A creep-considered anisotropic coal rock permeability tensor prediction method

Abstract

The present invention relates to a method for predicting the anisotropic coal rock permeability tensor taking creep into account, comprising the following steps: S1, constructing a strain constitutive equation for the anisotropic coal rock matrix under linear elastic conditions, taking into account the deformation caused by coal rock creep, the desorption expansion effect, and the compression effect of the cleat / bedding aperture, and establishing a nonlinear constitutive equation for the coal rock; S2, establishing a relationship between the permeability ratio and the cleat / bedding aperture based on the cubic law, substituting the nonlinear constitutive relationship into the equation to derive the intrinsic permeability of the coal rock, and introducing the rarefied gas effect to correct the flow state; coupling the nonlinear constitutive equation in step S1 to obtain a permeability model corresponding to the cleat / bedding, and correcting the anisotropic permeability tensor using the tortuosity connection coefficients in the three principal stress directions to obtain a permeability tensor prediction model. The present invention establishes an anisotropic coal rock permeability prediction model for the cleat / bedding plane system under the combined effects of matrix creep, desorption shrinkage / expansion, and cleat / bedding compression.

Description

Technical Field

[0001] The present invention relates to the technical field of oil and natural gas exploration and development, and in particular to a creep-considered anisotropic coal rock permeability tensor prediction method. Background Art

[0002] New unconventional areas, represented by deep coal-rock formations, are in the initial research stages and are a key focus for increasing reserves and production. Deep coal-rock gas exploration has opened up new frontiers for exploration in coal-bearing basins and provided new avenues for natural gas exploration. Deep coal-rock gas exploration is of paramount importance and urgency to rapidly establish new strategic replacement areas for large-scale reserves. Accurately assessing the mass transfer capacity of coal-rock formations is crucial for efficient development.

[0003] Reservoir permeability is one of the most important parameters characterizing seepage patterns, and the dynamic evolution of permeability directly affects coalbed methane production and extraction efficiency. Within deep coal-rock gas reservoirs, the in situ spatiotemporal evolution of permeability is difficult to directly measure through core-scale laboratory experiments. Deep coal-rock gas reservoirs have complex pore structures and mineral compositions, and their gas content and porosity are generally higher than those in medium- and deep-layer formations. Natural fractures and cleats / bedding are well developed, and the rock has a high elastic modulus and strong plasticity, exhibiting high-temperature and high-pressure gas adsorption characteristics. Matrix permeability is influenced by a combination of factors, including effective stress, rarefied gas effects (flow regimes), surface diffusion, gas desorption, adsorption deformation, and nonlinear creep deformation.

[0004] In addition, due to the difference in interfacial strength between coal seams and the different compressibility between face / end cleats and bedding, the permeability exhibits strong anisotropy. The time-varying effect of creep is different from that of desorption and aperture compression, and is affected by pressure and loading time. Existing coal rock permeability models also have the following deficiencies: (1) There is a lack of quantitative modeling methods for permeability anisotropy, which leads to errors in the calculation of permeability in different principal stress directions; (2) There is a lack of coupling for the full-stage creep effect, which leads to the neglect of the loss of coal rock permeability during the mining process; (3) There is a lack of representation of gas flow state, which makes it impossible to reveal the flow state transition in confined space. Summary of the Invention

[0005] To overcome the challenges of existing technologies, the present invention provides a creep-inclusive anisotropic coal rock permeability tensor prediction method. This method establishes a nonlinear constitutive equation for the cleat (face cleat, butt cleat) / bedding plane system under the competing conditions of matrix creep, desorption shrinkage / expansion, and cleat / bedding compression. Furthermore, the rarefied gas effect is introduced to characterize the influence of flow regime transitions on permeability, enabling accurate prediction of coal rock permeability under anisotropic conditions.

[0006] A creep-considered anisotropic coal rock permeability tensor prediction method comprises the following steps:

[0007] S1. Construct the strain constitutive equation of the anisotropic coal rock matrix under linear elastic conditions, consider the deformation caused by coal rock creep, desorption expansion effect and cleat / bedding opening compression effect, and establish the nonlinear constitutive equation of coal rock;

[0008] S2. Based on the cubic law, a relationship between the permeability ratio and the cleat / bedding aperture is established, and the nonlinear constitutive relationship is substituted into it to derive the intrinsic permeability of the coal rock, and the rarefied gas effect is introduced to correct the flow state; the nonlinear constitutive equation in the coupling step S1 is used to obtain the permeability model corresponding to the cleat / bedding, and the anisotropic permeability tensor is corrected by the tortuosity connection coefficients in the three principal stress directions to obtain the permeability tensor prediction model.

[0009] Furthermore, in step S1, the matrix strain constitutive equation under linear elastic conditions is:

[0010]

[0011] Among them, Δε v Indicates the total amount of strain increment in the x, y, and z directions, dimensionless; Δε x , Δε y , Δε z represents the strain increment in the x, y, and z directions, dimensionless; σ e represents effective stress, MPa; K represents bulk modulus, GPa; f represents internal expansion coefficient, dimensionless; represents the stress increment due to desorption expansion, MPa;

[0012]

[0013] Among them, Δσ ex , Δσ ey , Δσ ez Indicates the effective stress increment in different directions, MPa; E ex , E ey , E ez represents the Young's modulus in the x, y, and z directions, GPa; v xy , v xz , v yx , v yz , v zx , v zy Represents the Poisson's ratio in the xy, yx, xz, zx, zy, and yz directions, dimensionless; It represents the desorption expansion strain increment in the x, y, and z directions and is dimensionless.

[0014] Furthermore, in step S1, the deformation constitutive equation considering the creep of coal rock is:

[0015]

[0016] in:

[0017]

[0018] Among them, E vex , E vey , E vez represents the viscoelastic modulus in the x, y, and z directions, GPa; η vex , η vey , η vez and η vpx , η vpy , η vpz Represent the viscoelastic and viscoplastic coefficients in the x, y, and z directions, Pa·h γ ; ω represents the 0-1 correction function, dimensionless; σ ex , σ ey , σ ez Indicates the effective stress in the x, y, and z directions, MPa; σ s Represents stress increment, MPa.

[0019] Furthermore, in step S1, the deformation constitutive equation considering the desorption and expansion effect of coal rock is:

[0020]

[0021] in, represents the desorption expansion strain increment in the x, y, and z directions, dimensionless; ε L represents the Langmuir strain constant, dimensionless; p L represents the Langmuir pressure, MPa; p represents the pore pressure, MPa; p0 represents the initial pore pressure, MPa; S Lx , S Ly , S Lz It represents the equivalent Langmuir strain in the x, y, and z directions and is dimensionless.

[0022] Furthermore, in step S1, the deformation constitutive equation considering the compression effect of coal rock cleat / bedding aperture is:

[0023]

[0024] The opening compression coefficient is defined as:

[0025]

[0026] Among them, Δε fx , Δε fy , Δε fz represents the strain caused by the opening compression in the x, y, and z directions, dimensionless; b face Indicates the face cleat opening, m; bface0 represents the initial opening of the face cleat, m; b butt Indicates the end cleat opening, m; b butt0 Indicates the initial opening of the end cleat, m; b bed Indicates bedding aperture, m; b bed0 represents the initial opening of the bedding, m; σ bx , σ by , σ bz Indicates the overburden pressure in the x, y, and z directions, MPa; σ netx =σ bx -αp,σ nety =σ by -αp,σ netz =σ bz -αp represents the net pressure inside the face, butt cleat / bedding, MPa; C fx , C fy , C fz and C fx0 , C fy0 , C fz0 Represent the compression coefficients in the dynamic and initial states in the x, y, and z directions, 1 / MPa.

[0027] Furthermore, in step S1, the nonlinear constitutive equation of the coal rock is:

[0028]

[0029] Furthermore, in step S2, the relationship between the permeability ratio and the cleat / bedding aperture is:

[0030]

[0031] Among them, k face represents the face cleat permeability, m 2 ;k butt represents the end cleat permeability, m 2 ;k bed represents the bedding permeability, m 2 ; b face represents the cleat strain, m; b butt represents the end cleat strain, m; b bed represents bedding strain, m; φ face represents the porosity of face cleat, dimensionless; φ butt represents the end cleat porosity, dimensionless; φ bed represents the bedding porosity, dimensionless; k face0 represents the initial face cleat permeability, m 2 ;k butt0 represents the initial end cleat permeability, m 2 ;k bed0represents the initial bedding permeability, m 2 .

[0032] Furthermore, in step S2, introducing the rarefied gas effect to correct the flow state further includes: introducing a function of the Knudsen number to correct the rarefied gas effect, and the relationship between the corrected permeability ratio and the cleat / bedding aperture is:

[0033]

[0034] Among them, Kn face , Kn butt , Kn bed It represents the Knudsen number within face cleats, butt cleats, and beddings, and is dimensionless.

[0035] Furthermore, in step S2, the nonlinear constitutive equation in step S1 is coupled to obtain the permeability model corresponding to the cleat / bedding:

[0036]

[0037] Furthermore, in step S2, the permeability tensor prediction model is:

[0038]

[0039] Where k represents the anisotropic permeability tensor, m 2 ;k x represents the permeability in the x direction, m 2 ;k y represents the permeability in the y direction, m 2 ;k z represents the permeability in the z direction, m 2 ;c x represents the tortuosity coefficient in the x-direction, dimensionless; c y represents the tortuosity coefficient in the y direction, dimensionless; c z It represents the tortuosity coefficient in the z direction and is dimensionless.

[0040] On the other hand, the present invention provides a computer 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 computer program, the steps of the anisotropic coal rock permeability tensor prediction method described in any one of the above items are implemented.

[0041] On the other hand, the present invention provides a computer-readable storage medium having a computer program stored thereon, characterized in that when the computer program is executed by a processor, the steps of the anisotropic coal rock permeability tensor prediction method described in any one of the above are implemented.

[0042] This method fully considers the long-term loading and large-scale pressure reduction characteristics of deep coal rock volume fracturing development. By coupling the creep effects under different stress loading conditions, it establishes a nonlinear constitutive equation for the cleat (face cleat, end cleat) / bedding plane system under the competing conditions of matrix creep, desorption shrinkage / expansion, and cleat / bedding compression. Furthermore, the rarefied gas effect is introduced to characterize the impact of flow regime transitions on permeability, and the tortuosity connection coefficient is used to modify the anisotropic permeability tensor, achieving accurate prediction of coal rock permeability under anisotropic conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0044] Figure 1 Graph showing the predicted results of two-stage creep permeability under different pressures in an embodiment of the present invention;

[0045] Figure 2 Graph showing the predicted results of creep permeability in two stages at different times in an embodiment of the present invention;

[0046] Figure 3 Graph showing the prediction results of three-stage creep permeability under different pressures in an embodiment of the present invention;

[0047] Figure 4 Graph showing the predicted results of creep permeability at three stages at different times in an embodiment of the present invention;

[0048] Figure 5 Graph showing the prediction results of anisotropic permeability under different viscoplastic coefficients in an embodiment of the present invention;

[0049] Figure 6 Graph showing the predicted results of anisotropic permeability under different viscoelastic coefficients in an embodiment of the present invention;

[0050] Figure 7 Graph showing the predicted results of anisotropic permeability under different viscoelastic moduli in an embodiment of the present invention. DETAILED DESCRIPTION

[0051] The present invention is further described below with reference to the accompanying drawings and examples. It should be noted that, in the absence of conflict, the embodiments in this application and the technical features in the embodiments can be combined with each other. It should be noted that, unless otherwise specified, all technical and scientific terms used in this application have the same meanings as those commonly understood by those of ordinary skill in the art to which this application belongs. The use of similar words such as "include" or "comprising" in the present invention means that the elements or objects appearing before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects.

[0052] In order to solve the technical problem raised in the present invention, the present invention provides a method for predicting the anisotropic coal rock permeability tensor considering creep, comprising the following steps:

[0053] S1. Construct the strain constitutive equation of the anisotropic coal rock matrix under linear elastic conditions, consider the deformation caused by coal rock creep, desorption expansion effect and cleat / bedding opening compression effect, and establish the nonlinear constitutive equation of coal rock;

[0054] S11. Coal rock matrix strain constitutive model

[0055] In the absence of potential creep effects, coal rock behaves as a linear elastic material, that is, the poroelastic stress-strain equation is established, specifically:

[0056]

[0057] Since the porosity of coal is much less than 1, formula (1) can be simplified as follows:

[0058]

[0059] Among them, Δε ij Represents the strain increment in different directions, dimensionless; Indicates the stress increment due to desorption expansion, MPa; Δσ ij represents the stress increment in different directions, MPa; G = E / (1+2ν) represents the shear modulus, GPa; K = E / (3(1-2ν)) represents the bulk modulus, GPa; E represents the coal rock elastic model, GPa; α represents the Biot coefficient, dimensionless; δ ij represents the Kroneckerdelta function; σ e =σ-αp represents effective stress, MPa; σ kk Represents σ x +σ y +σ z ;φ represents the porosity of coal rock, dimensionless; f represents the internal expansion coefficient, dimensionless;.

[0060] For anisotropic coal rock, its constitutive relationship follows the principle of linear elasticity and can be expressed as follows:

[0061]

[0062] Among them, Δε x , Δε y , Δε z represents the strain increment in the x, y, and z directions, dimensionless; E x , E y , E z represents the Young's modulus in the x, y, and z directions, GPa; v xy , v xz , v yx , v yz , v zx , v zy Poisson's ratio in the xy, yx, xz, zx, zy, and yz directions, dimensionless; E x , E y , E z represents the Young's modulus in the x, y, and z directions, GPa; represents the desorption expansion strain increment in the x, y, and z directions, dimensionless; Δσ ex , Δσ ey , Δσ ez Represents the effective stress increment in different directions, MPa.

[0063] S12. Deformation caused by coal rock creep

[0064] The constitutive relation of coal rock with unstable creep is given by the following formula:

[0065]

[0066] Among them, Δε c (t) represents the strain increment caused by creep, dimensionless; E ve represents the viscoelastic modulus of coal rock, GPa; γ represents the fractional derivative; η ve and η vp Represent the viscoelastic and viscoplastic coefficients, Pa·h γ ;α0 represents the viscosity coefficient, 0.17; σ s Indicates yield stress, MPa; E 1,1+γ and E γ,1 represents different fractional-order Mittag-Leffler functions, dimensionless; t represents time, in hours.

[0067] Substituting equation (4) into equation (3), the nonlinear constitutive relations of coal rock under unsteady creep under different stress conditions are as follows:

[0068]

[0069] in:

[0070]

[0071] Where: E ex , E ey , E ez Indicates Young's modulus in the x, y, and z directions, GPa; E vex , E vey , E vez represents the viscoelastic modulus in the x, y, and z directions, GPa; η vex , η vey , η vez and η vpx , η vpy , η vpz Represent the viscoelastic and viscoplastic coefficients in the x, y, and z directions, Pa·h γ ; ω represents the 0-1 correction function, dimensionless; σ ex , σ ey , σ ez Indicates the effective stress in the x, y, and z directions, in MPa.

[0072] S13. Deformation caused by adsorption and expansion of coal rock

[0073] The permeability of coal is affected by effective stress and gas adsorption. Therefore, the changes in the volume of fractures, matrix, and bulk coal caused by gas adsorption can be expressed as:

[0074]

[0075] The porosity definition includes the internal expansion process caused by adsorption, and the deformation of the cracks and coal body can be determined:

[0076]

[0077] in, It represents the deformation of coal rock under adsorption, dimensionless; It represents the deformation of coal rock matrix under adsorption, dimensionless; It represents the deformation of coal rock cleats / beddings under adsorption, dimensionless; represents the matrix strain increment caused by desorption expansion, dimensionless; represents the crack strain increment caused by desorption expansion, dimensionless;.

[0078] In the above equation, a Langmuir-type equation can be used to describe the deformation caused by adsorption in the matrix as follows:

[0079]

[0080] For anisotropic coal rock, the deformation caused by adsorption in different principal stress directions is as follows:

[0081]

[0082] Among them, ε L represents the Langmuir strain constant, dimensionless; p L represents the Langmuir pressure, MPa; p represents the pore pressure, MPa; p0 represents the initial pore pressure, MPa; S Lx , S Ly , S Lz It represents the equivalent Langmuir strain in the x, y, and z directions and is dimensionless.

[0083] S14, deformation caused by coal rock cleat / bedding compression

[0084] In the early stages of gas production, the cleat / bedding system has a large aperture. As gas production continues, the subsequent stages see compression and closure of the cleats and bedding, which can be expressed by the following relationship:

[0085]

[0086] During the gas production process, the stress of the overburden does not change, and the change of effective stress is mainly determined by the pore pressure. Therefore, Equation (13) can be simplified as follows:

[0087]

[0088] The opening compression coefficient is defined as:

[0089]

[0090] Among them, Δε fx , Δε fy , Δε fz represents the strain caused by the opening compression in the x, y, and z directions, dimensionless; b face Indicates the face cleat opening, m; b face0 represents the initial opening of the face cleat, m; b butt Indicates the end cleat opening, m; b butt0 Indicates the initial opening of the end cleat, m; b bed Indicates bedding aperture, m; b bed0 represents the initial opening of the bedding, m; σ bx , σ by , σ bz Indicates the overburden pressure in the x, y, and z directions, MPa; σ netx =σ bx-αp,σ nety =σ by -αp,σ netz =σ bz -αp represents the net pressure inside the face, butt cleat / bedding, MPa; C fx , C fy , C fz and C fx0 , C fy0 , C fz0 Represent the compression coefficients in the dynamic and initial states in the x, y, and z directions, 1 / MPa.

[0091] S15. Nonlinear constitutive equation of coal and rock

[0092] When gas is extracted, the evolution of cleat porosity is determined by both matrix creep and cleat / beam compression and internal contraction due to desorption. Substituting equations (12), (14), and (15) into equation (5), the total deformation of anisotropic coal rock with adsorption-induced expansion, unsteady creep, and cleat / beam compression satisfies the following constitutive relation:

[0093]

[0094] Step 2: Based on the cubic law, a relationship between the permeability ratio and the cleat / bedding aperture is established, the nonlinear constitutive relationship is substituted into it to derive the intrinsic permeability of the coal rock, and the rarefied gas effect is introduced to correct the flow state; the nonlinear constitutive equation in step S1 is coupled to obtain the permeability model corresponding to the cleat / bedding, and the anisotropic permeability tensor is corrected by the tortuosity connection coefficients in the three principal stress directions to obtain the permeability tensor prediction model.

[0095] Deep coal rocks contain face / butt cleats and bedding, which contribute to their anisotropy, especially during gas extraction. According to the cubic law, the permeability of face / butt cleats and bedding is related to the aperture as follows:

[0096]

[0097] The changes in face / butt cleats and bedding apertures can be described by the strains in the principal stress directions:

[0098]

[0099] Substituting equation (18) into equation (17), we can obtain the corresponding relationship between the anisotropic permeability ratio and the coal rock strain:

[0100]

[0101] The Knudsen number function is introduced to correct the rarefied gas effect, and then quantitatively characterize the influence of flow regime conversion in confined space on permeability evolution. Equation (19) can be further written as:

[0102]

[0103] Among them, k face represents the face cleat permeability, m 2 ;k face0 represents the initial face cleat permeability, m 2 ;k butt represents the end cleat permeability, m 2 ;k but0t represents the initial end cleat permeability, m 2 ;k bed represents the bedding permeability, m 2 ;k bed0 represents the initial bedding permeability, m 2 ;φ face represents the porosity of face cleat, dimensionless; φ butt represents the end cleat porosity, dimensionless; φ bed Kn represents the bedding porosity, dimensionless; face =K B T / (2πd m 2 p) / b face , Kn butt =K B T / (2πd m 2 p) / b butt , Kn bed =K B T / (2πd m 2 p) / b bed K represents the Knudsen number within the face, butt cleat / bedding, dimensionless; B is the Boltzmann constant, J / K; T is the temperature, K; β is the Beskok-Karniadakis constant, dimensionless.

[0104] By combining equations (20) and (16), the permeabilities corresponding to face / butt cleats and bedding can be derived as follows:

[0105]

[0106] With the face / butt cleat directions as x and y and the bedding direction as z, the permeability in the vertical flow direction x is provided by the butt cleat and bedding. The same is true for the other two principal stress directions. Therefore, the tortuosity connection coefficient is introduced to correct the permeability in the three principal stress directions. The anisotropic permeability tensor of coal rock is:

[0107]

[0108] Where k represents the anisotropic permeability tensor, m 2 ;k x represents the permeability in the x direction, m 2 ;k y represents the permeability in the y direction, m 2 k z represents the permeability in the z direction, m 2 ;c x represents the tortuosity coefficient in the x-direction, dimensionless; c y represents the tortuosity coefficient in the y direction, dimensionless; c z It represents the tortuosity coefficient in the z direction and is dimensionless.

[0109] In order to facilitate those skilled in the art to understand and apply the anisotropic coal rock permeability tensor prediction method considering creep provided by the present invention, a practical example is used to perform prediction and result analysis. The basic parameters used in the practical example are shown in Table 1.

[0110] Table 1 Basic parameters

[0111]

[0112] The prediction results are as follows Figure 1-7 As shown by Figure 1 It can be seen that when the effective stress is less than the yield stress, the creep of coal rock presents a two-stage characteristic, which only causes the permeability to decrease in the initial 0-5 hours. When the pressure decreases from 20MPa to 8MPa, the effect of creep on the initial permeability loss increases. As the pressure further decreases, desorption and expansion increase the overall permeability.

[0113] Depend on Figure 2 It can be seen that within the entire pressure range, the permeability first decreases and then increases with pressure. At the same time, the closing effect of cleats / bedding and the expansion effect of desorption compete with each other, resulting in a permeability conversion pressure (about 4.6 MPa). At different times, as the creep time increases, the two-stage creep effect causes a partial loss of permeability only in the initial stage.

[0114] Depend on Figure 3 It can be seen that when the effective stress is greater than the yield stress, the creep of coal rock presents a three-stage characteristic. After the initial creep action, as the effective stress further decreases, a rapid creep stage (the third stage) appears, which causes a significant decrease in permeability. This effect on permeability reduction is negatively correlated with pressure before the conversion pressure. After it is less than the conversion pressure, the desorption and expansion effect causes the permeability to further recover.

[0115] Depend on Figure 4It can be seen that: under the action of full pressure, the accelerated deformation and damage in the third stage causes the permeability-pressure curve to drop significantly with the increase of creep time. From 0h to 20h, the permeability loss rate at the conversion pressure is as high as 80%. Although under the effect of desorption and permeation enhancement, the permeability only recovers to 72.6% of the initial state.

[0116] Depend on Figure 5 It can be seen that: when the viscoplastic coefficient in the y and z directions is increased by two times and the other directions remain unchanged, the permeability in the x direction and y and z directions deviates significantly. As the creep time increases, the creep effect in the third stage in the y and z directions is significantly enhanced. The larger the viscoplastic coefficient, the faster and higher the degree of plastic deformation in the third stage of creep, which makes the permeability loss in this direction significantly stronger than that in other directions. The higher the pressure, the stronger the anisotropy. Under the pressure condition of 20MPa, the permeability difference at 20h is stronger than that at 10MPa.

[0117] Depend on Figure 6 It can be seen that doubling the viscoelastic coefficient in the y and z directions, while keeping the other directions unchanged, leads to significant deviations in the permeability in the x, y, and z directions. The viscoelastic coefficient primarily determines the elastic deformation in the first and second creep stages. The larger the viscoelastic coefficient, the faster and more severe the initial elastic deformation. This results in significant anisotropy in the permeability during the initial creep phase. This effect decreases with increasing creep time and decreasing pore pressure.

[0118] Depend on Figure 7 It can be seen that: when the viscoelastic modulus in the y and z directions is increased by two times and the other directions remain unchanged, the permeability in the x direction and the y and z directions will show significant deviations. The viscoelastic modulus determines the difficulty of the coal rock to undergo viscoelastic deformation. Increasing the viscoelastic modulus makes the viscoelastic deformation of the coal rock in the second stage of creep more obvious. Therefore, the permeability in the y and z directions shows a significant difference from that in the x direction after about 2 hours, and remains until entering the viscoplastic deformation stage. The influence of pressure on it also satisfies the negative correlation.

[0119] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with this profession can make some changes or modifications to equivalent embodiments of the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A method for predicting anisotropic coal rock permeability tensor considering creep, characterized in that: The following steps are involved: S1. Construct the strain constitutive equation of the anisotropic coal rock matrix under linear elastic conditions, consider the deformation caused by coal rock creep, desorption expansion effect and cleat / bedding opening compression effect, and establish the nonlinear constitutive equation of coal rock; S2. Establish a relationship between the permeability ratio and the cleat / bedding aperture based on the cubic law, substitute the nonlinear constitutive relationship into it to derive the intrinsic permeability of the coal rock, and introduce the rarefied gas effect to correct the flow state; couple the nonlinear constitutive equation in step S1 to obtain the permeability model corresponding to the cleat / bedding, and correct the anisotropic permeability tensor using the tortuosity connection coefficients in the three principal stress directions to obtain the permeability tensor prediction model; In step S1, the matrix strain constitutive equation under linear elastic conditions is: ； in, It represents the total amount of strain increment in the x, y, and z directions, dimensionless; , , express x , y , z The strain increment in the direction is dimensionless; represents effective stress, MPa; K represents the bulk modulus, GPa; represents the internal expansion coefficient, dimensionless; represents the stress increment due to desorption expansion, MPa; ； in, , , Indicates the effective stress increment in different directions, MPa; E ex , E ey , E ez express x , y , z Young's modulus in the direction, GPa; v xy , v xz , v yx , v yz , v zx , v zy express xy , yx , xz , zx , zy , yz Poisson's ratio of direction, dimensionless; , , express x , y , z The desorption expansion strain increment in the direction is dimensionless; In step S1, the deformation constitutive equation considering the creep of coal rock is: ； in: ； ； in, E vex , E vey , E vez express x , y , z Viscoelastic modulus in the direction, GPa; η vex , η vey , η vez and η vpx , η vpy , η vpz Respectively x , y , z Viscoelastic and viscoplastic coefficients in the direction, Pa•h γ ; γ represents fractional derivative; ω represents the 0-1 correction function, dimensionless; σ ex , σ ey , σ ez express x , y , z Effective stress in the direction, MPa; σ s represents the stress increment, MPa; E 1,1+γ and E γ,1 represents different fractional-order Mittag-Leffler functions, dimensionless; t Indicates time, hours; α 0 represents the viscosity coefficient; In step S1, the deformation constitutive equation considering the desorption and expansion effect of coal rock is: ； in, , , express x , y , z The desorption expansion strain increment in the direction is dimensionless; ε L represents the Langmuir strain constant, dimensionless; p L represents the Langmuir pressure, MPa; p represents pore pressure, MPa; p 0 represents the initial pore pressure, MPa; S Lx , S Ly , S Lz express x , y , z Equivalent Langmuir strain in the direction, dimensionless; In step S1, the deformation constitutive equation considering the compression effect of coal rock cleat / bedding aperture is: ； The opening compression coefficient is defined as: ； in, , , express x , y , z The strain caused by the opening compression in the direction is dimensionless; b face represents the face cleat opening, m; b face0 represents the initial opening of the face cleat, m; b butt represents the end cleat opening, m; b butt0 represents the initial opening of the end cleat, m; b bed represents the bedding aperture, m; b bed0 represents the initial opening of the bedding, m; σ bx , σ by , σ bz express x , y , z Overburden pressure in the direction, MPa; σ netx = σ bx -αp , σ nety = σ by -αp , σ netz = σ bz -αp Indicates the net pressure inside the face, butt cleat / bedding, MPa; C fx , C fy , C fz and C fx0 , C fy0 , C fz0 Respectively x , y , z The dynamic and initial compressibility of the direction, 1 / MPa; α represents the Biot coefficient, dimensionless; In step S1, the nonlinear constitutive equation of the coal rock is: ； In step S2, the relationship between the permeability ratio and the cleat / bedding aperture is: ； in, k face represents the face cleat permeability, m 2 ; k butt represents the end cleat permeability, m 2 ; k bed represents the bedding permeability, m 2 ; b face represents the cleat strain, m; b butt represents the end cleat strain, m; b bed represents bedding strain, m; represents the porosity of face cleat, dimensionless; represents the end cleat porosity, dimensionless; represents the bedding porosity, dimensionless; k face0 represents the initial face cleat permeability, m 2 ; k butt0 represents the initial end cleat permeability, m 2 ; k bed0 represents the initial bedding permeability, m 2 ; In step S2, introducing the rarefied gas effect to correct the flow pattern further includes: introducing a function of the Knudsen number to correct the rarefied gas effect. The relationship between the corrected permeability ratio and the cleat / bedding aperture is: ； in, Kn face , Kn butt , Kn bed represents the Knudsen number within face cleats, end cleats, and beddings, dimensionless; β represents the Beskok−Karniadakis constant, dimensionless; In step S2, the nonlinear constitutive equation in step S1 is coupled to obtain the permeability model corresponding to cleat / bedding: ； In step S2, the permeability tensor prediction model is: ； in, k represents the anisotropic permeability tensor, m 2 ; k x express x Permeability in the direction, m 2 ; k y express y Permeability in the direction, m 2 ；k z express z Permeability in the direction, m 2 ; c x express x The tortuosity coefficient of the direction, dimensionless; c y express y The tortuosity coefficient of the direction, dimensionless; c z express z The tortuosity coefficient of the direction, dimensionless.

2. A computer 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 computer program, the steps of the anisotropic coal rock permeability tensor prediction method according to claim 1 are implemented.

3. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the anisotropic coal rock permeability tensor prediction method according to claim 1 are implemented.

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