Method and device for determining borehole wall instability radius and storage medium

Abstract

The embodiment of the invention provides a method and device for determining the borehole wall instability radius and a storage medium, and belongs to the technical field of oil and gas industry drilling. The method for determining the borehole wall instability radius comprises the steps that according to contact stress and a first well axis distance, well circumference stress of an initial well circumference position in multiple preset directions is obtained; according to the multiple well circumference stresses, the maximum well circumference principal stress and the minimum well circumference principal stress are obtained; under the condition that the maximum well circumference principal stress and the minimum well circumference principal stress do not meet the Moire-Coulomb criterion, changing the initial well circumference position to change the first well axis distance until the maximum well circumference principal stress and the minimum well circumference principal stress corresponding to the changed target well circumference position meet the Moire-Coulomb criterion, a second well axis distance corresponding to the target well circumferential position is obtained, and the second well axis distance is the well wall instability radius when the well wall instability phenomenon happens to the target well. According to the method, the borehole wall instability radius can be determined.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of drilling technology in the oil and gas industry, in particular to a method and device for determining a wellbore instability radius and a storage medium. BACKGROUND

[0002] In order to increase the exploitation of oil and gas resources, the application of deep wells and extended reach wells is gradually widespread. In the drilling process, the stability of the wellbore is crucial for safe drilling operations. The existing technology only exists for the judgment of whether the wellbore is unstable, such as qualitative analysis of wellbore instability according to rock mineral composition analysis, rock geostress analysis of wellbore instability mechanism, judgment of whether the wellbore is unstable; according to the method of three pressure profiles, the collapse pressure is used to judge whether the wellbore is unstable; according to the two action forms of drill string disturbance and drill string vibration, whether the drill string exceeds the critical speed of drill string vibration is judged to determine whether the wellbore is unstable. The above existing technology can only determine whether the wellbore is unstable, but cannot determine the wellbore instability radius when the wellbore instability occurs.

[0003] Therefore, how to determine the wellbore instability radius is a technical problem to be solved. SUMMARY

[0004] The purpose of the embodiments of the present application is to provide a method, device and storage medium for determining a wellbore instability radius, so as to solve the problem of how to determine the wellbore instability radius in the prior art.

[0005] In order to achieve the above purpose, the first aspect of the embodiments of the present application provides a method for determining a wellbore instability radius, the method comprising: obtaining a contact stress between a pipe string lowered into a target well and a wellbore of the target well, a first well axis distance between an initial well circumference position and a wellbore axis of the target well; obtaining well circumference stresses of the initial well circumference position in a plurality of preset directions according to the contact stress and the first well axis distance; obtaining a maximum well circumference principal stress and a minimum well circumference principal stress according to the plurality of well circumference stresses; in a case where the maximum well circumference principal stress and the minimum well circumference principal stress do not satisfy the Mohr-Coulomb criterion, changing the initial well circumference position to change the first well axis distance until the maximum well circumference principal stress and the minimum well circumference principal stress corresponding to the changed target well circumference position satisfy the Mohr-Coulomb criterion, so as to obtain a second well axis distance corresponding to the target well circumference position, wherein the second well axis distance is a wellbore instability radius when the target well occurs a wellbore instability phenomenon.

[0006] In this embodiment, the contact stress includes continuous contact stress. Obtaining the contact stress between the tubing string and the wellbore wall in the target well includes: obtaining the actual tubing string length, the gap between the tubing string and the wellbore wall, the equivalent radius of curvature of the contact surface between the tubing string and the wellbore wall, the contact force between the tubing string and the wellbore wall, and the equivalent elastic modulus of the contact surface between the tubing string and the wellbore wall; determining the actual tubing string deformation based on a preset tubing string deformation algorithm, according to the actual tubing string length; if the actual tubing string deformation is greater than the gap, determining the point contact limit length of the tubing string based on the preset tubing string deformation algorithm, where the preset tubing string deformation is the gap; determining the deviation between the actual tubing string length and the point contact limit length to obtain the continuous contact length between the tubing string and the wellbore wall; and determining the continuous contact stress based on a preset continuous contact stress algorithm, according to the continuous contact length, the equivalent radius of curvature, the contact force, and the equivalent elastic modulus.

[0007] In this embodiment of the application, the preset continuous contact stress algorithm includes the following formula:

[0008] Where pmax is the continuous contact stress, Nw is the contact force, E* is the equivalent elastic modulus, Lw is the continuous contact length, and R* is the equivalent radius of curvature.

[0009] In this embodiment, the contact stress includes point contact stress. Obtaining the contact stress between the tubing string run into the target well and the wellbore wall includes: obtaining the actual tubing string length, the gap between the tubing string and the wellbore wall, the wellbore radius of the target well, the upper limit of the distance from the contact point on the contact cross-section of the tubing string and the wellbore wall to the contact direction axis, the equivalent elastic modulus of the contact surface between the tubing string and the wellbore wall, the depth of the tubing string pressed into the wellbore wall, and the distance from the contact point on the contact cross-section of the tubing string and the wellbore wall to the contact direction axis; determining the actual tubing string deformation based on the actual tubing string length using a preset tubing string deformation algorithm; and determining the point contact stress based on the wellbore radius, contact half-width, tubing string elastic modulus, and depth when the actual tubing string deformation equals the gap.

[0010] In this embodiment, the preset point contact stress algorithm includes the following formula:

[0011] Where Pp is the point contact stress, w is the upper limit of the value, Rw is the wellbore radius, E* is the equivalent elastic modulus, d is the depth, and x is the distance from the contact point to the axis of the contact direction.

[0012] In this embodiment, the wellbore stress includes axial normal stress, circumferential normal stress, radial normal stress, in-plane shear stress, first axial shear stress, and second axial shear stress. Based on the contact stress and the first wellbore axis distance, the wellbore stress at the initial wellbore position in multiple preset directions is obtained, including: acquiring stress parameters, target well parameters, and Poisson's ratio of the wellbore wall. The stress parameters include the maximum wellbore principal stress, the minimum wellbore principal stress, the first normal stress in the direction of the maximum wellbore principal stress, the second normal stress in the direction of the minimum wellbore principal stress, and the direction of the wellbore axis. The parameters of the target well include the third normal stress, the first shear stress in the plane containing the maximum and minimum principal stresses, the second shear stress in the plane containing the minimum principal stress and the wellbore axis, and the third shear stress in the plane containing the maximum principal stress and the wellbore axis. The target well parameters include the wellbore angle, the wellbore radius, and the fluid pressure inside the target well. Based on the contact stress, the first well-axis distance, the stress parameters, the target well parameters, and Poisson's ratio, the wellbore stress at the initial wellbore position in multiple preset directions is determined. The determination of the wellbore stress includes using the following formula:

[0013]

[0014]

[0015]

[0016]

[0017]

[0018] in, P i The pressure of the fluid inside the well. P Let r be the contact stress and r be the distance from the first well axis. It is radial normal stress. For circumferential normal stress, It is the axial normal stress. In-plane shear stress, The first axial shear stress, For the second axial shear stress, The first normal stress, This is the second normal stress. The third normal stress, For the first shear stress, This is the second shear stress. The third shear stress is θ, and the wellbore angle is θ. Let v be the wellbore radius and v be Poisson's ratio.

[0019] In this embodiment, the wellbore stress includes axial normal stress, circumferential normal stress, radial normal stress, in-plane shear stress, first axial shear stress, and second axial shear stress. The maximum and minimum wellbore principal stresses are obtained based on these multiple wellbore stresses, including: obtaining a wellbore stress matrix based on the multiple wellbore stresses; determining multiple eigenvalues ​​of the wellbore stress matrix; and determining the maximum and minimum values ​​among the multiple eigenvalues ​​to obtain the maximum and minimum wellbore principal stresses, respectively.

[0020] In this embodiment of the application, the method further includes: obtaining the wellbore radius of the target well; determining the deviation between the wellbore instability radius and the wellbore radius; and determining the ratio of the deviation to the wellbore radius to obtain the wellbore disturbance coefficient.

[0021] A second aspect of this application provides an apparatus for determining the wellbore instability radius, comprising: a memory configured to store instructions; and a processor configured to retrieve instructions from the memory and, when executing the instructions, to implement the method for determining the wellbore instability radius as described above.

[0022] A third aspect of this application provides a machine-readable storage medium storing instructions that cause a machine to perform the method described above for determining the wellbore instability radius.

[0023] The above technical solution obtains multiple wellbore stresses at the initial wellbore position by acquiring the contact stress between the tubing string and the wellbore wall, and the first well axis distance between the initial wellbore position and the wellbore axis of the target well. Based on these multiple wellbore stresses, the maximum and minimum principal wellbore stresses are determined. Then, based on the maximum and minimum principal wellbore stresses, it is determined whether the initial wellbore position satisfies the Mohr-Coulomb criterion. If the maximum and minimum principal wellbore stresses at the initial wellbore position do not satisfy the Mohr-Coulomb criterion, the initial wellbore position is changed until the maximum and minimum principal wellbore stresses at the changed target wellbore position satisfy the Mohr-Coulomb criterion, thus obtaining the wellbore instability radius corresponding to the target wellbore position. Therefore, this application determines multiple wellbore stresses based on contact stress and the first well axis distance, thereby determining whether the maximum and minimum wellbore principal stresses determined by the wellbore stresses satisfy the Mohr-Coulomb criterion, in order to determine the wellbore instability radius. Thus, this application not only considers the influence of the tubing string run into the target well on the wellbore instability radius, but also determines the wellbore instability radius by changing the initial wellbore position, thereby realizing the determination of the wellbore instability radius.

[0024] Other features and advantages of the embodiments of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0025] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings: Figure 1 The schematic diagram illustrates a process for determining the wellbore instability radius according to an embodiment of this application; Figure 2 The diagram illustrates the parameters of the contact cross section between the tubing and the wellbore in a point contact situation according to an embodiment of this application. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only for illustration and explanation of the embodiments of this application and are not intended to limit the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0027] It should be noted that the acquisition, transmission, storage, use, and processing of data in the technical solution of this application all comply with the relevant provisions of national laws and regulations. In the embodiments of this application, certain existing industry solutions such as software, components, and models may be mentioned. These should be considered exemplary, intended only to illustrate the feasibility of implementing the technical solution of this application, and do not imply that the applicant has already used or necessarily used such solutions.

[0028] It should be noted that if the embodiments of this application involve directional indicators (such as up, down, left, right, front, back, etc.), the directional indicators are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.

[0029] Furthermore, if the embodiments of this application involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, features defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed in this application.

[0030] It should be noted that the acquisition, transmission, storage, use, and processing of data in the technical solution of this application all comply with relevant laws and regulations. In the embodiments of this application, certain existing industry solutions such as software, components, and models may be mentioned. These should be considered exemplary, intended only to illustrate the feasibility of implementing the technical solution of this application, and do not imply that the applicant has already used or necessarily used such solutions.

[0031] Figure 1 The illustration shows a schematic diagram of a process for determining the wellbore instability radius in one embodiment of this application. Figure 1 As shown in the figure, this application provides a method for determining the wellbore instability radius. Taking the application of this method to a processor as an example, the method may include the following steps: Step S101: Obtain the contact stress between the tubing string lowered into the target well and the wellbore wall, and the first well axis distance between the initial wellbore position and the wellbore axis of the target well.

[0032] Step S102: Based on the contact stress and the first well axis distance, obtain the well perimeter stress in multiple preset directions at the initial well perimeter position.

[0033] Step S103: Based on multiple wellbore stresses, obtain the maximum and minimum wellbore principal stresses.

[0034] Step S104: If the maximum and minimum principal stresses around the well do not satisfy the Mohr-Coulomb criterion, change the initial well position to change the first well axis distance until the maximum and minimum principal stresses around the well corresponding to the changed target well position satisfy the Mohr-Coulomb criterion, so as to obtain the second well axis distance corresponding to the target well position, wherein the second well axis distance is the well instability radius when the target well experiences wellbore instability.

[0035] The initial wellbore position is understood to be a predetermined location around the wellbore. The first well-axis distance is the distance between the initial wellbore position and the wellbore axis of the target well. Wellbore stress includes axial normal stress, circumferential normal stress, radial normal stress, in-plane shear stress, first axial shear stress, and second axial shear stress. The maximum wellbore principal stress refers to the maximum value of the normal stress in all directions at a point in the rock surrounding the wellbore. The minimum wellbore principal stress refers to the minimum value of the normal stress in all directions at a point in the rock surrounding the wellbore. The maximum and minimum wellbore principal stresses are perpendicular. The target wellbore position is the location around the wellbore where wellbore instability occurs. The second well-axis distance is the distance between the target wellbore position and the wellbore axis of the target well, which is also the wellbore instability radius of the target well when wellbore instability occurs.

[0036] Specifically, the processor acquires the contact stress between the tubing string and the wellbore wall, and the first wellbore axis distance between the initial wellbore position and the wellbore axis of the target well. Based on the contact stress and the first wellbore axis distance, it obtains the wellbore stress at the initial wellbore position in multiple preset directions. Then, based on these multiple wellbore stresses, it obtains the maximum and minimum wellbore principal stresses. The processor determines whether the maximum and minimum wellbore principal stresses satisfy the Mohr-Coulomb criterion. If the maximum and minimum wellbore principal stresses at the initial wellbore position do not satisfy the Mohr-Coulomb criterion, the processor changes the initial wellbore position and determines whether the maximum and minimum wellbore principal stresses at the changed wellbore position satisfy the Mohr-Coulomb criterion. This process continues until the maximum and minimum wellbore principal stresses at the changed wellbore position satisfy the Mohr-Coulomb criterion. The wellbore axis distance corresponding to the wellbore position that satisfies the Mohr-Coulomb criterion is determined as the wellbore instability radius when wellbore instability occurs in the target well.

[0037] The above technical solution obtains multiple wellbore stresses at the initial wellbore position by acquiring the contact stress between the tubing string and the wellbore wall, and the first well axis distance between the initial wellbore position and the wellbore axis of the target well. Based on these multiple wellbore stresses, the maximum and minimum principal wellbore stresses are determined. Then, based on the maximum and minimum principal wellbore stresses, it is determined whether the initial wellbore position satisfies the Mohr-Coulomb criterion. If the maximum and minimum principal wellbore stresses at the initial wellbore position do not satisfy the Mohr-Coulomb criterion, the initial wellbore position is changed until the maximum and minimum principal wellbore stresses at the changed target wellbore position satisfy the Mohr-Coulomb criterion, thus obtaining the wellbore instability radius corresponding to the target wellbore position. Therefore, this application determines multiple wellbore stresses based on contact stress and the first well axis distance, thereby determining whether the maximum and minimum wellbore principal stresses determined by the wellbore stresses satisfy the Mohr-Coulomb criterion, in order to determine the wellbore instability radius. Thus, this application not only considers the influence of the tubing string run into the target well on the wellbore instability radius, but also determines the wellbore instability radius by changing the initial wellbore position, thereby realizing the determination of the wellbore instability radius.

[0038] In one embodiment, the contact stress includes continuous contact stress. Obtaining the contact stress between the tubing string run into the target well and the wellbore wall includes: obtaining the actual tubing string length, the gap between the tubing string and the wellbore wall, the equivalent radius of curvature of the contact surface between the tubing string and the wellbore wall, the contact force between the tubing string and the wellbore wall, and the equivalent elastic modulus of the contact surface between the tubing string and the wellbore wall; determining the actual tubing string deformation based on a preset tubing string deformation algorithm, according to the actual tubing string length; if the actual tubing string deformation is greater than the gap, determining the point contact limit length of the tubing string based on the preset tubing string deformation algorithm, where the preset tubing string deformation is the gap; determining the deviation between the actual tubing string length and the point contact limit length to obtain the continuous contact length between the tubing string and the wellbore wall; and determining the continuous contact stress based on a preset continuous contact stress algorithm, according to the continuous contact length, the equivalent radius of curvature, the contact force, and the equivalent elastic modulus.

[0039] It is understood that the preset tubing deformation calculation algorithm is a pre-defined tubing deformation calculation algorithm, including the following formula: When the axial force of the tubing is pressure:

[0040] When the axial force on the tubing is 0:

[0041] When the axial force on the tubing string is tensile:

[0042] Where Y is the tubing deformation, q is the tubing linear weight, L is the tubing length, E is the tubing elastic modulus, I is the tubing moment of inertia, α is the well inclination angle, R is the wellbore curvature radius, Mi and Mi+1 are the bending moments of the hinged supports at both ends of the tubing, u is the longitudinal and transverse bending beam stability coefficient, and P is the tubing axial force.

[0043] Understandably, contact stress includes continuous contact stress, which is the contact stress under conditions of continuous contact between the tubing and the wellbore. Actual tubing length is the actual length of the tubing, which can be 10 meters. Actual tubing deformation is the actual tubing deformation calculated based on the actual tubing length and a preset tubing deformation algorithm. Wellbore clearance is the gap between the tubing and the wellbore. Equivalent radius of curvature is the radius of curvature formed by the contact surfaces of the tubing and the wellbore. Contact force is the force distinct from contact stress generated by the contact between the tubing and the wellbore. Equivalent elastic modulus is the elastic modulus of the contact surface between the tubing and the wellbore. Preset tubing deformation is the wellbore clearance. The tubing point contact limit length refers to the tubing length determined based on the preset tubing deformation (wellbore clearance). Continuous contact length is the contact length resulting from continuous contact between the tubing and the wellbore. The preset continuous contact stress algorithm is a pre-set stress algorithm for conditions of continuous contact between the tubing and the wellbore.

[0044] Specifically, the processor first calculates the actual tubing deformation based on a preset tubing deformation algorithm, taking into account the actual tubing length and axial force. It then determines the relationship between the tubing deformation and the wellbore clearance. If the tubing deformation exceeds the wellbore clearance, the continuous contact length is determined. This continuous contact length is determined by defining the tubing deformation Y as the wellbore clearance, and then, based on the preset tubing deformation algorithm, determining the limit length of the tubing point contact (the independent variable L in the preset tubing deformation algorithm) according to the wellbore clearance. Finally, based on a preset continuous contact stress algorithm, the contact stress under continuous contact conditions between the tubing and the wellbore is determined according to the continuous contact length, contact radius of curvature, contact force, and the tubing's elastic modulus.

[0045] In this embodiment, the continuous contact length is obtained based on the deviation between the actual tubing length and the limit length of the tubing point contact. The method for determining the continuous contact length in this application simplifies the acquisition of the continuous contact length and improves the accuracy of determining the continuous contact length.

[0046] In one embodiment, the preset continuous contact stress algorithm includes the following formula:

[0047] Where pmax is the continuous contact stress, Nw is the contact force, E* is the equivalent elastic modulus, Lw is the continuous contact length, and R* is the equivalent radius of curvature.

[0048] It can be understood that the preset continuous contact stress algorithm is a stress algorithm for the pre-defined continuous contact condition between the tubing and the wellbore. Contact force is the force distinct from contact stress generated by the contact between the tubing and the wellbore. The equivalent elastic modulus is the elastic modulus of the contact surface between the tubing and the wellbore. The continuous contact length is the contact length resulting from the continuous contact between the tubing and the wellbore. The equivalent radius of curvature is the radius of curvature formed by the contact surface between the tubing and the wellbore.

[0049] Specifically, the processor, based on a preset continuous contact stress algorithm, determines the contact stress under continuous contact conditions between the tubing and the wellbore, according to the continuous contact length, contact radius of curvature, contact force, and tubing elastic modulus. The preset continuous contact stress algorithm in this application is completely different from traditional continuous contact stress algorithms, and can improve the accuracy and simplicity of continuous contact stress calculation.

[0050] In one embodiment, the contact stress includes point contact stress. Obtaining the contact stress between the tubing string run into the target well and the wellbore wall includes: obtaining the actual tubing string length, the gap between the tubing string and the wellbore wall, the wellbore radius of the target well, the upper limit of the distance from the contact point on the contact cross-section between the tubing string and the wellbore wall to the contact direction axis, the equivalent elastic modulus of the contact surface between the tubing string and the wellbore wall, the depth of the tubing string pressed into the wellbore wall, and the distance from the contact point on the contact cross-section between the tubing string and the wellbore wall to the contact direction axis; determining the actual tubing string deformation based on the actual tubing string length using a preset tubing string deformation algorithm; and determining the point contact stress based on the wellbore radius, contact half-width, tubing string elastic modulus, and depth when the actual tubing string deformation equals the gap.

[0051] It is understandable that contact stress includes point contact stress. Point contact stress is the contact stress under point contact conditions between the tubing and the wellbore. The actual tubing length is simply the actual length of the tubing, which can be 10 meters. The well clearance is the gap between the tubing and the wellbore.

[0052] Specifically, the processor first calculates the actual tubing deformation based on the preset tubing deformation algorithm, taking into account the actual tubing length and axial force, and then determines the relationship between the tubing deformation and the well clearance. When the tubing deformation is equal to the well clearance, the processor determines the point contact stress based on the pre-obtained wellbore radius, contact half-width, tubing elastic modulus, and depth.

[0053] In this embodiment, the point contact stress is determined by four parameters: wellbore radius, contact half-width, tubing elastic modulus, and depth. This eliminates the need for calculations that use multiple complex parameters to calculate the point contact stress, greatly simplifying the calculation process.

[0054] In one embodiment, the preset point contact stress algorithm includes the following formula:

[0055] Where Pp is the point contact stress, w is the upper limit of the value, Rw is the wellbore radius, E* is the equivalent elastic modulus, d is the depth, and x is the distance from the contact point to the axis of the contact direction.

[0056] It can be understood that point contact stress is the contact stress under point contact conditions between the tubing and the wellbore. The upper limit of the wellbore cross-sectional width can be the contact half-width, which is the distance from the centerline of the contact area to the edge in a specific direction when two objects are in contact. The wellbore radius is the radius of the wellbore. The depth is the depth to which the tubing is pressed into the wellbore. The equivalent elastic modulus is the elastic modulus of the contact surface between the tubing and the wellbore. Figure 2 This diagram schematically illustrates the parameters of the contact cross-section between the tubing and the wellbore in a point contact situation according to an embodiment of this application. For example... Figure 2As shown, the red circle represents the tubing string, the black dashed circle represents the wellbore, d is the depth of the tubing string pressed into the wellbore, and w is the upper limit of the distance from the contact point to the axis of the contact direction. Figure 2 The y-axis in the figure is the contact direction axis mentioned above. x is the distance from the contact point on the contact cross section between the tubing and the well wall to the contact direction axis. In other words, x is the value of any point on the contact surface on the x-axis in the figure. Rw is the wellbore radius.

[0057] Specifically, the processor determines the point contact stress based on a preset point contact stress algorithm, taking into account the wellbore radius, contact half-width, tubing elastic modulus, and depth. This preset point contact stress algorithm differs significantly from traditional point contact stress algorithms, improving both the accuracy and ease of point contact stress calculation.

[0058] In this embodiment, the wellbore stress includes axial normal stress, circumferential normal stress, radial normal stress, in-plane shear stress, first axial shear stress, and second axial shear stress. Based on the contact stress and the first wellbore axis distance, the wellbore stress at the initial wellbore position in multiple preset directions is obtained, including: acquiring stress parameters, target well parameters, and Poisson's ratio of the wellbore wall. The stress parameters include the maximum wellbore principal stress, the minimum wellbore principal stress, the first normal stress in the direction of the maximum wellbore principal stress, the second normal stress in the direction of the minimum wellbore principal stress, and the direction of the wellbore axis. The parameters of the target well include the third normal stress, the first shear stress in the plane containing the maximum and minimum principal stresses, the second shear stress in the plane containing the minimum principal stress and the wellbore axis, and the third shear stress in the plane containing the maximum principal stress and the wellbore axis. The target well parameters include the wellbore angle, the wellbore radius, and the fluid pressure inside the target well. Based on the contact stress, the first well-axis distance, the stress parameters, the target well parameters, and Poisson's ratio, the wellbore stress at the initial wellbore position in multiple preset directions is determined. The determination of the wellbore stress includes using the following formula:

[0059]

[0060]

[0061]

[0062]

[0063]

[0064] in, P i The pressure of the fluid inside the well. P Let r be the contact stress and r be the distance from the first well axis. It is radial normal stress. For circumferential normal stress, It is the axial normal stress. In-plane shear stress, The first axial shear stress, For the second axial shear stress, The first normal stress, This is the second normal stress. The third normal stress, For the first shear stress, This is the second shear stress. The third shear stress is θ, and the wellbore angle is θ. Let v be the wellbore radius and v be Poisson's ratio.

[0065] It can be understood that the directions of the maximum and minimum wellbore principal stresses are perpendicular. Wellbore stresses include axial normal stress, circumferential normal stress, radial normal stress, in-plane shear stress, first axial shear stress, and second axial shear stress. Stress parameters include the first normal stress (…). ), second normal stress ( ), third normal stress ( ), first shear stress ( ), second shear stress ( ) and the third shear stress ( The value of ) is determined according to the following formula:

[0066] in, For the pressure of the overlying, For the maximum ground stress, The minimum ground stress is given by ψ, the well inclination angle is given by Ω, and the well inclination azimuth angle is given by Ω.

[0067] Specifically, the processor determines the wellbore stress (axial normal stress, circumferential normal stress, radial normal stress, in-plane shear stress, first axial shear stress, and second axial shear stress) in multiple preset directions at the initial wellbore position based on the continuous contact stress or point contact stress (P), the first well axis distance, stress parameters, target well parameters, and Poisson's ratio.

[0068] In the embodiments of this application, the method for obtaining wellbore stress takes into account the contact stress between the tubing and the well wall, thus better reflecting actual working conditions and improving the accuracy of wellbore stress determination, thereby improving the accuracy of well wall instability radius determination.

[0069] In one embodiment, the wellbore stress includes axial normal stress, circumferential normal stress, radial normal stress, in-plane shear stress, first axial shear stress, and second axial shear stress. Obtaining the maximum and minimum wellbore principal stresses based on the multiple wellbore stresses includes: obtaining a wellbore stress matrix based on the multiple wellbore stresses; determining multiple eigenvalues ​​of the wellbore stress matrix; and determining the maximum and minimum values ​​among the multiple eigenvalues ​​to obtain the maximum and minimum wellbore principal stresses, respectively.

[0070] It can be understood that wellbore stress includes axial normal stress, circumferential normal stress, radial normal stress, in-plane shear stress, first axial shear stress, and second axial shear stress. The principal stresses around the wellbore can be obtained by solving the eigenvalues ​​of the characteristic equation of the wellbore stress tensor matrix, which are represented from largest to smallest as the maximum principal stress σ1, intermediate principal stress σ2, and minimum principal stress σ3, respectively.

[0071] The stress tensor at the wellbore can be expressed as:

[0072] The principal stresses around the wellbore can be obtained by solving the characteristic equation of the wellbore stress tensor matrix:

[0073] in: The eigenvalue solutions of the stress tensor are represented, from largest to smallest, as the maximum principal stress σ1, intermediate principal stress σ2, and minimum principal stress σ3, respectively. Specifically, the processor obtains a wellbore stress matrix based on multiple wellbore stresses, and then determines multiple eigenvalues ​​based on the wellbore stress matrix, thereby determining the maximum and minimum values ​​among the multiple eigenvalues, so as to obtain the maximum and minimum wellbore principal stresses respectively. Since the wellbore stress matrix obtained by the processor takes into account the contact stress between the tubing and the wellbore, the accuracy of determining the maximum and minimum wellbore principal stresses is improved.

[0074] In one embodiment, the method further includes: obtaining the wellbore radius of the target well; determining the deviation between the wellbore instability radius and the wellbore radius; and determining the ratio of the deviation to the wellbore radius to obtain the wellbore disturbance coefficient.

[0075] As can be understood, the wellbore disturbance coefficient refers to the degree to which the original stress state and physical and mechanical properties of the rock surrounding the wellbore are altered by drilling operations (such as mechanical breaking, drilling fluid soaking, etc.).

[0076] Specifically, this application determines the wellbore disturbance coefficient by determining the deviation between the wellbore instability radius and the wellbore radius, and by determining the ratio of the deviation to the wellbore radius.

[0077] In this embodiment of the application, the wellbore instability can be more intuitively reflected by determining the wellbore disturbance coefficient.

[0078] A specific embodiment of this application provides a method for determining the instability radius of a wellbore, the specific steps of which are as follows: Step S11: Solve for the deformation of the tubing string based on the longitudinal and transverse bending beam model, and determine the contact status between the tubing string and the well wall (no contact, point contact, continuous contact) based on the deformation of the tubing string. Step S11 may include the following steps S111 to S113.

[0079] Step S111: Considering the wellbore clearance, the downhole tubing is simplified as a longitudinally and transversely bent beam constrained by the wellbore. Under running conditions, the tubing often has a neutral point; above this point, the tubing is under tension, and below it, it is under compression. Considering the effects of uniformly distributed force, axial force, bending moment, and initial bending on the tubing within the wellbore, based on the superposition principle, the formula for tubing deformation is: When the axial force on the tubing string is compressive:

[0080] When the axial force on the tubing is 0:

[0081] When the axial force on the tubing string is tensile:

[0082] Where: Y is the tubing deformation, m; q is the tubing linear weight, kg / m; L is the tubing length, m; E is the tubing elastic modulus, Pa; I is the tubing moment of inertia, m⁴; α is the wellbore inclination angle, °; R is the wellbore radius of curvature, m; Mi and Mi+1 are the bending moments of the hinged supports at both ends of the tubing, respectively. , N·m; u is the longitudinal and transverse bending beam stability coefficient, dimensionless, where P is the axial force of the pipe column, N.

[0083] Step S112: Compare the calculated tubing deformation with the gap between the tubing and the wellbore. If the tubing deformation is less than the gap between the tubing and the wellbore, it indicates no contact. If the tubing deformation is equal to the gap between the tubing and the wellbore, it indicates point contact. If the tubing deformation is greater than the gap between the tubing and the wellbore, it indicates continuous contact.

[0084] Step S113: If it is determined that the tubing string and the wellbore are in continuous contact, then the length of continuous contact between the tubing string and the wellbore needs to be calculated. The specific calculation method is as follows: Assuming the length of the tubing string in point contact is unknown, the length of the tubing string in point contact with the wellbore is calculated iteratively using the tubing string deformation calculation formula, and this length is defined as the limit length of point contact between the tubing string and the wellbore. At this point, the formula for calculating the continuous contact length of the tubing string is:

[0085] Where: Lw is the continuous contact length of the tubing, in meters; Lp is the limit length of the point contact of the tubing, in meters; and L is the length of the tubing.

[0086] Step S12 involves establishing a calculation model for the contact stress between the tubing and the wellbore during the tubing run, considering both point contact and continuous contact. The contact stress between the tubing and the wellbore is then calculated based on this model. Step S12 may include steps S121 to S122.

[0087] Step S121, establishing the contact stress calculation model between the tubing and the wellbore under point contact conditions, specifically involves:

[0088] Where: Pp is the point contact stress, w is the upper limit of the distance from the contact point to the contact direction axis, Rw is the wellbore radius, E* is the equivalent elastic modulus, d is the depth, and x is the distance from the contact point to the contact direction axis.

[0089] Based on the crescent-shaped geometric cross-section of the tubing inserted into the wellbore, the upper limit value w for the point contact condition between the tubing and the wellbore can be calculated using the following formula:

[0090] Where Rp and Rw are the radii of the tubing and the wellbore, respectively, in meters (m).

[0091] Step S122, establishing the contact stress calculation model between the tubing and the wellbore under continuous contact conditions, specifically involves:

[0092] Where: Nw is the contact force between the tubing and the wellbore under continuous contact conditions, N; E* is the equivalent elastic modulus of the contact surface between the tubing and the wellbore, Pa; R* is the equivalent radius of curvature of the contact surface between the tubing and the wellbore, m; pmax is the maximum contact stress, Pa; p is the contact pressure, Pa; b is the contact half-width, m; x is the distance from the contact point to the centerline of the contact surface, m.

[0093] The equivalent elastic modulus E* and equivalent radius of curvature R* of the contact surface between the tubing and the wellbore can be calculated using the following formulas:

[0094]

[0095] Where: Et and Ew are the elastic moduli of the tubing and wellbore rock, respectively, in Pa; μ p and μ w These are the Poisson's ratios of the tubing and the wellbore rock, respectively, and are dimensionless.

[0096] Step S13: Establish a wellbore stress calculation model considering the operation of the tubing string being lowered, and solve for the maximum and minimum principal stresses around the wellbore based on the wellbore stress calculation model.

[0097] Assuming the formation is a homogeneous, isotropic, linearly elastic porous material, the following mechanical model can be used to solve the wellbore stress for any inclined wellbore: On an infinitely large plane, the circular borehole is subjected to the fluid pressure Pi inside the well and the contact stress P of the tubing string. At the same time, it is subjected to the maximum and minimum horizontal principal stresses at an infinite distance from this plane, and is also subjected to the pressure of the overlying formation in the vertical direction.

[0098] Considering that rock is a small-deformation elastic body, the principle of linear superposition is applicable. Therefore, the overall stress state of the wellbore surrounding rock can be obtained by first studying the influence of each stress component on the wellbore surrounding rock stress, and then by superposition. Considering the additional radial stress generated by the contact between the tubing string and the wellbore, the expression for the wellbore stress distribution can be obtained as follows:

[0099]

[0100]

[0101]

[0102]

[0103]

[0104] in:

[0105] in, P i The pressure of the fluid inside the well. P Let r be the contact stress and r be the distance from the first well axis. It is radial normal stress. For circumferential normal stress, It is the axial normal stress. In-plane shear stress, The first axial shear stress, For the second axial shear stress, The first normal stress, This is the second normal stress. The third normal stress, For the first shear stress, This is the second shear stress. The third shear stress is θ, and the wellbore angle is θ. Let v be the wellbore radius and v be Poisson's ratio. For the pressure of the overlying, For the maximum ground stress, The minimum ground stress is given by ψ, the well inclination angle is given by Ω, and the well inclination azimuth angle is given by Ω.

[0106] The principal stresses around the well can be obtained by solving the characteristic equation of the stress tensor matrix of the well wall. They are represented as the maximum principal stress σ1, the intermediate principal stress σ2, and the minimum principal stress σ3, respectively, from largest to smallest.

[0107] Step S14: Based on the maximum and minimum principal stresses around the well, and combined with the Mohr-Coulomb failure criterion, the wellbore instability radius is calculated. A wellbore disturbance coefficient is proposed to quantify the degree of wellbore instability caused by the running tubing, and a method for analyzing wellbore disturbance caused by the running tubing is established.

[0108] Based on the wellbore stress calculation results, the wellbore instability radius can be determined using the Mohr-Coulomb criterion, which is expressed as follows:

[0109]

[0110] Where: τ f σ is the shear strength on the shear plane, Pa; σ is the normal stress on the shear plane, Pa; φ is the internal friction angle, °; c is the cohesion, Pa.

[0111] During the calculation process, the distance r from the wellbore rock to the wellbore axis is gradually reduced. When the wellbore rock is in a critical state of collapse, the distance from the wellbore rock to the wellbore axis is the wellbore instability radius.

[0112] The wellbore disturbance coefficient is defined as:

[0113] Where Rs is the wellbore instability radius, in meters.

[0114] Furthermore, this application provides a specific application of a method for determining the wellbore instability radius. Based on the Mohr-Coulomb failure criterion, this application analyzes the disturbance of the wellbore caused by the running tubing. Based on the data in Table 1, the influence of contact force, wellbore angle, well inclination angle, azimuth angle, wellbore curvature radius, wellbore diameter, wellbore rock elastic modulus, and Poisson's ratio on the wellbore disturbance coefficient is calculated and analyzed.

[0115] Table 1. Parameters related to the application of the wellbore disturbance analysis method during tubing string installation.

[0116] The calculation and analysis of the impact of the wellbore disturbance coefficient in this application leads to the following conclusions: The wellbore disturbance coefficient increases with increasing contact force, exhibiting an approximately linear relationship. When the contact force is less than 1900 N, the wellbore does not become unstable, and the disturbance coefficient is zero. At a contact force of 5000 N, the disturbance coefficient is 0.13, and at 10000 N, it reaches 0.25. The wellbore disturbance coefficient changes periodically with increasing azimuth angle. When the azimuth angle is between 67.5° and 112.5°, the wellbore remains stable. The disturbance coefficient reaches its maximum value of 0.14 at azimuth angles of 0° and 180°. The wellbore disturbance coefficient decreases with increasing wellbore radius of curvature.

[0117] The wellbore disturbance coefficient increases with increasing elastic modulus and Poisson's ratio.

[0118] In one embodiment, this application provides an apparatus for determining the wellbore instability radius, comprising: a memory configured to store instructions; and a processor configured to retrieve instructions from the memory and, when executing the instructions, to implement the method for determining the wellbore instability radius as described above.

[0119] In one embodiment, this application provides a machine-readable storage medium storing instructions for causing a machine to perform the method described above for determining the wellbore instability radius.

[0120] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0121] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for determining the wellbore instability radius, characterized in that, The method includes: The contact stress between the tubing string lowered into the target well and the wellbore wall, and the first well axis distance between the initial wellbore position and the wellbore axis of the target well are obtained. Based on the contact stress and the first well axis distance, the well perimeter stress at the initial well perimeter position in multiple preset directions is obtained; Based on the multiple wellbore stresses, the maximum and minimum wellbore principal stresses are obtained; If the maximum and minimum principal stresses around the well do not satisfy the Mohr-Coulomb criterion, the initial well position is changed to change the first well axis distance until the maximum and minimum principal stresses around the well corresponding to the changed target well position satisfy the Mohr-Coulomb criterion, so as to obtain the second well axis distance corresponding to the target well position, wherein the second well axis distance is the well instability radius when the target well experiences wellbore instability.

2. The method according to claim 1, characterized in that, The contact stress includes continuous contact stress, and obtaining the contact stress between the tubing string lowered into the target well and the wellbore wall of the target well includes: The actual length of the tubing string, the gap between the tubing string and the wellbore, the equivalent radius of curvature of the contact surface between the tubing string and the wellbore, the contact force between the tubing string and the wellbore, and the equivalent elastic modulus of the contact surface between the tubing string and the wellbore are obtained. Based on the preset tubing deformation algorithm, the actual tubing deformation is determined according to the actual tubing length. When the actual tubing deformation is greater than the well gap, the point contact limit length of the tubing is determined based on the preset tubing deformation algorithm, wherein the preset tubing deformation is the well gap. Determine the deviation between the actual tubing length and the limit length of the tubing point contact, so as to obtain the continuous contact length between the tubing and the well wall; Based on a preset continuous contact stress algorithm, the continuous contact stress is determined according to the continuous contact length, the equivalent radius of curvature, the contact force, and the equivalent elastic modulus.

3. The method according to claim 2, characterized in that, The preset continuous contact stress algorithm includes the following formula: Where pmax is the continuous contact stress, Nw is the contact force, E* is the equivalent elastic modulus, Lw is the continuous contact length, and R* is the equivalent radius of curvature.

4. The method according to claim 1, characterized in that, The contact stress includes point contact stress, and obtaining the contact stress between the tubing string lowered into the target well and the wellbore wall of the target well includes: The following parameters are obtained: actual tubing length, gap between tubing and wellbore, wellbore radius of target well, upper limit of distance from contact point on contact cross-section of tubing and wellbore to contact direction axis, equivalent elastic modulus of contact surface between tubing and wellbore, depth of tubing indentation into wellbore, and distance from contact point on contact cross-section of tubing and wellbore to contact direction axis. Based on the preset tubing deformation algorithm, the actual tubing deformation is determined according to the actual tubing length. When the actual tubing deformation is equal to the well gap, the point contact stress is determined based on the wellbore radius, the contact half-width, the tubing elastic modulus, and the depth, according to a preset point contact stress algorithm.

5. The method according to claim 4, characterized in that, The preset point contact stress algorithm includes the following formula: Wherein, Pp is the point contact stress, w is the upper limit of the value, Rw is the wellbore radius, E* is the equivalent elastic modulus, d is the depth, and x is the distance of the contact point from the contact direction axis.

6. The method according to claim 1, characterized in that, The wellbore stress includes axial normal stress, circumferential normal stress, radial normal stress, in-plane shear stress, first axial shear stress, and second axial shear stress. The step of obtaining the wellbore stress at the initial wellbore position in multiple preset directions based on the contact stress and the first well axis distance includes: The stress parameters, target well parameters, and Poisson's ratio of the wellbore are obtained. The stress parameters include the maximum principal stress around the wellbore, the minimum principal stress around the wellbore, the first normal stress in the direction of the maximum principal stress around the wellbore, the second normal stress in the direction of the minimum principal stress around the wellbore, the third normal stress in the direction of the wellbore axis, the first shear stress in the plane containing the maximum and minimum principal stresses around the wellbore, the second shear stress in the plane containing the minimum principal stress around the wellbore axis, and the third shear stress in the plane containing the maximum and minimum principal stresses around the wellbore axis. The target well parameters include the wellbore angle of the target well, the wellbore radius of the target well, and the fluid pressure inside the target well. Based on the contact stress, the first well axis distance, the stress parameter, the target well parameter, and the Poisson's ratio, the well perimeter stress at the initial well perimeter position in multiple preset directions is determined; The determination of the wellbore stress includes the following formula: in, P i The pressure of the fluid inside the well. P The contact stress is r, and the first well axis distance is r. The radial normal stress, The circumferential normal stress, The axial normal stress, The in-plane shear stress The first axial shear stress, This is the second axial shear stress. The first normal stress, This is the second normal stress. The third normal stress, This is the first shear stress. This is the second shear stress. The third shear stress is θ, and the wellbore angle is θ. Let v be the wellbore radius and v be the Poisson's ratio.

7. The method according to claim 1, characterized in that, The wellbore stress includes axial normal stress, circumferential normal stress, radial normal stress, in-plane shear stress, first axial shear stress, and second axial shear stress. The process of obtaining the maximum and minimum wellbore principal stresses based on the multiple wellbore stresses includes: Based on the multiple wellbore stresses, the wellbore stress matrix is ​​obtained; Determine multiple eigenvalues ​​of the wellbore stress matrix; The maximum and minimum values ​​among the plurality of characteristic values ​​are determined to obtain the maximum and minimum wellbore principal stresses, respectively.

8. The method according to claim 1, characterized in that, The method further includes: Obtain the wellbore radius of the target well; Determine the deviation between the wellbore instability radius and the wellbore radius; The ratio of the deviation to the wellbore radius is determined to obtain the wellbore disturbance coefficient.

9. A device for determining the instability radius of a wellbore, characterized in that, include: The memory is configured to store instructions; as well as The processor is configured to retrieve the instructions from the memory and, when executing the instructions, to implement the method for determining the wellbore instability radius according to any one of claims 1 to 7.

10. A machine-readable storage medium, characterized in that, The machine-readable storage medium stores instructions for causing the machine to perform the method for determining the wellbore instability radius according to any one of claims 1 to 7.

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