Calculation method for the influence of density reduction operation during cement setting on wellbore integrity

Abstract

The invention discloses a calculation method for the influence of density reduction operation during cement setting on wellbore integrity. Based on the relevant knowledge of elastoplastic mechanics, a mathematical model of casing-cement sheath-formation is established considering elastic and plastic deformation of the cement sheath under the condition of casing eccentricity. Taking the casing-cement sheath-formation combination as the main research object, the influence of wellbore density reduction operation on the interfacial micro-gap is studied. This method can analyze the influence law of density reduction operation during cement setting on the change of the micro-gap size at the first interface between the cement sheath and the casing under different eccentric states of deep well casings, effectively avoiding the problem of downhole fluid channeling caused by errors in the evaluation results using the casing centering model, and further providing a real calculation method for the wellbore density reduction range.

Description

Technical Field

[0001] The present invention relates to the field of well cementing engineering in oil and gas wells, and particularly relates to a calculation method for the influence of density reduction operation during cement setting on wellbore integrity. Background Art

[0002] Maintaining the structural integrity of the wellbore without damage and ensuring the normal function of the wellbore are important guarantees for safe, high-quality, and efficient drilling and production operations. Wellbore integrity can be divided into three parts: casing integrity, cement sheath integrity, and formation integrity. Cement sheath integrity is the weak link in the overall wellbore integrity. A complete cement sheath can effectively seal off oil, gas, and water layers in the formation and support the casing. Damage to the cement sheath will cause the failure of interlayer sealing and the deterioration of the casing stress condition, leading to the loss of oil and gas resources or the intrusion of other formation fluids into the production layer, resulting in safety hazards and environmental pollution, seriously affecting production capacity construction, and increasing the cost of oil and gas resource development. Therefore, maintaining the mechanical integrity of the cement sheath is of great significance for maintaining a normal oil and gas passage and extending the service life of oil and gas wells.

[0003] After cementing, there are many subsequent operations to reduce the density of the working fluid in the casing. Firstly, after liner cementing, when performing tie-back cementing, in order to improve the cement displacement efficiency in the tie-back section, sometimes the density in the pipe is reduced. Secondly, when logging, density reduction logging is used. In addition, when continuing drilling or performing underbalanced perforation operations after sealing the technical casing, it is often necessary to reduce the density of the perforating fluid. Thirdly, during operations such as stimulation, fluid drainage, production testing, and gas blowdown and pressure relief, there is a phenomenon of density reduction of the working fluid in the casing. When the density of the wellbore fluid is relatively high during drilling or cementing, the casing will expand outwards. At the initial stage of cement slurry setting, the strength is relatively low and it has large plasticity. At this time, the expansion and deformation of the casing cause residual deformation of the cement sheath. During subsequent density reduction operations, at this time the cement sheath has hardened and lost plasticity. The reduction in density causes the hydrostatic pressure in the casing to decrease. Under the action of elastic deformation, the casing contracts towards the center of the wellbore. If the radial tensile stress caused by the contraction is greater than the bonding strength of the cement sheath at the first interface, it will cause micro-gaps at the first interface of the cement sheath.

[0004] At present, regarding the research on the sealing integrity of the cement sheath, many scholars have considered the analysis of wellbore sealing integrity under the conditions of casing centering and when the internal pressure in the pipe changes, with the cement sheath undergoing elastic or elastoplastic changes. At the beginning of 2015, Wei established an elastoplastic analysis model for the casing-cement sheath-surrounding rock composite based on the Mohr-Coulomb criterion, calculated the tensile stress on the two interfaces of the cement sheath under alternating internal pressure of the casing, and used this to judge whether micro-gaps are generated at the interfaces; Yang Yan et al. studied the influence of the reduction in the density of the cement slurry for well cementing on the bonding strength of Interface I and Interface II. Through the establishment of a stress calculation model, it is known that the reduction in the density of the cement slurry for well cementing will increase the tensile stress on the interface and ultimately form cracks on the interface. However, during the actual well cementing process, the well inclination angle, azimuth angle, and well diameter continuously change with the well depth. Although centralizers are installed on the casing, it is still difficult to ensure that the casing is in a centered state. This easily causes casing eccentricity, which leads to uneven thickness of the cement sheath. There are significant differences in the stress states of the cement sheath when the casing is eccentric and centered. Especially at the narrow side of the cement sheath when it is eccentric, under a certain internal pressure change, it will induce micro-gaps or damage to occur at the interface of the cement sheath. If the evaluation model when the casing is centered is applied to the eccentric state of the casing, the evaluation result will be distorted. Summary of the Invention

[0005] Aiming at the above deficiencies in the prior art, the calculation method for the influence of the density reduction operation during cement setting on wellbore integrity provided by the present invention solves the problem that when the evaluation model when the casing is centered is applied to the eccentric state of the casing, the evaluation result of wellbore integrity will be distorted.

[0006] In order to achieve the above invention purpose, the technical solution adopted by the present invention is as follows:

[0007] Provide a calculation method for the influence of the density reduction operation during cement setting on wellbore integrity, which includes the following steps:

[0008] S1. After cementing, the casing, cement sheath, and formation are consolidated into a whole. Ignoring the axial load, the three-dimensional wellbore model is simplified into a plane strain model, and the casing, cement sheath, and formation are jointly regarded as a thick-walled cylinder of homogeneous isotropic material;

[0009] S2. Consider the axial strain of the thick-walled cylinder in the plane strain model as 0 to obtain the radial deformation model of the thick-walled cylinder; regard the casing as an elastic body and obtain the Lame solution of the stress in the plane strain model in polar coordinates;

[0010] S3. Calculate the casing eccentricity according to the eccentricity of the casing, the outer radius of the cement sheath, and the outer wall radius of the casing during cement setting;

[0011] S4. Substitute the inner radius of the casing, the outer radius of the casing wall, the distance from the target point to the central axis of the thick-walled cylinder, the elastic modulus of the casing, the Poisson's ratio of the casing, the internal pressure of the casing, and the stress at the first interface into the radial deformation model of the thick-walled cylinder and the Lame solution of the stress in polar coordinates to obtain the radial stress of the casing, the tangential stress of the casing, and the displacement of the outer wall of the casing respectively;

[0012] S5. Substitute the eccentricity of the casing, the outer radius of the formation wall, the contact force at the second interface, the in-situ stress at the outer radius of the formation, the elastic modulus of the formation, the Poisson's ratio of the formation, the linear expansion coefficient of the formation, the average temperature change value of the thick-walled cylinder, the outer radius of the cement sheath, and the distance from the target point to the central axis of the thick-walled cylinder into the radial deformation model of the thick-walled cylinder and the Lame solution of the stress in polar coordinates to obtain the radial stress of the surrounding rock of the wellbore, the tangential stress of the surrounding rock of the wellbore, and the displacement of the inner wall of the formation respectively;

[0013] S6. Substitute the outer radius of the casing, the outer radius of the cement sheath, the eccentricity of the casing, the contact force at the second interface, the stress at the first interface, the distance from the target point to the central axis of the thick-walled cylinder, the elastic modulus of the cement sheath, the Poisson's ratio of the cement sheath, the linear expansion coefficient of the cement sheath, and the average temperature change value of the thick-walled cylinder into the radial deformation model of the thick-walled cylinder and the Lame solution of the stress in polar coordinates to obtain the radial stress of the cement sheath when only elastic deformation occurs, the tangential stress of the cement sheath, the displacement of the inner wall of the cement sheath, and the displacement of the outer wall of the cement sheath respectively;

[0014] S7. Substitute the cohesive force of the cement sheath, the internal friction angle of the cement sheath, the stress at the first interface, the distance from the target point to the central axis of the thick-walled cylinder, and the outer radius of the casing into the Lame solution of the stress in polar coordinates to obtain the radial stress of the cement sheath and the tangential stress of the cement sheath when the cement sheath is in elastoplastic state respectively;

[0015] S8. Substitute the Poisson's ratio of the cement sheath, the elastic modulus of the cement sheath, the radius of the elastoplastic interface, the eccentricity of the casing, the stress at the elastoplastic interface of the cement sheath, the contact force at the second interface, the stress at the first interface, the outer radius of the casing, the outer radius of the cement sheath, the linear expansion coefficient of the cement sheath, and the average temperature change value of the thick-walled cylinder into the radial deformation model of the thick-walled cylinder to obtain the displacement of the inner wall of the plastic zone of the cement sheath and the displacement of the outer wall of the plastic zone of the cement sheath respectively;

[0016] S9. Let the stress at the first interface be 0 in the calculation formula of the displacement of the outer wall of the casing in step S4 and the calculation formula of the displacement of the inner wall of the plastic zone of the cement sheath in step S8 to obtain the displacement of the outer wall of the narrow-gap casing and the displacement of the inner wall of the cement sheath when a micro-gap is generated at the first interface respectively;

[0017] S10. Let the stress at the second interface be 0 in the calculation formula of the displacement of the inner wall of the formation in step S5 and the calculation formula of the displacement of the outer wall of the plastic zone of the cement sheath in step S8 to obtain the displacement of the inner wall of the formation and the displacement of the outer wall of the cement sheath when a micro-gap is generated at the second interface respectively;

[0018] S11. When a micro-gap is generated at the first interface, the displacement of the outer wall of the narrow-gap casing and the displacement of the inner wall of the cement sheath are subtracted to obtain the micro-gap value of the first interface gap; when a micro-gap is generated at the second interface, the displacement of the inner wall of the formation and the displacement of the outer wall of the cement sheath are subtracted to obtain the micro-gap value of the second interface gap.

[0019] The beneficial effects of the present invention are as follows:

[0020] 1. The present invention takes into account the influence of eccentricity on the stress of the cement sheath, establishes a calculation model for the stress and displacement of the cement sheath under the condition of casing eccentricity, and provides a reliable calculation method for evaluating the sealing integrity of the cement sheath under the actual downhole cement sheath stress state.

[0021] 2. The present invention can analyze the influence law of the density reduction operation during the cement setting period on the change of the micro-gap size between the cement sheath and the casing at different eccentric states of the deep well casing, effectively avoid the error caused by the evaluation result of applying the casing centering model, which leads to the downhole crossflow problem, and further provides a real calculation method for the wellbore density reduction range. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 is a schematic flow chart of the method;

[0023] Figure 2 is a physical model diagram of the casing-cement sheath-formation combination;

[0024] Figure 3 is a diagram of the change of the micro-gap size with the change of the internal pressure of the casing when the casing is centered;

[0025] Figure 4 is a diagram of the change of the micro-gap size with the change of the internal pressure of the casing when the casing is eccentric. DETAILED DESCRIPTION OF THE INVENTION

[0026] The following describes the specific embodiments of the present invention to facilitate the understanding of those skilled in the art of the present technology. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those ordinary skilled in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0027] As Figure 1 shown, the calculation method for the influence of the density reduction operation during the cement setting period on the wellbore integrity includes the following steps:

[0028] S1. After cementing, the casing, the cement sheath, and the formation are consolidated into a whole. Ignoring the axial load, the three-dimensional wellbore model is simplified into a plane strain model, and the casing, the cement sheath, and the formation are regarded as a thick-walled cylinder of homogeneous isotropic material.

[0029] S2. Consider the axial strain of the thick-walled cylinder in the plane strain model as 0 to obtain the radial deformation model of the thick-walled cylinder; consider the casing as an elastic body and obtain the Lame solution of the stress in the plane strain model in polar coordinates.

[0030] S3. According to the eccentricity e of the casing during the cement setting period, the outer radius of the cement sheath , the outer wall radius of the casing calculate the eccentricity of the casing l .

[0031] S4. Substitute the inner radius of the casing , the outer wall radius of the casing , the distance r from the target point to the central axis of the thick-walled cylinder, the elastic modulus of the casing , the Poisson's ratio of the casing , the internal pressure of the casing and the stress at the first interface into the radial deformation model of the thick-walled cylinder and the Lame solution of the stress in polar coordinates to obtain the radial stress of the casing , the tangential stress of the casing and the displacement of the outer wall of the casing ;

[0032] S5. Substitute the eccentricity of the casing l , the outer wall radius of the formation , the contact force at the second interface , the in-situ stress at the outer radius of the formation , the elastic modulus of the formation , the Poisson's ratio of the formation , the linear expansion coefficient of the formation , the average temperature change value of the thick-walled cylinder , the outer radius of the cement sheath and the distance r from the target point to the central axis of the thick-walled cylinder into the radial deformation model of the thick-walled cylinder and the Lame solution of the stress in polar coordinates to obtain the radial stress of the surrounding rock of the wellbore , the tangential stress of the surrounding rock of the wellbore and the displacement of the inner wall of the formation ;

[0033] S6. Substitute the outer wall radius of the casing , the outer radius of the cement sheath , the eccentricity of the casing l , the contact force at the second interface , the stress at the first interface , the distance r from the target point to the central axis of the thick-walled cylinder, the elastic modulus of the cement sheath , the Poisson's ratio of the cement sheath , the linear expansion coefficient of the cement sheath , the average temperature change value of the thick-walled cylinder Substitute the radial deformation model of the thick-walled cylinder and the Lame solution of the stress in polar coordinates to obtain the radial stress of the cement sheath when the cement sheath only undergoes elastic deformation , the circumferential stress of the cement sheath , the displacement of the inner wall of the cement sheath and the displacement of the outer wall of the cement sheath ;

[0034] S7. Substitute the cohesion C of the cement sheath, the internal friction angle of the cement sheath , the stress at the first interface , the distance r from the target point to the central axis of the thick-walled cylinder, and the outer radius of the casing into the Lame solution of the stress in polar coordinates to obtain the radial stress of the cement sheath and the circumferential stress of the cement sheath when the cement sheath is in the elastic-plastic state;

[0035] S8. Substitute the Poisson's ratio of the cement sheath , the elastic modulus of the cement sheath , the radius of the elastic-plastic interface , the eccentricity of the casing l , the stress at the elastic-plastic interface of the cement sheath , the contact force at the second interface , the stress at the first interface , the outer radius of the casing , the outer radius of the cement sheath , the linear expansion coefficient of the cement sheath , and the average temperature change value of the thick-walled cylinder into the radial deformation model of the thick-walled cylinder to obtain the displacement of the inner wall of the plastic zone of the cement sheath and the displacement of the outer wall of the plastic zone of the cement sheath ;

[0036] S9. Set the stress at the first interface in the calculation formula of the displacement of the outer wall of the casing in step S4 and the calculation formula of the displacement of the inner wall of the plastic zone of the cement sheath in step S8 to 0, and obtain the displacement of the outer wall of the narrow-gap casing and the displacement of the inner wall of the cement sheath when a micro-gap is generated at the first interface; ;

[0037] S10. Set the stress at the second interface in the calculation formula of the displacement of the inner wall of the formation in step S5 and the calculation formula of the displacement of the outer wall of the plastic zone of the cement sheath in step S8 to 0, and obtain the displacement of the inner wall of the formation and the displacement of the outer wall of the cement sheath when a micro-gap is generated at the second interface ;

[0038] S11. Subtract the outer wall displacement of the narrow-gap casing from the inner wall displacement of the cement sheath when a micro-gap is generated at the first interface to obtain the micro-gap value at the first interface; subtract the inner wall displacement of the formation from the outer wall displacement of the cement sheath when a micro-gap is generated at the second interface to obtain the micro-gap value at the second interface.

[0039] In a specific implementation process of the present invention, after cementing, the casing, cement sheath, and formation are consolidated into an integral body. The axial load can be ignored, and the three-dimensional wellbore model is simplified into a plane strain model. Assuming that the casing, cement sheath, and formation are thick-walled cylinders and are homogeneous isotropic materials, in this embodiment, the calculation of the influence of the density reduction operation during cement setting on the wellbore integrity is completed by considering the influence of the internal pressure change on the stress and displacement of the cement sheath under elastic and elastoplastic conditions.

[0040] The expression of the radial deformation model of the thick-walled cylinder in step S2 is:

[0041] ;

[0042] The expression of the Lame solution of the stress in the plane strain model in polar coordinates is:

[0043] .

[0044] The calculation expression of the casing eccentricity l in step S3 is:

[0045] .

[0046] Since the stress on the narrow gap is more concentrated and plastic deformation is more likely to occur, the thickness of the narrow-gap cement sheath is selected as , the inner radius of the casing is , the outer wall of the casing is , the outer radius of the cement sheath when the casing is centered is ; the outer radius of the cement sheath when the casing is eccentric is . According to the Lame solution of the plane axisymmetric problem, the calculation expressions of the radial stress of the casing, the tangential stress of the casing, and the displacement of the outer wall of the casing in step S4 are respectively:

[0047]

[0048] .

[0049] An infinitely large formation can also be assumed to be an elastic material, and its boundary condition is at the inner wall of the formation, i.e., ​​The force at this point is the contact force at the second interface, with a value of P c2 ; at the force is the in-situ stress, with a value of P f , according to the Lame solution formula for plane strain, the radial stress of the surrounding rock of the wellbore, the tangential stress of the surrounding rock of the wellbore, and the displacement of the inner wall of the formation in step S5 are calculated as follows:

[0050]

[0051]

[0052] .

[0053] In step S6, when the cement sheath only undergoes elastic deformation, the radial stress of the cement sheath, the tangential stress of the cement sheath, the displacement of the inner wall of the cement sheath, and the displacement of the outer wall of the cement sheath are calculated as follows:

[0054]

[0055]

[0056]

[0057] .

[0058] Figure 2 shows a schematic diagram of the elastoplastic deformation of the cement sheath, where is the radius of the elastoplastic interface. As the internal pressure increases, the cement sheath first yields from the inner side and gradually extends outward. In step S7, when the cement sheath is in the elastoplastic state, the radial stress and the tangential stress of the cement sheath are calculated as follows:

[0059]

[0060]

[0061] where when , ; when , .

[0062] In step S8, the displacement of the inner wall of the plastic zone of the cement sheath and the displacement The calculation expressions are respectively:

[0063]

[0064] 。

[0065] As the internal pressure increases, the plastic boundary of the cement sheath continuously develops from the inner side to the outer side of the cement sheath until it completely enters the plastic stage. When the density is reduced, the internal pressure in the wellbore decreases. When the internal pressure decreases to a certain extent, the cement sheath that is locally in the elastic state deflects towards the inner side of the wellbore, while the displacement of the plastic part of the cement sheath remains unchanged; at the same time, the casing undergoes elastic deformation towards the inner side of the wellbore. When the displacement of the casing is greater than the total displacement of the cement sheath, a micro-gap is generated at the interface between the casing and the cement sheath. Therefore, the displacement difference between the two is the micro-gap between the casing and the cement sheath. Taking the first interface as an example, when a micro-gap is generated at the interface, the stress will become 0. Substitute into the outer wall equation of the casing and the inner wall equation of the cement sheath. When a micro-gap is generated at the first interface in step S9, the outer wall displacement of the narrow-gap casing and the inner wall displacement of the cement sheath are respectively:

[0066]

[0067] 。

[0068] The difference between the outer wall displacement of the narrow-gap casing and the inner wall displacement of the cement sheath when a micro-gap is generated at the first interface is the size of the micro-gap at the first interface:

[0069] 。

[0070] Similarly, when a micro-gap is generated at the second interface, the stress on the second interface. When a micro-gap is generated at the second interface in step S10, the calculation expressions for the inner wall displacement of the formation and the outer wall displacement of the cement sheath are respectively:

[0071]

[0072] 。

[0073] The difference between the inner wall displacement of the formation and the outer wall displacement of the cement sheath when a micro-gap is generated at the second interface is the size of the micro-gap at the narrow-gap second interface:

[0074] .

[0075] In an embodiment of the present invention, a certain deep well adopts a five - opening wellbore structure, with a total drilled depth of 8166 m. The 273.05 mm casing (wall thickness 13.84 mm) in the fourth opening is run to a depth of 6566 m; the length of the open - hole section in the fifth opening is 6566 - 8166 m, and the average well diameters are 260 mm from 6566 - 6893 m, 251.4 mm from 6893 - 7981 m, and 228.2 mm from 7981 - 8166 m. This well adopts the liner cementing method, using 168.3 mm (wall thickness 14.7 mm) and 139.7 mm (wall thickness 15.8 mm) casings to isolate 6059 - 6693 m and 6693 - 8166 m respectively, and the hanger is run to a depth of 6060 m. The liner is run to the bottom of the well using a φ139.7 mm drill pipe (wall thickness 15.8 mm). The density of the drilling fluid in the wellbore is 2.17 g / cm 3 , and during cement injection, pilot slurry, front spacer fluid, lead slurry, tail slurry, rear spacer fluid, well slurry, central pipe protection fluid, pilot slurry, and well slurry are injected into the wellbore. The fluid densities and volumes are as follows: 2.12 g / cm 3 (50 m 3 ), 2.18 g / cm 3 (35 m 3 ), 2.25 g / cm 3 (52 m 3 ), 1.90 g / cm 3 (20 m 3 ), 1.90 g / cm 3 (4 m 3 ), 2.17 g / cm 3 (14.7 m 3 ), 1.90 g / cm 3 (6.0 m 3 ), 2.12 g / cm 3 (20 m 3 ), 2.17 g / cm 3 (43.6 m 3 ). After the liner cementing operation, in order to improve the displacement efficiency during cement injection in the overlap section, the density of the drilling fluid in the wellbore is reduced from 2.17 g / cm 3 to 1.92 g / cm 3 .

[0076] According to the well diameter and string size, the fluid distribution in the pipe during the cementing process is as follows: from 0 to 3550 m is the well slurry with a density of 2.17 g / m³; from 3550 to 5730 m is the pilot slurry with a density of 2.12 g / m³; from 5730 to 6270 m is the protection fluid with a density of 1.90 g / m³; from 6270 to 7600 m is the well slurry with a density of 2.17 g / m³; from 7600 to 8040 m there is a post-isolation fluid with a density of 1.9 g / m³, and from 8040 to 8166 m is the tail slurry with a density of 1.9 g / m³. When the density reduction operation is carried out during the waiting-on-cement period, the density of the working fluid above the hanger is reduced to 1.92 g / m³. At the end of cementing, the internal pressure distribution in the casing of the liner section from 6060 to 8166 m is 127 - 169.7 MPa; when the density of the drilling fluid is reduced to 1.92 g / m³, the internal pressure distribution in the casing is 114 - 156.8 MPa. The density reduction operation results in a 13 MPa reduction in the internal pressure of the casing. Given that the stress on the first interface of the cement sheath is higher than that on the second interface, leading to the easier occurrence of micro-annuli at the first interface, the development of micro-annuli at the first interface is selected for analysis.

[0077] Based on the well diameter and string size of the liner section, various parameters of the casing, cement sheath, and formation are obtained. The inner radius of the casing is 69.54 mm, and the outer radius is 84.15 mm; the inner radius of the cement sheath is 84.15 mm, and the outer radius is 128 mm, and the yield strength of the cement sheath is 20 MPa; the inner radius of the formation is 128 mm, and the force on the outer boundary is the in-situ stress; the elastic modulus of the casing is 21 GPa, and the Poisson's ratio is 0.3; the elastic modulus of the cement sheath is 6 GPa, and the Poisson's ratio is 0.1; the elastic modulus of the formation is 2.5 GPa, and the Poisson's ratio is 0.2.

[0078] Calculations are carried out according to this method and on-site parameters. When the casing is centered, the internal pressure of the casing drops from 127 MPa to 114 MPa, and the pressure drop amplitude is 13 MPa. At this time, the radial stress on the outer wall of the casing is calculated to be 26.2 MPa, the tangential stress is 12 MPa, and the displacement is 0.344 mm; the radial stress on the inner wall of the cement sheath is 19.1 MPa, the tangential stress is 9.9 MPa, and the displacement is 0.338 mm. The displacement difference between the outer wall of the casing and the inner wall of the cement sheath is the size of the micro-annulus, which is 0.006 mm.

[0079] When the eccentricity of the casing is 0.3, the radial stress on the outer wall of the casing is 26.2 MPa, the tangential stress is 12 MPa, and the displacement is 0.405 mm; the radial stress on the inner wall of the cement sheath is 22.9 MPa, the tangential stress is 10.8 MPa, and the displacement is 0.39 mm. The size of the micro-annulus is 0.015 mm.

[0080] The development of the size of the micro-annulus is as shown in Appendix Figure 3 、Appendix Figure 4As shown, when the casing is centered and when the casing is eccentric by 0.3, the corresponding casing pressures when the micro-gap just appears are 114.7 MPa and 116.4 MPa respectively. Considering the distribution characteristics of the pressure and well depth in the wellbore, the failure lengths of the centered casing and the casing with an eccentricity of 0.3 below a relatively large depth (6060 m) can be calculated to be 1476 m and 2160 m respectively. Therefore, the eccentric casing is more likely to cause the failure of the cement sheath.

Claims

1. A calculation method for the influence of density reduction operation during cement setting on wellbore integrity, characterized in that, It includes the following steps: S1. Consolidate the casing, cement sheath and formation after cementing into an integral whole. Ignoring the axial load, simplify the three-dimensional wellbore model into a plane strain model, and regard the casing, cement sheath and formation together as a thick-walled cylinder of homogeneous isotropic material; S2. Consider the axial strain of the thick-walled cylinder in the plane strain model as 0 to obtain the radial deformation model of the thick-walled cylinder; regard the casing as an elastic body and obtain the Lamé solution of the stress in the plane strain model in polar coordinates; S3. Calculate the eccentricity of the casing according to the eccentricity of the casing during cement setting, the outer radius of the cement sheath and the outer wall radius of the casing; S4. Substitute the inner radius of the casing, the outer wall radius of the casing, the distance from the target point to the central axis of the thick-walled cylinder, the elastic modulus of the casing, the Poisson's ratio of the casing, the internal pressure of the casing and the stress at the first interface into the radial deformation model of the thick-walled cylinder and the Lamé solution of the stress in polar coordinates to obtain the radial stress of the casing, the tangential stress of the casing and the displacement of the outer wall of the casing respectively; S5. Substitute the eccentricity of the casing, the outer wall radius of the formation, the contact force at the second interface, the in-situ stress at the outer radius of the formation, the elastic modulus of the formation, the Poisson's ratio of the formation, the linear expansion coefficient of the formation, the average temperature change value of the thick-walled cylinder, the outer radius of the cement sheath and the distance from the target point to the central axis of the thick-walled cylinder into the radial deformation model of the thick-walled cylinder and the Lamé solution of the stress in polar coordinates to obtain the radial stress of the surrounding rock of the wellbore wall, the tangential stress of the surrounding rock of the wellbore wall and the displacement of the inner wall of the formation respectively; S6. Substitute the outer wall radius of the casing, the outer radius of the cement sheath, the eccentricity of the casing, the contact force at the second interface, the stress at the first interface, the distance from the target point to the central axis of the thick-walled cylinder, the elastic modulus of the cement sheath, the Poisson's ratio of the cement sheath, the linear expansion coefficient of the cement sheath and the average temperature change value of the thick-walled cylinder into the radial deformation model of the thick-walled cylinder and the Lamé solution of the stress in polar coordinates to obtain the radial stress of the cement sheath when only elastic deformation occurs, the tangential stress of the cement sheath, the displacement of the inner wall of the cement sheath and the displacement of the outer wall of the cement sheath respectively; S7. Substitute the cohesive force of the cement sheath, the internal friction angle of the cement sheath, the stress at the first interface, the distance from the target point to the central axis of the thick-walled cylinder and the outer wall radius of the casing into the Lamé solution of the stress in polar coordinates to obtain the radial stress of the cement sheath and the tangential stress of the cement sheath when the cement sheath is in elastoplastic state respectively; S8. Substitute the Poisson's ratio of the cement sheath, the elastic modulus of the cement sheath, the radius of the elastoplastic interface, the eccentricity of the casing, the stress at the elastoplastic interface of the cement sheath, the contact force at the second interface, the stress at the first interface, the outer wall radius of the casing, the outer radius of the cement sheath, the linear expansion coefficient of the cement sheath and the average temperature change value of the thick-walled cylinder into the radial deformation model of the thick-walled cylinder to obtain the displacement of the inner wall of the plastic zone of the cement sheath and the displacement of the outer wall of the plastic zone of the cement sheath respectively; S9. Let the stress at the first interface be 0 in the calculation formula of the displacement of the outer wall of the casing in step S4 and the calculation formula of the displacement of the inner wall of the plastic zone of the cement sheath in step S8 to obtain the displacement of the outer wall of the narrow-gap casing and the displacement of the inner wall of the cement sheath when a micro-gap is generated at the first interface respectively; S10. In the calculation formulas of the displacement of the inner wall of the formation in step S5 and the displacement of the outer wall of the plastic zone of the cement sheath in step S8, let the stress at the second interface be 0, and respectively obtain the displacement of the inner wall of the formation and the displacement of the outer wall of the cement sheath when a micro-gap is generated at the second interface; S11. Subtract the displacement of the outer wall of the narrow-gap casing and the displacement of the inner wall of the cement sheath when a micro-gap is generated at the first interface to obtain the micro-gap value of the first interface; Subtract the displacement of the inner wall of the formation and the displacement of the outer wall of the cement sheath when a micro-gap is generated at the second interface to obtain the micro-gap value of the second interface.

2. The calculation method for the impact of density reduction operation during cement setting on wellbore integrity according to claim 1, wherein The expression of the radial deformation model of the thick-walled cylinder in step S2 is: Among them is the radial deformation at a distance r from the axis of the thick-walled cylinder; E represents the elastic modulus of the thick-walled cylinder; represents the Poisson's ratio of the thick-walled cylinder; represents the tangential stress of the thick-walled cylinder; represents the radial stress of the thick-walled cylinder; is the expansion coefficient of the thick-walled cylinder; is the average temperature change value of the thick-walled cylinder; The expression of the Lame solution of the stress in the plane strain model in polar coordinates is: wherein is the inner radius of the casing; is the outer wall radius of the casing; is the internal pressure of the casing; is the stress at the first interface; is the distance from the central axis of the thick-walled cylinder.

3. The calculation method for the influence of density reduction operation during the cement setting period on wellbore integrity according to claim 1, wherein The calculation expression for the casing eccentricity in step S3 l is as follows: where e is the eccentricity of the casing during the cement setting period; is the outer radius of the cement sheath or the inner radius of the formation; is the outer radius of the casing wall or the inner radius of the cement sheath.

4. The calculation method for the influence of density reduction operation during cement setting on wellbore integrity according to claim 2, characterized in that The calculation expressions of the radial stress of the casing, the tangential stress of the casing, and the displacement of the outer wall of the casing in step S4 are respectively: wherein is the radial stress of the casing; is the tangential stress of the casing; is the displacement of the outer wall of the casing; is the Poisson's ratio of the casing; is the elastic modulus of the casing.

5. The calculation method for the influence of density reduction operation during cement setting on wellbore integrity according to claim 2, characterized in that The radial stress of the shaft wall surrounding rock in step S5 , the tangential stress of the shaft wall surrounding rock and the displacement of the inner wall of the formation The calculation expressions are respectively as follows: Among them is the radial stress of the wellbore surrounding rock; is the tangential stress of the wellbore surrounding rock; is the displacement of the inner wall of the formation; l is the casing eccentricity; is the outer radius of the formation; is the contact force at the second interface; is the in-situ stress at the outer radius of the formation; is the Poisson's ratio of the formation; is the linear expansion coefficient of the formation; is the outer radius of the cement sheath; is the elastic modulus of the formation.

6. The calculation method for the influence of density reduction operation during cement setting on wellbore integrity according to claim 2, characterized in that, The radial stress of the cement sheath when only elastic deformation occurs in step S6 , the circumferential stress of the cement sheath , the displacement of the inner wall of the cement sheath and the displacement of the outer wall of the cement sheath The calculation expressions are respectively as follows: Among them is the radial stress of the cement sheath when only elastic deformation occurs in the cement sheath; is the tangential stress of the cement sheath when only elastic deformation occurs in the cement sheath; is the displacement of the inner wall of the cement sheath when only elastic deformation occurs in the cement sheath; is the displacement of the outer wall of the cement sheath when only elastic deformation occurs in the cement sheath; is the outer radius of the cement sheath; l is the eccentricity of the casing; is the contact force at the second interface; is the elastic modulus of the cement sheath; is the Poisson's ratio of the cement sheath; is the linear expansion coefficient of the cement sheath.

7. The calculation method for the impact of density reduction operation during cement setting on wellbore integrity according to claim 2, characterized in that The radial stress and tangential stress of the cement sheath when it is in elastoplastic state in step S7 are calculated by the following expressions respectively: Among them is the radial stress of the cement sheath when it is in the elastoplastic state; is the tangential stress of the cement sheath when it is in the elastoplastic state; C is the cohesion of the cement sheath; is the internal friction angle of the cement sheath; when is the case, ; when is the case, ; is the contact force at the second interface.

8. The calculation method for the influence of density reduction operation during cement setting on wellbore integrity according to claim 2, characterized in that Inner wall displacement of the cement sheath plastic zone in step S8 and outer wall displacement of the cement sheath plastic zone The calculation expressions are respectively as follows: wherein is the displacement of the inner wall of the plastic zone of the cement sheath; is the displacement of the outer wall of the plastic zone of the cement sheath; is the Poisson's ratio of the cement sheath; is the elastic modulus of the cement sheath; is the outer radius of the cement sheath; is the radius of the elastic-plastic interface; l is the casing eccentricity; is the stress at the elastic-plastic interface of the cement sheath; is the contact force at the second interface; is the linear expansion coefficient of the cement sheath.

9. The calculation method for the influence of density reduction operation during cement setting on wellbore integrity according to claim 1, characterized in that, Outer wall displacement of the narrow-gap casing and inner wall displacement of the cement sheath when a micro-gap is generated at the first interface in step S9 and inner wall displacement of the cement sheath The expressions are respectively as follows: Among them is the outer wall displacement of the narrow-gap casing when a micro-gap is generated at the first interface; is the inner wall displacement of the cement sheath when a micro-gap is generated at the first interface; is the elastic modulus of the casing; is the Poisson's ratio of the casing; is the Poisson's ratio of the cement sheath; is the elastic modulus of the cement sheath; is the outer radius of the cement sheath; is the radius of the elastic-plastic interface; l is the eccentricity of the casing; is the stress at the elastic-plastic interface of the cement sheath; is the contact force at the second interface; is the linear expansion coefficient of the cement sheath; is the inner radius of the casing; is the outer wall radius of the casing; is the average temperature change value of the thick-walled cylinder.

10. The calculation method for the influence of the density reduction operation during the cement setting period on the wellbore integrity according to claim 2, characterized in that, The displacement of the formation inner wall and the displacement of the outer wall of the cement sheath when a micro-gap is generated at the second interface in step S10 are respectively expressed by the following calculation formulas: wherein is the displacement of the inner wall of the formation when a micro-gap is generated at the second interface; is the displacement of the outer wall of the cement sheath when a micro-gap is generated at the second interface; is the outer radius of the cement sheath; is the elastic modulus of the formation; is the Poisson's ratio of the formation; is the coefficient of linear expansion of the formation; is the outer radius of the formation; l is the eccentricity of the casing; is the in-situ stress at the outer radius of the formation; is the radius of the elastic-plastic interface; is the elastic modulus of the cement sheath; is the Poisson's ratio of the cement sheath; is the stress at the elastic-plastic interface of the cement sheath; is the coefficient of linear expansion of the cement sheath.

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