A method for improving the fracture plugging effect of drilling fluid by combining a three-pore medium flow model with dislocation fracture mechanics

Abstract

The application discloses a method for improving the fracture plugging effect of drilling fluid by combining a three-pore medium flow model with dislocation fracture mechanics, and comprises the following steps: inputting a parameter set, constructing a three-pore medium flow model, configuring a solving mode, and solving and calculating to obtain the fluid pressure p in the fracture f , distributing simulation results, constructing an equation group by writing program codes, importing p f data, running the program, calculating a dislocation distribution function f(t k ), and further obtaining a fracture width W(t k ), a fracture tip stress intensity factor K I ; the fracture intensity factor K I under different conditions is obtained by modifying parameters, a K I vs. related parameter graph is drawn, a toughness coefficient K IC of a target formation is imported, for example, K IC >= K I , which indicates that the fracture will continue to expand; the fracture width and fracture re-expansion during the drilling process are predicted in real time, the plugging material is reasonably designed, the one-time plugging success rate of the fracture leakage is improved, and the continuous leakage and malignant leakage are avoided.

Description

Technical Field

[0001] This invention belongs to the field of drilling fluid fracture leakage and plugging, specifically involving a method for improving the drilling fluid fracture plugging effect by combining a three-pore medium flow model with dislocation fracture mechanics. Background Technology

[0002] During oil and gas well drilling, leakage of working fluid caused by fractured formations in the wellbore results in significant additional costs and can even lead to wellbore instability, causing serious safety issues. To address this leakage problem, sealing materials (LCMs) are added to the drilling fluid for plugging. LCMs typically need to be selected and designed based on the fracture width to ensure effective plugging.

[0003] To accurately estimate fracture size, researchers attempted to develop mechanical models related to fluid loss in the wellbore. Studies showed that, compared to numerical modeling and analytical models, semi-analytical models not only accurately predicted fracture width and stress intensity factors under different conditions but also offered higher computational efficiency. In natural fractures, fluid loss occurs at initially high and gradually decreasing flow velocities, with the amount of loss determined by fracture width, porosity, proppant conductivity, and fluid flow. Therefore, researchers developed models to describe the fluid flowing within the fracture.

[0004] However, these models neglect the fluid flowing through the wellbore toward the matrix, which may increase the pressure of the matrix around the fracture, leading to increased pressure at the fracture tip and poor plugging effect. Summary of the Invention

[0005] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0006] In view of the problems existing in the above and / or prior art, the present invention is proposed.

[0007] Therefore, the purpose of this invention is to overcome the shortcomings of the prior art and provide a method for improving the drilling fluid fracture plugging effect by combining a three-pore medium flow model with dislocation fracture mechanics.

[0008] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a method for improving the drilling fluid fracture plugging effect by combining a three-pore medium flow model with dislocation fracture mechanics, comprising,

[0009] include,

[0010] Determine the data parameter set for the actual fracture width in the well;

[0011] Input parameter set, construct three-pore medium flow model, add flow control equation, set boundary conditions, perform mesh generation, configure solution mode, and solve to obtain the fluid pressure p inside the crack. f Distributed simulation results;

[0012] By writing program code to construct a system of equations, the obtained p f Import the data, run the program, and calculate the dislocation distribution function f(t). k Then the crack width W(t) is obtained. k ), stress intensity factor K at the crack tip I ;

[0013] By modifying the parameters, the crack strength factor K under different conditions can be obtained. I Draw K I The relationship diagram with relevant parameters is used to import the toughness coefficient K of the target formation. IC , such as K IC ≥K I This indicates that the crack will continue to expand, K IC <K I The cracks remain stable;

[0014] By predicting fracture width and fracture re-expansion in real time during drilling, and designing appropriate plugging materials, the success rate of plugging fracture-related leaks in one attempt can be improved, thus avoiding continuous and malignant leaks.

[0015] As a preferred embodiment of the method described in this invention, the system of equations is constructed by means of:

[0016] The net pressure along the fracture is the superposition of the tangential stress component around the intact wellbore and the stress distributed along the fracture, expressed as follows:

[0017]

[0018] Where, σ θθ σ represents the tangential stress in the wellbore. H and σ h These represent the maximum and minimum horizontal stresses, respectively; θ represents the angle between the crack and the maximum horizontal stress; R is the wellbore radius; r is the distance from the wellbore center; and p... w This refers to the pressure inside the wellbore.

[0019] When two axisymmetric cracks exist, according to the potential of the complex function, the stress distribution on the fracture surface is equal to:

[0020]

[0021] in, The stress distribution on the fracture surface is represented by R, the radius of the wellbore, b, the position of the fracture tip, f(ξ), the dislocation distribution function that determines the fracture width distribution and the stress intensity factor at the fracture tip, ξ, the position of each dislocation tip, and x, the position of the stress field.

[0022]

[0023] Supplementary conditions for the maximum opening of the crack:

[0024] f(R)=0 (4)

[0025] The traction force along the fracture surface can be expressed as:

[0026]

[0027] Where E' is the plane strain modulus, E'=2G / (1-v) (v is Poisson's ratio, G is shear modulus), This represents the stress distribution on the fracture surface, σ. θθ p represents the tangential stress in the wellbore. f The fluid pressure inside the crack;

[0028] Based on the properties of Chebyshev polynomials, by using equations (2), (4), and (5), the integration interval is transformed from [a, b] to [-1, 1], and the following system of equations is constructed:

[0029]

[0030]

[0031]

[0032] Normalization process:

[0033]

[0034]

[0035] in, The stress distribution on the fracture surface is represented by R, the wellbore radius, b, the location of the fracture tip, m, a constant, ξ, and t. k Let ξ be the normalized value, x be the calculated location of the stress field, and y be the normalized value of x. By simultaneously solving equations (6) and (7), the distribution function f(t) is obtained. k );

[0036] The crack width and stress intensity factor are expressed using a semi-analytical model based on dislocation theory as follows:

[0037]

[0038]

[0039] As a preferred embodiment of the method described in this invention, the step of determining the data parameter set of the actual fracture width in drilling includes collecting historical drilling data of the target formation, plugging cases, and imaging logging data of the actual fracture width. The parameter set is obtained by collecting, organizing, and verifying the data.

[0040] As a preferred embodiment of the method described in this invention, the parameter set includes matrix porosity φ. m Matrix permeability k m Matrix elastic modulus K m Porosity φ of the filling and sealing material f , Permeability k of the filling and sealing material f Fluid bulk modulus K w Fluid viscosity μ, fluid volume compressibility C bf Initial pore pressure p0, wellbore pressure p w Matrix pore pressure p m The filtration coefficient ω, crack length L, and operation time t are also considered.

[0041] 5. The method as described in claim 1, wherein the flow control equation is as follows:

[0042]

[0043]

[0044]

[0045]

[0046] Among them, K w and K m These are the fluid bulk modulus and the matrix bulk modulus, respectively, k m k represents the matrix permeability. f The permeability of the filling and sealing material is given by φ, where φ is the porosity. m For matrix porosity, φ f The porosity of the sealing material is given by μ, the fluid viscosity by ρ, the fluid density by p, and the fluid pressure by C. b α is the volume compressibility coefficient, α is the cake permeability coefficient, and the subscripts m, f, c are the matrix, fluid, and cake, respectively. m p is the matrix pore pressure. f Where ω is the fluid pressure in the crack, C is the filtration coefficient, and ω is the fluid loss coefficient. bf t is the fluid volume compressibility coefficient, and t is time.

[0047] In a preferred embodiment of the method described in this invention, the boundary conditions are set as follows:

[0048] p m (R,t)=p f (R,t)=p w (16)

[0049] p m (R,∞)=p0 (17)

[0050] q f (R+L,t)=ω(p f -p m (18)

[0051] p m (x,t0)=p f (x,t0)=p0 (19)

[0052] Where p0 is the initial pore pressure, p w p is the wellbore pressure. m p is the matrix pore pressure. f R is the fluid pressure in the fracture, L is the wellbore radius, L is the fracture length, t is the operating time, t0 is the initial time, and q is the fluid pressure in the fracture. f Let ω be the fluid flow rate, ω be the filtration loss coefficient, and x be the location of the stress field.

[0053] As a preferred embodiment of the method described in this invention, the input parameter set is used to construct a three-pore medium flow model, which includes launching the commercial finite element software COMSOL Multiphysics to create a three-pore medium flow model.

[0054] In a preferred embodiment of the method described in this invention, the step of writing program code includes writing program code using MATLAB software.

[0055] In a preferred embodiment of the method described in this invention, the step of constructing a system of equations by writing program code is as follows:

[0056]

[0057]

[0058]

[0059] f(R)=0 (4)

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068] Where, σ θθ σ represents the tangential stress in the wellbore, θ represents the angle between the fracture and the maximum horizontal stress, and σ represents the tangential stress in the wellbore. H and σ h These represent the maximum and minimum horizontal stresses, respectively; R is the wellbore radius; r is the distance from the wellbore center; p w For wellbore pressure, The stress distribution on the fracture surface is represented by f(ξ), which is the dislocation distribution function that determines the crack width distribution and the stress intensity factor at the crack tip. ξ represents the position of each dislocation tip, x represents the calculated stress field position, y represents the normalized value of x, E' is the plane strain elastic modulus, E'=2G / (1-v), v is Poisson's ratio, G is the shear modulus, and p f K represents the fluid pressure within the fracture. I This represents the crack pressure intensity factor, b is the location of the crack tip, m is a constant, and t is the crack pressure intensity factor. k Let ξ be the value after normalization, and W(t) be the value of ξ. k () indicates the crack width.

[0069] Beneficial effects of this invention:

[0070] (1) Compared with the previous method of ignoring the change of fluid pressure in the crack during the leakage process, the present invention introduces a three-pore medium flow model, which is closer to the real scene of the operation site, and the calculation results are more accurate and have guiding significance.

[0071] (2) The method adopted in this invention combines the three-pore medium flow model with the semi-analytical analysis method of dislocation fracture mechanics. Through theoretical derivation, a method for calculating the crack width and evaluating crack propagation under the condition of fluid pressure change inside the crack is obtained. The leakage crack width and evaluation of crack propagation calculated by this method can provide a basis for judgment on the design and method selection of sealing materials in drilling and plugging operations, provide technicians with more accurate and effective decision-making basis, improve operation efficiency and success rate, and save construction costs. Attached Figure Description

[0072] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0073] Figure 1 This is a mechanical model of the wellbore and adjacent fractures, and a schematic diagram of fluid flow in a three-pore medium.

[0074] Figure 2 This is a flowchart illustrating the implementation of the present invention.

[0075] Figure 3 The variations in crack width and stress intensity factor under different case conditions of this invention are shown.

[0076] Figure 4 This is a comparison chart of the crack width results calculated by the original model and the model of this invention. Detailed Implementation

[0077] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the examples in the specification.

[0078] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0079] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0080] Example 1

[0081] This invention is based on the theory of dislocation fracture mechanics, which treats cracks as discontinuities in the matrix, crack propagation as translation of particles on the fracture surface, and the critical pressure for crack propagation as the stress intensity factor, which controls the stress field and displacement field near the crack tip, thereby affecting the crack propagation law.

[0082] Meanwhile, a three-porosity medium flow model was introduced. The mud cake attached around the wellbore and on the fracture surface is the third type of porosity medium. The other two types of porosity media are the formation matrix and the sealing material filling the fracture. During the fluid flow, the fluid pressure in the fracture is in a state of change, and the formation matrix far away from the fracture does not transfer fluid with the fracture.

[0083] The distributed stress on the crack surface is calculated, the dislocation distribution function is further solved, and finally the crack width and stress intensity factor are solved.

[0084] The relationship between wellbore pressure, fracture stress intensity factor, and rock fracture toughness coefficient is used to evaluate fracture propagation. Details are as follows:

[0085] (1) Establish a mechanical model of the wellbore and its adjacent fractures. Figure 1 A semi-analytical analysis was performed on the fracture geometry and stress intensity: It was assumed that if the wellbore pressure Pw is higher than the fracturing pressure, two axisymmetric induced fractures will be generated near the wellbore. Whether the fractures propagate depends on the magnitude of the resistance generated by the combined action of in-situ anisotropic stresses in the near-wellbore stress field. If the fractures propagate, they generally follow the path of least resistance, i.e., the direction perpendicular to the direction of the minimum horizontal stress in the vertical well.

[0086] This model is divided into two parts: a complete wellbore with anisotropic stress and a fractured wellbore with surface pressure on the fractures. By superimposing the stress conditions of the two parts, a mechanical model of the wellbore and its adjacent fractures is obtained, leading to the following conclusions:

[0087] The net pressure along the fracture is the superposition of the tangential stress component around the intact wellbore and the stress distributed along the fracture, expressed as follows:

[0088]

[0089] Where, σ θθ σ represents the tangential stress in the wellbore. H and σ h These represent the maximum and minimum horizontal stresses, respectively; θ represents the angle between the crack and the maximum horizontal stress; R is the wellbore radius; r is the distance from the wellbore center; and p... w This refers to the pressure inside the wellbore.

[0090] like Figure 1 As shown in the model, when two axisymmetric cracks exist, according to the potential of the complex function, the stress distribution on the fracture surface is equal to:

[0091]

[0092] in, Let f(ξ) represent the stress distribution on the fracture surface, R be the wellbore radius, b be the position of the fracture tip, f(ξ) be the dislocation distribution function that determines the fracture width distribution and the stress intensity factor at the fracture tip, ξ be the position of each dislocation tip, and x be the position of the stress field.

[0093]

[0094] Supplementary condition for maximum crack opening (Rubinstein 1987):

[0095] f(R)=0 (4)

[0096] The traction force along the fracture surface can be expressed as (Carbonell, 1995):

[0097]

[0098] Where E' is the plane strain modulus, E'=2G / (1-v) (v is Poisson's ratio, G is shear modulus), This represents the stress distribution on the fracture surface, σ. θθ p represents the tangential stress in the wellbore. f The pressure is the fluid pressure inside the crack.

[0099] Based on the properties of Chebyshev polynomials, by using equations (2), (4), and (5), the integration interval is transformed from [a, b] to [-1, 1], and the following system of equations is constructed:

[0100]

[0101]

[0102]

[0103] Normalization process:

[0104]

[0105]

[0106] in, The stress distribution on the fracture surface is represented by R, the wellbore radius, b, the location of the fracture tip, m, a constant, ξ, and t. k Let ξ be the normalized value, x be the calculated location of the stress field, and y be the normalized value of x. By simultaneously solving equations (6) and (7), the distribution function f(t) can be obtained. k ).

[0107] Using a semi-analytical model based on dislocation theory (Warren et al., 1982; Carbonell et al., 1995; Shahri et al., 2014), the crack width and stress intensity factor are expressed as:

[0108]

[0109]

[0110] (2) Data collection of historical drilling data, plugging cases, and actual fracture width from imaging logging in the target block. Through the collection, organization, and verification of the data, a parameter set was determined:

[0111] Matrix porosity φ m Matrix permeability k m Matrix elastic modulus K m Porosity φ of the filling and sealing material f , Permeability k of the filling and sealing material f Fluid bulk modulus K w Fluid viscosity μ, fluid volume compressibility C bf Initial pore pressure p0, wellbore pressure p w Matrix pore pressure p m The filtration coefficient ω, the crack length L, and the operation time t.

[0112] (3) Launch the commercial finite element software COMSOL Multiphysics, configure the solution mode to transient mode, enter the parameters in step (2) in the model developer window, add three line segments with lengths of 500m, 5mm and L in the geometry toolbar to complete the geometric construction of the three-pore medium model, add the flow control equations and set the boundary conditions in sequence, locate the physical field control grid in the mesh settings window, set the mesh size to regular, and complete the mesh generation settings.

[0113] The governing equations for fluid flow in a three-pore medium are as follows:

[0114]

[0115]

[0116]

[0117]

[0118] Among them, K w and K m These are the fluid bulk modulus and the matrix bulk modulus, respectively, k m k represents the matrix permeability. fThe permeability of the filling and sealing material is given by φ, where φ is the porosity. m For matrix porosity, φ f The porosity of the sealing material is given by μ, the fluid viscosity by ρ, the fluid density by p, and the fluid pressure by C. b α is the volume compressibility coefficient, α is the cake permeability coefficient, and the subscripts m, f, c are the matrix, fluid, and cake, respectively. m p is the matrix pore pressure. f Where ω is the fluid pressure in the crack, C is the filtration coefficient, and ω is the fluid loss coefficient. bf t is the fluid volume compressibility coefficient, and t is time.

[0119] The boundary conditions are set as follows:

[0120] p m (R,t)=p f (R,t)=p w (16)

[0121] p m (R,∞)=p0 (17)

[0122] q f (R+L,t)=ω(p f -p m (18)

[0123] p m (x,t0)=p f (x,t0)=p0 (19)

[0124] Where p0 is the initial pore pressure, p w p is the wellbore pressure. m p is the matrix pore pressure. f R is the fluid pressure in the fracture, L is the wellbore radius, L is the fracture length, t is the operating time, t0 is the initial time, and q is the fluid pressure in the fracture. f Let ω be the fluid flow rate, ω be the filtration loss coefficient, and x be the location of the stress field.

[0125] The fluid pressure p inside the fracture was obtained by performing the calculation. f Distribution simulation results.

[0126] (4) Write program code using MATLAB software to construct the system of equations in step (1) and convert the p obtained in step (3) into the system of equations in step (3). f Import the data, run the program, and calculate the crack width and crack strength factor.

[0127] (5) By modifying the selected condition parameters, the crack strength factor K under different condition parameters is calculated. I Launch the commercial software Origin and obtain the K IImport the data and selected conditional parameters, and plot K. I The relationship diagram with different condition parameters is used to import the toughness coefficient K of the target formation. IC (constant), if K IC >K I Under these conditions, the crack will continue to expand.

[0128] Example 2

[0129] Figure 2 This is a flowchart of the implementation method of the present invention.

[0130] The actual data pertains to a tight sandstone reservoir in a certain block. Based on the geological background data, the target formation has a matrix porosity of 0.06 and a matrix permeability of 1*10⁻⁶. -16 m 2 The matrix bulk modulus is 2.5 GPa, the fluid bulk modulus is 2.2 GPa, and the initial pore pressure is 4800 psi.

[0131]

[0132] The commercial finite element software COMSOL Multiphysics was used to solve the three cases, and the fluid pressure p inside the crack was obtained respectively. f distributed.

[0133] Write program code using MATLAB software to construct the system of equations in step (1), and convert the p obtained in step (2) into the system of equations in step (2). f Import the data, run the program, and calculate the crack width and crack strength factor; launch the commercial software Origin, and use the obtained K... I Import data and conditional parameters, and plot K. I The relationship diagram with various condition parameters is used to import the toughness coefficient K of the target formation. IC , such as K IC ≥K I This indicates that the crack will continue to expand, K IC <K I The cracks remained stable. Figure 3 ).

[0134] Comparative Example 1

[0135] Using the same parameter settings as in Example 2, without introducing a three-pore medium flow model, the original model (Shahri et al., 2014) was applied, and p was taken as... f =p w p at time f The values ​​are imported into a MATLAB program to calculate the crack width, such as... Figure 4 As shown.

[0136] Compared with the three-pore medium flow model, the crack width calculated by the original model is a constant value that does not change with time. The crack width calculated by the model used in this invention increases with time and eventually tends to stabilize, which is more in line with reality.

[0137] If the sealing material is designed based on the unchanged crack width, continuous leakage is likely to occur due to the continuous expansion of the crack, leading to the failure of the sealing. Only a sealing material design scheme that matches the actual crack width can improve the success rate of sealing a leak in one attempt.

[0138] This invention establishes a three-pore medium model to solve for the pressure distribution on the fracture surface, and combines it with a dislocation fracture mechanics model to solve for the fracture geometry and tip stress intensity. In the three-pore medium model, the mud cake adhering to the wellbore and fracture surface is considered as the third type of porous medium, while the other two porous media are the sealing material and formation matrix filling the fracture. Parametric studies were conducted using both models to explore the influence of fluid flow on fracture width and propagation. The conditions for effectively isolating the fracture tip to achieve leakage plugging were studied, thereby enabling drilling fluid optimization and sealing material design. This model explicitly considers the fluid flow process during leakage and evaluates the time-dependent fracture width and propagation.

[0139] In summary, by calculating a more realistic and accurate fracture width and evaluating fracture propagation, and further exploring the variation patterns of fracture width and stress intensity factor under different conditions, appropriate LCM and operation plans can be designed for field operations, improving the plugging effect during drilling operations and increasing the success rate of plugging in a single operation.

[0140] This invention establishes a three-porosity medium model to characterize the pressure distribution on the fracture surface, and combines it with dislocation fracture mechanics theory to characterize the fracture geometry and tip stress intensity. In the three-porosity medium model, the mud cake adhering to the wellbore and fracture surface is considered as the third type of porous medium, while the other two types of porous media are LCMs and the matrix filling the fracture.

[0141] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the present invention.

Claims

1. A method for improving the sealing effect of drilling fluid fractures by combining a three-pore medium flow model with dislocation fracture mechanics, characterized in that: include, Determine the data parameter set for the actual fracture width in the well; Input parameter set, construct a three-pore medium flow model, add flow control equations, set boundary conditions, perform mesh generation, configure the solution mode, and calculate the fluid pressure inside the fracture. p f Distributed simulation results; By writing program code to construct a system of equations, the obtained p f Import the data, run the program, and calculate the dislocation distribution function. f(t k ) This leads to the determination of the crack width. W(t k ) Crack tip stress intensity factor K I ; By modifying the parameters, the crack strength factor under different conditions can be obtained. K I ,draw K I A graph showing the relationship between the target formation and relevant parameters was used to import the toughness coefficient of the target formation. K IC ,like K IC ≥ K I This indicates that the crack will continue to expand. K IC < K I The cracks remain stable; By predicting fracture width and fracture re-expansion in real time during drilling, and designing appropriate plugging materials, the success rate of plugging fracture-related leakage can be improved, thus avoiding continuous and malignant leakage. The flow control equations are as follows: in, K w and K m These are the fluid bulk modulus and the matrix bulk modulus, respectively, k m k represents the matrix permeability. f To reduce the permeability of the sealing material, Porosity For matrix porosity, The porosity of the sealing material is given by µ, and the fluid viscosity is given by µ. ρ For fluid density, p For fluid pressure, C b α is the volume compressibility coefficient, and α is the cake permeability coefficient. (Subscript) m,f,c They are respectively matrix, fluid, and mud cake. p m For matrix pore pressure, p f Where ω is the fluid pressure in the crack, C is the filtration coefficient, and ω is the fluid loss coefficient. bf t is the fluid volume compressibility coefficient, and t is time.

2. The method as described in claim 1, characterized in that: The system of equations is constructed using the following methods: The net pressure along the fracture is the superposition of the tangential stress component around the intact wellbore and the stress distributed along the fracture, expressed as follows: Where, σ θθ σ represents the tangential stress in the wellbore. H and σ h These represent the maximum and minimum horizontal stresses, respectively; θ represents the angle between the crack and the maximum horizontal stress; R is the wellbore radius; and r is the distance from the wellbore center. P w This refers to the pressure inside the wellbore. When two axisymmetric cracks exist, according to the potential of the complex function, the stress distribution on the fracture surface is equal to: in, This represents the stress distribution on the fracture surface, where R is the wellbore radius and b is the location of the crack tip. f (ξ) is the dislocation distribution function that determines the crack width distribution and the stress intensity factor at the crack tip, where ξ is the position of each dislocation tip and x is the position of the stress field; Supplementary conditions for the maximum opening of the crack: The traction force along the fracture surface can be expressed as: Where E' is the plane strain modulus, E'=2G / (1-v) (v is Poisson's ratio, G is shear modulus), This represents the stress distribution on the fracture surface, σ. θθ p represents the tangential stress in the wellbore. f The fluid pressure inside the crack; Based on the properties of Chebyshev polynomials, by using equations (2), (4), and (5), the integration interval is transformed from [a, b] to [-1, 1], and the following system of equations is constructed: Normalization process: in, The stress distribution on the fracture surface is represented by R, the wellbore radius, b, the location of the fracture tip, m, a constant, ξ, and t. k Let ξ be the normalized value, x be the calculated location of the stress field, and y be the normalized value of x. By simultaneously solving equations (6) and (7), the distribution function f(t) is obtained. k ); The crack width and stress intensity factor are expressed using a semi-analytical model based on dislocation theory as follows: 。 3. The method as described in claim 1, characterized in that: The parameter set for determining the actual fracture width in drilling includes collecting historical drilling data, plugging cases, and imaging logging data on the target formation. The parameter set is obtained by collecting, organizing, and verifying the data.

4. The method as described in claim 1 or 2, characterized in that: The parameter set includes matrix porosity. Matrix permeability k m Matrix elastic modulus K m Porosity of filling and sealing materials , Permeability k of the filling and sealing material f Fluid bulk modulus K w Fluid viscosity μ, fluid volume compressibility C bf Initial pore pressure p0, wellbore pressure p w Matrix pore pressure p m The filtration loss coefficient ω, the crack length L, and the operation time t are all factors.

5. The method as described in claim 1, characterized in that: Set the boundary conditions as follows: Where p0 is the initial pore pressure, p w p is the wellbore pressure. m p is the matrix pore pressure. f R is the fluid pressure in the fracture, L is the wellbore radius, L is the fracture length, t is the operating time, t0 is the initial time, and q is the fluid pressure in the fracture. f Let ω be the fluid flow rate, ω be the filtration coefficient, and x be the location of the stress field.

6. The method as described in claim 1, characterized in that: The input parameter set is used to construct a three-pore medium flow model, which includes launching the commercial finite element software COMSOL Multiphysics three-pore medium flow model.

7. The method as described in claim 1, characterized in that: The process of writing program code includes writing program code using MATLAB software.

8. The method as described in claim 1, characterized in that: The system of equations is constructed by writing program code, and the constructed system of equations is as follows: Where, σ θθ σ represents the tangential stress in the wellbore, θ represents the angle between the fracture and the maximum horizontal stress, and σ represents the tangential stress in the wellbore. H and σ h These represent the maximum and minimum horizontal stresses, respectively; R is the wellbore radius; r is the distance from the wellbore center; p w For wellbore pressure, The stress distribution on the fracture surface is represented by f(ξ), which is the dislocation distribution function that determines the crack width distribution and the stress intensity factor at the crack tip. ξ represents the position of each dislocation tip, x represents the calculated stress field position, y represents the normalized value of x, E' is the plane strain elastic modulus, E' = 2G / (1-v), v is Poisson's ratio, G is the shear modulus, pf is the fluid pressure inside the crack, and K... I This represents the crack pressure intensity factor, b is the location of the crack tip, m is a constant, and t is the crack pressure intensity factor. k Let ξ be the value after normalization, and W(t) be the value of ξ. k () indicates the crack width.

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