A perforation fracture pressure prediction method considering wellbore deformation and mudcake sealing

Abstract

The application discloses a perforation breakdown pressure prediction method considering wellbore deformation and mud cake plugging, and relates to the technical field of oil and gas development.The method comprises the following steps: firstly, obtaining formation parameters, wellbore geometric parameters, perforation construction parameters and mud cake physical property parameters of a target well section; using a conformal transformation to map a non-circular wellbore shape after elliptical deformation into a standard circular ring; calculating a circumferential stress distribution induced by wellbore geometric deformation; constructing a mud cake seepage-pore elasticity coupling model; analytically describing a shielding effect of the mud cake on pressure transmission in the wellbore and an additional pore stress field generated by the mud cake; coupling a three-dimensional unequal ground stress field, wellbore internal pressure and a mud cake induced stress field; constructing an effective stress tensor of a perforation tip; introducing a vertical stress component to determine a main stress state of cracking; and finally outputting a three-dimensional explicit analytical solution of perforation breakdown pressure.The method overcomes the defects of the prior art, i.e., neglecting wellbore deformation and mud cake plugging effect, and can realize accurate prediction of perforation cracking pressure in an ultra-deep layer under an extreme environment.

Description

Technical Field

[0001] This invention relates to the field of oil and gas development technology, specifically a method for predicting perforation fracture pressure that takes into account wellbore deformation and mud cake blockage. Background Technology

[0002] In (ultra)deep unconventional oil and gas development operations, high horizontal stress gradients, high formation temperatures, and high pore pressures create an extreme high-stress, high-temperature, and high-pressure engineering environment, resulting in high hydraulic fracturing fracture pressure and low fracture initiation efficiency. Against this backdrop, perforation technology plays a crucial role in reducing rock mass fracturing pressure and directionally controlling fracture initiation location and propagation direction. The core parameter controlling perforation fracturing pressure—the perforation peri-stress field—is closely related to wellbore deformation, mud cake plugging effect, and three-dimensional in-situ in-situ stress. However, conventional linear elastic solutions based on ideal circular open-hole wellbores cannot reflect the impact of elliptical deformation of deep wellbores on the near-wellbore stress field, nor can they accurately describe the mechanism of mud cake seepage-pore elastic coupling on the effective stress of the perforation wall, thus failing to accurately predict the fracturing pressure and related parameters of perforated hydraulic fracturing.

[0003] The aforementioned multi-effect coupling is manifested in several ways. First, the high stress differential environment in deep formations causes the wellbore to undergo elliptic deformation due to the biaxial unequal horizontal principal stresses. This renders near-wellbore stress analysis, which was originally based on the assumption of a circular wellbore, ineffective. The degree of ellipticization alters the non-uniform distribution of tangential stress around the well, directly affecting the stress concentration at the perforation tip. Second, during drilling operations, drilling fluid is lost to the formation and forms a low-permeability mud cake on the perforation wall. This mud cake, on the one hand, alters the proportion of pressure transmitted to the rock skeleton within the perforation through a shielding effect; on the other hand, the mud cake itself enters a plastic yielding state under pressure differential, resulting in an actual effective radial pressure applied to the formation that is significantly lower than the fluid column pressure within the wellbore, thus systematically altering the fracturing initiation conditions. Finally, ultra-deep perforations are in a true three-dimensional stress state, where vertical stress contributes significantly to the circumferential stress at the perforation root through the Poisson effect. Previous two-dimensional models based on plane stress or plane strain assumptions cannot capture this effect, leading to a systematic underestimation of the fracture pressure. In summary, the fracturing pressure of ultra-deep perforated hydraulic fracturing is controlled by the coupling of multiple effects of wellbore deformation, mud cake plugging, and three-dimensional stress. Accurate prediction of fracturing pressure requires consideration of the interaction of the above three effects simultaneously within a unified analytical framework.

[0004] Therefore, establishing a three-dimensional analytical prediction method for ultra-deep perforation fracturing pressure that integrates wellbore elliptic deformation, perforation stress concentration, and mud cake plugging effect, and providing an explicit closed solution, provides analytical basis for the coordinated optimization of perforation direction angle, perforation length, and drilling fluid plugging performance. This is particularly important for ensuring the safety and effectiveness of ultra-deep fracturing operations and improving reservoir stimulation efficiency.

[0005] Currently, methods exist for predicting fracture pressure in perforated wells. For example, the invention patent CN 117195773A, published by Southwest Petroleum University, discloses a method and system for calculating the fracture pressure of perforated wells in deep shale gas formations. This method addresses the common elliptical deformation of wellbores in deep shale gas reservoirs. Based on the conformal mapping theory of complex variable functions, it maps the physical model formed by the elliptical wellbore and the perforation hole to a complex plane unit circle region, introducing the concept of complex stress intensity factor. Following the superposition principle, the load is decomposed into loading mode I (only subject to in-situ geostress) and loading mode II (only subject to perforation hydraulic pressure), deriving the derivatives of the stress functions respectively, and then superimposing them to obtain the type I and type II stress intensity factors at the fracture tip. Using the maximum circumferential stress criterion as the fracture criterion, the hydraulic fracture initiation angle is calculated. Finally, by progressively setting the perforation hydraulic pressure and iteratively verifying it, the rock fracture pressure corresponding to achieving the rock fracture toughness of the type I stress intensity factor at the fracture tip is determined. This invention is the first to propose an analytical calculation method for the fracturing pressure of planar perforation in deformable wellbores based on conformal transformation, filling the technical gap in the analytical calculation of fracturing pressure of perforation in elliptical deformable wellbores and providing a certain theoretical basis for the fracturing design of deep shale gas-cased deformable wells.

[0006] A patent published by Southwest Petroleum University, with publication number CN119102595A, discloses a method for predicting the initiation pressure of directional perforation hydraulic fracturing using thermo-fluid-structure interaction. This method obtains the elastic mechanical parameters, thermo-coupling parameters, porous media mechanical parameters, and strength parameters of the casing, cement sheath, and formation rock through laboratory experiments and well logging data. It derives the analytical solution of the stress field of the surrounding rock under non-uniform geostress conditions caused by the casing, cement sheath, and thermal coupling using the deformation control equation of the "casing-cement sheath-formation assembly." Then, using this as boundary conditions, it solves the analytical solution of the field variables of the surrounding rock under the thermo-fluid-structure interaction of the perforation channel. By integrating the rock tensile fracturing initiation criterion, it finally predicts the initiation angle and dynamic initiation pressure of directional perforation hydraulic fracturing, and can optimize the perforation depth, phase angle, and drilling displacement. This invention provides theoretical and technical guidance for the design of directional perforation hydraulic fracturing.

[0007] While the two patents and other existing technologies have their own technical contributions, they all share the following shortcomings: First, neither patent incorporates the mud cake effect formed by drilling fluid loss on the perforation wall into the mechanical analysis framework, neglecting the profound impact of mud cake seepage-pore elastic coupling on the effective stress boundary conditions of the perforation wall. On the one hand, the mud cake shields the transmission of pressure from the wellbore to the formation rock skeleton through its own plastic yielding; on the other hand, its seepage effect alters the pore pressure distribution around the perforation, thus systematically affecting the magnitude of the fracture pressure. The current methods' neglect of this effect will lead to unpredictable prediction results under strong mud cake plugging conditions. First, there are several shortcomings. The first is the neglect of systematic biases. The second is that the former, based on the plane stress assumption, only considers the influence of two-dimensional horizontal principal stresses on perforation initiation behavior, failing to incorporate the contribution of vertical stress to the local principal stress state at the perforation root through the Poisson effect into a unified calculation system. This results in a systematic underestimation of the fracture pressure prediction under ultra-deep, real three-dimensional high-stress environments. The latter, while introducing a three-dimensional stress field analysis framework, establishes its near-wellbore stress field based on the assumption of an ideal circular cross-section wellbore, failing to consider the influence of the elliptic deformation of the wellbore, which is common under ultra-deep, high-stress-difference environments, on the stress concentration at the perforation tip and the direction of fracture initiation. These shortcomings combine to make the accuracy of perforation fracture pressure prediction under ultra-deep, high-stress-difference, and strong mud cake sealing conditions insufficient to meet engineering requirements. Summary of the Invention

[0008] In view of this, the present invention provides a perforation fracture pressure prediction method that considers wellbore deformation and mud cake plugging. It can simultaneously couple wellbore elliptic deformation, perforation dual stress concentration and mud cake seepage-pore elasticity effect under three-dimensional stress state to perform explicit analytical prediction of perforation fracture pressure, so as to make up for the above-mentioned deficiencies of the prior art.

[0009] The technical solution of this invention is a method for predicting perforation fracture pressure considering wellbore deformation and mud cake blockage, comprising the following steps: Step S1: Obtain the elastic mechanical parameters, strength parameters, and pore medium mechanical parameters of the target well formation rock; Step S2: Calculate the triaxial in-situ in-situ stress and original formation pore pressure at the target well depth using logging data; Step S3: Compile wellbore structural data, including wellbore elliptic geometry parameters, perforation geometry parameters, and mud cake physical properties parameters; Step S4: Based on the conformal transformation theory of complex functions, establish a conformal mapping model for an elliptical wellbore containing symmetrical perforations, and map the irregular geometric region formed by the elliptical wellbore and perforations in the physical plane to the unit circle region in the complex plane. Step S5: Under the conformal mapping plane established in step S4, the total load is decomposed into far-field in-situ stress loading mode and hydraulic pressure loading mode. The perforation complex stress function under each loading mode is solved respectively. The two types of stress intensity factors at the perforation tip and the circumferential stress at the perforation tip are further calculated. Step S6: Based on the Darcy radial flow model, establish the flow continuity equations for the cake zone and the formation zone at the perforation scale, solve the perforation wall pore pressure, establish the cake seepage-pore elastic coupling equation, and calculate the additional stress field induced by pore pressure changes. Step S7: Based on the principle of linear superposition, the stress field at the perforation tip obtained in step S5 is superimposed with the additional elastic stress field in the pore obtained in step S6 to obtain the basic equation of two-dimensional perforation rupture pressure. Step S8: Based on the magnitudes of the vertical stress and the circumferential stress at the perforation tip, substitute the values ​​into the fundamental equation for perforation rupture pressure, and calculate the three-dimensional explicit analytical solution for the rupture pressure of ultra-deep perforations. The technical effects of this invention are: The prediction method proposed in this invention achieves, for the first time, a three-dimensional coupling of three effects—wellbore elliptic deformation, perforation stress concentration, and mud cake seepage-pore elasticity—within a unified analytical framework. It directly incorporates fracture toughness into the explicit solution of fracture pressure, avoiding the uncertainty of characteristic distance. It provides three-dimensional explicit closed analytical solutions for different cases, with high computational efficiency and no convergence issues, and can directly serve the collaborative optimization design of perforation direction angle, perforation length, and drilling fluid plugging performance in ultra-deep formations. Attached Figure Description

[0010] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below.

[0011] Figure 1 This is an overall flowchart of the present invention; Figure 2 This is a diagram showing the rupture pressure curves calculated at different perforation azimuth angles in an embodiment of the present invention. Detailed Implementation

[0012] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings.

[0013] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. The described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0014] See Figure 1 A method for predicting perforation fracture pressure considering wellbore deformation and mud cake plugging includes the following steps: Step S1: Using well logging data and laboratory rock mechanics experiments, obtain the elastic mechanical parameters, strength parameters, and pore medium mechanical parameters of the formation rock in the target well; Using a gas permeameter to measure core permeability ; Measuring the elastic modulus of formation rocks using a high-temperature, high-pressure triaxial rock tester Compared to Poisson Tensile strength of rock determined by Brazilian splitting test Fracture toughness was determined by a three-point bending fracture test. The effective stress coefficient of Biot was determined by testing the porosity elastic parameters. and porosity elastic coefficient .

[0015] Step S2: Calculate the triaxial in-situ in-situ stress and original formation pore pressure at the target well depth by inverting the logging data; The formula for calculating geostress includes: The pressure of the overlying strata, i.e., the vertical stress, is shown in the following formula: The calculation of far-field pore pressure (Eaton method) is shown in the following formula: The calculation of the maximum and minimum horizontal principal stresses is shown in the following formula: In the formula, Density of the rock mass, g / cm³; The acceleration due to gravity is m / s². 2 ; Let the vertical depth be m; The hydrostatic pressure is MPa. The acoustic time difference is for the normal compaction trend line. ; To measure the P-wave time difference, ; The Eaton exponent is dimensionless. and , representing the tectonic strains in the directions of maximum and minimum horizontal stress, respectively, are dimensionless.

[0016] Step S3: Compile wellbore structural data, including wellbore elliptic geometry parameters, perforation geometry parameters, and mud cake physical properties parameters; Wellbore ellipticization geometry parameters include the major semi-axis of the ellipse. a (m) and short half-axis b (m), determined by caliper logging or imaging logging data; perforation geometry parameters include perforation length. lp (m), inner radius of the perforation hole (m) and perforation direction angle (i.e., perforation and maximum horizontal principal stress) (Angle of direction); total distance from the perforation tip to the center of the wellbore. c (satisfy c = a + lp ); Mud cake physical properties include mud cake permeability (mD), outer radius of the mud cake (m) (satisfies) ), radius of influence zone (m), mud cake thickness The permeability of the drilling fluid was determined using drilling fluid loss tests and mud cake tests. and mud cake yield strength .

[0017] Step S4: Based on the conformal transformation theory of complex functions, establish a conformal mapping model for an elliptical wellbore with symmetrical perforations. Map the irregular geometric region formed by the elliptical wellbore and perforations in the physical plane to the unit circle region in the complex plane, providing a geometric transformation basis for subsequent stress analysis.

[0018] The specific method is as follows: Based on the conformal transformation theory of complex functions, the external region of the elliptical wellbore containing symmetrical perforations is mapped to the unit circle region, and then based on the Cartesian coordinate system after co-mapping... The complex stress in the plane is transformed into an expression in polar coordinates.

[0019] The calculation formula includes: Governing equations of the symmetric perforation problem in, The Airy stress function, when transformed into complex form, has the following expression: , and Let each represent a complex variable and an analytic complex function. By combining the above formulas, the complex stress form of the elliptical well shaft can be expressed as: The outer region of the elliptical wellbore containing symmetrical perforations is mapped to the unit circle region using a conformal mapping function, which is: intermediate variables and It can be represented as: To facilitate the solution, we can use the Cartesian coordinate system after co-mapping. Transform the complex stress in the formula into an expression in polar coordinates in the plane: The formula for the intermediate complex variable is as follows: In the above formula, and These represent stress components in different directions along the spatial coordinate axes; and It is the complex plane The real and imaginary components in ( = + ); intermediate coefficient and The expressions are respectively and ; , and These represent the lengths of the major and minor semi-axes of the ellipse and the length of the perforation, respectively, in meters (m). It equals the sum of the perforation length and the semi-major axis of the ellipse ( = + ); , and These represent the tangential stress, radial stress, and shear stress components in polar coordinates, respectively, with units of MPa. and It is the complex plane The two complex stress functions in the equation.

[0020] Step S5: Under the conformal mapping plane established in step S4, the total load is decomposed into far-field in-situ stress loading mode and hydraulic pressure loading mode. The complex stress function under each loading mode is solved respectively. The two types of stress intensity factors at the perforation tip and the circumferential stress at the perforation tip are further calculated. Based on linear elastic conditions, the stress problem of double-symmetric radial perforation after wellbore deformation can be divided into two sub-problems: loading mode I (far-field in-situ stress) and loading mode II (hydraulic pressure). Derivative of complex stress function for loading mode I: The derivative of the complex stress function for loading mode II is: By differentiating the conformal mapping function ω(ζ) with respect to ζ, and combining this with the Cauchy integral formula at infinity... Based on the superposition principle, the stress intensity factors of loading mode I and loading mode II at the perforation tip are... and They are respectively According to fracture mechanics theory, the circumferential stress at the perforation tip for: In the above formula, , These are the Type I and Type II stress intensity factors under the far-field in-situ stress loading mode and the hydraulic pressure loading mode at the perforation tip, respectively. The maximum principal stress at the perforation point and horizontal direction is given in MPa. The minimum principal stress for the perforation and horizontal direction is given in MPa. The pressure inside the perforation hole is in MPa. The direction angle of the perforation. ; The stress concentration factor is related to the geometric parameters of the elliptical wellbore and the perforation length. ; ; and These represent the hydraulic pressure applied to the elliptical wellbore and the pressure inside the perforation, respectively, in MPa; The direction angle of the perforation. The distance from a point around the crack to the tip of the crack. Defined as ; It is the angle between the direction of the perforation and the straight line between that point and the tip of the perforation crack.

[0021] Step S6: Based on the Darcy radial flow model, establish the flow continuity equation between the cake zone and the formation zone at the perforation scale, solve the perforation wall pore pressure, and establish the cake seepage-pore elastic coupling equation to calculate the additional stress field induced by pore pressure changes. The flow continuity equations for the cake zone and formation zone at the perforation scale are established as follows: when , When the two are equal, solve for the perforation wall gap pressure. : in, The difference between the perforation pressure and the pore pressure is calculated using the following formula: Where the permeability coefficient For characterizing the system's size and permeability: In the formula, , These are the permeabilities of the mud cake and the formation, respectively. , These represent the viscosity of the fluid in the two regions, respectively. , , These are the inner radius of the perforation, the outer radius of the mud cake (perforation wall), and the outer radius of the affected zone, respectively. , These are the pressure inside the perforation hole and the far-field pore pressure, respectively. The aforementioned radial Darcy flow was established directly at the perforation scale, rather than the open-hole scale. This is because the radial geometry of the perforation orifice is similar to that of the open-hole casing, both exhibiting cylindrical seepage boundaries, with the mud cake deposited directly on the perforation wall and the seepage direction being radially inward or outward, consistent with the basic assumptions of Darcy radial flow. This approach avoids the insufficient spatial resolution problem caused by placing the mud cake at the far-field wellbore scale, allowing for precise analysis of the mud cake's influence on the local stress field at the perforation tip.

[0022] Because the mud cake is soft, it enters a fully plastic yielding state under pressure differential. Based on the von Mises yield criterion, the radial stress distribution inside the mud cake is as follows: The integral constant is determined by the boundary conditions of the perforation wall. The effective radial pressure transmitted from the mud cake to the formation. : The change in pore pressure in the formation zone is reflected at the perforation wall ( The additional tangential stress induced at point () is: In the formula, the porosity elasticity correction coefficient and They are respectively: In the formula, Intermediate coefficients related to formation geometry parameters are defined as follows: , dimensionless.

[0023] Step S7: Based on the principle of linear superposition, the mechanical stress field at the perforation tip obtained in step S5 and the additional elastic stress field in the pore obtained in step S6 are linearly superimposed at the perforation wall to construct the complete and effective tangential stress of the perforation wall. Substituting the maximum tensile stress crack initiation criterion, the basic equation of the two-dimensional perforation fracture pressure is derived.

[0024] The tangential stress generated at the perforation wall by the far-field stress and the effective boundary pressure of the mud cake is: The minimum effective tangential stress at the perforation wall is determined by the superimposed elastic stress in the pores: It should be noted that the above superposition operation occurs at the specific spatial location of the perforation wall. The physical logic of the superposition is as follows: the tangential stress of the perforation wall under the combined action of geostress and hydraulic pressure calculated in step S5 (without considering the redistribution of pore pressure at the wall) and the additional tangential stress induced by the mud cake seepage-pore elastic coupling at the same spatial point calculated in step S6 (reflecting the correction of the effective stress boundary by the mud cake) can be linearly added within the linear elastic range to form the complete effective tangential stress of the perforation wall. The physical basis of this operation is: (1) the linear superposition of the Biot pore elastic equation within the linear elastic range; (2) the pore pressure change induced by mud cake seepage only affects the effective stress boundary conditions and does not change the basic structure of the far-field stress loading mode.

[0025] Let the minimum effective tangential stress be equal to the negative value of the rock's tensile strength, that is... (Maximum tensile strength crack initiation criterion), after simplification, the basic form of perforation fracture pressure based on a two-dimensional plane is obtained: Step S8: Considering the influence of vertical stress on the local principal stress state at the root of the perforation, a three-dimensional stress discrimination criterion is introduced. Based on the relative magnitudes of vertical stress and circumferential stress at the perforation tip, the two-dimensional perforation rupture pressure basic equation is substituted into the equation to calculate the three-dimensional explicit analytical solution of the ultra-deep perforation rupture pressure. Under actual ultra-deep vertical well perforation conditions, the local principal stress state at the perforation root changes from vertical stress. and the tangential stress at the tip of the perforation obtained in step S5 A joint decision-making process is required; it cannot be based solely on one approach. and Description. To achieve the extension from two-dimensional plane stress to three-dimensional stress state, in order to... and Replace the corresponding values ​​in the formula of step S7 respectively and First, it is necessary to determine the relative size relationship between the two. Specifically, we can use... Replace the basic equation for perforation rupture pressure in ,use Replace the basic equation for perforation rupture pressure in ,in, This represents the minimum value between the circumferential stress and the vertical stress at the perforation tip. It is the maximum value between the circumferential stress and the vertical stress at the tip of the perforation hole; make , And respectively used to replace the step S7 and Substituting into the final rupture pressure equation, we obtain the three-dimensional explicit analytical solution: when hour: when hour: In the formula, , By changing the perforation direction angle (Influence Value), perforation length (Influence (value) and mud cake parameters and (Influence , , The influence of each parameter on the fracturing pressure can be directly analyzed by the above explicit analytical solution, and the fracturing pressure of ultra-deep perforation hydraulic fracturing can be predicted. Based on this structure, the perforation direction angle, perforation length and mud cake plugging performance parameters can be further optimized to achieve accurate control of perforation design and drilling fluid plugging performance.

[0026] Example: Taking a well in a clastic rock block in the Tarim Basin of China as an example. The vertical stress of the formation where the well is located is 147 MPa, the maximum horizontal principal stress is 162 MPa, the minimum horizontal principal stress is 132 MPa, the perforation length is 0.8 m, the pore stress is 90 MPa, the perforation radius is 5 mm, the Poisson's ratio is 0.25, and the fracture toughness is 2 MPa·m. 1 / 2 The tensile strength is 6MPa. The wellbore has an elliptical major-to-minor axis ratio of 1.2 and a Boit coefficient of 0.9.

[0027] Based on the above calculation parameters and the fundamental parameters, the rock fracture pressure was calculated, and the predicted rock fracture pressure for this well was 159.5 MPa. The results are as follows: Figure 2As shown; however, the actual fracture pressure of the well was 155 MPa, and the error between the calculated result and the actual value was 2.90%, which is within the allowable range of engineering errors, thus demonstrating the reliability of the method proposed in this invention.

[0028] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the embodiments of the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting perforation fracture pressure considering wellbore deformation and mud cake plugging, characterized in that, Includes the following steps: Step S1: Obtain the elastic mechanical parameters, strength parameters, and pore medium mechanical parameters of the target well formation rock; Step S2: Calculate the triaxial in-situ in-situ stress and original formation pore pressure at the target well depth using logging data; Step S3: Compile wellbore structural data, including wellbore elliptic geometry parameters, perforation geometry parameters, and mud cake physical properties parameters; Step S4: Based on the conformal transformation theory of complex functions, establish a conformal mapping model for an elliptical wellbore containing symmetrical perforations, and map the irregular geometric region formed by the elliptical wellbore and perforations in the physical plane to the unit circle region in the complex plane. Step S5: Under the conformal mapping plane established in step S4, the total load is decomposed into far-field in-situ stress loading mode and hydraulic pressure loading mode. The perforation complex stress function under each loading mode is solved respectively. The two types of stress intensity factors at the perforation tip and the circumferential stress at the perforation tip are further calculated. Step S6: Based on the Darcy radial flow model, establish the flow continuity equations for the cake zone and the formation zone at the perforation scale, solve the perforation wall pore pressure, establish the cake seepage-pore elastic coupling equation, and calculate the additional stress field induced by pore pressure changes. Step S7: Based on the principle of linear superposition, the stress field at the perforation tip obtained in step S5 is superimposed with the additional elastic stress field in the pore obtained in step S6 to obtain the basic equation of two-dimensional perforation rupture pressure. Step S8: Based on the magnitude of the vertical stress and the circumferential stress at the perforation tip, substitute the values ​​into the basic equation for perforation rupture pressure for different cases to calculate the three-dimensional explicit analytical solution for the rupture pressure of ultra-deep perforations.

2. The method for predicting perforation fracture pressure considering wellbore deformation and mud cake plugging according to claim 1, characterized in that: The elastic mechanical parameters mentioned in step S1 include elastic modulus and Poisson's ratio; the strength parameters include rock tensile strength and fracture toughness; and the porous media mechanical parameters include Biot effective stress coefficient and pore elastic coefficient.

3. The method for predicting perforation fracture pressure considering wellbore deformation and mud cake plugging according to claim 1, characterized in that: The triaxial in-situ stress mentioned in step S2 includes vertical stress, horizontal maximum principal stress, and horizontal minimum principal stress.

4. The method for predicting perforation fracture pressure considering wellbore deformation and mud cake plugging according to claim 1, characterized in that: The wellbore elliptic geometric parameters in the wellbore structure data described in step S3 include the length of the major semi-axis and the length of the minor semi-axis of the ellipse; the perforation geometric parameters include the perforation length, the inner radius of the perforation, the perforation direction angle, and the total distance from the perforation tip to the center of the wellbore; the mud cake physical property parameters include the mud cake permeability, the outer radius of the mud cake, the outer radius of the influence zone, and the mud cake yield strength.

5. The method for predicting perforation fracture pressure considering wellbore deformation and mud cake plugging according to claim 1, characterized in that: The specific method for step S4 is as follows: Based on the conformal transformation theory of complex functions, the outer region of the elliptical wellbore containing symmetrical perforations is mapped to the unit circle region, and based on the Cartesian coordinate system after co-mapping... The complex stress in the plane is transformed into an expression in polar coordinates.

6. The method for predicting perforation fracture pressure considering wellbore deformation and mud cake plugging according to claim 1, characterized in that: The calculation method for the two types of stress intensity factors at the perforation tip in step S5 is shown in the following formula: In the formula, , These are the Type I and Type II stress intensity factors under the far-field in-situ stress loading mode and the hydraulic pressure loading mode at the perforation tip, respectively. The maximum principal stress at the perforation point and horizontal direction is given in MPa. The minimum principal stress for the perforation and horizontal direction is given in MPa. The pressure inside the perforation hole is in MPa. The direction angle of the perforation. ; The stress concentration factor is related to the geometric parameters of the elliptical wellbore and the perforation length; The circumferential stress at the perforation tip is obtained by substituting two types of stress intensity factors into fracture mechanics theory, as shown in the following formula: In the formula, The circumferential stress at the tip of the perforation hole; Let m be the distance from a point around the crack to the crack tip; To study the angle between the point and the perforation direction, .

7. The method for predicting perforation fracture pressure considering wellbore deformation and mud cake plugging according to claim 1, characterized in that: The additional stress field induced by the pore pressure change in step S6 is shown in the following equation: In the formula, The variation of pore pressure in the formation zone on the perforation wall Additional tangential stress induced at the location; The porosity elastic coefficient is dimensionless. M , N These are dimensionless porosity elasticity correction coefficients related to the geometric parameters of mud cake and formation seepage. The pressure inside the perforation hole is in MPa. ρ represents the far-field pore pressure, in MPa.

8. The method for predicting perforation fracture pressure considering wellbore deformation and mud cake plugging according to claim 1, characterized in that: The basic equation for the two-dimensional perforation rupture pressure in step S7 is shown below: In the formula, The two-dimensional perforation rupture pressure is expressed in MPa. The maximum principal stress at the perforation point and horizontal direction is given in MPa. The minimum principal stress for the perforation and horizontal direction is given in MPa. The porosity elastic coefficient is dimensionless. M , N These are dimensionless porosity elasticity correction coefficients related to the geometric parameters of mud cake and formation seepage. The seepage coefficient; Far-field pore pressure, MPa; Let be the inner radius of the perforation hole, in meters. Let the outer radius of the mud cake be m; Y The yield strength of the mud cake.

9. The method for predicting perforation fracture pressure considering wellbore deformation and mud cake plugging according to claim 8, characterized in that: The specific process for substituting the basic equation for the perforation rupture pressure under different conditions in step S8 is as follows: use Replace the basic equation for perforation rupture pressure in ,use Replace the basic equation for perforation rupture pressure in ,in, This represents the minimum value between the circumferential stress and the vertical stress at the perforation tip. It is the maximum value between the circumferential stress and the vertical stress at the tip of the perforation hole; The three-dimensional explicit expression of the fracturing pressure in ultra-deep perforations is shown in the following equation: When the vertical stress is less than the circumferential stress at the perforation tip: When the vertical stress is greater than the circumferential stress at the perforation tip: In the formula, The three-dimensional perforation rupture pressure; Tensile strength of rock; This represents vertical stress.

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