A shale bedding fracture propagation geometry parameter calculation method

Abstract

The application discloses a shale bedding fracture propagation geometric parameter calculation method, which comprises the following steps: establishing a differential equation group of a shale bedding standard layer according to an elastic mechanics theory, integrating the differential equation group into a partial differential equation group; transforming the partial differential equation group into a common differential equation group, and solving a general solution of the common differential equation group; solving constants in the general solution of the common differential equation group by using a linear spring controlled bedding boundary condition; obtaining a shear slip calculation model of the shale bedding under a space coordinate system; establishing a geometric parameter calculation equation of a shale bedding fracture, and coupling the shear slip calculation model of the shale bedding to obtain a shale bedding fracture propagation geometric parameter calculation model; and performing dynamic simulation on a fracture propagation in a shale gas volume fracturing process, and obtaining a calculation result of a shale bedding fracture propagation geometric parameter. The calculation result of the shale bedding fracture propagation geometric parameter obtained by the application is reliable, and provides a technical reference for shale gas exploration and development and other related work.

Description

Technical Field

[0001] This invention relates to the field of petroleum engineering technology, specifically to a method for calculating geometric parameters of shale bedding fracture propagation. Background Technology

[0002] In recent years, the exploration and development of shale gas has received increasing attention. As an unconventional gas reservoir, shale reservoirs have extremely poor physical properties, characterized by high porosity and low permeability. They are complex sedimentary rocks with strong heterogeneity. Currently, the main method for enhancing shale gas production is horizontal well volumetric fracturing technology, which achieves economic benefits through artificial modification. A key focus in the development of shale volumetric fracturing technology is to theoretically calculate the geometric parameters of shale fracture propagation and to evaluate the fracturing effects of different geological and operational parameters to explore the optimal fracturing scheme. It is well known that, compared to other oil and gas reservoirs, the presence of bedding in shale reservoirs significantly affects the final fracturing effect. Therefore, the impact of shale bedding on fracture propagation must be fully considered during volumetric fracturing.

[0003] Existing methods for calculating the geometric parameters of shale bedding fractures generally treat shale, which exhibits significant anisotropy, as a transversely isotropic composite material. However, in reality, shale is isotropic in the sedimentary plane but anisotropic in the cross-section perpendicular to the sedimentary plane. The distribution of fracture width and length varies greatly across different regions, making it difficult to establish a universal model to describe the morphological distribution of shale fractures in different areas. The strength and fracture toughness of shale bedding have a significant impact on the propagation behavior of hydraulic fractures.

[0004] Shale volumetric fracturing fracture propagation mechanics couples processes such as formation rock mechanical deformation, fracture network fluid flow, and fracture propagation. Existing theories and numerical software often simplify shale as a non-porous, isotropic material. However, due to the presence of bedding and natural fractures, shale exhibits anisotropy and randomness not only in its elastic and permeability parameters but also in its fracture and strength.

[0005] Existing hydraulic fracturing theoretical models include two-dimensional, pseudo-three-dimensional, and three-dimensional models. Two-dimensional models calculate fracture length and width based on a fixed fracture height, but the calculation error is relatively large. Three-dimensional models can simulate fracture extension in three directions (length, width, and height), but their computational efficiency is low and the modeling is complex. While pseudo-three-dimensional models have certain limitations when calculating large vertical fracture extensions, they have become a commonly used calculation model because they consider the change in fracture height during fracture propagation and have a significant advantage in computational efficiency compared to full three-dimensional models. However, current pseudo-three-dimensional models are all established under the assumption of well-cemented stratigraphy, without considering the mechanical characteristics of bedding and their influence on fracture propagation. Therefore, it is necessary to fully consider bedding factors and establish a reasonable, effective, accurate, and feasible method for calculating the geometric parameters of shale bedding fracture propagation. Summary of the Invention

[0006] This invention proposes a method for calculating the geometric parameters of shale bedding fracture propagation. This method can take the properties of shale bedding planes into account in the calculation model, and can simulate the geometric parameters of shale bedding fracture propagation considering the properties of bedding planes. The method is simple to operate, the results are reliable, and it can provide a technical reference for related work.

[0007] This invention provides a method for calculating the geometric parameters of shale bedding fracture propagation, comprising the following steps:

[0008] Based on the geometric parameters of the standard shale bedding layer, a set of differential equations for the standard shale bedding layer was established using the theory of elasticity.

[0009] Based on the principle of two-dimensional Fourier transform, the system of differential equations is integrated into a system of partial differential equations;

[0010] The partial differential equation system is transformed into an ordinary differential equation system using the two-dimensional Fourier forward transform, and the general solution of the ordinary differential equation system is obtained.

[0011] The constants in the general solution of the ordinary differential equation system are obtained by using the bedding boundary conditions controlled by the linear spring.

[0012] Using the two-dimensional inverse Fourier transform, the obtained set of ordinary differential equations is transformed into a calculation model of shear slip of shale bedding in a spatial coordinate system;

[0013] Based on the geometric parameters of shale bedding fractures, establish the calculation equations for the geometric parameters of shale bedding fractures;

[0014] By coupling the calculation model of shear slip of shale bedding with the calculation equation of geometric parameters of shale bedding cracks, a calculation model of geometric parameters of shale bedding crack propagation is obtained.

[0015] A calculation model of geometric parameters for shale bedding fracture propagation was used to dynamically simulate fracture propagation during the volumetric fracturing process of shale gas, and the calculation results of geometric parameters for shale bedding fracture propagation were obtained.

[0016] Furthermore, the step of establishing a set of differential equations for the standard shale bedding layer based on its geometric parameters and using elasticity theory includes:

[0017] The differential equations for the standard shale bedding layer are established using the constitutive equations for transversely isotropic linear elastic materials; the set of differential equations for the standard shale bedding layer is as follows:

[0018] σ ij,j l +f i l =0 (1)

[0019] σ ij l =λ l ε kk l δ ij +2G l ε ij l (2)

[0020] ε ij l =(u i,j l +u j,i l ) / twenty three)

[0021] Where 'l' represents the layer number of the standard shale layer;

[0022] i, j, and k are all 1, 2, 3, ...;

[0023] f represents the stress gradient at any point within the l-th layer; i l The physical strength within the l-th layer; The stress within the l-th layer;

[0024] λ l G l Let be the Lamé constant within the l-th layer, and its expressions are as follows:

[0025]

[0026] E and ν are Young's modulus and Poisson's ratio, respectively; The shear strain within the l-th layer;

[0027] δ ij For Kronecker notation, when i = j, δij When δ is 1 and i ≠ j, ij =0;

[0028] These are all displacement gradients at any point within the l-th layer, and their expressions are as follows:

[0029]

[0030] The sum of strain within the l-th layer is expressed as:

[0031]

[0032] Normal strain within the l-th layer.

[0033] Furthermore, the process of integrating the system of differential equations into a system of partial differential equations based on the principle of two-dimensional Fourier transform includes:

[0034] Based on the principle of two-dimensional Fourier transform, the system of differential equations is integrated to obtain a system of partial differential equations concerning the y-coordinate in the vertical direction, as follows:

[0035]

[0036] in This refers to the normal stress within the l-th layer; This refers to the shear stress within the l-th layer;

[0037] These represent the displacements in the x, y, and z directions within the l-th layer, respectively.

[0038] These represent the body forces in the x, y, and z directions within the l-th layer.

[0039] Furthermore, the step of transforming the system of partial differential equations into a system of ordinary differential equations using the two-dimensional Fourier forward transform, and then obtaining the general solution of the system of ordinary differential equations, includes:

[0040] For transversely isotropic shale bedding, the Fourier transform object is determined by using the two-dimensional Fourier transform criterion and properties and based on the aforementioned partial differential equations.

[0041] The coordinate axes parallel to the shale bedding are transformed using a two-dimensional positive Fourier transform, converting the partial differential equations into a system of ordinary differential equations. The two-dimensional Fourier transform formula is as follows:

[0042]

[0043] in Let be the stress or displacement expression in the Fourier transform domain; m and n are the coordinates in the Fourier transform domain, where m corresponds to the x-axis in the spatial coordinate system and n corresponds to the z-axis in the spatial coordinate system.

[0044] The general solution to the system of ordinary differential equations is as follows:

[0045]

[0046] Where k is the polar coordinate in the Fourier transform domain, and its calculation formula is:

[0047]

[0048] Solving the system of ordinary differential equations, we obtain its general solution form as follows:

[0049]

[0050] in This refers to the shear stress within the l-th layer;

[0051] C1, C2, C3, C4, C5, and C6 are coefficients to be determined.

[0052] Furthermore, the method of using the bedding boundary conditions controlled by a linear spring to obtain the constants in the general solution of the system of ordinary differential equations includes:

[0053] By using the bedding deformation boundary conditions controlled by linear springs, the continuity conditions of displacement and stress at the bedding between upper and lower standard layers are established, and this continuity condition is used as the shale bedding boundary condition.

[0054] The condition for bedding deformation controlled by the linear spring is:

[0055] τ yx l =S l Δu x l (13)

[0056] τ yz l =S l Δu z l (14)

[0057] Δσ yy l =0 (15)

[0058] Δσ yx l =0 (16)

[0059] Δσ yz l =0 (17)

[0060] Δu y l =0 (18)

[0061] Where S l Let be the bedding stiffness of the l-th bedding layer;

[0062] These represent the displacement rates along the x, y, and z directions at the l-th layer, respectively.

[0063] These represent the stress variation rates along the x, y, and z directions at the l-th layer, respectively.

[0064] The conditions for bedding deformation controlled by the linear spring are transformed by two-dimensional Fourier transform and substituted into equation (12) to obtain the constants in the general solution of the ordinary differential equation system.

[0065] Furthermore, the shear slip calculation model for shale bedding in a spatial coordinate system obtained by using two-dimensional inverse Fourier transform includes:

[0066] Substituting the constants from the obtained general solution of the system of ordinary differential equations into the general solution of the system of ordinary differential equations, the coordinate axes parallel to the shale bedding are transformed using the two-dimensional inverse Fourier transform and its properties. The formula for the two-dimensional inverse Fourier transform is as follows:

[0067]

[0068] By taking the thickness of the standard layer of each shale bedding as the ordinate of the shale bedding, the calculation model of bedding shear slip in the spatial coordinate system is obtained as follows:

[0069]

[0070] Where d l The thickness of the l-th layer is given.

[0071] Furthermore, the geometric parameter calculation equations for shale bedding fractures include the continuity equation for shale bedding fractures, the pressure drop equation, the fracture width calculation equation, the fracture propagation criterion, and the fracture length calculation equation.

[0072] The continuity equation for the shale bedding fractures is:

[0073]

[0074] Where x is the coordinate along the crack length; q is the flow rate within the crack;

[0075] w represents the crack opening at time t;

[0076] The pressure drop equation for the shale bedding fractures is:

[0077]

[0078] Where p is the pressure inside the fracture; h is the fracture height at x; and μ is the viscosity of the fracturing fluid.

[0079] The equation for calculating the width of the shale bedding fracture is:

[0080]

[0081] Where u1 and u2 are both fractions of the vertical half-slit height h / 2;

[0082] f(y) is the stress function acting on the crack wall;

[0083] The shale bulk propagation criterion for the shale bedding fractures satisfies the following formula:

[0084] K I =K Ic (twenty four)

[0085] When the fractures in the shale bedding fractures cross the layers, the following conditions must be met:

[0086]

[0087] Hydraulic fractures can penetrate shale bedding;

[0088] When the fractures in the shale bedding satisfy the following conditions:

[0089]

[0090] The hydraulic fracture terminates at the shale bedding and extends upwards;

[0091] The equation for calculating the length of the shale bedding fracture is as follows:

[0092] L = a * t b (27)

[0093] Where a and b are undetermined constants; t is the fracturing time.

[0094] Furthermore, based on programming software and a database, and using the shale bedding fracture propagation geometric parameter calculation model, dynamic simulation of fracture propagation during shale gas volumetric fracturing is performed, and the calculation results of shale bedding fracture propagation geometric parameters are obtained.

[0095] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0096] This invention establishes standard layer differential equations based on elasticity theory; transforms the partial differential equations into ordinary differential equations using a two-dimensional Fourier forward transform and obtains their general solution; uses bedding boundary conditions controlled by linear springs to obtain constants in the general solution; and uses a two-dimensional Fourier inverse transform to obtain a calculation model of bedding shear slip in a spatial coordinate system. Based on the continuity equation, pressure drop equation, fracture width calculation equation, fracture propagation criterion, and fracture length calculation equation of shale bedding fractures, a calculation model of geometric parameters for shale bedding fracture propagation is established by coupling the bedding shear slip calculation formula. The method for calculating geometric parameters of shale bedding fracture propagation in this invention considers the mechanical characteristics of shale bedding and their influence on fracture propagation. Furthermore, this method incorporates the properties of shale bedding surfaces into the calculation model, enabling the simulation of geometric parameters for shale bedding fracture propagation considering the properties of bedding surfaces. This method is simple to operate, and the obtained results for shale bedding fracture propagation are reliable, providing a technical reference for shale gas exploration and development. Attached Figure Description

[0097] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0098] Figure 1 This is a flowchart illustrating a method for calculating geometric parameters of shale bedding fracture propagation proposed in this invention.

[0099] Figure 2 This is a schematic diagram of a layered shale with mutually parallel bedding, established in an embodiment of a method for calculating geometric parameters of shale bedding crack propagation proposed in this invention.

[0100] Figure 3 This is a schematic diagram of bedding deformation controlled by a linear spring, established in an embodiment of a method for calculating geometric parameters of shale bedding crack propagation proposed in this invention.

[0101] Figure 4 This is a schematic diagram of the numerical simulation calculation process in an embodiment of the method for calculating geometric parameters of shale bedding fracture propagation proposed in this invention;

[0102] Figure 5 This is a schematic diagram of the curve of fracture height change with fracturing pumping time obtained by numerical simulation calculation in an embodiment of the method for calculating geometric parameters of shale bedding fracture propagation proposed in this invention;

[0103] Figure 6 This is a schematic diagram of the crack height result obtained from numerical simulation calculation in an embodiment of the method for calculating the geometric parameters of shale bedding crack propagation proposed in this invention. Detailed Implementation

[0104] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. However, it should be understood that the scope of protection of the present invention is not limited to the specific implementation.

[0105] Example 1

[0106] like Figure 1-6 As shown, this invention provides a method for calculating the geometric parameters of shale bedding fracture propagation, comprising the following steps:

[0107] Step 1: Based on the geometric parameters of the standard shale bedding layer, establish a set of differential equations for the standard shale bedding layer using the theory of elasticity.

[0108] Currently, research on shale constitutive relations focuses on the relatively simple elastic stage. Layered shale with well-developed bedding is generally regarded as a transversely isotropic material. This invention uses the constitutive equation of transversely isotropic linear elastic material to establish the differential equation of standard shale layer.

[0109] The differential equation for the standard shale bedding layer is then established using the constitutive equation for transversely isotropic linear elastic materials:

[0110] σ ij,j l +f i l =0 (1)

[0111] σ ij l =λ l ε kk l δ ij +2G l ε ij l (2)

[0112] ε ij l =(u i,j l +u j,i l ) / twenty three)

[0113] Where 'l' represents the layer number of the standard shale layer;

[0114] i, j, and k are all 1, 2, 3, ...;

[0115] f represents the stress gradient at any point within the l-th layer; i l The physical strength within the l-th layer; The stress within the l-th layer;

[0116] λl G l Let be the Lamé constant within the l-th layer, and its expressions are as follows:

[0117]

[0118] E and ν are Young's modulus and Poisson's ratio, respectively; The shear strain within the l-th layer;

[0119] δ ij For Kronecker notation, when i = j, δ ij When δ is 1 and i ≠ j, ij =0;

[0120] These are all displacement gradients at any point within the l-th layer, and their expressions are as follows:

[0121]

[0122] The sum of strain within the l-th layer is expressed as:

[0123]

[0124] Normal strain within the l-th layer.

[0125] Shale contains numerous bedding planes parallel to sedimentary planes, and most shale bedding is weak. Therefore, bedding factors are necessary in establishing a method for calculating the geometric parameters of shale bedding fracture propagation. A linear spring model is used to describe bedding deformation. Based on the linear spring model, the cemented bedding between standard layers is accurately described, and the constitutive model of the linear spring is determined.

[0126] Step 2: Based on the principle of two-dimensional Fourier transform, integrate the system of differential equations into a system of partial differential equations, including:

[0127] Step 2.1: For transversely isotropic shale bedding, a simplified schematic diagram of layered shale with parallel bedding is presented using a Cartesian coordinate system, as shown below. Figure 2 As shown. The schematic diagram includes the standard shale layer and bedding;

[0128] Step 2.2: Based on the principle of two-dimensional Fourier transform, the standard layer differential equations are integrated to obtain the partial differential equations about the y-coordinate in the vertical direction, as follows:

[0129]

[0130] in This refers to the normal stress within the l-th layer; This refers to the shear stress within the l-th layer;

[0131] These represent the displacements in the x, y, and z directions within the l-th layer, respectively.

[0132] These represent the body forces in the x, y, and z directions within the l-th layer.

[0133] Step 3: Transform the partial differential equation system into an ordinary differential equation system using the two-dimensional Fourier forward transform, and obtain the general solution of the ordinary differential equation system, including:

[0134] For transversely isotropic shale bedding, the Fourier transform object is determined by using the two-dimensional Fourier transform criterion and properties and based on the partial differential equation system.

[0135] The two-dimensional Fourier transform is used to transform the coordinate axes parallel to the shale bedding, transforming the partial differential equations into ordinary differential equations. The two-dimensional Fourier transform formula is as follows:

[0136]

[0137] in This is the expression for stress or displacement in the Fourier transform domain;

[0138] m and n are the coordinates in the Fourier transform domain, where m corresponds to the x-axis in the spatial coordinate system and n corresponds to the z-axis in the spatial coordinate system.

[0139] The general solution to the system of ordinary differential equations is as follows:

[0140]

[0141] Where k is the polar coordinate in the Fourier transform domain, and its calculation formula is:

[0142]

[0143] Solving the system of ordinary differential equations, we obtain its general solution form as follows:

[0144]

[0145] in This refers to the shear stress within the l-th layer;

[0146] C1, C2, C3, C4, C5, and C6 are coefficients to be determined.

[0147] Step 4: Use the bedding boundary conditions controlled by the linear spring to obtain the constants in the general solution of the system of ordinary differential equations, including:

[0148] By using the bedding deformation boundary conditions controlled by linear springs, the continuity conditions of displacement and stress at the bedding between upper and lower standard layers are established, and this continuity condition is used as the shale bedding boundary condition.

[0149] The condition for bedding deformation controlled by the linear spring is:

[0150] τ yx l =S l Δu x l (13)

[0151] τ yz l =S l Δu z l (14)

[0152] Δσ yy l =0 (15)

[0153] Δσ yx l =0 (16)

[0154] Δσ yz l =0 (17)

[0155] Δu y l =0 (18)

[0156] Where S l Let be the bedding stiffness of the l-th bedding layer;

[0157] These represent the displacement rates along the x, y, and z directions at the l-th layer, respectively.

[0158] These represent the stress variation rates along the x, y, and z directions at the l-th layer, respectively.

[0159] The conditions for bedding deformation controlled by the linear spring are transformed by two-dimensional Fourier transform and substituted into equation (12) to obtain the constants in the general solution of the ordinary differential equation system.

[0160] Step 5: Using the two-dimensional inverse Fourier transform, the obtained system of ordinary differential equations is transformed into a shear slip calculation model of shale bedding in a spatial coordinate system, including:

[0161] Substituting the constants from the obtained general solution of the ordinary differential equation system into the general solution of the ordinary differential equation system, the coordinate axes parallel to the shale bedding are transformed using the two-dimensional inverse Fourier transform and its properties. The formula for the two-dimensional inverse Fourier transform is as follows:

[0162]

[0163] By taking the thickness of the standard layer of each shale bedding as the ordinate of the shale bedding, the calculation model of bedding shear slip in the spatial coordinate system is obtained as follows:

[0164]

[0165] Where d l The thickness of the l-th layer is given.

[0166] Step 6: Based on the geometric parameters of shale bedding fractures, establish the calculation equations for the geometric parameters of shale bedding fractures.

[0167] The geometric parameter calculation equations for shale bedding fractures include the continuity equation, pressure drop equation, fracture width calculation equation, fracture propagation criterion, and fracture length calculation equation for shale bedding fractures.

[0168] Step 6.1: Assuming the fluid within the fracture exhibits one-dimensional flow and is an incompressible Newtonian fluid flowing on a planar plate, neglecting filtration loss, the continuity equation for the shale bedding fracture is:

[0169]

[0170] Where x is the coordinate along the crack length; q is the flow rate within the crack;

[0171] w represents the crack opening at time t;

[0172] The pressure drop equation for shale bedding fractures is:

[0173]

[0174] Where p is the pressure inside the fracture; h is the fracture height at x; and μ is the viscosity of the fracturing fluid.

[0175] Step 6.2: The equation for calculating the width of shale bedding fractures is:

[0176]

[0177] Where u1 and u2 are both fractions of the vertical half-slit height h / 2;

[0178] f(y) is the stress function acting on the crack wall;

[0179] Step 6.3: The shale bulk propagation criterion for shale bedding fractures satisfies the following formula:

[0180] K I =K Ic (twenty four)

[0181] When the fractures in shale bedding fractures cross the bedding planes, the following conditions must be met:

[0182]

[0183] Hydraulic fractures can penetrate shale bedding;

[0184] When the fractures in the shale bedding satisfy the following conditions:

[0185]

[0186] The hydraulic fracture terminates at the shale bedding and extends upwards;

[0187] Step 6.4: As the fracturing time increases, the extension of the fracture length is initially rapid and then slows down. Therefore, in the calculation process, the relationship between fracture length and time is assumed, i.e., the equation for calculating the length of shale bedding fractures is:

[0188] L = a * t b (27)

[0189] Where a and b are undetermined constants; t is the fracturing time.

[0190] Step 7: Couple the shear slip calculation model of shale bedding with the geometric parameter calculation equation of shale bedding fracture to obtain the geometric parameter calculation model of shale bedding fracture propagation.

[0191] By coupling the geometric parameter calculation equations of shale bedding fractures with the shear slip calculation model of shale bedding, a system is established as follows: Figure 4 The flowchart shows the calculation process for the geometric parameters of shale bedding fracture propagation.

[0192] Step 8: Use the shale bedding fracture propagation geometric parameter calculation model to perform dynamic simulation of fracture propagation during the shale gas volumetric fracturing process, and obtain the calculation results of the shale bedding fracture propagation geometric parameters.

[0193] Based on programming software and databases, and utilizing a shale bedding fracture propagation geometric parameter calculation model, dynamic simulation of fracture propagation during shale gas volumetric fracturing and calculation of shale bedding fracture propagation geometric parameters are performed.

[0194] The technical solutions of the present invention will be further described below with reference to specific embodiments.

[0195] Specifically, based on a database and the C# development platform, software for calculating the geometric parameters of shale bedding fractures was developed using a calculation model and process for shale bedding. This software simulates shale bedding and calculates the geometric parameters of fracture propagation during shale gas volumetric fracturing. The specific methods are as follows:

[0196] (1) Based on the database and C# development platform, using the calculation model and process of geometric parameters of shale bedding fracture, a software for calculating the geometric parameters of shale gas volumetric fracturing bedding fracture propagation with the ability to simulate shale bedding was developed.

[0197] (2) Two equally spaced bedding planes were established to simulate the propagation of shale bedding cracks. The geometric model of the layered shale is defined as shown in Table 1, and the basic data is shown in Table 2.

[0198] Table 1 Definition of Geometric Model for Layered Shale

[0199] Top (m) Bottom (m) 70 46 46 23 23 0

[0200] Table 2 Basic Data

[0201] parameter Parameter value Young's modulus of shale bulk (GPa) 12 Shale bulk Poisson's ratio 0.25 Shale tensile strength MPa 6 Shale body tensile stiffness GPa / m 8 Layer tensile strength (MPa) 1.5 Layered tensile stiffness GPa / m 2 coefficient of friction of bedding plane 0.4 Formation pore pressure / MPa 50 Minimum horizontal principal stress / MPa 58～62 Vertical principal stress / MPa 70～75 Displacement m3 / min 12 fracturing fluid viscosity (mPa·s) 5

[0202] (3) Dynamic simulation of shale bedding fracture propagation and calculation of geometric parameters were achieved using the basic data in Table 2. The calculation results are as follows: Figure 5 and Figure 6 As shown.

[0203] Finally, it should be noted that the above-disclosed embodiment is only one specific embodiment of the present invention. However, the embodiments of the present invention are not limited thereto, and any variations that can be conceived by those skilled in the art should fall within the protection scope of the present invention.

Claims

1. A method for calculating geometric parameters of shale bedding fracture propagation, characterized in that, Includes the following steps: Based on the geometric parameters of the standard shale bedding layer, a set of differential equations for the standard shale bedding layer was established using the theory of elasticity. Based on the principle of two-dimensional Fourier transform, the system of differential equations is integrated into a system of partial differential equations; The partial differential equation system is transformed into an ordinary differential equation system using the two-dimensional Fourier forward transform, and the general solution of the ordinary differential equation system is obtained. The constants in the general solution of the ordinary differential equation system are obtained by using the bedding boundary conditions controlled by the linear spring. Using the two-dimensional inverse Fourier transform, the obtained set of ordinary differential equations is transformed into a calculation model of shear slip of shale bedding in a spatial coordinate system; Based on the geometric parameters of shale bedding fractures, establish the calculation equations for the geometric parameters of shale bedding fractures; By coupling the calculation model of shear slip of shale bedding with the calculation equation of geometric parameters of shale bedding cracks, a calculation model of geometric parameters of shale bedding crack propagation is obtained. A calculation model of geometric parameters for shale bedding fracture propagation was used to dynamically simulate fracture propagation during the volumetric fracturing process of shale gas, and the calculation results of geometric parameters for shale bedding fracture propagation were obtained.

2. The method for calculating geometric parameters of shale bedding fracture propagation according to claim 1, characterized in that: The process of establishing a set of differential equations for the standard shale bedding layers based on their geometric parameters and using elasticity theory includes: The constitutive equations of transversely isotropic linear elastic materials are used to establish the differential equations of the standard shale bedding layer. The differential equations for the standard shale bedding layer are as follows: （1） （2） （3） in, l Indicates the layer number of the standard shale layer; i , j , k All are 1, 2, 3, ...; For the first l Stress gradient at any point within the layer; For the first l Physical strength within the layer; For the first l Intralayer stress; , For the first l The expressions for the Lamé constants within the layer are as follows: （4） （5） E , ν These are Young's modulus and Poisson's ratio, respectively. For the first l Shear strain within the layer; The symbol for Kronecker. i = j hour, =1, i ≠ j hour, =0; , All are the first l The displacement gradient at any point within the layer is expressed as follows: or (6) For the first l The total strain within the layer is expressed as: （7） For the first l Normal strain within the layer.

3. The method for calculating geometric parameters of shale bedding fracture propagation according to claim 2, characterized in that: The process of integrating a system of differential equations into a system of partial differential equations based on the principle of two-dimensional Fourier transform includes: Based on the principle of two-dimensional Fourier transform, the system of differential equations is integrated to obtain the equations concerning the vertical direction. y The system of partial differential equations for the coordinates is as follows: （8） in, For the first l Normal stress within the layer; , For the first l Shear stress within the layer; , , The first l Inside the layer x, y , z Displacement in the direction; , , The first l Inside the layer x , y , z Physical strength in a direction.

4. The method for calculating geometric parameters of shale bedding fracture propagation according to claim 3, characterized in that: The process of transforming a system of partial differential equations into a system of ordinary differential equations using a two-dimensional positive Fourier transform, and then obtaining the general solution of the system of ordinary differential equations, includes: For transversely isotropic shale bedding, the Fourier transform object is determined by using the two-dimensional Fourier transform criterion and properties and based on the aforementioned partial differential equations. The coordinate axes parallel to the shale bedding are transformed using a two-dimensional positive Fourier transform, converting the partial differential equations into a system of ordinary differential equations. The two-dimensional Fourier transform formula is as follows: （9） in, This is the expression for stress or displacement in the Fourier transform domain; m、n These are the coordinates in the Fourier transform domain. m Corresponding to the spatial coordinate system x axis; n Corresponding to the spatial coordinate system z axis; The general solution to the system of ordinary differential equations is as follows: （10） in, k The polar coordinates in the Fourier transform domain are calculated using the following formula: （11） Solving the system of ordinary differential equations, we obtain its general solution form as follows: （12） in, , For the first l Shear stress within the layer; , , , , , These are coefficients to be determined.

5. The method for calculating geometric parameters of shale bedding fracture propagation according to claim 4, characterized in that: The method of using line spring-controlled layered boundary conditions to obtain constants in the general solution of a system of ordinary differential equations includes: By using the bedding deformation boundary conditions controlled by linear springs, the continuity conditions of displacement and stress at the bedding between upper and lower standard layers are established, and this continuity condition is used as the shale bedding boundary condition. The condition for bedding deformation controlled by the linear spring is: （13） （14） （15） （16） （17） （18） in, For the first l The bedding stiffness of bedding; , , The first l Stratification along x , y , z The rate of change of displacement in the direction; , , The first l Stratification along x , y , z The rate of change of stress in the direction; The conditions for the layered deformation controlled by the linear spring are transformed by the two-dimensional Fourier transform and substituted into equation (12) to obtain the constants in the general solution of the ordinary differential equation system.

6. The method for calculating geometric parameters of shale bedding fracture propagation according to claim 5, characterized in that: The shear slip calculation model for shale bedding in a spatial coordinate system obtained by using two-dimensional inverse Fourier transform includes: Substituting the constants from the obtained general solution of the system of ordinary differential equations into the general solution of the system of ordinary differential equations, the coordinate axes parallel to the shale bedding are transformed using the two-dimensional inverse Fourier transform and its properties. The formula for the two-dimensional inverse Fourier transform is as follows: （19） By taking the thickness of the standard layer of each shale bedding as the ordinate of the shale bedding, the calculation model of bedding shear slip in the spatial coordinate system is obtained as follows: （20） in, For the first l Layer thickness.

7. The method for calculating geometric parameters of shale bedding fracture propagation according to claim 1, characterized in that: Based on programming software and database, and using the shale bedding fracture propagation geometric parameter calculation model, dynamic simulation of fracture propagation during shale gas volumetric fracturing process is performed, and calculation results of shale bedding fracture propagation geometric parameters are obtained.

Images