density. Indicating quasi-longitudinal waves in The intrinsic stiffness term corresponding to the direction.

[0121] ,

[0122] ,

[0123] ,

[0124] ,

[0125] ,

[0126] in, , , It is an intermediate function defined to simplify the equations; its essence is the elastic constant in different directions. From the perspective of dissemination The weighted combination of mineral particle density in the equivalent medium kg / m 3 Volume fraction , This represents the temperature-dependent porosity of the directional fractures obtained through inversion. Based on the above formulas and parameters, the equivalent medium under an isotropic background with superimposed directional fractures can finally be obtained. Five independent anisotropic velocity sets.

[0127] Example 2: In Example 1, the independent anisotropic velocities under an isotropic background have been calculated. Further, the directional characterization of the background pore structure can be introduced into the substrate medium to form an equivalent medium model of anisotropic background and crack directional superposition. Then, the independent anisotropic velocities under anisotropic background and their evolution law with temperature can be calculated, thereby realizing the quantitative inversion of thermal crack evolution parameters, the construction of anisotropic velocities, and the revelation of the coupling relationship between equivalent crack parameters and wave velocity anisotropy.

[0128] Specifically, the background medium is composed of mineral particles and rigid porous inclusions. In this embodiment of the invention, the bulk modulus of the mineral particles is expressed as... The shear modulus is expressed as The background porosity of granite measured at standard temperature (20℃) is denoted as . The aspect ratio of the rigid porous inclusion phase is ,

[0129] (1) The stiffness of the matrix phase (i.e., the mineral grain composition phase) in the background medium is characterized, denoted as , means as follows:

[0130] ,

[0131] (2) The rigid porous inclusion phases in the background medium are oriented and arranged. Using an anisotropic DEM model, the equivalent stiffness of the medium when the background is anisotropic is obtained. , means as follows:

[0132] ,

[0133] in, Represents the stiffness of rigid porous inclusions. Background porosity, The aspect ratio of the rigid porous inclusion phase in the background medium is given by F(·), which represents the iterative function of the anisotropic DEM model. In Example 2, water was also used as the saturated fluid for filling. ;

[0134] (3) with As the stiffness of the substrate medium, the equivalent crack porosity obtained by inversion in step two above is used. and the aspect ratio of the crack As a superposition of fracture inclusions, the equivalent stiffness of the medium with background anisotropy and directional fracture alignment is obtained through calculation. ,

[0135] ;

[0136] In this embodiment, water is still used as the saturated fluid for the cracks, therefore ;

[0137] (4) Equivalent stiffness By inputting the components into the Christoffel equation, the independent anisotropic velocities in an anisotropic background can be calculated:

[0138] ,

[0139] in, For quasi-longitudinal wave velocity, For horizontal shear wave velocity, This represents the angle between the propagation direction and the axis of symmetry of the medium. For equivalent stiffness The component represents the elastic constant of the medium. Represents the equivalent medium density. Indicating quasi-longitudinal waves in The intrinsic stiffness term corresponding to the direction.

[0140] ,

[0141] ,

[0142] ,

[0143] ,

[0144] ,

[0145] in, , , It is an intermediate function defined to simplify the equations; its essence is the elastic constant in different directions. From the perspective of dissemination The weighted combination of mineral particle density in the equivalent medium kg / m 3 Volume fraction , This represents the temperature-dependent porosity of the directional fractures obtained through inversion. Based on the above formulas and parameters, the equivalent medium under an anisotropic background with superimposed directional fractures can finally be obtained. Five independent anisotropic velocity sets.

[0146] like Figure 2 As shown, five independent velocities exist in a transversely isotropic medium formed after random thermal cracks are oriented. The left figure (a) shows the anisotropic P-wave velocity in the transversely isotropic medium; the solid line represents the P-wave velocity response of a directional crack superimposed on an isotropic background, and the dashed line represents the P-wave velocity response of a directional crack superimposed on a TI background. The right figure (b) shows the anisotropic S-wave velocity in the transversely isotropic medium; the solid line represents the S-wave velocity response of a directional crack superimposed on an isotropic background, and the dashed line represents the S-wave velocity response of a directional crack superimposed on a TI background.

[0147] The embodiments of the present invention described above do not constitute a limitation on the scope of protection of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for inverting rock thermal fracture evolution parameters and constructing anisotropic velocities, characterized in that, Includes the following steps: S1. In an isotropic background, the porosity of the thermal crack and the longitudinal and transverse wave velocities of the thermal crack medium caused by temperature rise within a preset temperature range are obtained by the THM model. Under S11 standard conditions, the initial porosity of the hot crack is estimated from two-dimensional measurement data, using the following formula: ， in, Indicates the average width of the pores. Indicates the length of the pore. Indicates the areal density of pores; S12 is obtained through normalization coefficients. By fitting the measured data of rock thermal fractures, an empirical relationship between thermal fracture porosity and temperature was obtained: ， in, Where T represents the porosity of the thermal crack, and T is the temperature. S13 constructs the THM coupling equations and uses the plane wave analysis method to solve for the complex phase velocities corresponding to different wave modes, thereby obtaining the P-wave and S-wave velocities of the hot crack medium: ， in, For the longitudinal wave velocity, The root of the complex phase velocity corresponding to the longitudinal wave mode. For transverse wave velocity, This is the root of the complex phase velocity corresponding to the transverse wave mode; S2. Based on the isotropic DEM model, the P-wave and S-wave velocities of the thermal fracture medium are equivalent to the equivalent medium P-wave and S-wave velocities of oriented fractures in an isotropic background. Combining the P-wave and S-wave velocities of the thermal fracture medium, an inversion process is constructed with the minimization of velocity error as the objective function to solve for the equivalent oriented fracture porosity and fracture aspect ratio. The equivalent medium P-wave and S-wave velocities are obtained by adding ellipsoidal fracture inclusions to the isotropic background medium based on the DEM model. The inversion process formula is as follows: ， in, The aspect ratio of the equivalent directional crack is... For equivalent directional crack porosity, These represent the longitudinal and transverse wave velocities of the hot fracture medium, respectively. These are the equivalent medium longitudinal and transverse wave velocities, respectively. S3. Establish a functional mapping relationship between the thermal crack porosity and the equivalent directional crack porosity and crack aspect ratio; the functional mapping relationship reflects the variation law of equivalent directional crack porosity and equivalent directional crack aspect ratio with thermal crack porosity at different temperatures, and establish a calculable functional mapping between thermal crack porosity and equivalent directional crack porosity and equivalent directional crack aspect ratio. S4. Based on the function mapping relationship and the equivalent directional fracture porosity and fracture aspect ratio, construct a transversely anisotropic equivalent medium and calculate the independent anisotropic velocity.

2. The method for inverting rock thermal fracture evolution parameters and constructing anisotropic velocities according to claim 1, characterized in that, Step S4 is implemented as follows: S401 determines the stiffness tensor of the background medium without cracks. , ， in, For the longitudinal wave velocity, For transverse wave velocity, Indicates the density of the background medium. is the first Lamé constant, a constant describing the stress-strain relationship of a material under volumetric deformation. Let be the second Lamé constant, describing the material's resistance to shear deformation, then the stiffness tensor of the background medium is... Represented as: ； After S402 develops cracks due to temperature increase, the Lamé constant is expressed using the bulk modulus and shear modulus of the inclusions in the cracks, as shown in the following formula: ， in, Indicates bulk modulus, Indicates shear modulus; Then the stiffness tensor of the fracture inclusion phase as follows: ； S403 uses an anisotropic DEM model to construct the coupling effect equation between the background medium and the crack inclusions, and obtains the equivalent stiffness of the crack-introduced medium. , means as follows: ， in, The aspect ratio of the equivalent crack is given. For equivalent crack porosity, This represents the iterative function for an anisotropic DEM model; S404, and utilizes equivalent medium stiffness Calculate independent anisotropic velocities in an isotropic background: ， in, For quasi-longitudinal wave velocity, For horizontal shear wave velocity, This represents the angle between the propagation direction and the axis of symmetry of the medium. It is equivalent stiffness The component represents the elastic constant of the medium. Represents the equivalent medium density. Indicating quasi-longitudinal waves in The intrinsic stiffness term corresponding to the direction.

3. The method for inverting rock thermal fracture evolution parameters and constructing anisotropic velocities according to claim 1, characterized in that, Another way to implement step S4 is as follows: S411 characterizes the stiffness of the matrix phase in the background medium at standard temperature, denoted as... , ， in, Indicates the bulk modulus of the matrix phase. The shear modulus of the matrix phase; S412 orients the rigid porous inclusion phases in the background medium and uses an anisotropic DEM model to construct the equivalent stiffness of the medium when the background is anisotropic. , means as follows: ， in, Indicates the stiffness of the rigid porous inclusion phase. Background porosity, The aspect ratio of the rigid porous inclusion phase in the background medium is given. This represents the iterative function for an anisotropic DEM model; S413 Equivalent stiffness of the medium when the background is anisotropic. As the stiffness of the substrate medium, an anisotropic DEM model is used. The equivalent directional crack porosity and crack aspect ratio obtained from the inversion in step S2 are used as the superposition of crack inclusions to calculate the equivalent stiffness of the medium under anisotropic background and crack orientation. , means as follows: ， in, The aspect ratio of the equivalent crack is given. For equivalent crack porosity, This represents the iterative function for an anisotropic DEM model; S414 utilizes equivalent medium stiffness Calculate independent anisotropic velocities in anisotropic backgrounds: ， in, For quasi-longitudinal wave velocity, For horizontal shear wave velocity, This represents the angle between the propagation direction and the axis of symmetry of the medium. For equivalent stiffness The component represents the elastic constant of the medium. Represents the equivalent medium density. Indicating quasi-longitudinal waves in The intrinsic stiffness term corresponding to the direction.

4. The method for inverting rock thermal fracture evolution parameters and constructing anisotropic velocities according to claim 2 or 3, characterized in that, The independent anisotropic velocity includes at least the following: , , , , Five independent anisotropic velocities.

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